Chapter of Dissolution

A. Release mechanism and LoC

How an amorphous solid dispersion releases its drug.

What this chapter covers

whether drug and polymer leave the dissolving surface together (congruent, polymer-controlled release) or the polymer leaves first and the drug dissolves from a drug-rich surface at about the rate of the neat amorphous drug (drug-controlled release); how the two regimes are measured, with constant-area compacts, both components assayed, and media presaturated with drug; the nanodroplets that only polymer-controlled release produces and their origin from dissolved drug; the limit of congruency (LoC), the drug loading above which release switches, and how narrow that switch is; the drug-rich, porous surface layer above the limit; water-induced amorphous–amorphous phase separation of the hydrating surface as the authors' explanation of the limit, imaged from 2022 in the gel layer of dissolving compacts; drug properties tested against it (log P, molecular weight, drug–polymer hydrogen and halogen bonding, the drug's wet glass transition against the test temperature, salt formation) and, from 2023, the polymer that a hydrogen-bonding drug carries into its drug-rich phase, read on schematic ternary phase diagrams and from 2024 on measured drug–polymer–water diagrams whose critical point lay near the limit; the polymer's molecular weight, which with short PVP chains let drug-rich droplets agglomerate in the gel before inversion; the polymer's own dissolution rate inside the dispersion, and for the enteric polymers HP-50 and HPMCAS its dependence on the buffer capacity, buffer species and pH of the medium through an acidic gel layer, and its pre-ionization as a polymer salt; from 2024 the insoluble complexes that lipophilic weak bases ionized at the gel pH form with HPMCAS, the HPMCAS grade, and the bile salt–lecithin micelles of biorelevant fluids that suppress these complexes; the size and stability of the released nanodroplets; crystals on the dissolving surface that end congruent release after minutes; the shape of the drug-rich phase that water separates; the polymer (hydrophilic PVP, PVPVA and HPMC against hydrophobic HPMCAS and Eudragit S 100), humid storage, a surfactant or a plasticizer in the dispersion, the manufacturing route, the drug content and the wettability of the particle surface as levers near the limit. The papers and their findings are in sources.md and findings.md. The twenty-nine papers run from 2017 to 2025 and study nifedipine, ritonavir, itraconazole, ledipasvir, nilvadipine, cilnidipine, felodipine, indomethacin and its methyl ester, four phenolphthalein analogues, loratadine, miconazole, danazol, elbasvir, paclitaxel, ivacaftor, clopidogrel, atazanavir, lumefantrine with eight of its amorphous salts, grazoprevir, clotrimazole, cinnarizine and bedaquiline, in PVPVA, PVP (six grades from K12 to K90), HPMC-E5, HPMC, HPMCAS (LF, MF, HF and LG grades and a triethylamine salt), HP-50 and nine of its salts and Eudragit S 100, with and without SDS, CTAB, TPGS, Tween 80, poloxamer 407, Span 20, 80 and 85, vinylpyrrolidone, PEG 3350, glycerol and its esters, citric acid and citrate esters in the dispersion or, with PVP, gelatin and poloxamer 407, on the particle surface, in buffers and simulated intestinal fluids, as films, spray-dried and melt-extruded dispersions, rotary-evaporated powders, co-precipitated particles and compacts.

29 papers2017–202535 findings

01Findings map

From basic to applied. The colour shows the strength of the evidence; click a card to read the finding.

Topic 3 · F6–F10, F17–F20, F25, F27, F29–F30

Limit of congruency and its causes

F6One loading step above the limit of congruency, drug release falls by one to three orders of magnitude.strongF7Above the limit the dissolving surface turned drug-rich and porous within minutes; below it the surface kept its composition.strongF8Wetted films phase-separated above the limit of congruency and not below it; that separation outpaces dissolution is proposed, not measured.moderateF9Drug log P and molecular weight did not set the limit of congruency in PVPVA.moderateF10Drug–polymer hydrogen bonding did not predict the limit of congruency in a consistent direction.weakF17In PVPVA, drugs that hydrogen-bond to the polymer had lower limits of congruency than close analogues that cannot.moderateF18The drug's glass transition against the test temperature moved the limit: a glassy drug-rich phase lowered it.moderateF19Congruent release can stop when crystals cover the dissolving surface, a failure that a read-out over the first minutes misses.strongF20After water separated a dispersion, release followed the shape of the drug-rich phase: discrete domains released, a continuous phase did not.weakF25In dissolving compacts release stayed congruent while the drug-rich phase formed discrete droplets, and failed once it connected into a network.moderateF27Drugs that hydrogen-bond to PVPVA carried it into their drug-rich phase; the more polymer that phase held, the lower the limit.moderateF29The molecular weight of PVP set the limit of congruency of clotrimazole, from below 5% with short chains to about 33–38% with long ones.strongF30Measured drug–PVPVA–water phase diagrams placed the limit of congruency near the critical point, where the drug-rich phase becomes the majority.strong

Topic 5 · F11–F14, F21–F22, F24, F26, F28, F31, F35

Formulation levers near the limit

F11Hydrophilic polymers release fastest at low loading but fall off a cliff; HPMCAS and EUDS release more slowly but stay congruent to 50%.strongF12Humid storage before dissolution removed nanodroplets and congruent release from PVP and PVPVA dispersions, but not from HPMCAS films.moderateF13Five parts SDS per 100 raised the ledipasvir–PVPVA limit of congruency from 5 to 30%; three other surfactants did not help.strongF14Near the switch the manufacturing route and the spray-drying solvent decided whether release was polymer- or drug-controlled.moderateF21A few percent of surfactant inside a PVPVA dispersion raised the limit of congruency, but the effective surfactant differed between drugs.strongF22Amorphous salts of lumefantrine raised its Tg and storage stability but lowered the loading with good release from PVPVA.moderateF24Pre-ionizing an enteric polymer as a salt sped its dissolution about threefold and removed most of its dependence on the buffer.moderateF26A few percent of a lipophilic plasticizer raised the limit of congruency of high-Tg drugs in PVPVA three- to fivefold.moderateF28In high-loading HPMCAS particles the drug content of the particle surface, not of the bulk, separated good from poor release.moderateF31With surfactant in ritonavir–PVPVA compacts, release followed whether a continuous drug-rich layer persisted at the dissolving surface.moderateF35On 75% grazoprevir–HPMCAS particles a secondary excipient helped release only when it made the particles wettable.strong

02Which paper supports which finding

Show the table of papers and findings
Two release regimes and their measurementNanodroplets from dissolving dispersionsLimit of congruency and its causesWeakly basic drugs in HPMCASFormulation levers near the limit
paperF1F2F3F15F23F4F5F16F6F7F8F9F10F17F18F19F20F25F27F29F30F32F33F34F11F12F13F14F21F22F24F26F28F31F35
2017indulkar2017borigin of nanodroplets from dissolving nifedipine dispersions, isotope scrambling
2017purohit2017britonavir dispersions during hydration and dissolution
2018bhardwaj2018surface-area-normalized dissolution of spray-dried and melt-extruded itraconazole–PVPVA
2019indulkar2019aritonavir–copovidone tablets, congruent release and the limit of congruency
2019que2019ledipasvir–copovidone, drug loading and drug–polymer interactions
2019saboo2019congruent release as a "sweet spot", nilvadipine and cilnidipine in PVPVA
2020saboo2020arelease against drug loading for five polymers, felodipine
2020saboo2020indomethacin and its methyl ester in PVPVA: hydrogen bonding, surface crystallization and glass transition
2021que2021four phenolphthalein analogues in PVPVA: hydrogen bonding, halogen bonding and the limit
2021saboo2021TPGS in felodipine–PVPVA dispersions at higher loading
2021yang2021six drugs of different Tg and log P in PVPVA and HPMCAS
2022correasoto2022asurfactants in clopidogrel–copovidone dispersions: drug loading and nanodroplet stability
2022correasoto2022bsurfactants and vinylpyrrolidone in atazanavir–PVPVA dispersions
2022hiew2022bamorphous salts of lumefantrine in PVPVA: Tg, release and stability
2022indulkar2022surfactants in ritonavir–copovidone dispersions above the limit
2022qi2022polymer salts of the enteric polymer HP-50 and their miconazole dispersions
2022yang2022arelease mechanisms of ritonavir–copovidone: phase separation and its morphology
2023bapat2023media choice for HPMCAS dispersions: buffer capacity, gel pH and release
2023correasoto2023plasticizers in PVPVA dispersions of high-Tg drugs
2023deac2023athe dissolution interface of two phenolphthalein analogues in PVPVA
2023deac2023bdrug load and molecular interactions: polymer in the drug-rich phase
2023hiew2023hierarchical co-precipitated particles of grazoprevir–HPMCAS
2023yang2023surfactants in ritonavir–PVPVA dispersions and the drug-rich barrier at the dissolving interface
2024bapat2024drug charge and insoluble drug–HPMCAS complexes
2024deac2024apolymer molecular weight and a new failure mode
2024deac2024bternary phase diagrams and the limit of congruency
2025bapat2025aHPMCAS grade and the release of weak bases
2025hiew2025surface composition and wettability of high-loading particles
2025kaur2025bedaquiline–HPMCAS complexation and biorelevant media
other library papers27 papers outside the chapter

Dot size = number of citations of the paper in the finding (long version C). Click a dot to open the finding.

03Connections to other subcategories

Takes from

and gives to [Amorphous solubility and LLPS](../c-amorphous-solubility-and-llps/index.md)

Taken: LLPS above the amorphous solubility and its UV extinction measurement (Ilevbare 2013 on LLPS) indulkar2017b C3; ritonavir LLPS at a similar concentration by several routes purohit2017b C47; the ritonavir amorphous solubility and wet Tg (builds_on of Indulkar 2019) indulkar2019a M1; the rule of about 10 °C Tg depression per 1% water ilevbare2013a E15; the SDS CMC used to judge the surfactant level of the ledipasvir dispersions indulkar2017a R1. Given: evidence from dissolving dispersions that their nanodroplets form from dissolved drug (F5) and appear only where release stays polymer-controlled (F4); that chapter lists the nanodroplet and glass–liquid picture as given to this subcategory (builds_on). From 2020 the chapter also takes the water-plasticized Tg as deciding whether a drug-rich phase is liquid or glassy at the test temperature, here applied to the drug-rich surface layer (F18), and the polymer effect on droplet stability, here for droplets released by dissolving dispersions (F16). From 2023 the chapter also takes entropy-driven polymer partitioning into drug-rich phases ueda2022 C48; deac2023b C45, on which the PVPVA content of the phenolphthalein drug-rich phases of F27 is read, and steric stabilization of drug-rich droplets by adsorbed HPMC, cited for the Spans of F16 ueda2020b C51; indulkar2022 C50. See Amorphous solubility and LLPS F1, F2, F12, F22. From 2024 the chapter reads the critical-point picture of F30 beside that chapter's polymer partitioning into drug-rich phases (Amorphous solubility and LLPS F19, F20), the agglomeration of F29 beside polymer effects on droplet dispersion (Amorphous solubility and LLPS F22), and the complexation of weak bases with HPMCAS in F32 beside the ionization dependence of their amorphous solubility (Amorphous solubility and LLPS F10).

Takes from

and gives to [Supersaturation from ASD dissolution](../b-supersaturation-from-asd-dissolution/index.md)

Taken: nanodroplets from low-loading dispersions and the dependence of LLPS on polymer and drug loading (Alonzo 2011, Jackson 2015) indulkar2017b C6, C7; LLPS from low-loading dispersions and impaired release at high loading (Alonzo 2011, builds_on of Purohit 2017 and Indulkar 2019); Corrigan's condition for polymer- and drug-controlled release xie2016a E2. Given: the falling-off-the-cliff effect and the gradual decline of HPMCAS release, tested and not found for praziquantel dispersions polyzois2024 C16, C18. From 2020 the chapter also takes the two crystallization routes of wetted amorphous solids, which the methyl ester of indomethacin follows on a congruently releasing compact (F19); additive effects on droplet size and life (F16); surfactants that promote crystallization of celecoxib from HPMCAS particles, set against the surfactant gains of F21 chen2015a C6; and a delamanid salt that raised the Tg and gave near-complete release from HPMCP, set against the lumefantrine salts of F22 duong2022a C67. See Supersaturation from ASD dissolution F1, F2, F9, F10, F12, F14, F16, F18, F23, F6, F11. Taken from 2025: delamanid dispersions without a biorelevant-media effect, the contrast to bedaquiline in F34 kaur2025 C52; duong2022a R13, and the biorelevant-media and grade effects of that chapter (Supersaturation from ASD dissolution F25, F28), beside F33 and F34; SDS and polysorbate 80 promoting crystallization (Supersaturation from ASD dissolution F14) beside the SDS crystals of F31.

Takes from

[Crystallization from solution](../d-crystallization-from-solution/index.md)

The cilnidipine amorphous solubility (Raina 2015 on dihydropyridines, builds_on of Saboo 2019); surfactants below their CMC that speed ritonavir crystal growth ilevbare2012a R17, set against the surfactant result of F13; HPMCAS grades that release posaconazole poorly at low pH because release is polymer-controlled shah2025 C17, beside the medium dependence of HPMCAS release in F23; the same paper's mass balance for the polymer content of drug-rich droplets shah2025 E3, beside F27. From 2021 also HPMC-AS keeping danazol and enzalutamide droplets small, beside the HPMCAS result of F16, and SDS cutting the inhibition of atazanavir nucleation by PVPVA, beside the surfactant results of F21. See Crystallization from solution F15, F18, F38, F44. From 2025 also the HPMCAS grade trade-off of posaconazole (Crystallization from solution F44) beside the grade ranking of F33, and SDS shortening induction times (Crystallization from solution F38) beside F31.

Takes from

and gives to [Physical stability](../../solid-state-stability/physical-stability/index.md)

Taken: moisture-induced AAPS of PVP dispersions and its dependence on polymer hygroscopicity (Rumondor 2009, 2010, 2011) purohit2017b C9; rumondor2010c C38; the Δχ argument for felodipine–PVP marsac2010 C43; the polymer hygroscopicity ranking xie2016b C23; the confocal method for water-induced separation (Saboo 2017, builds_on of Saboo 2019 and 2020); the felodipine NH band (Konno 2006, builds_on of Saboo 2020). Given: the shift from polymer- to drug-controlled release with loading, cited by a lumefantrine granule study, and water-induced separation slowing ritonavir release, cited by a surfactant phase-separation study that placed SDS in the polymer-rich phase and the more hydrophobic surfactants in drug-rich domains yang2022b C61 (builds_on), beside the surfactant partitioning of the clopidogrel and atazanavir papers (F21); Taken from 2022: the lever rule on a ritonavir–PVPVA–water diagram and dye partitioning into drug-rich domains yang2022b E1, C50 (builds_on of Yang 2022 on release mechanisms), used in F25 and F27. Taken from 2020: the hypothesis that drug–polymer hydrogen bonding resists moisture-induced separation (Rumondor 2009, 2011, builds_on of Saboo 2020 on indomethacin), which the analogue pairs of F17 did not support. See F8, F12, F13, F17, F21. Taken from 2023: the vapour-sorption study of the same four surfactant dispersions, with Span partitioning and lowered Tgs yang2023 R24 (builds_on of Yang 2023), used in F31; protonation of lumefantrine by enteric polymers in dry dispersions bhujbal2021 R8 and a lumefantrine granule study that set an insoluble complex aside trasi2020 C43, beside F32.

Takes from

and gives to [ASD process](../../asd-process/asd-process/index.md)

Taken: TEM of drug-rich domains and water in the solvent as their cause (Li 2017, Mugheirbi 2017) bhardwaj2018 C37. Given: the surface-normalized method and XPS of spray-dried particles, used for spray-dried ritonavir–PVPVA, where water-induced separation lowered release most at congruent loadings li2020 E13, R10, C67; surface drug enrichment of spray-dried particles impairing release (Li 2020), taken by the grazoprevir particle study (F28) hiew2023 C44; the tablet-edge imaging of F25, used for coated ritonavir tablets benson2025 C28; reduced release of humidified ritonavir dispersions, cited by a lopinavir–HPMC study that found the opposite for phase-separated films li2019 C38; the limit and the two regimes, cited by bicalutamide studies in which SDS kept release congruent and TPGS did not moseson2022b R13; the ritonavir limit of 25%, below which coated tablets were formulated benson2025 R20; surface crystallization of PVPVA dispersions during release, cited by a nanocoating study moseson2023 C40 (F19); TPGS making bicalutamide release incongruent, against its gains for felodipine moseson2022b R13 (F21). See F1, F12, F14, F19, F21. From 2024–2025: acid–base interactions read as stabilizing erlotinib in HPMCAS moseson2022a C33, set against the release cost of drug–polymer ion pairs in F32.

Takes from

and gives to [Bioperformance](../../bioperformance/bioperformance/index.md)

Taken: nanodroplets as a reservoir that sustains maximum flux (Indulkar 2016) indulkar2017b C4; que2019 C3. Given: the aggregate-formation route of Indulkar 2017, invoked for enzalutamide (builds_on). Taken from 2021: the reason to keep released droplets small (Indulkar 2016, builds_on of Correa Soto 2022 on clopidogrel) correasoto2022a C1; pre-dissolved HPMCAS inhibiting coarsening of drug-rich droplets ueda2020a C18, beside F16. Given from 2022: polymer salt formation by base addition at one mole per mole of HPMCAS-HF acid groups, taken over for pretomanid dispersions nguyen2023a E7, C67 (F24). See F4, F5, F13, F16. Taken from 2024: HPMCAS solubility of about 5 mg/mL at pH 6 (Nguyen 2023, builds_on of Bapat 2024) bapat2024 M9; atazanavir droplets agglomerating with PVPVA in a dissolution–absorption run hate2018 C27, beside F29.

Gives to

[Miscibility and drug-polymer interactions](../../solid-state-stability/miscibility-and-drug-polymer-interactions/index.md)

Congruent release, the limit and the surface-normalized method, used for lumefantrine, whose release from PVPVA at 5% was about 5 times that from HPMCP in line with the neat polymer rates hiew2022a C44. Taken: pyrene fluorescence to detect phase separation in spray-dried ITZ (Purohit 2015 on ITZ–HPMC, builds_on of Bhardwaj 2018); halogen bonding to the vinylpyrrolidone carbonyl and the Me-TIPP data (Que 2020, builds_on of Que 2021) que2020 C1, used in F17; the critical ionization of HP-50 and CAP, about 0.83 and 0.94, and the HPMCAS-MF pKa, taken by the enteric-polymer papers of 2022–2023 hiew2022a R27; qi2022 R19; bapat2023 M3 (F23); the free-base lumefantrine–PVPVA results, compact dissolution and FTIR methods (Hiew 2022 on lumefantrine polymers, builds_on of Hiew 2022 on salts), against which the salts of F22 are read. See F2, F11, F17, F22. Taken from 2024–2025: the ionic weak base–HPMCAS interaction proposed for lumefantrine, the acid content per gram and pKa of HPMCAS-MF and the critical-ionization model (Hiew 2022 on lumefantrine polymers, builds_on of Bapat 2024, Bapat 2025 and Kaur 2025) bapat2024 C5; bapat2025a C2, M4; kaur2025 C3, on which F32 and F33 rest; the lumefantrine ion pair that leaves too few carboxylates free hiew2022a C57.

Gives to

[Peptide permeability](../../peptide-permeability/peptide-permeability/index.md)

Congruent release from copovidone dispersions and the release patterns of the five polymers, used for a peptide permeation enhancer whose normalized release was read the same way bapat2025b E1, C12. Beside F23, a permeation-enhancer study measured a raised surface pH at insulin minitablets fagan2025 C36. See F1, F11. Given from 2024: PVP grades with different erosion rates as further gel-forming polymers, cited by the peptide study (Deac 2024 on polymer molecular weight, builds_on) (F29).

Takes from

[Solid-state methods](../../characterization-methods/solid-state-methods/index.md) and [Solution methods](../../characterization-methods/solution-methods/index.md)

The fluorescence methods for phase behaviour of dispersions and the separation of 50% ritonavir dispersions within 10 s (Purohit 2015 on phase separation kinetics) purohit2017b R20; the pyrene I/III method for LLPS (Raina 2015 on fluorescent probes, builds_on of Purohit 2017); the prodan and rhodamine 6G dye pair (Saboo 2017, builds_on of Deac 2023 on the interface), used in the imaging of F25; phase inversion in dry dextran–PVP blends by AFM-IR vaneerdenbrugh2012c C43, beside the inversion of F25. See F8, F25.

Left to other subcategories: the amorphous solubility itself and the drug-rich phase that separates above it (Amorphous solubility and LLPS, written before this chapter); how fast crystals form from supersaturated solutions with polymers and surfactants (Crystallization from solution, written before this chapter); what happens to the supersaturation a dissolving dispersion produces, crystallization of the wetted solid and from solution, and the polymer ranking for holding supersaturation (Supersaturation from ASD dissolution, written before this chapter); moisture-induced phase separation and crystallization in storage (Physical stability); manufacturing processes as such (ASD process); membrane transport and absorption (Bioperformance); and the fluorescence, XPS and NMR techniques as methods (Solid-state methods, Solution methods).

How to read this page. Each finding is one conclusion: a headline, a plain statement, one picture and what it means for your drug. Open How it works for the steps and numbers, and Evidence for the data and conditions, at medium (B) or full (C) length. The coloured tag grades the evidence as strong, moderate or weak. Dotted words show a definition. An id such as hate2017 R15 names a paper and an item in its card. Text marked (synthesis: …) joins several papers and is not one paper's claim.

Evidence length

Topic 1 of 5 · 5 findings · F1–F3, F15, F23

Two release regimes and their measurement

F1

Topic 1Two release regimes and their measurement1 of 5

Assay the polymer beside the drug, or dissolve into drug-saturated medium, to tell polymer-controlled from drug-controlled release.

Five papers of 2018–2020 pressed the dispersion into a die so that one face of about 0.5 cm² dissolved, and assayed drug and polymer in the same samples. Each rate was divided by the component's weight fraction, so equal values mean that both leave in the ratio in which they are present bhardwaj2018 P6, P7, E4; indulkar2019a P2, P3, P4; saboo2019 P9, E4; saboo2020a P6, E3. A second test dissolves the dispersion into medium already at the amorphous solubility: release that continues is polymer-controlled, release that stops is drug-controlled indulkar2019a R12, C43, C42.

moderateModerate to strong: drug and polymer were assayed separately in triplicate on compacts of fixed area in four papers, but the limits are brackets between loadings usually 5% apart and no paper states a numerical criterion for "congruent" saboo2019 K1; indulkar2019a K1, X7; saboo2020a X11.

amorphous felodipine ≈0.0008amorphous nilvadipine 0.00210% nilvadipine–PVPVA, drug 2.13neat PVPVA 3.49≈ 1700× polymer over amorphous drug0.00010.0010.010.1110dissolution rate of neat compacts, mg/min/cm² (log scale)

Neat references set the scale; the 10% dispersion releases its drug near the polymer rate. saboo2019 R5, R7, R8; saboo2020a R13

Ritonavir–PVPVA tablets: plain against ritonavir-saturated buffer10% · plain bufferdrug released by 30 min≈99.5%10% · saturated bufferdrug released by 30 min≈90%50% · plain bufferdrug released up to 50 min≈0.44%50% · saturated bufferdrug released up to 50 min0

Release that continues into saturated medium is polymer-controlled; release that stops is drug-controlled. indulkar2019a R12, R13

For your drug

  1. Press compacts of the dispersion, the neat polymer and the neat amorphous drug of the same mass into the same die, assay the polymer in the same samples, and compare normalized rates by a statistical test.
  2. Run the lowest and the target loading once more in medium presaturated at the amorphous solubility.
  3. Near an expected switch use loading steps finer than 5%, and run the test for at least 30–60 min, since 5-min rates missed surface crystallization.

saboo2019 P10, P20; saboo2020a P7, X11; indulkar2019a R12, C43, C42; saboo2020 R8

How it works and key numbers
  1. A single solid dissolves by \frac{dm}{dt} = A\,\frac{D}{h}\,(C_s - C_b) indulkar2017b E4.
  2. If the drug controls the surface, C_s is the amorphous solubility; in medium already at it, C_s = C_{amorph} = C_b and there is no driving force indulkar2017b E5.
  3. If the polymer controls, the drug leaves at the polymer rate times the mass ratio, (dC/dt)_{drug} = (dC/dt)_{polymer}\, m_{drug}/m_{polymer}; at 10% ritonavir and 20 min, ≈67 mg PVPVA × 10/90 gives ≈7.4 mg against ≈7.6 mg ritonavir read from the plot indulkar2019a E3, R1, R2.
  4. Normalized by weight fraction, the same relation predicts equal drug and polymer rates, which is how congruency is read saboo2020a E2, E3.
  5. The constant face removes the particle-size and disintegration effects of powders indulkar2019a C15.
≈1700×neat PVPVA (3.49) against amorphous nilvadipine (0.002 mg/min/cm²)saboo2019 R5, R7
0 against ≈0.44%50% ritonavir tablet in saturated against plain buffer, up to 50 minindulkar2019a R12
5% stepsthe limits found are brackets between tested loadingsindulkar2019a X7; saboo2020a X11
Evidence: data, conditions and papers

Finding F1. Assaying the polymer beside the drug from a compact of constant area, and dissolving it into medium already at the amorphous solubility, tells polymer-controlled from drug-controlled release; the drug concentration alone does not

In short. Five papers of 2018–2020 pressed 25–100 mg of dispersion into a die so that one face of about 0.5 cm² dissolved, assayed drug and polymer in the same samples and divided each rate by the component's weight fraction, so that equal values mean that both leave in the ratio in which they are present bhardwaj2018 P6, P7, E4; indulkar2019a P2, P3, P4; que2019 P3, P4; saboo2019 P9, E4; saboo2020a P6, E3. Against compacts of the neat components the gap is large: neat PVPVA dissolved about 1700 times faster than amorphous nilvadipine (3.49 against 0.002 mg/min/cm²), and five polymers 290–4600 times faster than amorphous felodipine saboo2019 R5, R7; saboo2020a R13. Dissolving into a medium presaturated with drug separates the regimes: 10% ritonavir–PVPVA tablets released as in plain buffer while 50% tablets released no drug, and nifedipine dispersions kept dissolving into water already at their amorphous solubility of 110 µg/mL indulkar2019a R12, R13; indulkar2017b R8, R9, R1. The limits of congruency these tests give are brackets between tested loadings, usually 5% apart, and no paper states a numerical criterion for "congruent" indulkar2019a X7; saboo2019 X11; saboo2020a X11.

Type. method comparison Strength. to strong: drug and polymer were assayed separately in triplicate on compacts of fixed area in four papers, with t-tests in one, and the presaturated-medium test gave the clearest single contrast of the chapter saboo2019 K1: strong; indulkar2019a K1: strong, K3: moderate to strong; weaker where the normalization, the presaturation or the neat-compact mass is not stated saboo2020a X10; indulkar2019a X8; que2019 X13.

How it was shown

Five papers of 2018–2020 pressed 25–100 mg of dispersion into a die so that one face of about 0.50 cm² dissolved, assayed drug and polymer in the same samples and divided each rate by the component's weight fraction bhardwaj2018 P6, P7, E4; indulkar2019a P2, P3; saboo2019 P9, E4; saboo2020a P6, E3. Indulkar and co-workers also dissolved nifedipine (2017) and ritonavir–PVPVA (2019) dispersions into medium presaturated with the drug indulkar2017b P1, P7; indulkar2019a P4, P5.

What the data show

Normalized drug and polymer rates of congruent dispersions were statistically equal (2.13 against 2.35 mg/min/cm² for 10% nilvadipine, "ns"), and those of incongruent ones differed at p ≤ 0.001 to 0.0001 saboo2019 R5, R8.

testsystem and conditionsresultids
neat compactsPVPVA and amorphous nilvadipine, pH 6.8, 100 rpm3.49 and 0.002 mg/min/cm² (≈1700-fold)saboo2019 R5, R7
neat compactsfive polymers and amorphous felodipinepolymers ≈0.23–3.6, felodipine ≈0.0008 mg/min/cm² (290–4600-fold)saboo2020a R13
normalized rates, t-testnilvadipine and cilnidipine in PVPVAdrug = polymer (ns) up to 10% and 15%; p ≤ 0.001 abovesaboo2019 R8
presaturated bufferritonavir–PVPVA 10, 30, 50%, 37 °C10% unchanged; 30% still releasing; 50% zeroindulkar2019a R12, R13
presaturated D2O, 110 µg/mLnifedipine 10, 20%, HPMC-E5 and PVPVA, 5 °Crelease continued to ≈214–218 µg/mLindulkar2017b R8, R9
5-min rates against 30-min profilesindomethacin methyl ester–PVPVAlimit ≥25% by 5-min rates, congruent over 30 min only at 5%saboo2020 C14, R8
Fig. 4 of indulkar2019a: ritonavir release from 10, 30 and 50% dispersions into plain and ritonavir-saturated buffer
Fig. 4 · indulkar2019aritonavir release from 10, 30 and 50% dispersions into plain and ritonavir-saturated buffer

The 10% curves overlap in both media, while the 50% tablet (inset) shows a small rise in plain buffer and none in saturated buffer indulkar2019a R12.

Why

For a drug-controlled surface with C_s = C_{amorph} = C_b the dissolution equation of a single solid gives no driving force, so the authors read continued release into a saturated medium as polymer control ("clearly indicate"; "confirming") and zero release as a drug-rich surface indulkar2017b E4, E5, C35; indulkar2019a C43, C42. (synthesis: the drug concentration alone cannot separate the regimes, because a slow polymer-controlled dispersion and a drug-controlled one can give similar drug curves; only the polymer curve or the saturated-medium test shows which component sets the rate.)

Limits and transfer

How the medium was presaturated is not stated indulkar2019a X8, and the later papers differ in limit criterion, so their limits compare only to the loading step saboo2020 P5; que2021 P9; yang2021 P17; hiew2022b P8, X6. Press compacts of the dispersion, the neat polymer and the neat amorphous drug into the same die, compare normalized rates by a statistical test, and rerun the lowest and the target loading in presaturated medium for at least 30–60 min saboo2019 P10, P20; indulkar2019a R12, C43; saboo2020 R8.

How it was shown

Indulkar and co-workers (2017) asked whether nifedipine dispersions dissolve by a drug- or a polymer-controlled route; they dissolved 10 and 20% dispersions with HPMC-E5 or PVPVA (150–250 µm) at 5 °C in 20 mL D2O at 300 rpm, once into plain D2O to 220 µg/mL drug and once into D2O presaturated with nifedipine at 110 µg/mL plus a further 110 µg/mL from the dispersion, following the drug by UV at 360 nm indulkar2017b P1, P7. Purohit and Taylor (2017) dissolved ritonavir films cast on vial walls in 18 mL of 100 mM pH 6.8 phosphate at 25 °C, followed the drug by UV (240 nm minus 400 nm) and the polymer by colorimetry of 1 µm-filtered aliquots (phenol–sulfuric acid for HPMCAS, potassium triiodide for PVP and PVPVA), and measured the free drug after ultracentrifugation; the film area was not controlled purohit2017b P14, P16, P19, P20. Bhardwaj and co-workers (2018) pressed 25 ± 5 mg of itraconazole (ITZ)–PVPVA at 500 psi in an 8 mm die, backed it with ethyl cellulose pressed at 1000 psi and sealed it with a silicone septum so that one face of about 0.50 cm² dissolved, in 70 mL 0.1 N HCl at 37 °C and 300 rpm; ITZ was read at 253 nm and PVPVA from the residual absorbance at 220 nm (quadratic calibration), n = 3, and rates were the 0–20 min slopes bhardwaj2018 P6, P7, E7. They expressed the ITZ rate relative to crystalline ITZ and divided both rates by the component's weight fraction bhardwaj2018 E2, E4. Indulkar and co-workers (2019) used Wood's apparatus with 100 mg compressed at 1600 lbs in an 8 mm die, rotated at 100 rpm in 100 mL 50 mM pH 6.8 phosphate at 37 °C, assayed unfiltered samples for ritonavir (HPLC, 210 nm) and PVPVA (size-exclusion chromatography, 205 nm), ran neat amorphous ritonavir and neat PVPVA tablets, and repeated the 10, 30 and 50% tablets in buffer presaturated with ritonavir at about 30 µg/mL indulkar2019a P2, P3, P4, P5. Que and co-workers (2019) used the same set-up at 1500 psi, mixing each drug sample with ethanol to dissolve drug-rich colloids and filtering the polymer sample through 0.2 µm, with a 250 mg neat PVPVA compact que2019 P3, P4, X13. Saboo and co-workers (2019) used 100 mg at 1500 psi in 100 mL 100 mM pH 6.8 phosphate at 100 rpm, took rates from the initial linear part of percent release normalized to each component's content, compared drug and polymer rates by t-test, and added powder dissolution at a nominal 100 µg/mL saboo2019 P9, P10, E4, P20, P19. Saboo and co-workers (2020) wrote the rate as A = kV/(SN) and assayed HPMC and HPMCAS by HPLC with evaporative light scattering and PVP, PVPVA and Eudragit S 100 (EUDS) by size-exclusion chromatography, with EUDS at pH 7.4 saboo2020a E3, P6, P7. The papers of 2020–2022 kept the 100 mg, 0.5 cm² compact but varied the read-out: Saboo and co-workers (2020) took rates from samples every minute over the first 5 min, each drug in its own medium saboo2020 P5, X5; Que and co-workers (2021) defined the limit as the last loading with simultaneous release and at least 80% of the drug in 90 min que2021 P9; Yang and co-workers (2021) compared drug and polymer rates by t-test at each loading and also dissolved powders, the PVPVA powders in medium holding 400 µg/mL HPMCAS yang2021 P17, P12, X18; Correa Soto and co-workers (2022) normalized by R = k/(Sx) without the medium volume and sampled to 120 min correasoto2022a E1, P11; and Hiew and Taylor (2022) dissolved into 250 mL and read the limit from drug release alone, without a stated criterion hiew2022b P8, X6. Indulkar and co-workers (2022) kept the 100 mg Wood's set-up with unfiltered samples so that drug held in colloids was counted, and set early PVPVA release of ternary tablets against a binary tablet reprinted from the 2019 paper, in amounts not normalized to the polymer content indulkar2022 P3, C7, P2, X6. Yang and co-workers (2022) printed the normalized rate as R = kV/(Ax) but reported only percent-release profiles, so no normalized rates are available from that paper yang2022a E1, X12. Bapat and co-workers (2023) kept the 100 mg, 0.5 cm² compact at 100 rpm and 37 °C but varied the medium (phosphate pH 6.8 at 3–51 mM/ΔpH buffer capacity, FaSSIF, FeSSIF, glycine and pH 7.5 and 9.0 buffers), assayed HPMCAS by HPLC with evaporative light scattering calibrated in each medium, and took rates from the initial linear part of each curve by R = kV/(Sx) bapat2023 P7, P8, P14, E1. Deac and co-workers (2023) added the drug content of the gel scraped from the compact at 10, 20 and 30 min, which they consider a more sensitive test of congruency than separate release rates because the drug gathers in the gel while release is incongruent (F25) deac2023a P4, C13, R3; their percent release is calculated on a 100 mg basis for compacts of 100–200 mg deac2023a X9.

What the data show

The neat references set the scale on which every dispersion is read. Melt-quenched ITZ dissolved at 51 ± 2 and crystalline ITZ at 2.8 ± 0.2 µg/min/cm², a ratio of about 18 that the authors equate with the amorphous-to-crystalline solubility ratio, which they did not measure bhardwaj2018 R4, R5, C45. Neat PVPVA dissolved at 10.4 mg/min/cm² in 0.1 N HCl at 300 rpm, 3.49 mg/min/cm² in pH 6.8 phosphate at 100 rpm, and ≈3.4 in the 2020 paper, where an extractor check of the plotted curve gives ≈1.7 bhardwaj2018 R9; saboo2019 R5; saboo2020a R13, X10 (synthesis: the three values come from different media, paddle speeds and compact masses and are not comparable). Amorphous nilvadipine dissolved at 0.002 mg/min/cm² and amorphous felodipine at ≈0.0008, neat amorphous ritonavir released essentially nothing in 120 min, and neat amorphous ledipasvir nothing detectable in 2 h saboo2019 R5; saboo2020a R13; indulkar2019a R1; que2019 R2. Against these, normalized drug and polymer rates of congruent dispersions were statistically equal (for example 2.13 against 2.35 mg/min/cm² for 10% nilvadipine, "ns"), and those of incongruent ones differed at p ≤ 0.001 to 0.0001 saboo2019 R5, R8. In ritonavir-saturated medium the 10% tablet released ≈90% by 30 min against ≈99.5% in plain buffer, the 30% tablet ≈40.5% by 120 min against ≈29.5%, and the 50% tablet 0 at every point up to 50 min against ≈0.44% in plain buffer indulkar2019a R12. Nifedipine dispersions in medium already at 110 µg/mL rose to ≈201 (10% HPMC-E5) and ≈211 µg/mL (10% PVPVA) within 5 and 1 min, and to ≈214–218 µg/mL at 60 min indulkar2017b R8, R9. Powders behaved like compacts: nilvadipine powders reached ≈89–91 µg/mL at 5–10% and ≈13.5–15 µg/mL at 15–20%, cilnidipine ≈96–99 up to 15% and ≈0.65–1.33 µg/mL at 20–25% saboo2019 R20, R21; ritonavir powders formed LLPS for the same combinations as films (data not shown) purohit2017b R19. In the papers of 2020–2022 the read-outs agreed where both were taken: at the limits of four phenolphthalein analogues drug and polymer rates differed with p = 0.022–0.67, and powders of six drugs showed the same cliff as compacts que2021 R21; yang2021 C41. The 5-min read-out of indomethacin methyl ester gave a limit of at least 25%, but over 30 min the ester released congruently only at 5% because crystals formed on the surface (F19) saboo2020 C14, R8.

papersystemmethod and conditionsresultids
bhardwaj2018crystalline and melt-quenched ITZ; PVPVA0.5 cm² compacts, 0.1 N HCl, 37 °C, 300 rpm2.8 and 51 µg/min/cm² (ratio ≈18); PVPVA 10.4 mg/min/cm²bhardwaj2018 R4, R5, R9
saboo2019PVPVA, amorphous nilvadipineWood's, pH 6.8, 100 rpm3.49 and 0.002 mg/min/cm² (≈1700-fold)saboo2019 R5, R7
saboo2020afive polymers, amorphous felodipinesame; EUDS pH 7.4polymers ≈0.23–3.6; felodipine ≈0.0008 (290–4600-fold)saboo2020a R13
saboo2019Nil and Cil in PVPVAnormalized rates, t-testdrug = polymer (ns) up to 10% and 15%; p ≤ 0.001 abovesaboo2019 R8
indulkar2019aritonavir–PVPVA 10, 30, 50%plain against presaturated buffer, 37 °C10% unchanged; 30% still releasing; 50% zeroindulkar2019a R12, R13
indulkar2017bnifedipine HPMC-E5 and PVPVA 10, 20%D2O presaturated at 110 µg/mL, 5 °Crelease continued to ≈214–218 µg/mLindulkar2017b R8, R9
saboo2019Nil and Cil powders100 µg/mL nominal, 300 rpmsame cliff as compactssaboo2019 R20, R21
purohit2017britonavir powders100 mL buffersame LLPS combinations as films (not shown)purohit2017b R19
saboo2020IND, INDester–PVPVA5-min rates against 30-min profilesINDester limit ≥25% by 5-min rates, congruent over 30 min only at 5%saboo2020 C14, R8
que2021four analogueslimit = congruent and ≥80% in 90 min; t-test at 99%drug against polymer p = 0.022–0.67 at the limitsque2021 P9, R21
yang2021six drugs, PVPVA and HPMCASpowders (PVPVA media with 400 µg/mL HPMCAS) and compactssame cliff in powders and compactsyang2021 P12, C41, X18
hiew2022blumefantrine formsdrug release only, 250 mLlimit read without a stated criterionhiew2022b P8, X6
li2020 (ASD process)spray-dried ritonavir–PVPVAdrug rate normalized by area and DL onlypolymer not assayed in the rateli2020 E13
benson2025 (ASD process)coated ritonavir–PVPVA tabletsdrug onlycongruency not measuredbenson2025 X18

Figure

Fig. 15 of saboo2019: normalized drug and PVPVA release rates of nilvadipine and cilnidipine dispersions with t-test marks
Fig. 15 · saboo2019normalized drug and PVPVA release rates of nilvadipine and cilnidipine dispersions with t-test marks

Red (drug) and black (PVPVA) bars stand together and are marked "ns" up to 10% nilvadipine and 15% cilnidipine; one 5% step higher the drug bar collapses below the break of the y-axis while the polymer bar remains saboo2019 R8, R5, R6.

Fig. 4 of indulkar2019a: ritonavir release from 10, 30 and 50% dispersions into plain and ritonavir-saturated buffer
Fig. 4 · indulkar2019aritonavir release from 10, 30 and 50% dispersions into plain and ritonavir-saturated buffer

The 10% curves overlap in both media, while the 50% tablet (inset) shows a small rise in plain buffer and none in saturated buffer indulkar2019a R12.

Why

The presaturated-medium test rests on the dissolution equation of a single solid,

\frac{dm}{dt} = A\,\frac{D}{h}\,\left(C_s - C_b\right)

indulkar2017b E4, which for a drug-controlled surface with C_s = C_{amorph} = C_b gives no driving force indulkar2017b E5. The authors therefore read continued release into a saturated medium as polymer control ("clearly indicate"; "confirming") and zero release as a drug-rich surface "in agreement with" the Nernst–Brunner form dC/dt = (DA/Vh)(C_s - C) indulkar2017b C35; indulkar2019a C43, C42, E2. For the polymer-controlled case they write the drug rate as the polymer rate times the mass ratio, (dC/dt)_{drug} = (dC/dt)_{polymer}\, m_{drug}/m_{polymer}; at 10% ritonavir and 20 min, ≈67 mg PVPVA × 10/90 gives ≈7.4 mg against ≈7.6 mg ritonavir read from the plot indulkar2019a E3, R1, R2. Normalized by weight fraction, the same relation predicts equal drug and polymer rates, which is how congruency is read in the 2020 paper saboo2020a E2, E3. The constant face removes the particle-size and disintegration effects of powders (the authors' stated reason), although packed particle layers present a renewed surface during dissolution indulkar2019a C15; bhardwaj2018 C47, C64. Reading the amorphous-to-crystalline IDR ratio as a solubility ratio is carried over from polymorphs ("should be the same") bhardwaj2018 E3, C45. (synthesis: the drug concentration alone cannot separate the regimes, because a slow polymer-controlled dispersion and a drug-controlled one can give similar drug curves; only the polymer curve or the saturated-medium test shows which component sets the rate.)

Conditions and limits

Compacts of 25–100 mg at 37 °C in 0.1 N HCl (ITZ), 50 or 100 mM pH 6.8 phosphate, or pH 7.4 for EUDS; ritonavir films at 25 °C; nifedipine at 5 °C bhardwaj2018 P7; indulkar2019a P2; saboo2019 P9; saboo2020a X8; purohit2017b P14; indulkar2017b P7. The weight-fraction normalization assumes similar component densities saboo2020a C8. How the medium was presaturated, and whether the starting concentration was subtracted, is not stated indulkar2019a X8; the two nifedipine media received different amounts of dispersion indulkar2017b X10. Some percent releases exceed 100% without a stated basis indulkar2019a X12. The neat PVPVA compact of the ledipasvir study weighed 250 mg against 100 mg for the dispersions, and the compact mass of the neat polymers of the 2020 study is not stated que2019 X13; saboo2020a X10. High-loading HPMCAS and EUDS rates are slopes after a lag saboo2020a X9. In the ritonavir films polymer release was measured only at 10:90 and 50:50 purohit2017b X12. The later papers differ in medium volume, sampling window and limit criterion (5-min rates, at least 80% in 90 min, t-test of rates, drug release alone), so their limits compare only to the loading step saboo2020 P5; que2021 P9; yang2021 P17; hiew2022b P8, X6. In the 2022 ritonavir surfactant paper the axis of the early polymer-release plot is labelled mg/mL but the values behave as milligrams released per vessel indulkar2022 X5. From 2024 the PVP molecular-weight paper counted release as congruent when more than 80% of both components left and took the limit as the highest loading passing 80% of the drug, over 90–120 min, and the bedaquiline paper of 2025 dispersed powders without assaying the polymer deac2024a C36, X6; kaur2025 P11, X14.

Counterexamples and conflicts

None found against the test itself. Papers that measured only the drug inferred the regime: the spray-dried ritonavir study normalized the drug rate by area and loading only, a coated-tablet study did not measure PVPVA, and a fluorescence study read the regime from whether the amorphous solubility was reached li2020 E13; benson2025 X18; tres2018 X10. A congruency test over the first 5 min missed the later failure of a fast crystallizer (F19) saboo2020 X7.

Transfer check

Press compacts of the target dispersion and of the neat polymer and the neat amorphous drug of the same mass into the same die, assay the polymer in the same samples (size-exclusion chromatography, light-scattering detection or colorimetry), and compare normalized rates by a statistical test saboo2019 P10, P20; saboo2020a P7. Run the lowest and the target loading once more in medium presaturated at the amorphous solubility: release that continues is polymer-controlled, release that stops is drug-controlled indulkar2019a R12, C43, C42. Near an expected switch use loading steps finer than 5%, since every limit reported here is a bracket saboo2020a X11; indulkar2019a X7. Run the test for at least 30–60 min, since 5-min rates missed surface crystallization saboo2020 R8. For an enteric polymer, record the buffer capacity of the medium beside its pH, since the HPMCAS rate changed about sixfold between 3 and 51 mM/ΔpH at pH 6.8 (F23) bapat2023 R5. Scrape and assay the gel layer at 10–30 min: a rising drug content of the gel marks incongruent release even while percent release still matches the neat polymer deac2023a R3, C13.

History

Compacts of sulfathiazole–PVP had shown crystalline-drug-, amorphous-drug- and polymer-controlled regimes as loading fell (Simonelli 1969, cited), and normalized ketoconazole release had tracked polymer release at 20% loading (Chen 2016, cited) bhardwaj2018 R22, R23. In the library Indulkar and co-workers (2017) first used a drug-saturated medium to show polymer control, and Purohit and Taylor (2017) first assayed drug and polymer together, on films indulkar2017b C35; purohit2017b C52. Bhardwaj and co-workers (2018) introduced the constant-area compact with both components and loading-normalized rates bhardwaj2018 C65. Indulkar and co-workers (2019) combined both components, neat references and the presaturated medium in Wood's apparatus indulkar2019a C15, C16; Saboo and co-workers (2019) took over the surface-normalized method (builds_on) and added t-tests and powders, and Que and co-workers (2019) and Saboo and co-workers (2020) carried it to ledipasvir and to five polymers saboo2019 R8; que2019 P3; saboo2020a E3. The papers of 2020–2022 kept the method for indomethacin and its ester, four phenolphthalein analogues, felodipine with TPGS, loratadine at two temperatures, clopidogrel, atazanavir and lumefantrine salts, and added powder release of six drugs saboo2020 P5; que2021 P9; saboo2021 P6; yang2021 P15, P12; correasoto2022a P11; correasoto2022b P5; hiew2022b P8. The HPMCAS papers of 2024–2025 kept the constant-area compact with drug and polymer assayed for eight drugs and three grades, while the bedaquiline study of 2025 used powders and drug assay only (F32, F33, F34) bapat2024 P7; bapat2025a P6; kaur2025 P11.

F2

Topic 1Two release regimes and their measurement2 of 5

At low loading drug and polymer leave together at the polymer's pace, far faster than the neat amorphous drug.

Ritonavir–PVPVA tablets at 10–25% drug released both components together, ≈97–100% of the drug by 60 min, while neat amorphous ritonavir released essentially nothing in 120 min indulkar2019a R11, R3, R1. 10% nilvadipine–PVPVA released its drug at 2.13 mg/min/cm², equal to its polymer rate of 2.35, against 0.002 for amorphous nilvadipine saboo2019 R5, R8.

strongStrong for the regime itself, which rests on separate drug and polymer assays from constant-area compacts with neat references; moderate for the mechanism, which is argued, not measured indulkar2019a K1, C25, C36; saboo2019 K1; saboo2020a K1.

Drug rate of a 10% dispersion ÷ neat amorphous drugfelodipine–PVP3.8 against 0.0008 mg/min/cm²≈4800×nilvadipine–PVPVA2.13 against 0.002 mg/min/cm²≈1100×itraconazole–PVPVA199 against 51 µg/min/cm², 0.1 N HCl≈3.9×

The gain is large where the amorphous drug alone is very slow and small where it is relatively fast. saboo2019 R5; saboo2020a R14, R13; bhardwaj2018 R4

Polymer rate from a congruent dispersion ÷ neat polymeritraconazole 10%spray-dried · extruded0.22–0.29nilvadipine 10%2.35 against 3.490.67cilnidipine 15%2.36 against 3.490.68felodipine–PVPVA 10%≈2.6 against ≈3.4≈0.76

In the 2018–2020 papers the polymer left more slowly than from a neat compact; later papers found the neat rate or faster (F15). bhardwaj2018 R12; saboo2019 R5, R8; saboo2020a R14

For your drug

  1. Measure the neat polymer and the neat amorphous drug in the same die and medium; compacts at 5 and 10% loading should give equal normalized drug and polymer rates and continued release into presaturated medium.
  2. Expect most gain where the neat amorphous drug is three orders slower than the polymer and little where it is within about an order of magnitude; a polymer fraction of 0.2–0.3 of its neat rate means the drug is already slowing the polymer.

saboo2019 R8, R7; indulkar2019a R12; bhardwaj2018 R4, R12, C49

How it works and key numbers
  1. At low loading there is too little drug to form an intact surface layer, so the dissolving polymer is thought to bring the drug into solution indulkar2019a C25.
  2. For ritonavir the authors suggest that a drug–polymer interaction persists during hydration and hinders amorphous–amorphous phase separation (AAPS), and that dissolution is faster than AAPS, keeping the interface composition constant indulkar2019a C36, C37.
  3. Higuchi's diffusion model allows only one mixture ratio, \frac{N_{drug}}{N_{polymer}} = \frac{D_{drug}\,C_{s(drug)}}{D_{polymer}\,C_{s(polymer)}}, about 1.7 × 10⁻³ for felodipine–PVPVA; congruent release over a range of polymer-rich compositions contradicts it saboo2020a E4, R27, C36, C37.
  4. Because the drug follows the polymer, the step that limits polymer dissolution also limits drug release: in HPMCAS the 10% indomethacin drug rate rose from about 0.12 to 0.80 mg/min/cm² as buffer capacity rose from 3 to 26 mM/ΔpH (F23) bapat2023 R9, C35.
2.13 against 0.002 mg/min/cm²10% nilvadipine–PVPVA against amorphous nilvadipinesaboo2019 R5
0.22–0.29polymer rate of 10% itraconazole compacts as a fraction of neat PVPVAbhardwaj2018 R12
5 → 60%loading range over which indomethacin and its ester stayed coupled in HPMCAS-MFbapat2024 R2, R3
Evidence: data, conditions and papers

Finding F2. Below a drug-specific loading a dispersion releases drug and polymer at one normalized rate, at about the polymer's pace and far faster than the neat amorphous drug, while in the 2018–2020 papers the polymer itself left more slowly than from a neat compact

In short. Ritonavir–PVPVA tablets at 10–25% drug released both components together, ≈97–100% of the drug by 60 min, while neat amorphous ritonavir released essentially nothing in 120 min indulkar2019a R11, R3, R1. Nilvadipine at 5–10% and cilnidipine at 5–15% in PVPVA gave drug rates of 2.13–2.53 mg/min/cm², equal to their polymer rates, against 0.002 for amorphous nilvadipine, and felodipine with PVP gave ≈3.3–3.8 at 5–10% against ≈0.0008 for amorphous felodipine saboo2019 R5, R6, R8; saboo2020a R14, R13. 10% itraconazole–PVPVA released 199 µg/min/cm², about 4 times amorphous ITZ and 71 times the crystal bhardwaj2018 R4, R6. In every set the polymer left more slowly than from a neat compact: 0.22–0.29 of neat PVPVA for 10% ITZ and 2.35–2.76 against 3.49 mg/min/cm² for nilvadipine bhardwaj2018 R12; saboo2019 R5, R8. In the papers of 2020–2022, IND, indomethacin methyl ester and four phenolphthalein analogues released congruently at about the neat PVPVA rate (about 2.8–4.2 against 3.0–3.8 mg/min/cm²), and clopidogrel at about twice it (F15) saboo2020 R3; que2021 R21; correasoto2022a R18. With HPMCAS, 10% indomethacin and 10% indomethacin methyl ester dispersions released drug and polymer at one normalized rate in every medium, so the drug rate rose about sevenfold to eightfold with the buffer capacity of the medium (about 0.12 against 0.10 mg/min/cm² at 3 mM/ΔpH, 0.80 against 0.78 at 26 mM/ΔpH for IND) (F23) bapat2023 R9, R13, R10. In 2024–2025 the same coupling held in HPMCAS-MF for indomethacin and its ester from 5 to 60% loading, both rates falling from about 0.85 to 0.50 and 0.66 to 0.39 mg/min/cm² against about 0.91 for the neat polymer, and in PVP for clotrimazole up to 20–38% depending on the grade, where the higher grades released more slowly (F29, F32) bapat2024 R2, R3; deac2024a R1, R3.

Type. observation in 7 drugs (nifedipine, ritonavir, itraconazole, ledipasvir, nilvadipine, cilnidipine, felodipine) with five polymers, and 15 further drugs in 2020–2022, and indomethacin and its methyl ester with HPMCAS-MF in 2023 Strength. for the regime itself, which rests on separate drug and polymer assays from constant-area compacts with neat references indulkar2019a K1: strong; saboo2019 K1: strong; saboo2020a K1: strong; moderate for the mechanism, which is argued, not measured indulkar2019a C25, C36.

How it was shown

The constant-area compacts of F1 were run for ritonavir, nilvadipine and cilnidipine in PVPVA, felodipine in five polymers and itraconazole (ITZ)–PVPVA, later for eight drugs in HPMCAS-MF at 5–60% and clotrimazole in six PVP grades indulkar2019a A1; saboo2019 A2; saboo2020a A2; bhardwaj2018 A1; bapat2024 P7; deac2024a P5.

What the data show

Nilvadipine at 5 and 10% gave drug rates of 2.53 and 2.13 against polymer rates of 2.76 and 2.35 mg/min/cm², and every polymer rate from a dispersion was below the 3.49 of neat PVPVA (p ≤ 0.05 to 0.01) saboo2019 R5, R6, R8.

systemconditionsdrug and polymer releaseids
ritonavir–PVPVA 10–25%compacts, pH 6.8, 37 °Ccongruent, ≈97–100% at 60 minindulkar2019a R3, R11
nilvadipine 5–10%, cilnidipine 5–15% in PVPVApH 6.8, 37 °Cdrug 2.13–2.53 = polymer; neat PVPVA 3.49 mg/min/cm²saboo2019 R5, R6, R8
felodipine in PVP, PVPVA, HPMC (≤10–15%); HPMCAS, EUDS (≤50%)pH 6.8 or 7.4congruent at ≈0.07–4.1 mg/min/cm²; amorphous felodipine ≈0.0008saboo2020a R14, R13
ITZ–PVPVA 10%, spray-dried and extruded0.1 N HCl, 37 °C199 µg/min/cm²; polymer 0.22–0.29 of neatbhardwaj2018 R4, R12
indomethacin and its ester in HPMCAS-MF, 5–60%pH 6.8, 37 °Cdrug ≈0.85 → 0.50 and 0.66 → 0.39 with the polymer alongside; neat ≈0.91 mg/min/cm²bapat2024 R2, R3
clotrimazole–PVP K25 20%, K29/32 30%, K60 35%, K90 38%pH 8.0, 90–120 mindrug ≈83–96%, PVP ≈93–103%deac2024a R1
Fig. 3A of indulkar2019a: percent release of ritonavir and PVPVA from the 10% dispersion
Fig. 3A · indulkar2019apercent release of ritonavir and PVPVA from the 10% dispersion

The red (ritonavir) and blue (PVPVA) curves lie on top of each other and both reach about 100% by 30 min indulkar2019a R3.a–b.

Why

The authors' explanation is that at low loading there is too little drug to form an intact surface layer, so that the dissolving polymer brings the drug into solution ("is thought to occur") indulkar2019a C25. Higuchi's diffusion model allows only one mixture ratio to release both components at once, so congruent release over a range of compositions contradicts it saboo2020a E4, C36, C37. The slower polymer is put down "most likely" to the hydrophobicity of the formulation or to drug–polymer interactions saboo2019 C13.

Limits and transfer

Congruent does not mean fast: 10% felodipine–HPMC released ≈0.14 mg/min/cm², about a sixth of 10% felodipine–HPMCAS saboo2020a R14. In 2020–2022 the polymer left congruent compacts at about its neat rate or faster, up to about twice for clopidogrel que2021 R21; correasoto2022a R18. A drug whose neat amorphous rate is within about an order of magnitude of the polymer's (ITZ in acid) gains little from polymer control; one three orders slower gains most bhardwaj2018 R4; saboo2019 R7.

How it was shown

The set-ups are those of F1. Indulkar and co-workers (2017) tested 10 and 20% nifedipine with HPMC-E5 or PVPVA at 5 °C indulkar2017b P1, P7. Purohit and Taylor (2017) followed ritonavir and polymer from 10:90 and 50:50 films of PVP K-90, PVPVA and HPMCAS-MF at a dose of 60 µg/mL drug (540 or 60 µg/mL polymer) purohit2017b P14, A1, A2. Bhardwaj and co-workers (2018) compared spray-dried and melt-extruded ITZ–PVPVA at 50, 25, 20 and 10% bhardwaj2018 A1, A2. Indulkar and co-workers (2019) tested ritonavir–PVPVA at 10, 20, 25, 30, 35, 40 and 50% indulkar2019a A1. Que and co-workers (2019) tested ledipasvir–PVPVA at 2, 5, 7.5, 10 and 20% que2019 A1. Saboo and co-workers tested nilvadipine at 5–20% and cilnidipine at 5–25% in PVPVA (2019) and felodipine in PVP, PVPVA and HPMC at 5–30% and in HPMCAS and EUDS at 10–50% (2020) saboo2019 A2; saboo2020a A2. Bapat and co-workers (2024) used the same constant-area compact for HPMCAS-MF dispersions of eight drugs at 5–60% with drug and polymer assayed, and Bapat and Taylor (2025) for 25% loratadine and cinnarizine in three HPMCAS grades (F32, F33) bapat2024 P7, E1; bapat2025a P6. Deac and co-workers (2024, polymer molecular weight) released clotrimazole from six PVP grades in pH 8.0 buffer and counted release as congruent when both components passed 80% deac2024a P5, C36.

What the data show

Ritonavir: the 10% tablet was essentially done by 30 min (drug ≈99.5%, PVPVA ≈94%), the 20% by 40 min and the 25% by 60–75 min; within this range release slowed with loading (≈77% against ≈46% of the drug at 20 min for 10 and 25%) indulkar2019a R3. In mass the 10% tablet released ≈67 mg PVPVA by 20 min against ≈46 mg for the neat PVPVA tablet indulkar2019a R2. Nilvadipine at 5 and 10% gave drug rates of 2.53 and 2.13 against polymer rates of 2.76 and 2.35 mg/min/cm², cilnidipine at 5, 10 and 15% 2.51, 2.26 and 2.18 against 2.74, 2.41 and 2.36, and every polymer rate from a dispersion was below the 3.49 of neat PVPVA (p ≤ 0.05 to 0.01) saboo2019 R5, R6, R8. Ledipasvir at 2 and 5% gave ≈54 and ≈50% drug with ≈55 and ≈49% polymer at 30 min and about 100% of both by 60 min que2019 R3, R4. ITZ at 10% gave 199 µg/min/cm² from both processes, with normalized rates of ≈2000 (drug) against ≈2265 µg/min/cm² (polymer) for the spray-dried compact and ≈555 against ≈810 at 20%, while the polymer left at about 0.22 (spray-dried) and 0.29 (extruded) of the rate of neat PVPVA bhardwaj2018 R4, R11, R12. Felodipine: PVP gave ≈3.3/≈3.3 (5%) and ≈3.8/≈4.1 mg/min/cm² (10%, drug/polymer), PVPVA ≈2.4/≈2.6 at 5 and 10% and ≈1.9/≈1.9 at 15%, HPMC ≈0.26/≈0.29 and ≈0.14/≈0.17, against neat PVP ≈3.6, PVPVA ≈3.4 and HPMC ≈0.37; HPMCAS stayed congruent at ≈0.82–0.93 up to 30% and EUDS at ≈0.07–0.16 up to 50% (see F11) saboo2020a R14, R13. Nifedipine dispersions released completely in under 5 min (PVPVA) and about 20 min (HPMC-E5) at 5 °C, also into drug-saturated water indulkar2017b R8, R9, C23. From 10:90 ritonavir films the polymer reached ≈500 of 540 µg/mL PVP by 10 min and ≈565 (PVPVA) and ≈550 µg/mL (HPMCAS) by about 5 min, while ritonavir reached ≈83, ≈116 and ≈113 µg/mL purohit2017b R15, R16, R17. (synthesis: the drug gain over the neat amorphous drug is 2.13/0.002 ≈ 1100-fold for 10% nilvadipine, 3.8/0.0008 ≈ 4800-fold for 10% felodipine–PVP and 199/51 ≈ 3.9-fold for 10% ITZ in 0.1 N HCl; the polymer from the dispersion ran at 2.35/3.49 = 0.67 (nilvadipine 10%), 2.36/3.49 = 0.68 (cilnidipine 15%) and ≈2.6/≈3.4 ≈ 0.76 (felodipine–PVPVA 10%) of neat PVPVA.) The papers of 2020–2022 add IND at 5 and 10% (drug and polymer about 3.44/3.47 and 3.14/3.19 mg/min/cm², against about 0.002 for amorphous IND) and INDester at 5–25% (about 3.3–4.2) saboo2020 R3; the four analogues at their limits (about 2.8–3.7 for drug and polymer) que2021 R21; felodipine with 5% TPGS at 10–30% (about 2.6–3.2) saboo2021 R9; loratadine–PVPVA at 20 and 30% (about 3.33/3.37 and 2.70/2.88) and loratadine–HPMCAS at 5–20% (about 0.40–0.61) yang2021 R21, R18; clopidogrel at 40% (about 4.5 for the drug and 5.2 for the polymer) correasoto2022a R18; ATZ at 5% (about 100% of both by 90 min) correasoto2022b R1; and lumefantrine free base at 5–35% (about 3.15–3.9 mg/min/cm² for the drug) hiew2022b R12. The 2023 HPMCAS study adds IND at 10% (drug and polymer about 0.12/0.10, 0.24/0.23, 0.55/0.54, 0.80/0.78 and 0.82/0.76 mg/min/cm² at 3, 5, 13, 26 and 51 mM/ΔpH, and 0.51/0.49 in FaSSIF) and INDester at 10% (about 0.13/0.11 to 0.57/0.59) bapat2023 R9, R13. Neat amorphous IND gave about 0.40 against 0.80 for IND from the dispersion, a comparison per unit of drug in the compact; per unit area the dispersion released about 0.08 mg IND/min/cm², about five times less than the neat amorphous drug bapat2023 R9, X14. In HPMCAS-MF the polymer left indomethacin dispersions at about 0.84 (5%) to 0.51 mg/min/cm² (60%) beside drug rates of 0.85 to 0.50, and indomethacin methyl ester dispersions at about 0.67 to 0.37 beside 0.66 to 0.39, against about 0.91 for the neat polymer; at 25% the ritonavir, loratadine, clotrimazole and cinnarizine dispersions released drug and polymer at about 0.40 and 0.43, 0.10 and 0.12, 0.05 and 0.08, and 0.03 and 0.05 bapat2024 R2, R3, R4. Loratadine dispersions in HPMCAS LF, MF and HF released drug and polymer at about 0.25 and 0.27, 0.10 and 0.12, and 0.01 and 0.02 at pH 6.8 bapat2025a R2. Clotrimazole–PVP released about 86–88% of the drug and 103% of the polymer (K25, 20%), 87–93% of both (K29/32, 30%), 96 and 101% (K60, 35%) and, at 120 min, 83 and 96% (K90, 38%), and neat PVP and the congruent dispersions released more slowly as molecular weight rose deac2024a R1, R3, C19.

papersystemmethod and conditionsresultids
indulkar2017bnifedipine 10, 20% with HPMC-E5 or PVPVA5 °C, D2O, 300 rpmcomplete in ~20 and < 5 min, also into saturated mediumindulkar2017b R8, R9, C35
purohit2017britonavir 10:90 films, three polymers25 °C, pH 6.8polymer and drug out within ≈5–10 minpurohit2017b R15, R16, R17
bhardwaj2018ITZ–PVPVA 10% (SD, HM)0.1 N HCl, 37 °C199 µg/min/cm²; polymer 0.22–0.29 of neatbhardwaj2018 R4, R12
indulkar2019aritonavir–PVPVA 10–25%pH 6.8, 37 °Ccongruent, ≈97–100% at 60 minindulkar2019a R3, R11
que2019ledipasvir–PVPVA 2, 5%pH 6.8, 37 °Ccongruent, about 100% by 60 minque2019 R3, R4
saboo2019Nil 5–10%, Cil 5–15% in PVPVApH 6.8, 37 °Cdrug 2.13–2.53 = polymer; neat PVPVA 3.49saboo2019 R5, R6, R8
saboo2020afelodipine in PVP, PVPVA, HPMC (≤10–15%); HPMCAS, EUDS (≤50%)pH 6.8 or 7.4congruent at ≈0.07–4.1 mg/min/cm²saboo2020a R14
saboo2020IND 5, 10%; INDester 5–25% in PVPVA5-min rates, pH 2.1 / 6.8≈3.1–4.2 mg/min/cm², drug = polymersaboo2020 R3
que2021four analogues at their limits (5–40%)rates, pH 6.8 (TIPP 2.5)≈2.8–3.7; p = 0.022–0.67que2021 R21
saboo2021felodipine–PVPVA with 5% TPGS, 10–30%rates≈2.6–3.2 for drug, polymer and TPGSsaboo2021 R9
yang2021loratadine–PVPVA 20, 30%; –HPMCAS 5–20%compacts, 37 °C, t-test≈2.7–3.4; ≈0.40–0.61yang2021 R21, R18
correasoto2022aCPD–PVPVA 40%compactsdrug ≈4.5, polymer ≈5.2correasoto2022a R18
correasoto2022bATZ–PVPVA 5%compacts, 90 min≈100% of bothcorreasoto2022b R1
hiew2022blumefantrine free base 5–35%compacts, drug only≈3.15–3.9 mg/min/cm²hiew2022b R12
bapat2023IND, INDester–HPMCAS-MF 10%compacts, pH 6.8 phosphate 3–51 mM/ΔpH, FaSSIFdrug = polymer at every buffer capacity; IND ≈0.12 → 0.82 mg/min/cm²bapat2023 R9, R13
hiew2022a (Miscibility)lumefantrine–PVPVA 5–35%compacts, pH 6.8normalized ratio 1.2–1.6, congruent to 35%hiew2022a C14, C31
moseson2022b (ASD process)bicalutamide–PVPVA 5, 10%powders> 90% of drug and polymer within 10 minmoseson2022b R6, R7, C17
bapat2025b (Peptide permeability)SNAC:PVPVA 50:50compacts, pH 6.8congruent; PVPVA about twice its neat ratebapat2025b C13
bapat2024indomethacin and its ester in HPMCAS-MF, 5–60%compacts, pH 6.8, 37 °Cdrug ≈0.85 → 0.50 and 0.66 → 0.39 with the polymer alongside; neat ≈0.91 mg/min/cm²bapat2024 R2, R3
bapat2025aloratadine 25% in HPMCAS LF, MF, HFsamedrug/polymer ≈0.25/0.27, 0.10/0.12, 0.01/0.02bapat2025a R2
deac2024aclotrimazole–PVP K25 20%, K29/32 30%, K60 35%, K90 38%compacts, pH 8.0, 90–120 mindrug ≈83–96%, PVP ≈93–103%deac2024a R1

Figure

Fig. 3A of indulkar2019a: percent release of ritonavir and PVPVA from the 10% dispersion
Fig. 3A · indulkar2019apercent release of ritonavir and PVPVA from the 10% dispersion

The red (ritonavir) and blue (PVPVA) curves lie on top of each other and both reach about 100% by 30 min indulkar2019a R3.a–b.

Why

The authors' explanation is that at low loading there is too little drug to form an intact surface layer, so that the dissolving polymer brings the drug into solution ("is thought to occur") indulkar2019a C25. For ritonavir they add that congruent release "suggests" a drug–polymer interaction that persists during hydration and hinders amorphous–amorphous phase separation (AAPS), and that dissolution is faster than AAPS, keeping the interface composition constant indulkar2019a C36, C37. The classic two-component theory does not predict this: in Higuchi's diffusion model only one mixture ratio releases both components at once,

\frac{N_{drug}}{N_{polymer}} = \frac{D_{drug}\,C_{s(drug)}}{D_{polymer}\,C_{s(polymer)}}

saboo2020a E4, and with an amorphous solubility of 8 µg/mL, a PVPVA solubility of 46 mg/mL and a diffusion-coefficient ratio of 10 that ratio is about 1.7 × 10⁻³ for felodipine–PVPVA (printed 1.7 × 10⁻⁶) saboo2020a R27, X1. Congruent release over a range of polymer-rich compositions therefore contradicts the model, as Corrigan had noted (cited) indulkar2019a C23, C24; saboo2020a C36, C37. Saboo and co-workers (2020) go further: because the PVPVA limit varies from 5 to 25% with the drug and HPMCAS and EUDS stay congruent to 50%, the amount of drug alone "doesn't seem to hold true" as the cause, and water-induced phase separation at the interface must be considered (see F8) saboo2020a C38. The slower polymer in dispersions is put down "most likely" to the higher hydrophobicity of the formulation or to drug–polymer interactions, as seen before for ketoconazole (cited) saboo2019 C13; bhardwaj2018 C49, R23. The non-linear 10% ITZ profiles "might" reflect initial hydration and swelling of the polymer bhardwaj2018 C20. (synthesis: since the drug follows the polymer, the polymer's own dissolution rate in the medium caps polymer-controlled release; the gain over the amorphous drug is then large where the amorphous drug alone is very slow (nilvadipine, felodipine at pH 6.8) and small where it is relatively fast (ITZ in 0.1 N HCl).) Bapat and co-workers (2023) take the equal rates to mean that the step limiting polymer dissolution also limits drug release ("expected"), and generalize to HPMCAS dispersions of acidic and neutral drugs ("demonstrate"), although drug release was measured at 10% loading only bapat2023 C35, C49, X4. Bapat and co-workers read matching drug and polymer rates in HPMCAS as polymer control ("indicates"), and Deac and co-workers describe the release mechanism of a congruent dispersion as "similar to that of neat glassy polymers" bapat2024 C10; deac2024a C31. (synthesis: the HPMCAS-MF series of 2024 shows the coupling without a cliff up to 60% for drugs that do not bind the polymer, the clotrimazole–PVP series shows the polymer's own rate, set by its molecular weight, capping the coupled release (F29), and for drugs that complex HPMCAS the coupled rate falls with the polymer's to about zero at 25–30% (F32).)

Conditions and limits

Shown for PVPVA with six drugs, for PVP, HPMC and EUDS with felodipine, for HPMC-E5 with nifedipine and for HPMCAS with felodipine and ritonavir; non-disintegrating compacts at 37 °C, nifedipine at 5 °C, ritonavir films at 25 °C; drug loadings of 2–25% (to 50% for HPMCAS and EUDS) saboo2020a A2; indulkar2017b P7; purohit2017b P14. No disintegrating tablet with excipients was tested saboo2020a C53; bhardwaj2018 C63.

Counterexamples and conflicts

Congruent does not mean fast: 10% felodipine–HPMC released ≈0.14 mg/min/cm², about a sixth of 10% felodipine–HPMCAS (≈0.82) saboo2020a R14. At 25% ritonavir the drug trailed the polymer mid-release (≈60 against ≈73% at 30 min) although the tablet is classed as congruent indulkar2019a X7. From 50:50 ritonavir–PVPVA films the polymer took about 2 h to dissolve, against "less than 10 min" in the text purohit2017b X4. Outside the subcategory a peptide-enhancer–PVPVA dispersion released its polymer about twice as fast as the neat polymer, the opposite of the slowing seen here bapat2025b C13. In the papers of 2020–2022 the polymer left congruent compacts at about its neat rate or faster, up to about twice for clopidogrel (F15) que2021 R21; correasoto2022a R18. Congruent release at a limit raised by a surfactant was about half as fast as at lower loadings saboo2021 X3. In the slowest HPMCAS-HF systems of 2025 the drug left at about half the polymer's rate bapat2025a X6.

Transfer check

Measure the neat polymer and the neat amorphous drug in the same die and medium; compacts at 5 and 10% loading should give equal normalized drug and polymer rates (no significant difference) and continued release into presaturated medium saboo2019 R8; indulkar2019a R12. A drug whose neat amorphous rate is within about an order of magnitude of the polymer's (as for ITZ in acid) gains little from polymer control; one that is three orders slower gains most bhardwaj2018 R4; saboo2019 R7. Check the polymer fraction of its neat rate: values of 0.2–0.3 (ITZ) mean the drug is already slowing the polymer bhardwaj2018 R12, C49.

History

Simonelli and co-workers (1969, cited) described polymer-controlled release of sulfathiazole–PVP at very low loading indulkar2017b R14. In the ASD dissolution chapter Alonzo and co-workers (2011) proposed polymer control for 90:10 dispersions from particle disintegration, without measuring polymer release (Supersaturation from ASD dissolution F10) alonzo2011 C37, C38. Indulkar and co-workers (2017) showed it for nifedipine through release into saturated medium indulkar2017b C35. Bhardwaj and co-workers (2018) found the normalized drug and polymer rates converging at 10–20% ITZ bhardwaj2018 C51. Indulkar and co-workers (2019) named the regime congruent release and wrote the rate relation indulkar2019a C1, E3; Saboo and co-workers (2019) called it the "sweet spot" and showed equal rates by t-test; Saboo and co-workers (2020) extended it to five polymers saboo2019 C30; saboo2020a C16, C17. Que and co-workers (2021) found that at the limit the polymer controls release whatever the compound, so that drug release can be predicted from polymer release que2021 C39, C41, and Correa Soto and co-workers (2022) found the polymer released faster than from a neat compact (F15) correasoto2022a C30; the second half of the title therefore now holds for the papers of 2018–2020 only. Bapat and co-workers (2023) showed for HPMCAS that the polymer-paced drug rate follows the medium's buffer capacity (F23) bapat2023 C18. Bapat and co-workers (2024) extended the drug-and-polymer assay to eight drugs in HPMCAS-MF, Bapat and Taylor (2025) to three HPMCAS grades, and Deac and co-workers (2024) to six PVP grades, where the coupled rate followed the polymer's molecular weight bapat2024 C23; bapat2025a C13; deac2024a C19.

F3

Topic 1Two release regimes and their measurement3 of 5

Above the switch the polymer leaves first and the drug dissolves near its neat amorphous rate, never above the amorphous solubility.

Ritonavir–PVPVA at 40 and 50% released ≈3% and ≈0.65% of its drug and ≈13% and ≈6% of its polymer in 180 min, about as little as neat amorphous ritonavir; the 50% tablet released no drug into ritonavir-saturated medium indulkar2019a R3, R7, R12. Nilvadipine–PVPVA at 15 and 20% released 0.035 and 0.013 mg/min/cm², 20–40 times below its polymer but 17 and 6.5 times above the neat amorphous drug saboo2019 R5, X9.

strongStrong for the slow, incongruent release, measured with both components; moderate for "near the amorphous drug", since several drug rates lie well above the neat amorphous rate indulkar2019a K3; saboo2019 K1, X9; saboo2020a C16.

drug releasedpolymer releasedritonavir–PVPVA 40%180 min≈2.95≈13.2ritonavir–PVPVA 50%180 min≈0.65≈6.2miconazole–PVPVA 50%powders, 60 min≈297clotrimazole–PVP K12 5%90 min35≈107ritonavir–PVPVA 40% + Span 2090 min≈8≈780102030405060708090100110percent released

In every incongruent system the polymer leaves well ahead of the drug. indulkar2019a R3; yang2021 R13; deac2024a R1; yang2023 R2, R3

itraconazole 50% ≈1.0itraconazole 25% ≈1.3nilvadipine 20% ≈6.5nilvadipine 15% ≈17felodipine–PVP 15% 25110drug rate above the switch ÷ neat amorphous drug (log scale)

Drug-controlled rates lie from about the neat amorphous rate up to 25 times above it. bhardwaj2018 R4; saboo2019 R5; saboo2020a R14

For your drug

  1. Compare the drug rate of the target loading with a compact of the neat amorphous drug in the same die: within about one order of magnitude, and with the polymer leaving several times faster, the dispersion is drug-controlled and will not exceed its amorphous solubility.
  2. Confirm with a run in medium presaturated at the amorphous solubility.

saboo2019 R5, X9; purohit2017b C50; indulkar2019a R12, C42

How it works and key numbers
  1. The hydrophilic polymer dissolves faster than the drug, so the surface loses polymer and becomes drug-rich, and the drug then dissolves on its own bhardwaj2018 C51; indulkar2019a C39; saboo2019 C38.
  2. A drug-controlled surface dissolves by \frac{dx}{dt} = C\,(S - x), with S the amorphous solubility, so the rate falls to zero as the solution approaches S and the concentration cannot pass it purohit2017b E3, C50.
  3. Liquid–liquid phase separation (LLPS) therefore "can only occur" when components that dissolve faster than the drug control release (F4) indulkar2019a C48.
  4. Short PVP chains gave polymer-first release without a continuous layer: in the K12 dispersion the polymer left completely while the drug stayed behind as droplets agglomerated in the gel (F29) deac2024a R10, C26.
47–64 against 51 µg/min/cm²itraconazole at 25 and 50% against amorphous itraconazolebhardwaj2018 R4
≈6–25×nilvadipine and felodipine–PVP above the switch, relative to the neat amorphous drugsaboo2019 R5; saboo2020a R14
0ritonavir released from the 50% tablet into saturated buffer up to 50 minindulkar2019a R12
Evidence: data, conditions and papers

Finding F3. Above the switch the polymer leaves first and the drug dissolves near the rate of the neat amorphous drug, often a few to tens of times faster; this release stops in medium already at the amorphous solubility and does not pass it

In short. At 25 and 50% loading, spray-dried and extruded itraconazole–PVPVA released 47–64 µg/min/cm², close to the 51 of amorphous ITZ, while the polymer left 3.5–4 times faster than the drug on a loading-normalized basis bhardwaj2018 R4, R11. Ritonavir–PVPVA at 40 and 50% released ≈3% and ≈0.65% of its drug and ≈13% and ≈6% of its polymer in 180 min, about as little as neat amorphous ritonavir, and the 50% tablet released no drug into ritonavir-saturated medium indulkar2019a R3, R7, R12. Nilvadipine–PVPVA at 15 and 20% released 0.035 and 0.013 mg/min/cm², 20–40 times below its polymer but 17 and 6.5 times above the neat amorphous drug saboo2019 R5, X9. From 50:50 ritonavir films the PVP or PVPVA dissolved while ritonavir reached only ≈18 and ≈9 µg/mL, below its amorphous solubility of about 27 µg/mL purohit2017b R15, R16, R10, R1. IND at 15–25% released drug at about 0.01–0.04 mg/min/cm² against 0.002 for amorphous IND and 0.50–0.72 for its polymer, and TIPP at 15–20% and Me-TIPP at 50% released no detectable drug saboo2020 R3; que2021 R15, C22. Short PVP chains gave the same polymer-first pattern without a continuous layer: clotrimazole–PVP K12 at 5% released about 107% of its polymer but 35% of its drug, as did ritonavir–PVPVA with Span 20 at 40% (about 78 and 8%) (F29, F31) deac2024a R1; yang2023 R2, R3.

Type. observation in 6 drugs (itraconazole, ritonavir, nilvadipine, cilnidipine, ledipasvir, felodipine), and 10 further drugs in 2020–2022, and miconazole with HP-50 in 2022 Strength. for the slow, incongruent release, measured with both components indulkar2019a K3: moderate to strong; saboo2019 K1: strong; moderate for "near the amorphous drug", since several drug rates lie well above the neat amorphous rate saboo2019 X9; saboo2020a C16.

How it was shown

As in F1 and F2, with loadings above the switch: ITZ at 20–50%, ritonavir tablets at 30–50% and films at 20–50%, nilvadipine at 15–20%, cilnidipine at 20–25% and felodipine at 15–30% bhardwaj2018 A1; indulkar2019a A1; purohit2017b A2; saboo2019 A2; saboo2020a A2.

What the data show

The 50% ritonavir tablet released 0 at every point up to 50 min into saturated buffer indulkar2019a R12. For ITZ at 50% the loading-normalized polymer rate ran ahead of the drug (≈395 against ≈100 µg/min/cm², spray-dried) bhardwaj2018 R11.

systemconditionsdrug against polymerids
ITZ–PVPVA 25, 50% (and 20% extruded)0.1 N HCl, 37 °C47–64 µg/min/cm² against 51 for amorphous ITZbhardwaj2018 R4, R6
ritonavir–PVPVA 40, 50%pH 6.8, 37 °C≈2.95% and ≈0.65% drug, ≈13.2% and ≈6.2% PVPVA in 180 minindulkar2019a R3
nilvadipine 15–20%, cilnidipine 20–25% in PVPVApH 6.8, 37 °Cdrug 0.002–0.035, polymer 0.21–0.72 mg/min/cm²saboo2019 R5, R6
felodipine–PVP 15–30%pH 6.8, 37 °Cdrug ≈0.005–0.020 against PVP ≈1.7–1.9 mg/min/cm²saboo2020a R14
indomethacin–PVPVA 15–25%5-min ratesdrug ≈0.01–0.04, PVPVA ≈0.50–0.72 mg/min/cm²saboo2020 R3
clotrimazole–PVP K12, K17 at 5%pH 8.0, 90 minPVP ≈107 and 101–103%; drug ≈35 and 74–77%deac2024a R1
Fig. 5 of bhardwaj2018: ITZ release rate relative to crystalline ITZ against polymer content for spray-dried and extruded dispersions
Fig. 5 · bhardwaj2018ITZ release rate relative to crystalline ITZ against polymer content for spray-dried and extruded dispersions

Points near the amorphous-ITZ value (about 18) at 50 and 75% polymer are drug-controlled; the points at 90% polymer (about 72) lie far above it bhardwaj2018 R6.

Why

The authors' common reading is that the hydrophilic polymer dissolves faster than the drug, so the surface becomes drug-rich and the drug then dissolves on its own bhardwaj2018 C51; indulkar2019a C39; saboo2019 C38. A drug-controlled surface dissolves by \frac{dx}{dt} = C\,(S - x), so the rate falls to zero as the solution approaches the amorphous solubility S ("can be rationalized") purohit2017b E3, C50. (synthesis: the measured drug rates lie up to 25 times above a flat compact of neat amorphous drug; a drug-rich layer that is porous or still holds some polymer would give such values, but neither the area nor the composition of the layer was followed over time.)

Limits and transfer

The zero release into saturated medium was shown for one loading of one drug indulkar2019a X8. High loading is not drug-controlled with every polymer: felodipine–HPMCAS stayed congruent to 50% saboo2020a R14. Compare the drug rate of the target loading with a compact of the neat amorphous drug in the same die: within about one order of magnitude, with the polymer leaving several times faster, the dispersion is drug-controlled and will not exceed its amorphous solubility saboo2019 R5, X9; purohit2017b C50.

How it was shown

As in F1 and F2, with the loadings above the switch: ITZ at 20 (extruded), 25 and 50% bhardwaj2018 A1; ritonavir tablets at 30–50% and ritonavir films at 20–50% with PVP and PVPVA indulkar2019a A1; purohit2017b A2; ledipasvir at 7.5, 10 and 20% que2019 A1; nilvadipine at 15–20%, cilnidipine at 20–25% saboo2019 A2; felodipine at 15–30% in PVP, PVPVA and HPMC saboo2020a A2.

What the data show

ITZ: 53 ± 4 (spray-dried) and 47 ± 2 µg/min/cm² (extruded) at 50%, 64 ± 1 and 55 ± 1 at 25%, about 17–23 times crystalline ITZ against about 18 for melt-quenched ITZ; the extruded 20% compact (48.8 ± 0.9) stayed on this plateau bhardwaj2018 R4, R6. The loading-normalized rates show the polymer ahead: ≈395 against ≈100 µg/min/cm² at 50% and ≈880 against ≈250 at 25% for the spray-dried series, and after 20 min the 50:50 compacts had released about 5.0 (spray-dried) and 12.2 (extruded) mg/cm² PVPVA against about 1.0 mg/cm² ITZ bhardwaj2018 R11, R8. Ritonavir: at 40% the drug rose from ≈0.15% at 10 min to ≈2.95% at 180 min and PVPVA from ≈2.2 to ≈13.2%; at 50% ≈0.1 to ≈0.65% and ≈2.05 to ≈6.2%; in mass both stayed below ≈0.5 mg in 120 min, like the neat amorphous tablet indulkar2019a R3.k–n, R1. The 50% tablet released 0 at every point up to 50 min into saturated buffer against ≈0.155–0.44% in plain buffer indulkar2019a R12. Ledipasvir at 7.5 and 10% released no drug up to 60 min and at most ≈7% by 90 min, with ≈17 and ≈23% polymer; the 20% dispersion released no drug and ≈19% of its polymer by 90 min que2019 R3, R4, R11, X6. Nilvadipine at 15 and 20% gave 0.035 and 0.013 mg/min/cm² drug against 0.72 and 0.52 polymer, cilnidipine at 20 and 25% 0.006 and 0.002 against 0.24 and 0.21 saboo2019 R5, R6. Felodipine with PVP fell to ≈0.020, ≈0.010 and ≈0.005 mg/min/cm² at 15, 20 and 30% while PVP still dissolved at ≈1.7–1.9, and the medium stayed below 1 µg/mL against an amorphous solubility of 8 µg/mL saboo2020a R14, R6, R1. In 50:50 ritonavir films PVP reached ≈57 of 60 µg/mL within 5 min and PVPVA ≈65 near 120 min, while ritonavir reached ≈18 (PVP) and ≈9 µg/mL (PVPVA) by 240 min; the free drug of the non-LLPS PVP and PVPVA films was 10–25 µg/mL after 4 h purohit2017b R15, R16, R10. (synthesis: relative to the neat amorphous drug, the drug-controlled rates are 0.035/0.002 ≈ 17 and 0.013/0.002 ≈ 6.5 for nilvadipine and 0.020/0.0008 = 25 to 0.005/0.0008 ≈ 6 for felodipine–PVP, but 53/51 ≈ 1.0 and 64/51 ≈ 1.3 for ITZ.) The papers of 2020–2022 add IND at 15, 20 and 25% (drug about 0.04, 0.02 and 0.01, PVPVA about 0.72, 0.64 and 0.50 mg/min/cm²) saboo2020 R3; TIPP at 15 and 20% and Me-TIPP at 50% (about 0% drug and 13–18% PVPVA in 90 min) que2021 R15; miconazole–PVPVA at 50% (about 2% drug against 97% polymer in 60 min) and elbasvir–PVPVA at 50% (about 5 against 34%) yang2021 R13; ATZ at 10% (about 0.07 against 0.24 mg/min/cm²) correasoto2022b R3; clopidogrel at 60% (about 0.2 against 4.1) correasoto2022a R18; and the benzoate salt of lumefantrine at 30%, which released about 20% of its PVPVA before any drug hiew2022b R13. (synthesis: IND at 15–25% released 0.01/0.002 = 5 to 0.04/0.002 = 20 times faster than amorphous IND alone.) Miconazole at 20% in the enteric polymer HP-50 released about 8.6% of its drug by 60 min and 11.7% by 120 min while the polymer reached about 23.3 and 42.2%, which the authors call incongruent release qi2022 R14, C22. Ritonavir–PVPVA compacts of the 2022 imaging study released about 35% of the drug against 69% of the polymer by 90 min at 30%, and at most about 3% of the drug with about 14 and 10.5% of the polymer at 40 and 50%, while neat amorphous ritonavir released at most about 0.5% yang2022a R2, X1, X2. In 2023–2024 incongruent release showed the same pattern: clotrimazole–PVP K12 at 5% released about 107% of its polymer and 35% of its drug, K17 at 5% about 101–103% and 74–77%, K29/32 at 33% about 103% and 77%; ritonavir–PVPVA with Span 20 at 40% about 78% and 8%, with SDS at 40% about 70–79% and 48–54%, and with Tween 80 at 50% about 85% and 22% deac2024a R1; yang2023 R2, R3.

papersystemmethod and conditionsresultids
purohit2017britonavir 50:50 films, PVP and PVPVA25 °C, pH 6.8polymer dissolves; ritonavir ≈18 and ≈9 µg/mLpurohit2017b R15, R16
bhardwaj2018ITZ–PVPVA 25, 50% (and 20% HM)0.1 N HCl, 37 °C47–64 µg/min/cm² against 51 for amorphous ITZbhardwaj2018 R4, R6
indulkar2019aritonavir–PVPVA 40, 50%pH 6.8, 37 °C≈3% and ≈0.65% drug in 180 min; 0 into saturated mediumindulkar2019a R3, R12
que2019ledipasvir–PVPVA 7.5, 10, 20%pH 6.8, 37 °C≤ ≈7% drug at 90 min; polymer ≈17–23%que2019 R3, R4, R11
saboo2019Nil 15–20%, Cil 20–25% in PVPVApH 6.8, 37 °Cdrug 0.002–0.035, 20–105 times below polymersaboo2019 R5, R6
saboo2020afelodipine–PVP 15–30%pH 6.8, 37 °Cdrug ≈0.005–0.020 against PVP ≈1.7–1.9saboo2020a R14
saboo2020IND–PVPVA 15–25%5-min rates, pH 2.1drug ≈0.01–0.04, PVPVA ≈0.50–0.72saboo2020 R3
que2021TIPP 15, 20%; Me-TIPP 50%90 min≈0% drug; 13–18% PVPVAque2021 R15
yang2021miconazole, elbasvir–PVPVA 50%powders, 60 min≈2 against 97%; ≈5 against 34%yang2021 R13
correasoto2022aCPD–PVPVA 60%compactsdrug ≈0.2, PVPVA ≈4.1correasoto2022a R18
correasoto2022bATZ–PVPVA 10%compactsATZ ≈0.07, PVPVA ≈0.24correasoto2022b R3
hiew2022blumefantrine benzoate 30%drug and PVPVA≈20% PVPVA, no drug at 30 minhiew2022b R13
qi2022miconazole–HP-50 20%compacts, 50 mM pH 6.8, 37 °Cdrug ≈8.6 / 11.7%, HP-50 ≈23.3 / 42.2% at 60 / 120 minqi2022 R14
yang2022aritonavir–PVPVA 30, 40, 50%compacts, pH 6.8, 37 °C, 90 mindrug ≈35 / 3 / 3% against PVPVA ≈69 / 14 / 10.5%yang2022a R2
hiew2022a (Miscibility)lumefantrine with HPMCP, HPMCAS, PVPVAcompacts near 50%polymer rates converge, read as drug controlhiew2022a C40
moseson2022b (ASD process)bicalutamide–PVPVA 30%powderspolymer ahead of drug (incongruent)moseson2022b C16
deac2024aclotrimazole–PVP K12, K17 at 5%compacts, pH 8.0, 90 minPVP ≈107 / 101–103%; drug ≈35 / 74–77%deac2024a R1
yang2023ritonavir–PVPVA 40% + Span 20; 50% + Tween 80compacts, pH 6.8, 90 minpolymer ≈78 / 85%; drug ≈8 / 22%yang2023 R2, R3

Figure

Fig. 5 of bhardwaj2018: ITZ release rate relative to crystalline ITZ against polymer content for spray-dried and extruded dispersions
Fig. 5 · bhardwaj2018ITZ release rate relative to crystalline ITZ against polymer content for spray-dried and extruded dispersions

Points near the amorphous-ITZ value (about 18) at 50 and 75% polymer are drug-controlled; the spray-dried point at 80% polymer (about 40) and both points at 90% (about 72) lie far above it bhardwaj2018 R6.

Why

The authors' common reading is that the hydrophilic polymer dissolves faster than the drug, so the surface loses polymer and becomes drug-rich, and the drug then dissolves on its own bhardwaj2018 C51; indulkar2019a C39; saboo2019 C38. A drug-controlled surface dissolves by

\frac{dx}{dt} = C\,(S - x)

with S the amorphous solubility, so the rate falls to zero as the solution approaches S and the concentration cannot pass it ("can be rationalized") purohit2017b E3, C50. Indulkar and co-workers state the consequence for the colloid: LLPS "can only occur" when components that dissolve faster than the drug control release (see F4) indulkar2019a C48. Bhardwaj and co-workers call the drug-rich outer layer a "supposition", which also explains the curving 50:50 polymer profiles, the polymer having to pass through a thickening drug-rich layer bhardwaj2018 C52. That ritonavir at 40–50% released at about the rate of the neat drug "suggests" rapid AAPS and early surface enrichment indulkar2019a C39, and the gap of more than three orders between neat PVPVA and amorphous nilvadipine "explains" the size of the drop when the mechanism changes saboo2019 C43. The authors describe the drug-controlled rates as close to the amorphous drug saboo2019 C12; saboo2020a C16. (synthesis: the measured drug rates lie up to 25 times above a flat compact of neat amorphous drug; a drug-rich layer that is porous or still holds some polymer would give such values, but neither the area nor the composition of the layer was followed over time, see F7.) (synthesis: in the K12 dispersion the polymer left completely while the drug stayed behind as droplets agglomerated in the gel, a route to polymer-first release that needs no continuous drug-rich layer (F29) deac2024a R10, C26.)

Conditions and limits

PVPVA (all drugs), PVP and HPMC (felodipine, ritonavir films); compacts at 37 °C except the ritonavir films at 25 °C; ITZ in 0.1 N HCl, where the weak base is relatively soluble bhardwaj2018 M1. The zero release into saturated medium was shown for one loading of one drug, with the presaturation and baseline not described indulkar2019a X8.

Counterexamples and conflicts

High loading is not drug-controlled with every polymer: 50:50 ritonavir–HPMCAS films released drug with the polymer (≈32–34 µg/mL within 5 min) and formed LLPS, and felodipine–HPMCAS stayed congruent to 50% (see F11) purohit2017b R17, C38; saboo2020a R14. In the ASD dissolution chapter a 50:50 PVP danazol dispersion dissolved as fast as a 90:10 one jackson2015 X9. Praziquantel–HPMCAS showed a gradual decline with loading rather than a switch, read as polymer control polyzois2024 C17. Partly incongruent release of low-Tg drugs still passed the amorphous solubility: loratadine–PVPVA at 35% released about 23% of its drug by 90 min against an amorphous-solubility line of about 3.2%, and clopidogrel–PVPVA at 50% about 52% with the polymer about twice as fast (F4) yang2021 R19, C15; correasoto2022a R17, R18.

Transfer check

Compare the drug rate of the target loading with a compact of the neat amorphous drug in the same die: within about one order of magnitude, and with the polymer leaving several times faster, the dispersion is drug-controlled and will not exceed its amorphous solubility saboo2019 R5, X9; purohit2017b C50. Confirm with a run in medium presaturated at the amorphous solubility indulkar2019a R12, C42.

History

The amorphous-drug-controlled regime at intermediate loading goes back to sulfathiazole–PVP compacts (Simonelli 1969, cited) bhardwaj2018 R22. In the ASD dissolution chapter Alonzo and co-workers (2011) proposed a drug-rich layer at the dissolving surface of 50:50 dispersions, without observing it alonzo2011 C46. Purohit and Taylor (2017) first measured the polymer leaving 50:50 ritonavir films ahead of the drug, Bhardwaj and co-workers (2018) the amorphous-drug plateau of ITZ, and Indulkar and co-workers (2019) the zero release into saturated medium purohit2017b C36; bhardwaj2018 C48; indulkar2019a C42; Saboo and co-workers (2019, 2020) and Que and co-workers (2019) added nilvadipine, cilnidipine, felodipine and ledipasvir saboo2019 C12; saboo2020a C16; que2019 C31. Saboo and co-workers (2020) and Que and co-workers (2021) added hydrogen-bonding IND and phenols, Yang and co-workers (2021) six drugs in powders, and Hiew and Taylor (2022) lumefantrine salts, whose lag-phase compacts released polymer before drug saboo2020 C12; que2021 C22; yang2021 C13; hiew2022b C18. Deac and co-workers (2024) found polymer-first release already at 5% with short PVP chains and named its cause Failure Mode I (F29) deac2024a C38.

F15

Topic 1Two release regimes and their measurement4 of 5

The drug or an additive in a dispersion changed how fast the polymer itself dissolved, up or down.

Congruent dispersions of indomethacin, its methyl ester and four phenolphthalein analogues released PVPVA at about the neat rate saboo2020 R3; que2021 R21, C40. Clopidogrel, with a Tg of −9 °C, made PVPVA dissolve at about 5.2–6.7 mg/min/cm² against about 2.6–2.7 for the neat compact, which the authors attribute to plasticization by the drug correasoto2022a R18, M1, C30, C48. Weak bases at 25% slowed HPMCAS-MF about 1.6-fold (ritonavir) to 18–30-fold (cinnarizine) bapat2024 R5, X2.

moderateModerate: drug and polymer rates come from constant-area compacts in triplicate with neat references run in the same paper, but the causes (plasticization, water uptake, hydrogen bonding) were argued, not measured correasoto2022a K2, C48; que2021 K5, C44; yang2021 C31.

polymer leaving the dispersion or blendPVPVA · 10% nilvadipineneat 3.492.35PVPVA · 10% indomethacinneat 3.43.19PVPVA · 50% clopidogrelneat 2.76.7PVPVA · 12.5 wt% SDS, no drugneat 3.66.9HPMCAS-MF · 25% ritonavirneat 0.900.43HPMCAS-MF · 25% cinnarizineneat 0.900.050.1110polymer dissolution rate, mg/min/cm² (log scale)

Dashed ticks: the neat polymer in the same paper and medium; the dispersion can run below, at or above it. saboo2019 R5, R8; saboo2020 R3; correasoto2022a R18; yang2023 R5; bapat2024 R4, R5

For your drug

  1. Dissolve a neat polymer compact in the same die and medium as the dispersion and compare the polymer rate of a low-loading compact with it: a ratio above 1 points to plasticization by the drug or an additive, one well below 1 to a drug or additive that slows the polymer.
  2. Repeat with each candidate surfactant, and for an enteric polymer compare dispersion and neat polymer at the buffer capacity of use.

correasoto2022a R18; saboo2019 R8; correasoto2022b R22; bapat2023 R12, C48

How it works and key numbers
  1. A glassy polymer dissolves by water ingress into a plasticized gel layer and chain disentanglement, which is faster above its Tg, so the polymer rate depends on the water the gel takes up and on the Tg of the hydrated matrix against the test temperature saboo2020 C54, C55; correasoto2022b C33, C36; yang2021 C30.
  2. Hiew and Taylor quantify the water a glassy polymer needs before its chains disentangle with the critical polymer volume fraction v_p^{*}; for PVPVA at 37 °C it is 0.89, at least 11% water hiew2022b E1, R21, C40.
  3. A low-Tg drug or a plasticizer speeds the polymer: drug-free PVPVA with 10% w/w glycerol tributyrate or tributyl citrate dissolved at about 4.8 and 6.1 against 2.7 mg/min/cm² correasoto2022a C48; correasoto2023 R13.
  4. A drug–polymer hydrogen bond that persists in water occupies polymer solvation sites, cuts water uptake and slows disentanglement ("could explain", F17) que2021 C44.
  5. In HPMCAS a lipophilic drug "most likely" lowers the amount and rate of water the polymer takes up, leaving a more viscous gel; uptake at 95% RH fell from about 6.2% (neat) to 2.4% (50% INDester) bapat2023 C46, R20.
  6. Cationic drugs also form an insoluble ion-pair complex with HPMCAS that lowers its interfacial solubility (F32) bapat2024 C32; bapat2025a C34.
≈6.7 against ≈2.7 mg/min/cm²PVPVA from 50% clopidogrel compacts against neat PVPVAcorreasoto2022a R18
0.22–0.68polymer rate as a fraction of neat in the 2018–2019 papersbhardwaj2018 R12; saboo2019 R5, R8
≈1.6 to 18–30-foldslowing of HPMCAS-MF by 25% ritonavir and by 25% cinnarizinebapat2024 R5, X2
Evidence: data, conditions and papers

Finding F15. The drug or an additive inside a dispersion changed how fast the polymer itself dissolved: congruent dispersions released PVPVA at about the neat rate for indomethacin, its ester and four phenolphthalein analogues, at about twice the neat rate for low-Tg clopidogrel, surfactants and plasticizers changed it again, and drugs slowed the enteric polymers HP-50 and HPMCAS

In short. In the congruent range, indomethacin and indomethacin methyl ester dispersions released PVPVA at about 3.2–4.0 mg/min/cm² against about 3.4–3.8 for neat PVPVA, and four phenolphthalein analogues at their limits at about 2.8–3.4 against 3.0, with no difference at the 99% level saboo2020 R3; que2021 R21, C40. Clopidogrel, with a Tg of −9 °C, made PVPVA dissolve at about 5.2, 6.7 and 4.1 mg/min/cm² at 40, 50 and 60% loading against about 2.6–2.7 for the neat compact, which the authors attribute to plasticization by the drug ("is thought to") correasoto2022a R18, M1, C30, C48. TPGS and Tween 80 in the clopidogrel dispersion brought the polymer back to about 2.1–3.0, 10% SDS almost doubled the rate of neat PVPVA, and 5% TPGS left it unchanged correasoto2022a R18; correasoto2022b R22; saboo2021 R14. In the 2018–2019 papers the polymer had left congruent compacts at 0.22–0.68 of its neat rate (F2) bhardwaj2018 R12; saboo2019 R5, R8, so the polymer rate that caps polymer-controlled release belongs to the formulation, not to the polymer alone (synthesis: comparison of the rates above). In 2023–2025 SDS and Tween 80 raised the PVPVA rate of blends from about 3.6 to 6.9 and 5.7 mg/min/cm² while the Spans did not, higher PVP grades dissolved more slowly neat and in congruent dispersions, and weak bases at 25% slowed HPMCAS-MF about 1.6-fold (ritonavir) to 18–30-fold (cinnarizine), most where they were ionized (F31, F29, F32) yang2023 R5; deac2024a R3, C19; bapat2024 R5, X2.

Type. observation in 11 drugs (indomethacin, its methyl ester, TIPP, PHPH, Me-TIPP, Me-PHPH, clopidogrel, loratadine, atazanavir, ritonavir, miconazole) with PVPVA, HPMCAS and HP-50 Strength. : drug and polymer rates from constant-area compacts in triplicate with neat references run in the same paper correasoto2022a K2: strong; que2021 K5: moderate; the causes (plasticization, water uptake, hydrogen bonding) were argued, not measured correasoto2022a C48; que2021 C44; yang2021 C31.

How it was shown

Constant-area compacts of indomethacin (IND), its methyl ester (INDester), four phenolphthalein analogues and clopidogrel (CPD), with and without surfactant, were dissolved beside neat PVPVA compacts, and IND and INDester dispersions also beside neat HPMCAS-MF saboo2020 P5; que2021 P9, P10; correasoto2022a P10, P11; bapat2023 A1, A3.

What the data show

Binary CPD–PVPVA compacts released PVPVA at about 5.2, 6.7 and 4.1 mg/min/cm² at 40, 50 and 60% against about 2.6 and 2.7 for neat PVPVA correasoto2022a R18.

systemconditionspolymer rate from the dispersion against neatids
IND, INDester–PVPVA 5–25%5-min rates, pH 2.1 / 6.8, 37 °Ccongruent PVPVA ≈3.2–4.0 against neat ≈3.4 / ≈3.8saboo2020 R3
four analogues at their limitsrates, t-test at 99%PVPVA ≈2.8–3.4 against ≈3.0; p = 0.37–0.48que2021 R21
CPD–PVPVA 40–60% ± surfactantscompacts, pH 6.8, 37 °Cbinary PVPVA ≈4.1–6.7 against neat ≈2.6–2.7; TPGS, Tween 80 ≈2.1–3.0 at 40%correasoto2022a R18
PVPVA + 12.5 wt% Span 85, Span 20, Tween 80 or SDScompacts, pH 6.8≈3.8 / 3.6 / 5.7 / 6.9 against 3.6 mg/min/cm²yang2023 R5
HPMCAS from IND, INDester dispersions 10, 50%compacts, pH 6.8, 51 mM/ΔpH≈0.76, 0.58, 0.58, 0.45 against neat ≈1.01 mg/min/cm²bapat2023 R11
HPMCAS-MF with 25% ritonavir, loratadine, clotrimazole, cinnarizinecompacts, pH 6.8neat-to-dispersion polymer rate ≈1.6 / 7.4 / 11.2 / 30 (≈18 from the bars)bapat2024 R5, X2
Fig. 9 of correasoto2022a: percent release and normalized release rates of clopidogrel and PVPVA at 40, 50 and 60% loading, with neat PVPVA
Fig. 9 · correasoto2022apercent release and normalized release rates of clopidogrel and PVPVA at 40, 50 and 60% loading, with neat PVPVA

In panels d–f the blue PVPVA bars of the binary dispersions stand above the neat-PVPVA bar at the right of each panel, while the TPGS and Tween 80 bars fall back to about its height correasoto2022a R18.

Why

A glassy polymer dissolves by water ingress into a plasticized gel layer and chain disentanglement, which is faster above its Tg, so the papers expect the polymer rate to depend on the water the gel takes up and on the Tg of the hydrated matrix saboo2020 C54, C55; correasoto2022b C33, C36; yang2021 C30. Correa Soto and co-workers read the faster PVPVA as plasticization by CPD ("is thought to"), and Bapat and co-workers the slower HPMCAS "most likely" as less water taken up by the polymer correasoto2022a C48; bapat2023 C46.

Limits and transfer

Gel hydration in the medium was not measured bapat2023 X9. Dissolve a neat polymer compact in the same die and medium and compare the polymer rate of a low-loading compact with it: a ratio above 1 points to plasticization by the drug or an additive, one well below 1 to slowing; repeat with each candidate surfactant correasoto2022a R18; saboo2019 R8; correasoto2022b R22.

How it was shown

Saboo and co-workers (2020) dissolved 100 mg compacts (0.5 cm², 1500 psi, 100 rpm, 100 mL, 37 °C) of indomethacin (IND)–PVPVA in pH 2.1 buffer and of indomethacin methyl ester (INDester)–PVPVA in pH 6.8 buffer, each with HPMC-606 in the medium, sampled every minute for 5 min and normalized each component's rate by area and weight fraction, R = kV/(Sx) saboo2020 P5, E1, M5, M6. Que and co-workers (2021) dissolved compacts of four phthalide analogues at their limits in 50 mM phosphate buffer (pH 6.8; pH 2.5 for TIPP) and compared drug, polymer and neat-polymer rates by t-tests at 99% confidence que2021 P9, P10. Yang and co-workers (2021) dissolved loratadine compacts with PVPVA or HPMCAS-MF and the neat polymers at 37 and 5 °C, and polymer and drug from powders yang2021 P15, P12, R18, R21. Saboo and co-workers (2021) dissolved a drug-free PVPVA matrix containing 5% TPGS saboo2021 P7. Correa Soto and co-workers (2022) dissolved clopidogrel (CPD)–PVPVA compacts at 40, 50 and 60% with and without 5 g surfactant per 100 g, with neat PVPVA as reference, and normalized by R = k/(Sx); in the atazanavir (ATZ) study they dissolved neat PVPVA containing 10% SDS or a Span correasoto2022a P10, P11, E1; correasoto2022b R22. Indulkar and co-workers (2022) compared the PVPVA released in the first 20 min from 30:70 ritonavir–PVPVA tablets with 5 parts of SDS, Tween 80, TPGS, Span 20 or Span 85 per 100 parts of drug and polymer with that of a binary 25:75 tablet at the limit, taken from the 2019 paper indulkar2022 P1, P3, P2, R20. Qi and Taylor (2022) dissolved 100 mg compacts of the enteric polymer HPMCP (HP-50) alone and of its 20% miconazole dispersion in 100 mL 50 mM pH 6.8 phosphate at 37 °C and 100 rpm, with the polymer assayed colorimetrically qi2022 P10, P11, P12, A6. Bapat and co-workers (2023) compared HPMCAS released from 10 and 50% indomethacin and indomethacin methyl ester dispersions with neat HPMCAS-MF in pH 6.8 phosphate of 3 to 51 mM/ΔpH and measured the water uptake of the powders at 95% RH and 37 °C for 12 h bapat2023 A1, A3, P11.

What the data show

IND–PVPVA at 5 and 10% released drug and polymer at about 3.44/3.47 and 3.14/3.19 mg/min/cm² against about 3.4 for neat PVPVA in that medium, and INDester at 5–25% at about 3.3–4.2 against about 3.8 saboo2020 R3, X5. At their limits TIPP (10%), Me-TIPP (30%), PHPH (5%) and Me-PHPH (40%) released PVPVA at about 3.2, 3.2, 2.8 and 3.4 mg/min/cm² against about 3.0 for neat PVPVA (p = 0.37–0.48 against neat) que2021 R21. Loratadine–PVPVA compacts at 20 and 30% gave PVPVA at about 3.33 and 2.70 against about 3.45 for neat PVPVA; with HPMCAS the 5% compact released polymer faster than neat HPMCAS (about 0.61 against 0.47 mg/min/cm²) yang2021 R21, R18. CPD–PVPVA binary compacts gave PVPVA at about 5.2 (40%), 6.7 (50%) and 4.1 mg/min/cm² (60%) against about 2.6 and 2.7 for neat PVPVA in two panels; with SDS and CTAB the 40% compacts kept about 5.4 and 5.2, with TPGS and Tween 80 about 2.1 and 3.0 correasoto2022a R18. Neat PVPVA with 10% SDS dissolved at almost twice the neat rate, with Spans unchanged, and a drug-free PVPVA matrix with 5% TPGS released at about 3.2 against 3.4 correasoto2022b R22; saboo2021 R14. In 10% ATZ–PVPVA compacts with additives the PVPVA rate ran from about 1.7 (TPGS) to 5.1 mg/min/cm² (CTAB) against about 2.7 for neat PVPVA correasoto2022b R3. At high loading the drug held the polymer back: elbasvir–PVPVA powders at 50% released about 34% of their polymer in 60 min against about 97% for miconazole–PVPVA at 50% yang2021 R13. (synthesis: polymer rate from the dispersion over the neat rate: 3.19/3.4 ≈ 0.94 for 10% IND, 3.4/3.0 ≈ 1.1 for 40% Me-PHPH, 6.7/2.7 ≈ 2.5 for 50% CPD, against 2.35/3.49 = 0.67 for 10% nilvadipine in F2.) In the ritonavir surfactant tablets the SDS dispersion had released about 35.4 against 14.0 units of PVPVA for the binary tablet at the limit by 10 min and 48.8 against 26.2 by 15 min, while Span 20, Span 85 and TPGS followed the binary curve (about 12.7–15.0 at 10 min) and Tween 80 lagged (about 6.6) indulkar2022 R20, C34. The values are amounts not normalized to the larger polymer content of the 25:75 tablet, and the SDS ratio falls from about 2.5 at 10 min to about 1.2 at 20 min indulkar2022 X5, X6. With an enteric polymer the drug slowed the polymer: HP-50 left its 20% miconazole dispersion at about 23.3% by 60 min and 42.2% by 120 min against about 28.4 and 60.3% for neat HP-50 compacts in the same medium, a comparison the authors do not comment on qi2022 R14, R9. With HPMCAS both drugs slowed the polymer, most at high buffer capacity and high loading: at 51 mM/ΔpH HPMCAS left at about 1.01 mg/min/cm² neat, 0.76 and 0.58 from 10% IND and INDester and 0.58 and 0.45 from the 50% dispersions, while at 3 mM/ΔpH all lay between 0.04 and 0.16 bapat2023 R11, R12. In relative terms the slowing at 3 mM/ΔpH was not smaller (dispersion over neat about 0.25–0.69), and the INDester-over-IND ranking held only at 26–51 mM/ΔpH bapat2023 X3, X12. Water uptake after 12 h fell from about 6.2% (neat) to 5.1 and 4.6% (10% IND, INDester) and 3.9 and 2.4% (50%) bapat2023 R20. A plasticizer alone sped PVPVA: drug-free PVPVA compacts with 10% w/w glycerol tributyrate or tributyl citrate dissolved at about 4.8 and 6.1 against 2.7 mg/min/cm², and plasticized atazanavir dispersions at 20% released drug at about 4.6–5.1 with PVPVA at 3.8–4.2 (F26) correasoto2023 R13, R6. In 2023 MePHPH–PVPVA compacts released drug and polymer together at a total of about 4.4, 6.4 and 4.3 mg/min/cm² at 5, 20 and 40%, and 5% PHPH at about 5.5, against 3.7 for neat PVPVA, with the shortest gel residence time (1.9 min) at 20% MePHPH deac2023a R4, C20. PVPVA blends with 12.5 wt% surfactant dissolved at about 3.6 (neat), 3.8 (Span 85), 3.6 (Span 20), 5.7 (Tween 80) and 6.9 mg/min/cm² (SDS) yang2023 R5, X9. Neat PVP compacts released more slowly as molecular weight rose (profiles in an unsupplied SI) deac2024a R3. In HPMCAS-MF at 25% and pH 6.8 the polymer left at about 0.43 (ritonavir), 0.12 (loratadine), 0.08 (clotrimazole) and 0.05 mg/min/cm² (cinnarizine) against 0.90 for the neat polymer, and at about 0.70 (loratadine, pH 7.5) and 0.28 (clotrimazole, pH 9.0), where these drugs are un-ionized bapat2024 R4, R5. Neat HPMCAS LF, MF and HF dissolved at about 1.50, 0.90 and 0.45 mg/min/cm², and a 25% cinnarizine dispersion left HF too slowly to measure bapat2025a R1, R3.

papersystemmethod and conditionsresultids
saboo2020IND, INDester–PVPVA 5–25%5-min rates, pH 2.1 / 6.8, 37 °Ccongruent PVPVA ≈3.2–4.0 against neat ≈3.4 / ≈3.8saboo2020 R3
que2021four analogues at their limitsrates, t-test at 99%PVPVA ≈2.8–3.4 against ≈3.0; p = 0.37–0.48que2021 R21
saboo2021PVPVA with 5% TPGS, no drugcompact≈3.2 against ≈3.4saboo2021 R14
yang2021loratadine–PVPVA 20, 30%; –HPMCAS 5%compacts, 37 °CPVPVA ≈3.33, ≈2.70 against ≈3.45; HPMCAS ≈0.61 against ≈0.47yang2021 R21, R18
yang2021elbasvir, miconazole–PVPVA 50%powders, 60 minpolymer ≈34% against ≈97%yang2021 R13
correasoto2022aCPD–PVPVA 40–60% ± surfactantscompacts, pH 6.8, 37 °Cbinary PVPVA ≈4.1–6.7 against neat ≈2.6–2.7; TPGS, Tween 80 ≈2.1–3.0 at 40%correasoto2022a R18
correasoto2022bATZ–PVPVA 10% with additives; PVPVA + 10% SDScompactsPVPVA ≈1.7–5.1 against ≈2.7; SDS almost doubles neat PVPVAcorreasoto2022b R3, R22
saboo2019nilvadipine–PVPVA 10%compacts2.35 against 3.49saboo2019 R5, R8
indulkar2022ritonavir–PVPVA 30:70 with five surfactants against binary 25:75 (cited)compacts, first 20 min, unnormalizedSDS ≈35.4 against ≈14.0 at 10 min; Spans, TPGS ≈12.7–15.0; Tween 80 ≈6.6indulkar2022 R20, X6
qi2022HP-50 alone and with 20% miconazolecompacts, 50 mM pH 6.8 phosphate, 37 °CHP-50 ≈23.3 / 42.2% at 60 / 120 min from the dispersion against ≈28.4 / 60.3% neatqi2022 R14, R9
bapat2023HPMCAS from IND, INDester dispersions 10, 50%compacts, pH 6.8, 51 mM/ΔpH≈0.76, 0.58, 0.58, 0.45 against neat ≈1.01 mg/min/cm²bapat2023 R11
bapat2023same powders95% RH, 37 °C, 12 hwater uptake ≈6.2 (neat) → 2.4% (50% INDester)bapat2023 R20
correasoto2023PVPVA alone and with 10% w/w GTB or TBCcompacts, pH 6.8, 37 °C≈2.7 → 4.8 and 6.1 mg/min/cm²correasoto2023 R13
deac2023aMePHPH–PVPVA 5, 20, 40%; PHPH 5%total release rate, gel residence time≈4.4 / 6.4 / 4.3; 5.5 against neat ≈3.7 mg/min/cm²; 1.9 min at 20%deac2023a R4
hiew2022a (Miscibility)lumefantrine–PVPVAcompactsPVPVA release constant with loadinghiew2022a C59
bapat2025b (Peptide permeability)SNAC:PVPVA 50:50compacts, pH 6.8PVPVA about twice its neat ratebapat2025b C13
yang2023PVPVA + 12.5 wt% Span 85, Span 20, Tween 80 or SDScompacts, pH 6.8≈3.8 / 3.6 / 5.7 / 6.9 against 3.6 mg/min/cm²yang2023 R5
deac2024aneat PVP K12 to K90compacts, pH 8.0slower with molecular weightdeac2024a R3
bapat2024HPMCAS-MF with 25% ritonavir, loratadine, clotrimazole, cinnarizinecompacts, pH 6.8neat-to-dispersion polymer rate ≈1.6 / 7.4 / 11.2 / 30 (≈18 from the bars)bapat2024 R5, X2
bapat2025aneat HPMCAS LF, MF, HFcompacts, pH 6.8≈1.50 / 0.90 / 0.45bapat2025a R1

Figure

Fig. 9 of correasoto2022a: percent release and normalized release rates of clopidogrel and PVPVA at 40, 50 and 60% loading, with neat PVPVA
Fig. 9 · correasoto2022apercent release and normalized release rates of clopidogrel and PVPVA at 40, 50 and 60% loading, with neat PVPVA

In panels d–f the blue PVPVA bars of the binary dispersions stand above the neat-PVPVA bar at the right of each panel, while the TPGS and Tween 80 bars fall back to about its height correasoto2022a R18.

Fig. 7 of que2021: drug and PVPVA release rates of four analogues at their limits against neat PVPVA
Fig. 7 · que2021drug and PVPVA release rates of four analogues at their limits against neat PVPVA

All bars lie near 3 mg/min/cm², with p-values for drug against polymer and for dispersion polymer against neat polymer que2021 R21.

Why

A glassy polymer dissolves by water ingress into a plasticized gel layer and chain disentanglement, which is faster above its Tg; the papers therefore expect the polymer rate to depend on the water the gel layer takes up and on the Tg of the hydrated matrix relative to the test temperature saboo2020 C54, C55; correasoto2022b C33, C36; yang2021 C30. Correa Soto and co-workers (2022) state that CPD lowers the dispersion Tg (data in the SI) and read the faster PVPVA as a plasticization effect, as 20 wt% PEO doubled the dissolution rate of PMMA ("is thought to") correasoto2022a R26, R30, C48. Yang and co-workers find it "feasible" that a little low-Tg loratadine plasticizes HPMCAS, while more low-polarity drug "would be anticipated" to reduce water entry and slow the polymer yang2021 C31, C32. Que and co-workers rationalize the opposite case: a drug–polymer hydrogen bond that persists in water occupies polymer solvation sites, cuts water uptake and slows disentanglement ("could explain"; see F17), whereas without specific interactions release is "agnostic" to the compound and drug release can be predicted from polymer release que2021 C44, C41. Hiew and Taylor (2022) quantify the water a glassy polymer needs before its chains disentangle with the critical polymer volume fraction,

v_p^{*} = \frac{1/\rho_p}{1/\rho_p + \frac{T_g - T}{\beta/\alpha_f}\cdot\frac{1}{\rho_s}}

hiew2022b E1, which for PVPVA at 37 °C gives 0.89, at least 11% water hiew2022b R21, C40. SDS, which interacts with PVPVA, sped the neat polymer, and the non-ionic surfactants that interacted with CPD slowed both components, which the authors call "likely unfavorable" correasoto2022b R22, C43; correasoto2022a C56, C57. (synthesis: the ceiling of polymer-controlled release in F2 is the rate of the polymer in the dispersion; a low-Tg drug or SDS can raise it above the neat rate and a non-ionic surfactant or a high-Tg drug at high loading can lower it, so the neat rate bounds the dispersion only roughly.) Indulkar and co-workers (2022) suggest that SDS "perhaps" speeds release by forming micellar aggregates on the PVPVA chains, a complex that "may" dissolve faster than the polymer alone, so that release outruns phase separation; SDS–PVPVA complexation was not measured in that paper indulkar2022 C33. They group the effect by charge: ionic SDS "may" act on the polymer and raise the overall release rate, the non-ionic surfactants on drug–polymer phase separation indulkar2022 C56, X11. Qi and Taylor (2022) explain the slower enteric polymer by a lipophilic drug lowering the water fraction of the gel layer that chain disentanglement needs, which the higher hydration of a pre-ionized polymer salt "likely" helps to offset (F24) qi2022 C40. Bapat and co-workers (2023) attribute the slower HPMCAS "most likely" to the drug lowering the amount and rate of water the polymer takes up, which leaves a more viscous gel from which the polymer escapes less easily; at low buffer capacity the polymer's solubility at the acidic interface still dominates, so the drug matters less there (F23) bapat2023 C46, C21. Gel hydration in the medium was not measured; the uptake came from humid air bapat2023 X9. Correa Soto and co-workers (2023) read the faster plasticized PVPVA through free-volume theory: a plasticizer raises the fractional free volume of the hydrated gel, chain mobility and so the disengagement rate (Devotta, cited), which they find "reasonable to suggest" as one mechanism; chain mobility was not measured (F26) correasoto2023 C40, C41, C39. Deac and co-workers (2023) propose that the congruent rate is set by water penetration and chain disentanglement, both faster up to 20% MePHPH because the gel is thinner and the low-Tg drug (onset 22.5 °C) plasticizes the polymer, and slower above it as the drug's lipophilicity lowers the driving force for water uptake ("may be due") deac2023a C73, C50, C51, C53. The residence times printed match the dry gel mass rather than the total gel weight deac2023a X3. Yang and co-workers suggest that faster water uptake, plasticization and, for SDS, a soluble SDS–PVPVA complex "could" explain the faster polymer, none measured on the blends yang2023 C49. For HPMCAS the 2024–2025 papers attribute the slowing by cationic drugs to an insoluble ion-pair complex that lowers the polymer's interfacial solubility (F32) bapat2024 C32; bapat2025a C34.

Conditions and limits

PVPVA except one HPMCAS series; compacts of about 100 mg at 37 °C; IND at pH 2.1 and TIPP at pH 2.5, so their neat-polymer references ran in other media saboo2020 X5; que2021 X5. How the rates of the analogue study were derived and how many runs lie behind them is not printed que2021 X6, X13. The CPD dispersion Tg is in an SI that was not supplied correasoto2022a R26. The ternary CPD and ATZ loadings are drug:polymer ratios with 5 g surfactant on top correasoto2022a X9; correasoto2022b X12. The surfactant blends held 12.5 wt% surfactant, more than the 9.1 wt% of the ternary dispersions of the same paper yang2023 X9.

Counterexamples and conflicts

In the 2018–2019 papers the polymer left congruent compacts more slowly than from a neat compact (0.22–0.29 for 10% itraconazole, 0.67–0.68 for the dihydropyridines) (F2) bhardwaj2018 R12; saboo2019 R5, R8. TPGS raised the felodipine limit although it did not speed PVPVA in a drug-free matrix, so its gain did not come from a faster polymer (F21) saboo2021 R14, C17, X15.

Transfer check

Dissolve a neat polymer compact in the same die and medium as the dispersion and compare the polymer rate of a low-loading compact with it: a ratio above 1 points to plasticization by the drug or an additive, one well below 1 to a drug or additive that slows the polymer correasoto2022a R18; saboo2019 R8. Repeat with each candidate surfactant, since non-ionic surfactants slowed PVPVA and SDS sped it correasoto2022a R18; correasoto2022b R22. For an enteric polymer, compare dispersion and neat polymer at the buffer capacity of use, since the drug's effect on HPMCAS grew with buffer capacity in absolute terms bapat2023 R12, C48.

History

Bhardwaj and co-workers (2018) and Saboo and co-workers (2019) found the polymer slowed in congruent dispersions, "most likely" by the hydrophobicity of the formulation or drug–polymer interactions bhardwaj2018 C49; saboo2019 C13. Saboo and co-workers (2020) and Que and co-workers (2021) found it at about the neat rate with indomethacin, its ester and four analogues saboo2020 R3; que2021 C39. Yang and co-workers (2021) saw a little loratadine speed up HPMCAS yang2021 C31. Correa Soto and co-workers (2022) were the first in the library to report PVPVA from a dispersion at about twice its neat rate ("Surprisingly") correasoto2022a C30, and a companion study showed SDS doubling neat PVPVA correasoto2022b R22. Hiew and Taylor (2022) brought in the critical polymer volume fraction hiew2022b E1. Indulkar and co-workers (2022) found the same SDS acceleration of PVPVA inside ritonavir dispersions, with Tween 80 slowing the polymer indulkar2022 C32, C34. Qi and Taylor (2022) extended the observation to an enteric polymer, which miconazole slowed qi2022 R14, R9. Bapat and co-workers (2023) found that the slowing of HPMCAS by a drug depends on the buffer capacity of the medium bapat2023 C21, C25. Correa Soto and co-workers (2023) sped neat PVPVA with plasticizers that are not surfactants correasoto2023 C18. Deac and co-workers (2023) showed the polymer-paced rate rising and then falling with loading below the limit deac2023a C22. Yang and co-workers (2023) measured surfactants in PVPVA blends, Deac and co-workers (2024) the effect of PVP molecular weight, and Bapat and co-workers (2024) and Bapat and Taylor (2025) the slowing of HPMCAS by weak bases and its dependence on grade yang2023 C6; deac2024a C19; bapat2024 C14; bapat2025a C12.

Other chaptersextends B F10
F23

Topic 1Two release regimes and their measurement5 of 5

For enteric polymers the buffer capacity, buffer species and pH of the medium set how fast polymer and drug are released.

Neat HPMCAS-MF released about 0.16 mg/min/cm² in pH 6.8 phosphate of 3 mM/ΔpH buffer capacity and 1.01 at 51 mM/ΔpH, and HP-50 fell from about 0.92 to 0.14 between 29 and 3 mM/ΔpH bapat2023 R5; qi2022 R12. The HPMCAS gel was more acidic than the medium (pH 5.6–6.2 against 6.8), and the rate rose with the gel pH bapat2023 R15, R16. Because 10% indomethacin left HPMCAS dispersions at the polymer's pace, drug release followed the medium in the same way bapat2023 R9, R10, R13.

strongStrong for the dependence of the rate on buffer capacity, large, monotonic and in triplicate in both papers; moderate for the acidic surface as the cause, which rests on an averaged gel pH and on cited surface-pH and solubility data bapat2023 K1, K3; qi2022 K3, K1, K6, X16.

Neat HPMCAS-MF in pH 6.8 phosphate, mg/min/cm²3 mM/ΔpH≈0.165 mM/ΔpH≈0.2613 mM/ΔpHgel pH 5.6≈0.5926 mM/ΔpHgel pH 6.0 · usual 50 mM buffer≈0.8951 mM/ΔpHgel pH 6.2≈1.01

Same polymer, same pH; only the buffer capacity changes. FaSSIF (12 mM/ΔpH) matched its blank buffer. bapat2023 R5, R7, R15

HP-50 dissolved in 60 min at pH 6.8, by buffer species, %BIS-TRISbuffer pKa 6.5≈44.8phosphatepKa 7.2≈28.4TrispKa 8.1≈6.6TEApKa 10.2≈1.8

Buffers whose pKa lies near the acidic surface pH carry protons away best. qi2022 R2, M23, M24, M25

For your drug

  1. For a dispersion in HPMCAS, HPMCP or another enteric polymer, run the constant-area release test in pH 6.8 phosphate at 3–5 mM/ΔpH as well as at 26 mM/ΔpH, with the polymer assayed.
  2. Run several rotation speeds, since a rise with the square root of speed without a plateau places the limit in diffusion of the polymer, and compare FaSSIF with its blank buffer before attributing a medium effect to micelles.

bapat2023 R5, R24, C30, R7, C20

How it works and key numbers
  1. A carboxylic polymer that is insoluble at low pH must ionize before its chains dissolve; ionization releases protons at the surface, which leave by diffusion, by meeting hydroxyl ions or on buffer species qi2022 C11, C24; bapat2023 C33, C36.
  2. The surface pH therefore lies below the bulk pH, and with a polymer pKa near 4–5 and HPMCAS solubility rising steeply between pH 5.0 and 6.5, a small drop cuts the polymer's solubility at the surface qi2022 R18, C23; bapat2023 C38, M3.
  3. In the diffusion-controlled regime the flux is J_p = \frac{D_p}{\delta}\, C_p, with C_p the polymer solubility at the interface and \delta = 1.612\, D_p^{1/3}\, \nu^{1/6}\, \omega^{-1/2} at a rotating disk, so release rises with the square root of rotation speed, as measured up to 700 rpm bapat2023 E2, E3, R18, R19.
  4. A buffer whose pKa lets it take up a proton at the surface pH lifts the interfacial pH: BIS-TRIS carries protons better than phosphate, while Tris and TEA "cannot act as proton carriers" qi2022 C26, C27; bapat2023 C39.
  5. Because the rate rose with the square root of speed without a plateau, the authors consider control by chain disentanglement "unlikely" bapat2023 R25, R27, C45.
0.16 → 1.01 mg/min/cm²neat HPMCAS-MF from 3 to 51 mM/ΔpH in pH 6.8 phosphatebapat2023 R5
pH 5.6–6.2gel of HPMCAS in pH 6.8 phosphate of 13–51 mM/ΔpHbapat2023 R15
≈5.6×HPMCAS in the usual 50 mM phosphate (26 mM/ΔpH) against 3 mM/ΔpHbapat2023 R5
Evidence: data, conditions and papers

Finding F23. For enteric polymers the buffer capacity, buffer species and pH of the medium set polymer and drug release through an acidic polymer surface: HP-50 and HPMCAS-MF dissolved about six times faster in strong than in weak pH 6.8 phosphate, the HPMCAS gel was 0.6–1.2 pH units more acidic than the medium, and FaSSIF micelles changed nothing for the neat polymer or a drug that does not complex it

In short. HP-50 compacts dissolved at about 0.92 mg/min/cm² in 50 mM pH 6.8 phosphate (29 mM/ΔpH buffer capacity) and 0.14 in 5 mM phosphate (3 mM/ΔpH), and at pH 6.8 about 45% of the polymer dissolved in 60 min in BIS-TRIS buffer against 2% in TEA buffer, the order of buffer pKa qi2022 R12, R2. Neat HPMCAS-MF released about 0.16, 0.26, 0.59, 0.89 and 1.01 mg/min/cm² at 3, 5, 13, 26 and 51 mM/ΔpH, FaSSIF matched its blank buffer, and at pH 5.0 nothing dissolved bapat2023 R5, R7, R8. A pH dye in the HPMCAS gel read 5.6, 6.0 and 6.2 in pH 6.8 phosphate of 13, 26 and 51 mM/ΔpH, and the rate rose with the gel pH bapat2023 R15, R16. Because 10% indomethacin and its ester left HPMCAS dispersions at the polymer's pace, drug release followed the medium in the same way, about sevenfold to eightfold over the buffer series (F2) bapat2023 R9, R10, R13. The authors name polymer solubility at the polymer–solution interface as the rate-limiting step ("likely"; "was elucidated as"); the interfacial pH and solubility were not measured qi2022 C2; bapat2023 C52, X5. In 2024–2025 the gel pH of 6.0 in 50 mM pH 6.8 phosphate became the reference pH for complexation of weak bases with HPMCAS; a 25% loratadine dispersion released about 2.5 times faster in 100 mM than in 50 mM phosphate against 1.1 times for the neat polymer, and FaSSIF-V1 raised bedaquiline release about fivefold over pH 6.5 buffer by suppressing complexation (F32, F34) bapat2024 R6, X3; kaur2025 R13, R15.

Type. observation in 2 enteric polymers (HP-50, HPMCAS-MF) with 3 drugs (miconazole, indomethacin, indomethacin methyl ester) Strength. for the dependence of the rate on buffer capacity, large, monotonic and in triplicate in both papers bapat2023 K1: strong; qi2022 K3: moderate, K1: moderate; moderate for the acidic surface as the cause, which rests on an averaged gel pH, a cited surface-pH shift and cited solubility data bapat2023 K3: moderate; qi2022 K6: weak to moderate, X16.

How it was shown

Qi and Taylor (2022) dissolved HP-50 compacts in pH 6.8 buffers of different species and buffer capacity qi2022 P10, A2, A4. Bapat and co-workers (2023) dissolved neat HPMCAS-MF and its indomethacin (IND) dispersions in pH 6.8 phosphate of 3–51 mM/ΔpH and in biorelevant media, read the gel pH with pH dyes and varied the rotation speed bapat2023 A3, P14, P10, A4.

What the data show

The HP-50 rate fell from about 0.92 to 0.14 mg/min/cm² between 29 and 3 mM/ΔpH, the "6-fold reduction" of the paper qi2022 R12, C4.

systemmethod and conditionsresultids
HP-50 in BIS-TRIS, phosphate, Tris, TEA buffers, pH 6.8compacts, 60 min≈44.8 / 28.4 / 6.6 / 1.8% (buffer pKa 6.5 / 7.2 / 8.1 / 10.2)qi2022 R2, M23, M24, M25
neat HPMCAS-MF, pH 6.8 phosphate 3–51 mM/ΔpHcompacts, 100 rpm, 37 °C≈0.16 / 0.26 / 0.59 / 0.89 / 1.01 mg/min/cm²bapat2023 R5
neat HPMCAS-MF in FaSSIF, blank buffer, FeSSIF-V2, FeSSIF V1same≈0.56, 0.57, 0.58; none at pH 5.0bapat2023 R5, R7, R8
HPMCAS gel in pH 6.8 phosphate 13, 26, 51 mM/ΔpH; pH 7.5pH dye in the polymer, scraped gelgel pH 5.6 / 6.0 / 6.2; 6.3; rates ≈0.60–1.09bapat2023 R15, R16
neat HPMCAS-MF, 100–700 rpmrotating disklinear in √rpm, ≈2.9–3.3× at 700 rpm, no plateaubapat2023 R18, R19
IND–HPMCAS 10%3–51 mM/ΔpH and FaSSIFIND = HPMCAS; ≈0.12 → 0.82 mg/min/cm²bapat2023 R9, R10
Fig. 2 of bapat2023: normalized release rate of neat HPMCAS against buffer capacity in several media
Fig. 2 · bapat2023normalized release rate of neat HPMCAS against buffer capacity in several media

The grey pH 6.8 phosphate squares rise steeply from 3 to 26 mM/ΔpH and level off; FaSSIF and its blank buffer overlap at 12 mM/ΔpH; FeSSIF-V2 at pH 5.8 lies low and pH 7.5 phosphate highest bapat2023 R5.

Why

Both papers take the Nguyen and Fogler framework (cited): a carboxylic polymer must ionize before its chains dissolve, ionization releases protons at the surface, and these leave by diffusion, by meeting hydroxyl ions or on buffer species, so the surface pH lies below the bulk pH and a small drop cuts the polymer's solubility there qi2022 C11, C24, C23; bapat2023 C33, C36, C38. Tris and TEA, mostly protonated at both pH values, "cannot act as proton carriers" qi2022 C27. With a diffusion flux J_p = \frac{D_p}{\delta}\, C_p and a Levich boundary layer, release rises with the square root of rotation speed, and without a plateau disentanglement control is "unlikely" bapat2023 E2, E3, C45.

Limits and transfer

The surface pH and the interfacial polymer solubility were not measured qi2022 X16; bapat2023 X5. For a drug that complexes HPMCAS the micelles of FaSSIF-V1 changed release several-fold kaur2025 R13, R15, C49. Run the release test of an enteric dispersion at 3–5 mM/ΔpH as well as at 26 mM/ΔpH with the polymer assayed, and compare FaSSIF with its blank buffer before attributing a medium effect to micelles bapat2023 R5, R24, R7, C20.

How it was shown

Qi and Taylor (2022) asked what limits the dissolution of hydroxypropylmethyl cellulose phthalate HP-50 (phthalic acid 1.61 mmol per gram, pKa about 4.2) at pH 6.8 qi2022 M1, C1. They compressed 100 mg into an 8 mm die (0.5 cm²) and rotated it at 100 rpm in 100 mL buffer at 37 °C, n = 3, assaying the polymer by the phenol–sulfuric acid method, in pH 6.8 phosphate with K, NH4, Cs, Na or tetrabutylammonium as cation, in 50 mM BIS-TRIS, Tris and TEA buffers (calculated pKa 6.5, 8.1 and 10.2, against 7.2 for phosphate), and in 50 and 5 mM phosphate, whose buffer capacities were measured as 29 and 3 mM/ΔpH qi2022 P10, P12, A1, A2, A4, M16, M17, M23, M24, M25. Bapat and co-workers (2023) used the same compact and speed for HPMCAS-MF (pKa 4.92 or 5.0 cited, about 18,000 Da), its triethylamine salt and 10 and 50% dispersions with indomethacin (IND, ionized at pH 6.8) or its methyl ester (INDester, neutral), assaying the polymer by HPLC with light-scattering detection calibrated in each medium bapat2023 M3, M4, A3, P7, P8. They varied the buffer capacity of pH 6.8 phosphate from 3 to 51 mM/ΔpH (5 to 100 mM), compared FaSSIF with its blank buffer, FeSSIF-V2 (pH 5.8), FeSSIF V1 (pH 5.0), phosphate at pH 7.5 and 9.0 and glycine at pH 9.0, and doubled the ionic strength with NaCl bapat2023 P14, A1, A2, P12. They imaged the gel layer of partly dissolved compacts with prodan by confocal microscopy, read the pH of gel scraped from compacts containing chlorophenol red or bromothymol blue against a calibration in solution, and ran the rotation speed from 100 to 700 rpm bapat2023 P9, P10, A4.

What the data show

HP-50: with five phosphate cations of 182–415 pm about 22.6–35.7% of the polymer dissolved in 60 min, the authors seeing little effect of cation size; with different buffer species at the same pH it was about 44.8% (BIS-TRIS), 28.4% (phosphate), 6.6% (Tris) and 1.8% (TEA) qi2022 R1, R2, C13. At 3 against 29 mM/ΔpH the rate fell from about 0.92 to 0.14 mg/min/cm², the "6-fold reduction" of the paper qi2022 R12, C4. HPMCAS-MF in pH 6.8 phosphate: about 0.16, 0.26, 0.59, 0.89 and 1.01 mg/min/cm² at 3, 5, 13, 26 and 51 mM/ΔpH, levelling at high buffer capacity ("may be approaching a plateau"); ionic strength 98 against 196 mM made no difference bapat2023 R5, C9, R6. FaSSIF (pH 6.5, 12 mM/ΔpH) gave about 0.56 and its blank buffer 0.57; FeSSIF-V2 (pH 5.8, 25 mM/ΔpH) about 0.58 against 0.89 in pH 6.8 phosphate of similar capacity; FeSSIF V1 (pH 5.0) dissolved no polymer bapat2023 R5, R7, R8. Phosphate at pH 7.5 (18 mM/ΔpH) gave about 1.09, phosphate at pH 9.0 (2 mM/ΔpH) about 0.67, glycine at pH 9.0 about 0.67 and 0.99 at 25 and 51 mM/ΔpH bapat2023 R5. A gel layer formed only from 13 mM/ΔpH, 3 ± 1 µm thick there and 19 ± 5 µm at 51 mM/ΔpH; at 5 mM/ΔpH the surface kept its grain boundaries bapat2023 R14. The gel pH read 5.6 ± 0.2, 6.0 ± 0.1 and 6.2 ± 0.2 in pH 6.8 phosphate of 13, 26 and 51 mM/ΔpH and 6.3 ± 0.1 in pH 7.5 phosphate, against rates of about 0.60, 0.90, 1.01 and 1.09; the pre-ionized salt read 6.7 ± 0.1 with about 1.62 (F24) bapat2023 R15, R16. The rate rose linearly with the square root of the rotation speed in every medium, to about 2.9–3.3 times the 100 rpm value at 700 rpm, without a plateau bapat2023 R18, R19. The drug followed: from the 10% IND dispersion IND and HPMCAS left at about 0.12/0.10 at 3, 0.55/0.54 at 13 and 0.80/0.78 mg/min/cm² at 26 mM/ΔpH and 0.51/0.49 in FaSSIF bapat2023 R9. (synthesis: 1.01/0.16 ≈ 6.3 for neat HPMCAS over 3–51 mM/ΔpH and 0.92/0.14 ≈ 6.6 for HP-50 over 3–29 mM/ΔpH; in the usual 50 mM phosphate (26 mM/ΔpH) HPMCAS ran 0.89/0.16 ≈ 5.6 times faster than at 3 mM/ΔpH.) Neat HPMCAS-MF released at about 0.91 in 50 mM and 1.00 mg/min/cm² in 100 mM pH 6.8 phosphate and the 25% loratadine dispersion at about 0.10 and 0.12 and 0.25 and 0.29 (drug and polymer), and neat HPMCAS-MF at about 0.63 in 50 mM pH 9.0 glycine buffer against 0.90 at pH 6.8 bapat2024 R6, R4. Neat HPMCAS LF, MF and HF dissolved at about 1.50, 0.90 and 0.45 mg/min/cm² at pH 6.8 and 1.73, 1.09 and 0.63 at pH 7.5 bapat2025a R1. Bedaquiline dispersions released about 17–19.5% at 10% in pH 6.5 buffer and 87.5–97% in FaSSIF-V1 kaur2025 R13, R15.

papersystemmethod and conditionsresultids
qi2022HP-50 in pH 6.8 phosphate, five cationscompacts, 100 rpm, 37 °C, 60 min≈22.6–35.7% dissolvedqi2022 R1
qi2022HP-50 in BIS-TRIS, phosphate, Tris, TEA buffers, pH 6.8same≈44.8 / 28.4 / 6.6 / 1.8% (buffer pKa 6.5 / 7.2 / 8.1 / 10.2)qi2022 R2, M23, M24, M25
qi2022HP-50; HP-50-Na at 29 and 3 mM/ΔpHnormalized rates≈0.92 → 0.14; ≈2.80 → 2.45 mg/min/cm²qi2022 R12
bapat2023neat HPMCAS-MF, pH 6.8 phosphate 3–51 mM/ΔpHcompacts, 100 rpm, 37 °C≈0.16 / 0.26 / 0.59 / 0.89 / 1.01 mg/min/cm²bapat2023 R5
bapat2023neat HPMCAS-MF in FaSSIF, blank buffer, FeSSIF-V2, FeSSIF V1same≈0.56, 0.57, 0.58; none at pH 5.0bapat2023 R5, R7, R8
bapat2023HPMCAS gel in pH 6.8 phosphate 13, 26, 51 mM/ΔpH; pH 7.5pH dye in the polymer, scraped gelgel pH 5.6 / 6.0 / 6.2; 6.3; rates ≈0.60–1.09bapat2023 R15, R16
bapat2023neat HPMCAS-MF, 100–700 rpmrotating disklinear in √rpm, ≈2.9–3.3× at 700 rpm, no plateaubapat2023 R18, R19
bapat2023IND–HPMCAS 10%same, 3–51 mM/ΔpH and FaSSIFIND = HPMCAS; ≈0.12 → 0.82 mg/min/cm²bapat2023 R9, R10
shah2025 (Crystallization from solution)posaconazole–HPMCAS gradesrelease at pH 5.5–7.5poor release of the least succinoylated grades at low pHshah2025 C17
bapat2024neat HPMCAS-MF and 25% loratadine dispersion, 50 and 100 mM pH 6.8 phosphatecompactsneat ≈0.91 → 1.00; loratadine ≈0.10 → 0.25 mg/min/cm²bapat2024 R6, X3
bapat2024neat HPMCAS-MF, 50 mM pH 9.0 glycinesame≈0.63 against 0.90 at pH 6.8bapat2024 R4
bapat2025aneat HPMCAS LF, MF, HF, pH 6.8 and 7.5same≈1.50 / 0.90 / 0.45 and ≈1.73 / 1.09 / 0.63bapat2025a R1
kaur2025bedaquiline–HPMCAS 10%, pH 6.5 buffer against FaSSIF-V1powder, 120 min≈17–19.5% against ≈87.5–97%kaur2025 R13, R15

Figure

Fig. 2 of bapat2023: normalized release rate of neat HPMCAS against buffer capacity in several media
Fig. 2 · bapat2023normalized release rate of neat HPMCAS against buffer capacity in several media

The grey pH 6.8 phosphate squares rise steeply from 3 to 26 mM/ΔpH and level off; FaSSIF and its blank buffer overlap at 12 mM/ΔpH; FeSSIF-V2 at pH 5.8 lies low and pH 7.5 phosphate highest bapat2023 R5.

Fig. 10 of bapat2023: HPMCAS release rate against the apparent pH of the gel layer
Fig. 10 · bapat2023HPMCAS release rate against the apparent pH of the gel layer

Four HPMCAS points rise with gel pH from 5.6 to 6.3; the pre-ionized salt stands alone at gel pH 6.7 with the highest rate; the gel pH is an average over gel scraped from the compact bapat2023 R16, X5, X6.

Why

Both papers take the framework of Nguyen and Fogler (cited) for carboxylic polymers: a polymer insoluble at low pH must ionize before its chains dissolve, ionization releases protons at the surface, and the protons have to leave by diffusion, by meeting hydroxyl ions or on buffer species that take them up at the surface and release them in the bulk qi2022 C11, C24; bapat2023 C33, C36. The surface pH therefore lies below the bulk pH (about 0.4 units for HP-50 films, cited), and with a polymer pKa near 4–5 and HPMCAS solubility rising steeply between pH 5.0 and 6.5 (cited) a small drop cuts the polymer's solubility at the surface qi2022 R18, C23; bapat2023 C38, M3. In the diffusion-controlled regime the flux is

J_p = \frac{D_p}{\delta}\, C_p

with C_p the polymer solubility at the interface and \delta the boundary layer, which at a rotating disk follows

\delta = 1.612\, D_p^{1/3}\, \nu^{1/6}\, \omega^{-1/2}

so that diffusion-controlled release rises with the square root of rotation speed bapat2023 E2, E3. A buffer with more species, or a pKa that lets it take up a proton at the surface pH, lifts the interfacial pH: BIS-TRIS (6.5) carries protons better than phosphate (7.2), while Tris and TEA, mostly protonated at both surface and bulk pH, "cannot act as proton carriers" qi2022 C26, C27; bapat2023 C39. The authors read the gel pH series as "strong" support, and the HPMCAS salt, which releases no protons, as further support (F24) bapat2023 C39, C41. Because release rose with √rpm without the plateau that marked disentanglement control for Eudragit (cited), and because HPMCAS-MF lies below the entanglement molecular weights estimated for other polysaccharides (about 22–34 kDa), they consider disentanglement control "unlikely" bapat2023 R25, R27, C45. For HP-50 the absence of a cation-size effect makes a percolation model "likely not appropriate" qi2022 C29. Surface pH is also said to set the hydration of the gel layer and hence disentanglement qi2022 C30. (synthesis: in the polymer-controlled regime of F2 the polymer's rate caps drug release; for an enteric polymer that cap is set by the medium as well as by the polymer, so the same dispersion can release several times faster in 50 mM phosphate than in a weak buffer; in the crystallization chapter the least succinoylated HPMCAS grades released posaconazole poorly at low pH for the same reason, release being polymer-controlled (Crystallization from solution F44) shah2025 C17.) Bapat and co-workers put the slow neat polymer in pH 9.0 glycine down to the low buffer capacity of that buffer at the acidic surface, and place three loratadine results on a gel-pH axis (6.0, 6.2, 6.3), only the first value with a stated source bapat2024 C13, R15, X6.

Conditions and limits

HP-50 and HPMCAS-MF compacts at 37 °C and 100 rpm (100–700 rpm in one series) in phosphate, amine, glycine and maleate buffers; no bicarbonate buffer was used, and the FaSSIF the authors call physiological has 12 mM/ΔpH against the cited 2–8 mM/ΔpH of fasted intestinal fluid qi2022 P10; bapat2023 P7, X8, R24. The surface pH, the proton flux and the polymer solubility at the interfacial pH were not measured; the gel pH is an average over scraped gel, near the upper limit of the dye for the salt, and the cited HPMCAS solubility data stop at pH 6.5 qi2022 X16; bapat2023 X5, X6. The buffer capacities of the amine buffers and the composition of the 77 mM/ΔpH medium are not printed, and the medium of the HPMCAS salt is labelled 26 or 51 mM/ΔpH in different figures qi2022 X12; bapat2023 X2, X1. Drug release was measured at 10% (HPMCAS) and 20% (HP-50) loading only bapat2023 X4; qi2022 A6.

Counterexamples and conflicts

Cation size changed HP-50 dissolution little, but sodium (about 28.4% at 60 min) lay below potassium, ammonium and cesium (33.5–35.7%), and the cation concentrations of that series differed qi2022 R1, X11. At pH 9.0, phosphate of only 2 mM/ΔpH still gave HPMCAS about 0.67 mg/min/cm², faster than pH 6.8 phosphate of 3–5 mM/ΔpH, so bulk pH acts beside buffer capacity bapat2023 R5, C15. The rotation data are linear in √rpm but rise above the Levich prediction at 700 rpm (about 2.9–3.3 against 2.65) bapat2023 X10. The stop of HPMCAS release near a gel pH of 5 is an extrapolation of four points bapat2023 R17, X13. In the ASD dissolution chapter the gastric pH and the enteric polymer grade decided the release of delamanid and praziquantel dispersions after a pH shift (Supersaturation from ASD dissolution F25), and SDS dissolved far more HPMCAS from suspended particles at pH 3 (Supersaturation from ASD dissolution F15) chen2015a R18. For a drug that complexes HPMCAS the micelles of FaSSIF-V1 and FeSSIF-V2 changed release several-fold, so the absence of a FaSSIF effect holds for the polymer and non-complexing drugs only (F34) kaur2025 R13, R15, C49. In 100 mM phosphate loratadine complexation also fell from about 70 to 48% at equal pH, a second route for the buffer effect that the authors do not discuss bapat2024 R16, X11.

Transfer check

For a dispersion in HPMCAS, HPMCP or another enteric polymer, run the constant-area release test in pH 6.8 phosphate at 3–5 mM/ΔpH as well as at 26 mM/ΔpH, with the polymer assayed, since the usual 50 mM buffer ran HPMCAS about 5.6 times faster than a 3 mM/ΔpH buffer (synthesis above) bapat2023 R5, R24. A run at several rotation speeds that rises with √rpm without a plateau places the limit in diffusion of the polymer, not in disentanglement bapat2023 C30. Compare FaSSIF with its blank buffer before attributing a medium effect to micelles bapat2023 R7, C20.

History

Lower surface pH at dissolving enteric coatings was known from coating work (Ozturk 1988, Harianawala 2002, cited), and the Nguyen and Fogler model (2005, cited) tied carboxylic polymer dissolution to interfacial solubility and proton carriers qi2022 C7, R18, C11. In the library the critical ionization of HP-50 (about 83%) and the HPMCAS-MF pKa came from a lumefantrine study of the Miscibility chapter qi2022 R19; bapat2023 M3. Qi and Taylor (2022) were the first in this subcategory to vary buffer species and capacity for an enteric dispersion polymer qi2022 C14, C4. Bapat and co-workers (2023) added the gel pH, the rotation test and drug release that follows the polymer across media bapat2023 C51, C30, C49. Bapat and co-workers (2024), Bapat and Taylor (2025) and Kaur and co-workers (2025) took the gel pH of 6.0 in 50 mM pH 6.8 phosphate as the pH at which to measure complexation of HPMCAS by weak bases (F32, F33) bapat2024 C9; bapat2025a C28; kaur2025 C44, and Kaur and co-workers found that micelle-containing fluids change release where the drug complexes the polymer (F34) kaur2025 C49. The title's statement on FaSSIF was narrowed after these papers to the neat polymer and drugs that do not complex it (synthesis).

Topic 2 of 5 · 3 findings · F4–F5, F16

Nanodroplets from dissolving dispersions

F4

Topic 2Nanodroplets from dissolving dispersions1 of 3

Drug-rich nanodroplets formed only where the released drug passed the amorphous solubility, which polymer-controlled release did and drug-controlled release did not.

In ritonavir films the dispersions that formed nanodroplets were exactly those whose free drug reached the amorphous solubility (27–30 µg/mL): every HPMCAS film, PVP at 10–20% and PVPVA at 10% purohit2017b R10, R11, R7. Nilvadipine and cilnidipine dispersions gave droplets of 237–366 nm only at the congruent loadings saboo2019 R10, R11, R12. From 2021 the rule had exceptions: loratadine–PVPVA at 35% passed the amorphous solubility and formed droplets although the polymer ran ahead yang2021 R19, C15.

strongStrong where free drug, a probe and particle counting agree, as for ritonavir films and the dihydropyridines; moderate where the colloid was sized at one loading only or inferred from concentration, and the link also follows from how much drug had been released purohit2017b K3; saboo2019 K2, X14; indulkar2019a X5; saboo2020a X12.

above the amorphous solubilitybelow itritonavir filmsfree drug after 4 hother films 10–25LLPS films 27–30nilvadipine–PVPVAreleased at 1 h15% ≈1.5, none10% ≈59, dropletsfelodipine–PVP60 min; colloid not measuredamorphous solubility 85% ≈3510% ≈67110100drug in the medium, µg/mL (log scale)

Droplets were found where the released drug passed the amorphous solubility, and not where it stayed below. purohit2017b R10, R1; saboo2019 X14, R12; saboo2020a R6

nifedipine 10, 20%190–222ritonavir 10:90 films200–315ledipasvir 5%225–257nilvadipine, cilnidipine237–366four phenolphthalein analogues179–364150200250300350400nanodroplet size, nm

Sizes by NTA or DLS from congruently releasing dispersions. indulkar2017b R7; purohit2017b R8; que2019 R12; saboo2019 R11; que2021 R22

For your drug

  1. Measure the free drug (ultracentrifugation or flux) and a colloid signal (DLS, NTA or an environment-sensitive probe) in the same release run, and compare the released amount with the amorphous solubility measured in that medium.
  2. Expect droplets only at loadings that release congruently and only once the released amount passes the amorphous solubility; size the droplets at more than one loading.

purohit2017b P16, P17, P12; saboo2019 P12; que2019 R12

How it works and key numbers
  1. When the polymer sets the rate, release continues past the amorphous solubility, and the excess drug then separates as drug-rich droplets (F5) indulkar2019a C49, R24.
  2. A drug-controlled release slows toward zero as the drug approaches its amorphous solubility and "never" produces liquid–liquid phase separation (LLPS) indulkar2019a C48; purohit2017b C50.
  3. In the ritonavir films the apparent concentration spiked and then decayed while the free drug stayed near 28 µg/mL and no crystals formed; the authors put the decay down to nanodroplets that scatter UV light and coalesce purohit2017b R12, R10, C39.
  4. An alternative reading is that droplets were absent above the switch simply because the concentration at 1 h was far below the amorphous solubility; the two readings agree on the outcome saboo2019 X14.
  5. The exceptions are low-Tg drugs whose drug still left at a substantial fraction of the polymer rate during incongruent release, 0.33 for loratadine and 0.54 for clopidogrel (F18) yang2021 R21, C15; correasoto2022a R18, R16.
190–370 nmsize range of the nanodropletsindulkar2017b R7; saboo2019 R11
59 against 1.5 µg/mLnilvadipine released at 1 h from the 10% and the 15% compactsaboo2019 X14
23% against 3.2%loratadine–PVPVA 35% released with droplets, against its amorphous-solubility lineyang2021 R19
Evidence: data, conditions and papers

Finding F4. In 2017–2020 only release that stayed under polymer control passed the amorphous solubility and formed drug-rich nanodroplets of about 190–370 nm, and drug-controlled release stayed at or below it and formed none; from 2021 partly incongruent release of low-Tg drugs also passed it

In short. In ritonavir films the dispersions that formed nanodroplets were exactly those whose free drug reached the amorphous solubility (27–30 µg/mL) and whose solution lowered the pyrene I/III ratio (1.50–1.66 against 1.90 in buffer): every HPMCAS film, PVP at 10–20% and PVPVA at 10% purohit2017b R10, R11, R7. Ritonavir–PVPVA tablets at 10–25% passed the amorphous solubility within 5–10 min and the 10% medium held 218 ± 15 nm droplets; the 30% tablet passed it during its fast phase and 35–50% never did indulkar2019a R9, R20. Nilvadipine and cilnidipine dispersions gave a probe blue shift, 237–366 nm droplets and NTA scattering only at the congruent loadings saboo2019 R10, R11, R12. Saboo and co-workers call this "a clear link", but at 1 h the 10% nilvadipine compact had released about 59 µg/mL against about 1.5 µg/mL from 15%, so the link also follows from how much drug had been released saboo2019 C30, X14. The papers of 2020–2022 confirm the link for IND (droplets of 250–350 nm at 5 and 10% only), felodipine with TPGS (up to its limit) and four analogues (179–364 nm), but loratadine–PVPVA at 35% and loratadine–HPMCAS at 30–40% passed the amorphous solubility although the polymer ran ahead saboo2020 R6, R7; saboo2021 R16, R17; que2021 R18, R22; yang2021 R19, R16, C14, C15.

Type. observation in 6 drugs (ritonavir, nifedipine, nilvadipine, cilnidipine, ledipasvir, felodipine), and 12 further drugs in 2020–2022 Strength. where free drug, a probe and particle counting agree, as for ritonavir films and the dihydropyridines purohit2017b K3: moderate to strong; saboo2019 K2: strong; moderate where the colloid was sized at one loading only or inferred from concentration indulkar2019a X5; saboo2020a X12.

How it was shown

Purohit and Taylor (2017) measured free ritonavir after ultracentrifugation of film solutions and added pyrene and NTA; Indulkar and co-workers (2019) compared the released amount with the amorphous solubility line; Saboo and co-workers (2019) read 4-Di-2-Asp fluorescence (a blue shift marks a drug-rich environment), DLS and NTA at about 1 h purohit2017b P16, P17, P12; indulkar2019a R1, P6; saboo2019 P12, C9.

What the data show

In ritonavir films the free drug after 4 h was 27–30 µg/mL for every HPMCAS film and 28 µg/mL for 10:90 and 20:80 PVP and 10:90 PVPVA, all at the amorphous solubility, against 10–25 µg/mL for the other films purohit2017b R10, R1, R11.

systemread-outresultids
ritonavir films, three polymersfree drug, pyrene, NTA, 25 °CLLPS only in HPMCAS (all), PVP 10–20%, PVPVA 10%; 200–315 nmpurohit2017b R7, R8, R10, R11
ritonavir–PVPVA tabletsamount against 3.3 mg line; DLScrossed at 10–30%; 218 ± 15 nm at 10%indulkar2019a R9, R20
nilvadipine, cilnidipine in PVPVA4-Di-2-Asp, DLS, NTA at 1 hdroplets only ≤10% Nil, ≤15% Cil; 237–366 nmsaboo2019 R10, R11, R12
indomethacin–PVPVA 5–25%NTA at 30 min250–350 nm particles at 5 and 10% onlysaboo2020 R6, R7
loratadine–PVPVA 35, 40%compactsabout 23% released at 35% (line about 3.2%) with droplets; about 0.2% at 40% withoutyang2021 R19, R16
Fig. 4 of saboo2019: normalized 4-Di-2-Asp emission spectra of the media after compact dissolution
Fig. 4 · saboo2019normalized 4-Di-2-Asp emission spectra of the media after compact dissolution

Spectra of the congruent loadings peak near 560–565 nm, blue-shifted from the buffer curve near 595 nm; the incongruent loadings lie on the buffer curve saboo2019 R10.

Why

The authors' reading is that a polymer-driven release continues past the amorphous solubility because the polymer sets the rate, after which the excess drug separates as drug-rich droplets, while a drug-controlled release slows toward zero there and "never" produces LLPS indulkar2019a C49, C48; purohit2017b C50. Alternatively, the droplets were absent above the switch because the concentration at 1 h was far below the amorphous solubility saboo2019 X14.

Limits and transfer

Loratadine–PVPVA at 35% formed droplets with incongruent release, and clopidogrel at 50% passed its LLPS concentration with PVPVA running ahead; both are low-Tg drugs yang2021 R21, C15; correasoto2022a R18, R16. Measure the free drug and a colloid signal in the same release run, compare the released amount with the amorphous solubility measured in that medium, and expect droplets only once the released amount passes it purohit2017b P16, P17, P12; saboo2019 P12.

How it was shown

Purohit and Taylor (2017) took the solutions of fresh films after 4 h of dissolution and measured free ritonavir in the supernatant after ultracentrifugation (35000 rpm, 30 min), added pyrene (0.4 ppm) to 1 µm-filtered solutions, imaged and sized particles by NTA and checked for crystals by polarized light purohit2017b P16, P17, P12, P18. Indulkar and co-workers (2019) compared the released amount with the amorphous solubility line (≈3.3 mg in 100 mL), noted turbidity and sized the 10% medium at 30 min by DLS indulkar2019a R1, R9, P6. Saboo and co-workers (2019) sampled the medium of each compact at about 1 h for 4-Di-2-Asp fluorescence (a blue shift marks a drug-rich environment), DLS and NTA saboo2019 P12, C9. Que and co-workers (2019) recorded cloudiness and sized 3 mL aliquots by DLS from 10 to 60 min (PDI below 0.3) que2019 R5, P9. Indulkar and co-workers (2017) sized the nanodroplets of four nifedipine dispersions by NTA at 5 °C and followed extinction at a non-absorbing wavelength indulkar2017b P6, R10. Saboo and co-workers (2020) compared felodipine concentrations with its amorphous solubility of 8 µg/mL, on unfiltered samples saboo2020a R6, R8, X12.

What the data show

Ritonavir films: free drug after 4 h was 27–30 µg/mL for every HPMCAS film and 28 µg/mL for 10:90 and 20:80 PVP and 10:90 PVPVA, all at the amorphous solubility of 26.8–28.5 µg/mL, against 10–25 µg/mL for the other PVP and PVPVA films; pyrene gave 1.50–1.61 (HPMCAS), 1.63 and 1.66 (PVP 10:90, 20:80) and 1.53 (PVPVA 10:90) against 1.88–1.90 for the rest purohit2017b R10, R1, R11. The LLPS films spiked to apparent concentrations of ≈130 (10:90 PVP), ≈116 (10:90 PVPVA) and ≈119 µg/mL (10:90 HPMCAS); the spikes decayed (for example to ≈17 and ≈21 µg/mL at 240 min) while the free drug stayed near 28 µg/mL and no crystals formed purohit2017b R12, R13, R14, R10, R18. Fresh 10:90 films gave mean droplet sizes of 200 (PVPVA), 250 (HPMCAS) and 315 nm (PVP) purohit2017b R8. Ritonavir tablets: 10% reached ≈3.5 mg in 100 mL by 10 min against the ≈3.3 mg line, the 30% tablet crossed between 30 and 40 min, the 35% tablet reached only ≈1.5 mg by 120 min, and the 10–25% media were visibly turbid indulkar2019a R1, R20, R9. Nilvadipine and cilnidipine: emission maxima of about 560–565 nm for 5 and 10% of both drugs and ≈570 nm for 15% cilnidipine against ≈593–595 nm in buffer and at higher loadings; DLS 237 ± 8 and 246 ± 3 nm (nilvadipine 5, 10%) and 255 ± 1, 300 ± 2 and 366 ± 7 nm (cilnidipine 5, 10, 15%); NTA scattering at these loadings and none above saboo2019 R10, R11, R12. Powders gave turbid media at 5–10% nilvadipine and clear ones at 15–20% saboo2019 R20. Ledipasvir at 2 and 5% turned the medium cloudy above an amorphous solubility below 1 µg/mL, with droplets of ≈225–257 nm over 10–60 min que2019 R5, R12. Nifedipine dispersions at 5 °C gave ≈190–222 nm droplets and extinction that rose once the amorphous solubility was passed indulkar2017b R7, R10. Felodipine from PVP at 5 and 10% reached ≈35 and ≈67 µg/mL at 60 min against 8 µg/mL, and every HPMCAS loading exceeded 8 µg/mL saboo2020a R6, R8. IND at 5 and 10% passed its amorphous solubility of 22.1 µg/mL between 25 and 30 and between 15 and 20 min, the media held 250–350 nm particles and were turbid without birefringence, while 15–25% stayed at 0.1–0.6% release without particles; every INDester medium exceeded 3.9 µg/mL, also after crystallization saboo2020 R6, R7, R12, R8. Felodipine with 5% TPGS reached about 68–165 µg/mL at 10–35% against 9.5 µg/mL, with particles to the limit and none at 40% saboo2021 R11, R16. The analogue media were turbid at or below the limits que2021 R18. Loratadine–PVPVA compacts released about 23% at 35% (line about 3.2%) with droplets and about 0.2% at 40% without, and loratadine–HPMCAS compacts at 30–40% stayed above the line while the polymer ran ahead yang2021 R19, R16, C14, C15. Clopidogrel dispersions at 40 and 50% passed the LLPS concentration within 10 min, the 50% binary although PVPVA ran ahead correasoto2022a R16, R18. With ATZ only the SDS and CTAB dispersions released enough to form colloids correasoto2022b R8, C8. Clotrimazole–PVP dispersions passed the amorphous solubility of 10.3 µg/mL in every release, with a turbid medium, and loratadine from HPMCAS LF reached 17.6 µg/mL at pH 6.8 and 59.1 µg/mL at pH 7.5 after 1 h against amorphous solubilities of 9.0 and 7.6 µg/mL, which the authors did not discuss deac2024a R4, M1; bapat2025a R5, X9.

papersystemmethod and conditionsresultids
indulkar2017bnifedipine 10, 20%, HPMC-E5 and PVPVANTA, 5 °C≈190–222 nm in all fourindulkar2017b R7
purohit2017britonavir films, freshfree drug, pyrene, NTA, 25 °CLLPS only in HPMCAS (all), PVP 10–20%, PVPVA 10%; 200–315 nmpurohit2017b R7, R8, R10, R11
indulkar2019aritonavir–PVPVA tabletsamount against 3.3 mg line; DLScrossed at 10–30%; 218 ± 15 nm at 10%indulkar2019a R9, R20
que2019ledipasvir–PVPVA 2, 5%cloudiness; DLSdroplets ≈225–257 nm at 5%que2019 R5, R12
saboo2019Nil, Cil in PVPVA4-Di-2-Asp, DLS, NTA at 1 hdroplets only ≤10% Nil, ≤15% Cil; 237–366 nmsaboo2019 R10, R11, R12
saboo2020afelodipine in PVP; HPMCASconcentration against 8 µg/mLabove at 5–10% PVP and at all HPMCAS loadings; colloid not measuredsaboo2020a R6, R8, X12
saboo2020IND 5–25%; INDester 5–25%NTA at 30 minparticles at 5, 10% IND only; all INDestersaboo2020 R7
saboo2021felodipine with 5% TPGSNTA, DLS at 60 minparticles to 35%, none at 40%; 237–280 nmsaboo2021 R16, R17
que2021four analogues at their limitsDLS, NTA at 30 min179–364 nmque2021 R22, R23
yang2021loratadine–PVPVA 35, 40%; –HPMCAS 30–40%compactsdroplets at 35% (incongruent), none at 40%; HPMCAS above the lineyang2021 R19, R16, C15
correasoto2022aCPD 40, 50%compactsabove the LLPS concentration within 10 min, also at 50% (incongruent)correasoto2022a R16
alonzo2011 (ASD dissolution)felodipine–HPMC 90:10particle sizing, birefringence≈185–300 nm particles read as crystallinealonzo2011 R8, C33
deac2024aclotrimazole–PVP, all grades and loadingscompacts, pH 8.0apparent concentration above 10.3 µg/mL, turbid mediumdeac2024a R4, M1
bapat2025aloratadine 25% in HPMCAS LFcompacts, 1 h17.6 (pH 6.8) and 59.1 µg/mL (pH 7.5) against 9.0 and 7.6bapat2025a R5, X9

Figure

Fig. 4 of saboo2019: normalized 4-Di-2-Asp emission spectra of the media after compact dissolution
Fig. 4 · saboo2019normalized 4-Di-2-Asp emission spectra of the media after compact dissolution

Spectra of the congruent loadings peak near 560–565 nm, blue-shifted from the buffer curve near 595 nm; the incongruent loadings lie on the buffer curve saboo2019 R10.

Fig. 2A of indulkar2019a: ritonavir released in mg against time with the amorphous solubility line
Fig. 2A · indulkar2019aritonavir released in mg against time with the amorphous solubility line

The 10–25% curves pass the dashed line within minutes, the 30% curve after 30–40 min; 40%, 50% and neat amorphous ritonavir stay at the bottom indulkar2019a R1, R20.

Why

The authors' reading is that a polymer-driven release continues past the amorphous solubility because the polymer, not the drug, sets the rate, after which the excess drug separates as drug-rich droplets, as they had shown for nifedipine (F5) indulkar2019a C49, R24. A drug-controlled release slows toward zero as the drug approaches its amorphous solubility and "never" produces LLPS indulkar2019a C48; purohit2017b C50. Purohit and Taylor generalize that colloids form where release is "congruent or close to congruent" purohit2017b C52. The decay of the apparent concentration after the spike is put down to nanodroplets that absorb and scatter UV light and coalesce, since no crystals were seen and the free drug stayed at the amorphous solubility purohit2017b C39. The larger droplets at higher cilnidipine loading "could indicate" lower stability against agglomeration or an effect of loading on the formation route saboo2019 C19. An alternative reading of the dihydropyridine result is that the droplets were absent above the switch simply because the concentration at 1 h was far below the amorphous solubility saboo2019 X14; the two readings agree on the outcome and differ only on whether congruency carries information beyond the release extent. (synthesis: in every system of these papers the colloid appeared when, and only when, the released drug passed the amorphous solubility; congruent release is the way a dispersion of a slowly dissolving amorphous drug gets there within the test time.)

Conditions and limits

Ritonavir films at 25 °C and compacts at 37 °C in pH 6.8 phosphate; nifedipine at 5 °C; DLS at one loading for ritonavir tablets; colloid not measured for felodipine purohit2017b X18; indulkar2019a X5; saboo2020a X12. The NTA images of the ritonavir films do not state the loading, and the pyrene table does not state whether the films were fresh or humidity-exposed purohit2017b X8, X6.

Counterexamples and conflicts

The 20:80 cilnidipine powder rose to ≈0.70–1.33 µg/mL, above its amorphous solubility of 0.6 µg/mL, for most of 4 h without reported LLPS saboo2019 X4, R21. In the ASD dissolution chapter the colloid shed by 90:10 felodipine–HPMC dispersions was read as crystalline, not as drug-rich droplets (Supersaturation from ASD dissolution F9) alonzo2011 R8, C33. Loratadine–PVPVA at 35% formed droplets with incongruent release (rates about 0.36 against 0.12 mg/min/cm²) yang2021 R21, C15, and clopidogrel at 50% passed its LLPS concentration with PVPVA running ahead correasoto2022a R18, R16; both are low-Tg drugs (F18) (synthesis: in both the drug still left at a substantial fraction of the polymer rate, 0.12/0.36 = 0.33 and 3.6/6.7 = 0.54).

Transfer check

Measure the free drug (ultracentrifugation or flux) and a colloid signal (DLS, NTA or an environment-sensitive probe) in the same release run, and compare the released amount with the amorphous solubility measured in that medium purohit2017b P16, P17, P12; saboo2019 P12. Expect droplets only at loadings that release congruently and only once the released amount passes the amorphous solubility; a polymer- or a surfactant-specific size (about 200–370 nm here, about 60–130 nm with surfactant, F13) should be checked by sizing at more than one loading que2019 R12.

History

Nanodroplets from dissolving dispersions at low loading were known from the ASD dissolution chapter (Alonzo 2011, Jackson 2015) indulkar2017b C6. Purohit and Taylor (2017) first tied their formation to congruent or near-congruent release and to a matrix that stays mixed, and Indulkar and co-workers (2019) to at least partly polymer-controlled release purohit2017b C52, C6; indulkar2019a C49. Saboo and co-workers (2019) confirmed the cut-off with three read-outs for two drugs saboo2019 C30, and Que and co-workers (2019) stated that colloids form only below the limit of congruency que2019 C10, C55. Saboo and co-workers (2020, 2021) and Que and co-workers (2021) confirmed the link for further drugs saboo2020 C16; saboo2021 C19; que2021 C21; Yang and co-workers (2021) found droplets from incongruent release of loratadine, which revises the "only" of the title for low-Tg drugs yang2021 C15, C2. In 2024–2025 clotrimazole–PVP and loratadine–HPMCAS dispersions passed the amorphous solubility as well, the latter without comment by the authors deac2024a R4, C18; bapat2025a X9.

F5

Topic 2Nanodroplets from dissolving dispersions2 of 3

The nanodroplets formed from drug that had first dissolved, not from drug-rich domains released intact from the solid.

Nifedipine dispersions were dissolved at 5 °C into water already saturated with deuterated nifedipine. The deuterated share of the dissolved drug fell to about the values that full mixing predicts, far below the 100% expected if droplets had left the solid intact indulkar2017b R11, P8, X2. Ritonavir films at 10% drug looked uniform after 10 s in buffer, and imaging of dissolving ritonavir–PVPVA compacts in 2022 placed droplet formation at the gel–solution interface purohit2017b R4; yang2022a R6, R10, C50.

moderateModerate: the isotope design makes the two routes predict very different results, but the key values are single bars without error bars and the slow-exchange control used different droplets; the ritonavir argument rests on imaging at about the droplet size indulkar2017b K1, X2, X5; purohit2017b K5, X11.

measured, four dispersions36 µg/mL added75intact droplets 100≈69–79110 µg/mL added50100≈45–56330 µg/mL added25100≈24–30770 µg/mL added12.5100≈11–180102030405060708090100deuterated share of the dissolved nifedipine, %

Ticks: expected share for full mixing, and 100% for droplets released intact; measured shares lie near full mixing. indulkar2017b R11, P8, X2

For your drug

  1. The isotope test needs droplets that exchange slowly with the solution: check first, with droplets made from the dispersion itself, that the water-saturated drug-rich phase is glassy at the test temperature.
  2. To exclude droplets born in the matrix, image the wetted surface at better than 200 nm resolution.

indulkar2017b C13, X5; purohit2017b X11

How it works and key numbers
  1. Two routes were compared: dissolution of the drug followed by LLPS in solution (mechanism I), or water-induced amorphous–amorphous phase separation in the wet solid with the drug-rich domains released intact (mechanism II) indulkar2017b C7, C8.
  2. If the drug dissolves first, it mixes with the deuterated drug and lowers the deuterated share to a dose-dependent value; intact droplets have no reason to dissolve in a saturated medium, so the solution stays all deuterated indulkar2017b C11.
  3. Exchange between glassy droplets and solution was slow at 5 °C (≈39.5–47% for about an hour, against ≈26.7% at 25 °C), so the ordinary drug in solution is read as dissolved dispersion drug indulkar2017b R3, R4, C27.
  4. The authors attribute the slow exchange to droplets below their wet Tg, estimated by T_{g,wet} \approx T_{g,dry} - 10\ ^{\circ}\mathrm{C} \times w, that is 42 - 10 \times 2.5 = 17 °C indulkar2017b C18, E6.
  5. In 2022 droplets of 0.5–2 µm appeared only at the gel surface of 10% ritonavir compacts and passed into the solution with the dissolving polymer, read as water-induced separation where the water content is highest yang2022a R6, R10, C50.
  6. In 2023 droplets of the methyl ether of phenolphthalein began 45–155 µm from the glass–gel boundary, inside the gel, while at 5% phenolphthalein they began about 601 µm away, beyond the 356 µm gel deac2023a R8, R4, C31, C47.
≈11–18% against 100%deuterated share at the highest dose, against intact dropletsindulkar2017b R11, P8
1–10 µm against 200–315 nmdomains of phase-separated films against droplets in solutionpurohit2017b R3, R5, R8
601 against 356 µmonset distance of phenolphthalein droplets against the gel thicknessdeac2023a R8, R4
Evidence: data, conditions and papers

Finding F5. The nanodroplets of congruently releasing dispersions formed from drug that had first dissolved: a deuterium label in the medium was diluted as full mixing predicts, and low-loading ritonavir films showed no drug-rich domains after 10 s in buffer; imaging of dissolving compacts in 2022–2023 placed their formation at or beyond the surface of the gel layer

In short. Nifedipine dispersions with HPMC-E5 or PVPVA (10 and 20%) dissolved at 5 °C into water already saturated with deuterated nifedipine lowered the deuterated share of the dissolved drug to ≈69–79, ≈45–56, ≈24–30 and ≈11–18% at 36, 110, 330 and 770 µg/mL added drug, close to the 75, 50, 25 and 12.5% of full mixing and 20 points or more below the 100% expected if droplets had left the solid intact indulkar2017b R11, P8, X2. The test relied on slow exchange of drug between glassy droplets and solution at 5 °C (≈39.5–47% for about an hour against ≈26.7% at 25 °C), shown with solvent-made droplets in an HPMC-E5 medium only indulkar2017b R3, R4, X5. Ritonavir films at 10% drug looked uniform after 10 s in buffer, and the domains of phase-separated films measured 1–10 µm against droplets of 200–315 nm, which the authors read the same way ("likely") purohit2017b R4, R9, R3, R5, R8, C57. Real-time and cross-section imaging of ritonavir–PVPVA compacts in 2022 placed the formation of the droplets at the gel–solution interface: at 10% drug-rich droplets of 0.5–2 µm appeared only at the surface of the gel and passed into the solution with the dissolving polymer, which the authors read as water-induced separation where the water content is highest, compatible with the isotope result ("would presumably") yang2022a R6, R10, C50. In 2023 droplets of the methyl ether of phenolphthalein began 45–155 µm from the glass–gel boundary, inside the gel, while at 5% phenolphthalein they began about 601 µm away, beyond the 356 µm gel, which the authors read as droplets forming in solution or the diffusion layer ("appear to originate outside the gel layer") deac2023a R8, R4, C31, C47.

Type. observation in 2 drugs (nifedipine, ritonavir), with imaging of ritonavir and two phenolphthalein analogues in 2022–2023 Strength. : the isotope design makes the two routes predict very different results, but the key values are single bars without error bars and the slow-exchange control used different droplets indulkar2017b K1: moderate to strong, X2, X5; the ritonavir argument rests on imaging at about the droplet size purohit2017b K5: weak to moderate, X11.

How it was shown

Indulkar and co-workers (2017) added ordinary (proteated) nifedipine dispersions in four amounts to D2O saturated at 110 µg/mL with deuterated nifedipine and measured the dissolved H- and D-forms by ¹H NMR, after checking with solvent-made droplets how fast the label exchanges indulkar2017b P8, P9, P5, C13. Purohit and Taylor (2017) imaged ritonavir films after 10 s in buffer, and Yang and co-workers (2022) imaged dissolving compacts in real time purohit2017b P9, P13; yang2022a P7.

What the data show

The D-share fell with the dose close to the values of full mixing (75.3, 50.0, 25.0 and 12.5%) indulkar2017b R11, R12, X1.

systemmethodresultids
nifedipine dispersions, four doses¹H NMR of D-share in D-saturated D2O, 5 °C≈69–79 / ≈45–56 / ≈24–30 / ≈11–18% against 75 / 50 / 25 / 12.5% (100% for mechanism II)indulkar2017b R11, P8
solvent-made droplets with D-solutionsame, 5–25 °C≈39.5–47% for an hour at 5 °C, ≈26.7% at 25 °Cindulkar2017b R3, R4
ritonavir 10:90 and 50:50 films10 s in buffer, confocal, SEM10:90 uniform; 50:50 PVP and PVPVA separatedpurohit2017b R4, R9
ritonavir–PVPVA 10, 20% compactsreal-time confocal; cross-sectionsdroplets of 0.5–2 µm form at the gel–solution interface and leave with the polymeryang2022a R10, R11, R6
MePHPH 5–30%, PHPH 5% compactsin situ confocal, onset from the glass–gel boundaryMePHPH 155 / 57 / 45 µm (inside the gel); PHPH 601 µm (beyond a 356 µm gel)deac2023a R8, R4
Fig. 9 of indulkar2017b: deuterated share of the dissolved drug after dissolution of four dispersions at four doses
Fig. 9 · indulkar2017bdeuterated share of the dissolved drug after dissolution of four dispersions at four doses

Bars near the solid red lines and far below the dashed line at 100% support mechanism I; compare the bars with the Table 1 values (75, 50, 25, 12.5%), since the drawn lines differ from them at three doses indulkar2017b R11, X1.

Why

If the drug dissolved first it mixes with the deuterated drug and lowers the D-share; if droplets left the solid intact, a saturated medium gives them no reason to dissolve and the solution stays all deuterated, so the authors conclude that the droplets form by dissolution followed by LLPS ("strongly suggest") indulkar2017b C11, C26. Purohit and Taylor "find no evidence" of a matrix origin, since matrix domains are an order of magnitude larger than the droplets purohit2017b C56, C57. Yang and co-workers place the separation at the gel–solution interface, which "would presumably" meet the conditions of the isotope test yang2022a C35, C50.

Limits and transfer

The isotope test covers nifedipine at 5 °C only, and the ritonavir images resolve about 300 nm, comparable with the droplets indulkar2017b A2, A4; purohit2017b X11, C25. The test suits a drug whose drug-rich phase is glassy at the test temperature; for a low wet Tg such as ritonavir (about 0 °C) the slow exchange must first be checked indulkar2017b C13, X5; indulkar2019a M1.

How it was shown

Indulkar and co-workers (2017) asked whether the droplets form by dissolution of the drug followed by LLPS in solution (mechanism I) or by water-induced AAPS in the wet solid, whose drug-rich domains are released intact (mechanism II, proposed for anacetrapib–PVPVA by Harmon and co-workers, cited) indulkar2017b C7, C8. They added dispersions of ordinary (proteated) nifedipine to D2O saturated at 110 µg/mL with nifedipine deuterated at its four aromatic positions, in four amounts (0.36–7.70 mg/mL of 10% dispersion), and measured the dissolved H- and D-forms by ¹H NMR right after complete dissolution: the methyl peak (2.29 ppm, 6 H) is common to both, the aromatic peaks (7–8 ppm, 4 H) belong to the H-form only, and the droplets give no NMR signal indulkar2017b P8, P9, E1, C11. For PVPVA a maleic acid external standard replaced the methyl reference indulkar2017b E2. Because exchange between droplets and solution would scramble the label under either mechanism, they first mixed a D-form solution (1× amorphous solubility) with H-form droplets (3×) made by solvent shift in D2O with 1 mg/mL HPMC-E5 and followed the D-share at 5–25 °C indulkar2017b P5, C13. The amorphous solubility was measured by UV extinction at 450 nm with 1 mg/mL HPMC-E5 in D2O, and the wet Tg of amorphous nifedipine was estimated from its dry Tg and an extrapolated water uptake indulkar2017b P2, P3, P4. Purohit and Taylor (2017) dipped ritonavir films (10:90 and 50:50) in buffer for 10 s, dried them and imaged them by confocal microscopy (nile red, brighter in drug-rich regions) and SEM, and sized the droplets of dissolving films by NTA purohit2017b P9, P13, P12. Yang and co-workers (2022) fused 100 mg ritonavir–PVPVA compacts with Nile red and Alexa Fluor 488 to a glass dish, sealed the top so that buffer entered from the edge only, and took confocal images every 30 s at 37 °C for 15–30 min, with manual agitation that the authors state makes rates incomparable between samples yang2022a P7, C31.

What the data show

At 36 µg/mL the four dispersions gave ≈78.1, ≈69.4, ≈77.8 and ≈78.6% D (10% HPMC-E5, 20% HPMC-E5, 10% PVPVA, 20% PVPVA), at 110 µg/mL ≈48.1, ≈44.5, ≈49.4 and ≈55.8%, at 330 µg/mL ≈30.4, ≈25.6, ≈24.2 and ≈27.3%, and at 770 µg/mL ≈11.4 and ≈17.6% for the HPMC-E5 dispersions, the PVPVA signal overlapping the aromatic peaks at that dose indulkar2017b R11, R12. The expected values of Table 1 equal 100 \times 110/(110 + c_H) with c_H the H-form added (extractor arithmetic: 75.3, 50.0, 25.0, 12.5), while the red lines of the figure sit at ≈57.9, ≈29.1 and ≈14.4% for the three higher doses without explanation indulkar2017b X1. In the exchange control the D-share fell from the starting 50% to ≈41.1, ≈39.9, ≈39.3, ≈30.2 and ≈26.7% at 5, 10, 15, 20 and 25 °C, full exchange giving 25%, and at 5 °C 29 points from ≈5 to ≈61 min stayed between ≈39.5 and ≈47% indulkar2017b R3, R4. About 2.5% of the H-form was estimated to sit on droplet surfaces, which explains only a small part of the early ≈9-point drop indulkar2017b R5, X3. The amorphous solubility rose from 110 µg/mL at 5 °C to 156 µg/mL at 25 °C, and the estimated wet Tg was about 17 °C (dry 42 °C, 2.5% water) indulkar2017b R1, M1, E6. Ritonavir: after 10 s in buffer the 10:90 PVP film was uniform while the 50:50 PVP film showed dark domains of about 1–3 µm in a bright drug-rich phase; SEM showed smooth 10:90 surfaces purohit2017b R4, R9. After humidity the domains were about 1–3 µm by confocal microscopy and 5–10 µm by AFM, against droplets of 200–315 nm purohit2017b R3, R5, R8. Ritonavir–PVPVA, real time: at 10% small red droplets formed near the gel–solution interface from the first minute and entered the solution, not throughout the gel; at 20% the same, with droplets starting closer to the water front; cross-sections at 10% showed droplets of 500 nm to 2 µm only at the compact surface yang2022a R10, R11, R6. Dissolving MePHPH–PVPVA compacts formed droplets below 1 µm starting 155 ± 43, 57 ± 14 and 45 ± 20 µm from the glass–gel boundary at 5, 20 and 30%, nearer the core as loading rose and less than the gel thickness of the release set-up, and some were seen leaving into the solution; at 5% PHPH the onset lay at 601 ± 68 µm against a 356 ± 18 µm gel deac2023a R6, R8, R4, C27.

papersystemmethod and conditionsresultids
indulkar2017bnifedipine dispersions, four doses¹H NMR of D-share in D-saturated D2O, 5 °C≈69–79 / ≈45–56 / ≈24–30 / ≈11–18% against 75 / 50 / 25 / 12.5% (100% for mechanism II)indulkar2017b R11, P8
indulkar2017bsolvent-made droplets with D-solutionsame, 5–25 °C≈39–41% at 5–15 °C, ≈26.7% at 25 °C; ≈39.5–47% for an hour at 5 °Cindulkar2017b R3, R4
indulkar2017bnifedipine amorphous solubilityUV extinction, 1 mg/mL HPMC-E5, D2O110 (5 °C) to 156 µg/mL (25 °C)indulkar2017b R1
purohit2017britonavir 10:90 and 50:50 films10 s in buffer, confocal, SEM10:90 uniform; 50:50 PVP and PVPVA separatedpurohit2017b R4, R9
purohit2017bdomains against dropletsconfocal, AFM, NTAdomains 1–10 µm; droplets 200–315 nmpurohit2017b R3, R5, R8
yang2022aritonavir–PVPVA 10, 20% compactsreal-time confocal, edge wetting, 37 °C; cross-sectionsdroplets of 0.5–2 µm form at the gel–solution interface and leave with the polymeryang2022a R10, R11, R6
deac2023aMePHPH 5–30%, PHPH 5% compactsin situ confocal, onset from the glass–gel boundaryMePHPH 155 / 57 / 45 µm (inside the gel); PHPH 601 µm (beyond a 356 µm gel)deac2023a R8, R4

Figure

Fig. 3 of indulkar2017b: the logic of the isotope test
Fig. 3 · indulkar2017bthe logic of the isotope test

In a medium saturated with the deuterated drug, mechanism I gives mixed droplets and the ordinary drug in solution; mechanism II gives droplets of the ordinary drug and a solution that stays all deuterated indulkar2017b C11.

Fig. 9 of indulkar2017b: deuterated share of the dissolved drug after dissolution of four dispersions at four doses
Fig. 9 · indulkar2017bdeuterated share of the dissolved drug after dissolution of four dispersions at four doses

Bars near the solid red lines and far below the dashed line at 100% support mechanism I; compare the bars with the Table 1 values (75, 50, 25, 12.5%), since the drawn lines differ from them at three doses indulkar2017b R11, X1.

Why

The authors' reasoning: if the drug dissolved first it mixes with the deuterated drug and lowers the D-share to a dose-dependent value; if droplets left the solid intact, a saturated medium gives them no reason to dissolve and the solution stays all deuterated indulkar2017b C11. Because exchange is slow at 5 °C, they read the ordinary drug in solution as dissolved dispersion drug that replaced the deuterated drug, not as drug released from droplets indulkar2017b C27. They attribute the slow exchange to droplets below their wet Tg ("presumably" faster exchange above it; glassy droplets "appear" to slow it), with the wet Tg taken from the rule

T_{g,wet} \approx T_{g,dry} - 10\ ^{\circ}\mathrm{C} \times w

(w in % water), 42 - 10 \times 2.5 = 17 °C indulkar2017b C18, E6. Their conclusion is that the droplets form by dissolution followed by LLPS ("strongly suggest"), that mechanism II cannot be taken as general for PVPVA dispersions ("we cannot concur"), and that drug–PVPVA dispersions that stay miscible in water "are expected" to follow mechanism I indulkar2017b C26, C37, C38. Purohit and Taylor "find no evidence" of a matrix origin: low-loading films stay uniform after 10 s, and matrix domains are an order of magnitude larger than the droplets, so their release "cannot account for" the nanosized species purohit2017b C56, C57. (synthesis: both tests concern dispersions that release congruently; the regime in which mechanism II was proposed, a matrix that separates on wetting, is the incongruent regime of F3 and F8, where no droplets formed at all in these papers.) Yang and co-workers (2022) propose that drug-rich and polymer-rich domains form together by water-induced separation where the gel's water content brings the drug–polymer–water mixture past the binodal, which is at the gel–solution interface, and that this separation, at the surface in contact with the bulk solution, "would presumably" meet the conditions of the isotope test; for them separation in the gel and LLPS in the solution are parts of one process on one three-component phase diagram ("In reality") yang2022a C34, C35, C48, C50, C51. They set this against drug-rich domains formed throughout the matrix and stabilized by surfactant (Harmon and co-workers, cited) and against the "particle and glue" picture of phase-separated lopinavir films (Li and Taylor 2019, ASD process), since their droplets formed only at the surface yang2022a C48, C49. (synthesis: the 2017 test showed that the droplet drug had mixed with the solution, the 2022 images that droplets form within the outermost wet gel; both concern low loadings where release is congruent, and neither measured the composition of the forming droplets.) Deac and co-workers (2023) infer that during congruent release the drug is "carried" into the diffusion layer by the swelling and dissolving polymer, separating either inside the gel (MePHPH) or after leaving it (PHPH at 5%), and they cite the isotope result as placing droplet formation in a high-mobility environment, in solution or in a low-viscosity region near the interface deac2023a C47, C3.

Conditions and limits

Nifedipine at 10 and 20% with HPMC-E5 or PVPVA at 5 °C only; ritonavir films at 25 °C indulkar2017b A2, A4; purohit2017b P14. The amorphous solubility was measured only for the H-form with 1 mg/mL HPMC-E5, while the NMR samples held up to about 7 mg/mL polymer and the D-form indulkar2017b X6, X7. The 17 °C wet Tg is an estimate from a rule taken from indomethacin indulkar2017b X8. Diffusion of the D-form into the solid dispersion is excluded by inference indulkar2017b X9. The real-time ritonavir set-up wetted the compact from its edge under manual agitation, and the binodal composition and water profile of the gel were not measured yang2022a C31, X10. The onset distances of 2023 come from gently mixed in situ imaging and are compared with gel thicknesses measured at 100 rpm deac2023a X4.

Counterexamples and conflicts

Harmon and co-workers (2016, cited, not a card of the library) found mechanism II for anacetrapib–PVPVA and suggested it may be general for PVPVA indulkar2017b C8; purohit2017b C51. The ritonavir images resolve about 300 nm, comparable with the droplets, so nanoscale domains in low-loading films are not excluded purohit2017b X11, C25. Saboo and co-workers (2021) still describe the origin as unresolved, matrix domains released intact (cited) against phase separation of dissolved drug, "not necessarily" exclusive, and their humid-film domains were larger than the 200–300 nm particles in solution saboo2021 C46, C47.

Transfer check

The isotope test needs droplets that exchange slowly with the solution, so it suits a drug whose water-saturated drug-rich phase is glassy at the test temperature (nifedipine about 17 °C at 5 °C); for a drug with a low wet Tg such as ritonavir (about 0 °C) the premise would have to be checked first with droplets made from the dispersion itself indulkar2017b C13, X5; indulkar2019a M1. For any drug, imaging of the wetted surface at better than 200 nm resolution would be needed to exclude matrix-born droplets purohit2017b X11.

History

Mechanism II was proposed by Harmon and co-workers (2016, cited) indulkar2017b C7, C8. Indulkar and co-workers (2017) and Purohit and Taylor (2017) answered it in the same year for nifedipine and ritonavir indulkar2017b C26; purohit2017b C57, and the 2019 copovidone study builds on the nifedipine result for polymer-assisted dissolution followed by LLPS indulkar2019a R24. Saboo and co-workers (2019) note that the effect of loading on the formation route "has not been widely explored and is under debate" saboo2019 C19. Saboo and co-workers (2021) left open whether TPGS lets molecular drug release first or keeps matrix-born droplets from ripening saboo2021 C52. The temperature dependence of the nifedipine amorphous solubility adds a steady rise from 5 to 25 °C to the ritonavir and efavirenz profiles of the LLPS chapter indulkar2017b R1, C15. Yang and co-workers (2022) imaged the forming droplets in real time and placed them at the gel–solution interface, reconciling the isotope result with water-induced separation at that interface yang2022a C50, C51; this adds the last clause to the title. Deac and co-workers (2023) found both places of formation in two analogues: inside the gel for the methyl ether, beyond it for phenolphthalein deac2023a C27, C31.

F16

Topic 2Nanodroplets from dissolving dispersions3 of 3

The size and stability of the released nanodroplets depended on drug, polymer and surfactant.

Elbasvir droplets from a PVPVA dispersion grew from about 670 to 1190 nm in 60 min and crystallized, while droplets from the HPMCAS dispersion stayed at about 280–390 nm yang2021 R3. Clopidogrel droplets in buffer grew about 12-fold by 2 h, while 50 µg/mL SDS, 4 µg/mL TPGS or 5 µg/mL Tween 80 kept them at about 0.8–1.0 times their starting size for 4 h, and 50 µg/mL CTAB gave about 12-fold growth within 1 h correasoto2022a R6. Built into 30% ritonavir–PVPVA, the Spans kept the droplets at about 330–1410 nm while TPGS and Tween 80 let them grow to about 4–10 µm indulkar2022 R11, R13.

moderateModerate: DLS in triplicate over 1–4 h with NTA and zeta potential, but the polymer advantage holds for two of four drugs and the adsorption mechanism was inferred correasoto2022a K5, K6; yang2021 K6, X9, C39.

droplets grewdroplets stayed smallelbasvir · PVPVA5–60 min; crystals after 30 min670 → 1190elbasvir · HPMCAS280 → 390loratadine · PVPVA820 → 2120loratadine · HPMCAS420 → 570ritonavir 30% · Span 85to 90 min330 → 960ritonavir 30% · TPGS10 → 90 min1320 → 384005001000150020002500300035004000droplet size by DLS, start → end of the test, nm

Sizes in the release medium of dissolving dispersions. yang2021 R3, R6; indulkar2022 R11, R13

Clopidogrel droplets: size relative to time zerobufferafter 2 h≈12×CTAB 50 µg/mLafter 1 h≈12×SDS 50 µg/mLafter 4 h≈0.92TPGS 4 µg/mLafter 4 h≈0.96Tween 80 5 µg/mLafter 4 h≈0.81

Droplets made by solvent shift and held at 37 °C. correasoto2022a R6

For your drug

  1. Size the droplets of the target dispersion by DLS every 15–60 min for 1–4 h in the release medium, with the dissolved polymer at the concentration release produces, and check for crystals by polarized light.
  2. If the droplets grow, test HPMCAS in the medium or in the dispersion, or 5–50 µg/mL of a non-ionic or anionic surfactant, and avoid a cationic surfactant until it has been tested.
  3. For a surfactant built into the dispersion, size the droplets in the release medium over the whole test, since the ranking with preformed droplets differed.

yang2021 P16, R3; correasoto2022a P6, R6, C43; indulkar2022 R11

How it works and key numbers
  1. The droplets are metastable and coarsen by ripening, flocculation and coalescence; the fast coarsening of clopidogrel droplets is "consistent with" the high interfacial energy of a lipophilic drug-rich phase correasoto2022a C2, C37.
  2. The low effective surfactant levels are "consistent with" stabilization by surfactant adsorbed at the droplet surface, and the zeta potential changed from about −16 mV in buffer to −69 with SDS and +29 with CTAB correasoto2022a C39, C13, R7.
  3. HPMCAS, charged at the study pH, can add electrostatic to steric hindrance at the droplet surface, which neutral PVPVA cannot; its adsorption "has been hypothesized" yang2021 C39, C40.
  4. For ritonavir the poorly water-soluble Spans "probably" mix into the droplets and lower the chemical potential of ritonavir, which "may" inhibit Ostwald ripening, while Tween 80 and TPGS "could possibly" lower the droplet Tg and make them coalesce indulkar2022 C49, C48.
  5. Dissolved PVP did not slow droplet growth in dilute suspension; in the gel, short PVP chains let the droplets agglomerate (F29) deac2024a R5, C44, C45.
≈670 → 1190 nmelbasvir droplets from PVPVA in 60 min, against ≈280–390 nm from HPMCASyang2021 R3
≈12-foldgrowth of clopidogrel droplets in buffer by 2 h, and with 50 µg/mL CTAB within 1 hcorreasoto2022a R6
4–50 µg/mLSDS, TPGS or Tween 80 that held clopidogrel droplets at constant size for 4 hcorreasoto2022a R6
Evidence: data, conditions and papers

Finding F16. The size and stability of the nanodroplets that congruent release produced depended on drug, polymer and surfactant: HPMCAS kept elbasvir and loratadine droplets at about 250–570 nm where PVPVA let them grow to 1190–2120 nm, and 4–50 µg/mL SDS, TPGS or Tween 80 held clopidogrel droplets at constant size for 4 h while CTAB agglomerated them, and built into 30% ritonavir dispersions the Spans kept droplets near 1 µm while TPGS and Tween 80 let them grow to about 4–10 µm

In short. Elbasvir droplets from a 2.5% PVPVA dispersion grew from about 670 to 1190 nm in 60 min and crystallized, whereas droplets from the HPMCAS dispersion stayed at about 280–390 nm and those from the PVPVA dispersion with 400 µg/mL HPMCAS in the medium at about 250–300 nm; loratadine droplets grew from about 820 to 2120 nm with PVPVA against about 420–570 nm with HPMCAS yang2021 R3, R6. Clopidogrel droplets in buffer grew about 12-fold by 2 h, while 50 µg/mL SDS, 4 µg/mL TPGS or 5 µg/mL Tween 80 kept them at about 0.8–1.0 times their starting size for 4 h and 50 µg/mL CTAB gave about 12-fold growth within 1 h correasoto2022a R6. The size also differed with the drug: about 179–193 nm for two iodinated analogues against 348–364 nm for two others, and 237–280 nm for felodipine with or without TPGS que2021 R22; saboo2021 R17. Danazol droplets grew to about 2780 nm even with dissolved HPMCAS, and miconazole droplets grew alike in all three media yang2021 R4, R5, X9. In ritonavir–PVPVA dispersions at 30%, built-in Span 85 and Span 20 kept the released droplets at about 330–1410 nm over 90 min, while without surfactant they grew to about 2200 nm, with SDS to about 2400, with TPGS to about 3840 nm, and Tween 80 gave droplets of about 10 µm indulkar2022 R11, R13. Clotrimazole droplets grew from about 540 nm to 1 µm without PVP and from about 290–340 to 610–630 nm with 1 mg/mL PVP K12 or K29/32, at the same relative rate, whereas in the gel the short chains let droplets agglomerate (F29) deac2024a R5, R10; with built-in Tween 80 ritonavir droplets agglomerated at the gel surface and left in chunks yang2023 R10.

Type. observation in 11 drugs (elbasvir, loratadine, danazol, miconazole, clopidogrel, TIPP, Me-TIPP, PHPH, Me-PHPH, felodipine, ritonavir) Strength. : DLS in triplicate over 1–4 h with NTA and zeta potential correasoto2022a K5: moderate; yang2021 K6: moderate; the polymer advantage holds for two of four drugs and the adsorption mechanism was inferred yang2021 X9, C39; correasoto2022a K6: weak to moderate.

How it was shown

Droplets were sized by DLS for 60 min from four dissolving dispersions, for 4 h after solvent shift of clopidogrel (CPD) with or without surfactant, and for 90 min from dissolving ritonavir–PVPVA–surfactant tablets yang2021 P16, A6; correasoto2022a P6, P7; indulkar2022 P7, P8.

What the data show

The zeta potential of CPD droplets was about −16 mV in buffer, −69 with SDS, +29 with CTAB and −1 to −5 mV with the non-ionics correasoto2022a R7.

systemconditionsdroplet sizeids
elbasvir 2.5%DLS 5–60 min, bufferPVPVA ≈670 → 1190 nm, crystals; HPMCAS ≈280 → 390; PVPVA + dissolved HPMCAS ≈250 → 300yang2021 R3
loratadine 10%samePVPVA ≈820 → 2120 nm; HPMCAS ≈420 → 570yang2021 R6
danazol 2.5%; miconazole 10%samedanazol ≈2780 nm with dissolved HPMCAS; miconazole alike in all mediayang2021 R4, R5
CPD droplets ± surfactantDLS 4 h, 37 °Cbuffer ≈12× by 2 h; SDS, TPGS, Tween 80 ≈0.8–1.0×; CTAB ≈12× in 1 hcorreasoto2022a R6
ritonavir–PVPVA 30:70:5 with five surfactants; binaryDLS of the release medium, 5–90 minSpan 85 ≈330 → 960, Span 20 ≈550 → 1410; none ≈940 → 2200; SDS ≈2400; TPGS ≈3840 nm; Tween 80 ≈10 µmindulkar2022 R11, R13
clotrimazole droplets ± 1 mg/mL PVP K12 or K29/32DLS, 37 °C≈540 → 1000; ≈340 → 610; ≈290 → 630 nmdeac2024a R5
Fig. 2 of yang2021: elbasvir nanodroplet z-average and PDI over 60 min in three media
Fig. 2 · yang2021elbasvir nanodroplet z-average and PDI over 60 min in three media

Black (PVPVA dispersion in buffer) rises and broadens; red (HPMCAS dispersion) and blue (PVPVA dispersion with dissolved HPMCAS) stay small and narrow yang2021 R3.

Why

The droplets are metastable and coarsen by ripening, flocculation and coalescence, and the low effective surfactant levels are "consistent with" stabilization by surfactant adsorbed at the droplet surface, which the zeta changes "support" correasoto2022a C2, C39, C13. Adsorption of HPMCAS on droplet surfaces "has been hypothesized"; charged at the study pH, HPMCAS can add electrostatic to steric hindrance, which neutral PVPVA cannot yang2021 C39, C40. For ritonavir the Spans "probably" mix into the droplets and lower the chemical potential of ritonavir, which "may" inhibit Ostwald ripening, while Tween 80 and TPGS "could possibly" partition into the droplets, lower their Tg and make them coalesce indulkar2022 C49, C48.

Limits and transfer

Dissolved HPMCAS did not hold danazol droplets, and miconazole droplets grew alike with either polymer yang2021 X9. TPGS and Tween 80, which held clopidogrel droplets at constant size, let ritonavir droplets grow to about 4 and 10 µm when built into the dispersion correasoto2022a R6; indulkar2022 R11, R13. Size the droplets of the target dispersion by DLS for 1–4 h in the release medium and check for crystals; if they grow, test HPMCAS or 5–50 µg/mL of a non-ionic or anionic surfactant yang2021 P16, R3; correasoto2022a P6, R6, C43.

How it was shown

Yang and co-workers (2021) followed the z-average and PDI by DLS over 60 min for 2.5% elbasvir and danazol and 10% miconazole and loratadine dispersions dissolving in buffer, the PVPVA dispersions also in buffer containing 400 µg/mL HPMCAS yang2021 P16, A6. Correa Soto and co-workers (2022) made CPD droplets by solvent shift into pH 6.8 phosphate with or without surfactant, held them at 37 °C and 200 rpm and sized them hourly for 4 h by DLS and NTA in triplicate; they measured the zeta potential at 70 µg/mL CPD (about 50 µg/mL as droplets), estimated the surfactant needed for a monolayer from droplet size and literature molecular areas, and sized the media of dissolving dispersions at 90 min correasoto2022a P6, P7, E2, P16. Que and co-workers (2021) sized the 30-min media of the analogue dispersions by DLS and imaged them by NTA, and Saboo and co-workers (2021) the 60-min media of felodipine dispersions que2021 P11, P12; saboo2021 P9, P10. Indulkar and co-workers (2022) sized the droplets in the medium of dissolving 30:70:5 ritonavir–PVPVA–surfactant tablets by DLS from the time the ritonavir concentration passed its amorphous solubility to 90 min, single values without error bars, and viewed the precipitates of the Tween 80 and Span 20 tablets under crossed polarizers indulkar2022 P7, P8, X12.

What the data show

Elbasvir: z-average about 670, 900, 940, 1110 and 1190 nm at 5–60 min from the PVPVA dispersion in buffer, PDI about 0.32 → 0.57, crystals after 30 min; about 280 → 390 nm (HPMCAS dispersion) and 250 → 300 nm (PVPVA dispersion with dissolved HPMCAS), PDI below about 0.21 yang2021 R3. Loratadine: about 820 → 2120 nm (PDI 0.07 → 1.0) from PVPVA against about 420 → 570 nm from HPMCAS yang2021 R6. Danazol: the PVPVA dispersion with dissolved HPMCAS gave about 200 nm at 10 min and about 2780 nm at 60 min, the HPMCAS dispersion about 360–390 nm; miconazole: all three series about 330–370 → 520–560 nm yang2021 R4, R5. CPD in buffer: size about 1.5 times the start after 1 h and about 12 times after 2 h, PDI about 4.2–4.6 times; with SDS (50 µg/mL), TPGS (4) and Tween 80 (5) size ratios about 1.01 → 0.92, 0.99 → 0.96 and 0.89 → 0.81 over 4 h; CTAB (50) about 12 after 1 h with floating agglomerates correasoto2022a R6. More surfactant gave smaller starting droplets, about 520 nm in buffer against 280 nm with 4 µg/mL TPGS correasoto2022a R5. Zeta potential: about −16 mV in buffer, −69 with SDS, +29 with CTAB and −1 to −5 mV with the non-ionics correasoto2022a R7. The calculated monolayer coverage was 0.3–17.8 (SDS), 2.4 (CTAB), 10.4 (TPGS) and 3.1 µg/mL (Tween 80) against effective levels of 50, none, 4 and 5 µg/mL correasoto2022a R24. In dissolution media at 90 min the 40% dispersions gave about 790 nm (binary), 510 (Tween 80), 580 (TPGS), 690 (SDS) and over 2000 nm (CTAB), the 50% dispersions about 1960, 780, 890, 1260 and over 2000 nm correasoto2022a R19. Analogues: 179 ± 8 (TIPP), 193 ± 5 (Me-TIPP), 348 ± 16 (PHPH) and 364 ± 5 nm (Me-PHPH), PDI below 0.3 que2021 R22. Felodipine: about 276–279 nm at 10–20% and 237–270 nm at 30–35% with 5% TPGS, about 278 nm at 10% without saboo2021 R17. Ritonavir: without surfactant the droplets grew from about 940 nm at 20 min to 2200 nm at 90 min; with SDS about 1180 nm when release levelled off at 20 min and about 2400–2470 nm later; with TPGS about 1320 nm at 10 min and 3840 nm at 90 min; with Span 20 about 550 → 1410 nm and with Span 85 about 330 → 960 nm; the Tween 80 precipitate was spherical droplets of about 10 µm, too large for DLS, and the Span 20 precipitate held needle crystals indulkar2022 R11, R13, R14. Clotrimazole droplets made by solvent injection grew from about 540 nm to 1 µm without PVP, from about 340 to 610 nm with K12 and from about 290 to 630 nm with K29/32, at the same normalized rate deac2024a R5. Ritonavir droplets agglomerated in the gel of 30% Tween 80 compacts and entered the medium as chunks at 2 and 5 min yang2023 R10. Bedaquiline precipitated at 100 µg/mL formed particles above 6000 nm without polymer and 413–967 nm with 400 µg/mL HPMCAS, about 98–107 nm in FeSSIF-V2 and 241–1002 nm in FaSSIF-V1 kaur2025 R18.

papersystemmethod and conditionsresultids
yang2021elbasvir 2.5%DLS 5–60 min, bufferPVPVA ≈670 → 1190 nm, crystals; HPMCAS ≈280 → 390; PVPVA + dissolved HPMCAS ≈250 → 300yang2021 R3
yang2021loratadine 10%samePVPVA ≈820 → 2120 nm; HPMCAS ≈420 → 570yang2021 R6
yang2021danazol 2.5%; miconazole 10%samedanazol ≈2780 nm with dissolved HPMCAS; miconazole alike in all mediayang2021 R4, R5
correasoto2022aCPD droplets ± surfactantDLS 4 h, 37 °Cbuffer ≈12× by 2 h; SDS, TPGS, Tween 80 ≈0.8–1.0×; CTAB ≈12× in 1 hcorreasoto2022a R6
correasoto2022asamezeta potential≈−16 / −69 / +29 mV (buffer, SDS, CTAB); non-ionics ≈−1 to −5correasoto2022a R7
correasoto2022aCPD dispersions 40, 50%DLS at 90 min of releasebinary ≈790, ≈1960 nm; surfactants smaller except CTAB (> 2000)correasoto2022a R19
que2021four analogues at their limitsDLS at 30 min≈179–193 (iodo) against ≈348–364 nmque2021 R22
saboo2021felodipine 10–35% ± TPGSDLS at 60 min≈237–280 nm, no trendsaboo2021 R17
que2019ledipasvir ± surfactantDLS 10–60 min≈60 (SDS), ≈96–130 (poloxamer 407), ≈225–257 nm (none)que2019 R12
indulkar2022ritonavir–PVPVA 30:70:5 with SDS, TPGS, Span 20, Span 85, Tween 80; binaryDLS of the release medium, 5–90 minSpan 85 ≈330 → 960, Span 20 ≈550 → 1410; none ≈940 → 2200; SDS ≈2400; TPGS ≈3840 nm; Tween 80 ≈10 µmindulkar2022 R11, R13
correasoto2023plasticized ATZ dispersions (systems not named)DLS after 90 min of releasedrug-rich droplets 500–1500 nmcorreasoto2023 R5, X18
ueda2020a (Bioperformance)ATZ and CLZ droplets with HPMCASDLS under agitation, 3 hHPMCAS limited coarsening; AS-HF kept the initial sizeueda2020a C18, C19
deac2024aclotrimazole droplets ± 1 mg/mL PVP K12 or K29/32DLS, 37 °C≈540 → 1000; ≈340 → 610; ≈290 → 630 nmdeac2024a R5
yang2023ritonavir–PVPVA 30% + Tween 80confocal, compactsdroplets agglomerated, left in chunksyang2023 R10
kaur2025bedaquiline 100 µg/mL ± 400 µg/mL HPMCASDLS, buffers and fluids>6000 nm without; 413–967 nm with polymer; ≈98–107 nm in FeSSIF-V2kaur2025 R18

Figure

Fig. 2 of yang2021: elbasvir nanodroplet z-average and PDI over 60 min in three media
Fig. 2 · yang2021elbasvir nanodroplet z-average and PDI over 60 min in three media

Black (PVPVA dispersion in buffer) rises and broadens; red (HPMCAS dispersion) and blue (PVPVA dispersion with dissolved HPMCAS) stay small and narrow yang2021 R3.

Fig. 2 of correasoto2022a: size and PDI of clopidogrel nanodroplets relative to time zero over 4 h
Fig. 2 · correasoto2022asize and PDI of clopidogrel nanodroplets relative to time zero over 4 h

Buffer and CTAB bars break the axis; missing bars mean growth that could not be measured, not stable size correasoto2022a R6, X10.

Why

The droplets are metastable and coarsen by ripening, flocculation and coalescence, and the fast coarsening of CPD droplets is "consistent with" the high interfacial energy of a lipophilic drug-rich phase correasoto2022a C2, C37. The low effective surfactant levels are "consistent with" stabilization by surfactant adsorbed at the droplet surface, sterically and/or electrostatically, and the zeta changes "support" adsorption correasoto2022a C39, C13; SDS needs more "most likely" because of its high HLB, and CTAB coarsens the droplets "by an unknown mechanism" correasoto2022a C42, C38. The non-ionic surfactants also partition into the drug-rich phase (aqueous TPGS 50 → 33 ± 5.4 µg/mL, a droplet composition of about 50:17 CPD:TPGS), which the authors judge unrelated to stabilization ("does not appear") correasoto2022a R12, C19, C40. For the polymers, adsorption of HPMCAS on droplet surfaces "has been hypothesized"; charged at the study pH, HPMCAS can add electrostatic to steric hindrance, which neutral PVPVA cannot, and the exact mechanism "clearly requires more investigation" yang2021 C39, C40. Que and co-workers expect colloid size to depend on the compound and excipients ("is likely") and smaller colloids to "potentially" improve absorption through faster reservoir replenishment que2021 C38, C37. (synthesis: because every PVPVA powder test of the 2021 drug-property study was run with 400 µg/mL HPMCAS in the medium to keep grown droplets from being lost on centrifugation, its PVPVA release data already include stabilization by a second polymer yang2021 P12, X18.) For ritonavir Indulkar and co-workers (2022) offer two explanations: the poorly water-soluble Spans "probably" mix into the droplets and lower the chemical potential of ritonavir, which "may" inhibit Ostwald ripening, as a poorly soluble oil did for amorphous felodipine particles (cited), or "may" prevent coalescence by steric repulsion; Tween 80 and TPGS "could possibly" partition into the droplets, lower their Tg and make them coalesce indulkar2022 C49, R25, C50, C48. Droplet composition and Tg were not measured indulkar2022 C48, C49. Deac and co-workers set aside steric stabilization by adsorbed PVP, since neither grade slowed droplet growth in dilute suspension, and propose entanglement in the gel instead ("may be contributing") (F29) deac2024a C44, C45. Yang and co-workers attribute the Tween 80 agglomeration "likely" to Tween 80 accumulating on the droplet surfaces yang2023 C22.

Conditions and limits

Buffers of pH 6.8, 7.5 and 9.0 at 37 °C; droplets made by solvent shift (CPD) or by dissolving dispersions (the others); one level per surfactant in the 4-h series, lower levels in an SI that was not supplied correasoto2022a P6, X10. The DLS series of the drug-property study are single drugs at one loading each, and the third series of two panels is unclear yang2021 A6, X7. Colloid sizes of the analogues were compared at different loadings, Me-PHPH below its limit que2021 X3.

Counterexamples and conflicts

Dissolved HPMCAS did not hold danazol droplets, and miconazole droplets grew alike with either polymer yang2021 X9. CTAB failed although its level was 20 times its calculated monolayer coverage, and TPGS worked below its calculated coverage correasoto2022a R24, X15. TPGS did not change felodipine droplet size, unlike a cited anacetrapib study in which size fell with TPGS saboo2021 C21, R28. TPGS and Tween 80, which held clopidogrel droplets at constant size, let ritonavir droplets grow to about 4 and 10 µm when built into the dispersion, and the Spans, which partitioned into atazanavir droplets, kept ritonavir droplets smallest correasoto2022a R6; indulkar2022 R11, R13; correasoto2022b R17 (synthesis: the surfactants were dissolved with preformed clopidogrel droplets but released from the dispersion together with ritonavir, so the comparison is between set-ups as well as drugs). The abstract of the ritonavir paper names TPGS instead of Span 85 among the smallest droplets, which contradicts its figure and table indulkar2022 X1.

Transfer check

Size the droplets of the target dispersion by DLS every 15–60 min for 1–4 h in the release medium, with the dissolved polymer at the concentration release produces, and check for crystals by polarized light yang2021 P16; correasoto2022a P6. If the droplets grow, test an ionizing polymer (HPMCAS) in the medium or in the dispersion, or 5–50 µg/mL of a non-ionic or anionic surfactant, and avoid a cationic surfactant until it has been tested yang2021 R3; correasoto2022a R6, C43. For a surfactant built into the dispersion, size the droplets in the release medium over the whole test, since the ritonavir ranking of surfactants differed from the clopidogrel ranking obtained with preformed droplets indulkar2022 R11; correasoto2022a R6.

History

Que and co-workers (2019) found smaller colloids with SDS and poloxamer 407 (F13) que2019 R12. Que and co-workers (2021) found the iodinated analogues giving colloids about half the size que2021 C24, and Saboo and co-workers (2021) no size effect of TPGS saboo2021 C20. Yang and co-workers (2021) compared the polymers and ran PVPVA powders with dissolved HPMCAS yang2021 C4, P12. Correa Soto and co-workers (2022) first screened surfactants for 4-h droplet stability and compared the effective levels with monolayer coverage, and propose this screen for selecting surfactants correasoto2022a C12, C41, C43. In the earlier chapters of this category additives decided the size and life of ritonavir and delamanid droplets (Supersaturation from ASD dissolution F12), the polymer decided whether ibuprofen droplets stayed dispersed (Amorphous solubility and LLPS F22), and HPMC-AS kept danazol and enzalutamide droplets small (Crystallization from solution F15); the papers here extend the polymer comparison to droplets released by dispersions. Indulkar and co-workers (2022) sized droplets released by surfactant-containing ritonavir dispersions and found the Spans best indulkar2022 C47; this adds the ritonavir clause to the title. Deac and co-workers (2024) separated droplet growth in solution, unchanged by the PVP grade, from agglomeration in the gel, which the grade decided deac2024a C20, C38.

Topic 3 of 5 · 13 findings · F6–F10, F17–F20, F25, F27, F29–F30

Limit of congruency and its causes

F6

Topic 3Limit of congruency and its causes1 of 13

One loading step above the limit of congruency, drug release falls by one to three orders of magnitude.

Ritonavir–PVPVA tablets released ≈97% of their drug at 60 min at 25% loading, ≈29% at 30% and at most ≈2% at 35–50%, which the authors call "falling off a cliff". The limit of congruency (LoC) is the highest loading that still releases congruently, 25% here indulkar2019a R11, C2, C31. In PVPVA the limits of the six drugs of 2018–2020 lay between 5 and 30%; later papers found 2 to 40% que2019 C10; saboo2019 R7; saboo2020a R15; indulkar2019a X7; hiew2022b R20; correasoto2022a C46; que2021 R19.

strongStrong for the existence and size of the drop, measured with both components in triplicate; the position of the limit is known only to the loading step indulkar2019a K2, X7; saboo2019 K1; saboo2020a K1, X11.

last congruent → first failing loadingledipasvir5–7.5nilvadipine10–15cilnidipine15–20felodipine15–20itraconazole (spray-dried)20–25ritonavir25–3005101520253035drug loading in PVPVA, %

The six drugs of 2018–2020; extruded itraconazole switched at 10–20%. que2019 C10; saboo2019 R7; saboo2020a R15; bhardwaj2018 X6; indulkar2019a X7

Fall of the drug rate one loading step past the limitcilnidipine–PVPVA2.18 → 0.006363×felodipine–PVPVA1.9 → 0.009211×felodipine–PVP3.8 → 0.020190×indomethacin–PVPVA3.14 → 0.04≈80×nilvadipine–PVPVA2.13 → 0.03561×lumefantrine sulfate–PVPVA4.5 → 0.1045×itraconazole, extruded199 → 48.8 µg/min/cm², 0.1 N HCl4.1×itraconazole, spray-dried113 → 64 µg/min/cm², 0.1 N HCl1.8×

Rates in mg/min/cm² unless stated; the cliff is steepest where the amorphous drug alone dissolves most slowly. saboo2019 R5, R6; saboo2020a R14; saboo2020 R3; hiew2022b R12; bhardwaj2018 R4

For your drug

  1. Dissolve the drug–polymer pair at 37 °C in 2.5–5% loading steps around the expected switch, with both components assayed.
  2. Treat the last congruent loading as an upper bound, choose the product loading with a margin below it, and repeat the first failing loading.
  3. Check the switch at the temperature of use, since the cited room-temperature limit of ritonavir–PVPVA lay below the 37 °C one.

que2019 A1; saboo2019 A2; indulkar2019a X3; benson2025 R21

How it works and key numbers
  1. The authors attribute the drop to water-induced phase separation that becomes faster than dissolution at high loading (F8) indulkar2019a C33.
  2. Below the switch the drug leaves at the polymer rate, above it at about the rate of the neat amorphous drug; the amorphous nilvadipine compact dissolves more than three orders of magnitude more slowly than PVPVA, "explaining" the fall saboo2019 C43.
  3. The drop therefore cannot exceed the ratio of the polymer-controlled to the neat-amorphous rate: about 1700 for nilvadipine–PVPVA and about 4600 for felodipine–PVP at pH 6.8, but about 200 for itraconazole in 0.1 N HCl saboo2019 R7; saboo2020a R13; bhardwaj2018 R9, R4.
  4. At the switch itself release is mixed: the 30% ritonavir tablet lagged for about 15 min, released both components together to about 40 min, and then PVPVA ran ahead (≈96 against ≈48.5% at 120 min) indulkar2019a R5, R6, R3.
≈97 → ≈29 → ≈2%ritonavir released at 60 min from 25, 30 and 35–50% tabletsindulkar2019a R11
61–363×fall of the drug rate one 5% step past the limit, nilvadipine and cilnidipinesaboo2019 R5, R6, X8
1.6-foldvariation of the first failing loading (30% ritonavir) between two seriesindulkar2019a X3
Evidence: data, conditions and papers

Finding F6. The limit of congruency is a narrow switch: one loading step above it drug release fell by one to three orders of magnitude, and in PVPVA the limit lay between 5 and 30% drug for the six drugs tested in 2018–2020

In short. Ritonavir–PVPVA tablets released ≈97% of their drug at 60 min at 25% loading, ≈29% at 30% and at most ≈2% at 35–50%, which the authors call "falling off a cliff"; they define the limit of congruency (LoC) as the highest loading that still releases congruently, 25% here indulkar2019a R11, C2, C31. One 5% step past the limit cut the drug rate about 60-fold for nilvadipine (2.13 → 0.035 mg/min/cm²), about 360-fold for cilnidipine (2.18 → 0.006) and about 200-fold for felodipine with PVP or PVPVA saboo2019 R5, R6, X8; saboo2020a R14. In PVPVA the brackets were 5–7.5% for ledipasvir, 10–15% for nilvadipine, 15–20% for cilnidipine and felodipine, 20–25% for spray-dried and 10–20% for extruded itraconazole, and 25–30% for ritonavir tablets que2019 C10; saboo2019 R7; saboo2020a R15; bhardwaj2018 X6; indulkar2019a X7. Every limit is the last congruent loading tested, so the switch itself lies inside the next step. The papers of 2020–2022 found PVPVA limits from 2% (lumefantrine sulfate) to 40% (clopidogrel and a non-interacting phenolphthalein analogue) for 22 further drug forms, with the same collapse one step above hiew2022b R20; correasoto2022a C46; que2021 R19, R15. In 2024 the polymer grade alone moved the limit of clotrimazole–PVP from below 5% (K12, K17) through 20% (K25) to about 33–38% (K29/32 to K90), each limit again bracketed by the next tested loading (F29) deac2024a R12, X5.

Type. observation in 6 drugs in PVPVA, and felodipine in PVP and HPMC Strength. for the existence and size of the drop, measured with both components in triplicate indulkar2019a K2: strong; saboo2019 K1: strong; saboo2020a K1: strong; the position is known only to the loading step indulkar2019a X7; saboo2020a X11.

How it was shown

Each paper dissolved a loading series under the conditions of F1: ritonavir–PVPVA tablets at 10–50%, ledipasvir at 2–20%, nilvadipine at 5–20% and cilnidipine at 5–25% in 5% steps, felodipine with PVP, PVPVA and HPMC at 5–30%, and itraconazole (ITZ) at 10–50% indulkar2019a A1; que2019 A1; saboo2019 A2; saboo2020a A2; bhardwaj2018 A1.

What the data show

Ritonavir tablets released (drug/polymer at 60 min) ≈97/≈100% at 25%, ≈29/≈62% at 30%, ≈1.7/≈8% at 35% and ≈0/≈3.1% at 50% indulkar2019a R11. Later PVPVA limits ranged from 2 to 40% hiew2022b R20; correasoto2022a C46.

systemread-outlimit and dropids
ritonavir–PVPVA tabletspH 6.8, 37 °CLoC 25%; ≈97 → ≈29 → ≤ ≈2% at 60 minindulkar2019a R11, C2
ledipasvir–PVPVApH 6.8, 37 °CLoC 5% (between 5 and 7.5%)que2019 C10, R3
nilvadipine, cilnidipine in PVPVAnormalized ratesswitch 10–15% and 15–20%; drop ≈60- and ≈360-foldsaboo2019 R5, R6, R7, X8
felodipine in PVP, PVPVA, HPMCnormalized ratesLoC 10, 15, 10%; drop ≈200-fold (PVP, PVPVA)saboo2020a R14, R15
ITZ–PVPVA spray-dried, extruded0.1 N HClswitch 20–25% and 10–20%; step 1.8–4.1-foldbhardwaj2018 R4, X6
clotrimazole–PVP K12 to K90pH 8.0, >80% drugbrackets <5, <5, 20–23, 33–35, 35–38, 38–40%deac2024a R12, X5
Fig. 8 of indulkar2019a: percent of ritonavir and PVPVA released at 60 min against drug loading
Fig. 8 · indulkar2019apercent of ritonavir and PVPVA released at 60 min against drug loading

Both bars are near 100% at 10–25%, both fall at 30% (the drug more than the polymer), and both are near zero from 35% on indulkar2019a R11.

Why

The authors stress that the range over which release switches is "very narrow" and that the switch changes drug release by "orders of magnitude", and they attribute the drop to faster water-induced phase separation relative to dissolution at high loading ("can be attributed") indulkar2019a C52, C33. The amorphous nilvadipine compact dissolves more than three orders of magnitude more slowly than PVPVA, "explaining" the precipitous fall saboo2019 C43. (synthesis: the drop cannot exceed the ratio of the polymer-controlled to the neat-amorphous rate; the observed drops are 60–360-fold for nilvadipine and felodipine and 2–4-fold for ITZ, so the cliff is steepest where the amorphous drug alone dissolves most slowly saboo2019 R7; saboo2020a R13; bhardwaj2018 R9, R4.)

Limits and transfer

The limit depends on how it is defined (last congruent loading, release of at least 80%, or LLPS), and gel drug content gave a lower MePHPH limit than release did hiew2022a X17; purohit2017b R11; deac2023a C14, X18. Dissolve the pair at 37 °C in 2.5–5% steps around the expected switch with both components assayed, treat the last congruent loading as an upper bound, and check the switch at the temperature of use que2019 A1; saboo2019 A2; indulkar2019a X3; benson2025 R21.

How it was shown

Each paper dissolved a loading series under the conditions of F1: ritonavir–PVPVA tablets at 10, 20, 25, 30, 35, 40 and 50% indulkar2019a A1; ledipasvir–PVPVA at 2, 5, 7.5, 10 and 20% que2019 A1; nilvadipine at 5–20% and cilnidipine at 5–25% in 5% steps saboo2019 A2; felodipine with PVP, PVPVA and HPMC at 5, 10, 15, 20 and 30% saboo2020a A2; spray-dried and extruded ITZ–PVPVA at 10, 20, 25 and 50% bhardwaj2018 A1. Purohit and Taylor (2017) tested ritonavir films at 10–50% in 10% steps with LLPS, not congruency, as read-out purohit2017b A2, R11.

What the data show

Ritonavir: percent released at 60 min (drug/polymer) was ≈100/≈96.5 (10%), ≈100/≈94 (20%), ≈97/≈100 (25%), ≈29/≈62 (30%), ≈1.7/≈8 (35%), ≈0.8/≈5.5 (40%) and ≈0/≈3.1 (50%) indulkar2019a R11. The 30% tablet lagged for about 15 min, released both components together to about 40 min and then let PVPVA run ahead (≈96 against ≈48.5% at 120 min); the 35% tablet released ≈49% polymer and ≈11% drug by 300 min indulkar2019a R5, R6, R3. The authors sort the tablets into three categories, fast, complete and congruent (10–25%), initially congruent and then incongruent (30%), and slow and incomplete (35–50%, with 35% mixed) indulkar2019a C32. The 30% extent differed about 1.6-fold between two series indulkar2019a X3. Ledipasvir: about 100% of both components by 60 min at 2 and 5%, no drug up to 60 min at 7.5% que2019 R3, R4. Nilvadipine and cilnidipine: polymer/drug ratios about 1 up to 10% and 15%, then about 20, 40, 40 and 105 saboo2019 R5, R6. Felodipine: PVP 3.8 → 0.020, PVPVA ≈1.9 → ≈0.009, HPMC ≈0.14 → ≈0.04 → ≈0.005 mg/min/cm² across the switch, the HPMC drop coming in two steps saboo2020a R14, X11. ITZ: spray-dried 64 (25%) → 113 (20%) → 199 µg/min/cm² (10%), extruded 55 → 48.8 → 199 bhardwaj2018 R4. Ritonavir films formed LLPS up to 20% with PVP and only at 10% with PVPVA purohit2017b R10, R11. (synthesis: the drops across the switch are 2.13/0.035 = 61 and 2.18/0.006 = 363 for nilvadipine and cilnidipine, 3.8/0.020 = 190 and 1.9/0.009 = 211 for felodipine with PVP and PVPVA, but only 113/64 = 1.8 (spray-dried) and 199/48.8 = 4.1 (extruded) for ITZ in 0.1 N HCl.) Limits in PVPVA from the papers of 2020–2022: IND 10% and INDester at least 25% (5-min rates) saboo2020 C14; PHPH 5, TIPP 10, Me-TIPP 30 and Me-PHPH 40% que2021 R19; felodipine 15% without TPGS saboo2021 R12; loratadine 30% in compacts, and drops at 25% (loratadine), 40% (miconazole), 5% (danazol) and 10% (elbasvir) in powders, with paclitaxel and ivacaftor dropping between 5 and 10% yang2021 R22, R7, R8, R9, R10, R11, R12, X26; clopidogrel about 40% correasoto2022a C46; ATZ 5% correasoto2022b C12; lumefantrine free base at least 35% and its eight salts 2–25% hiew2022b R20, X7. The one-step drops were large again: IND 3.14 → 0.04 mg/min/cm² (10 → 15%), ATZ from about 100 to below 3% released (5 → 10%) and lumefantrine sulfate 4.5 → 0.10 mg/min/cm² (2 → 5%) saboo2020 R3; correasoto2022b R1; hiew2022b R12. (synthesis: 3.14/0.04 ≈ 80-fold and 4.5/0.10 = 45-fold; 22 forms = 14 drugs and 8 salts in the rows below.) A second ritonavir–PVPVA series of 2022 released about 97–100% of drug and polymer by 60–90 min at 20% and about 35% of the drug at 30%, placing the switch between 20 and 30% in that paper's own data, next to the 25% of 2019 yang2022a R2, X7, R15. In 2023 MePHPH–PVPVA released at least as fast as neat PVPVA to 40% and about 15% of its drug at 50% after a lag, with nothing at 70%, and PHPH–PVPVA about 75% at 5% and nothing at 20%, in line with the cited limits of 40 and 5% deac2023a R1, R2, R14. The drug content of the gel rose at 40 and 50% MePHPH and not at 20%, so by that criterion the MePHPH limit lies between 20 and 40% deac2023a R3, C14, X18. Clotrimazole–PVP dispersions passed the 80% criterion at 20% but not 23% (K25), at 33% but not 35% (K29/32), at 35% but not 38% (K60) and at 38% but not 40% (K90), and failed at 5% with K12 and K17 deac2024a R1, R12, X5. With 10 parts of a Span per 100 parts of drug and polymer, ritonavir–PVPVA released about 87–97% at 30% but 1–8% at 40% (F31) yang2023 R2.

papersystemmethod and conditionsresultids
purohit2017britonavir films, PVP, PVPVALLPS read-out, 25 °CLLPS up to 20% (PVP), 10% (PVPVA)purohit2017b R10, R11
bhardwaj2018ITZ–PVPVA SD, HM0.1 N HClswitch 20–25% (SD), 10–20% (HM); step 1.8–4.1-foldbhardwaj2018 R4, X6
indulkar2019aritonavir–PVPVA tabletspH 6.8, 37 °CLoC 25%; ≈97 → ≈29 → ≤ ≈2% at 60 minindulkar2019a R11, C2
que2019ledipasvir–PVPVApH 6.8, 37 °CLoC 5% (between 5 and 7.5%)que2019 C10, R3
saboo2019Nil, Cil in PVPVApH 6.8, 37 °Cswitch 10–15% and 15–20%; drop ≈60- and ≈360-foldsaboo2019 R5, R6, R7, X8
saboo2020afelodipine in PVP, PVPVA, HPMCpH 6.8, 37 °CLoC 10, 15, 10%; drop ≈200-fold (PVP, PVPVA)saboo2020a R14, R15
saboo2020IND; INDester–PVPVA5-min rates10%; at least 25%saboo2020 C14
que2021PHPH, TIPP, Me-TIPP, Me-PHPH≥80% in 90 min5, 10, 30, 40%que2021 R19
yang2021loratadine, miconazole, danazol, elbasvir, paclitaxel, ivacaftorpowders; loratadine compactsdrops at 25, 40, 5, 10, 5–10, 5–10%; compact limit 30%yang2021 R7, R8, R9, R10, R11, R12, R22
correasoto2022aclopidogrelcompactsabout 40%correasoto2022a C46
correasoto2022batazanavircompacts5%correasoto2022b C12
hiew2022blumefantrine and eight saltsdrug release2–35%hiew2022b R20
yang2022aritonavir–PVPVA 20, 30, 40, 50%compacts, 90 min20% congruent and complete; switch between 20 and 30%yang2022a R2, X7
deac2023aMePHPH–PVPVA 20–70%; PHPH 5, 20%release at 30 min; gel drug contentMePHPH good to 40% (gel criterion 20–40%), 15% at 50%; PHPH good at 5%, none at 20%deac2023a R1, R2, R3, X18
hiew2022a (Miscibility)lumefantrine–PVPVAcompactsLoC 35%; 40% failshiew2022a C31, X17
moseson2022b (ASD process)bicalutamide–PVPVApowdersbetween 10 and 20%, not locatedmoseson2022b X15
li2020 (ASD process)copovidone dispersions (cited)review of boundaries5% to about 30%li2020 C63
benson2025 (ASD process)ritonavir–PVPVA (cited)room temperature20% beyond the limit, against 25% at 37 °Cbenson2025 R21, R20
duong2022a (ASD dissolution)delamanid edisylate–HPMCPpH 6.5≈95–99 → ≈59 → ≈21 µg/mL at 25, 30, 40%duong2022a R24
polyzois2024 (ASD dissolution)praziquantel–HPMCAS-MFPBS pH 6.5no cliff; gradual declinepolyzois2024 C16, C18
deac2024aclotrimazole–PVP K12, K17, K25, K29/32, K60, K90compacts, pH 8.0, >80% drugbrackets <5, <5, 20–23, 33–35, 35–38, 38–40%deac2024a R12, X5
yang2023ritonavir–PVPVA + Span 20 or Span 85compacts, pH 6.8, 90 min≈87–97% at 30%; ≈1–8% at 40%yang2023 R2

Figure

Fig. 8 of indulkar2019a: percent of ritonavir and PVPVA released at 60 min against drug loading
Fig. 8 · indulkar2019apercent of ritonavir and PVPVA released at 60 min against drug loading

Both bars are near 100% at 10–25%, both fall at 30% (the drug more than the polymer), and both are near zero from 35% on indulkar2019a R11.

Why

The authors stress that the range over which release switches from polymer- to drug-controlled is "very narrow" and that the switch changes drug release by "orders of magnitude" indulkar2019a C52. They attribute the drop to faster water-induced phase separation relative to dissolution at high loading ("can be attributed"), see F8, and propose that key ritonavir–PVPVA interactions in water are "likely" saturated around 25–30% (see F10) indulkar2019a C33, C34. The size of the drop follows from the two regimes of F2 and F3: the amorphous nilvadipine compact dissolves more than three orders of magnitude more slowly than PVPVA, "explaining" the precipitous fall saboo2019 C43. (synthesis: the drop cannot exceed the ratio of the polymer-controlled to the neat-amorphous rate, about 1700 for nilvadipine–PVPVA and about 4600 for felodipine–PVP at pH 6.8 but about 10.4/0.051 ≈ 200 for ITZ in 0.1 N HCl saboo2019 R7; saboo2020a R13; bhardwaj2018 R9, R4; the observed drops are 60–360-fold for the first two and 2–4-fold for ITZ, so the cliff is steepest where the amorphous drug alone dissolves most slowly.)

Conditions and limits

Compacts at 37 °C in pH 6.8 phosphate (ITZ in 0.1 N HCl), ritonavir films at 25 °C; loading steps of 2.5–10% que2019 A1; purohit2017b A2. Congruency is defined only as simultaneous release indulkar2019a X7. The limit depends on how it is defined and measured: last congruent loading, release of at least 80%, or LLPS hiew2022a X17; purohit2017b R11. Gel drug content gave a lower MePHPH limit (between 20 and 40%) than release did (40%), so the criterion matters deac2023a C14, X18.

Counterexamples and conflicts

Felodipine dispersions in HPMCAS and EUDS showed no limit up to 50%, and 50:50 ritonavir–HPMCAS films still formed LLPS (see F11) saboo2020a R15; purohit2017b R11. The same pair gave different limits by different tests: ritonavir–PVPVA films formed LLPS only at 10% (25 °C, LLPS read-out) while tablets released congruently to 25% (37 °C, congruency read-out), and a cited room-temperature value puts 20% beyond the limit (synthesis: a lower limit at lower temperature is consistent with both) purohit2017b R11; indulkar2019a C2; benson2025 R21. In the ASD dissolution chapter delamanid–HPMCP fell gradually from 25 to 40% and praziquantel–HPMCAS showed no cliff (Supersaturation from ASD dissolution F10) duong2022a R24; polyzois2024 C16. HPMCAS dispersions of three more drugs declined gradually with loading, and SDS dispersions of ATZ declined gradually above 10% (about 60.5 and 39% at 15 and 20%) instead of collapsing yang2021 C2; correasoto2022b R4, X11. The release data shown in the 2024 phase-diagram paper place the MePHPH limit only between 30 and 50%, against the cited 40% deac2024b X9.

Transfer check

Dissolve the candidate drug–polymer pair at 37 °C in 2.5–5% loading steps around the expected switch, with both components assayed que2019 A1; saboo2019 A2. Treat the last congruent loading as an upper bound, choose the product loading with a margin below it, and repeat the first failing loading, whose extent varied 1.6-fold between runs for ritonavir indulkar2019a X3. Check the switch at the temperature of use, since the cited room-temperature limit of ritonavir–PVPVA lay below the 37 °C one benson2025 R21.

History

Simonelli and co-workers (1969, cited) described a loading-dependent change of regime for sulfathiazole–PVP bhardwaj2018 R22. Bhardwaj and co-workers (2018) proposed a threshold drug-to-polymer ratio above which the amorphous drug controls release ("suggests") bhardwaj2018 C66. Indulkar and co-workers (2019) named the limit of congruency and the cliff for ritonavir–PVPVA indulkar2019a C2, C31. Saboo and co-workers (2019) located it for two dihydropyridines and recommended loadings below the "drop-off" concentration when rapid release is needed saboo2019 C33, Que and co-workers (2019) found the lowest value of the period for ledipasvir que2019 C10, and Saboo and co-workers (2020) showed that two polymers have no limit up to 50% saboo2020a R15. Purohit and Taylor's films of 2017 show the same loading switch through LLPS before the term was introduced purohit2017b C52. The papers of 2020–2022 added limits for 22 further drug forms and expressed them per mole when molecular weights differ que2021 E3, R20; this extends the range given in the short part from 5–30% to 2–40%. Deac and co-workers (2024, polymer molecular weight) showed the polymer grade moving the limit at least sevenfold, and Deac and co-workers (2024, ternary phase diagrams) located the limit near the critical point of the drug–polymer–water diagram (F29, F30) deac2024a R12; deac2024b R37.

Other chaptersexplains B F10
F7

Topic 3Limit of congruency and its causes2 of 13

Above the limit the dissolving surface turned drug-rich and porous within minutes; below it the surface kept its composition.

XPS of a 20% ledipasvir–PVPVA compact showed surface drug rising from 17 to 54 wt% in 10 min of dissolution, and of cilnidipine 20:80 compacts from 20 to 60%, while congruently releasing compacts did not change que2019 R15; saboo2019 R18; indulkar2019a R16, R15; saboo2020a R22. Micro-CT and SEM showed a porous layer with pits up to about 20 µm saboo2019 R13, R14. In 2022 cross-sections showed a continuous drug-rich layer 5–10 µm thick on 30% ritonavir compacts within 5 min yang2022a R5, R6.

strongStrong for the drug-rich surface, shown by IR, XPS, EDX, micro-CT and SEM in four papers; moderate for the barrier role, which is inferred from composition and from tablets dried before imaging saboo2019 K3; indulkar2019a K3; que2019 K2, X22.

before dissolutionafter dissolutionledipasvir–PVPVA 20%XPS, 10 min1754ledipasvir–PVPVA 50%XPS, 10 min4061nilvadipine–PVPVA 15:85XPS, 10 min232cilnidipine–PVPVA 20:80XPS, 10 min2060indomethacin–PVPVA 25%EDX, 20 min2572ritonavir–PVPVA 40%XPS, 30 min357201020304050607080drug at the compact surface, wt% (before → after dissolution)

All six compacts lie above their limit of congruency; congruently releasing compacts did not change. que2019 R15; saboo2019 R18; saboo2020 R21; yang2022a R14

Ritonavir–PVPVA: gel–glass front at 20 min, % of compact thicknessneat PVPVA and 10–20%all of it30%≈29%, then stopped40%17%, then stopped

Read by the authors as water entry slowed by the hydrophobic drug-rich layer. yang2022a R8

For your drug

  1. For a candidate loading, eject compacts after 5 and 10 min and compare the surface with the dry compact by ATR-IR or XPS, or by EDX of an element that only the drug carries (Cl, F, or the N/O ratio).
  2. A surface that gains drug within minutes and turns porous marks the drug-controlled side of the switch; an unchanged surface marks the congruent side.

indulkar2019a P7; que2019 P7; saboo2019 E2, R18; saboo2020a P9, R22

How it works and key numbers
  1. In incongruent release the polymer leaves faster, so the interface "must" become enriched in drug, and the porous structure is "consistent with" polymer loss saboo2019 C38, C21, C22.
  2. The authors trace the pits to rapid phase separation at the interface followed by dissolution of the polymer-rich regions; the pit rims were drug-rich (N/O ≈0.50 against ≈0.35 inside) saboo2019 C39, C40, R16.
  3. For ledipasvir the drug-rich layer makes dissolution drug-controlled and "it appears" to stop release even of the soluble PVPVA: only ≈2% of the polymer had left the 20% compact by 10 min que2019 C31, C32, R11.
  4. In 2022 the gel–glass front of 30 and 40% ritonavir compacts stopped early, read as water ingress "significantly retarded" by the hydrophobic drug-rich layer, which "effectively acts as a barrier" yang2022a R8, C30.
  5. For the phenolphthalein analogues the surface layer approached the composition of the drug-rich phase that the drug forms in water, a "pseudo-equilibrium" (F27) deac2023b C61, C59.
  6. An alternative reading is that preferential polymer dissolution alone gives a porous, drug-rich surface whether or not phase separation precedes it saboo2020a X6.
17 → 54 wt%ledipasvir at the surface of the 20% compact after 10 minque2019 R15
5–10 µmcontinuous drug-rich layer on the 30% ritonavir compact within 5 minyang2022a R5, R6
≈2%PVPVA released from the 20% ledipasvir compact in 10 minque2019 R11
Evidence: data, conditions and papers

Finding F7. Above the limit the dissolving surface turned drug-rich and porous within minutes, read as a barrier that slows even the polymer; below the limit the surface kept its composition

In short. XPS of ledipasvir–PVPVA compacts showed surface drug rising from 17 to 54 wt% (20% loading) and from 40 to 61 wt% (50%) in 10 min of dissolution, and of nilvadipine 15:85 and cilnidipine 20:80 compacts from 2 to 32% and from 20 to 60% que2019 R15; saboo2019 R18. The 50% ritonavir tablet surface gave the IR spectrum of amorphous ritonavir from 5 min, and felodipine tablets at 30% with PVP, PVPVA or HPMC gained surface chlorine (≈3.0 → ≈6.7, ≈4.6 → ≈6.4, ≈2.6 → ≈7.3 atomic %), whereas congruently releasing compacts (20% ritonavir; HPMCAS and EUDS) did not change indulkar2019a R16, R15; saboo2020a R22. Micro-CT and SEM showed a porous layer, pits up to about 20 µm and drug-rich pit rims (N/O ≈0.50 against ≈0.35 inside) saboo2019 R13, R14, R16. The authors read the layer as a barrier ("it appears"), and in the 20% ledipasvir compact only ≈2% of the polymer had left after 10 min que2019 C32, R11. IND tablets at 25% went from 25 to about 40–50 wt% surface drug at 5 min and about 60–72 wt% at 20 min by FTIR, EDX and nanoTA, and micro-CT showed a porous surface layer on incongruent felodipine–TPGS tablets only saboo2020 R17, R21, R28; saboo2021 R19. In ritonavir–PVPVA compacts imaged during dissolution in 2022, a continuous drug-rich layer 5–10 µm thick covered the 30% compact within 5 min and one of about 12 µm the 40% compact by 30 min, and XPS of the 40% surface rose from 35 to 72 wt% drug in 30 min yang2022a R5, R6, R14. Surfaces of partly dissolved compacts above the limit drifted toward the composition of the drug-rich phase that the drug forms in water (15% phenolphthalein from about 13.5 to 21% drug, 50% of its methyl ether from about 44 to 90–101%), while compacts at or below the limit kept their composition, and the 50% surfaces carried a porous, continuous drug-rich phase (F25, F27) deac2023b R6, R7; deac2023a R9.

Type. observation in 6 drugs (ritonavir, ledipasvir, nilvadipine, cilnidipine, felodipine, itraconazole), and indomethacin and lumefantrine salts in 2020–2022, and ritonavir, phenolphthalein and its methyl ether in 2022–2023 Strength. for the drug-rich surface, shown by IR, XPS, EDX, micro-CT and SEM in four papers saboo2019 K3: strong; indulkar2019a K3: moderate to strong; moderate for the barrier role, which is inferred from composition and dried-tablet morphology que2019 K2: moderate, X22.

How it was shown

Compacts were ejected after 0–15 min and their surfaces compared with the dry compact by ATR-IR, XPS, micro-CT, SEM and SEM-EDX indulkar2019a P7, P8; que2019 P7, P5; saboo2019 P14, P15, P16, P17; saboo2020a P8, P9. Yang and co-workers (2022) imaged cross-sections of dye-labelled ritonavir–PVPVA compacts by confocal microscopy and measured how far the gel–glass front advanced yang2022a P1, P5, P6, P10.

What the data show

Only ≈2% of the PVPVA of the 20% ledipasvir compact had left by 10 min que2019 R11. The gel–glass front advanced alike for neat PVPVA and 10–20% compacts but reached only about 29 and 17% of the thickness by 20 min at 30 and 40% and then stopped yang2022a R8.

systemmethodresultids
ritonavir–PVPVA 50% tabletATR-IR, SEM, 0–15 minamorphous ritonavir spectrum from 5 min; flaky at 15 minindulkar2019a R16, R17
ledipasvir–PVPVA 20, 50%XPS, 10 min17 → 54 and 40 → 61 wt% drugque2019 R15
nilvadipine 15:85, cilnidipine 20:80XPS, EDX, micro-CT, 10 min2 → 32% and 20 → 60%; rim N/O ≈0.50saboo2019 R18, R16, R13
felodipine 30%, five polymersEDX chlorine, micro-CTenriched with PVP, PVPVA, HPMC; not with HPMCAS, EUDSsaboo2020a R22, R19
ritonavir–PVPVA 10–50%confocal surfaces and cross-sections, 5–30 mindiscrete droplets at 10–25%; continuous drug-rich layer 5–10 µm (30%), ≈12 µm (40%)yang2022a R4, R5, R6
PHPH 5, 15, 50%; MePHPH 30, 50%ATR-FTIR of dried surfaces, 0–60 minconstant at 5% PHPH, 30% MePHPH; 13.5 → 21% and 44 → 90–101% above the limitdeac2023b R6, R7
Fig. 8 of saboo2019: SEM of dissolving compact surfaces after 10 min either side of the switch
Fig. 8 · saboo2019SEM of dissolving compact surfaces after 10 min either side of the switch

Smooth surfaces below the switch (a, c) against pits with raised rims above it (b, d); note the different scale bars (10, 20, 1 and 1 µm) saboo2019 R14.

Why

In incongruent release the polymer leaves faster, so the interface "must" become enriched in drug, and the porous structure is "consistent with" polymer loss saboo2019 C38, C21. For felodipine the surface enrichment is "a physical barrier to polymer release from subsurface layers" saboo2020a C42. Yang and co-workers read the stalled gel–glass front as water ingress "significantly retarded" by the hydrophobic drug-rich layer, which "effectively acts as a barrier" yang2022a C30, C55. An alternative reading is that preferential polymer dissolution alone gives a porous, drug-rich surface whether or not phase separation precedes it saboo2020a X6.

Limits and transfer

Most systems were examined at one loading above the switch, on dried samples saboo2019 A5; indulkar2019a X11; que2019 X22. From felodipine compacts PVP release only about halved and HPMC release did not fall saboo2020a X15. Eject compacts after 5 and 10 min and compare the surface with the dry compact; a surface that gains drug within minutes marks the drug-controlled side of the switch indulkar2019a P7; que2019 P7; saboo2019 R18; saboo2020a R22.

How it was shown

Purohit and Taylor (2017) imaged 50:50 and 10:90 ritonavir films by SEM after 10 s in buffer purohit2017b P13. Bhardwaj and co-workers (2018) inferred a drug-rich layer from the curving polymer profiles of 50:50 ITZ compacts, without surface analysis bhardwaj2018 C52. Indulkar and co-workers (2019) ejected ritonavir tablets at 0–15 min, blotted them and recorded ATR-IR against amorphous ritonavir and PVPVA, and imaged vacuum-dried tablets by SEM indulkar2019a P7, P8. Que and co-workers (2019) analysed compact surfaces before and after 10 min by XPS (N 1s fitting with pure-component spectra, F 1s components) and imaged dried compacts by micro-CT at 8 µm/pixel que2019 P7, P5. Saboo and co-workers (2019) took compacts either side of the switch after 10 min for micro-CT (3 µm pixels), SEM, SEM-EDX of the N/O ratio (0.5 for nilvadipine, ~0.3 for PVPVA) and XPS of the top ≈10 nm saboo2019 P14, P15, P16, P17, E2. Saboo and co-workers (2020) examined 30% felodipine tablets after 10 min by micro-CT, SEM and EDX of chlorine, which only felodipine contains saboo2020a P8, P9. Yang and co-workers (2022) dissolved ritonavir–PVPVA compacts at 10–50% containing trace Nile red (drug-rich phase) and Alexa Fluor 488 (polymer- and water-rich phase), removed them after 5–30 min, dried the surface with air and imaged surfaces and cut cross-sections by confocal microscopy, measured how far the gel–glass front had advanced into the compact, and analysed the 40% surface by XPS (C 1s fits, five spots on one compact) before and after 30 min yang2022a P1, P5, P6, P10, P9. Deac and co-workers (2023) blotted and dried compacts after 10–60 min of dissolution and read their surface drug content by ATR-FTIR against standard curves, with the PHPH medium spiked with 40 µg/mL PHPH, and imaged the surfaces of dye-labelled compacts by confocal microscopy after 2–20 min deac2023b P12; deac2023a P8.

What the data show

Ritonavir: the 50% surface still resembled the unexposed dispersion at 2 min, resembled amorphous ritonavir from 5 min with the PVPVA peaks diminished, and was closest to it at 15 min; the 20% surface was unchanged at 5 min, and SEM showed a rough, flaky 50% surface at 15 min against smooth 20% surfaces indulkar2019a R16, R15, R17. Ledipasvir: surface drug matched the nominal loading before dissolution (17 against 20, 40 against 50 wt%) and reached ≈54 ± 5 and ≈61 ± 2 wt% after 10 min; the share of the lower-binding-energy fluorine fell from ≈73, ≈42 and ≈18% to ≈9, ≈3 and ≈2% at 10, 20 and 50% que2019 R15, R17. The 10% compact kept its thickness with a distinct top layer at 10 min and bulged with pores and cracks by 30 min que2019 R13. Nilvadipine and cilnidipine: compacts below the switch were homogeneous and smooth, those above it had a porous layer at the dissolving face within 10 min, pits with raised rims up to about 20 µm (nilvadipine) or about 0.1–1 µm (cilnidipine), and porosity that grew at 20 and 30 min saboo2019 R13, R14. EDX on a nilvadipine 15:85 compact gave N/O ≈0.50 ± 0.03 on a pit rim, ≈0.35 ± 0.04 inside and ≈0.31 ± 0.01 before dissolution saboo2019 R16. XPS gave 2 ± 0 → 32 ± 1% (nilvadipine 15:85) and 20 ± 1 → 60 ± 4% (cilnidipine 20:80), while the congruent compacts did not change saboo2019 R18. Felodipine 30%: porous layers for PVP, PVPVA and HPMC, none for HPMCAS and EUDS; pits on PVP and PVPVA, voids on HPMC, angular particles on HPMCAS and EUDS; chlorine as in the short part, with HPMCAS ≈2.9 → ≈3.1 and EUDS ≈3.0 → ≈2.7 (not significant) saboo2020a R19, R21, R22. Ritonavir films after 10 s in buffer: a rough porous network on 50:50 PVP, a granular surface on 50:50 PVPVA, smooth 10:90 films and a smooth 50:50 HPMCAS film purohit2017b R9. Polymer release under the layer: ≈2% of the PVPVA of the 20% ledipasvir compact by 10 min, and PVPVA from felodipine compacts fell from ≈1.9 to ≈0.14–0.19 mg/min/cm² across the switch, whereas PVP only about halved and HPMC did not fall que2019 R11; saboo2020a R14, X15. IND: the 10% tablet surface was unchanged by IR after 5 min while the 15% surface gained the 1634 and 1591 cm⁻¹ bands; the 25% surface reached about 40–50, 50 and 60% drug by matching IR spectra at 5, 10 and 20 min, 41 ± 3, 55 ± 11 and 72 ± 9 wt% by EDX (from 25 ± 2) and 44 ± 5, 52 ± 7 and 60 ± 5 wt% by nanoTA on immersed films; SEM showed smooth 10% and rough, porous 15 and 25% surfaces, and AFM height features grew from about 15 nm at 2 s to about 150 nm at 20 min saboo2020 R15, R16, R17, R21, R28, R19, R24. Felodipine with TPGS: after 10 min the 30% tablets with 0 and 2% TPGS (incongruent) had a porous surface layer, those with 5 and 10% (congruent) a homogeneous section saboo2021 R19. Lumefantrine benzoate at 30%: large pits after 10 min and a rough, irregular surface, read as a PVPVA-rich phase dissolving first ("postulated") hiew2022b R17, C22. Ritonavir–PVPVA in 2022: surfaces carried small discrete drug-rich domains at 10–25%, a mixture of continuous drug-rich patches and discrete dots at 30%, and an interconnected, porous drug-rich network at 40–50% after 5 min that covered the whole surface by 30 min; neat amorphous ritonavir and neat PVPVA gave uniform images yang2022a R4. Cross-sections showed a glassy core, a gel layer with a sharp boundary to the core and, from 30%, a drug-rich surface layer, 5–10 µm at 30% after 5 min and about 12 µm at 40% after 30 min, with polymer- and water-rich regions under it yang2022a R5, R6, R7. The gel–glass front advanced alike for neat PVPVA and 10–20% compacts (about 44–54% of the thickness by 10 min, all of it by 20 min) but reached only about 29 and 17% by 20 min at 30 and 40% and then stopped yang2022a R8. XPS: 35 ± 0.5 wt% ritonavir before and 72 ± 10 wt% after 30 min at 40% yang2022a R14, X13. PHPH and MePHPH in 2023: surface drug of 5% PHPH about 5.6 → 6.2% over 60 min, 15% PHPH about 13.5 → 21.3% by 30 min, 50% PHPH about 49 → 53% in buffer and about 49 → 26% with 1 mg/mL PVPVA in the medium; 30% MePHPH about 33–43%, 50% MePHPH about 44 → 101 → 91% deac2023b R6, R7. Confocal surfaces were uniform at 30% MePHPH, patchy at 40%, a continuous porous drug-rich phase with water-rich pockets at 50%, and porous at 20% PHPH; neat drugs and polymer did not separate deac2023a R9, R10.

papersystemmethod and conditionsresultids
purohit2017britonavir 50:50 PVP, PVPVA filmsSEM after 10 s in bufferporous or granular; 10:90 and HPMCAS smoothpurohit2017b R9
indulkar2019aritonavir–PVPVA 50% tabletATR-IR, SEM, 0–15 minamorphous ritonavir spectrum from 5 min; flaky at 15 minindulkar2019a R16, R17
que2019ledipasvir–PVPVA 20, 50%XPS, 10 min17 → 54 and 40 → 61 wt% drugque2019 R15
saboo2019Nil 15:85, Cil 20:80XPS, EDX, micro-CT, 10 min2 → 32% and 20 → 60%; rim N/O ≈0.50saboo2019 R18, R16, R13
saboo2020afelodipine 30%, five polymersEDX chlorine, micro-CTenriched with PVP, PVPVA, HPMC; not with HPMCAS, EUDSsaboo2020a R22, R19
saboo2020IND–PVPVA 25%FTIR, EDX (tablets), nanoTA (films)25 → ≈40–50 → ≈60–72 wt% at 0, 5, 20 minsaboo2020 R17, R21, R28
saboo2020IND–PVPVA 10, 15, 25%SEM after 5 minsmooth at 10%; rough, porous at 15, 25%saboo2020 R19
saboo2021felodipine 30% with 0–10% TPGSmicro-CT after 10 minporous layer at 0, 2%; homogeneous at 5, 10%saboo2021 R19
hiew2022blumefantrine benzoate 30%SEM 0–90 minlarge pits, rough surfacehiew2022b R17
yang2022aritonavir–PVPVA 10–50%confocal surfaces and cross-sections, 5–30 mindiscrete droplets at 10–25%; continuous drug-rich layer 5–10 µm (30%), ≈12 µm (40%)yang2022a R4, R5, R6
yang2022asamegel–glass front at 20 min≈100% of thickness (0–20%) against ≈29 and 17% (30, 40%)yang2022a R8
yang2022aritonavir–PVPVA 40%XPS, 0 and 30 min35 → 72 wt% drugyang2022a R14
deac2023bPHPH 5, 15, 50%; MePHPH 30, 50%ATR-FTIR of dried surfaces, 0–60 minconstant at 5% PHPH, 30% MePHPH; 13.5 → 21% and 44 → 90–101% above the limitdeac2023b R6, R7
deac2023aMePHPH 30–50%, PHPH 5–20%confocal surfaces after 2–20 minuniform; patchy; porous continuous drug-rich phase (50% MePHPH, 20% PHPH)deac2023a R9, R10
hiew2022a (Miscibility)lumefantrine–PVPVA 40–50%; 25%ATR after 2 h; XPSdrug-rich, polymer-depleted; ≈27 → ≈65% drug carbon (PVPVA)hiew2022a R18, R21, C23
moseson2022b (ASD process)bicalutamide–PVPVA 30%SEM-EDX cross-section, 1 hboundary layer 94 ± 8 µm, F/F0 1.41 ± 0.10moseson2022b R15

Figure

Fig. 8 of saboo2019: SEM of dissolving compact surfaces after 10 min either side of the switch
Fig. 8 · saboo2019SEM of dissolving compact surfaces after 10 min either side of the switch

Smooth surfaces below the switch (a, c) against pits with raised rims above it (b, d); note the different scale bars (10, 20, 1 and 1 µm) saboo2019 R14.

Fig. 7 of que2019: surface ledipasvir content by XPS before and after 10 min of dissolution
Fig. 7 · que2019surface ledipasvir content by XPS before and after 10 min of dissolution

Both compacts start near their nominal loading and end far above it que2019 R15.

Why

In incongruent release the polymer leaves faster, so the interface "must" become enriched in drug; the porous structure is "consistent with" polymer loss and the pits "most likely" arise from faster polymer than drug release saboo2019 C38, C21, C22. The authors trace the pits to rapid phase separation at the interface followed by dissolution of the polymer-rich regions ("can likely be attributed"), and compare the drug-rich rims with the drug-rich rings of humidified films ("remarkably similar"; see F8) saboo2019 C39, C40. For ritonavir they add that drug molecules "can" move laterally and that drug-rich nanodomains "can" coalesce into contiguous regions, ritonavir being a supercooled liquid at 37 °C (wet Tg ~0 °C) indulkar2019a C28, C40, M1. For ledipasvir the drug-rich layer makes dissolution drug-controlled, "too slow to detect" for this drug, and "it appears" to stop release of drug and even of soluble PVPVA, leading to swelling que2019 C31, C32, C36. For felodipine the surface enrichment is "a physical barrier to polymer release from subsurface layers" saboo2020a C42. An alternative reading of the felodipine data is that preferential polymer dissolution alone gives a porous, drug-rich surface whether or not phase separation precedes it saboo2020a X6. In the ASD dissolution chapter such a layer had been proposed for 50:50 felodipine–HPMC but not observed alonzo2011 C46. For IND the authors find the agreement of three methods with different probe depths "compelling evidence" of enrichment, take the absence of the acid-dimer band to mean that some hydrogen-bonded polymer remains, and favour phase separation over plain polymer loss because the surface roughened over about 500 nm, a length not measured saboo2020 C44, C22, C42, X14. Yang and co-workers (2022) read the stalled gel–glass front as water ingress "significantly retarded" by the hydrophobic drug-rich layer, which "effectively acts as a barrier" to water, and "may serve" as a physical barrier to polymer release even where water gets in, which they say explains why poor drug release often comes with poor polymer release yang2022a C30, C55. They attribute the surface enrichment to preferential polymer release and the persistence of the layer to a medium saturated at the amorphous solubility, which was not measured yang2022a C40, C53, X11. For the phenolphthalein analogues the surface layer in contact with nearly pure water takes the composition of the dilute drug-rich phase, a "pseudo-equilibrium", while deeper layers do not; the layer of the polymer-binding PHPH therefore holds much polymer (F27) deac2023b C61, C59, C4.

Conditions and limits

Surfaces were examined after 2–15 min (micro-CT of nilvadipine to 30 min) and at one loading above the switch for most systems; SEM and micro-CT samples were dried before imaging saboo2019 A5; indulkar2019a X11; que2019 X22. The 15:85 nilvadipine surface started polymer-rich (2% drug by XPS against 15% nominal) saboo2019 X13. Below 20% ledipasvir the N 1s signal of the drug could not be separated from the polymer's, and there is no XPS at 7.5%, the first failing loading que2019 R15, X21. The low-loading ritonavir surface was examined at 5 min only, while its release continued to ≈40 min indulkar2019a X9. The 2022 ritonavir images are of compacts removed from the medium and air-dried, and the front position is a proxy for water entry; water content was not measured yang2022a P5, C28. The 2023 surface values carry calibration offsets, come from dried compacts, and the MePHPH values near 90–101% lie beyond the highest standard deac2023b X8, X17.

Counterexamples and conflicts

The barrier did not suppress polymer release in every polymer: from felodipine compacts PVP release about halved and HPMC release did not fall across the switch saboo2020a X15. The 20% ritonavir surface showed round features of ≈0.5–3 µm at 5 min that the text does not discuss indulkar2019a X10. Polymer still left the 40% ritonavir compact in the release test (about 14% in 90 min) although no polymer dye was seen beyond its drug-rich layer in real-time images yang2022a R2, R13, X8.

Transfer check

For a candidate loading, eject compacts after 5 and 10 min and compare the surface with the dry compact by ATR-IR or XPS, using an element that only the drug carries (Cl, F, or the N/O ratio) for EDX indulkar2019a P7; que2019 P7; saboo2019 E2; saboo2020a P9. A surface that gains drug within minutes and turns porous marks the drug-controlled side of the switch; an unchanged surface the congruent side saboo2019 R18; saboo2020a R22.

History

A drug-rich layer at the dissolving surface was proposed for sulfathiazole–PVP (Simonelli 1969, cited) and for 50:50 felodipine dispersions in the ASD dissolution chapter purohit2017b R23; alonzo2011 C46. Purohit and Taylor (2017) first imaged a porous surface on high-loading films after 10 s in buffer purohit2017b R9; Indulkar and co-workers (2019) recorded the drug-rich tablet surface by IR indulkar2019a C41; Saboo and co-workers (2019) and Que and co-workers (2019) quantified it by XPS and EDX saboo2019 C25; que2019 C17; and Saboo and co-workers (2020) showed its absence with HPMCAS and EUDS saboo2020a C22. Later studies outside the subcategory measured the same enrichment for lumefantrine and bicalutamide hiew2022a C67; moseson2022b C39. Saboo and co-workers (2020) followed the time course of enrichment by three methods, and Saboo and co-workers (2021) showed the porous layer forming only where release was incongruent saboo2020 C44; saboo2021 C22. Yang and co-workers (2022) imaged the layer in cross-sections of dissolving compacts and showed that it slows the advance of water yang2022a C21, C30. Deac and co-workers (2023) found the layer's composition to approach that of the drug-rich phase the drug forms in water, polymer-rich for a hydrogen-bonding drug deac2023b C59, C4.

Other chaptersexplains B F10
F8

Topic 3Limit of congruency and its causes3 of 13

Wetted films phase-separated above the limit of congruency and not below it; that separation outpaces dissolution is proposed, not measured.

After a brief dip in water, ritonavir–PVPVA films stayed uniform at 20% and showed drug-rich domains at 30 and 40%, against a limit of 25% in tablets indulkar2019a R18, C2. Felodipine films at 30% separated at 97% RH with PVP, PVPVA and HPMC but stayed uniform with HPMCAS and EUDS, the two polymers without a limit up to 50% saboo2020a R23, R15. In dissolving compacts imaged in 2022–2023, separation appeared below the limit as well, as discrete droplets yang2022a R4, R6, R10; deac2023a R6, C46.

moderateModerate for the co-occurrence of phase separation and the limit; weak to moderate for the race as the cause, since no rate of separation or of dissolution was measured on the same compact purohit2017b K1, K2; que2019 K3; indulkar2019a K5, X6; saboo2019 K6, X10; saboo2020a K4.

film uniform after waterfilm phase-separatedritonavirdipped in waterlimit 25203040ledipasvir3 days at 100% RH5limit 5–7.51050clopidogrel5 min at 100% RHlimit ≈40405060atazanavir3 h at 100% RH, 37 °C10, uniform although release fails0102030405060drug loading in PVPVA, %

Film separation lies within or just above the release bracket; high-Tg atazanavir failed without visible separation. indulkar2019a R18, C2; que2019 R14, C10; correasoto2022a R20, C46; correasoto2022b R9, R1

For your drug

  1. Cast films at the target loading and one step above and below, dip them in the medium for seconds and expose them to 97–100% RH, then image with a drug-rich probe (nile red or prodan).
  2. Read separation at the target loading, especially within seconds, as a prediction of incongruent release; uniform films are consistent with congruent release but do not prove it.

indulkar2019a P9, X6; saboo2020a P10

How it works and key numbers
  1. The Flory–Huggins free energy of mixing of water, drug and polymer contains \chi_{WD} and \chi_{WP}; a hydrophobic drug interacts unfavourably with water and the polymer favourably, and a large \Delta\chi = |\chi_{WD} - \chi_{WP}| drives separation, "a classic case of solvent-induced immiscibility" purohit2017b E2, E4, C43, C44.
  2. All five papers then propose a race: if the hydrating surface dissolves faster than it separates, drug and polymer leave together; if it separates first, the polymer-rich domains dissolve and leave a drug-rich surface purohit2017b C5; indulkar2019a C10, C30; que2019 C35; saboo2019 C42; saboo2020a C41.
  3. Higher loadings, closer to the miscibility limit, "can be expected" to separate more readily and faster indulkar2019a C30; saboo2020a C42.
  4. Humidity that turned a congruent compact incongruent is taken as "further evidence": the conditioned 10:90 nilvadipine compact released ≈0.34% of its drug in 15 min against ≈15% for the control saboo2019 R9, C41.
  5. For the high-Tg forms the failure is placed in low mobility instead: a glassy matrix hydrates and disentangles slowly, and a high-Tg salt cannot separate from the hydrated polymer (F18, F22) correasoto2022b C37; hiew2022b C47.
  6. In dissolving compacts the separation sits in the gel next to the solution, where the water content is highest; below the limit it formed droplets and from 30% ritonavir a continuous layer, so at the limit the shape of the separated phase changed, not its presence (F25) yang2022a C44, R4, R6, C58.
20 against 30–40%ritonavir films uniform against phase-separated after a dip in water; tablet limit 25%indulkar2019a R18, C2
14.0 → 24.5%water needed to separate 30% ritonavir films, without and with SDSyang2023 R21
below 15 wt%water that separated MePHPH–PVPVA films at every loading of 10–50%deac2024b R1, R2
Evidence: data, conditions and papers

Finding F8. Water-induced amorphous–amorphous phase separation appeared in films and humidified compacts above the limit of congruency and not below it, except for two high-Tg drug forms that failed without visible separation; the authors explain the switch as phase separation outpacing dissolution at the hydrating surface, a race that none of the papers measured; in dissolving compacts imaged in 2022–2023 it appeared below the limit as well, as discrete droplets (F25)

In short. After a brief dip in water, ritonavir–PVPVA films stayed uniform at 20% and showed drug-rich domains at 30 and 40%, against a limit of 25% in tablets indulkar2019a R18, C2. Ledipasvir–PVPVA films held 3 days at 100% RH were mostly homogeneous at 5%, had small domains at 10% and large ones (≈10–20 µm) at 50%, against a limit of 5–7.5% que2019 R14, C10. Felodipine films at 30% separated after 24 h at 97% RH with PVP, PVPVA and HPMC but stayed uniform with HPMCAS and EUDS, the two polymers without a limit up to 50% saboo2020a R23, R15. In buffer 50:50 ritonavir films with PVP or PVPVA separated within 10 s while 10:90 and HPMCAS films did not purohit2017b R4, R9. Each paper proposes a competition between phase separation and dissolution, but phase separation was never imaged in a dissolving compact and no rate of either process was measured purohit2017b C5; saboo2019 C42, X10; indulkar2019a X6. Clopidogrel films stayed uniform at 40% and separated at 50 and 60%, matching a limit of about 40%, but a 10% atazanavir film stayed uniform for 3 h although that loading failed, and the sulfate salt of lumefantrine did not separate yet released only at 2% (F20) correasoto2022a R20, C46; correasoto2022b R9, R1; hiew2022b R19, R20. In 2022 water-induced separation was imaged in dissolving ritonavir–PVPVA compacts for the first time in the library, as droplets at the gel–solution interface at 10–20% and as a continuous drug-rich layer from 30% (F25) yang2022a R4, R6, R10, R12, R13. In 2023–2024 less than 15 wt% water separated MePHPH–PVPVA films at every loading of 10–50%, SDS raised the water needed to separate 30% ritonavir films from 14.0 to 24.5%, and clotrimazole films with short- and long-chain PVP separated alike, so the limit follows the amount and shape of the separated phase rather than whether separation occurs (F30, F31, F29) deac2024b R1, R2; yang2023 R21; deac2024a R7, R8.

Type. observation in 5 drugs (ritonavir, ledipasvir, nilvadipine, felodipine, with PVP, PVPVA, HPMC, HPMCAS and EUDS) and 3 further drugs in 2021–2022 (clopidogrel, atazanavir, lumefantrine), and dissolving compacts of ritonavir and two phenolphthalein analogues in 2022–2023, with a proposed mechanism Strength. for the co-occurrence of phase separation and the limit purohit2017b K1: strong, K2: moderate; que2019 K3: moderate; weak to moderate for the race as the cause indulkar2019a K5: weak to moderate; saboo2019 K6: weak to moderate; saboo2020a K4: weak to moderate.

How it was shown

Films with a drug-rich probe were dipped in water or buffer for seconds or held at 97–100% RH for hours to days, then imaged by confocal microscopy purohit2017b P8, P13; indulkar2019a P9, P10; que2019 P6; saboo2020a P10.

What the data show

A 10:90 nilvadipine compact conditioned at 97% RH released ≈0.34% of its drug and ≈2.6% of its PVPVA in 15 min against ≈15% of both for the control saboo2019 R9, R19.

systemconditionsresultids
ritonavir–PVPVA filmsseconds in wateruniform at 20%; domains at 30, 40% (LoC 25%)indulkar2019a R18
ledipasvir–PVPVA films3 days, 100% RH, 37 °C5% mostly uniform; 10, 50% domains (LoC 5%)que2019 R14
felodipine 30% films, five polymers24 h, 97% RHdomains with PVP, PVPVA, HPMC; uniform with HPMCAS, EUDSsaboo2020a R23
clopidogrel–PVPVA films 40, 50, 60%5 min, 100% RHuniform; bicontinuous; drug-continuous (limit about 40%)correasoto2022a R20, C46
atazanavir–PVPVA 10% film3 h, 100% RH, 37 °Cuniform although the 10% dispersion failscorreasoto2022b R9, R1
ritonavir–PVPVA 10–50% compactsconfocal during and after dissolutionseparation at every loading; droplets at 10–25%, continuous layer from 30%yang2022a R4, R6, R10, R13
Fig. 7 of indulkar2019a: nile red films of ritonavir–PVPVA before and after dipping in water
Fig. 7 · indulkar2019anile red films of ritonavir–PVPVA before and after dipping in water

All films are uniform before water; afterwards the 20% film stays uniform while the 30% and 40% films show bright drug-rich spots, more at 40% indulkar2019a R18.

Why

A hydrophobic drug interacts unfavourably with water (large \chi_{WD}) and the polymer favourably (small \chi_{WP}), and a large \Delta\chi drives separation, "a classic case of solvent-induced immiscibility" purohit2017b E4, C43, C44. All five papers then propose a race: if the hydrating surface dissolves faster than it separates, drug and polymer leave together; if it separates first, the polymer-rich domains dissolve and leave a drug-rich surface purohit2017b C5; indulkar2019a C10, C30; que2019 C35; saboo2019 C42; saboo2020a C41. For high-Tg forms the atazanavir and lumefantrine papers place the failure in low mobility instead correasoto2022b C37; hiew2022b C47.

Limits and transfer

No rate of separation was measured, also not in the dissolving compacts imaged from 2022 saboo2019 X10; indulkar2019a X6; yang2022a P7, C31. MePHPH gels separated at 5–30%, below the limit, into discrete droplets deac2023a R6, C46. Image films at the target loading and one step either side after dipping and at 97–100% RH: separation predicts incongruent release, while uniform films do not prove congruent release indulkar2019a P9, X6; saboo2020a P10.

How it was shown

Purohit and Taylor (2017) followed ritonavir films at 97% RH by the pyrene I/III ratio (0–96 h), confocal microscopy with nile red, AFM after 4 days and DSC of powders after 24 h and drying, and dipped films in buffer for 10 s before confocal imaging and SEM purohit2017b P7, P8, P9, P10, P11, P13. Indulkar and co-workers (2019) dipped nile red films at 10–50% (20, 30 and 40% shown) in water for a few seconds and checked them under polarized light indulkar2019a P9, P10. Que and co-workers (2019) held nile red films at 5, 10 and 50% at 100% RH and 37 °C for 3 days que2019 P6. Saboo and co-workers (2019) held a 10:90 nilvadipine compact in its die and a matching film with prodan and rhodamine 6G at 97% RH for 12 h, then dissolved the compact for 15 min and imaged the film saboo2019 P13, P18. Saboo and co-workers (2020) held 30% felodipine films with prodan at 97% RH for 24 h saboo2020a P10.

What the data show

Ritonavir: at 97% RH the pyrene ratio of 50:50 PVP fell from ≈1.50 to ≈1.30 within 1 h and every 20–50% PVP and PVPVA film fell to ≈1.25–1.35 by 72–96 h, near pure amorphous ritonavir (≈1.27–1.30), while 10:90 films fell slowly (to ≈1.35 PVP and ≈1.45 PVPVA at 96 h) and HPMCAS films stayed at ≈1.39–1.47 purohit2017b R2, X9. Confocal images showed drug-rich domains in PVP and PVPVA films and uniform HPMCAS films; AFM showed 5–10 µm domains on 10:90 PVP and PVPVA; DSC showed a ritonavir-rich step at ≈47–50 °C in every PVP and PVPVA powder and one step (≈63–97 °C) for HPMCAS purohit2017b R3, R5, R6. After 10 s in buffer, 50:50 PVP showed 1–3 µm dark domains in a bright drug-rich continuous phase and SEM showed porous and granular surfaces on 50:50 PVP and PVPVA, while 10:90 films and both HPMCAS films stayed uniform; 50% ritonavir–PVP and –PVPVA dispersions had separated within 10 s of water contact in earlier work purohit2017b R4, R9, R20. Ritonavir–PVPVA films dipped in water: 20% uniform, 30% sparse bright spots of a few µm, 40% dense spots, none birefringent indulkar2019a R18, R19. Ledipasvir films after 3 days: as in the short part que2019 R14. Felodipine films: discrete prodan-rich domains for PVP, PVPVA and HPMC, uniform HPMCAS and EUDS at two magnifications saboo2020a R23. Humidity also changed release: the conditioned 10:90 nilvadipine compact released ≈0.34% of its drug and ≈2.6% of its PVPVA in 15 min against ≈15% of both for the control, and its film showed drug-rich circles and rings of roughly 5–15 µm in a continuous polymer-rich phase (see F12) saboo2019 R9, R19. Clopidogrel films after 5 min at 100% RH: uniform at 40%, bicontinuous at 50%, drug-continuous at 60% correasoto2022a R20. Felodipine films at 30% with 0–10% TPGS all separated after 12 h, with different morphology (F20) saboo2021 R21. The binary 10% atazanavir film showed no separation for 3 h at 37 °C and separated within 10 min at 50 °C correasoto2022b R9, R12. Lumefantrine free-base and benzoate films separated, the sulfate film did not hiew2022b R19. In dissolving ritonavir–PVPVA compacts imaged in 2022, phase separation appeared at every loading from 10 to 50% at the gel–solution interface; its shape changed with loading, discrete droplets at 10–25% and a continuous drug-rich layer from 30% (F25) yang2022a R4, R6, R10, R11, R12, R13. In 2023 dissolving MePHPH–PVPVA gels separated at every loading imaged (5–50%), segregatively, and PHPH gels associatively, with both dyes in the drug-rich phase (F25, F27) deac2023a R6, R7, C25, C28. MePHPH–PVPVA films at 10–50% stayed clear at 62 and 75% RH and separated from 80% RH, where matching powders held 9.6–14.6 wt% water deac2024b R1, R2. Ritonavir–PVPVA 30% films separated at 84% RH and 14.0% water, with SDS at 92% and 24.5%, and with Span 20 or Tween 80 already at 75% and 10.5–12.5% yang2023 R21. Clotrimazole films with PVP K12 or K29/32 at 10% separated into droplets within 3 h at 100% RH deac2024a R7.

papersystemmethod and conditionsresultids
purohit2017britonavir films, PVP, PVPVA, HPMCAS97% RH, pyrene, confocal, AFM, DSCPVP and PVPVA separated at every loading (10% slowly); HPMCAS notpurohit2017b R2, R3, R5, R6
purohit2017britonavir 10:90 and 50:50 films10 s in buffer50:50 PVP and PVPVA separated; 10:90 and HPMCAS uniformpurohit2017b R4, R9
indulkar2019aritonavir–PVPVA filmsseconds in wateruniform at 20%; domains at 30, 40% (LoC 25%)indulkar2019a R18
que2019ledipasvir–PVPVA films3 days, 100% RH, 37 °C5% mostly uniform; 10, 50% domains (LoC 5%)que2019 R14
saboo2019nilvadipine–PVPVA 10:90 film and compact12 h, 97% RHrings and circles; release incongruentsaboo2019 R19, R9
saboo2020afelodipine 30% films, five polymers24 h, 97% RHdomains with PVP, PVPVA, HPMC; uniform with HPMCAS, EUDSsaboo2020a R23
correasoto2022aCPD–PVPVA films 40, 50, 60%5 min, 100% RHuniform; bicontinuous; drug-continuous (limit about 40%)correasoto2022a R20, C46
correasoto2022bATZ–PVPVA 10% film3 h, 100% RH, 37 °Cuniform although the 10% dispersion failscorreasoto2022b R9, R1
hiew2022blumefantrine sulfate filmhigh RH, 37 °Chomogeneous; limit 2%hiew2022b R19, R20
yang2022aritonavir–PVPVA 10–50% compactsconfocal during and after dissolutionseparation at every loading; droplets at 10–25%, continuous layer from 30%yang2022a R4, R6, R10, R13
rumondor2010c (Physical stability)felodipine, quinidine with PVP, PVPVA, HPMCASmoistureseparation PVP > PVPVA > HPMCAS, following hygroscopicityrumondor2010c C38
marsac2010 (Physical stability)felodipine–PVPwater–drug and water–polymer χ≈3.3 against ≈0.5; large Δχmarsac2010 C43
deac2024bMePHPH–PVPVA films 10–50%62–97% RH, 37 °Cclear to 75% RH, domains from 80% RH (<15 wt% water)deac2024b R1, R2
yang2023ritonavir–PVPVA 30% films ± 10 parts surfactantRH steps, 12 hwater for separation 14.0% (none), 24.5% (SDS), 10.5–16.0% (others)yang2023 R21
deac2024aclotrimazole–PVP K12, K29/32 10% films100% RH, 3 hdroplets in a continuous water-rich phase for bothdeac2024a R7

Figure

Fig. 7 of indulkar2019a: nile red films of ritonavir–PVPVA before and after dipping in water
Fig. 7 · indulkar2019anile red films of ritonavir–PVPVA before and after dipping in water

All films are uniform before water; afterwards the 20% film stays uniform while the 30% and 40% films show bright drug-rich spots, more at 40% indulkar2019a R18.

Fig. 4 of purohit2017b: ritonavir–PVP films after 10 s in buffer
Fig. 4 · purohit2017britonavir–PVP films after 10 s in buffer

The 10:90 film (a) is uniform; the 50:50 film (b) has split into dark domains in a bright drug-rich phase purohit2017b R4.

Why

The thermodynamic argument is the Flory–Huggins free energy of mixing of water, drug and polymer,

\frac{\Delta G_{mix}}{RT} = n_w \ln\phi_w + n_D \ln\phi_D + n_p \ln\phi_p + n_w \phi_D \chi_{WD} + n_w \phi_p \chi_{WP} + n_D \phi_p \chi_{DP}

purohit2017b E2, in which a hydrophobic drug interacts unfavourably with water (large \chi_{WD}) and the polymer favourably (small \chi_{WP}); a large \Delta\chi = |\chi_{WD} - \chi_{WP}| drives separation, which the authors call "a classic case of solvent-induced immiscibility" purohit2017b E4, C43, C44. They expect PVP and PVPVA, more hygroscopic and with acceptors only, to separate more readily than HPMCAS ("can be expected") purohit2017b C45, C46. All five papers then propose a race: if the hydrating surface dissolves faster than it separates, drug and polymer leave together; if it separates first, the polymer-rich domains dissolve and leave a drug-rich surface purohit2017b C5; indulkar2019a C10, C30; que2019 C35; saboo2019 C42; saboo2020a C41. Higher loadings "can be expected" to separate more readily and faster, being closer to the miscibility limit, and at low loading there may be too little drug for a barrier indulkar2019a C30; saboo2020a C42. Humidity that converts a congruent compact into an incongruent one is "further evidence" for this role of matrix phase separation saboo2019 C41. Saboo and co-workers (2020) add that the water absorbed matters, so the low uptake of HPMCAS and EUDS "conceivably" keeps them below the separation threshold (F11) saboo2020a C44. Outside the subcategory moisture-induced separation followed polymer hygroscopicity for felodipine and quinidine, and felodipine–PVP has a large Δχ (χ about 3.3 against 0.5) rumondor2010c C38, C31; marsac2010 C43. (synthesis: in four drug–polymer pairs the loading at which films separate on wetting lies within or just above the release bracket, which is the main support for the race; neither the time to separate nor the time to dissolve was measured on the same compact, so the race remains an inference.) Saboo and co-workers (2020) and Yang and co-workers (2021) keep the race for IND and for the cliff in general ("would be expected"; "It has been suggested") saboo2020 C40, C41; yang2021 C17, Yang and co-workers explain the tendency to separate by the Δχ effect rather than log P yang2021 C21, E2, and Correa Soto and co-workers write that at high loading "AAPS is proposed to occur rapidly" correasoto2022a C53. For high-Tg forms the atazanavir and lumefantrine papers place the failure in low mobility instead: a glassy matrix hydrates and disentangles slowly, and a high-Tg salt cannot separate from the hydrated polymer (F18, F22) correasoto2022b C37; hiew2022b C47. Indulkar and co-workers (2022) restate the race for ritonavir with a third process: dissolution, water-induced separation and crystallization are concurrent kinetic processes, and separation is "inevitable" for hydrophobic drugs in PVPVA at high loading, so a dispersion has to release faster than it separates and crystallizes, or resist both indulkar2022 C23, C24, C25. Yang and co-workers (2022) place the separation in the gel layer, whose water content is highest next to the solution, so that separation is "favored" there yang2022a C44. (synthesis: the measured diagrams of 2024 put most of the MePHPH gel-layer compositions inside the miscibility gap, so separation occurs below the limit as well, as the compact images of 2022–2023 showed (F25, F30) deac2024b R28, C37.)

Conditions and limits

Phase separation was tested on spin-coated or cast films and on compacts held at 97–100% RH for 12 h to 4 days, or dipped in water for seconds and then dried, never on a compact during dissolution saboo2019 X10; indulkar2019a X6; que2019 X17. Films were imaged at 20, 30 and 40% (ritonavir), 5, 10 and 50% (ledipasvir) and 30% (felodipine), so the separation was not followed across each bracket indulkar2019a X6; que2019 K3; saboo2020a X5. Confocal resolution was about 300 nm purohit2017b P9. From 2022 separation was also imaged in dissolving ritonavir compacts, after removal from the medium and in real time with edge wetting, but still without a rate of separation yang2022a P5, P7, C31.

Counterexamples and conflicts

A cited study found that water-induced phase separation did not change the dissolution of a 40% dispersion, which the authors explain by that dispersion being drug-controlled already or by different test conditions saboo2019 R22, C44. Outside the subcategory phase separation raised release of lopinavir–HPMC films at 33–85% loading, where polymer-rich phases dissolve first (F12) li2019 C38. A drug-rich porous surface also follows from faster polymer dissolution alone, so the surface data do not prove the separation saboo2020a X6. Water uptake of the neat polymers does not rank the limits within the hydrophilic group: HPMC takes up less water than PVPVA yet has the lower limit saboo2020a X7. The binary 10% atazanavir film and the lumefantrine sulfate film failed without visible separation, while atazanavir films with surfactants separated within 10 min and released correasoto2022b R9, R10, R11, R2; hiew2022b R19. Since separation appeared at the gel–solution interface of ritonavir compacts below the limit as well (droplets at 10–25%), it is the shape of the separated phase, not its presence, that changed at the limit in that system (F20, F25) yang2022a R4, R6, C58. MePHPH gels separated at 5–30%, below the limit, into discrete droplets, so separation alone does not mark the limit there either deac2023a R6, C46.

Transfer check

Cast films of the drug–polymer pair at the target loading and one step above and below, dip them in the dissolution medium for seconds and expose them to 97–100% RH, then image with a drug-rich probe (nile red or prodan) indulkar2019a P9; saboo2020a P10. Separation at the target loading, especially within seconds, predicts incongruent release; uniform films are consistent with congruent release but do not prove it, because the race has not been measured indulkar2019a X6.

History

Moisture-induced AAPS was established for PVP dispersions in storage work of the library (Rumondor 2009, 2010, 2011, cited), and 50% ritonavir dispersions in PVP or PVPVA were known to separate within 10 s of water contact (Purohit 2015) purohit2017b C9, R20; que2019 C34; saboo2020a C39. Purohit and Taylor (2017) first linked such separation to the loss of LLPS on dissolution purohit2017b C53. Indulkar and co-workers (2019), Que and co-workers (2019) and Saboo and co-workers (2019) placed the film separation against the limit of congruency and proposed the race indulkar2019a C9; que2019 C35; saboo2019 C42; Saboo and co-workers (2020) added the polymer contrast and named water-induced AAPS "likely" the cause of the limit saboo2020a C43. Correa Soto and co-workers (2022) matched film separation with the clopidogrel limit, and the atazanavir and lumefantrine studies of 2022 found failure without visible separation for high-Tg forms, which adds the exception to the title (F20) correasoto2022a C52; correasoto2022b C18; hiew2022b C48. Yang and co-workers (2022) were the first to image the separation in dissolving compacts, and found it below the limit too, which qualifies "above the limit and not below it" of the title for that system yang2022a C5, C45; the last clause of the title was added for this reason. Deac and co-workers (2024) measured the water at which separation starts and the compositions of the separated phases, and Yang and co-workers (2023) the shift of that water by surfactants (F30, F31) deac2024b C13; yang2023 C9.

Other chapterssame mechanism C F1
F9

Topic 3Limit of congruency and its causes4 of 13

Drug log P and molecular weight did not set the limit of congruency in PVPVA.

Nilvadipine (ClogP 3.04) switched between 10 and 15% and cilnidipine (ClogP 5.54) between 15 and 20%, about 6–9 and 7–9 mol%; the authors found their hypothesis that the more lipophilic drug switches earlier "incorrect for the systems evaluated" saboo2019 R7, M1, M2, C6, C35. Ledipasvir (MW 889, Tg 160.9 °C) had a limit of 5–7.5% against 25% for ritonavir (log P 4.3, Tg 50 °C) que2019 M1, R27, R28, C48. Later papers found no log P trend among four phenolphthalein analogues or across six further drugs que2021 C29; yang2021 C19.

moderateModerate: the log P test rests on two analogues in 5% steps whose hydrogen bonding with PVPVA was assumed similar, the Tg idea is an untested observation, and the HPMCAS series is one polymer at one loading saboo2019 K4, X2, X11; que2019 C49; saboo2020a K6, X13.

nilvadipineClogP 3.0410–15ritonavirlog P 4.325cilnidipineClogP 5.5415–20miconazolelog P 5.69 · powdersdrop at 40ledipasvirlog P 3.8 or 6.8 · MW 8895–7.5lumefantrinelog P 8.34good release to 35051015202530354045limit of congruency or drop-off loading in PVPVA, %

Rows in order of rising log P (ledipasvir's is unresolved); the limits do not follow it. saboo2019 R7, M1, M2; que2019 R28, M1, X1, C10; yang2021 M2, R8; hiew2022b M1, R20

Congruent release at 40% in HPMCAS-MF, mg/min/cm²nilvadipinelog P 4.060.42felodipinelog P 4.460.34cilnidipinelog P 5.400.26

In HPMCAS at high loading release fell as log P rose; all pairs differed. saboo2020a R16, R17, C19

For your drug

  1. Do not estimate the limit of a new drug in PVPVA from its log P, molecular weight or amorphous solubility; dissolve a loading series instead.
  2. Record the dry and, if possible, the wet Tg of the drug against 37 °C.
  3. For HPMCAS at 40% and above, expect slower congruent release for more lipophilic drugs.

saboo2019 C35; que2019 C48, C49; saboo2020a R16

How it works and key numbers
  1. The original hypothesis was that a more lipophilic drug lowers the hydrophilicity of the blend faster and so loses congruent release at a lower loading saboo2019 C6.
  2. Having rejected it, the authors state that several drug and polymer properties are "likely" to set the switch and that the causes "are not well understood" saboo2019 C34, C45.
  3. Que and co-workers offer the glass transition as "One interesting difference": ritonavir, with a wet Tg near 0 °C, is a supercooled liquid at 37 °C, ledipasvir a glass (tested from 2020, F18) que2019 C48, C49.
  4. Yang and co-workers (2021) explain why log P fails by the Δχ effect, hygroscopicity and drug–polymer interactions yang2021 C21, C22, C42.
  5. In congruent HPMCAS dispersions at high loading the authors read the log P series as support for the "supposition" that drug hydrophobicity slows release once the drug dominates the hydrophobicity of the system saboo2020a C32, C33.
  6. In HPMCAS-MF in 2024 the charge of a weak base at the gel pH, not its log P, ordered the loss of release with loading (F32) bapat2024 C26, X18.
ClogP 3.04 against 5.54nilvadipine and cilnidipine, which switched at about 6–9 and 7–9 mol%saboo2019 R7, M1, M2
5–7.5% against 25%limit of ledipasvir (Tg 160.9 °C) against ritonavir (Tg 50 °C)que2019 R27, R28, M1
0.42 → 0.26 mg/min/cm²congruent release at 40% in HPMCAS as log P rose from 4.06 to 5.40saboo2020a R16, R17
Evidence: data, conditions and papers

Finding F9. Drug log P and molecular weight did not set the limit of congruency in PVPVA: two dihydropyridines 2.5 log units apart switched at about the same molar loading, and two lipophilic, high-molecular-weight drugs at 5 and 25%; the authors point instead to the drug's glass transition against the test temperature, tested only from 2020 (F18), and at 40% in HPMCAS release fell with log P

In short. Nilvadipine (ClogP 3.04) switched between 10 and 15% and cilnidipine (ClogP 5.54) between 15 and 20% w/w, about 6–9 and 7–9 mol%, so the authors found their hypothesis that the more lipophilic drug switches earlier "incorrect for the systems evaluated" saboo2019 R7, M1, M2, C6, C35. Ledipasvir (MW 889, Tg 160.9 °C) had a limit of 5–7.5% against 25% for ritonavir (log P 4.3, Tg 50 °C, wet Tg about 0 °C); the authors conclude that the limit "does not appear to depend" on hydrophobicity or molecular weight and note that under the test conditions ritonavir is a supercooled liquid and ledipasvir a glass que2019 M1, R27, R28, C48, C49. In HPMCAS at 40% loading, where release stayed congruent, drug and polymer rates fell from 0.42 (nilvadipine, log P 4.06) through 0.34 (felodipine, 4.46) to 0.26 mg/min/cm² (cilnidipine, 5.40), all pairs different saboo2020a R16, R17, C19. The papers of 2021–2022 found no log P, amorphous-solubility, Tg or molecular-weight trend among four phenolphthalein analogues and no log P trend across six drugs, and lumefantrine (log P 8.34) reached 35% que2021 C29; yang2021 C19; hiew2022b M1, R20. In HPMCAS-MF in 2024 drugs of log P 4.1–5.9 lost release with loading according to their charge at the gel pH rather than their log P, ritonavir (log P 5.7) far less than loratadine (4.55) (F32) bapat2024 C26, X18, R2.

Type. observation in 6 drugs (nilvadipine, cilnidipine, ledipasvir, ritonavir, felodipine, itraconazole), and 11 further drugs in 2021–2022 Strength. : the log P test rests on two analogues in 5% steps whose hydrogen bonding with PVPVA was assumed similar, and on a molar conversion that cannot be reproduced with one convention saboo2019 K4: moderate, X2, X11; the Tg idea is an untested observation que2019 C49; the HPMCAS series is one polymer at one loading saboo2020a K6: moderate, X13.

How it was shown

Saboo and co-workers (2019) dissolved PVPVA dispersions of two 1,4-dihydropyridines 2.5 units of calculated log P apart in 5% steps, and Que and co-workers (2019) chose ledipasvir as a contrast for its molecular weight, lipophilicity and very high Tg saboo2019 C7, A1; que2019 C7. Saboo and co-workers (2020) compared three drugs at 40% in HPMCAS-MF saboo2020a A3.

What the data show

Across the two possible molar conventions the switch ranges of nilvadipine and cilnidipine become about 5.4–9.0 and 6.6–10.0 mol%, still overlapping saboo2019 X2.

systemmethodresultids
nilvadipine, cilnidipine in PVPVAcompacts, 5% stepsswitch 10–15% and 15–20% w/w, about 6–9 and 7–9 mol%saboo2019 R5, R6, R7
ledipasvir against ritonavir (cited)compacts5% against 25%; Tg 160.9 against 50 °Cque2019 C10, R28, M1
nilvadipine, felodipine, cilnidipine at 40% in HPMCAScompacts, congruent0.42 → 0.34 → 0.26 mg/min/cm² with log P 4.06 → 5.40saboo2020a R16, R17
four analogues in PVPVAcompactsno trend with log P, amorphous solubility, Tg or MWque2021 C29
six drugs in PVPVA and HPMCASpowdersno log P trendyang2021 C19
HPMCAS-MF, five drugs of log P 4.1–5.9compacts, pH 6.8decline with loading ordered by charge at the gel pH, not by log Pbapat2024 R2, C26, X18
Fig. 8 of saboo2020a: drug and polymer release rates of 40% HPMCAS dispersions of three drugs of rising log P
Fig. 8 · saboo2020adrug and polymer release rates of 40% HPMCAS dispersions of three drugs of rising log P

Drug and polymer bars stay equal for each drug and fall together from nilvadipine to felodipine to cilnidipine; the dashed line is a guide for the eye saboo2020a R16.

Why

The original hypothesis was that a more lipophilic drug lowers the hydrophilicity of the blend faster and so loses congruent release at a lower loading; having rejected it, the authors state that several drug and polymer properties are "likely" to set the switch saboo2019 C6, C34. Que and co-workers offer the glass transition as "One interesting difference": ritonavir, with a wet Tg near 0 °C, is a supercooled liquid at 37 °C, ledipasvir a glass que2019 C48, C49. Yang and co-workers (2021) explain why log P fails by the Δχ effect, hygroscopicity and drug–polymer interactions yang2021 C21, C22. (synthesis: the papers give no mechanism that links Tg to the position of the limit.)

Limits and transfer

The log P test rests on two analogues whose interactions with the polymer were assumed similar, and ledipasvir's log P is unresolved between 3.8 and 6.8 saboo2019 X11; saboo2020a X13; que2019 X1. Do not estimate the limit of a new drug in PVPVA from its log P, molecular weight or amorphous solubility; dissolve a loading series instead, and record the dry and, if possible, the wet Tg of the drug against 37 °C saboo2019 C35; que2019 C48, C49.

How it was shown

Saboo and co-workers (2019) chose two 1,4-dihydropyridines of the same class that differ mainly in their ester side chains and by 2.5 units of calculated log P (ChemDraw fragment method), both non-ionizing slow crystallizers assumed to hydrogen-bond alike with PVPVA, and dissolved their PVPVA dispersions in 5% steps; loadings were also expressed in mol% with an average monomer molecular weight for the polymer saboo2019 C7, P21, A1, E1. Que and co-workers (2019) chose ledipasvir as a contrast to the low-Tg drugs studied before, with its molecular weight, lipophilicity and very high Tg, and compared its limit with cited values que2019 C7, R27, R28. Saboo and co-workers (2020) compared nilvadipine, felodipine and cilnidipine (shake-flask log P for the first and third, literature for felodipine) at 40% in HPMCAS-MF, and extrapolated the water uptake of the three dispersions to 100% RH saboo2020a A3, P13, P15, E5.

What the data show

Nilvadipine: congruent at 5 and 10% (3 and 6 mol% as printed), incongruent at 15 and 20% (9 and 13 mol%); cilnidipine: congruent at 5, 10 and 15% (2, 4, 7 mol%), incongruent at 20 and 25% (9, 12 mol%) saboo2019 R5, R6. The printed molar values cannot all be reproduced with one convention; across the two possible conventions the switch ranges become about 5.4–9.0 (nilvadipine) and 6.6–10.0 mol% (cilnidipine), still overlapping saboo2019 X2. The authors add cited cases with other log P values (itraconazole, ClogP 5.4, drop above 20%; ritonavir, ClogP 4.5, above 25%; sulfathiazole, ClogP −0.5, above 25% in PVP) as "further support", noting that the PVP case is hard to compare saboo2019 R22, C36. Ledipasvir has a molecular weight of 889 g/mol, a log P given as 6.8 in one place and 3.8 in another, and a Tg of 160.9 ± 0.8 °C; its dispersions had single Tgs of 106.7–135.5 °C que2019 M1, X1, R1. Ritonavir has log P 4.3, Tg 50 °C and a wet Tg around 0 °C (cited), and a limit of 25% in PVPVA; cilnidipine and nilvadipine have 15 and 10% (cited) que2019 R28, R27. In HPMCAS at 40% the drug rates were 0.42 ± 0.01, 0.34 ± 0.01 and 0.26 ± 0.00 and the polymer rates 0.42 ± 0.02, 0.32 ± 0.04 and 0.24 ± 0.01 mg/min/cm² for nilvadipine, felodipine and cilnidipine, with drug p < 0.0001 for each pair and polymer p = 0.0004–0.0249; the extrapolated water uptake fell slightly in the same order (≈5.83, ≈5.67, ≈5.45 wt%, overlapping error bars) saboo2020a R16, R17, R18. (synthesis: the amorphous solubility of the drugs does not rank the limits either: cilnidipine (0.6 µg/mL) switched later than nilvadipine (≈31 µg/mL), ledipasvir (below 1 µg/mL) earliest and ritonavir (about 27 µg/mL) latest saboo2019 R1; que2019 M1; purohit2017b R1; of the three drugs whose dry Tg is printed, ledipasvir, with by far the highest (160.9 °C), has the lowest limit (5%), but felodipine (46.9 °C) and ritonavir (about 45–50 °C) have similar Tgs and limits of 15 and 25% que2019 M1; saboo2020a M1, R15; purohit2017b M1; que2019 R28, so the dry Tg does not rank them either.) Four phenolphthalein analogues with calculated log P of 2.63 to 8.14 and amorphous solubilities from below 0.01 to 27.5 µg/mL had limits of 5–40% with no obvious correlation; the two iodo compounds, both below 0.01 µg/mL, reached 10 and 30% que2021 M1, M2, M3, M4, R19, C29. Miconazole, elbasvir and ivacaftor, with log P of 5.69, 5.33 and 5.68, dropped off at 40%, 10% and between 5 and 10% in PVPVA, and danazol and elbasvir (3.8 and 5.33) both at low loading yang2021 M2, M3, M4, M6, R8, R10, R12, C19. Lumefantrine free base (log P 8.34) released well to 35% hiew2022b M1, R20. Among HPMCAS-MF dispersions indomethacin (log P 4.1), its ester (4.5), ritonavir (5.7), loratadine (4.55) and cinnarizine (5.9) lost release with loading at very different speeds, cinnarizine to about 0.01 mg/min/cm² at 25% and indomethacin only to 0.50 at 60%; at 25% ritonavir released at 0.45 (table value) with 11–15% complexation and loratadine at 0.17 with 63–70% bapat2024 M1, M2, M3, M5, M7, R2, R12, X18.

papersystemmethod and conditionsresultids
saboo2019nilvadipine, cilnidipine in PVPVAcompacts, 5% stepsswitch 10–15% and 15–20% w/w, about 6–9 and 7–9 mol%saboo2019 R5, R6, R7
saboo2019 (cited)itraconazole, ritonavir in PVPVA; sulfathiazole in PVPliteraturedrop above 20%, 25%, 25%saboo2019 R22
que2019ledipasvir against ritonavir (cited)compacts5% against 25%; Tg 160.9 against 50 °Cque2019 C10, R28, M1
saboo2020aNil, Fel, Cil at 40% in HPMCAScompacts, congruent0.42 → 0.34 → 0.26 mg/min/cm² with log P 4.06 → 5.40saboo2020a R16, R17
que2021four analogues in PVPVAcompactsno trend with log P, amorphous solubility, Tg or MWque2021 C29
yang2021six drugs in PVPVA and HPMCASpowdersno log P trendyang2021 C19
hiew2022blumefantrine free base, log P 8.34compactsgood release to 35%hiew2022b M1, R20
rumondor2009c (Physical stability)six drugs in PVPmoisture-induced AAPSlog P does not predict uptake or AAPSrumondor2009c C27
rumondor2011 (Physical stability)PVP dispersionsmultivariate modelstronger interactions, low hygroscopicity, less hydrophobic API resist AAPS; log P excluded from the modelrumondor2011 C1, X5
bapat2024HPMCAS-MF, five drugs of log P 4.1–5.9compacts, pH 6.8decline with loading ordered by charge at the gel pH, not by log Pbapat2024 R2, C26, X18

Figure

Fig. 8 of saboo2020a: drug and polymer release rates of 40% HPMCAS dispersions of three drugs of rising log P
Fig. 8 · saboo2020adrug and polymer release rates of 40% HPMCAS dispersions of three drugs of rising log P

Drug and polymer bars stay equal for each drug and fall together from nilvadipine to felodipine to cilnidipine; the dashed line is a guide for the eye saboo2020a R16.

Why

The authors' original hypothesis was that a more lipophilic drug lowers the hydrophilicity of the blend faster and so loses congruent release at a lower loading saboo2019 C6. Having rejected it for the two analogues, they state that several drug and polymer properties are "likely" to set the switch and that the physicochemical causes "are not well understood" saboo2019 C34, C45. Que and co-workers find no dependence on hydrophobicity or molecular weight between ritonavir and ledipasvir and offer the glass transition as "One interesting difference": ritonavir, with a wet Tg near 0 °C, is a supercooled liquid at 37 °C, ledipasvir a glass que2019 C48, C49. Indulkar and co-workers use the same property for ritonavir, whose drug-rich nanodomains "can" coalesce into contiguous regions because it is a supercooled liquid at 37 °C indulkar2019a C40, M1. In the LLPS chapter the water-plasticized Tg decides whether a drug-rich phase is a liquid or a glass (Amorphous solubility and LLPS F2). (synthesis: the papers use the mobility of the drug-rich phase in two directions: it is invoked for the coalescence of ritonavir domains into a barrier above the limit, yet ritonavir has the higher limit; they give no mechanism that links Tg to the position of the limit.) For congruent HPMCAS dispersions at high loading the authors read the log P series as support for the "supposition" that drug hydrophobicity slows release once the drug dominates the hydrophobicity of the system, with a cutover loading that "seems likely" but was not located; at low loading an earlier study found no log P effect saboo2020a C32, C33, C34. Yang and co-workers (2021) explain why log P fails by the Δχ effect, hygroscopicity and drug–polymer interactions ("highlights why") and conclude that the formulation space "is not limited by" log P yang2021 C21, C22, C42. The Tg idea was tested from 2020 (F18), and hydrogen bonding with analogue pairs (F17). Bapat and co-workers read the spread among drugs of "somewhat comparable" log P as "strongly" suggesting a role for drug–polymer interactions, and attribute the slower release of non-complexing drugs at high loading "likely" to lipophilicity through slower hydration bapat2024 C26, C42.

Conditions and limits

Two dihydropyridine analogues in PVPVA; ledipasvir and ritonavir compared across two papers (tablets at 37 °C in 50 mM pH 6.8 phosphate in both); three analogues at 40% in HPMCAS only saboo2019 X11; que2019 P3; indulkar2019a P2; saboo2020a X13. The analogues' interactions with HPMCAS were assumed similar, not measured saboo2020a X13. Ledipasvir's log P is unresolved between 3.8 and 6.8 que2019 X1.

Counterexamples and conflicts

The highlights of the 2019 paper state that the switch "is independent of drug logP for PVPVA ASDs", wider than the two analogues tested saboo2019 C37, X11. In storage work outside the subcategory a less hydrophobic drug resisted moisture-induced AAPS in the authors' summary, while log P was excluded from their multivariate model as insignificant; another storage study found that log P does not predict moisture-induced AAPS rumondor2011 C1, X5; rumondor2009c C27.

Transfer check

Do not estimate the limit of a new drug in PVPVA from its log P, molecular weight or amorphous solubility; dissolve a loading series instead saboo2019 C35; que2019 C48. Record the dry and, if possible, the wet Tg of the drug against 37 °C so that the Tg idea can be tested across drugs que2019 C49. For HPMCAS at 40% and above, expect slower congruent release for more lipophilic drugs saboo2020a R16.

History

Before 2019 the library had no test of drug properties against the switch saboo2019 C4. Saboo and co-workers (2019) tested log P with two analogues and rejected it; Que and co-workers (2019) added molecular weight and raised the Tg idea; Saboo and co-workers (2020) found a log P effect on congruent release at high loading in HPMCAS saboo2019 C35; que2019 C48, C49; saboo2020a C32. Saboo and co-workers (2020) and Que and co-workers (2021) tested hydrogen bonding with analogue pairs (F17), and the papers of 2020–2022 tested Tg by temperature and across drugs (F18); Que and co-workers (2021) and Yang and co-workers (2021) confirmed the absence of a log P trend for ten further drugs, which replaces "which was not tested" in the title que2021 C29; yang2021 C19. Bapat and co-workers (2024) showed that in HPMCAS the charge of a weak base at the gel pH outweighs its log P (F32) bapat2024 C26.

F10

Topic 3Limit of congruency and its causes5 of 13

Drug–polymer hydrogen bonding did not predict the limit of congruency in a consistent direction.

In ledipasvir–PVPVA, two measures of the drug–polymer interaction (an XPS F 1s component of dry compacts and a ¹⁹F NMR splitting in toluene) levelled off between about 7 and 10% loading, near the limit of 5–7.5%; the authors say this "may be coincidental" que2019 R25, C43, C45. For felodipine the NH band moved down about 50 cm⁻¹ with PVP and PVPVA, the strongest bonds, and up with HPMCAS and EUDS, while the limits were 10 and 15% for the first two and above 50% for the last two: "no positive correlation" saboo2020a R24, R15, C48.

weakWeak to moderate: the ledipasvir link is a coincidence of two thresholds measured in proxy systems (toluene, dry compacts), and in the felodipine polymer set bond strength and hydrophilicity rise together que2019 K5, X8, X17; saboo2020a K7, X14.

polymer with a limit of 10–15%no limit up to 50%PVPlimit 10%amorphous felodipine 33423292PVPVAlimit 15%33423293HPMClimit 10%33423344EUDSnone to 50%33423354HPMCASnone to 50%334233623280329033003310332033303340335033603370felodipine NH stretch in 30% films, cm⁻¹

A lower NH wavenumber marks stronger hydrogen bonding; the strongest bonds went with the lowest limits. saboo2020a R24, R15, C25

Ledipasvir–PVPVA: fluorine at the lower F 1s binding energy (XPS)5% loading77%10%73%20%42%50%18%

Read as the share of drug NH bonded to the polymer instead of to fluorine; none in the neat drug. que2019 R16

For your drug

  1. Do not take a spectroscopic sign of drug–polymer interaction in the dry dispersion as a predictor of the limit; if you use one, follow how its extent changes with loading and compare its saturation loading with a measured release series.
  2. Compare polymers of similar hydrophilicity when testing an interaction effect.

que2019 R25; saboo2020a C48, X14

How it works and key numbers
  1. In neat ledipasvir an amine NH donates a hydrogen bond to fluorine; the vinylpyrrolidone carbonyl takes over this NH, leaving the fluorine electron-richer and giving the lower-binding-energy peak que2019 C38, C39, C40.
  2. The polymer's capacity to do this saturates below about 10%, above which drug–drug interactions predominate ("suggest"), and this "may contribute" to the surface enrichment above the limit que2019 C43, C44.
  3. The authors "speculate" that the competition of drug–drug and drug–polymer interactions, in particular in water, "may be a key factor" que2019 C45, C47.
  4. For felodipine the authors conclude that the role of drug–polymer interactions in the limit, "if any", "clearly needs further evaluation"; the polymers with the weakest bonds are also the least hydrophilic saboo2020a C48, X14.
  5. Analogue pairs of 2020–2021 pointed the same way within one scaffold: hydrogen-bonding drugs had limits of 5–10% against 25–40% for analogues without donors (F17) saboo2020 C14, C48; que2021 R19, C33.
77 → 18%fluorine at the lower binding energy from 5 to 50% ledipasvirque2019 R16
7–10%loading at which both interaction measures level off, against a limit of 5–7.5%que2019 R25, C43
≈50 cm⁻¹downward NH shift of felodipine with PVP and PVPVA, the polymers with the lowest limitssaboo2020a R24
Evidence: data, conditions and papers

Finding F10. PVPVA's vinylpyrrolidone carbonyl breaks ledipasvir's drug–drug hydrogen bonds only up to about 7–10% loading, near the limit of congruency, a match the authors call possibly coincidental; across five polymers for felodipine the strongest drug–polymer hydrogen bonding went with the lowest limits

In short. In ledipasvir–PVPVA dispersions part of the fluorine appears at a 3 eV lower F 1s binding energy (77, 73, 42 and 18% of fluorine at 5, 10, 20 and 50% loading, none in the neat drug), and in toluene the drug's ¹⁹F splitting, read as drug–drug NH···F bonding, shrinks with PVPVA and vinylpyrrolidone but not with polyvinyl acetate que2019 R16, R20, R22, R23. Both measures level off between about 7 and 10% loading, near the limit of 5–7.5%; the authors say this "may be coincidental" in the discussion, while the abstract states that drug–polymer interactions "play a central role" que2019 R25, C43, C45, X16. For felodipine the NH band moved down about 50 cm⁻¹ with PVP and PVPVA (strongest bonds), barely with HPMC, and up with HPMCAS and EUDS, while the limits were 10, 15 and 10% for the first three and above 50% for the last two: "no positive correlation" saboo2020a R24, R15, C48. In this polymer set bond strength and hydrophilicity rise together, so their effects cannot be separated saboo2020a X14.

Type. observation in 2 drugs (ledipasvir with PVPVA; felodipine with five polymers) Strength. to moderate: the ledipasvir link is a coincidence of two thresholds measured in proxy systems (toluene, dry compacts) que2019 K5: weak to moderate, X8, X17; the felodipine contrast is clear but confounded saboo2020a K7: moderate, X14.

How it was shown

Que and co-workers (2019) recorded XPS F 1s spectra of dry ledipasvir–PVPVA compacts and ¹⁹F NMR of ledipasvir in toluene-d8 with PVPVA, polyvinyl acetate or vinylpyrrolidone (VP) monomer, and converted both to a loading axis que2019 P7, P8, P10. Saboo and co-workers (2020) followed the felodipine NH stretch by FTIR in films with five polymers saboo2020a P11, C24.

What the data show

On the loading axis the NMR splitting rose to ≈0.16 ppm at ≈7% equivalent loading and then flattened, and the lower-binding-energy fluorine rose from ≈0.0087 mmol at 5% to ≈0.0165 at 10% and then levelled que2019 R25.

systemmethodresultids
ledipasvir–PVPVA, dry compactsXPS F 1slower-BE share 77 / 73 / 42 / 18% at 5 / 10 / 20 / 50%que2019 R16
ledipasvir in toluene with PVPVA, polyvinyl acetate, VP¹⁹F and ¹H NMRsplitting reduced by PVPVA and VP, not polyvinyl acetateque2019 R22, R23, R24
both measures against loadingconversion to a loading axislevel off near 7–10% against LoC 5–7.5%que2019 R25, C43
felodipine 30% films, five polymersFTIR NH stretchdown ≈50 cm⁻¹ (PVP, PVPVA), up (HPMCAS, EUDS)saboo2020a R24
same polymerslimits10 / 15 / 10% against none to 50%saboo2020a R15, C48
Fig. 16 of que2019: NMR splitting and lower-binding-energy fluorine against drug loading with the congruent-release band
Fig. 16 · que2019NMR splitting and lower-binding-energy fluorine against drug loading with the congruent-release band

Both curves rise steeply and then flatten between about 7 and 10% loading; the shaded band (≈3–10%) is wider than the measured congruent range (2–5%) que2019 R25, X7.

Why

In Que and co-workers' picture the VP carbonyl takes over the amine NH that in neat ledipasvir donates a hydrogen bond to fluorine, leaving the fluorine electron-richer and so giving the lower-binding-energy peak que2019 C38, C39, C40. The polymer's capacity to do this saturates below about 10%, above which drug–drug interactions predominate ("suggest"), a match with the limit that "may be coincidental" que2019 C43, C45. Saboo and co-workers (2020) conclude that the role of drug–polymer interactions in the limit, "if any", "clearly needs further evaluation" saboo2020a C48. (synthesis: the two felodipine polymers with the weakest NH bonding are also the least hygroscopic and the only ones that must ionize to dissolve, so the felodipine data show only that strong bonding with a very hydrophilic polymer did not prevent the cliff.)

Limits and transfer

The ledipasvir evidence comes from toluene solutions and dry compacts, not from the hydrated dispersion que2019 X17, X8. A spectroscopic sign of interaction in the dry dispersion does not predict the limit; compare the loading at which it saturates with a measured release series, and compare polymers of similar hydrophilicity que2019 R25; saboo2020a C48, X14.

How it was shown

Que and co-workers (2019) recorded XPS F 1s spectra of dry ledipasvir–PVPVA compacts at 5–50% and of the neat drug, and ¹⁹F and ¹H NMR of ledipasvir in toluene-d8, a solvent of minimal hydrogen-bonding ability, at 0.5–4 mg/mL, at 278–318 K, with 2 mg/mL PVPVA or polyvinyl acetate, and with 2–80 mg/mL vinylpyrrolidone (VP) monomer que2019 P7, P8, C24. They converted each VP level to the PVPVA mass that carries as many VP units, and each fluorine share to the moles of lower-binding-energy fluorine in a 100 mg compact, to plot both on a loading axis que2019 P10, E2, E3, E4. Saboo and co-workers (2020) recorded transmission FTIR of 30% felodipine films with the five polymers and of amorphous felodipine, following the NH stretch at 3342 cm⁻¹ saboo2020a P11, C24. Indulkar and co-workers (2019) proposed, without measurement, that ritonavir–PVPVA interactions in water saturate near the limit indulkar2019a C34.

What the data show

Ledipasvir: the neat drug gave one F 1s peak at 687.1 ± 0.1 eV, the dispersions an additional peak at 684.0 ± 0.2 eV, whose share fell with loading as in the short part and dropped to ≈9, ≈3 and ≈2% after 10 min of dissolution at 10, 20 and 50% que2019 R16, R17. In toluene the outer satellite peaks of the ¹⁹F pattern lay ≈1.31, ≈1.40 and ≈1.46 ppm apart at 0.5, 2 and 4 mg/mL and ≈1.59, ≈1.41 and ≈1.28 ppm apart at 278, 298 and 318 K; 2 mg/mL PVPVA reduced the splitting, polyvinyl acetate did not, and VP merged the peaks progressively, while two NH protons moved downfield by ≈0.4 ppm and two intramolecularly bonded ones by at most ≈0.1 ppm que2019 R20, R21, R22, R23, R24. On the loading axis the NMR splitting rose to ≈0.16 ppm at ≈7% equivalent loading and then flattened (≈0.19 at ≈37.5%), and the lower-binding-energy fluorine rose from ≈0.0087 mmol at 5% to ≈0.0165 at 10% and then levelled (≈0.0188–0.0197) que2019 R25. The SI prints 0.165 mmol for the 10% point, a factor-10 slip que2019 E4, X3. Felodipine: NH positions 3292 (PVP), 3293 (PVPVA), 3344 (HPMC), 3354 (EUDS) and 3362 cm⁻¹ (HPMCAS) in the table, the last two swapped in the figure (≈3362 and ≈3355), against 3342 for amorphous felodipine; with HPMC the carbonyl doublet merged into one band at 1699 cm⁻¹ saboo2020a R24, X2, R25. The authors' order of bond strength is PVP ≅ PVPVA > HPMC > HPMCAS > EUDS, and a residual 3342 cm⁻¹ shoulder in most dispersions means the extent of bonding cannot be quantified saboo2020a C25.

papersystemmethod and conditionsresultids
que2019ledipasvir–PVPVA, dry compactsXPS F 1slower-BE share 77 / 73 / 42 / 18% at 5 / 10 / 20 / 50%que2019 R16
que2019ledipasvir in toluene with PVPVA, PVA, VP¹⁹F and ¹H NMRsplitting reduced by PVPVA and VP, not PVAque2019 R22, R23, R24
que2019both measures against loadingconversion to a loading axislevel off near 7–10% against LoC 5–7.5%que2019 R25, C43
saboo2020afelodipine 30% films, five polymersFTIR NH stretchdown ≈50 cm⁻¹ (PVP, PVPVA), up (HPMCAS, EUDS)saboo2020a R24
saboo2020asame polymerslimits10 / 15 / 10% against none to 50%saboo2020a R15, C48
rumondor2011 (Physical stability)PVP dispersions in humid storagemultivariate modelstronger interactions resist moisture-induced AAPSrumondor2011 C1
rumondor2010c (Physical stability)indomethacin–PVPVAIR red shift, moisturestronger interaction, no demixingrumondor2010c C28

Figure

Fig. 16 of que2019: NMR splitting and lower-binding-energy fluorine against drug loading with the congruent-release band
Fig. 16 · que2019NMR splitting and lower-binding-energy fluorine against drug loading with the congruent-release band

Both curves rise steeply and then flatten between about 7 and 10% loading; the shaded band (≈3–10%) is wider than the measured congruent range (2–5%) que2019 R25, X7.

Why

Que and co-workers' picture is that in neat ledipasvir an amine NH donates a hydrogen bond to fluorine, and that the VP carbonyl takes over this NH, leaving the fluorine electron-richer and so giving the lower-binding-energy peak que2019 C38, C39, C40. The polymer's capacity to do this saturates below about 10%, above which drug–drug interactions predominate ("suggest"), and the low extent of drug–polymer interaction with more drug–drug interaction "may contribute" to the surface enrichment above the limit que2019 C43, C44. They allow that the match with the limit "may be coincidental" and "speculate" that the competition of drug–drug and drug–polymer interactions, in particular in water, "may be a key factor" que2019 C45, C47. Indulkar and co-workers make the analogous proposal for ritonavir at 25–30% ("It is likely") indulkar2019a C34, and Purohit and Taylor expect the donor and acceptor groups of HPMCAS to interact "more numerously and diversely" with ritonavir than PVP or PVPVA purohit2017b C46. Saboo and co-workers (2020), with the hydrogen-bonding evidence on the other side, conclude that the role of drug–polymer interactions in the limit, "if any", "clearly needs further evaluation" saboo2020a C48. Storage work outside the subcategory found that stronger drug–polymer interactions resist moisture-induced AAPS rumondor2011 C1; rumondor2010c C28. (synthesis: the two felodipine polymers with the weakest NH bonding are also the least hygroscopic and the only ones that must ionize to dissolve, so the felodipine data do not show that hydrogen bonding is irrelevant; they show that strong bonding with a very hydrophilic polymer did not prevent the cliff.)

Conditions and limits

Interaction evidence for ledipasvir comes from toluene solutions with VP monomer up to 80 mg/mL and from dry compacts, not from the hydrated dispersion where release occurs; there is no XPS point at 7.5% que2019 X17, X8. Some NMR points of the loading plot cannot be mapped to the stated VP series que2019 X9. Table 2 lists ¹H shifts with concentration and temperature that are not shown que2019 X10. The felodipine IR was recorded on 30% films only saboo2020a P11.

Counterexamples and conflicts

The abstract of the ledipasvir paper states the interaction role more strongly ("play a central role") than its discussion ("may be coincidental") and conclusions ("may play a role") que2019 X16. The storage-stability view that strong drug–polymer interactions protect against water-induced separation rumondor2011 C1 is not borne out for release in the felodipine polymer set, where the strongest bonding went with the lowest limits saboo2020a C48. Analogue pairs of 2020–2021 showed the same direction within one scaffold: hydrogen-bonding IND and two phenols had limits of 5–10% against 25–40% for analogues without donors (F17) saboo2020 C14, C48; que2021 R19, C33.

Transfer check

A spectroscopic sign of drug–polymer interaction in the dry dispersion (IR band shift, XPS component) does not predict the limit; if used, follow how its extent changes with loading and compare the loading at which it saturates with a measured release series que2019 R25; saboo2020a C48. Compare polymers of similar hydrophilicity when testing an interaction effect, to avoid the confounding of F11 saboo2020a X14.

History

Indulkar and co-workers (2019) first proposed interaction saturation near the limit, without data indulkar2019a C34. Que and co-workers (2019) measured it for ledipasvir by XPS and NMR and found it near the limit que2019 C43. Saboo and co-workers (2020) found the opposite ordering of bond strength and limit across five polymers saboo2020a C48. Saboo and co-workers (2020) and Que and co-workers (2021) compared drugs with and without specific interactions in PVPVA directly and found hydrogen bonding to lower the limit (F17) saboo2020 C59; que2021 C35. Deac and co-workers (2023) measured where the polymer goes when a hydrogen-bonding analogue separates in water: into its drug-rich phase (F27) deac2023b C26.

F17

Topic 3Limit of congruency and its causes6 of 13

In PVPVA, drugs that hydrogen-bond to the polymer had lower limits of congruency than close analogues that cannot.

Indomethacin, whose carboxylic acid hydrogen-bonds to the PVPVA carbonyl, released congruently at 5 and 10% and collapsed from 15%, while its methyl ester, without a donor, released congruently up to 25% over the first 5 min saboo2020 R3, C14. Among four phenolphthalein analogues the two phenols had limits of 5% (PHPH) and 10% (TIPP), against 30 and 40% for the methyl ethers que2021 R7, R19, C33. The authors' hypothesis that hydrogen bonding would raise the limit "appears to be incorrect" saboo2020 C48.

moderateModerate: the limit gaps are large and measured with both components, but each pair also differs in Tg, crystallization tendency, medium or drug–drug bonding, and the mechanism is argued saboo2020 K1, X6; que2021 K3, K6, X12.

hydrogen-bond donorno donorindomethacinacid · Tg 43.5 °C10indomethacin methyl esterTg 1.7 °C · 5-min ratesat least 25PHPHphenol · Tg 99.0 °C5TIPPphenol and iodine · Tg 86.1 °C10Me-TIPPiodine only · Tg 122.7 °C30Me-PHPHneither · Tg 25.2 °C40051015202530354045limit of congruency in PVPVA, %

In both analogue series the donor drug had the lower limit; Tg does not rank the four phenolphthalein analogues. saboo2020 R3, C14, M1, M2; que2021 R19, M1, M2, M3, M4

PVPVA in the drug-rich phase of the four analogues, wt%PHPHlimit 5%≈77TIPPlimit 10%≈36.5Me-TIPPlimit 30%≈9Me-PHPHlimit 40%≈5

The order is the reverse of the limits (F27). deac2023b R3; que2021 R19

For your drug

  1. Count the donors of the candidate that can bond to the vinylpyrrolidone carbonyl and record the carbonyl band of dry films (a new band near 1650 cm⁻¹, a shift of about 30 cm⁻¹).
  2. If a strong shift is present, expect a PVPVA limit of 5–10%, dissolve a loading series from 5% in 2.5–5% steps with both components assayed, and compare limits per mole when candidates differ greatly in molecular weight.

que2021 R7, R19, R20, E3; saboo2020 R14

How it works and key numbers
  1. In the IR the indomethacin acid-dimer band at 1705 cm⁻¹ disappeared and a hydrogen-bonded carbonyl band at 1634 cm⁻¹ grew with loading, while the ester left the PVPVA carbonyl region unchanged saboo2020 R13, R14, R18.
  2. The authors' rationalization: a drug–polymer hydrogen bond that persists in water occupies a polymer solvation site, lowers water uptake and so slows plasticization, chain disentanglement and polymer dissolution ("could explain") que2021 C44.
  3. Halogen bonds are weaker, and hydrogen bonds prevail where both compete que2021 C7, C17, C18.
  4. Deac and co-workers (2023) give a second mechanism: the phenols draw PVPVA into their drug-rich phase, which makes that phase "volumetrically larger", so that it forms a continuous barrier at a lower loading ("are hypothesized", F27) deac2023b C46, C63; deac2023a C65.
  5. Measured phase diagrams of 2024 put the critical point at about 3.7% for phenolphthalein and 33% for its methyl ether (F30) deac2024b R35, R37.
  6. Methylation also removed drug–drug hydrogen bonds and lowered Tg (indomethacin 43.5 → 1.7 °C), so the series show the role of the OH group, not uniquely of the drug–polymer bond que2021 X12; saboo2020 M1, M2.
10 against at least 25%limit of indomethacin against its methyl ester in PVPVAsaboo2020 R3, C14
5–10 against 30–40%limits of the two phenols against their methyl ethersque2021 R19
≈77 against ≈5 wt%PVPVA in the drug-rich phase of PHPH against Me-PHPHdeac2023b R3
Evidence: data, conditions and papers

Finding F17. In PVPVA, drugs that hydrogen-bond to the polymer had lower limits of congruency than close analogues that cannot: indomethacin 10% against at least 25% for its methyl ester, and two phenols 5 and 10% against 30 and 40% for their methyl ethers; the analogue pairs also differ in Tg and in drug–drug bonding, and in 2023 the phenols were found to carry PVPVA into their drug-rich phase (F27)

In short. Indomethacin, whose carboxylic acid hydrogen-bonds to the PVPVA carbonyl, released congruently at 5 and 10% and collapsed from 15% (drug about 0.01–0.04 against 3.1–3.5 mg/min/cm²), while its methyl ester, without a donor, released congruently up to 25% over the first 5 min; the authors' hypothesis that hydrogen bonding would raise the limit "appears to be incorrect" saboo2020 R3, C6, C14, C48. Among four phthalide analogues, the two phenols that shift the PVPVA vinylpyrrolidone carbonyl by up to 30 cm⁻¹ had limits of 5% (PHPH) and 10% (TIPP), the halogen-bonding-only Me-TIPP 30% and the non-interacting Me-PHPH 40%, and no bulk property tracked the limit que2021 R7, R19, C29, C33. Clopidogrel and lumefantrine free base, without hydrogen-bond donors, reached about 40% and 35% correasoto2022a C46, C47; hiew2022b M1, R20. Methylation removed drug–drug hydrogen bonds and lowered Tg too, and the authors' mechanism, bonds that persist in water slowing polymer hydration, was not measured que2021 X12, C44; saboo2020 X6. In 2023 the hydrogen-bonding analogues were found to carry PVPVA into their insoluble drug-rich phase (about 77 and 36.5 wt% for PHPH and TIPP against about 9 and 5 wt% for the methyl ethers), in the reverse order of their limits, and phenolphthalein's polymer-rich phase connected into a network at 10–20% where its methyl ether still formed droplets (F27, F25) deac2023b R3, R8; deac2023a R7, R6. In 2024 measured phase diagrams put the critical point at about 3.7% for phenolphthalein and 33% for its methyl ether, and the critical-point loadings of all four analogues followed their limits (F30) deac2024b R35, R37; phenolphthalein also took 60% of HPMCAS out of solution at pH 6.0 (F32) bapat2024 R12.

Type. observation in 2 analogue series (indomethacin and its methyl ester; four phenolphthalein analogues) with support from 2 further drugs Strength. : the limit gaps are large and measured with both components saboo2020 K1: moderate to strong; que2021 K3: moderate, but each series is confounded (Tg, crystallization tendency, medium, drug–drug bonding) and the mechanism is argued saboo2020 X6; que2021 X12, K6: weak.

How it was shown

Saboo and co-workers (2020) compared indomethacin (IND), whose acid hydrogen-bonds to the pyrrolidone carbonyl, with its methyl ester (INDester) as PVPVA compacts at 5–25% saboo2020 C6, P4, P5. Que and co-workers (2021) switched the phenolic OH and iodine of one phenolphthalein scaffold on or off (TIPP, PHPH, Me-TIPP, Me-PHPH) and read interactions by IR and XPS que2021 A1, P2, P3.

What the data show

In the IR a hydrogen-bonded carbonyl band at 1634 cm⁻¹ grew with IND loading, while INDester left the PVPVA carbonyl region unchanged saboo2020 R14, R18.

systemmethodresultids
IND (acid donor) against INDester (no donor), PVPVA5-min rates, 37 °Climits 10% against at least 25%saboo2020 R3, C14
TIPP, PHPH, Me-TIPP, Me-PHPH in PVPVAcompacts, ≥80% in 90 minlimits 10, 5, 30, 40%; 0.012, 0.016, 0.035, 0.115 mol/100 gque2021 R19, R20
sameIR films; I 3d XPSVP carbonyl shift up to 30 cm⁻¹ (phenols), ≤7 cm⁻¹ (Me-TIPP); halogen-bonded iodineque2021 R7, R12
clopidogrel (no donor)compactslimit about 40%correasoto2022a C46, C47
four analoguesPVPVA in drug-rich nanoparticles, 60 °C≈77 / 36.5 / 9 / 5 wt% (PHPH / TIPP / MeTIPP / MePHPH)deac2023b R3
four analogues in PVPVAPC-SAFT drug activity in the dry dispersion; critical pointactivity ≈10⁻¹³ to 0.06; critical point ≈3.7 to 33%deac2024b R36, R37
Fig. 2 of saboo2020: normalized drug and polymer release rates of IND and INDester dispersions over the first 5 min
Fig. 2 · saboo2020normalized drug and polymer release rates of IND and INDester dispersions over the first 5 min

Panel A: the IND bars collapse below the axis break from 15:85 while PVPVA bars stay above it; panel B: INDester and PVPVA match at every loading to 25:75; the media of the two panels differ saboo2020 R3, X5.

Why

Saboo and co-workers conclude that hydrogen bonding "appears to be somewhat detrimental" to release, while allowing that the lower Tg of the ester may have contributed saboo2020 C59, C50. Que and co-workers reason that a drug–polymer hydrogen bond that persists in water occupies a polymer solvation site, lowers water uptake and so slows plasticization, disentanglement and polymer dissolution ("could explain") que2021 C33, C44. Deac and co-workers (2023) add that the phenols draw PVPVA into their drug-rich phase, which makes that phase "volumetrically larger" so that it forms a continuous barrier at a lower loading ("are hypothesized") deac2023b C46, C63; deac2023a C65.

Limits and transfer

Methylation removes drug–drug hydrogen bonds as well, and IND and INDester were tested in different media que2021 X12; saboo2020 X5. Record the carbonyl band of dry drug–PVPVA films: with a new band near 1650 cm⁻¹ or a shift of about 30 cm⁻¹, expect a limit of 5–10% and dissolve a loading series from 5% in 2.5–5% steps que2021 R7, R19, R20; saboo2020 R14.

How it was shown

Saboo and co-workers (2020) asked whether drug–polymer hydrogen bonding raises the limit, expecting so because stronger bonding appears to resist water-induced phase separation in humid storage saboo2020 C5, C7. They chose IND, whose acid hydrogen-bonds to the pyrrolidone carbonyl, and INDester, in which OCH3 replaces the OH, made rotary-evaporated dispersions at 5–25% in PVPVA and dissolved them as compacts with drug and polymer assayed every minute for 5 min and up to 30 min (conditions in F15); IND was tested at pH 2.1 and INDester at pH 6.8 to avoid ionization and hydrolysis saboo2020 C6, P4, P5, P6, M5, M6. ATR-IR of dispersions of 10–90% followed the hydrogen-bonded carbonyl band saboo2020 P11, R14. Que and co-workers (2021) used one phenolphthalein scaffold with phenolic OH and iodine switched on or off: TIPP (OH and iodine), PHPH (OH), Me-TIPP (iodine) and Me-PHPH (neither); they read interactions by transmission IR of films at 10–90% and by I 3d XPS of compacts at 10–40%, and defined the limit as the last loading with simultaneous release and at least 80% drug in 90 min, expressed also per mole que2021 A1, P2, P3, P9, E3. Deac and co-workers (2023) measured the PVPVA content of drug-rich nanoparticles of the four analogues and imaged dissolving PHPH and MePHPH compacts (F25, F27) deac2023b P1, P2; deac2023a P7.

What the data show

IND at 5 and 10% released drug and polymer at about 3.44/3.47 and 3.14/3.19 mg/min/cm²; at 15, 20 and 25% the drug fell to about 0.04, 0.02 and 0.01 and PVPVA to about 0.72, 0.64 and 0.50, and only 0.04–0.13% of the drug had dissolved at 5 min against 1.8–2.3% of the polymer saboo2020 R3, R4. INDester released both at about 3.3–4.2 at every loading up to 25% saboo2020 R3. In the IR the IND acid-dimer band at 1705 cm⁻¹ disappeared and a hydrogen-bonded carbonyl band at 1634 cm⁻¹ grew with loading, while INDester left the PVPVA carbonyl region unchanged saboo2020 R13, R14, R18, C23. The two drugs also differ in Tg onset (43.5 against 1.7 °C), melting point (160.7 against 91.4 °C), crystallization class (III against II) and amorphous solubility (22.1 against 3.9 µg/mL) saboo2020 M1, M2, R1. In the analogue series the PVPVA vinylpyrrolidone carbonyl (about 1684 cm⁻¹) shifted by up to 30 cm⁻¹ with TIPP and PHPH, at most 7 cm⁻¹ with Me-TIPP and minimally with Me-PHPH; a lower-binding-energy iodine doublet (618.1 against 620.7 eV) marked halogen bonding, with about 0.042–0.050 mmol per 100 mg for Me-TIPP against 0.017–0.026 for TIPP from 20% loading que2021 R7, R9, R12, X1. The limits were 5, 10, 30 and 40% for PHPH, TIPP, Me-TIPP and Me-PHPH, or 0.016, 0.012, 0.035 and 0.115 mol per 100 g dispersion que2021 R19, R20. One step above, TIPP at 15–20% and Me-TIPP at 50% released about 0% drug and 13–18% PVPVA in 90 min, PHPH at 10% about 30 and 44%, Me-PHPH at 50% about 17 and 26% que2021 R15. Tg (86.1, 122.7, 99.0 and 25.2 °C), calculated log P and amorphous solubility (below 0.01 µg/mL for both iodo compounds) did not track the limit que2021 M1, M2, M3, M4, C29, C31. (synthesis: in both series the donor drug had a limit at least 2.5 times lower by weight, 10 against at least 25% and 5–10 against 30–40%.) The computed drug activity in the dry dispersion was about 10^{-13} (PHPH), 10^{-9} (TIPP), 2 \times 10^{-3} (MeTIPP) and 0.06 (MePHPH), the order of interaction and the reverse of the limits deac2024b R36, R37. Dry PHPH–PVPVA dispersions had Tgs above both components from 5 to 50%, while MePHPH–PVPVA followed the Gordon–Taylor equation with K = 0.65 deac2024b R31. PHPH at one drug per succinoyl group complexed 60 ± 4% of HPMCAS-MF and released at 0.22 mg/min/cm² at 27% bapat2024 R12, R2.

papersystemmethod and conditionsresultids
saboo2020IND (acid donor) against INDester (no donor), PVPVA5-min rates, 37 °Climits 10% against at least 25%saboo2020 R3, C14
saboo2020sameATR-IR1634 cm⁻¹ hydrogen-bonded carbonyl with IND; none with INDestersaboo2020 R14, R18
que2021TIPP, PHPH, Me-TIPP, Me-PHPH in PVPVAcompacts, ≥80% in 90 minlimits 10, 5, 30, 40%; 0.012, 0.016, 0.035, 0.115 mol/100 gque2021 R19, R20
que2021sameIR films; I 3d XPSVP carbonyl shift up to 30 cm⁻¹ (phenols), ≤7 cm⁻¹ (Me-TIPP); halogen-bonded iodineque2021 R7, R12
correasoto2022aCPD (no donor)compactslimit about 40%correasoto2022a C46, C47
hiew2022blumefantrine free base (no available donor)compactsgood release to 35%, the highest loading testedhiew2022b M1, R20, X7
yang2021six drugspowdershigh-Tg drugs all carry donors, low-Tg drugs noneyang2021 C8, C25
saboo2020afelodipine with five polymersIR, compactsstrongest NH bonding with the lowest limitssaboo2020a C48
deac2023bfour analoguesPVPVA in drug-rich nanoparticles, 60 °C≈77 / 36.5 / 9 / 5 wt% (PHPH / TIPP / MeTIPP / MePHPH)deac2023b R3
deac2023aPHPH, MePHPH compactsin situ confocaldrug-rich network from 10–20% (PHPH) against 40–50% (MePHPH)deac2023a R7, R6
que2020 (Miscibility)four halogen compounds without donorsXPS, NMR, IRhalogen bonds to the VP carbonylque2020 C1
rumondor2011 (Physical stability)PVP dispersions in humid storagemultivariate modelstronger interactions resist moisture-induced phase separationrumondor2011 C1
deac2024bfour analogues in PVPVAPC-SAFT drug activity in the dry dispersion; critical pointactivity ≈10⁻¹³ to 0.06; critical point ≈3.7 to 33%deac2024b R36, R37
bapat2024PHPH with HPMCAS-MFpH 6.0 spike test; compacts60% complexed; 0.22 mg/min/cm² at 27%bapat2024 R12, R2

Figure

Fig. 2 of saboo2020: normalized drug and polymer release rates of IND and INDester dispersions over the first 5 min
Fig. 2 · saboo2020normalized drug and polymer release rates of IND and INDester dispersions over the first 5 min

Panel A: the IND bars collapse below the axis break from 15:85 while PVPVA bars stay above it; panel B: INDester and PVPVA match at every loading to 25:75; the media of the two panels differ saboo2020 R3, X5.

Fig. 6 of que2021: limit of congruency of the four analogues by weight and by moles
Fig. 6 · que2021limit of congruency of the four analogues by weight and by moles

The two OH-bearing compounds sit low in both panels; TIPP, which can form both bonds, is lowest per mole que2021 R19, R20, C34.

Why

Saboo and co-workers read the IND switch as polymer- to drug-controlled release, the lower PVPVA rate "most likely" reflecting a drug-rich interface, and favour water-induced phase separation at the interface, inferred from enrichment and roughness, over plain polymer loss (F7, F8) saboo2020 C12, C13, C41, C42, X8. They conclude that hydrogen bonding "appears to be somewhat detrimental" to release, while allowing that the lower Tg of the ester may have contributed saboo2020 C59, C50. Que and co-workers find that the limit "appears to trend" with interaction ability and "can rationalize" it: a drug–polymer hydrogen bond that persists in water occupies a polymer solvation site, lowers water uptake (as in vapour sorption of hydrogen-bonded dispersions, cited) and so slows plasticization, disentanglement and polymer dissolution ("could explain") que2021 C33, C44. Halogen bonds are weaker and hydrogen bonds prevail where both compete ("most likely due to competition") que2021 C7, C17, C18. Yang and co-workers draw the same conclusion from the indomethacin pair ("are likely to") and Correa Soto and co-workers note that the effects of hydrogen bonding and Tg are "somewhat difficult to deconvolute" yang2021 C29; correasoto2022a C49. (synthesis: in both series methylation also lowered Tg (IND 43.5 → 1.7 °C; PHPH 99.0 → Me-PHPH 25.2 °C), but Me-TIPP kept a limit of 30% with a Tg of 122.7 °C, so within the analogue series the donor ranked the limits better than the Tg did saboo2020 M1, M2; que2021 M2, M3, M4, R19; across unrelated drugs the two properties go together (F18) yang2021 C25.) Deac and co-workers (2023) give a second mechanism: the phenols draw PVPVA into their drug-rich phase ("it is reasonable to infer"), which makes that phase "volumetrically larger" so that it forms a continuous barrier at a lower loading ("are hypothesized") (F27) deac2023b C46, C63; deac2023a C65. (synthesis: the 2024 diagrams give a thermodynamic route for the analogue pairs: hydrogen bonding ("likely") draws PVPVA into the drug-rich phase and moves the critical point to low loading (F30) deac2024b C56; with HPMCAS the phenol complexes the carboxylate by what the authors call, as a "conjecture", hydrophobic hydrogen bonding bapat2024 C41.)

Conditions and limits

PVPVA only; rotary-evaporated dispersions; compacts at 37 °C; IND and INDester in different media, TIPP at pH 2.5 saboo2020 X5; que2021 X5. INDester's limit rests on 5-min rates and the ester crystallized later (F19) saboo2020 X7. Each limit is resolved to the tested step, Me-PHPH at 40% sits at the edge of the 80% criterion, and the TIPP drug–polymer difference has p = 0.022 que2021 X11, X4. Hydrogen bonds were measured in dry films and compacts, not in the hydrated gel where release occurs que2021 C44.

Counterexamples and conflicts

Ritonavir hydrogen-bonds to PVP through three NH donors and has a PVPVA limit of 25%, while itraconazole, without a donor, has 20% purohit2015b C27; indulkar2019a C2; saboo2020 R35, C58. Methylation removes drug–drug hydrogen bonds as well, so the series show the role of the phenolic OH, not uniquely of the drug–polymer bond que2021 X12. The storage view that stronger drug–polymer interactions protect against water-induced separation rumondor2011 C1 is the hypothesis both papers set out to test and did not confirm for release saboo2020 C48; que2021 C35.

Transfer check

Count the donors of the candidate that can bond to the vinylpyrrolidone carbonyl and record the carbonyl band of dry films (a new band near 1650 cm⁻¹, a shift of about 30 cm⁻¹) que2021 R7; saboo2020 R14. If a strong shift is present, expect a PVPVA limit of 5–10% and dissolve a loading series from 5% in 2.5–5% steps with both components assayed; compare limits per mole when candidates differ greatly in molecular weight que2021 R19, R20, E3.

History

The storage studies of the library found that drug–polymer hydrogen bonding resists moisture-induced separation rumondor2011 C1. Indulkar and co-workers (2019) and Que and co-workers (2019) proposed a role of drug–polymer interactions near the limit (F10) indulkar2019a C34; que2019 C43, and Saboo and co-workers (2020, five polymers) found the strongest bonding with the lowest limits saboo2020a C48. Saboo and co-workers (2020, indomethacin) made the first analogue-pair test and rejected the hypothesis saboo2020 C48. Que and co-workers (2021) extended it to four analogues and "believe" this to be the first correlation between compound chemistry and release que2021 C46. Yang and co-workers (2021), Correa Soto and co-workers (2022) and Hiew and Taylor (2022) found high limits for drugs without donors and noted the confounding with Tg yang2021 C25; correasoto2022a C49; hiew2022b C29. Deac and co-workers (2023) measured the polymer content of the analogues' drug-rich phases and the loading at which the phase connects in the dissolving gel, which revises "the proposed cause was not measured" of the title to a partly measured cause (F27) deac2023b C67; deac2023a C72. Deac and co-workers (2024, ternary phase diagrams) placed the four limits near the computed critical points, and Bapat and co-workers (2024) found phenolphthalein complexing HPMCAS as well (F30, F32) deac2024b C59; bapat2024 C19.

Other chapterssame mechanism B F18
F18

Topic 3Limit of congruency and its causes7 of 13

The drug's glass transition against the test temperature moved the limit: a glassy drug-rich phase lowered it.

The indomethacin–PVPVA limit stayed at 10% from 25 to 57 °C, fell to 5% at 17 °C and below 5% at 10 °C; a water-saturated 70% dispersion standing in for the drug-rich surface has a wet Tg onset of 18 °C saboo2020 R29, R30, C53. A 10% atazanavir dispersion (wet Tg 55 °C) released about 3% of its drug at 37 °C and about 64% at 55 °C, until it crystallized correasoto2022b R6, R5, M1. Across drugs, low-Tg drugs reached 25–40% in PVPVA where high-Tg drugs failed at 5–10%, but the high-Tg drugs all carried hydrogen-bond donors yang2021 R7, R8, R9, R10, C8, C25.

moderateModerate: the temperature shifts are large and repeated in four papers, but the limits are in 5% steps, temperature also changes the polymer, and Tg goes with hydrogen-bond donors across drugs yang2021 K4, X16, C25; saboo2020 K5, X9; correasoto2022b K3; hiew2022b K5, X10.

37 °C (indomethacin 25–57 °C)cooledindomethacin–PVPVA5 at 17 °C10loratadine–PVPVAcompacts2 at 5 °C30loratadine–HPMCAScompacts5 at 5 °C2005101520253035limit of congruency, %

Indomethacin fell below 5% at 10 °C; the wet Tg of its drug-rich surface is about 18 °C, that of loratadine 13.8 °C. saboo2020 R29, R30; yang2021 R22, M1

low Tghigh Tg (all with hydrogen-bond donors)miconazolewet Tg −4.7 °C40clopidogrelTg −9 °Cabout 40loratadinewet Tg 13.8 °C · powders25danazolwet Tg 73.3 °C5elbasvirTg 129.1 °C10ledipasvirTg 160.9 °C5051015202530354045loading at which PVPVA release failed, %

Clopidogrel and ledipasvir values are limits from compacts; the others are drop-off loadings of powders. yang2021 R7, R8, R9, R10, M1, M2, M3, M4, C25; correasoto2022a M1, C46; que2019 M1, C10

For your drug

  1. Measure or estimate the wet Tg of the drug, and if possible of a drug-rich (about 70%) dispersion, from water sorption at 37 °C with the 10 °C per 1% rule.
  2. A wet Tg above 37 °C, or a dry Tg above about 70 °C, places the drug among those that failed at 2–10% in PVPVA; test release at 37 °C, not at room temperature, and consider an additive that plasticizes the dispersion.

saboo2020 P22, P23, R29; yang2021 P9; hiew2022b R16; correasoto2022b C40

How it works and key numbers
  1. Water plasticizes the drug, T_{g,\mathrm{wet}} \approx T_{g,\mathrm{dry}} - 10\,w with w the water content in % saboo2020 E6; yang2021 E3.
  2. Above its wet Tg the drug-rich phase is a supercooled liquid, below it a glass; the authors link the indomethacin effect "plausibly" to the wet Tg of the drug-enriched surface (about 70% drug, 18 °C), not of the neat drug saboo2020 C32, C52, C53.
  3. Lower temperature impedes chain mobility and disentanglement ("may explain"); for low-Tg drugs a mobile drug-rich phase lets the polymer dissolve past it, while a high-Tg drug impedes polymer dissolution at high loading saboo2020 C55; yang2021 C33, C34.
  4. A glassy matrix takes up water slowly and needs more water before its chains disentangle, which the authors think likely underlies the poor release of high-Tg drugs correasoto2022b C34, C36, C37.
  5. Cooling also slowed neat PVPVA from about 3.45 to 1.68 mg/min/cm², but neat HPMCAS was not slowed, so a slower polymer alone "cannot explain" the drop for loratadine yang2021 R21, X16, C26.
  6. Plasticizers raised the limit of atazanavir and ledipasvir three- to fivefold but that of ritonavir only 1.2-fold (F26) correasoto2023 R16, C20.
10 → below 5%indomethacin–PVPVA limit from 25–57 °C down to 10 °Csaboo2020 R29
≈3 → ≈64%10% atazanavir released at 37 against 55 °Ccorreasoto2022b R6, R5
30 → 2%loratadine–PVPVA compact limit at 37 against 5 °Cyang2021 R22
Evidence: data, conditions and papers

Finding F18. The drug's glass transition against the dissolution temperature moved the limit: cooling below the wet Tg of the drug or of the drug-rich layer lowered it (indomethacin 10 → below 5%, loratadine 30 → 2% in PVPVA and 20 → 5% in HPMCAS), heating a high-Tg drug restored release (atazanavir at 10% from about 3 to 64%), and drugs of low wet Tg reached 25–40% in PVPVA where high-Tg drugs failed at 5–10%; plasticizers raised the limit of two high-Tg drugs three- to fivefold and that of ritonavir 1.2-fold (F26)

In short. The IND–PVPVA limit stayed at 10% at 25, 37 and 57 °C, fell to 5% at 17 °C and below 5% at 10 °C, where a water-saturated 70% dispersion standing in for the drug-rich surface has a wet Tg onset of 18 °C saboo2020 R29, R30, C53. Loratadine (wet Tg 13.8 °C) had compact limits of 30% (PVPVA) and 20% (HPMCAS) at 37 °C and 2% and 5% at 5 °C yang2021 R22, M1. A 10% ATZ dispersion (wet Tg 55 °C) released about 3% of its drug at 37 °C and about 64% at 55 °C until it crystallized, and two lumefantrine salt dispersions that released well at 37 °C released almost nothing at 10 °C correasoto2022b R6, R5, M1; hiew2022b R16. Across drugs, PVPVA powders failed at 25 and 40% for loratadine and miconazole (wet Tg 13.8 and −4.7 °C) but at 5–10% for danazol, elbasvir, paclitaxel and ivacaftor, all with high Tg and hydrogen-bond donors, so Tg and donor were not separated yang2021 R7, R8, R9, R10, R11, R12, M1, M2, M3, M4, C8, C25. Cooling also slowed neat PVPVA from about 3.45 to 1.68 mg/min/cm² yang2021 R21, X16. In 2023 lipophilic plasticizers raised the limit of the high-Tg drugs atazanavir and ledipasvir three- to fivefold but that of ritonavir (Tg 50 °C) only 1.2-fold, which the authors read as confirming that mobility limits release more for high-Tg drugs (F26) correasoto2023 R16, C20.

Type. observation in 9 drugs by temperature or Tg (indomethacin, loratadine, atazanavir, lumefantrine salts, miconazole, danazol, elbasvir, paclitaxel, ivacaftor), and 3 drugs with plasticizers in 2023 Strength. : the temperature shifts are large and repeated in four papers yang2021 K4: moderate; saboo2020 K5: weak to moderate; correasoto2022b K3: moderate; hiew2022b K5: weak to moderate, but the limits are in 5% steps without rates at the other temperatures, temperature also changes the polymer, and Tg goes with hydrogen-bond donors across drugs saboo2020 X9; yang2021 X16, C25; hiew2022b X10.

How it was shown

Compacts were dissolved at temperatures above and below the wet Tg of the drug: IND–PVPVA at 10–57 °C, loratadine at 37 and 5 °C and atazanavir (ATZ) at 37 and 55 °C, and powders of six drugs were grouped by wet Tg saboo2020 P7; yang2021 A1, P12, P15; correasoto2022b A3, P5.

What the data show

A 70% IND dispersion standing in for the drug-rich surface took up about 6% water, and its Tg onset fell from 62.64 to 18.48 °C saboo2020 R30.

systemconditionsresultids
IND–PVPVA5-min rates at 10–57 °Climit 10% (25–57 °C), 5% (17 °C), below 5% (10 °C)saboo2020 R29
loratadine compactsrates, t-test, 37 and 5 °CPVPVA 30 → 2%; HPMCAS 20 → 5%yang2021 R22
neat PVPVA, HPMCAScompacts, 37 and 5 °C≈3.45 → 1.68; 0.472 → 0.469 mg/min/cm²yang2021 R21, R18
six drugs in PVPVApowders, 37 °Cdrops at 25, 40% (low Tg) and 5–10% (high Tg)yang2021 R7, R8, R9, R10, R11, R12
lumefantrine benzoate 20%, besylate 10%37 and 10 °C≈59 → 0 and ≈38 → 1 µg/mLhiew2022b R16
ATZ, LED, RTV with TBC or GTB in PVPVAcompacts, 37 °Climit ×5, ×3–4, ×1.2 (cited binary limits 5, 5, 25%)correasoto2023 R16, X7
Fig. 11 of saboo2020: limit of congruency of IND–PVPVA dispersions at five dissolution temperatures
Fig. 11 · saboo2020limit of congruency of IND–PVPVA dispersions at five dissolution temperatures

The limit is flat at 10% from 57 to 25 °C and drops only below 25 °C; only limits, not rates, are shown, in 5% steps saboo2020 R29, X9.

Why

The wet Tg comes from the rule T_{g,\mathrm{wet}} \approx T_{g,\mathrm{dry}} - 10\,w, with w the water content in % saboo2020 E6; yang2021 E3. Saboo and co-workers link the effect "plausibly" to the wet Tg of the drug-enriched surface (about 70% drug, 18 °C) rather than of the neat drug, and propose that lower temperature impedes chain mobility and disentanglement ("may explain") saboo2020 C52, C53, C55. Correa Soto and co-workers argue that a glassy matrix takes up water slowly and needs more water before its chains disentangle, which "likely underpin[s]" the poor release of high-Tg drugs correasoto2022b C34, C36. (synthesis: no paper measured mobility or the wet Tg of the dissolving surface.)

Limits and transfer

Temperature also moved the polymer (neat PVPVA halved at 5 °C), and Me-TIPP (Tg 122.7 °C) reached 30% yang2021 X16; que2021 M3, R19, C31. Estimate the wet Tg of the drug, and if possible of a 70% dispersion, with the 10 °C per 1% rule; a wet Tg above 37 °C places the drug among those that failed at 2–10% in PVPVA, and release should be tested at 37 °C, not at room temperature saboo2020 P22, P23, R29; yang2021 P9; hiew2022b R16.

How it was shown

Saboo and co-workers (2020) dissolved IND–PVPVA compacts for 5 min at 10, 17, 25, 37 and 57 °C, estimated the wet Tg of neat IND (29 °C) from its sorption at 37 °C with a rule of 10 °C per 1% water, and measured the wet Tg of a 70% dispersion by DSC after 4 h at 100% RH saboo2020 P7, P22, P23, E6, M1. Yang and co-workers (2021) placed four drugs on a grid of wet Tg (above or below 37 °C, measured by DSC for loratadine and estimated from sorption for the others) against log P (above or below 5), added paclitaxel and ivacaftor as high-Tg drugs, dissolved PVPVA and HPMCAS powders over loading series, and dissolved loratadine compacts at 37 and 5 °C with drug and polymer rates compared by t-test yang2021 A1, P8, P9, P12, P15, P17, E3. Correa Soto and co-workers (2022) dissolved binary and ternary ATZ–PVPVA compacts at 37 and 55 °C (the wet Tg of ATZ) and imaged binary films at 100% RH at 37 and 50 °C correasoto2022b A3, P5, P8. Hiew and Taylor (2022) dissolved benzoate (20%) and besylate (10%) lumefantrine salt dispersions at 37 and 10 °C hiew2022b A4, P8.

What the data show

IND: the limit was 10% at 57, 37 and 25 °C, 5% at 17 °C and below 5% at 10 °C, with no crystals on partly dissolved tablets; the 70% dispersion took up about 6% water and its Tg onset fell from 62.64 to 18.48 °C saboo2020 R29, R30. INDester at 25%, where crystallization was suppressed at 15 °C, released congruently for 60 min (F19) saboo2020 R10. Loratadine compacts: PVPVA rates matched at 20 and 30% at 37 °C (about 3.33/3.37 and 2.70/2.88) but only at 2% at 5 °C (about 0.97/0.84); HPMCAS matched up to 20% at 37 °C and up to 5% at 5 °C; neat HPMCAS dissolved at 0.472 and 0.469 mg/min/cm² at 37 and 5 °C, neat PVPVA at about 3.45 and 1.68 yang2021 R21, R18, R22. ATZ: at 37 °C the binary compact released about 100% at 5% and less than 3% at 10%; at 55 °C the 10% compact released about 63–64% ATZ and 84% PVPVA by 90 min, the rates rising from about 0.07 to 1.6 (ATZ) and 0.23 to 2.2 mg/min/cm² (PVPVA), while neat PVPVA rose from about 2.7 to 3.7; crystals appeared at 90 min correasoto2022b R1, R6, R7, R5. The binary ATZ film stayed uniform for 3 h at 100% RH and 37 °C but separated within 10 min at 50 °C correasoto2022b R9, R12. Lumefantrine: the benzoate 20% dispersion reached about 59 µg/mL at 37 °C and about 0 at 10 °C, the besylate 10% dispersion about 38 and about 1 µg/mL hiew2022b R16. Across drugs in PVPVA powders the stated drops were at 25% (loratadine), 40% (miconazole), 5% (danazol, wet Tg 73.3 °C) and 10% (elbasvir, 129.1 °C), and paclitaxel and ivacaftor (dry Tg 152 and 175 °C) dropped between 5 and 10% yang2021 R7, R8, R9, R10, R11, R12, M1, M2, M3, M4, M5, M6, X26. (synthesis: the low-Tg drugs of the chapter with limits of 25–40% in PVPVA are loratadine, miconazole, clopidogrel (Tg −9 °C, about 40%), ritonavir (wet Tg about 0 °C, 25%) and lumefantrine free base (19.7 °C, 35%); the high-Tg drugs with 2–10% are danazol, elbasvir, paclitaxel, ivacaftor, ATZ (5%), ledipasvir (160.9 °C, 5%) and lumefantrine sulfate (about 101 °C, 2%) yang2021 R7, R8; correasoto2022a M1, C46; indulkar2019a M1, C2; hiew2022b R2, R20; correasoto2022b C12; que2019 M1, C10.) With plasticizer inside the dispersion the limit rose fivefold for atazanavir (dry Tg about 105 °C, 5 g per 100 g of plasticizer), three- to fourfold for ledipasvir (about 160 °C, 10 g per 100 g needed) and 1.2-fold for ritonavir (50 °C) (F26) correasoto2023 R16, M1, M2, M3.

papersystemmethod and conditionsresultids
saboo2020IND–PVPVA5-min rates at 10–57 °Climit 10% (25–57 °C), 5% (17 °C), below 5% (10 °C)saboo2020 R29
saboo2020IND–PVPVA 70%DSC after 100% RHTg onset 62.64 → 18.48 °C, ≈6% watersaboo2020 R30
yang2021loratadine compactsrates, t-test, 37 and 5 °CPVPVA 30 → 2%; HPMCAS 20 → 5%yang2021 R22
yang2021neat PVPVA, HPMCAScompacts, 37 and 5 °C≈3.45 → 1.68; 0.472 → 0.469 mg/min/cm²yang2021 R21, R18
yang2021six drugs in PVPVApowders, 37 °Cdrops at 25, 40% (low Tg) and 5–10% (high Tg)yang2021 R7, R8, R9, R10, R11, R12
correasoto2022bATZ–PVPVA 10%compacts, 37 and 55 °CATZ ≈2.8 → 63%, PVPVA ≈7.8 → 84% at 90 min; crystalscorreasoto2022b R6, R5
hiew2022blumefantrine benzoate 20%, besylate 10%37 and 10 °C≈59 → 0 and ≈38 → 1 µg/mLhiew2022b R16
correasoto2022aCPD, Tg −9 °Ccompactslimit about 40%correasoto2022a M1, C46
que2019ledipasvir, Tg 160.9 °C, against ritonavircompacts5% against 25%que2019 M1, R28, C49
que2021Me-TIPP, Tg 122.7 °Ccompactslimit 30%que2021 M3, R19, C31
correasoto2023ATZ, LED, RTV with TBC or GTB in PVPVAcompacts, 37 °Climit ×5, ×3–4, ×1.2 (cited binary limits 5, 5, 25%)correasoto2023 R16, X7

Figure

Fig. 11 of saboo2020: limit of congruency of IND–PVPVA dispersions at five dissolution temperatures
Fig. 11 · saboo2020limit of congruency of IND–PVPVA dispersions at five dissolution temperatures

The limit is flat at 10% from 57 to 25 °C and drops only below 25 °C; only limits, not rates, are shown, in 5% steps saboo2020 R29, X9.

Fig. 11 of yang2021: normalized rates of loratadine–PVPVA compacts at 37 and 5 °C
Fig. 11 · yang2021normalized rates of loratadine–PVPVA compacts at 37 and 5 °C

At 37 °C polymer (red) and drug (grey) match to 30%; at 5 °C only at 2%; the neat PVPVA bar at the left of each panel halves on cooling yang2021 R21, X16.

Why

The wet Tg comes from the rule

T_{g,\mathrm{wet}} \approx T_{g,\mathrm{dry}} - 10\,w

with w the water content in % (stated in words) saboo2020 E6; yang2021 E3; hiew2022b E3. Saboo and co-workers place the IND-rich phase in the supercooled-liquid state at 25–57 °C and in the glassy state at 10 °C, link the effect "plausibly" to the wet Tg of the drug-enriched surface (about 70% drug, 18 °C) rather than of the neat drug, and separate it from temperature as such because the limit did not move over more than 30 °C above that Tg saboo2020 C32, C52, C53. Their mechanism is that lower temperature impedes chain mobility and disentanglement ("may explain"); an alternative, that temperature only changes the relative rates of separation and dissolution, is "not supported" by the ester run, and the role of Tg "needs further investigation" saboo2020 C55, C57. Yang and co-workers reason that at 5 °C loratadine "becomes a high Tg compound" with glassy droplets, call the result "a Tg effect" ("appears"), and offer lower drug–polymer miscibility in water at 5 °C, because the ternary phase diagram changes with temperature, as "an alternative explanation"; since neat HPMCAS was not slowed by cooling, a slower polymer alone "cannot explain" the drop yang2021 C16, C35, C36, C26. For low-Tg drugs a mobile drug-rich phase lets the polymer dissolve past it, while a high-Tg drug impedes polymer dissolution at high loading yang2021 C33, C34. Correa Soto and co-workers argue that a glassy matrix takes up water slowly and needs more water before its chains disentangle, which "likely underpin[s]" the poor release of high-Tg drugs, and link the low ATZ limit to its Tg ("may be linked"), citing ritonavir (Tg 50 °C, limit about 25%) correasoto2022b C34, C36, C37, C15, C32. Hiew and Taylor see a role of the dissolution temperature relative to Tg ("appears to play a role") but note that by the water rule every dispersion's wet Tg would be below 37 °C, so wet Tg alone is "difficult to rationalize" hiew2022b C21, C44. In the LLPS chapter the water-plasticized Tg decides whether a drug-rich phase is liquid or glassy at the test temperature (Amorphous solubility and LLPS F2). (synthesis: the papers agree that the mobility of the hydrated drug or drug-rich phase at the test temperature matters, but give two routes, polymer leaving past a mobile drug-rich phase saboo2020 C55; yang2021 C33 and a glassy drug salt unable to separate from the hydrated polymer (F22) hiew2022b C47; no paper measured mobility or the wet Tg of the dissolving surface.) Yang and co-workers (2022) use the low wet Tg of ritonavir (about 14 °C, cited) to explain why drug-rich domains at the surface of high-loading compacts coalesce into a contiguous coating ("can further agglomerate") yang2022a C54, M1. Deac and co-workers (2023) note that both drug-rich phases released in their study had Tgs below 37 °C (16.8 and −5.8 °C), mobile enough to approach equilibrium compositions, and that a high-Tg drug-rich phase "can kinetically trap" the polymer, as for the slowly equilibrating iodinated analogues deac2023a R12, C70; deac2023b C40. (synthesis: the 2024 phase-diagram paper expects dispersions of high-Tg drugs not to follow its local-equilibrium picture ("may not"), which leaves the Tg effects of this finding outside the critical-point reading of F30 deac2024b C54.)

Conditions and limits

PVPVA (and HPMCAS for loratadine); compacts or powders at 5–57 °C in phosphate buffers; temperature limits in 5% steps without rates at 10–57 °C for IND saboo2020 X9. Wet Tg values are estimates from the water rule except loratadine and the 70% IND dispersion, which is a model composition yang2021 P9; saboo2020 X16. The amorphous solubility of loratadine was not measured at 5 °C yang2021 X17. The paclitaxel and ivacaftor classes rest on dry Tg yang2021 X24.

Counterexamples and conflicts

Me-TIPP (Tg 122.7 °C) reached 30% and Me-PHPH (25.2 °C) 40%, and the authors find it "unlikely" that Tg per se explains the series que2021 M3, M4, R19, C31. Ritonavir (wet Tg about 0 °C) has a lower limit (25%) than CPD (Tg −9 °C, about 40%) and the IND ester failed by crystals, so a low Tg does not guarantee a high limit indulkar2019a M1, C2; correasoto2022a C46; saboo2020 C17. Temperature also moved the polymer: neat PVPVA halved at 5 °C and rose from about 2.7 to 3.7 at 55 °C yang2021 X16; correasoto2022b R7. At 55 °C ATZ trailed the polymer and crystallized correasoto2022b X9, C14. In the ASD dissolution chapter a sulfonate salt that raised the Tg of delamanid gave near-complete release from HPMCP (Supersaturation from ASD dissolution F23) duong2022a C67. The wet Tg of ritonavir is cited as about 0 °C in the 2019 papers and about 14 °C in the 2022 imaging study, both below 37 °C indulkar2019a M1; yang2022a M1.

Transfer check

Measure or estimate the wet Tg of the drug, and if possible of a drug-rich (about 70%) dispersion, from water sorption at 37 °C with the 10 °C per 1% rule saboo2020 P22, P23; yang2021 P9. A wet Tg above 37 °C, or a dry Tg above about 70 °C, places the drug among those that failed at 2–10% in PVPVA; test release at 37 °C, not at room temperature, since cooling to 17 °C halved the IND limit and cooling to 10 °C stopped two good releasers saboo2020 R29; hiew2022b R16. For such drugs consider an additive that plasticizes the dispersion (F21) correasoto2022b C40.

History

Que and co-workers (2019) raised the glass transition as "One interesting difference" between ledipasvir and ritonavir without testing it (F9) que2019 C49. Saboo and co-workers (2020) made the first test by temperature saboo2020 C51, C53. Yang and co-workers (2021) compared six drugs and cooled loratadine, Correa Soto and co-workers (2022) heated ATZ to its wet Tg and attributed the high clopidogrel limit to its low Tg, and Hiew and Taylor (2022) raised the Tg of one drug by salt formation and cooled two of its dispersions yang2021 C35; correasoto2022b C15; correasoto2022a C47; hiew2022b C33, C21. Correa Soto and co-workers (2023) lowered the effective Tg with plasticizers instead of raising the temperature and found the gain largest for the highest-Tg drugs (F26) correasoto2023 C21; this adds the last clause to the title. Deac and co-workers (2024, ternary phase diagrams) restricted their critical-point reading of the limit to drug-rich phases that are rubbery at 37 °C (F30) deac2024b C50, C54.

F19

Topic 3Limit of congruency and its causes8 of 13

Congruent release can stop when crystals cover the dissolving surface, a failure that a read-out over the first minutes misses.

Indomethacin methyl ester–PVPVA at 10–25% released drug and polymer together at first; then drug release levelled off after 7.5–20 min while PVPVA kept dissolving saboo2020 R8. XRD, polarized light and SEM showed crystals on the surface from 10 min; at 15 °C, where crystallization was suppressed, the 25% compact released both components together to about 84–88% in 60 min saboo2020 R9, R22, R10. With SDS built in, 30% ritonavir–PVPVA stopped near 80% with needle crystals on the surface by 15 min indulkar2022 R5, R15, R16.

strongStrong for surface crystallization ending congruent release, seen by XRD, PLM, IR and SEM and removed at 15 °C; shown for one drug, whose Tg, crystallization class and medium also differ from its comparator saboo2020 K4, X6.

drugPVPVA5%no crystals576510%22.73415%10.52220%8.41625%12.82125% at 15 °Ccrystallization suppressed≈43, both together010203040506070% released at 30 min, indomethacin methyl ester–PVPVA

At 37 °C crystals covered the surface of the 10–25% compacts and the drug fell behind the polymer. saboo2020 R8, R9, R10

For your drug

  1. For a drug of crystallization class I or II or of low Tg, run the release test for at least 30–60 min with both components assayed and inspect the compact surface at 5, 10 and 20 min by XRD or polarized light.
  2. Read a drug curve that flattens while the polymer continues and the medium stays supersaturated as surface crystallization; confirm at a lower temperature, and do not rely on an inhibitor dissolved in the medium.

saboo2020 P8, P9, M2, R10, C37

How it works and key numbers
  1. At the compact–water interface rapid, polymer-controlled release competes with crystallization of the matrix, which "appears to show a dependency" on loading saboo2020 C39.
  2. Once crystals cover the surface, release depends on dissolution from the remaining amorphous surface, and the crystal layer impedes polymer release saboo2020 C36.
  3. The medium stayed above both solubilities (amorphous 3.9, crystalline 0.6 µg/mL) without net desupersaturation, so crystallization did not start in the solution, and neither the polymer nor 1000 µg/mL HPMC-606 in the medium prevented it at the hydrated interface saboo2020 R1, C37, M6.
  4. The susceptibility of the ester "may arise, in part" from its low Tg (1.7 °C) saboo2020 C38, M2.
  5. SDS is "a double-edged sword": its fast release nearly completes dissolution, but it promotes crystallization before dissolution is complete, and the crystals "likely served as a barrier" indulkar2022 C38, C39.
  6. A drug whose crystallization induction time is shorter than the gel residence time (about 5 min in these compacts) may crystallize in the matrix and lose congruent release deac2023a C48.
7.5–20 mintime after which ester release levelled off at 10–25% loadingsaboo2020 R8
≈84–88%25% ester compact released congruently in 60 min at 15 °Csaboo2020 R10
≈80%plateau of 30% ritonavir–PVPVA with SDS, needle crystals by 15 minindulkar2022 R5, R15
Evidence: data, conditions and papers

Finding F19. A dispersion that released congruently at first could stop when crystals covered the dissolving surface: indomethacin methyl ester at 10–25% levelled off after 7.5–20 min with the medium still supersaturated, suppressing crystallization at 15 °C kept release congruent for 60 min, and SDS built into 30% ritonavir–PVPVA stopped release near 80% with surface crystals by 15 min, so a congruency read-out over the first minutes misses this failure

In short. INDester–PVPVA at 10, 15, 20 and 25% released drug and polymer together at first, then drug release levelled off from about 20, 7.5–10, 10 and 12.5–15 min while PVPVA kept dissolving (about 22.7, 10.5, 8.4 and 12.8% drug against 34, 22, 16 and 21% polymer at 30 min) saboo2020 R8. XRD showed Bragg peaks at 30 min for 10–25%, polarized light showed needles at 10 min and SEM a crystal-covered 25% surface by 20 min; at 15 °C the 25% compact released both components together to about 84–88% in 60 min saboo2020 R9, R22, R10. The medium stayed above both solubilities without measurable desupersaturation, which the authors read as crystallization at the hydrated surface that the polymer, and 1000 µg/mL HPMC-606 in the medium, did not prevent saboo2020 R8, R1, M6, C36, C37. Even so, 8.4–12.8% of INDester had dissolved by 30 min at 15–25% against about 0.1–0.6% of IND, which the authors take as showing the "extremely deleterious effects" of surface enrichment (F17) saboo2020 R6, R8, C46. With 10 parts of SDS, ritonavir–PVPVA plateaued after about 30 min at about 70% (30%), 48–54% (40%) and 33–39% (50%), with needle crystals on the 30% surface and SDS covering about 98 wt% of the 40% surface (F31) yang2023 R2, R16, R17; the weak-base HPMCAS dispersions of 2025 released poorly without crystallizing kaur2025 R14; bapat2025a R6.

Type. observation in 2 systems (indomethacin methyl ester–PVPVA; ritonavir–PVPVA with SDS), with supporting rows for atazanavir, danazol and elbasvir Strength. for surface crystallization ending congruent release, seen by XRD, PLM, IR and SEM and removed at 15 °C saboo2020 K4: strong; one drug, whose Tg, crystallization class and medium also differ from its comparator saboo2020 X6.

How it was shown

Saboo and co-workers (2020) dissolved indomethacin methyl ester (INDester)–PVPVA compacts at 5–25% in pH 6.8 phosphate with 1000 µg/mL HPMC-606 at 37 °C for 30 min, examined the surfaces by XRD, polarized light, SEM and ATR-IR, and dissolved a 25% compact at 15 °C for 60 min saboo2020 P6, P8, P9, P13, P11, P7. Indulkar and co-workers (2022) examined the surfaces of ritonavir–PVPVA–SDS tablets after 2 and 15 min by SEM and ATR-IR indulkar2022 P9, P11.

What the data show

At 5 min no INDester surface had crystallized and drug and polymer rates matched, and after crystallization every medium stayed above the amorphous solubility of 3.9 µg/mL saboo2020 R5, R3, R1, C36.

systemmethod and conditionsresultids
INDester–PVPVA 10–25%30-min profiles, pH 6.8, 37 °Cdrug levels off after ≈7.5–20 min; polymer continuessaboo2020 R8
sameXRD, PLM, SEM, IRcrystals from 10 min; 25% surface covered by 20 minsaboo2020 R9, R22, R18
INDester 25%15 °C, 60 mincongruent, ≈84–88%saboo2020 R10
IND 5–25%XRD at 30 minno crystalssaboo2020 R11
ritonavir–PVPVA 30:70:5 with SDScompacts; SEM and ATR-IR at 2 and 15 mincongruent to ≈75% at 15 min, then flat near 80%; needle crystals and crystalline bands at 15 minindulkar2022 R5, R15, R16
ritonavir–PVPVA 30–50% + 10 parts SDScompacts, 90 min; PLM, SEM, XPSplateau from ≈30 min at ≈70 / 48–54 / 33–39%; needles at 30%; SDS ≈98 wt% of the surfaceyang2023 R2, R16, R17
Fig. 4 of saboo2020: INDester dispersions over 30 min, with NTA frames
Fig. 4 · saboo2020INDester dispersions over 30 min, with NTA frames

INDester (red) tracks PVPVA (black) at 5% but flattens at 10–25% while the polymer keeps rising; every medium lies above the amorphous-solubility level and shows particles saboo2020 R8, R7.

Why

The authors' picture is a competition at the compact–water interface between rapid, polymer-controlled release and matrix crystallization saboo2020 C39. Because there was no net desupersaturation, crystallization was not triggered in the solution, and the polymer cannot prevent crystallization at the hydrated interface ("it is apparent"); the suppression at 15 °C "lends support" to this over the alternative of too little polymer left at the interface saboo2020 C37, C18. Indulkar and co-workers read the ritonavir crystals as having "likely served as a barrier" and call SDS "a double-edged sword" indulkar2022 C38, C39.

Limits and transfer

Surfaces were examined after removal and drying, and IND failed by a drug-rich surface, not by crystals saboo2020 P11, R11, C62. For a drug of crystallization class I or II or a low Tg, run the release test for at least 30–60 min and inspect the surface at 5, 10 and 20 min; a drug curve that flattens while the polymer continues and the medium stays supersaturated points to surface crystallization saboo2020 P8, P9, M2, R10, C37.

How it was shown

Saboo and co-workers (2020) dissolved INDester–PVPVA compacts at 5–25% in pH 6.8 phosphate containing 1000 µg/mL HPMC-606 at 37 °C, sampling drug and polymer to 30 min, and examined the tablet surfaces at 0, 5 and 30 min by XRD, at 0, 5 and 10 min by polarized light, at 5, 10 and 20 min by SEM and at 0, 5 and 20 min by ATR-IR, where crystalline INDester has a band at 1607 cm⁻¹ saboo2020 P6, P8, P9, P13, P11, R18, M6. A 25% compact was dissolved for 60 min at 15 °C, where crystallization was suppressed; dissolution below the Tg of INDester (about 2 °C) was impossible in water saboo2020 P7, C9. Correa Soto and co-workers (2022) checked dissolving ATZ compacts at 55 °C by polarized light correasoto2022b P11. Yang and co-workers (2021) followed danazol and elbasvir in solution yang2021 R9, R14, R3. Indulkar and co-workers (2022) ejected 30:70:5 ritonavir–PVPVA–SDS tablets after 2 and 15 min of dissolution in pH 6.8 phosphate at 37 °C and examined the surface by SEM and by ATR-IR against crystalline ritonavir; the tablets with the other surfactants were checked the same way indulkar2022 P9, P11, R17.

What the data show

At 5 min no surface had crystallized and every INDester loading released drug and polymer at matching rates of about 3.3–4.2 mg/min/cm² saboo2020 R5, R3. Over 30 min the 5% compact released drug and polymer together (about 57 and 65%) without crystals, whereas at 10–25% drug release levelled off at the times in the short part while PVPVA continued saboo2020 R8, R9. The 25% surface was smooth at 5 min, carried scattered needles at 10 min and was covered with crystals at 20 min, and the 1607 cm⁻¹ band was absent at 5 min and present at 20 min saboo2020 R22, R18. Every INDester medium exceeded the amorphous solubility of 3.9 µg/mL (crystalline 0.6 µg/mL) and held nanoparticles, and after crystallization the concentration stayed on a plateau above both saboo2020 R1, R7, R8, C36. At 15 °C the 25% compact released drug and polymer along overlapping curves (about 21% at 15 min, 43% at 30 min, 84–88% at 60 min) saboo2020 R10. IND (crystallization class III) showed no Bragg peaks at 30 min at any loading, against class II for INDester saboo2020 R11, M1, M2. With ATZ at 55 °C drug release stopped at about 70 min and crystals were seen at 90 min, and the TPGS dispersion crystallized after 1 h correasoto2022b R5, R6. Danazol released from 2% PVPVA powder fell from about 91% at 15 min to about 17% at 60 min while the polymer reached about 94%, and elbasvir droplets from PVPVA crystallized after 30 min, both in solution yang2021 R14, R3. (synthesis: the INDester–PVPVA pair has a limit of at least 25% from 5-min rates but released congruently over 30 min only at 5%, so the two read-outs differ by at least four loading steps for a class II drug.) Ritonavir with SDS: drug and polymer were released together and fast, about 60% of the drug at 10 min and 75% at 15 min, and then both levelled off at about 80% to 90 min indulkar2022 R5. At 2 min the tablet surface was smooth and its IR spectrum matched the dry dispersion; at 15 min SEM showed needle-shaped crystals and IR showed bands of crystalline ritonavir, while the other surfactant tablets showed no surface crystals indulkar2022 R15, R16, R17. The two SEM images differ in detector and magnification, and the IR band list of the text differs from the arrows of the figure indulkar2022 X17, X7. Ritonavir–PVPVA with 10 parts of SDS released about 68–70% by 30 min at 30% and then stayed, 53–54% from 30 min at 40% and 33–39% at 50%; PLM and SEM showed needles on the 30% surface at 30 min, and XPS put SDS at about 60 wt% of the 40% surface before and 98 wt% after 30 min yang2023 R2, R16, R17. Bedaquiline–HPMCAS residues were non-birefringent with PXRD halos, and loratadine and cinnarizine HPMCAS dispersions showed no crystals during 1 h or for 12 h after, except small crystals for loratadine–LF after about 10 h kaur2025 R14; bapat2025a R6.

papersystemmethod and conditionsresultids
saboo2020INDester–PVPVA 10–25%30-min profiles, pH 6.8, 37 °Cdrug levels off after ≈7.5–20 min; polymer continuessaboo2020 R8
saboo2020sameXRD, PLM, SEM, IRcrystals from 10 min; 25% surface covered by 20 minsaboo2020 R9, R22, R18
saboo2020INDester 25%15 °C, 60 mincongruent, ≈84–88%saboo2020 R10
saboo2020IND 5–25%XRD at 30 minno crystalssaboo2020 R11
correasoto2022bATZ 10% binary and with TPGS55 °C, PLMcrystals at 90 min and after 1 h; ATZ release stops near 70 mincorreasoto2022b R5, R6
yang2021danazol–PVPVA 2% powder60 min≈91 → ≈17% drug; polymer ≈94%yang2021 R14
correasoto2022aCPD with CTAB120 min, PLMdissolved drug falls without crystalscorreasoto2022a R16, C26
indulkar2022ritonavir–PVPVA 30:70:5 with SDScompacts, pH 6.8, 37 °C; SEM and ATR-IR at 2 and 15 mincongruent to ≈75% at 15 min, then flat near 80%; needle crystals and crystalline bands at 15 minindulkar2022 R5, R15, R16
moseson2023 (ASD process)posaconazole–HPMCAS particles, oxide coatingSHG after releasecoating delayed matrix crystallization and raised releasemoseson2023 C40
yang2023ritonavir–PVPVA 30–50% + 10 parts SDScompacts, 90 min; PLM, SEM, XPSplateau from ≈30 min at ≈70 / 48–54 / 33–39%; needles at 30%; SDS ≈98 wt% of the surfaceyang2023 R2, R16, R17
kaur2025bedaquiline–HPMCAS residuesPLM, PXRDamorphouskaur2025 R14
bapat2025aloratadine, cinnarizine in three HPMCAS gradesPLM during 1 h and up to 12 h afterno crystals except loratadine–LF after ≈10 hbapat2025a R6

Figure

Fig. 4 of saboo2020: INDester dispersions over 30 min, with NTA frames
Fig. 4 · saboo2020INDester dispersions over 30 min, with NTA frames

INDester (red) tracks PVPVA (black) at 5% but flattens at 10–25% while the polymer keeps rising; every medium lies above the amorphous-solubility level and shows particles saboo2020 R8, R7.

Fig. 8 of saboo2020: SEM of the 25% INDester tablet surface after 5, 10 and 20 min
Fig. 8 · saboo2020SEM of the 25% INDester tablet surface after 5, 10 and 20 min

Smooth at 5 min, needles at 10 min, crystal-covered at 20 min; use the instrument data bars, not the caption, for sizes saboo2020 R22, X12.

Why

The authors' picture is a competition at the compact–water interface between rapid, polymer-controlled release and matrix crystallization, which "appears to show a dependency" on loading saboo2020 C39. Once crystals cover the surface, release depends on dissolution from the remaining amorphous surface against surface nucleation and growth; the solution sits above both solubilities with little driving force for further dissolution, and the crystal layer impedes polymer release saboo2020 C36. Because there was no net desupersaturation, they conclude that crystallization was not triggered by or in the solution, and that the polymer cannot prevent crystallization at the hydrated interface ("it is apparent") saboo2020 C37. The suppression at 15 °C "lends support" to this over the alternative that a loss of congruency left too little polymer at the interface saboo2020 C18. The susceptibility of INDester "may arise, in part" from its low Tg (1.7 °C) saboo2020 C38, M2. In the ASD dissolution chapter wetted amorphous felodipine, nifedipine and celecoxib crystallized in or on the solid, a polymer dissolved in the medium did not stop it for nifedipine and celecoxib, and matrix crystallization depended on the polymer and its content (Supersaturation from ASD dissolution F1, F2, F16); the INDester result is the same route in a compact that was releasing congruently (synthesis: the routes and polymer effects of those findings). Indulkar and co-workers (2022) read the ritonavir crystals on the SDS tablet as having "likely served as a barrier" to further release, and call SDS "a double-edged sword": its fast release nearly completes dissolution, but it promotes crystallization before dissolution is complete under the non-sink conditions used indulkar2022 C38, C39. Surfactants are known to promote crystallization by lowering the interfacial energy of new surfaces, by templating and by plasticizing the matrix (cited), and they "can" make a crystallization-inhibiting polymer ineffective even in a homogeneous dispersion indulkar2022 C40, C42. Whether phase separation preceded the crystals is "difficult to ascertain" indulkar2022 C41. Deac and co-workers (2023) add that a drug whose crystallization induction time is shorter than the gel residence time (about 5 min in their compacts) may crystallize in the matrix and lose congruent release, and that a polymer with a short residence time "may be worthwhile" then deac2023a C48. Yang and co-workers write that the SDS plateau "can be attributed" to crystallization at the compact surface, which SDS accumulating there "conceivably" promotes through higher surface mobility; crystals were imaged only at 30% and not identified yang2023 C24, C50, X12.

Conditions and limits

One drug–polymer pair at pH 6.8 with HPMC-606 in the medium, 30 min at 37 °C and 60 min at 15 °C; surfaces examined ex situ after removal and drying saboo2020 P6, P7, P11. The crystallizing range is stated as above 5% and above 10% in two places; the figures support 10–25% saboo2020 X1. The 55 °C ATZ runs mix crystallization with higher mobility and faster polymer (F18) correasoto2022b X9. The ritonavir surface was examined at two times only, and the crystallization of the binary tablet surface under the same conditions was not reported indulkar2022 A5, C39.

Counterexamples and conflicts

IND did not crystallize within 30 min, and its failure came from a drug-rich surface instead saboo2020 R11, C62. With CTAB the clopidogrel concentration fell without crystals, attributed to droplet agglomeration ("can be attributed") correasoto2022a C26. The table-of-contents graphic lists surface crystallization among factors that lower the limit, although the INDester limit from 5-min rates was not lowered saboo2020 X7. Poor release of weak bases from HPMCAS came without crystals, from complexation of the polymer (F32) kaur2025 C23; bapat2025a C17.

Transfer check

For a drug of crystallization class I or II or a low Tg, run the release test for at least 30–60 min with both components assayed and inspect the compact surface at 5, 10 and 20 min by XRD or polarized light saboo2020 P8, P9, M2. A drug curve that flattens while the polymer continues and the medium stays supersaturated points to surface crystallization; repeat at a lower temperature to confirm, and do not rely on an inhibitor dissolved in the medium saboo2020 R10, C37.

History

In the ASD dissolution chapter Alonzo and co-workers (2010) set out the two crystallization routes of dissolving amorphous solids (Supersaturation from ASD dissolution F1). Saboo and co-workers (2020) were the first in this subcategory to show surface crystallization ending congruent release and named it one of two failure mechanisms saboo2020 C62. An ASD process paper of 2021 cites the result for surface crystallization of PVPVA dispersions during release, and an oxide nanocoating later delayed matrix crystallization during release of posaconazole particles (as listed in the evidence index of this subcategory) moseson2023 C40. Indulkar and co-workers (2022) found the same surface failure for ritonavir, a drug that did not crystallize on the binary tablet in these papers, once SDS was built into the dispersion, which widens the title from a fast-crystallizing drug to surfactant-promoted crystallization indulkar2022 C38, C39. Yang and co-workers (2023) found the SDS-related surface crystals of the 2022 ritonavir study again at 10 parts SDS, and the HPMCAS papers of 2025 excluded crystallization by PLM and PXRD yang2023 C51; kaur2025 C23; bapat2025a C17.

F20

Topic 3Limit of congruency and its causes9 of 13

After water separated a dispersion, release followed the shape of the drug-rich phase: discrete domains released, a continuous phase did not.

At 30% felodipine in PVPVA every film separated after 12 h at about 100% RH, into semi-continuous drug-rich domains at 0 and 2% TPGS and round, discrete domains at 5 and 10% TPGS; only the latter released congruently saboo2021 R21, R23, R9, R10. Clopidogrel films were uniform at 40%, bicontinuous at 50% and drug-continuous at 60%, matching good release at 40% and its loss from 50% correasoto2022a R20, R21, R17. A 10% atazanavir film stayed uniform for 3 h although that loading released less than 3%, so a uniform film did not guarantee release correasoto2022b R9, R1.

weakWeak to moderate: film morphology and release change at the same loadings or additive levels, but the films were held 5 min to 12 h in humid air and the gel layer of the dissolving compact was not imaged in these papers saboo2021 K4, K5, X5; correasoto2022a K7, X13.

Clopidogrel–PVPVA: drug released, % (film morphology after 5 min at 100% RH)40%film uniform≈7750%bicontinuous≈5250% with SDSnearly uniform≈7060%drug-continuous≈7

Release fell where the drug-rich phase of the wetted film became continuous. correasoto2022a R17, R20, R21

30% felodipine–PVPVA: felodipine release rate, mg/min/cm²2% TPGSsemi-continuous drug-rich domains0.0085–10% TPGSdiscrete round domains≈2.6–3.25

Both films had separated after 12 h at about 100% RH; only the shape of the drug-rich phase differed. saboo2021 R9, R10, R21, R23

For your drug

  1. Cast films at the target loading and one step above, expose them to about 100% RH for 5 min and for 12 h, and image with a drug-selective and a polymer-selective dye.
  2. Read discrete round drug-rich domains in a continuous polymer-rich phase as consistent with congruent release, and a bicontinuous or drug-continuous structure as predicting loss of release; a uniform film of a high-Tg drug is no assurance, so check the Tg (F18).

correasoto2022a P17; saboo2021 P13, C53; correasoto2022b R9; hiew2022b R19

How it works and key numbers
  1. At high loading, whether release is drug- or polymer-controlled "depends largely" on the architecture of the drug-rich phase formed in the hydrated matrix saboo2021 C37.
  2. A contiguous drug-rich network "likely also forms" in the gel layer and leaves a porous, insoluble drug-rich layer once the polymer-rich phase has dissolved saboo2021 C39.
  3. Discrete domains, "rationalized" by a lower interfacial energy and slower coarsening with TPGS, "can release" intact as the gel layer recedes saboo2021 C50, C40, C41.
  4. Yang and co-workers "anticipate" that the lower-volume phase forms the discrete phase, so that the drug-rich phase inverts to the continuous one as loading rises, and call a continuous drug-rich phase "catastrophic" for release yang2022a C58, C46, C59.
  5. The binary atazanavir and lumefantrine sulfate films failed without separating, which the authors read through low mobility of a high-Tg drug (F18, F22) correasoto2022b C22; hiew2022b C47.
  6. In dissolving compacts of 2023 the same correspondence appeared: discrete droplets inside the gel with good release, networks with failure (F25) deac2023a R6, R7, C72.
≈77 / 52 / 7%clopidogrel released at 40, 50 and 60%: films uniform, bicontinuous, drug-continuouscorreasoto2022a R17, R20
0.008 against 2.6–3.25 mg/min/cm²30% felodipine with 2% TPGS (semi-continuous domains) against 5–10% TPGS (discrete)saboo2021 R10, R9
≈2.4%10% atazanavir released by 90 min although its film stayed uniformcorreasoto2022b R2, R9
Evidence: data, conditions and papers

Finding F20. When water separated a dispersion, release followed the shape of the drug-rich phase rather than the separation itself: discrete drug-rich domains went with congruent release and a continuous or bicontinuous drug-rich phase with its loss, while films of two high-Tg drug forms failed without visible separation and the surfactant films of one of them separated within minutes yet released

In short. At 30% felodipine in PVPVA every film separated after 12 h at about 100% RH, into semi-continuous drug-rich domains at 0 and 2% TPGS and round, discrete domains at 5 and 10% TPGS; only the latter released congruently, and micro-CT showed a porous surface layer on the 0 and 2% tablets and none at 5 and 10% saboo2021 R21, R23, R19, R9, R10. Clopidogrel films after 5 min at 100% RH were uniform at 40%, bicontinuous at 50% and drug-continuous at 60%, matching good release at 40% and its loss from 50%; with SDS the 50% film stayed nearly uniform and the dispersion released correasoto2022a R20, R21, R17. A 10% atazanavir film stayed uniform for 3 h at 100% RH although that loading released less than 3%, while every surfactant film separated within 10 min and the surfactant dispersions released 11–106% correasoto2022b R9, R10, R11, R1, R2; the high-Tg lumefantrine sulfate film did not separate yet released only at 2% hiew2022b R19, R20. All morphologies were seen on films or dried tablets, not in a dissolving compact saboo2021 C42; correasoto2022a X13. In 2023–2024 a persistent continuous drug-rich layer went with failure in ten surfactant–ritonavir compacts while a layer swept away by flow did not block release, droplets that agglomerated into strands failed with short PVP chains, and phenolphthalein and its ether switched from droplets to a continuous phase in films at 10–15% and near 40% (F31, F29, F30) yang2023 C40, R8; deac2024a R7, R10; deac2024b R18, R19.

Type. observation in 4 drugs in films (felodipine, clopidogrel, atazanavir, lumefantrine), with ritonavir and two phenolphthalein analogues in dissolving compacts in 2022–2023 (F25) Strength. to moderate: film morphology and release change at the same loadings or additive levels saboo2021 K4: moderate, K5: weak to moderate; correasoto2022a K7: weak to moderate, but at one loading (felodipine), on films held 5 min to 12 h in humid air, and with the gel layer of the dissolving compact not imaged saboo2021 X5; correasoto2022a X13.

How it was shown

Saboo and co-workers (2021) held 30% felodipine–PVPVA films with 0–10% TPGS for 12 h at about 100% RH and imaged them by AFM and nanoIR, and scanned dissolving tablets by micro-CT saboo2021 P12, P13, P14, P11. Correa Soto and co-workers (2022) imaged clopidogrel and atazanavir films with a drug-selective and a polymer-selective dye by confocal microscopy after 5 min to 3 h at 100% RH correasoto2022a P17; correasoto2022b P8.

What the data show

At 30% felodipine release failed with 0 and 2% TPGS and was congruent with 5 and 10%, and binary clopidogrel dispersions released about 77, 52 and 7% of the drug at 40, 50 and 60% saboo2021 R10, R9; correasoto2022a R17.

systemmethod and conditionsresultids
felodipine–PVPVA 30% ± TPGSfilms, 12 h ≈100% RH; AFM, nanoIRsemi-continuous (0, 2%) against discrete drug-rich domains (5, 10%)saboo2021 R21, R23
clopidogrel–PVPVA 40–60%films, 5 min 100% RH, confocaluniform, bicontinuous, drug-continuous; SDS 50% nearly uniformcorreasoto2022a R20, R21
atazanavir–PVPVA 10% binaryfilms, 3 h 100% RH, 37 °Cuniform; release ≈2.4% at 90 mincorreasoto2022b R9, R2
atazanavir 10% with additivesfilms, 10 minall separated; release 11–106%correasoto2022b R10, R11, R2
lumefantrine free base, benzoate, sulfatefilms, high RH, 37 °Cseparated, separated, homogeneoushiew2022b R19
ritonavir–PVPVA 10–50% compactsconfocal during and after dissolutiondroplets (10–20%), porous continuous layer (30%), rigid layer (40–50%); release complete, ≈35%, ≤3%yang2022a R4, R6, R12, R13, R2
Fig. 13 of saboo2021: nanoIR maps of 30% felodipine films without and with 10% TPGS after high humidity
Fig. 13 · saboo2021nanoIR maps of 30% felodipine films without and with 10% TPGS after high humidity

Top, no TPGS: connected drug-rich (red) regions; bottom, 10% TPGS: separate round drug-rich domains in a drug-lean (blue) matrix saboo2021 R23, X19.

Why

Saboo and co-workers (2021) state that at high loading whether release is drug- or polymer-controlled "depends largely" on the architecture of the drug-rich phase: a contiguous network "likely also forms" in the gel layer and leaves a porous, insoluble drug-rich layer, while discrete domains "can release" intact as the gel layer recedes saboo2021 C37, C39, C40. Hiew and Taylor argue that a high-Tg salt cannot separate at all ("potential explanation") hiew2022b C47. (synthesis: film separation predicted release in neither direction, while the shape of the separated drug-rich phase tracked release for felodipine and clopidogrel.)

Limits and transfer

The films were thin, held in humid air and mostly dried before imaging saboo2021 P12, P13; correasoto2022a P17. With PVP K12 discrete droplets agglomerated into a network anchored in the gel deac2024a R10, R1. In films of the target loading and one step above, discrete round drug-rich domains are consistent with congruent release, a bicontinuous or drug-continuous structure predicts its loss, and a uniform film of a high-Tg drug is no assurance correasoto2022a P17; saboo2021 C53; correasoto2022b R9; hiew2022b R19.

How it was shown

Saboo and co-workers (2021) spin-coated 30% felodipine–PVPVA films with 0–10% TPGS under nitrogen below 20% RH, held them 12 h at about 100% RH, dried them and imaged them by AFM, and at 0 and 10% TPGS by AFM-nanoIR at a felodipine band (1213 cm⁻¹) and a PVPVA band (1243 cm⁻¹); 30% tablets were scanned by micro-CT after 10 min of dissolution saboo2021 P12, P13, P14, P16, P11. Correa Soto and co-workers (2022) imaged spin-coated films of 40–60% clopidogrel with Nile red (drug-rich phase) and Alexa 488 (polymer-rich phase) by confocal microscopy, fresh and after 5 min at 100% RH, with a detection limit of about 500 nm correasoto2022a P17, C7. In the atazanavir study the same dyes were imaged at 100% RH and 37 °C for up to 3 h (binary) or 10 min (ternaries), and the binary film also at 50 °C correasoto2022b P8. Hiew and Taylor (2022) imaged Nile red films at 37 °C and high RH, with the images in an SI that was not supplied hiew2022b P15, P16, R19.

What the data show

Felodipine: fresh films were featureless; after 12 h all four films had separated, "irregularly shaped semi-continuous domains" at 0 and 2% TPGS and "circular, discrete domains" at 5 and 10%, and nanoIR placed the drug in elongated, connected regions without TPGS and in separate round domains with 10% TPGS saboo2021 R20, R21, R23, C24, C25. At 30% release failed with 0 and 2% TPGS (PVPVA about 0.2–0.3 and felodipine 0.008 mg/min/cm² at 2%) and was congruent with 5 and 10% TPGS (about 2.6–3.25) saboo2021 R10, R9, R12. The micro-CT sections of the 0 and 2% tablets showed a porous zone at the dissolving face, those of the 5 and 10% tablets a homogeneous section saboo2021 R19. Clopidogrel: after 5 min at 100% RH the binary film was unchanged at 40%, bicontinuous at 50% and drug-continuous with discrete polymer-rich domains at 60%; with SDS the 50% film showed at most a small heterogeneity and the 60% film a continuous drug-rich phase with smaller polymer domains; with TPGS the 50% film was bicontinuous and the 60% film coarse; with Tween 80 the 50 and 60% films separated correasoto2022a R20, R21, R22, R23, X12. Release matched: about 77, 52 and 7% of the drug at 40, 50 and 60% for the binary, 70% at 50% with SDS correasoto2022a R17. Atazanavir: the binary 10% film showed no separation within the resolution for 3 h at 37 °C and separated within 10 min at 50 °C; films with SDS, CTAB or TPGS formed low-contrast domains that appear to contain drug and polymer, those with Tween 80 or Spans high-contrast drug-rich domains on a polymer-rich background correasoto2022b R9, R12, R10, R11, C20, C21. The binary 10% dispersion released about 2.4% of its drug in 90 min and the additive dispersions 11–106% correasoto2022b R2. Lumefantrine: free base and benzoate films separated, the sulfate film stayed visually homogeneous; the free base released well to 35% and the sulfate only at 2% hiew2022b R19, R20. Ritonavir at 30% with surfactants: every dry dispersion had one Tg (midpoints 70.90–84.93 °C against 82.24 °C for the binary), and after dissolution the surface material of the Tween 80 and Span 20 tablets had a Tg onset of 40.25 and 42.18 °C against 66.01 and 67.85 °C before, which the authors read as a separated ritonavir-rich phase; these two dispersions stalled at about 25 and 41% release indulkar2022 R18, R19, C19, R6, R7. No second, polymer-rich Tg and no water content were reported, and the Span 85, TPGS and SDS tablets were not tested for separation although the summary table lists "No" indulkar2022 X10, X4. Ritonavir–PVPVA compacts imaged during dissolution in 2022 showed the same correspondence: discrete drug-rich droplets at 10–20%, where release was congruent and complete; a continuous but porous drug-rich layer at 30%, through which air and polymer escaped while drug release stalled at about 35%; and a rigid continuous layer at 40–50%, where at most about 3% of the drug was released (F25) yang2022a R4, R6, R12, R13, R2. Dissolving compacts of 2023 showed the correspondence directly: discrete droplets inside the gel and good release at 5–30% MePHPH, networks and failing release from 40–50% MePHPH and 10–20% PHPH (F25) deac2023a R6, R7, R1, R2. In ritonavir–PVPVA compacts with four surfactants every releasing dispersion showed discrete droplets or a one-phase gel and every one with a persistent continuous drug-rich layer released minimal drug yang2023 C40. Clotrimazole films with PVP K12 formed strands of touching droplets by 11 h at 100% RH, those with K29/32 kept separate droplets deac2024a R7. MePHPH films at 100% RH kept droplets at 10–30%, were co-continuous at 1 h and droplets at 6 h at 40%, and continuous at 50–60%; PHPH films held droplets at 5–10% and a continuous drug-rich phase at 15–20% deac2024b R18, R19.

papersystemmethod and conditionsresultids
saboo2021felodipine–PVPVA 30% ± TPGSfilms, 12 h ≈100% RH; AFM, nanoIRsemi-continuous (0, 2%) against discrete drug-rich domains (5, 10%)saboo2021 R21, R23
saboo2021same, tabletsmicro-CT after 10 minporous layer (0, 2%); homogeneous (5, 10%)saboo2021 R19
correasoto2022aCPD–PVPVA 40–60%films, 5 min 100% RH, confocaluniform, bicontinuous, drug-continuous; SDS 50% nearly uniformcorreasoto2022a R20, R21
correasoto2022bATZ–PVPVA 10% binaryfilms, 3 h 100% RH, 37 °Cuniform; release ≈2.4% at 90 mincorreasoto2022b R9, R2
correasoto2022bATZ 10% with additivesfilms, 10 minall separated; release 11–106%correasoto2022b R10, R11, R2
hiew2022blumefantrine free base, benzoate, sulfatefilms, high RH, 37 °Cseparated, separated, homogeneoushiew2022b R19
indulkar2022ritonavir–PVPVA 30:70:5 with Tween 80, Span 20DSC of surface material after dissolutionTg onset 66.01 → 40.25 and 67.85 → 42.18 °C; release stalls ≈25 and ≈41%indulkar2022 R19, R6, R7
yang2022aritonavir–PVPVA 10–50% compactsconfocal during and after dissolutiondroplets (10–20%), porous continuous layer (30%), rigid layer (40–50%); release complete, ≈35%, ≤3%yang2022a R4, R6, R12, R13, R2
deac2023aMePHPH 5–50%, PHPH 5–20% compactsin situ confocal of the dissolving geldroplets with good release; networks with failuredeac2023a R6, R7, C72
yang2022b (Physical stability)ritonavir–PVPVA 30% ± surfactantsfilms, confocal, O-PTIRbinary bicontinuous; SDS and Tween 80 discrete, Span 85 continuous drug-richyang2022b C9, R22
saboo2021 (cited)ritonavir–PVP; lopinavir–HPMC filmsliteraturerelease switch where domains became continuous; discrete domains and complete dissolution at 15%saboo2021 R24, R25
yang2023ritonavir–PVPVA 30–50% + four surfactantscompacts, confocalrelease with droplets or a one-phase gel; none with a persistent continuous layeryang2023 C40, R6, R7, R9, R13
deac2024aclotrimazole–PVP K12, K29/32 10% films100% RH, 11 hstrands of droplets (K12); separate droplets (K29/32)deac2024a R7
deac2024bMePHPH 10–60%, PHPH 5–20% films100% RH, confocaldroplets to 30% and 10%; continuous from 50% and 15%deac2024b R18, R19

Figure

Fig. 13 of saboo2021: nanoIR maps of 30% felodipine films without and with 10% TPGS after high humidity
Fig. 13 · saboo2021nanoIR maps of 30% felodipine films without and with 10% TPGS after high humidity

Top, no TPGS: connected drug-rich (red) regions; bottom, 10% TPGS: separate round drug-rich domains in a drug-lean (blue) matrix; read the ratio colours as relative only saboo2021 R23, X19.

Fig. 11 of correasoto2022a: binary clopidogrel–PVPVA films before and after 5 min at 100% RH
Fig. 11 · correasoto2022abinary clopidogrel–PVPVA films before and after 5 min at 100% RH

The 40% film stays uniform, the 50% film turns bicontinuous, and at 60% the red drug-rich phase is continuous around dark polymer-rich domains correasoto2022a R20.

Why

Saboo and co-workers (2021) extend the transient-gel-layer model: at high loading, whether release is drug- or polymer-controlled "depends largely" on the architecture of the drug-rich phase formed in the hydrated matrix saboo2021 C37. A contiguous network "likely also forms" in the gel layer and leaves a porous, insoluble drug-rich layer once the polymer-rich phase has dissolved, and rapid coarsening is "clearly a feasible explanation" for the loss of release; with TPGS the discrete domains, "rationalized" by a lower interfacial energy and slower coarsening, "can release" intact as the gel layer recedes, or the surfactant "may" slow the separation itself saboo2021 C39, C50, C40, C41. The film domains appear larger than the 200–300 nm particles in solution, which the authors read as separation running under different conditions in a slowly wetted film and a fast-wetted compact ("likely") saboo2021 C47, C48. Correa Soto and co-workers (2022) state that separation leaving enough drug-rich phase for a continuous or semi-continuous barrier degrades release ("support a link"), that SDS "may prevent, delay, or change the domain size", and that the significance of these differences, "if any, is currently unknown" correasoto2022a C53, C58, C61. In the atazanavir study separation is taken as a sign of mobility that the surfactants supply ("suggest"), with drug–polymer miscibility in water possibly changed ("may") correasoto2022b C22, C41, C49. Hiew and Taylor argue that separated drug and polymer both leave at the polymer's rate as long as the drug cannot form a continuous barrier, and that a high-Tg salt cannot separate at all ("potential explanation"; F22) hiew2022b C46, C47. (synthesis: across the four drugs, film separation predicted release in neither direction: the binary ATZ and sulfate films failed without separating, and the ATZ surfactant films separated and released; the shape of the separated drug-rich phase tracked release for felodipine, clopidogrel and the cited ritonavir–PVP study, which qualifies the link between separation and the limit drawn in F8.) Indulkar and co-workers (2022) propose that Span 85 and TPGS, which released ritonavir completely without a faster polymer, "can potentially" act by changing the kinetics of separation or the composition and morphology of the separated regions, and that Tween 80 and Span 20 lose the race against separation because they do not raise the release rate above that of the polymer ("may") indulkar2022 C35, C45; neither morphology nor rate was measured in that paper indulkar2022 X4, C24. Yang and co-workers (2022) call a continuous drug-rich phase "catastrophic" for release and the loss of congruency "likely dependent" on the morphology after separation, in agreement with Han and co-workers (cited); they "anticipate" that the lower-volume phase forms the discrete phase, so that the drug-rich phase inverts to the continuous one as loading rises, helped by coalescence of the low-Tg drug-rich phase yang2022a C58, C46, C59.

Conditions and limits

Spin-coated films of about 100–200 nm, exposed to humid air for 5 min to 12 h and in most cases dried before imaging; confocal resolution about 500 nm saboo2021 P12, P13; correasoto2022a P17. Felodipine morphology at 30% only, nanoIR at 0 and 10% TPGS only, domain sizes not measured saboo2021 X5, X6, X7. CTAB films were not imaged; the lumefantrine images and their loadings are in an SI that was not supplied correasoto2022a X13; hiew2022b X20.

Counterexamples and conflicts

The ATZ films with Tween 80 and Span 85 showed irregular, connected drug-rich domains, yet these dispersions released 56.5 and 38% at 10% against about 2.4% for the uniform binary correasoto2022b R11, R2. Phase separation raised release of lopinavir–HPMC films at 33–85% (F12) li2019 C38. A cited study found that water-induced separation did not change the dissolution of a 40% dispersion saboo2019 R22. Discrete droplets did not guarantee release: with PVP K12 they agglomerated into a network anchored in the gel and the drug stayed while the polymer left (F29) deac2024a R10, R1. A continuous layer that formed on 30% Span 85 compacts in a quiet chamber was removed under rotation, and the dispersion released about 86% yang2023 R8, R2.

Transfer check

Cast films of the target composition at the target loading and one step above, expose them to about 100% RH for 5 min and for 12 h, and image with a drug-selective and a polymer-selective dye correasoto2022a P17; saboo2021 P13. Discrete round drug-rich domains in a continuous polymer-rich phase are consistent with congruent release; a bicontinuous or drug-continuous structure predicts loss of release; a uniform film of a drug with a high Tg is no assurance, so check the Tg (F18) saboo2021 C53; correasoto2022b R9; hiew2022b R19.

History

Purohit and Taylor (2017) and the papers of 2019–2020 placed water-induced separation of films above the limit of congruency (F8) purohit2017b C53; indulkar2019a C9. Saboo and co-workers (2021) were the first in this subcategory to tie the morphology of the separated phase to release, citing ritonavir–PVP and lopinavir–HPMC studies saboo2021 C30. Correa Soto and co-workers (2022) showed the morphology changing with loading and surfactant, and the atazanavir and lumefantrine studies of 2022 showed release failing without visible separation for high-Tg forms correasoto2022a C32, C33; correasoto2022b C18; hiew2022b C48. Yang and co-workers (2022) carried the morphology link from humidified films to dissolving compacts (F25) yang2022a C58. Deac and co-workers (2023) showed the morphology link in the dissolving gel of two analogues (F25) deac2023a C72. Yang and co-workers (2023) and Deac and co-workers (2024) carried the correspondence to surfactant-containing compacts, to the persistence of the layer under flow, to agglomerating droplets and to measured phase diagrams yang2023 C37; deac2024a C42; deac2024b C65.

F25

Topic 3Limit of congruency and its causes10 of 13

In dissolving compacts release stayed congruent while the drug-rich phase formed discrete droplets, and failed once it connected into a network.

Ritonavir–PVPVA compacts imaged in cross-section and in real time carried drug-rich droplets of 0.5–2 µm at the surface of the gel at 10–20%, which passed into the solution with the dissolving polymer; at 30% a continuous porous drug-rich layer formed and at 40% a rigid one yang2022a R6, R10, R11, R12, R13. In the phenolphthalein analogues the switch from droplets to a network came at 40–50% for the methyl ether (MePHPH) and at 10–20% for phenolphthalein (PHPH) deac2023a R6, R7. Release followed: ritonavir about 100, 35 and at most 3% at 20, 30 and 40–50% yang2022a R2.

moderateModerate: release and three imaging modes agree in both papers, but the link is a co-occurrence across set-ups with different stirring, and a partial network at 40% MePHPH came with good release yang2022a K2, K5; deac2023a K1, X10, X4, C60.

discrete drug-rich dropletsconnected drug-rich phaseritonavirdroplets 0.5–2 µmcontinuous layerMePHPHdroplets inside the gelnetwork → continuousPHPHdroplets beyond the gelnetwork0510152025303540455055drug loading in PVPVA, %

Morphology of the dissolving gel by confocal microscopy; each drug failed where its drug-rich phase connected. yang2022a R4, R6, R10, R12, R13; deac2023a R6, R7, R8

Drug released (ritonavir at 90 min, analogues at 30 min), %ritonavir 20%≈100ritonavir 30%≈35ritonavir 40–50%at most 3MePHPH 20%≈96MePHPH 40%≈61MePHPH 50%≈15, after a lagPHPH 5%≈75PHPH 20%none

Release follows the morphology above. yang2022a R2; deac2023a R1, R2

For your drug

  1. Dissolve dye-labelled compacts at the target loading and one step above, image the dissolving edge or cut cross-sections after 5–30 min, and measure the drug content of the scraped gel at 10–30 min.
  2. Read discrete droplets below about 2 µm at the gel surface as congruent release, and a continuous drug-rich layer, a stalled gel–glass front or a rising gel drug content as failure.

deac2023a C13, R3, R6; yang2022a P5, R6, R8

How it works and key numbers
  1. Water plasticizes the compact into a rubbery gel with a sharp boundary to the glassy core, and chains disentangle at the gel–solution side once diluted enough yang2022a C23, C41; deac2023a C42, C43.
  2. Because the water content of the gel is highest next to the solution, water-induced separation is "favored" there yang2022a C44.
  3. Discrete drug-rich domains in the continuous, water-soluble polymer-rich phase are carried out as nanodroplets when that phase dissolves, and do not coalesce within the 2–6 min residence time of the gel yang2022a C47; deac2023a C47.
  4. As loading rises the drug-rich phase inverts to the continuous one, helped by coalescence of a mobile drug-rich phase (ritonavir wet Tg about 14 °C) yang2022a C46, C54, C59.
  5. A continuous drug-rich layer slows the entry of water that polymer dissolution needs and "may serve" as a barrier to polymer release; anchored in the gel, it "acts as an insoluble barrier" yang2022a C30, C55; deac2023a C56.
  6. Drug gathering in the gel flags the failure: the drug content of the gel rose from 40 to about 49% and from 50 to about 59.5% within 30 min at 40 and 50% MePHPH deac2023a R3, C14.
0.5–2 µmdrug-rich droplets at the gel surface of 10–20% ritonavir compacts, carried out with the polymeryang2022a R6, R10
≈100 / 35 / 3%ritonavir released at 20, 30 and 40–50%yang2022a R2
≈29 and 17%how far water had advanced into 30 and 40% ritonavir compacts by 20 min, against all of it at 0–20%yang2022a R8
Evidence: data, conditions and papers

Finding F25. In dissolving PVPVA compacts water separated the gel layer below as well as above the limit; release stayed congruent while the drug-rich phase formed discrete droplets of up to about 2 µm that left with the polymer, and failed where that phase connected into a network that stayed on the surface as a porous drug-rich layer (ritonavir from 30%, the methyl ether of phenolphthalein at 40–50%, phenolphthalein at 10–20%)

In short. Ritonavir–PVPVA compacts imaged in cross-section and in real time carried drug-rich droplets of 0.5–2 µm at the surface of the gel at 10–20%, which passed into the solution with the dissolving polymer, a continuous but porous drug-rich layer at 30% and a rigid one at 40% yang2022a R6, R10, R11, R12, R13. For the methyl ether of phenolphthalein (MePHPH) discrete droplets below 1 µm formed inside the gel at 5–30%, networks appeared at 40% and the drug-rich phase became continuous within 60 s at 50%; for phenolphthalein (PHPH) the drug-rich phase was partly connected at 10% and fully at 20% deac2023a R6, R7. Release followed: ritonavir about 100, 35 and at most 3% at 20, 30 and 40–50%; MePHPH at least as fast as neat PVPVA to 40%, about 15% after a lag at 50% and nothing at 70%; PHPH about 75% at 5% and nothing at 20% yang2022a R2; deac2023a R1, R2. The drug-rich layer slowed the advance of water into the ritonavir compacts, and drug gathered in the gel of 40 and 50% MePHPH compacts yang2022a R8; deac2023a R3. Images and release came from separate set-ups, and transport through the network was not measured deac2023a X10; yang2022a C31. In 2023–2024 the imaging was carried to ritonavir compacts with surfactants, where a layer that formed but was swept away did not block release, and to clotrimazole–PVP, where droplets with short chains agglomerated at the gel–solution boundary within 2 min and stayed (F31, F29) yang2023 R8; deac2024a R10.

Type. observation in 3 drugs in PVPVA (ritonavir, phenolphthalein, its methyl ether) Strength. : release and three imaging modes agree in both papers yang2022a K2: strong, K5: moderate; deac2023a K1: moderate, but the link is a co-occurrence across set-ups with different stirring, and a partial network at 40% MePHPH came with good release deac2023a X10, X4, C60.

How it was shown

Yang and co-workers (2022) dissolved dye-labelled ritonavir–PVPVA compacts at 10–50% with drug and polymer assayed, and imaged surfaces, cut cross-sections and edge-wetted compacts in real time by confocal microscopy yang2022a P1, P2, P5, P6, P7. Deac and co-workers (2023) did the same for phenolphthalein (PHPH) and its methyl ether (MePHPH), and scraped the gel at 10–30 min for its thickness, water and drug content deac2023a P3, P4, P7, P8.

What the data show

The drug content of the gel rose from 40 to about 49% at 40% MePHPH and from 50 to about 59.5% at 50% within 30 min, and stayed constant at 20% deac2023a R3, C14.

systemmethod and conditionsresultids
ritonavir–PVPVA 20–50%compacts, pH 6.8, 37 °C, 90 mindrug ≈100 / 35 / 3 / 3%yang2022a R2
ritonavir–PVPVA 10–50%confocal cross-sections and real timedroplets 0.5–2 µm (10–20%); porous layer (30%); rigid layer ≈12 µm (40%)yang2022a R6, R10, R12, R13
samegel–glass front at 20 min≈100% (0–20%) against ≈29 and 17% (30, 40%)yang2022a R8
MePHPH–PVPVA 20, 40, 50, 70%release at 30 mindrug ≈96 / 61 / 15 / 0%deac2023a R1
MePHPH 5–50%; PHPH 5–20%in situ confocal of the dissolving edgedroplets inside the gel (5–30%), networks (40%), inversion (50%); PHPH network from 10%deac2023a R6, R7, R8
clotrimazole–PVP K12, K29/32 10%in situ edge of the compact, pH 8.0agglomerated network at the gel–solution boundary (K12); none (K29/32)deac2024a R10
Fig. 8 of yang2022a: real-time hydration of a 10% ritonavir–PVPVA compact
Fig. 8 · yang2022areal-time hydration of a 10% ritonavir–PVPVA compact

Red drug-rich droplets appear at the gel–solution side and drift into the solution, not throughout the gel yang2022a R10.

Why

Water plasticizes the compact into a rubbery gel whose chains disentangle at the gel–solution side, and because the water content of the gel is highest there, water-induced separation is "favored" there yang2022a C23, C41, C44; deac2023a C42. Discrete drug-rich domains in the continuous, water-soluble polymer-rich phase are carried out as nanodroplets when that phase dissolves ("it can be inferred") deac2023a C47; yang2022a C47. A continuous drug-rich layer slows the entry of water that polymer dissolution needs and "may serve" as a barrier to polymer release, and anchored in the gel it "acts as an insoluble barrier" yang2022a C30, C55; deac2023a C56.

Limits and transfer

The real-time images are not comparable with the release test, and phase compositions in the gel were not measured yang2022a C31, X10; deac2023a X4, X10. At 40% MePHPH a partial network coexisted with good release deac2023a C60, R1. Image dye-labelled compacts at the target loading and assay the scraped gel: a rising gel drug content flags incongruent release before percent release looks poor, and a continuous drug-rich layer or a stalled gel–glass front predicts failure deac2023a C13, R3; yang2022a P5, R6, R8.

How it was shown

Yang and co-workers (2022) asked why ritonavir–PVPVA release collapses above a loading and whether the shape of the drug-rich phase at the dissolving surface explains it yang2022a C10. They made rotary-evaporated dispersions at 10–50% with trace Nile red (drug-rich phase) and Alexa Fluor 488 (polymer- and water-rich phase), dissolved 100 mg compacts in 100 mL 50 mM pH 6.8 phosphate at 37 °C and 100 rpm with drug and polymer assayed (n = 3), removed compacts after 5–30 min for confocal images of the surface and of cut cross-sections, measured how far the gel–glass front had advanced, imaged compacts fused to a glass dish and wetted from the edge every 30 s, and analysed the 40% surface by XPS yang2022a P1, P2, P5, P6, P7, P9, P10. Deac and co-workers (2023) used phenolphthalein, which hydrogen-bonds to PVPVA (cited limit 5%), and its methyl ether, which does not (cited 40%), with prodan (drug-rich phase) and rhodamine 6G (water- and polymer-rich phase) deac2023a M1, M2, M4, M5, R14. They dissolved 100–200 mg compacts under the same medium, temperature and speed, assayed drug and polymer at 10, 20 and 30 min, scraped and analysed the gel at each time for thickness, water, drug content and residence time, imaged the dissolving edge of dye-labelled compacts every 30 s at 230 nm resolution and the surfaces and cross-sections of compacts removed after 2–20 min, and analysed the drug-rich phase released from fully dissolved compacts (F27) deac2023a P2, P3, P4, P5, P7, P8, P9, P10. Yang and co-workers (2023) imaged ritonavir–PVPVA compacts with four surfactants after 5–20 min and in situ, and Deac and co-workers (2024, polymer molecular weight) the dissolving edge of 10% clotrimazole compacts with PVP K12 and K29/32 yang2023 P7, P8; deac2024a P8.

What the data show

Ritonavir: release at 90 min was about 100% (drug) and 97% (polymer) at 20%, 35 and 69% at 30%, and at most 3 and 10–14% at 40–50% yang2022a R2. Surfaces showed small discrete drug-rich domains at 10–25%, a mixture of continuous patches and dots at 30%, and an interconnected, porous drug-rich network at 40–50% after 5 min that covered the surface by 30 min yang2022a R4. Cross-sections showed a glassy core, a gel layer with a sharp boundary to it at every loading, droplets of 500 nm to 2 µm only at the surface at 10%, a continuous drug-rich layer of 5–10 µm at 30% after 5 min that later broke into green regions with embedded droplets, and a continuous layer of about 12 µm over polymer-rich regions at 40% yang2022a R5, R6, R7. In real time droplets formed near the gel–solution interface from the first minute at 10 and 20% and entered the solution; at 30% a porous red layer formed at once, with air bubbles and polymer signal passing through it; at 40% a rigid layer formed with no polymer signal beyond it and separation 50–100 µm deep yang2022a R10, R11, R12, R13. The gel–glass front reached the whole compact by 20 min at 0–20% but only about 29 and 17% at 30 and 40%, and stopped there yang2022a R8. MePHPH: at 20% release reached about 96% of the drug and 105% of the polymer by 30 min against 53% for neat PVPVA, at 40% about 61 and 72%, at 50% about 15 and 22% after a lag of more than 10 min, at 70% nothing; PHPH at 5% about 75 and 83%, at 20% nothing deac2023a R1, R2. The gel's drug content (dry basis) rose from 40 to about 49% at 40% and from 50 to about 59.5% at 50% within 30 min, and stayed at 20% and 5% for 20% MePHPH and 5% PHPH, which the authors read as a true MePHPH limit below 40% deac2023a R3, C14. Gels were 140–227 µm thick at 5–40% MePHPH and 334 µm and still growing at 50%, with water falling from 18–19% to 11% and 1.5% at 50 and 70% deac2023a R4. In situ, MePHPH droplets below 1 µm began 155, 57 and 45 µm from the glass–gel boundary at 5, 20 and 30%, inside the gel, and some left into the solution; at 40% domains linked into networks that intermittently ruptured; at 50% the morphology inverted by 60 s and coarsened to 2100 s deac2023a R6, R8. PHPH particles at 5% began about 601 µm from the boundary, beyond the 356 µm gel; at 10% the drug-rich phase was partly and at 20% fully connected, and the PHPH network deformed under flow where the MePHPH networks did not deac2023a R7, R8, R4. Surfaces after 20 min: uniform with domains of about 1 µm at 30% MePHPH, patchy at 40%, a continuous porous drug-rich phase with water-rich pockets at 50%, and porous at 20% PHPH; neat drug and polymer surfaces did not separate deac2023a R9, R10. No crystallization was seen yang2022a R3; deac2023a R13. With Span 20 at 30% a one-phase gel lay beneath droplets forming at the gel–solution interface, and at 40% a drug-rich layer of about 50–100 µm covered the surface from 5 min; with SDS at 40% the gel stayed one phase with droplets only at its boundary yang2023 R6, R7, R13. In the K12 compact droplets formed a strand-like network near the gel–solution boundary within 2 min and accumulated there; in the K29/32 compact none agglomerated over more than 7 min deac2024a R10.

papersystemmethod and conditionsresultids
yang2022aritonavir–PVPVA 20–50%compacts, pH 6.8, 37 °C, 90 mindrug ≈100 / 35 / 3 / 3%yang2022a R2
yang2022aritonavir–PVPVA 10–50%confocal cross-sections and real timedroplets 0.5–2 µm (10–20%); porous layer (30%); rigid layer ≈12 µm (40%)yang2022a R6, R10, R12, R13
yang2022asamegel–glass front at 20 min≈100% (0–20%) against ≈29 and 17% (30, 40%)yang2022a R8
deac2023aMePHPH–PVPVA 20, 40, 50, 70%release at 30 mindrug ≈96 / 61 / 15 / 0%deac2023a R1
deac2023aPHPH–PVPVA 5, 20%same≈75 / 0%deac2023a R2
deac2023aMePHPH 20, 40, 50%drug content of the scraped gelconstant; 40 → 49%; 50 → 59.5%deac2023a R3
deac2023aMePHPH 5–50%; PHPH 5–20%in situ confocal of the dissolving edgedroplets inside the gel (5–30%), networks (40%), inversion (50%); PHPH network from 10%deac2023a R6, R7, R8
deac2023aMePHPH 30–50%; PHPH 5–20%surfaces after 2–20 minuniform; patchy; porous drug-rich continuous phase (50% MePHPH, 20% PHPH)deac2023a R9, R10
benson2025 (ASD process)ritonavir–PVPVA tabletstablet edge, confocaldiscrete droplets in the gel move into solution as the polymer disentanglesbenson2025 C28
yang2023ritonavir–PVPVA 30, 40% + Span 20; 40% + SDScompacts, cross-sections and in situdroplets at the interface; layer ≈50–100 µm; one-phase gelyang2023 R6, R7, R13
deac2024aclotrimazole–PVP K12, K29/32 10%in situ edge of the compact, pH 8.0agglomerated network at the gel–solution boundary (K12); none (K29/32)deac2024a R10

Figure

Fig. 8 of yang2022a: real-time hydration of a 10% ritonavir–PVPVA compact
Fig. 8 · yang2022areal-time hydration of a 10% ritonavir–PVPVA compact

Red drug-rich droplets appear at the gel–solution side and drift into the solution, not throughout the gel yang2022a R10.

Fig. 7 of deac2023a: 50% MePHPH–PVPVA compact dissolving in situ
Fig. 7 · deac2023a50% MePHPH–PVPVA compact dissolving in situ

At 60 s the blue drug-rich phase is continuous with red water-rich pockets near the surface, and it coarsens by 2100 s deac2023a R6.

Why

Both papers start from the dissolution of a glassy polymer: water plasticizes the compact into a rubbery gel with a sharp boundary to the glassy core, and chains disentangle at the gel–solution side once diluted enough yang2022a C23, C41; deac2023a C42, C43. Because the water content of the gel is highest next to the solution, water-induced separation is "favored" there yang2022a C44. The authors "anticipate" that the lower-volume phase forms the discrete phase and the larger one the continuous phase, so that the drug-rich phase inverts to the continuous one as loading rises, helped by coalescence of a mobile drug-rich phase (ritonavir wet Tg about 14 °C, cited) yang2022a C46, C54, C59. Discrete drug-rich domains in the continuous, water-soluble polymer-rich phase are carried out as nanodroplets when that phase dissolves ("potentially provide an explanation"; "it can be inferred"), and do not coalesce within the 2–6 min residence time of the gel ("It appears") yang2022a C47; deac2023a C47. A continuous drug-rich layer cannot dissolve once the medium is at the amorphous solubility (assumed, not measured), slows the entry of water that polymer dissolution needs, and "may serve" as a barrier to polymer release yang2022a C53, X11, C30, C55. For Deac and co-workers a water-poor network becomes viscous, adds strength to the gel and, anchored in it, "acts as an insoluble barrier"; its pores first hold water-rich phase, which lets some drug and polymer out just above the limit and lets water reach the core, so the gel keeps growing deac2023a C56, C58. The 40% MePHPH network ruptured intermittently, "possibly" because swelling pressure overcame it, and the authors expect it to cover the surface with time deac2023a C60, C62. They propose that congruent release is set by water penetration and chain disentanglement ("it was proposed"), and that MePHPH speeds both up to 20% by plasticizing the polymer (F15) deac2023a C73, C50. Why the phenol connects at a lower loading is the subject of F27 deac2023a C65. (synthesis: these are the first observations in the library of what F7 and F20 inferred from dried surfaces and humidified films: separation occurred in the dissolving gel below the limit too, and the limit coincided with the drug-rich phase becoming continuous; the AAPS of the gel and the LLPS of the solution merge at the gel–solution interface, as Yang and co-workers argue yang2022a C51.) (synthesis: the 2024 PVP paper adds a failure in which discrete droplets join in the gel before the polymer carries them out, and the 2023 surfactant paper one in which a continuous layer fails only if it persists under flow; both fit the reading that release follows the shape of the drug-rich phase at the gel–solution boundary (F29, F31).)

Conditions and limits

PVPVA compacts of three drugs, two of them close analogues, in 50 mM pH 6.8 phosphate at 37 °C yang2022a P2; deac2023a P3. The real-time images used edge wetting and manual pipette mixing, so their rates are not comparable with the release test or between samples, and the inside- or outside-gel conclusions compare two set-ups yang2022a C31; deac2023a C24, X4. Ex situ images were of compacts removed from the medium and dried in air, and the dyes stand for the phases yang2022a P5, C11; deac2023a C10. Phase volumes and compositions in the gel were not measured, nor transport through the network yang2022a X10; deac2023a X10. No release was measured at 25% ritonavir or 30% MePHPH, and the MePHPH limit is given as 40% by release and below 40% by gel drug content yang2022a X7; deac2023a X1, X18. The authors expect high-Tg drugs or polymers to dissolve differently, for example by cracking yang2022a C43; deac2023a C70.

Counterexamples and conflicts

At 40% MePHPH a partial network coexisted with release at least as fast as neat PVPVA deac2023a C60, R1. In the release test about 14% of the polymer left the 40% ritonavir compact although no polymer dye appeared beyond its layer in real time yang2022a X8. At 5% PHPH the droplets formed beyond the gel, not in it, so not every droplet forms inside the gel deac2023a C31. Films of two high-Tg drug forms failed without visible separation (F20); no high-Tg drug was imaged in a dissolving compact correasoto2022b R9; hiew2022b R19. Release failed with discrete droplets in the gel when short PVP chains let them agglomerate (F29) deac2024a C38.

Transfer check

For a PVPVA dispersion near its expected limit, dissolve dye-labelled compacts at the target loading and one step above, image the dissolving edge or cut cross-sections after 5–30 min, and measure the drug content of the scraped gel at 10–30 min: a rising gel drug content flags incongruent release before percent release looks poor deac2023a C13, R3; yang2022a P5. Discrete droplets below about 2 µm at the gel surface go with congruent release; a continuous drug-rich layer or a stalled gel–glass front predicts failure yang2022a R6, R8; deac2023a R6.

History

Han and co-workers (2019, cited) proposed that a continuous hydrophobic network gives incongruent and discrete domains congruent release deac2023a C7. In the library films had shown the same correspondence (F20) saboo2021 C53; correasoto2022a C53. Yang and co-workers (2022) were the first to image the separation in dissolving compacts, in cross-section and in real time yang2022a C5. Deac and co-workers (2023) added the gel layer's thickness, water, drug content and residence time and compared two analogues of different limits deac2023a C71. Yang and co-workers (2023) extended the imaging to surfactant-containing compacts (F31) yang2023 C1, Deac and co-workers (2024, polymer molecular weight) to the PVP grade, finding droplet agglomeration in the gel (F29) deac2024a C38, and Deac and co-workers (2024, ternary phase diagrams) tied the switch from droplets to a network to the critical point of the measured diagram (F30) deac2024b C64; an ASD process study of 2025 used the tablet-edge method benson2025 C28.

F27

Topic 3Limit of congruency and its causes11 of 13

Drugs that hydrogen-bond to PVPVA carried it into their drug-rich phase; the more polymer that phase held, the lower the limit.

Drug-rich nanoparticles formed in buffer with dissolved PVPVA held about 77, 36.5, 9 and 5 wt% PVPVA for phenolphthalein (PHPH), tetraiodophenolphthalein (TIPP) and their methyl ethers (MeTIPP, MePHPH), the reverse order of their cited limits of 5, 10, 30 and 40% deac2023b R3, R8. PVPVA lowered the amorphous solubility of PHPH from 200 to 27.5 µg/mL deac2023b R1. Measured phase diagrams of 2024 confirmed the two kinds of separation and placed the critical points at about 3.7 and 33% loading for PHPH and MePHPH deac2024b R17, R35.

moderateModerate to strong for the partitioning, measured by NMR and HPLC by two routes and at two temperatures; moderate for its rank against the cited limits; weak for the plait-point mechanism, drawn on schematic diagrams deac2023b K1, K3, K7; deac2023a K6.

PVPVA in the drug-rich nanoparticles at 60 °C, wt%PHPHcited limit 5%≈77TIPPcited limit 10%≈36.5MeTIPPcited limit 30%≈9MePHPHcited limit 40%≈5

The phenols take the polymer in (associative separation); the methyl ethers leave it out (segregative). deac2023b R3, R8

startafter 48 hMePHPH 70%≈1.530PHPH 10%≈74–7990PHPH 50%50≈690102030405060708090100PVPVA in dispersion particles held 48 h in PVPVA solution, wt%

Above about 28% PHPH the polymer moved into the particles instead of out; 28% particles barely changed. deac2023b R4, R5

For your drug

  1. For a candidate drug in PVPVA, make drug-rich nanoparticles by solvent shift into buffer with 0.5 mg/mL polymer by both routes and measure the polymer in the particles, and measure the amorphous solubility with and without 1 mg/mL polymer.
  2. Read a polymer-rich particle phase or a large drop in amorphous solubility as a sign of an associative system, for which these papers predict a low limit.

deac2023b P1, P2, R1, C65

How it works and key numbers
  1. The authors read the polymer-rich PHPH and TIPP phases as insoluble drug–polymer complexes, as PVP forms with many phenols deac2023b C43, C44, C15.
  2. Polymer partitioning into a drug-rich phase is entropy-driven, and "it is reasonable to infer" that the phenols draw PVPVA in by hydrogen bonding while the methyl ethers do not deac2023b C45, C46.
  3. By the lever rule the drug-rich phase is the minority below the drug-to-polymer ratio of the plait point and the majority above it, so its volume rises in a step near the plait point deac2023b C32, C33, C34, C36.
  4. In an associative system the plait point lies at low drug content, so the step, and the limit, comes at a lower loading ("are hypothesized"); the polymer makes the drug-rich phase "volumetrically larger", and PHPH connects at 10–20% (F25) deac2023b C48, C49, C63; deac2023a C65.
  5. PVPVA can leave the drug-rich phase only while the dispersion holds more polymer than that phase; above about 28% PHPH the driving force reverses, a loading above the limit deac2023b C54, C56, C57.
≈77 against ≈5 wt%PVPVA in the drug-rich nanoparticles of PHPH against MePHPHdeac2023b R3
200 → 27.5 µg/mLamorphous solubility of PHPH without and with PVPVAdeac2023b R1
26.2 against 98.8 wt%drug in the drug-rich phase released by dissolving 5% PHPH and 30% MePHPH compactsdeac2023a R12
Evidence: data, conditions and papers

Finding F27. Drugs that hydrogen-bond to PVPVA carried it into their insoluble drug-rich phase: phenolphthalein nanoparticles held about 71–78 wt% PVPVA against about 0.5–7.5 wt% for its methyl ether, the order of four analogues was the reverse of their limits of congruency, and the authors propose that the polymer enlarges the drug-rich phase so that it connects at a lower loading, which measured phase diagrams of 2024 supported (F30)

In short. Equilibrated drug-rich nanoparticles formed in buffer with dissolved PVPVA held about 77, 36.5, 9 and 5 wt% PVPVA at 60 °C for phenolphthalein (PHPH), tetraiodophenolphthalein (TIPP), its methyl ether (MeTIPP) and the methyl ether of PHPH (MePHPH), the order of their interaction with the polymer and the reverse of their cited limits of 5, 10, 30 and 40% deac2023b R3, R8. The drug-rich phase released by a dissolving 5% PHPH compact held 26.2 wt% drug (dry basis) against 98.8 wt% for 30% MePHPH deac2023a R12. PVPVA lowered the amorphous solubility of PHPH from 200 to 27.5 µg/mL and raised that of MePHPH from 2.81 to 4.40 µg/mL deac2023b R1. PVPVA left 10% PHPH and 70% MePHPH particles but entered 50% PHPH particles, so above about 28% PHPH the polymer has no driving force to leave, a limit that lies above the limit of congruency deac2023b R4, R5, R15, C56, C57. The authors call the phenols associative and the ethers segregative and "hypothesize" that a shifted plait point makes the polymer-rich drug phase continuous at a lower loading (F25); no phase diagram was measured deac2023b C47, C63, X14; deac2023a C65. Measured drug–PVPVA–water diagrams of 2024 confirmed the two kinds of separation (PVPVA 42–52 wt% in the PHPH-rich phase, rising with water, against 13.7 → 2.5 wt% for MePHPH) and placed the critical points at about 3.7 and 33% loading (F30) deac2024b R17, R35.

Type. observation in 4 phenolphthalein analogues in PVPVA, with release and gel imaging of two of them Strength. to strong for the partitioning, by NMR and HPLC, two routes and two temperatures deac2023b K1: moderate to strong; moderate for its rank against the cited limits deac2023b K3: moderate; weak for the plait-point mechanism, drawn on schematic diagrams deac2023b K7: weak; deac2023a K6: weak.

How it was shown

Deac and co-workers (2023) made drug-rich nanoparticles of four phenolphthalein analogues by solvent shift into buffer containing PVPVA and measured the polymer in the particles by NMR and HPLC deac2023b P1, P2, P8, P9. They also stirred dispersion particles above the limit in buffer with 1 mg/mL PVPVA for 48 h to see which way the polymer moves deac2023b P7.

What the data show

In suspension 70% MePHPH particles fell from 30 to about 1.5 wt% PVPVA in 48 h, whereas 50% PHPH particles rose from 50 to about 69 wt% deac2023b R4, R5.

systemmethod and conditionsresultids
PHPH, MePHPH nanoparticlessolvent shift, 37 °C, NMR and HPLC, two routesPVPVA 71.4–78.0 against 0.5–7.5 wt%deac2023b R2
four analogues60 °C, NMRPVPVA ≈77 / 36.5 / 9 / 5 wt% (PHPH / TIPP / MeTIPP / MePHPH)deac2023b R3
same, against cited limitsrankinglimits 5 / 10 / 30 / 40% in the reverse orderdeac2023b R8
PHPH, MePHPHUV extinction, ± 1 mg/mL PVPVAamorphous solubility 200 → 27.5; 2.81 → 4.40 µg/mLdeac2023b R1
drug-rich phase from 5% PHPH, 30% MePHPH compactsHPLC, DSC26.2 against 98.8 wt% drug; Tg −5.8 against 16.8 °Cdeac2023a R12
PHPH, MePHPH–PVPVA–buffer, 25–99 wt% waterequilibrated up to 147 days, NMRPVPVA in the drug-rich phase ≈42 → 52 (PHPH) and ≈13.7 → 2.5 wt% (MePHPH)deac2024b R15, R17
Fig. 7 of deac2023b: cited limit of congruency against PVPVA in the drug nanoparticles, ordered by interaction strength
Fig. 7 · deac2023bcited limit of congruency against PVPVA in the drug nanoparticles, ordered by interaction strength

Grey bars (limit, left axis) fall from 40 to 5% while black bars (PVPVA in the particles, right axis) rise from about 5 to 73 wt%; the limits are cited from the 2021 analogue study deac2023b R8, X6.

Why

The authors read the polymer-rich PHPH and TIPP phases as insoluble drug–polymer complexes and, since polymer partitioning is entropy-driven, find "it is reasonable to infer" that the phenols draw PVPVA in by hydrogen bonding deac2023b C43, C45, C46. By the lever rule the drug-rich phase turns from the minority to the majority near the plait point, and in an associative system the plait point lies at low drug content, so the limit comes at a lower loading ("are hypothesized") deac2023b C34, C36, C48, C63. The polymer thus makes the drug-rich phase "volumetrically larger" deac2023a C65.

Limits and transfer

Release was not measured in the drug-load paper, and no phase diagram was measured in either 2023 paper deac2023b X6, X14; deac2023a X12. Make drug-rich nanoparticles of a candidate in buffer with 0.5 mg/mL polymer and measure the polymer in them and the amorphous solubility with and without polymer: a polymer-rich particle phase or a large drop in amorphous solubility flags an associative system, for which these papers predict a low limit deac2023b P1, P2, R1, C65.

How it was shown

Deac and co-workers (2023, drug load and interactions) asked why the analogues that bind PVPVA most strongly have the lowest limits (F17) deac2023b A1, C2. They made drug-rich nanoparticles by injecting the drug (10 mg/mL in an organic solvent) into 3 mL buffer containing 0.5 mg/mL PVPVA (method A) or by injecting drug and polymer together (method B), at about 100 µg/mL drug in the particle phase, 37 or 60 °C, pH 6.8 phosphate (pH 2.5 for TIPP), and took the PVPVA content of the particles as equilibrated once the two routes converged deac2023b P1, P2, C10, C11. They measured the aqueous phase by ¹H NMR with water suppression and HPLC and the pellets after dissolution in DMSO, computing the dry-basis polymer content by mass balance,

W_{p,2} = 100 \times \frac{C_{p,T} - C_{p,1}}{\left(C_{p,T} - C_{p,1}\right) + \left(C_{d,T} - C_{d,1}\right)}

deac2023b P8, P9, P10, E1. They stirred dispersion particles above the limit (MePHPH 70%; PHPH 10, 28 and 50%) in buffer with 1 mg/mL PVPVA for 48 h to see which way the polymer moves, followed the surface composition of partly dissolved compacts by ATR-FTIR (PHPH compacts in medium spiked with 40 µg/mL PHPH), and measured the amorphous solubility by UV extinction deac2023b P7, P12, P6. Deac and co-workers (2023, interface) analysed the drug-rich phase released from fully dissolved compacts by HPLC and DSC (F25) deac2023a P10, P11.

What the data show

At 37 °C PHPH nanoparticles held 71.4–71.5 wt% PVPVA by NMR and 77.6–78.0 by HPLC, MePHPH nanoparticles 5.3–7.5 by NMR and 0.5–4.9 by HPLC, the two routes agreeing within 5 min deac2023b R2, C16. At 60 °C, needed for TIPP and MeTIPP to equilibrate, the values were about 77, 36.5, 9 and 5 wt% for PHPH, TIPP, MeTIPP and MePHPH; TIPP was not fully converged and MeTIPP crystallized after 1 h, so its value is an upper bound deac2023b R3, R9, X12. The cited limits fall in the reverse order (40, 30, 10 and 5% for MePHPH, MeTIPP, TIPP and PHPH) deac2023b R8. In suspension, 70% MePHPH particles fell from 30 to about 1.5 wt% PVPVA in 48 h and 10% PHPH particles from 90 to about 74–79 wt%, whereas 50% PHPH particles rose from 50 to about 69 wt% and took almost all the PVPVA out of the solution (1.0 to 0.01 mg/mL); 28% PHPH particles barely changed and released almost no polymer into plain buffer deac2023b R4, R5. Compact surfaces drifted toward the composition of the drug-rich phase above the limit (15% PHPH from about 13.5 to 21% drug in 30 min; 50% MePHPH from about 44 to 90–101%), stayed put at 5% PHPH and 30% MePHPH, and the 50% PHPH surface fell to about 26% drug only when 1 mg/mL PVPVA was in the medium deac2023b R6, R7. The drug-rich phase released from dissolving compacts held 98.8 ± 0.6 wt% MePHPH with an onset Tg of 16.8 °C and 26.2 ± 0.5 wt% PHPH with −5.8 °C, against 22.5 and 84.5 °C for the neat drugs and 101.3 °C for PVPVA; both dyes partitioned into the PHPH drug-rich phase deac2023a R12, M1, M2, M3, R7. The authors convert the particle compositions into drug loads of the drug-rich phase of roughly 30, 65, above 90 and above 95%, all above the limits deac2023b R14, X18. (synthesis: 200/27.5 ≈ 7.3 and 4.40/2.81 ≈ 1.6, the ratios the authors state; 26.2 wt% PHPH means about three parts polymer per part drug in the released phase.) In equilibrated mixtures with buffer the PHPH-rich phase held 5.7–16.7 wt% drug and 41.9–52.2 wt% PVPVA and the MePHPH-rich phase 82.9–94.1 wt% drug and 2.5–13.7 wt% PVPVA; at 80 wt% total water about 47 against 5 wt% PVPVA deac2024b R15, R17.

papersystemmethod and conditionsresultids
deac2023bPHPH, MePHPH nanoparticlessolvent shift, 37 °C, NMR and HPLC, two routesPVPVA 71.4–78.0 against 0.5–7.5 wt%deac2023b R2
deac2023bfour analogues60 °C, NMRPVPVA ≈77 / 36.5 / 9 / 5 wt% (PHPH / TIPP / MeTIPP / MePHPH)deac2023b R3
deac2023bsame, against cited limitsrankinglimits 5 / 10 / 30 / 40% in the reverse orderdeac2023b R8
deac2023bPHPH, MePHPHUV extinction, ± 1 mg/mL PVPVA200 → 27.5; 2.81 → 4.40 µg/mLdeac2023b R1
deac2023bPHPH particles 10, 28, 50%; MePHPH 70%48 h in buffer with PVPVApolymer out (10%, 70%), none (28%), in (50%)deac2023b R4, R5
deac2023bPHPH 5, 15, 50%; MePHPH 30, 50% compactsATR-FTIR of dried surfaces, 0–60 minconstant at or below the limit; toward the drug-rich phase above itdeac2023b R6, R7
deac2023adrug-rich phase from 5% PHPH, 30% MePHPH compactsHPLC, DSC26.2 against 98.8 wt% drug; Tg −5.8 against 16.8 °Cdeac2023a R12
ueda2022 (Amorphous solubility and LLPS)PVP, PVP-VA, HPMC and ibuprofen-rich dropletsvariable-temperature NMRpolymer transfer into the drug-rich phase endothermic and entropy-drivenueda2022 C48, R23
deac2024bPHPH, MePHPH–PVPVA–buffer, 25–99 wt% waterequilibrated up to 147 days, NMRPVPVA in the drug-rich phase ≈42 → 52 (PHPH) and ≈13.7 → 2.5 wt% (MePHPH)deac2024b R15, R17
deac2024bfour analoguesPC-SAFT critical point≈3.7 / 13.7 / 32.6 / 33.2% against limits 5 / 10 / 30 / 40%deac2024b R37
bapat2024PHPH with HPMCAS-MFpH 6.0 spike test60% of the polymer complexedbapat2024 R12

Figure

Fig. 7 of deac2023b: cited limit of congruency against PVPVA in the drug nanoparticles, ordered by interaction strength
Fig. 7 · deac2023bcited limit of congruency against PVPVA in the drug nanoparticles, ordered by interaction strength

Grey bars (limit, left axis) fall from 40 to 5% while black bars (PVPVA in the particles, right axis) rise from about 5 to 73 wt%; the limits are cited from the 2021 analogue study deac2023b R8, X6.

Fig. 4 of deac2023b: PVPVA exchange between PHPH dispersion particles and solution
Fig. 4 · deac2023bPVPVA exchange between PHPH dispersion particles and solution

Orange bars (polymer in the particles) fall for 10%, rise for 50% while the blue bars (polymer in solution) empty, and barely move for 28% PHPH deac2023b R5.

Why

The authors read the polymer-rich PHPH and TIPP phases as insoluble drug–polymer complexes, as PVP forms with many phenols (cited), and the lower PHPH amorphous solubility with PVPVA as "likely due to" such complexes deac2023b C43, C44, C15. Polymer partitioning into a drug-rich phase is entropy-driven, and drug–polymer interactions were "postulated" to lower its enthalpic cost (Ueda 2021, cited), so "it is reasonable to infer" that the phenols draw PVPVA in by hydrogen bonding while the methyl ethers do not deac2023b C45, C46. For the limit they assume that water enters at a constant drug-to-polymer ratio, that separation starts where the hydration path crosses the spinodal, and that both phases reach their binodal compositions at once; by the lever rule the drug-rich phase is the minority below the plait point's ratio and the majority above it, so its volume rises in a step near the plait point deac2023b C32, C33, C34, C36. In an associative system the tie lines slope so that the plait point lies at low drug content, and the step, hence the limit, comes at a lower loading ("are hypothesized"; "It is speculated herein") deac2023b C48, C49, C63. The interface paper states it as the reason PHPH's network forms at 10–20% where MePHPH still forms droplets: the polymer makes the drug-rich phase "volumetrically larger" (F25) deac2023a C65. Separately, PVPVA can leave the drug-rich phase only while the dispersion holds more polymer than that phase; above composition X (about 28% PHPH) the driving force reverses, "an important conclusion" that lies above the limit, so the limit comes from a barrier at the surface that needs only part of the dispersion to change deac2023b C54, C56, C57, C64. The surface in contact with nearly pure water can reach the composition of the dilute drug-rich phase, a "pseudo-equilibrium" deac2023b C61, C59. The framework assumes near-equilibrium compositions along the hydration path, which "may" hold because both drug-rich phases have Tgs below 37 °C deac2023a C70, C39. (synthesis: this gives a second explanation of the analogue pairs of F17 beside the 2021 one, in which bonds persisting in water slow polymer hydration; both act through the hydrated matrix and neither was measured there; in the LLPS chapter dissolved polymers entering a drug-rich phase lowered the amorphous solubility of ibuprofen, as PVPVA lowered that of PHPH here (Amorphous solubility and LLPS F19).) (synthesis: the plait-point hypothesis drawn here on schematic diagrams was tested in 2024 on measured and computed diagrams, which put the switch near the critical point for MePHPH but at 10–15% in PHPH films against a computed 3.7% (F30) deac2024b X5.)

Conditions and limits

Four analogues on one scaffold and PVPVA only; the four-drug ranking uses 60 °C, TIPP at pH 2.5, and compositions on a dry basis because the water content of the drug-rich phase is unknown deac2023b X13, C50. Release was not measured in the drug-load paper; its limits are cited from the 2021 study deac2023b X6. The flux reversal was shown for PHPH only, over 48 h in suspension deac2023b X15. Surface values carry calibration offsets and come from dried compacts, and the 40 µg/mL PHPH spike lies below the drug's amorphous solubility in plain buffer deac2023b X8, X17, X20. The released-phase compositions were measured once per drug, at different loadings, on particles released in bulk at 500 rpm deac2023a X11. No ternary phase diagram, tie line or plait point was measured or computed in either paper deac2023b X14; deac2023a X12. The 2024 diagrams were measured for PHPH and MePHPH only; TIPP and MeTIPP were computed from one tie-line slope each deac2024b A1, R25.

Counterexamples and conflicts

The PHPH binode is given between about 70 and 78 wt% PVPVA depending on method and temperature, and the composition-X value rests on it deac2023b X3. TIPP and MeTIPP equilibrated slowly, which the authors relate to a high-Tg drug-rich phase that can trap the polymer, so local equilibrium is "unclear" for them deac2023b C39, C40. In the analogue pairs the donor drugs also differ in Tg (F17, F18) que2021 M1, M2, M3, M4.

Transfer check

For a candidate drug in PVPVA, make drug-rich nanoparticles by solvent shift into buffer with 0.5 mg/mL polymer by both routes and measure the polymer in the particles, and measure the amorphous solubility with and without 1 mg/mL polymer deac2023b P1, P2, R1. A polymer-rich particle phase or a large drop in amorphous solubility flags an associative system, for which these papers predict a low limit; the authors suggest a polymer or additive that keeps the polymer out of the drug-rich phase, which was not tested deac2023b C65.

History

Que and co-workers (2021) ranked the same analogues by interaction and limit (F17) deac2023b C2. Ueda and co-workers (2021, cited; LLPS chapter) found polymer partitioning into drug-rich phases entropy-driven deac2023b C45. Deac and co-workers (2023) were the first in the subcategory to measure where the polymer goes when the analogues separate, and in the interface paper tied it to the loading at which the drug-rich phase connects deac2023b C26, C67; deac2023a C65. Deac and co-workers (2024, ternary phase diagrams) measured the diagrams of PHPH and MePHPH with PVPVA and water, computed those of all four analogues and found the critical-point loadings in the order of the limits (F30) deac2024b C59, and Bapat and co-workers (2024) cited the insoluble PHPH–PVPVA complex when PHPH took HPMCAS out of solution as well (F32) bapat2024 C41. The title was extended after the 2024 diagrams (synthesis).

Formulaslever rule
F29

Topic 3Limit of congruency and its causes12 of 13

The molecular weight of PVP set the limit of congruency of clotrimazole, from below 5% with short chains to about 33–38% with long ones.

Clotrimazole dispersions in six PVP grades (2,500 to 1,300,000 g/mol) had limits below 5% with K12 and K17, of 20% with K25 and of about 33, 35 and 38% with K29/32, K60 and K90 deac2024a R1, R12, C36. The rise lies near the computed entanglement molecular weight of 46,620 g/mol, between K25 and K29/32 deac2024a E1, C37. With short chains the drug-rich droplets clustered into strands in the gel layer and stayed there, a failure the authors call "Failure Mode I" deac2024a R7, R10, C38.

strongStrong for the dependence of the limit on molecular weight, from drug and polymer release in triplicate for twelve grade–loading pairs; moderate for agglomeration as the failure of short chains, imaged for one grade at another loading; weak for entanglement as the cause deac2024a K1, K2, K6, X11.

below the entanglement weightabove itK12 · limit below 5%K17 · below 5%K25 · 20%K29/32 · ≈33%K60 · 35%K90 · ≈38%1000100001000001e+06PVP molecular weight, g/mol (log scale)

The limit rose at least sevenfold across the computed entanglement weight (46,620 g/mol) and little above it. deac2024a R12, E1, M5, M6, M7, A2

For your drug

  1. For a weakly interacting, low-Tg drug in PVP, PVPVA or another vinyl polymer, compare a grade below M_c with one above it at two loadings 2.5–5% apart, with drug and polymer assayed for 90–120 min.
  2. Read a low-grade dispersion whose polymer leaves completely while the drug stays below 80%, with droplets that join into strands in a humid film or at the edge of a dissolving compact, as agglomeration; an entangling grade releases more slowly, and its limit can be no higher than the inversion loading, about 30–40% here.

deac2024a E1, P5, A2, R1, R7, R10, R3, C41

How it works and key numbers
  1. Congruent release resembles that of a neat glassy polymer: water turns the glass into a gel, a miscibility gap opens, drug-rich droplets form in a PVP-rich water phase, and they stay held until the polymer is dilute enough to leave at the gel–solution boundary deac2024a C31, C34.
  2. With chains too short to entangle (below M_c \approx 30\,C_\infty M_0) there is no "fishnet": the droplets move, meet and agglomerate into strings anchored in the gel, and the low limits of K12, K17 and K25 "appear to be caused" by this deac2024a E1, C38, C26, C47.
  3. Above M_c entanglement raises viscosity sharply, droplets of a few hundred nanometres are too large for a mesh of at most 80 nm, and the swollen gel "is expected to" keep them apart; entanglement "may be contributing" deac2024a C45, C46, E5.
  4. Steric stabilization by adsorbed PVP is "not the likely mechanism", because neither grade slowed droplet growth in dilute suspension deac2024a C44, C47, R5.
  5. Above about 30–40% the drug-rich phase becomes continuous whatever the grade ("Failure Mode II"), because the phase compositions did not change with molecular weight; this inversion sets the limit of the long grades deac2024a R8, R11, C39, C40, C41.
below 5 → about 38%clotrimazole–PVP limit from K12 to K90deac2024a R12
46,620 g/molcomputed entanglement molecular weight, between K25 and K29/32deac2024a E1
≈35 against ≈107%drug against PVP released from the 5% K12 compactdeac2024a R1
Evidence: data, conditions and papers

Finding F29. The molecular weight of the polymer set the limit of congruency of clotrimazole–PVP from below 5% (K12, K17) through 20% (K25) to about 33–38% (K29/32 to K90), near the computed entanglement weight; with short chains the drug-rich droplets agglomerated in the gel layer, a failure that came before phase inversion

In short. Clotrimazole dispersions in six PVP grades (2,500 to 1,300,000 g/mol), released as compacts in pH 8.0 buffer and counted as below the limit when more than 80% of the drug left, had limits below 5% with K12 and K17, of 20% with K25 and of about 33, 35 and 38% with K29/32, K60 and K90 deac2024a R1, R12, C36. The rise lies near the entanglement weight computed as M_c \approx 30\,C_\infty M_0 = 46,620 g/mol, between K25 and K29/32, with little gain above it deac2024a E1, C37. In humid films and in a dissolving 10% compact the drug-rich droplets of K12 clustered into strands, near the gel–solution boundary within 2 min, and stayed in the gel; those of K29/32 stayed apart deac2024a R7, R10. The authors name this "Failure Mode I", distinct from phase inversion ("Failure Mode II"), which both grades showed between 30 and 40% loading in films with the same phase compositions deac2024a C38, R8, R11, C40. Agglomeration was imaged for K12 only, and the "fishnet" of entangled chains that they propose holds the droplets apart was not measured deac2024a X7, C45, X10.

Type. single-system observation (clotrimazole with six PVP grades) Strength. for the dependence of the limit on molecular weight, from release of drug and polymer in triplicate for twelve grade–loading pairs deac2024a K1: strong; moderate for agglomeration as the failure of short chains, imaged for one grade at a loading other than the one released deac2024a K2: moderate, X11; weak for entanglement as the cause deac2024a K6: weak.

How it was shown

Deac and co-workers (2024) released compacts of clotrimazole, a low-Tg drug that interacts weakly with PVP, in six PVP grades in pH 8.0 buffer with drug and polymer assayed, and imaged humid films and the edge of dissolving compacts of K12 and K29/32 deac2024a M1, C10, P5, P6, P10, P8.

What the data show

The computed M_c of 46,620 g/mol lies between K25 and K29/32 deac2024a E1.

systemmethod and conditionsresultids
clotrimazole–PVP K12, K17 at 5%compacts, pH 8.0, 37 °C, 90 minPVP ≈101–107%; drug ≈35% (K12), ≈74–77% (K17)deac2024a R1, R2
six gradeslimit = highest loading with >80% drug<5, <5, 20, ≈33, 35, ≈38%deac2024a R12, X5
PVP chain parametersM_c \approx 30 C_\infty M_0, c_eM_c = 46,620 g/mol; c_e 0.80 / 0.12 / 0.04 v/v (K29/32 / K60 / K90)deac2024a E1, E2, M5, M6, M7
10% K12 against K29/32 films and compacts100% RH, 3 and 11 h; in situ edge of the compactstrands of droplets and a network near the gel–solution boundary (K12); separate droplets (K29/32)deac2024a R7, R10
K12, K29/32 films 20–40%100% RH, 1 hdroplets to 30%, continuous drug-rich phase at 40% for bothdeac2024a R8
clotrimazole droplets ± 1 mg/mL K12 or K29/32DLS, dilute≈540 → 1000; ≈340 → 610; ≈290 → 630 nm, same relative growthdeac2024a R5
Fig. 7 of deac2024a: limit of congruency against PVP molecular weight, with the entanglement weight and the phase-inversion band
Fig. 7 · deac2024alimit of congruency against PVP molecular weight, with the entanglement weight and the phase-inversion band

Left of the red dashed M_c line the limits lie far below the grey phase-inversion band (30–40%); right of it they lie inside it; the band is observed for K12 and K29/32 and drawn by inference for the other grades deac2024a R12, X8.

Why

The authors read congruent release as that of a neat glassy polymer, the drug-rich droplets being held in the gel until the polymer is dilute enough to leave deac2024a C31, C34. With chains too short to entangle there is no "fishnet", the droplets meet and agglomerate into strings anchored in the gel, and the low limit of the short grades "appears to be caused" by this deac2024a C38, C26, C47. Above about 30–40% the drug-rich phase becomes continuous whatever the grade, and this phase inversion sets the limit of K29/32 deac2024a C39, C40, C41.

Limits and transfer

Agglomeration was imaged only for K12 at 10%, while K12 release was tested only at 5%, and entanglement in the gel was not measured deac2024a X7, X11, X10. Compare a PVP grade below M_c with one above it at two loadings with drug and polymer assayed: polymer leaving completely while the drug stops below 80%, with droplets that join into strands, points to agglomeration rather than inversion deac2024a E1, P5, R1, R7, R10.

How it was shown

Deac and co-workers (2024, polymer molecular weight) asked whether the molecular weight of the polymer, which shapes the gel layer, changes the limit, and whether release can fail in a way other than through a continuous drug-rich phase deac2024a C2, C10. They chose clotrimazole (Tg 28.0 °C, amorphous solubility 10.3 µg/mL at pH 8.0, calculated pKa 6.26) because it does not interact strongly with PVP and crystallizes slowly, and combined it with PVP K12, K17, K25, K29/32, K60 and K90 (nominal 2,500, 10,000, 34,000, 58,000, 400,000 and 1,300,000 g/mol) deac2024a M1, M2, M3, M4, M5, M6, M7, C10. Rotary-evaporated dispersions (K60 from its aqueous solution through a propanol azeotrope) were pressed into 100 mg compacts of 0.5 cm² and rotated at 100 rpm in 100 mL pH 8.0, 50 mM phosphate at 37 °C, where the drug is "largely unionized", for 90 min (K12 to K29/32) or 120 min (K60, K90), with the drug assayed by HPLC after dissolving the droplets in ethanol and PVP by size-exclusion HPLC or, for K12, an iodine assay (n = 3) deac2024a P1, P2, P5, P6, P7, C12. Release was called congruent when more than 80% of drug and polymer left, and the limit was the highest loading whose drug release passed 80% deac2024a P5, C36. Loadings were 5% (K12, K17), 20 and 23% (K25), 30, 33 and 35% (K29/32), 35 and 38% (K60) and 38, 40 and 45% (K90) deac2024a A2. Dye-labelled films of K12 and K29/32 (prodan in the drug-rich, Alexa Fluor 488 in the water-rich phase) were held at 100% RH and 37 °C and imaged by confocal microscopy after 1 h (20–40%) and 3 and 11 h (10%); dye-labelled 10% compacts were fused to a glass dish and their edge imaged every 30 s in buffer deac2024a P10, P8, A3, A4. Mixtures of 10% dispersions with buffer (40:60) were heated to 90 °C, cooled and centrifuged at 37 °C, and both phases analysed by ¹H NMR; droplets made by solvent injection were followed by DLS without PVP and with 1 mg/mL K12 or K29/32 deac2024a P9, P11. Entanglement weight, entanglement concentration, tube diameter and radius of gyration were computed for each grade with C_\infty = 14 and M_0 = 111 g/mol deac2024a P12, E1, E2, E3, E4, E5.

What the data show

At 5% the K12 dispersion released about 107% of its PVP but only about 35% of its drug, and K17 about 101–103% of its PVP and about 74–77% of its drug deac2024a R1, R2. K25 released about 86–88% of the drug at 20% and about 58% (SD about ±23) at 23%, with PVP at about 103 and 91% deac2024a R1. K29/32 released both components to about 87–93% at 30%; at 33% the drug peaked at about 82% at 50 min and ended at about 77% while PVP reached about 103%, and at 35% about 64% drug and 73% PVP at 90 min deac2024a R1. K60 released about 96% drug and 101% PVP at 35% and about 69–73% and 86–87% at 38%; K90 reached about 83% drug and 96% PVP at 38% only at 120 min, and about 64 and 70% at 40% and 50 and 72% at 45%, still rising deac2024a R1, X6. The limits read from these are below 5%, below 5%, 20, about 33, 35 and about 38% (Fig. 7 bars about 20, 32.5, 35 and 37.5%), each bracketed by the next tested loading deac2024a R12, X5. The computed M_c of 46,620 g/mol lies between K25 and K29/32; entanglement needs at least 0.80, 0.12 and 0.04 v/v polymer for K29/32, K60 and K90, where the maximum tube diameter is 10, 36 and 80 nm, against a tube diameter of 8.7 nm for undiluted PVP and a radius of gyration of 1 (K12) to 27 nm (K90) deac2024a E1, E3, E4, E5, M5, M6, M7. Neat PVP compacts released more slowly as the molecular weight rose, and so did the congruent dispersions, compared at different loadings deac2024a R3, C19, R1. Every release passed the amorphous solubility, with a turbid medium deac2024a R4, C18. In 10% films after 3 h at 100% RH both grades held small drug-rich droplets in a continuous water-rich phase; by 11 h the K12 droplets had formed strands of touching droplets while the K29/32 droplets stayed separate deac2024a R7. In the dissolving 10% K12 compact the droplets, first dispersed, formed a strand-like network near the gel–solution boundary within 2 min, with denser agglomerates nearest the solution, and accumulated there instead of leaving; the K29/32 compact showed no agglomeration after more than 7 min, in the gel or in the released droplets deac2024a R10. After 1 h at 100% RH, films held droplets at 20–30% and a continuous drug-rich phase with water-rich droplets at 40%, for K12 and K29/32 alike, though the K12 domains at 30% were several micrometres across and many touched deac2024a R8, X15. The 40:60 mixtures gave a drug-rich phase of about 83 ± 5.5 and 84 ± 2.5 wt% clotrimazole and a water-rich phase of about 41 and 39 wt% PVP for K12 and K29/32 deac2024a R11. In dilute suspension droplets grew from about 540 nm to 1 µm without PVP, from about 340 to 610 nm with K12 and from about 290 to 630 nm with K29/32, at the same relative rate deac2024a R5. (synthesis: the limit rose at least sevenfold from K17 to K29/32, 33/5 ≈ 7, and by 38/33 ≈ 1.15 over the next 22-fold rise in molecular weight, 1,300,000/58,000 ≈ 22.)

papersystemmethod and conditionsresultids
deac2024aclotrimazole–PVP K12, K17 at 5%compacts, pH 8.0, 37 °C, 90 min, drug and polymerPVP ≈101–107%; drug ≈35% (K12), ≈74–77% (K17)deac2024a R1, R2
deac2024aK25 20, 23%; K29/32 30, 33, 35%; K60 35, 38%; K90 38, 40, 45%same, 90 or 120 mindrug ≈86–88 / 58; ≈87–91 / 77 / 64; ≈96 / 69–73; ≈83 / 64 / 50%deac2024a R1
deac2024asix gradeslimit = highest loading with >80% drug<5, <5, 20, ≈33, 35, ≈38%deac2024a R12, X5
deac2024aPVP chain parametersM_c \approx 30 C_\infty M_0, c_e, d_TM_c = 46,620 g/mol; c_e 0.80 / 0.12 / 0.04 v/v (K29/32 / K60 / K90)deac2024a E1, E2, M5, M6, M7
deac2024a10% K12 against K29/32 films and compacts100% RH, 3 and 11 h; in situ edge of the compactstrands of droplets and a network near the gel–solution boundary (K12); separate droplets (K29/32)deac2024a R7, R10
deac2024aK12, K29/32 films 20–40%100% RH, 1 hdroplets to 30%, continuous drug-rich phase at 40% for bothdeac2024a R8
deac2024a10% K12, K29/32 with buffer 40:60¹H NMR of both phasesdrug-rich phase ≈83–84 wt% drug; water-rich phase ≈39–41 wt% PVPdeac2024a R11
deac2024aclotrimazole droplets ± 1 mg/mL K12 or K29/32DLS, dilute≈540 → 1000; ≈340 → 610; ≈290 → 630 nm, same relative growthdeac2024a R5
ueda2020b (Amorphous solubility and LLPS)ibuprofen droplets with HPMC, PVP-VA or EUD-EDLS, 3 h stirringPVP-VA less effective against flocculation and creaming than HPMCueda2020b C18, C29

Figure

Fig. 7 of deac2024a: limit of congruency against PVP molecular weight, with the entanglement weight and the phase-inversion band
Fig. 7 · deac2024alimit of congruency against PVP molecular weight, with the entanglement weight and the phase-inversion band

Left of the red dashed M_c line the limits lie far below the grey phase-inversion band (30–40%); right of it they lie inside it; the band is observed for K12 and K29/32 and drawn by inference for the other grades deac2024a R12, X8.

Fig. 5 of deac2024a: dissolution front of 10% compacts with K12 at 2 min and K29/32 after more than 7 min
Fig. 5 · deac2024adissolution front of 10% compacts with K12 at 2 min and K29/32 after more than 7 min

In panel a the blue drug-rich droplets join into strands near the gel–solution boundary (region 2 to 3); in panel b they stay separate; the two compacts were fused to the glass differently deac2024a R10, X12.

Why

The authors read congruent release as the release of a neat glassy polymer: water turns the glass into a viscous gel, a miscibility gap opens in it, the drug-rich phase forms droplets in a PVP-rich water phase, and the droplets stay held until the polymer is dilute enough to leave at the gel–solution boundary, so that release is limited by water penetration and the release of chains deac2024a C31, C34. With chains too short to entangle (below M_c) there is no "fishnet", the droplets can move and meet, and they agglomerate into strings anchored in the gel, strong enough to resist the flow, which collapse into dense agglomerates as the surrounding phase is diluted; the low limit of K12, K17 and K25 "appears to be caused" by this deac2024a C38, C26, C47. Above M_c entanglement raises viscosity sharply, droplets of a few hundred nanometres are too large for a mesh of at most 80 nm, and an entangled gel swells more, which "is expected to" space the droplets so that they do not meet when the chains finally disentangle; the authors say the coincidence with M_c "gives support to the hypothesis" that entanglement "may be contributing" to droplet stability deac2024a C45, C46. Steric stabilization by adsorbed PVP is "not the likely mechanism", because neither grade slowed droplet growth in dilute suspension, where K29/32 cannot entangle deac2024a C44, C47. Above about 30–40% loading the drug-rich phase becomes continuous whatever the grade, because the phase compositions, and hence phase volumes, did not change with molecular weight; this phase inversion then sets the limit of K29/32 and "possibly" of K60 and K90 deac2024a C39, C40, C41. "It appears" that two independent mechanisms underlie the limit, and that agglomeration comes at lower loadings than inversion deac2024a C42, C48. (synthesis: in the earlier findings of this chapter discrete drug-rich droplets in the gel went with congruent release (F20, F25); here discrete droplets that formed in the gel failed when they joined before the polymer carried them out, so the shape of the drug-rich phase at the moment the polymer leaves, not at the moment it separates, is what the release follows. In the LLPS chapter PVP-VA also kept ibuprofen droplets dispersed less well than HPMC (Amorphous solubility and LLPS F22), and in the ASD dissolution chapter PVP and PVPVA kept ritonavir droplets small no better than no additive (Supersaturation from ASD dissolution F12); that is droplet growth in solution, which in this paper did not differ between grades, whereas the agglomeration that failed release happened inside the gel.)

Conditions and limits

One drug with low Tg and weak interaction with PVP, one polymer family, pH 8.0 where the drug is mostly un-ionized, 37 °C and one stirring rate deac2024a C10, C12, X13. The limits are bracketed by coarse steps, and the 80% criterion was applied over 90- or 120-min tests at an unstated time, with some profiles still rising deac2024a X5, X6. Agglomeration was imaged only for K12, at 10% loading, while K12 release was tested only at 5%, and failure by agglomeration for K17 and K25 is inferred from their limits lying below the inversion band deac2024a X7, X11. Inversion was imaged only for K12 and K29/32 films at 30 and 40%, after 1 h deac2024a X8, X15. The phase compositions come from a 90 °C heating–cooling protocol, not from the gel during release, with no named statistical test and n of 3 or 4 deac2024a X16, X14, X3. Entanglement in the gel, droplet diffusion and gel swelling were not measured; K29/32 entangles only above 0.80 v/v polymer, and the polymer content where its droplets stayed dispersed is not reported deac2024a X10. The K60 dispersions were processed differently, and whether crystals contributed to poor release was checked by PLM but not reported deac2024a X12, X13.

Counterexamples and conflicts

The rise is not a single step: K25, below M_c, already reached 20% deac2024a X9. The K12 film at 30% already showed coarse, touching domains, so inversion and agglomeration overlap there deac2024a X15. PVP did not stabilize droplets in dilute suspension, which leaves open why entangled grades kept them apart in the gel deac2024a C43, X10. In the earlier papers of this chapter drugs in PVPVA (about 65,000 g/mol as the PC-SAFT input of the 2024 phase-diagram paper, above M_c for PVP) failed at 5–40% by a continuous drug-rich phase, not by agglomeration (F6, F25) deac2024b M5.

Transfer check

For a dispersion in PVP, PVPVA or another vinyl polymer of a weakly interacting, low-Tg drug, compare a low-molecular-weight grade (below M_c \approx 30\,C_\infty M_0) with a grade above it at two loadings 2.5–5% apart, with drug and polymer assayed for 90–120 min deac2024a E1, P5, A2. A low-grade dispersion whose polymer leaves completely while the drug stops below 80% at 5% loading, together with droplets that join into strands in a humid film or at the edge of a dissolving compact, points to agglomeration rather than inversion deac2024a R1, R7, R10. An entangling grade will release more slowly, and its limit can then be no higher than the loading at which the drug-rich phase inverts, about 30–40% here deac2024a R3, C41.

History

Earlier papers of this chapter attributed the limit to drug–polymer interactions (F17) and the drug's Tg (F18), and imaged failure as a continuous drug-rich phase in the gel (F25) deac2024a C2, C9. Deac and co-workers (2024, polymer molecular weight) were the first in the library to vary the polymer grade and to describe failure by droplet agglomeration in the gel layer deac2024a C2, C54. They name phase inversion Failure Mode II and expect it to "always occur" under un-ionized conditions as loading rises, with surfactants or partial ionization as possible means against Failure Mode I, which they did not test deac2024a C53, C52. A 2025 peptide study of the Peptide permeability chapter cites the PVP grades with different erosion rates as further gel-forming polymers (as listed in the evidence index of this subcategory).

F30

Topic 3Limit of congruency and its causes13 of 13

Measured drug–PVPVA–water phase diagrams placed the limit of congruency near the critical point, where the drug-rich phase becomes the majority.

Equilibrated mixtures of dispersion and buffer gave a drug-rich phase of 82.9–94.1 wt% drug with little PVPVA for the methyl ether of phenolphthalein (MePHPH), but a "drug-rich" phase of only 5.7–16.7 wt% drug and 41.9–52.2 wt% PVPVA for phenolphthalein (PHPH) deac2024b R15, R17. A thermodynamic model (PC-SAFT) put the critical point at about 33% loading for MePHPH and 3.7% for PHPH deac2024b R22, R23, R35. The critical-point loadings of four analogues followed their cited limits in order deac2024b R37.

strongStrong for the opposite partitioning of the polymer, measured directly; moderate for the agreement of measured and computed diagrams and for the critical point as predictor, which rests on cited limits and misses the PHPH film switch three- to fourfold deac2024b K1, K2, K3, K4, X9, X5.

computed critical pointcited limit of congruencyMePHPH≈33.240MeTIPP30≈32.6TIPP10≈13.7PHPH≈3.75051015202530354045drug loading in PVPVA, %

Each prediction lies within 7% of the limit; release was not measured in the paper. deac2024b R37, X9

Computed fraction of drug-rich phase at the onset of separationMePHPH 27%≈0.15MePHPH 39.5%≈0.82PHPH 3.0%≈0.16PHPH 4.5%≈0.82

Above 0.5 the drug-rich phase is taken as continuous; the jump comes around the critical point. deac2024b R35, C51

For your drug

  1. For a candidate in PVPVA, measure where the polymer goes when dispersion and buffer separate (NMR of both phases after equilibration at two or more ratios), or fit a thermodynamic model to the drug's solubility data and one dilute tie line.
  2. Read tie lines sloping up or a polymer-rich drug phase as an associative system whose limit can lie near 5%, and confirm with dye-labelled films at 100% RH around the predicted critical point and a release test in 2.5–5% steps.

deac2024b P4, P19, R17, R36, R37, R18, R19, C54

How it works and key numbers
  1. Water enters the gel faster than drug or polymer leave, so the gel hydrates at a constant drug-to-polymer ratio, crosses the binodal and separates at the spinodal deac2024b C48, C23.
  2. Both drug-rich phases are rubbery at 37 °C, so they stay near local equilibrium and their amounts follow the lever rule, W^{\alpha} = \frac{W_i^{T} - W_i^{\beta}}{W_i^{\alpha} - W_i^{\beta}} deac2024b C49, C50, E12.
  3. Below the critical point the drug-rich phase is the minority and forms droplets that leave as the chains disentangle; above it the drug-rich phase is the majority, forms a network and stays as a surface barrier, a change that "appears to underpin" the fall-off deac2024b C47, C65.
  4. PHPH hydrogen bonding to PVPVA ("likely") pulls the polymer into the drug-rich phase, inflates it and moves the critical point, and with it the limit, to low loading deac2024b C21, C22, C56.
  5. Less than 15 wt% water splits MePHPH–PVPVA, so it separates in the gel at all but the lowest loadings, while PHPH separates there only above its limit deac2024b R1, R2, R28, C37.
≈0.15 → 0.82computed drug-rich fraction from 27 to 39.5% MePHPH, around the critical pointdeac2024b R35
≈47 against ≈5 wt%PVPVA in the drug-rich phase with PHPH and with MePHPH at 80 wt% total waterdeac2024b R17
10–15% against 3.7%PHPH film switch against its computed critical pointdeac2024b R19, X5
Evidence: data, conditions and papers

Finding F30. Measured drug–PVPVA–water phase diagrams placed the limit of congruency near the critical point: there the computed fraction of drug-rich phase jumps from about 0.15 to 0.82, and the critical-point loadings of four phenolphthalein analogues (about 33, 33, 14 and 4%) followed their cited limits (40, 30, 10 and 5%) because a hydrogen-bonding drug draws the polymer into its drug-rich phase

In short. Equilibrated mixtures of dispersion and buffer at 37 °C gave a drug-rich phase of 82.9–94.1 wt% drug for the methyl ether of phenolphthalein (MePHPH), whose PVPVA fell from about 13.7 to 2.5 wt% as total water rose from 25 to 99 wt%, and a drug-rich phase of only 5.7–16.7 wt% drug and 41.9–52.2 wt% PVPVA for phenolphthalein (PHPH), whose polymer rose with water deac2024b R15, R17. PC-SAFT fitted to solubility data and one dilute tie line reproduced both diagrams and put the critical (plait) point at about 33% loading for MePHPH and 3.7% for PHPH deac2024b R22, R23, R35. Along a hydration path at constant drug-to-polymer ratio the lever rule gave a drug-rich fraction that jumps from about 0.15 at 27% to about 0.82 at 39.5% MePHPH, and films at 100% RH switched from droplets to a continuous drug-rich phase near 40% MePHPH and between 10 and 15% PHPH deac2024b R35, R18, R19. The critical-point loadings of MePHPH, MeTIPP, TIPP and PHPH (about 33.2, 32.6, 13.7 and 3.7%) followed the cited limits of 40, 30, 10 and 5% in order, each within 7% deac2024b R37. The authors propose the critical point as a "surrogate" for the limit; release was not measured in the paper, and for PHPH the prediction misses the film switch three- to fourfold deac2024b C64, X9, X5.

Type. model result checked against measured diagrams and films for 2 drugs, and against cited limits for 4 analogues in PVPVA Strength. for the opposite partitioning of the polymer, measured directly with replicate SDs deac2024b K1: strong; moderate for the agreement of measured and computed diagrams deac2024b K2: moderate; moderate for the critical point as predictor of the limit, which rests on cited limits and misses the PHPH films deac2024b K3: moderate, K4: moderate, X9, X5.

How it was shown

Deac and co-workers (2024) equilibrated phenolphthalein (PHPH) and methyl ether (MePHPH) dispersions with pH 6.8 buffer at 37 °C and analysed both phases by NMR, imaged dye-labelled films at 100% RH, and applied the lever rule to PC-SAFT diagrams along a hydration path at constant drug-to-polymer ratio deac2024b P4, P7, P3, P19, P20, E12.

What the data show

Less than 15 wt% water split MePHPH–PVPVA films deac2024b R1, R2.

systemmethod and conditionsresultids
MePHPH–PVPVA–buffer, 25–99 wt% waterequilibrated up to 147 days, 37 °C, NMR and HPLCdrug-rich phase 82.9–94.1 wt% drug; PVPVA ≈13.7 → 2.5 wt% (segregative)deac2024b R15, R17
PHPH–PVPVA–buffer, 60–99 wt% watersamedrug-rich phase 5.7–16.7 wt% drug, 41.9–52.2 wt% PVPVA, rising with water (associative)deac2024b R15, R17
MePHPH films 10–60%; PHPH films 5–20%confocal, 100% RH, 37 °C, to 14 hdroplets to 30%, continuous from 50%; droplets to 10%, continuous from 15%deac2024b R18, R19
PC-SAFT diagrams, lever rule at the spinodalhydration at constant drug:polymer ratioW^{\alpha} ≈0.15 → 0.82 between 27 and 39.5% MePHPH; critical point ≈33 and 3.7%deac2024b R35
four analoguescritical-point loading against cited limit≈33.2 / 32.6 / 13.7 / 3.7 against 40 / 30 / 10 / 5%deac2024b R37
Fig. 16 of deac2024b: fraction of drug-rich phase at the onset of separation against drug loading, with film images
Fig. 16 · deac2024bfraction of drug-rich phase at the onset of separation against drug loading, with film images

The curve stays low and then jumps across the orange critical point; the overlaid films show blue droplets below the jump and a blue network above it; no computed MePHPH point lies between about 27 and 39.5% except the critical point deac2024b R35, X8.

Why

The gel hydrates at a constant drug-to-polymer ratio, crosses the binodal and separates by spinodal decomposition, and because both drug-rich phases are rubbery at 37 °C their amounts follow the lever rule deac2024b C48, C23, C49, C50. Below the critical point the drug-rich phase is the minority and forms droplets that leave as the chains disentangle; above it the majority forms a network that stays as a surface barrier, which "appears to underpin" the fall-off deac2024b C47, C65. PHPH hydrogen bonding to PVPVA, "likely", pulls the polymer into the drug-rich phase and moves the critical point, and with it the limit, to low loading deac2024b C22, C56.

Limits and transfer

Release was not measured, the limits being cited, and for PHPH the predicted inversion at about 3.7% misses the film switch between 10 and 15% deac2024b X9, X5, C53. High-Tg drugs "may not" reach local equilibrium deac2024b C54. For a candidate drug, measure where the polymer goes when dispersion and buffer separate, or fit a model to solubility data and one dilute tie line: tie lines sloping up or a polymer-rich drug phase flag an associative system whose limit can lie near 5% deac2024b P4, P19, R17, R37.

How it was shown

Deac and co-workers (2024, ternary phase diagrams) asked whether the limit of a drug–PVPVA dispersion can be read from the drug–polymer–water phase diagram without a release test deac2024b A1, A7. They used PHPH and MePHPH, the strongest and weakest PVPVA binders of the four phthalide analogues of the 2021 study, measured both experimentally, and computed TIPP and MeTIPP as well deac2024b M1, M2, M3, M4, R39. Dispersion powders at 5–20% were mixed with pH 6.8 phosphate at dispersion-to-water ratios of 20:80 to 70:30, stored at 37 °C for up to 147 days, separated by centrifugation and analysed by quantitative ¹H NMR and HPLC, giving coexisting compositions and tie lines; very dilute points (99% water) came from dispersed compacts deac2024b P4, P7, A4, A5. Spin-coated MePHPH–PVPVA films were held at 62–97% RH to find the onset of separation, with the water of matching powders weighed deac2024b P2, P8, A2. Dye-labelled films (prodan in the hydrophobic, Alexa Fluor 488 in the hydrophilic phase) were imaged by confocal microscopy at 100% RH and 37 °C every minute for 30 min and up to 14 h, at 10–60% MePHPH and 5–20% PHPH deac2024b P3, P11, A3. Tgs of hydrated dispersions and of the separated phases were measured by DSC deac2024b P16. PC-SAFT parameters were fitted to crystalline solubilities in several solvents (PHPH, TIPP, MeTIPP) or amorphous binodals (MePHPH), each drug–PVPVA binary parameter k_{ij} to the most dilute measured tie line in u_{ij} = (1-k_{ij})\sqrt{u_i u_j}, and binodal, spinodal and critical point computed at 37 °C deac2024b P19, E7, E19, E20. Hydration was drawn as a straight path from the dry dispersion to the water corner at constant drug-to-polymer ratio, separation was taken to start at the spinodal with both phases at local equilibrium, and the lever rule

W^{\alpha} = \frac{m^{\alpha}}{m^{T}} = \frac{W_i^{T} - W_i^{\beta}}{W_i^{\alpha} - W_i^{\beta}}

gave the mass fraction W^{\alpha} of drug-rich phase at onset, the drug-rich phase being taken as continuous above 0.5 deac2024b P20, E12, C48, C51. The critical-point loading was compared with the film switch and with the limits measured by release in the 2021 study deac2024b R37, X9.

What the data show

MePHPH films stayed clear at 62 and 75% RH and showed domains from 80% RH, where matching powders held 9.6–14.6 wt% water (4.9–9.4 wt% at 75% RH), so less than 15 wt% water splits MePHPH–PVPVA, below the cited average gel-layer water of about 10–20 wt% deac2024b R1, R2, R40, C13. Every MePHPH mixture split into a drug-rich phase of 82.9–94.1 wt% drug, 2.5–13.7 wt% PVPVA and 2.6–4.0 wt% water and a water-rich phase of less than 1 wt% drug except in the driest mixture; PVPVA in the drug-rich phase fell from about 13.7 to 6.9, 4.2 and 2.5 wt% at 25, 50, 80 and 99 wt% total water, and the tie lines sloped down (segregative) deac2024b R15, R17, C18. Three PHPH mixtures stayed one phase; in the others the "drug-rich" phase held 5.7–16.7 wt% PHPH, 41.9–52.2 wt% PVPVA and 31–52 wt% water, its polymer rising from about 42 to 52 wt% between 60 and 99 wt% total water (from about 69 wt% water strictly), and the tie lines sloped up (associative); at 80 wt% total water the drug-rich phase held about 47 wt% PVPVA with PHPH against about 5 wt% with MePHPH deac2024b R15, R17, C18, C20, X14. The computed critical point lay at about 29 wt% drug, 59 wt% PVPVA and 12 wt% water for MePHPH and about 2.6 wt% drug, 59.5 wt% PVPVA and 38 wt% water for PHPH; the real MePHPH gap is slightly larger and the real PHPH gap smaller than computed deac2024b R22, R23, C34. The fitted binary parameter was −0.040 for PVPVA–PHPH and 0.015–0.020 for the other three drugs, and computed drug activity in the dry dispersion (5% by volume) was about 10^{-13}, 10^{-9}, 2 \times 10^{-3} and 0.06 for PHPH, TIPP, MeTIPP and MePHPH deac2024b R50, R36. MePHPH films became co-continuous within 8–15 min at every loading and broke into droplets at 14–31 min; the lasting structure was droplets at 10–30%, co-continuous at 1 h and large droplets at 6 h at 40%, and a continuous drug-rich phase at 50 and 60% deac2024b R18. PHPH films showed no co-continuous stage: droplets at 5 and 10%, continuous at 15 and 20% deac2024b R19. Vapour took 25–60 min to reach the lasting structure against less than 5 min cited for compacts in water deac2024b R20, R21. The computed drug-rich fraction rose slowly to about 0.15 at 27% MePHPH and jumped to about 0.82 at 39.5%, and for PHPH from about 0.16 at 3.0% to about 0.82 at 4.5%, around critical points at about 33 and 3.7% deac2024b R35. The 30% MePHPH dispersion had one Tg falling from about 75 °C dry to about 25 °C at 0.10 g/g water and two Tgs from 0.15 g/g, its drug-rich phase at about 14–20 °C up to 0.99 g/g; the 5% PHPH dispersion stayed one phase to at least 70% water, with a single measured drug-rich-phase Tg of about −5 °C deac2024b R29, R30, C42, X6. Critical-point loadings were about 33.2, 32.6, 13.7 and 3.7% for MePHPH, MeTIPP, TIPP and PHPH against cited limits of 40, 30, 10 and 5% deac2024b R37. The release data shown for MePHPH (cited) are at 20, 30 and 50% only: drug and polymer about 5.3 and 5.15 at 20%, 5.45 and 5.2 at 30%, and 0.65 and 1.1 wt%·min⁻¹·cm⁻² at 50% deac2024b R38, X9. (synthesis: the predicted minus the cited limit is −6.8, 2.6, 3.7 and −1.3% for MePHPH, MeTIPP, TIPP and PHPH; the PHPH film switch at 10–15% is 2.7–4 times the predicted 3.7%.)

papersystemmethod and conditionsresultids
deac2024bMePHPH–PVPVA–buffer, 25–99 wt% waterequilibrated up to 147 days, 37 °C, NMR and HPLCdrug-rich phase 82.9–94.1 wt% drug; PVPVA ≈13.7 → 2.5 wt% (segregative)deac2024b R15, R17
deac2024bPHPH–PVPVA–buffer, 60–99 wt% watersamedrug-rich phase 5.7–16.7 wt% drug, 41.9–52.2 wt% PVPVA, rising with water (associative)deac2024b R15, R17
deac2024bMePHPH–PVPVA films 10–50%62–97% RHclear to 75% RH, domains from 80% RH; powders 9.6–14.6 wt% water at 80% RHdeac2024b R1, R2
deac2024bMePHPH films 10–60%; PHPH films 5–20%confocal, 100% RH, 37 °C, to 14 hdroplets to 30%, continuous from 50%; droplets to 10%, continuous from 15%deac2024b R18, R19
deac2024bPC-SAFT diagrams, lever rule at the spinodalhydration at constant drug:polymer ratioW^{\alpha} ≈0.15 → 0.82 between 27 and 39.5% MePHPH; critical point ≈33 and 3.7%deac2024b R35
deac2024bfour analoguescritical-point loading against cited limit≈33.2 / 32.6 / 13.7 / 3.7 against 40 / 30 / 10 / 5%deac2024b R37
deac2024aclotrimazole–PVP K12, K29/3240:60 with buffer, NMR; films 100% RHsame phase compositions; inversion between 30 and 40% for both gradesdeac2024a R11, R8
yang2023ritonavir–PVPVA 30% films ± 10 parts surfactantRH steps, 12 h, confocalwater for separation 14.0% (no surfactant), 24.5% (SDS), 10.5–16.0% (Spans, Tween 80)yang2023 R21

Figure

Fig. 16 of deac2024b: fraction of drug-rich phase at the onset of separation against drug loading, with film images
Fig. 16 · deac2024bfraction of drug-rich phase at the onset of separation against drug loading, with film images

The curve stays low and then jumps across the orange critical point; the overlaid films show blue droplets below the jump and a blue network above it; no computed MePHPH point lies between about 27 and 39.5% except the critical point deac2024b R35, X8.

Fig. 6 of deac2024b: PVPVA in the drug-rich phase against total water for MePHPH (a) and PHPH (b)
Fig. 6 · deac2024bPVPVA in the drug-rich phase against total water for MePHPH (a) and PHPH (b)

Panel a falls to a few percent, panel b rises to about half the phase; the y-axes differ by an order of magnitude deac2024b R17.

Why

The authors start from the gel layer: water enters faster than drug or polymer leave, because entanglement holds the polymer and the hydrophobic drug has little drive to dissolve, so the gel hydrates at a constant drug-to-polymer ratio, crosses the binodal and separates at the spinodal by spinodal decomposition, the co-continuous onset and its breakup in MePHPH films being "the signature" of this route deac2024b C48, C23. Because both drug-rich phases are rubbery at 37 °C, they stay close to local equilibrium, their amounts follow the lever rule, and the majority phase becomes continuous over a narrow co-continuous range deac2024b C49, C50, C51, C57. Below the critical point the drug-rich phase is the minority and forms droplets that leave as the chains disentangle; above it the drug-rich phase is the majority, forms a network that traps water-rich domains and stays as a surface barrier, and this change "appears to underpin" the fall-off deac2024b C47, C65. PVPVA prefers water to MePHPH but PHPH to water ("the data suggest"), and PHPH hydrogen bonding to PVPVA is "a potential explanation", later "likely": it pulls the polymer into the drug-rich phase, inflates it, and moves the critical point, and with it the limit, to low loading deac2024b C19, C21, C22, C56. The miscibility gap of MePHPH covers most of the gel-layer region, so it separates in the gel at all but the lowest loadings, while PHPH separates there only above its limit, matching the cited observation that at 5% MePHPH separated in the gel and PHPH in the solution deac2024b R28, C37, R41. For ritonavir with surfactants Yang and co-workers (2023) argue on a schematic diagram in the same way: by the lever rule a low loading yields little drug-rich phase, which stays discrete, a high loading more, which "is expected" to be continuous; SDS, which raised the water needed for separation from 14.0 to 24.5%, enlarges the miscible region, so that less drug-rich phase forms (F31) yang2023 C41, C42, R21. (synthesis: this turns the hypothesis of F27, stated in 2023 on schematic diagrams, into measured and computed diagrams for two of the analogues; it gives a second, thermodynamic route to the lowering of the limit by hydrogen-bonding drugs in F17, next to the slower hydration of the matrix proposed in 2021; and the clotrimazole–PVP paper of 2024 shows the limit tracking inversion only when the droplets below it do not agglomerate first (F29). In the LLPS chapter dissolved polymers that enter a drug-rich phase also lowered the amorphous solubility, as PVPVA lowered that of PHPH (Amorphous solubility and LLPS F19, Amorphous solubility and LLPS F20) deac2023b R1.)

Conditions and limits

One polymer (PVPVA), four analogues on one scaffold, 37 °C and pH 6.8, no additives; release was not measured, all limits being cited from the 2021 study, and for MePHPH the release data shown place the limit only between 30 and 50% deac2024b X9. No critical point was measured; W^{\alpha} was computed from the PC-SAFT diagrams only, and the film morphology of TIPP and MeTIPP was not checked deac2024b X7, X16, C66. The TIPP tie line that sets its prediction was measured at pH 2.5, and the MePHPH parameters were fitted at 22 °C deac2024b X10, X17. Some PHPH mixtures were still changing at 105 days, one MePHPH tie line fails the mass balance, and the stated fit deviation of 2.94% cannot be reproduced (3.48% from the tabulated pairs) deac2024b X15, X3, X2, E9. Hydrogen bonding in the wet phases was not measured deac2024b C35. The authors expect high-Tg drugs, which "may not" reach local equilibrium, to behave differently deac2024b C54.

Counterexamples and conflicts

For PHPH the predicted inversion at about 3.7% matches the cited limit of 5% but not the film switch between 10 and 15% seen in the same paper, which the authors attribute to the computed critical point differing from the real one deac2024b X5, C53. The loading at which MePHPH becomes continuous is stated as above 40%, 40% or higher, and 35–40% in different parts of the paper, and the 40% film was co-continuous at 1 h but droplets at 6 h deac2024b X4, R18. In the 2023 interface paper MePHPH compacts already showed networks at 40% and inversion at 50% in situ (F25) deac2023a R6. Release can fail below inversion when droplets agglomerate, as with short PVP chains (F29) deac2024a C48. High-Tg drugs whose films stayed uniform yet failed, such as atazanavir and lumefantrine sulfate, fall outside the local-equilibrium picture (F20) correasoto2022b R9; hiew2022b R19.

Transfer check

For a candidate drug in PVPVA or another hydrophilic polymer, measure where the polymer goes when dispersion and buffer separate (two or more dispersion-to-water ratios, NMR of both phases after equilibration), or fit a thermodynamic model to the drug's solubility data and one dilute tie line deac2024b P4, P19. Tie lines sloping up, a polymer-rich drug phase or a very low computed drug activity in the dry dispersion flag an associative system whose limit can lie near 5%; a drug-rich phase of more than 80% drug and tie lines sloping down place the critical point, and the limit, at high loading deac2024b R17, R36, R37. Confirm with dye-labelled films at 100% RH at loadings around the predicted critical point, and with a release test 2.5–5% apart, since the prediction was checked only against cited limits and the drug-rich phase must be rubbery at 37 °C for the local-equilibrium picture to apply deac2024b R18, R19, C54.

History

Yang and co-workers (2022) and Deac and co-workers (2023) argued from phase volumes and schematic diagrams that the drug-rich phase becomes continuous as loading rises, and that an associative system reaches this at a lower loading (F25, F27) yang2022a C46; deac2023b C48, C63. A PC-SAFT diagram of ritonavir–PVPVA–water (Krummnow 2022, cited) had shown that little water separates that system, without considering morphology yang2023 R26. Yang and co-workers (2023) read surfactant effects on the lever rule of a schematic diagram yang2023 C41, C42. Deac and co-workers (2024, ternary phase diagrams) were the first in the library to measure the drug–polymer–water diagrams of dispersions, to compute them, and to compare the critical-point loading with the limit, calling the agreement "remarkably good" and the critical point a possible route to in silico screening ("may lead") deac2024b C59, C62. In the same year Deac and co-workers (2024, polymer molecular weight) found the phase compositions and the inversion loading of clotrimazole–PVP unchanged by molecular weight (F29) deac2024a C27, C40.

Topic 4 of 5 · 3 findings · F32–F34

Weakly basic drugs in HPMCAS

F32

Topic 4Weakly basic drugs in HPMCAS1 of 3

Lipophilic weak bases ionized at the pH of the HPMCAS gel took the polymer out of solution as an insoluble complex and released poorly.

When drug and HPMCAS-MF were added together to pH 6.0 buffer at one drug per succinoyl acid group, the polymer lost from solution was 5% (indomethacin) to 17% (cilnidipine) for non-basic drugs and ritonavir, but 70% (loratadine) and 90% (cinnarizine) for the weak bases bapat2024 R12. At 25% loading and pH 6.8 the polymer left the ritonavir, loratadine, clotrimazole and cinnarizine dispersions about 1.6, 7.4, 11.2 and 30 times more slowly than neat HPMCAS, and the drug left with it bapat2024 R5, R4, X2. Bedaquiline removed about 89–96% of HPMCAS at pH 6.0, and its 5 and 10% dispersions released only about 17–30% while staying amorphous kaur2025 R5, R7, R13, R14.

strongStrong for the complexation and its pH dependence, measured with controls and replicate SDs; moderate for the link to release, a correlation across drugs and media, with the complex measured in dilute solution, not in the dissolving gel bapat2024 K3, K4, K6, K7, X10; kaur2025 K1, K4, X14.

HPMCAS-MF taken out of pH 6.0 buffer at 1 drug per acid group, %indomethacinacid5indomethacin methyl esterneutral7ritonavirpKa 2.615cilnidipineneutral17phenolphthaleinneutral phenol60loratadinepKa 5.270clotrimazolepKa 5.9 · at 0.8:180cinnarizinepKa 8.490

Weak bases with pKa above 5, and the phenol, complexed the polymer; the others hardly did. bapat2024 R12, M1, M2, M3, M4, M5, M6, M7, M8

25% dispersions in HPMCAS-MF, pH 6.8: drug release rate, mg/min/cm²ritonavir15% complexed≈0.40loratadine70%≈0.10clotrimazole80% at 0.8:1≈0.05cinnarizine90%≈0.03

Neat HPMCAS-MF dissolved at about 0.90; drug and polymer left together in every case. bapat2024 R4, R12

For your drug

  1. For a weakly basic drug planned with HPMCAS, compare its pKa with about 6.0, the gel pH in 50 mM pH 6.8 phosphate; a base with pKa above about 5 and a high log P is at risk.
  2. Run the spike test (drug and polymer from THF into pH 6.0 buffer, polymer in the supernatant) at drug:COOH ratios from 0.125:1 to 1:1; above about 30% complexed at the target ratio predicts poor release even at low loading.
  3. Confirm with release of drug and polymer at pH 6.8 and 7.5: a dispersion that speeds up at the higher pH, where the neat drug slows down, shows that complexation controls release.

bapat2024 C45, R20, R12, R14, R4, R7; kaur2025 R5

How it works and key numbers
  1. HPMCAS dissolves only once a critical fraction of its acid groups ionizes and the chains hydrate, and drug release follows polymer release bapat2024 C24, C30; kaur2025 C27, C40.
  2. Ionization releases protons, so the gel of a compact in 50 mM pH 6.8 phosphate sits near pH 6.0, where a weak base is more ionized than in the bulk bapat2024 C9, C48.
  3. There a lipophilic drug cation pairs with the polymer carboxylate as a hydrophobic ion pair, held by electrostatic attraction plus hydrophobic interaction, and the complex is insoluble bapat2024 C33, C34, C35.
  4. Through J_p = \frac{D_p}{\delta}\, C_p, a lower interfacial polymer solubility C_p slows polymer and drug release, and the complex "likely largely accounts" for the poor release of the high-complexation drugs bapat2024 E3, C32.
  5. Bedaquiline was already about half protonated (52%) in the dry dispersion, so its ion pairs form during manufacture; a little pairing brings HPMCAS below the about 77% ionization it needs to dissolve ("may explain") kaur2025 R20, C25, C32, C33.
Loratadine at 1:1: HPMCAS-MF complexed against buffer pH, %pH 5.8≈85pH 6.0≈70pH 6.2≈60pH 6.3≈50pH 6.5≈25pH 6.8≈5pH 7.5≈2

Less ionized drug, less complex; the loratadine dispersion released faster at pH 7.5 than at 6.8. bapat2024 R13, R4

70–96% against 5–17%HPMCAS complexed at pH 6.0 by the weak bases against the acid, the neutral drugs and ritonavirbapat2024 R12; kaur2025 R5
1.6 to 30-foldslowing of HPMCAS by 25% ritonavir and by 25% cinnarizinebapat2024 R5, X2
≈17–30%bedaquiline released in 120 min at pH 6.5 from 5–10% dispersions, residues amorphouskaur2025 R13, R14
Evidence: data, conditions and papers

Finding F32. Lipophilic weak bases that are ionized at the pH of the HPMCAS gel took the polymer out of solution as an insoluble complex and released poorly even at 5–10% loading: loratadine, clotrimazole, cinnarizine and bedaquiline complexed 70–96% of HPMCAS at pH 6.0, against 5–17% for an acid, a neutral ester, ritonavir and cilnidipine

In short. When drug and HPMCAS-MF were added together from THF to pH 6.0 buffer, the polymer lost from solution at one drug per succinoyl acid group was 5% (indomethacin), 7% (its methyl ester), 15% (ritonavir), 17% (cilnidipine), 60% (phenolphthalein), 70% (loratadine) and 90% (cinnarizine), and 80% for clotrimazole at 0.8:1 bapat2024 R12. At 25% loading and pH 6.8 the polymer left the ritonavir, loratadine, clotrimazole and cinnarizine dispersions about 1.6, 7.4, 11.2 and 30 times more slowly than neat HPMCAS, and drug and polymer left together bapat2024 R5, R4, X2. Bedaquiline (pKa 8.5) removed about 89–96% of HPMCAS LF or MF at pH 6.0 and 43–54% at the ratio of a 5% dispersion; its 5 and 10% dispersions released only about 17–30% in pH 6.5 buffer while staying amorphous, and XPS put the drug at 52–55% protonated in the complex and in a dry 40% dispersion kaur2025 R5, R7, R13, R14, R20. Loratadine complexation fell from about 85% at pH 5.8 to 2% at pH 7.5, and its dispersion released faster at pH 7.5 than at 6.8, the reverse of neat amorphous loratadine bapat2024 R13, R4, R7. The authors attribute the poor release to the complex lowering polymer solubility at the gel–solution interface ("likely largely accounts"); the complex was measured in a solution test, not in the dissolving gel bapat2024 C32, X10; kaur2025 C56, X14.

Type. observation in 9 drugs (8 with HPMCAS-MF, 1 with HPMCAS LF and MF) Strength. for the complexation itself, measured with controls and replicate SDs, and for its pH dependence bapat2024 K3: strong, K4: strong; kaur2025 K1: strong; moderate for the link to release, a correlation across drugs and media with complexation and release measured at different pH bapat2024 K6: moderate, K7: weak to moderate; kaur2025 K4: moderate.

How it was shown

Bapat and co-workers (2024) released compacts of HPMCAS-MF dispersions of eight drugs at 5–60%, and spiked drug and HPMCAS from THF into pH 6.0 buffer, the gel-layer pH estimated in 2023, measuring the polymer left in solution bapat2024 P3, P7, P9, E2, C9. Kaur and co-workers (2025) ran the same test for bedaquiline (BDQ) at pH 5.8–10.5 kaur2025 P7, P11.

What the data show

BDQ was 4 ± 4% protonated as free base, 55 ± 4% in the complex and 52 ± 7% in a dry 40% dispersion kaur2025 R20.

systemmethod and conditionsresultids
8 drugs with HPMCAS-MF, 1:1 drug:COOHTHF spike into pH 6.0, 50 mM phosphatecomplexed 5 / 7 / 15 / 17 / 60 / 70 / 90% (IND / INDester / RTV / CIL / PHPH / LOR / CNZ); CLO 80% at 0.8:1bapat2024 R12
25% dispersions of RTV, LOR, CLO, CNZcompacts, pH 6.8, 37 °C, 1 hdrug ≈0.40 / 0.10 / 0.05 / 0.03 against neat HPMCAS ≈0.90 mg/min/cm²bapat2024 R4
IND, INDester 5–60%samedrug ≈0.85 → 0.50 and 0.66 → 0.39, polymer alongsidebapat2024 R2, R3
25% LOR dispersion pH 6.8, 7.5; neat amorphous LOR pH 3.0, 6.8, 7.5compactsdispersion ≈0.10 → 0.62; neat ≈0.22 / 0.05 / 0.01bapat2024 R4, R7
BDQ with HPMCAS LF, MF, pH 5.8–10.5spike test, 30 minup to ≈96 / 94.5% at pH 6.0; ≈7 / 5.5% at pH 10.5kaur2025 R5, R7
BDQ–HPMCAS 5, 10%powder, pH 6.5 buffer, 120 min, in situ UV≈28–30 and 17–19.5% released; residues amorphouskaur2025 R13, R14
Fig. 12 of bapat2024: drug release rate against percent HPMCAS complexed, two trendlines
Fig. 12 · bapat2024drug release rate against percent HPMCAS complexed, two trendlines

The low-complexation drugs sit at the upper left even at high loading; LOR, CNZ, CLO and PHPH fall along a second line to about zero at 90% complexation; labels give the loading, and some values differ from the paper's table bapat2024 R14, X1.

Why

HPMCAS dissolves only once a critical fraction of its acid groups ionizes, and the gel of a compact sits near pH 6.0, where a weak base is more ionized than in the bulk bapat2024 C24, C9, C48. There a lipophilic drug cation pairs with the polymer carboxylate as an insoluble hydrophobic ion pair bapat2024 C33, C34, C35. A lower interfacial polymer solubility slows polymer and drug release, and the complex "likely largely accounts" for the high-complexation drugs bapat2024 E3, C32, C28. BDQ ion pairs form already during manufacture kaur2025 C25.

Limits and transfer

Complexation was measured in dilute buffer, not in a dissolving gel, and unionized PHPH complexed 60% bapat2024 X10, R12, C41; kaur2025 X14. For a weak base planned with HPMCAS, run the spike test at drug:COOH ratios of 0.125:1 to 1:1: above about 30% complexation at the target ratio predicts poor release even at low loading, and a dispersion that speeds up at pH 7.5 shows that complexation controls release bapat2024 R12, R14, R4, R7.

How it was shown

Bapat and co-workers (2024) tested the hypothesis that lipophilic drug cations lower the solubility of HPMCAS by forming an ionic complex and so release poorly even at low loading, whereas anionic or neutral drugs can be loaded higher bapat2024 C6. They made rotary-evaporated HPMCAS-MF dispersions of indomethacin (IND, acid, pKa 4.5), its methyl ester (INDester, neutral), ritonavir (RTV, pKa 2.6), cilnidipine (CIL, neutral), loratadine (LOR, pKa 5.2), clotrimazole (CLO, pKa 5.9), cinnarizine (CNZ, pKa 8.4) and phenolphthalein (PHPH, neutral phenol) at 5–60% loading bapat2024 P3, M1, M2, M3, M4, M5, M6, M7, M8. They pressed 100 mg compacts (0.5 cm²), rotated them at 100 rpm in 100 mL 50 mM pH 6.8 phosphate at 37 °C for 1 h, assayed drug by HPLC-UV and HPMCAS by HPLC with light-scattering detection (n = 3), and normalized rates by R = kV/(Sx); the 25% LOR dispersion was also run at pH 7.5 and in 100 mM phosphate, the 25% CLO dispersion in pH 9.0 glycine buffer, and neat amorphous LOR at pH 3.0, 6.8 and 7.5 bapat2024 P7, E1, A3, A4. For complexation, drug and HPMCAS dissolved together in THF at set molar ratios of drug to succinoyl (COOH) groups were spiked into agitated pH 6.0 buffer (0.5–1.0 mg/mL polymer, far below its solubility), chosen as the gel-layer pH estimated in 2023, and the polymer left after ultracentrifugation gave

\text{complexed}\ (\%) = \left(1 - \frac{\text{polymer in the supernatant}}{\text{total polymer}}\right) \times 100

bapat2024 P9, E2, C9, R20. LOR was also tested at pH 5.8–7.5 and at higher ionic strength, and the protonation of CNZ in compacts was measured by XPS bapat2024 A6, A7, P8. Kaur and co-workers (2025) used bedaquiline (BDQ, pKa 8.5, log P 7.13) with HPMCAS LF (1.54 mM COOH per gram) and MF (1.19), made dispersions at 5–30%, measured complexation by the same spike test (100 µL THF stock into 5 mL medium, 0.5 mg/mL polymer, 30 min, ultracentrifuged at 25 °C) in buffers of pH 5.8–10.5 and in two biorelevant fluids, and released powders equal to 5 mg drug in 50 mL at 37 °C and 150 rpm with in situ UV for 120 min (100 µg/mL = complete), single-stage at pH 6.5 or after 60 min at pH 1.6, 3.0 or 5.0 kaur2025 M1, M2, M3, P1, P7, P11, P12. They checked residues by PLM and PXRD, measured induction times with and without polymer, and measured the protonated fraction of BDQ nitrogen by XPS against the maleate salt kaur2025 P13, P14, P15.

What the data show

In the HPMCAS-MF series drug and polymer left together throughout: IND from about 0.85 to 0.50 and INDester from 0.66 to 0.39 mg/min/cm² between 5 and 60%, with polymer rates within a few hundredths, against about 0.91 for neat HPMCAS bapat2024 R2, R3. Drug rates fell with loading at very different speeds: RTV 0.66 (10%) to 0.12 (47%), LOR 0.49 (10%) to 0.1 (30%), CNZ 0.6 (5%) to 0.01 (25%), PHPH 0.22 at 27% bapat2024 R2. At 25% and pH 6.8 drug and polymer left at about 0.40 and 0.43 (RTV), 0.10 and 0.12 (LOR), 0.05 and 0.08 (CLO) and 0.03 and 0.05 (CNZ) against 0.90 for neat HPMCAS; at pH 7.5 the LOR dispersion released at about 0.62 and 0.70, and at pH 9.0 the CLO dispersion at about 0.25 and 0.28 bapat2024 R4. Complexation at pH 6.0 and 1:1 was 5 ± 2% (IND), 7 ± 2 (INDester), 15 ± 3 (RTV), 17 ± 3 (CIL), 60 ± 4 (PHPH), 70 ± 5 (LOR) and 90 ± 5% (CNZ), and 80 ± 3% for CLO at 0.8:1; it rose with ratio, LOR from 30 ± 5% at 0.25:1 (10% loading) and CNZ from 12 ± 3% at 0.125:1 (5%) to about 99–100% from 1.5:1 bapat2024 R12, R11. LOR complexation was about 85, 70, 60, 50, 25, 5 and 2% at pH 5.8, 6.0, 6.2, 6.3, 6.5, 6.8 and 7.5, while neat amorphous LOR released at about 0.22 (pH 3.0), 0.05 (6.8) and 0.01 (7.5) bapat2024 R13, R7. Release against complexation fell on two lines: drugs complexing at most 17% released about 0.43–0.68 up to 30% loading (IND still 0.50 at 60%), and LOR, CNZ, CLO and PHPH fell from about 0.47 (LOR 10%, 30% complexed) to about 0 (CNZ 30%, 90%) bapat2024 R14. Only about 20% of CNZ was protonated in the dry 25% dispersion and 11% after partial dissolution bapat2024 R8. LOR complexation was about 70% in 50 mM phosphate, 65% with NaCl to 150 mM ionic strength and 48% in 100 mM phosphate bapat2024 R16. BDQ: at the highest ratio complexation with LF was about 96% at pH 6.0, 90% at 5.8, 58.5% at 6.5, 50% at 7.0, 18% at 8.5 and 7% at 10.5, and with MF about 94.5, 84.5, 65.5, 57, 22 and 5.5% kaur2025 R5, R7. Complexes from pH 6.0–7.0 held the polymer's carbonyl band and broadened bands of disordered BDQ; from pH 8.5 and 10.5 the drug was crystalline kaur2025 R11. BDQ was 4 ± 4% protonated as free base, 55 ± 4% in the complex and 52 ± 7% in a dry 40% MF dispersion; after 1 h at pH 6.5 the dispersion surface was 15 ± 3% protonated and held 55 ± 2 wt% drug against 32 ± 2 before kaur2025 R20. In pH 6.5 buffer the 5% dispersions reached about 30 (LF) and 28% (MF) and the 10% dispersions about 17 and 19.5% in 120 min, and after a 60 min acid stage (under 10% released) about 20–25% kaur2025 R13, R12. Residues were non-birefringent with PXRD halos, and with 400 µg/mL HPMCAS the precipitate stayed amorphous for 12–24 h kaur2025 R14, R18. The amorphous solubility of BDQ was 13.4, 1.9 and 0.63 µg/mL at pH 5.0, 5.8 and 6.5 kaur2025 R2. (synthesis: at 25% loading the polymer rate of the CNZ dispersion, 0.05, is about 1/18 of neat HPMCAS, 0.90/0.05 = 18, the value the extractor finds against the printed 30; at 1:1 drug:COOH LOR and CNZ correspond to about 30% loading, so the complexation values of 70–90% describe dispersions near 30%.)

papersystemmethod and conditionsresultids
bapat20248 drugs with HPMCAS-MF, 1:1 drug:COOHTHF spike into pH 6.0, 50 mM phosphatecomplexed 5 / 7 / 15 / 17 / 60 / 70 / 90% (IND / INDester / RTV / CIL / PHPH / LOR / CNZ); CLO 80% at 0.8:1bapat2024 R12
bapat202425% dispersions of RTV, LOR, CLO, CNZcompacts, pH 6.8, 37 °C, 1 hdrug ≈0.40 / 0.10 / 0.05 / 0.03 against neat HPMCAS ≈0.90 mg/min/cm²bapat2024 R4
bapat2024IND, INDester 5–60%samedrug ≈0.85 → 0.50 and 0.66 → 0.39, polymer alongsidebapat2024 R2, R3
bapat2024LOR 1:1, pH 5.8–7.5spike test≈85 → 2% complexedbapat2024 R13
bapat202425% LOR dispersion pH 6.8, 7.5; neat amorphous LOR pH 3.0, 6.8, 7.5compactsdispersion ≈0.10 → 0.62; neat ≈0.22 / 0.05 / 0.01bapat2024 R4, R7
kaur2025BDQ with HPMCAS LF, MF, pH 5.8–10.5spike test, 30 minup to ≈96 / 94.5% at pH 6.0; ≈7 / 5.5% at pH 10.5kaur2025 R5, R7
kaur2025BDQ free base, complex, dry 40% dispersionXPS N 1sprotonated ≈4 / 55 / 52%kaur2025 R20
kaur2025BDQ–HPMCAS 5, 10%powder, pH 6.5 buffer, 120 min, in situ UV≈28–30 and 17–19.5% released; residues amorphouskaur2025 R13, R14

Figure

Fig. 12 of bapat2024: drug release rate against percent HPMCAS complexed, two trendlines
Fig. 12 · bapat2024drug release rate against percent HPMCAS complexed, two trendlines

The low-complexation drugs sit at the upper left even at high loading; LOR, CNZ, CLO and PHPH fall along a second line to about zero at 90% complexation; labels give the loading, and some values differ from the paper's table bapat2024 R14, X1.

Fig. 1 of kaur2025: HPMCAS LF complexed by bedaquiline against drug:COOH ratio in buffers (A) and in simulated intestinal fluids (B)
Fig. 1 · kaur2025HPMCAS LF complexed by bedaquiline against drug:COOH ratio in buffers (A) and in simulated intestinal fluids (B)

In panel A the pH 6.0 and 5.8 curves plateau near 90–96% from a ratio of about 0.3:1, pH 8.5 and 10.5 stay low; 0.0625:1 to 1.2:1 corresponds to 5–50% loading kaur2025 R5, C12.

Why

The authors start from the group's earlier picture: HPMCAS dissolves only once a critical fraction of its acid groups ionizes and the chains hydrate, and drug release follows polymer release bapat2024 C24, C30; kaur2025 C27, C40. Ionization releases protons, so the gel of a compact in 50 mM pH 6.8 phosphate sits near pH 6.0 (2023 study), where a weak base is more ionized than in the bulk bapat2024 C9, C48. There a lipophilic drug cation pairs with the polymer carboxylate as a hydrophobic ion pair, driven by electrostatic attraction plus hydrophobic interaction, as polyelectrolytes do with oppositely charged amphiphiles, and the complex is insoluble bapat2024 C33, C34, C35. Through the boundary-layer flux

J_p = \frac{D_p}{\delta}\, C_p

a lower interfacial polymer solubility C_p slows polymer and drug release; the authors say this "can be used to partially rationalize" the data, that the complex "likely largely accounts" for the high-complexation drugs, and that lipophilicity, through slower hydration, "is likely the dominant factor" for the others bapat2024 E3, C32, C28, C42. Ionization of LOR "is necessary" for complexation, and its high complexation at only 14% calculated ionization "could" come from a higher apparent pKa of bound LOR or cooperative hydrophobic binding bapat2024 C38, C39. PHPH, unionized, is explained by "hydrophobic hydrogen bonding" of its phenols to the carboxylate, a "conjecture" bapat2024 C41. For BDQ the authors place the maximum at pH 5.8–6.0 rather than near pH 6.7, where both species are about 98% ionized, because at 5.8–6.0 HPMCAS is about 88–92% ionized while BDQ is above 99%, so a little pairing brings the polymer below the about 77% ionization it needs to dissolve ("may explain") kaur2025 C32, C33, C28. The complex leaves ionization intact but "is expected to impede hydration", and the surface loses polymer and gains drug, a second, "highly unfavorable" factor; the poor release in pH 6.5 buffer "was attributed" to the complex, with crystallization excluded kaur2025 C46, C43, C56, C23. Since BDQ is already about half protonated in the dry dispersion, ion pairs form during manufacture from the organic solvent, not only on contact with water kaur2025 C25. (synthesis: for a weak base in HPMCAS the decline of release with loading is set by how much of the polymer the drug ties up, not by the drug's log P: RTV, more lipophilic than LOR (log P 5.7 against 4.55), complexed 15% and released 0.45 at 25%, LOR 63–70% and about 0.10–0.17 bapat2024 X18, M3, M5; this replaces, for cationic drugs, the gradual decline of HPMCAS dispersions of F11, and it parallels the polymer-rich drug phase that hydrogen-bonding phenols form with PVPVA (F27, F30), PHPH taking HPMCAS out as well. In the LLPS chapter the amorphous solubility of weak bases rose with ionization as the Henderson–Hasselbalch relation predicts (Amorphous solubility and LLPS F10); here the same ionization that raises solubility binds the drug to the polymer.)

Conditions and limits

HPMCAS-MF (and LF for BDQ) only, 37 °C; compacts in 50 mM phosphate (Bapat) and powder dispersion in buffers and biorelevant fluids (Kaur) bapat2024 P7; kaur2025 P11. Complexation was measured in dilute buffer spiked from THF, at an unstated temperature (Bapat) or at 25 °C (Kaur), not in a dissolving gel; the gel pH of 6.0 is cited, and no complex was isolated from, or polymer solubility measured at, a dissolving compact bapat2024 X10, X13; kaur2025 X14. Kaur and co-workers did not measure polymer release, and the surface enrichment comes from a 40% dispersion that was not release-tested kaur2025 X14, X9, X10. Release values for the same 25% dispersions differ between table and figures in the 2024 paper (LOR 0.17 against about 0.10; CNZ 0.01 against about 0.03), and the CNZ slowdown is 18- or 30-fold bapat2024 X1, X2. Buffer recipes for several pH values are inconsistent with their labels bapat2024 X5. Three weak bases with pKa above 5 and one with pKa 8.5; no in vivo data bapat2024 C45, C51.

Counterexamples and conflicts

PHPH, unionized, complexed 60% and released on the cationic line bapat2024 R12, C41. CNZ at 5% (12% complexed) released at about 0.60, with the low-complexation group bapat2024 R14. LOR complexation was not zero far above its pKa (about 2–5% at pH 6.8–7.5), and it fell most steeply between pH 6.3 and 6.8, not in the gel pH range 6.0–6.3 the authors match to release bapat2024 X17. In 100 mM phosphate LOR complexation fell to about 48%, a second route for the 2.5-fold faster release in that buffer that the authors do not discuss bapat2024 X11, R6. With poly(acrylic acid), which dissolves even when un-ionized, proton transfer to a basic drug (loperamide, cited) went with rapid release, which the 2025 grade paper relates to polymer hydrophilicity (F33) bapat2025a C21, C22. Delamanid, a weak base of low pKa, showed no effect of medium in earlier work because it is barely ionized where HPMCAS is anionic kaur2025 C52.

Transfer check

For a weakly basic drug planned with HPMCAS, compare its pKa with about 6.0, the gel pH in 50 mM pH 6.8 phosphate: a base with pKa above about 5 and a high log P is at risk bapat2024 C45, R20. Run the spike test (drug and polymer from THF into pH 6.0 buffer, polymer in the supernatant) at drug:COOH ratios from 0.125:1 to 1:1, computed from the grade's acid content; complexation above about 30% at the target ratio predicts poor release even at low loading, at most 17% predicts release limited by lipophilicity bapat2024 R12, R14; kaur2025 R5. Confirm with constant-area release of drug and polymer at pH 6.8 and 7.5: a dispersion that speeds up at the higher pH, where the neat drug slows down, shows that complexation, not drug solubility, controls release bapat2024 R4, R7.

History

A lumefantrine study of the Miscibility chapter (2022) had attributed poor release from enteric polymers to drug–polymer ionic interactions that reduce polymer hydration bapat2024 C5; kaur2025 C3. The 2023 media study placed the HPMCAS gel near pH 6.0 (F23) bapat2024 R20. Bapat and co-workers (2024) were the first in the library to measure insoluble drug–HPMCAS complexes across drug charge and to set them against release; they cite the insoluble PHPH–PVPVA complex of 2023 (F27) bapat2024 C41. Bapat and Taylor (2025) carried the test to three HPMCAS grades (F33), and Kaur and co-workers (2025) to bedaquiline, showing ion pairs already in the dry dispersion and their disruption in biorelevant fluids (F34) bapat2025a C5; kaur2025 C25, C49.

F33

Topic 4Weakly basic drugs in HPMCAS2 of 3

For lipophilic weak bases the HPMCAS grade ranked release LF > MF > HF, in the order of acid groups per gram.

Dispersions of 25% loratadine released drug at about 0.25, 0.10 and 0.01 mg/min/cm² from HPMCAS LF, MF and HF at pH 6.8, but 0.73, 0.62 and 0.44 at pH 7.5, where loratadine is barely ionized bapat2025a R2, R13. Cinnarizine at 25% released at about 0.13 (LF) and 0.014 (MF), and from HF too slowly to determine bapat2025a R3. The grades carry 1.52, 1.19 and 0.76 mmol/g of acid groups, and cinnarizine complexed HF more than LF at every ratio bapat2025a M3, M4, M5, R9, R10.

strongStrong for the release and complexation rankings, direct and in triplicate; moderate for the pH effect and for complexation as the cause; weak to moderate for the grade mechanism, which was not measured bapat2025a K1, K3, K2, K5, K6, X11.

pH 6.8pH 7.5HPMCAS-LF1.52 mmol/g acid groups0.250.73HPMCAS-MF1.19 mmol/g0.100.62HPMCAS-HF0.76 mmol/g0.010.440.010.1125% loratadine: drug release rate, mg/min/cm² (log scale)

The 25-fold grade gap at pH 6.8 closes to under twofold at pH 7.5. bapat2025a R2, M3, M4, M5

from 0.25 to 1 drug per acid groupHPMCAS-HF70 → 99HPMCAS-MFcited41 → 90HPMCAS-LF30 → 700102030405060708090100polymer complexed by cinnarizine at pH 6.0, %

All grades approach 100% at 3:1. bapat2025a R9, R10

For your drug

  1. For a weakly basic drug planned with HPMCAS, compute the drug:COOH ratio at the target loading from the grade's acid content (about 1.5, 1.2 and 0.8 mmol/g for LF, MF and HF) and run the pH 6.0 spike test at that ratio for each grade.
  2. Start with LF when the drug is cationic at pH 6–7, and test release of drug and polymer at pH 6.8 and 7.5; a grade gap at 6.8 that closes at 7.5 marks complexation.

bapat2025a M3, M4, M5, R9, R2, C24

How it works and key numbers
  1. An acidic polymer dissolves only after a critical fraction of its acid groups ionizes and hydrates, and a hydrophobic drug bound to the carboxylate "can impact" its solubility and rate bapat2025a C2, C3.
  2. At the dissolving surface near pH 6.0 a cationic drug forms hydrophobic ion pairs with the carboxylates, and because drug release is coupled to polymer dissolution, the complex holds back both (F32) bapat2025a C28, C29, C34.
  3. LF carries twice the carboxylates per gram of HF, so at 25% loading it keeps "spare" carboxylates to hydrate; by analogy with maleic anhydride copolymers, the more succinoylated LF may also need less ionization to dissolve bapat2025a C26, C25.
  4. Loratadine leaves LF faster than cinnarizine "most likely" because it complexes less (about 50 against 70% at 1:1), accounted for "at least partially" by its lower ionization at pH 6.0 (about 14%) bapat2025a C30, C31, R13.
  5. At pH 7.5 loratadine is only about 0.5% ionized, its complexation of LF fell to about 0%, and the grade gap closed bapat2025a R13, R11, R2.
0.25 / 0.10 / 0.01 mg/min/cm²25% loratadine from LF / MF / HF at pH 6.8bapat2025a R2
1.52 / 1.19 / 0.76 mmol/gsuccinoyl acid groups of LF / MF / HFbapat2025a M3, M4, M5
95 against 50%loratadine complexation of HF against LF at 1:1 and pH 6.0bapat2025a R11
Evidence: data, conditions and papers

Finding F33. For lipophilic weak bases the HPMCAS grade ranked release LF > MF > HF, in the order of acid groups per gram (1.52, 1.19, 0.76 mmol/g) and the reverse of complexation: at 25% loading and pH 6.8 loratadine left LF about 25 times faster than HF and cinnarizine left HF too slowly to measure, while at pH 7.5, where loratadine is barely ionized, the grade gap fell below twofold

In short. Neat compacts of HPMCAS LF, MF and HF dissolved at about 1.50, 0.90 and 0.45 mg/min/cm² in pH 6.8 phosphate and 1.73, 1.09 and 0.63 at pH 7.5 bapat2025a R1. Dispersions of 25% loratadine released drug at about 0.25, 0.10 and 0.01 mg/min/cm² from LF, MF and HF at pH 6.8 and 0.73, 0.62 and 0.44 at pH 7.5, with the polymer alongside; 25% cinnarizine released at about 0.13 (LF) and 0.014 (MF), and from HF too slowly to determine bapat2025a R2, R3. Titration gave 1.52 (LF) and 0.76 mmol/g (HF) of succinoyl acid groups at pKa 4.91 and 5.06, against a cited 1.19 mmol/g for MF bapat2025a M3, M4, M5. In pH 6.0 buffer cinnarizine took 70% of HF and 30% of LF out of solution at 0.25 drug per acid group and 99% and 70% at 1:1, and loratadine complexation fell with pH for every grade as its calculated ionization fell from 14% to 0.5% bapat2025a R9, R10, R11, R13. The authors read LF's advantage as more, "spare" carboxylates and a lower critical ionization, neither of which was measured; MF data are cited from earlier work bapat2025a C26, C25, X11, X7.

Type. observation in 2 drugs (loratadine, cinnarizine) with 3 HPMCAS grades at one loading Strength. for the release ranking and the complexation ranking, direct and in triplicate bapat2025a K1: strong, K3: strong; moderate for the pH effect and for complexation as the cause bapat2025a K2: moderate, K5: moderate; weak to moderate for the grade mechanism bapat2025a K6: weak to moderate.

How it was shown

Bapat and Taylor (2025) released compacts of 25% loratadine (LOR, pKa 5.2) and cinnarizine (CNZ, pKa 8.4) dispersions in HPMCAS LF, MF and HF with drug and polymer assayed, titrated the grades and ran the pH 6.0 spike test of the 2024 study bapat2025a M1, M2, P5, P6, P8, P9.

What the data show

Moving to pH 7.5 raised the LOR rate from HF more than tenfold, from MF about fivefold and from LF about threefold bapat2025a C14.

systemmethod and conditionsresultids
neat HPMCAS LF, MF, HFcompacts, pH 6.8 and 7.5, 37 °C≈1.50 / 0.90 / 0.45 and ≈1.73 / 1.09 / 0.63 mg/min/cm²bapat2025a R1
LOR 25% in LF, MF, HFsame, drug and polymerdrug ≈0.25 / 0.10 / 0.01 (pH 6.8); ≈0.73 / 0.62 / 0.44 (pH 7.5)bapat2025a R2
CNZ 25% in LF, MF, HFpH 6.8drug ≈0.13 / 0.014 / not measurablebapat2025a R3
LF, MF, HFtitration1.52 / 1.19 (cited) / 0.76 mmol/g COOH; pKa 4.91 / 4.97 / 5.06bapat2025a M3, M4, M5
CNZ:COOH 0.25:1 to 1:1, pH 6.0spike testHF 70 → 99%; LF 30 → 70%bapat2025a R9, R10
LOR 1:1, pH 5.8–7.5spike testHF 95 → 15%; LF 70 → 0%bapat2025a R11
Fig. 3 of bapat2025a: drug and polymer release rates of 25% loratadine dispersions in three HPMCAS grades at pH 6.8 (a) and 7.5 (b)
Fig. 3 · bapat2025adrug and polymer release rates of 25% loratadine dispersions in three HPMCAS grades at pH 6.8 (a) and 7.5 (b)

At pH 6.8 the HF bars barely rise; at pH 7.5 the three grades lie close; drug and polymer bars are nearly equal; the y-axis of panel a ends at 0.30, of panel b at 0.8 bapat2025a R2.

Why

An acidic polymer dissolves only after a critical fraction of its acid groups ionizes and hydrates, and a hydrophobic drug bound to the carboxylate "can impact" its solubility and rate bapat2025a C2, C3. A cationic drug forms hydrophobic ion pairs with the carboxylates, and the complex holds back both polymer and drug bapat2025a C28, C29, C34. LF carries twice the carboxylates per gram of HF, so at 25% loading it keeps "spare" carboxylates free to hydrate ("fairly straightforward to rationalize") and, by analogy with maleic anhydride copolymers, needs less ionization to dissolve bapat2025a C26, C25.

Limits and transfer

Two drugs were tested at one loading, the MF data were cited, and the grade mechanism was not measured bapat2025a A1, X7, X11. Compute the drug:COOH ratio at the target loading from the grade's acid content (about 1.5, 1.2 and 0.8 mmol/g for LF, MF and HF), run the spike test at that ratio, and start with LF when the drug is cationic at pH 6–7; a gap between grades at pH 6.8 that closes at 7.5 marks complexation bapat2025a M3, M4, M5, R9, R2, C24.

How it was shown

Bapat and Taylor (2025) tested the hypothesis that at equal loading a lipophilic cation impairs release from HPMCAS-HF more than from MF, with LF best bapat2025a C7. They made 25:75 dispersions of loratadine (LOR, pKa 5.2, log P 5.2, partly cationic at pH 6.8) and cinnarizine (CNZ, pKa 8.4, log P 5.8, fully cationic) with each grade by rotary evaporation, confirmed them amorphous, and released 100 mg compacts (0.5 cm²) at 100 rpm in 100 mL 50 mM phosphate at 37 °C for 60 min, drug by HPLC-UV and polymer by HPLC-ELSD (n = 3), at pH 6.8 and 7.5 (LOR and neat polymers), pH 6.8 (CNZ) and pH 1.6 (drug only); MF data at pH 6.8 and 7.5 were taken from the 2023 and 2024 studies bapat2025a M1, M2, P5, P6, X7. They titrated LF and HF for acid content and pKa, measured the pH of polymer slurries in water, and ran the spike test of the 2024 study (drug and polymer from THF into pH 6.0 buffer, 0.5 mg/mL polymer, phenol–sulfuric acid assay of the supernatant) at CNZ:COOH ratios of 0.25:1 to 3:1, for LOR at 1:1 from pH 5.8 to 7.5, and for CNZ also at pH 5.8 bapat2025a P8, P10, P9, E2. They checked solution and compact surfaces for crystals by PLM for up to about 12 h bapat2025a P7.

What the data show

Neat polymers: LF about 1.50, MF 0.90 and HF 0.45 mg/min/cm² at pH 6.8, and about 1.73, 1.09 and 0.63 at pH 7.5 bapat2025a R1. LOR dispersions released drug and polymer at about 0.25 and 0.27 (LF), 0.10 and 0.12 (MF) and 0.01 and 0.02 (HF) at pH 6.8, and 0.73 and 0.76, 0.62 and 0.68, 0.44 and 0.48 at pH 7.5; after 1 h the medium held 17.6, 7.0 and 2.4 µg/mL at pH 6.8 and 59.1, 39.9 and 29.2 µg/mL at pH 7.5 bapat2025a R2, R5. Moving to pH 7.5 raised the HF rate more than tenfold, MF about fivefold and LF about threefold bapat2025a C14. CNZ dispersions released drug and polymer at about 0.130 and 0.140 (LF) and 0.014 and 0.025 (MF); the HF rate was too slow to determine, with 0.0 µg/mL after 1 h against 5.3 (LF) and 2.7 (MF) bapat2025a R3, R5. At pH 1.6 all six dispersions released 2.1–5.5% in 1 h bapat2025a R4, X2. No crystals formed during the 1 h tests or for 12 h after release from MF and HF; small crystals appeared after about 10 h only for LOR–LF bapat2025a R6. Acid content was 1.52 ± 0.03 (LF), 1.19 ± 0.01 (MF, cited) and 0.76 ± 0.02 mmol/g (HF), pKa 4.91, 4.97 and 5.06, and slurry pH 4.52, 4.61 and 4.73 bapat2025a M3, M4, M5. CNZ complexation at pH 6.0 was 70, 86, 98 and 99% for HF and 30, 45, 65 and 70% for LF at 0.25, 0.5, 0.75 and 1:1, with the cited MF values (about 41, 67, 82 and 90%) between, all near 100% at 3:1; at a fixed loading the ratio depends on the grade, 1:1 being 36% loading for LF but 22% for HF bapat2025a R9, R10. LOR at 1:1 and pH 6.0 complexed 95% of HF and 50% of LF; HF fell to about 67, 40 and 15% at pH 6.5, 6.8 and 7.5, LF from about 70% at pH 5.8 to 13% at 6.5 and about 2 and 0% at 6.8 and 7.5, while calculated LOR ionization fell from about 20% (pH 5.8) and 14% (6.0) to 2.5% (6.8) and 0.5% (7.5) bapat2025a R9, R11, R13. Lowering the pH to 5.8 raised CNZ complexation with LF from 30–70% to about 40–81% bapat2025a R12. (synthesis: 0.25/0.01 = 25 for LOR at pH 6.8 and 0.73/0.44 ≈ 1.7 at pH 7.5; 1.50/0.45 ≈ 3.3 for the neat grades; 1.52/0.76 = 2.0 for acid content; 25% loading lies between 0.5:1 and 0.75:1 for LF and between 1:1 and 1.5:1 for HF in the paper's own conversion, so in an HF dispersion of CNZ the drug cations can outnumber the carboxylates.)

papersystemmethod and conditionsresultids
bapat2025aneat HPMCAS LF, MF, HFcompacts, pH 6.8 and 7.5, 37 °C≈1.50 / 0.90 / 0.45 and ≈1.73 / 1.09 / 0.63 mg/min/cm²bapat2025a R1
bapat2025aLOR 25% in LF, MF, HFsame, drug and polymerdrug ≈0.25 / 0.10 / 0.01 (pH 6.8); ≈0.73 / 0.62 / 0.44 (pH 7.5)bapat2025a R2
bapat2025aCNZ 25% in LF, MF, HFpH 6.8drug ≈0.13 / 0.014 / not measurablebapat2025a R3
bapat2025aLF, MF, HFtitration1.52 / 1.19 (cited) / 0.76 mmol/g COOH; pKa 4.91 / 4.97 / 5.06bapat2025a M3, M4, M5
bapat2025aCNZ:COOH 0.25:1 to 1:1, pH 6.0spike testHF 70 → 99%; LF 30 → 70%bapat2025a R9, R10
bapat2025aLOR 1:1, pH 5.8–7.5spike testHF 95 → 15%; LF 70 → 0%bapat2025a R11
kaur2025bedaquiline 5, 10% in LF and MFpowder, pH 6.5 buffer, 120 min≈30 / 28% (5%); ≈17 / 19.5% (10%)kaur2025 R13
shah2025 (Crystallization from solution)posaconazole with HPMCAS gradesrelease at pH 5.5–7.5grades with less succinoyl released poorly at low pHshah2025 C17

Figure

Fig. 3 of bapat2025a: drug and polymer release rates of 25% loratadine dispersions in three HPMCAS grades at pH 6.8 (a) and 7.5 (b)
Fig. 3 · bapat2025adrug and polymer release rates of 25% loratadine dispersions in three HPMCAS grades at pH 6.8 (a) and 7.5 (b)

At pH 6.8 the HF bars barely rise; at pH 7.5 the three grades lie close; drug and polymer bars are nearly equal; the y-axis of panel a ends at 0.30, of panel b at 0.8 bapat2025a R2.

Fig. 6 of bapat2025a: cinnarizine complexation against drug:COOH ratio for HF, MF and LF
Fig. 6 · bapat2025acinnarizine complexation against drug:COOH ratio for HF, MF and LF

At every ratio HF lies above MF (cited) and MF above LF; all reach about 100% at 3:1 bapat2025a R9, R10.

Why

The authors use the critical-ionization model: an acidic polymer dissolves only after a critical fraction of its acid groups ionizes and hydrates, and anything that hinders hydration, such as a hydrophobic drug bound to the carboxylate, "can impact" its solubility and rate bapat2025a C2, C3. With the dissolving surface near pH 6.0 (cited), a cationic drug forms hydrophobic ion pairs with the carboxylates, and because drug release is coupled to polymer dissolution through interfacial polymer solubility, the complex holds back both (F32) bapat2025a C28, C29, C34. LF carries twice the carboxylates per gram of HF, so at 25% loading it keeps "spare" carboxylates not paired with the drug to hydrate ("fairly straightforward to rationalize"), and by analogy with maleic anhydride copolymers (Heller, cited), whose critical ionization rose from 3 to 91% with a larger hydrophobic group at unchanged pKa, the more succinoylated LF needs less ionization to dissolve ("A similar explanation can be applied") bapat2025a C26, C25. LOR releases faster than CNZ from LF "most likely" because it complexes less (about 50 against 70% at 1:1), not because it is less lipophilic, and this is accounted for "at least partially" by its lower ionization at pH 6.0 bapat2025a C30, C31. At pH 5.8 CNZ complexed more because the polymer itself is less ionized and less soluble ("This is because") bapat2025a C19. Release "was compromised by drug/polymer electrostatic interactions leading to the formation of an insoluble complex", more for HF than LF bapat2025a C34. (synthesis: for a cationic drug the grade acts through two numbers, the polymer's own dissolution rate, which ranks LF > MF > HF, and the ratio of drug cations to its acid groups at the chosen loading; the more succinoylated grade is better on both. In the crystallization chapter the more acetylated, less succinoylated grades held posaconazole supersaturated longer but limited its release at low pH (Crystallization from solution F44), and in the ASD dissolution chapter the grade decided release after a gastric stage (Supersaturation from ASD dissolution F25), so for weak bases the grade is a trade-off between inhibition and release on more than one count.)

Conditions and limits

Two lipophilic weak bases at one loading (25%), 50 mM phosphate at pH 6.8 and 7.5 (CNZ at 6.8 only), 1 h tests bapat2025a A1, A3. MF release, neat rate and pH 6.0 complexation are cited from earlier batches and studies bapat2025a X7. Complexation and surface pH were not measured in the dissolving dispersion, and the grade mechanism (critical ionization, spare carboxylates, substituent contents of the lots) was not measured bapat2025a X10, X11. In the slowest systems the drug rate is about half the polymer rate, so release there is not strictly congruent bapat2025a X6. Several LOR concentrations after 1 h exceed the amorphous solubility (9.0 µg/mL at pH 6.8, 7.6 at pH 7.5) without comment, the CNZ concentrations do not match the plotted rates, and the printed 88% loading for LF at 2:1 is out of line bapat2025a X9, X8, X1.

Counterexamples and conflicts

Raising the pH also raised the neat polymers' own rates (HF from 0.45 to 0.63), so drug and polymer ionization are not separated in the pH comparison bapat2025a R1, K2. For bedaquiline, which tied up 89–96% of either polymer at pH 6.0, LF and MF released alike in pH 6.5 buffer (about 17–30%) and in biorelevant fluids, so with a drug that saturates the carboxylates of both grades the grade made little difference (F34) kaur2025 R13, R15, R5, R7. In acid all grades released 2.1–5.5%, and the pH 1.6 rates exceeded the pH 6.8 rates of LOR–HF and CNZ–MF bapat2025a R4, X12.

Transfer check

For a weakly basic drug planned with HPMCAS, compute the drug:COOH molar ratio at the target loading from the grade's acid content (about 1.5, 1.2 and 0.8 mmol/g for LF, MF and HF) and run the pH 6.0 spike test at that ratio for each grade bapat2025a M3, M4, M5, R9. Start with LF when the drug is cationic at pH 6–7, and test release of drug and polymer at pH 6.8 and 7.5: a large gap between grades at pH 6.8 that closes at 7.5 marks complexation bapat2025a R2, C24. Where a more acetylated grade is wanted for crystallization inhibition, check that its release penalty with the cationic drug is acceptable bapat2025a C23.

History

Grade comparisons in the library had concerned crystallization inhibition and nanodroplets (cited), and the 2024 study had shown complexation with HPMCAS-MF only (F32) bapat2025a C4, C5. Bapat and Taylor (2025) were the first in the library to compare HPMCAS grades for release of weak bases and to titrate their acid content bapat2025a C24, R8. Kaur and co-workers (2025) used LF and MF with bedaquiline and found them alike in release kaur2025 R13, R15.

F34

Topic 4Weakly basic drugs in HPMCAS3 of 3

Intestinal-fluid micelles raised release from HPMCAS several-fold only where the drug complexed the polymer.

In pH 6.5 buffer 10% bedaquiline dispersions in HPMCAS LF or MF released about 17–19.5% in 120 min; in FaSSIF-V1, at the same pH, they released about 87.5–97% kaur2025 R13, R15. In the fluids the complexation of HPMCAS by bedaquiline fell, for LF from about 58.5 to 25% (FaSSIF-V1) and from about 90 to 17% (FeSSIF-V2) kaur2025 R5, R6. FaSSIF had left neat HPMCAS-MF and a 10% indomethacin dispersion at their blank-buffer rates bapat2023 R5, R7, R9.

strongStrong for the suppression of complexation in the fluids; weak to moderate for micelles raising release by disrupting the complex, since micellar solubilization was not separated and buffer and fluid share only the 10% loading kaur2025 K3, K5, X15, X13.

pH 6.5 bufferFaSSIF-V1, pH 6.5FeSSIF-V1, pH 5.010% in HPMCAS-LF≈17≈9710% in HPMCAS-MF≈19.5≈87.520% in LF and MFpolymer hardly dissolves at pH 5.0≈22.5–250102030405060708090100bedaquiline released in 120 min, %

Same pH, with and without bile salt–lecithin micelles; at pH 5.0 a high drug solubility did not help. kaur2025 R13, R15, R16

blank bufferbiorelevant fluidLF · FaSSIF-V1≈25≈58.5LF · FeSSIF-V2≈17≈90MF · FaSSIF-V1≈26.5≈65.5MF · FeSSIF-V2≈29≈84.50102030405060708090100HPMCAS complexed by bedaquiline at the highest ratio, %

The micelles cut complexation to at most about 29% in both fluids. kaur2025 R5, R6, R7, R8

For your drug

  1. For an HPMCAS dispersion of a lipophilic base with pKa well above that of HPMCAS (about 5), run release at the same loading in the blank buffer and in FaSSIF-V1 (and FeSSIF-V2), with the spike complexation test in both.
  2. Read a several-fold gain in the fluid with a large drop in complexation as a complexation-limited dispersion whose poor release in plain buffer may not reflect its behaviour with intestinal micelles, and keep FeSSIF-V1 (pH 5.0) as a check on polymer solubility.

kaur2025 R13, R15, R5, R6, C54, R16, C51

How it works and key numbers
  1. Release from HPMCAS is polymer-controlled: low at acidic pH even where bedaquiline is far more soluble, and rising only when HPMCAS ionizes kaur2025 C40.
  2. In plain buffer bedaquiline cations pair with HPMCAS carboxylates as an insoluble complex (F32) kaur2025 C42, C56.
  3. In the fluids the cations "clearly" interact with the bile salt–lecithin mixed micelles, as the rise of crystalline solubility from undetected at pH 6.5 to 7.8 µg/mL in FaSSIF-V1 shows; this lowers complexation, so more polymer dissolves, "likely the predominant mechanism" in FaSSIF-V1 kaur2025 R2, C38, C36, C39, C49.
  4. In FeSSIF-V2 the crystalline solubility (258.8 µg/mL) exceeds the 100 µg/mL maximum, so release no longer runs under non-sink conditions kaur2025 C50.
  5. In FeSSIF-V1 (pH 5.0) HPMCAS hardly dissolves, so release stayed low despite a crystalline solubility of 628 µg/mL, "in line with" polymer control kaur2025 R16, R2, C51.
≈17–19.5 → 87.5–97%10% bedaquiline released in pH 6.5 buffer and in FaSSIF-V1kaur2025 R13, R15
≈90 → 17%HPMCAS LF complexed in blank FeSSIF-V2 buffer and in FeSSIF-V2kaur2025 R5, R6
0.56 against 0.57 mg/min/cm²neat HPMCAS-MF in FaSSIF and in its blank bufferbapat2023 R5, R7
Evidence: data, conditions and papers

Finding F34. Bile salt–lecithin micelles changed release from HPMCAS only where the drug complexed the polymer: bedaquiline dispersions released about 17–30% in pH 6.5 buffer but about 80–97% in FaSSIF-V1 and FeSSIF-V2, where complexation fell from up to 90% to at most about 29%, whereas FaSSIF left neat HPMCAS and an indomethacin dispersion at their blank-buffer rates

In short. In pH 6.5 buffer 5 and 10% bedaquiline (BDQ) dispersions in HPMCAS LF or MF released about 17–30% in 120 min; in FaSSIF-V1 (pH 6.5) the 10% dispersions released about 87.5–97% and the 20% about 80%, and in FeSSIF-V2 (pH 5.8) 20 and 30% dispersions about 87.5–95% kaur2025 R13, R15, R17. At the highest drug:COOH ratio HPMCAS LF complexed about 58.5% in blank FaSSIF-V1 buffer and 25% in FaSSIF-V1, and about 90% in blank FeSSIF-V2 buffer and 17% in FeSSIF-V2; MF stayed at or below about 29% in both fluids kaur2025 R5, R6, R8. In FeSSIF-V1 (pH 5.0), where HPMCAS hardly dissolves, 20% dispersions released only about 22.5–25% although the crystalline solubility of BDQ there was 628 µg/mL kaur2025 R16, R2. In the 2023 media study FaSSIF had matched its blank buffer for neat HPMCAS-MF (about 0.56 against 0.57 mg/min/cm²) and for a 10% indomethacin dispersion (F23) bapat2023 R5, R7, R9. The authors explain the gain by BDQ binding to the micelles, "likely the predominant mechanism" in FaSSIF-V1, while FeSSIF-V2 dissolves so much BDQ that release is no longer under non-sink conditions; micellar solubilization and complex disruption were not separated kaur2025 C39, C49, C50, X13.

Type. single-system observation (bedaquiline with HPMCAS LF and MF in four media), against a non-complexing drug in the 2023 study Strength. for the suppression of complexation in the fluids kaur2025 K3: strong; weak to moderate for micelles raising release by disrupting the complex, since solubilization was not separated and buffer and fluid share only the 10% loading kaur2025 K5: weak to moderate, X15.

How it was shown

Kaur and co-workers (2025) spiked bedaquiline (BDQ) and HPMCAS LF or MF from THF into blank FaSSIF-V1, FaSSIF-V1, blank FeSSIF-V2 and FeSSIF-V2 at six drug:COOH ratios, and released dispersion powders in buffer and in three fluids kaur2025 P7, P8, P9, P11, P12. Bapat and co-workers (2023) had compared FaSSIF with its blank buffer for neat HPMCAS-MF and 10% indomethacin (IND) dispersions bapat2023 P14, R7.

What the data show

The crystalline solubility of BDQ rose from undetected at pH 6.5 to 7.8 µg/mL in FaSSIF-V1, 258.8 in FeSSIF-V2 and 628 µg/mL in FeSSIF-V1 kaur2025 R2.

systemmethod and conditionsresultids
BDQ + HPMCAS LF, highest ratiospike test in blank buffers and fluids≈58.5 → 25% (pH 6.5 → FaSSIF-V1); ≈90 → 17% (pH 5.8 → FeSSIF-V2)kaur2025 R5, R6
BDQ + HPMCAS MFsamefluids ≤ ≈29% against ≈65.5 and 84.5% in blank bufferskaur2025 R7, R8
BDQ 10% in LF, MFpowder, 120 min, pH 6.5 buffer against FaSSIF-V1≈17 / 19.5% against ≈97 / 87.5%kaur2025 R13, R15
BDQ 20, 30% in LF, MFFeSSIF-V2 (pH 5.8)≈87.5–95%kaur2025 R17
BDQ 20% in LF, MFFeSSIF-V1 (pH 5.0)≈25 / 22.5%kaur2025 R16
neat HPMCAS-MF; IND 10%compacts, FaSSIF against blank buffer≈0.56 against 0.57; IND ≈0.51 in FaSSIFbapat2023 R5, R7, R9
Fig. 6 of kaur2025: release of 10 and 20% bedaquiline dispersions in FaSSIF-V1
Fig. 6 · kaur2025release of 10 and 20% bedaquiline dispersions in FaSSIF-V1

The 10% curves reach about 97 (LF) and 87.5% (MF) and the 20% curves about 80% at 120 min, against about 17–19.5% for the same 10% dispersions in pH 6.5 buffer (Fig. 4 of the paper) kaur2025 R15, R13.

Why

Release is polymer-controlled, and in plain buffer BDQ cations pair with the HPMCAS carboxylates as an insoluble complex kaur2025 C40, C42, C56. In the fluids BDQ cations "clearly" interact with the mixed micelles, and this affinity "explains" the lower complexation, so more polymer dissolves and release rises, "likely the predominant mechanism" in FaSSIF-V1 kaur2025 C38, C36, C39, C49. In FeSSIF-V2 the crystalline solubility exceeds the 100 µg/mL maximum, so release is no longer under non-sink conditions, while in FeSSIF-V1 the polymer is poorly soluble at pH 5.0 and release stays low, "in line with" polymer control kaur2025 C50, C51.

Limits and transfer

Polymer release was not measured, buffer and fluid were compared at the same loading only at 10%, and micellar solubilization was not separated from complex disruption kaur2025 X14, X15, X13. For an HPMCAS dispersion of a lipophilic base, run release and the spike test at the same loading in the blank buffer and in FaSSIF-V1: a several-fold gain in the fluid with a large drop in complexation marks a complexation-limited dispersion kaur2025 R13, R15, R5, R6, C54.

How it was shown

Kaur and co-workers (2025) tested the hypotheses that BDQ–HPMCAS complexation falls with the solubilizing components of simulated intestinal fluids, and that release is low where much complex forms and high where little forms kaur2025 C5. They measured complexation by spiking BDQ and HPMCAS LF or MF from THF into blank FaSSIF-V1 (pH 6.5), FaSSIF-V1, blank FeSSIF-V2 (pH 5.8) and FeSSIF-V2 at six drug:COOH ratios equal to 5–50% dispersions, polymer in the fluids measured by HPLC with light-scattering detection; FeSSIF-V1 (pH 5.0) was left out because HPMCAS alone does not dissolve there kaur2025 P7, P8, P9, C11. They released powders equal to 5 mg drug in 50 mL at 37 °C and 150 rpm for 120 min with in situ UV: 5 and 10% dispersions in pH 6.5 buffer, 10 and 20% in FaSSIF-V1, 20% in FeSSIF-V1 and 20 and 30% in FeSSIF-V2 kaur2025 P11, P12, A5. They measured crystalline BDQ solubility in all media, and induction times and particle sizes at 100 µg/mL with and without 400 µg/mL polymer in buffers and fluids kaur2025 P4, P13. Bapat and co-workers (2023) had compared FaSSIF (pH 6.5, 12 mM/ΔpH) with its blank buffer for neat HPMCAS-MF and for 10% dispersions of indomethacin (IND) and its methyl ester in rotating compacts (F23) bapat2023 P14, R7.

What the data show

HPMCAS LF complexation rose with ratio from about 9 to 25% in FaSSIF-V1 against 5 to 58.5% in its blank buffer, and from about 2.5 to 17% in FeSSIF-V2 against 29.5 to 90% in its blank buffer; for MF from about 15.5 to 26.5% and 3 to 29% against 6 to 65.5% and 45.5 to 84.5% kaur2025 R6, R5, R8, R7. Crystalline BDQ solubility rose from undetected at pH 6.5 to 7.8 µg/mL in FaSSIF-V1, from below 0.1 µg/mL at pH 5.8 to 258.8 µg/mL in FeSSIF-V2, and to 628 µg/mL in FeSSIF-V1 kaur2025 R2. The 10% dispersions released about 17 (LF) and 19.5% (MF) in pH 6.5 buffer and about 97 and 87.5% in FaSSIF-V1; the 20% dispersions about 80 and 80.5% in FaSSIF-V1 kaur2025 R13, R15. In FeSSIF-V2 all four dispersions passed about 66% by 20 min and ended at about 95 and 94% (LF 20 and 30%) and 92.5 and 87.5% (MF) kaur2025 R17. In FeSSIF-V1 the 20% dispersions rose slowly to about 25 (LF) and 22.5% (MF), with HPMCAS solubility at pH 5.0 cited as about 250 and 110 µg/mL kaur2025 R16, R4. With polymer, precipitated BDQ stayed uncrystallized for 12–24 h in both fluids, at about 98–107 nm in FeSSIF-V2 and 241–1002 nm in FaSSIF-V1 kaur2025 R18. In the 2023 study neat HPMCAS-MF dissolved at about 0.56 mg/min/cm² in FaSSIF and 0.57 in its blank buffer, and the 10% IND dispersion released drug and polymer at about 0.51 and 0.49 in FaSSIF bapat2023 R5, R7, R9. (synthesis: for 10% BDQ the fluid raised release about fivefold, 97/17 ≈ 5.7 for LF and 87.5/19.5 ≈ 4.5 for MF, while for neat HPMCAS FaSSIF changed the rate by 0.56/0.57 ≈ 0.98.)

papersystemmethod and conditionsresultids
kaur2025BDQ + HPMCAS LF, highest ratiospike test in blank buffers and fluids≈58.5 → 25% (pH 6.5 → FaSSIF-V1); ≈90 → 17% (pH 5.8 → FeSSIF-V2)kaur2025 R5, R6
kaur2025BDQ + HPMCAS MFsamefluids ≤ ≈29% against ≈65.5 and 84.5% in blank bufferskaur2025 R7, R8
kaur2025BDQ 10% in LF, MFpowder, 120 min, pH 6.5 buffer against FaSSIF-V1≈17 / 19.5% against ≈97 / 87.5%kaur2025 R13, R15
kaur2025BDQ 20, 30% in LF, MFFeSSIF-V2 (pH 5.8)≈87.5–95%kaur2025 R17
kaur2025BDQ 20% in LF, MFFeSSIF-V1 (pH 5.0)≈25 / 22.5%kaur2025 R16
kaur2025crystalline BDQeight media, 37 °Cundetected (pH 6.5); 7.8 (FaSSIF-V1); 258.8 (FeSSIF-V2); 628 µg/mL (FeSSIF-V1)kaur2025 R2
bapat2023neat HPMCAS-MF; IND 10%compacts, FaSSIF against blank buffer≈0.56 against 0.57; IND ≈0.51 in FaSSIFbapat2023 R5, R7, R9
duong2022a (Supersaturation from ASD dissolution)delamanid dispersionsrelease in FaSSIF and buffersame release although the amorphous solubility was ten times higher in FaSSIFduong2022a R13, R1

Figure

Fig. 6 of kaur2025: release of 10 and 20% bedaquiline dispersions in FaSSIF-V1
Fig. 6 · kaur2025release of 10 and 20% bedaquiline dispersions in FaSSIF-V1

The 10% curves reach about 97 (LF) and 87.5% (MF) and the 20% curves about 80% at 120 min, against about 17–19.5% for the same 10% dispersions in pH 6.5 buffer (Fig. 4 of the paper) kaur2025 R15, R13.

Fig. 4 of kaur2025: release in plain buffer, after a pH shift and at pH 6.5
Fig. 4 · kaur2025release in plain buffer, after a pH shift and at pH 6.5

Under 10% in the acid stage, about 20–25% after the switch to pH 6.5 (5% dispersions), about 28–30% (5%) and 17–20% (10%) in pH 6.5 buffer alone kaur2025 R12, R13.

Why

The authors start from polymer-controlled release: release stays low at acidic pH, where BDQ is far more soluble, and rises only when HPMCAS ionizes kaur2025 C40. In plain buffer BDQ cations pair with HPMCAS carboxylates as an insoluble complex (F32) kaur2025 C42, C56. In the fluids, BDQ cations, though still ionized, "clearly" interact with the mixed micelles, as the large rise in crystalline solubility shows; this affinity "explains" the lower complexation, so more polymer dissolves and release rises, "likely the predominant mechanism" in FaSSIF-V1 kaur2025 C38, C36, C39, C49. In FeSSIF-V2 the crystalline solubility (258.8 µg/mL) exceeds the 100 µg/mL maximum, so release is no longer under non-sink conditions and the driving force is very high kaur2025 C50. In FeSSIF-V1 the polymer is poorly soluble at pH 5.0, so release stays low despite the highest drug solubility, "in line with" polymer control kaur2025 C51. The authors expect media effects to vary "from drug to drug" with the drug's tendency to interact with the polymer and to be solubilized, citing delamanid, a weak base of low pKa barely ionized where HPMCAS is anionic, whose release did not change in biorelevant media kaur2025 C53, C52. (synthesis: the 2023 conclusion that FaSSIF micelles change nothing (F23) holds for the polymer and for a drug that does not bind it; for a lipophilic cation that binds HPMCAS the micelles compete for the drug and lift release several-fold, so the blank buffer and its fluid can rank the same dispersion very differently. In the ASD dissolution chapter biorelevant media also changed release in both directions, through crystallization (praziquantel) and solubility (delamanid) (Supersaturation from ASD dissolution F28), and in the LLPS chapter micelles raised crystalline and amorphous solubility together (Amorphous solubility and LLPS F12); here the micelles act on a drug–polymer complex as well.)

Conditions and limits

One drug, two HPMCAS grades, powder dissolution at 150 rpm with drug assayed only; polymer release was not measured, and the complex was measured in a solution test, not in a dissolving gel kaur2025 P11, X14. Buffer and fluid were compared at the same loading only at 10%, FeSSIF-V2 has no blank-buffer release run, and the fluids were tested at higher loadings (20–30%) than the buffer (5–10%) kaur2025 X15. Micellar solubilization of BDQ was not separated from complex disruption, and the amorphous solubility in the fluids was not measured kaur2025 X13, X12. Several solubility values lie below the stated HPLC quantification limit kaur2025 X11. The 2023 FaSSIF comparison concerned neat HPMCAS-MF and a weak acid and its ester, not a cationic drug bapat2023 R7, R9.

Counterexamples and conflicts

The text gives "~20% or less" complexation for LF in the fluids, while LF in FaSSIF-V1 reached about 24–25% at the two highest ratios kaur2025 X5. FaSSIF-V1 10% LF reached about 97% where the text says 80–90% kaur2025 X4. A high drug solubility alone did not give release: FeSSIF-V1, with the highest crystalline solubility, gave the lowest release of the fluids because the polymer did not dissolve kaur2025 R16, R2. Delamanid dispersions released alike in FaSSIF and buffer, and fed fluid lowered praziquantel release through crystallization (ASD dissolution chapter) duong2022a R13; kaur2025 C52.

Transfer check

For an HPMCAS dispersion of a lipophilic base with pKa well above that of HPMCAS (about 5), run release at the same loading in the blank buffer and in FaSSIF-V1 (and FeSSIF-V2), and the spike complexation test in both; a several-fold gain in the fluid with a large drop in complexation marks a complexation-limited dispersion whose poor release in plain buffer may not reflect its behaviour with intestinal micelles kaur2025 R13, R15, R5, R6, C54. Keep FeSSIF-V1 (pH 5.0) as a check on polymer solubility, since below about pH 5.5 HPMCAS does not release the drug whatever its solubility kaur2025 R16, C51.

History

Bapat and co-workers (2023) found FaSSIF micelles without effect on neat HPMCAS and on non-complexing dispersions (F23) bapat2023 R7, C20. Bapat and co-workers (2024) and Bapat and Taylor (2025) established complexation of HPMCAS by cationic drugs in buffer and named biorelevant fluids as the next test (F32, F33) bapat2025a C36. Kaur and co-workers (2025) were the first in the library to measure drug–polymer complexation in simulated intestinal fluids and to show its suppression there, and urge caution in screening such dispersions in simple buffers kaur2025 C57, C54.

Topic 5 of 5 · 11 findings · F11–F14, F21–F22, F24, F26, F28, F31, F35

Formulation levers near the limit

F11

Topic 5Formulation levers near the limit1 of 11

Hydrophilic polymers release fastest at low loading but fall off a cliff; HPMCAS and EUDS release more slowly but stay congruent to 50%.

Felodipine dispersions with PVP, PVPVA and HPMC lost congruent release above 10, 15 and 10%, while HPMCAS and EUDS stayed congruent to 50% saboo2020a R15. At 10% PVP and PVPVA released felodipine at ≈3.8 and ≈2.4 mg/min/cm² against ≈0.82 for HPMCAS, but at 20 and 30% HPMCAS released about 100–225 times faster than PVPVA saboo2020a R14. The authors call the polymer choice a "trade-off" between fast release at low loading and workable release at higher loading saboo2020a C55.

strongStrong for the two patterns, measured with both components; moderate to strong for the trade-off; weak to moderate for water uptake as the cause, since HPMC takes up less water than PVPVA yet has the lower limit saboo2020a K1, K2, K5, X7; purohit2017b K3.

PVPVAHPMCAS10% loading≈0.82≈2.420%≈0.009≈0.9330%≈0.004≈0.9040%≈0.3450%≈0.13, after a lag0.0010.010.1110felodipine release rate, mg/min/cm² (log scale)

PVPVA is faster at 10% and falls off a cliff above 15%; HPMCAS stays congruent and declines only above 30%. saboo2020a R14, R15

Water uptake of the neat polymers at 95% RH, wt%PVPlimit 10%≈71PVPVAlimit 15%≈47HPMClimit 10%≈28EUDSnone to 50%≈13HPMCASnone to 50%≈10

Water uptake separates the two groups but does not rank the limits within the hydrophilic one. saboo2020a R3, R15, X7

For your drug

  1. Measure the neat polymer dissolution rates in the intended medium and the water uptake of the dispersions at 95% RH.
  2. If the dose allows a loading below the limit with PVP or PVPVA, use them for the fastest release; if the loading must exceed it, test HPMCAS in a medium above its dissolution pH, whose release may stay congruent to 30–50%.
  3. Check high-loading HPMCAS compacts for a lag before reading their rates.

saboo2020a R13, R3, C55, R14, X9

How it works and key numbers
  1. At low loading the polymer sets the pace, so the fastest-dissolving polymers give the fastest drug release (F2) saboo2020a C54.
  2. Water-induced amorphous–amorphous phase separation "is likely the cause" of the limit with the three hydrophilic polymers; the lower water uptake of HPMCAS and EUDS "conceivably" stays below what is needed, supported by uniform humidified films saboo2020a C43, C44, R23.
  3. HPMCAS and EUDS must ionize to dissolve, so their interactions with water and drug differ between the dry and the hydrated state saboo2020a C30.
  4. For ritonavir, HPMCAS can hydrogen-bond through donors and acceptors, and because its dispersions resist phase separation the drug "can enter the solution together with the polymer" purohit2017b C46, C55.
  5. From 2024 the gradual decline in HPMCAS held for indomethacin and its ester to 60% but not for lipophilic weak bases that complex the polymer, whose release fell to about zero by 25–30% (F32, F33) bapat2024 R2; bapat2025a R2, R3.
≈100–225×HPMCAS over PVPVA felodipine release at 20 and 30% loadingsaboo2020a R14
≈71 against ≈10 wt%water uptake at 95% RH of neat PVP and neat HPMCASsaboo2020a R3
86 against 4 µg/mLloratadine released from HPMCAS and PVPVA powders at 40%yang2021 R7
Evidence: data, conditions and papers

Finding F11. Polymer hydrophobicity separated two release patterns: hydrophilic, neutral PVP, PVPVA and HPMC gave the fastest release at low loading and a cliff at 10–15% felodipine, while hydrophobic, ionizing HPMCAS and EUDS released felodipine congruently up to 50% but more slowly, and HPMCAS dispersions of three more drugs declined gradually instead of falling off a cliff; water uptake separated the two groups but did not rank the limits within the first

In short. Neat PVP took up ≈71 wt% water at 95% RH, PVPVA ≈47, HPMC ≈28, EUDS ≈13 and HPMCAS ≈10, and buffer contact angles ran from 11.9° (PVP) to 46.8° (HPMCAS) in the same order saboo2020a R3, R4. Felodipine dispersions with PVP, PVPVA and HPMC lost congruent release above 10, 15 and 10%, while HPMCAS and EUDS stayed congruent to 50% saboo2020a R15. At 10% PVP and PVPVA released felodipine at ≈3.8 and ≈2.4 mg/min/cm² against ≈0.82 for HPMCAS and ≈0.16 for EUDS, but at 20 and 30% HPMCAS (≈0.93 and ≈0.90) released about 100–225 times faster than PVPVA (≈0.009 and ≈0.004) saboo2020a R14. Ritonavir films showed the same split: HPMCAS films formed nanodroplets at every loading to 50% where PVP stopped at 20% and PVPVA at 10%, and the authors call the polymer choice a "trade-off" between fast release at low loading and workable release at higher loading purohit2017b R11, R10; saboo2020a C55. For loratadine, miconazole and danazol, HPMCAS powders declined over a wide loading range where PVPVA fell off a cliff within about 10%, and released more at high loading (loratadine about 86 against 4 µg/mL at 40%), but elbasvir behaved alike with both polymers and loratadine compacts had a lower limit with HPMCAS (20%) than with PVPVA (30%) yang2021 R7, R8, R9, R10, C2, R22. From 2024 the gradual decline in HPMCAS held for indomethacin and its ester to 60% but not for lipophilic weak bases that complex the polymer, whose release fell to about zero by 25–30%, and the grade with the most acid groups (LF) released them best (F32, F33) bapat2024 R2; bapat2025a R2, R3.

Type. observation in 2 drugs (felodipine with five polymers; ritonavir with three), and six drugs with PVPVA and HPMCAS in 2021, and grazoprevir with HPMCAS-LF in 2023 Strength. for the two patterns, measured with both components for felodipine and with three read-outs for ritonavir saboo2020a K1: strong; purohit2017b K3: moderate to strong; moderate to strong for the trade-off saboo2020a K2: moderate to strong; weak to moderate for water uptake as the cause saboo2020a K5: weak to moderate, X7.

How it was shown

Saboo and co-workers (2020) ranked the neat polymers by water sorption at 37 °C up to 95% RH and by buffer contact angles, then dissolved felodipine dispersions with PVP, PVPVA and HPMC at 5–30% and with HPMCAS-MF and EUDS at 10–50%, EUDS at pH 7.4 saboo2020a P3, P4, A2, M6.

What the data show

Felodipine–HPMCAS released congruently at ≈0.82, ≈0.93, ≈0.90, ≈0.34 and ≈0.13 mg/min/cm² at 10–50%, which the authors call a "penalty" of high loading, a negative "slope" rather than a "cliff" saboo2020a R14, C29, X4.

systemmethodresultids
neat PVP, PVPVA, HPMC, EUDS, HPMCASsorption at 95% RH; contact angle≈71 / 47 / 28 / 13 / 10 wt%; 11.9° to 46.8°saboo2020a R3, R4
felodipine in five polymerscompacts, pH 6.8 (EUDS 7.4)LoC 10 / 15 / 10% (PVP / PVPVA / HPMC); none to 50% (HPMCAS, EUDS)saboo2020a R15
felodipine 10% and 20–30%normalized drug ratesPVP ≈3.8, PVPVA ≈2.4, HPMCAS ≈0.82 at 10%; HPMCAS ≈0.90–0.93 against PVPVA ≈0.004–0.009 at 20–30%saboo2020a R14
loratadine, miconazole, danazol, elbasvir with PVPVA and HPMCASpowders, 37 °CPVPVA cliff within ≈10%; HPMCAS gradual (elbasvir alike)yang2021 R7, R8, R9, R10, C2
indomethacin, cinnarizine, loratadine in HPMCAS-MFcompacts, pH 6.8≈0.85 → 0.50 (5–60%); ≈0.6 → 0.01 (5–25%); ≈0.49 → 0.1 (10–30%)bapat2024 R2
Fig. 14 of saboo2020a: normalized felodipine release rate against loading for PVPVA, HPMCAS and EUDS
Fig. 14 · saboo2020anormalized felodipine release rate against loading for PVPVA, HPMCAS and EUDS

PVPVA is highest to 15% and near zero from 20%; HPMCAS is flat to 30% and then falls; EUDS is low and flat; the PVPVA and HPMCAS curves cross between 15 and 20% saboo2020a R14.

Why

The authors conclude that the patterns "appear to depend" on polymer hydrophobicity: water-induced AAPS "is likely the cause" of the limit with the three hydrophilic polymers, and the lower water uptake of HPMCAS and EUDS "conceivably" stays below what is needed to induce it saboo2020a C49, C43, C44. The polymers with a distinct limit are neutral, whereas HPMCAS and EUDS must ionize to dissolve saboo2020a C30. At low loading the polymer sets the pace, so the fastest-dissolving polymers give the fastest drug release, while HPMCAS and EUDS release relatively better above 15% saboo2020a C54, C55.

Limits and transfer

Water uptake was measured on the neat polymers only, and HPMC, less hygroscopic than PVPVA, had the lower limit saboo2020a X7, R14. For loratadine compacts the HPMCAS limit (20%) lay below the PVPVA limit (30%), and weak bases that complex HPMCAS lost release steeply in it yang2021 R22; bapat2024 R2, R12. If the dose allows a loading below the limit with PVP or PVPVA, these give the fastest release; if the loading must exceed it, test HPMCAS in a medium above its dissolution pH saboo2020a C55, R14.

How it was shown

Saboo and co-workers (2020) ranked the neat polymers by gravimetric water sorption at 37 °C from 5 to 95% RH (single runs) and by static contact angles of dissolution buffer on spin-coated films (triplicate), then dissolved felodipine dispersions as in F1: PVP, PVPVA and HPMC at 5–30%, HPMCAS-MF and EUDS at 10–50%, EUDS at pH 7.4 because it dissolves only above pH 7 saboo2020a P3, P4, A2, M6. Purohit and Taylor (2017) dissolved fresh and humidity-exposed ritonavir films with PVP K-90, PVPVA and HPMCAS-MF at 10–50% and followed LLPS by free drug, pyrene and NTA purohit2017b A1, A2, P14.

What the data show

Neat polymer rates were ≈3.6 (PVP), ≈3.4 (PVPVA), ≈0.37 (HPMC), ≈0.77 (HPMCAS) and ≈0.23 mg/min/cm² (EUDS), 290–4600 times the ≈0.0008 of amorphous felodipine, and did not follow the hydrophobicity ranking (HPMCAS dissolved faster than HPMC) saboo2020a R13, C15. Felodipine–HPMCAS released congruently at ≈0.82 (10%), ≈0.93 (20%), ≈0.90 (30%), ≈0.34 (40%) and ≈0.13 mg/min/cm² (50%), up to 30% at about the rate of neat HPMCAS, and every loading passed the amorphous solubility of 8 µg/mL (≈21–76 µg/mL at 60 min, ≈10 µg/mL at 50%); release from 50% began only after a lag saboo2020a R14, R8, R7, C13. EUDS stayed congruent at ≈0.16 to ≈0.07 mg/min/cm², with lags of 25–120 min at 30–50% that the text does not mention saboo2020a R14, R11, X9. The decline of HPMCAS between 30 and 40% the authors call a "penalty" of high loading that keeps congruency, a negative "slope" rather than a "cliff" saboo2020a C29, X4. Ritonavir: fresh HPMCAS films gave free drug of 27–30 µg/mL and pyrene ratios of 1.50–1.61 at every loading, and the 50:50 HPMCAS film released ritonavir with its polymer (≈32–34 µg/mL within 5 min, HPMCAS ≈53 of 60 µg/mL by 20 min) purohit2017b R10, R11, R17; HPMCAS films did not phase separate at 97% RH or after 10 s in buffer, unlike PVP and PVPVA (F8) purohit2017b R2, R4, C55. (synthesis: the crossover of Fig. 14 is 0.93/0.009 = 103-fold at 20% and 0.90/0.004 = 225-fold at 30% in favour of HPMCAS, against 3.8/0.82 = 4.6-fold (PVP) and 2.4/0.82 = 2.9-fold (PVPVA) in favour of the hydrophilic polymers at 10%.) Yang and co-workers (2021): with PVPVA, loratadine released about 85, 41 and 8 µg/mL (of 100) at 20, 25 and 30%, with HPMCAS about 86, 46 and 12 at 40, 50 and 70%; miconazole fell from about 93 to 3 between 40 and 50% with PVPVA and from about 83 to 4 between 40 and 70% with HPMCAS; danazol (at 15 min) fell from about 78 to 9.5 between 5 and 10% with PVPVA and from about 98 to 8 between 5 and 70% with HPMCAS; elbasvir gave similar curves with both yang2021 R7, R8, R9, R10. HPMCAS was not ahead at every loading: miconazole released about 93–103 from PVPVA against 83–97 from HPMCAS at 10–40% yang2021 X15. Loratadine–HPMCAS compacts released slowly (about 23% by 90 min at 10%), and their limit was 20% against 30% for PVPVA at 37 °C yang2021 R16, R22. HPMCAS also kept released droplets smaller (F16) yang2021 C4. Grazoprevir–HPMCAS-LF dispersions of 2023 declined gradually in a two-stage test, from about 102% released at 5% through 63% at 20% and 43% at 30% to 27–30% at 50–75%, which the authors call a sloped profile as expected for an enteric polymer hiew2023 R8, C18, C36. In HPMCAS-MF indomethacin fell only from about 0.85 to 0.50 mg/min/cm² between 5 and 60%, whereas cinnarizine fell from 0.6 at 5% to 0.01 at 25% and loratadine from 0.49 at 10% to 0.1 at 30% bapat2024 R2. At 25% loratadine released at about 0.25, 0.10 and 0.01 mg/min/cm² from HPMCAS LF, MF and HF bapat2025a R2. Grazoprevir–HPMCAS dispersions released about 63, 43 and 30% at 90 min of a two-stage test at 20, 30 and 75% hiew2025 R10.

papersystemmethod and conditionsresultids
purohit2017britonavir films, PVP K-90, PVPVA, HPMCAS-MF25 °C, pH 6.8LLPS to 20%, 10% and ≥50%purohit2017b R10, R11
saboo2020aneat polymerssorption at 95% RH; contact angle≈71 / 47 / 28 / 13 / 10 wt%; 11.9° to 46.8°saboo2020a R3, R4
saboo2020afelodipine in five polymerscompacts, pH 6.8 (EUDS 7.4)LoC 10 / 15 / 10% (PVP / PVPVA / HPMC); none to 50% (HPMCAS, EUDS)saboo2020a R15
saboo2020afelodipine 10% and 20–30%normalized drug ratesPVP ≈3.8, PVPVA ≈2.4, HPMCAS ≈0.82 at 10%; HPMCAS ≈0.90–0.93 against PVPVA ≈0.004–0.009 at 20–30%saboo2020a R14
hiew2023grazoprevir–HPMCAS-LF 5–75%two-stage SGF → FaSSIF, 90 min≈102 → 63 → 43 → 27–30%, no cliffhiew2023 R8
xie2016b (Physical stability)neat polymerssorption, 25 °CPVP > PVP/VA > HPMC > HPMCASxie2016b C23
hiew2022a (Miscibility)lumefantrine 5% in PVPVA and HPMCPcompactsrelease ≈5 times higher from PVPVA, matching neat polymer rateshiew2022a C44
saboo2020a (cited)grazoprevir–PVPVA tablets, humans30% against 40% loading intermediatebioavailability halvedsaboo2020a R30
yang2021loratadine, miconazole, danazol, elbasvir with PVPVA and HPMCASpowders, 37 °CPVPVA cliff within ≈10%; HPMCAS gradual (elbasvir alike)yang2021 R7, R8, R9, R10, C2
yang2021loratadine compactsrates, t-testlimit 30% (PVPVA) against 20% (HPMCAS)yang2021 R22
bapat2024indomethacin, cinnarizine, loratadine in HPMCAS-MFcompacts, pH 6.8≈0.85 → 0.50 (5–60%); ≈0.6 → 0.01 (5–25%); ≈0.49 → 0.1 (10–30%)bapat2024 R2
bapat2025aloratadine 25% in HPMCAS LF, MF, HFsame≈0.25 / 0.10 / 0.01bapat2025a R2
hiew2025grazoprevir–HPMCAS-LG 20, 30, 75%two-stage SGF → FaSSIF, 90 min≈63 / 43 / 30%hiew2025 R10

Figure

Fig. 14 of saboo2020a: normalized felodipine release rate against loading for PVPVA, HPMCAS and EUDS
Fig. 14 · saboo2020anormalized felodipine release rate against loading for PVPVA, HPMCAS and EUDS

PVPVA is highest to 15% and near zero from 20%; HPMCAS is flat to 30% and then falls; EUDS is low and flat; the PVPVA and HPMCAS curves cross between 15 and 20% saboo2020a R14.

Fig. 15 of saboo2020a: neat-polymer dissolution rate and limit of congruency of each polymer
Fig. 15 · saboo2020aneat-polymer dissolution rate and limit of congruency of each polymer

The fastest-dissolving polymers (PVP, PVPVA) have the lowest limits; the 50% points for HPMCAS and EUDS mean "no limit up to the highest loading tested" saboo2020a R13, R15, X11.

Why

Saboo and co-workers (2020) conclude that the patterns "appear to depend" on polymer hydrophobicity saboo2020a C49. Their mechanism is the race of F8: water-induced AAPS "is likely the cause" of the limit with the three hydrophilic polymers, and the lower water uptake of HPMCAS and EUDS "conceivably" stays below what is needed to induce it, supported by the uniform humidified films saboo2020a C43, C44, R23. They note that the polymers with a distinct limit are neutral, whereas HPMCAS and EUDS must ionize to dissolve, so their interactions with water and drug differ between the dry and the hydrated state saboo2020a C30. Purohit and Taylor expect PVP and PVPVA, more hydrophilic and hygroscopic and with acceptors only, to be more prone to moisture-induced AAPS than HPMCAS, which can hydrogen-bond ritonavir through donors and acceptors ("can be expected"), and conclude that because HPMCAS dispersions resist AAPS the drug "can enter the solution together with the polymer" purohit2017b C45, C46, C55. In the low-loading regime the polymer sets the pace, so the fastest-dissolving polymers give the fastest drug release saboo2020a C54; HPMCAS and EUDS, dissolving more slowly, are at a release disadvantage there but release relatively better above 15% saboo2020a C54, C55. For congruent HPMCAS dispersions at high loading the drug slows the polymer, as earlier reported for HPMCAS (cited) saboo2020a C17, C31. (synthesis: in this polymer set a fast neat dissolution rate, which sets the ceiling of polymer-controlled release (F2), comes with high water uptake, which brings the limit down; HPMCAS combines a moderate neat rate (≈0.77 mg/min/cm²) with the lowest water uptake, which is why it releases best above the PVPVA limit.)

Conditions and limits

One drug for five polymers, at pH 6.8 (EUDS pH 7.4); ritonavir with three polymers in films at 25 °C saboo2020a X8; purohit2017b X18. Water uptake was measured once on neat polymers, not on the dispersions saboo2020a X7. High-loading HPMCAS and EUDS rates are slopes after a lag saboo2020a X9. The neat PVPVA rate is uncertain by about a factor of two saboo2020a X10. HPMCAS and EUDS must be in a medium where they ionize; the pH 6.8 and 7.4 media of the tests ensure this saboo2020a C30. HPMCAS rates depend strongly on the medium: neat HPMCAS-MF released about 0.16 and 1.01 mg/min/cm² in pH 6.8 phosphate of 3 and 51 mM/ΔpH buffer capacity, so HPMCAS rates of different papers compare only at the same buffer capacity (F23) bapat2023 R5.

Counterexamples and conflicts

HPMC, hydrophilic but less hygroscopic than PVPVA (≈28 against ≈47 wt%), had the lower limit (10 against 15%) and the slowest congruent release of the three neutral polymers (≈0.14 mg/min/cm² at 10%) saboo2020a X7, R14. HPMCAS release declined above 30% felodipine, and in the crystallization chapter the least succinoylated HPMCAS grades released posaconazole poorly at low pH (Crystallization from solution F44) saboo2020a C29; shah2025 C17. For loratadine compacts the HPMCAS limit (20%) lay below the PVPVA limit (30%), and elbasvir released alike from both polymers yang2021 R22, C2. The PVPVA powders of that comparison dissolved in medium containing 400 µg/mL HPMCAS, so the polymer comparison is not like for like yang2021 X18. Lipophilic weak bases that complex HPMCAS lost release steeply in it, cinnarizine about 60-fold between 5 and 25% (synthesis: 0.6/0.01 = 60) bapat2024 R2, R12.

Transfer check

For a new drug, measure the neat polymer dissolution rates in the intended medium and the water uptake of the dispersions at 95% RH saboo2020a R13, R3. If the dose allows a loading below the limit with PVP or PVPVA, these give the fastest release; if the loading must exceed it, test HPMCAS (in a medium above its dissolution pH), whose release may stay congruent to 30–50% saboo2020a C55, R14. Check the high-loading HPMCAS compacts for a lag before reading their rates saboo2020a X9.

History

In the ASD dissolution chapter the cellulosic polymers held felodipine and danazol supersaturation longer than PVP (Supersaturation from ASD dissolution F4), and in storage work PVP and PVPVA dispersions separated with moisture more than HPMCAS ones rumondor2010c C38. Purohit and Taylor (2017) first showed HPMCAS ritonavir films forming nanodroplets at every loading where PVP and PVPVA failed purohit2017b C4. Saboo and co-workers (2020) generalized the contrast to five polymers, measured their hydrophobicity and named the trade-off saboo2020a C49, C55, and linked the PVPVA pattern to the halved human bioavailability of a 40% against a 30% grazoprevir tablet intermediate ("may underlie") saboo2020a C52, R30. Yang and co-workers (2021) extended the PVPVA–HPMCAS contrast to six drugs and called the HPMCAS decline a negative "slope" yang2021 C2, C1; this adds the HPMCAS behaviour of further drugs to the title. Bapat and co-workers (2023) showed that the rate of HPMCAS and its dispersions follows the buffer capacity, species and pH of the medium (F23) bapat2023 C50. Hiew and co-workers (2023) found the same sloped decline for grazoprevir–HPMCAS hiew2023 C36. Bapat and co-workers (2024) and Bapat and Taylor (2025) found the gradual pattern limited to drugs that do not complex HPMCAS (F32, F33) bapat2024 C43; bapat2025a C24.

F12

Topic 5Formulation levers near the limit2 of 11

Humid storage before dissolution removed nanodroplets and congruent release from PVP and PVPVA dispersions, but not from HPMCAS films.

After storage at 97% RH the 10:90 ritonavir–PVP film no longer spiked (≈130 µg/mL apparent when fresh) but crept to ≈30 µg/mL at 240 min, and NTA found no nanodroplets from any exposed PVP or PVPVA film purohit2017b R12, R13, R7. A 10:90 nilvadipine–PVPVA compact held 12 h at 97% RH released ≈0.34% of its drug and ≈2.6% of its polymer in 15 min, against ≈15% of both for the control saboo2019 R9. Exposed ritonavir–HPMCAS films still spiked and formed nanodroplets, and no crystals formed in these tests purohit2017b R14, R7, R18; saboo2019 R3.

moderateModerate: three read-outs agree for the ritonavir films and the nilvadipine compact released incongruently in triplicate, but the storage time before dissolution is not stated for the films and the compact was followed for 15 min only purohit2017b K3, X7; saboo2019 K5, R9.

fresh film, spikeafter 97% RHPVPcreeps to ≈30 at 240 min≈130 spikePVPVA≈25–26≈116 spikeHPMCAS≈131, still spikes020406080100120140apparent ritonavir from 10:90 films, µg/mL

After humidity the PVP and PVPVA films no longer pass the amorphous solubility; the HPMCAS film does. purohit2017b R12, R13, R14

10:90 nilvadipine–PVPVA compact, % released in 15 mincontroldrug≈14.7controlPVPVA≈15.2after 12 h at 97% RHdrug≈0.34after 12 h at 97% RHPVPVA≈2.6

Humidity slowed both components and the drug much more: congruent release became incongruent. saboo2019 R9

For your drug

  1. For a PVP or PVPVA dispersion formulated at or below its limit, expose the powder or compact to 97% RH for 12 h to several days and repeat the release test with both components and a colloid read-out.
  2. Read loss of the spike, of nanodroplets or of congruency without crystals as water-induced separation; where humid storage cannot be excluded, compare with an HPMCAS dispersion.

purohit2017b R7, R12, R14; saboo2019 R9

How it works and key numbers
  1. At 97% RH water induces amorphous–amorphous phase separation; on the nilvadipine compact it was confined to the exposed surface, which looked wrinkled saboo2019 C24, R17.
  2. A matrix separated by humidity dissolves by drug control instead of polymer control ("can be readily explained"), so it dissolves more slowly and no longer reaches LLPS purohit2017b C53, C54.
  3. After the separated surface layer of the nilvadipine compact peeled off at 15–20 min, drug release was much faster, "presumably" from a fresh surface saboo2019 R9, C16.
  4. Above the limit a dispersion is drug-controlled whether or not it has separated, so humidity matters most at congruent loadings; the high-loading ritonavir profiles changed little purohit2017b R12, C33.
≈130 → ≈30 µg/mL10:90 ritonavir–PVP film, fresh spike against exposed film at 240 minpurohit2017b R12
≈0.34 against ≈14.7%drug released in 15 min by the exposed nilvadipine compact and its controlsaboo2019 R9
12 h at 97% RHstorage that turned the congruent nilvadipine compact incongruentsaboo2019 R9
Evidence: data, conditions and papers

Finding F12. Humid storage before dissolution removed nanodroplets and congruent release from PVP and PVPVA dispersions without crystallizing them, but not from HPMCAS films

In short. After 97% RH the 10:90 ritonavir–PVP film no longer spiked (≈130 µg/mL apparent when fresh) but crept to ≈25 µg/mL after ≈25 min and ≈30 µg/mL at 240 min, the 10:90 PVPVA film fell from a ≈116 µg/mL spike to ≈25–26 µg/mL, and NTA found no nanodroplets from any exposed PVP or PVPVA film purohit2017b R12, R13, R7. A 10:90 nilvadipine–PVPVA compact held 12 h at 97% RH released ≈0.34% of its drug and ≈2.6% of its polymer in 15 min, against ≈15% of both for the control, until its surface layer peeled off after 15–20 min saboo2019 R9, C16. Exposed ritonavir–HPMCAS films still spiked (≈131, ≈124 and ≈90 µg/mL at 10, 20 and 30%) and formed nanodroplets purohit2017b R14, R7. No crystals formed in these tests purohit2017b R18; saboo2019 R3.

Type. observation in 2 drugs (ritonavir, nilvadipine) Strength. : three read-outs agree for the ritonavir films and the nilvadipine compact released incongruently in triplicate purohit2017b K3: moderate to strong; saboo2019 K5: moderate, but the storage time before dissolution is not stated for the films and the compact was followed for 15 min only purohit2017b X7; saboo2019 R9.

How it was shown

Purohit and Taylor (2017) stored ritonavir films over saturated K2SO4 (97% RH) for 24 h to 4 days and dissolved them as fresh films were, measuring apparent and free drug, pyrene and NTA purohit2017b P7, P14, P12. Saboo and co-workers (2019) held a 10:90 nilvadipine–PVPVA compact in its die at 97% RH for 12 h and dissolved it for 15 min against an unexposed control saboo2019 P13, P15, P18.

What the data show

The control compact released ≈14.7% drug and ≈15.2% polymer in 15 min, the exposed one ≈0.34% and ≈2.6%, and the exposed film showed drug-rich circles and rings in a continuous polymer-rich phase saboo2019 R9, R19.

systemmethod and conditionsresultids
ritonavir 10:90 PVP film97% RH, then dissolution at 25 °Cspike ≈130 → creep to ≈25–30 µg/mL; no nanodropletspurohit2017b R12, R7
ritonavir 10:90 PVPVA filmsamespike ≈116 → ≈25–26 µg/mLpurohit2017b R13
ritonavir–HPMCAS films 10–30%samestill spiking ≈90–131 µg/mL; nanodropletspurohit2017b R14, R7
nilvadipine–PVPVA 10:90 compact12 h 97% RH, 15 min dissolution≈0.34% drug, ≈2.6% polymer against ≈15% of bothsaboo2019 R9
spray-dried ritonavir–PVPVA 25% (ASD process)water in the spray solventsurface-normalized rate ≈3.5 → ≈2.27 → ≈0.90li2020 R10
Fig. 9 of purohit2017b: dissolution of fresh and humidity-exposed ritonavir films with PVP, PVPVA and HPMCAS
Fig. 9 · purohit2017bdissolution of fresh and humidity-exposed ritonavir films with PVP, PVPVA and HPMCAS

Spikes above the dashed amorphous-solubility line for fresh low-loading PVP and PVPVA films (a, c) vanish after humidity (b, d), while the HPMCAS spikes remain (e, f) purohit2017b R12, R13, R14.

Why

Purohit and Taylor conclude "very clearly" that a matrix phase-separated by humidity dissolves more slowly and no longer reaches LLPS, a switch from polymer-controlled dissolution of the miscible matrix to drug-controlled dissolution of the separated one ("can be readily explained") purohit2017b C53, C54. Saboo and co-workers call the conversion of a congruent into an incongruent dispersion "further evidence" for the role of matrix phase separation saboo2019 C41. (synthesis: humidity matters most where release is congruent, because only there does a separated surface change the regime; above the limit the dispersion is drug-controlled whether or not it has separated purohit2017b C33.)

Limits and transfer

The storage time of the dissolution films is not stated, and the exposed compact was followed for 15 min only purohit2017b X7; saboo2019 R9. For a PVP or PVPVA dispersion at or below its limit, repeat the release test after 97% RH storage with both components and a colloid read-out: loss of the spike, of nanodroplets or of congruency without crystals marks water-induced separation purohit2017b R7, R12; saboo2019 R9.

How it was shown

Purohit and Taylor (2017) stored films and powders over saturated K2SO4 (97% RH) for 24 h to 4 days depending on the test, then dissolved the films as fresh films were, measuring apparent and free drug, pyrene in solution and NTA purohit2017b P7, P14, P12. Saboo and co-workers (2019) held a 10:90 nilvadipine–PVPVA compact in its die at 97% RH for 12 h, dissolved it for 15 min against an unexposed control, imaged its surface by SEM and imaged a matching film by confocal microscopy saboo2019 P13, P15, P18.

What the data show

Ritonavir–PVP after exposure: the 10:90 film reached ≈25 µg/mL after ≈25 min and ≈30 at 240 min instead of spiking, the 20:80 film ≈27 µg/mL at 240 min, and higher loadings changed little (≈14–25 µg/mL), all at or below the amorphous solubility purohit2017b R12, C33. PVPVA: only the 10% profile changed, the others staying at ≈10–21 µg/mL purohit2017b R13, C35. HPMCAS: the exposed films spiked as in the short part and stayed higher at 240 min (≈65, ≈45 and ≈42 µg/mL) than fresh films; the authors' "did not impact" holds for the fast rise and LLPS, not for the height of the profiles purohit2017b R14, C37, X5. Nilvadipine: the control released ≈14.7% drug and ≈15.2% polymer in 15 min, the exposed compact ≈0.34% and ≈2.6%, so both slowed and the drug much more; SEM showed a wrinkled surface after exposure whose features were gone after 15 min of dissolution, and the exposed film showed drug-rich circles and rings in a continuous polymer-rich phase saboo2019 R9, R17, R19. After the surface layer peeled off, drug release was much faster (data in a supplementary figure not supplied) saboo2019 R9.

papersystemmethod and conditionsresultids
purohit2017britonavir 10:90 PVP film97% RH, then dissolution at 25 °Cspike ≈130 → creep to ≈25–30 µg/mL; no nanodropletspurohit2017b R12, R7
purohit2017britonavir 10:90 PVPVA filmsamespike ≈116 → ≈25–26 µg/mLpurohit2017b R13
purohit2017britonavir–HPMCAS films 10–30%samestill spiking ≈90–131 µg/mL; nanodropletspurohit2017b R14, R7
saboo2019nilvadipine–PVPVA 10:90 compact12 h 97% RH, 15 min dissolution≈0.34% drug, ≈2.6% polymer against ≈15% of bothsaboo2019 R9
li2020 (ASD process)spray-dried ritonavir–PVPVA 25%water in the spray solventsurface-normalized rate ≈3.5 → ≈2.27 → ≈0.90li2020 R10
li2019 (ASD process)lopinavir–HPMC filmswater in the casting solventphase-separated films released faster at 33–85%li2019 C38
saboo2019 (cited)a 40% dispersionwater-induced phase separationno effect on dissolutionsaboo2019 R22

Figure

Fig. 9 of purohit2017b: dissolution of fresh and humidity-exposed ritonavir films with PVP, PVPVA and HPMCAS
Fig. 9 · purohit2017bdissolution of fresh and humidity-exposed ritonavir films with PVP, PVPVA and HPMCAS

Spikes above the dashed amorphous-solubility line for fresh low-loading PVP and PVPVA films (a, c) vanish after humidity (b, d), while the HPMCAS spikes remain (e, f) purohit2017b R12, R13, R14.

Fig. 3 of saboo2019: release of a 10:90 nilvadipine–PVPVA compact after 12 h at 97% RH and of a control
Fig. 3 · saboo2019release of a 10:90 nilvadipine–PVPVA compact after 12 h at 97% RH and of a control

After humidity (a, y-axis to 4%) the drug barely leaves while PVPVA does; the control (b, y-axis to 20%) releases both together saboo2019 R9.

Why

Purohit and Taylor conclude "very clearly" that a matrix phase-separated by humidity dissolves more slowly and no longer reaches LLPS, and explain it by a switch from polymer-controlled dissolution of the miscible matrix to drug-controlled dissolution of the separated one ("can be readily explained") purohit2017b C53, C54. Saboo and co-workers attribute the wrinkled surface "most likely" to water-induced AAPS confined to the exposed surface, which disappeared within 15 min of dissolution, and call the conversion of a congruent into an incongruent dispersion "further evidence" for the role of matrix phase separation (F8) saboo2019 C24, C41. The peeled layer "presumably" revealed a fresh surface saboo2019 C16. For the 40% dispersion of a cited study, where phase separation had no effect, the authors suggest that it was already drug-controlled or tested under other conditions saboo2019 C44. (synthesis: humidity matters most where release is congruent, because only there does a separated surface change the regime; above the limit the dispersion is drug-controlled whether or not it has separated, as the unchanged high-loading ritonavir profiles show purohit2017b C33.)

Conditions and limits

97% RH for 12 h (compact) or an unstated time (dissolution films; other tests 24 h–4 days); ritonavir films at 25 °C; release of the exposed compact followed for 15 min purohit2017b X7, P7; saboo2019 R9. Whether the exposed films were dried before dissolution is not stated purohit2017b X7. No intermediate humidities or storage times were tested.

Counterexamples and conflicts

Outside the subcategory, phase separation raised release where it produced polymer-rich phases that dissolve first: lopinavir–HPMC films cast with water released faster at 33–85% loading li2019 C38. Spray-dried ritonavir–PVPVA phase-separated by water in the spray solvent released more slowly at 25% loading, as here, and the effect is expected to be largest at congruent loadings li2020 R10, C67.

Transfer check

For a PVP or PVPVA dispersion formulated at or below its limit, expose the powder or compact to high humidity (97% RH for 12 h to several days) and repeat the release test with both components and a colloid read-out; loss of the spike, of nanodroplets or of congruency without crystals marks water-induced separation purohit2017b R7, R12; saboo2019 R9. Where humid storage cannot be excluded, compare with an HPMCAS dispersion, which kept its behaviour purohit2017b R14.

History

Moisture-induced AAPS had been studied for crystallization in storage (cited) purohit2017b C9. Purohit and Taylor (2017) were the first in the library to show that it removes LLPS from dissolving dispersions purohit2017b C53, and Saboo and co-workers (2019) that it turns a congruent compact incongruent saboo2019 C41. Li and co-workers (2020, ASD process) found the same loss of release for spray-dried ritonavir–PVPVA phase-separated during manufacture li2020 C67.

F13

Topic 5Formulation levers near the limit3 of 11

Five parts SDS per 100 raised the ledipasvir–PVPVA limit of congruency from 5 to 30%; three other surfactants did not help.

At 7.5% ledipasvir, where the binary dispersion released no drug by 60 min, 5 parts SDS per 100 parts drug and polymer gave congruent release of ≈102% of the drug by 60 min, and poloxamer 407 about 100% by 110 min; Span 85, Tween 80 and TPGS left drug release at ≤ ≈4% by 60 min que2019 R7, R6, R3. With SDS release stayed congruent up to 30% and failed at 40% que2019 R8, R9, C12. Why SDS works was not tested que2019 C53.

strongStrong for the effect on release, with clear positives and negatives at one loading; moderate for the colloid sizes, compared across formulations that released at different rates; the mechanism is untested que2019 K6, K7, X11, C53.

7.5% ledipasvir–PVPVA: drug released by 60 min, %no surfactantnoneSpan 85none detectedTPGS≈1Tween 80≈4poloxamer 407≈45 (≈100 by 110 min)SDS≈102

5 parts surfactant per 100 parts drug and polymer. que2019 R3, R6, R7

SDS, 7.5%≈60–63poloxamer 407, 5%≈96–130no surfactant, 5%≈225–257050100150200250300colloid size by DLS over 10–60 min, nm

The three formulations differ in loading and release rate, so the sizes compare only roughly. que2019 R12, X11

For your drug

  1. At the first failing loading of the binary dispersion, add 5 parts per 100 of SDS and of poloxamer 407, dissolve compacts with both components assayed, and raise the loading in 5–10% steps until congruency fails.
  2. Keep the delivered surfactant below its CMC in the medium (calculate it from the dose) and, for a drug that crystallizes, test supersaturation with the surfactant present.

que2019 R7, R9, X19; chen2015a C6

How it works and key numbers
  1. If release depends on the race between dissolution and phase separation (F8), "it is possible" that SDS and poloxamer 407 reduce the rate or tendency of phase separation, SDS much more than poloxamer 407 que2019 C53.
  2. SDS did not raise the limit by changing the polymer release rate: the SDS dispersions released like pure PVPVA que2019 C52.
  3. At complete release the medium held at most 0.048 mg/mL surfactant, about a tenth of the SDS critical micelle concentration (CMC) of 0.5 mg/mL, so bulk micellar solubilization "should be negligible" que2019 X19, C51; indulkar2017a R1.
  4. Smaller colloids, with more surface area, "can potentially" speed replenishment of absorbed drug que2019 C54.
  5. In humidified ritonavir–PVPVA films SDS sat mainly in the polymer-rich phase and the Spans in drug-rich domains; where the surfactant sat in the ledipasvir dispersions was not measured yang2022b C61.
5 → 30%limit of congruency without and with 5 parts SDS per 100que2019 R8, R9, C12
≈60 against ≈225–257 nmcolloid size with SDS and without surfactantque2019 R12
≤ ≈4%drug released by 60 min at 7.5% with Span 85, Tween 80 or TPGSque2019 R6
Evidence: data, conditions and papers

Finding F13. Five parts SDS per 100 raised the ledipasvir–PVPVA limit of congruency from 5 to 30% and poloxamer 407 to 7.5%, while Span 85, Tween 80 and vitamin E TPGS did not help at 7.5%; the surfactant colloids were smaller, and why SDS works was not tested

In short. At 7.5% ledipasvir, where the binary dispersion released no drug by 60 min, 5 parts SDS per 100 parts drug and polymer gave congruent release of ≈102% drug and ≈113% polymer by 60 min, and poloxamer 407 ≈45 and ≈42% by 60 min and about 100% by 110 min; Span 85, Tween 80 and TPGS left drug release at ≤ ≈4% by 60 min que2019 R7, R6, R3. With SDS release stayed congruent at 10, 20 and 30% (≈97% of both at 90 min at 30%) and failed at 40% (≈7–8%), whereas poloxamer 407 failed at 10% que2019 R8, R9, C12. The colloids measured about 60 nm with SDS (7.5%) and ≈96–130 nm with poloxamer 407 (5%) against ≈225–257 nm without surfactant (5%) que2019 R12. The authors offer that the surfactants "possibly" reduce the rate or tendency of phase separation; at complete release the medium held at most about 0.05 mg/mL surfactant, below the critical micelle concentration que2019 C53, C51, X19.

Type. single-system observation (ledipasvir–PVPVA with five surfactants) Strength. for the effect on release, with clear positives and negatives at one loading que2019 K6: strong; moderate for the colloid sizes, compared across formulations that released at different rates que2019 K7: moderate, X11; the mechanism is untested que2019 C53.

How it was shown

Que and co-workers (2019) added surfactant to the ethanol solution before rotary evaporation, so that every ternary dispersion held 5 parts surfactant per 100 parts drug plus polymer que2019 P1, C60. They screened Span 85, Tween 80, vitamin E TPGS, poloxamer 407 and SDS at 7.5% loading, then tested poloxamer 407 at 5 and 10% and SDS at 10–40% as compacts, and sized the colloids by DLS que2019 A2, A3, P3, P9.

What the data show

The SDS dispersions released like pure PVPVA, so SDS did not raise the limit by changing the polymer release rate que2019 C52.

systemconditionsresultids
7.5% with Span 85, Tween 80, TPGS5 parts surfactant, compactsno rescue: ≤ ≈4% drug at 60 minque2019 R6
7.5% with poloxamer 407 or SDSsamecongruent; ≈45% (P407) and ≈102% drug (SDS) at 60 minque2019 R7
SDS at 10–40%samecongruent to 30%; ≈7–8% at 40%que2019 R8, R9
colloids, three formulationsDLS 10–60 min≈60 (SDS), ≈96–130 (P407), ≈225–257 nm (none)que2019 R12
Fig. 3a of que2019: drug and polymer release of 7.5% ledipasvir–PVPVA dispersions with poloxamer 407 or SDS
Fig. 3a · que2019drug and polymer release of 7.5% ledipasvir–PVPVA dispersions with poloxamer 407 or SDS

Both pairs of curves overlap, the SDS pair reaching 100% by about 60 min and the poloxamer 407 pair by about 110 min, where the binary 7.5% dispersion released no drug que2019 R7, R3.

Why

If release depends on the race between dissolution and phase separation, "it is possible" that SDS and poloxamer 407 reduce the rate or tendency of phase separation, SDS much more than poloxamer 407; the mechanism "certainly needs more investigation" que2019 C53. Because the medium stays below the CMC after complete release, bulk micellar solubilization "should be negligible" que2019 C51. Smaller colloids, with more surface area, "can potentially" speed replenishment of absorbed drug que2019 C54.

Limits and transfer

One drug, one polymer and one surfactant level were tested, at 37 °C in pH 6.8 phosphate que2019 A2, P3. SDS and polysorbate 80 promoted crystallization of celecoxib from HPMCAS particles and of ritonavir drug-rich droplets in the ASD dissolution chapter chen2015a C6. At the first failing loading add 5 parts per 100 of SDS or poloxamer 407, dissolve compacts with both components assayed and raise the loading in 5–10% steps, keeping the delivered surfactant below its CMC and, for a drug that crystallizes, testing supersaturation in its presence que2019 R7, R9, X19; chen2015a C6.

How it was shown

Que and co-workers (2019) added 500 mg surfactant to the ethanol solution of 10 g drug and polymer before rotary evaporation, so that every ternary dispersion held 5 parts surfactant per 100 parts drug plus polymer at the drug-to-polymer ratio of the binary que2019 P1, C60. They screened Span 85, Tween 80, vitamin E TPGS, poloxamer 407 and SDS at 7.5% loading, then tested poloxamer 407 at 5 and 10% and SDS at 10, 20, 30 and 40%, by the compact method of F1, and sized the colloids of three formulations by DLS from 10 to 60 min que2019 A2, A3, P3, P9.

What the data show

Span 85 gave no detectable drug and ≈12% polymer by 60 min, Tween 80 ≈4% and ≈11%, TPGS ≈1% and ≈14%, each reaching ≈20–37% polymer at 90 min que2019 R6. Poloxamer 407 at 7.5% released both components together from ≈3–5% at 10 min to ≈102–106% at 110 min, and at 5% to ≈101–103% at 90 min; at 10% it gave ≈2% drug and ≈17% polymer by 90 min que2019 R7, R10, R8. SDS at 7.5% released ≈15 and ≈17% (drug, polymer) at 10 min and ≈102 and ≈113% at 60 min; at 10% ≈106 and ≈113% at 90 min; at 20% ≈101 and ≈113% at 90 min; at 30% ≈60 and ≈61% at 60 min and ≈97% of both at 90 min; at 40% ≈8 and ≈7% at 90 min que2019 R7, R8, R9. The authors note that SDS did not raise the limit by changing the polymer release rate, the SDS dispersions releasing like pure PVPVA, while the 7.5% poloxamer 407 and 30% SDS dispersions released congruently but more slowly que2019 C52. Colloid sizes: ≈60–63 nm with SDS throughout, ≈96 → ≈130 nm with poloxamer 407 and ≈225 → ≈257 nm without surfactant between 10 and 60 min que2019 R12, X12. (synthesis: at most 0.048 mg/mL surfactant in the medium que2019 X19 is about a tenth of the SDS CMC of 0.5 mg/mL measured in 50 mM pH 6.8 phosphate at 37 °C in the LLPS chapter indulkar2017a R1: 0.048/0.5 ≈ 0.1.)

papersystemmethod and conditionsresultids
que2019ledipasvir–PVPVA 7.5% with Span 85, Tween 80, TPGS5 parts surfactant, compactsno rescue: ≤ ≈4% drug at 60 minque2019 R6
que20197.5% with poloxamer 407 or SDSsamecongruent; ≈45% (P407) and ≈102% drug (SDS) at 60 minque2019 R7
que2019SDS at 10–40%samecongruent to 30%; ≈7–8% at 40%que2019 R8, R9
que2019colloids, three formulationsDLS 10–60 min≈60 (SDS), ≈96–130 (P407), ≈225–257 nm (none)que2019 R12
indulkar2017a (LLPS chapter)SDSpyrene carboxaldehyde, 50 mM pH 6.8, 37 °CCMC 0.5 mg/mLindulkar2017a R1
moseson2022b (ASD process)bicalutamide–PVPVA 30% with 1.5% SDS or TPGSpowdersSDS congruent, > 80% in 30 min; TPGS incongruentmoseson2022b R9, R13
yang2022b (Physical stability)ritonavir–PVPVA with four surfactantshumidified filmsSDS mainly in the polymer-rich phase, Spans in drug-rich domainsyang2022b C61

Figure

Fig. 3a of que2019: drug and polymer release of 7.5% ledipasvir–PVPVA dispersions with poloxamer 407 or SDS
Fig. 3a · que2019drug and polymer release of 7.5% ledipasvir–PVPVA dispersions with poloxamer 407 or SDS

Both pairs of curves overlap, the SDS pair reaching 100% by about 60 min and the poloxamer 407 pair by about 110 min, where the binary 7.5% dispersion released no drug que2019 R7, R3.

Fig. 4 of que2019: Z-average size of the drug-rich colloids against sampling time
Fig. 4 · que2019Z-average size of the drug-rich colloids against sampling time

The SDS colloids stay at about 60 nm, the poloxamer 407 colloids at about 100–130 nm and the surfactant-free colloids at about 225–257 nm; the three formulations differ in loading and in release rate que2019 R12, X11.

Why

The authors argue that if release depends on the race between dissolution and phase separation (F8), "it is possible" that SDS and poloxamer 407 reduce the rate or tendency of phase separation, SDS much more than poloxamer 407, which would explain the rise of the congruency boundary from about 5 to about 30%; the mechanism "certainly needs more investigation" que2019 C53. They call poloxamer 407 and SDS the more hydrophilic surfactants, without printing HLB values que2019 C12, X19. Because the medium stays below the CMC after complete release, bulk micellar solubilization "should be negligible" que2019 C51. Smaller colloids, with more surface area, "can potentially" speed replenishment of absorbed drug, so colloid size is "definitely another factor" when designing formulations with comparable release que2019 C54. Outside the subcategory a hydrophilic surfactant (SDS) was found mainly in the polymer-rich phase and hydrophobic Spans in drug-rich domains of humidified ritonavir–PVPVA films yang2022b C61, and SDS in the medium raised bicalutamide release only slightly, so the SDS dispersion's fast release came from a change of mechanism to polymer-controlled release rather than from wetting moseson2022b C24. (synthesis: the surfactants that helped are the two whose location would be the hydrophilic, polymer-rich side, but none of these papers measured where the surfactant sat in the ledipasvir dispersions.)

Conditions and limits

One drug, one polymer, one surfactant level (5 parts per 100), 37 °C in pH 6.8 phosphate que2019 A2, P3. Ledipasvir has no reported crystal forms, so the effect of the surfactants on crystallization was not at issue here que2019 M1. The release replicates and error bars are not stated que2019 X15. The 20% SDS dispersion plots ≈4% drug at time 0, and the 40% SDS dispersion released slightly more drug than polymer que2019 R9.

Counterexamples and conflicts

In the ASD dissolution chapter SDS and polysorbate 80 promoted crystallization of celecoxib from HPMCAS particles and of ritonavir drug-rich droplets, the SDS effect occurring even below its CMC (Supersaturation from ASD dissolution F14) chen2015a C6, and in the crystallization chapter TPGS and Tween 80 at 5 µg/mL, far below their CMC, about doubled the growth rate of ritonavir crystals (Crystallization from solution F18) ilevbare2012a R17. For a drug that crystallizes, a surfactant that raises the limit may therefore cost supersaturation later (synthesis: not tested for any crystallizing drug in this paper). TPGS, ineffective here at 7.5%, made bicalutamide release incongruent in an ASD process study moseson2022b R13. TPGS raised the felodipine limit from 15 to 45% at 10% of the polymer portion (F21) saboo2021 R12.

Transfer check

At the first failing loading of the binary dispersion, add 5 parts per 100 of a hydrophilic anionic surfactant (SDS) and of a nonionic block copolymer (poloxamer 407) and dissolve compacts with both components assayed; raise the loading in 5–10% steps until congruency fails que2019 R7, R9. Keep the delivered surfactant below its CMC in the medium (calculate it from the dose) and, for a drug that crystallizes, test supersaturation in the presence of the surfactant que2019 X19; chen2015a C6. Size the colloids at matched release extents before attributing a size difference to the surfactant que2019 X11.

History

Surfactants are part of marketed dispersions (Span 20 in Kaletra, SDS in Kalydeco, cited) que2019 R30. Que and co-workers (2019) were the first in the library to raise a limit of congruency with a surfactant and proposed it as "a formulation strategy to increase the LoC" que2019 C56. Saboo and co-workers (2021) and Correa Soto and co-workers (2022) raised the limits of felodipine, clopidogrel and atazanavir with surfactants and found the effective surfactant to differ between drugs (F21) saboo2021 C16; correasoto2022a C55; correasoto2022b C12; Indulkar and co-workers (2022) built five surfactants into ritonavir–PVPVA above its limit and found Span 85 and TPGS best and SDS stopped by crystals on the tablet (F21, F19) indulkar2022 C54, C38, and the ASD process chapter found the same contrast between SDS and TPGS for bicalutamide moseson2022b R13.

F14

Topic 5Formulation levers near the limit4 of 11

Near the switch the manufacturing route and the spray-drying solvent decided whether release was polymer- or drug-controlled.

Spray-dried and melt-extruded itraconazole (ITZ)–PVPVA released ITZ alike at 10, 25 and 50% loading, but at 20% the spray-dried compact released 113 and the extruded one 48.8 µg/min/cm² bhardwaj2018 R4. Spray-drying the 20% dispersion from five solvent systems changed ITZ release several-fold, and XPS put the surface drug between 4.2 and 35.7% against 20% in the bulk bhardwaj2018 R13, R14, R20.

moderateModerate for the process difference at 20%, a tabulated rate with n = 3 at one composition; weak to moderate for the surface–release link, a correlation over four XPS batches confounded with particle morphology bhardwaj2018 K4, X6, K5, X12.

spray-driedmelt-extruded10% loading199 (both)20%48.811325%556450%4753020406080100120140160180200220ITZ release rate in 0.1 N HCl, µg/min/cm²

The two processes differ only at 20%, the loading at the switch. bhardwaj2018 R4

20% ITZ–PVPVA spray-dried from five solvents: ITZ released at 60 min, mg/cm²DCM–methanol–watersurface drug 4.2%≈7.5DCM≈6.0DCM–methanol (reference)surface drug 28.1%≈5.2DCM with n-hexane or cyclohexanesurface drug 31.8–35.7%1.35–2.0

Bulk loading 20%; PVPVA release was similar for all batches. bhardwaj2018 R13, R14, R20

For your drug

  1. For a product whose loading lies near the switch, compare candidate processes (spray drying, extrusion, different spray solvents) by constant-area release with the polymer assayed.
  2. Measure the surface composition of spray-dried particles by XPS using an element of the drug: a surface richer in drug than the bulk predicts drug-controlled release, and equivalence of two processes cannot be assumed at that loading.

bhardwaj2018 C65, P11, C57, C2

How it works and key numbers
  1. The authors find that XPS "can be readily correlated" with dissolution: drug-enriched surfaces (n-hexane) go with drug-controlled release, near-bulk or drug-depleted surfaces (water) with polymer-controlled release bhardwaj2018 C57.
  2. With water in the solvent the droplet dries fast relative to polymer diffusion, a large Peclet number \mathrm{Pe}_i = \frac{k}{8 D_i}, which "is thought" to give the polymer-rich surface bhardwaj2018 E1, C60.
  3. With DCM–hexane, DCM evaporates first so that ITZ, poorly soluble in hexane, "could conceivably" precipitate early at the surface; the authors add that this "may be an over simplification" bhardwaj2018 C62.
  4. The large solvent effect at 20% is "perhaps unexpected" because the reference releases under polymer control there; 20% lies between the polymer-controlled 10% and the drug-controlled 25–50% (F6) bhardwaj2018 C54, R4.
  5. In 2023 grazoprevir–HPMCAS particles with 10–34% surface drug released 47–72% against 8–17% for particles with 53–84%, at nearly the same bulk loading (F28) hiew2023 R14.
113 against 48.8 µg/min/cm²20% ITZ–PVPVA spray-dried against melt-extrudedbhardwaj2018 R4
4.2 → 35.7%surface drug of 20% particles from the water to the n-hexane solvent; bulk 20%bhardwaj2018 R20
≈7.5 against 1.35–2.0 mg/cm²ITZ released at 60 min, water-containing against hydrocarbon solventsbhardwaj2018 R13
Evidence: data, conditions and papers

Finding F14. Near the switch the manufacturing route and the spray-drying solvent decided the regime: 20% itraconazole–PVPVA released 113 µg/min/cm² spray-dried against 48.8 melt-extruded, and spray solvents that left 4–36% drug at the particle surface changed ITZ release several-fold

In short. At 50, 25 and 10% loading spray-dried and extruded ITZ–PVPVA released ITZ alike (53 and 47, 64 and 55, 199 and 199 µg/min/cm²), although their polymer release differed, for example ≈12.2 against ≈5.0 mg/cm² PVPVA in 20 min at 50% with the extruded material ahead bhardwaj2018 R4, R8. At 20% the spray-dried compact released 113 and the extruded one 48.8 µg/min/cm² bhardwaj2018 R4. Spray-drying the 20% dispersion from five solvent systems gave ITZ at 60 min of about 7.5 (DCM–methanol–water), 6.0 (DCM), 5.2 (DCM–methanol) and 1.35–2.0 mg/cm² (DCM with n-hexane or cyclohexane), with similar PVPVA release, and XPS put the surface drug at 4.2% (water), 28.1% (DCM–methanol) and 31.8–35.7% (n-hexane) against 20% in the bulk bhardwaj2018 R13, R14, R20. Pyrene fluorescence and TEM found no separate drug-rich and polymer-rich phases inside the particles bhardwaj2018 R15, R16, C35. In 2023 high-loading grazoprevir–HPMCAS co-precipitates with a water-soluble polymer deposited from the anti-solvent had 10–34% surface drug and released 47–72% against 8–17% for binary particles with 53–84%, at nearly the same bulk loading (F28) hiew2023 R14.

Type. single-system observation (itraconazole–PVPVA), with grazoprevir–HPMCAS particles in 2023 (F28) Strength. for the process difference at 20%, a tabulated rate with n = 3 at one composition bhardwaj2018 K4: moderate, X6; weak to moderate for the surface–release link, a correlation over four XPS batches confounded with particle morphology bhardwaj2018 K5: weak to moderate, X12.

How it was shown

Bhardwaj and co-workers (2018) spray-dried ITZ–PVPVA from DCM–methanol and melt-extruded it at 175 °C, at 50, 25, 20 and 10% loading, and at 20% also spray-dried it from four other solvent systems bhardwaj2018 P2, P4, P3. All were dissolved as constant-area compacts in 0.1 N HCl, and particle surfaces were analysed by XPS bhardwaj2018 P7, P11.

What the data show

The extruded 20% compact (about 17.5 times crystalline ITZ) stayed on the amorphous-drug plateau and the spray-dried one (about 40 times) left it, while PVPVA release was similar for all solvent batches bhardwaj2018 R4, R6, R14, C34.

systemmethodresultids
ITZ–PVPVA spray-dried against extruded, 10–50%compacts, 0.1 N HClsame ITZ rate except at 20% (113 against 48.8)bhardwaj2018 R4
20% spray-dried from five solventsITZ at 60 min≈7.5 / 6.0 / 5.2 / 1.35–2.0 mg/cm²bhardwaj2018 R13
20% spray-dried, four batchesXPS N 1ssurface drug 4.2 / 28.1 / 31.8–35.7% (bulk 20%)bhardwaj2018 R20
grazoprevir–HPMCAS co-precipitates, 60–75%XPS; two-stage release at 90 min≤34% surface drug with ≈47–72% release; ≥53% with ≈8–17%hiew2023 R14
spray-dried ritonavir–PVPVA 25% (ASD process)XPS; releasemore water in the spray solvent: surface ritonavir ≈21 → 43 → 70%; rate ≈3.5 → ≈2.27 → ≈0.90li2020 R7, R10
Fig. 7 of bhardwaj2018: ITZ release from 20-80 spray-dried batches made with different solvents
Fig. 7 · bhardwaj2018ITZ release from 20-80 spray-dried batches made with different solvents

The water (black), DCM (light green) and reference (blue) batches run above amorphous ITZ (dark green); the hexane batches (light blue, magenta, brown) below it bhardwaj2018 R13.

Why

The authors find that XPS "can be readily correlated" with dissolution: drug-enriched surfaces go with drug-controlled release, near-bulk or drug-depleted surfaces with polymer-controlled release bhardwaj2018 C57. They explain the polymer-rich surface with water by fast drying relative to polymer diffusion, a large Peclet number ("is thought", "it appears"), and the drug-rich surface with DCM–hexane by early precipitation of ITZ ("could conceivably") bhardwaj2018 E1, C60, C62. (synthesis: the effect appears only at the loading that sits at the switch, where a few percent of drug more or less at the surface can move the dispersion from one regime to the other.)

Limits and transfer

One drug–polymer pair was tested in 0.1 N HCl only, and surface composition and particle morphology changed together bhardwaj2018 C27, X12. For ritonavir–PVPVA water in the spray solvent had the opposite effect li2020 R7, R10. Near the switch compare candidate processes by constant-area release with the polymer assayed and measure the particle surface by XPS: a surface richer in drug than the bulk predicts drug-controlled release, and equivalence of two processes cannot be assumed at that loading bhardwaj2018 C65, P11, C57, C2.

How it was shown

Bhardwaj and co-workers (2018) spray-dried ITZ–PVPVA from 50:50 DCM–methanol in a Büchi B-290 (outlet 48 ± 2 °C) and melt-extruded physical mixtures at 175 °C for 3–4 min, milling the extrudates, at 50, 25, 20 and 10% loading bhardwaj2018 P2, P4. At 20% they also spray-dried from DCM–methanol–water 50:50:20, DCM alone, DCM–n-hexane (about 55:45) and DCM–cyclohexane (about 40:60), adding the hydrocarbon up to polymer turbidity, and dried the n-hexane batch also at 70 °C outlet bhardwaj2018 P3. All were dissolved as constant-area compacts in 0.1 N HCl (F1) and characterized by pyrene fluorescence, TEM, SEM of whole and fractured particles and XPS of the outer ~10 nm (N 1s and O 1s fits, Cl 2p/C 1s, Cl 2p components) bhardwaj2018 P7, P8, P9, P10, P11.

What the data show

Process: ITZ rates as in the short part, the extruded 20% compact (48.8 ± 0.9, about 17.5 times crystalline) staying on the amorphous-drug plateau and the spray-dried one (113 ± 2, about 40 times) leaving it bhardwaj2018 R4, R6. Polymer release differed without matching ITZ changes: at 25% about 13.9 (spray-dried) against 8.6 mg/cm² (extruded) by 20 min, stated as "twice as fast" (about 1.5–1.7 times in the plot), and at 20% about 12.2 against 9.0 bhardwaj2018 R8, C25, X9. Solvent: the water batch released ITZ "unexpectedly" faster than the reference (≈2.5 against ≈2.0 mg/cm² at 20 min, ≈7.5 against ≈5.2 at 60 min), the DCM batch about like the reference, and the hexane batches "significantly slower" (≈0.5–0.75 mg/cm² at 20 min), slightly below melt-quenched ITZ but well above the crystal, with crystal-free compacts bhardwaj2018 R13, R3, C32, C33. PVPVA release was about 15–18 mg/cm² by 30 min for all batches bhardwaj2018 R14, C34. Pyrene I/III ratios were 1.75–1.79 for the 20-80 batches (pure drug 1.29, pure polymer 2.06) bhardwaj2018 R15. Particles were hollow shells, raisin-like from DCM–methanol with or without water and smooth with pitted shells from the hexane solvents bhardwaj2018 R17, R18. XPS: a homogeneous 20% surface would give a polymer:drug ratio of 4; N 1s gave 2.1 and 1.8 (n-hexane, 48 and 70 °C), 2.8 (reference; 2.6 from its own percentages) and 22.9 (water), and Cl 2p/C 1s 0.0067, 0.0072, 0.0050 and 0.0011 against 0.0421 for pure ITZ bhardwaj2018 R20, E6, X1. The second Cl 2p component at about 197 eV made up 9.0–9.5% (n-hexane), 15.8% (reference) and 62.5% (water), read as ITZ chlorine in a more polymer-rich environment ("suggests") bhardwaj2018 R20, R21, C42.

papersystemmethod and conditionsresultids
bhardwaj2018ITZ–PVPVA SD against HM, 10–50%compacts, 0.1 N HClsame ITZ rate except at 20% (113 against 48.8)bhardwaj2018 R4
bhardwaj2018samePVPVA releasediffers by process at 20–50%bhardwaj2018 R8
bhardwaj201820% SD from five solventsITZ at 60 min≈7.5 / 6.0 / 5.2 / 1.35–2.0 mg/cm²bhardwaj2018 R13
bhardwaj201820% SD, four batchesXPS N 1ssurface drug 4.2 / 28.1 / 31.8–35.7% (bulk 20%)bhardwaj2018 R20
hiew2023grazoprevir–HPMCAS cPADs, 60–75%XPS; two-stage release at 90 min≤34% surface drug with ≈47–72% release; ≥53% with ≈8–17%hiew2023 R14
li2020 (ASD process)spray-dried ritonavir–PVPVA 25%XPS; releasemore water in the spray solvent: surface ritonavir ≈21 → 43 → 70%; rate ≈3.5 → ≈2.27 → ≈0.90li2020 R7, R10

Figure

Fig. 7 of bhardwaj2018: ITZ release from 20-80 spray-dried batches made with different solvents
Fig. 7 · bhardwaj2018ITZ release from 20-80 spray-dried batches made with different solvents

The water (black), DCM (light green) and reference (blue) batches run above amorphous ITZ (dark green); the hexane batches (light blue, magenta, brown) below it bhardwaj2018 R13.

Table 6 of bhardwaj2018: XPS surface composition of the spray-dried particles
Table 6 · bhardwaj2018XPS surface composition of the spray-dried particles

Read the polymer:drug ratios against 4 for a homogeneous 20% surface: below 4 is drug-enriched (n-hexane), far above it drug-depleted (water) bhardwaj2018 R20, E6.

Why

The authors find that XPS differentiates the samples best and "can be readily correlated" with dissolution: drug-enriched surfaces (n-hexane) go with drug-controlled release, near-bulk (reference) or drug-depleted (water) surfaces with polymer-controlled release bhardwaj2018 C57. They explain the polymer-rich surface with water by drying fast relative to polymer diffusion, a large Peclet number,

\mathrm{Pe}_i = \frac{k}{8 D_i}

("is thought", "it appears"), and the drug-rich surface with DCM–hexane by DCM evaporating first so that ITZ, poorly soluble in hexane, precipitates early ("could conceivably"), adding that PVPVA is also poorly soluble in hexane, so this "may be an over simplification" bhardwaj2018 E1, C60, C62. The different polymer release of spray-dried and extruded compacts is "likely" a different speed of the receding polymer solid–liquid boundary, whose reasons are "currently unknown" bhardwaj2018 C53. The large solvent effect at 20% is "perhaps unexpected" because the reference releases under polymer control there bhardwaj2018 C54. (synthesis: the effect appears only at the loading that sits at the switch, where a few percent of drug more or less at the surface can move the dispersion from one regime to the other (F6); at 10% and at 25–50% both processes stay in one regime and give the same ITZ release.)

Conditions and limits

One drug–polymer pair, in 0.1 N HCl only bhardwaj2018 C27, P7. XPS covered four of the six 20% batches and no extruded material, and surface composition and particle morphology change together, so their roles are not separated bhardwaj2018 X12. The regime of each solvent batch is inferred from the drug and polymer profiles; no normalized rates are given for this series bhardwaj2018 X11. The 70 °C outlet batch released more slowly than the 48 °C one, although the authors report no effect bhardwaj2018 X10. n-Hexane and cyclohexane are not typical spray solvents and were used to widen the design space bhardwaj2018 C59.

Counterexamples and conflicts

The direction of the water effect differs between drugs: water in the spray solvent depleted the ITZ surface of drug and gave faster release, whereas for spray-dried ritonavir–PVPVA more water raised the surface drug and lowered release bhardwaj2018 R20, R13; li2020 R7, R10. A cited case also found drug enrichment with water, in a system with a surfactant bhardwaj2018 R24, C61. In the grazoprevir co-precipitates the anti-solvent changed the surface drug of a 75% binary particle from about 53% (acidified water) to 84% (MTBE), with release of about 17 and 8% (F28) hiew2023 R14, C29.

Transfer check

For a product whose loading lies near the switch, compare candidate processes (spray drying, extrusion, different spray solvents) by constant-area release with the polymer assayed, and measure the surface composition of spray-dried particles by XPS using an element of the drug bhardwaj2018 C65, P11. A surface richer in drug than the bulk predicts drug-controlled release; equivalence of two processes or manufacturers cannot be assumed at that loading bhardwaj2018 C57, C2.

History

Bhardwaj and co-workers (2018) were the first in the library to compare spray-dried and extruded dispersions of one composition by constant-area release and to link the spray solvent to the release regime through surface composition bhardwaj2018 C5, C58. Their method and their itraconazole drop above 20% were taken up by the dihydropyridine study saboo2019 R22, and Li and co-workers (2020, ASD process) took the surface-normalized method with an ethyl cellulose backing and the XPS of spray-dried particles to ritonavir–PVPVA (builds_on) li2020 R7. Hiew and co-workers (2023) cite it for surface drug enrichment impairing release and lowered the surface drug of high-loading co-precipitates on purpose (F28) hiew2023 C44, C45. In 2025 a high-shear treatment with HPMC or SDS solution lifted a 75% grazoprevir–HPMCAS dispersion from about 30 to 43–57% release, near that of 20–30% dispersions, and wettability rather than surface drug content separated good from poor surface treatments (F35) hiew2025 R10, C40.

F21

Topic 5Formulation levers near the limit5 of 11

A few percent of surfactant inside a PVPVA dispersion raised the limit of congruency, but the effective surfactant differed between drugs.

With TPGS replacing 2, 5 or 10% of the polymer, felodipine–PVPVA released congruently up to 25, 35 and 45% against 15% without it, while TPGS dissolved in the medium did nothing saboo2021 R12, R15. In clopidogrel–PVPVA only SDS helped, and in atazanavir–PVPVA all eight additives raised release at 10% from about 2.4% to 11–106% correasoto2022a R17, C55; correasoto2022b R2. The gain was not micellar solubilization, since the released surfactant stayed below its critical micelle concentration (CMC) saboo2021 C33; que2019 C51.

strongStrong for the gains in limit, measured with drug and polymer assayed; weak for the mechanisms (morphology, plasticization), which were not measured in a dissolving compact saboo2021 K1, K6; correasoto2022b K2, K5; correasoto2022a K3.

binary dispersionwith surfactant insideledipasvir · SDS530felodipine · 10% TPGS1545clopidogrel · SDS4050atazanavir · Span 8051505101520253035404550limit of congruency in PVPVA, %

Each drug needed a different surfactant; TPGS raised felodipine but did not help ledipasvir at 7.5%. que2019 C12, R6; saboo2021 R12; correasoto2022a C55; correasoto2022b R4, C12

10% atazanavir–PVPVA: drug released at 90 min, %binary≈2.4CTAB≈106Span 80≈103.5SDS≈93Span 20≈70Tween 80≈56.5Span 85≈38TPGS≈11

5 g additive per 100 g of drug and polymer; the plasticizer vinylpyrrolidone gave ≈87. correasoto2022b R2

For your drug

  1. At the first failing loading of the binary dispersion, co-process 2–10% of SDS, a sorbitan ester and TPGS into the dispersion, dissolve compacts with drug and polymer assayed for 60–90 min, and raise the loading in 5% steps until congruency fails.
  2. Size the released droplets and check crystallization at 37 °C and on storage before adopting the surfactant, and judge it by the extent released at 60–90 min and by the tablet surface, not by the removal of a lag phase.

saboo2021 R12; correasoto2022b R4, C53; correasoto2022a R19; indulkar2022 R6, R7, X3

How it works and key numbers
  1. Micellar solubilization is ruled out: 2% TPGS raised the felodipine limit with at most 18 µg/mL TPGS at full release, below its CMC of 41–49 µg/mL saboo2021 C33, R1.
  2. TPGS dissolved in the medium did nothing, "indicating" that the surfactant must be in the dispersion; the authors place the effect in the hydrated matrix or at the dispersion–solution interface saboo2021 C18, C35, C36.
  3. Saboo and co-workers favour a changed morphology of the separated drug-rich phase (F20), and allow that the lower Tg "may also play a role" saboo2021 C53, C43.
  4. For atazanavir the authors "speculate" that the additives act as plasticizers; additives below about 430 g/mol gave 24- to 35-fold gains and larger ones 4- to 19-fold correasoto2022b C40, C47, R21.
  5. The dry Tg depression did not rank the additives (Span 85 7 °C and 13-fold, TPGS 14 °C and 4-fold) correasoto2022b R20, X16.
  6. Yang and co-workers propose that preventing or disrupting a continuous drug-rich layer is the most critical surfactant effect (F31) yang2023 C37, C9, C11.
15 → 45%felodipine–PVPVA limit with 10% of the polymer replaced by TPGSsaboo2021 R12
≈2.4 → 11–106%10% atazanavir released by 90 min, binary against eight additivescorreasoto2022b R2
≈0.4%drug released in 60 min by a 30% felodipine binary in medium with 35 µg/mL TPGSsaboo2021 R15
Evidence: data, conditions and papers

Finding F21. A few percent of surfactant inside a PVPVA dispersion raised the limit of congruency of four drugs (ledipasvir 5 → 30% with SDS, felodipine 15 → 45% with TPGS, clopidogrel 40 → 50% with SDS, atazanavir 5 → 15% with Span 80) and restored near-complete release of ritonavir at 30% (Span 85, TPGS), but the effective surfactant differed between drugs, the gain was not micellar solubilization, and TPGS dissolved in the medium did nothing

In short. With TPGS replacing 2, 5 or 10% of the polymer, felodipine–PVPVA released congruently up to 25, 35 and 45% against 15% without it, while 35 µg/mL TPGS dissolved in the medium left a 30% binary dispersion releasing about 0.4% of its drug in 60 min saboo2021 R12, R15. In clopidogrel–PVPVA only SDS (5 g per 100 g) helped, raising release at 50% from about 52 to 70% with drug and polymer rates of about 5.1 and 5.3 mg/min/cm², while TPGS and Tween 80 roughly halved the rates and CTAB let dissolved drug fall correasoto2022a R17, R18, R15, C55. In atazanavir–PVPVA all eight additives raised release at 10% from about 2.4% to 11–106%, giving limits of 10% with SDS or CTAB and 15% with Span 80; additives below about 430 g/mol gave 24- to 35-fold gains and larger ones 4- to 19-fold, and the plasticizer vinylpyrrolidone matched the best surfactants at 10% but released about 6% at 15% correasoto2022b R2, R4, C12, R20, R21, X21. TPGS raised the felodipine limit but not that of ledipasvir at 7.5%, slowed clopidogrel and gave atazanavir only a 4-fold gain (F13) que2019 R6; correasoto2022a C56; correasoto2022b R20. In 2023, 10 parts of SDS, Tween 80, Span 20 or Span 85 raised ritonavir release at 30% to about 50–97%, but only SDS and Tween 80 kept partial release (about 48–57%) at 40%, which the authors trace to whether a continuous drug-rich layer persists (F31) yang2023 R2, C37.

Type. observation in 5 drugs (ledipasvir, felodipine, clopidogrel, atazanavir, ritonavir) with 8 surfactants and one plasticizer in PVPVA Strength. for the gains in limit, measured with drug and polymer assayed saboo2021 K1: strong; correasoto2022b K2: moderate to strong; correasoto2022a K3: moderate; weak for the mechanisms (morphology, plasticization), not measured in a dissolving compact saboo2021 K6: weak; correasoto2022b K5: weak to moderate.

How it was shown

Surfactants were built into PVPVA dispersions of felodipine (TPGS at 2–10% of the polymer portion), clopidogrel (CPD) and atazanavir (ATZ) (5 g per 100 g) and ritonavir (5 parts per 100), and compacts were dissolved over loading series saboo2021 P4, P6; correasoto2022a P10, P11; correasoto2022b P3, A1; indulkar2022 P1, P3. A binary felodipine dispersion was also run in medium containing TPGS saboo2021 P8.

What the data show

The TPGS CMC was 49 ± 4 µg/mL in buffer saboo2021 R1.

systemconditionsresultids
felodipine–PVPVA, TPGS 0–10%compacts, pH 6.8limit 15 / 25 / 35 / 45%saboo2021 R12
30% binary in 35 µg/mL TPGScompacts≈4.9% polymer, ≈0.4% drug in 60 minsaboo2021 R15
CPD–PVPVA 40–60%, four surfactantscompacts, 120 minSDS 40 → 50%; TPGS, Tween 80 slower; CTAB drug losscorreasoto2022a R17, R18, C55
ATZ–PVPVA 10%, eight additives90-min release≈11–106% against ≈2.4%; gains 4–35-foldcorreasoto2022b R2, R20
ATZ 15, 20%90-min releaselimit 10% (SDS, CTAB), 15% (Span 80)correasoto2022b R4, C12
ritonavir–PVPVA 30:70, five surfactants or PEG 3350compacts, pH 6.8, 37 °C, 90 minRTV ≈87 (Span 85), ≈89 (TPGS), ≈78 (SDS), ≈41 (Span 20), ≈25% (Tween 80); binary ≈45%, PEG 3350 ≈46%indulkar2022 R1, R4, R5, R6, R7, R8, R9
Fig. 5 of saboo2021: limit of congruency of felodipine–PVPVA against TPGS level
Fig. 5 · saboo2021limit of congruency of felodipine–PVPVA against TPGS level

Bars of 15, 25, 35 and 45% at 0, 2, 5 and 10% TPGS; each bar is the highest loading tested that still released congruently saboo2021 R12, X2.

Why

The authors rule out micellar solubilization: 2% TPGS raised the felodipine limit with at most 18 µg/mL TPGS at full release, below the CMC, so micelles play "a negligible role", and TPGS in the medium did nothing, "indicating" that the surfactant must be in the dispersion saboo2021 C33, C18, C35. Saboo and co-workers favour a changed morphology of the separated drug-rich phase, and for ATZ Correa Soto and co-workers "speculate" that the additives act as plasticizers saboo2021 C53; correasoto2022b C40. (synthesis: no surfactant worked for every drug, and the dry Tg depression did not rank the additives, so the effective additive has to be found for each drug correasoto2022b X16; saboo2021 X15.)

Limits and transfer

Release at the new felodipine limit was about half as fast, and no storage stability or in vivo data were reported saboo2021 X3, C54; correasoto2022b C53. With ritonavir SDS stopped near 80% because crystals formed on the tablet indulkar2022 R5, R15. At the first failing loading co-process 2–10% of SDS, a sorbitan ester and TPGS, raise the loading in 5% steps with both components assayed, and check droplets and crystallization before adopting the surfactant saboo2021 R12; correasoto2022b R4, C53; correasoto2022a R19.

How it was shown

Saboo and co-workers (2021) made rotary-evaporated felodipine–PVPVA dispersions with TPGS at 2, 5 or 10% of the polymer portion, stepped the loading up, dissolved 100 mg compacts in pH 6.8, 100 mM phosphate at 37 °C with drug, polymer and TPGS assayed, measured the TPGS CMC by drug solubility and pyrene with and without 900 µg/mL PVPVA, and ran a binary dispersion in medium containing TPGS and a drug-free PVPVA–TPGS matrix saboo2021 P4, P6, P1, P2, P8, P7. Correa Soto and co-workers (2022) built SDS, CTAB, TPGS or Tween 80 into clopidogrel–PVPVA dispersions at 5 g per 100 g of drug and polymer and dissolved 40, 50 and 60% compacts for 120 min, with ANOVA against the binary correasoto2022a P10, P11, P15. In the atazanavir study eight additives (SDS, CTAB, TPGS, Tween 80, Spans 20, 80 and 85, and vinylpyrrolidone) at 5 g per 100 g were screened at 10% and the best taken to 15 and 20%, with the 90-min release, dispersion Tg, water sorption and additive partitioning into drug-rich droplets measured correasoto2022b P3, A1, A2, P1, P9, P10. Que and co-workers (2019) had screened five surfactants with ledipasvir (F13) que2019 A2. Indulkar and co-workers (2022) built PEG 3350 or one of five surfactants (SDS, Tween 80, TPGS, Span 20 and Span 85, HLB 40 to 1.8) at 5 parts per 100 parts of drug and polymer into 30:70 ritonavir–PVPVA dispersions, one loading above the binary limit of about 25%, dissolved 100 mg compacts in 100 mL pH 6.8 phosphate at 37 °C for 90 min with drug and polymer assayed, and ran a binary tablet in medium containing 50 µg/mL SDS as a wetting control indulkar2022 P1, P3, P4, A1, M4, M5, M6, M7, M8.

What the data show

Felodipine: with 5% TPGS drug, polymer and TPGS left at about 2.6–3.2 mg/min/cm² up to 30%, at about 1.7–1.8 at 35% after a lag of about 15 min, and drug release collapsed to about 0.003 at 40%; with 2% TPGS release was congruent to 25% and failed at 30%, with 10% TPGS congruent to 45% and failed at 50% saboo2021 R9, R8, R10. The 30% dispersion with 5% TPGS reached about 165 µg/mL against an amorphous solubility of 9.5 µg/mL with PVPVA saboo2021 R11, R4. The TPGS CMC was 49 ± 4 µg/mL in buffer and 41 ± 3 with PVPVA, and the TPGS a dispersion would release in full ranged from 14 to 90 µg/mL saboo2021 R1, P4. TPGS lowered the Tg of the 30% dispersion from 89.2 to 86.0, 80.8 and 71.1 °C at 2, 5 and 10% saboo2021 R5. Clopidogrel: at 50% SDS gave about 70% drug and 81% polymer against 52 and 103% for the binary; at 40% SDS changed little, TPGS and Tween 80 cut the drug rate to about 1.9 and 2.5 mg/min/cm² against 4.5, and with CTAB dissolved drug peaked at about 45% at 50 min and fell to about 25% by 120 min at 50%; at 60% every dispersion stayed at 7–11% correasoto2022a R17, R18, R15. Atazanavir: at 10% ATZ release at 90 min was about 106% (CTAB), 103.5% (Span 80), 93% (SDS), 87% (vinylpyrrolidone), 70% (Span 20), 56.5% (Tween 80), 38% (Span 85) and 11% (TPGS) against 2.4% for the binary, with polymer release following correasoto2022b R2. At 15% Span 80 released about 100%, SDS 60.5%, CTAB 11% and vinylpyrrolidone 6%; at 20% Span 80 about 4% and SDS 39% correasoto2022b R4. The additives lowered the dispersion Tg by 7–16 °C without ordering the gains (Span 85 7 °C and 13-fold, CTAB 9 °C and 32-fold, TPGS 14 °C and 4-fold), raised water uptake at 95% RH from 44 to 49% (SDS, Span 80), and partitioned into ATZ droplets from 0% (vinylpyrrolidone) and 7% (SDS) to 68% (Span 80) correasoto2022b R20, R13, X16, R16, R17. Ritonavir at 30%: the binary dispersion released almost nothing for about 15 min and about 45% of its drug by 90 min (48.5% at 120 min); with any surfactant release began at once, and at 90 min ritonavir release was about 87% with Span 85 and 89% with TPGS (PVPVA about 94–95%), 78% with SDS, 41% with Span 20 and 25% with Tween 80, against about 46% with PEG 3350 indulkar2022 R1, R8, R9, R5, R7, R6, R4. SDS dissolved in the medium did not change release of the binary dispersion indulkar2022 R10. The ternary dispersions hold 28.6 wt% ritonavir indulkar2022 X13. With 10 parts of surfactant per 100 parts of ritonavir and PVPVA, release at 90 min was about 87% (Span 85), 87–97% (Span 20), 50% (Tween 80) and 70% (SDS) at 30%, about 1, 8, 57 and 48–54% at 40%, and about 22% (Tween 80) and 33–39% (SDS) at 50%, against a cited 30% at 30% without surfactant yang2023 R2, R1.

papersystemmethod and conditionsresultids
que2019ledipasvir–PVPVA, five surfactants5 parts per 100, compactsSDS 5 → 30%, poloxamer 407 7.5%; Span 85, Tween 80, TPGS no helpque2019 C12, R6
saboo2021felodipine–PVPVA, TPGS 0–10%compacts, pH 6.8limit 15 / 25 / 35 / 45%saboo2021 R12
saboo202130% binary in 35 µg/mL TPGScompacts≈4.9% polymer, ≈0.4% drug in 60 minsaboo2021 R15
correasoto2022aCPD–PVPVA 40–60%, four surfactantscompacts, 120 minSDS 40 → 50%; TPGS, Tween 80 slower; CTAB drug losscorreasoto2022a R17, R18, C55
correasoto2022bATZ–PVPVA 10%, eight additives90-min release≈11–106% against ≈2.4%; gains 4–35-foldcorreasoto2022b R2, R20
correasoto2022bATZ 15, 20%90-min releaselimit 10% (SDS, CTAB), 15% (Span 80)correasoto2022b R4, C12
indulkar2022ritonavir–PVPVA 30:70 with five surfactants or PEG 3350 (5 parts per 100)compacts, pH 6.8, 37 °C, 90 minRTV ≈87 (Span 85), ≈89 (TPGS), ≈78 (SDS), ≈41 (Span 20), ≈25% (Tween 80); binary ≈45%, PEG 3350 ≈46%indulkar2022 R1, R4, R5, R6, R7, R8, R9
indulkar2022binary 30:70 in medium with 50 µg/mL SDScompactsrelease unchangedindulkar2022 R10
moseson2022b (ASD process)bicalutamide–PVPVA 30% with SDS or TPGSpowdersSDS congruent; TPGS incongruentmoseson2022b R9, R13
yang2022b (Physical stability)ritonavir–PVPVA films with four surfactantsO-PTIRSDS in the polymer-rich phase, Spans in drug-rich domainsyang2022b C61
yang2023ritonavir–PVPVA 30, 40, 50% + 10 parts of four surfactantscompacts, 90 min30%: ≈50–97%; 40%: ≈1–8% (Spans), ≈48–57% (SDS, Tween 80); 50%: ≈22–39%yang2023 R2

Figure

Fig. 5 of saboo2021: limit of congruency of felodipine–PVPVA against TPGS level
Fig. 5 · saboo2021limit of congruency of felodipine–PVPVA against TPGS level

Bars of 15, 25, 35 and 45% at 0, 2, 5 and 10% TPGS; each bar is the highest loading tested that still released congruently saboo2021 R12, X2.

Fig. 12 of correasoto2022b: release enhancement of 10% atazanavir dispersions against additive molecular weight
Fig. 12 · correasoto2022brelease enhancement of 10% atazanavir dispersions against additive molecular weight

The five additives below about 430 g/mol sit at about 24–36; Span 85, Tween 80 and TPGS at about 13, 19.5 and 4 correasoto2022b R21.

Why

Micellar solubilization is ruled out by the authors: 2% TPGS raised the felodipine limit with at most 18 µg/mL TPGS at full release, below the CMC, so micelles play "a negligible role" saboo2021 C33; the ledipasvir media also stayed below the CMC que2019 C51. TPGS in the medium did nothing, "indicating" that the surfactant must be in the dispersion, and the authors place the effect in the hydrated matrix or at the dispersion–solution interface ("suggest") saboo2021 C18, C35, C36. For the mechanism, Saboo and co-workers favour a changed morphology of the separated drug-rich phase (F20) and allow that higher mobility from the lower Tg "may also play a role" saboo2021 C53, C43; Correa Soto and co-workers propose that SDS "may prevent, delay, or change the domain size" of separation in clopidogrel correasoto2022a C58; for atazanavir they "speculate" that the additives act as plasticizers that raise polymer-chain mobility, and read the larger gains from small additives as kinetic factors that "appear to be very important", with charge, hydrophilicity and affinity for the drug making little difference correasoto2022b C40, C47, C52, C45, C50. SDS also nearly doubled the dissolution rate of neat PVPVA (F15) correasoto2022b R22. (synthesis: no surfactant worked for every drug, and the dry Tg depression did not rank the additives, so the papers give candidate mechanisms that each fit part of the data; the effective additive has to be found for each drug correasoto2022b X16; saboo2021 X15.) Indulkar and co-workers (2022) see the ritonavir outcome as "a balance" between dissolution rate and the rate and extent of phase transformation: SDS "perhaps" outruns separation through faster-dissolving SDS–PVPVA complexes but then crystallizes the drug (F19), Span 85 and TPGS "can potentially" change the kinetics or morphology of separation without a faster polymer, and Tween 80 and Span 20 "may" only improve the initial wetting; no correlation with HLB or charge was found indulkar2022 C59, C33, C35, C44, C64. Their SDS-in-medium control argues against a wetting effect, so the role of wetting stays unresolved indulkar2022 C13, X8. Yang and co-workers propose that preventing or disrupting a continuous drug-rich layer is the most critical surfactant effect, SDS by widening the drug–polymer–water miscible region and the Spans by plasticizing the drug-rich phase (F31) yang2023 C37, C9, C11.

Conditions and limits

PVPVA, rotary-evaporated dispersions, compacts in pH 6.8 phosphate at 37 °C; 5 g additive per 100 g of drug and polymer, TPGS as a share of the polymer portion correasoto2022b P3; saboo2021 P4. Each new limit is the last passing loading, release at it was about half as fast in the felodipine series, and the ATZ limits rest on 90-min release with the rate data in an unavailable SI saboo2021 X2, X3; correasoto2022b X11. TPGS was only about half released at 60 min, so even the nominally above-CMC case stayed below the CMC in the bulk saboo2021 X14. No storage stability or in vivo data saboo2021 C54; correasoto2022b C53, C54. The ritonavir series tested one loading and one surfactant level, so it shows that the surfactant restored release above the limit but not a new limit indulkar2022 A1, P1.

Counterexamples and conflicts

The atazanavir authors note that the same plasticization may raise crystallization on storage, and cite Span 20 and SDS improving ritonavir release while inducing crystallization correasoto2022b C53, R30. In the ASD dissolution chapter SDS and polysorbate 80 promoted crystallization of celecoxib from HPMCAS particles (Supersaturation from ASD dissolution F14) chen2015a C6, and in the crystallization chapter TPGS and Tween 80 far below their CMC doubled ritonavir crystal growth and SDS cut the inhibition of atazanavir nucleation by PVPVA (Crystallization from solution F18, F38) ilevbare2012a R17. TPGS made bicalutamide release incongruent in an ASD process study moseson2022b R13. For ritonavir SDS released fastest but stopped near 80% because crystals formed on the tablet (F19), Tween 80 and Span 20 removed the lag but released no more drug than the binary dispersion, and Span 20 induced needle crystals in solution; the abstract's claim that every surfactant improved release holds only for the lag indulkar2022 R5, R15, R6, R7, R14, X3. In 2023 plasticizers that are not surfactants raised the atazanavir limit to 25% and the ledipasvir limit to 15–20%, more than any surfactant did for atazanavir, so surface activity is not needed for the gain (F26) correasoto2023 R1, R11; correasoto2022b C12. At 5 parts per 100, Span 20 and Tween 80 released ritonavir only to about 40% and 25–28% at 30% in the 2022 study, at 10 parts about 87–97% and 50% in 2023, so the surfactant level matters as well as the surfactant indulkar2022 R6, R7; yang2023 R2. The 2023 paper cites the ledipasvir gain with SDS as 7.5 → 30%, against the 5 → 30% read from the 2019 study in F13 yang2023 R27.

Transfer check

At the first failing loading of the binary dispersion, co-process 2–10% of SDS, a sorbitan ester and TPGS into the dispersion, dissolve compacts with drug and polymer assayed for 60–90 min and raise the loading in 5% steps until congruency fails saboo2021 R12; correasoto2022b R4. Size the released droplets and check crystallization at 37 °C and on storage before adopting the surfactant, and expect slower release at the new limit correasoto2022a R19; saboo2021 X3; correasoto2022b C53. Judge a surfactant by the extent released at 60–90 min and by the tablet surface, not by the removal of a lag phase indulkar2022 R6, R7, X3.

History

Que and co-workers (2019) first raised a limit with a surfactant (F13) que2019 C56. Saboo and co-workers (2021) showed the gain scaling with TPGS level and excluded micelles and dissolved TPGS saboo2021 C16, C33, C18. Correa Soto and co-workers (2022) found only SDS effective for clopidogrel and, for atazanavir, gains in all eight additives with size as the best predictor correasoto2022a C55; correasoto2022b C47. Indulkar and co-workers (2022) built five surfactants into ritonavir–PVPVA above its limit and found that each acts on release rate, phase separation, crystallization and droplet size, Span 85 and TPGS restoring near-complete release, which adds ritonavir to the title indulkar2022 C51, C58; Correa Soto and co-workers (2023) raised the limits of high-Tg drugs with plasticizers that are not surfactants (F26) correasoto2023 C28. Yang and co-workers (2023) imaged the interface of the ritonavir system with four surfactants and measured how each changed the water needed for separation and the Tg of the drug-rich phase (F31) yang2023 C1, R21, R22.

F22

Topic 5Formulation levers near the limit6 of 11

Amorphous salts of lumefantrine raised its Tg and storage stability but lowered the loading with good release from PVPVA.

The onset Tg of amorphous lumefantrine rose from 19.7 °C to about 28–42 °C with carboxylate counterions, about 70–85 °C with sulfonates, about 96 °C (HCl) and about 101 °C (sulfate) hiew2022b R2. In PVPVA compacts at 37 °C good release reached 35% for the free base but only 20–25% for the carboxylates, 10% for the sulfonates, 15% for HCl and 2% for the sulfate hiew2022b R20, R10. The neat HCl and sulfate salts did not crystallize for at least 16 weeks at 40 °C/75% RH, whereas the carboxylate-salt dispersions crystallized within a week hiew2022b R7, R8.

moderateModerate: nine drug forms at several loadings in triplicate, but the limits are last-good points of a coarse grid read from drug release only, Tg goes with counterion class, and the mechanism is untested hiew2022b K2, K3, X7, X6, X9, X20.

low-Tg formshigh-Tg saltsfree baseonset Tg 19.7 °C35 (highest tested)carboxylate salts≈28–42 °C20–25sulfonate salts≈70–85 °C10HCl salt≈96 °C15sulfate salt≈101 °C20510152025303540highest loading with good release in PVPVA, %

Release capacity fell as the salt Tg rose, though HCl did better than the sulfonates. hiew2022b R2, R20, R10

Good release to 20–35% in PVPVA
free basecarboxylate salts
No crystals for at least 16 weeks (neat)
HCl saltsulfate salt

hiew2022b R20, R7, R8

For your drug

  1. Before choosing a counterion for a PVPVA dispersion, measure the Tg of the amorphous salt: above about 70 °C expect good release only to 2–15%, and dissolve compacts at the intended loading with the polymer assayed.
  2. Test the chosen form for crystallization in open-dish storage at 40 °C/75% RH at that loading.

hiew2022b R20, R2, R8

How it works and key numbers
  1. In PVPVA, release "should ideally" be polymer-controlled: if drug and polymer separate in the gel layer, both still leave at the polymer's rate as long as the drug cannot form a continuous barrier hiew2022b C26, C46.
  2. Separation needs mobility; most neat salts took up less than 2% water at 95% RH, so a high-Tg salt is plasticized much less than the hydrated polymer hiew2022b R4, C47.
  3. This Tg asymmetry can arrest separation, a "potential explanation" supported by the stopped release at 10 °C and by the homogeneous sulfate film hiew2022b C47, C48, R16, R19.
  4. As Tg rises, any separation becomes "increasingly detrimental" because the drug-enriched phase needs more water to reach v_p^{*}; PVPVA itself needs at least 11% water at 37 °C hiew2022b C49, E1, R21.
  5. For stability the drug or salt Tg "appears to be an important predictor": the low-Tg free base was "predisposed" to water-induced separation and then crystallization hiew2022b C35, C36, C37.
19.7 → ≈101 °Conset Tg of amorphous lumefantrine, free base to sulfate salthiew2022b R2
35 → 2%highest loading with good release in PVPVA, free base to sulfate salthiew2022b R20
at least 16 weeks against under 1 weektime to crystals at 40 °C/75% RH: neat HCl and sulfate salts against carboxylate-salt dispersionshiew2022b R7, R8
Evidence: data, conditions and papers

Finding F22. Making amorphous salts of low-Tg lumefantrine raised its Tg from about 20 °C to as much as 101 °C and delayed crystallization in storage, but lowered the highest loading with good release from PVPVA from 35% to 10–15% for sulfonate and HCl salts and 2% for the sulfate, a trade-off between stability and release

In short. The onset Tg of amorphous lumefantrine rose from 19.7 °C to about 28–42 °C with carboxylate counterions, about 70–85 °C with sulfonates, about 96 °C (HCl) and about 101 °C (sulfate) hiew2022b R2. In PVPVA compacts at 37 °C good release reached 35% for the free base, 20–25% for the carboxylate salts, 10% for the sulfonates, 15% for HCl and 2% for the sulfate, and at the next loading tested release lagged or nearly stopped hiew2022b R20, R10. The neat HCl and sulfate salts did not crystallize for at least 16 weeks at 40 °C/75% RH and the 10% camsylate dispersion held 12 weeks, whereas the carboxylate-salt dispersions crystallized within a week hiew2022b R7, R8. The authors see a trade-off ("It appears") and advise attention to the salt Tg "at least for PVPVA-based ASDs"; Tg varies with counterion class, and "good release" has no stated criterion hiew2022b C53, C54, X9, X6.

Type. single-system observation (lumefantrine–PVPVA, free base and eight salts) Strength. : nine drug forms at several loadings in triplicate hiew2022b K2: moderate, K3: moderate, but the limits are last-good points of a coarse grid read from drug release only, Tg goes with counterion class, and the mechanism is untested hiew2022b X7, X6, X9, X20.

How it was shown

Hiew and Taylor (2022) made amorphous lumefantrine salts with eight counterions and PVPVA dispersions at 2–35%, measured onset Tg by modulated DSC, stored salts and dispersions at 40 °C/75% RH with PXRD, and dissolved compacts in 250 mL pH 6.8 buffer at 37 °C hiew2022b P1, P2, P5, P7, P8.

What the data show

Dispersions of the high-Tg salts kept a Tg of about 101–105.5 °C, near that of PVPVA hiew2022b R3, R2.

systemmethod and conditionsresultids
lumefantrine free base and eight saltsmodulated DSConset Tg 19.7 to ≈101 °Chiew2022b R2
PVPVA dispersions 2–35%compacts, pH 6.8, 37 °Cgood release to 35 / 20–25 / 10 / 15 / 2% (free base / carboxylates / sulfonates / HCl / sulfate)hiew2022b R20, R10
benzoate 30%drug and PVPVApolymer first: ≈20% PVPVA, no drug at 30 minhiew2022b R13
neat salts and dispersions40 °C/75% RH, PXRDHCl, sulfate salts ≥16 weeks; carboxylate dispersions < 1 week; camsylate 10% 12 weeks; besylate 10% 3 dayshiew2022b R7, R8
free base, benzoate, sulfate filmshigh RH, confocalseparated, separated, homogeneoushiew2022b R19
Fig. 13 of hiew2022b: highest loading with good release against the onset Tg of the neat drug form
Fig. 13 · hiew2022bhighest loading with good release against the onset Tg of the neat drug form

The free base (about 20 °C) sits at 35%, the sulfate (about 101 °C) at 2%; each point is the last good loading tested, so the limits are intervals hiew2022b R20, X7.

Why

The authors argue that separated drug and polymer both leave at the polymer's rate as long as the drug cannot form a continuous barrier hiew2022b C46. Separation needs mobility: the neat salts take up far less water than PVPVA, so a high-Tg salt is plasticized much less than the hydrated polymer, and the Tg asymmetry can arrest separation, a "potential explanation" supported by the 10 °C result and the homogeneous sulfate film hiew2022b C47, C48. (synthesis: this route, a glassy drug phase that cannot separate, runs opposite to the barrier argument of F8, in which separation causes the failure; both rest on films, not on the dissolving compact.)

Limits and transfer

Each limit is the last good loading on a coarse grid, read from drug release alone hiew2022b X7, X6. The ranking is not monotonic, HCl (about 96 °C) releasing to 15% where the sulfonates stopped at 10%, and Tg is confounded with counterion class hiew2022b X8, X9. Measure the Tg of the amorphous salt before choosing a counterion for a PVPVA dispersion: above about 70 °C expect good release only to 2–15%; test the chosen form at 40 °C/75% RH, since low-Tg carboxylate salts crystallized within a week hiew2022b R20, R2, R8.

How it was shown

Hiew and Taylor (2022) reacted lumefantrine (pKa 8.73, log P 8.34, no available hydrogen-bond donor) with benzoic acid, PEG 250 diacid (1:1 and 2:1), benzene-, toluene- and camphorsulfonic acid, HCl and sulfuric acid (2:1) by solvent evaporation, made PVPVA dispersions at 2–35%, measured onset Tg by modulated DSC (n = 2) and water uptake by DVS, stored salts and dispersions in open dishes at 40 °C/75% RH with PXRD up to 32 weeks, and dissolved compacts in Wood's apparatus in 250 mL pH 6.8 buffer at 37 °C (two at 10 °C), with PVPVA assayed for two lag-phase formulations, SEM of dissolving surfaces, FTIR of films and confocal imaging of films at high RH hiew2022b M1, P1, P2, P5, P13, P7, P8, P9, P11, P10, P16, A2, A4.

What the data show

Dispersions of the free base and carboxylate salts lost about 5 °C of Tg per 5% loading (free base about 99 °C at 5% to 73 °C at 35%), whereas dispersions of the high-Tg salts stayed at about 101–105.5 °C, near PVPVA (102.9 °C) hiew2022b R3, R2. Free-base compacts released about 63–84% by 25–30 min at every loading to 35%, at about 3.15–3.9 mg/min/cm² hiew2022b R10, R12. Benzoate released about 60% at 20%, about 14% at 25% and about 10.5% at 30% after a lag; the sulfonates released about 58–81% at 10% and about 0–9% at 15%; HCl about 78–93% at 5–15%, about 26% at 20% and none at 25%; the sulfate about 94% at 2% and about 3.5% (about 0.1 mg) at 5% hiew2022b R10, R11. Good releasers had rates of about 1.9–4.5 and failing ones about 0.10–0.84 mg/min/cm² hiew2022b R12. In the benzoate 30% compact about 20% of the PVPVA but no drug had left at 30 min and about 50% against 8.5% at 90 min hiew2022b R13. Cooling to 10 °C stopped release of the benzoate 20% and besylate 10% dispersions (F18) hiew2022b R16. FTIR showed no shift of the PVPVA carbonyls except with the tosylate hiew2022b R18. Most neat salts took up less than 2% water at 95% RH (sulfate 3.3%, PEG 250 diacid 1:1 6.6%), the dispersions 35–55%, and PVPVA needs at least 11% water to start disentangling at 37 °C (v_p^{*} = 0.89) hiew2022b R4, R5, R21. In storage the neat benzoate, PEG 250 diacid and besylate salts crystallized within 4 weeks, the camsylate after 32 weeks, and the HCl and sulfate salts not within 16 weeks; carboxylate-salt dispersions crystallized within a week, besylate dispersions after 3 days (10%) and 2 weeks (15%) with disproportionation, the camsylate dispersion at 10% after 12 weeks hiew2022b R7, R8. FTIR of the salt films showed the PVPVA carbonyl peaks (1736 and 1684 cm⁻¹) unshifted at every loading for all salts except the tosylate, which the authors read as at most a "minor extent" of interaction hiew2022b R18, C24.

papersystemmethod and conditionsresultids
hiew2022blumefantrine free base and eight saltsmodulated DSConset Tg 19.7 to ≈101 °Chiew2022b R2
hiew2022bPVPVA dispersions 2–35%compacts, pH 6.8, 37 °Cgood release to 35 / 20–25 / 10 / 15 / 2% (free base / carboxylates / sulfonates / HCl / sulfate)hiew2022b R20, R10
hiew2022bbenzoate 30%drug and PVPVApolymer first: ≈20% PVPVA, no drug at 30 minhiew2022b R13
hiew2022bneat salts and dispersions40 °C/75% RH, PXRDHCl, sulfate salts ≥16 weeks; carboxylate dispersions < 1 week; camsylate 10% 12 weeks; besylate 10% 3 dayshiew2022b R7, R8
hiew2022bfree base, benzoate, sulfate filmshigh RH, confocalseparated, separated, homogeneoushiew2022b R19
hiew2022a (Miscibility)lumefantrine free base–PVPVAcompactscongruent to 35%; 40% failshiew2022a C31, X17
duong2022a (ASD dissolution)delamanid sulfonate salts with HPMCPpH 6.5Tg raised; ≈95–97 µg/mL of 100 at 25% against ≈20 for the free baseduong2022a R20, R26

Figure

Fig. 13 of hiew2022b: highest loading with good release against the onset Tg of the neat drug form
Fig. 13 · hiew2022bhighest loading with good release against the onset Tg of the neat drug form

The free base (about 20 °C) sits at 35%, the sulfate (about 101 °C) at 2%; each point is the last good loading tested, so the limits are intervals hiew2022b R20, X7.

Fig. 7 of hiew2022b: drug release profiles of all lumefantrine dispersions at 37 °C
Fig. 7 · hiew2022bdrug release profiles of all lumefantrine dispersions at 37 °C

Panel a releases at every loading; panels b–i fail one step above 20–25% (carboxylates), 10% (sulfonates), 15% (HCl) and 2% (sulfate) hiew2022b R10.

Why

The authors start from polymer-controlled release, which "should ideally" govern dispersions, and argue that if drug and polymer separate in the gel layer, both leave at the polymer's rate as long as the drug cannot form a continuous barrier hiew2022b C26, C46. Separation needs mobility; the neat salts take up far less water than PVPVA, so a high-Tg salt is plasticized much less than the hydrated polymer, and the Tg asymmetry can arrest a thermodynamically favoured separation, a "potential explanation" supported by the 10 °C result and by the absence of separation in the sulfate film hiew2022b C47, C48. As Tg rises, any separation becomes "increasingly detrimental" because the drug-enriched phase needs more water to reach v_p^{*} hiew2022b C49, E1. By the water rule every dispersion's wet Tg would lie below 37 °C, so wet Tg alone is "difficult to rationalize" as the cause hiew2022b C44. For stability, the lack of specific interactions and the high log P "predisposed" the free base to water-induced separation, after which the low Tg raised the crystallization risk, and drug or salt Tg "appears to be an important predictor" of stability hiew2022b C35, C36, C37. (synthesis: the salt series agrees with the Tg trend of F18, but its proposed route, a glassy drug phase that cannot separate, runs opposite to the barrier argument of F8, in which separation causes the failure; both rest on films, not on the dissolving compact.)

Conditions and limits

One drug and PVPVA; drug-only release except two lag-phase formulations; the basis of the loading (free base or salt mass) is not stated and samples were not filtered, so "released" means total drug in the medium hiew2022b X6, X14, X15. Each limit is the last good loading on a grid of 5% steps (2 and 5% for the sulfate), and the free-base value is the highest loading tested hiew2022b X7. The 57% effective loading stated for the benzoate lag phase cannot be reproduced and is about 35–38% by the stated polymer loss hiew2022b X3.

Counterexamples and conflicts

The ranking is not monotonic: HCl (about 96 °C) released to 15% where the sulfonates (about 70–85 °C) stopped at 10%, and the besylate dispersion crystallized fastest of all despite a Tg of about 70 °C hiew2022b X8, X11. Tg is confounded with counterion class, hygroscopicity and disproportionation hiew2022b X9. In the ASD dissolution chapter salt formation raised the Tg of delamanid and gave near-complete release at 25% from HPMCP where free-base dispersions left crystals (Supersaturation from ASD dissolution F23) duong2022a C56, C67 (synthesis: there the salt removed residual crystallinity of a fast crystallizer in an enteric polymer; here it raised the Tg of a slow-releasing drug in a neutral polymer).

Transfer check

Before choosing a counterion for a PVPVA dispersion, measure the Tg of the amorphous salt: above about 70 °C expect good release only to 2–15%, and dissolve compacts at the intended loading with the polymer assayed hiew2022b R20, R2. Test the chosen form for crystallization in open-dish storage at 40 °C/75% RH at that loading, since low-Tg carboxylate salts released to 20–25% but crystallized within a week hiew2022b R8, R20.

History

Amorphous salts with raised Tg (sodium indomethacin, propranolol salts; cited) and a polymer-dependent stability of free-base lumefantrine dispersions came from earlier work hiew2022b C6, C3. In the ASD dissolution chapter delamanid salts were formed in the dispersion to overcome crystallization (Supersaturation from ASD dissolution F23). Hiew and Taylor (2022) were the first in this subcategory to vary the Tg of one drug by salt formation and to show the stability–release trade-off hiew2022b C55, C53.

Other chapterscontradicts B F23
F24

Topic 5Formulation levers near the limit7 of 11

Pre-ionizing an enteric polymer as a salt sped its dissolution about threefold and removed most of its dependence on the buffer.

HP-50 neutralized with sodium or one of eight amines dissolved at about 2.35–3.09 mg/min/cm² against 0.92 for HP-50 in 50 mM pH 6.8 phosphate, whatever the counterion qi2022 R3, R10, C18. In 5 mM phosphate the sodium salt kept about 2.45 while HP-50 fell to 0.14 qi2022 R12. Dispersions of 20% miconazole on the sodium and triethylamine salts released about 89.5 and 83.7% of the drug by 60 min, against about 8.6% on HP-50 qi2022 R14.

moderateModerate to strong for the effects, three-, six- and 12–14-fold in triplicate; weak to moderate for the mechanism, inferred from rates; one drug at one loading qi2022 K2, K3, K5, K6, K7, C41.

HP-50sodium salt of HP-5029 mM/ΔpH50 mM phosphate0.922.803 mM/ΔpH5 mM phosphate0.142.4500.511.522.53polymer dissolution rate, mg/min/cm²

The salt barely changes with buffer capacity; HP-50 falls about sixfold. qi2022 R12

20% miconazole dispersions: drug released by 60 min, %on HP-50polymer ran ahead≈8.6on the sodium salt≈89.5on the triethylamine salt≈83.7

With the salts the polymer left alongside the drug. qi2022 R14

For your drug

  1. To speed release from an enteric-polymer dispersion of a lipophilic drug, neutralize the polymer's acid groups with about one equivalent of a pharmaceutically acceptable base before making the dispersion, and compare with the protonated polymer in 5 and 50 mM pH 6.8 phosphate with drug and polymer assayed.
  2. Then test loadings above 20%, release after an acidic stage and water uptake on humid storage, none of which was covered.

qi2022 P1, R12, R14, C41, R11

How it works and key numbers
  1. A pre-ionized polymer generates no protons at its surface, so its solubility there is not suppressed; it hydrates faster and more, giving a more mobile gel layer at a rate that does not depend on the buffer ("is attributed to") qi2022 C42, C31.
  2. The triethylamine salt of HPMCAS had a gel pH of 6.7, close to the medium, and dissolved at about 1.62 against 0.89 mg/min/cm² for HPMCAS (F23) bapat2023 R16, R15, C41.
  3. The rate rose most steeply between 80 and 100% neutralization, "perhaps explained" by a minimum ionization that hydrophobic ionizable polymers need, estimated at about 83% for HP-50 qi2022 R13, C36, R19.
  4. In the dispersion the higher hydration of the salt "likely" offsets the lipophilic drug's lowering of the water fraction in the gel layer (F15) qi2022 C40.
  5. Water uptake did not rank the salts: the sodium salt took up the most water (about 42.4%) without dissolving faster than the amine salts qi2022 R11, X17.
  6. A drug cation that pairs with the polymer's acid groups works the other way: bedaquiline tied up HPMCAS carboxylates as an insoluble complex (F32) kaur2025 R20, C25.
≈2.35–3.09 against 0.92 mg/min/cm²nine HP-50 salts against HP-50, 50 mM pH 6.8 phosphateqi2022 R10
2.80 → 2.45 against 0.92 → 0.14sodium salt and HP-50 from 29 to 3 mM/ΔpHqi2022 R12
≈89.5 against ≈8.6%miconazole released by 60 min from 20% dispersions on the sodium salt and on HP-50qi2022 R14
Evidence: data, conditions and papers

Finding F24. Pre-ionizing an enteric polymer as a salt removed most of its dependence on the medium and sped release: nine HP-50 salts dissolved about three times faster than HP-50 whatever the counterion, the sodium salt kept its rate at a tenth of the buffer capacity, and 20% miconazole dispersions on two salts released about 84–90% of the drug in 60 min against about 9% on HP-50

In short. HP-50 neutralized with sodium or one of eight amines (91–95% sodium content for the sodium salt) dissolved at about 2.35–3.09 mg/min/cm² against 0.92 for HP-50 in 50 mM pH 6.8 phosphate, with little effect of counterion size, pKa or lipophilicity qi2022 R3, R10, C18. In 5 mM phosphate the sodium salt kept about 2.45 while HP-50 fell to 0.14 qi2022 R12. The rate rose with the share of acid groups neutralized, most steeply between 80 and 100% qi2022 R13. At 20% miconazole, dispersions on the sodium and triethylamine salts released about 89.5 and 83.7% of the drug by 60 min with the polymer alongside, against about 8.6% from the HP-50 dispersion, whose polymer ran ahead; normalized drug rates were about 3.15, 2.70 and 0.22 mg/min/cm² qi2022 R14, R15. The triethylamine salt of HPMCAS released about 1.62 against 0.89 mg/min/cm² for HPMCAS, with a gel pH of 6.7 close to the medium bapat2023 R16, R15. The authors call salt formation "a successful strategy" and see a "potential" to raise drug loading, which was tested at one loading of one drug qi2022 C6, C39, C41.

Type. single-system observation (HP-50 and nine of its salts, one drug), with a second polymer salt (HPMCAS-TEA) Strength. to strong: three-, six- and 12–14-fold effects in triplicate qi2022 K2: strong, K3: moderate, K5: moderate to strong; weak to moderate for the mechanism, inferred from rates qi2022 K6: weak to moderate, K7: weak.

How it was shown

Qi and Taylor (2022) added 1.61 mmol of base per gram of HP-50 (1.0 equivalent of its phthalic acid) to make a sodium salt and eight amine or ammonium salts, plus partial BIS-TRIS salts, and dissolved compacts as in F23 qi2022 P1, M2, P10. They dissolved 20% miconazole dispersions on HP-50, the sodium salt and the triethylamine salt with drug and polymer assayed qi2022 P2, P11, P12, A6. Bapat and co-workers (2023) made the triethylamine salt of HPMCAS-MF bapat2023 P4.

What the data show

The sodium salt held 3.38–3.52 wt% sodium, read as 91–95% of the acid groups, and was about 99% dissolved at 80 min against about 39% of HP-50 qi2022 R3, R9.

systemconditionsresultids
HP-50 and nine saltscompacts, 50 mM pH 6.8 phosphate, 37 °C≈2.35–3.09 against ≈0.92 mg/min/cm²qi2022 R10
HP-50-Na; HP-5029 and 3 mM/ΔpH≈2.80 → 2.45; ≈0.92 → 0.14qi2022 R12
BIS-TRIS salts, 20–100 mol% basesame≈1.22 → 2.93; largest step 80 → 100%qi2022 R13
HP-50-Na, amine salts, HP-50100% RH, 37 °C, 96 hwater ≈42.4 / 24.6–30.1 / 9.7%qi2022 R11
miconazole 20% on HP-50, HP-50-Na, triethylamine saltcompacts, drug and polymerdrug ≈8.6 / 89.5 / 83.7% at 60 min; ≈0.22 / 3.15 / 2.70 mg/min/cm²qi2022 R14, R15
HPMCAS-TEA against HPMCAS-MFcompacts, pH 6.8 phosphate≈1.62 against ≈0.89; gel pH 6.7 against 6.0bapat2023 R16, R15
Fig. 8 of qi2022: normalized dissolution rate of HP-50-Na and HP-50 at two buffer capacities
Fig. 8 · qi2022normalized dissolution rate of HP-50-Na and HP-50 at two buffer capacities

The red sodium-salt bars barely change between 29 and 3 mM/ΔpH; the blue HP-50 bars fall about sixfold qi2022 R12.

Why

The authors' reading is that a pre-ionized polymer generates no protons at its surface, so its solubility there is not suppressed and it hydrates faster and more, at a rate that does not depend on the buffer ("is attributed to") qi2022 C42, C31. They relate the steep step between 80 and 100% neutralization to a critical ionization of about 83% estimated for HP-50 (cited) ("may explain") qi2022 C36, R19. The HPMCAS salt's gel pH close to the bulk supports the interfacial-pH picture of F23 bapat2023 C41.

Limits and transfer

One drug was tested at 20% loading, without a gastric stage, biorelevant medium or storage test, and water uptake did not rank the salts' rates qi2022 A6, C41, X17. Neutralize the polymer's acid groups with about one equivalent of a pharmaceutically acceptable base before making the dispersion, compare release with the protonated polymer in 5 and 50 mM pH 6.8 phosphate with drug and polymer assayed, and then test higher loadings, an acidic stage and humid storage qi2022 P1, R12, R14, C41, R11.

How it was shown

Qi and Taylor (2022) added 1.61 mmol of base per gram of HP-50 (1.0 equivalent of its phthalic acid) in methanol–dichloromethane and dried the solution, making a sodium salt and eight amine or ammonium salts whose counterions span calculated pKa 6.5–10.8, log P −4.7 to 2.1 and van der Waals volume 90–300 ų, plus BIS-TRIS salts neutralized to 20, 50, 80, 90 and 95 mol% qi2022 P1, M2, M3, M4, M5, M6, M7, M8, M9, M10. They confirmed ionization by elemental analysis, NMR and FTIR, measured water uptake at 100% RH and 37 °C for 96 h and Tg by DSC and DMA, and dissolved compacts as in F23 qi2022 P8, P6, P7, P3, P4, P5, P10. They made 20% miconazole dispersions (a lipophilic weak base, pKa 6.5, amorphous solubility about 5 µg/mL, cited) on HP-50, the sodium salt and the triethylamine salt by rotary evaporation and dissolved them with drug (HPLC) and polymer assayed qi2022 P2, M11, P11, P12, A6. Bapat and co-workers (2023) made the triethylamine salt of HPMCAS-MF (2.38 mmol per 2 g) and compared its rate and gel pH with HPMCAS bapat2023 P4, R15, R16.

What the data show

HP-50-Na held 3.38–3.52 wt% sodium, read as 91–95% of the acid groups, and showed a new carboxylate band near 1600 cm⁻¹ qi2022 R3, R6. At 100% RH it took up about 42.4% water in 96 h, three amine salts about 24.6–30.1% and HP-50 about 9.7% qi2022 R11. The salts dissolved at about 3.09 (tetrabutylammonium), 2.93 (BIS-TRIS), 2.87, 2.86, 2.85, 2.80 (sodium), 2.53 (triethylamine), 2.39 and 2.35 mg/min/cm² against about 0.92 for HP-50, and the sodium salt was about 99% dissolved at 80 min against about 39% of HP-50 qi2022 R10, R9. From 29 to 3 mM/ΔpH the sodium salt went from about 2.80 to 2.45 mg/min/cm² (overlapping SD bars) and HP-50 from about 0.92 to 0.14 qi2022 R12, X6. The partial BIS-TRIS salts gave about 1.22, 1.52, 1.68, 2.10, 2.23 and 2.93 mg/min/cm² at 20, 50, 80, 90, 95 and 100 mol% base, where the percentages are base added, not measured ionization qi2022 R13, X9. The salts had DSC onset Tgs of 54.9–92.1 °C against 127.1 °C for HP-50 qi2022 R8. Miconazole dispersions: HP-50 released about 8.6% of the drug and 23.3% of the polymer by 60 min (11.7 and 42.2% by 120 min); the sodium salt about 89.5% of the drug and 106.7% of the polymer by 60 min, levelling at about 91%, with a turbid medium above the amorphous solubility; the triethylamine salt about 83.7% and 93.4%, levelling at about 87% qi2022 R14, C22. The normalized drug rates were about 0.22, 3.15 and 2.70 mg/min/cm², per unit mass of dispersion rather than of drug qi2022 R15, X5. HPMCAS-TEA: gel pH 6.7 ± 0.1 and about 1.62 mg/min/cm² in pH 6.8 phosphate, rising to about 4.78 at 700 rpm, against 0.89–1.01 for HPMCAS at 100 rpm bapat2023 R15, R16, R18. (synthesis: 3.15/0.22 ≈ 14 and 2.70/0.22 ≈ 12 for the drug, 2.35/0.92 ≈ 2.6 to 3.09/0.92 ≈ 3.4 for the neat salts, 1.62/0.89 ≈ 1.8 for HPMCAS-TEA.)

papersystemmethod and conditionsresultids
qi2022HP-50 and nine saltscompacts, 50 mM pH 6.8 phosphate, 37 °C≈2.35–3.09 against ≈0.92 mg/min/cm²qi2022 R10
qi2022HP-50-Na; HP-5029 and 3 mM/ΔpH≈2.80 → 2.45; ≈0.92 → 0.14qi2022 R12
qi2022BIS-TRIS salts, 20–100 mol% basesame≈1.22 → 2.93; largest step 80 → 100%qi2022 R13
qi2022HP-50-Na, amine salts, HP-50100% RH, 37 °C, 96 hwater ≈42.4 / 24.6–30.1 / 9.7%qi2022 R11
qi2022miconazole 20% on HP-50, HP-50-Na, PTEAcompacts, drug and polymerdrug ≈8.6 / 89.5 / 83.7% at 60 min; ≈0.22 / 3.15 / 2.70 mg/min/cm²qi2022 R14, R15
bapat2023HPMCAS-TEA against HPMCAS-MFcompacts, pH 6.8 phosphate≈1.62 against ≈0.89; gel pH 6.7 against 6.0bapat2023 R16, R15

Figure

Fig. 8 of qi2022: normalized dissolution rate of HP-50-Na and HP-50 at two buffer capacities
Fig. 8 · qi2022normalized dissolution rate of HP-50-Na and HP-50 at two buffer capacities

The red sodium-salt bars barely change between 29 and 3 mM/ΔpH; the blue HP-50 bars fall about sixfold qi2022 R12.

Fig. 10 of qi2022: drug and polymer release from 20% miconazole dispersions on HP-50 (A), HP-50-Na (B) and the triethylamine salt (C)
Fig. 10 · qi2022drug and polymer release from 20% miconazole dispersions on HP-50 (A), HP-50-Na (B) and the triethylamine salt (C)

Panel A: the polymer runs ahead and the drug stays near 10%; panels B and C: drug near 85–92% with the polymer slightly ahead and above 100%, which points to an assay offset qi2022 R14, X4.

Why

The authors' reading is that a pre-ionized polymer generates no protons at its surface, so its solubility there is not suppressed and it hydrates faster and more, giving a more mobile gel layer from which chains are released, at a rate that does not depend on the buffer ("is attributed to"); they take the HP-50 against HP-50-Na comparisons to "confirm" the role of proton generation and removal qi2022 C42, C31. Higher hydration is "likely a key contributor", although the sodium salt took up the most water without dissolving faster than the amine salts, which they call "somewhat surprising" qi2022 C35, X17. The steep step between 80 and 100% neutralization is "perhaps explained" by a minimum ionization that hydrophobic ionizable polymers need, and the critical ionization of about 83% estimated for HP-50 (cited) "may explain" it qi2022 C36, R19. In the dispersion the higher hydration of the salt "likely" offsets the lipophilic drug's lowering of the water fraction in the gel layer, which chain disentanglement needs (F15) qi2022 C40. For HPMCAS the salt's gel pH close to the bulk supports the interfacial-pH picture of F23 bapat2023 C41. (synthesis: the polymer salt acts on the polymer, not on the drug, so it raises the ceiling of polymer-controlled release of F2 and turned an incongruent 20% miconazole dispersion into a nearly congruent one; in F22 a salt of the drug raised its Tg and lowered release from PVPVA.) (synthesis: a drug that pairs with the polymer's acid groups works the other way: bedaquiline was already about half protonated in a dry HPMCAS dispersion and tied up the carboxylates as an insoluble complex, so neutralizing the acid groups helps release only with a counterion that leaves the polymer soluble (F32) kaur2025 R20, C25.)

Conditions and limits

HP-50 salts in 50 and 5 mM pH 6.8 phosphate at 37 °C; one drug at 20% loading, no gastric stage, biorelevant medium or storage test qi2022 A6, C41. "Complete" drug release in the text is about 84–92%, and polymer release above 100% from the salt dispersions points to an assay offset qi2022 X3, X4. The normalized rates are per dispersion mass, the ionization of the partial salts is nominal, and the amorphous state of the dispersions was not verified by diffraction qi2022 X5, X9, X14. The counterion effect of about 25% between salts was not tested statistically qi2022 X7.

Counterexamples and conflicts

Water uptake did not rank the salts' rates, so hydration is at most one contributor qi2022 X17. The counterion changed the Tg of the salt from about 55 to 92 °C (DSC onset) without changing its rate qi2022 R8, R10. The salts take up 25–42% water at 100% RH and the sodium salt dissolves in plain water, so the acid resistance that makes the polymer enteric was not tested qi2022 R11, R16. Drug–polymer salt formation, pursued for physical stability, lowered release of cationic weak bases from HPMCAS, a loss the 2025 grade paper says should "ideally" be balanced against the stability gain (F33) bapat2025a C23.

Transfer check

To speed release from an enteric-polymer dispersion of a lipophilic drug, neutralize the polymer's acid groups with about one equivalent of a pharmaceutically acceptable base before making the dispersion, and compare release with the protonated polymer in 5 and 50 mM pH 6.8 phosphate with drug and polymer assayed qi2022 P1, R12, R14. Then test the loading above 20%, release after an acidic stage and water uptake on humid storage, none of which was covered qi2022 C41, R11.

History

Neutralization had been used for aqueous enteric coatings, and partial neutralization was proposed to speed enteric coating dissolution (cited) qi2022 C37. Qi and Taylor (2022) were the first in the library to pre-ionize an enteric dispersion polymer as a salt qi2022 C44. Bapat and co-workers (2023) used the triethylamine salt of HPMCAS as a control for the gel pH bapat2023 C41. A pretomanid study of the Bioperformance chapter took over base addition at 1:1 to the polymer's acid groups (as listed in the evidence index of this subcategory). The HPMCAS papers of 2024–2025 showed that ion pairs with a lipophilic drug cation, unlike salts with small counterions, make the polymer insoluble (F32) bapat2024 C33; kaur2025 C35.

F26

Topic 5Formulation levers near the limit8 of 11

A few percent of a lipophilic plasticizer raised the limit of congruency of high-Tg drugs in PVPVA three- to fivefold.

With 5 g plasticizer per 100 g of drug and polymer, atazanavir–PVPVA released congruently up to 25% with glycerol tributyrate (GTB) or three citrate esters, against a cited 5% without correasoto2023 R1. Ledipasvir needed 10 g per 100 g, which took its limit to 15–20%, and ritonavir (Tg 50 °C) went only from a cited 25% to 30% correasoto2023 R11, R14, R16. Drug-free PVPVA with 10% w/w GTB or tributyl citrate (TBC) dissolved at about 4.8 and 6.1 against 2.7 mg/min/cm² correasoto2023 R13.

moderateModerate to strong for the gains in limit, three- to fivefold against steps of 2.5–5%; weak to moderate for the mechanism, which was not measured, and the binary limits are cited from earlier papers correasoto2023 K1, K2, K5, X7.

without plasticizer (cited)with GTB or a citrate esteratazanavirTg about 105 °C · 5 g per 100 g525ledipasvirTg about 160 °C · 10 g per 100 g515–20ritonavirTg 50 °C · 5 g per 100 g253005101520253035limit of congruency in PVPVA, %

The gain was largest for the highest-Tg drugs: fivefold, three- to fourfold and 1.2-fold. correasoto2023 R1, R11, R14, R16, M1, M2, M3

Atazanavir–PVPVA limit with 5 g plasticizer per 100 g, %glycerol7.5glycerol diacetate7.5citric acid7.5triacetin10triethyl citrate20GTB25TEAC25TBC25

Tributyl acetylcitrate also gave 25%; the binary limit was 5%. correasoto2023 R1

For your drug

  1. For a high-Tg drug with a PVPVA limit of 5–10%, co-process 5 g (dry Tg near 100 °C) or 10 g (near 160 °C) per 100 g of a citrate ester or GTB, and dissolve compacts with drug and polymer assayed for 120 min in 2.5–5% loading steps, expecting lags near the new limit.
  2. Screen several plasticizers, since neither LogP nor Tg depression picked the best one, and test physical stability before adopting one.

correasoto2023 R1, R11, R4, X14, X15, C46

How it works and key numbers
  1. Below the limit drug release is tied to PVPVA dissolution, which for this glassy, high-molecular-weight polymer under stirring is "most likely" limited by chain disengagement from the gel correasoto2023 C33.
  2. By free-volume theory a low-Tg small molecule separates the chains and raises free volume and mobility; in Devotta's model the highest chain mobility in the gel rises with its fractional free volume, m_{p,\infty} = A_d\, \exp\left(-\frac{B_d}{f_g}\right) correasoto2023 C37, C40, E2.
  3. A plasticizer that raises the free volume of the hydrated gel should therefore speed polymer dissolution and the coupled drug release ("is predicted"), which the authors find "reasonable to suggest" as one mechanism correasoto2023 C41, C39.
  4. Water ingress is not the lever, since water vapour uptake changed little correasoto2023 C34, R21.
  5. Ritonavir, whose mobility is "expected" to limit release less, gained little, "confirming" the hypothesis correasoto2023 C19, C20.
  6. The Tg drops of the 8:1 drug:plasticizer glasses did not rank the gains: triacetin lowered the atazanavir Tg most (43.3 °C) and gave a limit of only 10% correasoto2023 R17, R18, X14.
5 → 25%atazanavir–PVPVA limit with 5 g per 100 g of GTB or a citrate estercorreasoto2023 R1
≈4.8 and 6.1 against 2.7 mg/min/cm²drug-free PVPVA with GTB and with TBC against neat PVPVAcorreasoto2023 R13
5 / 3–4 / 1.2-foldgain in limit for atazanavir, ledipasvir and ritonavircorreasoto2023 R16
Evidence: data, conditions and papers

Finding F26. A few percent of a lipophilic plasticizer that is not a surfactant raised the limit of congruency of high-Tg drugs in PVPVA (atazanavir 5 → 25% with 5 g per 100 g of glycerol tributyrate or citrate esters, ledipasvir 5 → 15–20% with 10 g), against 25 → 30% for lower-Tg ritonavir; the plasticizer also sped neat PVPVA, while Tg depression and water uptake did not rank the gains

In short. With 5 g plasticizer per 100 g of drug and polymer, atazanavir–PVPVA released congruently up to 25% with glycerol tributyrate (GTB), triethyl acetylcitrate (TEAC), tributyl citrate (TBC) or tributyl acetylcitrate (TBAC), 20% with triethyl citrate and only 7.5–10% with glycerol, glycerol diacetate, triacetin or citric acid, against a cited 5% without correasoto2023 R1. Ledipasvir needed 10 g per 100 g, which took the limit to 15% (TEAC, TBC) and 20% (GTB), and ritonavir with GTB or TBC went from a cited 25% to 30% correasoto2023 R11, R14, R16. Drug-free PVPVA with 10% w/w GTB or TBC dissolved at about 4.8 and 6.1 against 2.7 mg/min/cm² correasoto2023 R13. The plasticizers lowered the Tg of 8:1 drug:plasticizer glasses by 30–53 °C and changed water vapour uptake little, and the Tg drops did not rank the limits correasoto2023 R17, R18, C34, X14. The authors find it "reasonable to suggest" faster chain disentanglement in a gel of higher free volume and call plasticizers "a potential new strategy" for high-Tg drugs with a low tendency to crystallize; stability was not tested correasoto2023 C39, C48, X21.

Type. observation in 3 drugs (atazanavir, ledipasvir, ritonavir) with 9 plasticizers in PVPVA Strength. to strong for the gains in limit, three- to fivefold against steps of 2.5–5% correasoto2023 K1: moderate to strong, K2: moderate to strong; weak to moderate for the mechanism, which was not measured, and the binary limits are cited correasoto2023 K5: weak to moderate, X7.

How it was shown

Correa Soto and co-workers (2023) made PVPVA dispersions of atazanavir (ATZ, Tg about 105 °C), ledipasvir (LED, about 160 °C) or ritonavir (RTV, 50 °C) with 5 g (ATZ, RTV) or 10 g (LED) of a plasticizer per 100 g of drug and polymer, and dissolved compacts for 120 min with drug and polymer assayed correasoto2023 P1, P2, M1, M2, M3, P3, P4.

What the data show

At the 25% ATZ limit the plasticized dispersions released at about 2.0–3.1 mg/min/cm² after a lag, at or below neat PVPVA correasoto2023 R7, R4.

systemconditionsresultids
ATZ–PVPVA, nine plasticizers at 5 g per 100 gcompacts, pH 6.8, 37 °C, >80% in 120 minlimit 7.5–25% against 5% (cited)correasoto2023 R1
LED–PVPVA with 10 g TEAC, TBC, GTBsamelimit 15, 15, 20% against 5% (cited)correasoto2023 R11
RTV with 5 g GTB or TBCcompactscomplete at 30%, not at 35% (cited 25%)correasoto2023 R14
8:1 ATZ and LED glassesmodulated DSCTg lowered by 30.4–43.3 and 47.6–53.1 °Ccorreasoto2023 R17, R18
PVPVA with 10% w/w GTB or TBCcompacts≈4.8 and 6.1 against ≈2.7 mg/min/cm²correasoto2023 R13
ATZ 10% with vinylpyrrolidonecompacts, 90 minrelease ≈87% against ≈2.4%; 15% failscorreasoto2022b R2, R4
Fig. 9 of correasoto2023: fold increase of the limit of congruency with TBC or GTB for atazanavir, ledipasvir and ritonavir
Fig. 9 · correasoto2023fold increase of the limit of congruency with TBC or GTB for atazanavir, ledipasvir and ritonavir

Fivefold for ATZ, three- and fourfold for LED, 1.2-fold for RTV; ATZ and RTV at 5 g, LED at 10 g per 100 g, and the binary limits are cited correasoto2023 R16, X7.

Why

Below the limit drug release is tied to PVPVA dissolution, "most likely" limited by chain disengagement from the gel correasoto2023 C33. In Devotta's model (cited) chain mobility rises with the fractional free volume of the gel, m_{p,\infty} = A_d\, \exp\left(-\frac{B_d}{f_g}\right), so a plasticizer that raises it should speed polymer dissolution and the coupled drug release ("is predicted"), which the authors find "reasonable to suggest" as one mechanism correasoto2023 C40, E2, C41, C39. Ritonavir gained little, "confirming" that mobility limits release more for high-Tg drugs correasoto2023 C19, C20. (synthesis: the Tg drops of the 8:1 glasses did not rank the gains, so the plasticizer's effect on the dissolving gel or on the drug-rich phase is what the data leave open correasoto2023 X14, C45.)

Limits and transfer

The binary limits are cited from earlier papers, and no storage or crystallization data were reported correasoto2023 X7, X21. For a high-Tg drug with a PVPVA limit of 5–10%, co-process 5–10 g per 100 g of a citrate ester or GTB, screen several plasticizers and test physical stability correasoto2023 R1, R11, X14, X15, C46.

How it was shown

Correa Soto and co-workers (2023) tested the hypothesis that non-surfactant plasticizers raise the limit of PVPVA dispersions of high-Tg drugs correasoto2023 C8. They made rotary-evaporated dispersions of atazanavir (ATZ, Tg about 105 °C), ledipasvir (LED, about 160 °C) or ritonavir (RTV, 50 °C) with a glycerol series (glycerol, glycerol diacetate, triacetin, GTB; LogP −1.33 to 2.58) or a citric acid series (citric acid, triethyl citrate, TEAC, TBC, TBAC; LogP −1.68 to 3.06), at 5 g (ATZ, RTV) or 10 g (LED) per 100 g of drug and polymer, with drug loading counted on drug and polymer only correasoto2023 P1, P2, M1, M2, M3, M5, M6, M7, M8, M9, M10, M11, M12, M13. They dissolved 100 mg compacts (0.5 cm², 2500 psi) at 100 rpm in 100 mL 50 mM pH 6.8 phosphate at 37 °C for 120 min with drug (HPLC) and PVPVA (SEC) assayed, took normalized rates by R = k/(Sx) (from 30–60 min after a lag), and counted a loading as below the limit if more than 80% of the drug left in 120 min at about the polymer's rate correasoto2023 P3, P4, P6, E1. They measured the Tg of 8:1 drug:plasticizer glasses and of 10% LED dispersions by modulated DSC, water vapour uptake at 95% RH and 37 °C, and the dissolution of drug-free PVPVA with plasticizer correasoto2023 P7, P8, P9, A6.

What the data show

ATZ with 5 g per 100 g: limits of 7.5% (glycerol, glycerol diacetate, citric acid), 10% (triacetin), 20% (triethyl citrate) and 25% (GTB, TEAC, TBC, TBAC), against 5% for the binary dispersion of the 2022 study correasoto2023 R1, R2. At 20% the TEAC, TBC and TBAC dispersions released ATZ at about 4.6–5.1 and PVPVA at 3.8–4.2 mg/min/cm², above neat PVPVA (about 2.7 ± 0.5); at the 25% limit the rates were about 2.0–3.1, at or below neat PVPVA, after a lag of about 20 min for TEAC and TBAC correasoto2023 R6, R7, R4. LED: with 5 g per 100 g only citric acid released a 10% dispersion completely; with 10 g TEAC lowered the dispersion Tg from 99.1 to 85.8 °C and raised release by 90 min from 20 to 94%, and the limit rose to 15% (TEAC, TBC) and 20% (GTB), with LED and PVPVA rates of about 4.3–7.0 and 4.6–6.2 mg/min/cm² at the limit correasoto2023 R8, R9, R11, R12. RTV with GTB or TBC released completely at 30% and not at 35% correasoto2023 R14. The fold gains were 5 (ATZ), 3–4 (LED) and 1.2 (RTV) correasoto2023 R16. The 8:1 glasses fell from 105.5 to 62.2–75.1 °C (ATZ) and from 162 to 109.1–114.6 °C (LED), triacetin giving the largest ATZ drop (43.3 °C) with a limit of only 10% correasoto2023 R17, R18. Drug-free PVPVA dissolved at about 4.8 (GTB) and 6.1 mg/min/cm² (TBC) against 2.7 correasoto2023 R13. Water uptake at 95% RH of 20% ATZ dispersions was about 25–28.5% with the citrate esters and 31.6% with GTB against about 25% without plasticizer, and GTB or TBC lowered the uptake of PVPVA from about 42 to 32–34% correasoto2023 R21, R19, R22. Drug-rich droplets of 500–1500 nm formed "in all cases" correasoto2023 R5. (synthesis: 25/5 = 5 for ATZ, 15/5 = 3 and 20/5 = 4 for LED, 30/25 = 1.2 for RTV.)

papersystemmethod and conditionsresultids
correasoto2023ATZ–PVPVA, nine plasticizers at 5 g per 100 gcompacts, pH 6.8, 37 °C, >80% in 120 minlimit 7.5–25% against 5% (cited)correasoto2023 R1
correasoto2023ATZ 20% with TEAC, TBC, TBAC; at the limitnormalized rates≈4.6–5.1 drug; ≈2.0–3.1 at 25% against neat PVPVA ≈2.7correasoto2023 R6, R7
correasoto2023LED–PVPVA with 10 g TEAC, TBC, GTBsamelimit 15, 15, 20% against 5% (cited)correasoto2023 R11
correasoto2023LED 10% with 5 and 10 g TEACDSC; release by 90 minTg 99.1 → 85.8 °C; 20 → 94%correasoto2023 R9
correasoto2023RTV with 5 g GTB or TBCcompactscomplete at 30%, not at 35% (cited 25%)correasoto2023 R14
correasoto20238:1 ATZ and LED glassesmodulated DSCTg lowered by 30.4–43.3 and 47.6–53.1 °Ccorreasoto2023 R17, R18
correasoto2023PVPVA with 10% w/w GTB or TBCcompacts≈4.8 and 6.1 against ≈2.7 mg/min/cm²correasoto2023 R13
correasoto2022bATZ 10% with vinylpyrrolidonecompacts, 90 minrelease ≈87% against ≈2.4%; 15% failscorreasoto2022b R2, R4

Figure

Fig. 9 of correasoto2023: fold increase of the limit of congruency with TBC or GTB for atazanavir, ledipasvir and ritonavir
Fig. 9 · correasoto2023fold increase of the limit of congruency with TBC or GTB for atazanavir, ledipasvir and ritonavir

Fivefold for ATZ, three- and fourfold for LED, 1.2-fold for RTV; ATZ and RTV at 5 g, LED at 10 g per 100 g, and the binary limits are cited correasoto2023 R16, X7.

Fig. 8 of correasoto2023: PVPVA dissolution with and without plasticizer
Fig. 8 · correasoto2023PVPVA dissolution with and without plasticizer

Neat PVPVA about 2.7, with GTB about 4.8, with TBC about 6.1 mg/min/cm² correasoto2023 R13.

Why

The authors start from the trend that high-Tg drugs have low limits in PVPVA (F18) and from the suggestion of the 2022 atazanavir study that surfactants act by plasticizing (F21) correasoto2023 C4, C6. Below the limit drug release is tied to PVPVA dissolution, which for this glassy, high-molecular-weight polymer under stirring is "most likely" limited by chain disengagement from the gel correasoto2023 C33. By free-volume theory a low-Tg small molecule separates the chains and raises free volume and mobility; in Devotta's model (cited) the highest chain mobility in the gel rises with its fractional free volume f_g,

m_{p,\infty} = A_d\, \exp\left(-\frac{B_d}{f_g}\right)

and the disengagement rate is proportional to chain mobility, with f_g taken as additive over the components correasoto2023 C37, C40, E2, E3, E4. A plasticizer that raises the free volume of the hydrated gel should therefore speed polymer dissolution and the coupled drug release ("is predicted"), while more high-Tg drug and less water lower the free volume as loading rises correasoto2023 C41, C42. The authors find it "reasonable to suggest" this as one mechanism and add that other factors are "likely" correasoto2023 C39, C43. Water ingress is not the lever, since vapour uptake changed little, which they ascribe to the lipophilic plasticizers' unfavourable interaction with water ("may be due") correasoto2023 C34, C35. Lipophilic plasticizers "appear" more effective, which "suggests" that their interaction with the drug matters, and a plasticizer "may also affect" the drug-rich barrier above the limit correasoto2023 C44, C31. Ritonavir, whose mobility is "expected" to limit release less, gained little, "confirming" the hypothesis correasoto2023 C19, C20. (synthesis: the gains agree with the Tg ordering of F18, but the Tg drops of the 8:1 glasses did not rank them, so the plasticizer's effect on the dissolving gel or on the drug-rich phase, not the dry Tg, is what the data leave open correasoto2023 X14, C45.) (synthesis: in 2023 the Spans, which lowered the Tg of amorphous ritonavir to 7.7–27.8 °C, were read as softening the drug-rich layer so that flow removes it, a second way in which plasticization can raise release near the limit (F31) yang2023 R22, C18.)

Conditions and limits

PVPVA, rotary-evaporated dispersions, compacts in 50 mM pH 6.8 phosphate at 37 °C; 5 or 10 g plasticizer per 100 g of drug and polymer, about 4.8 and 9.1 wt% of the solid correasoto2023 P2, X8. The binary limits are cited from three earlier papers, so the fold gains compare across studies and plasticizer levels correasoto2023 X7. Whether loadings above 25% (ATZ) or 20% (LED) were tested is not stated, and the release profiles are in an SI that was not supplied correasoto2023 X6. Tg was measured on drug:plasticizer glasses without polymer, water uptake from vapour at 200–300 min, and no rate test was statistical correasoto2023 X8, X19, X20. No storage, post-dissolution or crystallization data were reported correasoto2023 X21.

Counterexamples and conflicts

Triacetin lowered the ATZ Tg most and gave a limit of 10%, TEAC lowered it least and gave 25% correasoto2023 X14. "Lipophilic is better" has exceptions: TEAC (LogP 0.35) matched the lipophilic esters with ATZ, TBAC (the most lipophilic) released less than 30% of 10% LED, and only citric acid released 10% LED with 5 g per 100 g correasoto2023 X15, R10, R8. At their limits the plasticized ATZ dispersions released no faster than neat PVPVA, against the conclusion's "in all cases" correasoto2023 X5. In the 2022 atazanavir study vinylpyrrolidone, a plasticizer, matched the best surfactants at 10% but failed at 15% (F21) correasoto2022b R2, R4. The authors warn that the lower Tg may raise crystallization risk correasoto2023 C46.

Transfer check

For a drug of high Tg with a PVPVA limit of 5–10%, co-process 5 g (dry Tg near 100 °C) or 10 g (near 160 °C) per 100 g of a citrate ester or GTB, dissolve compacts with drug and polymer assayed for 120 min at 2.5–5% loading steps, and expect lags near the new limit correasoto2023 R1, R11, R4. Screen several plasticizers, since neither LogP nor Tg depression picked the best one, and test physical stability before adopting the plasticizer correasoto2023 X14, X15, C46.

History

Plasticizers were used in the library's processes to lower extrusion temperatures, not to change release correasoto2023 C5, C1. The 2022 atazanavir study proposed plasticization as the action of surfactants and tested vinylpyrrolidone (F21) correasoto2023 C6; correasoto2022b C40. Correa Soto and co-workers (2023) were the first in the library to raise the limit with non-surfactant plasticizers and to compare drugs of different Tg correasoto2023 C1, C21. Yang and co-workers (2023) attributed the action of lipophilic surfactants on the drug-rich barrier to plasticization (F31) yang2023 C11.

F28

Topic 5Formulation levers near the limit9 of 11

In high-loading HPMCAS particles the drug content of the particle surface, not of the bulk, separated good from poor release.

Binary grazoprevir–HPMCAS particles co-precipitated at 75% had 53 and 84% drug at the surface by XPS and released about 17 and 8% in 90 min hiew2023 R10, R14. "Hierarchical" particles precipitated into acidified water that already held dissolved HPMC or HPC had about 10–25% surface drug and released about 56–72% hiew2023 R14, R10, R11, R12. In six dogs the hierarchical particle gave an AUC of 135 against 73 µM·h for the binary one hiew2023 R15.

moderateModerate: large release differences and a dog crossover agree, but the surface link rests on eight XPS points in two groups, and several comparisons are confounded by anti-solvent and particle size hiew2023 K2, K6, K3, X7, X13, X14.

Grazoprevir release at 90 min, % (note: surface drug by XPS)hierarchical HPMC (rotary-evaporated)surface ≈10%≈6320% solvent-evaporatedsurface ≈12%≈63hierarchical HPC, 90 °Csurface ≈21.5%≈56hierarchical HPC, 60 °Csurface ≈24%≈72hierarchical HPMC (filtered)surface ≈25%≈71HPMC washsurface ≈34%≈47binary, acidified watersurface ≈53%≈17binary, MTBEsurface ≈84%≈8

Two groups rather than a grade: low surface drug with good release, high surface drug with poor release. hiew2023 R14

Dogs, n = 6: AUC 0–24 h, µM·hbinary particle73.8% drug73hierarchical particle73.4% drug135

≈1.8-fold exposure at nearly equal bulk loading. hiew2023 R15

For your drug

  1. For a high-loading particle dispersion, measure the surface drug by XPS against a solvent-evaporated dispersion of known loading, and assay the isolated solid.
  2. When co-precipitating, dissolve the water-soluble polymer in the anti-solvent rather than suspending it or washing it on afterwards, and test release in a two-stage medium at the amorphous-solubility dose.

hiew2023 P14, C46, R6, C50, P12

How it works and key numbers
  1. Drug enrichment at the particle surface impairs release (F14) hiew2023 C44.
  2. A secondary polymer dissolved in the anti-solvent is "postulated" to deposit as a predominantly continuous coat, which dilutes the surface drug, and this depletion "drove improved release performance" hiew2023 C22, C45.
  3. At 50% or more surface drug, release is read as "dominated by the drug dissolution rather than the polymer"; polymer release was not measured to test this hiew2023 C53, X10.
  4. Poor wetting of the binary powder, which aggregated and floated, "could have resulted" in its poor release hiew2023 C20, R9.
  5. The polymer has to be in the anti-solvent at precipitation to coat well: a wash of the filtered cake gave 34% surface drug and 47% release hiew2023 C50, R14.
  6. In 2025, among surfaces already diluted, wettability rather than surface drug decided (F35) hiew2025 R14, R15, R17.
≈10–34% against 53–84%surface grazoprevir of the good and the poor releasershiew2023 R14
≈71 against 17%release at 90 min, filtered hierarchical against binary particle at nearly equal bulk loadinghiew2023 R10, R14
135 against 73 µM·hAUC in dogs, hierarchical against binary particlehiew2023 R15
Evidence: data, conditions and papers

Finding F28. In high-loading HPMCAS particles the drug content of the particle surface, not of the bulk, separated good from poor release: grazoprevir co-precipitates with a water-soluble polymer deposited from the anti-solvent had about 10–34% surface drug and released 47–72% in 90 min against 8–17% for binary particles with 53–84%, and one of them gave 1.8-fold exposure in dogs; among surfaces already diluted, wettability decided (F35)

In short. Solvent-evaporated grazoprevir–HPMCAS dispersions released about 102% of the dose at 5%, 63% at 20%, 43% at 30% and 27–30% at 50–75% after 90 min of a two-stage test, a gradual decline hiew2023 R8, C18. Binary co-precipitated particles at 75% released about 17% (precipitated into acidified water) and 8% (into MTBE), with 53 and 84% grazoprevir at the surface by XPS hiew2023 R10, R14. "Hierarchical" particles precipitated into acidified water that already held dissolved HPMC or HPC had about 10–25% surface drug and released about 56–72%; a wash of the filtered wet cake with HPMC solution gave 34% and 47%, and HPMC suspended in MTBE about 8–15% hiew2023 R14, R10, R11, R12. A 60% hierarchical particle and a 20% solvent-evaporated dispersion, both near 10–12% surface drug, released about 63% hiew2023 R14, C31. In six dogs the hierarchical particle (73.4% drug) gave AUC 135 against 73 µM·h for the binary (73.8%) hiew2023 R15. Surface drug separates two groups rather than grading release, and coat continuity and wetting were inferred hiew2023 X7, X15, X12. In 2025, 75% grazoprevir–HPMCAS co-precipitates with seven secondary excipients had surface drug contents of about 32–50% whether they released well or not, and the FaSSIF contact angle (0–52° against 119–137°) separated about 37–52% from 8–20% release (F35) hiew2025 R14, R15, R17.

Type. single-system observation (grazoprevir–HPMCAS-LF with HPMC or HPC) Strength. : large release differences and a dog crossover in agreement hiew2023 K2: moderate to strong, K6: moderate, but the surface link rests on eight XPS points in two groups and several comparisons are confounded by anti-solvent and particle size hiew2023 K3: moderate, X7, X13, X14.

How it was shown

Hiew and co-workers (2023) made solvent-evaporated grazoprevir–HPMCAS-LF dispersions at 5–75% and co-precipitated dispersions (cPADs) at 75% by shearing a THF solution into acidified water or MTBE, with HPMC or HPC dissolved in the anti-solvent, suspended in it or washed on afterwards hiew2023 P5, P6, P8. They tested release in a two-stage SGF → FaSSIF test, measured the surface drug by XPS and dosed one pair to six dogs hiew2023 P12, P14, P15.

What the data show

In dogs the hierarchical particle gave an AUC of 135 ± 47 against 73 ± 31 µM·h and a Cmax of 19.2 ± 4.6 against 13.1 ± 5.1 µM hiew2023 R15.

systemmethod and conditionsresultids
solvent-evaporated dispersions, 5–75%two-stage SGF → FaSSIF, 90 min≈102 → 63 → 43 → 27–30%hiew2023 R8
binary cPADs 60, 75%same≈37.5, 17% (acidified water); 8% (MTBE)hiew2023 R10, R14
hierarchical cPADs, HPMC or HPC dissolved in the anti-solventsame≈56–72%; wash ≈47%; HPMC suspended in MTBE ≈8–15%hiew2023 R10, R11, R12
eight materialsXPS surface drug against release at 90 min≤34% with ≈47–72%; ≥53% with ≈8–17%hiew2023 R14
binary against hierarchical cPAD, ≈73% drugdogs, n = 6, crossoverAUC 73 against 135 µM·hhiew2023 R15
75:25 co-precipitates, seven secondary excipients (2025)XPS; contact angle; two-stage releasesurface drug ≈32–50% for good and poor; 0–52° with ≈37–52%, ≈119–137° with ≈8–20%hiew2025 R14, R15, R17
Fig. 7 of hiew2023: release at 90 min against XPS surface grazoprevir (a) and against bulk loading (b)
Fig. 7 · hiew2023release at 90 min against XPS surface grazoprevir (a) and against bulk loading (b)

Panel a: the materials fall into a low-surface, high-release group and a high-surface, low-release group; panel b: bulk loading does not order them hiew2023 R14, X7.

Why

The authors build on the finding that drug enrichment at the particle surface impairs release hiew2023 C44. They "postulated" that a secondary polymer dissolved in the anti-solvent deposits as a predominantly continuous coat, and conclude that the coat dilutes the surface drug and that this depletion "drove improved release performance" hiew2023 C22, C45. Poor wetting of the binary powder "could have resulted" in its poor release hiew2023 C20. (synthesis: the 2025 paper shows a drug-poor surface to be necessary but not sufficient, since PVP and poloxamer 407 diluted the surface yet left it poorly wettable hiew2025 C35, C51.)

Limits and transfer

Within the low-surface group release did not follow surface drug, and the particles dosed to dogs also differed in size, without a statistical test of AUC hiew2023 X7, X13, X19. Measure the surface drug of high-loading particles by XPS and assay the isolated solid, since filtration drained most of a dissolved secondary polymer, and dissolve the water-soluble polymer in the anti-solvent rather than suspending it or washing it on hiew2023 P14, C46, R6, C50.

How it was shown

Hiew and co-workers (2023) tested the hypothesis that the drug loading at the particle surface, rather than in the bulk, sets the extent of release hiew2023 C6. They made rotary-evaporated grazoprevir–HPMCAS-LF dispersions at 5–75% as a reference, and co-precipitated dispersions (cPADs) by shearing a THF solution of drug and polymer (75% target loading, 20% solids) into ten volumes of 0.001 N HCl or MTBE, with HPMC or HPC (5 mg/mL) dissolved in the acidified water, suspended in MTBE (as received or jet-milled) or dissolved in a wash of the filtered wet cake, isolated by filtration and drying or by rotary evaporation with a 60 or 90 °C bath hiew2023 P5, P6, P8. Release was a two-stage non-sink test: 15 mg drug into 50 mL SGF at 37 °C and 100 rpm, then 50 mL double-strength FaSSIF at 30 min, so that 100% equals 150 µg/mL, the amorphous solubility in FaSSIF, followed by in situ UV to 90 min hiew2023 P12, R2. Surface grazoprevir was measured by XPS over about 10 nm (five spots), and two materials of equal loading were dosed as 100 mg capsules to six dogs in a crossover hiew2023 P14, P15.

What the data show

Grazoprevir (weak acid, pKa 4.68, Tg 149.4 °C) has an amorphous solubility of about 1 µg/mL in SGF, 26–29 in pH 6.5 buffer and 149–186 µg/mL in FaSSIF hiew2023 M1, R2. Every dispersion released about 0–1% in SGF; after FaSSIF the solvent-evaporated series released at 90 min about 102, 84, 83, 63, 43, 27, 29 and 30% at 5, 10, 15, 20, 30, 50, 60 and 75% hiew2023 R7, R8. Binary cPADs released about 37.5% (60%) and 17% (75%) from acidified water and 8% (75%) from MTBE, and the powders aggregated and floated hiew2023 R10, R14, R9. With HPMC dissolved in the acidified water release reached about 71% (filtered) and 63% (rotary-evaporated); the filtered material assayed 73.4% drug, read as only about 1.6 wt% HPMC retained hiew2023 R10, R6, C15. The wash gave about 47%, HPMC suspended in MTBE about 8% (15% when jet-milled), and HPC dried with a 60 or 90 °C bath about 72 and 56% hiew2023 R10, R11, R12. XPS put the surface grazoprevir at about 10 (rotary-evaporated HPMC), 12 (20% solvent-evaporated), 21.5 and 24 (HPC, 90 and 60 °C), 25 (filtered HPMC), 34 (washed), 53 (binary, acidified water) and 84% (binary, MTBE), with release at 90 min of about 63, 63, 56, 72, 71, 47, 17 and 8% hiew2023 R14. Dogs: AUC0–24h 135 ± 47 against 73 ± 31 µM·h and Cmax 19.2 ± 4.6 against 13.1 ± 5.1 µM, median Tmax 2 against 3 h, with plasma concentrations higher at 0.5–2 h (p < 0.05) hiew2023 R15, R16. The hierarchical particles were also smaller (median 28.8 against 36.9 µm) hiew2023 R5. (synthesis: 135/73 ≈ 1.8 and 19.2/13.1 ≈ 1.5, the ratios printed; 71/17 ≈ 4.2 for the filtered hierarchical against the binary particle at nearly equal bulk loading.)

papersystemmethod and conditionsresultids
hiew2023grazoprevir–HPMCAS solvent-evaporated, 5–75%two-stage SGF → FaSSIF, 90 min≈102 → 63 → 43 → 27–30%hiew2023 R8
hiew2023binary cPADs 60, 75%same≈37.5, 17% (acidified water); 8% (MTBE)hiew2023 R10, R14
hiew2023hierarchical cPADs, HPMC or HPC dissolved in the anti-solventsame≈56–72%; wash ≈47%; HPMC suspended in MTBE ≈8–15%hiew2023 R10, R11, R12
hiew2023eight materialsXPS surface drug against release at 90 min≤34% with ≈47–72%; ≥53% with ≈8–17%hiew2023 R14
hiew2023binary against hierarchical cPAD, ≈73% drugdogs, n = 6, crossoverAUC 73 against 135 µM·hhiew2023 R15
bhardwaj2018ITZ–PVPVA 20% spray-dried from five solventsXPS; releasesurface drug 4–36%; release several-fold differentbhardwaj2018 R20, R13
li2020 (ASD process)spray-dried ritonavir–PVPVA 25%XPS; releasesurface ritonavir ≈21 → 70%; rate ≈3.5 → 0.90li2020 R7, R10
hiew2025grazoprevir–HPMCAS 75:25 co-precipitates, seven secondary excipientsXPS; contact angle; two-stage releasesurface drug ≈32–50% for good and poor; 0–52° with ≈37–52%, ≈119–137° with ≈8–20%hiew2025 R14, R15, R17

Figure

Fig. 7 of hiew2023: release at 90 min against XPS surface grazoprevir (a) and against bulk loading (b)
Fig. 7 · hiew2023release at 90 min against XPS surface grazoprevir (a) and against bulk loading (b)

Panel a: the materials fall into a low-surface, high-release group and a high-surface, low-release group; panel b: bulk loading does not order them hiew2023 R14, X7.

Fig. 9 of hiew2023: co-precipitated particles against the release curve of solvent-evaporated dispersions
Fig. 9 · hiew2023co-precipitated particles against the release curve of solvent-evaporated dispersions

The hierarchical particle at about 73% drug sits above the solvent-evaporated curve at 20%; the binary particles sit on or below its plateau hiew2023 R17.

Why

The authors build on the earlier finding that drug enrichment at the particle surface impairs release (F14) hiew2023 C44. They "postulated" that a secondary polymer dissolved in the anti-solvent deposits as a predominantly continuous coat and one insoluble in it as discrete particles, and conclude that the coat dilutes the surface drug and that this depletion "drove improved release performance" ("we demonstrated") hiew2023 C22, C45. Carrying the solvent-evaporated curve over to the surface, they read release at 50% or more surface drug as "dominated by the drug dissolution rather than the polymer", which polymer release was not measured to test hiew2023 C53, X10. Poor wetting of the binary powder "could have resulted" in its poor release, and the large surface area of co-precipitates "could predispose" them to it hiew2023 C20, C39. Filtration "could" have removed dissolved polymer from the surface, and the wash results "implied" that the polymer has to be in the anti-solvent at precipitation to coat well hiew2023 C49, C50. For HPC, drying above its cloud point (about 40 °C) "should" give a discrete coat, which XPS did not show hiew2023 C25, X8. For HPMCAS the decline with loading is expected to be "sloped" rather than a cliff, because the polymer must ionize (F11, F23) hiew2023 C36. (synthesis: this is the surface principle of F14, shown there near the PVPVA switch with spray solvents, carried to high loading in HPMCAS, where release declines gradually; a drug-poor surface let a 73% particle release like a 20% dispersion.) (synthesis: the 2025 paper shows a drug-poor surface to be necessary but not sufficient: PVP and poloxamer 407 diluted the surface like HPMC yet left it poorly wettable (F35) hiew2025 C35, C51.)

Conditions and limits

One drug, HPMCAS-LF as primary polymer, HPMC or HPC as secondary polymer, a two-stage test of 90 min at a dose equal to the amorphous solubility in FaSSIF, drug release only by in situ UV, and one dog study of one pair hiew2023 A3, P12, P15. XPS reports only the surface drug, not the polymer fractions, and the MTBE hierarchical materials were not measured hiew2023 X15, X6. Replicate numbers are not stated, whether the dose used target or assayed loading is not stated, and the bulk-loading axis mixes target and assay values hiew2023 X18, X2, X16. Storage stability was not studied hiew2023 A3.

Counterexamples and conflicts

Within the low-surface group release did not follow surface drug (about 10% surface with 63%, 25% with 71%, 21.5% with 56%) hiew2023 X7. The 90 °C HPC material released less than the 60 °C one with no higher surface drug hiew2023 X8. The discrete-coat materials were also precipitated in MTBE, whose binary core alone had the highest surface drug, so coat type and anti-solvent are confounded hiew2023 X14. Both 75% binaries released less than the 75% solvent-evaporated dispersion (about 17 and 8% against 30%) hiew2023 X20, X10. The hierarchical particles dosed to dogs were also smaller, and AUC and Cmax were not tested statistically hiew2023 X13, X19. Among diluted surfaces surface drug content did not separate good from poor excipients in 2025: PVP (about 33%) and poloxamer (about 45%) particles released poorly beside SDS (about 32%) and HPMC (about 50%) ones hiew2025 R14, R9.

Transfer check

For a high-loading particle dispersion, measure the surface drug by XPS against a solvent-evaporated dispersion of known loading, and assay the isolated solid, since filtration drained most of a dissolved secondary polymer hiew2023 P14, C46, R6. When co-precipitating, dissolve the water-soluble polymer in the anti-solvent rather than suspending it or washing it on afterwards, and test release in a two-stage medium at the amorphous solubility dose hiew2023 C50, P12.

History

Hierarchical co-precipitates with an HPMC coat had been made to fix wetting at moderate loading (Schenck 2021, cited) hiew2023 C5. Bhardwaj and co-workers (2018) and Li and co-workers (2020, ASD process) linked surface drug enrichment of spray-dried particles to poor release hiew2023 C44. Hiew and co-workers (2023) were the first in the library to lower the surface drug of high-loading particles on purpose and to test the result in dogs hiew2023 C47, C43. Hiew and co-workers (2025) screened seven secondary excipients on 75% grazoprevir–HPMCAS particles, found wettability rather than surface drug content separating good from poor release, and applied HPMC or SDS by high shear to a solvent-evaporated dispersion (F35) hiew2025 C35, C40, C21; the title was extended after that paper (synthesis).

Other chaptersextends B F10
F31

Topic 5Formulation levers near the limit10 of 11

With surfactant in ritonavir–PVPVA compacts, release followed whether a continuous drug-rich layer persisted at the dissolving surface.

At 30% ritonavir all four surfactants (10 parts per 100 parts of drug and polymer) gave about 50–97% release in 90 min against a cited 30% without; at 40% the Spans released about 1–8% while Tween 80 and SDS released about 57% and 48–54% yang2023 R2, R1, X5. Every dispersion that released showed discrete drug-rich droplets or a one-phase gel at the dissolving surface, and every one with a persistent continuous drug-rich layer released almost none yang2023 R6, R13, R7, R9, C40. SDS raised the water at which 30% films separated from 14.0 to 24.5% yang2023 R21.

moderateModerate to strong for the link between a persistent layer and failed release, consistent over ten formulations and two imaging modes; moderate for the SDS miscibility effect; weak for plasticization by the Spans; the surfactant-free comparator is cited yang2023 K2, K4, K5, X5.

30% loading40% loadingSpan 85continuous layer persists at 40%≈1≈87Span 20layer 50–100 µm at 40%≈887–97Tween 80droplets agglomerate≈50≈57SDSone-phase gel; surface crystals48–54≈700102030405060708090100ritonavir released in 90 min, %

10 parts surfactant per 100 parts drug and polymer; without surfactant about 30% at 30% (cited). yang2023 R2, R1, R7, R10, R13, R16

Water needed to phase-separate 30% ritonavir–PVPVA films, %no surfactant14.0Span 8516.0Span 2010.5Tween 8012.5SDS24.5

Only the SDS shift exceeds the resolution of the humidity steps. yang2023 R21, X15

For your drug

  1. One or two loading steps above the binary limit, make ternary dispersions with a few parts of an ionic surfactant that raises the water needed for separation (test films at stepped RH against the binary) and with a lipophilic plasticizing surfactant, and dissolve compacts with drug and polymer assayed.
  2. Image cross-sections after 5–20 min: a one-phase gel or droplets at the gel–solution boundary predicts release, a persistent drug-rich layer predicts failure; with SDS, check the dissolved surface for crystals.

yang2023 R21, R22, P4, R13, R7, X12

How it works and key numbers
  1. On a schematic ritonavir–PVPVA–water diagram, by the lever rule a low loading yields little drug-rich phase, which stays discrete, and a high loading much, which is continuous and acts as a barrier if it resists the flow (F30) yang2023 C41.
  2. SDS enlarges the miscible region, so the gel can dissolve without separating; the 40% SDS gel stayed one phase with an unenriched surface (ritonavir about 41% before and 40% after 30 min) yang2023 C9, C10, C42, R13, R19.
  3. The Spans lowered the Tg of amorphous ritonavir from 46.8 °C to 7.7–27.8 °C, so a continuous layer "is expected to be more liquid-like" and is removed by shear as fast as it forms yang2023 R22, C18, C35.
  4. Tween 80 on the droplet surfaces "likely" causes agglomeration, which "could potentially explain" its slower release yang2023 C22, C20.
  5. SDS accumulating at the dissolving surface (about 98 wt% of the 40% surface after 30 min) "conceivably" promotes crystallization, and release stopped at about 30 min with needle crystals on the 30% surface yang2023 R17, C50, C24, R16.
14.0 → 24.5%water needed to separate 30% films, without and with SDSyang2023 R21
≈1–8% against ≈48–57%release at 40%: the Spans against SDS and Tween 80yang2023 R2
≈86%release of 30% Span 85, whose continuous layer formed in situ but was swept awayyang2023 R8, R2
Evidence: data, conditions and papers

Finding F31. In ritonavir–PVPVA compacts with 10 parts of surfactant, release followed whether a continuous drug-rich layer persisted at the dissolving surface: SDS kept the gel in one phase by raising the water needed for separation from 14.0 to 24.5%, the Spans plasticized the drug-rich phase so that flow removed a layer that formed, Tween 80 let droplets agglomerate, and SDS brought surface crystals

In short. At 30% ritonavir all four surfactants (10 parts per 100 parts of drug and polymer) gave release of about 50–97% in 90 min against a cited 30% without surfactant; at 40% the Span dispersions released about 1–8% while Tween 80 and SDS released about 57% and 48–54% yang2023 R2, R1, X5. Every dispersion that released showed discrete drug-rich droplets or a one-phase gel at the dissolving surface, and every one with a persistent continuous drug-rich layer (Span 20 at 40%, about 50–100 µm by 5 min; Span 85 at 40%) released almost none yang2023 R6, R13, R7, R9, C40. A continuous layer that formed in situ at 30% Span 85 was swept away by agitation and the dispersion released about 86% yang2023 R8, R2. SDS raised the water at which 30% films separated from 14.0 to 24.5% and its 40% gel stayed one phase with an unenriched surface (ritonavir about 41% before and 40% after 30 min), while the Spans lowered the Tg of amorphous ritonavir from 46.8 °C to 7.7–27.8 °C yang2023 R21, R13, R19, R22. The authors "propose" that preventing or disrupting the continuous layer is the most critical surfactant effect; SDS release stopped at about 30 min with needle crystals on the 30% surface yang2023 C37, C40, R16, C24.

Type. observation in 1 drug–polymer pair with 4 surfactants at 30–50% loading Strength. to strong for the link between a persistent continuous layer and failed release, consistent over ten formulations and two imaging modes yang2023 K2: moderate to strong; moderate for the SDS miscibility effect, from one threshold per formulation yang2023 K4: moderate; weak for plasticization by the Spans and weak to moderate for crystallization as the cause of the SDS plateau yang2023 K5: weak, K6: weak to moderate; the surfactant-free comparator is cited yang2023 X5.

How it was shown

Yang and co-workers (2023) made ritonavir–PVPVA dispersions at 30–50% with 10 parts of SDS, Tween 80, Span 20 or Span 85 per 100 parts of drug and polymer and dissolved compacts with drug and polymer assayed; the binary comparator was cited yang2023 P1, P4, P5, P6, X5. They imaged surfaces, cross-sections and edge-wetted compacts, found the lowest RH at which 30% films separated, and measured the Tg of ritonavir–Span mixtures yang2023 P7, P8, P12, P17.

What the data show

A continuous layer that formed in situ on 30% Span 85 was removed by agitation at 4 min, releasing the droplets beneath, and re-formed yang2023 R8.

systemmethod and conditionsresultids
ritonavir–PVPVA 30% + 10 parts Span 85, Span 20, Tween 80, SDScompacts, pH 6.8, 37 °C, 90 mindrug ≈87 / 87–97 / 50 / 70% against 30% citedyang2023 R2, R1
same at 40%same≈1 / 8 / 57 / 48–54%yang2023 R2
ten formulationsconfocal, surfaces, cross-sections, in siturelease with discrete droplets or one-phase gel; none with a persistent continuous layeryang2023 R6–R14, C40
30% films ± surfactantRH steps, 12 hwater for separation 14.0 / 16.0 / 10.5 / 12.5 / 24.5% (none / Span 85 / Span 20 / Tween 80 / SDS)yang2023 R21
amorphous ritonavir ± Span 20 or Span 85DSC onset46.8 → 7.7–27.8 °Cyang2023 R22
SDS 40% compact, before and after 30 minXPS; ATR-FTIRSDS ≈60 → 98 wt% of the surface; ritonavir ≈41 → 40%yang2023 R17, R19
Fig. 6 of yang2023: Span 85, 30% ritonavir, in situ: a continuous layer forms, is swept away and forms again
Fig. 6 · yang2023Span 85, 30% ritonavir, in situ: a continuous layer forms, is swept away and forms again

A red drug-rich rim at the interface (panels h, i) is removed by agitation, releasing the droplets beneath (j), and re-forms (k); the rotated compacts of the same dispersion showed only small domains yang2023 R8.

Why

On a schematic phase diagram a low loading yields little drug-rich phase, which stays discrete, and a high loading much, which is continuous and a barrier if it resists the flow yang2023 C41. SDS enlarges the miscible region, and separation confined to the wettest surface of the gel is "likely responsible" for its better release yang2023 C9, C42. The Spans partition into the drug-rich phase and lower its Tg, so a continuous layer "is expected to be more liquid-like" and is removed under shear yang2023 C18, C35. The authors "propose" that preventing or disrupting a continuous drug-rich layer is the most critical surfactant effect yang2023 C37.

Limits and transfer

One drug and one surfactant level were tested against a cited comparator, and only the SDS shift exceeded the RH step resolution yang2023 A1, X5, X15. Image cross-sections of ternary dispersions after 5–20 min: a one-phase gel or droplets at the gel–solution boundary predict release, a persistent drug-rich layer predicts failure; with SDS check the surface for crystals yang2023 R13, R7, X12.

How it was shown

Yang and co-workers (2023) tested the hypothesis that surfactants that improve release hinder the formation or persistence of a continuous drug-rich barrier at the dispersion–water interface yang2023 C1. They made rotary-evaporated ritonavir–PVPVA dispersions at 30–50% loading (drug as a share of drug and polymer) with 10 parts of SDS (HLB 40), Tween 80 (15.0), Span 20 (8.6) or Span 85 (1.8) per 100 parts of drug and polymer, 9.1 wt% of the solid yang2023 P1, M3, M4, M5, M6, X9, X10. They pressed 100 mg compacts (8 mm die) and rotated them at 100 rpm in 100 mL 50 mM pH 6.8 phosphate at 37 °C for 90 min, with ritonavir by HPLC and PVPVA by size-exclusion HPLC (n = 3); the binary comparator was cited from the 2019 ritonavir study, not re-run yang2023 P4, P5, P6, R1, X5. With Nile red (drug-rich) and Alexa Fluor 488 (polymer- and water-rich) they imaged compact surfaces and cut cross-sections after 5, 10 and 20 min and, in situ, compacts fused to a glass dish and wetted from the side, agitated by a pipette yang2023 P7, P8, C55. They measured gel thickness, water uptake at 95% RH, the lowest RH at which 30% films separated within 12 h (converted to water content from a sorption isotherm), the Tg of ritonavir–Span mixtures, the surface composition of the SDS 40% compact before and after 30 min by XPS and ATR-FTIR, the release rate of PVPVA–surfactant blends, and crystals on dissolved surfaces by PLM and SEM yang2023 P9, P10, P12, P17, P13, P14, P2, P15, P16.

What the data show

At 30% ritonavir release at 90 min was about 87% (Span 85, about 86% from 45 min), 87–97% (Span 20, 92–97% at 30–60 min), 50% (Tween 80) and 70% (SDS, from 30 min), with PVPVA at about 101, 98–106, 71 and 86% yang2023 R2, R3. At 40% Span 85 released about 1% of the drug and 8% of the polymer, Span 20 about 8 and 78%, Tween 80 about 57 and 86%, and SDS plateaued near 53–54% from 30 min (about 48% at 90 min) with polymer about 70–79%, already incongruent at 15 min (about 38 against 52%) yang2023 R2, R3, X4. At 50% Tween 80 released about 22% after a lag and SDS about 33–39%, with polymer about 85 and 89% yang2023 R2, R3. Span 20 at 30% showed a one-phase gel beneath a top layer in which drug-rich droplets formed at the gel–solution interface and left with the polymer yang2023 R6. Span 20 at 40% carried a drug-rich layer of about 50–100 µm from 5 min, crossed by pores that closed in situ by 3–5 min, and Span 85 at 40% a thick, high-coverage layer (SI figure, described in the text) yang2023 R7, R9. Span 85 at 30% showed only small domains on rotated compacts, while in situ a continuous layer formed at once, was removed by agitation at 4 min releasing the droplets beneath, and re-formed yang2023 R8. Tween 80 droplets stayed discrete but agglomerated and left in chunks yang2023 R10. The SDS 40% gel looked homogeneous with droplets only at the gel–solution boundary; at 50% Tween 80 and SDS formed porous or bicontinuous drug-rich layers with droplets in the pores yang2023 R13, R12, R14. Films separated at 84% RH and 14.0% water without surfactant, 84% and 16.0% with Span 85, 75% and 10.5% with Span 20, 75% and 12.5% with Tween 80, and 92% and 24.5% with SDS yang2023 R21. Span 20 and Span 85 lowered the onset Tg of amorphous ritonavir from 46.8 °C to 14.8 and 7.7 °C (80–20 and 60–40) and to 27.8 and 12.7 °C yang2023 R22. XPS put SDS at about 60 wt% of the SDS 40% compact surface before dissolution (9.1% in the bulk) and about 98 wt% after 30 min, while ATR-FTIR gave ritonavir about 41% before and 40% after on a drug-plus-polymer basis yang2023 R17, R19. Needle crystals covered the SDS 30% surface at 30 min; no other surfactant gave crystals (SI figure, described in the text) yang2023 R16. PVPVA blends dissolved at about 6.9 (SDS) and 5.7 mg/min/cm² (Tween 80) against 3.6 for neat PVPVA, and the Spans did not change it yang2023 R5. Gel layers grew with time for Tween 80 (147.6 to 279.6 at 30%, unit not printed) and thinned from 90.7 to 50.7 for Span 20 at 40% yang2023 R15, X8. (synthesis: 30 parts of ritonavir in 110 parts of solid is about 27 wt%, close to the cited binary limit of 25%, so part of the gain at "30%" is dilution by the surfactant.)

papersystemmethod and conditionsresultids
yang2023ritonavir–PVPVA 30% + 10 parts Span 85, Span 20, Tween 80, SDScompacts, pH 6.8, 37 °C, 90 mindrug ≈87 / 87–97 / 50 / 70% against 30% citedyang2023 R2, R1
yang2023same at 40%same≈1 / 8 / 57 / 48–54%yang2023 R2
yang2023Tween 80 and SDS at 50%same≈22 / 33–39%, polymer ≈85 / 89%yang2023 R2, R3
yang2023ten formulationsconfocal, surfaces, cross-sections, in siturelease with discrete droplets or one-phase gel; none with a persistent continuous layeryang2023 R6–R14, C40
yang202330% films ± surfactantRH steps, 12 hwater for separation 14.0 / 16.0 / 10.5 / 12.5 / 24.5% (none / Span 85 / Span 20 / Tween 80 / SDS)yang2023 R21
yang2023amorphous ritonavir ± Span 20 or Span 85DSC onset46.8 → 7.7–27.8 °Cyang2023 R22
yang2023SDS 40% compact, before and after 30 minXPS; ATR-FTIRSDS ≈60 → 98 wt% of the surface; ritonavir ≈41 → 40%yang2023 R17, R19
indulkar2022ritonavir–PVPVA 30% with 5 parts of SDS, Tween 80, Span 20, Span 85 or TPGScompacts, 90 minSDS ≈80% then stop, needles by 15 min; Tween 80 ≈25–28%; Span 20 plateau ≈40%; Span 85 and TPGS near completeindulkar2022 R5, R6, R7, R8, R9, R15
correasoto2022aclopidogrel–PVPVA 50% film ± SDS100% RH, 5 minbicontinuous without, nearly uniform with SDScorreasoto2022a R21

Figure

Fig. 6 of yang2023: Span 85, 30% ritonavir, in situ: a continuous layer forms, is swept away and forms again
Fig. 6 · yang2023Span 85, 30% ritonavir, in situ: a continuous layer forms, is swept away and forms again

A red drug-rich rim at the interface (panels h, i) is removed by agitation, releasing the droplets beneath (j), and re-forms (k); the rotated compacts of the same dispersion showed only small domains yang2023 R8.

Fig. 9 of yang2023: SDS, 40% ritonavir, after partial dissolution: a one-phase gel
Fig. 9 · yang2023SDS, 40% ritonavir, after partial dissolution: a one-phase gel

The cross-sections (d–f) show a uniform orange gel with red domains only at the gel–solution boundary, where the binary dispersion of the 2022 study carried a continuous layer at 40% yang2023 R13, X18.

Why

The authors read their results on a schematic ritonavir–PVPVA–water diagram: as water enters, the gel moves into the miscibility gap below the vitrification line, and by the lever rule a low loading yields little drug-rich phase (discrete) and a high loading much (continuous, a barrier if it resists the flow) (F30) yang2023 C41. SDS enlarges the miscible region, so the gel can dissolve without separating and, at high loading, yields less drug-rich phase; separation confined to the wettest surface of the gel is "likely responsible" for the better SDS release yang2023 C9, C10, C42. The Spans partition into the drug-rich phase (cited) and lower its Tg, so a continuous layer "is expected to be more liquid-like" and is removed as fast as it forms under rotating-disk shear; the authors attribute barrier disruption by the non-ionic surfactants to plasticization ("is attributed to") and judge that the Spans act "most likely" kinetically, since they did not raise the water needed for separation yang2023 C18, C35, C11, C36. Tween 80 on droplet surfaces "likely" causes agglomeration, which "could potentially explain" its slower release yang2023 C22, C20. SDS accumulating at the dissolving surface "conceivably" promotes ritonavir crystallization, to which the plateau "can be attributed", so SDS has a positive and a negative effect yang2023 C50, C24, C51. Faster polymer dissolution with SDS and Tween 80 "is expected" to speed congruent release at low loading yang2023 C48. They "propose" that, of the many surfactant effects, preventing or disrupting a continuous drug-rich layer is the most critical for release yang2023 C37. (synthesis: this puts the surfactant gains of F21 on the interface picture of F25: the same surfactant can act through the phase diagram (SDS) or through the mobility of the drug-rich phase (Spans), which is why the best surfactant differed between drugs; the SDS crystals agree with SDS shortening ritonavir and atazanavir induction times in solution (Supersaturation from ASD dissolution F14, Crystallization from solution F38), and the Tween 80 agglomeration is a form of the droplet agglomeration that failed short-chain PVP dispersions (F29).)

Conditions and limits

One drug, one polymer, one surfactant level (10 parts), loadings of 30–50% counted on drug and polymer only, one rotation speed yang2023 A1, X10. The surfactant-free release and morphology are cited from the 2019 and 2022 studies yang2023 X5, X18. Text and figures disagree on the extent of release for Span 85 at 30%, Tween 80 at 30%, Span 20 at 40% and SDS at 40%; figure values are used here yang2023 X1, X2, X3, X4. The separation thresholds are single values bracketed by RH steps, so only the SDS shift exceeds the step resolution, and Span 20 and Tween 80 separated at less water than the binary yang2023 X15, X16. Plasticization of the layer formed in situ is inferred from ritonavir–Span mixtures at 20–40% Span; Tween 80 and SDS were not tested for Tg yang2023 X17. Crystals were imaged only at 30% SDS and not identified yang2023 X12. The 40% Span 85 and Tween 80 morphologies and the crystal check of the other surfactants rest on text descriptions of SI figures; in-situ agitation was uncontrolled yang2023 R9, R11, R16, C16.

Counterexamples and conflicts

The same Span 85 dispersion formed a continuous layer in the quiet chamber and none under rotation, so the morphology depends on the shear yang2023 R8, C16. Water uptake at 95% RH was faster with every surfactant only at first; by 30 min only Tween 80 and SDS stayed above the binary yang2023 R20, X13. In the 2022 surfactant study of the same system, with 5 instead of 10 parts of surfactant, Span 20 levelled near 40% and Tween 80 near 25–28% at 30% loading, where 10 parts gave about 87–97% and 50%, while SDS stopped near 80% with needle crystals by 15 min and Span 85 and TPGS released nearly completely, and 50 µg/mL SDS in the medium did nothing (F21, F19) indulkar2022 R7, R6, R5, R15, R8, R9, R10; yang2023 R2. For atazanavir every surfactant film separated within 10 min yet released, so a surfactant need not suppress separation to help (F20) correasoto2022b R11, R2.

Transfer check

For a PVPVA dispersion at one or two steps above its binary limit, make the ternary dispersion with a few parts of an ionic surfactant that raises the water needed for separation (test films at stepped RH against the binary) and with a lipophilic plasticizing surfactant, and dissolve compacts with drug and polymer assayed yang2023 R21, R22, P4. Image cross-sections after 5–20 min: a one-phase gel or droplets at the gel–solution boundary predicts release, a persistent drug-rich layer predicts failure yang2023 R13, R7. With SDS, check the dissolved surface for crystals and compare the plateau with the crystalline solubility, which this paper did not do; test physical stability before adopting a surfactant yang2023 X12, C52.

History

Surfactants were known to raise the limits of ledipasvir, felodipine, clopidogrel and atazanavir in PVPVA (F13, F21), and a vapour-sorption study of the same four ternary dispersions (Physical stability chapter) had found that the Spans partition into the ritonavir-rich phase, Tween 80 adsorbs on the droplets and all four lower the Tg yang2023 R27, R24. The 2022 interface study had imaged the binary system at 10–50% (F25) yang2023 R25. Yang and co-workers (2023) were the first in the library to image the interface of surfactant-containing dispersions in water and to measure the water needed for separation with each surfactant yang2023 C1. The polymer molecular-weight paper of 2024 lists surfactants among the additives that "may prevent" droplet agglomeration, untested (F29) deac2024a C52.

F35

Topic 5Formulation levers near the limit11 of 11

On 75% grazoprevir–HPMCAS particles a secondary excipient helped release only when it made the particles wettable.

Co-precipitated 75:25 grazoprevir–HPMCAS particles with a secondary excipient in the anti-solvent released, at 90 min of a two-stage test, about 37–52% when the excipient was SDS or 10 mg/mL HPMC, but about 8–20% with PVP, poloxamer 407 or HPMC dispersed rather than dissolved hiew2025 R9, R17. FaSSIF contact angles on powder beds split the materials the same way, 0–52° against about 119–137° hiew2025 R15. XPS surface grazoprevir was about 32–50% for good and poor particles alike hiew2025 R14.

strongStrong for the excipient screen, sixteen co-precipitates and six treated dispersions in one test with n = 3; moderate for wettability as the separating property, which rests on two clusters of seven materials with HPMC at twice the concentration of the others; weak to moderate for surface dilution being secondary hiew2025 K1, K2, K3, X11, X8.

wettablepoorly wettableSDS0° · release ≈37%HPMC 10 mg/mL30–52° · ≈52%PVP≈121° · ≈20%poloxamer 407≈131° · ≈13%MTBE-treated dispersion≈119° · ≈8%HPMC dispersed in heptane137° · ≈9%020406080100120140FaSSIF contact angle on the powder bed, °

Release at 90 min after a two-stage test; surface drug by XPS was about 32–50% in both groups. hiew2025 R15, R17, R14

as madeafter 1 min sonicationSDS≈37≈82HPMC5 mg/mL, 120 min mixing≈24≈73PVP≈20≈33poloxamer 407≈13≈140102030405060708090release at 90 min, %, without and with 1 min sonication

Breaking agglomerates helped mainly the wettable particles. hiew2025 R13, R18

For your drug

  1. For a high-loading particle dispersion of a hydrophobic drug, measure the FaSSIF contact angle of the powder bed alongside the XPS surface composition; an angle above 90° predicts poor release even with a diluted surface.
  2. Choose a secondary excipient that lowers the angle below 90° (here HPMC at 10 mg/mL or SDS), dissolve it in the anti-solvent rather than dispersing it, avoid strong gel formers, and test the physical stability of SDS-treated particles.

hiew2025 R15, R17, R14, C27, C55, C58

How it works and key numbers
  1. The high drug fraction makes the particle surfaces hydrophobic, so they wet poorly, which the authors found "hardly surprising" hiew2025 C38, R20.
  2. An excipient dissolved in the anti-solvent is left on the particles by the liquid held in the filter cake as it dries, and dilutes the surface drug hiew2025 C7, C16.
  3. Release "largely correlated" with contact angle, and "regardless of the surface grazoprevir concentration" the excipient type governed release: PVP and poloxamer diluted the surface like HPMC but released poorly hiew2025 C40, C35, C51.
  4. HPMCAS does not dissolve in SGF, so extra surface counts only in FaSSIF, and accessible surface area "enhances drug release only if the particles demonstrate good wettability" hiew2025 C32, C50.
  5. Gel strength ("could" form a barrier; poloxamer 407 and gelatin "may be less suitable") and affinity for drug or polymer are proposed, not measured, and SDS "likely" acted as a wetting agent hiew2025 C53, C55, C54, C57.
0–52° against ≈119–137°FaSSIF contact angle of the good and the poor releasershiew2025 R15
≈37–52% against ≈8–20%release at 90 min of the wettable and the poorly wettable grouphiew2025 R17
≈30 → 57%75% solvent-evaporated dispersion after high shear in 72.5 mg/mL HPMC, against ≈63% for a 20% dispersionhiew2025 R10
Evidence: data, conditions and papers

Finding F35. On 75% grazoprevir–HPMCAS particles a secondary excipient helped release only when it made the particles wet: HPMC and SDS gave FaSSIF contact angles of 0–52° and about 37–52% release, PVP, poloxamer 407 and undissolved HPMC 119–137° and about 8–20%, while XPS surface drug contents of good and poor particles overlapped

In short. Co-precipitated 75:25 grazoprevir–HPMCAS particles with 5 mg/mL of a secondary excipient in the acidified anti-solvent released, at 90 min of a two-stage SGF → FaSSIF test, about 37% (SDS), 31% (TPGS, PEG), 23% (HPMC), 21% (PVP), 14% (gelatin) and 13% (poloxamer 407), against about 30% for a 75% solvent-evaporated dispersion and 17% for the binary co-precipitate; 10 mg/mL HPMC, or 5 mg/mL HPMC with 0.5 mg/mL SDS, gave about 47–52%, near a 30% dispersion (about 43%) hiew2025 R9, R13. FaSSIF contact angles on powder beds split the materials into a wettable group (SDS 0°, HPMC about 30–52°) releasing about 37–52% and a poorly wettable group (PVP about 121°, poloxamer about 131°, an MTBE-treated dispersion about 119°, HPMC dispersed in heptane 137 ± 5°) releasing about 8–20% hiew2025 R15, R17. XPS surface grazoprevir before the acid stage was about 32–50% for good and poor particles alike hiew2025 R14. One minute of sonication raised release to about 73–82% for HPMC and SDS particles but only about 14–33% for PVP and poloxamer hiew2025 R13. The authors conclude that "proper wetting of the particles is pivotal"; the correlation is two clusters of seven materials, with HPMC compared at twice the concentration of the others hiew2025 C59, C40, X11, X8.

Type. single-system observation (grazoprevir–HPMCAS-LG at 75% with seven secondary excipients) Strength. for the excipient screen, sixteen co-precipitates and six treated dispersions in one test, n = 3 hiew2025 K1: strong; moderate for wettability as the separating property hiew2025 K2: moderate; weak to moderate for surface dilution being secondary to wettability hiew2025 K3: weak to moderate.

How it was shown

Hiew and co-workers (2025) co-precipitated 75:25 grazoprevir–HPMCAS-LG under high shear into 0.001 N HCl holding 5 or 10 mg/mL HPMC or 5 mg/mL of six other excipients hiew2025 P5, P6, P7. They tested release in a two-stage SGF → FaSSIF test and measured surface drug by XPS, FaSSIF contact angles on powder beds and the effect of 1 min sonication hiew2025 P13, P16, P17, P14.

What the data show

High-shear treatment in HPMC or SDS solution raised a 75% solvent-evaporated dispersion from about 30% to 43–57%, against about 63% for a 20% dispersion hiew2025 R10.

systemmethod and conditionsresultids
75:25 particles, 5 mg/mL secondary excipienttwo-stage SGF → FaSSIF, 90 minSDS ≈37, TPGS / PEG ≈31, HPMC ≈23, PVP ≈21, gelatin ≈14, poloxamer ≈13%; SE-75 ≈30%hiew2025 R9
particles with 10 mg/mL HPMC; HPMC + SDSsame≈47–52%; ≈47% (SE-30 ≈43%)hiew2025 R9
seven materialsFaSSIF contact angle on powder beds, 10 s0–52° (SDS, HPMC) against ≈119–137°hiew2025 R15
samerelease at 90 min against contact angle≈37–52% against ≈8–20%hiew2025 R17
five materialsXPS surface grazoprevir before SGF≈32–50% for good and poor alikehiew2025 R14
nine particles1 min sonication in SGFHPMC ≈24 → 73%, SDS ≈37 → 82%; PVP ≈20 → 33%, poloxamer ≈13 → 14%hiew2025 R13
Fig. 11 of hiew2025: release at 90 min against FaSSIF contact angle without (a) and with (b) 1 min sonication
Fig. 11 · hiew2025release at 90 min against FaSSIF contact angle without (a) and with (b) 1 min sonication

The wettable materials (SDS, HPMC) sit at the upper left, the poorly wettable ones (PVP, poloxamer, heptane cPAD, MTBE-treated dispersion) at the lower right; it is two groups, not a line, and SDS at 0° sits below the HPMC points hiew2025 R17, R18, X11.

Why

The authors read the high drug fraction as making the particle surfaces very hydrophobic, so that poor wetting is "hardly surprising" hiew2025 C38, R20. Release "largely correlated" with contact angle, "suggesting a relationship between wettability and effective drug release", and the excipient type governed release regardless of the surface drug content, since PVP and poloxamer diluted the surface like HPMC but released poorly hiew2025 C40, C35, C51. Accessible surface area "enhances drug release only if the particles demonstrate good wettability" hiew2025 C50.

Limits and transfer

HPMC was best only at 10 mg/mL, compared against 5 mg/mL of the other excipients, and within the wettable group the fully wetting SDS particles released less than the HPMC ones hiew2025 X8, R17, X11. For a high-loading particle dispersion, measure the FaSSIF contact angle of the powder bed beside the XPS surface composition: an angle above 90° predicts poor release even with a diluted surface; choose an excipient that lowers it, dissolve it in the anti-solvent and avoid strong gel formers hiew2025 R15, R17, R14, C27, C55.

How it was shown

Hiew and co-workers (2025) asked why some secondary excipients deposited on high-loading co-precipitated amorphous dispersions (cPADs) improve release and others do not hiew2025 C8. They injected grazoprevir and HPMCAS-LG (75:25) in THF into the high-shear zone of a rotor–stator homogenizer in ice-cold 0.001 N HCl holding 5 or 10 mg/mL HPMC, or 5 mg/mL PVP K29/32, PEG 3350, gelatin, poloxamer 407, SDS or TPGS, mixed the slurry 5–120 min, and filtered and dried the particles; controls were a binary cPAD, a cPAD precipitated into heptane with micronized HPMC dispersed afterwards, and wet-mill material made at 100 g scale, sieved or not hiew2025 P5, P6, P7, P8, P9. They also stirred a cryomilled 75% rotary-evaporated dispersion for 5 min at high shear in 10 or 72.5 mg/mL HPMC (acidified water), 5 mg/mL SDS (water) or briefly in MTBE hiew2025 P4. Release was a non-sink two-stage test at 37 °C and 100 rpm, a dose equal to 150 µg/mL (the amorphous solubility in FaSSIF) in SGF for 30 min, then FaSSIF to 90 min, with in-line UV (n = 3), against rotary-evaporated dispersions at 20, 30 and 75% hiew2025 P13, P2. They measured surface grazoprevir by XPS (about 10 nm, five spots) before and after 30 min in SGF, FaSSIF and SGF contact angles of drops on powder beds over 10 s (n = 4), particle structure by SEM, the effect of 1 min sonication in SGF before release, and the HPMC taken up by precipitating HPMCAS hiew2025 P16, P17, P15, P14, P18.

What the data show

All particles released about 1% or less in SGF hiew2025 R9. At 5 mg/mL excipient, release at 90 min was about 37% (SDS), 31% (TPGS and PEG), 23% (HPMC), 21% (PVP), 14% (gelatin) and 13% (poloxamer 407), against reference lines of about 30% (75%), 43% (30%) and 63% (20% dispersion), and about 17% for the binary cPAD; the calculated loadings of the gelatin, PEG, PVP and poloxamer cPADs were similar to the 73.9% of the 5 mg/mL HPMC cPAD hiew2025 R9, R13, R8. HPMC at 10 mg/mL gave about 47% (5 min mixing) and 52% (120 min, 71.6% loading), and 5 mg/mL HPMC with 0.5 mg/mL SDS about 47% hiew2025 R9, R8. All cPADs showed the same porous network of rod-like structures hiew2025 R5. FaSSIF contact angles started at about 93–137°; the SDS cPAD wetted completely from 1 s, the 10 mg/mL HPMC cPADs fell to about 30° and 51–52°, and PVP (about 121°), poloxamer (about 131°), the MTBE-treated dispersion (about 119°) and the heptane cPAD (137 ± 5°) stayed constant hiew2025 R15. Release at 90 min was about 37% (SDS) and 52% (both HPMC cPADs) in the wettable group, and about 20% (PVP), 13% (poloxamer), 9% (heptane) and 8% (MTBE) in the other hiew2025 R17. After 1 min sonication release was about 82% (SDS), 66% (HPMC), 33% (PVP) and 14% (poloxamer) hiew2025 R18. Sonication raised the 5 mg/mL HPMC cPAD made with 120 min mixing from about 24 to 73%, the binary cPAD from about 17 to 27%, TPGS from 31 to 49% and PEG from 31 to 42%, and sieving the wet-mill HPMC material raised it from about 43 to 59% and 36 to 52% hiew2025 R13, R11. XPS surface grazoprevir before and after SGF was about 45 → 46% (dispersion treated with 72.5 mg/mL HPMC), 50 → 69% (10 mg/mL HPMC cPAD), 32 → 56% (SDS), 33 → 53% (PVP) and 45 → 46% (poloxamer) hiew2025 R14. High-shear treatment raised the 75% dispersion from about 30% to 57% (72.5 mg/mL HPMC), 43% (10 mg/mL HPMC) and 54% (SDS), against about 63% for a 20% and 43% for a 30% dispersion hiew2025 R10. The heptane cPAD released 9.2%, and precipitating HPMCAS took up 0.62 of 2.5 mg and 1.13 of 5 mg HPMC added hiew2025 R12, R6. (synthesis: the wettable and poorly wettable groups differ by at least 67° in contact angle, 119 − 52, and by at least 17 points in release, 37 − 20.)

papersystemmethod and conditionsresultids
hiew2025grazoprevir–HPMCAS 75:25 cPADs, 5 mg/mL secondary excipienttwo-stage SGF → FaSSIF, 90 minSDS ≈37, TPGS / PEG ≈31, HPMC ≈23, PVP ≈21, gelatin ≈14, poloxamer ≈13%; SE-75 ≈30%hiew2025 R9
hiew2025cPADs with 10 mg/mL HPMC; HPMC + SDSsame≈47–52%; ≈47% (SE-30 ≈43%)hiew2025 R9
hiew2025seven materialsFaSSIF contact angle on powder beds, 10 s0–52° (SDS, HPMC) against ≈119–137°hiew2025 R15
hiew2025samerelease at 90 min against contact angle≈37–52% against ≈8–20%hiew2025 R17
hiew2025five materialsXPS surface grazoprevir before SGF≈32–50% for good and poor alikehiew2025 R14
hiew2025nine cPADs1 min sonication in SGFHPMC ≈24 → 73%, SDS ≈37 → 82%; PVP ≈20 → 33%, poloxamer ≈13 → 14%hiew2025 R13
hiew202575% solvent-evaporated dispersionhigh shear in HPMC or SDS solution≈30 → 57% (72.5 mg/mL HPMC), 43% (10 mg/mL), 54% (SDS)hiew2025 R10
hiew2023grazoprevir–HPMCAS-LF cPADs ± HPMC or HPCXPS against release at 90 min≤34% surface drug with ≈47–72%; ≥53% with ≈8–17%hiew2023 R14

Figure

Fig. 11 of hiew2025: release at 90 min against FaSSIF contact angle without (a) and with (b) 1 min sonication
Fig. 11 · hiew2025release at 90 min against FaSSIF contact angle without (a) and with (b) 1 min sonication

The wettable materials (SDS, HPMC) sit at the upper left, the poorly wettable ones (PVP, poloxamer, heptane cPAD, MTBE-treated dispersion) at the lower right; it is two groups, not a line, and SDS at 0° sits below the HPMC points hiew2025 R17, R18, X11.

Fig. 9 of hiew2025: XPS surface grazoprevir before and after 30 min in SGF
Fig. 9 · hiew2025XPS surface grazoprevir before and after 30 min in SGF

Before SGF all five materials lie at about 32–50%, well below the 75% loading, and the poorly releasing PVP and poloxamer particles lie among the good ones hiew2025 R14.

Why

The authors read the high drug fraction as making the particle surfaces very hydrophobic, so that they wet poorly, which they found "hardly surprising" hiew2025 C38, R20. A secondary excipient dissolved in the anti-solvent is left on the particles by the liquid held in the filter cake as it dries, helped for HPMC by its partial co-precipitation with HPMCAS, and dilutes the surface drug hiew2025 C7, C16. Whether this helps depends on the excipient: release "largely correlated" with contact angle, "suggesting a relationship between wettability and effective drug release", and "regardless of the surface grazoprevir concentration" the excipient type governed release, since PVP and poloxamer diluted the surface to similar extents as HPMC but released poorly hiew2025 C40, C35, C51. In SGF HPMCAS does not dissolve, so extra surface counts only in FaSSIF, where breaking agglomerates exposes area and aids wetting; accessible surface area "enhances drug release only if the particles demonstrate good wettability" ("suggest") hiew2025 C32, C50. Molecular weight did not predict an excipient's effect; gel strength ("could" form a barrier; poloxamer 407 and gelatin "may be less suitable") and affinity for the drug or primary polymer ("may be another important attribute") are proposed, not measured hiew2025 C52, C53, C55, C54. SDS sat mainly on the surface and "likely" acted as a wetting agent rather than a plasticizer; HPMC must be "dissolved rather than dispersed" in the anti-solvent hiew2025 C57, C27. (synthesis: this limits F28: in the 2023 grazoprevir study a low surface drug content separated good from poor co-precipitates, but here, among particles whose surfaces were already diluted to 32–50% drug, wettability separated them; a surface diluted by a non-wetting or gel-forming polymer did not release, so the surface must be both drug-poor and wettable. In the ASD dissolution chapter drug loading and polymer set how fast a dispersion released and whether it reached the ceiling (Supersaturation from ASD dissolution F10); here a surface treatment let a 75% dispersion release like a 20–30% one.)

Conditions and limits

One drug, one primary polymer (HPMCAS-LG), one high loading, a two-stage test of 90 min at a dose equal to the amorphous solubility in FaSSIF, drug release only hiew2025 P13, P1. HPMC was the best excipient only at 10 mg/mL, and the contact-angle and XPS comparisons set 10 mg/mL HPMC against 5 mg/mL of the others hiew2025 X8. Contact angles were measured for seven materials, not for the TPGS, PEG, gelatin or 5 mg/mL HPMC cPADs hiew2025 X8. XPS covers five materials without an untreated baseline, and "similar" surface contents differ by up to about 17 points hiew2025 X10, X9. The heptane control differs in several process steps and its profile is not shown; sonication conditions are not stated hiew2025 X18, X12. No storage stability, crystallinity or Tg of the treated particles was reported hiew2025 C46, C58.

Counterexamples and conflicts

Within the wettable group the fully wetting SDS cPAD (0°) released less than the HPMC cPADs (30–52°) hiew2025 R17, X11. At 5 mg/mL HPMC (about 23%) was below SDS, TPGS and PEG, so its advantage needed the higher concentration hiew2025 R9, X8. PVP, PEG, TPGS and gelatin particles also gained about 11–18 points on sonication hiew2025 X19. In the 2023 study surface drug content did separate two groups of co-precipitates whose surfaces ranged from 10 to 84% drug (F28) hiew2023 R14. The MTBE-treated dispersion released less than the untreated 75% dispersion, which is not explained hiew2025 X14.

Transfer check

For a high-loading particle dispersion of a hydrophobic drug, measure the FaSSIF contact angle of the powder bed alongside XPS surface composition: an angle above 90° predicts poor release even with a diluted surface hiew2025 R15, R17, R14. Choose a secondary excipient that lowers the angle below 90° (HPMC at 10 mg/mL or SDS in the anti-solvent here), dissolve it in the anti-solvent rather than dispersing it, avoid strong gel formers, and de-agglomerate larger batches by sieving hiew2025 C27, C55, C30. Test physical stability of SDS-treated particles before adopting them hiew2025 C58.

History

Hierarchical co-precipitates with an HPMC coat had been made to fix wetting at moderate loading (Schenck 2021, cited), and Hiew and co-workers (2023) linked a low surface drug content to good release and exposure at 70–75% grazoprevir (F28) hiew2025 R22, C7. Hiew and co-workers (2025) were the first in the library to screen secondary excipients on such particles against wettability and to apply them by high shear to a solvent-evaporated dispersion; they call the approach "promising" for high-loading formulations hiew2025 C11, C46.

Other chaptersextends B F10

01Development line

One entry per paper in year order: what the library already knew, what the paper added, and how it relates to earlier entries.

  1. 2017
    indulkar2017borigin of nanodroplets from dissolving nifedipine dispersions, isotope scramblingfirst proposed

    Origin of Nanodroplet Formation upon Dissolution of an Amorphous Solid Dispersion: A Mechanistic Isotope Scrambling Study

    Note
    Known in the library (builds_on: Alonzo 2011, Ilevbare 2013 on LLPS, Jackson 2015, Indulkar 2016): certain dispersions form nanodroplets on dissolution, more often at low loading, depending on polymer type and loading indulkar2017b C6; above the amorphous solubility excess drug separates as water-saturated drug-rich droplets indulkar2017b C3; the droplets sustain the maximum membrane flux as a reservoir indulkar2017b C4; two proposed origins, dissolution followed by LLPS (mechanism I) or release of drug-rich domains formed by AAPS in the hydrated matrix (mechanism II, cited) indulkar2017b C7, C8.
    Added
    a deuterium label in the medium diluted as full mixing predicts when nifedipine dispersions with HPMC-E5 or PVPVA dissolved at 5 °C, with slow droplet–solution exchange at that temperature, and release that continued into water saturated at the amorphous solubility indulkar2017b R11, R3, R8, R9.
    Relation
    first in the library to test where the nanodroplets of a dissolving dispersion come from; supports mechanism I for these systems ("strongly suggest") indulkar2017b C26.
    Note
    Findings: F1, F2, F4, F5.
  2. 2017
    purohit2017britonavir dispersions during hydration and dissolutionfirst proposed

    Phase Behavior of Ritonavir Amorphous Solid Dispersions during Hydration and Dissolution

    Note
    Known in the library (builds_on: Rumondor 2009, 2010 and 2011, Alonzo 2011, Ilevbare 2013 on LLPS, Purohit 2015 on phase separation kinetics, Raina 2015 on fluorescent probes): water can separate a hydrated dispersion into drug-rich and drug-lean domains (AAPS) purohit2017b C9; hygroscopic polymers favour it purohit2017b C45; 50% ritonavir–PVP and –PVPVA dispersions had separated within 10 s of water contact purohit2017b R20; LLPS above the amorphous solubility, for ritonavir at a similar concentration by several routes purohit2017b C10, C47.
    Added
    all PVP and PVPVA films separated at 97% RH and HPMCAS films did not purohit2017b C1; only low-loading PVP and PVPVA and all HPMCAS films passed the amorphous solubility and formed nanodroplets, and drug kept pace with the polymer only where they formed purohit2017b R11, R7, C52; humid storage removed LLPS from PVP and PVPVA dispersions purohit2017b C53.
    Relation
    first in the library to link water-induced phase separation with loss of LLPS on dissolution; argues against matrix domains as the source of the droplets ("we find no evidence") purohit2017b C56.
    Note
    Findings: F3, F4, F5, F8, F11, F12.
  3. 2018
    bhardwaj2018surface-area-normalized dissolution of spray-dried and melt-extruded itraconazole–PVPVAfirst proposed

    Surface area normalized dissolution to study differences in itraconazole-copovidone solid dispersions prepared by spray-drying and hot melt extrusion

    Note
    Known in the library (builds_on: Purohit 2015 on ITZ–HPMC miscibility, Li 2017, Mugheirbi 2017): pyrene fluorescence and TEM contrast to detect drug-rich domains, and water in the solvent as a cause of drug-rich domains bhardwaj2018 C37.
    Added
    constant-area compacts with drug and polymer assayed and loading-normalized rates bhardwaj2018 P6, P7, E4, R11; amorphous ITZ dissolving about 18 times faster than the crystal bhardwaj2018 R5; a switch between 25 and 20% (spray-dried) and 20 and 10% (melt-extruded) bhardwaj2018 X6; the spray solvent changing surface drug content and release at 20% bhardwaj2018 R13, R20.
    Relation
    first in the library with the surface-normalized two-component method, which the later papers take over saboo2019 P9; saboo2020a P6.
    Note
    Findings: F1, F2, F3, F6, F14.
  4. 2019
    indulkar2019aritonavir–copovidone tablets, congruent release and the limit of congruencyextends

    Insights into the dissolution mechanism of ritonavir-copovidone amorphous solid dispersions: importance of congruent release for enhanced performance

    Note
    Known in the library (builds_on: Alonzo 2011, Ilevbare 2013 on LLPS, Purohit 2015 on phase separation kinetics, Indulkar 2017, Purohit 2017): the ritonavir amorphous solubility (about 30 µg/mL) and wet Tg (about 0 °C) indulkar2019a M1; impaired release without droplets at high loading for some compounds indulkar2019a C13; water-induced AAPS indulkar2019a C14; the Higuchi two-component model and Corrigan's note that it fails for low-loading dispersions indulkar2019a C23, C24.
    Added
    the limit of congruency, defined as the highest loading with congruent release (25%), and release "falling off a cliff" above it indulkar2019a C2, C31, R11; release into ritonavir-saturated medium that separates the regimes indulkar2019a R12; a drug-rich tablet surface by IR within minutes at 50% indulkar2019a R16; films that separate on contact with water above the limit and not below indulkar2019a R18.
    Relation
    names the limit; extends Purohit 2017 from films to tablets and takes the dissolution-then-LLPS route of Indulkar 2017 for the droplets indulkar2019a C49.
    Note
    Findings: F1, F2, F3, F4, F6, F7, F8.
  5. 2019
    que2019ledipasvir–copovidone, drug loading and drug–polymer interactionsextends

    Insights into the Dissolution Behavior of Ledipasvir-Copovidone Amorphous Solid Dispersions: Role of Drug Loading and Intermolecular Interactions

    Note
    Known in the library (builds_on: Rumondor 2009, Purohit 2015 on phase separation kinetics, Indulkar 2016, Purohit 2017, Indulkar 2019, Saboo 2019): the LoC concept and its variability in PVPVA (ritonavir 25%, cited limits for other drugs) que2019 C6, R27; colloids form only under polymer control que2019 C4; colloids as a reservoir que2019 C3; AAPS on contact with water que2019 C34; phase segregation at the dissolution front of polyphase mixtures forming a barrier layer que2019 C5.
    Added
    a limit of 5–7.5% for a high-Tg drug que2019 C10; surface drug enrichment by XPS within 10 min que2019 R15; drug–drug hydrogen bonds broken by PVPVA up to about 7–10% loading, near the limit que2019 R25, C45; SDS raising the limit to 30% and poloxamer 407 to 7.5%, with smaller colloids que2019 C12, R12.
    Relation
    extends the limit to a drug with a low value; first in the library to raise it with a surfactant que2019 C56.
    Note
    Findings: F3, F4, F6, F7, F8, F9, F10, F13.
  6. 2019
    saboo2019congruent release as a "sweet spot", nilvadipine and cilnidipine in PVPVAconfirmsrevises

    Congruent release of drug and polymer: A “sweet spot” in the dissolution of amorphous solid dispersions

    Note
    Known in the library (builds_on: Ilevbare 2013 on LLPS, Mosquera-Giraldo 2015, Raina 2015 on dihydropyridines, Saboo 2017, Bhardwaj 2018, Indulkar 2019): polymer-controlled release at low and drug-controlled release at high loading, a picture "likely" oversimplified, with the switch loading poorly understood saboo2019 C4; high RH known to induce phase separation in some dispersions saboo2019 C15; the surface-normalized method and the ritonavir and itraconazole drop-offs (builds_on).
    Added
    the cliff for two drugs 2.5 log units apart at about the same molar loading, refuting the log P hypothesis saboo2019 R7, C35; nanodroplets only from congruent dispersions ("a clear link") saboo2019 C30; a porous, drug-rich surface above the switch saboo2019 R13, R18; humidity turning a congruent compact incongruent saboo2019 C41; the same cliff in powder dissolution saboo2019 R20, R21.
    Relation
    confirms the ritonavir cliff for two more drugs; revises the expectation that the more lipophilic drug switches earlier saboo2019 C6, C35.
    Note
    Findings: F1, F2, F3, F4, F6, F7, F8, F9, F12.
  7. 2020
    saboo2020arelease against drug loading for five polymers, felodipineextends

    Patterns of drug release as a function of drug loading from amorphous solid dispersions: A comparison of five different polymers.

    Note
    Known in the library (builds_on: Konno 2006, Purohit 2015 on phase separation kinetics, Purohit 2017, Saboo 2017, Bhardwaj 2018, Indulkar 2019, Que 2019, Saboo 2019): congruent release seen only at low loading, mostly with PVPVA, and a limit thought to depend on drug properties and interactions saboo2020a C4; no correlation between polymer properties and the limit established saboo2020a C5; water-induced AAPS turning congruent into incongruent release saboo2020a C40; no log P effect at low loading saboo2020a C33.
    Added
    limits of 10, 15 and 10% with PVP, PVPVA and HPMC and none to 50% with HPMCAS and Eudragit S 100 saboo2020a R15; polymer hydrophobicity by water sorption and contact angle saboo2020a R3, R4; the trade-off between fast release at low loading and workable release at higher loading saboo2020a C55; release falling with log P at 40% in HPMCAS saboo2020a R16, C19; no positive correlation between drug–polymer hydrogen bonding and the limit saboo2020a C48; the Higuchi critical ratio far below practical loadings saboo2020a R27.
    Relation
    extends the limit from a drug property to a polymer property; generalizes Purohit 2017's HPMCAS contrast to five polymers saboo2020a C49.
    Note
    Findings: F1, F2, F3, F6, F7, F8, F9, F10, F11.
  8. 2020
    saboo2020indomethacin and its methyl ester in PVPVA: hydrogen bonding, surface crystallization and glass transitionfirst proposedrevises

    Congruent release of drug and polymer from amorphous solid dispersions: insights into the role of drug-polymer hydrogen bonding, surface crystallization and glass transition

    Note
    Known in the library (builds_on: Taylor and Zografi 1997 on indomethacin–PVP hydrogen bonding, Rumondor 2009 and 2011, Purohit 2017, Indulkar 2019, Saboo 2019): polymer-controlled, congruent release at low loading with an abrupt decrease at a loading that varies between drug–polymer pairs saboo2020 C2; the same limit for two PVPVA dispersions of very different log P saboo2020 C4; drug–polymer hydrogen bonding considered advantageous to physical stability, with its role in release poorly understood saboo2020 C5.
    Added
    a limit of 10% for indomethacin against at least 25% for its methyl ester over 5 min, so that the hypothesis that hydrogen bonding raises the limit "appears to be incorrect" saboo2020 C14, C48; the surface of the 25% indomethacin compact followed by EDX, nanoTA and FTIR to about 60–72 wt% drug at 20 min saboo2020 R21, R28, R17, X15; congruent release of the ester stopped after 7.5–20 min by crystals on the surface saboo2020 R8, R22, C17; the indomethacin limit at 10% from 25 to 57 °C, 5% at 17 °C and below 5% at 10 °C, against a wet Tg onset of 18 °C for a 70% dispersion saboo2020 R29, R30.
    Relation
    first in the library to set a matched analogue without a donor, and the test temperature, against the limit; revises the hypothesis taken from Rumondor 2009 and 2011 that hydrogen bonding favours release saboo2020 C7, C48.
    Note
    Findings: F1, F2, F3, F4, F6, F7, F8, F10, F15, F17, F18, F19.
  9. 2021
    que2021four phenolphthalein analogues in PVPVA: hydrogen bonding, halogen bonding and the limitextends

    Impact of Drug−Polymer Intermolecular Interactions on Dissolution Performance of Copovidone-Based Amorphous Solid Dispersions

    Note
    Known in the library (builds_on: Indulkar 2019, Saboo 2019, Que 2019, Que 2020 on halogen bonding, Saboo 2020 on five polymers, Saboo 2020 on indomethacin, Crowley and Zografi 2002): phenolic OH groups can hydrogen-bond to the PVPVA carbonyl and iodine atoms can potentially halogen-bond to the same acceptor que2021 C2; halogen bonding to the VP carbonyl and the Me-TIPP data (Que 2020, builds_on); a lower limit for indomethacin than for its ester (Saboo 2020, builds_on).
    Added
    limits of 5% (PHPH) and 10% (TIPP) for the two phenols against 30% (Me-TIPP) and 40% (Me-PHPH) for their methyl ethers, 0.012–0.115 mol per 100 g que2021 R19, R20; VP carbonyl shifts of up to 30 cm⁻¹ for the phenols, 7 cm⁻¹ for Me-TIPP and minimal for Me-PHPH que2021 R7; the share of halogen-bonded iodine by XPS falling with loading que2021 R11, R12; drug and PVPVA leaving at the neat-polymer rate at every limit que2021 R21, C39; no obvious correlation of log P, amorphous solubility, Tg or molecular weight with the limit que2021 C29.
    Relation
    extends the indomethacin–ester comparison of Saboo 2020 to two analogue pairs and adds halogen bonding; proposes, without measuring it, that bonds persisting in water slow polymer hydration que2021 C44.
    Note
    Findings: F1, F2, F3, F4, F6, F9, F10, F15, F16, F17, F18.
  10. 2021
    saboo2021TPGS in felodipine–PVPVA dispersions at higher loadingextends

    Exploring the Role of Surfactants in Enhancing Drug Release from Amorphous Solid Dispersions at Higher Drug Loadings

    Note
    Known in the library (builds_on: Saboo 2019, Indulkar 2019, Li 2019, Que 2019, Saboo 2020 on five polymers, Saboo 2020 on indomethacin, Han 2019): surfactants raised the limit of ledipasvir–PVPVA but the mechanism "remains elusive" saboo2021 C6; hydrophobic polymers give higher limits but slower release saboo2021 C3; a drug-rich surface layer formed during hydration slows release saboo2021 C28; the transient gel layer model (Saboo 2020 on indomethacin, builds_on).
    Added
    limits of 25, 35 and 45% with 2, 5 and 10% TPGS against 15% without saboo2021 R12; the gain with TPGS below its CMC, so that micelles play "a negligible role", and no gain with TPGS dissolved in the medium saboo2021 R1, C33, R15; semi-continuous drug-rich domains at 0 and 2% TPGS against discrete domains at 5 and 10% in humidified films, and a porous surface layer only on the 0 and 2% tablets saboo2021 R21, R23, R19; TPGS lowering the dispersion Tg from 89.2 to 71.1 °C saboo2021 R5.
    Relation
    extends the surfactant result of Que 2019 to a second drug and a graded level; first in the library to tie release to the shape of the drug-rich phase ("appeared to be linked") saboo2021 C53.
    Note
    Findings: F1, F2, F4, F5, F6, F7, F8, F13, F15, F16, F20, F21.
  11. 2021
    yang2021six drugs of different Tg and log P in PVPVA and HPMCASextends

    Drug Release and Nanodroplet Formation from Amorphous Solid Dispersions: Insight into the Roles of Drug Physicochemical Properties and Polymer Selection

    Note
    Known in the library (builds_on: Indulkar 2019, Saboo 2019, Saboo 2020 on indomethacin, Que 2019, Jackson 2015, Mosquera-Giraldo 2018, Ilevbare 2013 on LLPS, Saboo 2017): high log P drugs were expected to undergo phase separation in the wet matrix more readily and impair release yang2021 C6, and high-Tg drugs to be detrimental to release and nanodroplet formation yang2021 C7.
    Added
    PVPVA powders failing at 25 and 40% for low-Tg loratadine and miconazole and at 5–10% for danazol, elbasvir, paclitaxel and ivacaftor, with no log P trend yang2021 R7, R8, R9, R10, R11, R12, C19; a cliff within a 10% loading span in every PVPVA system against a gradual decline with HPMCAS yang2021 C2; the loratadine limit falling from 30 to 2% (PVPVA) and 20 to 5% (HPMCAS) on cooling from 37 to 5 °C, below its wet Tg of 13.8 °C yang2021 R22, M1; HPMCAS keeping elbasvir and loratadine droplets smaller yang2021 R3, R6.
    Relation
    extends the temperature test of Saboo 2020 to a second drug and two polymers; Tg and hydrogen-bond donors went together across the drugs and were not separated yang2021 C25, C38.
    Note
    Findings: F1, F2, F3, F4, F6, F8, F9, F11, F15, F16, F17, F18, F19.
  12. 2022
    correasoto2022asurfactants in clopidogrel–copovidone dispersions: drug loading and nanodroplet stabilityextends

    Impact of Surfactants on the Performance of Clopidogrel-Copovidone Amorphous Solid Dispersions: Increased Drug Loading and Stabilization of Nanodroplets

    Note
    Known in the library (builds_on: Indulkar 2019, Que 2019, Saboo 2021, Saboo 2019, Saboo 2020 on indomethacin, Yang 2021, Indulkar 2017 on SDS, Indulkar 2016, Ueda 2020): drug-rich nanodroplets benefit bioavailability as a reservoir correasoto2022a C1; a supersaturated solution with a drug-rich phase is metastable and its droplets coarsen correasoto2022a C2; reported limits in PVPVA range from below 5 to about 30% correasoto2022a C45.
    Added
    a limit of about 40% for a low-Tg drug without hydrogen-bond donors, and 50% with SDS correasoto2022a C46, C47, C55; PVPVA dissolving about twice as fast from the binary dispersions as from the neat compact correasoto2022a R18, C30; SDS, TPGS or Tween 80 keeping the droplets at constant size for 4 h and CTAB agglomerating them correasoto2022a R6, C12; TPGS taken up into the droplets at about 50:17 w/w drug:TPGS correasoto2022a R12; uniform, bicontinuous and drug-continuous films at 40, 50 and 60% correasoto2022a R20.
    Relation
    raises the limit of a third drug with SDS, as Que 2019 did for ledipasvir, and extends the morphology link of Saboo 2021 to a binary dispersion correasoto2022a C55, C32.
    Note
    Findings: F1, F2, F3, F4, F6, F8, F13, F15, F16, F17, F18, F19, F20, F21.
  13. 2022
    correasoto2022bsurfactants and vinylpyrrolidone in atazanavir–PVPVA dispersions

    Role of surfactants in improving release from higher drug loading amorphous solid dispersions

    Note
    Known in the library (builds_on: Indulkar 2019, Que 2019, Saboo 2020 on indomethacin, Yang 2021, Saboo 2021, Indulkar 2015, Indulkar 2017 on SDS, Ueda 2021, Devotta 1995, Cooper 1986): the drug Tg plays a role in the limit and high-Tg drugs release poorly unless the loading is very low correasoto2022b C3; surfactants can raise release at higher loading, with selection mostly empirical correasoto2022b C4; the dry and wet Tg of atazanavir, 105 and 55 °C correasoto2022b M1.
    Added
    a limit of 5% for the binary dispersion, 10% with SDS or CTAB and 15% with Span 80 correasoto2022b R1, C12; every additive raising release at 10% by 4- to 35-fold, vinylpyrrolidone as well as the best surfactants correasoto2022b R20; release of the 10% binary dispersion restored at 55 °C until the drug crystallized correasoto2022b R5; additives lowering the dispersion Tg by 7–16 °C and making wet films separate within 10 min correasoto2022b R20, R10, R11.
    Relation
    tests plasticization as the cause of the surfactant effect with a plasticizer that is not a surfactant correasoto2022b C9, C40; a high-Tg drug where the clopidogrel paper of the same year studied a low-Tg one (synthesis).
    Note
    Findings: F1, F2, F3, F4, F6, F8, F13, F15, F18, F19, F20, F21.
  14. 2022
    hiew2022bamorphous salts of lumefantrine in PVPVA: Tg, release and stabilityfirst proposed

    Combining drug salt formation with amorphous solid dispersions – a double edged sword

    Note
    Known in the library (builds_on: Hiew 2022 on lumefantrine polymers, Towler 2008, Tong 1999 and 2002, Saboo 2020 on indomethacin, Yang 2021, Que 2019, Indulkar 2019, Narasimhan and Peppas 1996 and 1997): salt formation as a way to raise Tg and reduce recrystallization hiew2022b C6; impaired release from systems with a high Tg against the dissolution temperature hiew2022b C7; congruent release from fast-releasing PVPVA dispersions hiew2022b C25.
    Added
    salts raising the onset Tg from 19.7 °C to as much as about 101 °C hiew2022b R2; the highest loading with good release falling from 35% (free base) to 2% (sulfate) as the salt Tg rose hiew2022b R20; higher-Tg forms crystallizing later in storage hiew2022b R7, R8; the critical polymer volume fraction of PVPVA, 0.89 at 37 °C hiew2022b R21.
    Relation
    first in the subcategory to vary the Tg of one drug by salt formation and to show the stability–release trade-off hiew2022b C55, C53.
    Note
    Findings: F1, F2, F3, F6, F7, F8, F9, F15, F17, F18, F20, F22.
  15. 2022
    indulkar2022surfactants in ritonavir–copovidone dispersions above the limitextends

    Role of Surfactants on Release Performance of Amorphous Solid Dispersions of Ritonavir and Copovidone

    Note
    Known in the library (builds_on: Indulkar 2016, Purohit 2017, Indulkar 2019): the ritonavir–PVPVA limit of about 25%, with polymer-controlled, congruent release below it indulkar2022 R2; water-induced separation impeding release and nanodroplet formation in ritonavir dispersions (Purohit 2017, builds_on); the 30% binary dispersion with a lag, a period of congruent release and then incongruent, incomplete drug release indulkar2022 C30, R1; strategies that raise the limit called "essential" indulkar2022 C5.
    Added
    five surfactants at 5 parts per 100 parts of 30:70 ritonavir–PVPVA, every one removing the lag and giving congruent release for at least 20 min indulkar2022 C31; near-complete release with Span 85 and TPGS, release stopped near 80% by surface crystals with SDS, and about 41 and 25% with Span 20 and Tween 80 indulkar2022 R8, R9, R5, R15, R7, R6; early PVPVA release about doubled by SDS indulkar2022 C32, R20; a lowered Tg of surface material after dissolution with Tween 80 and Span 20, read as phase separation indulkar2022 R19, C19; released droplets from about 1 µm with the Spans to about 10 µm with Tween 80 indulkar2022 R11, R13.
    Relation
    extends the surfactant results of Que 2019, Saboo 2021 and the 2022 clopidogrel and atazanavir papers to a drug above its limit (synthesis); first in the subcategory to show a surfactant bringing surface crystallization to a drug that did not crystallize on the binary tablet indulkar2022 C38.
    Note
    Findings: F1, F8, F13, F15, F16, F19, F20, F21.
  16. 2022
    qi2022polymer salts of the enteric polymer HP-50 and their miconazole dispersionsfirst proposed

    Improved dissolution of an enteric polymer and its amorphous solid dispersions by polymer salt formation

    Note
    Known in the library (builds_on: Indulkar 2019, Saboo 2020 on five polymers, Yang 2021, Hiew 2022 on lumefantrine polymers): release worsening as the loading of a lipophilic drug rises; drug-dependent changes in enteric polymer dissolution; the miconazole pKa and amorphous solubility (builds_on); a critical ionization of about 83% for HP-50 qi2022 R19; the dependence of enteric polymer dissolution on buffer capacity, "well known" from coating work (cited) qi2022 C20.
    Added
    HP-50 dissolution set by the buffer species, fastest in BIS-TRIS and slowest in TEA, not by cation size qi2022 R1, R2, C14; nine salts dissolving about 3-fold faster than HP-50 whatever the counterion qi2022 R10, C3; HP-50-Na keeping its rate at 3 mM/ΔpH where HP-50 slowed 6-fold qi2022 R12, C4; dissolution rising with neutralization, the largest step from 80 to 100% qi2022 R13; 20% miconazole on HP-50-Na and its triethylamine salt releasing about 84–90% in 60 min against about 9% on HP-50 qi2022 R14.
    Relation
    first in the library to pre-ionize an enteric dispersion polymer as a salt qi2022 C44; adds an ionizing polymer whose own dissolution, not the drug, limits release to the hydrophobic-polymer contrast of Saboo 2020 (synthesis).
    Note
    Findings: F3, F15, F23, F24.
  17. 2022
    yang2022arelease mechanisms of ritonavir–copovidone: phase separation and its morphologyfirst proposed

    Release mechanisms of amorphous solid dispersions: Role of drug-polymer phase separation and morphology

    Note
    Known in the library (builds_on: Indulkar 2017, Purohit 2017, Indulkar 2019, Li 2019, Yang 2022 on surfactant-containing dispersions): solution-mediated nanodroplet formation (Indulkar 2017); fluorescent dyes for the phase behaviour of hydrating ritonavir dispersions (Purohit 2017); the limit of 25% yang2022a R15; the falling-off-the-cliff effect of PVPVA dispersions yang2022a C7; conflicting evidence on whether preformed discrete drug-rich domains help release (Li 2019, builds_on).
    Added
    drug release of about 100, 35 and at most 3% at 20, 30 and 40–50% yang2022a R2; cross-sections with a gel layer at every loading and a drug-rich crust from 30% yang2022a R5, R6, R7; the gel–glass front slowed above the limit yang2022a R8; real-time imaging of droplets of 0.5–2 µm leaving with the polymer at 10–20% and a continuous drug-rich layer at 30–40% yang2022a R10, R11, R12, R13; XPS surface ritonavir rising from 35 to 72% at 40% yang2022a R14.
    Relation
    first in the library to image the separation in dissolving compacts, in cross-section and in real time yang2022a C5; reconciles the solution route of Indulkar 2017 with water-induced separation at the gel–solution interface yang2022a C50, C51; carries the morphology link of Saboo 2021 and the 2022 clopidogrel paper from humidified films to dissolving compacts (synthesis).
    Note
    Findings: F1, F3, F5, F6, F7, F8, F18, F20, F25.
  18. 2023
    bapat2023media choice for HPMCAS dispersions: buffer capacity, gel pH and releaseconfirmsextends

    Does Media Choice Matter When Evaluating the Performance of Hydroxypropyl Methylcellulose Acetate Succinate-Based Amorphous Solid Dispersions?

    Note
    Known in the library (builds_on: Saboo 2020 on indomethacin, Hiew 2022 on lumefantrine polymers, Yang 2022 on release mechanisms, Nguyen 2023 on delamanid): polymer-controlled release in copovidone dispersions (Saboo 2020, Yang 2022); drug release linked to HPMCAS dissolution and the HPMCAS-MF pKa of 4.92 or 5.0 bapat2023 M3; HPMCAS solubility rising between pH 5.0 and 6.5 (Nguyen 2023, builds_on).
    Added
    the neat HPMCAS-MF rate rising about sixfold from 3 to 51 mM/ΔpH in pH 6.8 phosphate bapat2023 R5; FaSSIF equal to its blank buffer and no dissolution in FeSSIF V1 at pH 5.0 bapat2023 R7, R8; a gel layer only from 13 mM/ΔpH, 3 to 19 µm thick, with an apparent pH of 5.6–6.2 bapat2023 R14, R15; drug at the polymer's rate for 10% indomethacin and its methyl ester bapat2023 R9, R13; rate linear in the square root of rotation speed without a plateau bapat2023 R18, R19; the drugs lowering polymer release and water uptake bapat2023 R20, C46.
    Relation
    extends the buffer-capacity result of Qi 2022 from HP-50 to HPMCAS and adds the gel pH bapat2023 C51; confirms polymer-controlled release for HPMCAS dispersions of acidic and neutral drugs bapat2023 C49.
    Note
    Findings: F1, F2, F11, F15, F23, F24.
  19. 2023
    correasoto2023plasticizers in PVPVA dispersions of high-Tg drugsextends

    Release Enhancement by Plasticizer Inclusion for Amorphous Solid Dispersions Containing High Tg Drugs

    Note
    Known in the library (builds_on: Indulkar 2019, Que 2019, Saboo 2020 on indomethacin, Correa Soto 2022 on atazanavir): binary limits of 25% (ritonavir), 5% (ledipasvir) and 5% (atazanavir), cited correasoto2023 R14, R11, R1; the link between drug Tg and the limit (Saboo 2020, builds_on); surfactants raising the limit possibly by plasticization (Correa Soto 2022, builds_on).
    Added
    the atazanavir limit raised from 5 to 7.5–25% by 5 g per 100 g of nine plasticizers correasoto2023 R1, C12; ledipasvir from 5 to 15–20% with 10 g correasoto2023 R11, C17; ritonavir from 25 to 30% correasoto2023 R14; the Tg of 8:1 drug–plasticizer glasses lowered by 30–53 °C correasoto2023 R17, R18; neat PVPVA dissolving faster with GTB or TBC correasoto2023 R13; little change in water vapour uptake correasoto2023 C34.
    Relation
    extends the vinylpyrrolidone test of Correa Soto 2022 to plasticizers that are not surfactants and to two more drugs correasoto2023 C28; the gain was largest for the highest-Tg drugs correasoto2023 C21.
    Note
    Findings: F15, F16, F18, F21, F26.
  20. 2023
    deac2023athe dissolution interface of two phenolphthalein analogues in PVPVAextends

    Dissolution Mechanisms of Amorphous Solid Dispersions: A Close Look at the Dissolution Interface

    Note
    Known in the library (builds_on: Saboo 2017, Indulkar 2019, Que 2021, Deac 2023 on drug load): the prodan and rhodamine 6G dye pair for confocal imaging (Saboo 2017, builds_on); congruent release, the limit and the surface barrier; limits of 40% for MePHPH and 5% for PHPH deac2023a R14; the polymer-rich PHPH drug-rich phase and associative against segregative separation (Deac 2023 on drug load, builds_on).
    Added
    drug release at 30 min of about 96, 61, 15 and 0% for 20–70% MePHPH and 75 and 0% for 5 and 20% PHPH deac2023a R1, R2; drug piling up in the gel at 40 and 50% MePHPH deac2023a R3; gel thickness, water content and residence time deac2023a R4; in situ imaging of droplets within the gel up to 30% MePHPH, networks at 40% and inversion at 50%, and of PHPH particles beyond the gel at 5% and a network at 10–20% deac2023a R6, R7, R8; released drug-rich phases of 98.8 and 26.2 wt% drug deac2023a R12; porous drug-rich surfaces above the limit deac2023a R9, R10.
    Relation
    extends the real-time imaging of Yang 2022 to two analogues of different limit and adds gel-layer measurements deac2023a C71; ties the polymer-rich PHPH phase to the lower loading at which the drug-rich phase connects deac2023a C65.
    Note
    Findings: F1, F5, F6, F7, F8, F15, F17, F18, F19, F20, F25, F27.
  21. 2023
    deac2023bdrug load and molecular interactions: polymer in the drug-rich phasefirst proposed

    Dissolution Mechanisms of Amorphous Solid Dispersions: Role of Drug Load and Molecular Interactions

    Note
    Known in the library (builds_on: Indulkar 2019, Que 2019, Saboo 2020 on indomethacin, Que 2021, Ueda 2022): congruent release and the limit; the drug-rich surface layer of a PVPVA dispersion (Que 2019, builds_on); hydrogen bonding lowering the limit (Saboo 2020, builds_on); limits, interaction types and amorphous solubility with PVPVA of the four analogues deac2023b R8; entropy-driven polymer partitioning into drug-rich phases deac2023b C45.
    Added
    PVPVA lowering the amorphous solubility of PHPH from 200 to 27.5 µg/mL and raising that of MePHPH from 2.81 to 4.40 deac2023b R1; about 77, 36.5, 9 and 5 wt% PVPVA in the nanoparticles of PHPH, TIPP, MeTIPP and MePHPH, the reverse order of their limits deac2023b R3, R8; PVPVA moving into rather than out of PHPH particles above about 28% deac2023b R4, R5; compact surfaces drifting toward the drug-rich phase above the limit and constant below it deac2023b R6, R7; schematic ternary diagrams with plait points and the lever rule deac2023b C34, C48, C63.
    Relation
    first in the subcategory to measure where the polymer goes when the analogues separate deac2023b C26; proposes, on schematic diagrams, that associative separation lowers the limit deac2023b C63, X14; the interface paper of the same year builds on it.
    Note
    Findings: F7, F10, F17, F18, F27.
  22. 2023
    hiew2023hierarchical co-precipitated particles of grazoprevir–HPMCASfirst proposed

    Improving Dissolution Performance and Drug Loading of Amorphous Dispersions Through a Hierarchical Particle Approach

    Note
    Known in the library (builds_on: Bhardwaj 2018, Indulkar 2019, Saboo 2019, Li 2020, Yang 2021, Hiew 2022 on lumefantrine polymers): surface drug enrichment impairing release (Bhardwaj 2018, Li 2020) hiew2023 C44; polymer- against drug-controlled release, the limit and the drug-rich surface barrier hiew2023 C35; a sloped decline of release with loading in enteric-polymer dispersions (Hiew 2022, builds_on) hiew2023 C36.
    Added
    solvent-evaporated dispersions falling from about 102% released at 5% to 27–30% at 50–75% hiew2023 R8; binary co-precipitates at 60 and 75% releasing 8–37.5% and wetting poorly hiew2023 R10, R9; HPMC or HPC dissolved in the anti-solvent raising release to 56–72% hiew2023 R10, R12; surface drug of at most 34% against at least 53% separating good from poor release hiew2023 R14; AUC 135 against 73 µM·h in dogs hiew2023 R15.
    Relation
    first in the library to lower the surface drug of high-loading particles on purpose and to test the result in dogs hiew2023 C47, C43; carries the surface-composition result of Bhardwaj 2018 from spray-dried to co-precipitated particles (synthesis).
    Note
    Findings: F11, F14, F28.
  23. 2023
    yang2023surfactants in ritonavir–PVPVA dispersions and the drug-rich barrier at the dissolving interfacefirst proposedconfirms

    Drug Release from Surfactant-Containing Amorphous Solid Dispersions: Mechanism and Role of Surfactant in Release Enhancement

    Note
    Known in the library (builds_on: Purohit 2017, Indulkar 2019, Li 2019, Que 2019, Saboo 2021, Correa Soto 2022 on clopidogrel, Yang 2022 on release mechanisms, Yang 2022 on surfactant-containing dispersions): the binary ritonavir–PVPVA limit of 25% and its release yang2023 R1; discrete drug-rich domains released and a continuous layer blocking release at the dissolving interface yang2023 R25, C39; surfactants raising the limit of ledipasvir, felodipine and clopidogrel yang2023 R27; Span partitioning into the drug-rich phase and lowered Tgs of the same four ternary dispersions under water vapour yang2023 R24.
    Added
    release at 30–50% with 10 parts of SDS, Tween 80, Span 20 or Span 85 (about 50–97% at 30%, 1–57% at 40%) yang2023 R2; confocal images of the interface of ten ternary compacts after partial dissolution and in situ yang2023 R6, R7, R8, R9, R10, R12, R13, R14; the water needed for separation (14.0% without, 24.5% with SDS) yang2023 R21; Tg of ritonavir–Span mixtures yang2023 R22; SDS covering the dissolved surface and needle crystals at 30% yang2023 R17, R16.
    Relation
    first in the library to image the interface of surfactant-containing dispersions in water yang2023 C1; confirms the barrier picture of the 2022 interface study for ternary dispersions and adds that a layer must persist under flow to block release; confirms the SDS-related surface crystals of the 2022 surfactant study yang2023 C40, R8, C51.
    Note
    Findings: F3, F6, F8, F15, F16, F19, F20, F21, F25, F26, F30, F31.
  24. 2024
    bapat2024drug charge and insoluble drug–HPMCAS complexesfirst proposed

    Interplay of Drug−Polymer Interactions and Release Performance for HPMCAS-Based Amorphous Solid Dispersions

    Note
    Known in the library (builds_on: Indulkar 2019, Saboo 2020 on five polymers, Hiew 2022 on lumefantrine polymers, Bapat 2023, Deac 2023 on drug load, Nguyen 2023): congruent release and the limit bapat2024 C2; the gradual decline of HPMCAS release with loading bapat2024 C3; ionic drug–polymer interactions proposed to slow enteric polymer dissolution (Hiew 2022, builds_on) bapat2024 C5; the HPMCAS gel pH of 6.0 in 50 mM pH 6.8 phosphate bapat2024 R20; the insoluble PHPH–PVPVA complex bapat2024 C41.
    Added
    drug and HPMCAS-MF release of eight drugs of different charge at 5–60% bapat2024 R2, R3, R4; the polymer slowed 1.6- to 30-fold by weak bases, most where ionized bapat2024 R5; complexation of HPMCAS at pH 6.0 (5–17% against 60–90%), with drug:COOH ratio, pH and ionic strength bapat2024 R12, R11, R13, R16; a loratadine dispersion releasing faster at pH 7.5 than 6.8, the reverse of the neat drug bapat2024 R4, R7; release on two trendlines against complexation bapat2024 R14.
    Relation
    first in the library to measure drug–HPMCAS complexes across drug charge and to set them against release bapat2024 C6; limits the gradual HPMCAS pattern of the 2020 five-polymer study to drugs that do not complex the polymer (synthesis).
    Note
    Findings: F1, F2, F9, F11, F15, F17, F23, F24, F32.
  25. 2024
    deac2024apolymer molecular weight and a new failure modefirst proposedextends

    Dissolution mechanisms of amorphous solid dispersions: Role of polymer molecular weight and identification of a new failure mode

    Note
    Known in the library (builds_on: Indulkar 2019, Que 2020, Que 2021, Yang 2022 on release mechanisms, Deac 2023 on the interface, Deac 2024 on ternary phase diagrams): congruent, polymer-controlled release and the limit deac2024a C5; drug–polymer interactions and drug Tg lowering the limit deac2024a C2; dispersed droplets against a continuous drug-rich phase in the gel layer, here named Failure Mode II deac2024a C9; clotrimazole forming no strong interactions with PVP deac2024a C10.
    Added
    clotrimazole limits with six PVP grades, below 5% to about 38%, near the computed entanglement weight of 46,620 g/mol deac2024a R12, E1; droplet agglomeration in films and at the dissolution front of short-chain compacts deac2024a R7, R10; inversion between 30 and 40% and unchanged phase compositions for two grades deac2024a R8, R11; no droplet stabilization by PVP in dilute suspension deac2024a R5.
    Relation
    first in the library to vary the polymer grade and to describe failure by droplet agglomeration in the gel ("Failure Mode I") deac2024a C54; extends the interface picture of 2022–2023 to a failure in which the droplets are discrete when they form (synthesis).
    Note
    Findings: F1, F2, F3, F4, F6, F8, F15, F16, F20, F25, F29, F30, F31.
  26. 2024
    deac2024bternary phase diagrams and the limit of congruencyfirst proposed

    Dissolution Mechanisms of Amorphous Solid Dispersions: Application of Ternary Phase Diagrams To Explain Release Behavior

    Note
    Known in the library (builds_on: Indulkar 2019, Que 2021, Yang 2022 on release mechanisms, Deac 2023 on the interface, Deac 2023 on drug load): the limit and the cliff deac2024b C1; a continuous drug-rich phase in the gel above the limit deac2024b C2; strong interactions and high drug Tg lowering the limit deac2024b C4; limits and interaction ranks of the four analogues deac2024b R39; polymer partitioning into the drug-rich phases of the analogues deac2024b C5.
    Added
    measured drug–PVPVA–water diagrams of PHPH and MePHPH at 37 °C, with associative and segregative tie lines deac2024b R15, R17, R22, R23; PC-SAFT diagrams and critical points of all four analogues deac2024b R35, R37; the water that separates MePHPH–PVPVA (under 15 wt%) deac2024b R1, R2; the switch from droplets to a network in films deac2024b R18, R19; Tgs of the hydrated phases deac2024b R29, R30.
    Relation
    first in the library to measure and compute the phase diagrams of dispersions and to compare the critical-point loading with the limit deac2024b C59; tests the plait-point hypothesis of the 2023 drug-load paper, confirming its order and missing the PHPH film switch deac2024b X5.
    Note
    Findings: F6, F8, F17, F18, F20, F25, F27, F30.
  27. 2025
    bapat2025aHPMCAS grade and the release of weak basesfirst proposedextends

    Impact of HPMCAS Grade on the Release of Weakly Basic Drugs from Amorphous Solid Dispersions

    Note
    Known in the library (builds_on: Hiew 2022 on lumefantrine polymers, Bapat 2023, Bapat 2024): the titration method and critical ionization model for enteric polymers, and the MF acid content and pKa bapat2025a C2, M4; MF release and rate data and the surface pH of 6.0 bapat2025a R15, X7; hydrophobic ion pairs of weak bases with HPMCAS-MF and the complexation test bapat2025a C5.
    Added
    neat rates of HPMCAS LF, MF and HF bapat2025a R1; release of 25% loratadine and cinnarizine from the three grades at pH 6.8 and 7.5 bapat2025a R2, R3; titrated acid contents and pKa bapat2025a M3, M5, R8; complexation by grade, ratio and pH bapat2025a R9, R11, R12.
    Relation
    first in the library to compare HPMCAS grades for release of weak bases bapat2025a C24; extends the 2024 complexation result from one grade to three.
    Note
    Findings: F1, F2, F4, F11, F15, F19, F23, F24, F32, F33.
  28. 2025
    hiew2025surface composition and wettability of high-loading particlesfirst proposedrevises

    The importance of surface composition and wettability on the dissolution performance of high drug loading amorphous dispersion formulations

    Note
    Known in the library (builds_on: Indulkar 2019, Deac 2023 on the interface, Deac 2023 on drug load, Hiew 2023): the release decline above a threshold loading in copovidone hiew2025 C4; a hydrophobic continuous phase blocking release hiew2025 C4; the hierarchical co-precipitation method and 70% grazoprevir particles with HPMC diluting the surface hiew2025 R22, C7.
    Added
    release of 75% grazoprevir–HPMCAS particles with seven secondary excipients hiew2025 R9; FaSSIF contact angles splitting good from poor materials hiew2025 R15, R17; XPS surface drug of 32–50% for good and poor alike hiew2025 R14; de-agglomeration by sonication and sieving hiew2025 R13, R11; high-shear treatment of a 75% solvent-evaporated dispersion hiew2025 R10.
    Relation
    first in the library to screen secondary excipients against wettability hiew2025 C40; revises the surface-drug reading of the 2023 study: among diluted surfaces wettability, not surface drug content, separated good from poor release hiew2025 C35.
    Note
    Findings: F11, F14, F28, F35.
  29. 2025
    kaur2025bedaquiline–HPMCAS complexation and biorelevant mediafirst proposedextends

    Impact of drug-polymer complexation and media properties on the release performance of amorphous solid dispersions containing a weakly basic drug and hydroxypropyl methylcellulose acetate succinate

    Note
    Known in the library (builds_on: Duong 2022, Hiew 2022 on lumefantrine polymers, Bapat 2023, Nguyen 2023, Bapat 2024, Bapat 2025): ionic weak base–HPMCAS interactions impeding release kaur2025 C3; the gel pH of HPMCAS-MF and media effects on HPMCAS release kaur2025 R22; insoluble complexes of lipophilic cationic drugs with HPMCAS kaur2025 C3; delamanid dispersions without a biorelevant-media effect, as a contrast kaur2025 C52.
    Added
    bedaquiline–HPMCAS LF and MF complexation at pH 5.8–10.5 and in FaSSIF-V1 and FeSSIF-V2 kaur2025 R5, R6, R7, R8; drug protonation in the complex and in a dry dispersion by XPS kaur2025 R20; release in buffers after a pH shift and in three biorelevant fluids kaur2025 R12, R13, R15, R16, R17; amorphous residues and induction times with polymer kaur2025 R14, R18.
    Relation
    first in the library to measure drug–polymer complexation in simulated intestinal fluids kaur2025 C57; extends the complexation results of 2024–2025 to a drug of pKa 8.5 and shows that micelles change release where FaSSIF changed nothing for non-complexing drugs in 2023 (synthesis).
    Note
    Findings: F1, F16, F19, F23, F24, F32, F33, F34.
For the authors: coverage of each paper card's main findings

Every finding of section 0.3 of each card, with the findings of this chapter that use it.

paperfinding of section 0.3used in
indulkar2017bF1. Below about 15 °C the drug hardly moves between droplets and solutionF5
indulkar2017bF2. All four ASDs form nanodroplets of about 200 nmF4
indulkar2017bF3. The ASDs dissolve completely even in water already saturated with drugF1, F2
indulkar2017bF4. The label is diluted as full mixing predictsF5
purohit2017bF1. Ritonavir's amorphous solubility is about 27–28 µg/mL, and the polymers do not change itF3, F4
purohit2017bF2. Humidity splits the PVP and PVPVA dispersions but not the HPMCAS onesF8, F11
purohit2017bF3. In buffer, high-loading PVP and PVPVA films split within secondsF5, F8
purohit2017bF4. Only some fresh dispersions exceed the amorphous solubility and form nanodropletsF4, F11
purohit2017bF5. The polymer dissolves fast; the drug keeps pace only where LLPS occursF3, F4
purohit2017bF6. Humidity storage removes LLPS from PVP and PVPVA dispersions but not from HPMCASF12
bhardwaj2018F1. Amorphous ITZ dissolves about 18 times faster than crystalline ITZF1, F3
bhardwaj2018F2. Down to 25% loading, both processes release ITZ at the amorphous-drug rateF3
bhardwaj2018F3. The polymer dissolves much faster than the drug, at a rate that depends on the processF3, F14
bhardwaj2018F4. At 20% loading the processes diverge; at 10% both are polymer-controlled and fastF2, F6, F14
bhardwaj2018F5. At 20% loading the spray solvent changes ITZ release several-fold but not polymer releaseF14
bhardwaj2018F6. No phase separation in the bulk, but particle shape and shell differ with the solventF14
bhardwaj2018F7. Surface composition tracks the release groupF14
indulkar2019aF1. Up to 25% DL drug and polymer leave together at the polymer's rateF2
indulkar2019aF2. Above 25% DL release falls off a cliffF6
indulkar2019aF3. At 30–35% DL the polymer outruns the drugF3, F6
indulkar2019aF4. At 40–50% DL almost nothing dissolves, the drug at the pace of neat amorphous ritonavirF3
indulkar2019aF5. Only fast, near-congruent release exceeded the amorphous solubility and gave nanodropletsF4
indulkar2019aF6. Drug in the medium stops high-loading release but not low-loading releaseF1, F3
indulkar2019aF7. The high-loading tablet surface turns drug-rich within minutesF7
indulkar2019aF8. Water splits the films above the LoCF8
que2019F1. Release collapses between 5 and 7.5% DLF3, F6
que2019F2. Above the LoC the compact surface turns drug-rich within 10 minF7
que2019F3. Humid films phase-separate more at higher DLF8
que2019F4. PVPVA breaks ledipasvir's drug–drug hydrogen bondsF10
que2019F5. The polymer's effect saturates near the LoCF10
que2019F6. SDS raises the LoC to 30% DL and poloxamer 407 to 7.5%; three other surfactants do notF13
que2019F7. Surfactants make smaller colloidsF4, F13
saboo2019F1. Release falls off a cliff one loading step above the congruent rangeF2, F3, F6
saboo2019F2. The more hydrophobic drug did not switch earlierF9
saboo2019F3. Only congruent release produced drug-rich nanodropletsF4
saboo2019F4. Above the switch the dissolving surface turns porous and drug-richF7
saboo2019F5. Phase-separating the surface with humidity makes a congruent dispersion incongruentF8, F12
saboo2019F6. Powder dissolution shows the same cliffF1, F4
saboo2020aF1. The five polymers rank the same way by water uptake and by wettingF11
saboo2020aF2. The hydrophilic polymers release fast only at low loading, then fall off a cliffF6, F11
saboo2020aF3. The hydrophobic polymers stay congruent up to 50% drug but slow down above 30%F11
saboo2020aF4. Faster-dissolving polymers give faster release at low loading; HPMCAS wins at 20-30%F11
saboo2020aF5. Above the LoC the tablet surface turns porous and drug-rich, and humid films phase-separateF7, F8
saboo2020aF6. In HPMCAS at 40% loading, more lipophilic drugs release more slowlyF9
saboo2020aF7. The polymers that hydrogen-bond most strongly to felodipine have the lowest LoCsF10
saboo2020F1. Without the hydrogen bond, the limit of congruency is higherF17
saboo2020F2. Congruent IND release supersaturates; incongruent release does notF4
saboo2020F3. The IND surface becomes drug-rich and roughF7
saboo2020F4. INDester fails later, by crystals on the surfaceF19
saboo2020F5. Below the wet Tg of the drug-rich layer, the IND limit fallsF18
que2021F1. Both phenols hydrogen-bond to PVPVA; the iodo-only compound binds weakly; the ether not at allF17
que2021F2. Iodine halogen-bonds to PVPVA, but less so when OH groups competeF17
que2021F3. The hydrogen-bonding compounds have LoCs of 5–10 wt%, the others 30–40 wt%F6, F17
que2021F4. Above the LoC, release collapses, most completely for the iodo compoundsF3, F6
que2021F5. Lipophilicity, amorphous solubility, Tg and MW do not explain the LoCF9, F17
que2021F6. At the LoC, all four release at the neat polymer's rateF2, F15
saboo2021F1. TPGS raises the LoC in step with its levelF21
saboo2021F2. Congruent ASDs supersaturate the medium and shed nanoparticles; failing ones do neitherF4, F16
saboo2021F3. Micelles and dissolved TPGS do not explain the gainF21
saboo2021F4. With TPGS the wet drug-rich phase stays as discrete domainsF20
saboo2021F5. Tablets with little or no TPGS keep a porous surface layerF7, F20
saboo2021F6. TPGS plasticizes the ASDF21
yang2021F1. PVPVA dispersions fell off a cliff; HPMCAS dispersions declined graduallyF6, F11
yang2021F2. Wet Tg, not log P, ordered the drugsF9, F18
yang2021F3. Release failed when drug and polymer stopped dissolving togetherF2, F3, F4
yang2021F4. Cooling loratadine below its wet Tg cut the LoCF18
yang2021F5. HPMCAS kept nanodroplets small; PVPVA did notF16
correasoto2022aF1. Binary ASDs release well up to 40% DL and fall off the cliff aboveF6
correasoto2022aF2. CPD makes PVPVA dissolve about twice as fastF15
correasoto2022aF3. Only SDS improves release at 50% DLF21
correasoto2022aF4. TPGS and Tween 80 slow release; CTAB lets drug fall out of solutionF15, F21
correasoto2022aF5. A little surfactant stops nanodroplet growth, except CTABF16
correasoto2022aF6. The surfactants meet the drug in different placesF16
correasoto2022aF7. Humid air splits the films from 50% DL; SDS keeps the 50% DL film nearly uniformF8, F20
correasoto2022bF1. Without an additive, release collapses between 5 and 10% DLF6
correasoto2022bF2. Every additive raised release at 10% DL, by 4- to 35-foldF21
correasoto2022bF3. A plain plasticizer, VP, worked as well as the best surfactants at 10% DLF21
correasoto2022bF4. The LoC rose to 10% DL with SDS or CTAB and to 15% DL with Span 80F21
correasoto2022bF5. At 55 °C the binary ASD released again, until ATZ crystallizedF18, F19
correasoto2022bF6. Surfactants lowered the ASD Tg and made wet films phase separate within minutesF20, F21
correasoto2022bF7. Small additives helped most; charge and affinity for the drug did not decideF21
hiew2022bF1. Salt formation raised the Tg, by counterion, up to about 101 °CF22
hiew2022bF2. Dispersions of high-Tg salts keep the polymer's Tg at every loadingF22
hiew2022bF3. The higher the salt Tg, the lower the loading that still releasesF6, F18, F22
hiew2022bF4. In lag-phase dispersions the polymer leaves firstF3
hiew2022bF5. At 10 °C two well-releasing dispersions stopped releasingF18
hiew2022bF6. Higher-Tg forms crystallised later, with exceptionsF22
hiew2022bF7. FTIR shows little drug–polymer interactionF22
indulkar2022F1. Every surfactant removed the lag phase, but only Span 85 and TPGS released nearly all the drugF21
indulkar2022F2. Only SDS speeds up polymer releaseF15
indulkar2022F3. With SDS, ritonavir crystallises on the tablet surface within 15 min, and release stops near 80%F19
indulkar2022F4. Tween 80 and Span 20 do not prevent phase separation, and release stalls below 50%F20, F21
indulkar2022F5. The surfactant sets the size of the drug-rich dropletsF16
qi2022F1. The buffer species, not the cation size, sets how fast HP-50 dissolvesF23
qi2022F2. Salt formation ionizes HP-50 and multiplies its water uptakeF24
qi2022F3. Pre-ionized salts dissolve about three times faster than HP-50, whatever the counterionF24
qi2022F4. The sodium salt keeps its rate when buffer capacity drops; HP-50 slows 6-foldF23, F24
qi2022F5. The more of the polymer is neutralized, the faster it dissolves, with the largest step between 80 and 100%F24
qi2022F6. Polymer-salt ASDs release miconazole about 12 to 14 times faster, nearly together with the polymerF3, F15, F24
yang2022aF1. Release collapses between 20 and 30% drug loadingF3, F6
yang2022aF2. On the surface, drug-rich droplets turn into a continuous drug-rich layerF7, F25
yang2022aF3. Cross-sections show a gel layer, and from 30% DL a drug-rich crust on topF7, F25
yang2022aF4. The drug-rich layer slows water entryF7, F25
yang2022aF5. Real-time imaging: droplets leave with the polymer at low loading; a layer traps them at high loadingF5, F20, F25
yang2022aF6. The surface becomes drug-rich during dissolutionF7
bapat2023F1. Buffer capacity, not micelles, sets how fast HPMCAS dissolvesF23
bapat2023F2. The gel layer is more acidic than the medium, and release follows its pHF23, F24
bapat2023F3. At 10% loading the drug leaves at the polymer's paceF2, F23
bapat2023F4. Both drugs slow polymer release, most at high buffer capacity and high loadingF15
bapat2023F5. Faster stirring speeds release in step with the square root of rotation speed, with no plateauF23
bapat2023F6. The drugs reduce water uptake, INDester more than INDF15
correasoto2023F1. Lipophilic plasticizers raise the ATZ LoC up to fivefoldF26
correasoto2023F2. Plasticized ATZ dispersions release drug and polymer together, often faster than PVPVA aloneF26, F15
correasoto2023F3. LED needs twice the plasticizer, then its LoC triples or quadruplesF26
correasoto2023F4. The lower-Tg control RTV gains littleF18, F26
correasoto2023F5. All plasticizers lower the drug Tg by 30 to 53 °CF26
correasoto2023F6. A plasticizer alone speeds PVPVA dissolutionF15, F26
correasoto2023F7. Plasticizers change water vapour uptake littleF26
deac2023aF1. Release collapses above about 40% DL for MePHPH and above 5% DL for PHPHF6, F25
deac2023aF2. Drug piles up in the gel layer at 40 and 50% DLF1, F6, F25
deac2023aF3. Below the LoC the gel is thin and releases fast; above it the gel grows and dries outF15, F25
deac2023aF4. MePHPH: droplets inside the gel up to 30% DL, networks at 40%, inversion at 50%F5, F25
deac2023aF5. PHPH: particles form beyond the gel at 5% DL, and a network appears already at 10-20% DLF5, F25, F17
deac2023aF6. The PHPH drug-rich phase is three-quarters polymer and softF27
deac2023aF7. Above the LoC a porous drug-rich layer covers the surfaceF7, F25
deac2023bF1. PVPVA lowers PHPH's amorphous solubility but slightly raises MePHPH'sF27
deac2023bF2. The more strongly a drug binds PVPVA, the more PVPVA its nanoparticles holdF27, F17
deac2023bF3. The order of PVPVA partitioning mirrors the LoC orderF27, F17
deac2023bF4. Above about 28% PHPH, PVPVA moves into the particles instead of outF27
deac2023bF5. Above the LoC the compact surface drifts toward the drug-rich phase; at or below it, it stays putF7, F27
deac2023bF6. The thermodynamic limit lies well above the LoCF27
hiew2023F1. Release from solvent-evaporated ASDs falls with drug loading and levels off at about 30%F11, F28
hiew2023F2. Binary co-precipitated particles release little and wet poorlyF28
hiew2023F3. Polymer dissolved in the anti-solvent raises release; suspended polymer or a wash helps lessF28
hiew2023F4. Less drug at the particle surface goes with more releaseF14, F28
hiew2023F5. The hierarchical particle gave higher exposure in dogsF28
yang2023F1. Every surfactant helped at 30% DL; only Tween 80 and SDS kept partial release at 40% DLF21, F31
yang2023F2. Release followed the interface: discrete droplets were released, a persistent continuous layer blocked releaseF20, F25, F31
yang2023F3. A continuous layer that does not persist does not block releaseF20, F31
yang2023F4. SDS needed far more water to phase separate, and its gel stayed one phaseF8, F30, F31
yang2023F5. At 50% DL, Tween 80 and SDS formed porous drug-rich layers and released drug only in partF31
yang2023F6. SDS release stopped at about 30 min, with RTV crystals on the surfaceF19, F31
bapat2024F1. Drug and polymer leave together, and both slow as loading risesF2, F11, F32
bapat2024F2. Weak bases slow the polymer most when they are ionizedF15, F32
bapat2024F3. Cationic drugs take HPMCAS out of solution as an insoluble complexF17, F32
bapat2024F4. LOR binds HPMCAS only when ionized, and its dispersion releases faster at higher pHF32
bapat2024F5. Release falls along two trendlines with complexationF9, F32
deac2024aF1. The LoC jumps with PVP molecular weight, then levels offF6, F29
deac2024aF2. In humid films, drug-rich droplets cluster into strands with K12 but not with K29/32F20, F29
deac2024aF3. At the dissolution front, K12 droplets agglomerate and stay behind; K29/32 droplets leaveF25, F29
deac2024aF4. Phase inversion happens between 30 and 40% DL for both gradesF29, F30
deac2024aF5. Molecular weight does not change the phase compositionsF29, F30
deac2024aF6. PVP does not stabilise the droplets in dilute suspensionF16, F29
deac2024bF1. The two drugs push the polymer in opposite directionsF27, F30
deac2024bF2. Measured and computed diagrams agree, with the critical points at opposite endsF30
deac2024bF3. In wet films the drug-rich phase switches from droplets to a networkF20, F30
deac2024bF4. The switch sits at the critical pointF30
deac2024bF5. The predictions follow the reported LoCsF6, F17, F30
bapat2025aF1. Neat LF dissolves about 3 times faster than HFF15, F23, F33
bapat2025aF2. Loratadine ASDs: grade matters greatly at pH 6.8, much less at pH 7.5F11, F33
bapat2025aF3. Cinnarizine ASDs: LF releases about 9 times faster than MF, and HF does not release measurablyF33
bapat2025aF4. LF carries twice the acid groups of HF, at nearly the same pKaF33
bapat2025aF5. HF loses more polymer to an insoluble complex with cinnarizine than LFF32, F33
bapat2025aF6. Complex formation follows drug ionizationF32, F33
hiew2025F1. The excipient on the surface decides release, not the coating as suchF35
hiew2025F2. Wettability splits the materials into two groups that track releaseF28, F35
hiew2025F3. Surface drug content measured by XPS does not separate good from poor excipientsF28, F35
hiew2025F4. HPMC or SDS treatment lifts a 75% SE ASD to the release of a 20–30% DL ASDF11, F14, F35
hiew2025F5. More exposed surface helps only wettable particlesF35
hiew2025F6. HPMC works only when dissolved in the anti-solventF35
kaur2025F1. BDQ pulls HPMCAS out of solution, most at pH 5.8–6.0F32
kaur2025F2. Micelle-containing SIFs largely stop the complex from formingF34
kaur2025F3. In plain buffer the ASDs release little, even at 5% DLF32, F34
kaur2025F4. In FaSSIF-V1 and FeSSIF-V2 release is high; in FeSSIF-V1 it is notF23, F34
kaur2025F5. The drug did not crystallize, so crystallization is not the failureF19, F32
kaur2025F6. BDQ is half protonated in the complex and in the dry ASDF24, F32

01Concepts

congruent releasedrug and polymer leave in their dispersion ratio; the regime that gives fast release and nanodropletsincongruent releasethe polymer leaves faster than the drug, above the limit or after humid storagepolymer-controlled releasethe polymer carries the drug into the medium; release continues into medium at the amorphous solubilitydrug-controlled releasethe drug dissolves from a drug-rich surface at about the neat amorphous rate and stops at the amorphous solubilitylimit of congruencythe highest loading with congruent release; 5–30% in PVPVA for six drugs in 2018–2020, 2–40% for the drugs and salts of 2020–2022, none to 50% in HPMCAS and EUDS; raised by surfactants and, for high-Tg drugs, three- to fivefold by plasticizers; lowered by hydrogen bonding and by cooling below the wet Tg; from 2024 set by the PVP grade (below 5 to about 38% for clotrimazole) and placed near the critical point of the drug–polymer–water diagramfalling-off-the-cliff effectthe one-step drop of release by one to three orders of magnitude above the limitintrinsic dissolution rateconstant-area rate of neat drug and neat polymer, the scale on which dispersion rates are readHiguchi two-component dissolution modelthe older diffusion model whose critical ratio predicts drug control at every practical loadingNernst-Brunner equationthe diffusion-layer rate that goes to zero at the amorphous solubility, the basis of the saturated-medium testNoyes-Whitney equationrate of drug-controlled release; ceiling at the amorphous solubilitydiffusion boundary layerthe stagnant layer where drug released with the polymer can separate as dropletsStokes-Einstein equationNTA sizing of the droplets and the drug-to-polymer diffusion ratiopolymer swellingproposed for non-linear low-loading profiles and for compacts behind a drug-rich layerdrug-rich nanodropletsthe colloid that only polymer-controlled release forms, 60–370 nm in 2017–2020; from 2021 sized against time, about 180–2120 nm depending on drug, polymer and surfactant, and up to about 10 µm with Tween 80 built into ritonavir dispersions; imaged forming within or beyond the gel layernanodroplet reservoir effectthe reason given for wanting congruent release and small colloidssurface drug enrichmentthe dissolving surface above the limit turns drug-rich within minutes; spray solvents set it before dissolutiondrug-rich surface layerthe porous, drug-rich layer that sets drug-controlled releasedrug-rich barrier layerthat layer read as a barrier to further drug and polymer releaseamorphous-amorphous phase separationwater-induced separation of films above the limit, the authors' explanation of the switchphase separation kineticsthe proposed race between separation and dissolution at the hydrating surfacedrug-polymer-water miscibilitywhether drug and polymer stay mixed once water enters; raised by SDS in 2023 (14.0 → 24.5% water for separation)Flory-Huggins interaction parameterthe water–drug and water–polymer terms behind water-induced separationhygroscopicitywater uptake of the polymers, separating hydrophilic from hydrophobic polymerswettabilitybuffer contact angle on polymer films, the second hydrophobicity scale; from 2025 the FaSSIF contact angle that separated good from poor surface excipients on 75% particlesplasticization by waterwet Tg of the drug-rich phase; nifedipine droplets glassy at 5 °C; the indomethacin-rich layer and loratadine below their wet Tg on coolingsupercooled liquidritonavir above its wet Tg at 37 °C, offered as a reason for its higher limitlipophilicitythe drug property tested against the limit and found not to set itoctanol-water partition coefficientmeasured and calculated log P of the test drugscritical micelle concentrationthe released surfactant stays below it, so bulk solubilization is excluded; TPGS raised the felodipine limit below ithydrophilic-lipophilic balancethe hydrophilic surfactants (SDS, poloxamer 407) raised the limit, the hydrophobic ones did notgel layerthe hydrated polymer layer in which the release regime is set; imaged in dissolving compacts from 2022; for HPMCAS formed only above 13 mM/ΔpH and more acidic than the mediumpolymer chain disentanglementthe step that sets the polymer rate; below Tg it needs a critical water contentplasticizationthe drug or a surfactant lowering the dispersion Tg and speeding polymer releasewater sorptionwater uptake of salts and dispersions, a proxy for hydration of the compactternary phase diagramthe thermodynamic alternative for the lower limit at 5 °C; from 2023 the schematic drug–PVPVA–water diagram on which hydration paths, plait points and tie lines are drawn; measured and computed in 2024 for two analogues, the basis of the critical-point reading of the limitdrug-polymer hydrogen bondingwent with a lower limit in two analogue pairs; carries PVPVA into the drug-rich phase of the phenolshalogen bondingthe weaker bond of iodinated analogues without donorssurface-normalized dissolution ratethe per-component rate per area of a compact, read for drug and polymersurface crystallizationcrystals on the dissolving surface that end congruent release after minutescrystallization during dissolutionthe crystallization that stopped atazanavir release at 55 °Cphase separation morphologydiscrete against continuous drug-rich phase, which tracked releasedrug-rich phase coarseninggrowth of drug-rich domains and droplets, slowed by surfactantssurfactant partitioning into the drug-rich phasenon-ionic surfactants and Spans taken up into drug-rich droplets, SDS notmicellar solubilizationexcluded as the cause of the higher limit with TPGSpolymer-surfactant interactionlittle TPGS–PVPVA interaction at the CMCGordon-Taylor equationturns a local Tg into a local drug content; K = 0.65 for dry MePHPH–PVPVA in 2024 deac2024b E14drug loadingthe main variable of the chapter; grazoprevir–HPMCAS release falling to a plateau near 30%buffer capacitymM/ΔpH of the medium; sets enteric polymer dissolution about sixfold over 3–51 mM/ΔpHmicroenvironmental pHthe acidic gel or surface of a dissolving enteric polymer, 5.6–6.2 at bulk pH 6.8 for HPMCAS; from 2024 the pH (6.0) at which weak bases complex HPMCAScritical ionization for polymer dissolutionthe ionized fraction an enteric polymer needs to dissolve, about 83% for HP-50 (cited)polymer salt formationpre-ionized HP-50 and HPMCAS salts that dissolve faster and largely independent of the mediumionizationof the polymer: HP-50 dissolving more slowly as less of it is neutralizedpKaof buffer species, deciding which buffers carry protons away; of HP-50 and HPMCASunstirred water layerthe aqueous boundary layer through which polymer and protons leave; thinned by rotationpolymer chain entanglementgel-layer dissolution of entangled PVPVA; judged unlikely for HPMCAS-MF; proposed in 2024 to keep drug-rich droplets apart in long-chain PVP gelscritical entanglement molecular weightthe molecular weight HPMCAS-MF is judged to fall below; from 2024 the PVP weight (46,620 g/mol) near which the clotrimazole limit roseglass-gel interfaceinner boundary of the gel layer, its advance a measure of water penetrationphase inversionthe drug-rich phase turning from discrete to continuous as loading rises; located between 30 and 40% for clotrimazole–PVP and near the critical point for the analogues in 2024associative phase separationdrug and polymer together in the insoluble phase (PHPH, TIPP), with low limitssegregative phase separationpolymer left in the water (MePHPH, MeTIPP), with higher limitsbinodalthe water content at which a hydrating dispersion separates; hydrophobic binodal compositions of the analoguestie lineits slope distinguishes associative from segregative separationcritical pointthe plait point, proposed to approximate the maximum limit (schematic); from 2024 computed for four analogues, its loading following their limitslever rulephase amounts from the tie line; a step in hydrophobic-phase volume at the plait point; printed in 2024 as W^{\alpha} = (W_i^T - W_i^{\beta})/(W_i^{\alpha} - W_i^{\beta}) and used for the drug-rich fraction at the spinodal deac2024b E12local equilibriumthe assumption that gel-layer phases are at pseudo-equilibrium with the local water contentspinodal decompositionthe assumed mode of separation along the hydration pathdrug-polymer complexationthe insoluble PHPH–PVPVA complex that lowers the amorphous solubility; from 2024 the insoluble complexes of weak bases and phenolphthalein with HPMCASsteric stabilizationproposed for the Spans keeping ritonavir droplets small; set aside in 2024 for clotrimazole droplets with PVPhierarchical particle approachco-precipitated particles coated with a water-soluble polymer to dilute the surface drugdrug-polymer ionic interactionsa weak base cation bound to the polymer carboxylate, already in the dry dispersion for bedaquilineinsoluble drug-polymer complexHPMCAS taken out of solution by weak bases (70–96%) and phenolphthalein, lowering releasehydrophobic ion pairingthe authors' name for the drug cation–carboxylate pair that precipitatespolymer hydrationthe step through which loading, complexation and grade are proposed to slow HPMCASnanodroplet agglomerationdroplets joining in the gel of short-chain PVP dispersions (Failure Mode I) or with Tween 80pH-dependent polymer solubilitywhy HPMCAS releases nothing at low pH and why the grades differ

02Formulas

surface-normalized release rateA = \frac{k \times V}{S \times N}A = kV/(SN), the rate per area of each component as if it were pure; the read-out of congruency saboo2020a E3; R = kV/(Sx) and R = k/(Sx) in the papers of 2020–2022 saboo2020 E1; correasoto2022a E1, and R = kV/(Ax), R = kV/(Sx) and R = k/(Sx) again in 2022–2023 yang2022a E1; bapat2023 E1; correasoto2023 E1; printed again in 2023–2025 yang2023 E1; bapat2024 E1; bapat2025a E1congruent release relationG_D = \frac{G_C\,A_D}{A_C}drug rate = polymer rate × drug:polymer ratio; 7.4 against 7.6 mg ritonavir at 20 min indulkar2019a E3; printed again for the surfactant dispersions of ritonavir indulkar2022 E1Noyes-Whitney equationAs printed for crystals dissolving in a polymer melt (concentration C of dissolved drug in the liquid phase):six printed forms, a seventh as the Nernst–Brunner form of 2022 indulkar2022 E2; the rate of drug-controlled release and its zero at the amorphous solubility; named for HPMCAS as the form that fails under polymer control bapat2023 E4, C2Higuchi-Corrigan critical mixture ratio\frac{N_{drug}}{N_{polymer}} = \frac{D_{drug}\,C_{s(drug)}}{D_{polymer}\,C_{s(polymer)}}about 1.7 × 10⁻³ for felodipine–PVPVA (printed 1.7 × 10⁻⁶) saboo2020a E4, X1Stokes-Einstein equationD_{NMR} = \frac{k_B T}{6\pi\eta r}NTA sizing; D_{drug}/D_{polymer} = 10 saboo2020a E6polynomial calibration curveNot printed: a second-degree polynomial calibration of PVPVA absorbance at 220 nm, solved for concentrationPVPVA assay at 220 nm, coefficients not printed bhardwaj2018 E7; y = 5.1445x^2 - 0.2064x + 4.1749 for the PHPH content of compact surfaces by ATR-FTIR deac2023b E3water plasticization rule of thumbStated in words: the wet Tg equals the dry Tg less about 10 °C for each 1% of water sorbedwet Tg of nifedipine 42 − 10 × 2.5 = 17 °C indulkar2017b E6; indomethacin 29 °C, miconazole, danazol and elbasvir, and every lumefantrine dispersion below 37 °C saboo2020 E6; yang2021 E3; hiew2022b E3multicomponent Flory-Huggins free energy of mixingWater–drug–polymer system:water–drug–polymer form behind water-induced separation purohit2017b E2Δχ effect\left|\Delta\chi\right| = \left|\chi_{12} - \chi_{13}\right|\Delta\chi = \lvert\chi_{WD} - \chi_{WP}\rvert in words purohit2017b E4; printed with absolute-value bars to explain why log P fails yang2021 E2molar amount of halogen at the lower XPS binding energyn_{F,\mathrm{low}} = \frac{100\,\mathrm{mg} \times DL}{889\,\mathrm{g\,mol^{-1}}} \times 2 \times f_{\mathrm{low}}bonded fluorine against loading; printed example a factor-10 misprint que2019 E4, X3; bonded iodine of TIPP and Me-TIPP, 0.017–0.050 mmol per 100 mg que2021 E4, R12octanol-water partition coefficient\log P = \log\frac{[\mathrm{drug}]_{\mathrm{octanol}}}{[\mathrm{drug}]_{\mathrm{aqueous}}}shake-flask log P of nilvadipine and cilnidipine saboo2020a E5; of indomethacin and its ester, 4.07 and 4.53 saboo2020 E4, M1, M2amorphous solubility advantage from free energy difference\ln x_{SL,L_1} = \ln x_{C,L_1} + \frac{\Delta G_{a\to c}}{RT}\Delta G \approx -RT\ln(C_{amorph}/C_{xtal}), background indulkar2017b E3amorphous-to-crystalline solubility ratio\frac{\sigma_a}{\sigma_c} = \frac{\text{LLPS onset concentration}}{\text{crystalline solubility in the same medium}}nilvadipine 31/1.7 = 18, cilnidipine 0.6/0.05 = 12 saboo2019 E3Gordon-Taylor equationAs printed with a density-based constant:T_{g,mix} = (w_1T_{g1} + k\,w_2T_{g2})/(w_1 + k\,w_2) with k = 0.91, inverted to the local drug content saboo2020 E3, R28Fox equation\frac{1}{T_g} = \frac{x_1}{T_{g,1}} + \frac{x_2}{T_{g,2}}neat TIPP Tg of 84 °C from a 90% dispersion, named only que2021 E2, R1; printed in 2024 for wet dispersions with T_{g,water} = 135 K deac2024b E13theoretical monolayer adsorption capacityX_m = \frac{\mathrm{SSA} \times 10^{20} \times \mathrm{MW}}{S_c \times N_A}surfactant needed to cover the clopidogrel droplet surface, in words correasoto2022a E2boundary-layer diffusion flux (film model)J_p = \frac{D_p}{\delta}\,C_pJ_p = (D_p/\delta)\,C_p, polymer flux set by the interfacial polymer solubility bapat2023 E2; used in 2024–2025 for complexation lowering the interfacial solubility of HPMCAS bapat2024 E3; kaur2025 E1lever rulePrinted in words: the ratio of the amount of phase A to that of phase B equals the ratio of the length BX to AX, X being the overall composition on the tie line joining A and Bphase amounts from the tie line, named only deac2023b E5; printed in words in the Physical stability chapter yang2022b E1percent polymer complexed\text{complexed}\ (\%) = \left(1 - \frac{\text{polymer in the supernatant}}{\text{total polymer in the solution}}\right) \times 100(1 - \text{polymer in supernatant}/\text{total polymer}) \times 100, the complexation of HPMCAS by weak bases bapat2024 E2; bapat2025a E2Henderson-Hasselbalch equation\mathrm{pH} = \mathrm{p}K_a + \log_{10}\frac{[\mathrm{B}]}{[\mathrm{BH}^+]}ionization of HPMCAS and bedaquiline against pH kaur2025 E2
31 more formulas printed by one paper (table only)
formularole hereexpression
NMR isotope fraction from proton integralstable only: f_{\mathrm{H}} = N_{\mathrm{arom}}/4 with the methyl integral set to 6, deuterated share 100\,(1 - f_{\mathrm{H}}) in % indulkar2017b E1table only
external-standard quantitative NMRtable only: c_{\mathrm{NFD}} = c_{\mathrm{MA}}\,\frac{n_{\mathrm{NFD}}\,NF_{\mathrm{NFD}}}{n_{\mathrm{MA}}\,NF_{\mathrm{MA}}} with maleic acid as the standard indulkar2017b E2table only
Peclet number of a solute in a drying droplettable only: Pe_i = k/(8D_i); a large value gives surface enrichment of that solute bhardwaj2018 E1table only
relative dissolution ratetable only: ITZ rate over 0–20 min divided by the intrinsic rate of crystalline ITZ, in words bhardwaj2018 E2table only
normalized relative polymer dissolution ratetable only: polymer rate from the dispersion divided by that of neat PVPVA, in words bhardwaj2018 E5table only
expected surface polymer:drug ratio of a homogeneous dispersiontable only: 80/20 = 4 for a homogeneous 20% dispersion, in words bhardwaj2018 E6table only
PVPVA mass equivalent of added VP monomertable only: m_{PVPVA} = \frac{c_{VP}\,V}{M_{VP}} \times \frac{10}{5.4} \times M_{repeat}, 77 mg in the example que2019 E2table only
equivalent drug loading of an NMR titration sampletable only: 1.2 mg drug over (1.2 + 77) mg = 1.5% que2019 E3table only
molar composition and repeat-unit MW of PVPVAtable only: 60 wt% VP and 40 wt% VA give 5.4 : 4.6 and 99.62 g/mol, in words que2019 E5table only
XPS quantification with sensitivity factorstable only: atomic to weight percent from the chemical formulas, named only que2019 E6table only
atomic ratio from molecular formulatable only: N/O of nilvadipine 3/6 = 0.50 and of the PVPVA dimer 1/3, in words saboo2019 E2table only
Cliff-Lorimer methodtable only: standardless EDX quantification, named only saboo2019 E6table only
EDX atomic ratio to drug mole fractiontable only: the Cl/N atomic ratio read as mole % drug and converted to wt%, with an unstated unit weight for the polymer saboo2020 E2, X3table only
ATR penetration depth (Harrick equation)table only: d_p = \lambda/(2\pi(n_1^2\sin^2\theta - n_2^2)^{1/2}), the probe depth of the surface FTIR saboo2020 E5table only
percent release normalizationtable only: 100 × amount released over the amount of that component in the compact que2021 E1table only
polymer chain disentanglement ratetable only: k_d = B/(1 - v_p)^{1.9} above the critical volume fraction hiew2022b E2table only
salt formation pKa ruletable only: a pKa difference of more than 2 units between acid and base, in words hiew2022b E4table only
Tg/Tm two-thirds ruletable only: T_g/T_m = 2/3 for additives without a measured Tg correasoto2022b E2table only
gel layer thickness from component weightstable only: h = (w_1/\rho_1 + w_2/\rho_2 + w_3/\rho_3)/A with additive volumes deac2023a E1table only
Fick's first law for solvent penetrationtable only: \partial m_1/\partial t = D A\,\partial m_1/\partial x as printed, argument only deac2023a E2table only
gel layer residence timetable only: gel layer weight over total surface release rate, in words; 5.7 min printed against 7.9 recomputed for neat PVPVA deac2023a E3, X3table only
exponential calibration curvetable only: y = 0.1517\,e^{0.034x} for MePHPH surfaces by ATR-FTIR deac2023b E4table only
sphere volume-radius relationtable only: ion radius from the Van der Waals volume assuming a sphere, V = \frac{4}{3}\pi r^3, in words qi2022 E1table only
disengagement rate proportional to chain mobilitytable only: k_d \propto m_p correasoto2023 E3table only
additive fractional free volume of the geltable only: f_g as the sum of volume fraction × free volume of each component, in words correasoto2023 E4table only
binodal and spinodal conditionstable only: \mu_i^{(1)} = \mu_i^{(2)} and a zero determinant of the Hessian of G, for the PC-SAFT diagrams deac2024b E20, E19table only
PC-SAFT residual Helmholtz energy and combining rulestable only: a^{res} = a^{hc} + a^{disp} + a^{assoc}; u_{ij} = (1 - k_{ij})\sqrt{u_i u_j} with k_{ij} from one dilute tie line deac2024b E5, E7table only
linear gel-layer water gradienttable only: W_{w;g\text{-}s} = 2W_{w;avg} - W_{w;g\text{-}g} deac2024b E4table only
critical polymer concentration for entanglement and tube diametertable only: c_e = \rho M_c/M_w, d_T = b\sqrt{M_c/(2M_0)}, d_T(c_e) = d_T c_e^{-2/3} deac2024a E2, E3, E4table only
radius of gyration of an ideal chaintable only: R_g^2 = M_w b^2/(6M_0), 1–27 nm for K12 to K90 deac2024a E5table only
XPS surface composition from carbon attributiontable only: C 1s split among drug, HPMCAS and excipient for the surface drug fraction hiew2025 E1table only

Sources: A. Release mechanism and LoC

Every paper cited in the chapter A. Release mechanism and LoC (category Dissolution) and in the concept and formula drafts written from it. Keys are first-author surname plus year; a, b, c, d separate papers of the same author and year and are taken from synthesis/citation_keys.csv. The first twenty-nine rows are the papers of the chapter, 2017–2025, in year order (within 2017: Indulkar, Purohit; within 2019: Indulkar, Que, Saboo; within 2020: the five-polymer study, then the indomethacin study; within 2021: Que, Saboo, Yang; within 2022: the clopidogrel study, the atazanavir study, Hiew, Indulkar, Qi, Yang; within 2023: Bapat, Correa Soto, Deac on the dissolution interface, Deac on drug load, Hiew, Yang; within 2024: Bapat, Deac on polymer molecular weight, Deac on ternary phase diagrams; within 2025: Bapat, Hiew, Kaur); the other rows are papers of other subcategories cited in findings, drafts or the chapter page, in year order.

keyyeartitleslugcategory / subcategory
indulkar2017b2017Origin of Nanodroplet Formation upon Dissolution of an Amorphous Solid Dispersion: A Mechanistic Isotope Scrambling Study2017-indulkar-origin-nanodroplet-formation-asd-isotope-scramblingDissolution / A. Release mechanism and LoC
purohit2017b2017Phase Behavior of Ritonavir Amorphous Solid Dispersions during Hydration and Dissolution2017-purohit-ritonavir-asd-hydration-dissolution-phase-behaviorDissolution / A. Release mechanism and LoC
bhardwaj20182018Surface area normalized dissolution to study differences in itraconazole-copovidone solid dispersions prepared by spray-drying and hot melt extrusion2018-bhardwaj-surface-area-normalized-dissolution-itraconazole-pvpva-asdDissolution / A. Release mechanism and LoC
indulkar2019a2019Insights into the dissolution mechanism of ritonavir-copovidone amorphous solid dispersions: importance of congruent release for enhanced performance2019-indulkar-ritonavir-copovidone-asd-congruent-release-locDissolution / A. Release mechanism and LoC
que20192019Insights into the Dissolution Behavior of Ledipasvir-Copovidone Amorphous Solid Dispersions: Role of Drug Loading and Intermolecular Interactions2019-que-ledipasvir-copovidone-asd-loc-interactionsDissolution / A. Release mechanism and LoC
saboo20192019Congruent release of drug and polymer: A “sweet spot” in the dissolution of amorphous solid dispersions2019-saboo-congruent-drug-polymer-release-asd-sweet-spotDissolution / A. Release mechanism and LoC
saboo2020a2020Patterns of drug release as a function of drug loading from amorphous solid dispersions: A comparison of five different polymers.2020-saboo-asd-drug-loading-polymer-hydrophobicity-releaseDissolution / A. Release mechanism and LoC
saboo20202020Congruent release of drug and polymer from amorphous solid dispersions: insights into the role of drug-polymer hydrogen bonding, surface crystallization and glass transition2020-saboo-congruent-release-hbond-crystallization-tg-pvpva-asdDissolution / A. Release mechanism and LoC
que20212021Impact of Drug−Polymer Intermolecular Interactions on Dissolution Performance of Copovidone-Based Amorphous Solid Dispersions2021-que-drug-polymer-interactions-loc-copovidone-asdDissolution / A. Release mechanism and LoC
saboo20212021Exploring the Role of Surfactants in Enhancing Drug Release from Amorphous Solid Dispersions at Higher Drug Loadings2021-saboo-tpgs-felodipine-pvpva-asd-release-high-loadingDissolution / A. Release mechanism and LoC
yang20212021Drug Release and Nanodroplet Formation from Amorphous Solid Dispersions: Insight into the Roles of Drug Physicochemical Properties and Polymer Selection2021-yang-asd-nanodroplet-release-drug-properties-polymer-selectionDissolution / A. Release mechanism and LoC
correasoto2022a2022Impact of Surfactants on the Performance of Clopidogrel-Copovidone Amorphous Solid Dispersions: Increased Drug Loading and Stabilization of Nanodroplets2022-correa-soto-surfactants-clopidogrel-copovidone-asd-nanodropletsDissolution / A. Release mechanism and LoC
correasoto2022b2022Role of surfactants in improving release from higher drug loading amorphous solid dispersions2022-correa-soto-surfactants-higher-drug-loading-atazanavir-pvpva-asdsDissolution / A. Release mechanism and LoC
hiew2022b2022Combining drug salt formation with amorphous solid dispersions – a double edged sword2022-hiew-combining-drug-salt-formation-asd-double-edged-swordDissolution / A. Release mechanism and LoC
indulkar20222022Role of Surfactants on Release Performance of Amorphous Solid Dispersions of Ritonavir and Copovidone2022-indulkar-surfactants-ritonavir-copovidone-asd-release-performanceDissolution / A. Release mechanism and LoC
qi20222022Improved dissolution of an enteric polymer and its amorphous solid dispersions by polymer salt formation2022-qi-enteric-polymer-salt-hp50-miconazole-asd-dissolutionDissolution / A. Release mechanism and LoC
yang2022a2022Release mechanisms of amorphous solid dispersions: Role of drug-polymer phase separation and morphology2022-yang-release-mechanisms-rtv-pvpva-asd-phase-separation-morphologyDissolution / A. Release mechanism and LoC
bapat20232023Does Media Choice Matter When Evaluating the Performance of Hydroxypropyl Methylcellulose Acetate Succinate-Based Amorphous Solid Dispersions?2023-bapat-hpmcas-asd-media-choice-buffer-capacity-releaseDissolution / A. Release mechanism and LoC
correasoto20232023Release Enhancement by Plasticizer Inclusion for Amorphous Solid Dispersions Containing High Tg Drugs2023-correa-soto-plasticizer-release-enhancement-high-tg-pvpva-asdsDissolution / A. Release mechanism and LoC
deac2023a2023Dissolution Mechanisms of Amorphous Solid Dispersions: A Close Look at the Dissolution Interface2023-deac-asd-dissolution-interfaceDissolution / A. Release mechanism and LoC
deac2023b2023Dissolution Mechanisms of Amorphous Solid Dispersions: Role of Drug Load and Molecular Interactions2023-deac-asd-drug-load-molecular-interactions-locDissolution / A. Release mechanism and LoC
hiew20232023Improving Dissolution Performance and Drug Loading of Amorphous Dispersions Through a Hierarchical Particle Approach2023-hiew-grazoprevir-hierarchical-cpad-surface-drug-releaseDissolution / A. Release mechanism and LoC
yang20232023Drug Release from Surfactant-Containing Amorphous Solid Dispersions: Mechanism and Role of Surfactant in Release Enhancement2023-yang-surfactant-containing-asd-release-enhancementDissolution / A. Release mechanism and LoC
bapat20242024Interplay of Drug−Polymer Interactions and Release Performance for HPMCAS-Based Amorphous Solid Dispersions2024-bapat-hpmcas-drug-polymer-complexation-release-performanceDissolution / A. Release mechanism and LoC
deac2024a2024Dissolution mechanisms of amorphous solid dispersions: Role of polymer molecular weight and identification of a new failure mode2024-deac-asd-polymer-molecular-weight-failure-mode-locDissolution / A. Release mechanism and LoC
deac2024b2024Dissolution Mechanisms of Amorphous Solid Dispersions: Application of Ternary Phase Diagrams To Explain Release Behavior2024-deac-asd-ternary-phase-diagrams-releaseDissolution / A. Release mechanism and LoC
bapat2025a2025Impact of HPMCAS Grade on the Release of Weakly Basic Drugs from Amorphous Solid Dispersions2025-bapat-hpmcas-grade-weak-base-asd-release-complexationDissolution / A. Release mechanism and LoC
hiew20252025The importance of surface composition and wettability on the dissolution performance of high drug loading amorphous dispersion formulations2025-hiew-surface-composition-wettability-high-drug-loading-asdDissolution / A. Release mechanism and LoC
kaur20252025Impact of drug-polymer complexation and media properties on the release performance of amorphous solid dispersions containing a weakly basic drug and hydroxypropyl methylcellulose acetate succinate2025-kaur-bdq-hpmcas-complexation-media-asd-releaseDissolution / A. Release mechanism and LoC
rumondor2009c2009Phase Behavior of Poly(vinylpyrrolidone) Containing Amorphous Solid Dispersions in the Presence of Moisture2009-rumondor-pvp-asd-moisture-induced-immiscibilitySolid state stability / Physical stability
marsac20102010Effect of Temperature and Moisture on the Miscibility of Amorphous Dispersions of Felodipine and Poly(vinyl pyrrolidone)2010-marsac-temperature-moisture-miscibility-felodipine-pvp-asdSolid state stability / Physical stability
rumondor2010c2010Effect of Polymer Hygroscopicity on the Phase Behavior of Amorphous Solid Dispersions in the Presence of Moisture2010-rumondor-polymer-hygroscopicity-moisture-phase-separation-asdSolid state stability / Physical stability
alonzo20112011Dissolution and Precipitation Behavior of Amorphous Solid Dispersions2011-alonzo-asd-dissolution-precipitation-nanoparticlesDissolution / B. Supersaturation from ASD dissolution
rumondor20112011Understanding the Tendency of Amorphous Solid Dispersions to Undergo Amorphous–Amorphous Phase Separation in the Presence of Absorbed Moisture2011-rumondor-asd-moisture-aaps-pvp-oplsSolid state stability / Physical stability
ilevbare2012a2012Effect of Binary Additive Combinations on Solution Crystal Growth of the Poorly Water-Soluble Drug, Ritonavir2012-ilevbare-ritonavir-binary-additive-crystal-growthDissolution / D. Crystallization from solution
vaneerdenbrugh2012c2012Nanoscale Mid-Infrared Evaluation of the Miscibility Behavior of Blends of Dextran or Maltodextrin with Poly(vinylpyrrolidone)2012-van-eerdenbrugh-nanoscale-mid-ir-dextran-maltodextrin-pvp-miscibilityCharacterization methods / Solid-state methods
ilevbare2013a2013Liquid-Liquid Phase Separation in Highly Supersaturated Aqueous Solutions of Poorly-Water Soluble Drugs – Implications for Solubility Enhancing Formulations2013-ilevbare-llps-supersaturated-poorly-water-soluble-drugsDissolution / C. Amorphous solubility and LLPS
chen2015a2015Impact of Surfactants on the Crystallization of Aqueous Suspensions of Celecoxib Amorphous Solid Dispersion Spray Dried Particles2015-chen-surfactants-crystallization-celecoxib-hpmcas-asd-suspensionsDissolution / B. Supersaturation from ASD dissolution
jackson20152015Dissolution of Danazol Amorphous Solid Dispersions: Supersaturation and Phase Behavior as a Function of Drug Loading and Polymer Type2015-jackson-danazol-asd-dissolution-llps-drug-loading-polymer-typeDissolution / B. Supersaturation from ASD dissolution
purohit2015b2015Phase Separation Kinetics in Amorphous Solid Dispersions Upon Exposure to Water2015-purohit-phase-separation-kinetics-asd-waterCharacterization methods / Solid-state methods
xie2016a2016Improved Release of Celecoxib from High Drug Loading Amorphous Solid Dispersions Formulated with Polyacrylic Acid and Cellulose Derivatives2016-xie-celecoxib-high-drug-loading-asd-paa-cellulose-derivativesDissolution / B. Supersaturation from ASD dissolution
xie2016b2016Effect of Temperature and Moisture on the Physical Stability of Binary and Ternary Amorphous Solid Dispersions of Celecoxib2017-xie-temperature-moisture-celecoxib-binary-ternary-asd-stabilitySolid state stability / Physical stability
indulkar2017a2017Impact of Micellar Surfactant on Supersaturation and Insight into Solubilization Mechanisms in Supersaturated Solutions of Atazanavir2017-indulkar-micellar-surfactant-supersaturation-atazanavir-sdsDissolution / C. Amorphous solubility and LLPS
tres20182018Mechanistic Understanding of the Phase Behavior of Supersaturated Solutions of Poorly Water-Soluble Drugs2018-tres-asd-phase-behavior-fluorescence-lifetime-ritonavir-lopinavirCharacterization methods / Solution methods
mosqueragiraldo2018b2018Influence of Polymer and Drug Loading on the Release Profile and Membrane Transport of Telaprevir2018-mosquera-giraldo-telaprevir-asd-polymer-loading-release-membrane-transportBioperformance / Bioperformance
hate20182018Insight into Amorphous Solid Dispersion Performance by Coupled Dissolution and Membrane Mass Transfer Measurements2018-hate-asd-coupled-dissolution-membrane-mass-transferBioperformance / Bioperformance
li20192019Microstructure Formation for Improved Dissolution Performance of Lopinavir Amorphous Solid Dispersions2019-li-lopinavir-hpmc-asd-microstructure-dissolutionASD process / ASD process
li20202020Water-induced phase separation of spray dried amorphous solid dispersions2020-li-water-induced-phase-separation-spray-dried-asd-ritonavir-pvpvaASD process / ASD process
que20202020Evidence for Halogen Bonding in Amorphous Solid Dispersions2020-que-halogen-bonding-amorphous-solid-dispersionsSolid state stability / Miscibility and drug-polymer interactions
ueda2020a2020Impact of hypromellose acetate succinate grade on drug amorphous solubility and in vitro membrane transport2020-ueda-hpmcas-grade-amorphous-solubility-membrane-transportBioperformance / Bioperformance
wilson20202020Amorphous solid dispersions of enzalutamide and novel polysaccharide derivatives: investigation of relationships between polymer structure and performance2020-wilson-enzalutamide-polysaccharide-asd-polymer-performanceBioperformance / Bioperformance
ueda2020b2020Polymer type impacts amorphous solubility and drug-rich phase colloidal stability: A mechanistic study using nuclear magnetic resonance spectroscopy2020-ueda-polymer-type-amorphous-solubility-drug-rich-phase-colloidal-stabilityDissolution / C. Amorphous solubility and LLPS
trasi20202020Physical stability and release properties of lumefantrine amorphous solid dispersion granules prepared by a simple solvent evaporation approach2020-trasi-lumefantrine-asd-granules-solvent-evaporationSolid state stability / Physical stability
bhujbal20212021Physical Stability and Dissolution of Lumefantrine Amorphous Solid Dispersions Produced by Spray Anti-Solvent Precipitation2021-bhujbal-lumefantrine-asd-spray-antisolvent-precipitationSolid state stability / Physical stability
duong2022a2022Combining enabling formulation strategies to generate supersaturated solutions of delamanid: In situ salt formation during amorphous solid dispersion fabrication for more robust release profiles2022-duong-delamanid-in-situ-salt-asd-releaseDissolution / B. Supersaturation from ASD dissolution
hiew2022a2022Balancing Solid-State Stability and Dissolution Performance of Lumefantrine Amorphous Solid Dispersions: The Role of Polymer Choice and Drug−Polymer Interactions2022-hiew-lumefantrine-asd-stability-dissolution-polymer-choiceSolid state stability / Miscibility and drug-polymer interactions
moseson2022b2022Formulation and processing strategies which underpin susceptibility to matrix crystallization in amorphous solid dispersions2022-moseson-processing-strategies-matrix-crystallization-bcl-pvpva-asdASD process / ASD process
yang2022b2022Phase separation in surfactant-containing amorphous solid dispersions: Orthogonal analytical methods to probe the effects of surfactants on morphology and phase composition2022-yang-surfactant-containing-rtv-pvpva-asd-phase-separationSolid state stability / Physical stability
hate20222022A Mechanistic Study of Drug Mass Transport from Supersaturated Solutions Across PAMPA Membranes2021-hate-drug-mass-transport-supersaturated-pampa-membranesBioperformance / Bioperformance
ueda20222022Variable-Temperature NMR Analysis of the Thermodynamics of Polymer Partitioning between Aqueous and Drug-Rich Phases and Its Significance for Amorphous Formulations2022-ueda-polymer-partitioning-ibuprofen-drug-rich-phase-nmrDissolution / C. Amorphous solubility and LLPS
moseson2022a2022Atomic Layer Coating to Inhibit Surface Crystallization of Amorphous Pharmaceutical Powders2022-moseson-atomic-layer-coating-surface-crystallization-asd-powdersASD process / ASD process
moseson20232023Impact of Aluminum Oxide Nanocoating on Drug Release from Amorphous Solid Dispersion Particles2023-moseson-aluminum-oxide-nanocoating-drug-release-asd-particlesASD process / ASD process
nguyen2023a2023Fed- and Fasted-State Performance of Pretomanid Amorphous Solid Dispersions Formulated with an Enteric Polymer2023-nguyen-pretomanid-hpmcas-asd-fed-fasted-performanceBioperformance / Bioperformance
polyzois20242024Amorphous Solid Dispersion Formation for Enhanced Release Performance of Racemic and Enantiopure Praziquantel2024-polyzois-praziquantel-racemic-enantiopure-asd-releaseDissolution / B. Supersaturation from ASD dissolution
bapat2025b2025Modification of Peptide and Permeation Enhancer In Vitro Release Rates by Dispersion with a Gel-Forming Polymer2025-bapat-peptide-permeation-enhancer-pvpva-synchronous-releasePeptide permeability / Peptide permeability
benson20252025Dissolution of copovidone-based amorphous solid dispersions: Influence of atomic layer coating, hydration kinetics, and formulation2025-benson-alc-coated-rtv-pvpva-asd-hydration-releaseASD process / ASD process
shah20252025Chemistry and ionization of HPMCAS influences the dissolution and solution-mediated crystallization of posaconazole amorphous solid dispersions2025-shah-hpmcas-ionization-posaconazole-asd-crystallizationDissolution / D. Crystallization from solution
fagan20252025Impact of Permeation Enhancers on the Release of Insulin from Tablets in Biorelevant Media2025-fagan-permeation-enhancers-insulin-minitablet-biorelevant-mediaPeptide permeability / Peptide permeability
For the authors: card issues found while writing

Card issues: A. Release mechanism and LoC

Material problems found in the cards of the chapter while writing it (seven papers of 2017–2020: indulkar2017b, purohit2017b, bhardwaj2018, indulkar2019a, que2019, saboo2019, saboo2020a; seven papers of 2020–2022: saboo2020, que2021, saboo2021, yang2021, correasoto2022a, correasoto2022b, hiew2022b; eight papers of 2022–2023: indulkar2022, qi2022, yang2022a, bapat2023, correasoto2023, deac2023a, deac2023b, hiew2023; seven papers of 2023–2025: yang2023, bapat2024, deac2024a, deac2024b, bapat2025a, hiew2025, kaur2025). Extractor notes (X#) that the cards already contain are not repeated here.

Papers of 2017–2020: none found. No contradiction between card sections was met while writing the findings, and a script check showed that every id cited inside these seven cards resolves to a row or heading of the same card (the only unmatched id-like tokens are the names Rotavapor-R210 in indulkar2017b and indulkar2019a, Eclipse E600 in purohit2017b and the abbreviation P407 for poloxamer 407 in que2019). The source inconsistencies met while writing are recorded in the cards' own X notes and are carried into the chapter with that note: the critical mixture ratio printed 1.7 × 10⁻⁶ against 1.7 × 10⁻³ from its inputs (saboo2020a X1), the uncertain neat PVPVA rate (saboo2020a X10), the factor-10 misprint of the fluorine example (que2019 X3), the molar loadings that no single convention reproduces (saboo2019 X2), the shared equation label of the Noyes–Whitney and Flory–Huggins equations (purohit2017b X2), and the stated switch loadings of the itraconazole paper (bhardwaj2018 X6).

Papers of 2020–2022: none found. A script check showed that every id cited inside these seven cards resolves to a row or heading of the same card (142, 110, 124, 131, 133, 127 and 121 distinct cited ids). The inconsistencies met while writing are already recorded in the cards' own X notes and are carried into the chapter with that note: the unstated unit weight of the polymer in the EDX weight conversion (saboo2020 X3), the table-of-contents graphic that lists surface crystallization as lowering the limit although the ester released congruently over the first 5 min (saboo2020 X7), the different probe depths of the three surface methods (saboo2020 X15), the 18 °C wet Tg as the onset of a bulk model composition (saboo2020 X16), the undescribed normalization of the analogue release rates (que2021 X6), the unstated mass basis of the felodipine–TPGS rates and the TPGS levels that assume complete release (saboo2021 X4, X14), the untested exclusion of wetting (saboo2021 X13), the two printed log P values of miconazole and the mixed conventions of the stated cliff loadings (yang2021 X1, X26), the TPGS CMC printed as 40 and about 50 µg/mL and the drug-loading basis of the ternary dispersions (correasoto2022a X1, X9), the CTAB enhancement factor of 32 in the table against about 36 in the figure and the HLB of Span 80 printed as that of Tween 80 (correasoto2022b X2, X8), and the missing criterion for "good release" and the coarse loading steps of the salt paper (hiew2022b X6, X7).

Two points are not card errors and are noted for the merge into the shared pages. First, the shared page of incongruent release lists the 2019 XPS study saboo2019 C25 as "nilutamide and cilostazol–PVPVA compacts"; the drugs of that paper are nilvadipine and cilnidipine saboo2019 M1, M2. The draft of that concept in this chapter states the correction. Second, two papers of Saboo and co-workers from 2020 are cited: saboo2020a is the five-polymer felodipine study and saboo2020 the indomethacin study, as assigned in the library's key list; the shared concept pages of surface crystallization and of the Gordon–Taylor equation already carry rows of saboo2020, and the shared formula page of the Fox equation a row of que2021, from other chapters, so the drafts here add only the new aspects.

Papers of 2022–2023 (indulkar2022, qi2022, yang2022a, bapat2023, correasoto2023, deac2023a, deac2023b, hiew2023): none found. A script check showed that every id cited inside these eight cards resolves to a row or heading of the same card (149, 139, 129, 143, 139, 151, 152 and 145 distinct cited ids; the only unmatched id-like tokens are the instrument names Eclipse E600 and Rotavapor-R210 in indulkar2022, Eclipse E600 in yang2022a, Eclipse E200 in deac2023b and Vision G2 in correasoto2023 and hiew2023). The source inconsistencies met while writing are already recorded in the cards' own X notes and are carried into the chapter with that note: the abstract naming Span 20 and TPGS for the smallest droplets against the figure and table naming Span 20 and Span 85, the abstract saying every surfactant improved release against the discussion saying two did not, the axis of the early polymer-release plot printed as mg/mL for values that behave as mg per vessel, and the IR band positions of crystalline ritonavir in text and figure (indulkar2022 X1, X3, X5, X7); the 30% drug release given as 30% in the text against about 35% in the figure, and "no release" at 40–50% against about 3% drug and 10.5–14% polymer in the figure (yang2022a X1, X2); the MePHPH limit given as 40% and 30% in different sections, and the gel residence times shorter than the gel weight implies (deac2023a X1, X3); the PVPVA content of PHPH nanoparticles printed between about 69.6 and 78.0% across figures, tables and text, and the binode drug loads that do not exactly match the nanoparticle data (deac2023b X3, X18); and the best hierarchical particle called a 60% material in the discussion while it assays 73.4% drug, with dog AUCs that a recomputation from the plasma profile does not reproduce (hiew2023 X1, X4).

One point is not a card error and is noted for the merge into the shared pages: the same nominal medium, 50 mM pH 6.8 phosphate, is given a buffer capacity of 29 mM/ΔpH in the HP-50 paper qi2022 M16 and 26 mM/ΔpH in the HPMCAS paper bapat2023 A1; the draft of buffer capacity states both. The key hate2022 belongs to a card whose slug starts with 2021 and whose front matter gives 2022; the chapter uses the key list's year.

Papers of 2023–2025 (yang2023, bapat2024, deac2024a, deac2024b, bapat2025a, hiew2025, kaur2025): none found. A script check showed that every id cited inside these seven cards resolves to a row or heading of the same card (129, 118, 108, 148, 88, 133 and 127 distinct cited ids). The inconsistencies met while writing are already recorded in the cards' own X notes and are carried into the chapter with that note: text against figure values of release in the surfactant paper yang2023 X1, X2, X3, X4, the cinnarizine slowdown of 18- or 30-fold and the table against figure release values in the 2024 HPMCAS paper bapat2024 X1, X2, the bracketed limits and unstated time point of the PVP paper deac2024a X5, X6, the cited rather than measured limits and the PHPH film switch of the phase-diagram paper deac2024b X9, X5, the cited MF data of the grade paper bapat2025a X7, the two clusters and unequal HPMC concentration of the particle paper hiew2025 X11, X8, and the solution-test basis of complexation in the bedaquiline paper kaur2025 X14.

Three points are not card errors and are noted for the merge into the shared pages. First, the critical point of PHPH–PVPVA–water read from Fig. 10 (about 2.6 wt% PHPH and 59.5 wt% PVPVA) corresponds to about 4.2% drug loading (synthesis: 2.6/(2.6 + 59.5) ≈ 0.042), against the 3.7% the paper places in Figs. 16 and 18; the chapter uses 3.7%, the paper's own value, and the difference lies within the precision of reading 2.6 wt% from the plot deac2024b R23, R35, R37. Second, the acid content of HPMCAS-LF is 1.52 ± 0.03 mmol/g as titrated in the grade paper and 1.54 mM per gram as cited in the bedaquiline paper bapat2025a M3; kaur2025 M2; the drafts give each with its source. Third, the 2023 surfactant paper cites the ledipasvir gain with SDS as 7.5 → 30%, while the 2019 ledipasvir study read in this chapter gives 5 → 30% (F13) yang2023 R27; the chapter keeps the 2019 values and states the cited ones beside them in F21.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

absorptive dissolution testing

A dissolution test coupled to a membrane that removes dissolved drug into a receiver, as absorption would, so that release, phase behaviour and mass transfer are measured together [hate2020a P9; hate2020b P8, C12]. With sink maintained the donor concentration over time dictates the transport rate, so the receiver profile reflects dissolution, crystallization and the supersaturation reached [hate2017 C36]. In the mesoporous-silica papers it tests whether removal of drug frees drug held back by the silica [hate2020a C15].

Findings

F14, F11, F13, F15.

Related concepts

provides an absorptive sink and keeps sink conditions in the receiver; reads membrane flux; contrasts with closed non-sink dissolution; shifts the dynamic adsorption-desorption equilibrium.

Formulas

total release by mass balance, membrane flux in terms of solute activity.

How it is measured or obtained

A flow-through apparatus with a cellulosic hollow-fibre module (100 cm², 15 nm pores), co-current flow of 4 mL/min on both sides at 37 °C, a 50 mL donor with a 10 µm cannula filter, an in-line UV receiver fed with pH 6.8 buffer and HPLC of donor samples; total release is drug in the donor plus drug transferred [hate2020a P9, E4; hate2020b P8]. The closed-vessel comparison uses the same medium without the module [hate2020a P7].

Values in the library
materialvalue or classconditionspaper ids
atazanavir–SBA-15, 20% w/wtotal release about 89.5% against 46.5% closed at 240 minpH 6.8, 75 µg/mL, HPMC[hate2020a R20]
atazanavir–SBA-15, 5–50% w/wabout 73 / 80.5 / 66.5 / 52 / 36% in 90 minsame[hate2020a R15]
atazanavir–SBA-15, pH 1 → 6.8receiver peak about 6.4 against 3.6 µg/mL (pH 6.8 only)20% w/w[hate2020a R22]
10% atazanavir–SBA-15 against 10% HPMC ASDreceiver about 4.3–5.2 against 10.2–11.6 µg/mL200 µg/mL[hate2020a R25]
ketoconazole–SBA-15, pH 1 → 6.8about 54–60.5% → 69.5% over 4 h20% w/w[hate2020b R17]
nevirapine with 0.1% PVPVA (not silica)total drug constant 120 min with absorption; dissolved drug falling after 60 min closed500 µg/mL, pH 6.5[hate2017 R16, R17]

Evidence table: absorptive dissolution testing.

Pitfalls and disagreements

About 5–6% of the drug binds to the membrane, and whether total release counts it is not stated [hate2020a R16, X18]. Figures share data sets, so the sink, loading and pre-dissolved results are not independent repeats [hate2020a X9]. The total-release calculation of the ketoconazole run is not described [hate2020b X10]. Hate and co-workers state that a closed vessel may overestimate the supersaturation at any time and the risk of crystallization of slowly crystallizing solutions, and that an absorptive compartment gives more in vivo relevant insight for silica formulations [hate2017 C53, C55; hate2020a C49].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

absorptive sink

A membrane compartment that removes dissolved drug from the dissolution medium while dissolution and phase change go on, as the intestinal wall does in vivo; the test that couples a dissolving donor to such a compartment is called absorptive dissolution testing [hate2019 C9, C31, P4]. The sink changes concentration–time profiles: it lowers the supersaturation reached in the donor and so the driving force for crystal growth on residual seeds [hate2019 C15, C35]. In vivo, absorption keeps depleting the lumen after gastric emptying and may lower the driving force for secondary nucleation and growth, and may let a crystalline fraction dissolve once luminal concentrations fall low enough [purohit2019 C41]. It differs from a sink in the compendial sense, where the medium is large enough to dissolve the dose (sink conditions).

Findings

F14, F28, F29.

Related concepts

contrasts with sink conditions and non-sink dissolution; acts on desupersaturation and crystal seeding; measured with the membrane mass transfer coefficient.

Formulas

hollow-fibre donor depletion, power-law crystal growth rate, mass transferred from receiver AUC.

How it is measured or obtained

A cellulosic hollow-fibre module (100 cm² and 15 nm pores in the tacrolimus study) fed from the dissolution vessel, donor and receiver pumped co-currently at 2 mL/min, receiver read by in-line UV and donor by HPLC; total dissolved drug in donor plus receiver follows crystallization [hate2019 P4, P8, C19]. Receiver AUC and a test-to-reference ratio with 80–125% limits summarize the result [hate2019 P9, E6]. The module is described as having 115 cm² of membrane in the nevirapine study [hate2017 M10].

Values in the library
materialvalue or classconditionspaper ids
tacrolimus generic capsule, freshreceiver AUC0–120 about 362, 682 and 992 µg/mL·min in 240, 100 and 40 mLhollow fibre, 37 °C[hate2019 R12, C24]
tacrolimus crystalline suspensionAUC about 87 µg/mL·min at every volumesame[hate2019 R12]
tacrolimus generic, freshdid not crystallize at 240, 100 or 40 mL, unlike in an earlier closed vesselsame[hate2019 R11, C35]
tacrolimus generic, 20% crystallineat 40 mL only: total dissolved drug fell from about 2.35 to 1.9 mg after 60 min5 mg in 40 mL[hate2019 R11, C20]
nevirapine tablet donorabout 253 µg/mL after 270 min with absorption against about 525 in a closed vessel0.05% HPMC-AS[hate2017 R15, R7]
atazanavir 50% ASDstotal release at 120 min 6200, 6300, 5000 µg with absorption against 4200, 4600, 3600 closed (HPMCAS, HPMC, PVPVA)200 µg/mL dosehate2018 R18
Pitfalls and disagreements

The absorption rate is a property of the apparatus: a closed vessel may overstate crystallization, and an absorptive test may understate it if absorption in vivo is slower [hate2019 C12, C35]. Two explanations for the missing crystallization of fresh tacrolimus capsules, the polymer and the lower supersaturation from absorption, were not separated, because no run without the sink at the same volume exists [hate2019 X15, C22]. The area of the same module is 100 cm² in one card and 115 cm² in another [hate2019 P4; hate2017 M10]. The fitted model constants are not reproducible from the printed values (F29) [hate2019 X1, X3, X4].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

accelerated stability testing

Storage at raised humidity and/or temperature to provoke and rank physical instability in less time than at the intended storage condition. In the library the concern is that high RH can change the mechanism, not only the rate, of crystallization of susceptible dispersions rumondor2009c C52.

Findings

F16, F25.

Related concepts

related to moisture-induced phase separation, moisture-induced crystallization and physical stability.

Formulas

Arrhenius equation (temperature extrapolation; used here for nucleation, not for shelf life).

How it is measured or obtained

Storage over saturated salts at fixed RH (here 54–94% RH at room temperature) and read-out by IR, DSC, PXRD or microscopy [rumondor2009c P4; rumondor2009b P2, P3; marsac2010 P7].

Values in the library
materialvalue or classconditionspaper ids
pimozide–PVPpartial phase separation after 3 days54% RHrumondor2009c R10, C4
felodipine–PVP 30.3 wt%distinct separation after 1 week75% RHmarsac2010 R7, R8
felodipine with 25–50% PVP vs HPMCASindistinguishable at 0–52% RH in ≈490 days; 51–82% vs 9–28% crystallized at 75–93% RH22–25 °C[rumondor2009b R19, R9]
PEO compacts (outside)slow water uptake over months; partially crystalline polymers "may" defeat Arrhenius extrapolation94% RH[marsac2008b C40]
curcumin dispersions25 °C/0% RH and 90 °C/0% or 60 °C/98% RH separate no polymersix conditions[wegiel2014 R13, C23]
felodipine–3% PVP powder≈8-fold faster start and ≈85% against ≈45% plateau at 50 against 30 °Cdry storage[kestur2013b R17, C38]

Evidence table: accelerated stability testing.

Pitfalls and disagreements

In susceptible systems "the route of crystallization may be altered at high RH" and need not represent lower RH rumondor2009c C52; the separation threshold depends on time and composition marsac2010 X9. Dry and moderate-RH data could not rank PVP against HPMCAS for felodipine within the method error [rumondor2009b X4]. The 2013 papers state that their results "highlight the difficulty" of choosing accelerated conditions [wegiel2013b C41; kestur2013b C40].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

acid-base interaction

The transfer of a proton, or the formation of an ion pair, between an acidic and a basic group of drug and polymer, instead of a neutral hydrogen bond. In the papers of this chapter: the basic dimethylamino group of E100 with the weakly acidic OH groups of naringenin and quercetin (also resveratrol and curcumin); the carboxylic acids of HPMCAS, HPMCP, CAP and Eudragit L 100 with the tertiary amine of lumefantrine; and the strongly acidic sulfonic acid of PSSA with the amine or ring nitrogen of anthranilic acid, lidocaine and dibucaine [wegiel2013a C16, C17, C33; hiew2022a C25, C48; vaneerdenbrugh2011a C22, C38, C44]. The authors take ionic interactions to be "typically stronger" than hydrogen bonds, an assumption, and ascribe the unusual stability of E100 dispersions to them ("appear to be the reason") [wegiel2013a C16, C35]. For the enteric polymers the same contact is held to reduce hydration of the polymer carboxylates and so to slow release ("are postulated"; "is thought to") hiew2022a C53.

Findings

Miscibility and drug-polymer interactions: F21, F23, F24, F25, F26. Physical stability: F24, F34.

Related concepts

depends on pKa; contrasts with hydrogen bonding, halogen bonding and hydrogen-bond donor and acceptor groups; part of drug-polymer interactions; acts on crystallization inhibition and physical stability; an alternative where intramolecular hydrogen bonding limits hydrogen bonds [wegiel2014 C44].

Formulas

free carboxylate fraction after ion pairing, Fox equation.

How it is measured or obtained

By the loss of the E100 amine bands at 2820 and 2770 cm⁻¹ with rising drug content [wegiel2013a R6]; by a protonated component of the N 1s XPS peak and by carboxylate bands at 1594–1560 and 1410–1343 cm⁻¹ in subtraction IR spectra hiew2022a R19, R20; by ATR-FTIR of melts at equimolar functional groups (spectra not shown) [vaneerdenbrugh2011a R8, R15, R17]; by colour change (curcumin with E100) [wegiel2014 R10, C20]: dark red for curcumin–E100 against orange for the others, read as a change of the drug's ionization state; by a dispersion Tg above both components [wegiel2014 C41]. For the weak base lumefantrine with acidic enteric polymers in the physical-stability papers, XPS of the N 1s signal gives the share of protonated drug, and ATR-FTIR shows the polymer carbonyl band moving up and a band near 1560 cm⁻¹ read as carboxylate ("likely") trasi2020 P15, R9, C11, C12; bhujbal2021 P6, R6. The pKa of each group is calculated or titrated to judge whether a proton can move [vaneerdenbrugh2011a P7; hiew2022a P17].

Values in the library
materialvalue or classconditionspaper ids
quercetin–E100amine bands gone at 50% quercetinIR, films[wegiel2013a R6]
resveratrol–E100; curcumin–E100bands absent at 50% resveratrol; eradicated at 60% curcuminIR, films[wegiel2013b R7, C15; wegiel2014 R7, C16]
lumefantrine, 25% drug loadingprotonated 19% (HPMCAS), 46% (HPMCP), 55% (CAP), 49% (Eudragit L 100); 0% with PVPVAXPS, dry compactshiew2022a R20
same, after 2 h in pH 6.8 buffer3, 21, 54, 12%XPShiew2022a R20
anthranilic acid, lidocaine, dibucaine with PSSAproton transfer reported; not with PAAATR-FTIR of melts (not shown)[vaneerdenbrugh2011a R8, R15, R17]
cationic drugs with HPMCAS-MF, 1:1 drug to carboxyl, pH 6.0≥70% of the polymer complexedco-precipitationbapat2024 C19
curcumin–E100 (basic monomer pKa 8.4; curcumin pKa 10.51, 9.88, 8.38)dark red; Tg 62 °C, about 19 °C above the Fox line after recalculation75:25 powder[wegiel2014 M5, M1, R10, X1, C41]
resveratrol–E100highest amorphous loading of six polymers (60%); "could be responsible" for better manufacturabilityrotary evaporation[wegiel2013b R2, C16, C43]
curcumin–E100; resveratrol–E100amorphous > 350 and > 400 days at 84% RHstorage, 25 °C[wegiel2014 R13; wegiel2013b R12.g]
lumefantrine 40:60 with HPMCAS, Eudragit L100, HPMCP, CAP16, 33, 48, 61% protonated; neat drug 7%rotary-evaporated powders, XPStrasi2020 R11, C14
lumefantrine with HPMCP, HPMCAS (20–40% drug), CAP, Eudragit L100 (40%)14–42% protonated; amorphous drug 3%powders precipitated into dilute HCl, XPSbhujbal2021 R8
fluorescein in miconazole–PVPVA filmslocated in the drug-rich phase, read as a possible acid–base contact with the weakly basic drug ("may arise")confocal dye screen[saboo2017 C36]

Evidence table: acid-base interaction.

Pitfalls and disagreements

The strength of the contact was not measured, and the causal role of the E100 contact in stability was not separated from other properties of E100 [wegiel2013a X10]. The naringenin–E100 spectra are described but not shown, and no polyphenol-side marker is reported [wegiel2013a C17, X10]. The melt spectra behind the PSSA reactions are not shown, and no acid–base reaction was seen for bifonazole [vaneerdenbrugh2011a X13, R16]. The lumefantrine values come from dry compacts and fall after dissolution, except for CAP; an earlier XPS study found no protonation with HPMCAS where this one found 19% hiew2022a R20, R30, X14. An ion pair does not guarantee stability: the 50% HPMCAS dispersion, with 1.61 mol drug per mol acid groups, crystallized within a week hiew2022a R26, C63. For curcumin the extent of proton transfer was not measured, and no polymer with the same backbone without amine groups was tested [wegiel2014 C37]. For resveratrol the IR-based ranking that put E100 first did not hold in storage, where PVP outperformed it [wegiel2013b X10]. In the lumefantrine powder studies the share of protonated drug ordered the stability of powders made without water but not of powders precipitated into water, where residual water and drying time decided trasi2020 C36; bhujbal2021 C50, C51. The polymer that protonated the drug most, CAP, released the least drug at 40% loading trasi2020 R14; bhujbal2021 R15.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

activity coefficient

The ratio of the ideal solubility to the real solubility of a drug in a solvent, \gamma_d; a value below 1 means that the drug dissolves better than ideal, far above 1 that it mixes much worse [baird2011 E7, C23; marsac2008b E2, C14]. If the entropy of mixing is close to ideal, \gamma < 1 points to exothermic mixing and favourable drug–solvent interactions and \gamma > 1 to endothermic mixing [baird2011 C23; marsac2008a C34]. New aspect (C. Amorphous solubility and LLPS): the activity coefficient γ of the drug in the dilute aqueous solution links concentration to activity, a = C\gamma or a = x\gamma; the amorphous solubility estimate assumes that γ in the bulk is the same at the crystalline and at the amorphous solubility, a "reasonable assumption" for dilute solutions of poorly soluble compounds [ilevbare2013a E7, C55; indulkar2015 C43; mosqueragiraldo2015 E5]. Micelles break the assumption of equal activity coefficients at the crystalline and the amorphous concentration: for atazanavir in 3.6 mg/mL SDS the slope of free against total drug, labelled γ, was 0.047, so the concentration ratio is about half the activity ratio indulkar2017a R11, E8, C44. For telaprevir the ratio of flux slopes below the plateau gives the ratio of activity coefficients (Eq. 7) [lu2017b E7]. New aspects (Miscibility and drug-polymer interactions): For a drug in a polymer the activity coefficient γ carries any non-ideal entropy or heat of mixing, and the mole-fraction solubility of the crystal is its ideal value divided by γ [marsac2009 E1, C4]. It splits into a combinatorial (entropy) part and a residual (enthalpy) part; exothermic mixing lowers γ and endothermic mixing raises it [marsac2009 C10]. In a polymer γ is much higher than in a small-molecule analogue because the polymer contributes less mixing entropy [marsac2006b C50; marsac2009 C33]. Estimating the solubility of a drug in a liquid is essentially the problem of determining γ, which is exceedingly difficult for drugs in viscous glassy polymers [marsac2009 C4]. New aspect (Bioperformance): γ appears in a = \gamma C for the donor and as γm for the membrane in the flux equation, and additives change the donor value [raina2015c E3, E4, C35]. The concentration-based supersaturation ratio assumes \gamma/\gamma_{eq} = 1; this holds in simple buffers, where the dilute solution is nearly ideal, and fails in media with micelles, where the solubilized fraction differs between the saturated and the supersaturated solution [elkhabaz2019b E2, C28, C42]. New aspect (Physical stability): the activity coefficient of water in an amorphous drug, from water uptake by Raoult's law a_{water} = \gamma_{water} X_{water}, and of the drug in water, from aqueous solubility; both were tested as predictors of moisture-induced separation and showed no trend rumondor2009c E1, E2, C29.

Findings

PEG dispersions: F3, F11. C. Amorphous solubility and LLPS: F5, F12, F16. Miscibility and drug-polymer interactions: F8, F9. Bioperformance: F3, F6, F18. Physical stability: F2, F13.

Related concepts

depends on ideal solubility; measured by drug solubility in polymer; indicates enthalpy of mixing; related to Flory-Huggins interaction parameter and drug-polymer interactions, and chemical potential; part of thermodynamic activity; depends on combinatorial entropy of mixing.

Formulas

activity coefficient from solubility, Flory-Huggins melting point depression, activity from concentration, binodal condition, solid-liquid equilibrium solubility equation; Flory-Huggins activity equation.

How it is measured or obtained

From the mole-fraction solubility in a liquid analogue of the polymer, PEG 400, after 24 h at 25 °C with a UV assay, and the ideal solubility from the melting point and heat of fusion, \gamma_d = \frac{1}{x_d}\exp\left(\frac{-\Delta H_{fus}(T_m - T)}{R\,T_m^{2}}\right) [baird2011 P5, P9, E7; marsac2008b P5, P9]. PEG 400 is used because activity coefficients in viscous, semicrystalline PEG 3350 are hard to determine [baird2011 C21]. In the amorphous solubility papers it is not measured; in the liquid–liquid equilibrium form x_{L_1}\gamma_{L_1} = x_{L_2}\gamma_{L_2} it links the water-phase and drug-rich-phase compositions ilevbare2013a E12. For the PVP dispersions, from the solubility of the crystalline drug in 1-ethyl-2-pyrrolidone (excess drug, 25 °C, at least 24 h, UV–Vis, or HPLC with refractive-index detection for sucrose) and the ideal solubility from the melting point, heat of fusion and heat capacities; Eq. 8 then scales γ to PVP, assuming ideal entropy with EP, equal contacts and equal γ at both solubility limits [marsac2009 P2, P7, E1, E8, C11]. In the Bioperformance papers it was not measured; the slope of free against total drug is taken from atazanavir–SDS work indulkar2017a R11, E8, and the solubility split into a crystal term and an activity-coefficient term was used to compare ritonavir and atazanavir [alhalaweh2016 E3, E4, E5]. In the moisture study, the water activity coefficient from the uptake of the amorphous drug at 95% RH and the drug activity coefficient from mole-fraction solubility rumondor2009c P13.

Values in the library
materialvalue or classconditionspaper ids
chlorpropamide; aceclofenac; loratadine; haloperidol in PEG 4000.614; 0.121; 2.369; 0.84225 °C[baird2011 R9.a, R9.b, R9.c, R9.d]
acetaminophen, ketoprofen, naproxen, ibuprofen, felodipine, ketoconazole in PEG 4000.06, 0.31, 0.02, 0.64, 0.14, 0.0925 °C[marsac2008b R14.a, R14.b, R14.c, R14.d, R14.e, R14.f]
the same six drugs in water1.2 × 10¹, 1.4 × 10⁴, 3.8 × 10³, 3.1 × 10⁴, 2.4 × 10⁵, 5.3 × 10⁵cited aqueous solubilities[marsac2008b R14]
nifedipine; felodipine in water1.89 × 10³; 2.43 × 10⁵25 °C[marsac2008a R10.c, R10.d]
five compounds in an ethyl-pyrrolidone analogue of PVPbelow 1 for all25 °C[marsac2009 C23, R9]
felodipine, nifedipine, ketoconazole, sucrose, indomethacin in EP0.89, 0.26, 0.68, 0.37, 0.1525 °C[marsac2009 R9]
same five in PVP K123.94, 1.18, 5.04, 1.76, 0.50scaled with Eq. 8[marsac2009 R9]
same five in PVP K29/324.34, 1.30, 5.92, 1.93, 0.54scaled with Eq. 8[marsac2009 R9]
nifedipine, felodipineχ-based activity from melting depression; no direct γFlory–Huggins[marsac2006b E6]
ritonavir, atazanavirlog γ ordering RTV > ATV (recomputed 4.65 against 3.01)pH 6.8[alhalaweh2016 X1, X2]
felodipine / nifedipine fluxγ/γ* assumed 1 for dilute solutionsbuffer[raina2015c C32]
atazanavir, posaconazoleconcentration-based and activity-based ratios agree in the two buffers and differ in the four micellar mediasix media, 37 °C[elkhabaz2019b R8, R9, C42]
water in nifedipine, felodipine, droperidol, pimozide, indomethacin, ketoprofen3.19, 4.13, 3.00, 4.65, 2.54, 3.3525 °C, 95% RHrumondor2009c R24
same drugs in water4.95 × 10⁵ to 8.88 × 10⁶; ketoprofen 9.85 × 10⁴from solubilityrumondor2009c R24

The amorphous solubility chapter prints no activity coefficient value.

Pitfalls and disagreements

The conversion from mg/mL to mole fraction is not printed in Baird and Taylor; the printed values equal moles of drug per mole of PEG 400 in 1 mL, and a true mole fraction would give 0.766, 0.149, 2.49 and 0.856 instead of 0.614, 0.121, 2.369 and 0.842, leaving the split at 1 unchanged [baird2011 X4]. Loratadine, grouped with haloperidol as close to ideal, dissolves at about 0.42 of its ideal solubility [baird2011 X13]. Several rows of the Marsac and co-workers table are not internally consistent, aqueous solubilities come from three cited sources at unstated temperatures and the ideal solubility temperature is not stated, so the coefficients in water serve only as orders of magnitude [marsac2008b X5, X18]. Activity coefficients in PEG 400 were measured at 25 °C, far below the 52–61 °C of the molten dispersions, and are not values for molten PEG 3350 [baird2011 X16]. A value below 1 in PEG 400 did not separate the crystalline from the transforming drugs in PEO under humidity: all six were below 1 [marsac2008b R14, R16]. Ketoconazole has 0.09 in PEG 400 but a positive interaction parameter in PEG 3350 [marsac2008b R14.f; zhu2011 R5.f]. In the amorphous solubility papers the constancy of γ underlies the claim that a solubilizer leaves the maximum supersaturation unchanged, while a later study found the concentration ratio falling [ilevbare2013a C54; raina2015c C29]. There γ is estimated with the ideal dilute solution as standard state, from a buffer calibration indulkar2017a R11, and is the factor in a = C\gamma; the PEG dispersions chapter defines \gamma_d instead as the ratio of ideal to real solubility in a liquid polymer analogue, so the values tabulated above are not those of the aqueous solutions. The predicted γ in PVP exceeds 1 for four of five compounds (1.18–5.97), so the compounds that dissolve better than ideal in the analogue are predicted to dissolve worse than ideal in the polymer; only indomethacin stays below 1 [marsac2009 R9]. Lattice volume, heat capacities, ideal solubilities and the mole-fraction basis in PVP are not printed [marsac2009 X4, X13]. The value of indomethacin in K29/32 differs between table and text [marsac2009 X2]. In the Bioperformance papers γ/γ* = 1 breaks down with solubilizers [raina2015c C36]; the plotted log γ in the ritonavir–atazanavir figure does not match the recomputation [alhalaweh2016 X1, X2]. The value of \gamma/\gamma_{eq} is not measured; its departure from 1 is read from the gap between the flux ratio and the concentration ratio (F18) [elkhabaz2019b C21, C28]. In the 2009 moisture study the drug-in-water column of the table equals the inverse mole-fraction solubility rather than the printed equation, so it ranks drugs by solubility alone rumondor2009c X1; two text rankings disagree with the table rumondor2009c X2, X3.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

adsorption isotherm

The amount of solute held per gram of adsorbent, Q_a (mg/g), against the solute concentration left in solution at equilibrium, C_e, at constant temperature [dening2019 E1, R2]. In the mesoporous-silica papers it is measured from subsaturated into supersaturated solution, where the state is a metastable, transient equilibrium held only because no crystallization occurs [dening2019 C7; mccarthy2020 C9]. The shapes are type II: a rise, a gentler stretch and a second steep rise near the amorphous solubility [hate2020a C21; dening2019 R2].

Findings

F3, F4, F6, F2, F10.

Related concepts

measures drug adsorption onto silica; fitted by the BET isotherm, Langmuir adsorption isotherm and Freundlich isotherm; gives monolayer coverage and evidence for multilayer adsorption; plotted on the scale of thermodynamic activity relative to the amorphous solubility.

Formulas

adsorbed amount by solution depletion, liquid-phase BET isotherm, Langmuir isotherm, Freundlich isotherm, solute activity relative to amorphous solubility.

How it is measured or obtained

Batch solution depletion: silica suspended in the medium at 37 °C, drug added from a methanolic stock (methanol below 0.5%), equilibration for 30 min, 2 h or 8 h, centrifugation or 1 µm filtration, HPLC of the supernatant, Q_a = (C_i - C_e)V/m [dening2019 P3, E1; hate2020a P13, E3; hate2020b P2, E4; mccarthy2020 P7, E1]. Fits with linear Langmuir and Freundlich and nonlinear BET forms [dening2019 P12; mccarthy2020 P17; hate2020a P16]. Replotting against C_e over the amorphous solubility gives the activity scale [mccarthy2020 E2; hate2020b E3].

Values in the library
materialvalue or classconditionspaper ids
ritonavir on SBA-1539 → 424 mg/g over C_i 0.625–30 µg/mL; C_e ≤ about 25 µg/mL12.5 µg/mL silica, pH 6.8, 30 min[dening2019 R2, X8]
indomethacin on SBA-15up to about 289 mg/g at about 35 µg/mL125 µg/mL silica, pH 2.2, HPMC, 8 h[mccarthy2020 R7]
indomethacin methyl ester on SBA-15up to about 342 mg/g at about 7.7 µg/mLsame[mccarthy2020 R8]
atazanavir on SBA-15about 20.8 mg/g at about 64.5 µg/mL (300 µg/mL silica); about 193 mg/g at about 63.3 µg/mL (25 µg/mL silica)HPMC, 2 h[hate2020a R2, R4]
ketoconazole; clozapine; atazanavir on SBA-15top points at pH 6.8 about 66; 53; 21 mg/g2 h, HPMC[hate2020b R3, R4, R5]
HPMC on felodipine seed crystals (not silica)modified Langmuir K 58.1, n 6.9, adjusted R² 0.79supersaturated felodipine[alonzo2012 R7]
atazanavir into SDS micelles (not silica)Langmuir, R² 0.998, x_m 0.0173.6 mg/mL SDS, Region Iindulkar2017a R16

Evidence table: adsorption isotherm.

Pitfalls and disagreements

The silica concentration changed the atazanavir isotherm about sevenfold per gram (about 116 against 16.2 mg/g at C_e about 56–58 µg/mL), which a single isotherm should not do, and the low-silica data rest on small concentration changes [hate2020a R2, R4, X15]. The indomethacin values exceed the stated mass balance [mccarthy2020 X2]. Values near the top of the ritonavir isotherm vary by about 90 mg/g between runs [dening2019 X4]. No isotherm has a point at or above the amorphous solubility [dening2019 X8]. The pH of the atazanavir isotherm is not stated [hate2020a X17]. Isotherms from different papers differ in silica concentration, medium and equilibration time and are not directly comparable.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

amorphous-amorphous phase separation

The separation of an amorphous drug–polymer mixture into two amorphous phases of different composition, a drug-rich and a polymer-rich one, shown by two glass transitions or by imaging. In the miscibility papers it is the outcome of a miscibility test: solvent-cast films of itraconazole–HPMC (10–50% drug) and telaprevir with HPMC, PVPVA or HPMCAS carried discrete drug-rich domains in a polymer-rich matrix, and blends of long dextran and PVP chains split into a PVP-rich and a dextran-rich phase [purohit2015a C36, C37; li2016c C54; vaneerdenbrugh2012a C16, C17]. Both phases usually hold some of the other component, by partial miscibility or spectral mixing [li2016c C14]. The papers expect the drug-rich phase to crystallize faster, because less polymer surrounds the drug, and a polymer-rich phase to dissolve first [purohit2015a C51; li2016c C41]. Outside the subcategory it is produced by humidity (felodipine–PVP, miconazole–PVPVA, evacetrapib–HPMC) and by water or alcohol in the casting solvent (itraconazole–HPMC) [marsac2010 C14, C27; saboo2017 C42; li2017 C32; mugheirbi2017 C39; mugheirbi2018 R1]. New aspects (ASD process): it arises either because the pair is not miscible at the composition and temperature (thermodynamic) or because the solvent path through a miscibility gap, or later water, traps a separated state (kinetic) [mugheirbi2017 C3; li2017 C1]. The drug-rich phase can crystallize more readily and phase separation can lower the maximum concentration on dissolution [li2017 C1]. In spray-dried ritonavir–PVPVA powders it is read by aged DSC, a pyrene probe and XPS, and it lowered the 25% DL dissolution rate where the baseline release was fast li2020 R4, R6, R7, R10. In hydrating ritonavir–PVPVA tablets the drug-rich phase appears as small discrete droplets in a polymer- and water-rich gel (uncoated) or as connected drug-rich regions along particle boundaries (coated), imaged by confocal fluorescence microscopy benson2025 R14, R16. New aspect (Physical stability): the moisture-induced form in drug–PVP dispersions, its signatures (IR toward a non-interacting physical mixture, a second Tg near the drug's Tg, near-additive water uptake) and its consequence: crystallization then proceeds from a polymer-poor drug-rich phase rumondor2009c C15, C24, C5, C6; marsac2010 C49. New aspect (Release mechanism and LoC): water-induced AAPS of the hydrating dispersion is the authors' explanation of the limit of congruency. Two roles were proposed. As a source of nanodroplets (mechanism II, cited), drug-rich domains formed in the hydrated matrix would be released as droplets; the 2017 nifedipine and ritonavir papers found no evidence for this, the matrix domains being micron-sized against droplets an order of magnitude smaller indulkar2017b C7, C26; purohit2017b C56. As a cause of incongruent release, AAPS at the surface leaves a drug-rich layer once the polymer-rich domains dissolve; films above the limit separated on contact with water and films below it did not indulkar2019a C8, C33; que2019 C35; saboo2020a C43. If a drug-rich layer forms by AAPS, the drug controls release and the carrier effect of the polymer is lost indulkar2017b C33. Papers of 2020–2022 distinguish the morphology of the separated phase: discrete drug-rich domains went with congruent release and contiguous ones with incongruent release saboo2021 C30, C53; correasoto2022a C53, while release of two high-Tg drug forms failed without visible separation correasoto2022b R9; hiew2022b R19. In dissolving compacts the high water content of the gel layer makes water-induced separation possible, favoured close to the solution where water is highest yang2022a C44.

Findings

Miscibility and drug-polymer interactions: F18, F19, F22, F3, F23, F26. ASD process: F1, F6, F7, F14, F3, F20, F21, F48. Physical stability: F7, F12, F13, F14, F15, F23. Release mechanism and LoC: F5, F8, F12, F20, F22, F25, F27.

Related concepts

contrasts with drug-polymer miscibility; characterized by phase-separated domain size and spectral mixing; persists through kinetic trapping; lowers physical stability. Caused by moisture-induced phase separation or solvent-induced phase separation. Reversed by remixing of separated amorphous phases; driven in humid storage by the Δχ effect; set by drug-polymer-water miscibility. Its rate against dissolution is phase separation kinetics; produces surface drug enrichment; favoured by hygroscopicity; its morphology is phase separation morphology.

Formulas

Gibbs free energy of mixing, additive moisture sorption, multicomponent Flory-Huggins free energy of mixing, Δχ effect.

How it is measured or obtained

Two Tg events by DSC (one Tg is read as miscible, with the limits in single-Tg miscibility criterion) [vaneerdenbrugh2012a P3, C3]; pyrene and prodan fluorescence and fluorescence imaging, AFM-nanoIR, nanoTA, Lorentz contact resonance and AFM topography [purohit2015a P3, P4, P9, P10; li2016c P2, P4, P7, P8]; for polymer pairs also the hydrogen-bonded fraction of PVP carbonyls by FTIR [vaneerdenbrugh2012a P5]. In the later process papers: two Tgs by DSC, AFM with LCR or nanoTA, fluorescence microscopy and the drug's autofluorescence, TEM with EDX or HAADF [li2017 P9, P10, P13; mugheirbi2017 P8, P9; li2019 P10]. In the moisture papers: IR against a physical-mixture spectrum built from C–C band ratios; DSC wet and re-dried; sorption against additivity; AFM and TEM rumondor2009c P7, E7, P9, P12; marsac2010 P14, P15. In the release-mechanism papers: Pyrene I/III ratio, nile red or prodan confocal fluorescence, AFM and DSC of films and powders after 97–100% RH, or of films dipped in buffer for seconds purohit2017b R2, R3, R4, R5, R6; indulkar2019a R18; que2019 R14; saboo2019 R19; saboo2020a R23; pyrene and TEM of spray-dried particles bhardwaj2018 R15, R16.

Values in the library
materialvalue or classconditionspaper ids
itraconazole–HPMC 10:90 to 50:50drug-rich domains at every loading by four film methods; one broad Tg by DSC of powderssolvent-cast from methanol–dichloromethane[purohit2015a R1, R11, R13, R7]
telaprevir–HPMC, –PVPVAdomains from 10% drugspin-coated films[li2016c R4, R6]
telaprevir–HPMCASregular domains only from about 30–40% drugspin-coated films, humidity not controlled[li2016c R5, C17, X2, X9]
dextran–PVP, 20 pairsphase separated at 0, 0–5, 5–7, 5–9 of nine compositions for DEX1, DEX6, DEX40, DEX450DSC, freeze-dried[vaneerdenbrugh2012a R13]
felodipine–PVP, 30–50% PVPdrug-rich and polymer-rich phases after 94% RHIR, TEMmarsac2010 C14, C27
miconazole–PVPVA 50:50domains after film formation at 60% RH and after 75% RH storageAFM, confocal[saboo2017 R13, R15, C42]
telaprevir–PVPVA, 70% PVPVAtwo overlapping Tgs; "may have partially phase separated"mDSCmosqueragiraldo2018b R23, C53
ECP–polymerdrug-rich spheres (preparation) or drug-rich network (storage)TEM-EDX[li2017 R18, R19, R22]
ITZ–HPMCdiscrete drug-rich domains with self-associated ITZ (extra emission near 381 nm)FLOM, AFM, UV, emission[mugheirbi2017 R1, R22]
LPV–HPMCdiscrete drug-rich domains 50–500 nm high in a polymer-rich matrix; faster release at 33–85% DLAFM, nanoTA, releaseli2019 R8, R2
ritonavir–PVPVA spray-driedsecond non-reversing DSC event after ageing in 50% DL powders from 10:90 to 40:60; drug-rich surfaces (XPS) from 60:40; SNDR at 25% DL about 3.5 → 2.27 → 0.90 mg·min⁻¹·cm⁻¹BLD-35 dryerli2020 R4, R7, R10
pimozide–PVP 50:50Tgs −21/44 °C wet, 61/112 °C re-dried94% RH, 42 hrumondor2009c R17
felodipine–PVP 46.5 wt%event at ≈45–50 °C instead of one Tg near 80 °Cafter 75–94% RHmarsac2010 R14
felodipine–PVP 50% filmislands of about 300–500 nm (TEM, AFM)94% RHmarsac2010 C41
felodipine–PVP at 93% RHcrystallization independent of PVP level; plateau 70–80%powders[rumondor2009b R21, R11, C20]
felodipine, quinidine, pimozide with PVPVA; pimozide with HPMCAStwo Tgs after 94% RH50:50 powders, driedrumondor2010c R3.a, R3.c, R3.d, R3.e
indoprofen, clofoctol, probucol, nilutamide, loratadine with PVPseparation at 70–90% PVP for all; at every composition for nilutamide and loratadineIR, 54–94% RHrumondor2011 R14
ritonavir with PVP, PVPVA; HPMCASall PVP and PVPVA dispersions separated, from about 1 h; HPMCAS stayed miscible97% RH, films and powderspurohit2017b C1, C22
ritonavir 50:50 PVP filmdark domains of about 1–3 µm in a drug-rich continuous phase after 10 s in buffer; 10:90 uniformdried after immersionpurohit2017b R4
ritonavir–PVPVA films 20, 30, 40%uniform; sparse bright domains; dense domains (LoC 25%)seconds in waterindulkar2019a R18, C20
ledipasvir–PVPVA films 5, 10, 50%mostly homogeneous; small domains; ≈10–20 µm domains100% RH, 37 °C, 3 daysque2019 R14, C16
nilvadipine 10:90 film and compactdrug-rich circles and rings of roughly 5–15 µm; rough surface gone after 15 min of dissolution ("superficial")97% RH, 12 hsaboo2019 R19, R17, C24
felodipine 30% films with PVP, PVPVA, HPMC; HPMCAS, EUDSdiscrete domains; uniform97% RH, 24 hsaboo2020a R23, C23
ITZ–PVPVA 20% spray-dried particlesno separate drug-rich and polymer-rich phases by pyrene or TEM, also with water in the solventbefore dissolutionbhardwaj2018 C35, C37
felodipine 30% films with 0–10% TPGSall separated after 12 h; semi-continuous (0, 2%) against discrete (5, 10%) drug-rich domains≈100% RHsaboo2021 R21
clopidogrel 40, 50, 60% filmsuniform; bicontinuous; drug-continuous5 min, 100% RHcorreasoto2022a R20
atazanavir 10% filmuniform for 3 h at 37 °C; separated within 10 min at 50 °C100% RHcorreasoto2022b R9, R12
lumefantrine free base, benzoate; sulfate filmsseparated; homogeneoushigh RH, 37 °Chiew2022b R19
ritonavir–PVPVA 30:70:5 with Tween 80; Span 20Tg onset of surface material 66.01 → 40.25 and 67.85 → 42.18 °C after dissolution, read as a ritonavir-rich phaseDSC, scraped after dissolutionindulkar2022 R19, C19
ritonavir–PVPVA 10–40% compactsdroplets near the gel–solution boundary (10–20%); continuous drug-rich layer at the interface (30–40%)real-time confocal, pH 6.8yang2022a R10, R11, R12, R13
MePHPH–PVPVA; PHPH–PVPVA compactsseparation in the gel layer of most compacts; segregative (MePHPH) and associative (PHPH)in situ confocal with two dyesdeac2023a R6, R7, C25, C28, C71

Evidence table: amorphous-amorphous phase separation.

Pitfalls and disagreements

A single DSC Tg did not show the separation of itraconazole–HPMC, which the authors attribute to mixing during the scan, a reading supported only by the narrower second-run steps [purohit2015a C39, C26, X1]. Whether the separation is kinetic (solvent-induced, water-induced) or thermodynamic is not settled, and the phase compositions were not measured: the band-ratio and softening data rank the phases but give no weight fractions [purohit2015a C48; li2016c X3, X10]. The separation depended on preparation: humidity, solvent water and the alcohol of the solvent changed whether films separated [mugheirbi2017 C39; mugheirbi2018 R1, C50]. For polymer pairs the plot of the miscibility map is not monotonic cell by cell [vaneerdenbrugh2012a X10]. Separation during dissolution or storage was invoked for PVPVA dispersions of lumefantrine but not measured hiew2022a C43, C61, X11. DSC and polarised light microscopy may overestimate miscibility [mugheirbi2018 C4]. Whether separation helps or hurts release depends on the resulting microstructure li2019 C5, C58. The same separation can lower release (ritonavir–PVPVA at 25% DL) or raise it (lopinavir–HPMC at 33–85% DL) li2020 C64; li2019 R2. In the humid felodipine–PVP films the composition of the polymer-rich phase was not determined either; the DSC "second Tg" near 124 °C may be depressed melting marsac2010 X7, C18. Faster crystallization after moisture-induced separation was shown across different drugs, not for one drug with and without separation rumondor2009c X7. In the 2019 ritonavir–PVPVA study AAPS was seen only in films dipped for seconds or in humidified samples, not in a dissolving tablet, and neither its rate nor that of dissolution was measured indulkar2019a X6. A drug-rich porous surface also follows from faster polymer dissolution alone saboo2020a X6. In the 2022 ritonavir surfactant study separation was inferred from one lowered Tg of material scraped from the wet tablet, without a second Tg or water content, and was not tested for three of the five surfactants indulkar2022 X10, X4.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

amorphous salt

The amorphous form of a drug salt; salt formation adds an ionic interaction between the protonated base and the counterion, taken to dominate over hydrogen bonding in setting Tg [towler2008 C23]. Combining salt formation and amorphization "may be desirable", for example for a lyophilized product [towler2008 C18].

Findings

F20.

Related concepts

depends on glass transition temperature; related to crystallization tendency and physical stability.

Formulas

none in this chapter (counterion descriptors listed in the chapter table).

How it is measured or obtained

Prepared by freeze-drying or melt quenching and checked by DSC [towler2008 P3, P5, R1]; Tg, recrystallization on heating, moisture sorption and storage at high humidity are then measured [towler2008 P6, P8, P9]; later by open-dish storage at 40 °C/75% RH hiew2022b R7; duong2022a C32.

Values in the library
materialvalue or classconditionspaper ids
propranolol saltsTg 9.0–35.9 °C against −9.3 °C for the baseDSC[towler2008 R4]
nicardipine saltsTg 28.5–81.0 °C against 3.2 °C for the baseDSC[towler2008 R5]
20 salts of both bases11 amorphous after freeze-dryingDSC[towler2008 R1]
propranolol salts0.39–61.90% water uptake at 75% RHvapour sorption[towler2008 R8]
lumefantrine saltsbenzoate, PEG 250 diacid, besylate crystallized within 4 weeks; HCl and sulfate not for at least 16 weeks40 °C/75% RHhiew2022b R7
delamanid saltsstable 2 weeks; salt formation raised Tg40 °C/75% RHduong2022a C32, C47
Pitfalls and disagreements

Stoichiometry and ionization state of the amorphous salts were not reported [towler2008 X8]. Crystallization and moisture uptake did not follow counterion pKa [towler2008 C14, C34]; drug or salt Tg appeared an important predictor for lumefantrine hiew2022b C37, yet the highest-Tg propranolol salt crystallized [towler2008 R12]. Salt formation did not change delamanid crystallization in dispersion films at pH 3.0 [nguyen2023b C17].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

amorphous solid dispersion

A drug dispersed in a polymer in the amorphous state to raise dissolution rate and supersaturation. In the amorphous solubility and LLPS papers an ASD matters as a route to supersaturation: dissolved beyond the amorphous solubility it gives a drug-rich phase and a cap on the free drug (F8, F13) [ilevbare2013a C52, C5; almeidaesousa2016 C6]. The ASDs tested were ritonavir:PVP 1:9 and CRH1:HPMC 20:80 [ilevbare2013a P13; almeidaesousa2016 M7]. The ueda2020b, ueda2021 and ueda2022 studies add that the polymer of an ASD, once dissolved, enters the drug-rich phase and lowers the amorphous solubility, so a higher polymer:drug ratio in the ASD can "conceivably" reduce the supersaturation advantage further; the studies used dissolved polymers, melt-made ibuprofen ASDs for DVS and solid-state NMR, and no dissolving ASD [ueda2020b C37, C55; ueda2021 P6; ueda2022 P5]. New aspects (Miscibility and drug-polymer interactions): A molecularly mixed, single-phase, homogeneous mixture of drug and polymer, in older wording a "glass solution" in which a solute is dissolved in a glassy solvent [kestur2010b C4; taylor1997 C1]. Amorphous dispersions are used to raise apparent solubility and dissolution, but the amorphous phase is metastable and may crystallize during storage or dissolution [taylor1997 C1, C2; vaneerdenbrugh2010b C6, C7]. The miscibility papers hold that the polymer must be in the same amorphous phase as the drug to be effective ("it is generally accepted") and that maximum stabilization "can only be realized" with intimate mixing, so that a physical mix does not inhibit crystallization [kestur2010a C2; rumondor2009a C3]. Dispersions made by solvent evaporation were not always molecularly mixed: itraconazole–HPMC and telaprevir films carried drug-rich domains [purohit2015a C36; li2016c C54], and neat naringenin and quercetin could not be made amorphous by rotary evaporation, so a polymer was needed to make the dispersion at all [wegiel2013a R7, C46]. Ionizable polymers (E100, HPMCAS, HPMCP, CAP, Eudragit L 100, PAA) add acid–base contacts [wegiel2013a M4, M8; hiew2022a M3, M4, M5, M6]. New aspects (ASD process): the earliest paper of that chapter asks which carrier and process give a useful solid form of an extremely poorly soluble drug and finds that the carrier set whether probucol stayed amorphous [broman2001 C1, C14]. (synthesis: the paper's "solid dispersions" include samples that are not amorphous, since the probucol–PEO and probucol–PAA dispersions are mainly crystalline Form II [broman2001 R4.c–f].) The ASDs of the process papers were also made by solvent granulation of drug and polymer onto lactose and cellulose [trasi2019 C50], by spray drying from water-containing methanol li2020 P1 and by extrusion of physical mixtures of drug and polymer [moseson2020 P4]. New aspect (Bioperformance): the ASD is a drug dispersed amorphously in a polymer (or, in alhalaweh2016, in a mix with a second drug) that releases drug into supersaturation. Rotary-evaporated dispersions were used in alhalaweh2016, hate2018, mosqueragiraldo2018b and elkhabaz2017, and commercial capsules in purohit2018 [alhalaweh2016 P3; hate2018 P5; mosqueragiraldo2018b P1; elkhabaz2017 P6; purohit2018 M2]. Later papers dose such dispersions to animals: rotary-evaporated enzalutamide dispersions to rats, spray-dried pretomanid tablets to monkeys, and generic and innovator tacrolimus capsules to dogs, the generic being a mainly physical mixture of amorphous drug with HPMC and the innovator an intimate dispersion [wilson2018 P10; wilson2020 P1; nguyen2023a P4, P5; purohit2019 C21]. New aspect (Physical stability): the physical-stability papers call the drug–polymer glass a molecular (one-phase) dispersion when it shows a single Tg and drug–polymer hydrogen bonds by IR [konno2006 C8, R5; rumondor2009c C1], and stress that a polymer can inhibit crystallization only while it stays intimately mixed with the drug marsac2010 C31. In the study of marketed tacrolimus capsules the term is used strictly: a product that contains the polymer but holds the drug as an amorphous coating on lactose, not mixed with HPMC, is in the authors' belief not an amorphous solid dispersion, and molecular-level mixing is "considered to be essential" for stabilization [trasi2017 C47, C50].

Findings

C. Amorphous solubility and LLPS: F8, F13, F14, F19, F20, F21. Miscibility and drug-polymer interactions: F1, F3, F9, F15, F16, F18, F19, F23, F26. ASD process: F17, F18, F19, F22, F23, F24. Bioperformance: F6, F8, F9, F11, F16, F23, F24. Physical stability: F1, F12, F14, F23, F24, F26, F27, F28, F29, F30, F33, F35.

Related concepts

produces a drug-rich phase above the amorphous solubility; relieved by crystallization unless a polymer is present (F14); requires drug-polymer miscibility; stabilized by drug-polymer interactions and kinetic stabilization; related to crystallization inhibition and supercooled liquid. Processed in the HME operating design space. Sets drug loading effects; related to non-sink dissolution. Can undergo amorphous-amorphous phase separation; stabilized by crystallization inhibition by polymers.

Formulas

Gordon-Taylor equation.

How it is measured or obtained

Rotary evaporation from methanol (ritonavir) or methanol/dichloromethane (CRH1) and incremental or single-dose non-sink dissolution [ilevbare2013a P13, P14; almeidaesousa2016 P2, P11]. The dispersions of the miscibility papers were made by dissolving drug and polymer in a common solvent and removing it: rotary evaporation from methanol, ethanol, chloroform or dichloromethane–ethanol, followed by vacuum drying [taylor1997 P3; rumondor2009a P1; vaneerdenbrugh2010b P6]; spin coating on coverslips, ZnSe or KRS5 for films [vaneerdenbrugh2010b P1; marsac2009 P4]; cryomilling of a 10% w/w dispersion with crystalline drug and melt-quenching for the low-polymer growth samples [kestur2010a P1, P2]. A physical mix of amorphous drug and polymer is the control without molecular mixing [taylor1997 C24, C26]. Amorphous state is checked by XRPD or polarized light [taylor1997 R1; vaneerdenbrugh2010b P2]. Further preparations: rotary evaporation at 45–60 °C with 24 h vacuum drying and cryomilling [wegiel2013a P1; hiew2022a P5]; spin coating on KRS-5, ZnSe or quartz [purohit2015a P2, P9]; freeze-drying of aqueous polymer blends [vaneerdenbrugh2012a P2]; 50 mg compacts for release hiew2022a P9. In the process papers the solid form was read by Raman and DSC (single Tg between those of the components; polymer-free marker band) [broman2001 P1, P2, R1, R4]. In the Bioperformance papers the dispersions were made by rotary evaporation from methanol and cryomilling, and checked by PXRD, DSC, PLM and SHG [hate2018 P5, P10; elkhabaz2017 R8]. In the physical-stability papers: spin-coated films (dichloromethane:ethanol, ethanol or chloroform, heated to 90 °C) for nucleation, growth and IR; rotary-evaporated and, for low polymer contents, cryomilled powders for DSC, sorption and PXRD [konno2006 P1, P3; rumondor2009c P1; rumondor2009b P1; kestur2010b P1]. Spin-coated films and rotary-evaporated powders of nine 50:50 drug–polymer pairs rumondor2010c P1, P5; rotary evaporation in 5% steps to find the highest amorphous loading [wegiel2013b P1]; rotary evaporation followed by cryomilling [wegiel2014 P2, P3]; a 10% PVP dispersion diluted with crystalline drug by cryomilling, then melted, to reach 3% PVP [kestur2013a P4; kestur2013b P2].

Values in the library
materialvalue or classconditionspaper ids
ritonavir:PVP 1:96.4, 11.8, 18.3, 18.0 µg/mL with 6.0, 12.0, 18.0, 24.0 added100 mM pH 6.8, 37 °Cilevbare2013a R17
CRH1:HPMC 20:80about 12.9 µg/mL without polymer in the medium; HPLC maximum about 13.2pH 4.6, 25 °C[almeidaesousa2016 R8, R12]
indomethacin–PVP-K90, 5–70 wt% PVPamorphous by XRPD; interactions in dispersions, none in physical mixesmethanol, rotary evaporation[taylor1997 R1, R10, R11, R12]
felodipine–PVP, nifedipine–PVPone amorphous phaseIR, PXRD[rumondor2009a C38]
8 drugs × 7 polymers392 spin-coated compositions scored over 7 daysethanol or ethanol–dichloromethane[vaneerdenbrugh2010b R2]
50/50 drug–PAA, drug–PVP powderscrystalline with PAA for acidic drugs, amorphous with PVProtary evaporation, 7 days[vaneerdenbrugh2010b R9]
felodipine, 0.5–4.5% w/w polymermade by diluting a 10% dispersion by cryomillingmelt-quenched films[kestur2010a P1, C5]
naringenin, quercetin with six polymershighest X-ray amorphous polyphenol content about 20–85%; E100 highest, PAA lowestrotary evaporation at 60 °C, cryo-milled[wegiel2013a R8]
lumefantrine with PVPVA and four enteric polymersall X-ray amorphous with one Tg, except 50% HPMCAS (melted at 126.3 °C on heating)rotary evaporation at 45 °C, sieved below 250 µmhiew2022a R4, R6
itraconazole–HPMC, telaprevir–polymersdrug-rich domains in the filmsspin-coated from methanol–dichloromethane[purohit2015a R11; li2016c R4, R5, R6]
probucol–PVP K30 50:50amorphous; Tg 95 °C (solvent), 129 °C (moulded)Raman, DSC[broman2001 R4.a, R4.b]
probucol–PAA, –PEOmainly Form IIsame[broman2001 R4.c–f]
probucol–PVP–PAA 50:25:25mainly amorphousboth routes[broman2001 R4.g, R4.h]
ritonavir and lopinavir with PVPVA 1:1 on lactose:MCCX-ray amorphous granules, unchanged for one month at 40 °C/75% RHsolvent granulation[trasi2019 R1, R2]
ritonavir–PVPVA spray-dried, 25–75% DLX-ray amorphous (methanol powders); one Tg of 91, 75 and 63 °Cspray dryingli2020 R1, R2
ritonavir/atazanavir/lopinavir in PVP K29/3290% polymer, Tg 139–160 °C10% drug[alhalaweh2016 R4]
atazanavir in HPMCAS, HPMC, PVPVA10, 30, 50%X-ray amorphoushate2018 R10
telaprevir in HPMCAS, HPMC, PVPVA, CA Sub10, 30, 50%one Tg for HPMCAS 50%mosqueragiraldo2018b R15, R23
ezetimibe in PAA, PVP, HPMC-AS50:50no crystals by PLM or SHG[elkhabaz2017 R8]
tacrolimus capsulestacrolimus:HPMC 1:1; drug about 4% of fillgeneric[purohit2018 M2, R2]
enzalutamide in PVPVA or HPMCAS-MF10 and 50 wt% drug, rotary-evaporated, amorphous by XRPD and FTIRused within 2 weeks[wilson2018 P10, P11]
enzalutamide in CA Sub or CPHPC-106CA Sub 50%; CPHPC-106 10 and 50% drugrotary evaporationwilson2020 P1, A3
atazanavir in AS-LF or AS-HF1:9, spray-drieddissolution and transportueda2020a P1, M14
pretomanid in HPMCAS-HF, MF, LF blends20% drug in the monkey tablets, spray-dried; screening powders rotary-evaporatedwith TPGS or tris in two tabletsnguyen2023a P4, P5
felodipine with PVP, HPMCAS, HPMC 0–100%single Tg at every compositionrotary-evaporated, DSC[konno2006 R5, C8]
five drugs with PVPdry dispersions one phase by IR; single Tg for droperidol and pimozidespin-coated and rotary-evaporatedrumondor2009c R3, R5, C1
felodipine with 0.5–4.5 wt% PVPmade by cryomilling a 10% dispersion with crystalline drug, then meltingto avoid partial crystallization on rotary evaporation[kestur2010b P1]
resveratrol with E100, PVP, HPMC, HPMCAS, CMCAB, PAAhighest X-ray amorphous loading 60, 45, 40, 35, 35, 15%rotary evaporation[wegiel2013b R2]
curcumin with five polymers75:25 dispersionsrotary evaporation, cryomilling[wegiel2014 P2, P3]
tacrolimus–HPMC 1:1 (solvent cast) and six marketed capsulesdispersion amorphous 4 weeks at 40 °C/75% RH; one generic 57–95% crystalline at 4 weeksopen dish[trasi2017 R16, R13]
ATP enantiomers with 5% w/w polymermelt-quenched films from solvent-evaporated mixturesgrowth at 40–90 °C[sato2015 P1, P3]
indomethacin with 10% w/w HPMC, HPMCAS or PVPsolvent-evaporated dispersion, then melt-quenchedgrowth from 80 °C to near Tm[tian2017 P2]
Pitfalls and disagreements

One composition of one polymer each; the medium of the CRH1 ASD runs in Figs. 7 and 8 is unclear [ilevbare2013a X15; almeidaesousa2016 X5]. The preparation route changes the result: films, rotary-evaporated powders and melt-quenched powders of the same pair can differ (PH–PAA) and the three characterization methods of one study used differently prepared samples [vaneerdenbrugh2010b C44; rumondor2009a X4]. Direct rotary evaporation below 5% w/w polymer would let felodipine crystallize, hence the cryomilled dilution, whose uniformity at the molecular level is assumed, not measured [kestur2010a C5]. A single Tg does not prove a single phase (see single-Tg miscibility criterion). Thermodynamically stable dispersions are hard to achieve; most are supersaturated and kinetically stabilized [marsac2009 C34]. The amorphous and single-phase state of the halogen-bond dispersions (up to 50 wt% for XPS, 90 wt% for IR) was not verified que2020 X10. Neat naringenin gave an amorphous film only by spin coating, quercetin not at all [wegiel2013a R7]. Amorphous probucol occurred only with PVP present, so carrier and form are confounded [broman2001 X13]; amorphous does not mean fastest release [broman2001 C35]. Two drugs in one dispersion can form a co-amorphous system whose amorphous solubilities are lower than those of the single-drug dispersions [trasi2019 C38]. In the Bioperformance papers making an ASD does not by itself remove dissolution-rate-limited absorption (high loading) [indulkar2016 C41]. The lowest loading did not always give the best dispersion (10% enzalutamide in HPMCAS crystallized), and the best solution inhibitor of 24 polymers made a dispersion no better than the crystals (F8, F24) [wilson2018 R6, R16; wilson2020 R1, R6]. A dispersion that is one phase when dry can separate under humidity and stay separated after drying rumondor2009c C2; marsac2010 C53. Nucleation was measured on films and Tg on powders made differently, so "one phase" is shown on one sample form and assumed for the other [konno2006 X12]. In the later felodipine growth papers too, below about 5% polymer rotary evaporation was expected to crystallize felodipine partly, hence the two-step dilution [kestur2013b C5]. Interactions were read on spin-coated films at other compositions than the stored powders [wegiel2014 X8; wegiel2013b X12]. Equal composition does not mean equal structure: six tacrolimus products with about one part HPMC per part drug differed in stability because of the manufacturing route [trasi2017 R1, R6, C47].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

amorphous solubility advantage

The factor by which the amorphous drug is more soluble than the crystal, e^{\Delta G/RT} from the crystal–amorphous free-energy difference, reduced by the activity of the water-saturated amorphous drug [ilevbare2013a E1, C60; almeidaesousa2015 E1]. In the amorphous solubility and LLPS papers the measured counterpart is the supersaturation ratio at the LLPS onset (F6). The papers of 2017–2022 add measured values of the ceiling ratio of 63.6 (atazanavir, synthesis: 70 ÷ 1.1), 28.5 (telaprevir, synthesis: 148 ÷ 5.2), about 600 (pazopanib) and 2.5–5.9 (ibuprofen, falling with temperature), and that micelles lower the concentration-based advantage (atazanavir 65 → 33) without lowering the activity-based one [indulkar2017a R4, R6, R13; lu2017b R2, R1; sugihara2018 R4; ueda2022 R16]. New aspect (ASD process): it is the supersaturation an ASD can reach if it stays amorphous and dissolves; crystals in the dispersion "directly" lose their share of it ("potency") and may also consume what is generated [moseson2020a C3]. For bicalutamide the maximum advantage over the stable form is 35-fold [moseson2021 R2]. In the pH-shift test of posaconazole the dose was set at about 10 times the amorphous solubility in the intestinal medium (19.1 µg/mL), that is about 191 µg/mL, and 200 µg/mL at full release [shah2024 P11, X9]. New aspect (Bioperformance): the ratio is computed by the Hoffman estimate with water correction or taken as the LLPS onset over the crystalline solubility [raina2014a R7; raina2015c E8]. New aspect (Crystallization from solution): in the solution-crystallization papers the advantage fixes the highest supersaturation tested: the calculated amorphous solubility over the crystalline solubility gives S 15.3–15.4 for ritonavir and about 14.7 for celecoxib, and the "amorphous benchmark" S of about 10 for felodipine [ilevbare2012b R3; ilevbare2013c E1, R2; alonzo2012 C42]. The measured counterpart is the plateau after a pH shift or the onset of phase separation (F2). For six dihydropyridines the estimated ratios of amorphous to crystalline solubility in buffer were 16.1 (cilnidipine), 9.03, 8.42, 23.0, 11.7 and 22.9, not reproducible from the printed inputs (felodipine 5.93 recomputed against 6.68 µg/mL); for danazol the recalculated estimate of 7.8 µg/mL is a ratio of 8.7 against the earlier 19.6 [raina2015b X2; jackson2016 R3, R4]. New aspect (Supersaturation from ASD dissolution): the calculated advantage is the yardstick for what a dissolving amorphous solid or dispersion should reach, and the question is whether a dispersion can exceed that of the pure amorphous drug: by flux it did not for felodipine, and the authors add that thermodynamics gives "no reason to expect" the two to be equal alonzo2011 C22, C45. The advantage is "rarely achieved" because the solid or the solution crystallizes [konno2008a C4; alonzo2010 C2]. For six marketed tacrolimus capsules the advantage of about 35-fold was "sustained throughout" a 2 h non-sink test [trasi2016 C44, C16]; mixing the drug with a polymer that does not dissolve lowers the advantage a dispersion can realize [li2018 C67].

Findings

Amorphous solubility and LLPS: F5, F6, F7, F12, F14, F16, F21. ASD process: F23, F26, F27, F28, F39, F41. Bioperformance: F1, F4, F18. Crystallization from solution: F2, F9, F14, F19, F21, F22, F34. Supersaturation from ASD dissolution: F1, F5, F7, F18, F22, F23, F28, F29.

Related concepts

same as the ceiling supersaturation ratio; built from amorphous-crystalline free energy difference and water sorption correction of amorphous solubility; gives the amorphous solubility. Realised in non-sink dissolution; lost to residual crystallinity and matrix crystallization; lowered by mutual amorphous solubility reduction. Depends on Hoffman equation; estimated with the Gibbs-Duhem equation water correction; depends on crystalline solubility; related to free drug concentration.

Formulas

amorphous solubility advantage with water-sorption correction, amorphous solubility advantage from free energy difference, supersaturation ratio. Amorphous-to-crystalline solubility ratio, Hoffman equation.

How it is measured or obtained

By calculation (Hoffman or heat-capacity free energy, sorption isotherm) and by the onset [almeidaesousa2015 P9, P10]; also by dissolving an amorphous film ilevbare2013a P4. In the ASD process papers: crystalline solubility by 72 h shake flask; amorphous solubility as the onset of light scattering during solvent-shift addition (liquid–liquid phase separation), in some cases only with a polymer present because the drug crystallised too fast without it [moseson2020a P7, P8; moseson2021 R1, R27]. In the Bioperformance papers it is estimated from melting data or as onset ÷ crystalline solubility [raina2015c P3, P6]. In the crystallization-from-solution papers: calculated with the Hoffman equation and a water-sorption correction; measured by dissolving a spin-coated film (ritonavir), by pH-induced precipitation, and by the onset of phase separation of a solvent-shifted solution [ilevbare2012b P4–P6; hsieh2012 P11; jackson2014 P6, P7]. In the ASD dissolution papers: calculated from melting data with the Hoffman equation and the measured crystalline solubility [konno2008a P7; alonzo2010 P12; alonzo2011 P8]; tested against flux relative to the crystal alonzo2011 R14.

Values in the library
materialvalue or classconditionspaper ids
ibuprofen to griseofulvinpredicted 3.7/4.2, 7.0/6.4, 9.8/11.7, 28.9/52.5, 48.4/48.6, 34.8/30.9 (Hoffman / Cp method)25 °C[almeidaesousa2015 R13]
clotrimazole; atazanavirpredicted about 9.2 and 62; measured about 13 and about 6337 °C[indulkar2015 R3, R10]
felodipine, buffer; with 0.04% vitamin E TPGS; in FaSSIFabout 9.2; 4.5; 5.0 (concentration-based)37 °C[raina2015c C29]
tacrolimusabout 35 (49/1.4), about 33–36 by method; other drugs 5–65amorphous solubility by ultracentrifugation, pH 4.5, 37 °C[trasi2016 R16, R17, X9]
IDM, pH 4.5 acetatecrystalline about 8, amorphous about 80 µg/mL (about 10-fold, synthesis); unchanged by 50 µg/mL PVPVA37 °C[moseson2020a R1]
BCL, pH 6.8 phosphateform 1 4.3, form 2 15, amorphous 150 µg/mL; 35-fold37 °C[moseson2021 R1, R2]
RTV and LPV, pH 6.8crystalline 1.8 and 2.9, amorphous 31 and 19 µg/mL10 mM phosphate, 37 °C[trasi2019 M1, M2]
IDM–PVPVA with 25% residual crystalsC720 about 28.8 against about 43.1 µg/mL: the share of the advantage lost with the crystals50 µg/mL total dose[moseson2020a R6]
posaconazole in FaSSGF and FaSSIF V2LLPS concentration (taken as the amorphous solubility) 2326 and 19.1 µg/mL against crystalline 86.5 and 1.2 µg/mL, ratios about 27 and 16 (arithmetic on the cited values)37 °C[shah2024 R11, C14]
ritonavir / atazanavir / lopinavirabout 14 / 83 / 6pH 6.8[alhalaweh2016 R6]
clotrimazole15pH 8[indulkar2016 R3]
atazanavirobserved ratio in SDS about half that in buffer, with unchanged activityindulkar2017a C64, C45
atazanavir, posaconazoleconcentration ratio about 55 and 36 in the buffers, about 14 and 5 in pooled human fluid; flux ratio 50–56 and 29–37six media[elkhabaz2019b R8, R9]
atazanavir, darunavir58 and 1.37 from the printed solubilities (printed "almost 82-fold" and "1.30")pH 6.8, 37 °C[alkalla2026 R3, R6, X1]
pretomanid8–10 in buffers37 °Cnguyen2023a R1
tacrolimusabout 33pH 4.5[purohit2019 C30]
enzalutamideabout 14.5 (42/2.9); S "approximately 13" is the theoretical 39/2.9pH 6.5[wilson2018 R1, R3, X2]
felodipineS of about 10 over the crystal (theoretical and measured)benchmark for the supersaturation range S 3–12[alonzo2012 M1, C42]
ritonavir20.6 µg/mL calculated, 19.8 measured; S 15.3–15.4 over 1.3 µg/mL37 °C[ilevbare2012b R1, R2, R3]
efavirenz; celecoxib19.8 and 22.6 µg/mL calculated against 12.3 and 2.5 measured37 °C[ilevbare2013c R2]
five weak basesratios 22.2, 11.9, 20.4, 54.6, 7.0 without and 12.3, 9.8, 16.7, 15.3, 4.3 with water correction37 °C[hsieh2012 R10]
glyburide; warfarinabout 60 and 4825 °C[hsieh2014 R16]
danazol19.6 printed (15.4 recomputed); earlier estimates 13.7 and 26.525 °C[jackson2014 R2, R3, X1]
six dihydropyridinesestimated amorphous solubility 0.5, 6.68, 48, 20, 6.3, 19.0 µg/mLbuffer, Hoffman with water correction[raina2015b R10]
danazol7.8 µg/mL with heat-capacity data and the water correction; onset 8 µg/mL25 °C, pH 6.8[jackson2016 R3, R8]
posaconazolemeasured amorphous/crystalline 33.6 at pH 7.0 (32.4–37.3 from pH 2.0 to 7.0); estimate 37.9 printed37 °C[duong2022b R1, R6, R7, X5]
felodipineabout 10 times the crystal, about 9.5 µg/mL37 °C, pH 6.8 test fluid[konno2008a R17]
felodipineabout 9.1 µg/mL at 37 °C; 5–6 µg/mL at 25 °CpH 6.8alonzo2011 M1
felodipine, flux ratio to the crystal8.5 (pure amorphous), 9.5 (50:50), 10.5 (90:10 HPMC dispersion)dialysis, 37 °Calonzo2011 R14
indomethacinabout 21 µg/mL (crystal about 1.2 µg/mL)pH 2.0alonzo2011 M2
ritonavir; lopinavir (cited)25 and 17 µg/mL against 1.7 and 2.7 µg/mL crystallinepH 6.8[trasi2015b M1, M2]
lopinavirabout 5.6 (17.4/3.1)pH 3, 25 °C[li2018 E2, R1]
indomethacin with 100 µg/mL HPMC36 µg/mL against 1.61 (γ) and 2.8 µg/mL (α)pH 2.2, 37 °C[xie2017 R3, R1]
paclitaxel31.6 against 0.36 µg/mL, a ratio of about 88pH 6.8, 37 °C, three methods[que2018 R1, R2]
delamanid0.76 against 0.018 µg/mL at pH 6.5, a measured ratio of 42.3 against 31.8 from the Hoffman free energy37 °Cduong2022a R1, R27
praziquantel, racemate and R-enantiomerratios 5.6–7.7 and 4.0–5.8 across nine media; amorphous 1.17–1.74 and 1.20–1.70 mg/mL37 °C[alvarenga2025 R1]
posaconazoleabout 20 against 1.69 µg/mL in FaSSIF; 115.1 µg/mL crystalline in FaSSGF37 °C[elkhabaz2019a R2, R1]
Pitfalls and disagreements

The calculated advantage fails for high-melting drugs when the Hoffman free energy is used (F7) [mosqueragiraldo2015 C23, C24]. When additives raise crystalline solubility more than the LLPS concentration, the concentration-based ratio falls (felodipine, about 9.2 in buffer to 4.5 in 0.04% vitamin E TPGS and 5.0 in FaSSIF), while the maximum flux stays in the buffer band, so the advantage in activity is retained [raina2015c R9, R11, C29]. In dispersions, a dose below the amorphous solubility (IDM 50 against about 80 µg/mL) can still lose most of the advantage to crystals; a crystal-free bicalutamide dispersion never reached 40 µg/mL against 150 µg/mL [moseson2020a X17; moseson2021 C41]. The amorphous solubility of ritonavir alone is reduced to about 4 µg/mL in a co-amorphous granule [trasi2019 R4]. In the Bioperformance papers the ratio from concentrations falls with solubilizers although the flux advantage does not [raina2015c C43]; the atazanavir ratio differs between cards because the crystalline solubility differs (F1). In human fluid the flux of a solution at the amorphous solubility was about 30 times that of a crystalline suspension for posaconazole, so the advantage was not lost although the concentration ratio fell to about 5 (F18) [elkhabaz2019b C30, C45]. The printed atazanavir and darunavir ratios do not follow from the printed solubilities [alkalla2026 X1]. With a polymer in the medium the same ratio applied to the polymer-containing solubility overestimates the ceiling (danazol: 43 against an onset of 8–9 µg/mL) [jackson2014 X9]. Celecoxib's measured 2.5 µg/mL is far below the calculated value and is not discussed [ilevbare2013b X9]. The efavirenz run started at S about 2.3, the ratio of calculated amorphous to crystalline solubility being 2.4 [ilevbare2013c X4]. The printed estimates for the dihydropyridines differ between media in ways the equation does not allow [raina2015b X2]. Felodipine dispersion and solution readings of 14.1 and about 11 µg/mL exceed the 9.5 µg/mL estimate of the 2008 paper, measured by UV through a 70-µm filter [konno2008a X5]. The 25 °C indomethacin range (17–25 µg/mL) does not reproduce from its printed inputs (15.8–23.6) [alonzo2010 X2]. That a dispersion reached the same activity as the pure amorphous drug "may be purely coincidental" alonzo2011 C48. The tacrolimus ratio uses an ultracentrifugation value measured with 10 µg/mL HPMC in the buffer [trasi2016 X9]. For praziquantel the ratio is lower for the enantiomer because its crystal is more soluble, not because its amorphous solubility is lower [alvarenga2025 R1].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

amorphous solubility

The concentration of dissolved drug at which a supersaturated aqueous solution is in apparent, metastable equilibrium with the amorphous drug, more rigorously with the water-saturated supercooled liquid or glass; it is not a true thermodynamic solubility, which is why the authors keep it in quotation marks [almeidaesousa2015 C3, C39]. In this chapter it is operationally the concentration at which a drug-rich phase first separates (the LLPS or GLPS onset), and the free-drug ceiling above which added drug only makes more drug-rich phase [ilevbare2013a C3, C5; mosqueragiraldo2015 C34]. It exceeds the crystalline solubility by e^{\Delta G/RT} and is lowered by the water the amorphous drug absorbs ilevbare2013a C60. The papers of 2017–2022 add that the dissolved-drug concentration in the presence of a drug-rich phase can be read directly by NMR (ibuprofen 154 µg/mL in buffer against 151 µg/mL calculated) [ueda2021 R5, R6, C10], and that the value changes when a second component enters the drug-rich phase or the water phase: a dissolved polymer that enters the droplets lowers it (ibuprofen 177.1 → 96.9 and 90.7 µg/mL with 300 µg/mL HPMC and PVP-VA) and a polymer that complexes the drug in water raises it (256.3 µg/mL with EUD-E) ueda2020b R1; micelles raise the total concentration at the amorphous solubility but not its activity indulkar2017a R13; STCDC and SGCDC lower the activity at which it is reached [lu2017b R18]. New aspect (Bioperformance): the highest free-drug concentration that an amorphous (supercooled-liquid or glassy) drug can produce in a medium; above it a second, drug-rich phase separates and the free concentration stays at this value [raina2014a C24, C27; alhalaweh2016 C1; hate2018 C5]. Several papers treat the concentration at which the second phase appears (the LLPS or glass–liquid onset) as the amorphous solubility [indulkar2016 R2; hate2018 R2; alhalaweh2016 R6]. In ASD work it is the ceiling of the free concentration a dispersion can give, and the concentration at which flux stops rising (F2). Enzalutamide, atazanavir, darunavir, clozapine, ketoconazole, nifedipine and pretomanid all take the UV-extinction onset as the amorphous solubility, with the polymer or medium of the test present [wilson2018 R2, C16; ueda2020a R1; alkalla2026 R3; nguyen2023a R1, P2]. In rats the enzalutamide dispersions that reached the ceiling gave several times the exposure of the crystalline drug (F23) [wilson2018 R16, R18].

Findings

Amorphous solubility and LLPS: F3, F4, F5, F6, F7, F8, F9, F10, F11, F12, F13, F14, F15, F16, F17, F18, F19, F20, F21, F23. Bioperformance: F1, F2, F4, F6, F7, F8, F15, F18, F19, F20, F23, F27, F30.

Related concepts

depends on crystalline solubility and water sorption correction of amorphous solubility; measured as the onset of liquid-liquid phase separation; sets the ceiling of supersaturation; lowered by a second component in the drug-rich phase; gives the amorphous solubility advantage. Papers of 2017–2022: lowered by a dissolved polymer that enters the drug-rich phase (polymer partitioning into the drug-rich phase); not raised in activity terms by micelles (activity-based supersaturation); its upper limit on the activity scale is the maximum achievable supersaturation. Depends on Hoffman equation inputs; related to thermodynamic activity.

Formulas

amorphous solubility advantage with water-sorption correction, amorphous solubility advantage from free energy difference, Hoffman equation, amorphous-crystalline free energy difference from heat capacity. Amorphous-to-crystalline solubility ratio, ideal-mixing reduction of amorphous solubility.

How it is measured or obtained

(1) As the onset of scattering during slow addition of a drug stock, confirmed by a polarity probe [ilevbare2013a P5; almeidaesousa2015 P1, P2]. (2) As the drug concentration in the supernatant after ultracentrifugation of a phase-separated solution [trasi2015a P2; almeidaesousa2016 P7]. (3) By dissolving an amorphous film under non-sink conditions [ilevbare2013a P4; indulkar2015 P13]. (4) As the break point of flux against donor concentration [trasi2015a P6]. (5) By calculation from the crystalline solubility, the free-energy difference and the water activity of the amorphous drug ilevbare2013a E1. The papers of 2017–2022 add quantitative ¹H NMR of the dissolved drug beside the drug-rich phase [ueda2021 P3, P4], ultracentrifugation and the flux plateau in bile-salt media [lu2017b P3, P4], and an in-situ UV probe after a pH shift [sugihara2018 P6]. In the Bioperformance papers: (1) solvent-shift UV extinction, a methanol stock pumped into stirred buffer and the onset of scattering read at 350–455 nm [raina2014a P7; alhalaweh2016 P9; indulkar2016 P3; hate2018 P2; elkhabaz2017 P4]; (2) ultracentrifugation or centrifugation of a supersaturated solution and assay of the supernatant [mosqueragiraldo2018b P8; alhalaweh2016 P10]; (3) the flux plateau in a diffusion cell [raina2014a R16]; (4) estimate from the crystalline solubility with the Hoffman free-energy difference and a water-sorption correction [raina2014a E3, E5]; (5) the drug's own fluorescence, whose emission intensity rises, and whose peak may shift to shorter wavelengths, when the drug-rich phase forms, at the concentration found by ultracentrifugation in buffers and in pooled human intestinal fluid [elkhabaz2019b R3, C17]; (6) a solvent-shift or antisolvent addition into buffer with the polymer already dissolved, which gives the value in the presence of that polymer [ueda2020a R1; alkalla2026 R3, P7]; (7) for tacrolimus the value of about 50 µg/mL is taken from earlier work and used to define the dose-to-volume conditions of a dissolution test [hate2019 R7, C16; purohit2019 C15].

Values in the library
materialvalue or classconditionspaper ids
ritonavir37.2 µg/mL (onset); 39.2 predicted; 34.2 from filmwater, 37 °Cilevbare2013a R8, R13
ritonavir; lopinavir; paclitaxel hydrate26–28; 16–17.3; 27.2–30.1 µg/mL100 mM phosphate pH 6.8, 25 °C, four methods[trasi2015a R1]
telaprevir90–92 µg/mL (UV, NMR, fluorescence)pH 6.8, 37 °C[mosqueragiraldo2015 R13]
clotrimazole; atazanavir7.7; 65.1 µg/mL (un-ionized)37 °C, 0.1 M buffer[indulkar2015 R2]
ibuprofen; sorafenib; griseofulvin125.74; 0.532; 355.96 µg/mLpH 2 or 6.8, 25 °C; griseofulvin with HPMCAS-HF[almeidaesousa2015 R5, R6]
CRH1 free base12.49–13.73 µg/mLpH 4.6 citrate + 20 µg/mL HPMC, 25 °C[almeidaesousa2016 R4]
atazanavir70 µg/mL (onset); 68 predicted; with 3.6 mg/mL SDS about 1450 µg/mL total but 65–70 µg/mL freepH 6.8 buffer, 37 °Cindulkar2017a R5, R6, R11, R13
telaprevir146–149 µg/mL by three methods; 311–360 with 12 mM STDC or SGDC50 mM pH 6.5 buffer, 37 °C[lu2017b R2]
pazopanib19.8 µg/mL at pH 6.5; 9.2 at pH 8.4; 60 at pH 50.1 M buffers with 5 µg/mL HPMC, 37 °C[sugihara2018 R1]
ibuprofen177.1 (buffer); 96.9 (HPMC); 90.7 (PVP-VA); 256.3 µg/mL (EUD-E)pH 2.0 (D2O), 300 µg/mL polymer, 37 °Cueda2020b R1
ibuprofen154 µg/mL (buffer) → 89–131 µg/mL with 1000 µg/mL of six polymersNMR, pH 2.0 (D2O), 37 °C[ueda2021 R5]
ibuprofen in bufferabout 127 µg/mL at 15 °C, about 284 at 60 °CNMR, pH 2.0 (D2O)ueda2022 R9
felodipine5.99 / 8.70 µg/mL predicted; onset 6.01 / 8.70pH 6.8 buffer, 25 / 37 °C[raina2014a R16]
nifedipine72.09 µg/mL predicted; onset 72.85buffer with 1 mg/mL HPMC, 37 °C[raina2014a R16, X3]
felodipine, FaSSIFonset 214.6 µg/mL; estimate 308.037 °C[raina2015c R1]
ritonavir / atazanavir / lopinavir45.2 / 132.1 / 27.2 µMpH 6.8, 37 °C[alhalaweh2016 R6]
clotrimazole7.5 µg/mL (ratio 15)pH 8, 37 °C[indulkar2016 R2, R3]
atazanavir78 µg/mL (94 with 1.8 mg/mL PVPVA)pH 6.8, 1 mg/mL HPMCAShate2018 R2, R3
ezetimibe21.0 µg/mL buffer; 123 µg/mL FeSSIF37 °C[elkhabaz2017 R3]
telaprevir96–111 µg/mL with 1.05 mg/mL polymerpH 6.8, 37 °Cmosqueragiraldo2018b R13
tacrolimusabout 50 µg/mL (cited), ratio about 35USP medium I[purohit2018 R4; trasi2016 C16]
enzalutamideonset about 42 µg/mL (crystalline 2.9); the printed estimate of about 39 is not reproduced50 mM phosphate pH 6.5, 37 °C[wilson2018 R1, R2, R3, C16]
atazanavir, clozapine, ketoconazole81.5 / 233.0 / 75.0 µg/mL without polymer; with AS-HF 35.5 / 95.0 / 56.0; with AS-LF 75.8 / 219.0 / 71.2buffer, 37 °C, 1000–2700 µg/mL polymerueda2020a R1, C13
nifedipine123 µg/mL with AS-HF against 221 with AS-LFbuffer, 37 °C, 1000 µg/mL polymerueda2020a R1
atazanavir, darunavir93.1 ± 1.5 (crystalline 1.6) and 363.8 ± 2.1 µg/mL (hydrate 265.6)pH 6.8, 37 °C, antisolvent[alkalla2026 R3]
atazanavir, posaconazole79–102 and 8.1–43.3 µg/mL in six media (crystalline 1.4–7.1 and 0.22–3.2)FaSSIF-type media and human intestinal fluid pool, 37 °C[elkhabaz2019b R1, R2, C15, C16]
pretomanidabout 166 µg/mL in buffer, 226 with SLS, 275 with TPGS, 308 in FaSSIF; crystalline 15–18, ratio 8–10pH 6.5, 37 °Cnguyen2023a R1, R2
tacrolimusabout 50 µg/mL, crystalline 2.5 µg/mL, ratio about 33used to fix the dose-to-volume conditions[hate2019 R7; purohit2019 C30]
Pitfalls and disagreements

The onset depends on the method by up to about 25% (ritonavir in water at 37 °C, 34–40 µg/mL) and on the medium (water against 100 mM buffer, twofold), so values are comparable only within one medium ilevbare2013a X14, X16, C40. Four of the eight 2013 predictions cannot be recomputed from the printed inputs ilevbare2013a X1. The claim that the onset equals the amorphous solubility is partly circular in the free-energy comparison [almeidaesousa2015 X4]. For ionizable drugs the value is for the un-ionized form [indulkar2015 C47]. For ibuprofen the same medium gave 177.1 µg/mL by extinction and 154 µg/mL by NMR, with crystalline solubilities of 29.8 and 43.1 µg/mL, in two papers of one group [ueda2020b R1, X1; ueda2021 R5, R2]. In SDS a prediction from the crystalline solubility overshoots about twofold indulkar2017a C16. For a drug that degrades on melting (pazopanib) the calculation cannot be made [sugihara2018 C17]. In the Bioperformance papers the onset depends on stirring, addition rate and polymer [raina2014a X15]. The estimate fails in FaSSIF and for high-melting telaprevir [raina2015c C18; mosqueragiraldo2015 C24]; the nifedipine prediction cannot be reproduced [raina2014a X3]. The atazanavir crystalline solubility is 5 µg/mL in one card and about 1.1 µg/mL in two others, so ratios differ [hate2018 R1; alhalaweh2016 R6; indulkar2017a E3]. A second drug or a polymer in the drug-rich phase lowers it (F6, F7). The value depends on the medium and on the polymer in it: the more hydrophobic HPMCAS grade AS-HF lowered it for four drugs by a quarter to well over half, and a co-dissolved crystalline drug lowered it too (F19, F20) [ueda2020a R1, C13; alkalla2026 C1, C39]. In simulated and human intestinal fluids the amorphous solubility rose much less than the crystalline solubility, so the ratio of the two fell from about 36 to about 5 for posaconazole (F18) [elkhabaz2019b R1, R2]. The printed enzalutamide estimate cannot be reproduced from its inputs [wilson2018 R3, X1]. The amorphous solubility of atazanavir at 37 °C is 75 (cited), 79, 81.5 and 93.1 µg/mL in four later papers, with crystalline values of 1.4, 1.14 and 1.6 µg/mL, so the ratio is 56, 71 or 58 depending on the paper [hate2022 M1; elkhabaz2019b R1, R2; ueda2020a R1; alkalla2026 R3] (synthesis: 79/1.4, 81.5/1.14, 93.1/1.6).

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

amphiphilicity

The presence of both hydrophobic and hydrophilic parts in one molecule. For the cellulose ω-carboxyalkanoate esters the hydrophobic ester chains and the ionized terminal carboxyls (pKa about 4.43, nearly fully ionized at pH 6.8) make the polymer amphiphilic, which the authors think "may influence" its adsorbed conformation and so its growth inhibition [ilevbare2012c C40, R15]. CA 320S Sub, a relatively hydrophilic cellulose acetate backbone with an ionizable suberate chain, is said to have a structure that "may promote" interaction with drugs [ilevbare2013b C46]. For telaprevir the ionized carboxylate makes a cellulose polymer amphiphilic, with a free energy of solvation of −86 kcal/mol for ionized adipate against −33 for protonated adipate, but charged long side chains (A5b, A6, A7) fold onto the backbone and are "not truly amphiphilic" [mosqueragiraldo2016 R16, C37, C55].

Findings

F8, F11, F25, F37, F44.

Related concepts

related to polymer hydrophobicity, polymer ionization and degree of substitution.

Formulas

none.

How it is measured or obtained

Not measured; it follows from the polymer structure and the degree of ionization at the test pH [ilevbare2012c R15; ilevbare2013b R18].

Values in the library
materialvalue or classconditionspaper ids
CA 320S Sub 0.90; 0.63growth ratio 12.6; 10.8 on ritonavir; 7.2; 6.1 on celecoxib5 µg/mL[ilevbare2013b R9]
adipate esters, ionizedratio 2.98 (CAP Adp 0.85) at pH 6.8, 1.12 at pH 3.8ritonavir[ilevbare2012b R7]
hydrophobicity, rigidity and amphiphilicity"appear to be jointly responsible" for the advantage of the cellulose estersritonavir growth[ilevbare2012c C49, C50]
CA-A5a-079 (short spacer, COOH branch); CA-A5b-067 (long spacer)induction time about 90 against about 12 mintelaprevir 150 µg/mL, 5 µg/mL polymer[mosqueragiraldo2016 R6]
HPMCAS L, M, Hamphiphilic; affinity for posaconazole rises with A/S ratio and lower pH, for water the reversepH 5.5–7.5shah2025 C48
HPMCAS against Eudragit E POboth amphiphilic; HPMCAS "should" be drawn to enzalutamide dropletspH 6.5[wilson2021 C50, C51, C52]
Pitfalls and disagreements

Amphiphilicity, solubility parameter and carboxyl content are interrelated in the new esters and cannot be separated by the data [ilevbare2012c C42, X10]. PAA, with many ionized carboxyls but no hydrophobic part, failed for all three drugs [ilevbare2013b R9.b]. Amphiphilicity was inferred, not measured, and the simulations omit the ester groups of the real polymers [mosqueragiraldo2016 X10, X15].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

antiplasticization

The rise of the Tg of a drug on mixing in a polymer of higher Tg, and with it a lower mobility, proposed as a reason for the stabilization of amorphous dispersions [taylor1997 C4; kestur2011 M3]. PVP, with a Tg of 177 °C, "has been suggested" to raise the Tg of the mixture and lower the mobility [taylor1997 C4, M4]. For indomethacin, inhibition by PVP at relatively low levels was already known to be too large to be explained by antiplasticization alone [taylor1997 C5]. In the growth studies of this chapter, antiplasticization is ruled out as the cause at 3–5 wt% polymer, since the dispersion Tg changes by 2.2 °C or less [kestur2010a C32; kestur2011 C12]. New aspect (Physical stability): water undoes it: after 75% RH every felodipine dispersion with up to 25% polymer had a Tg below the dry drug [konno2008 C16].

Findings

Miscibility and drug-polymer interactions: F11, F1. Physical stability: F5, F6.

Related concepts

depends on and is measured by glass transition temperature; contrasts with drug-polymer interactions as an explanation of crystallization inhibition; related to supercooled liquid; contrasts with plasticization and plasticization by water.

Formulas

Gordon-Taylor equation.

How it is measured or obtained

By onset Tg of dispersions by DSC at 10 °C/min after erasing thermal history, against the drug alone and the pure polymer [kestur2010a P8; kestur2011 P5]. Growth rates may be normalized to Tm − T and T − Tg to separate driving force and mobility [kestur2010a C31, E2]. DSC Tg against polymer content, dry and after humid storage [konno2008 P6; marsac2006a R17].

Values in the library
materialvalue or classconditionspaper ids
felodipine with 3% PVP, PVP/VA, HPMCAS, PVAcTg 44.1, 43.7, 42.7, 43.5 °C against 43.3 °Conset DSC[kestur2010a R1]
bifonazole with 5% polymersTg 16.4–17.4 °C against 15.2 °Conset DSC[kestur2011 R6]
nimesulide with 5% polymersTg 19.9–20.8 °C against 19.5 °Conset DSC[kestur2011 R6]
felodipine with PVP, HPMC, HPMCAS (other chapter)PVP raised Tg by 10 °C at 25 wt%; HPMC and HPMCAS no change up to 25 wt%onset DSC[konno2006 R6, C25]
felodipine with PVP (other chapter)Tg largely unaffected (43.4–44.1 °C against 43.3 °C at 0.5–4.5 wt% PVP); antiplasticization not the cause, yet growth slowedPVP grades, 3–4.5 wt%; dry[kestur2010b R1, C34]
felodipine–PVP 10 wt%Tg 40.5 °C, below pure felodipine 43.1 °Cdry[marsac2006a R8, C22]
felodipine with ≤ 25% polymerTg ≈30–35 °C after 75% RH25 °C[konno2008 R7, C16]
celecoxib with 40% PVP K12 or PVPVA vs HPMCAS or HPMCdry Tg 84.4 and 81 °C vs 64 and 71 °C, although neat PVP K12 and PVPVA have lower Tg (97, 102 °C) than HPMCAS and HPMC (117, 140 °C)DSC, dryxie2016b R17, R14, C27

Evidence table: antiplasticization.

Pitfalls and disagreements

For nimesulide the inhibition order follows the polymer Tg, and the rank of dispersion Tg matches the inhibition rank for both drugs, within about ± 1 °C [kestur2011 X8]. At higher polymer contents the Tg does rise, and PVP is the strongest antiplasticizer of the three polymers in another study [konno2006 C25]. The authors conclude that Tg is not a good predictor of crystallization tendency in multicomponent amorphous systems [kestur2010a C33]. PVP raised felodipine Tg only from about 15% polymer, although the authors write "at all concentrations" [konno2006 X15]. The dry Tg gain did not carry over to humid storage: after 3 days at 94% RH four celecoxib dispersions had Tgs of 37.4–42.1 °C and very different stability xie2016b R17, C46.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

associative phase separation

Evidence table: associative phase separation. Content from the release-mechanism chapter (2023–2025).

Phase separation in which the insoluble phase is enriched in both drug and polymer, a complex coacervate, against segregative separation in which the polymer stays in the aqueous phase deac2023b C47. PHPH–PVPVA separates associatively, and TIPP is grouped with it in the conclusions deac2023b C47. Hydrogen bonding increases PVPVA distribution into the hydrophobic phase and makes it volumetrically larger, which is why the continuous hydrophobic phase formed at lower loading for PHPH, a high polymer content giving a low limit of congruency deac2023a C65. In the dissolving PHPH gel both dyes went into the hydrophobic phase, which is therefore "considerably less hydrophobic" than in MePHPH dispersions deac2023a C28. Associative separation gives positively sloped tie lines with the plait point on the low-drug side and can have a low maximum limit of congruency deac2023b C48; deac2023a C69. Measured in 2024: the PHPH-rich phase of PHPH–PVPVA–water held 41.9–52.2 wt% PVPVA, rising with total water, with tie lines sloping up, which the authors read as PVPVA preferring PHPH to water ("the data suggest"), hydrogen bonding being "a potential explanation" deac2024b R15, R17, C18, C21, C22. With HPMCAS the neutral phenol complexed 60% of the polymer bapat2024 R12, C41.

Findings

Release mechanism and LoC: F17, F27, F30, F32.

Related concepts

contrasts with segregative phase separation; high polymer partitioning into the drug-rich phase; related to drug-polymer complexation and hydrogen bonding; shifts the critical point on the ternary phase diagram and so the limit of congruency.

Formulas

drug-rich phase composition.

How it is measured or obtained

As for segregative separation: polymer content of nanoparticles by depletion mass balance deac2023b R2, R3, dye partitioning in dissolving compacts deac2023a R7 and composition and Tg of the released hydrophobic phase deac2023a R12.

Values in the library
materialvalue or classconditionspaper ids
PHPH nanoparticles with PVPVA71.4–78.0 wt% PVPVA37 °C, two preparation routesdeac2023b R2
PHPH; TIPP nanoparticles≈77; ≈36.5 wt% PVPVA60 °C, NMRdeac2023b R3
hydrophobic phase released from 5% PHPH–PVPVA26.2 wt% drug, Tg −5.8 °CHPLC, DSCdeac2023a R12
PHPH; TIPP–PVPVAlimit 5; 10% (cited)deac2023b R8
PHPH with PVPVA in solutionamorphous solubility 200 → 27.5 µg/mLUV extinctiondeac2023b R1, C15
PHPH–PVPVA–water, 60–99 wt% waterPVPVA in the drug-rich phase ≈42 → 52 wt%equilibrated, NMR, 37 °Cdeac2024b R17
Pitfalls and disagreements

The PVPVA content of PHPH nanoparticles is printed as about 69.6–78.0% across figures, tables and text, depending on temperature and method deac2023b X3. The link from associative separation to a low limit rests on schematic diagrams deac2023b X14.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

atomic layer coating

Deposition of a thin metal-oxide film on the surface of powder particles by repeated, self-limiting vapour-phase reactions in a rotating reactor. For Al2O3, trimethylaluminum reacts with surface hydroxyl groups and water regenerates them, giving overall 2 Al(CH3)3 + 3 H2O → Al2O3 + 6 CH4 [duong2022c E5, E6, E7]. In the ASD process papers it is applied at 35 °C to amorphous solid dispersion (ASD) particles made by spray drying, by rotary evaporation or by extrusion and milling, with Al2O3 in all four coating papers and ZnO in one [duong2022c P2, P4; moseson2022a P1, P2, P3; benson2025 P3]. The growth per cycle was varied from slow (under 0.4 nm per cycle) to average and fast, and thickness is reported in nm moseson2023 P3, P4; benson2025 P3. The coating was introduced to stop surface crystallization of ASD powders; it also changes flow, water uptake and release.

Findings

F42, F43, F44, F45, F46, F47, F48, F49.

Related concepts

characterised by coating conformality and coating defect density; acts through surface molecular mobility and the moisture barrier effect; targets surface crystallization; sized with the specific surface area; changes powder flowability.

Formulas

coating thickness from oxide content and specific surface area.

How it is measured or obtained

Thickness: residual oxide after heating the coated powder in dry air (800–850 °C, thermogravimetry, TGA) converted with the BET area (see coating thickness from oxide content and specific surface area), and cross-sectional TEM of focused-ion-beam lamellae of about 100 nm [moseson2022a P9, P10, R2; duong2022c P5, P10, R2]. Effects: SEM, XRPD and DSC of powders stored open at 40 °C; dynamic vapour sorption; shear-cell and tapped-density flow tests; release in non-sink tests; SEM/EDX of particles incubated in medium [moseson2022a P11, P12, P14; duong2022c P8, P9, P15, P16; moseson2023 P10, P13, P15].

Values in the library
materialvalue or classconditionspaper ids
ezetimibe–HPMCAS 50 and 70% DL, spray dried, thin and thick Al2O3about 12–40 nm by TEM (six places in one cut); oxide residue 1.7–9.2%rotating-tube reactor, 35 °C[duong2022c R2, R12]
erlotinib–HPMCAS, erlotinib–PVPVA, naproxen–HPMCAS, lumefantrine–PVPVA7.4–24 nm by TGA and BET; 4.4–37.7 nm by TEM; Al2O3 and one ZnOrotary reactor, 35 °Cmoseson2022a R2
posaconazole–HPMCAS 25 and 50% DL, twelve samples11–39 nm (oxide 0.40–3.68%); one slow-deposited 26 nmslow, average, fast growthmoseson2023 R1
ritonavir–PVPVA 10 and 20% DL, nine coated samples9.3–28.3 nm; oxide 0.92–5.30%; BET 0.22–0.76 m²/gbenson2025 R1
stored powders, uncoated → coatedcrystals by SEM within 1–3 weeks → 3–24 weeks, or none within 48 weeks to 2 yearsopen dishes, 40 °C, 31–75% RH[moseson2022a R11; duong2022c R16, R17]
tablets of coated ritonavir–PVPVA particlesabout 35–75% of the dose at 60 min against about 95% uncoatedpH 6.8, 37 °Cbenson2025 R10
Pitfalls and disagreements

The thickness label is a mass-balance estimate and differs from TEM by up to a factor of two inside one paper moseson2022a X10. The number of cycles is not printed in the coating papers [moseson2023 P3; moseson2022a P3; duong2022c X2; benson2025 M11]. The coating delays crystallization and does not stop it, and it can slow or block release depending on defects, not thickness (see coating defect density) moseson2022a R11; moseson2023 C53; benson2025 C21. Evidence is for Al2O3 on six drug–polymer pairs; other oxides, polymers and dosage forms were not tested [duong2022c C60; moseson2022a X20].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

BET isotherm

A multilayer adsorption isotherm in which the first layer is held most strongly and further layers more weakly, with no lateral interactions and a homogeneous surface [dening2019 C14; hate2020a C23]. For adsorption from solution the papers use the liquid-phase form of Ebadi and co-workers, with constants K_S (first layer) and K_L (upper layers) and an infinite number of layers, or a form in the relative concentration X = C_e/C_s with C_s set to the amorphous solubility [dening2019 E4; mccarthy2020 E8; hate2020a E1]. By analogy with the saturation vapour pressure of gas-phase BET, 1/K_L is proposed to be the saturation concentration of the liquid drug phase, the amorphous solubility ("We propose") [dening2019 C48, E7; mccarthy2020 C21].

Findings

F2, F3, F10.

Related concepts

model of multilayer adsorption; gives the BET monolayer coverage; fitted to an adsorption isotherm; contrasts with the Langmuir adsorption isotherm and Freundlich isotherm; 1/K_L related to the amorphous solubility.

Formulas

liquid-phase BET isotherm.

How it is measured or obtained

Nonlinear least-squares fit of the isotherm by solution depletion, in GraphPad Prism or Origin [dening2019 P12; mccarthy2020 P17; hate2020a P16]. The electrostatics paper names the fit and prints only Q_m [hate2020b E2, R21].

Values in the library
materialvalue or classconditionspaper ids
ritonavir on SBA-15R² 0.94; Q_m 103 mg/g; K_S 1.169, K_L 0.031 mL/µg; 1/K_L 32.7 µg/mLpH 6.8, 37 °C[dening2019 R6, X1]
indomethacin on SBA-15R² 0.94; Q_m 29 mg/g; K_L 0.025; 1/K_L 40 µg/mLpH 2.2, HPMC[mccarthy2020 R10, R11]
indomethacin methyl ester on SBA-15R² 0.98; Q_m 31 mg/g; K_L 0.118; 1/K_L 8.5 µg/mLsame[mccarthy2020 R10, R11]
atazanavir on SBA-15best of three models; Q_m 4.5 mg/g; K_{BET} not printed300 µg/mL silica, HPMC[hate2020a R3, E1]
three bases on SBA-15Q_m 0.006–0.275, unit printed "mg/mol"pH 1–6.8[hate2020b R21, X9]

Evidence table: BET isotherm.

Pitfalls and disagreements

The silica surface is heterogeneous, so deviations at low concentration are expected and were seen for atazanavir ("may result") [dening2019 C15; hate2020a C24]. The ritonavir 1/K_L lies 17% above the measured amorphous solubility, and no isotherm point lies at or above it [dening2019 X9, X8]. K_S and K_L are printed in "µg/mL⁻¹" where the dimension must be mL/µg [dening2019 X1]. The BET Q_m from water lies 2.5 to about 60 times below the geometric monolayer (synthesis: 253/103 and 278/4.5) [dening2018 R4; dening2019 R6; hate2020a R1, R3]. Langmuir and Freundlich fitted worse in all three studies [dening2019 R4, R5; mccarthy2020 R10; hate2020a R3].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

bile salt micelles

Aggregates of bile salt above its critical micelle concentration; in the telaprevir studies 1.86 mM is nominally the monomer and 12 mM the micellar level, with micelles of the dihydroxy salts STDC, SGDC and STCDC opposing the monomer effect on nucleation and those of STCDC and SGCDC on growth [lu2017 C14, C41; lu2017a C13, C33].

Findings

F32, F33.

Related concepts

part of critical micelle concentration; related to mixed micelles.

Formulas

none.

How it is measured or obtained

CMC by surface tension (Wilhelmy plate, 37 °C) for STC (about 4 mM) and SGDC (about 2 mM) only; the states of the other salts are cited from companion work [lu2017 R5, X7; lu2017a C13].

Values in the library
materialvalue or classconditionspaper ids
telaprevir δ 11.5, 12 mM STDC, SGDC, STCDCinduction time about 140, 125, 180 min against >960 at 1.86 mMpH 6.5, 37 °C[lu2017 R3]
telaprevir δ 12.5, 12 mM STCDC, SGCDC15 h residual 4.0 of 145.2 and 11.5 of 95.2 µg/mL against 60.5 and 91.7 at 1.86 mMpH 6.5, 37 °C[lu2017a R12]
ternary STC–STDC–STCDC at 5.58 mMabout 254 min against >960 for 12 mM STC; STC protection "reduced by the presence of the other bile salts"δ 11.5, 37 °C[lu2018 R4, C18]
Pitfalls and disagreements

The monomer share was not measured, 1.86 mM is close to the SGDC CMC, and the 18 mM evidence is given in words only [lu2017 X7, X8].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

binding constant

The equilibrium constant of the association of a drug molecule with a polymer group, here the indomethacin–PVP carbonyl species. In the indomethacin–PVP paper the constant is never given a value: the authors reason that spectral changes continue above the composition at which PVP monomer equals drug in moles, "which suggests" a low equilibrium constant and/or a stoichiometry below 1:1, so that dimers, PVP-bonded drug and free PVP coexist and "dimers may still be present depending on" the constant [taylor1997 C37, C38]. In the halogen-bond study K_F is the equilibrium constant of the 1:1 complex between a halogenated compound (donor D) and a monomer analogue of the polymer carbonyl (acceptor A), K_F = [AD]/([A][D]) que2020 E1. Unlike the indomethacin–PVP case it is measured: 0.56–1.11 M⁻¹ in cyclohexane and 0.21–0.39 M⁻¹ in toluene que2020 R12, R13.

Findings

F1, F20.

Related concepts

measured by hydrogen bonding; related to self-association and drug-polymer interactions; measures halogen bonding.

Formulas

none (the weight-fraction conversion is named in plain text only).

How it is measured or obtained

It was not measured. The stoichiometric compositions were computed from the weight fraction of PVP with a monomer molecular weight of 111: 1:1 at 24 wt% PVP, and 12 wt% printed for two hydrogen bonds per carbonyl, which the card recomputes as 13.6 wt% [taylor1997 E1, R18, X2]. The evidence for incomplete binding is a visual reading of overlapping bands, with no intensities, areas or fits [taylor1997 X5]. By ¹H and ¹³C NMR titration at 25 °C: 11 to 1219 mM 1-ethyl-2-pyrrolidone added to a 14.5 mM solution of the compound, fitted to a 1:1 hyperbolic model; three titrations each; a carbonyl-free titrant (1-ethylpyrrolidine) as control que2020 P6, E1, C4, R15.

Values in the library
materialvalue or classconditionspaper ids
indomethacin–PVP-K901:1 monomer:drug at 24 wt% PVP; changes continue aboveIR, 5–70 wt% PVP[taylor1997 R18, R11, R12]
indomethacin–PVP-K90two bonds per carbonyl: 12 wt% printed, 13.6 wt% recomputedsame[taylor1997 E1, X2]
clotrimazole0.63 ± 0.05 (¹H), 0.97 ± 0.04 (¹³C) M⁻¹ in cyclohexane; 0.32, 0.35 in tolueneNMR, 25 °Cque2020 R12, R13
loratadine0.65 ± 0.05, 1.11 ± 0.07 M⁻¹ in cyclohexane; 0.35, 0.39 in toluenesameque2020 R12, R13
brotrimazole0.56 ± 0.06, 0.81 ± 0.04 M⁻¹ in cyclohexane; 0.30, 0.21 in toluenesameque2020 R12, R13

Evidence table: binding constant.

Pitfalls and disagreements

The incomplete binding is qualitative: the growing PVP band overlaps the same region [taylor1997 X5]. The two-bond threshold is a halved weight fraction, not a halved mole ratio [taylor1997 X2]. The authors' "low equilibrium constant" is one reading; a stoichiometry below 1:1 is the other, and the data do not separate them [taylor1997 C37]. The ¹³C values are 1.45–1.71 times the ¹H values, which the authors call similar, and the tracked ¹³C peak of loratadine crosses a neighbour que2020 C13, X8. K_F belongs to a monomer analogue in a non-polar solvent, not to the solid dispersion que2020 C4. The lower constants in toluene are read as competition from π electrons, not tested que2020 C15.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

binodal

The coexistence curve of the water-rich and the drug-rich liquid phases: beyond it two liquid phases can coexist, and at a fixed temperature its concentration is the LLPS (coexistence) concentration CL-L; the spinodal lies inside it ilevbare2013a C30, C32. The drug concentration in the continuous phase after complete phase separation (the ultracentrifuge supernatant) is one binodal point [trasi2015a C10; jackson2016 C7]. New aspect (ASD process): in drying and humid films it is the boundary of the two-phase region on a phase diagram. In the evacetrapib (ECP)–methanol–water picture the drying path crosses the binodal while solvent is still present, and the drug leaves as droplets [li2017 C38, C42]. In the drying model of the ritonavir–PVPVA spray solution the two-phase region is computed from the minima of a four-component Flory–Huggins free energy along the drying path, and drug above its solubility marks a path inside it li2020 P12, R17. The papers of 2017–2022 add that for telaprevir the ultracentrifuge and flux onsets are read as the coexistence (binodal) concentration of the continuous phase [lu2017b C15, C16]. New aspect (Release mechanism and LoC): in a hydrating dispersion the binodal is crossed when the local water content is high enough. In dissolving ritonavir–PVPVA compacts at 10% droplets formed near the gel–solution interface once the drug–polymer–water system exceeded its binodal composition, rather than throughout the gel, because a certain water content must be reached first; since droplets formed deeper at 20% than at 10%, the water content needed to cross the binodal is higher at 10% yang2022a C34, C35, C36. For the phenolphthalein analogues PVPVA diffused out of the 10% PHPH and 70% MePHPH particles until the hydrophobic binodal composition was reached deac2023b C52, and the binode closer to the initial composition is the majority phase deac2023b C34. Measured in 2024 for two drug–PVPVA–water systems at 37 °C from equilibrated mixtures, with the condition \mu_i^{(1)} = \mu_i^{(2)} used for the PC-SAFT binodal deac2024b R15, R22, R23, E20. For MePHPH–PVPVA the binodal at low water lies between the film compositions at 75 and 80% RH, under 15 wt% water deac2024b C13.

Findings

Amorphous solubility and LLPS: F3, F9, F4. ASD process: F2, F6, F20. Release mechanism and LoC: F5, F25, F27, F30.

Related concepts

boundary of liquid-liquid phase separation; inside it lies the spinodal decomposition region; its concentration is the amorphous solubility. In films it is drawn on a ternary phase diagram. Joined by tie lines ending at the critical point; read with the local equilibrium assumption in the gel layer.

Formulas

binodal condition.

How it is measured or obtained

Cloud point on cooling at 0.5 °C/min and clear point on heating at a known concentration (90° scattering at 474 nm), taking their mean as TL-L; or titration onset at a fixed temperature, which agrees closely with it ilevbare2013a P12, C30. For ECP films the phase boundaries of the ECP–methanol–water diagram were not determined and Fig. 12 is a schematic [li2017 C38, X9]. For the ritonavir–PVPVA spray solution the region is computed along the trajectory, not mapped: pseudo-ternary sections (total solvent, PVPVA, ritonavir) at 11.5:88.5, 15:85 and 30:70 show the region growing with the water content of the feed li2020 R18. In the release-mechanism papers: Position of droplet formation in time-lapse confocal images yang2022a R10, R11; polymer content of particles held in buffer with PVPVA deac2023b R4, R5.

Values in the library
materialvalue or classconditionspaper ids
ritonavirTL-L about 11.4, 15.7, 20.0, 24.7 °C at about 58, 50, 46.5, 42.7 µg/mLbuffer or water (medium unresolved), 0.5 °C/minilevbare2013a R11, X6
ritonavirLLPS concentration about 57.9 at 10 °C, 37.1 at 35 °C, 54.8 µg/mL at 65 °Cwaterilevbare2013a R11
ECP–methanol–waterdrying path B → D crosses the binodal at C with less water than the spiking path B → E needsschematic[li2017 C38]
ECP–water–polymer (storage)high-DL films absorb little water and stay in the one-phase region; low-DL films cross the binodalschematic[li2017 C42]
drug–polymer mixturesbinodal points are the two minima of the free energy of mixing against compositionargument[rumondor2009a E6, C35]
MePHPH–PVPVA–waterexperimental binodes and tie lines at 37 °CPC-SAFTdeac2024b R15, R22
ritonavir–PVPVA–methanol–water (25% and 50% DL)the 25% DL path enters the two-phase region from about 12.5:87.5 water:methanol; the 50% DL path from about 11.5:88.5droplet modelli2020 R17, R19, C50, C53
ritonavir–PVPVA 10%; 20% compactsdroplets near the gel–solution interface; deeper in the gelreal-time confocal, pH 6.8yang2022a R10, R11
PHPH–PVPVA; MePHPH–PVPVA hydrophobic binodalabout 72% PVPVA; below 5% PVPVAparticles, 48 h in bufferdeac2023b C52
MePHPH–PVPVA films 10–50%binodal between 75 and 80% RH (≈4.9–9.4 and 9.6–14.6 wt% water)37 °Cdeac2024b R1, R2
Pitfalls and disagreements

The binodal was measured on the low-temperature branch only, four concentrations, and the scan direction on that branch is unresolved ilevbare2013a X6, X7, X17. Raina and co-workers describe the binodal points as the theoretical onset of LLPS in a partially miscible drug–buffer system [raina2014a C27]. In the film papers the quaternary system with polymer is "much more complex" than the ternary one drawn, and Fig. 12B lacks the letters that the text uses [li2017 C36, X9]. The computed binodal depends on χ values that are partly assumed and inconsistently described, and keeps the 10:90 path outside the region although the powders separate li2020 X10, X12. The binode drug loads stated in the 2023 text do not exactly match the nanoparticle data deac2023b X18. MePHPH films separated at 80% RH where the computation predicts one phase, and single-phase PHPH mixtures lie inside the computed gap deac2024b C34.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

buffer capacity

Evidence table: buffer capacity. Content from the release-mechanism chapter (2022–2025), with a note from the Peptide permeability chapter.

The ability of a medium to take up acid or base with little change of pH, given in mM per pH unit (mM/ΔpH). For an enteric polymer it measures how many buffer species are available to carry away the protons that the polymer releases as it ionizes at the dissolving surface. That the dissolution rate of enteric polymers depends on buffer capacity is described as "well known" (cited) qi2022 C20. For HP-50 in four pH 6.8 buffers the rate "appears to trend" with buffer pKa and buffer capacity: slow buffers had higher pKa and lower capacity, fast buffers higher capacity and a pKa near the dissolution pH qi2022 C14. HPMCAS-MF dissolution depends strongly on buffer capacity in pH 6.8 phosphate, particularly at low capacity, and "may be approaching" a plateau at higher capacity bapat2023 C9. A pre-ionized polymer salt keeps its rate whatever the buffer capacity qi2022 C4. In 2024 a stronger buffer (100 against 50 mM pH 6.8 phosphate) sped a 25% loratadine–HPMCAS dispersion about 2.5-fold but neat HPMCAS only about 1.1-fold, and neat HPMCAS dissolved more slowly in 50 mM pH 9.0 glycine (about 0.63 against 0.90 mg/min/cm²), put down to the low buffer capacity of that buffer at the acidic surface bapat2024 R6, X3, R4, C13.

Findings

Release mechanism and LoC: F23, F24, F32.

Related concepts

sets the microenvironmental pH at the dissolving surface; depends on buffer pKa; acts through the unstirred water layer; its effect is removed by polymer salt formation; related to critical ionization for polymer dissolution and the gel layer of enteric polymers.

Formulas

boundary-layer diffusion flux (film model).

How it is measured or obtained

Phosphate buffers of the same pH at different concentrations: 50 and 5 mM at pH 6.8, given as 29 and 3 mM/ΔpH, the 29 measured by a co-worker with the method not printed qi2022 R12, M16, M17; 5, 10, 25, 50 and 100 mM pH 6.8 phosphate given as 3, 5, 13, 26 and 51 mM/ΔpH bapat2023 A1. Rates are surface-normalized polymer release rates of compacts on a rotating disk qi2022 P10; bapat2023 R5.

Values in the library
materialvalue or classconditionspaper ids
HP-50; HP-50-Na compacts≈0.92 → 0.14; ≈2.80 → 2.45 mg/min/cm² from 29 to 3 mM/ΔpHpH 6.8 phosphate, 37 °Cqi2022 R12, C4
HP-50 in BIS-TRIS, phosphate, Tris, TEA buffers≈44.8 / 28.4 / 6.6 / 1.8% dissolved at 60 min (buffer pKa 6.5 / 7.2 / 8.1 / 10.2)50 mM, pH 6.8qi2022 R2, C14
neat HPMCAS-MF≈0.16 / 0.26 / 0.59 / 0.89 / 1.01 mg/min/cm² at 3 / 5 / 13 / 26 / 51 mM/ΔpHpH 6.8 phosphate, 100 rpmbapat2023 R5
neat HPMCAS-MFno gel at 5 mM/ΔpH; gel 3 ± 1 µm at 13 and 19 ± 5 µm at 51 mM/ΔpHconfocal, 60 minbapat2023 R14
neat HPMCAS-MF; 25% loratadine dispersion≈0.91 → 1.00; ≈0.10 → 0.25 mg/min/cm² (50 → 100 mM)compacts, pH 6.8 phosphatebapat2024 R6
Pitfalls and disagreements

The same nominal medium, 50 mM pH 6.8 phosphate, is given 29 mM/ΔpH in the HP-50 paper and 26 mM/ΔpH in the HPMCAS paper (synthesis: from qi2022 M16 and bapat2023 A1), so the two series compare by trend only. The composition and pH of the 5 mM buffer of the HP-50 paper are not printed qi2022 M17. In the Peptide permeability chapter a table row labelled "buffer capacity (Osm/L)" carries osmolality values and the buffer capacity is unreported fagan2025 X1. In 100 mM phosphate loratadine complexation also fell from about 70 to 48%, a second route for the buffer effect bapat2024 X11, R16.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

chemical potential

The partial molar free energy of the drug in a phase

The amorphous drug, treated as a supercooled liquid, has a higher chemical potential than the crystal, so its solubility is higher by \exp(\Delta\mu/RT); in an equilibrated two-phase system the chemical potential of the drug is the same in both phases, so transport driven by chemical potential responds non-linearly to total concentration and peaks where the drug-rich phase first forms [trasi2015a E1, C36, C5]. With ideal mixing in the drug-rich phase the chemical potential of each component falls by RT\ln x [trasi2015a E2, E3]. The papers of 2017–2022 add that a dissolved polymer which enters the drug-rich phase lowers the chemical potential of the drug there by dilution (and, for PVP-VA, by interaction), so the drug in the water is lowered to match: ibuprofen 154 → 89–131 µg/mL [ueda2021 R5, C11, C42]; and the fundamental supersaturation is defined by \ln\delta = (\mu - \mu^{\circ})/RT [lu2017b E3]. New aspect (Bioperformance): it is the driving quantity of passive transport; it is higher in a supersaturated solution than in a saturated one, and lowered by solubilizers and by a second component in the drug-rich phase [raina2014a C6, E8; raina2015c C7; alhalaweh2016 C25, C26]. Polymer or a second drug in the drug-rich phase dilutes the drug and lowers its chemical potential, and with it the amorphous solubility: HPMCAS-HF for four drugs, darunavir for atazanavir [ueda2020a C36; alkalla2026 C7, C12, C37]. The Crystallization from solution papers add that solubilization raises the solubility without raising the chemical potential, whereas supersaturation raises it, and derive the activity-based supersaturation δ = a/a° from the same relation [jackson2016 C31; raina2015b C2; lu2017 E1]. New aspect (Supersaturation from ASD dissolution): once a drug-rich phase forms in metastable equilibrium with the water-rich phase, the free drug is fixed at the amorphous solubility, so dispersions cannot raise it further jackson2015 C31, C32; mixing two drugs in the drug-rich phase lowers the chemical potential of each and with it each amorphous solubility, "as long as" they are miscible there [trasi2015b C36, C53]. Membrane flux into a sink follows the activity of the free drug, so the tacrolimus flux levelling off at the amorphous solubility marks the maximum chemical potential, which six marketed capsules reached [trasi2016 C23, C36, C38]. Complexed drug raises the total concentration without raising the free drug, so complexed solutions are thermodynamically "quite different" from supersaturated ones [wegiel2015 C23, C44]. Mixing an amorphous drug with a polymer that stays undissolved, and the water the dispersion takes up, lower the drug's chemical potential and with it the maximum concentration the dispersion can reach [li2018 C1, C2, C43].

Findings

Amorphous solubility and LLPS: F8, F11, F12, F15, F17, F19, F20, F21. Bioperformance: F6, F7, F19, F20. Crystallization from solution: F22, F31, F37, F44. Supersaturation from ASD dissolution: F7, F11, F17, F18, F25.

Related concepts

related to thermodynamic activity; lowered by ideal mixing in the drug-rich phase; determines the amorphous solubility advantage. Related to drug–drug miscibility and polymer partitioning into the drug-rich phase; related to supersaturation; related to amorphous solubility; lowered by mixing in solubility suppression.

Formulas

amorphous solubility advantage from free energy difference, ideal-mixing reduction of amorphous solubility, activity-based supersaturation ratio, Huang model of drug solubility in an ASD, Flory-Huggins activity equation.

How it is measured or obtained

Not measured; derived from solubility ratios and used to reason about the effect of a second component on the amorphous solubility (F11) [trasi2015a E1, E4]. In the Bioperformance papers it is inferred from flux or from the shift of the LLPS concentration [alhalaweh2016 R12, R13; mosqueragiraldo2018b C37]. Through the membrane flux ratio, which follows the activity [lu2017 E2]. In the ASD dissolution papers it is inferred from flux plateaus and from the fit of ideal mixing [jackson2015 R9; trasi2015b R5].

Values in the library

None printed in the amorphous solubility and LLPS chapter; the Bioperformance, Crystallization from solution and ASD dissolution papers give the following.

materialvalue or classconditionspaper ids
telaprevir with CA Sublowered in the drug-rich phase by polymer (fraction 0.90)inferredmosqueragiraldo2018b C37, R14
ritonavir, atazanavir mixtureeach drug's amorphous solubility times its mole fractionideal mixing[alhalaweh2016 E7]
ritonavir, lopinavir, paclitaxelmax flux drops with a second componentdiffusion cell[trasi2015a C35, E3]
ibuprofenpolymer dilution, extra water and interactions lower itdrug-rich phase[ueda2021 C42]
atazanavir, clozapine, ketoconazole, nifedipine with AS-HFamorphous solubility lowered by a quarter to well over half; AS-LF by under a tenth for threebuffer, 37 °Cueda2020a R1, C36
atazanavir with darunaviratazanavir ceiling and flux plateau lowered, darunavir partitioning into the atazanavir-rich phaseinferred from supernatant depletion and flux[alkalla2026 R9, R11, C37]
telaprevir with six bile saltsδ 11.5 and 28.8 set from the flux ratiopH 6.5, 37 °C[lu2017 R1]
enzalutamide above 42 µg/mLequal chemical potential in droplets and water; crystals can start in either phase or at the interfacepH 6.5[wilson2021 C3]
posaconazole droplets with HPMCASpolymer mixed into the droplets "serves to" lower the drug's chemical potential (not measured)pH 6.5shah2025 C46
ritonavir + lopinavir mixed drug-rich phasesfree RTV 14.2–15.8 and LPV 7.0–7.5 µg/mL at once and twice the single-drug onsets5 h[trasi2015b R16]
ritonavir with 180 µg/mL PVP, PAA, HPMC, HPMCASLLPS concentration unchanged, read as no change of the phase's activity37 °C[ilevbare2013d R10, C22]
tacrolimus solutions, 20–100 µg/mLflux plateau ≈0.0050–0.0055 µg/min from 60 µg/mLpH 4.5, 37 °C[trasi2016 R14]
resveratrol–HPMCAS solutionsup to ≈1610 µg/mL with flux ≈2.6–4.4 against 2.0 µg/min for the crystalpH 6.8, 37 °C[wegiel2015 R19, R20]
lopinavir with undissolved HPMCP, 15–85% drug≈0.6–10.5 against 17.4 µg/mLpH 3, 25 °C, 48 h[li2018 R3]
delamanid edisylate in HPMCP-55 against HPMCP-50, pH 1.6release ≈9% against ≈30% of the dose, polymer release ≈1–2% in both25% drug, 37 °C[nguyen2023c R11, R12]
Pitfalls and disagreements

A polymer mixing into the drug-rich phase is later reported to lower the drug's chemical potential and hence the amorphous solubility, as does a second drug in a co-amorphous system [ueda2020a C36; trasi2015b C36; alkalla2026 C12]. Ideal mixing was tested for one pair only [trasi2015a X9]. The chemical potential of the drug in the polymer-containing droplets was not measured in any of the polymer papers [ueda2020b X4; ueda2021 X5, X6]. The activity of telaprevir in the CA Sub-rich phase was not measured, so mixing and complexation are not separated mosqueragiraldo2018b X12. For the darunavir case the mixing is inferred; the centrifuged drug-rich phase was not analysed and the light-scattering onset with darunavir present was not measured (F20) [alkalla2026 X6]. A higher concentration is not a higher chemical potential in micellar media [jackson2016 C31]. In the two-drug dispersions the lower chemical potential is inferred, not measured [trasi2015b C36]. CAAdP 0.85 raised the ritonavir LLPS concentration by about 17%, unlike the other polymers [ilevbare2013d X7]. The lower chemical potential in the lopinavir dispersions is inferred from concentrations; χ was not measured and the model is used qualitatively [li2018 C46]. For delamanid in HPMCP-55 the authors invoke stronger or more extensive drug–polymer interactions lowering the chemical potential of the drug, which were not measured [nguyen2023c C41, C42].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

coating defect density

The number and size of pinholes, cracks and voids in an atomic layer coating through which water and medium reach the particle. It is the quantity the authors of the release papers hold responsible for whether a coating slows release: water enters through voids and defects, hydrates the particle, and the swelling substrate cracks the coating moseson2023 C58; "as long as defects were present" release of coated ritonavir–PVPVA powders was complete and rapid benson2025 C17. No paper measured defect density; it is inferred from the deposition regime and from sorption and release behaviour moseson2023 C15, X7; benson2025 X14.

Findings

F44, F45, F46, F47, F48.

Related concepts

the opposite of coating conformality; a property of the atomic layer coating; governs the moisture barrier effect and so wettability and release.

Formulas

none.

How it is measured or obtained

Not measured. Inferred from (i) deposition rate, with a slow rate (under 0.4 nm per cycle) taken to give fewer defects moseson2023 C50, C51; (ii) water uptake kinetics at 90% RH, near-zero uptake flagging a coating that lets little water in moseson2023 R8, C52; (iii) release that returns after the coating is broken, by cryomilling for 2 min or sonic sieving moseson2023 R19; benson2025 R9; (iv) SEM/EDX of particles incubated in buffer, showing cracks, buckling and flaking within 30–60 min for coatings that release normally moseson2023 R20, R21, R22, R23.

Values in the library
materialvalue or classconditionspaper ids
posaconazole–HPMCAS 50% DL, slow-deposited 26 nm (oxide 3.68%, the highest of twelve)uptake about 0.33% in 2 h against about 4.2–4.5%; release about 0.7 µg/mL at 3 h against about 3.35; intact coating at 60 minDVS 90% RH; pH 6.5; SEM/EDXmoseson2023 R1, R8, R15, R24
same, cryomilled 2 minrelease about 5.4 µg/mL at 60 min and about 6.55 at 180 minpH 6.5moseson2023 R19
posaconazole–HPMCAS 25% DL, 11–39 nm, average or fast growthabout 90% of the dose in 10–20 min; cracks and buckling after 30 min at pH 1.6 and 4.0pH 6.5 after acid; SEM/EDXmoseson2023 R9, R20, R21
ritonavir–PVPVA 20% DL slow-coated 20.5 nmuptake about 15.1% against about 20%; release plateau at 80% at pH 6.8 and in acid; sonic sieving restores hydrationDVS 3 h; powder release; confocalbenson2025 R3, R5, R6, R9
ritonavir–PVPVA, 9.3–28.3 nmseven of eight coated powders about 94–97% at 60 minpowder, pH 6.8benson2025 R4
same particles pressed into tabletsabout 35–75% at 60 min at pH 6.8, alike in 0.1 N HCl6 mm, 140 MPabenson2025 R10, R12
Pitfalls and disagreements

In the one blocked posaconazole sample slow growth, the highest oxide content and the small particle size coincide, and the intact coating is shown for one particle moseson2023 X7, X14. The recommendation of a thin coating "with a sufficient level of defects" is not a threshold found in the data: fast or average coatings of 23–39 nm released like uncoated particles moseson2023 C54, X16. Drying could also crack the coating in the SEM images moseson2023 X13. A second ritonavir sample (10% DL, 27 nm) levelled at about 85% for an unexplained reason benson2025 R4, X8.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

cold crystallization

Crystallization on heating a glass into its supercooled liquid (devitrification), as opposed to melt crystallization on cooling [lu2016 C2]. In the DSC classification it separates class II (crystallizes on reheating) from class III [baird2010 R1].

Findings

F7, F15.

Related concepts

process in supercooled liquid; contrasts with crystallization from the supercooled melt; measured by critical heating rate; related to glass stability and polymorphism.

Formulas

none.

How it is measured or obtained

As an exotherm on DSC reheating of a quenched glass, or by isothermal holds above Tg on a hot stage [lu2016 P2, P3; baird2010 P1]; the slowest heating that avoids it is the critical heating rate [baird2013 R9].

Values in the library
materialvalue or classconditionspaper ids
vemurafenib glassexotherms peaking at 157 and 217 °C, then α melting at 271.5 °CDSC at 10 °C/min[lu2016 R3]
11 class II moleculescrystallize on reheating at 10 °C/minDSC[baird2010 R1]
nifedipine glasscrystallized to a metastable form at 87 °C; felodipine did notheating at 2 °C/min[marsac2006a R5]
delamanid glassdevitrified just above Tgliquid-N2 quenchedduong2022a R3
propranolol saltsrecrystallization at 46.5–105.4 °C for four salts; none for nicardipine saltsDSC[towler2008 R4, C10]
rotary-evaporated drug–polymer powdersno exotherm on heatingDSC[vaneerdenbrugh2010b R10]
Pitfalls and disagreements

The polymorph formed on heating is often metastable and may convert later [lu2016 C54]. The rate at which the glass was made changes cold crystallization on reheating [baird2013 C28].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

competitive adsorption

Two additives competing for the same adsorption sites on a crystal, so that the pair does no better than the stronger one, or a surfactant displacing a polymer so that the polymer's inhibition is lost. Ilevbare and co-workers read the lack of any gain from adding HPMCAS or CAPh to CAP Adp 0.85 as competition for the same sites ("may compete"), and the loss of CAP Adp effectiveness with Tween 80 "most likely" as reduced polymer adsorption ilevbare2012a C39, C53. For felodipine, polymer in solution must compete with growth units for the active sites of the steps, and HPMCAS still adsorbed (phase images) when 100 µg/mL SDS had removed most of its inhibition [schram2016 C14, R17, R16]. New aspect (Mesoporous silica): two species competing for the same sites on a silica surface, so that one displaces the other. On silica the papers write three such exchanges: water against drug (adsorbed drug + solvent ⇌ adsorbed solvent + drug in solution), surfactant against drug, and a cation against a cationic drug at SiO⁻ sites; urea is used as a competitor for hydrogen bonds [dening2019 E9, E10, C5, C55; hate2020b C19, C21; dening2019 C16; mccarthy2020 C28]. Hate and co-workers explain the low uptake of atazanavir from water by water competing with drug for the surface [hate2020a C41]. The silica papers also note that in crystallization studies additives are described as competing for adsorption sites on a growing crystal [ilevbare2012a C33, C39; lu2018 C20].

Findings

Crystallization from solution: F17, F18, F24, F33, F43. Mesoporous silica: F5, F6, F9, F12.

Related concepts

related to synergistic crystallization inhibition, polymer-surfactant interaction and polymer adsorption; acts on drug-silanol hydrogen bonding and ionic interactions; part of the dynamic adsorption-desorption equilibrium; combined with micellar solubilization above the critical micelle concentration; reduces drug adsorption onto silica.

Formulas

none in the crystallization-from-solution papers; in the Mesoporous silica papers competitive solvent-drug adsorption equilibrium.

How it is measured or obtained

Not measured; it is inferred from growth-rate ratios of single additives and of pairs: a pair ratio at or below that of the better component points to shared sites, a pair above both to different sites or a complex ilevbare2012a R11, R17, C33. On silica it is measured directly, as adsorption or release with and without the competitor at fixed drug concentration: 5 M urea, 0.5 M urea, 50 mM triethylamine, Vit E TPGS or SDS below and above their CMC [dening2019 P4, P9; mccarthy2020 P9; hate2020b P3, P7].

Values in the library
materialvalue or classconditionspaper ids
CAP Adp 0.85 + HPMCAS; + CAPhpair 2.7; 2.85 against 3.0 for CAP Adp 0.85 aloneritonavir, S 7.6ilevbare2012a R11.j, R11.k
Tween 80 + CAP Adp 0.33; + CAP Adp 0.850.70; 0.83 against 1.64; 2.97 for the polymers alone and 0.53 for Tween 80 alone5 µg/mL each, S 7.6ilevbare2012a R17
HPMCAS 5 µg/mL ± SDS 100 µg/mL on felodipine seedsgrowth ratio 2.7 (HPMCAS), 1.07 (both), 0.81 (SDS)S 4, rotating disk[schram2016 R16]
telaprevir seeds with STDC and STCDC monomersboth adsorb with different effectiveness ("we can speculate"), giving intermediate growth inhibitionδ 7.9[lu2018 C20, C21, R5]
HPMC-AS in bile salt mediabile salts and lecithin "may" reduce polymer–drug interactionsix media[elkhabaz2021 C32]
ritonavir on SBA-15 + 5 M urea259 → 169 mg/gpH 6.8, initial 27.5 µg/mL[dening2019 R8]
indomethacin; methyl ester + 5 M urea12.4 → 6.1; 14.2 → 5.8 mg/gpH 2.2, activity about 0.2[mccarthy2020 R14]
ketoconazole; clozapine + 50 mM triethylamineabout 66 → 8.6; 53 → 25 mg/gpH 6.8[hate2020b R14]
ritonavir release + Vit E TPGS (28; 500 µg/mL)maximum 61; 69% against 50%; bound drug 90; 72 against 146 mg/gpH 6.8[dening2019 R17, R18, R19]
ritonavir release + SDS 28 µg/mLabout 50%; bound 135 mg/gpH 6.8[dening2019 R17, R19]
Pitfalls and disagreements

Two independent opposing effects (surfactant acceleration and polymer inhibition) would give the same pair ratios, so competition is untested ilevbare2012a X15. CAP Adp 0.85 with HPMCAS and CAPh lies in the SP range of HPMC, which did add to CAP Adp 0.85, so hydrophobicity does not explain the difference ilevbare2012a X8. Coverage with SDS was not quantified and the interfacial energy was not measured [schram2016 X8]. Mesoporous silica: the adsorption of the competitor itself (Vit E TPGS, triethylamine) on the silica was not measured [dening2019 C55; hate2020b X7]. Urea may lower adsorption by changing the drug's solubility and activity rather than by competing [dening2019 X12]. The "below monolayer" bound drug with Vit E TPGS depends on the drug load assumed [dening2019 X7]. The anionic SDS did not compete, which the authors attribute to repulsion from the negatively charged silica ("unlikely") [dening2019 C56]. The chapters differ in method: competition is inferred from growth-rate ratios on crystals ilevbare2012a X15 but measured as adsorbed amount on silica [dening2019 R8; hate2020b R14].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

conformational flexibility

The ability of a molecule to take different shapes by rotation about single bonds, counted in the library as the number of rotatable bonds [baird2010 P8]. More flexible molecules exist in the melt as many similar conformers, lowering the probability of the orientation needed to nucleate or grow, which is argued to raise glass-forming ability [baird2010 C59; vaneerdenbrugh2010a C37]. New aspect (Crystallization from solution): in solution crystallization the argument is turned around from the melt picture, as molecules with several low-energy forms (conformers or tautomers) are said to crystallize more slowly because only the right form joins a nucleus, which lowers the effective supersaturation of that form [hsieh2014 C31]. Ilevbare and co-workers attribute the slow nucleation of ritonavir, the largest molecule (720.9 g/mol), "most likely" to its higher molecular weight and greater conformational flexibility [ilevbare2013c C25, M1]. Among six dihydropyridines, rotatable bonds (6–11), molecular weight and polar surface area did not track the order of crystallization from the precipitate, and only cilnidipine stands out as larger and more flexible [raina2015b C31, M1–M6].

Findings

Crystallization tendency: F7, F13. Crystallization from solution: F3, F16, F21.

Related concepts

related to entropy of fusion and polymorphism; contributes to crystallization tendency; related to polymer chain stiffness.

Formulas

none.

How it is measured or obtained

Rotatable-bond counts from software or databases [baird2010 P8; baird2012 P7]; single-molecule conformer energy scans for one drug [trasi2014b P10]. In the solution papers not measured; rotatable-bond and tautomer counts are quoted: dipyridamole 12 rotatable bonds, warfarin 4; tautomers 6 (glyburide) and 9 (warfarin) [hsieh2014 X12, R19].

Values in the library
materialvalue or classconditionspaper ids
class I against class IIIrotatable bonds ≈−0.54 against ≈+0.66 SD51 molecules[baird2010 R22.a]
solvent classes I against III≈−0.42 against ≈+0.57 SD40 drugs[vaneerdenbrugh2010a R20.b]
ritonavir18 rotatable bonds, class IIImelt[baird2012 M34]
nilutamideone rotatable bond; crystal conformer at 54.4° against a computed minimum near 30°DFT, crystal structure[trasi2014b M1, R19, R24]
ritonavir in solution, against celecoxib and efavirenzslow nucleation attributed to higher MW and flexibility; induction time about 120 against 2.4 and 5.1 minaqueous buffer, 37 °C[ilevbare2013c R8, C25]
glyburide, warfarinseveral tautomers may explain slow crystallization; amorphous precipitates for at least 6 h with most polymerspH shift, 1 mg/mL polymer[hsieh2014 R4, R19, C31, C32]
papaverine, dipyridamolereduced conformational freedom proposed; crystalline with every polymer; papaverine adopts its crystal conformation in solutionpH shift[hsieh2014 R4, R19, C33]
six dihydropyridinesno correlation of rotatable bonds with the first crystalline time (0.25–12 h)10 mg/mL solvent shift[raina2015b R6, C31]
Pitfalls and disagreements

Conformer populations were never measured; the argument is inferred from class averages [baird2010 C59]. Nilutamide, with a single rotatable bond, is nonetheless a good glass former [trasi2014b C36]. In one solution study the rotatable-bond counts did not follow the conformational-freedom ranking used for dipyridamole and papaverine, and the argument rests on cited data [hsieh2014 X12]. Neither the ritonavir explanation nor the tautomer explanation was tested [ilevbare2013c C25; hsieh2014 C31]. Prediction from structure is called extremely difficult by the authors of the dihydropyridine study [raina2015b C6].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

congruent release

Drug and polymer leave a dispersion at the same normalised rate, so release is governed by the polymer; typical of low drug loading, and the condition for fast, complete release of a copovidone dispersion li2020 C63. Above a drug-specific loading release becomes incongruent and falls to roughly that of the neat amorphous drug (see limit of congruency). In the bicalutamide dispersion, congruent release at 5 and 10% DL went with escape from matrix crystallization; the authors conclude that it "may be a strategy to avoid" it, yet a congruently releasing dispersion with 3% SDS still lost one of three replicates moseson2022b C36, C48, C51. In the Peptide permeability papers: The criterion extends from two components to three, and from a small molecule to a peptide with its permeation enhancer: in an octreotide–SNAC–copovidone dispersion all three components released at one normalized rate, which the authors call synchronous release bapat2025b C3, C15. It also survives a component that is not amorphous: both enhancers stayed crystalline in the dispersions and were still carried out with the polymer, which the authors attribute "likely" to the gel-forming properties of copovidone bapat2025b R17, C44. A second usage appears in the same subcategory under the name corelease, judged not by rates but by the times at which each component reaches its maximum release from a tablet, which were about 30 min for insulin and about 10–20 min for the enhancer fagan2025 R20, C44, C46; see peptide-enhancer co-release. New aspect (Release mechanism and LoC): in the release-mechanism papers of 2017–2020 congruent release is read from drug and polymer assayed separately from a compact of constant area, as equal rates normalized to each component's weight fraction (no significant difference by t-test) or as overlapping percent-release curves saboo2019 R8, E4; indulkar2019a R3. Congruent dispersions keep releasing into a medium presaturated with drug, which the authors take as proof of polymer control indulkar2019a R12, C43; indulkar2017b C35. The 2017 ritonavir study ties the colloid to release that is "congruent or close to congruent" purohit2017b C52, and the 2019 dihydropyridine study calls congruent release the "sweet spot" of dispersion dissolution because only it gave drug-rich droplets ("a clear link") saboo2019 C30. Congruent release ends at the limit of congruency, which lay between 5 and 30% drug in PVPVA, and with HPMCAS or Eudragit S 100 it lasted to 50% felodipine que2019 C10; indulkar2019a C2; saboo2020a R15. The papers of 2020–2022 add that congruent release can end after minutes when crystals form on the dissolving surface (indomethacin methyl ester–PVPVA congruent at 5 min up to 25%, over 30 min only at 5%) saboo2020 R3, R8, C17, that at the limit the polymer controls release whatever the compound que2021 C39, and that congruent release at a limit raised by a surfactant is slower than at lower loadings (≈1.8 against ≈2.95–3.2 mg/min/cm² for felodipine with 5% TPGS) saboo2021 X3. For ritonavir at 30%, one loading above its limit, every surfactant built into the dispersion removed the lag phase and gave congruent release for at least 20 min, but only Span 85 and TPGS kept it congruent to about 87–95% at 90 min indulkar2022 C31, X14. For two phenolphthalein analogues in PVPVA the morphology of the two phases after separation "appears" to differentiate congruent from incongruent release; during congruent release the drug is carried into the diffusion boundary layer by swelling and release of the polymer chains deac2023a C46, C47. Below the limit the surface drug/polymer ratio of PHPH (5%) and MePHPH (30%) compacts stayed constant during dissolution, as it must if both components release in the dispersion ratio deac2023b C24, C58. The papers of 2023–2025 extend the reading to HPMCAS, where indomethacin, its ester and four weak bases released drug and polymer at matching normalized rates, so that release "appear[s] co-dependent" bapat2024 C10, C23, and to PVP, where congruency was counted as more than 80% of both components and congruent dispersions released more slowly with higher-molecular-weight grades deac2024a C36, C19. In the PVP paper droplets in the gel are held until the polymer is dilute enough to leave and then leave with it, so congruent release is limited by water penetration and the release of chains deac2024a C34.

Findings

ASD process: F21, F24, F38, F40, F48. Peptide permeability: F4, F5, F6. Release mechanism and LoC: F1, F2, F3, F4, F6, F11, F12, F13, F15, F17, F19, F21, F23, F24, F25, F26, F27, F29, F31, F32, F33.

Related concepts

ends at the limit of congruency; the opposite is incongruent release; belongs to polymer-controlled release; the three-component case for a peptide plus an enhancer is peptide-enhancer co-release; still bounded by the limit of congruency and opposed by incongruent release; the accelerating effect of a co-formulated enhancer connects it to water sorption of the excipient blend. Read by the intrinsic dissolution rate of each component; contradicts the Higuchi two-component dissolution model at low loading; the condition for drug-rich nanodroplets to form; ended early by surface crystallization; coupled to the polymer's own dissolution rate, which a cationic drug can lower through drug-polymer ionic interactions.

Formulas

The same surface-normalized rate is used, printed here as Eq. 1 with the medium volume in the numerator; see surface-normalized release rate bapat2025b E1. Also congruent release relation and saturated-medium condition.

How it is measured or obtained

Constant-area dissolution of compacts with drug and polymer both assayed, expressed as normalised release rates or as fractions released; in the ASD process papers the surface-normalised dissolution rate of ritonavir–PVPVA was used and the congruent boundary of 25% DL was cited from earlier work li2020 P9, E13, R23. In the Peptide permeability papers: As before by constant-area dissolution with every component assayed and converted to a normalized rate, here at 0.5 cm² in 100 mL of 50 mM pH 6.8 phosphate buffer at 37 °C, with reversed-phase HPLC for peptide and SNAC and aqueous size-exclusion chromatography for copovidone bapat2025b P4, P2, E1. The new practical limit is analytical: sodium decanoate could not be quantified at all, so in every decanoate dispersion congruence rests on the peptide and the polymer and the enhancer's co-release is inferred ("presumably") bapat2025b R6, C19, X1. In the release-mechanism papers: Wood's apparatus or a die with one face of about 0.5 cm², drug by HPLC or UV, polymer by size-exclusion chromatography, light-scattering detection or colorimetry, and the rate A = kV/(SN) for each component indulkar2019a P2, P3, P4; saboo2019 P9, P10; saboo2020a E3, P7; bhardwaj2018 P6, P7, E4. Later variants: 5-min rates sampled every minute saboo2020 P5; the last loading with simultaneous release and at least 80% of the drug in 90 min que2021 P9; t-tests of normalized rates yang2021 P17; drug release alone hiew2022b X6.

Values in the library
materialvalue or classconditionspaper ids
ritonavir–PVPVAcongruent up to 25% DL; at 40–50% DL drug release like neat amorphous drugcitedli2020 R23, C63
ritonavir–PVPVA spray-dried, 25% DLrate about 3.5 mg·min⁻¹·cm⁻¹ from methanol, falling to about 0.90 with 60:40 water:methanolpH 6.5, 100 rpmli2020 R10
ritonavir–PVPVA, 50% and 75% DLabout 0.003–0.006 mg·min⁻¹·cm⁻¹, near neat amorphous drug (about 0.0026)sameli2020 R10
ritonavir–PVPVA (outside)congruent up to 25% DL; polymer leaves first above ittabletsindulkar2019a C2
felodipine ASDs (outside)PVP and HPMC congruent to 10% DL, PVPVA to 15%; HPMCAS and EUDS congruent to 50% DL37 °Csaboo2020a C12, C14
BCL–PVPVA 5 and 10% DL, solvent evaporateddrug about 91 and 96% and polymer about 90 and 97% of the dose at 10 min; ends about 91 and 96%dose of at most 30 µg/mL, pH 6.8moseson2022b R6, R7
BCL–PVPVA 30% DL with 1.5% SDScongruent; more than 80% in 30 min, about 90–94% at 4 hsamemoseson2022b R9, R13
RTV–PVPVA 10 and 20% DL powders (below the limit of 25%)seven of eight coated powders about 94–97% at 60 minpH 6.8benson2025 R4
SNAC:copovidone 50:50congruent; ≈7.9 and ≈8.7 mg min⁻¹ cm⁻², about 4.4 and 2.7 times the neat rates; complete 25–30 minpH 6.8, 0.5 cm² compact, 37 °Cbapat2025b R2.d–e, R3, X18
octreotide:SNAC:copovidone, 1.6% peptidecongruent in three components; ≈8.1 / ≈8.4 / ≈8.9 mg min⁻¹ cm⁻²samebapat2025b R2.f–h, R5
octreotide:sodium decanoate:copovidone, 1.6% peptide≈23 and ≈25 mg min⁻¹ cm⁻² (peptide, polymer); complete in about 10 min; enhancer not assayedsamebapat2025b R2.j–k, R9, X1
SNAC:copovidone ratio seriescongruent within 30 min from 20:80 upward; 10:90 slower, complete within 40 minsame (SI, text only)bapat2025b R4, C14
sodium decanoate:copovidone ratio seriespolymer complete within about 10 min from 20:80 upward, by 25 min at 10:90same (SI, text only)bapat2025b R8, C18
cyclosporine:copovidone ± enhancer, 1.6% peptidepeptide follows polymer: about 50 min (binary), about 10 min (decanoate), ≈95% at 60 min (SNAC)samebapat2025b R10, C21
cyclosporine ternaries, 10–20% peptidenot congruent: polymer complete while peptide reaches ≈54.5% and ≈16% with decanoatesamebapat2025b R12.i, R13.i, C23
nifedipine 10 and 20% with HPMC-E5 or PVPVAcomplete release in ~20 and < 5 min, also into water saturated with drug5 °C, D2Oindulkar2017b R8, R9, C35
ritonavir 10:90 films, PVP, PVPVA, HPMCASdrug and polymer dissolved at the same rate; the polymer almost completely in < 10 min25 °C, pH 6.8purohit2017b C52, R15, R16, R17
ritonavir 50:50 HPMCAS filminitially congruent (≈32–34 µg/mL drug within 5 min)samepurohit2017b R17, C38
ITZ–PVPVA 10% spray-driednormalized drug ≈2000 against polymer ≈2265 µg/min/cm²0.1 N HCl, 37 °Cbhardwaj2018 R11
ritonavir–PVPVA 10, 20, 25% tablets≈97–100% of both by 60 minpH 6.8, 37 °Cindulkar2019a R3, R11
ledipasvir–PVPVA 2 and 5%about 100% of both by 60 minpH 6.8, 37 °Cque2019 R3, R4
ledipasvir–PVPVA with 5 parts SDS, 7.5–30%congruent to 30%; fails at 40%sameque2019 R7, R8, R9
nilvadipine 5–10%, cilnidipine 5–15% in PVPVAdrug 2.13–2.53 = polymer 2.35–2.76 mg/min/cm² (ns)pH 6.8, 37 °Csaboo2019 R5, R6, R8
felodipine with HPMCAS (10–50%) and EUDS (10–50%)drug = polymer at every loading; HPMCAS ≈0.13–0.93 mg/min/cm²pH 6.8; EUDS pH 7.4saboo2020a R14
nilvadipine, felodipine, cilnidipine 40% in HPMCAS0.42/0.42, 0.34/0.32, 0.26/0.24 mg/min/cm²samesaboo2020a R16
indomethacin; its methyl ester in PVPVAIND 5, 10%: ≈3.44/3.47, 3.14/3.19; INDester 5–25%: ≈3.3–4.2 mg/min/cm² (drug/polymer, 5 min)pH 2.1 / 6.8, 37 °Csaboo2020 R3, M5, M6
indomethacin methyl ester–PVPVA 10–25%congruent at first, drug levels off after 7.5–20 min30 min, 37 °Csaboo2020 R8
four phenolphthalein analogues at their limitsdrug ≈2.9–3.7, polymer ≈2.8–3.4 mg/min/cm² (p = 0.022–0.67)pH 6.8 (TIPP 2.5)que2021 R21, P9
felodipine–PVPVA with 2, 5, 10% TPGScongruent to 25, 35, 45%pH 6.8, 37 °Csaboo2021 R12, P6
loratadine–PVPVA; –HPMCASto 30% and 20% at 37 °C; 2% and 5% at 5 °Ccompacts, t-testyang2021 R22
clopidogrel–PVPVAclose to congruent to 40%; 50% with SDScompactscorreasoto2022a C46, C55
atazanavir–PVPVA5%; 10% with SDS or CTAB; 15% with Span 80compactscorreasoto2022b C12
ritonavir–PVPVA 30:70 with 5 parts Span 85, TPGS; SDS; Span 20; Tween 80congruent for at least 20 min with every surfactant; ≈87–89% (Span 85, TPGS), ≈78% (SDS), ≈41%, ≈25% of the drug at 90 minpH 6.8, 37 °Cindulkar2022 C31, R8, R9, R5, R7, R6
miconazole 20% on HP-50; on HP-50-Na; on PTEAincongruent and slow, drug ≈8.6% at 60 min; drug ≈89.5 and 83.7% at 60 min with the polymer aheadcompacts, 50 mM pH 6.8 phosphate, 37 °Cqi2022 R14, C22
ritonavir–PVPVA 20%; 30%; 40–50%congruent and complete; drug ≈35% with the polymer ahead; drug ≤3% at 90 mincompacts, pH 6.8, 37 °Cyang2022a R2, C12, C13
indomethacin–HPMCAS-MF 10%; its methyl ester 10%drug and polymer at the same normalized rate within error, ≈0.12 → 0.82 mg/min/cm² over 3–51 mM/ΔpH; rates comparablepH 6.8 phosphate and FaSSIFbapat2023 R9, R10, R13, C16
atazanavir–PVPVA 20% with TEAC, TBC, TBAC; at the limit, 25%drug ≈4.6–5.1 mg/min/cm²; ≈2.0–3.1 against neat PVPVA ≈2.7compacts, pH 6.8, 37 °Ccorreasoto2023 R6, R7, C13
MePHPH–PVPVA 20, 40, 50, 70%; PHPH–PVPVA 5, 20%drug ≈96 / 61 / 15 / 0%; ≈75 / 0% at 30 mincompacts, pH 6.8, 37 °Cdeac2023a R1, R2
PHPH–PVPVA 5%; MePHPH–PVPVA 30% compactssurface drug content constant over 60 minATR-FTIR of dried surfacesdeac2023b R6, R7
indomethacin, indomethacin methyl ester–HPMCAS-MF 5–60%drug ≈0.85 → 0.50 and 0.66 → 0.39 mg/min/cm² with the polymer alongsidecompacts, pH 6.8 phosphate, 37 °Cbapat2024 R2, R3, C10
loratadine 25% in HPMCAS LF, MF, HFdrug/polymer ≈0.25/0.27, 0.10/0.12, 0.01/0.02compacts, pH 6.8bapat2025a R2, C13
clotrimazole–PVP K25 20%, K29/32 30%, K60 35%, K90 38%congruent (>80% of both components)compacts, pH 8.0, 90–120 mindeac2024a R1, R2
ritonavir–PVPVA 30% + Span 20congruent for 20 min (≈48% drug, ≈50% polymer), then ≈92–97% drugcompacts, pH 6.8yang2023 R2, R3, C13
Pitfalls and disagreements

No numerical criterion is given for "congruent" in the ritonavir study indulkar2019a X7. Phase separation can raise or lower release depending on loading regime and on where the drug-rich phase ends up li2020 C64. The limit of the bicalutamide pair was not located and lies between 10 and 20% DL moseson2022b X15. A congruent SDS dispersion failed after milling moseson2022b C51. Peptide permeability: The loading boundary for a peptide is far lower than the values recorded for small molecules on this page: for cyclosporine in copovidone it lies between 1.6% and 5% peptide, and the paper gives neither a threshold nor a mechanism for the change bapat2025b C5, C22, C45. Congruence was asserted for systems where it was not computed: no normalized rate exists for any cyclosporine dispersion, and at 1.6% loading with SNAC the peptide in fact lagged (≈75.5% against ≈85% enhancer and ≈89.5% polymer at 30 min) bapat2025b X2, R10.f. The claim that a low peptide fraction removes the effect of peptide solubility holds for the decanoate ternaries but not for the SNAC ternaries bapat2025b C41, X3. The rates of the fastest systems rest on two or three points, because the compacts were nearly empty by the second sample bapat2025b X8. Several profiles plateau at ≈100–110% without a compact assay bapat2025b X9. Finally, congruent release of peptide and enhancer has not been shown to improve anything downstream: no permeability or absorption was measured bapat2025b C6; fagan2025 C45. In congruent dispersions the polymer still left more slowly than from a neat compact (2.35–2.76 against 3.49 mg/min/cm² for PVPVA; 0.22–0.29 of the neat rate for 10% ITZ), which the authors put "most likely" down to the drug's hydrophobicity or drug–polymer interactions saboo2019 R8, C13; bhardwaj2018 R12, C49. The link between congruency and droplets partly follows from how much drug had been released at the time of sampling saboo2019 X14. The neat PVPVA compact of the ledipasvir study weighed 250 mg against 100 mg for the dispersions que2019 X13. A congruency read-out over 5 min can miss later surface crystallization saboo2020 X7, and the criteria for the limit differ between papers que2021 P9; hiew2022b X6. For the miconazole dispersion on HP-50-Na the authors state polymer release "at the same normalized rate as the drug", but polymer percent release runs above drug release from 20 min (≈40.8 against ≈31.6%) qi2022 C22, X4. In the slowest HPMCAS-HF systems the drug left at about half the polymer's rate although the authors call release approximately congruent bapat2025a X6, C13. With SDS at 40% ritonavir release was already incongruent at 15 min, against the authors' "congruent" for the first 30 min yang2023 X4, C4.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

cosolvency

The change of a solute's solubility in a mixture of two solvents with their ratio; in this chapter water is an anti-solvent for hydrophobic drugs, and polymer plus sorbed water is treated as the drug's co-solvent inside a humid dispersion [marsac2008a C39, C26, C33; rumondor2009c C37].

Findings

F2, F10.

Related concepts

related to solid-liquid equilibrium solubility equation via activity coefficient; feeds supersaturation; related to Δχ effect.

Formulas

the log-linear cosolvency model of the 2008 paper is listed on the chapter page as table only.

How it is measured or obtained

Shake-flask solubility of the crystalline drug in a liquid analogue of the polymer (NMP for PVP), in water and in their mixtures at 25 °C, fitted with a log-linear cosolvency line; the water fraction of the polymer–water co-solvent is computed from sorption data [marsac2008a P8, E5, E6].

Values in the library
materialvalue or classconditionspaper ids
nifedipine, felodipine in NMP–watermole fraction 0.05 and 0.10 at 0% water; ≈0.015 and ≈0.017 at ≈24 wt% water25 °C[marsac2008a R12]
nifedipine with 10 and 25% PVPco-solvent 23 and 18 wt% water75% RH, 25 °C[marsac2008a R13]
felodipine with 10 and 25% PVP≈16 wt% water75% RH[marsac2008a R13.c, R13.d]
drug–PVP–water (argument)water–PVP "cosolvent" mixes less well with the drug as it takes up waterhumid dispersionsrumondor2009c C37, C44
drugs in PEO compacts (outside)water lowers solubility in the water–PEO co-solvent but enlarges the solvent volume94% RH[marsac2008b C33]

Evidence table: cosolvency.

Pitfalls and disagreements

The printed cosolvency fits do not reproduce their own points and cross at 16.5 rather than about 25 wt% water; the crossover rests on three water contents [marsac2008a X2, X3]. NMP stands in for PVP by assumption [marsac2008a C33, X4].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

Couchman-Karasz equation

An ideal-mixing prediction of the Tg of a miscible blend in which the constant is the ratio of the heat-capacity steps of the components at their Tg; a measured Tg below the line is read as non-ideal mixing [konno2006 E4, R7, C16; rumondor2009a E1, E2].

Findings

F5.

Related concepts

alternative to Gordon-Taylor equation; predicts glass transition temperature of a drug-polymer miscibility blend.

Formulas

the Gordon–Taylor form with a ΔCp-based constant; see Gordon-Taylor equation.

How it is measured or obtained

Calculated from the Tg and ΔCp of the pure components and compared with DSC Tgs of dispersions [konno2006 P5; marsac2006a R17].

Values in the library
materialvalue or classconditionspaper ids
felodipine with PVP, HPMCAS, HPMCHPMCAS and HPMC Tgs below the line at mid-range; PVP closeΔCp 0.33, 0.20, 0.31, 0.25 J/g/K[konno2006 R7, M1, M2, M3, M4]
nifedipine–PVP, felodipine–PVP"relatively ideal"DSC, 0–100 wt% PVP[marsac2006a R17, C21]
ketoconazole–PVP (outside)single Tg near the line at every ratioDSC[rumondor2009a R4]

Evidence table: Couchman-Karasz equation.

Pitfalls and disagreements

The 2006 felodipine paper prints the constant as \Delta C_{p1}/\Delta C_{p2}, and neither orientation reproduces its plotted lines; a logarithmic form evaluated with Tg in °C comes close, but the paper does not print it [konno2006 X4]. Ideality conclusions therefore depend on which form was used.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

critical entanglement molecular weight

Evidence table: critical entanglement molecular weight (names merged there: critical entanglement molecular weight, critical molecular weight for entanglement). Content from the release-mechanism chapter (2023–2025).

The molecular weight above which chains of a polymer entangle. Polymers above it are expected to form a gel layer in a good solvent because solvent penetrates faster than the chains disentangle; polymers near or below it may still form a swollen gel through viscosity effects (cited) bapat2023 C34. HPMCAS-MF, of about 18,000 Da, is below the critical values estimated for other polysaccharides, which with the rotation data led the authors to judge it "unlikely" to entangle bapat2023 C45. The 2024 PVP paper computes M_c \approx 30\,C_\infty M_0 = 46,620 g/mol for PVP (C_\infty = 14, M_0 = 111 g/mol), between K25 and K29/32, and places the rise of the clotrimazole limit from 20 to about 33% close to it deac2024a E1, C16, C37.

Findings

Release mechanism and LoC: F23, F29.

Related concepts

threshold for polymer chain entanglement; decides whether dissolution goes through polymer chain disentanglement in a gel layer.

Formulas

critical molecular weight for chain entanglement.

How it is measured or obtained

Taken from estimates for other polysaccharides, without a reference bapat2023 R27.

Values in the library
materialvalue or classconditionspaper ids
pullulan; curdlan; xanthan≈22; 24; 34 kDa (estimates, no reference given)bapat2023 R27
HPMCAS-MF≈18 kDabapat2023 C45
PVPM_c = 46,620 g/molWool estimatedeac2024a E1
Pitfalls and disagreements

The polysaccharide values carry no reference, and no value for HPMCAS itself is given bapat2023 R27. K25, below M_c, already reached a limit of 20%, so the rise spans K17 to K29/32 deac2024a X9.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

critical ionization for polymer dissolution

Evidence table: critical ionization for polymer dissolution (names merged there: critical ionization, critical ionization extent, critical ionization fraction, polymer ionization threshold). Content from the release-mechanism chapter (2022–2025), with rows from the Miscibility and drug-polymer interactions chapter.

The minimum fraction of the acid groups of an enteric polymer that must be ionized before its chains dissolve; below it the polymer does not dissolve, or dissolves slowly, whatever the bulk pH. In the Miscibility chapter it was written with the Willson model, dissolution rate ∝ [A⁻]/[HA], and used to explain why CAP and HPMCP dispersions with a basic drug that ties up some acid groups release poorly or slowly hiew2022a E2, C57. For HP-50 the critical ionization of about 83% taken from that work "may explain" the almost 2-fold drop of the dissolution rate of BIS-TRIS salts from 100 to 80% ionization, "perhaps" because hydrophobic ionizable polymers need a minimum ionization to dissolve qi2022 C36, R19. For HPMCAS-MF no polymer dissolved in FeSSIF V1 at pH 5.0, "presumably" because the threshold ionization was not reached, and near the threshold pH (FeSSIF-V2, pH 5.8) dissolution was slower than in phosphate of corresponding buffer capacity bapat2023 C14, C12. The 2025 papers apply the model to drug–polymer complexes: a drug that binds the carboxylates and blocks their hydration "can impact" dissolution, the more succinoylated HPMCAS-LF is proposed to need less ionization to dissolve by analogy with maleic anhydride copolymers, and about 77% ionization is estimated for HPMCAS from a threshold pH of 5.5 bapat2025a C2, C3, C25; kaur2025 C28, C46.

Findings

Release mechanism and LoC: F23, F24, F32, F33.

Related concepts

a threshold of polymer ionization and of ionization; reached or not according to the microenvironmental pH and the polymer pKa; bypassed by polymer salt formation; behind the pH-dependent polymer solubility of enteric polymers.

Formulas

The Willson relation is printed only in the Miscibility chapter hiew2022a E2; no shared formula page.

How it is measured or obtained

By extrapolating literature dissolution data of the neat polymer against the ionized fraction or pH hiew2022a R27; indirectly, from dissolution of partially neutralized salts against the amount of base added qi2022 R13 or from media of different pH bapat2023 R5, R8.

Values in the library
materialvalue or classconditionspaper ids
CAP; HPMCP (Miscibility chapter)≈0.94; slightly less than 0.83extrapolated from literature datahiew2022a R27
HP-50 (HPMCP)≈83% (cited)qi2022 R19
HP-50-BIS-TRIS salts, 20–100 mol% baserate ≈1.22 → 2.93 mg/min/cm², largest step from 80 to 100%50 mM pH 6.8 phosphateqi2022 R13
neat HPMCAS-MF in FeSSIF V1no dissolutionpH 5.0bapat2023 R8
HPMCAS (pKa ≈5.0), threshold pH 5.5≈77% ionization to start dissolvingestimatekaur2025 C28
HPMCAS LF, MF, HF1.52, 1.19 (cited), 0.76 mmol/g COOH; pKa 4.91, 4.97, 5.06titrationbapat2025a M3, M4, M5
Pitfalls and disagreements

The ionization of the partial BIS-TRIS salts was not measured: the axis is mol% base added, read as % ionization, and the 0% point is HP-50 in sodium phosphate buffer, not a salt qi2022 X9. The HPMCP value comes from an extrapolation whose relation is not printed hiew2022a R27. The critical ionization of the grades was not measured; the LF argument is an analogy bapat2025a X11. The acid content of HPMCAS-LF is 1.52 ± 0.03 mmol/g as titrated in the grade paper and 1.54 mmol/g (printed as mM per gram) as cited in the bedaquiline paper bapat2025a M3; kaur2025 M2.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

critical micelle concentration

The surfactant concentration above which micelles form; Tween 80 was used above its CMC of 23.6 µg/mL (0.018 mM) ilevbare2013a M11. The authors also invoke the U-shaped temperature dependence of surfactant CMCs (minimum typically at 20–40 °C) as an analogy for the U-shaped LLPS concentration of ritonavir ilevbare2013a C47. The papers of 2017–2022 add that the CMC of SDS in 50 mM pH 6.8 phosphate at 37 °C was 0.5 mg/mL against 2.4 mg/mL in water, attributed to ionic strength, with aggregation numbers of 60, 58 and 65 at 1, 2 and 3.6 mg/mL indulkar2017a R1, R2, R3, C10. The six bile salts have reported CMCs of 2–12 mM, and 1.86 and 12 mM were taken as monomeric and micellar levels, assuming telaprevir does not shift the CMC [lu2017b C42, M3]. New aspect (Bioperformance): above the CMC the micelles begin to solubilize drug, so the CMC marks where solubilization starts [raina2015c A2]. New aspect (Crystallization from solution): the binary-additive study kept both surfactants far below their CMC so that micellar solubilization was excluded and any effect on growth had to come from adsorption at the crystal interface: Tween 80 at about 0.018 mM (about 24 µg/mL) and TPGS at 0.02 wt% (printed as about 212 µg/mL) against 5 µg/mL used ilevbare2012a M16, M17, C52. Other CMCs used: STC 0.97% and SDS 0.24% in water (cited); STC 0.48% and SGC 0.46% w/v in the presence of celecoxib (about 8.9 and 9.4 mM by the card's conversion) [chen2015 M1, M4; li2016a R12, X16]. New aspect (Supersaturation from ASD dissolution): in the celecoxib suspension study the CMC is read with the drug present at saturation, because a drug can shift it: the break point where two straight lines of solubility against surfactant concentration meet chen2015a P8, E2. With lopinavir at saturation in pH 3 citrate buffer the CMCs were lower than with celecoxib in pH 3 HCl (SDS 0.050 against 0.23%), and dissolved polymer moved them: HPMCP shifted the SDS break to about 0.1%, and with PVPVA and HPMCAS-HF the lopinavir solubility rose from about 0.025% SDS [li2016b R1, R11, R18, X9; chen2015a R4]. New aspect (Release mechanism and LoC): for surfactants built into a dispersion, the CMC is the reference for whether the released surfactant can solubilize drug in the bulk medium; in the ledipasvir study the surfactant concentration after complete release stayed below the reported CMCs, so bulk solubilization is taken as negligible que2019 C51. With TPGS in felodipine dispersions and four surfactants with clopidogrel the CMC was measured in the release medium with and without dissolved polymer saboo2021 R1; correasoto2022a R1; 2% TPGS raised the felodipine limit while the released TPGS stayed below the CMC, so micelles play "a negligible role" saboo2021 C33.

Findings

Amorphous solubility and LLPS: F9, F12, F17, F18. Bioperformance: F3, F9, F22. Crystallization from solution: F18, F28, F29, F31, F32, F38, F39. Supersaturation from ASD dissolution: F14, F19. Release mechanism and LoC: F13, F21.

Related concepts

defines micellar solubilization; analogy used for liquid-liquid phase separation of ritonavir. Limits the micelle-water partition coefficient. Related to polymer-surfactant interaction, interfacial tension and hemimicelle; related to surfactant-induced crystallization; related to the hydrophilic-lipophilic balance of the surfactants.

Formulas

CMC from the solubilization break point (printed in words; no shared page) chen2015a E2.

How it is measured or obtained

The Tween 80 value is a footnote of Table 7 and not measured in the paper ilevbare2013a M11. Emission maximum of pyrene carboxaldehyde against SDS concentration, and static quenching of pyrene by dodecyl pyridinium chloride for the aggregation number indulkar2017a P1, P2; in a companion paper surface tension with 60 µg/mL telaprevir gave about 4 mM for STC and about 2 mM for SGDC [lu2017 R5]. In the additive study the CMC was taken from the literature [raina2015c A2]; elsewhere it was read from pyrene emission, surface tension or solubility breaks indulkar2017a R1, R2. In the PAMPA study of hate2022 it was measured by pyrene fluorescence for SDS and CTAB in a buffer at 37 °C hate2022 R12. In the binary-additive study not measured; the CMC values are literature values at 37 °C ilevbare2012a M16, M17. In the bile-salt papers from celecoxib solubility against bile salt concentration (intercept of two lines) or surface tension against log concentration [li2016a P7; lu2017 P5]. In the celecoxib suspension study: from Form III solubility at a series of surfactant levels in pH 3 HCl, 25 °C chen2015a P6, P8. In the release-mechanism papers: Cited CMCs compared with the surfactant delivered by the dose que2019 C51, X19. Drug solubility against surfactant level and the pyrene I1/I3 ratio, with 900 µg/mL PVPVA giving a critical aggregation concentration saboo2021 P1, P2; pyrene and Wilhelmy surface tension correasoto2022a P4, P5.

Values in the library
materialvalue or classconditionspaper ids
Tween 80CMC 23.6 µg/mL (0.018 mM)used at 500 µg/mLilevbare2013a M11, R16
SDSCMC 0.5 mg/mL (buffer); 2.4 mg/mL (water, cited); Nagg 58–6550 mM pH 6.8 phosphate, 37 °Cindulkar2017a R1, R2, R3
STC; SGDCCMC about 4 mM; about 2 mMpH 6.5 buffer, 37 °C, with and without 60 µg/mL telaprevir[lu2017 R5]
Vit E TPGS / Cremophor EL / RH40 / Tween 200.02 / 0.01 / 0.03 / 0.009%levels C1–C3 chosen around it[raina2015c A2]
SDS in the telaprevir ASDfinal about 15 µg/mL, far below CMC37 °Cmosqueragiraldo2018b R21, C48
taurocholate, glycocholate0.48% and 0.46% (w/v)pH 6.5[li2016a R12]
SDS; CTABSDS 0.5 mg/mL (0.05% w/v); CTAB 0.05 mg/mLpyrene fluorescence, 37 °C, bufferhate2022 R12
SDS in the PAMPA receiversink effect from 0.15%, no further rise up to 2%atazanavir 150 µg/mLhate2022 R13, C29
Tween 80CMC 0.018 mM, about 24 µg/mL5 µg/mL used (about a fifth)ilevbare2012a M17, R17
TPGSCMC 0.02 wt%, printed as about 212 µg/mL (about 200 µg/mL at unit density)5 µg/mL usedilevbare2012a M16, X16
TPGS with and without 900 µg/mL PVPVA (ASD dissolution chapter)about 50 µg/mL; about 40 µg/mL with PVPVA (49 ± 4 and 41 ± 3 µg/mL as printed)pH 6.8, 100 mM buffer, 37 °Csaboo2021 R1
SDS in 50 mM phosphate pH 6.8CMC 0.5 mg/mL (cited); induction-time effect from about 0.075 mg/mL, none further above the CMCatazanavir, 37 °C[indulkar2019b M2, R3]
SDS with 1 mg/mL polymercritical aggregation concentration 0.1 (PVPVA), 0.2 mg/mL (HPMC-606, HPMCAS-MF)pyrene I1/I3, no drug[indulkar2019b R8]
lyso-PC against PClower CMC and higher surface activity (cited)reasoning for faster nucleation with digests[enright2020 C22]
SDS with celecoxib at saturation0.23%pH 3, 25 °Cchen2015a R4
STC0.69% in the text, 0.668% on the figuresamechen2015a R4, X1
polysorbate 80; Poloxamer 188; Triton X1000.0058%; 0.16%; 0.022%samechen2015a R4
SDS / Poloxamer 188 / polysorbate 80 / STC with lopinavir0.050 / 1.40 / 0.020 / 0.73%pH 3 citrate, 25 °C[li2016b R1]
SDS with lopinavir and HPMCPbreak near 0.1%pH 3, 25 °C[li2016b R11]
ledipasvir–PVPVA with 5 parts surfactant per 100at most ≈0.048 mg/mL surfactant in the medium after complete release (synthesis: 0.048/0.5 ≈ 0.1 of the SDS CMC in buffer indulkar2017a R1)100 mg compacts, pH 6.8que2019 X19
SDS, CTAB, TPGS, Tween 80487 ± 34, 50, 40, ≈14 µg/mL50 mM pH 6.8, 37 °Ccorreasoto2022a R1
SDS, CTAB, TPGS, Tween 80, Span 20, Span 80, Span 85500, 50, 40, 14, 7.3, 14, 5–50 µg/mLas listedcorreasoto2022b M3, M4, M5, M6, M7, M8, M9
Pitfalls and disagreements

The micelle-like origin of the ritonavir profile is "surmised", with no structural data ilevbare2013a C47. The CMC of the other four bile salts in the telaprevir medium was not measured, and the CMC of SDS in buffer is lower than in water [lu2017 C14; indulkar2017a C10]. The CMC basis (w/v or w/w) and source are not printed in Table I of the additive study [raina2015c A2]. In the PAMPA study the receiver sink effect is said to be available at 0.15% SDS, three times the CMC read by pyrene (0.05%); whether 0.15% is a tested level or a misprint is unclear hate2022 R12, R13, X6. The two printed TPGS values (212 and about 200 µg/mL) agree only at unit density; both are far above the 5 µg/mL used ilevbare2012a X16. Ritonavir solubility in 5 µg/mL Tween 80 was 1.3 ± 0.02 µg/mL, so no solubilization is expected below the CMC ilevbare2012a R1.g. Most dihydroxy conjugates and SLC have literature CMCs at or below the 1.86–2.51 mM used, so the monomer assumption is uncertain; CMCs were measured for two bile salts only in the telaprevir study [li2016a X16; lu2017 X7]. The Poloxamer 188 CMC rests on solubility changes of 0.1–0.2 µg/mL and is weakly determined chen2015a X20. The test levels lie 6–14% above the printed CMCs, not exactly 11% chen2015a X2. SDS and STC acted below their CMC as well chen2015a C6. The authors place an aggregation onset with PVPVA below 0.01% SDS, whereas the plotted rise begins between 0.01 and 0.025% [li2016b X9]. Below the CMC in the bulk, the surfactant concentration at the dissolving surface was not known que2019 C53. Only about half the TPGS had been released at 60 min, so the bulk stayed below the CMC in every felodipine case saboo2021 X14; one paper prints the TPGS CMC as 40 and as about 50 µg/mL correasoto2022a X1.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

critical point

Evidence table: critical point (names merged there: critical point, plait point). Content from the release-mechanism chapter (2023–2025).

The point on the binodal of a ternary diagram at which the two coexisting phases have the same composition; the 2023 dissolution papers call it the plait point. Because the volume of the hydrophobic phase decides whether it forms a network, a hydration path entering the two-phase region on the high-drug side of the plait point (through the hydrophobic binodal) makes the hydrophobic phase the majority and "should" give a continuous network, one entering on the other side a discrete phase; the plait point position therefore approximates the maximum limit of congruency of a system deac2023a C68. Associative systems have the plait point on the low-drug side and can have a low maximum limit, segregative systems on the high-drug side and a higher one, and a smaller miscibility gap also favours a higher maximum limit deac2023a C69. Strong drug–polymer interactions are proposed to lower the limit by shifting the plait point to a lower drug/polymer ratio, which raises the polymer content of the hydrophobic binode and the hydrophobic-phase volume at a given load deac2023b C63, C49. In 2024 the critical point was computed for the four analogues, the drug-rich fraction jumping across it, and its loading followed the cited limits in order, so the authors propose it as "a surrogate" for phase inversion and the limit deac2024b R35, R37, C64.

Findings

Release mechanism and LoC: F27, F30.

Related concepts

end point of the binodal and of the tie lines on the ternary phase diagram; sets the step of the lever rule; shifted by associative phase separation; approximates the maximum limit of congruency.

Formulas

none.

How it is measured or obtained

Not measured in these papers; placed on schematic diagrams deac2023b X14. Computed in 2024 with PC-SAFT for four drug–PVPVA–water systems; not measured deac2024b P19, X7.

Values in the library
materialvalue or classconditionspaper ids
associative phenolphthalein analogues (PHPH, TIPP)plait point on the low-drug side, low limit (5, 10%, cited)schematicdeac2023b C49, R8
segregative analogues (MeTIPP, MePHPH)plait point on the high-drug side, higher limit (30, 40%, cited)schematicdeac2023b C48, R8
MePHPH–PVPVA–water≈29 wt% drug, 59 wt% PVPVA, 12 wt% water (≈33% loading)PC-SAFT, 37 °Cdeac2024b R22, R35
PHPH–PVPVA–water≈2.6 wt% drug, 59.5 wt% PVPVA, 38 wt% water (≈4.2% loading read from the diagram, synthesis: 2.6/(2.6 + 59.5) ≈ 0.042; 3.7% as the paper states)samedeac2024b R23, R35
four analogues≈33.2 / 32.6 / 13.7 / 3.7% loading against cited limits 40 / 30 / 10 / 5%samedeac2024b R37
Pitfalls and disagreements

The central mechanism of the 2023 paper is drawn on schematic diagrams, one with horizontal tie lines; no diagram, tie line or plait point was measured and the link to the limit rests on the rank order of four analogues deac2023b X14. For PHPH the computed critical point (3.7%) lies below the film switch (10–15%) of the same paper deac2024b X5. Two values stand for the PHPH critical point: the paper states 3.7% loading, while the point read from its PHPH–PVPVA–water diagram (about 2.6 wt% PHPH, 59.5 wt% PVPVA) corresponds to about 4.2% (synthesis: 2.6/(2.6 + 59.5) ≈ 0.042), a difference within the precision of reading the plot deac2024b R23, R35, R37.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

crystal dissolution into a polymer melt

The process by which drug crystals suspended in a softened polymer dissolve into it, below the drug's melting point and above the polymer Tg, forming the homogeneous melt that becomes an ASD on cooling. It is usually described by the Noyes–Whitney equation with a diffusion boundary layer [moseson2018 C50, C52; moseson2019 C39, C40]. Crystals also break up while dissolving (fragmentation-based dissolution), which the diffusion picture does not contain [moseson2019 C43, C44]. A crystalline physical mixture lags a dispersion in thermogravimetry when the crystals are large, because the crystals must first dissolve at a rate set by particle size and the drug then diffuse through the viscous melt; in DSC of miscible extrudates this process appears as a dissolution endotherm instead of a melting peak [moseson2020 C33, R13; moseson2021 C12]. At Tc the melt is most viscous, diffusion slowest and the gradient smallest, so differences between lots of input crystals show most there [moseson2022c C37, C39, C40]. A model with dissolution alone cannot finish within 20 min, whereas one with breakage scaled by the share of agglomerates fits four lots [moseson2022c R12, R16].

Findings

F9, F11, F12, F13, F10, F31, F36, F37.

Related concepts

limited by the diffusion boundary layer; includes fragmentation-based dissolution; governed by the HME operating design space; leaves residual crystallinity.

Formulas

Noyes–Whitney equation, Stokes–Einstein equation.

How it is measured or obtained

Isothermal hot-stage microscopy without mixing (time to loss of birefringence), variable-temperature XRD, SEM-EDX chlorine maps of drug in the polymer and TEM of films held at temperature [moseson2018 P10, R13; moseson2019 P3, P4, P5, P6, P7]. Nonisothermal TGA of a dispersion against crystalline physical mixtures with micronized (3.5 µm) or large (93 µm) crystals [moseson2020 P3, R13]; the broad endothermic shift of the non-reversing heat flow over 120–170 °C of a 30% crystalline extrudate [moseson2021 R7]. Residence-time series in a 5 mL recirculating micro-extruder (50 rpm, 145 ± 1 °C, 2–20 min) read by PXRD, with a population balance model fitted to the crystallinity [moseson2022c P15, P16, P18, P19].

Values in the library
materialvalue or classconditionspaper ids
IDM in PVPVA (117-2 powder, no mixing)≈0.01 h at 161 °C; ≈0.32 h at 138 °C; ≈1.86 h at 131 °C; ≈7.8 h at 126 °C; ≈20.2 h at 121 °Chot stage, n = 3[moseson2018 R13]
IDM crystals in copovidone 1:5 at 130 °Cgradient about 7–9 µm after 1 h; plateau about 2.8–3.1 atomic % Cl over about 31–73 µmSEM-EDX[moseson2019 R9]
IDM extrudate at Tcdefective crystals <100 nm, amorphous channels, a dissolution frontTEM[moseson2018a R9, R13, R14]
30/70 BCL–PVPVA, mixtures against the dispersion3.5 µm mixture tracks the dispersion; 93 µm mixture lags by about 10 °C at 1–10 °C/minnonisothermal TGA[moseson2020 R13]
diffusion layer of an IDM crystal in a polymer film (cited)on the order of 8 µmhigh temperature, quiescent[moseson2020 R21]
30:70 BCL–PVPVA extrudates at 155 °C from 3.5, 38 and 93 µm crystalsbelow 1%, 3.5% and 30% crystals left5 mL extruder[moseson2021 R6, M2, M3]
30% BCL–PVPVA at Tc = 145 °C, lots of D50 3.51 / 37.0 / 38.0 / 42.2 / 92.7 µmbelow the limit of detection at 2 / 5 / 6 min; about 2.5% and 15.0% at 20 min for the last twoPXRD[moseson2022c R10, R1]
population balance model, dissolution only26–73% crystallinity left at 20 min with 0.5 µm/s; 3–61% with 4 µm/sfour lots[moseson2022c R12]
same with breakage scaled by % agglomeratesdissolution rate constant 0.1002 ± 0.0511 µm/s; breakage rate constant 0.355 ± 0.111fitted to PXRD[moseson2022c R16]
BCL crystals in PVPVA film, 170 °C, no mixingthe rough-surfaced crystal splits at 10–15 min; the agglomerate breaks apart; fines of the milled lot vanish while a large crystal barely changeshot-stage PLM[moseson2022c R11]
Pitfalls and disagreements

The hot-stage sample was a partly dissolved extrudate, not a physical mixture [moseson2018 X8]. Between Tc and Tm dissolution was slower than melting because of lower thermal input, higher viscosity and no mixing [moseson2018 C33]. The nanoscale sequence of fragmentation is assembled from different particles [moseson2019 X11]. In DSC of miscible extrudates the crystals dissolve during the scan, so DSC under-reads them [moseson2021 C12, C36]. The fitted dissolution rate constant lies 5–40 times below the assumed values (0.5 and 4 µm/s), which the authors relate to melt viscosity; the printed sign conventions disagree and the size-dependence parameters are undetermined [moseson2022c R16, C30, X11, X21]. The supporting images are quiescent PLM at 170 °C, 25 °C above the melt temperature of the extrusions [moseson2022c X18].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

crystal growth inhibition

Reduction of the crystal growth rate by an additive, here dissolved PVPVA or HPMCAS, expressed as the effectiveness ratio E_G=R_{G,np}/R_{G,p}, the growth rate without polymer over the rate with it [moseson2020a E2; moseson2021 E1]. The mechanism proposed is surface poisoning: polymer globules adsorb on the crystal face and the adsorbed network "appears to limit the sites available for molecular integration" [moseson2020a C48, C50]. HPMCAS at nine times the drug concentration slowed seeded growth of posaconazole in FaSSIF V2 but did not stop it at 100 µg/mL drug: 10 µg/mL seeds left 43.5% at 30 min against 4.5% without polymer [shah2024 R22]. New aspect (Crystallization from solution): The slowing of the growth of drug crystals in a supersaturated aqueous solution by a dissolved additive, usually a polymer, expressed as the ratio of the initial growth rate without additive to that with it, E_g = R_{g0}/R_{gp}; above 1 the additive inhibits growth, below 1 it accelerates it [ilevbare2013b E5; ilevbare2012a E3, E4]. In these papers it is a kinetic effect at constant solubility, shown by solubility controls with the polymer [ilevbare2012c R1, C16]. It is the solution counterpart of the growth inhibition in supercooled liquids described below and is one of two steps of crystallization inhibition, the other being nucleation inhibition. Seeded growth ratios now include HPMCAS on felodipine (2.29 at pH 6.8, 1.28 at pH 3, and 2.7 to 12 depending on how the seeds were made) and bile salts on telaprevir seeds (E_G 1.0–4.6; complete stop with monomeric STCDC) [schram2015 R4; schram2016 R2; lu2017a R7, R10]. New aspect (Supersaturation from ASD dissolution): the 2008 felodipine study reads a flat concentration after an initial drop as growth inhibition: the drop takes the solution from the labile into the metastable zone ("it appears"), where only growth could lower the concentration further, so a plateau "strongly suggests" inhibited growth [konno2008a C27, C26]. The 2011 study reads slower growth of particles with HPMC than with PVP the same way alonzo2011 C18. For celecoxib, seeded desupersaturation with HPMCAS gave growth ratios R_0/R_p of about 70–158, less inhibition at the higher supersaturation, against an estimated nucleation ratio of ~4000, so both steps were slowed but nucleation far more ("it can be surmised") xie2016a R12, R13, C37, C40; the slow growth explains why crystals formed in dissolving PAA particles did not empty a medium holding HPMCAS xie2016a C36. In the supercooled liquid (formerly the page "crystal growth inhibition by polymers", from Crystallization tendency and Miscibility and drug-polymer interactions): the reduction of the crystal growth rate of a drug by a polymer dissolved in its supercooled liquid; the extent is thought to depend on specific drug–polymer interactions such as hydrogen bonding, and at higher levels on the polymer's effect on mobility [trasi2014a C33; trasi2014b C19]. The inhibition depends on the chemistry of the polymer at low levels, where it changes neither the Tg nor the melting point of the drug: at 3% w/w felodipine growth was slowed in the order PVP > PVP/VA > HPMCAS > PVAc [kestur2010a C17, C32, C36]. The factor is not a constant of the polymer: it grows as the temperature falls toward Tg and with polymer content [kestur2010a C12, R6, R8], and the best polymer depends on the drug (PAA for bifonazole, PVP and PVP/VA for nimesulide at low temperature) [kestur2011 C9, C10, C29]. The authors tie the order to the strength or extent of drug–polymer hydrogen bonding and propose, as a "speculation", that crystal growth needs the drug to demix from the polymer at the growth front [kestur2010a C40, C42].

Findings

ASD process: F25, F27, F29, F41. Crystallization from solution: F5, F6, F7, F8, F9, F10, F11, F12, F17, F18, F20, F23, F24, F27, F33. Supersaturation from ASD dissolution: F4, F5, F16, F22. Crystallization tendency: F19. Miscibility and drug-polymer interactions: F10, F11, F12, F13, F14, F17.

Related concepts

part of crystallization inhibition by polymers; acts on crystal seeding; slows desupersaturation; related to crystal growth rate; part of crystallization inhibition; contrasts with nucleation inhibition and with polymer effects on nucleation; related to polymer adsorption on crystal surfaces, step pinning and physical stability; contrasts with the polymer's effect on antiplasticization and thermodynamic driving force for crystallization; depends on hydrogen bonding and intramolecular hydrogen bonding.

Formulas

crystal growth inhibition effectiveness ratio, power-law crystal growth rate, initial growth rate from the desupersaturation slope, Kubota-Mullin model, overall mass crystal growth rate, relative nucleation rate from seeded and unseeded induction times, viscosity-limited normal growth law.

How it is measured or obtained

Seeded growth from a supersaturated solution at a stated supersaturation and polymer concentration, with the growth rate from the desupersaturation profile; adsorption by AFM in liquid (globule spacing) and crystal habit by SEM [moseson2020a P10, P15, P16; moseson2021 P12]. In the crystallization-from-solution papers: Seeded desupersaturation: a fixed mass of seed crystals (0.010 g in 50 mL for ritonavir, celecoxib and efavirenz; about 2.5 mg in 18 mL for felodipine) is placed in buffer with predissolved polymer, supersaturation is created by adding drug in methanol, and a fibre-optic UV probe on second-derivative spectra gives the slope of the first 2 min (5 min for felodipine) as the growth rate [ilevbare2013b P10; alonzo2012 P4]. Eg is the ratio of slopes, in triplicate [ilevbare2012c P12]. Rates can be normalized by seed mass and BET area [ilevbare2013b E6]. Unseeded controls and turbidity checks test that the slope is growth [ilevbare2012a R9; ilevbare2013b R5]. Rotating-disc seeds (felodipine) and seeds grown in situ in the vessel (telaprevir); the ratio is R_0/R [schram2015 P2; schram2016 P5; lu2017a P1, P2]. In the ASD dissolution papers: initial slopes of desupersaturation curves with equal crystal surface areas assumed (Eq. 5) [konno2008a E5, P6, C28]; particle size against time by light scattering alonzo2011 P5; seeded desupersaturation with 7 mg seeds in 50 mL, initial slope without polymer against the slope over 16 h with polymer xie2016a P4, P11. In the supercooled liquid: by comparing seeded growth rates of the neat drug and of drug with a low polymer level at the same temperatures [trasi2014a P3; trasi2014b P2], with FTIR to assess drug–polymer hydrogen bonding [trasi2014b P4]. For the felodipine, bifonazole and nimesulide dispersions: a 10% w/w polymer dispersion made by rotary evaporation is diluted with crystalline drug in a cryogenic mill to 0.5–4.5% w/w, melted between cover glasses, nucleated over P2O5 at 40 °C (or at ambient temperature) and grown on a hot stage at 70–110 °C (or 18–100 °C), the slope of spherulite diameter against time being the rate [kestur2010a P1, P2, P3, P4; kestur2011 P1, P2, P3]. Whether the slope is a diameter or radius rate is not always stated, and the felodipine Fig. 3 slopes are about twice the Fig. 4 rates [kestur2010a X3; kestur2011 X12]. Hydrogen bonding is read separately by IR on films with 20–50 wt% polymer [kestur2010a P6, C6].

Values in the library
materialvalue or classconditionspaper ids
IDM, PVPVAE_G 18 (5 µg/mL) and 56 (50 µg/mL polymer)50 µg/mL seeds, S = 6[moseson2020a R5]
BCL, PVPVA 70 µg/mL and HPMCAS 1 mg/mLE_G 8.6 and 158150 µg/mL, form 1 seeds[moseson2021 R5]
felodipine seeds, HPMCAS 5 µg/mL (outside)E_G about 2 to 12 depending on how the seed crystals were preparedS = 4[schram2016 R2, C13]
celecoxib, HPMCAS (outside)E_G about 130, 70 and 158 (R_0/R_p at 11/11, 22/5 and 22/22 µg/mL drug/polymer)11 and 22 µg/mL drug, pH 6.8, 37 °Cxie2016a R12
ritonavir with cellulose polymers (outside)inhibition large at low supersaturation, marginal at the amorphous "solubility"seeded growth[ilevbare2012b C56]
felodipine in buffer, PVP, HPMC, HPMCAS (outside)initial slopes about 0.1399, 0.0398, 0.0044 and 0.0021 µg/mL·min⁻¹9.5 µg/mL start, 150 µg/mL polymer[konno2008a R16]
PCZ 100 µg/mL in FaSSIF V2, HPMCAS 0 / 3 / 9 times the drug; seeds 0 / 10 µg/mL% left at 30 min about 13 / 4.5; 66 / 10.5; 95 / 43.5seeded solution[shah2024 R22]
ritonavir, 34 polymersE_g 0.83–3.25; Pn-IPAAmd 3.25, CAP Adp 0.85 2.98, CAB Adp 0.81 2.70, HPMCAS about 2.545 µg/mL polymer, S 7.6, 37 °C[ilevbare2012c R9]
ritonavir, CA 320S Sub 0.90; 0.6312.6; 10.8same[ilevbare2013b R9]
celecoxib, HPMC; HPMCAS; PVPVA10.2; 8.5; 7.45 µg/mL polymer, S 6.6[ilevbare2013b R9]
efavirenz, PVPVA; CA 320S Sub 0.90about 4.9S 1.2[ilevbare2013b R9]
ritonavir, CAP Adp 0.856.40, 2.99, 1.56S 3.8, 7.6, 15.3[ilevbare2012b R5]
ritonavir, CAP Adp 0.85 + Pn-IPAAmdabout 12.1 (S 7.6); 3.3 (S 15.4)5 + 5 µg/mLilevbare2012a R11, R16
felodipine, 1 µg/mL HPMCgrowth ratio 0.607S 10, 25 °C[alonzo2012 R5]
felodipine, HPMCAS-LF 5 µg/mLE_g 2.29 (pH 6.8), 1.28 (pH 3); 2.7 to 12 by seed route (pH 6.8)S 8 and S 4, 25 °C[schram2015 R4; schram2016 R2]
acetaminophen, 20 µg/mL polymerconcentration at 24 h 16.1 (HPMC), 15.8 (PVP), 13.4 (PAA), 13.0 (none) mg/mLS 1.5, 20 °C[trasi2015 R11]
telaprevir, 1.86 mM bile salts, δ 2.4E_G 3.2 (STC), 1.5, 1.4, 1.2; STCDC no desupersaturationpH 6.5, 37 °C[lu2017a R7, R10]
telaprevir seeds, 1:1 STDC–STCDC (binary-L, 1.86 mM; binary-H, 3.72 mM)E_G about 35.5 and 7.4, between STDC (3.8) and STCDC (>60)δ 7.9, 50 mM phosphate pH 6.5, 37 °C, first 10 min[lu2018 R5]
felodipine particles: none; 90:10 PVP dispersion; HPMC936 nm at 7 min; ≈218 → ≈459 nm (10–90 min); ≈280–307 nm at 90 min25 °Calonzo2011 R10, R8
felodipine particles at 37 °C, PVP against HPMC dispersions≈441 nm by 20 min against ≈287–307 nm37 °Calonzo2011 R11
paclitaxel seeds with 20 µg/mL HPMCASgrowth continued at S = 88 and left ≈7.9–25.3 µg/mL after 16 h; seeds grew dendritic fingers ≈10.5–16.8 nm widepH 6.8, 37 °C[que2018 R14, R12]
praziquantel with HPMCAS-MF against HPMC E5 LVno concentration drop with HPMCAS outside fed media; HPMC lost dissolved drug at 1.5 mg/mL37 °C[alvarenga2025 R14, C28]
five drugs with 10 mol% PVPgrowth reduced about 3- to 14-fold (authors: "around 5−10"), one point about 50-foldsupercooled liquid, 40–120 °C[trasi2014a R6, X6, C10]
nilutamide≈5 (alone), ≈3.8 (PAA), ≈1.1 µm/s (PVP)supercooled liquid, 80 °C[trasi2014b R3]
felodipine with PVP K-29/322- and 6-fold at 110 °C, 3- and 35-fold at 70 °C (1.5 and 4.5 wt%)supercooled liquid, melt[kestur2010b R13]
bifonazole with PAA5-fold at 100 °C, 15-fold at 18 °Csupercooled liquid, 5 wt%[kestur2011 R7]
flutamide with PVPabout one order of magnitudesupercooled liquid, 10 mol%[trasi2012b R3]
celecoxib with PVP; with TPGSmore than one order slower; about two orders faster at 70 °Csupercooled liquid, 10% w/w[mosqueragiraldo2014 R1, C9]
felodipine with 3% PVP, PVP/VA, HPMCAS, PVAcrate ratios at 70 °C ≈10.0, 6.5, 4.4, 1.2; at 110 °C ≈2.9, 1.1, 1.1, 1.1supercooled liquid, form II, hot stage, triplicate[kestur2010a R6]
felodipine, 4.5% w/w at 90 °C≈4.7 × 10⁻⁹ (PVP), 6.4 × 10⁻⁹ (PVP/VA), 1.7 × 10⁻⁸ (HPMCAS), 3.8 × 10⁻⁸ m/s (PVAc) against 6.7 × 10⁻⁸ m/ssupercooled liquid, log-linear in polymer content[kestur2010a R8]
bifonazole with 5% PAA; PVP; HPMCASratios ≈15, 5.9, 4.0 at 18 °C; ≈5.1, 2.1, 1.7 at 100 °Csupercooled liquid, melt-quenched films[kestur2011 R7]
nimesulide with 5% PVP; PVP/VA; PVAcratios ≈21, 16, 3.4 at 18 °C; ≈4.7, 3.1, 2.0 at 80 °Csupercooled liquid, melt-quenched films[kestur2011 R9]
Pitfalls and disagreements

E_G falls as supersaturation rises and depends on seed preparation, polymer concentration and polymer chemistry, so values from different systems are not comparable [ilevbare2012b C56; schram2016 C13; moseson2020a X12]. Adsorption was imaged on bulk crystals only, not on residual crystals [moseson2020a X5]. The threshold for "effective" is applied loosely: Eg above 1 is the stated rule, but counts of effective polymers match a cut-off near 1.2, and polymers at 1.0–1.4 are called ineffective [ilevbare2013b X3; ilevbare2012c X7]. Eg depends on supersaturation, polymer concentration, pH and buffer strength, so ratios from different papers are comparable only roughly; absolute rates cannot be compared because seed mass, volume and methanol fraction are often not printed [ilevbare2012c X16; ilevbare2012b X12]. Most 2013 ritonavir values were reported before [ilevbare2013b X15]. A polymer that raises the solubility lowers S and so flatters Eg [ilevbare2013c X7; ilevbare2012a X6]. The ratio depends on the seed route and the dose [schram2016 R2]; rates are not normalised to area in the felodipine and telaprevir papers [schram2016 X12; lu2017a C5]. For a bile salt mixture the "intermediate" ratio rests on an off-scale value for STCDC and a wide spread for the mixture (about 16.7–54.5), and secondary nucleation at δ 7.9 was assumed small [lu2018 X7, C8]. Polymers that form globules on an amorphous drug surface "may" need a higher concentration to block growth, which was not measured [mosqueragiraldo2018a C41]. No precipitate was examined in the 2008 felodipine study and surface areas were assumed equal [konno2008a X4, X7]. Seeded and unseeded tests of felodipine with HPMC later found growth at 0.607 of the polymer-free rate but an estimated nucleation-rate ratio of 7.05 × 10⁻⁴, placing the main effect on nucleation [alonzo2012 R5, R17]. For nifedipine polymorph conversion the polymers are read as inhibiting α nucleation, not growth [raina2014b C32]. The celecoxib slopes are not printed and R_p was taken over 16 h while the plot covers 4 h, so the ratios cannot be reproduced; seeded growth was measured with HPMCAS only, not HPMC xie2016a X8, X5. A polymer that blocks nucleation need not stop growth: HPMCAS held unseeded paclitaxel at S = 88 for more than 16 h but only slowed growth on seeds [que2018 R3, C30]. In the supercooled liquid: inhibition of growth and of nucleation need not coincide either: for acetaminophen, HPMCAS inhibited nucleation best but growth least [trasi2012a C46]. Some additives accelerate growth [sato2016 R11]. The molar basis of the PVP level was not defined [trasi2014a X7]. The text of the felodipine paper overstates two points against its own figures: the 105 → 70 °C fall is about 51-fold, not 3 orders of magnitude, and PVP still inhibits about 3-fold at 110 °C where the polymers "appear to have no effect" [kestur2010a X1, X2]. The nimesulide text gives 2–10-fold, the plot up to about 21-fold [kestur2011 X7]. The hydrogen-bond order was measured at 20–50 wt% polymer and one temperature, and bifonazole–polymer bonding was not measured [kestur2010a X5; kestur2011 X9]. The melting-point argument used form I in physical mixtures while form II grows [kestur2010a X7]. Only growth was measured, not nucleation [kestur2010a X10]. The two media are explained differently: in solution the authors propose surface poisoning by adsorbed polymer [moseson2020a C48, C50], in the supercooled liquid drug–polymer hydrogen bonding and mobility, with demixing at the growth front as a "speculation" [trasi2014a C33; kestur2010a C40, C42], so ratios from the two media are not interchangeable (synthesis: different media and proposed mechanisms).

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

crystal growth rate

The speed at which a crystal front advances into the surrounding supercooled liquid or glass, taken as the slope of crystal size (length, radius or diameter) against time [trasi2014a P1; trasi2014b E1]. Its temperature dependence is bell-shaped, with a maximum crystal growth velocity between Tg and Tm [trasi2014a C22]. This draft comes from the crystallization-tendency chapter (growth from melts); growth from supersaturated solution, measured by desupersaturation, is covered by other chapters [ilevbare2013b R7]. New aspects (Miscibility and drug-polymer interactions): Growth of felodipine from the supercooled liquid is expected to depend on a thermodynamic part (the free energy difference between liquid and crystal) and a kinetic part (viscosity), as in u = (k/\eta)[1 - \exp(-\Delta G/RT)], and also on molecular recognition at the crystal surface [kestur2010a C30, E1]. The growth rate of felodipine peaks at about 105 °C and a polymer at 3% shifts the apparent maximum to 110 °C (not for PVAc) [kestur2010a R5, C11]. The polymer effect, expressed as the ratio of growth rates without and with polymer, is not constant but grows toward the glass transition [kestur2010a R6; kestur2011 C8, C10]. New aspect (Crystallization from solution): growth from supersaturated aqueous solution is measured as the initial bulk growth rate of seed crystals, the slope of the dissolved drug amount against time over the first 2 min (5 min for felodipine), in µg/mL/min or µg/min, and normalized by seed mass and BET area (mg min⁻¹ m⁻²) to compare drugs [ilevbare2013b E6, E8; alonzo2012 P4]. It follows the empirical law R_G = k_G S^{g} with order g between 1 (diffusion control) and 2 (integration control) [alonzo2012 C3, E2]. New aspect (Physical stability): in the physical-stability papers the growth rate is the slope of crystal diameter (melt films) or radius (thin films at fixed RH) against time, of existing crystals nucleated first, so that growth is measured apart from nucleation [kestur2010b P3; rumondor2010 P1, P5, C7]. New aspect (Supersaturation from ASD dissolution): in the ASD dissolution papers a growth rate from solution is the mass gained by crystals per unit surface area and time, R_G = \frac{1}{A_c}\frac{dM_c}{dt}; with equal surface areas assumed, the slope of the falling concentration ranks growth rates [konno2008a E5, C28].

Findings

Crystallization tendency: F1, F2, F3, F5, F6, F7, F15, F19, F21. Miscibility and drug-polymer interactions: F10, F11, F12, F13. Crystallization from solution: F3, F5, F7, F9, F10, F23, F24, F33, F42. Physical stability: F3, F9, F11, F15, F17, F18, F19, F21, F22, F27, F28, F29, F35. Supersaturation from ASD dissolution: F5.

Related concepts

part of crystal growth; includes maximum crystal growth velocity; depends on melt viscosity and thermodynamic driving force for crystallization; contrasts with nucleation; related to crystal growth inhibition by polymers and surface crystallization; includes spherulitic growth; depends on supercooled liquid; lowered by crystal growth inhibition by polymers; inhibited in crystal growth inhibition; limited at high supersaturation by kinetic roughening; related to integration-controlled crystal growth. Regime diffusion-controlled crystal growth; modified by crystallization inhibition by polymers and moisture-induced crystallization; related to surface-enhanced crystal growth; faster mode near Tg: glass-crystal growth mode; split from nucleation and crystal growth; related to desupersaturation.

Formulas

temperature of maximum crystal growth rate, Jackson interface-kinetics growth rate, linear fit of melt viscosity on Tm − Tg, linear fit of normalized growth rate on melting entropy; viscosity-limited normal growth law, power-law crystal growth rate, initial growth rate from the desupersaturation slope; empirical log-linear growth-rate equation, linear crystal growth rate from size-time slope, crystal growth inhibition effectiveness ratio, overall mass crystal growth rate.

How it is measured or obtained

Hot-stage polarized light microscopy of melt-quenched films seeded at the edge with the form of interest, triplicate where stated [trasi2014a P1; trasi2014b P3]; with the top coverslip removed for surface growth [trasi2014a P2]; from the crystallized area when the front is irregular [trasi2014b P3]; the size–time plot is linear [trasi2012a R4; kestur2011 R4]. In the felodipine, bifonazole and nimesulide studies: the slope of spherulite diameter against time on a hot stage at 70–110 °C (felodipine) or 18–100 °C (bifonazole, nimesulide), triplicate; slower growth below 40 °C was followed in ovens or coolers with periodic pictures [kestur2010a P4; kestur2011 P3]. Whether the slope is a diameter or a radius rate is not always clear: the felodipine Fig. 3 slopes are about twice the Fig. 4 rates [kestur2010a X3; kestur2011 X12]. From solution, by seeded desupersaturation with a fibre-optic UV probe on second-derivative spectra, in triplicate (F5) [ilevbare2013b P10; ilevbare2012a P8]. In the physical-stability papers: melt-quenched felodipine between cover glasses, nuclei formed at 40 °C, grown on a hot stage at 70–110 °C, with crystals 5.5 ± 2 µm thick so that diameter slopes can be compared [kestur2010b P2, P3, R19, C5]. Uncovered spin-coated films, spherulites nucleated on a 90 °C hot plate, radius read from photomicrographs at four or more times for three or more crystals at each RH [rumondor2010 P1, P5]. Seeded edge growth of melt-quenched films of flutamide, acetaminophen and celecoxib, triplicate where stated; the flutamide paper reports diameter, the acetaminophen paper radial growth rates [trasi2012b P2, R3; trasi2012a P2, R6; mosqueragiraldo2014 P3]. Felodipine form I at a free surface or seeded in the bulk, form II unseeded between two cover glasses [kestur2013a P2, P3]. In the ASD dissolution papers: the initial linear slope of solvent-shift desupersaturation curves (felodipine from 9.5 µg/mL with 150 µg/mL polymer) [konno2008a P6].

Values in the library
materialvalue or classconditionspaper ids
nimesulideMCV 216 µm/s, the fastest of 31 drugsbulk melt[trasi2014a R1.a]
clotrimazoleMCV 0.02 µm/s, the slowestbulk melt[trasi2014a R1.ae]
vemurafenib α-needles; β≈106 µm/s at 250 °C; ≈110 µm/s at 230 °Csupercooled liquid[lu2016 R12.o, R12.m]
nilutamide stable form≈0.00015 µm/s at 30 °C to ≈40 µm/s at 100 °Cseeded films[trasi2014b R8]
felodipinemaximum near 105 °C, 3 orders lower at 70 °Cmelt films[kestur2010a R5, C10]
felodipine form Iabout 6 times faster at the surface than in the bulk30 °C, 0% RH[kestur2013b R12]
felodipine filmsabout 2-fold rise over 13–80% RH (≈0.030 → 0.066 mm/min), 40-fold at 87% RH (2.3–2.8 mm/min at 87–93% RH)25 °C[rumondor2010 R1]
bifonazoleabout 5.5 orders lower from 100 to 18 °Cmelt-quenched films[kestur2011 R7]
flutamidenearly 2 orders lower from 70 to 40 °Cfilms[trasi2012b R3]
acetaminophennearly 2 orders lower from 110 to 70 °Cfilms[trasi2012a R6]
indomethacin γ; α; δMCV 4.07 × 10⁻⁷; 4.34 × 10⁻⁶; ≈1.5 × 10⁻⁷ m/s, at 135, 135 and 110 °Cpure melt[tian2017 R7, R8, R9, R10]
celecoxib with TPGSabout two orders faster than celecoxib alone at 70 °C10% w/w[mosqueragiraldo2014 C9]
felodipine form II≈3.5 × 10⁻⁹ (70 °C), ≈6.9 × 10⁻⁸ (90 °C), ≈1.8 × 10⁻⁷ m/s (105 °C)neat, hot stage[kestur2010a R5.a]
felodipine, 3% PVP; PVP/VA; HPMCAS; PVAcat 70 °C ≈3.5 × 10⁻¹⁰, 5.4 × 10⁻¹⁰, 7.9 × 10⁻¹⁰, 3.0 × 10⁻⁹ m/sform II[kestur2010a R5.e, R5.d, R5.c, R5.b]
bifonazole neat; with 5% PAA≈1.7 × 10⁻¹² and ≈1.1 × 10⁻¹³ m/s at 18 °C; ≈4.7 × 10⁻⁶ and ≈9.2 × 10⁻⁷ m/s at 100 °Cmelt-quenched films[kestur2011 R7.a, R7.i]
nimesulide neat; with 5% PVP≈3.7 × 10⁻¹¹ and ≈1.8 × 10⁻¹² m/s at 18 °C; ≈8.5 × 10⁻⁶ and ≈1.8 × 10⁻⁶ m/s at 80 °Cmelt-quenched films[kestur2011 R9.a, R9.g]
ritonavir; celecoxib; efavirenznormalized 0.20; 0.91; 2.97 mg min⁻¹ m⁻² at S 1.2–1.3seeded, 37 °C[ilevbare2013b R7]
celecoxib; ritonavir at S 6.6; 7.66.23; 6.14 mg min⁻¹ m⁻²same[ilevbare2013b R7]
celecoxib; ritonavir at S 14.7; 15.419.08; 14.32 mg min⁻¹ m⁻² (217.5 and 181.5 µg min⁻¹)same[ilevbare2013b R7]
ritonavir without additive, 10 µg/mL1.56 µg mL⁻¹ min⁻¹ (text), about 1.4 (figure)100 mM buffer, S 7.6ilevbare2012a R10, X5
ritonavir without additive, S 3.8; 7.6; 15.4about 0.72; 1.4; 3.63 µg mL⁻¹ min⁻¹sameilevbare2012a R15
felodipine without HPMC, S 3 to 12about 0.078 to 0.62 µg mL⁻¹ min⁻¹; g about 1.5025 °C[alonzo2012 R4, R13]
telaprevir seeds, no bile salt5.4, 58.6, 89.2 µg/min at δ 2.4, 7.9, 12.5 (per 50 mL vessel)pH 6.5, 37 °C[lu2017a R2, X12]
felodipine seeds, no polymerconcentration 4.0 → 1.7 µg/mL in 50 minS 8, 25 °C, 1000 rpm[schram2015 R1]
atazanavir, posaconazole, six mediaSHG size growth about 2–55 (atazanavir) and 20–156 nm/min (posaconazole); highest in blank buffers37 °C, relative per field[elkhabaz2021 R15, X13]
felodipine form II (PVP grade study)3.5 × 10⁻⁹ m/s (70 °C) to 1.7 × 10⁻⁷ m/s (105 °C, maximum)melt films[kestur2010b R7, C9]
felodipine with 3 wt% PVP K-12, K-29/32, K-9011-, 15-, 21-fold slower at 70 °C; 3-, 3-, 6-fold at 110 °Cmelt films[kestur2010b R8]
felodipine with 0.5–4.5 wt% PVP K-29/32ln rate linear in concentration; slope −0.82 (70 °C) to −0.49 per wt% (105 °C)melt films[kestur2010b R15, E1]
felodipine with 10% PVP vs 10% HPMCAS5.8 × 10⁻⁵ vs 1.3 × 10⁻³ mm/min (13% RH); 7.3 × 10⁻² vs 2.4 × 10⁻³ (93% RH)room temperature[rumondor2010 R5, R3]
flutamide with 10 mol% PVP≈0.13 against ≈1.4 µm/s at 40 °Cmelt films, diameter rate[trasi2012b R3.a, R3.h]
acetaminophen with 10% w/w PAA≈0.43 against ≈5.3 µm/s at 80 °Cmelt films, radial rate[trasi2012a R6.a, R6.h]
celecoxib≈0.002 (70 °C) to ≈12 µm/s (120 °C); 19–38-fold slower with 10% PVPseeded melt films[mosqueragiraldo2014 R1.a, R1.b]
felodipine form I against form II, bulkform I faster at 40–100 °C: ≈4700-fold at 40 °C, 7–9-fold at 80–100 °Cmelt films[kestur2013a R8, X5]
felodipine form I with 3% PVPsurface 1.45 × 10⁻⁹, bulk 6.37 × 10⁻¹¹ m/s (ratio 22.8)30 °C, 0% RH[kestur2013b R12]
ATP(S), ATP(R)0.022–0.032 µm/s (40 °C) to 21–34 µm/s (90 °C); S 1.2–1.6 times fastermelt films[sato2015 R5.a, R5.b, X2]
griseofulvin with 5% PHB≈0.015 → ≈0.15 µm/s at 120 °C (diameter rate)melt films[sato2016 R4.a, R4.c]
celecoxib, alone and with 10% PVP K29/32≈0.010 and ≈0.00003 µm/s at 80 °Cmelt filmsxie2016b R21
felodipine, buffer / PVP / HPMC / HPMCASdMc/dt ~0.1399 / ~0.0398 / ~0.0044 / ~0.0021 µg/mL-minpH 6.8, 37 °C[konno2008a R16]
Pitfalls and disagreements

The MCVs of the 31-drug set have no stated derivation and some disagree with the plotted rates; no replicates are given [trasi2014a X3, X17]. Rankings change with the temperature scale (T/Tg against Tm − T) [trasi2014a C7] and between surface and bulk [trasi2014a C8]. Rates above Tg cannot readily be extrapolated to storage temperatures [trasi2014a C35], and surface-enhanced or sudden growth modes near Tg can make high-temperature data overpredict stability [kestur2013a C7]. Near Tg, diffusion decouples from viscosity [trasi2014a C21]. The text says the felodipine rate falls by 3 orders of magnitude from 105 to 70 °C (the figure in the table above), the plot gives about 51-fold [kestur2010a X1]. The text says the polymers "appear to have no effect" at 110 °C, but PVP still gives a ratio of about 2.9 [kestur2010a X2]. All rates of the felodipine, bifonazole and nimesulide studies are plot readings from log axes and the error bars are not defined [kestur2010a X9; kestur2011 X6]. The bifonazole orders of magnitude in the text (5.5, as in the table above) differ from the plot [kestur2011 X6]. In solution, the same no-polymer condition gives 71.0, 69.80 and about 68 µg min⁻¹ for celecoxib in three places of one paper [ilevbare2013b X7]. Seed amount, volume and methanol fraction are often not printed, so absolute solution growth rates cannot be compared across studies [ilevbare2012c X16]. Efavirenz shows secondary nucleation above 10 µg/mL, which confounds its seeded rate [ilevbare2013b R5]. The fall of pure felodipine growth from 105 to 70 °C is about 49-fold in the PVP grade paper (synthesis: 1.7 × 10⁻⁷/3.5 × 10⁻⁹ [kestur2010b R7]) but 3 orders of magnitude in the text of the other 2010 paper [kestur2010a C10]. The melt growth model takes the diameter slope as the radial front speed [kestur2010b X5]. Replicates and error-bar meaning are not stated for the melt study or for the polymer films at fixed RH [kestur2010b X17; rumondor2010 X7]. Diameter and radial growth rates differ by a factor of two, so flutamide and acetaminophen rates cannot be compared as printed [trasi2012b R3; trasi2012a R6]. The measured felodipine front changes habit with temperature [kestur2013a X12]. The PHB paper reports diameter rates, twice the radial rate [sato2016 X8]. Table 2 of the indomethacin polymorph paper interchanges the δ and γ maxima of the pure drug [tian2017 X1]. Two celecoxib papers differ about tenfold in the factor by which 10% PVP slows growth [mosqueragiraldo2014 R1; xie2016b R21]. The slopes come from one panel without uncertainty, from curves that start at different 5-min levels, and no surface area was measured [konno2008a X7]. The buffer slope reproduces from the plotted points (≈0.14 µg/mL-min) [konno2008a E5].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

crystalline solubility

The equilibrium solubility of the stable crystalline form of the free drug in a given medium, the reference against which supersaturation and the amorphous advantage are defined; Eq. 1 multiplies it by the free-energy and water terms to obtain the amorphous solubility [ilevbare2013a E1; indulkar2015 E2]. For ionizable drugs it is measured at each pH and follows the pH-solubility profile of the free base [indulkar2015 E8, R4]. The papers of 2017–2022 add that it rises steeply with temperature (ibuprofen about 23.5 µg/mL at 25 °C to about 116 µg/mL at 60 °C), that polymers do not change it except one that complexes the drug (EUD-E, 29.8 → 42.1 µg/mL), and that micelles raise it (atazanavir 1.1 → about 45.6 µg/mL at 3.6 mg/mL SDS; telaprevir about twofold with 12 mM dihydroxy bile salts) [ueda2022 R1, R2; ueda2020b R1; indulkar2017a R7; lu2017b R1].

Findings

F5, F6, F9, F10, F12, F4, F15, F17, F18, F23.

Related concepts

reference for amorphous solubility and supersaturation; raised by ionization (pH-dependent solubility) and by micellar solubilization; lowered by salt (F9).

Formulas

solid-liquid equilibrium solubility equation, pH-solubility profile, amorphous solubility advantage with water-sorption correction.

How it is measured or obtained

Shake flask with excess crystals, about 48 h at the test temperature, separation by ultracentrifugation, HPLC or UV assay [ilevbare2013a P1; almeidaesousa2015 P3; indulkar2015 P3; mosqueragiraldo2015 P1; trasi2015a P1; almeidaesousa2016 P5]. A small amount of the stock solvent was added in one study to mimic the onset composition [almeidaesousa2015 P3].

Values in the library
materialvalue or classconditionspaper ids
ritonavir2.4; 1.3; 0.95 µg/mLwater; 100 mM; 200 mM phosphate pH 6.8, 37 °Cilevbare2013a R13
ritonavir; lopinavir; paclitaxel (hydrate); felodipine1.7; 2.7; 0.32; 0.74 µg/mL100 mM pH 6.8, 25 °C[trasi2015a R1]
efavirenz; loratadine; ketoconazole; indomethacin; clotrimazole; clozapine8.2; 1.6; 3.7; 3.0; 0.4; 8.8 µg/mLun-ionizing media, 37 °Cilevbare2013a R8
ibuprofen; tolnaftate; sorafenib29.29; 27.87 × 10⁻³; 9.86 × 10⁻³ µg/mL25 °C[almeidaesousa2015 R5]
telaprevir4.6 ± 0.1 (4.7 with 5 µg/mL HPMCAS) µg/mLpH 6.8, 37 °C[mosqueragiraldo2015 R13]
clotrimazole; atazanavir0.55; 1.04 µg/mL (un-ionized)37 °C[indulkar2015 R2]
CRH1 free base1.20 (pH 6.8); 1.50 µg/mL (pH 4.6 + HPMC)25 °C[almeidaesousa2016 R2]
telaprevir5.2 ± 0.1 µg/mL; 9.6–12.4 with 12 mM STDC, STCDC, SGDC, SGCDC; 6.2–6.9 otherwise50 mM pH 6.5, 37 °C[lu2017b R1]
atazanavir1.1 µg/mL (buffer); about 45.6 µg/mL (3.6 mg/mL SDS)pH 6.8, 37 °Cindulkar2017a R4, R7
pazopanib free base0.018 µg/mL (pH 8.4); 0.033 (pH 6.5); about 0.60 (pH 5); 0.571 mg/mL (SGF)37 °C, 72 h[sugihara2018 R2]
ibuprofen29.8 (2020) and 43.1 µg/mL (2021) at 37 °C, pH 2.0 (D2O); about 23.5 (25 °C) to about 116 µg/mL (60 °C)shake flask[ueda2020b R1; ueda2021 R2; ueda2022 R1]
Pitfalls and disagreements

Crystalline nicardipine turned amorphous in water within 2 h, so no crystal solubility exists for it [indulkar2015 R1]. The paclitaxel value is that of a hydrate [trasi2015a X12]. Solubility at pH 8 is quoted at pH 9 in the text of one paper [indulkar2015 X2]. Media differ between drugs in the 2013 table ilevbare2013a X16. Pazopanib's value is very low and carries a high experimental uncertainty [sugihara2018 C16]; the same drug and medium gave 29.8 and 43.1 µg/mL for ibuprofen in two papers [ueda2020b R1; ueda2021 R2].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

crystallization during dissolution

Crystallization of an amorphous drug while it dissolves, either on the dissolving solid or from the supersaturated solution it creates, so that the solution never reaches the calculated amorphous solubility [ilevbare2013c C20, C24]. The induction-time runs of the chapter avoid the first route by starting from a solution [ilevbare2013c C24]. Seeds crystallized from a felodipine–HPMCAS melt in pH 3 buffer for up to a week are the dispersion route of the seed study [schram2016 P3, R10]. New aspect (Supersaturation from ASD dissolution): the frame of two routes (crystallization of the solid matrix and of the solution) and the claim that their kinetics relative to dissolution "in large part shape" the concentration–time profile [alonzo2010 C32, C47]; for nifedipine both routes pass through a metastable form first [raina2014b C29]. For resveratrol dispersions crystallization "appeared to occur in or at the surface of the matrix", also where an undissolved polymer blocked release, and the concentration reached depended on the extent of crystallization, the drug–polymer interactions and the amount of dispersion added [wegiel2015 C16, C48]. New aspect (Release mechanism and LoC): in the release papers of 2020–2022 crystallization on the dissolving compact ends release that began well. Heating 10% atazanavir–PVPVA compacts to 55 °C, near the drug's wet Tg, restored release, but drug release ceased at about 70 min at 64% released while PVPVA dissolved completely, and crystals were seen by PLM at 90 min; crystallization "is likely" why release stopped correasoto2022b R5, C14, M1. The TPGS dispersion crystallized after 1 h at 55 °C correasoto2022b R6. For indomethacin methyl ester the route was crystallization at the compact surface saboo2020 C17. The 2025 HPMCAS papers checked and excluded it as the cause of poor weak-base release: no crystals during 1 h or for 12 h after (except loratadine–LF after about 10 h), and amorphous bedaquiline residues bapat2025a R6, C17; kaur2025 R14.

Findings

Crystallization from solution: F2, F3, F24. Supersaturation from ASD dissolution: F1, F2, F3, F16. Release mechanism and LoC: F18, F19, F32.

Related concepts

limits amorphous solubility; related to crystallization tendency and desupersaturation; part: matrix crystallization and solution crystallization; related to solution-mediated phase transformation. At the compact surface it is surface crystallization; ends congruent release; the test temperature is set against the wet glass transition temperature.

Formulas

Noyes-Whitney equation, classical nucleation theory.

How it is measured or obtained

The maximum concentration reached on dissolving a solvent-evaporated or spin-coated amorphous solid by in-situ UV, compared with the calculated value; polarized-light microscopy of melt-quenched particles wetted with buffer [ilevbare2013c P7, P8, R2, R4, R5; ilevbare2012b P5, P6]. In the ASD dissolution papers: concentration–time profiles read side by side with in situ solid-state measurements of slurries (Raman, MCR) and polarized light [alonzo2010 P5; raina2014b P6, P10]. In the release-mechanism papers: polarized light microscopy of the compact after the run, besides the stop of drug release while the polymer keeps dissolving correasoto2022b R5.

Values in the library
materialvalue or classconditionspaper ids
ritonavir; efavirenz; celecoxibmaximum 19.8; 12.3; 2.5 µg/mL against calculated 20.6; 19.8; 22.6pH 6.8, 37 °C[ilevbare2013c R2]
amorphous celecoxib particlebirefringent spot within about 1 min, extensive crystals at 6 minbuffer, 20×[ilevbare2013c R4]
amorphous efavirenz particlesshrank over 3 h, no birefringencebuffer[ilevbare2013c R5]
felodipine slurry without polymer (ASD dissolution chapter)more than 50% crystalline at the first acquisition (1 min) at 37 °C; about 8 min to 50% at 25 °CpH 6.8[alonzo2010 R2]
danazol (cited)amorphous danazol reached less than a quarter of the expected concentrationrefs in the card[jackson2014 R27]
felodipine–HPMCAS melt (10% w/w)small rounded features, steps 0.77 nmpH 3, up to a week[schram2016 R10, R12]
indomethacin, neat amorphousconcentration maximum (≈11.2 µg/mL) near the onset of conversion to αpH 2, 37 °C[alonzo2010 R13, R7]
nifedipine glassglass gone by ≈6 min, γ then α; solution ≈6 µg/mLpH 6.8, 25 and 37 °C[raina2014b R6, R14]
nifedipine–HPMC 50:50≈100 µg/mL at ≈22 min, ≈41 µg/mL at 150 min5 mg/mL, 37 °C[raina2014b R14]
resveratrol–HPMCAS 25%, pH 6.8 against pH 1.2Raman ratio ≈0.96 and ≈0.93 after a day37 °C[wegiel2015 R17]
neat amorphous celecoxib≈1.70 against ≈1.85 µg/mL for the crystal at 16 hpH 6.8, 37 °C[xie2015 R7]
atazanavir–PVPVA 10%64% of the drug and all PVPVA released; drug release ceased at ≈70 min; crystals at 90 min55 °Ccorreasoto2022b R5
atazanavir–PVPVA 10% with TPGScrystals after 1 h55 °Ccorreasoto2022b R6
Pitfalls and disagreements

For efavirenz the shrinking particles suggest crystallization from the solution after dissolution, not on the solid ("suggesting") [ilevbare2013c C23]. The theoretical and experimental amorphous solids were made by different routes (melt-quench for the water sorption feeding the calculation, solvent evaporation for the measurement) [ilevbare2013c X17]. The Tg of the hydrated solid explains the felodipine temperature effect only in part; indomethacin crystallized more slowly despite a similar Tg drop [alonzo2010 C34, C42]. Supersaturation in the nifedipine slurries was not measured [raina2014b X10]. (synthesis: the higher temperature that restored release of the 10% dispersion also brought crystallization within the 90-min run) correasoto2022b R5, R6.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

crystallization from the supercooled melt

Crystallization of a drug melt as it is cooled below Tm, or while it is held below Tm; it is the route probed by the DSC classification and the one relevant to melt extrusion and melt quenching [baird2013 C1; vaneerdenbrugh2010a P10].

Findings

F9, F14.

Related concepts

contrasts with cold crystallization; measured by crystallization tendency classification; depends on degree of supercooling and melt viscosity; occurs in supercooled liquid.

Formulas

Barandiaran-Colmenero critical cooling rate.

How it is measured or obtained

DSC cooling at fixed rates [baird2010 P1]; rapid heat–cool DSC [baird2013 P2]; isothermal holds of the undercooled melt [moseson2020 R7]; rheometry while cooling [baird2012 P1].

Values in the library
materialvalue or classconditionspaper ids
51 molecules23 crystallize on cooling at 20 °C/minDSC[baird2010 R1]
vemurafenibcrystallized from 248.9 °Ccooling at 10 °C/min[lu2016 R1]
posaconazole, bicalutamide; indomethacincrystallization within 1 h; none in 4 hisothermal holds at 130–180 °C[moseson2020 R7]
acetaminophen with polymersrank orders for nucleation and growth inhibition differ, and differ from solutionundercooled melt (cited)[trasi2015 R14, C28]
Pitfalls and disagreements

Solid-state polymer rankings need not hold in solution [trasi2015 C28]. Melt and solvent classes agree only for rapid solidification [vaneerdenbrugh2010a X7].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

crystallization inhibition

The delay or slowing of crystallization of an amorphous drug by a polymer mixed with it. Several explanations are in circulation and none is accepted: reduced molecular mobility through a higher Tg (antiplasticization), a lower driving force through a lower chemical potential, a higher barrier, and drug–polymer specific interactions that disrupt the drug's self-association [taylor1997 C3, C4, C5; marsac2006b C2, C5; kestur2010a C29; rumondor2009a C2]. For indomethacin and PVP the proposal is that a nucleus of the stable γ form is built of acid dimers, so that nucleation "would require" breaking the PVP–drug hydrogen bond [taylor1997 C43]. The effect is measured on different quantities: the overall crystallinity of a film over days (the amorphicity index), the growth rate of crystals into the supercooled liquid, or nucleation separately [vaneerdenbrugh2010b E1; kestur2010a P4]. In later designs the effect is read as the amorphicity index of 105 spin-coated pairs of 15 drugs and 7 polymers [vaneerdenbrugh2011a R3], as the highest polyphenol content that stays X-ray amorphous and the days to crystals at five storage conditions [wegiel2013a R8, R9], and as the weeks to crystals of lumefantrine dispersions hiew2022a R6. The ranking of polymers follows complementary groups of drug and polymer (see F24). In the glass, melt and solution (formerly the page "crystallization inhibition by polymers", from ASD process, Crystallization from solution, Physical stability and Supersaturation from ASD dissolution): delay of nucleation and slowing of growth of a drug by a polymer in the glass, melt or solution. Two settings matter here. In solution, dissolved PVPVA prevented nucleation of indomethacin for more than 12 h and HPMCAS prevented that of bicalutamide for 8 h [moseson2020a C11; moseson2021 R3]. In the solid or melt, a polymer can stabilise the amorphous drug against recrystallisation and let degradation be tested on a dispersion [moseson2020 C32, C55]. A polymer inhibits in the solid only when intimately mixed with the drug in one phase, usually inferred from a single Tg rumondor2009c C26; marsac2010 C31. The polymer's help in solution does not carry into the hydrating solid or across drugs: HPMCAS slowed seeded growth of posaconazole in FaSSIF [shah2024 R22], but in the hydrating solid cryomilled and high-loading bicalutamide–PVPVA dispersions still crystallized moseson2022b R4, R6; and coated erlotinib–HPMCAS held 48 weeks at 43% RH where coated erlotinib–PVPVA failed at 6 weeks, a difference the authors attribute to the polymer moseson2022a R11, R12, C31. New aspect (Crystallization from solution): the delay of crystallization from a supersaturated aqueous drug solution by a dissolved polymer, through slowing nucleation, growth or both; for felodipine and HPMC both were slowed at µg/mL levels and nucleation far more [alonzo2012 C46]. The papers separate it into crystal growth inhibition and nucleation inhibition because polymers rank differently in the two (F6) [ilevbare2013c C40]. The solid-state version, in amorphous dispersions, is described at the start of this definition. New aspect (Physical stability): in dry felodipine films a few percent of polymer lowered nucleation by orders of magnitude, independent of polymer type and of any Tg rise, and the authors speculate that it raises the kinetic barrier to nucleation [konno2006 C13, C14, C40]. With water present the polymer still inhibits, competing with the water it brings, but the polymers then differ [konno2008 C13, C10]. New aspect (Supersaturation from ASD dissolution): one polymer can act differently on the two routes by which an amorphous solid loses supersaturation: PVP delayed crystallization of the wetted felodipine solid at least as well as HPMC and HPMC-AS but held felodipine solutions poorly [alonzo2010 C38]; the authors therefore "speculate" that some drugs "might" be formulated better with two polymers, one per route [alonzo2010 C46]. Because 1 mg/mL of each polymer left the crystalline solubility of felodipine unchanged, the higher concentrations from the dispersions are read as kinetically maintained supersaturation, not solubilization [konno2008a R1, C17, C22]. The papers of 2015–2018 add that a fast-releasing polymer can be paired with a minor inhibitor that then works in solution [xie2015 C6; xie2016a C69], that against matrix crystallization the inhibitor must stay in contact with the drug in the particle xie2016a C54, and that the polymer content needed to stop matrix crystallization depends on the polymer [wegiel2015 C11].

Findings

Miscibility and drug-polymer interactions: F1, F9, F10, F11, F12, F13, F15, F16, F17, F23, F24, F25, F26. ASD process: F25, F27, F31, F38, F41, F44. Crystallization from solution: F6, F7, F8, F13, F14, F15, F16, F20, F25, F26, F27, F36, F37, F41, F43, F44. Physical stability: F1, F3, F4, F10, F11, F15, F17, F18, F19, F21, F22, F24, F26, F27, F28, F29, F33, F35. Supersaturation from ASD dissolution: F2, F3, F4, F5, F6, F12, F16, F20.

Related concepts

includes crystal growth inhibition and nucleation inhibition; depends on drug-polymer interactions, drug-polymer miscibility, antiplasticization and thermodynamic driving force for crystallization; contrasts with crystallization tendency of the neat drug; limited by matrix crystallization; related to nucleation, crystal growth rate, kinetic stabilization, polymer hydrophobicity and supersaturation. Acts through kinetic barrier to nucleation and polymer rejection at the crystal growth front (proposed); not through antiplasticization at low content; lost by moisture-induced phase separation; decided by hydrogen-bond donor and acceptor groups and acid-base interaction; related to drug-polymer complexation.

Formulas

amorphicity index, viscosity-limited normal growth law, crystal growth inhibition effectiveness ratio, relative nucleation rate from seeded and unseeded induction times, induction time decomposition, empirical log-linear growth-rate equation, classical nucleation theory, supersaturation ratio, overall mass crystal growth rate.

How it is measured or obtained

Spin-coated films of drug and polymer at several ratios, scored by polarized light microscopy at day 0, 1, 3 and 7 and expressed as an amorphicity index [vaneerdenbrugh2010b P1, P2, E1]; hot-stage growth of spherulites in melt-quenched films with low polymer levels after nucleation at 40 °C [kestur2010a P2, P3, P4]; rotary-evaporated bulk powders by DSC crystallinity [vaneerdenbrugh2010b P8, E5]. Only growth, not nucleation, was measured in the felodipine and bifonazole–nimesulide studies [kestur2010a X10; kestur2011 P3]. Induction time and seeded desupersaturation in solution; DSC of undercooled melts for the dispersion (a melting peak on reheating means nucleation during the hold); matrix crystallisation by microscopy and Raman of particles in buffer [moseson2021 P12, P15, P16; moseson2020 P7]. In the crystallization-from-solution papers: seeded growth rates and unseeded induction times with and without predissolved polymer under identical conditions, combined into a relative nucleation rate (F5, F6) [alonzo2012 P10, E9, E10]; induction times by UV extinction or absorbance [ilevbare2013c P9]; pH-shift precipitation followed by polarized light, WAXS and HPLC [hsieh2014 P2–P7]; fluorescence and SHG for droplet and crystal read-outs [jackson2014 P7, P10]. In the physical-stability papers: nucleation-site counts in films [konno2006 P2; marsac2006a P4; konno2008 P4], melt or film growth rates [kestur2010b P3; rumondor2010 P5], PXRD crystallinity of stored powders [rumondor2009b P5]. In the ASD dissolution papers: non-sink dissolution of dispersions or of amorphous drug with polymer in the medium; solvent-shift solutions with predissolved polymer; induction times by extinction or pyrene; Raman of slurries for the solid [konno2008a P3, P5; alonzo2010 P2, P4, P5; jackson2015 P3; ilevbare2013d P6].

Values in the library
materialvalue or classconditionspaper ids
8 drugs, 7 polymersmean amorphicity index PVP = PVPVA 70 > E100 67 > HPMC 66 > HPMCAS 62 > PAA 49 > PSSA 48spin-coated films, 7 days dry[vaneerdenbrugh2010b R5]
amides, bases against acids with PAA and PSSAhighest for amides (64–78) and bases; lowest for acids (8–31)as above[vaneerdenbrugh2010b R3, C3]
felodipine, 3% PVP, PVP/VA, HPMCAS, PVAcgrowth ratio at 70 °C 10.0, 6.5, 4.4, 1.2hot stage[kestur2010a R6]
bifonazole with 5% PAA5-fold at 100 °C, 15-fold at 18 °Chot stage[kestur2011 R7]
nimesulide with 5% PVP, PVP/VA, PVAcabout 21-, 16-, 3-fold at 18 °Chot stage[kestur2011 R9, X7]
50/50 powders, acidic drugs with PAA against PVPabout 64–117% against at most about 3% crystallinerotary evaporation, DSC[vaneerdenbrugh2010b R9]
acids, acidic N–H drugs, alcohols (13 drugs)AI with E100, PVP, PVPVA about 54–100; with PAA, PSSA mostly about 4–31spin-coated films, 7 days dry[vaneerdenbrugh2011a R3, C20, C25]
naringenin, quercetinhighest X-ray amorphous content: E100 about 85 and 70%, PAA about 30 and 20%rotary evaporation, PXRD[wegiel2013a R8]
naringenin, quercetin with E100 and PVPno crystals for >200 to >450 days at five conditionsPXRD[wegiel2013a R9]
lumefantrine–PVPVA; –enteric polymerscrystals at 1–8 weeks; only at 50% drug loading (1–40 weeks)40 °C/75% RHhiew2022a R6
IDM, PVPVA in solutionno nucleation for more than 12 h at 5–50 µg/mL; about 40 min withoutS = 6[moseson2020a R3, C11]
BCL, PVPVA 70 µg/mL and HPMCAS 1 mg/mL in solutioninduction above 1 h; none in 8 h; without polymer under 30 min37 °C[moseson2021 R3]
BCL–PVPVA dispersion in the slurryHPMCAS in the medium delays crystallisation by about 10 min and leaves form 2 growth unchangedRaman[moseson2021 R19, R20, C51]
neat PCZ and BCL meltsnucleate within 1 h between Tg and Tm; IDM did not in 4 hDSC holds[moseson2020 R7]
twenty commercial polymers on ritonavir growth (outside)five effective: Pn-IPAAmd > HPMCAS > HPMC > CAPh > CMCABseeded growth[ilevbare2012c C22]
bifonazole in melt-quenched films (outside)PAA the most effective polymer; PAA ineffective on acetaminophen in solution5 wt%[kestur2011 C9; trasi2015 C26]
erlotinib–HPMCAS against erlotinib–PVPVA, coated, 43% RHnone at 48 weeks against about 6 weeks40 °C, SEMmoseson2022a R11, R12
felodipine, 1 µg/mL HPMCgrowth ratio 0.607; induction time 15.3 → 136.5 min; J/J_0 7.05 × 10⁻⁴S 10, 25 °C[alonzo2012 R5, R16, R17]
ritonavir, CAB Adp 0.81induction time ≈120 → ≈244 min5 µg/mL, 20 µg/mL drug[ilevbare2013c R9]
celecoxib, HPMC2.4 → 12.6 min (22 µg/mL); 27.5 → 855.5 min (11 µg/mL)5 µg/mL, 37 °C[ilevbare2013c R9, R15]
danazol, HPMC-AS6–10 → 250–516 min10 µg/mL polymer, 25 °C[jackson2014 R17]
warfarin, six polymersamorphous precipitate ≥ 6 h; 103–224 µg/mL1 mg/mL, pH shift[hsieh2014 R4]
celecoxib, 5 µg/mL HPMCASsupersaturation held 16 h; J_0/J_p about 4,00022 µg/mL drugxie2016a R3, R13
six dihydropyridines, 4.5 mg/mL polymerPVPVA = HPMC = HPMCAS > PVP > CMCAB = CAPAdp > P2VP = PAAnominal 10 mg/mL[raina2015b C16, R9]
telaprevir 150 µg/mL, 5 µg/mL polymerHPMC 243, HPMCAS 175–226, CA-Sub-090 106 min against 14–15 withoutpH 6.8, 37 °C[mosqueragiraldo2016 R4, R5]
acetaminophen S 1.5, 10 µg/mL95% of vials: none 26, PAA 11, HPMCAS 470, HPMC 1043 min20 °C[trasi2015 R1]
atazanavir, volunteer media V5 and V6, 1 mg/mL HPMC134 ± 23 and 45 ± 7 → >360 minpH 6.5, 37 °C[enright2020 R28]
telaprevir δ 28.8, 150 µg/mL HPMCAS-MF, four lecithin mediaabout 357–474 min, no difference37 °C[lu2018 R7]
enzalutamide 120 µg/mL, 50–100 µg/mL HPMCASabout 431–530 min; P177 about 71–125 minpH 6.5[wilson2021 R3]
felodipine with 3% PVP, HPMCAS or HPMCnucleation ≈1.3 × 10⁵ → ≈2–3 × 10³ m⁻³ s⁻¹, equal for all three0% RH, 22 °C[konno2006 R4, C14]
nifedipine and felodipine with 7 wt% PVPabout two orders of magnitude lower; 3–4-fold more to 25 wt%0% RH[marsac2006a R16, C18]
felodipine with 3% PVP vs HPMCAS≈8.6 × 10⁵ vs ≈1.3 × 10⁴ m⁻³ s⁻¹75% RH[konno2008 R3.b, C10]
felodipine with 3 wt% PVP K-90growth 21-fold slower at 70 °C, 6-fold at 110 °Cmelt[kestur2010b R8]
felodipine with 25–50% PVP vs HPMCAS51–82% vs 9–28% crystallized after ≈490 days75–93% RH[rumondor2009b R9, C13]
acetaminophen with PAA or HPMCASPAA the best growth inhibitor but most nuclei; HPMCAS the reverse10% w/w[trasi2012a C46, C53]
flutamide with acceptor or donor polymersacceptor polymers (PVP, PDMA, PIPA) slow growth; donor polymers do not10 mol%[trasi2012b C8, C50]
felodipine forms I and II with 3% PVPrate ratios ≈15.8 and ≈18.7 at 60 °C, ≈3.5 and ≈6.5 at 100 °Cmelt growth[kestur2013a R15]
celecoxib with PVP and TPGSslower than PVP alone at 70–120 °C at 10% PVPmelt growth[mosqueragiraldo2014 R2.b, C13]
resveratrol and curcumin dispersionsPVP and E100 best for resveratrol; E100 best, PVP worst for curcuminstorage at 84% RH[wegiel2013b R12; wegiel2014 R13]
ATP(S) vs ATP(R) with 5% HPMCAS-HF or -LFS 1.9–2.5 times faster than R (HF); R 1.5–1.9 times faster than S (LF)melt growth, 50–80 °C[sato2015 R5.i–l]
six compounds with 5% PHBratio with/without polymer ≈0.42–10, rising with compound Tgmelt growth[sato2016 R11]
indomethacin α vs γ with 10% HPMCratio without/with polymer ≈2900 vs ≈2.9 at 120 °Cmelt growth[tian2017 R12.i]
tacrolimus–HPMC 1:1 vs pure amorphous drugamorphous at 4 weeks vs crystalline after 2 weeks at 40 °C/75% RHopen dish[trasi2017 R16, C40]
felodipine dispersions 75% HPMCAS / HPMC / PVPmaxima 14.1 / 4.9 / 2.3 µg/mLpH 6.8, 37 °C[konno2008a R7]
felodipine 9.5 µg/mL, 150 µg/mL polymer8.5–9.1 (HPMCAS), 7.8–8.9 (HPMC) µg/mL held; PVP to ≈2.8solvent shift[konno2008a R14]
amorphous indomethacin, 250 µg/mL PVP≈23.8 µg/mL held 4 h at 25 °CpH 2[alonzo2010 R14]
indomethacin solvent shift, 37 °Cnone ≈42 → ≈7.3 µg/mL in 30 min; HPMC ≈39 held about 2.5 hpH 2[alonzo2010 R17]
danazol dispersions PVP / HPMC / HPMCASinduction ≈56–70 / ≈188–200 / ≈284–319 minpH 6.8, 25 °Cjackson2015 R5
ritonavir 20 µg/mL, 5 µg/mL of 15 additivesinduction 23.6 to 242.8 against 119.3 minpH 6.8, 37 °C[ilevbare2013d R12]
nifedipine γ → α, 1 mg/mL polymerγ intact ≈20 (PVP), ≈60 (HPMC), ≈110 min (HPMCAS) against ≈1325 °C[raina2014b R9]
celecoxib 22 µg/mL, 5 µg/mL PVP-K12 / PVP-K29/32 / HPMCAS, HPMC / PAAonset ≈1 h / ≈2 h / more than 8–16 h / as no polymerpH 6.8, 37 °C[xie2015 R1; xie2016a R3]
tacrolimus 50 µg/mL with 50 µg/mL HPMConset 6–8 h against within 3 hpH 4.5, 37 °C[trasi2016 R9]
indomethacin, 100 µg/mL HPMC against EPOheld ≈1.5 h against crystals during the titrationpH 2.2, 37 °C[xie2017 R5, R8]
resveratrol dispersionsno matrix crystallization from 80% HPMC, 85% HPMCAS, 95% CMCABpH 6.8, 37 °C[wegiel2015 R14]

Evidence table: crystallization inhibition.

Pitfalls and disagreements

Inhibition of growth, of nucleation and of overall crystallinity need not coincide: the best growth inhibitor of acetaminophen promoted nucleation [trasi2012a C46]. Polymers rank differently for different drugs [vaneerdenbrugh2010b C20; kestur2011 C29]. No polymer property tested at low levels (Tg, melting point, molecular weight) explained the order [kestur2010a C32, C34, C35]. The hydrogen-bond mechanism is a rank correlation over four polymers, and the demixing step is the authors' "speculation" [kestur2010a C38, C42]. Film results carried over to bulk powders for six of seven drugs [vaneerdenbrugh2010b C42, C43, C44]. The IR ranking of the polyphenol polymers separated the best and worst but not the middle ones, and polymer content differed from 30 to 80% in the stability comparison [wegiel2013a X4, X3]. The same ionic contact that protected lumefantrine dispersions slowed the dissolution of the enteric polymers hiew2022a C53. A polymer that inhibits in solution does not necessarily inhibit in the hydrating solid (HPMCAS and bicalutamide; polymers predissolved with amorphous nifedipine) [moseson2021 C51; raina2014b C11]. The mixing condition fails when the dispersion has phase separated, so water-induced separation can remove the benefit of the polymer rumondor2009c C6. Celecoxib with HPMC or HPMCAS at 22 µg/mL and 5 µg/mL polymer gave induction times of about 10–13 min in one laboratory and more than 8–16 h in another [ilevbare2013c R9; xie2015 R1; xie2016a R3]. Growth and nucleation data for the same polymers are often measured at different supersaturations [ilevbare2013b X15]. A polymer that raises the crystalline solubility or lowers the onset of phase separation changes the supersaturation it is credited with (F19) [jackson2014 X9]. In the solid state, equal effectiveness holds for felodipine nucleation when dry, not for growth (polymers differed several-fold) or in humid air [konno2006 C14; kestur2010a R6; konno2008 C10]. After moisture-induced phase separation the PVP level stopped mattering for crystallization at 93% RH [rumondor2009b C20]. The mechanism (barrier at the nucleus, hydrogen-bond coupling, polymer encaged in the crystal) was argued, not measured [konno2006 C40; kestur2010b C35, C42]. A polymer's effects on nucleation and on growth need not agree [trasi2012a C53]. Equal inhibition of two polymorphs is read as action in the liquid, unlike adsorption in solution [kestur2013a C6, C28]. PVP slowed felodipine bulk growth about sevenfold but surface growth only twofold [kestur2013b C32]. A polymer can also speed growth (PHB with high-Tg compounds) [sato2016 C29]; the factor depends on the polymorph and on the side of the growth maximum [tian2017 C37, C35]; and two grades of one polymer can favour opposite enantiomers [sato2015 C28]. PAA, the most effective polymer for bifonazole in melt-quenched films and the best growth inhibitor for acetaminophen melts, was ineffective on acetaminophen in solution (synthesis: contrast between papers) [kestur2011 C9; trasi2012a C46; trasi2015 C26]. In the ASD dissolution papers the ranking depends on the drug (PVP worked for indomethacin, not for felodipine, danazol or ritonavir) [alonzo2010 C22; konno2008a R7; jackson2015 R5; ilevbare2013d R12]. Solution screens predict only the rank order, and HPMC was misranked for felodipine [konno2008a C31; jackson2015 X8]. An additive can stabilize droplet size yet promote crystallization [ilevbare2013d R14].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

crystallization tendency classification

A sorting of neat drugs by when, if ever, they crystallize under a fixed protocol. From the melt: class I crystallizes on cooling (split into I-A, which still crystallizes on liquid-N2 quenching, and I-B, which vitrifies), class II only on reheating, class III on neither [baird2010 R1, C10]; the labels very high, high, moderate and low tendency are used for I-A, I-B, II and III [baird2013 P5]. After rapid solvent evaporation: rapid, intermediate and slow crystallizers [vaneerdenbrugh2010a P9]. An extended scheme combines nucleation behaviour and growth rate into classes IA, IB, II, III and IV [trasi2014a C17].

Findings

Crystallization tendency: F5, F9, F10, F14, F17, F18. Physical stability: F17, F24.

Related concepts

measures crystallization tendency; extended by extended nucleation and growth classification; related to glass-forming ability, glass stability, critical cooling rate and nucleation and crystal growth.

Formulas

none specific; the critical-rate formulas refine the classes: Barandiaran-Colmenero critical cooling rate.

How it is measured or obtained

DSC heat–cool–heat at 20 and 10 °C/min plus liquid-N2 quench [baird2010 P1, P6]; spin coating and polarized light microscopy over 7 days [vaneerdenbrugh2010a P8, P9]; growth rates for the extended scheme [trasi2014a P1].

Values in the library
materialvalue or classconditionspaper ids
51 molecules23 class I, 11 class II, 17 class IIImelt DSC[baird2010 R1]
93 drug–solvent combinations39 class I, 23 class II, 31 class IIIspin coating[vaneerdenbrugh2010a R9]
felodipineclass III (melt and solvent)both routes[baird2010 M37; vaneerdenbrugh2010a R8.ag]
nifedipineclass IImelt DSC[baird2010 M32; raina2015b C12]
celecoxibclass II (melt); class III (solvent)both routes[baird2010 M26; vaneerdenbrugh2010a R8.ae]
atenololclass I (melt); class III (solvent)both routes[vaneerdenbrugh2010a R17]
cilnidipine, nisoldipine, nitrendipineclass IIImelt DSC[raina2015b C12]
curcumin; resveratrolintermediate; rapid crystallizersolvent scheme[wegiel2014 R21; wegiel2013b C6]
naringenin; quercetinintermediate; rapidsolvent scheme[wegiel2013a C19]
lumefantrineclass 3melt DSCtrasi2020 R5
pretomanid, delamanidclass Imelt DSCnguyen2023a C59
nimesulide, nilutamide, celecoxibextended class II (fast growth, low nucleation)extended scheme[trasi2014a C17]
celecoxibslow crystallizer by the cited scheme, yet growth "quite fast"; "quite hard to nucleate"melt films[mosqueragiraldo2014 R17, R16, R15, C7]
acetaminophenforms a glass because nucleation and growth zones barely overlapDSC and hot stage[trasi2012a C39]
Pitfalls and disagreements

The class can be altered by the heating and cooling rates [trasi2012a C7], and 7 of 28 class II and III molecules changed behaviour at other rates [baird2010 X12]. Two schemes are mixed in some papers [trasi2014a X10]. Celecoxib is called a "slow crystallizer" by one later paper although the 2010 screen placed it in class II [mosqueragiraldo2014 R17; baird2010 M26]. The melt class predicts crystallization from aqueous solution only partly [raina2015b C28]. A slow class can hide a fast grower: celecoxib is class-slow because it nucleates poorly, not because it grows slowly [mosqueragiraldo2014 C7].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

crystallization tendency

The propensity of an amorphous or supercooled drug to crystallize, expressed as a class from the melt or after solvent evaporation, as a growth rate, or as a time to crystallize in storage or solution [baird2010 C8; vaneerdenbrugh2010a C33; trasi2014a R1]. The inherent crystallization tendency is called the most important parameter of physical instability and is said to depend on conformational flexibility, configurational entropy, driving force, viscosity and hydrogen bonding, factors "not fully elucidated" [trasi2017 C6]. New aspect (PEG dispersions): the tendency can also be read in a dispersion, relative to the neat drug; in 20/80 comelts with PEG 3350 at 25 °C PEG delayed benzocaine, left haloperidol unchanged and brought forward ibuprofen and fenofibrate, so the authors conclude that PEG "can delay, promote or have no influence" on drug crystallization and that both the neat-drug tendency and the interaction with PEG matter [zhu2012 C6, C38, C39]. New aspect (solution methods): in solution work the tendency decides whether a supersaturated drug first phase-separates or first crystallizes; very fast crystallizers (nifedipine; nimodipine at 37 °C) crystallize just below the LLPS concentration unless a polymer slows nucleation, slow crystallizers form a drug-rich phase first [raina2015a R17, C11, C37; ilevbare2013a C27]. New aspect (Miscibility and drug-polymer interactions): the tendency of the neat drug carries into polymer dispersions. In a spin-coating screen of eight drugs with seven polymers, drugs whose pure amorphous form crystallizes rapidly (class I) "tended to be" more difficult to stabilize and, the authors say, needed more polymer; the overall crystallization tendency of a drug in the dispersions is related to that of the pure amorphous drug prepared in a similar way [vaneerdenbrugh2010b C1, C15]. Class I compounds are therefore "ideal model compounds" for telling polymers apart, whereas the compounds usually used as models in solid-dispersion work are often class III [vaneerdenbrugh2010b C16, C17]. Knowledge of the pure drug's tendency is called "extremely important" early in development and a guide to whether a dispersion is feasible [vaneerdenbrugh2010b C18]. Further cases: naringenin (intermediate crystallizer) and quercetin (rapid crystallizer) could not be made amorphous by rotary evaporation, naringenin only as a spin-coated film, and needed 15–80% polymer to give an amorphous dispersion [wegiel2013a C19, R7, R8]; the 15 model drugs of the donor–acceptor screen all have an intermediate to rapid tendency [vaneerdenbrugh2011a C16]; lumefantrine is a class III glass former (no crystallization on heat–cool–heat; Tg 19.7 °C) whose PVPVA dispersions crystallized in 1–8 weeks hiew2022a R3, R6. New aspect (ASD process): in process papers the tendency is a precondition: a drug must resist crystallization while the solvent leaves in granulation, so slowly crystallizing, larger and more complex molecules are "most suitable" for solvent granulation [trasi2019 C35]; ritonavir crystallizes slowly, so amorphous phase separation can be studied without crystallization interfering li2020 C15. Bicalutamide is "a fast-crystallizing compound in solution" and also crystallizes inside the hydrating solid; the authors name its low Tg, high crystallization tendency, high loading and fast polymer dissolution as the reasons for its susceptibility to matrix crystallization [moseson2021 C6, C60]. The tendency decides whether a residual-crystal level is tolerable: posaconazole, a fast crystallizer, lost supersaturation with 0.3% crystals, whereas indomethacin–PVPVA, a slow crystallizer, was little affected (cited) [shah2024 C56, R26]. Spray-dried ezetimibe–HPMCAS crystallized within 12–19 days at 40 °C/75% RH uncoated [duong2022c R16, R17]. New aspect (Bioperformance): the tendency is used as a descriptor to explain why felodipine reaches LLPS and nifedipine crystallizes first [raina2014a C31, R20]. Pretomanid is a low-Tg, class I rapid crystallizer (reduced glass transition temperature 0.67): its melt-quenched glass crystallized on heating just above Tg and within minutes at room temperature, and its solution crystallized within 2 min near the amorphous solubility nguyen2023a C10, C59, C61, R1, R3, R4. New aspect (Crystallization from solution): the solution counterpart of the class from the melt, that is how fast a drug crystallizes from a supersaturated aqueous solution, read as the type 1 or type 2 behaviour of a pH shift, as the precipitate form (crystalline against amorphous), or as an induction time at a defined supersaturation [hsieh2012 C42; ilevbare2013c R8; hsieh2014 R4]. It is only partly predicted by the melt class (see Crystallization tendency F18). The synchrotron WAXS ranking of six dihydropyridine precipitates (nifedipine 0.25 h to cilnidipine 12 h) is wider than their melt classes (two Class II, four Class III) [raina2015b R1, R6]. New aspect (Physical stability): the relative crystallization tendency of drugs from dispersions "may be dependent" on that of the pure drugs: nifedipine stayed the faster nucleator over felodipine in PVP at every content, dry and humid [marsac2006a C52; marsac2008a C7]. New aspect (Supersaturation from ASD dissolution): behaviour of neat amorphous drugs on wetting: nifedipine, a "relatively fast crystallizer" (cited), crystallized in the particle within minutes even with polymer in the medium, and its faster inherent crystallization than felodipine "appears" to carry over to water [raina2014b M1, C10, C28]; Tg alone did not rank felodipine and indomethacin [alonzo2010 C42]. Resveratrol, classed as a rapid crystallizer (cited), crystallized in or at the matrix of cellulosic dispersions within the first hour of slurrying, and its high melting point and rapid crystallization make effective polymeric inhibitors "essential" [wegiel2015 R22, C27, C16]; lopinavir, a slow crystallizer from solution, was chosen so that leaching and solubility could be measured over hours without crystals [li2016b C5; li2018 C11].

Findings

Crystallization tendency: F9, F13, F14, F17, F18, F20. PEG dispersions: F8, F9. Solution methods: F8, F9. Miscibility and drug-polymer interactions: F15, F16, F23, F24, F26. ASD process: F22, F25, F27, F29, F31, F41, F43, F44. Bioperformance: F1, F10, F27. Crystallization from solution: F1, F3, F16, F21, F35, F36. Physical stability: F2, F17, F24, F33, F34. Supersaturation from ASD dissolution: F1, F2, F16, F23, F29.

Related concepts

measured by crystallization tendency classification; depends on nucleation, crystal growth rate, melt viscosity and thermodynamic driving force for crystallization; related to glass-forming ability, glass stability, physical stability, stochastic nucleation, nucleation induction time, heterogeneous nucleation, semicrystalline solid dispersion, liquid-liquid phase separation, crystallization and crystallization inhibition. Governs matrix crystallization; moderated by crystallization inhibition by polymers. Related to solution crystallization and reduced glass transition temperature. Measured in solution by chaser and non-chaser behaviour; related to conformational flexibility and nucleation rate; related to glass transition temperature.

Formulas

Hoffman equation, classical nucleation barrier; amorphicity index. Reduced glass transition temperature, printed in words for pretomanid (0.67; recomputed 0.673) nguyen2023a E2, M1.

How it is measured or obtained

By the DSC cooling–reheating classification [baird2010 P1]; by spin coating and dry storage [vaneerdenbrugh2010a P9]; by seeded growth rates [trasi2014a P1]; by induction times or precipitate crystallinity in supersaturated solution [ilevbare2013c R8; raina2015b R6]; by storage of neat glasses [baird2010 P7; nguyen2023a R4]. In dispersions: the fraction P(t) of 50 neat melts that had started to crystallize at 25 °C, followed for about 500 h [zhu2012 P3]; onset and t_{50} of the drug in the comelt by XRD and by two Raman bands [zhu2012 P5, P6, R23]; simultaneous SAXS/WAXS of the blend from 0.2 min to 24 h [zhu2011 P2]; crystallization of each neat melt cooled to room temperature under polarized light [zhu2011 P7, R6]. In solution: by the order of extinction onset and visible crystals, with and without a nucleation inhibitor [raina2015a R4, R5], and by how long a drug-rich phase persists before the probe signal returns to the aqueous value (lopinavir 94 min; ritonavir not within 213 min) tres2018 R20, R21. For drug–polymer films of the spin-coating screen, by scoring crystalline area over 7 days and expressing it as an amorphicity index, averaged over drug/polymer ratios, polymers or drugs [vaneerdenbrugh2010b P2, P3, E1, E2, E3, E4]. The class of the pure drug is cited from the group's melt and spin-coating classifications [vaneerdenbrugh2010b R11]. In the process papers: isothermal DSC holds of the undercooled melt between Tg and Tm followed by reheating (a melting peak means nucleation during the hold): posaconazole 1 h at 130–160 °C and bicalutamide 1 h at 130–180 °C nucleated, indomethacin did not in 4 h at 130–150 °C [moseson2020 P7, R7]; in solution by induction time and seeded growth [moseson2021 P12, R3]. In raina2014a the tendency is cited, not measured: felodipine a slow and nifedipine a faster crystallizer [raina2014a R20]. The crystallization-from-solution papers cite the classes from cooling the melt (Baird 2010) and from rapid solvent evaporation (Van Eerdenbrugh 2010), and measure the solution tendency by the pH-shift titration or the unseeded induction time [hsieh2012 P7; ilevbare2013c P9]. In the physical-stability papers, by nucleation in films and crystallization on heating of melt-quenched glasses [marsac2006a P4, P10]. In the ASD dissolution papers: by time to crystallize in aqueous slurry (Raman) and by microscopy of wetted particles [alonzo2010 P5; raina2014b P4, P6].

Values in the library
materialvalue or classconditionspaper ids
31 drugsMCV 216 to 0.02 µm/smelt growth[trasi2014a R1]
haloperidol, benzocainecrystallized within seconds after quench coolingpure melts[zhu2012 R1]
ibuprofen; fenofibratecrystallization probability 0.20 and 0.34 after 3 weekspure melts at 25 °C[zhu2012 R2, R3]
ketoconazoleamorphous after 24 h at room temperaturepure melt[zhu2011 R6]
nifedipine against felodipinegreater tendency for nifedipinemelt-quenched, heated at 2 °C/min[marsac2006a R5, C11]
propranolol against nicardipine saltspropranolol salts more prone to crystallizeamorphous salts[towler2008 C32]
dihydropyridinescilnidipine slowest, nifedipine fastest in solution; for six drugs the ranking is cilnidipine < felodipine = nisoldipine < nitrendipine = nimodipine < nifedipinesupersaturated buffer; synchrotron[raina2015b C13, C28]
nifedipine; nimodipinenifedipine a very fast crystallizer; nimodipine faster than the other four dihydropyridinesaqueous media (cited)[raina2015a R17]
felodipinerelatively slow; nifedipine fastercited[raina2014a R20, C31]
ritonavir, efavirenz (class III); celecoxib (class II)induction times about 120, 5.1 and 2.4 minsupersaturated buffer, 37 °C, calculated amorphous solubility[ilevbare2013c M1–M3, R8]
ritonavirlow tendency; drug-rich phase persists for 213 minno polymer, 24 °Ctres2018 P5, M1, C29, R20
lopinavirdrug-rich phase lost after an induction period of 94 minno polymer, 24 °Ctres2018 P5, R21
papaverine, warfarin, glyburide (slow); dipyridamole (rapid)slow from the melt but crystalline on rapid supersaturation; all crystallized without polymer within about 15–30 minpH shift, 25 °C[hsieh2014 R1, R18, C30]
pretomanidneat glass crystallized within minutesroom temperaturenguyen2023a R4, C10
drugs with polymerspure-drug tendency related to that in dispersionsspin coating[vaneerdenbrugh2010b C1]
haloperidol in PEG 3350onset −100 s, t_{50} 7 s; crystalline from the first SAXS/WAXS frame20/80, 25 °C[zhu2012 R23.a, R23.b; zhu2011 R9]
benzocaine in PEG 3350onset 120–180 min, t_{50} 110–170 min20/80, 25 °C[zhu2012 R23.a, R23.b]
ibuprofen in PEG 3350onset about 100 min, t_{50} about 70 min20/80, 25 °C[zhu2012 R23.a, R23.b]
fenofibrate in PEG 3350onset 120–180 min, t_{50} 140–200 min20/80, 25 °C[zhu2012 R23.a, R23.b]
chlorpropamide; nilutamide in PEG 3350partially crystalline at 24 h20/80, 25 °C[zhu2011 R18.c, R18.e]
ketoconazole in PEG 3350amorphous at 24 h20/80, 25 °C[zhu2011 R18.f]
phenacetin, chlorzoxazone, benzamide, lidocaine, flufenamic acid (class I)mean AI over 7 polymers 47, 47, 48, 55, 59%spin-coated films, 7 days dry[vaneerdenbrugh2010b R4]
flurbiprofen (class I/II); chlorpropamide, bifonazole (class II)mean AI 68, 73, 97%as above[vaneerdenbrugh2010b R4]
class I films with every polymer at 75/25 drug/polymeralmost all fully crystalline (AI 0)as above[vaneerdenbrugh2010b R2]
naringenin; quercetinintermediate; rapid crystallizerneat films, rotary evaporation and spin coating[wegiel2013a C19, R7]
lumefantrineclass III; melting onset 127.9 °C, Tg 19.7 °CDSC heat–cool–heathiew2022a R3
bicalutamide in pH 6.8 buffernucleation in under 30 min without polymer, under 5 min at the highest supersaturation; seeded growth near zero at 30 µg/mL, extremely rapid at 150 µg/mL37 °C[moseson2021 R3, R4]
posaconazole and bicalutamide neat meltsmelting endotherm on reheating after 1 h holds below TmDSC[moseson2020 R7]
indomethacin neat meltonly Tg after 4 h at 130–150 °CDSC[moseson2020 R7]
ritonavir and lopinaviramorphous granules unchanged for one month at 40 °C/75% RHXRPD[trasi2019 R2]
uncoated spray-dried ezetimibe–HPMCAS 50 and 70% DLcrystals by SEM at 19 and 12 daysopen dish, 40 °C/75% RH[duong2022c R16, R17]
uncoated ASD powders of four drug–polymer systemscrystals within about 1–2 weeks40 °C, 31–75% RHmoseson2022a R11
PCZ 100 µg/mL in FaSSIF V2, seeds 10 µg/mL, HPMCAS 0 / 3 / 9 times the drug% left at 30 min about 4.5 / 10.5 / 43.5seeded solution[shah2024 R22]
nevirapineinduction about 5 min at S 3.9 (fast without polymer)pH 6.5[hate2017 R2]
atazanavirrelatively slow; crystallization inhibited more than 4 h with enough polymercitedhate2018 C13
pretomanidinduction time under 2 min at 160 µg/mL in seven media; melting onset of the crystals 147 °CDSC, 37 °Cnguyen2023a R1, R3, R4
carvedilol, clotrimazole, clozapine, ketoconazoleclass III (melt) and III (solvent evaporation); type 2pH shift[hsieh2012 M2, M3, M4, M7, R1]
loratadineIII and II/III; type 2same[hsieh2012 M8, R1]
bifonazole; dipyridamole; droperidol; papaverine; pyrimethamineII/II; I/III; II/III; III/II; not classed; all type 1same[hsieh2012 M1, M5, M6, M9, M10, R1]
six dihydropyridinesmelt: nifedipine, nimodipine Class II; others Class III; solution: 0.25–12 hDSC; solvent shift[raina2015b R1, R6]
nine drugs (griseofulvin, celecoxib, ezetimibe, danazol fast; telaprevir, nifedipine, nevirapine intermediate; ritonavir, atazanavir slow)induction time without polymer about 1 to 66 min100 mM phosphate pH 6.8, 37 °C; basis of the classes not given[mosqueragiraldo2018a R1, M1–M9, X11]
nifedipine vs felodipine glass0.39 vs 0.17 × 10¹⁰ m⁻³ day⁻¹; only nifedipine crystallized on heating (87 °C)22 °C; 2 °C/min[marsac2006a R4.a, R5]
nifedipine vs felodipine with 25% PVP≈4.3 × 10⁵ vs ≈2.3 × 10³ m⁻³ s⁻¹75% RH[marsac2008a R1.f, R1.l]
resveratrolrapid crystallizer; a polymer is needed to make it amorphousspin coating, rotary evaporation, cryomilling[wegiel2013b R1, C6, C27]
curcuminintermediate crystallizer, relatively high tendencysolvent evaporation[wegiel2014 C9, C1]
celecoxibgrows fast but nucleates poorlymelt films[mosqueragiraldo2014 C7]
tacrolimus in a marketed generic capsulecrystallized within days at 40 °C/75% RH, faster than the pure amorphous drugopen dish[trasi2017 R12, R16, C28]
lumefantrine; artemetherclass 3; class 1DSC heat–cool–heattrasi2020 R5, R6, C7
felodipine, neat amorphous≈54% crystalline at 1 minpH 6.8 slurry, 37 °C[alonzo2010 R2]
indomethacin, neat amorphousamorphous for at least 4 hpH 2 slurry, 25 °C[alonzo2010 R11]
nifedipine, neat glasscrystalline (γ) by ≈6 min with or without dissolved polymerpH 6.8, 25 °C[raina2014b R6, R2]
resveratrolrapid crystallizer (cited); Tm 262 °Cstorage and solvent-evaporation class[wegiel2015 R22, M1]
celecoxib, 22 µg/mL without polymercrystallization within 5 minpH 6.8, 37 °Cxie2016a C13
lopinavirslow crystallization from aqueous solutionpH 3[li2016b C5]
delamanidinduction time 2.4 min at pH 1.6 and 10.7 min at pH 6.5 at the amorphous solubility; no glass on cooling the melt at 50 °C/min; Tg 43.3 °C37 °Cduong2022a R2, R3
praziquantel, racemate and R-enantiomerabout 5.5 and 5 min without polymer at their amorphous solubilities; 83 min and 37 min with HPMCAS-MFPBS pH 6.5, 37 °Cpolyzois2024 R3, R4
paclitaxelunseeded crystallization within 6 min at S = 88 without polymerpH 6.8, 37 °C[que2018 R3]
Pitfalls and disagreements

The tendency depends on route and medium: rapid and slow drying differ strongly [vaneerdenbrugh2010a C26], and the solid-state ranking need not hold in dilute aqueous solution [hsieh2014 C30]; in the dihydropyridine series, by contrast, the solution ranking and the two drugs that recrystallize from the melt coincide [raina2015b C28]. No single descriptor captures it [vaneerdenbrugh2010a C45]. In dispersions, heterogeneous nucleation by the carrier can break the link to the pure drug [zhu2012 C41]: the link "was found to break down for the slowly crystallizing compounds" ibuprofen and fenofibrate, because crystalline PEG apparently promotes their heterogeneous nucleation [zhu2012 C41]. The neat ibuprofen and fenofibrate statistics stop at 3 weeks and the dispersion runs have unstated replicates [zhu2012 X5, X6]. The neat-melt entries of the 2011 PEG paper (chlorpropamide, nilutamide and ibuprofen "within a few hours") come from single melts and sit beside the 50-sample statistics of the 2012 paper for ibuprofen [zhu2011 R6; zhu2012 R2]. The polymer fraction needed per drug is not tabulated, although the day-by-day scores show the highest drug fraction that stayed amorphous [vaneerdenbrugh2010b X13, R2]. The class of flurbiprofen depends on the solvent (class I from ethanol–dichloromethane, class II from ethanol), and the HPMC and HPMCAS films used the mixed solvent [vaneerdenbrugh2010b X2, X12]. Class III drugs were left out on the expectation of stability over a week [vaneerdenbrugh2010b C13]. Polymer and chemistry change the ranking within a class, so the class is a risk flag, not a prediction (see F15) [vaneerdenbrugh2010b C20]. The link from the neat drug to the dispersion held in the spin-coating screen [vaneerdenbrugh2010b C1] but broke down for ibuprofen and fenofibrate in PEG [zhu2012 C41] (synthesis: the two papers differ in carrier and test). Posaconazole, indomethacin and bicalutamide were chosen as class III glass formers, yet neat posaconazole and bicalutamide nucleated within an hour between Tg and Tm; an isothermal hold near Tm tests nucleation differently from the cooling and reheating test that defines the class (synthesis) [moseson2020 C5, R7]. The granulation conclusion rests on one pair of slow crystallizers [trasi2019 C53]. In the Bioperformance papers the tendency of the neat melt does not carry into solution with polymer (F10). A rapid crystallizer in the neat state and in solution can still be held by one polymer: HPMCAS-HF kept pretomanid in solution for over 1000 min at S = 5 while most enteric polymers failed within minutes (F27) nguyen2023a R5. In the pH-shift study class III covers all type 2 bases and also three of the four classifiable type 1 bases, so it does not separate the types [hsieh2012 X1]. Efavirenz is class III yet crystallizes in minutes at S about 2.3 [ilevbare2013c R9.a, X4]. Failing to crystallize in the DSC screen "does not guarantee" slow crystallization in solution [raina2015b C29]. The carry-over of the nifedipine–felodipine ranking into PVP dispersions rests on one drug pair and one polymer, and no PVP level giving equal stabilization of the two drugs was found [marsac2006a X7]. A favourable class did not protect a marketed product whose process left the drug outside the polymer: tacrolimus forms a stable glass, yet one generic crystallized faster than the pure amorphous drug [trasi2016 C13; trasi2017 C28, C47]. In the ASD dissolution papers nifedipine and felodipine have similar Tg and moisture sorption (cited) yet differ in water only when polymers are present [raina2014b C27, R17]; the felodipine–nifedipine comparison is cross-study [raina2014b X16]. Delamanid behaved like tacrolimus and bicalutamide, whose residual crystals the polymer does not poison, rather than like indomethacin duong2022a C58.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

crystallization

In this chapter, the formation of crystals from a supersaturated solution or from a drug-rich phase; it depletes the supersaturation, unlike a drug-rich phase, which keeps it [tres2017 C42].

Findings

F3, F8, F9.

Related concepts

contrasts with drug-rich phase and liquid-liquid phase separation; related to crystallization inhibition, crystallization tendency and nucleation induction time.

Formulas

none.

How it is measured or obtained

By visual particles and birefringence under polarized light [raina2015a P7]; by the return of a probe signal toward its aqueous value (pyrene I1/I3, PRODAN lifetime) [raina2015a R16; tres2018 R21]; by a long lifetime component of the drug itself [tres2017 R1.g]; in outside work by PXRD of compacts bhardwaj2018 R3.

Values in the library
materialvalue or classconditionspaper ids
nifedipinecrystals in buffer at ≈38 (25 °C) and ≈58 µg/mL (37 °C)extinction onset with visible crystals[raina2015a R4, R5]
nimodipinecrystals at ≈21.5 µg/mL (37 °C)same[raina2015a R4, R5]
nifedipine with HPMCpyrene I1/I3 back to ≈1.60 at 400 µg/mL after ≈0.76 at 200 µg/mL25 °C[raina2015a R16]
felodipine 108 µM, no HPMClifetime component 9.04 ns (17%) after 15 hpH 7.4[tres2017 R1.g]
lopinavir, no polymerlifetime 1.31 ns at 94 min to 1.06 ns at 213 minpH 7.4, 24 °Ctres2018 P5, R21
itraconazole dispersionsno crystallinity in compacts after dissolutionPXRDbhardwaj2018 R3, C14
Pitfalls and disagreements

Crystallization of a drug-rich phase was inferred from fluorescence in three papers and confirmed by an independent test in none of them [raina2015a X15; tres2017 X6; tres2018 X5]. Extinction cannot tell crystals from a liquid phase [raina2015a C9].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

degree of substitution

The average number of the three hydroxyl groups of an anhydroglucose unit of cellulose that carry a given substituent (maximum 3); DS (CO2H) counts the substituents that end in a free carboxyl (adipate, suberate, sebacate) [ilevbare2012c M23–M36, P8; ilevbare2013b M11–M13]. For the cellulose ω-carboxyalkanoate esters synthesized for ASDs the adipate chain adds hydrophobicity and its terminal carboxyl ionizes at intestinal pH [ilevbare2012c C9, C10]. For telaprevir a high carboxylic acid DS worked (CAP-Adp-085 and CA-Sub-090 about 70 and 106 min at 5 µg/mL; about 472 and 500 min at 50 µg/mL) and a low one failed (CAP-Seb-024, DS 0.24, about 9 min) [mosqueragiraldo2016 R5, M13].

Findings

F8, F11, F25, F36.

Related concepts

related to polymer ionization, polymer hydrophobicity and solubility parameter.

Formulas

none (a ratio of substituents from NMR integrals).

How it is measured or obtained

From ¹H NMR for each substituent; the molecular weight by SEC (polystyrene equivalents) and Tg by DSC complete the polymer description [ilevbare2012c P8, P9, P10]. Total DS runs from 2.16 to 2.98 for the 14 esters of the ritonavir screen and from 2.38 to 2.98 for the five adipates of the pH study [ilevbare2012c M42, X2; ilevbare2012b M2–M7].

Values in the library
materialvalue or classconditionspaper ids
CAP Adp 0.85; CAB Adp 0.81; CA 320S Adp; CAP Seb 0.67; CP Adp; CAP Adp 0.33; CAB Adp 0.25DS (CO2H) 0.85; 0.81; 0.67; 0.67; 0.48; 0.33; 0.25ritonavir growth ratios 2.98; 2.70; 1.83; 0.85; 1.68; 1.64; 0.99[ilevbare2012c R11]
eight esters with DS (CO2H) 0.19–0.26growth ratios 0.83–1.015 µg/mL[ilevbare2012c R11]
CAP Adp 0.85 against 0.33; CAB Adp 0.81 against 0.25same backbone, higher DS (CO2H) gives 2.98 against 1.64 and 2.70 against 0.99ritonavir[ilevbare2012c R11]
CA 320S Sub 0.63; CA 320S Sub 0.90; CA 320S SebDS (CO2H) 0.63; 0.90; 0.57ritonavir growth ratios 10.8; 12.6; 5.7[ilevbare2013b R9, M11–M13]
CAP-Adp-085; CA-Sub-090; CAP-Seb-02470, 106, 9 min (150 µg/mL telaprevir, 5 µg/mL polymer)pH 6.8, 37 °C[mosqueragiraldo2016 R5]
A5a, A5b (carboxylated side chain on cellulose acetate)DS 0.79 and 0.67; acetyl 1.82; modelled at DS 0.50synthesized; MD model[mosqueragiraldo2018a M10, M11, X9]
ECA–ECD (ethyl cellulose ethers)ethyl DS 2.3, side-chain DS 0.69synthesized[mosqueragiraldo2018a M12–M15]
dansyl-labelled HPMCASlabel DS about 0.003 from NMR integrals; hydroxypropyl MS 0.69¹H NMR[wilson2021 R23, E2]
Pitfalls and disagreements

DS (CO2H) and the solubility parameter co-vary within each backbone series, so only two single polymers (CA 398-30 Adp, CAP Seb 0.67) separate their effects [ilevbare2012c X10]. The DS (CO2H) ranks of Table 3 are inconsistent, the Fig. 8 order is not strictly by DS (CO2H), and the outlier is named "CAB Seb 0.67" in places [ilevbare2012c X3, X4]. The total DS of CAB Adp 0.81 is 2.84 or 2.94 [ilevbare2012c X2; ilevbare2012b X6]. The size of the pH 3.8 loss does not follow DS (CO2H) in the middle of the ranking [ilevbare2012b X17]. Polymer compositions are not repeated in the nucleation paper [ilevbare2013c X15]. A5a and A5b differ in side-chain DS (0.79 against 0.58 plus 0.09 unreacted), DS(OH) and Tg as well as spacer length [mosqueragiraldo2016 X25]. The tether pair A5a and A5b also differs in side-chain DS (0.79 against 0.67), so the tether effect is not isolated [mosqueragiraldo2018a X12].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

Δχ effect

Demixing of two miscible components caused by a third component, a solvent, that interacts very differently with each of them; the larger the difference between the solvent–component interaction parameters, the stronger the tendency to separate marsac2010 C36, E1; purohit2017b E4. In the library the solvent is water, the components a hydrophobic drug and a hydrophilic polymer marsac2010 C43.

Findings

F12, F13, F14, F31.

Related concepts

mechanism of moisture-induced phase separation; depends on Flory-Huggins interaction parameter; related to cosolvency and enthalpy of mixing.

Formulas

Δχ effect, multicomponent Flory-Huggins free energy of mixing.

How it is measured or obtained

From the absolute difference of the water–drug and water–polymer Flory–Huggins parameters, each obtained from water sorption marsac2010 E1, R22, E3.

Values in the library
materialvalue or classconditionspaper ids
felodipine–PVP–waterχ water–felodipine ≈3.3, water–PVP ≈0.5 (difference 2.8 by subtraction); felodipine–PVP slightly negativecited valuesmarsac2010 R22, E1
six drugs in PVP–waterseparating drugs had water–drug χ 2.84–3.58, non-separating 2.50–2.7125 °C sorptionrumondor2009c R24, C46
ritonavir with PVP, PVPVA, HPMCAS (outside)larger Δχ, higher tendency to phase separation (argument)stated in wordspurohit2017b E4, C43
loratadine-type ASDs (outside)separation predicted when the difference is large even if drug–polymer χ is negativeargumentyang2021 E2
miconazole–PVPVA 50:50no separation dry at 100 °C; separation with water during casting, storage and immersion, read as a water-driven change of the thermodynamics ("evidence is provided")films and powders[saboo2017 R22, C41, C43]

Evidence table: Δχ effect.

Pitfalls and disagreements

No ternary phase behaviour was measured; all χ values are cited or derived from sorption marsac2010 C43. Within the six-drug set the gap in water–drug χ between groups is only 0.13 and coincides with a difference in hydrogen-bond donor type, so the two explanations cannot be separated rumondor2009c X4, X13. The miconazole argument rests on one Tg after annealing (data not shown) and on images; no interaction parameters were measured [saboo2017 R22, C43].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

desupersaturation

The fall of the dissolved concentration after supersaturation was reached, because crystals nucleate or seeds grow; in an ASD it "corresponds to the crystal growth rate exceeding the dissolution rate" [moseson2020a C14]. A plateau is not the same as a fall: a crystal-free bicalutamide dispersion that stayed at about 18 µg/mL (30 µg/mL dose) without desupersaturation was read as crystallisation inside the dissolving solid, which caps the concentration without lowering it afterwards [moseson2021 C17, R14]. In the posaconazole pH-shift test the concentration falls below the LLPS concentration (about 19 µg/mL in the intestinal medium) when crystals present or newly formed consume the supersaturation; this is not a return to the crystalline solubility of 1.2 µg/mL [shah2024 R11, X15]. New aspect (Bioperformance): the loss of supersaturation, mostly by crystallization from solution or in the matrix; its onset is read from a concentration fall [elkhabaz2017 C19, C23]. In dissolution of enzalutamide–PVPVA dispersions and tacrolimus capsules the fall after the maximum was read as crystallization, from seeds in the product or formed in the medium; absorption lowers the donor too [wilson2018 C18; purohit2019 C17, C34; hate2019 C20, C30]. New aspect (Crystallization from solution): with seed crystals present it reflects growth of the seeds; without seeds the crystals must first nucleate, so the profile has a flat start (the induction time) followed by a fall [alonzo2012 P4, P5; ilevbare2013c R7]. New aspect (Supersaturation from ASD dissolution): the fall of the concentration after a dissolving amorphous solid or dispersion has supersaturated the medium, read as crystallization from solution, sometimes together with crystallization of the remaining solid [alonzo2010 C16, C21; jackson2015 C14].

Findings

ASD process: F25, F26, F27, F28, F38, F39, F40, F41, F46. Bioperformance: F9, F10, F11, F12, F14, F16, F23, F28, F29, F30. Crystallization from solution: F4, F5, F14, F20, F23, F24, F27, F33, F42. Supersaturation from ASD dissolution: F4, F5, F6, F15, F16, F20, F22, F26, F28.

Related concepts

read in non-sink dissolution; driven by crystal seeding; slowed by crystal growth inhibition; contrasts with matrix crystallization. Loss of supersaturation; caused by solution crystallization and secondary nucleation; also lowered by an absorptive sink; driven by crystal growth rate and nucleation induction time; summarized by supersaturation factor; related to residual crystallinity.

Formulas

power-law crystal growth rate, initial growth rate from the desupersaturation slope, supersaturation factor, supersaturation ratio, overall mass crystal growth rate.

How it is measured or obtained

From the concentration–time profile after the maximum, or from seeded runs: 50 µg/mL indomethacin made by antisolvent addition and 10–50 µg/mL bulk seeds added, with the growth rate R_G in µg/s taken from the profile (extraction method not printed) [moseson2020a P10, P20, X12]. In the Bioperformance papers: concentration–time profiles, UV at 233 and 350 nm for induction time, with SHG or PLM to confirm crystals [elkhabaz2017 P5, P8, P10]. In the crystallization-from-solution papers: concentration against time by a fibre-optic UV probe on second-derivative spectra (every 2–5 s), in seeded runs (slope of the first 2–5 min as initial growth rate) and unseeded runs (flat start, then fall); light-scattering extinction and pyrene fluorescence give the matching signals for droplets and crystals [alonzo2012 P3; ilevbare2012a P8; jackson2014 R15]. In the ASD dissolution papers: in situ UV during non-sink dissolution or after a solvent shift; a rise of the pyrene ratio confirms loss of the drug-rich phase [konno2008a P5; alonzo2010 P3, P4; jackson2015 P2, P3]; drug in the filtered liquid of suspensions chen2015a P11.

Values in the library
materialvalue or classconditionspaper ids
IDM, 50 µg/mL, no polymerunseeded about 50 → 25.6 µg/mL at 120 min; with 50 µg/mL seeds about 26.9pH 4.5, 37 °C[moseson2020a R3.a, R3.d]
IDM, 50 µg/mL, 5 µg/mL PVPVA, 50 µg/mL seedsabout 50 → 37.1 µg/mL in 720 minsame[moseson2020a R3.h, X6]
IDM–PVPVA extrudatesslight fall after the peak above 3% crystallinity (131-2 about 40.6 → 39.4; 117-2 about 30.9 → 28.8)50 µg/mL total dose[moseson2020a R6]
BCL–PVPVA S/155 and M/155about 32.4 → 24.5 and about 28.2 → 16.2 µg/mL150 µg/mL dose, 4 h[moseson2021 R12]
paclitaxel–HPMCAS with 18 wt% seeds (outside)desupersaturation by crystal growth; HPMCAS cannot block it completely16 h[que2018 C30]
tacrolimus capsules (outside)steep decline after the maximum shows that seeds grow rapidly in 100 mLpH 4.5[purohit2018 C43]
PCZ–HPMCAS 10% DL, 0.3% crystals against nonepeak about 178 → 18.5 µg/mL at 150 min against about 172.5 → 125 µg/mL at 300 minpH shift at 60 min, dose about 200 µg/mL[shah2024 R12, R14]
PCZ–HPMCAS 25% DL, 3.2% crystals against nonecrystallization after 45 min against about 1.5 hsame[shah2024 R15, C29]
BCL–PVPVA 30% DL, 3% SDS, cryomilled 5 minpeak about 84% at 45–60 min, then about 78% (about 23 µg/mL)dose of at most 30 µg/mLmoseson2022b R10
PCZ 20 µg/mL in FaSSIF V2, HPMCAS 0 / 9 times the drug; seeds 0 / 5 / 10 µg/mL% left at 30 min about 66 / 46.5 / 25; about 99.5 / 96 / 74.5seeded solution[shah2024 R22]
ezetimibe PVP ASD, FeSSIF195 µg/mL at 15 min to 41 at 30 min37 °C[elkhabaz2017 R14]
ezetimibe ASDs, bufferdecline after about 30 min[elkhabaz2017 R10, C19]
tacrolimus generic, 100 mLabout 98% released at 20–30 min, 39.5% at 120 minmedium I[purohit2018 R7]
felodipine, no polymer, unseededabout 5.35 → 1.54 µg/mL from about 10–15 min to 150 minS 10[alonzo2012 R15]
paclitaxel–HPMCASnone unseeded; present with 18 wt% seeds16 h[que2018 R13]
pazopanib19.8 to about 1 µg/mL at 60 minpH 6.5[sugihara2018 R8]
enzalutamide PVPVA ASDsmaximum close to the amorphous solubility, then fall; 10:90 HPMCAS peak only 10 µg/mL with crystals in the medium100 µg/mL total, 12.5 mL, pH 6.5[wilson2018 R6, C18]
tacrolimus, seeded solutionsrate about 0.39 at 50 µg/mL against 0.075 at 20 µg/mL; growth order 1.677seeds from the crystallized generic[hate2019 R17, R18, C30]
tacrolimus 50% and 100% crystalline capsule contents15 and 4 µg/mL at 2 h, still above the crystalline solubility5 mg in 100 mL, pH 4.5[purohit2019 R4]
felodipine, 1 µg/mL HPMC, seeded; unseeded5.1 → 2.17 µg/mL in 58 min; 5.38 → 5.03 over 198 minS 10, 25 °C[alonzo2012 R18]
ritonavir seeded, none; CAP Adp 0.8510.0 → 6.9; 10.15 → 9.25 µg/mL in 2 minS 7.6, 37 °C[ilevbare2012c R7]
danazol 20 µg/mL, no polymerapparent UV concentration 19.2 → 14.4 → 11.8 → 2.1 → 1.4 µg/mL at 1, 5, 10, 30, 60 min25 °C[jackson2014 R15]
celecoxib, HPMC, start S 14.7S 15 for 15 min, 7.8 at 35 min, 4.9 at 100 min, 4.3 at 200–240 min37 °C[ilevbare2013c R16]
paclitaxel with 18 wt% seeds (ASD dissolution chapter)desupersaturation immediate without polymer37 °C[que2018 R7]
telaprevir seeds, 1.86 mM STCDCflat at about 11.2 and 72 µg/mL for 240 min; buffer 4 and 6δ 2.4 and 12.5[lu2017a R11]
telaprevir after 15 h, δ 12.5residual 60.5 (STCDC), 91.7 (SGCDC), 9.0 (STC) of 65.2–95.2 µg/mLdiffusion cell[lu2017a R12]
acetaminophen seeded19.5–19.8 → 13.0 (none) and 16.1 mg/mL (HPMC) at 24 hS 1.5, 20 µg/mL polymer[trasi2015 R11]
atazanavir, posaconazole after nucleation, three mediaatazanavir 1.0, 4.2, 0.3; posaconazole 0.6, 1.9, 1.7 µg/mL·min (buffer-V1, FaSSIF-V1, composite)37 °C, slope after the break[elkhabaz2021 R8, E7]
posaconazole at S 33.6 with nanocrystal seedsfrom about 8.5 to 4.9 µg/mL by 4 min (2 µg/mL seeds), to about 3.4 within about 1 min (20 µg/mL)PBS pH 6.5[duong2022b R13]
felodipine 50 µg/mL nominal, 150 µg/mL PVP; none≈6.3 → ≈1.9 µg/mL in 240 min; ≈2.7 → ≈1.05solvent shift, 37 °C[konno2008a R12]
indomethacin, solvent shift, no polymer≈27.3 µg/mL held about 25 min, then ≈5.3 at 90 minpH 2, 25 °C[alonzo2010 R18]
felodipine 90:10 HPMC, 90 µg/mL addedapparent ≈75 µg/mL at 5 min, ≈22.6 at 50 min37 °Calonzo2011 R2
danazol 90:10 PVP dispersion≈9.2 µg/mL at 60 min to ≈2.2 at 420 min, pyrene ratio risingpH 6.8, 25 °Cjackson2015 R12
nifedipine–HPMC 50:50≈100 µg/mL at ≈22 min to ≈41 at 150 min37 °C[raina2014b R14]
celecoxib–HPMCAS suspension, SDSS ≈8.6 at about 5 min to ≈3.2 at 1 hpH 3, 25 °Cchen2015a R17
celecoxib 22 µg/mL: none / 5 µg/mL PVP-K12 / PVP-K29/32≈20.8 → ≈4.1 in 1 h / ≈20.9 → ≈4.4 by 8 h / ≈9.1 µg/mL at 8 hsolvent shift, pH 6.8, 37 °C[xie2015 R2]
celecoxib–PVP-K12 50% dispersion≈21.0 µg/mL near 6 h → ≈6.5 at 16 hpH 6.8, 37 °C[xie2015 R6]
celecoxib 22 µg/mL seeded: none / 5 µg/mL HPMCAS≈22.5 → ≈4.0 in 30 min / → ≈16.0 µg/mL at 4 hpH 6.8, 37 °Cxie2016a R11
tacrolimus 50 µg/mL: none / 50 µg/mL HPMCfall from ≈150 min / from ≈400 minpH 4.5, 37 °C[trasi2016 R9]
indomethacin–EPO 3:7 dispersion≈77 µg/mL (UV) → 8.8 µg/mL (HPLC) at 1 hpH 2.2, 37 °C[xie2017 R11]
lopinavir 50%: EUD, CAP / HPMCPloss within ≈10–12 h / none in 48 hpH 3, 25 °C[li2018 R6]
paclitaxel–HPMCAS 49/51 with 18 wt% seeds≈31–33 µg/mL reached, then ≈7.9–25.3 µg/mL left at 16 h depending on the seed typepH 6.8, 37 °C[que2018 R14]
posaconazole–HPMCAS 10% dispersion, high against low dose≈22–24 µg/mL to 120 min then ≈6–8; ≈17–21 µg/mL to 90 min then ≈8 µg/mLFaSSGF → FaSSIF, 37 °C[elkhabaz2019a R6, R12]
praziquantel–HPMC E5 LV dispersions, 1.5 mg/mLa 30% drop in FaSSIF after about 75–82%; R-enantiomer lost dissolved drug in every medium37 °C[alvarenga2025 R14, C36]
Pitfalls and disagreements

Growth rates are vessel mass rates, not normalised to seed area [moseson2020a X12]. In the bicalutamide tests the desupersaturation at 150 µg/mL is attributed to growth from solution, whereas the overall low plateau is attributed to growth in the solid [moseson2021 C21, C46, X4]. The IDM extrudates may have lost concentration by growth into the surrounding amorphous solid rather than from solution [moseson2020a X15]. In the posaconazole test the focused beam reflectance signature read as secondary nucleation for the crystal-containing 25% dispersion has the same form as the one read as primary nucleation for the crystal-free one [shah2024 K3, K4, X14]. For bicalutamide with cryomilled surfactant powders the loss is attributed to nuclei in the milled matrix and was not measured moseson2022b C26. In the Bioperformance papers concentration alone cannot separate LLPS from crystallization in turbid media [elkhabaz2017 C30]. Absorption also lowers the donor (F14). With an absorptive sink the fresh generic tacrolimus did not lose supersaturation at 240, 100 or 40 mL, unlike in a closed vessel; only at 40 mL did total dissolved drug fall for the 20% sample (F14, F28) [hate2019 R11, C20, C35]. Apparent UV concentration of a colloidal solution is distorted by droplet size changes: at 20 µg/mL danazol the early fall is attributed to droplet coalescence, not crystallization, and orthogonal methods are needed [jackson2014 C29, C54, C55]. The seeded profile includes any secondary nucleation [ilevbare2012b X18]. After crystallization with HPMC the celecoxib solution sat at S 4.3, not 1, at 240 min [ilevbare2013c R16]. In the ASD dissolution papers apparent UV falls above the amorphous solubility can come from particle growth or settling as well as from crystallization alonzo2011 C14; jackson2015 C12. With HPMC the felodipine solution kept falling slowly; the PVP and buffer solutions approached but did not reach the crystalline solubility in 4 h [konno2008a X10]. After crystallization the celecoxib readings settled at ≈2.6–2.9 µg/mL, above the 1.5 µg/mL crystalline solubility measured by HPLC xie2016a X4. With crystals present from the start, the onset of desupersaturation marks the time at which growth outpaces redissolution of amorphous material, not the onset of crystallization [elkhabaz2019a C49].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

diffusion boundary layer

The thin region at a dissolving surface across which drug moves by diffusion. In a polymer melt a dissolution boundary layer and a heat-transfer boundary layer form at each crystal–polymer interface; mixing thins them and so speeds dissolution, and large particles dissolve slowly [moseson2018 C50, C52, C53]. In the Noyes–Whitney form its thickness h stands in the denominator [moseson2018 E5]. In the bicalutamide population balance model it enters only as a lumped dissolution rate constant whose fit (0.1002 ± 0.0511 µm/s) lies far below the assumed values, which the authors relate to melt viscosity [moseson2022c R16, C30]. New aspect (Release mechanism and LoC): at a dissolving dispersion it is the stagnant layer in which, in the first of two proposed mechanisms, drug and polymer released together dissociate and the drug separates as nanodroplets once it passes the amorphous solubility indulkar2017b C7. Its thickness h stands in the denominator of the Nernst–Brunner form dC/dt = (DA/Vh)(C_s - C) indulkar2019a E2. During congruent release of MePHPH–PVPVA the drug is carried into the diffusion boundary layer by swelling and release of the polymer chains and can separate into nanoparticles within the gel during its residence time of about 2–6 min deac2023a C47. The 2025 bedaquiline paper writes polymer release as the flux across the aqueous boundary layer, J_p = (D_p/\delta)\,C_p, so that anything lowering interfacial polymer solubility lowers drug release kaur2025 E1, C41; the 2025 grade paper uses the same reading bapat2025a C29.

Findings

ASD process: F11, F9, F37. Release mechanism and LoC: F5, F25, F32, F34.

Related concepts

part of crystal dissolution into a polymer melt. Part of the Nernst-Brunner equation; where drug-rich nanodroplets form by liquid-liquid phase separation.

Formulas

Noyes–Whitney equation.

How it is measured or obtained

Not measured in the ASD process papers; the drug gradient around a dissolving crystal was mapped by EDX chlorine line scans (ramps of about 7 and 9 µm) [moseson2019 R9, C41]. In the release-mechanism papers: not measured in these papers; D and h are not given indulkar2019a E2.

Values in the library
materialvalue or classconditionspaper ids
IDM crystal in copovidone, 1 h at 130 °Cgradient about 8 µm on each side of a plateauEDX[moseson2019 R9, C41]
nifedipine ASDs in waternanodroplets form after the drug dissolves in the bulk medium or stagnant diffusion layerisotope scramblingindulkar2017b C26
ledipasvir–copovidonedissolution rate by the Noyes–Whitney form with diffusion layer hcompactsque2019 E1
ritonavir–PVPVAdiffusion-layer equation used for release from a drug-rich surfaceargumentindulkar2019a E2, C22
Pitfalls and disagreements

Boundary-layer thickness in the extruder was not measured [moseson2018 C52]. The isotope study does not separate the bulk medium from the stagnant layer as the place where the droplets form indulkar2017b C26.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

dipole-dipole interactions

Electrostatic interaction between permanent dipoles, proposed in this chapter as the contact of ketoconazole with PVP, since ketoconazole has no hydrogen-bond donor and its PVP carbonyl does not shift: "it seems reasonable to speculate" that the two interact through dipole–dipole forces, helped by the large size of ketoconazole and its van der Waals contacts [marsac2009 C40, C41, R14]. The slight changes in the ketoconazole carbonyl band in PVP dispersions are also "speculated" to come from dipole–dipole interactions, by analogy with ion–dipole interactions reported for PVP with another drug [rumondor2009a C23].

Findings

F2, F4.

Related concepts

contrasts with hydrogen bonding; part of drug-polymer interactions; related to drug-polymer miscibility.

Formulas

none.

How it is measured or obtained

Not measured as an interaction: only the dipole moments of single molecules were computed by DFT (B3LYP/6-311++G(2d,p)) [marsac2009 P5, R12], and the IR changes were compared with calculated physical mixtures [rumondor2009a R10].

Values in the library
materialvalue or classconditionspaper ids
ketoconazole6.03 D; no donor; PVP C=O shift 0DFT; FTIR[marsac2009 R12.h, R14]
nifedipine; felodipine; sucrose9.58; 5.30; 5.40 DDFT[marsac2009 R12.a, R12.b, R12.d]
indomethacin; ibuprofen; vinyl pyrrolidone2.68; 1.76; 3.91 DDFT[marsac2009 R12.c, R12.e, R12.g]

Evidence table: dipole-dipole interactions.

Pitfalls and disagreements

The dipole moment does not rank the carbonyl shift (nifedipine has the largest moment and no shift entry, indomethacin a small moment and the largest shift) [marsac2009 R12]. No dipole–dipole interaction was demonstrated in the mixture [marsac2009 C41; rumondor2009a C23]. The PXRD and DSC results on ketoconazole–PVP leave its phase state open [rumondor2009a X1].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

droplet coalescence

The merging of drug-rich droplets into larger ones; the growth of the ritonavir droplets from about 345 to about 842 nm in 64 min is "consistent with coalescence of the droplets, commonly observed in LLPS" ilevbare2013a R3, C18. The papers of 2017–2022 add ibuprofen droplets, which in buffer coarsened and creamed within 1–2 h, whereas with HPMC they stayed at 345–385 nm for 3 h; flocculation and coalescence were not told apart by DLS because the droplets creamed ueda2020b R7, R15, C39, C40. New aspect (Crystallization from solution): for danazol the authors attribute the early fall of the apparent UV concentration of a phase-separated solution (19.2 to 11.8 µg/mL over 10 min at 20 µg/mL) to coalescence of the drug-rich droplets, which changes how they absorb and scatter light, not to crystallization ("is attributed") [jackson2014 C29, R15]. Polymers adsorbed at the droplet surface are inferred to reduce coalescence because the droplets stay smaller ("it is inferred") [jackson2014 C33]. In the later danazol paper DLS sizes fell from about 350 to 103–136 nm with 1000 µg/mL polymer while NTA means stayed at about 181–270 nm, which the authors read as polymer reducing the formation of some larger droplets, "probably through coalescence" [jackson2016 R19, R21, C30].

Findings

Amorphous solubility and LLPS: F1, F22. Crystallization from solution: F4, F15.

Related concepts

changes the size of the drug-rich phase; occurs in liquid-liquid phase separation. Papers of 2017–2022: Ostwald ripening, colloidal stability. Reduced by polymer adsorption to drug-rich droplets; related to zeta potential.

Formulas

none.

How it is measured or obtained

DLS mean size against time after a single addition of stock at the onset concentration, 37 °C ilevbare2013a P11, R3. DLS Z-average over hours, UV absorbance and extinction, and pyrene fluorescence on the same solution [jackson2014 P8, P9].

Values in the library
materialvalue or classconditionspaper ids
ritonavir dropletsabout 345, 447, 536, 677, 842 nm at about 1, 10, 28, 46, 64 minwater, 37 °Cilevbare2013a R3
ibuprofen droplets, stirred 3 hbuffer below detection at 30 min; HPMC 345–385 nm; PVP-VA 320–440 nm with count rate 470 → 35 × 10⁶ cps; EUD-E 810 → 1110 nmpH 2.0 (D2O), 37 °C, 300 rpmueda2020b R7
danazol aloneabout 490 nm at once; about 9800 nm at 1 h25 °C, above the onset[jackson2014 R22]
with PVPabout 240–250 nm to 1 h; about 2900 nm at 2 h10 µg/mL polymer[jackson2014 R22]
with HPMC; HPMC-ASabout 305–345 nm to 2 h and 820 nm at 4 h; about 230–250 nm to 4 h and 1250 nm at 6 hsame[jackson2014 R22]
ritonavir nanodroplets (ASD dissolution chapter)stabilized against coalescence "likely" by charge repulsion between adsorbed polymers37 °C[ilevbare2013d C38]
danazol droplets, PVP, HPMC, HPMC-ASDLS z-diameter about 350 → 103–136 nm; NTA 181–270 nm1–1000 µg/mL, 25 °C[jackson2016 R19, R21]
Pitfalls and disagreements

Coalescence itself was not observed; size growth is read as its sign ilevbare2013a C18. Droplet size also differs with the technique and the drug (about 116–387 nm for the weak bases) [indulkar2015 R14]. For danazol no droplet size was measured in the first minutes for the drug alone: the DLS points are 0 and 1 h, the second after crystallization (induction 6–10 min), so coalescence is inferred from the UV signal [jackson2014 X6]. The danazol concentration for DLS is not printed [jackson2014 X11]. Time after supersaturation and drug level of the 2016 measurement are not stated [jackson2016 X12].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

drug adsorption onto silica

Uptake of dissolved drug onto a silica surface

For drug-loaded mesoporous silica the papers hold it responsible for incomplete release: dissolved drug returns to the surface in a dynamic equilibrium [dening2018 C23, C4; dening2019 C4]. Neutral drugs bind mainly by hydrogen bonds from silanols to their acceptor groups, and weak bases still charged at the test pH mainly electrostatically [dening2019 C52; mccarthy2020 C41; hate2020b C28, C35]. Adsorption grows with supersaturation, which the authors relate to the higher activity of the dissolved drug ("can be proposed") and which competes with solvation [dening2019 C39; hate2020b C9, C31].

Findings

F3, F4, F5, F6, F7, F9.

Related concepts

measured by an adsorption isotherm; occurs through drug-silanol hydrogen bonding or ionic interactions; part of a dynamic adsorption-desorption equilibrium; cause of incomplete drug release; grows with supersaturation.

Formulas

adsorbed amount by solution depletion, competitive solvent-drug adsorption equilibrium.

How it is measured or obtained

Solution depletion with blank silica added to a drug solution, or isotherms over a range of concentrations [dening2018 P8; dening2019 P3; hate2020a P13; hate2020b P2; mccarthy2020 P7].

Values in the library
materialvalue or classconditionspaper ids
ritonavir, blank SBA-15 about 100 µg/mL28 → about 22 µg/mL (about 20% adsorbed)pH 6.8, 2 h[dening2018 R13]
ritonavir, loaded SBA-15 in medium at 28 µg/mLabout 600 µg more taken up (27% w/w)pH 6.8[dening2018 R14, R15]
ritonavir on SBA-15up to 424 mg/gpH 6.8, isotherm[dening2019 R2]
atazanavir on SBA-15up to about 20.8 mg/g (300 µg/mL silica)HPMC, 2 h[hate2020a R2]
ketoconazole; clozapine; atazanavir on SBA-15pH 6.8 top points about 66; 53; 21 mg/gHPMC[hate2020b R3, R4, R5]
indomethacin; methyl ester on SBA-15up to about 289; 342 mg/gpH 2.2, HPMC[mccarthy2020 R7, R8]

Evidence table: drug adsorption onto silica.

Pitfalls and disagreements

The adsorbed amount is always derived from what is missing in solution; no paper measured drug on silica during release [dening2019 X18]. Per-gram values depend on the silica concentration used [hate2020a X15]. Blank silica took up only about 20% of ritonavir while loaded silica kept about 50%, so retention "may therefore depend only in part on the adsorption equilibrium" [dening2018 C47].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

drug-controlled release

Dissolution paced by the drug itself, slow and typical of high drug loading, in which the driving force vanishes once the amorphous solubility is reached and no droplets form li2019 C48; purohit2017b C50. New aspect (Supersaturation from ASD dissolution): at moderate to high drug loading the polymer leaves the dissolving surface faster than the drug, and a drug-rich interface, "possibly" amorphous, regulates dissolution; if it stays amorphous it "would presumably" cap the concentration at the amorphous level alonzo2011 C37, C46. For marketed tacrolimus capsules the authors "believe" that a 50% drug loading reported for the innovator makes dissolution drug controlled, so that no drug nanospecies form [trasi2016 C41]; a celecoxib paper recalls the cited analysis in which, at high loading, the polymer dissolves faster and leaves a drug-rich layer xie2016a C4. New aspect (Release mechanism and LoC): above the limit of congruency the polymer leaves first and the drug dissolves from a drug-rich surface, by dx/dt = C(S - x) with S the amorphous solubility, so the concentration cannot pass S and no LLPS occurs purohit2017b E3, C50; indulkar2019a C48. Release stops in a medium presaturated with drug indulkar2019a R12, C42. The authors describe the drug rates as close to the neat amorphous drug saboo2019 C12; saboo2020a C16, but several lie well above it saboo2019 X9. Above the limit indomethacin released at about 5–20 times the rate of amorphous indomethacin alone (synthesis: 0.01/0.002 to 0.04/0.002) saboo2020 R3. The 2022 ritonavir surfactant paper restates the regime with the Nernst–Brunner form and the 50% ritonavir result of 2019 indulkar2022 E2, C21, R3.

Findings

ASD process: F14, F15, F21, F23, F38, F48. Supersaturation from ASD dissolution: F7, F9, F10. Release mechanism and LoC: F1, F3, F6, F7, F14, F17.

Related concepts

contrasts with polymer-controlled release; promoted by surface drug enrichment; related to drug-rich surface layer and drug loading. Follows incongruent release; stops by the Nernst-Brunner equation at the amorphous solubility.

Formulas

Noyes-Whitney equation, saturated-medium condition.

How it is measured or obtained

From release rates close to those of amorphous drug alone, or release into saturated medium li2019 R2; indulkar2019a R13. In the ASD dissolution papers: by slow dissolution of intact particles and slowly rising UV curves alonzo2011 R4, R1; jackson2015 R13. In the release-mechanism papers: from drug rates near a compact of neat amorphous drug in the same die, polymer rates several times higher, and zero release into presaturated medium bhardwaj2018 R4, R11; saboo2019 R5; indulkar2019a R12.

Values in the library
materialvalue or classconditionspaper ids
miscible LPV–HPMC E5100% DL: about 1.2 µg/mL at 10 min30 µg/mL doseli2019 R2.f
ritonavir–copovidone 50% DLno release into drug-saturated mediumoutsideindulkar2019a R13, C42
itraconazole–copovidonea threshold drug-to-polymer ratio above which amorphous drug controls releaseoutsidebhardwaj2018 C66
ritonavir–PVPVA spray-dried, 50% and 75% DLabout 0.0053–0.0063 and 0.0031–0.0040 mg·min⁻¹·cm⁻¹, near neat amorphous ritonavir (about 0.0026), whatever the solventpH 6.5li2020 R10, C37
ritonavir/lopinavir co-granule, 50:50 drug:polymerexpected drug-controlled; polymer leaves first and the surface turns drug-richacid[trasi2019 C46]
IDM–PVPVA 1:1dissolution described as drug-controlled; the polymer is expected to dissolve quickly, leaving amorphous drug particlesnon-sink, pH 4.5[moseson2020a C30]
BCL–PVPVA 50% DLpolymer about 18% at 10 min and 80% at 2 h; drug plateau about 73% from about 120 mindose of at most 30 µg/mLmoseson2022b R6, R7
felodipine 50:50 HPMC dispersionparticle intact for at least 30 min; ≈8.9 µg/mL at 60 min37 °Calonzo2011 R4, R1
danazol 50:50 HPMC; HPMCAS dispersionspast 8 µg/mL after ≈270 min; ≈6.0 µg/mL plateau25 °Cjackson2015 R2, R13
celecoxib–HPMCAS 50% and 60% drug≈21.1 µg/mL only after 16 h; ≈15.8 of 22 µg/mL at 16 hpH 6.8, 37 °Cxie2016a R4
tacrolimus innovator (cited)50% drug loadingreport, no reference[trasi2016 R19]
ritonavir 50:50 films with PVP, PVPVApolymer dissolved; ritonavir ≈18 and ≈9 µg/mL at 240 min, below 27 µg/mL25 °C, pH 6.8purohit2017b R15, R16, R1
ITZ–PVPVA 25, 50%47–64 µg/min/cm² against 51 for amorphous ITZ; polymer 3.5–4 times faster (normalized)0.1 N HClbhardwaj2018 R4, R11
ritonavir–PVPVA 40, 50%≈3% and ≈0.65% of the drug in 180 min; 0 into saturated medium (50%)pH 6.8, 37 °Cindulkar2019a R3, R12
ledipasvir–PVPVA 7.5–20%≤ ≈7% drug and ≈17–23% polymer at 90 minsameque2019 R3, R4, R11
nilvadipine 15, 20%; cilnidipine 20, 25% in PVPVA0.035, 0.013; 0.006, 0.002 mg/min/cm² (neat nilvadipine 0.002)samesaboo2019 R5, R6
felodipine–PVP 15–30%≈0.005–0.020 mg/min/cm², 5–25 times neat felodipinesamesaboo2020a R14, R13
indomethacin–PVPVA 15–25%≈0.01–0.04 against 0.002 mg/min/cm² for amorphous drug; PVPVA ≈0.50–0.72pH 2.1, 37 °Csaboo2020 R3, M5
atazanavir–PVPVA 10%≈0.07 against PVPVA ≈0.24 mg/min/cm²pH 6.8, 37 °Ccorreasoto2022b R3, P5
Pitfalls and disagreements

In the lopinavir films phase separation turns a drug-controlled dissolution at high DL toward polymer-controlled release of the polymer-rich phase, but only partly (33% DL reached about 13 of 30 µg/mL against about 17 for miscible 15% DL) li2019 R2, C58. Drug-controlled release was inferred from the loading and the congruent boundary in the ritonavir studies, not from polymer release measured on the same powders li2020 C66, X13. In the ASD dissolution papers the drug-rich surface layer was not observed alonzo2011 C46. The 50:50 PVP danazol dispersion dissolved as fast as the 90:10 one jackson2015 X9, and the 50:50 danazol films were partly crystalline before dissolution jackson2015 X10. The 50% tacrolimus loading is unreferenced and the generics' loadings are unknown; release rates were not measured [trasi2016 X4]. The drug-rich layer of ITZ compacts is a "supposition" from the curving polymer profiles bhardwaj2018 C52. Nilvadipine above the switch released 17 and 6.5 times faster than the neat amorphous drug, a significant difference saboo2019 X9, R8. The presaturation of the medium is not described indulkar2019a X8.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

drug–drug miscibility

Mixing of two drugs in one amorphous phase; it makes a mixed drug-rich phase when both dissolve [alhalaweh2016 C9, C26]. A crystalline drug can also enter an amorphous drug-rich phase from solution: darunavir partitioned into the atazanavir-rich phase in water although the dry amorphous drugs were phase separated [alkalla2026 C4, C5, C30, C31].

Findings

F6, F20.

Related concepts

lowers amorphous solubility through the drug-rich phase; related to Fox equation.

Formulas

ideal-mixing reduction of amorphous solubility.

How it is measured or obtained

Melting-point depression of the crystalline drug by the amorphous second drug and one Tg of the melt-quenched mixture [alhalaweh2016 P7, P8].

Values in the library
materialvalue or classconditionspaper ids
ritonavir with atazanavirmelting onset 394.4 K to about 380.1 K at x_ATV 0.52; one Tg 349–323 KDSC[alhalaweh2016 R8, R9]
ritonavir with lopinavirliquid-state miscibility; one Tg in every mixture[trasi2015a C41; trasi2015b R2, C39]
atazanavir with darunavir, dry amorphous mixturestwo Tgs in every mixture (neat 105 and 62 °C); heterogeneous co-melt-quenched film with nanoTA softening at 118 ± 4 and 92 ± 2 °CDSC, nanoTA[alkalla2026 R15, R16, R17, C30, C31]
atazanavir with darunavir in waterdarunavir enters the atazanavir-rich phase; atazanavir's amorphous solubility falls as the darunavir fraction of the phase risesantisolvent, 150 µg/mL atazanavir, pH 6.8[alkalla2026 R11, C4, C39]
Pitfalls and disagreements

Only miscible, structurally similar drugs were tested; immiscible pairs are outside the evidence [alhalaweh2016 C40]. Miscibility in water and immiscibility in the dry state differ, the mixing in water is inferred from supernatant depletion, and the plotted mole fraction has no printed calculation (F20) [alkalla2026 X5, X6].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

drug leaching

Evidence table: drug leaching. Content from the ASD dissolution chapter (celecoxib, 2015) and the ASD process chapter.

Passage of drug, and of polymer, out of suspended ASD particles into the surrounding liquid while the particles stay largely undissolved, as in acid for dispersions of enteric polymers. Because the drug is amorphous, leaching can create a supersaturated liquid, whose concentration falls if the drug then crystallizes chen2015a C13. For lopinavir dispersions of three HPMCAS grades and HPMCP at pH 3 the leached drug settled between the crystalline and the amorphous solubility, the dispersions leached less polymer than the pure polymers ("consistent with a miscible solid dispersion"), surfactants raised the leached drug in step with its crystalline solubility, and SDS at pH 5 raised drug and polymer leaching together [li2016b R4, R3, C35, C39, C24].

Findings

F15, F18, F19, F24, F25, F27.

Related concepts

depends on pH-dependent polymer solubility and polymer-controlled release; raised by polymer-surfactant complexation; related to solubility suppression by an undissolved, mixed polymer.

Formulas

supersaturation ratio.

How it is measured or obtained

Filtering the suspension liquid (0.45 µm) and assaying drug by HPLC, divided by the crystalline solubility in the same medium, and polymer by colorimetry chen2015a P11, P12, E1; drug in acid over time in two-stage tests moseson2023 R11. Spray-dried dispersions, 100 mg in 10 mL citrate buffer at 25 °C and 300 rpm, 0.45-µm filtrates to 3 h, lopinavir by HPLC and polymer by phenol–sulfuric acid colorimetry [li2016b P4, P7, P8].

Values in the library
materialvalue or classconditionspaper ids
celecoxib–HPMCAS 33.3%, pH 3, no surfactantS ≈4.3 → ≈6.7 over 48 h, no crystals10 mg/mL, 25 °Cchen2015a R17, R14
same, 0.25% SDSS ≈8.6 at about 5 min, ≈3.2 at 1 h (crystals)25 °Cchen2015a R17
same, 0.025% Triton X100S ≈1.6–1.8 for 48 h25 °Cchen2015a R17
posaconazole–HPMCAS dispersions, gastric stage (ASD process)a low amount of amorphous drug leaches; a coating slows itpH 1.2 and 4.0 mediamoseson2023 C17, C20
lopinavir 33% with HPMCAS LF / MF / HF; HPMCP≈7 µg/mL each; ≈5 µg/mLpH 3, 25 °C, 3 h[li2016b R4]
same, polymerbelow 5 µg/mL from the dispersionspH 3[li2016b R3]
lopinavir–HF with STC; SDS at pH 5; PVPVA + SDS≈25.6; ≈33–39; ≈50 µg/mL25 °C[li2016b R19, R13, R17]
posaconazole–HPMCAS 10 / 25 / 50% drug7.5 / 10 / 11.5% of a 400 µg/mL dose in 60 min, below the 115.1 µg/mL crystalline solubilityFaSSGF pH 1.6, 37 °C[elkhabaz2019a R10, R1]
delamanid salt dispersions, acid stage≈30% (HPMCP-50), under 10% (HPMCP-55) and ≈21–36.5% (HPMCAS grades) at pH 1.6; about 0.5–3.5% at pH 3.025% drug, 37 °C[nguyen2023c R11]
uncoated against coated delamanid–HPMCP-50 tablets≈30–41 µg/mL against below 0.5 µg/mL in the gastric stagepH 1.6, 37 °C[nguyen2023b R2, R10]
Pitfalls and disagreements

The supersaturation in SDS assumes that about 860 µg/mL leached HPMCAS leaves the celecoxib solubility unchanged, which was not tested chen2015a X10, C11. The surfactant-free suspension leached to the highest supersaturation without crystallizing chen2015a X6. Polymer values from the dispersions lie below detection or near quantitation and differ between figures [li2016b X7, X6]; the amorphous solubility was measured only in plain pH 3 buffer, so leaching with additives cannot be set against it [li2016b X15]. Leaching from an undissolved enteric matrix is attributed to the drug being molecularly dispersed in the polymer, and rose with drug loading for posaconazole [nguyen2023b C35; elkhabaz2019a C29].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

drug loading

The weight fraction of drug in an ASD (10, 30, 50% in the earlier papers). Higher loading gave slower and lower release in the atazanavir and telaprevir dispersions hate2018 R11; mosqueragiraldo2018b R5, R16. Enzalutamide dispersions differ: 10% in HPMCAS crystallized while the 50% one reached the ceiling slowly, and 50:50 CPHPC-106 gave an exposure like a lipid formulation at a tenfold higher loading (F8, F24) [wilson2018 R6; wilson2020 C19, C22]. New aspect (Release mechanism and LoC): in the release-mechanism chapter drug loading is the main variable, and its limit for congruent release is a concept of its own (limit of congruency). For grazoprevir–HPMCAS solvent-evaporated dispersions release declined steeply with loading, complete at 5%, about 80% at 10 and 15%, and about 30% at 50, 60 and 75%, an apparent plateau hiew2023 C18, R8. At nearly the same bulk loading, the release of co-precipitated particles depended on how much drug sat at the particle surface (hierarchical particle approach) hiew2023 R14, R17. In 2025 75% grazoprevir–HPMCAS particles with a wetting secondary excipient released like 20–30% dispersions, and the calculated loadings of the treated particles were 71.6–73.9% hiew2025 R9, R10, R8.

Findings

Bioperformance: F8, F9, F23, F24, F27. Release mechanism and LoC: F11, F28, F35.

Related concepts

affects matrix crystallization and reaching the amorphous solubility; part of amorphous solid dispersion. Limited by the limit of congruency; raised at the particle level by the hierarchical particle approach; interacts with surface drug enrichment.

Formulas

none.

How it is measured or obtained

Set by preparation (rotary evaporation at 10, 30, 50 wt%); effect read from dissolution, flux and AUC hate2018 P5; mosqueragiraldo2018b P1.

Values in the library
materialvalue or classconditionspaper ids
atazanavir HPMCAS 10 / 30 / 50%apparent 248 / 99 / 84 µg/mL at 120 min; AUC 1220 / – / 660closed; absorptivehate2018 R11, R15
telaprevir HPMCAS 10 / 30 / 50%above 90 µg/mL at about 2 / 21 / 600 minpH 6.8mosqueragiraldo2018b R5, R16
grazoprevir ASDsrelease complete at 5%, about 80% at 10–15%, about 30% at 50–75%hiew2023 C18
tacrolimus commercial ASD50% loading; higher loading may not generate nanospeciescited[trasi2016 R19, C41]
enzalutamide in HPMCAS-MF 10 / 50%10%: peak about 10 µg/mL with crystals; 50%: ceiling reached in 3–4 h100 µg/mL total, pH 6.5[wilson2018 R6]
enzalutamide in CPHPC-106 10:90 / 50:50AUC0–inf 516 / 305 µg·h/mL; mass flow about 0.53 / 0.49 µg/minrats, 50 mg/kgwilson2020 R6, R8, C22
grazoprevir–HPMCAS-LF solvent-evaporated, 5–75%≈102 → 63 → 43 → 27–30% released at 90 mintwo-stage SGF → FaSSIFhiew2023 R8
binary cPADs at 60; 75%; hierarchical cPAD at ≈73%≈37.5; 17%; ≈71%samehiew2023 R17
grazoprevir–HPMCAS hierarchical particles73.9% (5 mg/mL HPMC), 71.6% (10 mg/mL, 120 min)calculatedhiew2025 R8
Pitfalls and disagreements

High loading is "normally preferred" for dose size and cost mosqueragiraldo2018b C59. The limit differs by drug and polymer (F8). Most polymers work well only at low loading, so dispersions are mostly polymer, which raises dose-form size wilson2020 C19; a polymer that works at 50% loading is the aim of the enzalutamide study (F24) wilson2020 C22.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

drug-polymer complexation

Evidence table: drug-polymer complexation. Content from the ASD dissolution chapter (2008, 2011) and from papers of the release-mechanism and miscibility chapters named in the table.

Association of drug and polymer in aqueous solution into a complex, which can raise the apparent solubility of the drug or, if the complex is insoluble, take drug and polymer out of solution. In the ASD dissolution chapter it was the alternative explanation of high dispersion concentrations, "discounted" for felodipine because 1 mg/mL PVP, HPMC or HPMCAS left the crystalline solubility at 0.98–1.01 against 0.94 µg/mL [konno2008a C17, C5, R1]. During dispersion dissolution it was shown for resveratrol: in PVP solution resveratrol formed soluble and then insoluble, non-crystalline complexes ("it is clear"), and the gain from HPMCAS dispersions is "mainly due to" a soluble resveratrol–HPMCAS complex, free drug being at most about twice saturation [wegiel2015 C33, C41]. For polymers the authors equate solubilization with complex formation [wegiel2015 C25]. New aspect (Release mechanism and LoC): an insoluble drug–polymer complex as the drug-rich phase of a dissolving dispersion. The lower amorphous solubility of PHPH with PVPVA is "likely" due to insoluble PHPH–PVPVA complexes, as reported for other compound–polymer pairs deac2023b C15. Complex formation "was further shown" for PHPH and TIPP by the large PVPVA content of their amorphous insoluble phase, while the MePHPH and MeTIPP insoluble phases held very little polymer deac2023b C44; the PHPH–PVPVA insoluble phase is described as a complex coacervate, the case of associative separation deac2023b C47. In 2024–2025 complexation with HPMCAS was measured by spiking drug and polymer from THF into buffer and assaying the polymer left in solution: at pH 6.0 and one drug per acid group 5–17% for an acid, a neutral ester, ritonavir and cilnidipine, 60–90% for phenolphthalein, loratadine and cinnarizine, up to about 96% for bedaquiline bapat2024 P9, R12; kaur2025 R5. See insoluble drug-polymer complex.

Findings

Supersaturation from ASD dissolution: F4, F7, F17. Release mechanism and LoC: F27, F32, F33.

Related concepts

related to drug-polymer interactions, free drug concentration and crystallization inhibition by polymers. The insoluble form gives associative phase separation and high polymer partitioning into the drug-rich phase; lowers the amorphous solubility measured with polymer.

Formulas

percent polymer complexed.

How it is measured or obtained

Crystalline solubility with and without dissolved polymer [konno2008a P4]; membrane flux, which sees only free drug alonzo2011 C23; elsewhere coprecipitation of drug and polymer bapat2024 R11. Rising drug addition to a fixed polymer solution with PXRD and IR of the precipitate; total concentration against membrane flux [wegiel2015 P3, P10].

Values in the library
materialvalue or classconditionspaper ids
crystalline felodipine with 1 mg/mL PVP / HPMCAS / HPMC0.98 / 1.01 / 1.00 against 0.94 µg/mLpH 6.8, 37 °C, 24 h[konno2008a R1]
felodipine with HPMC in solutionnot complexed, read from the flux result37 °Calonzo2011 C23
bifonazole and lidocaine with PAA, PSSA (Miscibility)non-crystalline precipitates read as drug–polymer complexessolutions in ethanol[vaneerdenbrugh2010b C25]
cinnarizine with HPMCAS-MF (Release mechanism and LoC)about 41, 67, 82 and 90% of HPMCAS complexed at drug/COOH 0.25, 0.5, 0.75 and 1pH 6.0bapat2024 R11
crystalline resveratrol in 20 mg/mL PVP709, 1610, 1193, 706, 99 µg/mL at 658–11,037 µg/mL added; amorphous drug–PVP precipitatepH 6.8, 37 °C, 24 h[wegiel2015 R6, R7]
resveratrol–HPMCAS 15:85up to ≈1610 µg/mL with flux at most about twice the crystal'spH 6.8, 37 °C[wegiel2015 R19, R20]
PHPH; MePHPH with 1 mg/mL PVPVAamorphous solubility 200 → 27.5; 2.81 → 4.40 µg/mLUV extinctiondeac2023b R1
PHPH, TIPP, MeTIPP, MePHPH nanoparticles≈77, 36.5, 9, 5 wt% PVPVA60 °C, NMRdeac2023b R3
eight drugs with HPMCAS-MF, 1:1 drug:COOH5 / 7 / 15 / 17 / 60 / 70 / 90% (IND / INDester / RTV / CIL / PHPH / LOR / CNZ)pH 6.0 spike testbapat2024 R12
cinnarizine with HPMCAS LF, HF30 → 70% and 70 → 99% (0.25:1 → 1:1)samebapat2025a R9
Pitfalls and disagreements

An unchanged crystalline solubility at one polymer level rules out solubilizing complexes at that level only [konno2008a C17]. The "no complex" reading from flux is indirect; association was not measured alonzo2011 C23. Neither resveratrol complex was detected directly: the HPMCAS complex rests on flux, the PVP complex on a precipitate formed from crystalline drug, and E100 complexation, named in the abstract, has no data [wegiel2015 C41, C33, X8].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

drug-polymer hydrogen bonding

Evidence table: drug-polymer hydrogen bonding. Content from the release-mechanism chapter (2020–2022), with rows from the Physical stability chapter.

A hydrogen bond between a donor group of the drug (NH, OH or COOH) and an acceptor of the polymer, in PVP and PVPVA the carbonyl of the vinylpyrrolidone unit, read from a shift of the polymer carbonyl band to lower wavenumber saboo2020 R14, C20; que2021 R7. In the release papers it is tested as a cause of a low limit of congruency: indomethacin, which hydrogen-bonds to PVPVA, had a much lower limit than its methyl ester, which does not, so the hypothesis that hydrogen bonding in the dry dispersion raises the limit "appears incorrect" saboo2020 C48; from the same pair Yang and co-workers (2021) conclude that strong interactions such as hydrogen bonding "are likely to" lower the polymer release rate and hence drug release yang2021 C29. In the Physical stability chapter, sorbed water disrupts drug–polymer hydrogen bonds of NH-donor drugs with PVP, producing a drug-rich phase purohit2015b C27, and a larger carbonyl shift with COOH donors than with NH donors is read as a stronger drug–polymer interaction rumondor2009c C48.

Findings

Release mechanism and LoC: F10, F17.

Related concepts

a case of hydrogen bonding and of drug-polymer interactions; the weaker alternative in donor-free analogues is halogen bonding; lowers the limit of congruency in the analogue pairs; may shift the ternary phase diagram.

Formulas

none.

How it is measured or obtained

Infrared spectra of the carbonyl region of dispersions against loading and, for tablets, against dissolution time saboo2020 R14, R16; que2021 R7; analogues without donor groups as controls saboo2020 R18; que2021 R7.

Values in the library
materialvalue or classconditionspaper ids
indomethacin–PVPVA 10–70%1705 cm⁻¹ dimer band absent; hydrogen-bonded PVP carbonyl band at 1634 cm⁻¹ growing with loadingdry tabletssaboo2020 R14
indomethacin methyl ester–PVPVA 25%PVP carbonyl region unchangeddry tabletssaboo2020 R18, C23
TIPP; PHPH in PVPVAVP carbonyl shifted by up to 30 cm⁻¹; new band at about 1650–1654 cm⁻¹films 10–90%que2021 R7
Me-TIPP; Me-PHPH in PVPVAmaximum shift 7 cm⁻¹ (halogen bond); minimal shiftsameque2021 R7
nifedipine, pimozide, droperidol; indomethacin, ketoprofen with PVP (Physical stability chapter)PVP carbonyl red shift 20–24; 42–44 cm⁻¹dry dispersionsrumondor2009c R29
ritonavir–PVP 80:20 (Physical stability chapter)hydrogen-bond band at 1654 cm⁻¹ lost after 97% RHfilms, driedpurohit2015b C17
Pitfalls and disagreements

In the analogue pairs hydrogen bonding goes with a higher Tg and with drug–drug bonding, so the two effects are hard to separate: all high-Tg drugs of the drug-property study can hydrogen-bond with both polymers while the low-Tg drugs lack donors yang2021 C25, and drugs that hydrogen-bond strongly to PVPVA also had high Tgs correasoto2022a C49. The release papers read the bonds in dry dispersions or after drying; whether they persist in the hydrated matrix was not measured que2021 C44.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

drug-polymer interactions

The contacts between drug and polymer in an amorphous dispersion, relative to the contacts in the pure components: strong adhesive (drug–polymer) interactions formed at the expense of weak cohesive (self) interactions make mixing exothermic, adhesive interactions that require breaking strong cohesive ones do not [marsac2009 C3, C36]. The interactions are hydrogen bonds where the drug has a donor and the polymer an acceptor, and, for a drug without donors, perhaps dipole–dipole forces and van der Waals contacts [taylor1997 C35; marsac2009 C41; rumondor2009a C23]. Specific interactions have been postulated as one way polymers stabilize amorphous drugs, and as a condition of single-phase dispersions [kestur2010a C3; marsac2009 C3]. In this chapter they are the common thread of the miscibility papers (whether the pair mixes) and the inhibition papers (whether the polymer slows crystallization). The later papers add ionic (acid–base) contacts of E100, enteric polymers and PSSA with basic or acidic drugs [wegiel2013a C16, C35; hiew2022a C25, C48; vaneerdenbrugh2011a C22] and a weak halogen bond between compounds with Cl, Br or I but no donor and the PVP carbonyl que2020 C1, C25. A polymer can also bond to itself (PAA, dextran), which competes with the drug [rumondor2009a C45; vaneerdenbrugh2012a C36].

Findings

F1, F2, F3, F4, F7, F8, F12, F13, F14, F15, F17, F20, F21, F23, F24, F25, F26.

Related concepts

includes hydrogen bonding and dipole-dipole interactions; measured by Flory-Huggins interaction parameter and activity coefficient; determines drug-polymer miscibility and crystal growth inhibition by polymers; related to enthalpy of mixing; includes acid-base interaction and halogen bonding.

Formulas

Flory-Huggins melting point depression, Flory-Huggins activity equation.

How it is measured or obtained

Spectroscopically, by shifts of IR bands of the drug and the polymer carbonyl in dispersions against physical mixes and amorphous references [taylor1997 C24, C26; marsac2009 P4]; by a second principal component of the IR spectra beyond calculated physical mixtures [rumondor2009a P5, C9]; thermodynamically, by the melting point depression of the crystalline drug in the polymer (χ) and by the solubility of the drug in a liquid analogue of the polymer (activity coefficient) [marsac2009 P6, P7]; by DSC and PXRD for the resulting phase state [rumondor2009a P2, P8, P9]. Interactions are not measured at the temperature and polymer level of the growth studies [kestur2010a X5]. Further methods: IR band shifts of the polyphenol OH and the polymer C=O in films [wegiel2013a P4]; XPS of N 1s and of halogen core levels hiew2022a P16; que2020 P5; solution NMR titration with a monomer analogue for a binding constant que2020 P6; crystal-structure statistics of competing groups [vaneerdenbrugh2011a P5].

Values in the library
materialvalue or classconditionspaper ids
indomethacin–PVPacid OH bonded to PVP carbonyl; dimers opened; incomplete bindingIR, 5–70 wt% PVP; physical mixes show none[taylor1997 C35, C26, C37]
felodipine–PVP, nifedipine–PVPone phase over 10–90% and 25–70% PVP; hydrogen bonding "presumably" behind the second PCIR, PXRD[rumondor2009a C38, C20]
felodipine–PAAlittle mixing at 30–70% PAA; competition from PAA self-association "speculated"DSC, IR, PXRD[rumondor2009a C44, C45]
ketoconazole–PVPnear-athermal mixing, no carbonyl shift; dipole–dipole forces "speculated"melting, FTIR[marsac2009 C40, C41, R12.h]
felodipine with PVP, PVP/VA, HPMCAS, PVAcstrength PVP > PVP/VA > HPMCAS ≥ PVAcNH shifts at 50 wt% polymer[kestur2010a C26, R9]
nimesulide with PVP, PVP/VA, PVAcpresent but small; limited by the intramolecular bondIR, 20–50 wt% polymer[kestur2011 C23, C24, C27]
amide and basic drugs with PAA, PSSAhighest crystallization resistance; acidic drugs lowestspin-coated films, 7 days[vaneerdenbrugh2010b C23, C24, C27]
indomethacin–PVP K12χ −0.82 (melting), −1.83 (EP solubility)most favourable of five pairs[marsac2009 R7.e, R9.e, C42]
naringenin, quercetin with PVP; with E100hydrogen bonding strongest with PVP; acid–base contact with E100 (amine bands lost at 50% quercetin)IR, films[wegiel2013a R2, R4, R6]
lumefantrine with enteric polymers and PVPVAprotonated 19–55% with HPMCAS, HPMCP, CAP, Eudragit L 100; 0% with PVPVAXPS, 25% drug loadinghiew2022a R20
clotrimazole, loratadine, brotrimazole, Me-DIBF with PVPVAhalogen bond: K_F 0.56–1.11 M⁻¹, carbonyl shift 2–6 cm⁻¹NMR, IRque2020 R12, R11
15 drugs, 7 polymerscomplementary donor and acceptor groups give the highest amorphicity indexspin-coated films[vaneerdenbrugh2011a R3, C20, C33]

Evidence table: drug-polymer interactions.

Pitfalls and disagreements

In every inhibition study cited here the interaction is inferred or measured under other conditions than the crystallization test, and its causal role is argued, not demonstrated [kestur2010a X5, X6; kestur2011 X9, X10; vaneerdenbrugh2010b C33]. The two thermodynamic routes agree in sign but not in size [marsac2009 X7]. A strong donor polymer is not enough when it bonds to itself (PAA with felodipine) or when the drug donor is tied up intramolecularly (nimesulide) [rumondor2009a C45; kestur2011 C27]. Interaction does not always decide the outcome: PAA, a strong donor, left flutamide growth almost unchanged [trasi2012b R3, C7]. The strength of the ionic and halogen contacts was not measured in the dispersions, and their evidence rests on band loss, binding-energy shifts or spectra that are not shown [wegiel2013a X10; que2020 X11, X12; vaneerdenbrugh2011a X13]. The ionic contact that protects against crystallization also slows the dissolution of the enteric polymers hiew2022a C53, C65. A complementary polymer did not always protect: the IR ranking of the polyphenol polymers held at the extremes only [wegiel2013a X4].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

drug-polymer ionic interactions

Evidence table: drug-polymer ionic interactions. Content from the release-mechanism chapter (2024–2025), with rows from the Physical stability and ASD process chapters.

Electrostatic attraction between an ionized drug and oppositely charged groups of the dispersion polymer, here a weakly basic drug cation and the carboxylate of an enteric polymer. In the release papers of 2024–2025 such interactions, when both partners are ionized at the pH of the polymer gel, form an insoluble complex that lowers polymer solubility and so polymer and drug release; ionization of loratadine "is necessary" for its complexation with HPMCAS, which it binds "mainly electrostatically" bapat2024 C38, C46; bapat2025a C34. The interaction can exist before water arrives: bedaquiline was about half protonated in a dry HPMCAS dispersion made from organic solvents kaur2025 C25, C35. In the stability papers the same proton transfer from an acidic polymer to a basic drug is read as a source of physical stability (lumefantrine, erlotinib) bhujbal2021 C21, C52; moseson2022a C33.

Findings

Release mechanism and LoC: F32, F33, F34, F24.

Related concepts

gives an insoluble drug-polymer complex by hydrophobic ion pairing; depends on ionization at the microenvironmental pH; contrasts with drug-polymer hydrogen bonding; lowers polymer hydration.

Formulas

Henderson-Hasselbalch equation (ionization of drug and polymer at the gel pH).

How it is measured or obtained

XPS of the drug nitrogen, with a protonated N 1s component near 402 eV beside the neutral one near 399 eV, calibrated against a salt kaur2025 R19, R20; bhujbal2021 C21; indirectly by the polymer lost from solution when drug and polymer meet in buffer at a set pH (insoluble drug-polymer complex) bapat2025a R9, R11.

Values in the library
materialvalue or classconditionspaper ids
bedaquiline free base; HPMCAS-MF complex; dry 40% dispersion4 ± 4; 55 ± 4; 52 ± 7% protonated NXPSkaur2025 R20
bedaquiline 40% dispersion after 1 h at pH 6.515 ± 3% protonated at the surfaceXPSkaur2025 R20
cinnarizine–HPMCAS-MF 25%20% protonated dry, 11% after partial dissolutionXPSbapat2024 R8
loratadine with HPMCAS LF, MF, HF at 1:1, pH 5.8–7.5complexation falling with calculated drug ionization (≈20 → 0.5%)spike testbapat2025a R11, R13
lumefantrine with HPMCP, HPMCAS, CAP, Eudragit L100 (Physical stability chapter)14–42% protonated against 3% for amorphous lumefantrineXPS, dry dispersionsbhujbal2021 R8
erlotinib with HPMCAS (ASD process chapter)acid–base interactions the "likely" reason for better stability (cited)—moseson2022a C33, R21
Pitfalls and disagreements

The same interaction is sought for stability and harms release: the 2025 grade paper says the stability gain of drug–polymer salt formation should "ideally" be balanced against reduced release under mutual ionization bapat2025a C23. For lumefantrine the extent of protonation did not rank stability bhujbal2021 C50. The release papers infer the interaction in the dissolving gel from solution tests and cited gel pH, not from measurements in the gel bapat2024 X10; kaur2025 X14.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

drug-polymer miscibility

A single amorphous phase formed by liquid–liquid mixing of amorphous drug and amorphous polymer, a description the authors themselves call "clearly" an oversimplification below Tg, where the system is not at equilibrium [marsac2006b C3]. A molecularly mixed system has one amorphous phase; more than one phase means regions of different drug:polymer ratio [rumondor2009a C4]. Three behaviours follow from the free energy of mixing: complete miscibility (one minimum), complete immiscibility (positive ΔGmix) and partial miscibility (two minima), with strict immiscibility rare, because some of each component always dissolves in the other [rumondor2009a C35, C36, C37]. Miscibility is not solubility: crystals in a dispersion after manufacture or storage do not necessarily mean the two liquids are immiscible, since the solubility limit of the crystal in the polymer may have been exceeded [marsac2006b C43]. Maximum stabilization of an amorphous drug "can only be realized" when drug and polymer are intimately mixed [rumondor2009a C3]. The concept also applies to pairs of polymers, whose miscibility falls with the molecular weights of both: from one phase at every composition for a 783 Da maltodextrin with all PVP grades to two phases at all nine compositions for a 450 kDa dextran with PVP K 90 [vaneerdenbrugh2012a C6, C23, C24, C38]. Solvent-cast films of itraconazole–HPMC (10–50% drug) and of telaprevir with HPMC, PVPVA or HPMCAS were not miscible at the loadings tested, with the onset of separation at 10% drug for HPMC and PVPVA and at about 30–40% for HPMCAS [purohit2015a C36; li2016c C17, C52]. New aspect (ASD process): mixing of drug and polymer at the molecular level in one amorphous phase, judged by a single Tg, featureless AFM and TEM images and spectroscopy, is considered essential for solid-state stability and for supersaturation on dissolution [li2017 C2, C30; broman2001 C14]. In the hot-melt extrusion context it is also the condition for melting point depression: miscible pairs show it, immiscible pairs do not [moseson2018 C8, C15].

Findings

Miscibility and drug-polymer interactions: F3, F4, F5, F6, F7, F17, F18, F19, F22. ASD process: F1, F5, F8, F17.

Related concepts

measured by single-Tg miscibility criterion, melting point depression and Flory-Huggins interaction parameter; depends on enthalpy of mixing, entropy of mixing and drug-polymer interactions; described by free energy of mixing; contrasts with drug solubility in polymer; required for an amorphous solid dispersion; contrasts with amorphous-amorphous phase separation. In films, miscibility is lost in amorphous-amorphous phase separation.

Formulas

Gibbs free energy of mixing, Flory-Huggins free energy of mixing, Flory-Huggins melting point depression, Flory-Huggins combinatorial entropy of mixing.

How it is measured or obtained

By counting glass transitions by DSC, with its limits [rumondor2009a C5, C6]; by IR with PCA against calculated physical mixtures [rumondor2009a C9]; by PXRD with PDF fitting and pure curve resolution [rumondor2009a C10, C11]; by the melting point depression of the crystalline drug in the polymer [marsac2009 C12]; by Flory–Huggins free energy curves from χ [marsac2006b C17]. A pair is classed miscible, partially miscible or immiscible from Tg, FTIR and microscopy in the earlier literature [marsac2009 R1]. Further methods: pyrene and prodan fluorescence, fluorescence imaging, AFM-nanoIR, nanoTA and Lorentz contact resonance on films [purohit2015a P3, P4, P9, P10; li2016c P4, P7, P8]; DSC together with the hydrogen-bonded fraction of PVP carbonyls for polymer blends [vaneerdenbrugh2012a P3, P5]. In the later process papers: a single Tg between those of the components (probucol–PVP 95 or 129 °C between 26 and 163 °C) [broman2001 R4.a, R4.b, C14, M1, M2]; featureless films at the 40 nm AFM resolution [li2017 C8]; melting point depression across the range [moseson2018 R5]; itraconazole's own UV and fluorescence [mugheirbi2017 C30].

Values in the library
materialvalue or classconditionspaper ids
nifedipine, felodipine, ketoconazole, sucrose, indomethacin with PVPmiscible (cited Tg, FTIR)classification used for χ[marsac2009 R1.a, R1.b, R1.c, R1.d, R1.e]
sucrose–dextranmiscible; ibuprofen–dextran, indomethacin–dextran immisciblecited and this study (Tg data not shown)[marsac2009 R1.f, R1.g, R1.h, X10]
itraconazole–Eudragit E100partially misciblecited[marsac2009 R1.i]
felodipine–PVP, nifedipine–PVPone amorphous phase over the compositions studiedIR, PXRD, DSC (cited)[rumondor2009a C38, X5]
felodipine–PAA"practically immiscible" at 30–70% PAA; some mixing at 10 and 90%DSC, IR, PXRD[rumondor2009a C44, C46]
ketoconazole–PVP"suspected" partially miscible, one phase at higher PVP onlyone Tg; IR; PXRD[rumondor2009a C40, X1]
nifedipine–PVP K29/32predicted miscible at all compositions from χ −3.8Flory–Huggins[marsac2006b R2, C33]
itraconazole–HPMC 10:90 to 50:50phase separated at every loading in solvent-cast films; one broad Tg of powdersfluorescence, AFM-nanoIR, nanoTA; mDSC[purohit2015a C36, R7]
telaprevir with HPMC, PVPVA, HPMCASdomains from 10% drug (HPMC, PVPVA); from about 30–40% (HPMCAS)AFM, AFM-IR, nanoTA, LCR[li2016c C17, C52]
dextran–PVP, 20 pairsmiscible at all compositions for 783 Da maltodextrin; phase separated at all nine for DEX450–PVP90DSC, FTIR[vaneerdenbrugh2012a R13, R14]
probucol–PVP K30 50:50single Tg, "seemed" one-phase; carbonyl shiftsolvent, moulded[broman2001 R4, R5, C14]
ECP–HPMC / PVPVAmiscible over 10–90% DL when dry18% RH[li2017 R3.a, C33]
ITZ–HPMCthermodynamically miscible when dry, trapped as two phases when wet ("suggest")7% RH vs 20–40% RH[mugheirbi2017 R1, C39]
IDM–PVPVAmelting point depression confirms miscibility at elevated temperatureDSC[moseson2018 C15]

Evidence table: drug-polymer miscibility.

Pitfalls and disagreements

A single Tg is a weak criterion: domains below 15–30 nm may give one Tg, heating can change miscibility during the scan, and ketoconazole–PVP gave one Tg at every ratio while PXRD suggested partial miscibility [rumondor2009a C6, R3, C40]. The ketoconazole–PVP conclusion conflicts with Table II of the same paper [rumondor2009a X1]. The felodipine–PAA phase state differs with the heating regimen, which the authors read as temperature-dependent mixing [rumondor2009a R1, C15]. The three methods used samples with different thermal histories [rumondor2009a X4]. Molecular-level mixing is assumed in the dilute dispersions of the growth studies but not measured there [kestur2010a C5]. Solvent-cast films and DSC powders of the same pair gave different verdicts, so the verdict depends on sample and method [purohit2015a X1]; heating to 165 °C mixed itraconazole–HPMC films [purohit2015a C38]. The telaprevir onset loadings rest on topography and moisture changed the HPMCAS films from day to day [li2016c X3, C18]. A pair classed miscible by DSC showed domains in films (DEX6–PVP90) vaneerdenbrugh2012c R16. A miscibility verdict on a solvent-made batch is a verdict on pair and process together [mugheirbi2017 C54]; a dry film may be trapped rather than miscible [li2017 C43]; low-resolution methods may overestimate miscibility [mugheirbi2018 C4].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

drug-polymer-water miscibility

Evidence table: drug-polymer-water miscibility. Content from the release-mechanism chapter (2017–2025).

Whether drug and polymer stay mixed once water enters the dispersion. Indulkar and co-workers (2017) state that AAPS depends on drug–polymer miscibility in the presence of water, set by the balance of drug, polymer and water interactions, and varies with drug, polymer type and composition; drug–PVPVA dispersions that dissolve rapidly while staying miscible in water "are expected" to form nanospecies by dissolution followed by LLPS indulkar2017b C38. Saboo and co-workers (2020) add that water can impair the miscibility of a dispersion on hydration, which "is expected" to harm dissolution saboo2020a C39. In the Flory–Huggins description a hydrophobic drug and a hydrophilic polymer interact very differently with water, which drives separation purohit2017b C43. Measured in 2023 as the water content at which 30% ritonavir–PVPVA films separated within 12 h: 14.0% without surfactant, 24.5% with SDS, 10.5–16.0% with Span 20, Span 85 or Tween 80; the authors read the SDS shift as a larger miscible region ("suggesting"), "likely responsible" for its better release yang2023 R21, C9, C10.

Findings

Release mechanism and LoC: F5, F8, F31.

Related concepts

lost through amorphous-amorphous phase separation; expressed by the Flory-Huggins interaction parameter and the Δχ effect; its loss in time is phase separation kinetics.

Formulas

multicomponent Flory-Huggins free energy of mixing, Δχ effect.

How it is measured or obtained

From films or powders exposed to water or high humidity, imaged by fluorescence or tested by DSC (see amorphous-amorphous phase separation) purohit2017b R3, R6; saboo2020a R23.

Values in the library
materialvalue or classconditionspaper ids
ritonavir–HPMCASmiscible after 97% RH; PVP and PVPVA dispersions separatedfilms and powderspurohit2017b C1
felodipine 30% with HPMCAS, EUDS; PVP, PVPVA, HPMCuniform; separated97% RH, 24 hsaboo2020a C23
ritonavir–PVPVA 30% films ± 10 parts surfactant14.0 / 16.0 / 10.5 / 12.5 / 24.5% water (none / Span 85 / Span 20 / Tween 80 / SDS)saturated-salt RH, 12 h, confocalyang2023 R21
Pitfalls and disagreements

No ternary phase diagram or interaction parameter was measured in these papers purohit2017b E4. The thresholds are single values bracketed by RH steps; only the SDS shift exceeds the step resolution yang2023 X15, X16.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

drug-rich barrier layer

Evidence table: drug-rich barrier layer. Content from the release-mechanism chapter (2019–2025).

A drug-rich layer at the dissolution front that blocks release of the drug and of the polymer beneath it. Que and co-workers (2019) take the idea from studies of polyphase mixtures, in which phase segregation at the dissolution front forms a barrier layer (cited), and state for ledipasvir–PVPVA above the limit of congruency that "it appears" the drug-rich layer acts as a physical barrier that stops further release of drug and even of water-soluble PVPVA, leading to swelling que2019 C5, C32. Saboo and co-workers (2020) describe surface drug enrichment of hydrophilic-polymer dispersions as "a physical barrier to polymer release from subsurface layers" saboo2020a C42. Hiew and Taylor (2022) use it for the release plateau after about 30 min ("could be attributed") and argue that drug and polymer leave together as long as separated drug cannot form a continuous barrier hiew2022b C16, C46; for clopidogrel, separation leaving a continuous or semi-continuous drug-rich barrier "is linked to" poor release correasoto2022a C53. In dissolving ritonavir–PVPVA compacts the drug-rich coating impedes polymer dissolution as a barrier to water penetration and "may" also be a physical barrier to polymer release when water penetrates yang2022a C55. The water-poor hydrophobic phase is expected to become more viscous and, once connected and anchored to the gel layer, to persist at the interface as an insoluble barrier, porous in top view deac2023a C56, C57. Above the limit the compact surface evolves toward the hydrophobic binodal composition measured under dilute conditions and is in pseudo-equilibrium with the aqueous phase deac2023b C59, C3. The 2023 surfactant study found every ritonavir–PVPVA–surfactant dispersion with a persistent continuous drug-rich layer releasing minimal drug: Span 20 at 40% carried a layer of about 50–100 µm from 5 min, through whose pores polymer but not drug left, and Span 85 at 40% a thick layer that released neither yang2023 R7, R9, C15, C19, C40. A layer that formed in situ on 30% Span 85 compacts was removed by agitation and did not block release yang2023 R8.

Findings

Release mechanism and LoC: F7, F20, F22, F25, F26, F27, F31.

Related concepts

part of the drug-rich surface layer; formed by surface drug enrichment; found above the limit of congruency; its formation depends on phase separation morphology.

Formulas

none.

How it is measured or obtained

Not measured as a barrier: inferred from surface composition by XPS, from micro-CT of dried tablets and from suppressed polymer release que2019 R15, R13, R11, X22.

Values in the library
materialvalue or classconditionspaper ids
ledipasvir–PVPVA 20%≈2% of the polymer released in 10 min while surface drug rose to ≈54 wt%pH 6.8, 37 °Cque2019 R11, R15, C36
felodipine–PVPVA 15 → 20–30%polymer rate ≈1.9 → ≈0.14–0.19 mg/min/cm²samesaboo2020a R14
felodipine–PVP and –HPMC across the limitPVP about halved; HPMC not reducedsamesaboo2020a X15
lumefantrine benzoate 20%, tosylate 10%plateau after ≈30 min at ≈58–60% releasedcompacts, 37 °Chiew2022b R10, C16
clopidogrel–PVPVA 50, 60%bicontinuous and drug-continuous films; ≈52 and 7% releasedfilms 5 min at 100% RH; compactscorreasoto2022a R20, R17
ritonavir–PVPVA 30%; 40%continuous porous drug-rich layer at the gel–solution interface; rigid layer ≈12 µmreal-time confocal, pH 6.8yang2022a R6, R12, R13
MePHPH–PVPVA 50%; PHPH–PVPVA 20%porous continuous drug-rich phase on the surfacesurfaces after 2–20 mindeac2023a R9, R10, C57
PHPH–PVPVA 15, 50%; MePHPH–PVPVA 50% compactssurface drug content moves toward the hydrophobic binodal compositionATR-FTIR of dried surfaces, 0–60 mindeac2023b R6, R7, C59
ritonavir–PVPVA + Span 20, 40%layer ≈50–100 µm from 5 min; drug ≈8%, polymer ≈78% at 90 minconfocal cross-sections; compactsyang2023 R7, R2, R3
ritonavir–PVPVA + Span 85, 30%layer formed, swept away and re-formed in situ; ≈86% released under rotationin situ confocal; compactsyang2023 R8, R2
Pitfalls and disagreements

The barrier function itself, its composition over time and its permeability were not measured que2019 X22. Suppression of polymer release above the limit is polymer-specific saboo2020a X15. Whether plasticizers act on barrier formation was not tested; the authors call for a more in-depth evaluation correasoto2023 C32. Persistence depends on the shear: the same Span 85 dispersion formed a layer in a quiet chamber and none under rotation yang2023 C16, R8.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

drug-rich nanodroplets

The dispersed drug-rich phase formed by LLPS, usually of 100–300 nm, which dissolves fast and is expected to replenish absorbed drug [indulkar2016 C4, C25]. Droplets are too large to cross the 3–4 nm (regenerated cellulose, 12–14 kDa) or 15 nm (hollow fibre) pores of the membranes used [indulkar2016 C11; hate2018 C52]. In enzalutamide dispersions the same species is called amorphous aggregates, about 100 nm; in simulated and pooled human intestinal fluids spheres of 0.1–0.5 µm were found [wilson2018 R11, C45; elkhabaz2019b R4, C19, C24]. New aspect (Supersaturation from ASD dissolution): fast-releasing dispersions put drug above the amorphous solubility into a submicron colloid within minutes, and additives decide its size and how soon it crystallizes [ilevbare2013d C59, C60; jackson2015 C29]. New aspect (Release mechanism and LoC): from dissolving dispersions, nanodroplets formed only where release was congruent or close to congruent, so that the drug concentration exceeded the amorphous solubility purohit2017b C52; indulkar2019a C5; saboo2019 C30. The 2017 isotope study concludes that they form from drug that has first dissolved, followed by LLPS ("strongly suggest"), not by release of drug-rich domains from the hydrated matrix indulkar2017b C26; Purohit and Taylor reach the same reading for ritonavir films ("likely") purohit2017b C57. When drug release is controlled by polymer dissolution, colloid formation is "highly dependent" on drug loading que2019 C55. Their size and life after release depend on the drug, the polymer and small amounts of surfactant: HPMCAS kept elbasvir and loratadine droplets small, and SDS, TPGS or Tween 80 at 4–50 µg/mL kept clopidogrel droplets stable for 4 h while CTAB agglomerated them yang2021 C4; correasoto2022a C12, C38. Built into ritonavir–PVPVA at 30%, the Spans kept the released droplets near 1 µm, while TPGS and Tween 80 let them grow to several micrometres, which the authors suggest "could possibly" come from these surfactants partitioning into the droplets and lowering their Tg indulkar2022 C47, C48. In dissolving ritonavir–PVPVA compacts at 10 and 20% droplets formed near the gel–solution interface and entered the solution with the dissolving polymer, which the authors explain by a water content needed to cross the binodal yang2022a C34, C35, R10, R11.

Findings

Bioperformance: F5, F8, F15, F19, F22, F23. Supersaturation from ASD dissolution: F8, F9, F12, F13. Release mechanism and LoC: F4, F5, F12, F13, F16, F25, F27.

Related concepts

produced by liquid-liquid phase separation; act as nanodroplet reservoir effect; part of the drug-rich phase; related to droplet coalescence and particle absorption of light; form under congruent release above the amorphous solubility. Coarsen by drug-rich phase coarsening.

Formulas

Stokes-Einstein equation.

How it is measured or obtained

NTA (scattering or fluorescence mode with Nile red), DLS, the 369 nm band of atazanavir [indulkar2016 P4; hate2018 P3, P4, P6]. Nile Red fluorescence of the pellet against aggregate mass, and DLS [wilson2018 R8, R11]; SEM of a centrifuged pellet with the drug's own fluorescence in human fluid [elkhabaz2019b R3, R4]; Z-average by DLS under agitation ueda2020a R5, R6; size and zeta potential with polymer or surfactant additives hate2022 R17. In the ASD dissolution papers: light scattering in a flow-through cell, nanoparticle tracking of samples or 0.45 µm filtrates, SEM of dried samples [ilevbare2013d P3, P8; jackson2015 P5; trasi2015b P8]. In the release-mechanism papers: NTA, DLS, visible turbidity, environment-sensitive probes in solution and free drug after ultracentrifugation indulkar2017b R6, R7; purohit2017b R7, R8; indulkar2019a R9; que2019 R5, R12; saboo2019 R11, R12.

Values in the library
materialvalue or classconditionspaper ids
clotrimazole111 / 223 / 246 / 257 nm at 8 / 10 / 15 / 20 µg/mL; 1.2 × 10⁸ to 12.5 × 10⁸ per mLpH 8, NTA[indulkar2016 R4]
atazanavir, solvent shift204–226 nm, PDI 0.08–0.15100–500 µg/mL, DLShate2018 R6
atazanavir 90:10 HPMCAS and HPMC ASDs294–326 nmclosed and absorptivehate2018 R12
atazanavir with PVPVAabout 245 nm rising to about 700 nm at 75 min and 10 µm at 105 minagglomerationhate2018 R20
telaprevir 90% HPMCAS ASDabout 300 nmDLS (data not shown)mosqueragiraldo2018b R3
ritonavir ASD (Tres 2018)696 / 294 nm (ritonavir / lopinavir)NTAtres2018 R18
enzalutamide 10:90 and 50:50 copovidone ASDsabout 100 nm; about 50 against about 3 µg/mL of 100 as aggregatespH 6.5, 1 h dissolution[wilson2018 R10, R11]
atazanavir, posaconazole in pooled human fluidspheres of 0.1–0.5 µm, no needlesSEM of pellet, 100 µg/mL HPMC-AS[elkhabaz2019b R4]
atazanavir, clozapine with HPMCAS-LF and -HFAS-LF droplets below 300 nm over 3 h; AS-HF kept the initial size; clozapine about 100 nm (AS-HF) against 250 (AS-LF)300 rpm, 37 °Cueda2020a R6
atazanavir 150 µg/mL with polymer or surfactant additivesdroplets of about 280 and about 1000 nm gave the same mass flowPAMPA, 2% SDS receiverhate2022 R17
ritonavir–PVP dispersion at 20 µg/mLabout 350 nm at onset; ≈5590 nm by 120 min100 mM buffer, 37 °C[ilevbare2013d R1, R5]
ritonavir 20 µg/mL with 5 µg/mL CAAdP 0.33210−214 nm before crystallizationsolvent shift[ilevbare2013d R12]
danazol 90:10 dispersions246–284 nm25 °Cjackson2015 R6
ritonavir; ritonavir + lopinavir, HPMCAS dispersionsabout 500 nm; about 160 nm in 0.45 µm filtrates1 h[trasi2015b R7]
felodipine 90:10 HPMC dispersion≈185 → ≈300 nm, read as crystalline25 °Calonzo2011 R8, C33
nifedipine 10, 20% with HPMC-E5 or PVPVA≈190–222 nmNTA, 5 °C, D2Oindulkar2017b R7
ritonavir 10:90 films with PVPVA, HPMCAS, PVP200, 250, 315 nmNTA, fresh filmspurohit2017b R8
ritonavir–PVPVA 10% tablet218 ± 15 nm; media of 10–25% turbidDLS at 30 minindulkar2019a R9
ledipasvir–PVPVA 2, 5%cloudy medium; ≈225–257 nm at 5%DLSque2019 R5, R12
nilvadipine 5, 10%; cilnidipine 5, 10, 15%237 ± 8, 246 ± 3; 255 ± 1, 300 ± 2, 366 ± 7 nm; none at higher loadingsDLS, about 1 hsaboo2019 R11
indomethacin–PVPVA 5, 10%250–350 nmNTA, 30 minsaboo2020 R7
felodipine with 5% TPGSZ-average ≈237–279 nmDLS, 60 minsaboo2021 R17
elbasvir 2.5%; loratadine 10%PVPVA ≈670 → 1190; ≈820 → 2120 nm; HPMCAS ≈280 → 390; ≈420 → 570 nmDLS, 60 minyang2021 R3, R6
clopidogrel≈520 nm in buffer; stable with SDS, TPGS or Tween 80; ≈12-fold growth with CTABDLS, 4 hcorreasoto2022a R5, R6
four phenolphthalein analogues179–364 nmDLS, 30 minque2021 R22
ritonavir–PVPVA 30:70:5 with Span 85; Span 20; none; SDS; TPGS; Tween 80≈330–960; ≈550–1410; ≈940–2200; ≈2400; ≈3840 nm; ≈10 µmDLS of the medium during releaseindulkar2022 R11, R13
plasticized dispersions (systems not specified)500–1500 nm after 90 minDLScorreasoto2023 R5
MePHPH–PVPVA 5–30%; PHPH–PVPVA 5%nanoparticles formed within the gel; onset 601 ± 68 µm beyond the 356 ± 18 µm gelin situ confocaldeac2023a C27, R8, C31
drug-rich phase released from 30% MePHPH; from 5% PHPH98.8 against 26.2 wt% drug; Tg 16.8 against −5.8 °CHPLC, DSCdeac2023a R12
PHPH; MePHPH nanoparticles with PVPVAPVPVA 71.4–78.0; 0.5–7.5 wt%37 °C, two preparation routesdeac2023b R2
Pitfalls and disagreements

The size is quoted as 110, 200, 220 or 250 nm in one paper [indulkar2016 X9]. Size depends on polymer and agglomeration hate2018 C26, C27. Counts stop at 150 µg/mL in the atazanavir study hate2018 X10. The enzalutamide aggregate amounts come from a Nile Red calibration, and the aggregate-rich ASD also dissolved fastest and left less solid in the dosed suspension (F23) [wilson2018 R8, X13, X14]. Size fell with polymer concentration and was smaller with AS-HF (F19) ueda2020a C18; in a PAMPA cell the polymer or surfactant type, not the size, shaped the transport gain (F22) hate2022 R17. Droplets pass 0.45 µm filters [trasi2015b C22]. Sizes depend on method (SEM of dried samples against DLS) and medium [ilevbare2013d X12, R9]. Whether the felodipine particles were droplets or crystals was not measured directly alonzo2011 X7. Nanodroplets of ritonavir tablets at 20–30% are inferred from turbidity and concentration, not sized indulkar2019a X5. The link between congruency and droplets partly follows from the amount of drug released by the sampling time saboo2019 X14. The larger cilnidipine droplets at higher loading "could indicate" lower stability or a different formation route saboo2019 C19. The slow-exchange premise of the isotope test was shown with solvent-made droplets only indulkar2017b X5.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

drug-rich phase coarsening

Evidence table: drug-rich phase coarsening. Content from the release-mechanism chapter (2021–2023), with rows from the Bioperformance chapter.

The growth of a separated drug-rich phase into fewer, larger domains or droplets after it has formed, in the hydrated dispersion or in the medium. In solution, clopidogrel nanodroplets grew in buffer, which the authors attribute to the high interfacial energy of the lipophilic drug-rich phase correasoto2022a C37, R6; surfactants "in general" slowed the coarsening of drug-rich nanodroplets formed by LLPS, CTAB excepted, at very low concentrations correasoto2022a C38. In the hydrated dispersion, persistent discrete drug-rich domains with 5 and 10% TPGS "can be rationalized" by TPGS lowering the interfacial energy between the phases and so reducing coarsening, so that the domains can be released intact as the gel layer recedes saboo2021 C40; rapid coarsening without surfactant is "a feasible explanation" for the loss of release saboo2021 C50. In the 40% MePHPH gel heterogeneous domains turned homogeneous between 2 and 20 min, "likely" by movement and coalescence into large domains deac2023a C38, C34.

Findings

Release mechanism and LoC: F16, F20, F25.

Related concepts

acts on drug-rich nanodroplets and on the phase separation morphology of the hydrated dispersion; follows amorphous-amorphous phase separation; slowed by surfactants with surfactant partitioning into the drug-rich phase or at the droplet surface.

Formulas

none.

How it is measured or obtained

Z-average and PDI of droplets by DLS against time, as ratios to the initial value correasoto2022a R6 or at 90 min of dispersion dissolution correasoto2022a R19; in the hydrated dispersion inferred from the morphology of humidified films saboo2021 C51, R21.

Values in the library
materialvalue or classconditionspaper ids
clopidogrel nanodroplets in buffer; with 50 µg/mL CTABZ-average ratio ≈1.5 at 1 h and ≈12 at 2 h; ≈12 at 1 h37 °C, DLScorreasoto2022a R6
clopidogrel nanodroplets with 50 µg/mL SDS, 4 µg/mL TPGS, 5 µg/mL Tween 80Z-average ratio ≈0.92–1.01, ≈0.96–0.99, ≈0.81–0.89 over 4 hsamecorreasoto2022a R6
clopidogrel–PVPVA 40%; 50%, binary and with Tween 80, TPGS, SDS≈790, ≈510, ≈580, ≈690 nm; ≈1960, ≈780, ≈890, ≈1260 nm90 min of dissolutioncorreasoto2022a R19
atazanavir- and clozapine-rich droplets with pre-dissolved HPMCAS-LF; -HF (Bioperformance chapter)grew slightly early and stayed below 300 nm; kept their initial size3 h agitation, 37 °Cueda2020a C19, R6
Pitfalls and disagreements

Coarsening in the hydrated dispersion was not followed in time; it is inferred from end-point morphology after 12 h at about 100% RH saboo2021 C51, R21. Why CTAB destabilized the clopidogrel droplets is not known correasoto2022a C38. In the Bioperformance chapter pre-dissolved HPMCAS inhibited coarsening and the droplets were smaller with AS-HF than with AS-LF regardless of the drug ueda2020a C18.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

drug-rich phase

The dispersed, non-crystalline phase that forms when a supersaturated drug solution phase-separates above the amorphous solubility: a water-saturated supercooled liquid or, for high-Tg drugs, a glass, that can later crystallize; "drug-rich phase" is judged a more appropriate term than "precipitate" [trasi2015a C3; mosqueragiraldo2015 C30]. In the papers of this chapter it is the object the probes enter [raina2015a C26] and the object that makes UV readings unreliable tres2018 C37. Other papers show that it can contain polymer and a second drug [mosqueragiraldo2018b C35; alkalla2026 C4; ueda2022 C10]. New aspects (C. Amorphous solubility and LLPS): the drug-rich phase can be liquid or glassy depending on its water-plasticized Tg (F2), is in equilibrium with the water-rich phase at the amorphous solubility, and keeps the drug activity of the continuous phase constant (F8) [ilevbare2013a C36, C61; mosqueragiraldo2015 C35]. It is a transient precursor of crystals whose lifetime ranges from minutes to hours (F3) [mosqueragiraldo2015 C36, R1]. A second unionized drug mixes into it and lowers the amorphous solubility of both (F11) [trasi2015a C42]. A dissolved ASD polymer also enters it: the polymer:drug weight ratio in the ibuprofen-rich phase was 0.40–1.14 for six polymers at 1000 µg/mL and rose with temperature (PVP-VA 0.46 → 1.32 from 15 to 60 °C), lowering the amorphous solubility (F19–F21) [ueda2021 R5; ueda2022 R10]. A micellar solubilizer is inferred to stay out of it, because the maximum activity is unchanged, whereas STCDC and SGCDC are inferred to mix into it [indulkar2017a C40; lu2017b C50, C51]. Where its drug is mobile (ibuprofen, Tg −45 °C), solution NMR sees it ueda2020b C7. New aspect (Bioperformance): the phase is treated as a hydrated amorphous phase in equal activity with the drug-lean solution; for telaprevir it contains polymer when the polymer is poorly soluble [raina2014a C33; mosqueragiraldo2018b C35]. A second, crystalline drug can enter the phase: darunavir partitioned into the atazanavir-rich phase and lowered what remained in solution [alkalla2026 C3, C4, C37]. New aspect (Supersaturation from ASD dissolution): dissolving dispersions form it: a ritonavir-rich phase appeared at about the LLPS concentration, redissolved on dilution and had a glass transition near 1 °C, a supercooled liquid at 37 °C [ilevbare2013d R1, R2, C7]; danazol dispersions formed it up to 30% drug with three polymers jackson2015 C36. A phase holding two drugs sets both concentrations by its composition [trasi2015b C44]. Tacrolimus separates a drug-rich phase between 40 and 50 µg/mL (220 nm after 0.7-µm filtration at 60 µg/mL), and six marketed capsules appeared to dissolve to, not beyond, that limit [trasi2016 C15, R11, C40]; indomethacin with HPMC formed a 70–100 nm droplet phase from about 40 µg/mL, detected by the drug's own fluorescence [xie2017 R6, R7, C17].

Findings

Solution methods: F3, F4, F5, F7, F8, F9, F10, F11. C. Amorphous solubility and LLPS: F1, F2, F3, F8, F11, F13, F15, F17, F19, F20, F21, F22, F23. Bioperformance: F5, F6, F7, F20. Supersaturation from ASD dissolution: F7, F9, F11, F13, F21.

Related concepts

measured by light scattering by particles and fluorescent probe partitioning; contrasts with crystallization; related to liquid-liquid phase separation and droplet coalescence. In the amorphous solubility chapter: formed by liquid-liquid phase separation or glass-liquid phase separation; acts as a nanodroplet reservoir (claimed); grows by droplet coalescence; receives dissolved polymer (polymer partitioning into the drug-rich phase); its stability against creaming depends on the polymer (colloidal stability, Ostwald ripening). Composition also set by drug–drug miscibility; dispersed as drug-rich nanodroplets; related to chemical potential and ideal mixing.

Formulas

none specific; see amorphous solubility advantage with water-sorption correction for the limit at which it forms. In the amorphous solubility chapter: binodal condition, ideal-mixing reduction of amorphous solubility.

How it is measured or obtained

By light-scattering extinction (F3), by probe or drug fluorescence (F4 to F6), by NTA or DLS sizing of filtered media [tres2018 P10; trasi2015a R15], by ultracentrifugation (the supernatant gives the concentration of the other phase) tres2018 P9, and by ¹H NMR peaks of the drug-rich phase [ueda2021 R3]. In the amorphous solubility papers it is isolated by ultracentrifugation at 274,356 × g with gravimetric water and DSC Tg of the pellet, and examined by polarized microscopy, XRPD, Nile red under a fluorescence filter and ¹H NMR of the dissolved drug [ilevbare2013a P7, P8, P9; indulkar2015 P12, P14, P15; mosqueragiraldo2015 P10]. The NMR-invisible polymer measures the polymer content (ratio of polymer lost from solution to phase-separated drug), which counts surface-bound polymer too [ueda2021 P4, X4]. In the Bioperformance papers: pellet analysis after centrifugation (polymer by colorimetry, drug by Nile red) mosqueragiraldo2018b P12–P14; NTA counts [alhalaweh2016 P13]; mass balance from antisolvent additions [alhalaweh2016 P12]. In the ASD dissolution papers: stepwise addition and dilution with light scattering; DSC of the ultracentrifuged phase; pyrene I1/I3 (lower in a hydrophobic phase); SEM; nanoparticle tracking; ultracentrifugation with assay of the pellet [ilevbare2013d P4, P9, P7, P8; jackson2015 P5; trasi2015b P9].

Values in the library
materialvalue or classconditionspaper ids
ritonavir, 10% Kollidon VA64 dispersionmean size 696.4 ± 213.6 nmNTA, medium filtered at 1 µm, about 60 mintres2018 R18
lopinavir, 10% dispersion294.3 ± 67.7 nmsametres2018 R18
ritonavir 30 µg/mL≈360 nmDLS, antisolvent[trasi2015a R15]
ritonavir–HPMCAS dispersion≈500 nmNTA of 0.45 µm filtrate, 1 h[trasi2015b R7]
tacrolimus, 60 µg/mL≈220 nm, a second phaseNTA of 0.7 µm filtrate, pH 4.5, 37 °C[trasi2016 R11]
telaprevir (glass, Tg 52 °C)≈300 nm; redissolves within about 2 min on dilution37 °C[mosqueragiraldo2015 R4, R5, R8, C13]
ibuprofenmicron-sized in buffer; ≈300 nm with HPMC or PVP-VApH 2.0, 37 °Cueda2020b R5
felodipine aggregatesτ2 ≈1.87–2.04 ns, share a2 14–39%24–38 µM, pH 7.4, HPMC 100 µg/mL[tres2017 R1.d–f]
clotrimazole; efavirenz drug-rich phasesPRODAN second band ≈435 and ≈450 nm; τ2 up to 3.40 and 3.89 nspH 7.4[tres2017 P1, R13, R10, R11]
ritonavir pellet94.85–95.97% drug, 4.03–5.15% water, Tg 0.4 °C10–50 °C, waterilevbare2013a R5, R6
weak-base precipitatesX-ray amorphous halos, no birefringence; Tg about 14 (clotrimazole) and about 51 °C (atazanavir)37 °C[indulkar2015 R19, R20, R21, R22]
lopinavir added to a ritonavir-rich phaseabout a third stays in bulk; about 0.21 at 85 µg/mL ritonavir25 °C[trasi2015a R9, R10]
ionized diclofenac with the ritonavir-rich phasefully recovered in bulk25 °C[trasi2015a R11]
ibuprofen-rich phasepolymer:drug weight ratio 0.40 (PVP K12), 0.52 (K25, K90), 0.87 (PVP-VA), 0.95 (HPMC 603), 1.14 (HPMC 615)1000 µg/mL polymer, 400 µg/mL drug, 37 °C[ueda2021 R5]
ibuprofen-rich phaseratio 0.24 → 0.62 (PVP), 0.46 → 1.32 (PVP-VA), 0.20 → 1.46 (HPMC, to 55 °C)15–60 °Cueda2022 R10
pazopanib precipitate (dried)Tg about 83 °C; non-birefringent aggregates then free-base crystalspH 6.5 after pH shift[sugihara2018 R11, R17]
telaprevir, 90% CA Sub ASDpolymer 9407 µg, drug 1080 µg; polymer fraction 0.90150 µg/mL, 15 mLmosqueragiraldo2018b R14
telaprevir, 90% HPMCAS / 70% HPMCAS / 90% PVPVApolymer fraction 0.21 / 0.27 / 0.22samemosqueragiraldo2018b R14
ritonavir, atazanavirNTA counts: buffer 4.74 × 10⁶; ATV 150 µg/mL 4.15 × 10⁸ per mLantisolvent[alhalaweh2016 R15]
clotrimazole1.2 × 10⁸ to 12.5 × 10⁸ per mL8–20 µg/mL[indulkar2016 R4]
atazanavir with darunavir hydrateatazanavir in the drug-lean phase about 61–63 instead of 91–96 µg/mL at about 196 µg/mL darunavir added150 µg/mL atazanavir, 400 µg/mL HPMCAS, pH 6.8[alkalla2026 R11, C1]
ritonavir phase from a PVP dispersionTg inflection 1.05 °C; pyrene I1/I3 ≈1.43–1.46water, 37 °C[ilevbare2013d R2, R3]
danazol, 90:10 dispersions246–284 nm, 4.1–4.5 × 10⁹ per mL25 °Cjackson2015 R6
lopinavir alone; with ritonavircrystallized at 1–2 h; no crystallization in 5 hpyrene I3/I1[trasi2015b R15]
indomethacin with 100 µg/mL HPMConset 36 µg/mL; droplets 70–100 nmpH 2.2, 37 °C[xie2017 R4, R6]
indomethacin EPO–HPMC dispersion≈75 nm species; redissolved within ≈2 min after a rise to pH 537 °C[xie2017 R15, R20]
Pitfalls and disagreements

Its amorphous nature was often inferred, not tested: the supernatant matched the amorphous solubility, but no solid-state measurement was made tres2018 X5. Size varies strongly with drug, medium and technique (about 160–700 nm in the rows above), so no size transfers. Filtration may not remove it [jackson2015 C12; trasi2016 R8]. Droplets coalesce and grow with time, which changes scattering [jackson2014 C29; tres2018 C28]. A glassy phase behaves much like a liquid one in these tests [mosqueragiraldo2015 C30]. In the amorphous solubility papers the ritonavir DSC trace shown stops at 20 °C, so the absence of melting is stated, not shown ilevbare2013a X8. The water content of the telaprevir pellet was not measured [mosqueragiraldo2015 X3]. The polymer in the phase is the NMR-invisible polymer and the droplet composition is not known [ueda2021 X4; ueda2020b X4]. The composition of the mixed ritonavir–atazanavir phase was calculated, not measured [alhalaweh2016 C17]; absolute pellet amounts of the telaprevir study are not mass balances mosqueragiraldo2018b X8. The NTA count of the ritonavir–atazanavir mixture is below that of buffer [alhalaweh2016 X6]. The centrifuged drug-rich phase of the darunavir study was not analysed; its composition is inferred from supernatant depletion and flux (F20) [alkalla2026 X6]. In the ASD dissolution papers the ritonavir phase's water content was not measured, and the probe run is described in two media [ilevbare2013d C8, X1]. Tracking cannot tell droplets from crystals jackson2015 X13. For ritonavir the phase "appears" to promote crystallization rather than protect against it [ilevbare2013d C41]. The non-crystalline state of the indomethacin droplets rests on optical methods; they crystallized after 3 h at pH 2.2 [xie2017 X18, R15].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

drug-rich surface layer

A polymer-depleted, drug-enriched layer at the surface of a dissolving ASD, left when the polymer dissolves ahead of the drug above the limit of congruency. Moseson (2022) shows it on bicalutamide–PVPVA compacts and says that this layer, hydrated and mobile, crystallizes within 20–30 min, which "could prevent release, promote surface crystallization, and prevent or slow continued hydration" moseson2022b C46, C43. In the 2021 paper it was inferred from the shape of the PVPVA release curve and pitted surfaces, "presumably drug-rich" [moseson2021 C32, C58]. It is the general case of surface drug enrichment applied to dissolution. New aspect (Release mechanism and LoC): the layer is the drug-controlled surface of the older two-component literature (sulfathiazole–PVP, cited) purohit2017b R23, and the nifedipine study states that if water-induced phase separation forms such a layer, the drug controls release and the carrier effect of the polymer is lost indulkar2017b C33. For ritonavir the authors add that drug molecules "can" move laterally on the dissolving surface and that drug-rich nanodomains "can" coalesce into contiguous regions, ritonavir being a supercooled liquid at 37 °C indulkar2019a C28, C40. Saboo and co-workers (2021) model it as what a contiguous drug-rich network leaves once the polymer-rich phase dissolves ("likely") saboo2021 C39; for clopidogrel, faster polymer loss leaves a drug-enriched compact that "likely accounts for" incomplete release correasoto2022a C25.

Findings

ASD process: F27, F38, F48. Release mechanism and LoC: F3, F7, F20.

Related concepts

forms above the limit of congruency during incongruent release; sits on the gel layer; leads to matrix crystallization and surface crystallization. Its barrier role is the drug-rich barrier layer; sets drug-controlled release; mobile where the drug is a supercooled liquid.

Formulas

None.

How it is measured or obtained

SEM-EDX of exposed compacts: fluorine occurs only in the drug, so F/F0 above 1 means drug enrichment; confocal fluorescence with a drug-rich dye; SEM of the surface for crystals moseson2022b P14, P15, P16, P17, C8. In the release-mechanism papers: IR of the tablet surface, micro-CT and SEM of dried compacts indulkar2019a P7, P8; que2019 P5; saboo2019 P14.

Values in the library
materialvalue or classconditionspaper ids
30% BCL–PVPVA compact surfaceF/F0 = 1.23 ± 0.07 (about 20% enrichment)30 min in buffermoseson2022b R14
same, cross-sectiondrug-rich boundary layer 94 ± 8 µm with crystals, F/F0 = 1.41 ± 0.10; gel layer below F/F0 = 0.93 ± 0.061 hmoseson2022b R15
same, confocalred layer 55 ± 6 µm at 5 min, 103 ± 9 µm at 30 minNile redmoseson2022b R16
50% BCL–PVPVA compact5–10 µm crust of crystals; red regions of 8 ± 2 µm at 5 min, a continuous layer of 1.9 ± 0.3 µm at 30 min, gone at 60 minSEM-EDX, confocalmoseson2022b R15, R17
10% BCL–PVPVA compactsurface smooth at 30 minSEMmoseson2022b R14
coated ritonavir–PVPVA tablet edgeconnected drug-rich regions along particle boundariesconfocalbenson2025 R14
ritonavir–PVPVA 50%amorphous-ritonavir IR spectrum from 5 min; flaky at 15 minpH 6.8, 37 °Cindulkar2019a R16, R17
ledipasvir–PVPVA 10%distinct top layer at 10 min; bulging, porous top by 30 minmicro-CT, driedque2019 R13
nilvadipine 15:85porous layer within 10 min, growing to 30 minmicro-CTsaboo2019 R13
felodipine 30% in PVP, PVPVA, HPMCporous layer at the dissolving facemicro-CT, 10 minsaboo2020a R19
felodipine 30% with 0, 2% TPGS; 5, 10% TPGSporous surface layer after 10 min; homogeneousmicro-CT, driedsaboo2021 R19
indomethacin–PVPVA 15, 25%rough, porous surface after 5 min; smooth at 10%SEMsaboo2020 R19
Pitfalls and disagreements

The layers were measured on compacts, and the crystals were identified by shape and not by diffraction moseson2022b X20, X18. The polymer-depleted state of the 50% crust is inferred from the dye, and the authors read the crust as formed and dissolved repeatedly, which would make its slow release only "seemingly congruent" moseson2022b X16, C47. A drug-rich surface is not the only consideration: a TPGS dispersion released incongruently yet completely because little solid was left when nucleation began moseson2022b C50. The layer of the ITZ compacts is a "supposition" bhardwaj2018 C52; SEM and micro-CT samples were dried indulkar2019a X11; que2019 X22.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

drug solubility in polymer

The amount of crystalline drug that a polymer can hold in solution at a given temperature. In the PEG papers it appears in three forms: the eutectic composition, "the maximum drug solubility at the eutectic temperature" of the molten polymer [baird2011 C1]; an extrapolated value at 25 °C, which refers to supercooled liquid PEG because 25 °C is below the PEG melting point [zhu2011 C8]; and the solubility in a liquid low-molecular-weight analogue, PEG 400, used as a stand-in for amorphous PEO because the true value cannot be measured when the transformation is too slow [marsac2008b C18]. For amorphous polymers it is predicted from the heat of fusion, the melting point and the sign of the mixing enthalpy, so that drugs with a high heat or temperature of fusion are less soluble [marsac2006b C52]. New aspects (Miscibility and drug-polymer interactions): For amorphous polymers, the solubility of the crystal in the polymer is the quantity that separates a thermodynamically stable dispersion from a supersaturated one; knowing it would allow the supersaturation, a measure of the driving force, to be evaluated, but it had been measured only in a low-Tg polymer [marsac2006b C44]. It depends on the melting temperature, the heat of fusion and the sign of the mixing enthalpy: high-melting, high-ΔHfus drugs without substantial polymer interaction have very low solubility, and a negative mixing enthalpy raises it [marsac2006b C52, C53]. Miscibility and solubility are different: crystals in a dispersion do not by themselves mean immiscibility [marsac2006b C43]. New aspect (ASD process, extrusion): the depressed melting point at a given composition is the temperature at which the polymer holds that amount of crystalline drug in solution; the authors treat the value from DSC melting point depression (heating a fixed composition until the last crystal dissolves) as thermodynamically equivalent to the solubility that isothermal dissolution during extrusion approaches from the under-saturated side [moseson2018 C10, C43]. New aspect (Physical stability): with water present, the solubility that matters is that in the polymer–water co-solvent, which falls as water is added, and the dispersion's supersaturation rises accordingly (reasoned from NMP–water) [marsac2008a C33, C46].

Findings

ASD process: F8, F9, F11. PEG dispersions: F1, F3, F4, F11. Miscibility and drug-polymer interactions: F4, F8, F9. Physical stability: F10, F15.

Related concepts

depends on melting point depression, crystal lattice energy and drug-polymer interactions; measured by van't Hoff equation and activity coefficient; related to eutectic, ideal solubility and semicrystalline solid dispersion; depends on ideal solubility and activity coefficient for the predicted values; contrasts with drug-polymer miscibility; related to kinetic stabilization. Expressed as formulation critical temperature. Related to cosolvency and supersaturation.

Formulas

van't Hoff equation, activity coefficient from solubility, drug mass solubilized by the amorphous polymer fraction, Flory-Huggins melting point depression; solid-liquid equilibrium solubility equation, Flory-Huggins activity equation.

How it is measured or obtained

From the drug-rich liquidus of the temperature–composition phase diagram: a straight line of \ln x against 1/T, extended to 25 °C and converted to weight percent [zhu2011 P6, E3]; by shake-flask in liquid PEG 400 (excess drug, 24 h at 25 °C, UV assay) [baird2011 P5; marsac2008b P5]; for amorphous PEO as the PEG 400 value times the amorphous volume of PEO in the compact, assuming that crystalline PEO dissolves no drug [marsac2008b E4, C20]; from melting point depression with the Flory–Huggins relation, or from the solubility in an analogue solvent scaled to the polymer, for drugs in PVP [marsac2006b R8, R17; marsac2009 R9]. For drugs in PVP it was not measured in the polymer. It is predicted by solving the solid–liquid equilibrium equation together with the Flory–Huggins activity coefficient and the melting-route χ (2006), checked against the measured solubility in methyl pyrrolidone at 25 °C [marsac2006b P9, P3, E5, E6]; or by measuring the activity coefficient in a liquid analogue (1-ethyl-2-pyrrolidone) and scaling it to PVP K12, K29/32 or K90 with Eq. 8 (2009) [marsac2009 P7, E8]. Estimates made by measuring solubility in a low-molecular-weight analogue "need to be corrected" for the smaller mixing entropy of the polymer [marsac2006b C51]. The fraction of drug in excess of the predicted solubility, at each polymer content, is the fraction "available for crystallization" [marsac2009 P9, R11]. In the extrusion papers it is read from the offset temperature extrapolated to 0 °C/min of cryomilled mixtures, or in a hot-stage test at constant temperature, where complete dissolution within about 8 h below Tc was read as a thermodynamic rather than kinetic limit [moseson2018 P2, R13, C35]; for IDM in copovidone at 1:5 a solubility temperature of about 78 °C is cited from the phase diagram [moseson2019 R21]. In the moisture papers it was not measured in PVP; NMP and NMP–water were used as stand-ins, and a dry-PVP value was cited for the plateau estimate [marsac2008a P8; rumondor2009b R26].

Values in the library
materialvalue or classconditionspaper ids
benzocaine; chlorpropamide; ibuprofen in PEG 335028; 26; 25 wt%extrapolated to 25 °C from the liquidus[zhu2011 R5.b, R5.c, R5.d]
nilutamide in PEG 335011 wt% (eutectic 10 wt% at 58.4 °C)as above[zhu2011 R5.e, X4]
haloperidol; ketoconazole in PEG 33500 wt%as above; text for haloperidol: under 1% w/w[zhu2011 R5.a, R5.f; zhu2012 X10]
fenofibrate in PEG 33506 wt%as above, from the supporting-information diagram[zhu2012 M2]
chlorpropamide; aceclofenac; loratadine; haloperidol in PEG 400194; 233; 49; 14 mg/mL24 h, 25 °C[baird2011 R9]
acetaminophen, ketoprofen, naproxen, ibuprofen, felodipine, ketoconazole in PEG 4000.32, 0.32, 0.22, 0.28, 0.16, 0.02 mole fraction24 h, 25 °C[marsac2008b R14]
the same six drugs in amorphous PEO (9% of 450 mg PEO)14, 24, 13, 17, 15, 2% of the 50 mg of drug dissolvablePEG 400 value used[marsac2008b R16]
nifedipine in PVPmore than 90% polymer needed for no crystallization on a thermodynamic basispredicted with \chi = −3.8[marsac2006b R18, R17]
most drugs in polymeric matriceslikely low at room temperature unless cohesive interactions are extremely favourablesolubility in an ethyl-pyrrolidone analogue[marsac2009 C46, R9]
nifedipine in PVP K29/32; K120.06; 0.07 g/g (0.001 g/g with χ = 0.5)χ −3.8, predicted[marsac2006b R17.a, R17.b]
felodipine in PVP K29/32; K120.25; 0.31 g/gχ −4.2, predicted[marsac2006b R17.a, R17.b]
nifedipine; felodipine in methyl pyrrolidonepredicted 0.15 and 0.48; measured 0.21 ± 0.02 and 0.45 ± 0.07 g/g25 °C[marsac2006b R17.c, R17.d]
felodipine, nifedipine, ketoconazole, sucrose, indomethacin in PVP K29/320.065, 0.049, 0.010, 0.015, 0.134 weight fractionscaled from EP[marsac2009 R9]
same five in EP0.268, 0.215, 0.079, 0.074, 0.396 weight fractionmeasured, 25 °C[marsac2009 R9]
same fivefraction above solubility reaches zero at polymer 0.93, 0.95, 0.99, 0.99, 0.86PVP K29/32[marsac2009 R11]
IDM in PVPVA, 50% DL132.3 ± 0.8 °C (predicted 131.0 °C)DSC offset, 0 °C/min[moseson2018 R5]
IDM in copovidone, 1:5about 78 °Ccited[moseson2019 R21]
felodipine in dry PVP (cited)about 0.25 g/g; taken as at most 0.025 g/g in PVP–waterused for the plateau estimate[rumondor2009b R26, C31]
felodipine–PVP 50% at 93% RHresidual ≈0.1 g drug per 0.86 g PVP–water, above that boundmass balance in words[rumondor2009b E4]
all dispersions studied (cited)supersaturated with respect to the estimated solubility in PVPnifedipine and felodipine[marsac2008a C47]
Pitfalls and disagreements

The 25 °C values are extrapolations below the PEG melting point and refer to supercooled liquid PEG, not to the largely crystalline polymer of a stored dispersion; one value (nilutamide) lies above its own eutectic content [zhu2011 C8, X4]. The eutectic composition is a ceiling at the eutectic temperature, about 49–58 °C, and not a solubility at storage temperature [baird2011 C1; zhu2011 R5]. Estimates of different kinds are not on one scale: weight percent of drug in the saturated PEG solution against percent of the drug in a compact that the amorphous polymer fraction could take up (synthesis: 25 wt% for ibuprofen in PEG 3350 against 17% in a PEO compact [zhu2011 R5.d; marsac2008b R16.d]). The PEG 400 estimate did not predict the humid-storage outcome in PEO [marsac2008b C22], and nominal solubilities above the 20% loading did not keep benzocaine and ibuprofen amorphous in PEG [zhu2012 X13]. PEG 400 may differ from PEG 3350 and PEO through its end groups [baird2011 C22; marsac2008b C19]. All values in PVP are predictions: the temperature and heat-capacity terms are not printed, the only check (methyl pyrrolidone) is about 30% low for nifedipine, and no solubility in a polymer was measured in either paper [marsac2006b X10, X11; marsac2009 X17]. The 2009 summary extends five compounds to "most drugs" [marsac2009 C46, X17]. The solubility in PVP K29/32 of indomethacin is 0.134 in the table and 0.144 in part of the text [marsac2009 X2]. The text and Fig. 6 of the 2009 paper do not agree on the definition of the fraction plotted [marsac2009 X13]. In the extrusion work, microscopy implied a lower Tc than DSC, which the authors attribute to degradation during long holds or crystals below about 600 nm going undetected ("could be due to"), and the agreement depends on the 2 h window [moseson2018 C37, C38, X9]. In the moisture papers the tenfold drop with water is transferred from the NMP system to PVP by assumption [rumondor2009b X9; marsac2008a X4].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

dynamic adsorption-desorption equilibrium

A reversible exchange between drug adsorbed on silica and drug in solution, written as adsorbed drug + solvent in solution ⇌ adsorbed solvent + drug in solution: water displaces drug from the surface, and more drug in solution shifts the balance toward the adsorbed side [dening2018 E4, C53; dening2019 E9, C2; mccarthy2020 E5, C47]. With a supersaturated solution the equilibrium is metastable, since crystallization would reach a lower energy [dening2019 C7]. The papers find it partly irreversible: part of the drug does not leave on dilution [dening2019 C32; mccarthy2020 C27].

Findings

F9, F8, F10, F14.

Related concepts

describes drug adsorption onto silica in contact with solution; quantified by an adsorption isotherm; involves competitive adsorption of water; shifted by absorptive dissolution testing; explains incomplete drug release.

Formulas

competitive solvent-drug adsorption equilibrium, adsorbed amount by solution depletion.

How it is measured or obtained

Not measured directly; inferred from order-of-addition tests (blank silica into drug solution, loaded silica into presaturated medium), release into medium with pre-dissolved drug, redissolution of the recovered solid, dilution and desorption at sink, and release against dose [dening2018 P7, P8, P9, A1; hate2020a P8; mccarthy2020 P15, P8].

Values in the library
materialvalue or classconditionspaper ids
ritonavir, blank SBA-15 in 28 µg/mLabout 22 µg/mL leftpH 6.8[dening2018 R13]
ritonavir residue redissolvedabout 12 µg/mL, 43% (n = 1)pH 6.8[dening2018 R17]
ritonavir, dilution to S about 1release about 40 → 60–66%; bound drug 170 → 100–110 mg/g (calculated)50 mL, 180 min[dening2018 R18; dening2019 R16]
atazanavir, 0 / 20 / 40 µg/mL pre-dissolvedreleased about 31.2 / 23.9 / 14.8 µg/mL at 90 minpH 6.8, closed[hate2020a R17]
indomethacin; methyl ester, recovered solidCmax 16.2; 3.5 µg/mL, as first run (n = 1)pH 2.2[mccarthy2020 R24]
indomethacin; methyl ester, dilution to sink73%; 57% desorbed in 24 hpH 2.2[mccarthy2020 R13]

Evidence table: dynamic adsorption-desorption equilibrium.

Pitfalls and disagreements

Forward release kept about 50% of ritonavir while blank silica took up only about 20%, so retention "may therefore depend only in part on the adsorption equilibrium" [dening2018 C47]. Diffusion of drug that is in the pores but not adsorbed would respond to the bulk concentration in the same way, and the tests do not separate it [hate2020a X16]. The redissolution tests are single runs [dening2018 R17; mccarthy2020 X15]. An absorptive sink freed little ketoconazole re-adsorbed after a pH shift, read as adsorption "at least partially irreversible" or very slow [hate2020b C32].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

enteric polymer

Evidence table: enteric polymer. Content from the ASD dissolution chapter (posaconazole 2019, delamanid 2022–2023, praziquantel 2024–2025) and the Bioperformance chapter.

A polymer with acidic groups, such as the succinoyl groups of HPMCAS, the phthalyl groups of HPMCP or the methacrylic acid of the Eudragit L grades, that stays largely undissolved at gastric pH and dissolves above a threshold pH set by its substitution [nguyen2023c R4, C14; nguyen2023b M11]. In a dispersion it holds most of the drug back in the stomach, which an enteric polymer is chosen for, but it is a poor crystallization inhibitor where it is unionized, so the drug in the wetted matrix can crystallize in acid [nguyen2023b C36, C37]. Around a tablet, as a coating, the same chemistry keeps the gastric medium away from the dispersion altogether [nguyen2023b C43]. Weakly acidic polymers with pH-responsive solubility are used more and more in dispersions, while release and crystallization at a pH where the polymer is insoluble are "not well understood" nguyen2023a C1.

Findings

F24, F25, F27, F28.

Related concepts

defined by pH-dependent polymer solubility and polymer ionization; governs drug leaching and polymer-controlled release; risk of surface crystallization in acid; read with gastric pH variability.

Formulas

pH-solubility profile.

How it is measured or obtained

Polymer solubility by hydrolysing the cellulose backbone of the dissolved polymer and assaying it by HPLC-ELSD, checked by phenol–sulfuric acid colorimetry, from pH 1.6 to 6.5 [nguyen2023c P3, P4]; polymer release alongside drug release during a two-stage test by the same assay [nguyen2023c P10]. Coat integrity by stirring coated tablets in gastric media overnight and photographing them, with a USP acid-stage tolerance test [nguyen2023b P6, P7].

Values in the library
materialvalue or classconditionspaper ids
HPMCP-50; HPMCP-55893 ± 95 and 189 ± 18 µg/mL at pH 5.0; insoluble below pH 4.550 mg in 15 mL, 48 h, 37 °C[nguyen2023c R4]
HPMCAS-LF; -MF1687 ± 47 and 1401 ± 69 µg/mL at pH 5.5the same[nguyen2023c R4]
HPMCAS-HFdissolves only from about pH 6.0the same[nguyen2023c R4]
HPMCAS-HF, cited threshold (Bioperformance)the most hydrophobic grade, with the highest acetyl:succinoyl ratio, needs the highest pHcitednguyen2023a C15
Eudragit L 100-55 as an Acryl-EZE II coat, 14–16% weight gainintact 15 to more than 17 h at pH 1.6–3.0; failed after ≈130–150 min at pH 4.5–5.0; dissolved in 10–15 min at pH 6.0500 mL, 37 °C[nguyen2023b R7]
posaconazole–HPMCAS-MF dispersions in FaSSGF7.5–11.5% of a 400 µg/mL dose released in 60 minpH 1.6, 37 °C[elkhabaz2019a R10]
praziquantel–HPMCAS-MF dispersions, first stage≈9–29% released against ≈88–106% for HPMC E5 LVpH 1.6–5.0 or FaSSGF, 37 °C[alvarenga2025 R7, R10, R13]
Pitfalls and disagreements

The polymer that releases best at intestinal pH is not the one that protects best in acid, and the ranking reverses with the gastric pH: delamanid dispersions of HPMCP-55 ended at ≈80.5% after pH 3.0 but ≈12.5% after pH 5.0, below HPMCAS-LF [nguyen2023c R11, X3]. Holding the drug back is incomplete: posaconazole and delamanid dispersions released 7.5–41% of the dose in acid, where the matrix can then crystallize [elkhabaz2019a R10; nguyen2023b R2]. The printed polymer solubilities above about 3.3 mg/mL exceed what the stated amounts allow [nguyen2023c X1].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

enthalpy of mixing

The heat effect of mixing drug and solvent or polymer, set by the strength of the cross (adhesive) interactions relative to the interactions in the pure components. Exothermic mixing is read from a Flory–Huggins parameter below zero [baird2011 C26, C27] or from an activity coefficient below 1, provided the entropy of mixing is close to ideal [baird2011 C23; marsac2008b C14]. In the library it is never measured calorimetrically in the PEG papers; it is inferred. Outside this chapter the entropy of mixing is taken as always favourable, so the enthalpy decides miscibility [marsac2009 C29]. New aspects (Miscibility and drug-polymer interactions): The sign and size of the enthalpy of mixing follow the strength and number of interactions in the mixture relative to the pure materials: exothermic only if the cross-interactions are stronger or more numerous, endothermic if a component self-associates more strongly, athermal if they are similar; hydrogen bonds, dipolar forces and van der Waals contacts all contribute, and van der Waals-only systems are expected to mix endothermically [marsac2009 C36, C37]. Since the entropy of mixing with a polymer is always favourable and nearly the same for any pair, the enthalpy, through χ, decides miscibility [marsac2006b C13; marsac2009 C26]. A pair can tolerate a certain maximum unfavourable enthalpy [marsac2009 C26]. In dextran–PVP blends the enthalpy of mixing is inferred to be positive because many blends phase separate, with dextran–dextran hydrogen bonds assumed to be stronger or more numerous than dextran–PVP ones; it was not measured [vaneerdenbrugh2012a C32, C36, X7]. For itraconazole–HPMC, which has no donor, any miscibility is "likely" entropy-driven with little favourable enthalpy [purohit2015a C42]. New aspect (Physical stability): moisture-induced separation "must" come from a positive mixing enthalpy of the ternary system, because the entropy of mixing favours mixing; it is expected when water, polymer and drug interact very differently rumondor2009c C42, C43. Miscibility of the dry pair is set by the balance of cohesive and adhesive interactions marsac2010 C4.

Findings

PEG dispersions: F2, F3, F11. Miscibility and drug-polymer interactions: F2, F5, F6, F7, F18, F22. Physical stability: F13, F23.

Related concepts

depends on Flory-Huggins interaction parameter and activity coefficient; related to hydrogen bonding, drug-polymer interactions and athermal mixing; part of free energy of mixing; contrasts with entropy of mixing; part of Flory-Huggins theory; drives Δχ effect.

Formulas

Flory-Huggins melting point depression, Flory-Huggins interaction parameter from interaction energy; Gibbs free energy of mixing; multicomponent Flory-Huggins free energy of mixing.

How it is measured or obtained

Inferred from the sign of \chi (melting point depression), of \gamma in PEG 400 or water, or from the interaction energy back-calculated from an eutectic composition [baird2011 E3, E8, E7; zhu2011 C6; marsac2008b C14]. Not by calorimetry in the miscibility papers. It is inferred from the sign of χ obtained by melting point depression or from the solubility of the drug in a liquid analogue, which assumes ideal entropy of mixing in that liquid [marsac2009 C29, C11; marsac2006b C35]. The papers on dispersions also define the quantity from component enthalpies: Rumondor and co-workers print ΔHmix as the pure-component minus the mixture enthalpy, so that a positive value is exothermic, but use the conventional sign elsewhere [rumondor2009a E4, X8]. In the moisture papers it is inferred from activity coefficients above or below 1 and from interaction parameters, assuming ideal mixing entropy [marsac2008a C34, C37; rumondor2009c C28].

Values in the library
materialvalue or classconditionspaper ids
chlorpropamide; aceclofenac with PEG 3350exothermic mixing implied by \chi_{dp} −2.53 and −6.68 and interaction energies −6.85 and −18.2 kJ/molback-calculated[baird2011 C18, C27, R1.a, R1.b, R9.a, R9.b]
loratadine; haloperidol with PEG 3350athermal mixing implied by \chi_{dp} 0.13 and −0.04back-calculated[baird2011 C27, R9.c, R9.d]
six drugs with PEG 400; with waterexothermic with PEG 400 (\gamma 0.02–0.64); endothermic with water (\gamma 10¹–10⁵)if mixing entropy is near ideal[marsac2008b C14]
nifedipine, felodipine with NMP and waterexothermic with NMP (γ 0.09, 0.30), endothermic with water (γ 1.89 × 10³, 2.43 × 10⁵)assuming near-ideal mixing entropy; 25 °C[marsac2008a R10, C37]
six drugs in waterγ water 2.54–4.65; unfavourable drug–water contacts95% RHrumondor2009c R24, C28
felodipine and quinidine with HPMCASless sorbed water gives a less positive mixing enthalpy, which "may explain" no separationqualitativerumondor2010c C31
indomethacin with PVPVAstronger drug–polymer bonds give a more favourable mixing enthalpyqualitativerumondor2010c C28
miscible pairs with PVP\chi near or below zero: athermal or slightly exothermic, miscibility largely driven by entropymelting point depression[marsac2009 C29]
indomethacin–PVPmost exothermic of five PVP pairs (χ −0.82 melting, −1.83 solubility route)melting at 1 °C/min; EP at 25 °C[marsac2009 R7.e, R9.e, C29]
felodipine, ketoconazole, nifedipine, sucrose with PVP K12athermal or slightly exothermic, miscibility "largely driven by entropy"offset melting[marsac2009 R7.a, R7.b, R7.c, R7.d, C29]
nifedipine, felodipine with PVP K12exothermic mixing indicated by χ −3.8 and −4.2melting at 1 °C/min[marsac2006b C35, R9]
dextran with ibuprofen or indomethacinadhesive interactions not more favourable than cohesive ones, "speculated"no depression[marsac2009 C43]
dextran–PVPpositive enthalpy inferred where blends separate; dextran–dextran bonds assumed stronger or more numerousphase map; OH band shift[vaneerdenbrugh2012a C36, C37, R13, R16]
itraconazole–HPMCentropy-driven mixing with little favourable enthalpyargument in words[purohit2015a C42]
Pitfalls and disagreements

The entropy of mixing was not measured, so an exothermic reading rests on an assumption [baird2011 C23]. The abstract of Baird and Taylor says the interactions were confirmed by infrared spectroscopy, while the spectra show shifts of drug bands against an additive spectrum and no PEG band was analysed [baird2011 X15]. (synthesis: in water the activity coefficient is far above 1 for all six drugs, which is endothermic mixing if the entropy is ideal, yet the drug with the smallest coefficient lost the most crystallinity in PEO [marsac2008b C14, C35].) The two sign conventions of ΔHmix within one paper change the reading of the PAA statement: with the conventional sign, intra-PAA hydrogen bonds make mixing with felodipine less favourable [rumondor2009a X8, C45]. The statement that the solubility of drugs in polymers is low "unless extremely favourable cohesive interactions" form uses "cohesive" where the paper's own definition would give "adhesive" [marsac2009 X14]. In the miscibility papers the enthalpy was never measured either, so every reading rests on an entropy assumption [marsac2009 C11, C29]. In the ternary water–drug–polymer case the χ terms also carry non-ideal entropy, so "positive enthalpy" is a statement about positive χ terms rumondor2009c X14. No mixing enthalpy was computed for the HPMCAS and PVPVA dispersions, and a mobility reading is offered alongside rumondor2010c X13, C32.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

enthalpy relaxation

The slow loss of excess enthalpy of a glass during ageing below Tg, recovered as an endotherm on reheating; fitted with a stretched exponential, it gives a mean relaxation time τ (longer means less mobile) and a width parameter β [konno2006 P6, E7; marsac2006a P9, E7].

Findings

F5.

Related concepts

measures molecular mobility; related to structural relaxation and structural relaxation time; uses Kohlrausch-Williams-Watts equation.

Formulas

Kohlrausch-Williams-Watts equation, maximum enthalpy recovery.

How it is measured or obtained

Glasses or dispersions are aged for set times (here at 2 °C or 23.5 °C), the recovered enthalpy is measured by DSC, divided by the maximum recovery \Delta C_p(T_g - T) and fitted with the Kohlrausch–Williams–Watts function [konno2006 P6, E5, E6; marsac2006a E8]. A strong recovery peak on the first DSC scan of a humidity-exposed dispersion was also reported marsac2010 R15.

Values in the library
materialvalue or classconditionspaper ids
felodipine with 10% PVP, HPMC, HPMCASτ 208, 319, 687 h; β 0.42, 0.47, 0.45aged at 2 °C[konno2006 R9]
amorphous nifedipine, felodipineτ 6.3 and 4.2 h; β 0.36 and 0.3723.5 °C[marsac2006a R4.m, R4.n]
nifedipine, felodipine with 10 wt% PVPτ 42.1 and 16.7 h23.5 °C[marsac2006a R7]
felodipine, alone and with 10% PVP84% and 65% of the maximum recovery after 16 h23.5 °C[marsac2006a R8]
felodipine–PVP 46.5 wt% after 94% RHstrong recovery peak at ≈55 °C on the first scanDSC cyclingmarsac2010 R15
HPMCAS dispersions and indomethacin–PVPVA after 94% RHendotherm with the single Tg read as enthalpic recoveryDSC after dryingrumondor2010c R17, C17

Evidence table: enthalpy relaxation.

Pitfalls and disagreements

Both papers print the KWW equation with the sign or exponent misplaced; the standard form reproduces the data [konno2006 X5; marsac2006a X4]. The relaxation times did not rank crystallization: the faster-nucleating nifedipine dispersion was the slower-relaxing one, and the τ order of the three felodipine dispersions differs from their Tg order [marsac2006a R7, C37; konno2006 X13].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

Etter's hydrogen-bond rules

Empirical rules from crystal engineering on which donors and acceptors pair in a crystal: all good proton donors and acceptors are used in hydrogen bonding; intramolecular hydrogen bonds that close a six-membered ring form in preference to intermolecular ones; and the best donors and acceptors left after intramolecular bonding pair with one another [vaneerdenbrugh2011a C11; wegiel2013a C29]. The library applies them to drug–polymer pairs: the free group of the drug with the highest donor or acceptor strength is matched to the polymer group that can compete with the drug's own self-association, which gives the expectation that acceptor-only polymers suit donor drugs and acidic donor polymers suit amide and basic drugs [vaneerdenbrugh2011a C19, C32, C33, C53]. The authors say the rules should be used as "a set of tools providing guidance, rather than a strict set of rules" [vaneerdenbrugh2011a C53].

Findings

F24, F25, F14, F17.

Related concepts

uses hydrogen-bond basicity and intramolecular hydrogen bonding; predicts crystallization inhibition by polymers; part of hydrogen bonding; related to steric hindrance and pKa.

Formulas

none.

How it is measured or obtained

By classifying every functional group of drug and polymer: donor strength from the bonding atom (O–H, N–H) and its acidity, adjusted by substituents, pKa and short contacts in crystal structures; acceptor strength from the pKBHX scale of a model compound; possible intramolecular rings from ring size, published surveys, crystal structures and DFT; and competition between groups from crystal-structure statistics [vaneerdenbrugh2011a P5, P6, P7, P8, C13, C14, C15]. The resveratrol paper used the same scheme for the polymers of its set [wegiel2013b P10, C30], and the polyphenol paper for naringenin and quercetin [wegiel2013a P8, C29].

Values in the library
materialvalue or classconditionspaper ids
carboxylic acid groups of the drugsvery strong donors, medium acceptors (ethyl acetate 1.07)Table 1 classes[vaneerdenbrugh2011a R1]
PVP, PVPVA pyrrolidonevery strong acceptor (1-methyl-2-pyrrolidone 2.38), no donorTable 2[vaneerdenbrugh2011a R2]
amide carbonyl of benzamide, phenacetinstrong acceptor (1.81, 1.69); amide N–H medium donorTable 1[vaneerdenbrugh2011a R1]
benzamide, phenacetin crystalsamide–amide only: 100 and 94% alone; 0% with COOH; 14 and 33% with C(O)NC2CSD survey[vaneerdenbrugh2011a R14]
naringenin, quercetinfree phenolic OH donors (two and three) after intramolecular bondsstructure[wegiel2013a M1, M2, C30]

Evidence table: Etter's hydrogen-bond rules.

Pitfalls and disagreements

The rules come from crystals and are applied to amorphous mixtures; the hydrogen bonds in the films were not measured and the melt spectra for acid–base reactions are not shown [vaneerdenbrugh2011a C50, X13]. The abstract speaks of an ab initio rank order that "agreed well", but no predicted order per drug was tabulated or scored, and the exceptions were explained afterwards [vaneerdenbrugh2011a C55, X5]. Footnotes of the group tables call the acceptor classes "donor strength" and cite two different references for the pKBHX values [vaneerdenbrugh2011a X2].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

falling-off-the-cliff effect

Evidence table: falling-off-the-cliff effect. Content from the release-mechanism chapter (2018–2022), with comparison rows from the ASD dissolution chapter.

The steep fall of drug release over a small increase of drug loading just above the limit of congruency, named "falling off a cliff" for ritonavir–PVPVA, whose drug release at 60 min fell from ≈97% at 25% loading to ≈29% at 30% and below ≈2% at 35–50% indulkar2019a C31, R11. The authors stress that the range of loadings over which release switches from polymer- to drug-controlled is "very narrow" and that the switch changes the drug release rate by "orders of magnitude" indulkar2019a C52. Saboo and co-workers (2020) contrast this "cliff" with the gradual "slope" of HPMCAS dispersions saboo2020a C29. Yang and co-workers (2021) saw the cliff in powders as well as compacts for six drugs in PVPVA and call the HPMCAS decline a negative "slope" instead yang2021 C2, C41. Yang and co-workers (2022) hypothesized that the cliff coincides with a continuous drug-rich barrier at the dispersion surface yang2022a C10, C7.

Findings

Release mechanism and LoC: F6, F8, F11, F22.

Related concepts

marks the limit of congruency; separates polymer-controlled release from drug-controlled release.

Formulas

surface-normalized release rate.

How it is measured or obtained

Percent released at a fixed time against loading, or normalized drug rates across the switch, from constant-area compacts indulkar2019a R11; saboo2019 R5, R6; saboo2020a R14.

Values in the library
materialvalue or classconditionspaper ids
ritonavir–PVPVA 25 → 30 → 35%≈97 → ≈29 → ≈1.7% drug at 60 minpH 6.8, 37 °Cindulkar2019a R11
nilvadipine–PVPVA 10 → 15%2.13 → 0.035 mg/min/cm² (60-fold)samesaboo2019 R5, R7
cilnidipine–PVPVA 15 → 20%2.18 → 0.006 mg/min/cm² (about 360-fold; described as "similar")samesaboo2019 R6, X8
felodipine–PVP 10 → 15%; –PVPVA 15 → 20%≈3.8 → ≈0.020; ≈1.9 → ≈0.009 mg/min/cm² (synthesis: 190- and 211-fold)samesaboo2020a R14
ITZ–PVPVA 20 → 25% (SD); 10 → 20% (HM)113 → 64; 199 → 48.8 µg/min/cm² (synthesis: 1.8- and 4.1-fold)0.1 N HClbhardwaj2018 R4
praziquantel–HPMCAS-MF, HPMC (ASD dissolution chapter)no cliff; release never declined massively with loadingPBS pH 6.5polyzois2024 C16, C18
indomethacin–PVPVA 10 → 15%3.14 → 0.04 mg/min/cm²5-min ratessaboo2020 R3
loratadine, miconazole, danazol, elbasvir in PVPVA≈85 → 41 → 8; 93 → 42 → 3; 78 → 9.5; 77 → 13 µg/mL of 100powdersyang2021 R7, R8, R9, R10
atazanavir–PVPVA 5 → 10%≈100 → below 3% releasedcompacts, 37 °Ccorreasoto2022b R1
lumefantrine sulfate–PVPVA 2 → 5%4.5 → 0.10 mg/min/cm²compactshiew2022b R12
ritonavir–PVPVA 20 → 30 → 40%drug ≈100 → 35 → 3% at 90 mincompacts, pH 6.8yang2022a R2
Pitfalls and disagreements

Loadings were tested in 5% steps, so the cliff is located only to the step saboo2020a X11. For HPMC the drop came in two steps (≈0.14 → ≈0.04 → ≈0.005 mg/min/cm²) saboo2020a X11, R14. (synthesis: the height of the cliff is bounded by the ratio of the polymer-controlled to the neat-amorphous rate, so it is small where the amorphous drug alone dissolves fast, as for ITZ in 0.1 N HCl.) Stated cliff loadings mix the last good and the first poor loading yang2021 X26.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

Flory-Huggins interaction parameter

The parameter \chi of Flory–Huggins lattice theory that expresses the energy of drug–polymer contacts relative to the contacts in the pure components. In the PEG papers \chi > 0, \chi = 0 and \chi < 0 mean endothermic, athermal and exothermic mixing [baird2011 C26], and more negative values are "consistent with" a negative enthalpy of mixing and favourable drug–polymer interactions [zhu2011 C6]. The three PEG papers that report it define it differently: Baird and Taylor divide a back-calculated interaction energy by R\,T_{eut,th}, Zhu and co-workers take the drug volume as lattice site and normalize per PEG segment [baird2011 E8; zhu2011 E1, E2]. Marsac and co-workers take the volume of a low-molecular-weight analogue as lattice site for polymers such as PVP [marsac2009 E2]. New aspects (Miscibility and drug-polymer interactions): χ reflects the relative strength of cohesive (drug–drug, polymer–polymer) and adhesive (drug–polymer) interactions and has an entropic part; it can vary with temperature and composition [marsac2006b C15]. A negative χ describes strong, numerous adhesive interactions that favour miscibility, a positive χ stronger cohesive interactions [marsac2006b C16]. In the simulations the χ needed for miscibility over the whole composition range of nifedipine–PVP is about 0.6 or less, and the critical value depends on the lattice definition and is system specific [marsac2006b R3, C18]. Because the entropy of mixing with a polymer is small and almost the same for any pair, differences between compounds come from the magnitude of χ [marsac2009 C26, C31]. A larger negative χ reflects a greater driving force for mixing near the drug's melting temperature [marsac2009 C18]. For dextran–PVP blends χ was not determined and was assumed independent of molecular weight so that only the combinatorial term differs between the 20 pairs [vaneerdenbrugh2012a C33]; for itraconazole–HPMC no χ was measured, and a positive χ is inferred from the lack of hydrogen-bond donors [purohit2015a C41, C42, C47]. New aspect (ASD process): in the 2018 hot-melt extrusion study the lattice volume is the drug's molecular volume (molecular weight divided by true density: IDM 273 cm³/mol, PVPVA 46,610 cm³/mol), \phi is the drug volume fraction from true densities and m the polymer-to-drug volume ratio (170.7 at 50/50) [moseson2018 M1, M2, E2, E6]. The same theory applied to water gives large positive water–drug parameters and a small water–polymer parameter; the asymmetry is the reason cited for moisture-induced demixing marsac2010 C43; rumondor2009c C45, C46. In the four-component drying model χ is estimated for each pair from vapour-sorption fits (Flory–Huggins sorption isotherm), a solubility or a heat of mixing: ritonavir–methanol 0.8, ritonavir–water 2.8, PVPVA–methanol 0.73, PVPVA–water 1.13, methanol–water −0.002, ritonavir–PVPVA 0.5 (assumed in the SI) li2020 R15, E12. In the later HME papers the same linearized fit gave a negative value for bicalutamide–PVPVA and a positive one for posaconazole–HPMCAS, so the sign differs between pairs [moseson2022c R8; shah2024 R4]. New aspect (Physical stability): water–component parameters from sorption isotherms rank drugs and polymers by their dislike of water, and the drug–water value split six drugs by moisture-induced separation in PVP [rumondor2010a R11; rumondor2009c R24, C46]. New aspect (Supersaturation from ASD dissolution): in an argument about dissolution, the enthalpy of solution of pure amorphous drug contains the water–drug term χ12, whereas a dispersion adds water–polymer (χ13) and drug–polymer (χ23) terms, so there is "no reason to expect" the two to give the same solution activity alonzo2011 E7, E8, C43, C45. In the lopinavir work χ enters the drug's chemical potential in a polymer that stays undissolved: a more negative χ, a stronger drug–polymer attraction, lowers the maximum concentration more than dilution alone, a χ above zero lowers it less, and a large χ gives phase separation with little suppression [li2018 C44, C51]. χ was not measured; the model is "probably best applied in a qualitative manner" [li2018 C46]. New aspect (Release mechanism and LoC): in the water–drug–polymer free energy of mixing, three pairwise parameters enter: \chi_{DP} is negative or small for a molecular dispersion, \chi_{WD} of a hydrophobic drug is large and positive, and \chi_{WP} is smaller because the polymer hydrogen-bonds with water; a large difference between \chi_{WD} and \chi_{WP} gives a tendency to phase separate on hydration purohit2017b C43, E2, E4. Yang and co-workers (2021) use the Δχ form to explain why log P fails: drugs have much larger χ with water than polymers (cited), so water–drug against water–polymer interactions, drug–polymer interactions and hygroscopicity, not one descriptor, decide separation yang2021 C21, C22, E2.

Findings

PEG dispersions: F2, F3, F5, F6. Miscibility and drug-polymer interactions: F2, F5, F6, F7, F8, F9, F18, F22. ASD process: F8, F1, F20, F41. Physical stability: F4, F8, F13, F23, F29. Supersaturation from ASD dissolution: F7, F18. Release mechanism and LoC: F8, F9.

Related concepts

depends on enthalpy of mixing and melting point depression; derived from drug-polymer interaction energy; contrasts with athermal mixing; related to drug-polymer interactions and activity coefficient; part of Flory-Huggins theory. Relates to drug solubility in polymer. Basis of Δχ effect; measured from water sorption isotherm; linked to water through hydrophobicity; related to drug-polymer miscibility and amorphous solubility advantage. Related to drug-polymer-water miscibility.

Formulas

Flory-Huggins melting point depression, Flory-Huggins interaction parameter from interaction energy, Lacoulonche liquidus model; Flory-Huggins interaction parameter from solubility parameters, Flory-Huggins free energy of mixing, Flory-Huggins activity equation. Extrusion work: molar volume from molecular weight and density, multicomponent Flory–Huggins free energy of mixing. Water sorption: Flory-Huggins water sorption isotherm, ternary Flory-Huggins water sorption isotherm. Dissolution of dispersions: Flory–Huggins enthalpy of mixing for two and three components (named, no shared page) alonzo2011 E7, E8; Huang model of drug solubility in an ASD, Δχ effect.

How it is measured or obtained

From the melting point depression of the drug: the slope of the linearized relation against the squared polymer volume fraction, at 50–80% drug in the PEG study [zhu2011 P5, E1]; from the interaction energy that closes the gap between the athermal and the observed eutectic [baird2011 P8, P10, E3, E8]; for PVP, from the slope of the melting-point plot at 0–25 wt% polymer, or from group-contribution solubility parameters [marsac2006b R8, R9, R4]. In the Marsac studies of drugs in PVP and other polymers, three routes appear. (1) Group-contribution solubility parameters, Eq. 2, which always give a non-negative χ [marsac2006b E2, R4]. (2) The slope of the linearized melting point depression against Φ_polymer², over 0–25 wt% polymer, with the lattice site set to the drug (2006) or to a liquid analogue (2009), using the offset of the melting peak in 2009 [marsac2006b E10, R8, R9; marsac2009 P6, C16]. (3) From the activity coefficient of the drug in a liquid analogue (1-ethyl-2-pyrrolidone, 25 °C), scaled to the polymer with Eq. 8 [marsac2009 P7, E8, E9]. A fourth route, the ternary Flory–Huggins fit to moisture sorption, was unable to give unambiguous values [rumondor2010a C30]. In the extrusion work χ is the slope of the linearized melting point depression plot A=\chi B, with A=\left(-\Delta H/R\right)(1/T_c-1/T_m)-[\ln\phi+(1-1/m)(1-\phi)] and B=(1-\phi)^2, fitted through 90/10 to 50/50 IDM:PVPVA; the printed value is reproduced only with a free intercept of about +0.02 (a line through the origin gives −1.86) [moseson2018 E4, R4, X7]. For water: binary Flory–Huggins sorption fits of pure amorphous components, and the drug–water χ from the 95% RH uptake [rumondor2010a P4; rumondor2009c P13, E5]. In the ASD dissolution papers no values were measured; binary parameters cannot simply be carried into the ternary model (cited) alonzo2011 C44, R27. In the release-mechanism papers: not measured in the release-mechanism papers; used in argument purohit2017b E2, E4.

Values in the library
materialvalue or classconditionspaper ids
chlorpropamide; haloperidol with PEG 3350−0.50 and 0.08; −2.53 and −0.04zhu2011 (per PEG segment); baird2011 (\Delta W/RT), same phase diagrams[zhu2011 R5.c, R5.a; baird2011 R9.a, R9.d]
aceclofenac; loratadine with PEG 3350−6.68; 0.13\Delta W_{d,p}/(R\,T_{eut,th})[baird2011 R9.b, R9.c]
benzocaine, ibuprofen, nilutamide, ketoconazole with PEG 3350−0.23, −0.19, −0.09, 0.02melting point depression at 50–80% drug[zhu2011 R5.b, R5.d, R5.e, R5.f]
nifedipine; felodipine with PVP K12−3.8; −4.2 near the melting point; solubility-parameter estimates 2.0 and 0.5slope of the linearized plot[marsac2006b R9, R4]
indomethacin with PVP K12−6.16 (onset), −1.94 (midpoint), −0.82 (offset)melting point depression[marsac2009 R6]
indomethacin with PVPVA−1.97 (R² = 0.9895); reproduces all predicted Tc of Table III within 0.05 °Cused to predict Tc; slope with free intercept, 50–90% DL[moseson2018 R4, R5, E2]
PVP-miscible pairsnegative or near zero; immiscible pairs larger positive values, from −0.82 to 0.72offset melting[marsac2009 C17]
indomethacin, felodipine, nifedipine, ketoconazole, sucrose with PVP K12offset χ −0.82, −0.08, 0.00, −0.08, 0.021 °C/min[marsac2009 R7.a, R7.b, R7.c, R7.d, R7.e]
same five compoundssolubility-route χ −1.83, −0.08, −0.81, −0.12, −0.5325 °C, EP[marsac2009 R9]
sucrose–dextran; ibuprofen–dextran; indomethacin–dextran; itraconazole–Eudragit E1000.20; ≥ 0.38; ≥ 0.72; ≥ 0.11 (lower limits for the last three)offset melting[marsac2009 R7.f, R7.g, R7.h, R7.i, C19]
felodipine–PVP; indomethacin–PVP−9.6 to 26.9; −20.4 to 22.0 (ranges only)ternary sorption fit[rumondor2010a R14]
IDM–PVPVA in four other studies−0.64, −2.06, −2.9, −4.5 (assignment to studies not printed)cited[moseson2018 R7]
water–felodipine, water–PVPabout 3.3 and about 0.5 (Δχ large)sorption isotherms, Flory–Huggins fitsmarsac2010 C43
water with amorphous felodipine, PVP, HPMC and HPMCAS3.27 for felodipine; above 0.5 for HPMC and HPMCAS; the PVP value close to but slightly below other authors' valueswater sorption isotherms, 25 °C[rumondor2010a R11, C19, C20]
BCL–PVPVA 30% DL−1.57, read as favourable miscibilityphase diagram, SI not supplied[moseson2021 M1, C10]
RTV–PVPVA (drying model)0.5 assumed in the SI; "likely <0.5, and possibly close to zero" in the text; varied −0.5 to 0.5sensitivity moved mainly the drug–polymer sideli2020 R15, R16, C72, X10
water–ritonavir and water–PVPVA (drying model)2.8 and 1.13fitted to dynamic vapour sorption, room temperatureli2020 R15
BCL–PVPVA 30–90% BCL−1.57 (R² 0.994); Tc 145 °C at 30% BCLDSC offsets extrapolated to 0 °C/min[moseson2022c R8, R9]
PCZ–HPMCAS MF, PCZ fractions 0.4–1.0+0.43 (R² 0.991); the fitted line meets B = 0 at A of about −0.05same[shah2024 R1, R4]
water with nifedipine, felodipine, droperidol, pimozide, indomethacin, ketoprofen2.84, 3.18, 2.85, 3.58, 2.50, 2.7125 °C, 95% RHrumondor2009c R24
nifedipine–PVP, felodipine–PVP (cited)−3.8 and −4.2 from melting point depressionused for activity[marsac2006a R18]
indomethacin–PVP vs nifedipine–PVP (cited)−0.8 vs 0.0used for susceptibilityrumondor2009c R26
indomethacin against felodipine, quinidine, pimozide with PVPVAlarger carbonyl red shift (42–44 against 19–22 cm⁻¹) "would result" in a lower \chi_{DP}IR of dry filmsrumondor2010c R20, C28
hydrophobic drugs with water\chi_{WD} expected positive from log Pqualitativerumondor2010c C30
indomethacin with HPMC, HPMCAS, PVPχ not measured; stronger interaction "would" lower the driving force for growthargument with the free energy of mixing[tian2017 E2, C30, X13]
lopinavir with HPMCP, EC, HPMCASranked HPMCP > EC > HPMCAS in suppression, read as interaction strengthpH 3, 25 °C[li2018 C54]
lopinavir with CA, EUDtwo Tgs, sorption on the additive line; little suppressionpH 3, 25 °C[li2018 C56]
ritonavir with PVP, PVPVA, HPMCASno values; the argument explains AAPS of PVP and PVPVA films at 97% RH25 °Cpurohit2017b C43, C1
six drugs with PVPVA and HPMCASno χ measured; argument—yang2021 E2, C21
Pitfalls and disagreements

The values of one paper are not comparable with those of another: for the same published diagram of chlorpropamide the two PEG papers give −2.53 and −0.50, and for haloperidol −0.04 and 0.08, so the sign near zero is not robust [baird2011 R9; zhu2011 R5]. The printed expression for the interaction energy in Baird and Taylor does not reproduce, and only signs and ranking are robust [baird2011 X3]. Zhu and co-workers fitted \chi at 50–80% drug, not at the 20/80 composition of the SAXS/WAXS samples, and the normalization cannot be reproduced from printed inputs [zhu2011 X10]. In the PEG study the size of \chi did not rank the size of the long-period increase: chlorpropamide has the most negative \chi and the smallest increase [zhu2011 X5]. The reading as exothermic mixing assumes a near-ideal entropy of mixing [baird2011 C23]. The printed solubility-parameter values (2.0, 0.5) were not reproduced from the inputs (2.36 and 0.70 at 298.15 K) [marsac2006b X1]. The melting-route χ of one pair spans 7.5-fold with the point of the melting peak read (synthesis: 6.16/0.82) [marsac2009 R6]. The two experimental routes differ by up to 1.01 and rank the compounds differently [marsac2009 X7]. The positive values for non-depressing pairs are lower limits [marsac2009 C19, X11]. The nifedipine volume fractions of the 2006 fit may use felodipine's density [marsac2006b X2]. A χ determined near the drug melting point is applied at storage temperature without correction [marsac2006b C32]. The χ of one pair differs between studies (indomethacin–PVPVA −1.97 against −0.64 to −4.5) [moseson2018 R4, R7]. The positive mixing enthalpy of dextran–PVP is inferred from the existence of phase separation, not measured [vaneerdenbrugh2012a C32, X7]. In the extrusion work a single \chi neglects temperature and composition dependence [moseson2018 C18]. Differences between studies "can be attributed" to sample preparation, DSC method or onset versus offset [moseson2018 C21]; the nature of the fit (with or without intercept) also shifts the value [moseson2018 X7]. For ritonavir–PVPVA the main text and the SI disagree on χ, and the basis of the other χ values (vapour sorption or solubility, room temperature or 37 °C) is described differently in the two; the DVS and solubility data are not shown li2020 X10, X11. For posaconazole–HPMCAS χ is a slope with a free intercept, and Tc below 40% PCZ are extrapolations from it [shah2024 R4, X7, X8]. Two values cited in the physical-stability papers for the same pair differ by an order of magnitude: −3.8 and −4.2 (melting onset route, used in 2006) against −0.8 and 0.0 (offset route, used in 2009) for nifedipine–PVP, which reflects the choice of melting-peak point (synthesis; see the onset, midpoint and offset values above) [marsac2006a R18; rumondor2009c R26]. The drug–water χ split rests on approximated densities and a gap of 0.13 rumondor2009c X4. No χ was computed in the 2010 polymer comparison: \chi_{DP} is ranked by red shift and \chi_{WD} by calculated log P rumondor2010c X13. In the dispersion-dissolution argument, with 90% polymer, fewer drug–drug contacts "would lead to a reduction in the barrier" to dissolution, an argument without χ values alonzo2011 C43. The "ideal" line of the lopinavir figure is proportional dilution, not χ = 0 of the equation [li2018 X2]. No χ values were measured or cited for the ritonavir systems purohit2017b E4.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

Flory-Huggins theory

Lattice solution theory for a small molecule and a polymer, used here with the amorphous drug treated as the solvent and one lattice site set equal to the molecular volume of the drug (or, in the 2009 paper, of a liquid analogue of PVP) [marsac2006b C9, E1; marsac2009 P6]. For a large and a small molecule the free energy of mixing is better written in volume fractions than in mole fractions, because the large molecule has far fewer configurations; the first terms of the expression are the entropy of mixing and the last carries the interaction parameter χ [marsac2006b C7, E1]. The authors call it "still considered" an excellent starting point despite documented limits and more advanced models [marsac2006b C8]. In the library the same lattice picture gives four quantities: the free energy of mixing and miscibility, the melting point depression, the activity coefficient of the drug and the solubility of the crystal in the polymer [marsac2006b E1, E3, E6; marsac2009 E2, E8, E10]. Two later uses: for two polymers the chain lengths enter through the lattice sites per chain, N_1 and N_2, in the combinatorial term [vaneerdenbrugh2012a E5, C31]; and for itraconazole–HPMC the equation is used in words to say that, without hydrogen-bond donors, any miscibility is entropy-driven [purohit2015a E1, C41, C42]. New aspect (ASD process): written for a small molecule and a polymer as \Delta G=RT[\phi\ln\phi+\frac{1-\phi}{m}\ln(1-\phi)+\chi\phi(1-\phi)], with the two entropy terms always favouring mixing and the \chi term carrying the enthalpy [moseson2018 E1; purohit2015a C41]. In the hot-melt extrusion papers it is used through the melting point depression relation to build the solubility line for HME [moseson2018 E2]. It was extended to four components in the drying model of a spray droplet, with volume fractions of methanol, water, ritonavir and PVPVA and six pairwise χ values, to locate the drug solubility along the drying path li2020 P12, E11. New aspect (Physical stability): extended to the ternary water–drug–polymer system, where separation requires the interaction terms to outweigh the entropy of mixing, and to water sorption of blends, where the drug–polymer term is too small to be fitted [rumondor2009c E4, C42; rumondor2010a C25].

Findings

Miscibility and drug-polymer interactions: F5, F6, F7, F8, F9, F18, F22. ASD process: F8, F20. Physical stability: F4, F8, F13, F23, F29.

Related concepts

gives Flory-Huggins interaction parameter, entropy of mixing, combinatorial entropy of mixing, free energy of mixing and activity coefficient; used for drug-polymer miscibility and drug solubility in polymer. Predicts melting point depression. Explains Δχ effect and moisture-induced phase separation.

Formulas

Flory-Huggins free energy of mixing, Flory-Huggins melting point depression, Flory-Huggins activity equation, Gibbs free energy of mixing, Flory-Huggins combinatorial entropy of mixing. Four-component form: multicomponent Flory–Huggins free energy of mixing. Water sorption: Flory-Huggins water sorption isotherm, ternary Flory-Huggins water sorption isotherm.

How it is measured or obtained

It is a model; its inputs are densities (helium pycnometry or cited), molecular volumes (molecular weight over density), heats of fusion and melting points from DSC, and χ from experiment [marsac2006b P4, P5, P6; marsac2009 P6, P7, P8]. Outside the binary case, a ternary water–drug–polymer form is used to discuss moisture rumondor2010c E1, C26. In the extrusion work χ is fitted to melting point depression data (see Flory–Huggins interaction parameter); the free energy itself is not evaluated there [moseson2018 E1, E4]. In the moisture papers the ternary free energy of mixing is used in words, and binary, ternary and pseudobinary sorption equations are fitted to isotherms [rumondor2009c E4; rumondor2010a E1, E2, E4].

Values in the library
materialvalue or classconditionspaper ids
nifedipine with PVP K12, K29/32, K90entropy minimum near Φ ≈ 0.6, against ≈ 0.44 with methyl pyrrolidoneχ = 0[marsac2006b R1]
nifedipine–PVP K29/32miscible over the whole range for χ ≲ 0.6; single deep minimum at χ −3.8, −4.2five χ values[marsac2006b R2, R3]
five compounds with PVPΔG/RT minima at polymer fractions ≈ 0.5–0.6; indomethacin deepestmelting-route and solubility-route χ[marsac2009 R10]
nifedipine, felodipine in PVPlittle activity lowering below polymer volume fraction ≈ 0.5χ from melting depression[konno2006 R20, C35; marsac2006a R19]
indomethacin–PVPVAχ −1.97 from the linearized melting relation; one χ describes Tc from 50 to 90% DL (HME phase diagram)offset extrapolated to 0 °C/min[moseson2018 R4, C19]
dextran–PVP, 20 pairscombinatorial entropy per site from about −27 × 10⁻²³ J (783 Da maltodextrin, PVP K 12) to about 0 (450 kDa dextran, PVP K 90)25 °C, no enthalpic term[vaneerdenbrugh2012a R15, E5]
itraconazole–HPMCentropy-driven miscibility, limited at room temperature (UCST-type); no χ measuredargument in words[purohit2015a C42, C47, E1]
ternary water–drug–polymer systemswater lowers the free energy entropically; large positive \chi_{WD} favours drug-rich separationstored ASDspurohit2017b C43
drug in polymer, melting point depression and activityfree energy of mixing and melting point depression from Flory–Hugginsfelodipine, nifedipine with PVP[marsac2006b E1, E3; marsac2006a E10]
ritonavir–PVPVA–methanol–waterthe computed solubility boundary is crossed from about 12.5:87.5 initial water:methanol at 25% DLfour-component modelli2020 R17, C50
indomethacin–PVP, felodipine–PVPdrug–polymer term 0.029–0.160% of the ternary adjustment25 °C sorption[rumondor2010a R13]
felodipine–PVP, indomethacin–PVPfitted χ23 −9.6 to 26.9 and −20.4 to 22.0same[rumondor2010a R14]
four blend seriesmean water–blend χ1,23 falls with polymer contentsame[rumondor2010a R15]
felodipine, quinidine, pimozide, indomethacin with PVP, PVPVA, HPMCASternary free energy of mixing used to explain why less hygroscopic polymers separate lessqualitativerumondor2010c E1, C26, C31, C39
indomethacin–polymer meltsfree energy of mixing used to argue a lower driving force with stronger interactiongrowth, 80–135 °C[tian2017 E2, C30, C31]

Evidence table: Flory-Huggins theory.

Pitfalls and disagreements

The glasses are non-equilibrium, χ is assumed independent of composition and temperature, and the critical χ for miscibility depends on how the lattice is defined and is system specific [marsac2006b C3, C18; marsac2009 P8]. The melting relation is linear only at low polymer content, so the fitted χ is a composite [marsac2009 C7]. The entropy curves exist for nifedipine only and carry no ordinate scale [marsac2006b X7, X8]. The hydrogen-bond picture cannot be represented by solubility parameters inside the theory [marsac2006b C24]. The ternary form fitted to moisture sorption gave ambiguous χ values [rumondor2010a C30]. The comparison of the 20 dextran–PVP pairs rests on a χ that is independent of molecular weight, which was assumed and not measured, and two of the 20 plotted entropy curves do not follow from the stated inputs [vaneerdenbrugh2012a C33, X1]. For itraconazole–HPMC no χ, n or φ was given [purohit2015a E1]. In the extrusion work the theory neglects the temperature and composition dependence of \chi and treats the polymer as a chain on a lattice; for IDM–PVPVA a single \chi fits 50–90% DL but not 40% DL, where viscosity hindered the measurement [moseson2018 R4, C18, C17]. The printed SI equation of the four-component model lacks the operator joining the combinatorial and χ sums and leaves the chain length undefined, so it is not directly implementable li2020 X15. The ternary sorption model assumes that binary interactions carry over unchanged into the blend, which the authors consider "unlikely" [rumondor2010a C26, C27]. χ in the ternary free energy also holds non-ideal entropy, so a positive χ term need not be enthalpic rumondor2009c X14. In the three-polymer moisture study it is applied without parameter values, and the data do not separate the thermodynamic from the mobility reading rumondor2010c X13, X12.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

food effect

Evidence table: food effect. Content from the ASD dissolution chapter (delamanid 2023, praziquantel 2025), the Bioperformance chapter and the Mesoporous silica chapter.

The change of release or exposure when a dose is taken with food rather than fasting. In this chapter it enters through the media: fed gastric and intestinal fluids hold more bile salt, lecithin and lipid than fasted ones, raise the solubility of the drug, and prolong gastric residence at a higher pH [nguyen2023b R13, C19]. The two effects can pull in opposite directions. Where food raised the solubility of delamanid several hundredfold, the release of the marketed tablet rose with it, which the authors say the higher solubility "likely accounts" for [nguyen2023b R14, C29]; where it raised praziquantel solubility only modestly, the fed intestinal medium instead "promoted crystallization" that neither polymer could inhibit [alvarenga2025 C29]. Clinically, a standard meal raised the Cmax and AUC of the delamanid product 3.4- and 2.9-fold [nguyen2023b R24].

Findings

F28, F27.

Related concepts

acts through micellar solubilization and gastric pH variability; changes nucleation and crystallization inhibition by polymers; relevant to enteric polymer coats.

Formulas

none.

How it is measured or obtained

By measuring crystalline and amorphous solubility in fasted and fed simulated fluids and running the same release test in each, with a fed gastric stage (FEDGAS or acetate pH 4.5) before a fed intestinal medium [nguyen2023b P13, P12; alvarenga2025 P7, P8, P12]; crystals in the residues are then sought by polarized light and PXRD [alvarenga2025 P6, P5].

Values in the library
materialvalue or classconditionspaper ids
delamanid, crystalline0.52 (FaSSIF V1), 2.30 (FeSSIF V2), 13.10 (FEDGAS pH 4.5), 57.97 µg/mL (FEDGAS pH 3.0)37 °C[nguyen2023b R13]
Deltyba tablet≈77 µg/mL in FeSSIF V2 against ≈31–37 µg/mL in FaSSIF V1 at 120 min500 mL, 37 °C[nguyen2023b R14]
coated delamanid edisylate tablets≈96 µg/mL in both media; ≈86–87 µg/mL after 17 h in FEDGAS37 °C[nguyen2023b R16, R17]
praziquantel, amorphous and crystalline1.74 and 0.31 mg/mL (racemate) in FeSSIF-V2 against 1.17 and 0.16 mg/mL in PBS pH 6.537 °C[alvarenga2025 R1]
praziquantel dispersions, both polymers≈68–80% at 0.667 mg/mL and ≈34–52% at 1.5 mg/mL in FeSSIF-V22 h, 37 °C[alvarenga2025 R16, R18]
pretomanid–HPMCAS-HF dispersion; crystalline reference (Bioperformance)negative food effect in monkeys for the dispersion; positive for the reference (Cmax +23%, AUC +49%)single 30 mg dosenguyen2023a C53, C78
Pitfalls and disagreements

A higher solubility in a fed medium does not predict the direction of the effect for a dispersion: the pretomanid dispersion lost exposure with food while its crystalline reference gained nguyen2023a C53, C78, and praziquantel release fell in fed fluid although its solubility rose [alvarenga2025 R18, C8]. Delamanid dispersion release was the same in FaSSIF as in buffer although the amorphous solubility was ten times higher duong2022a R13. The delamanid solubility method is not described, and text and figure values differ for the marketed tablet [nguyen2023b X8, X2].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

Fox equation

1/T_g = w_1/T_{g,1} + w_2/T_{g,2} for the glass transition of a miscible blend [alhalaweh2016 E6].

Findings

F6.

Related concepts

used for drug-drug miscibility.

Formulas

Fox equation.

How it is measured or obtained

Compared with DSC Tg of melt-quenched mixtures [alhalaweh2016 P8, R9].

Values in the library
materialvalue or classconditionspaper ids
ritonavir–atazanavirmeasured Tg lie 3–8 K below the Fox line; line from about 365 K (w_RTV 0.2) to 323 Kmelt-quenched[alhalaweh2016 R9, X7]
TIPP with PVPVAFox gives 84 °C for neat TIPP90:10 ASDque2021 R1, E2
enzalutamideFox-estimated water-saturated Tg 352 K, so the amorphous drug is glassy at 37 °C[wilson2018 E8, C14]
Pitfalls and disagreements

The authors call the fit "well described" although the measured values deviate negatively by 3–8 K [alhalaweh2016 C10, X7].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

fragility

How steeply molecular mobility or viscosity changes as a liquid approaches Tg: strong liquids follow Arrhenius behaviour, fragile ones depart from it [baird2012 C37]. It is expressed by the fragility index m (strong below 40, fragile above 75) or by the VTF strength parameter D (strong above 30, fragile below 10) [baird2010 R30]. Good glass formers were expected to be strong liquids [baird2010 C3].

Findings

F5, F12.

Related concepts

measured by melt viscosity; depends on glass transition temperature; proposed predictor of glass-forming ability; related to reduced glass transition temperature.

Formulas

Vogel-Tammann-Fulcher equation.

How it is measured or obtained

m from the heating- and cooling-rate dependence of Tg (Moynihan) and D from m, or D from the VTF equation with T0 set to the Kauzmann temperature [baird2010 P10, E14, E15, E18]; D also by fitting the VTF equation to melt viscosity [baird2012 P5, E4].

Values in the library
materialvalue or classconditionspaper ids
tolazamidem 18DSC rate dependence[baird2010 R18.k]
itraconazolem 731DSC rate dependence[baird2010 R18.r]
nifedipinem 33, D 36 from m, D 9 from VTF with TKDSC[baird2010 R18.i]
28 compounds of classes I-B to IIID 4.3–8.7VTF fit of melt viscosity[baird2012 R12]
Pitfalls and disagreements

The category depends on the estimate used: aceclofenac, tolazamide and nifedipine are strong by m but fragile by the VTF-based D [baird2010 X14]. Fitted T0 values do not satisfy the paper's own T0–D–Tg relation [baird2012 X5]. Fragility did not separate good from poor glass formers [baird2012 C43], and invoking it for outliers in growth data is untested [trasi2014a X18].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

free drug concentration

The concentration of molecularly dissolved drug that can cross a membrane, as against drug in micelles, complexes, droplets or aggregates [raina2015c C30, C49; alhalaweh2016 C1]. In rat studies of enzalutamide the free drug is inferred from flux: the cellulose acetate suberate dispersion gave free drug like the crystalline form, matching their equal exposure (F24, F25) wilson2020 C10, C40. In micellar media the buffer solubility is taken as the free drug and the excess as micelle-associated [elkhabaz2019b C26, C31]. New aspect (Supersaturation from ASD dissolution): the free drug concentration, not the total, sets the supersaturation that drives crystallization and membrane transport (cited), and it stops at the amorphous solubility once a drug-rich phase forms jackson2015 C26, C31. Flux separated free from complexed resveratrol: more HPMCAS dispersion gave more total but less free drug, free resveratrol being at most about twice saturation [wegiel2015 C19, C41]; six tacrolimus products reached the free-drug maximum of the pure drug [trasi2016 C38].

Findings

Bioperformance: F3, F6, F7, F15, F18, F24, F25. Supersaturation from ASD dissolution: F7, F8, F11, F17.

Related concepts

equals thermodynamic activity in effect; lowered by micellar solubilization; related to additive cases for amorphous solubility, speciation, micelle-water partition coefficient; measured by membrane flux; capped by amorphous solubility.

Formulas

activity from concentration, supersaturation from membrane flux ratio, membrane flux in terms of solute activity, activity-based supersaturation ratio, ideal-mixing reduction of amorphous solubility.

How it is measured or obtained

Supernatant after ultracentrifugation [alhalaweh2016 P10]; flux against a reference [raina2015c E9]; fluorescence or filtration are less reliable above the amorphous solubility hate2018 X15. In the ASD dissolution papers: by flux across a membrane against a standard curve jackson2015 P4, by flux relative to the crystal alonzo2011 P4, by solution NMR alonzo2011 P7, and by ultracentrifugation [trasi2015b P9].

Values in the library
materialvalue or classconditionspaper ids
ritonavir, atazanavir (PVP ASD)4.3–4.75 × 10⁻⁵ M and 1.38–1.54 × 10⁻⁴ M alone; falls linearly with mole fractionpH 6.8[alhalaweh2016 R12]
atazanavir + SDSabout 65 µg/mL at the amorphous solubility whatever the SDS level37 °Cindulkar2017a R11, C19
ritonavir, lopinavir HPMCAS and PVP dispersionsRTV-PVP maximum about 22 µg/mL even after 2 hultracentrifuged[trasi2015b R12, R13]
resveratrol–HPMCASat most about twice saturation; enhancement from a soluble complex[wegiel2015 C41]
telaprevir + CA Subnot measured; flux 0.91 µg/min with the predissolved polymermosqueragiraldo2018b R13
enzalutamideabout 42 µg/mL molecularly dissolved of 70 µg/mL added; the rest colloidal amorphous aggregatespH 6.5 buffer[wilson2020 R2; wilson2018 R10]
posaconazole, atazanavirfree concentration at either solid phase taken as the buffer value in every mediumsix media, 37 °C[elkhabaz2019b C26, C27, C31]
danazol dispersions with a drug-rich phase7.1–9.1 µg/mL (amorphous solubility 8)flux, 25 °Cjackson2015 R9
danazol 50:50 HPMCAS (no drug-rich phase)5.4 ± 0.8 µg/mLflux, 25 °Cjackson2015 R9
ritonavir + lopinavir drug-rich phasesRTV 14.2–15.8, LPV 7.0–7.5 µg/mL for 5 hultracentrifuged[trasi2015b R16]
felodipine 90:10 and 50:50 HPMC dispersionsflux ratios 10.5 and 9.5 to the crystal37 °Calonzo2011 R14
resveratrol–HPMCAS 15:85, 6–35 mg/mLtotal ≈530 → ≈1610 µg/mL while flux ≈4.4 → ≈2.6 µg/min (crystal 2.0)pH 6.8, 37 °C[wegiel2015 R19, R20]
six tacrolimus products0.0048–0.0054 µg/min against a pure-drug plateau of ≈0.0050–0.0055pH 4.5, 37 °C[trasi2016 R15, R14]
Pitfalls and disagreements

Free drug was not measured in the donor in the hollow-fibre studies, so statements that it equals the amorphous solubility are assumptions hate2018 X11. Equating the buffer solubility with the free drug assumes that bile salts and lecithin do not mix into the drug phases, which the small fall of the posaconazole flux ratio questions (F18) [elkhabaz2019b C31, C44]. Ueda 2024 (p. 39) gives the general form: the buffer value equals the free drug only in Case I, and in Case III the free drug at the limit falls. In the ASD dissolution papers in situ UV and 0.45 µm filtrates count droplets or particles as dissolved [alonzo2011 C27; trasi2015b C22]. The danazol standard curve does not pass through zero, so flux cannot be converted to concentration by proportion jackson2015 X5. The inverse link of flux and concentration for resveratrol holds only up to about 18.8 mg/mL loading [wegiel2015 X9].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

gastric pH variability

Evidence table: gastric pH variability. Content from the ASD dissolution chapter (delamanid 2023, praziquantel 2024–2025) and the Release mechanism and LoC chapter.

The spread of stomach pH between and within patients, from about 1.6 fasted to 5 or above after a meal, and with age or acid-reducing drugs, which changes how much drug and polymer dissolve during the gastric stage of a dispersion and how long the dispersion sits wetted before the pH rises [nguyen2023c C5, C57]. In vitro tests are usually standardized at one gastric pH and so do not see it [nguyen2023c C5]. Food also prolongs gastric residence, cited as 15–60 min fasted and 2–5 h fed, with a gastric pH of 6–6.5 about 30 min after a meal [nguyen2023b R22, C19].

Findings

F25, F27, F24.

Related concepts

acts through pH-dependent polymer solubility and pH-dependent solubility of weak bases; risk of surface crystallization; mitigated by an enteric polymer coat; read with food effect.

Formulas

none.

How it is measured or obtained

By repeating a two-stage test with the gastric stage set at several pH values (pH 1.6, 3.0 and 5.0, or FaSSGF and a fed gastric medium) and the same intestinal stage, so that only the gastric pH changes [nguyen2023c P8; alvarenga2025 P10, P11, P12]; by soaking a coated tablet across the same range to find where the coat fails [nguyen2023b P6].

Values in the library
materialvalue or classconditionspaper ids
delamanid salt dispersions, five enteric gradesfinal release ≈101 / ≈41 / ≈82% (HPMCP-50), ≈94.5 / ≈80.5 / ≈12.5% (HPMCP-55), down to ≈18 / ≈1 / ≈0% (HPMCAS-HF)60 min at pH 1.6 / 3.0 / 5.0 → pH 6.5[nguyen2023c R11]
delamanid free base with HPMCP-50≈62.5 / ≈33.5 / ≈6.5 µg/mL of 100the same[nguyen2023c R7]
uncoated delamanid–HPMCP-50 tablets, three drug forms≈0.3–93 µg/mL after the shift against ≈82–96 µg/mL in a single stagethe same[nguyen2023b R2, R1]
coated delamanid tablets, three drug forms≈76–86 µg/mL after every gastric pH, a spread of about 4–8 µg/mL within a formthe same, transfer to fresh medium[nguyen2023b R10]
praziquantel–HPMCAS dispersions, 0.667 mg/mL≈92–103% after pH 1.6 or FaSSGF against ≈62–77% after pH 3.0 or 5.01 h gastric stage → pH 6.5[alvarenga2025 R7, R10, R13]
bedaquiline–HPMCAS 5/95 dispersions (Release mechanism and LoC)≈19.5–25 µg/mL of 100 at 120 min from all three gastric pH values60 min at pH 1.6 / 3.0 / 5.0 → pH 6.5kaur2025 R12
Pitfalls and disagreements

The worst gastric pH is not the lowest and differs by drug form: pH 3.0 for the delamanid edisylate tablet and pH 5.0 for the free base and the chloride [nguyen2023b X5]. A neutral drug is not exempt: praziquantel, neutral above about pH 3, still recovered less after pH 3.0 and 5.0 starts, which the paper does not explain [alvarenga2025 R4, R10]. The gastric supersaturation reached does not order the final release [nguyen2023c C39]. All of these tests used one 60-min gastric stage and simple media without food components [nguyen2023c X8].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

gel layer

The swollen, porous, polymer- and water-rich layer that forms at a hydrating ASD surface, below any drug-enriched outer layer, and from which the polymer disentangles into the medium. For 30% bicalutamide–PVPVA compacts it has the starting composition (F/F0 of drug 0.93 ± 0.06) moseson2022b R15; in ritonavir–PVPVA tablet edges it is the green (polymer- and water-rich) phase that carries drug-rich droplets and moves into solution as the polymer disentangles benson2025 R14, R16. (synthesis: release is polymer-controlled while the gel layer lasts and drug-controlled once the polymer has gone and drug-rich material is left; see polymer-controlled release.) New aspect (Release mechanism and LoC): the release-mechanism papers of 2020–2022 place the switch between polymer- and drug-controlled release inside this layer. A glassy polymer dissolves by solvent ingress, swelling, plasticization and gel-layer formation, chain disentanglement and diffusion of the free chains (cited); above its Tg the polymer forms a gel layer, while below it the layer thins and dissolution changes from disentanglement to cracking (cited) correasoto2022b C33; saboo2020 C54. For dispersions the polymer rate "is expected to depend" on the water absorbed to form the gel layer, which falls with drug loading, and on the Tg of the hydrated matrix against the test temperature saboo2020 C55. Saboo and co-workers (2021) propose a transient gel layer in which water plasticizes the chains before they disentangle, and in which the shape of the drug-rich phase formed by phase separation largely decides between drug- and polymer-controlled release at high loading saboo2021 C37. Hiew and Taylor (2022) argue that drug and polymer that separate in the gel layer should still both leave at the neat-polymer normalized rate as long as the separated drug cannot form a continuous barrier layer hiew2022b C46. For the enteric polymer HP-50 the gel is tied to ionization: less hydration at lower ionization at the dissolving surface, with the solvent fraction of the gel setting the disentanglement rate (cited); the pre-ionized salts are said to hydrate faster and more and so give a more mobile gel layer qi2022 C30, C42. The gel forms when water plasticizes the polymer chains into a rubbery state, which greatly lowers the Tg of the matrix (cited); ritonavir–PVPVA compacts of 10–40% all formed a gel layer with a sharp boundary to the glassy core yang2022a C23, C42. HPMCAS-MF formed a gel layer only above a buffer capacity of 13 mM/ΔpH, thickening with buffer capacity, and its gel had a lower apparent pH than the bulk bapat2023 C27, C28. A gel layer formed on every PVPVA compact of two phenolphthalein analogues, which suggests the dispersions may dissolve by a mechanism similar to that of neat polymers deac2023a C44. The 2024 PVP paper places droplet release at the gel–solution boundary, where the viscosity of overlapping and, above the entanglement weight, entangled chains falls enough for the polymer to leave deac2024a C32, C33, C34. The 2024 phase-diagram paper draws the gel layer as a region of the drug–polymer–water diagram between the glass–gel boundary (water content at which Tg = 37 °C) and the gel–solution boundary (from the measured average water and a linear gradient), and finds the MePHPH miscibility gap covering most of it deac2024b C36, E4, R28.

Findings

ASD process: F27, F38, F48. Release mechanism and LoC: F15, F20, F23, F24, F25, F29, F30, F31.

Related concepts

lies under the drug-rich surface layer; controls polymer-controlled release; ends at the limit of congruency; delayed by a coating defect density that is too low. The site of polymer chain disentanglement; formed by plasticization by water; the place where phase separation morphology decides the release regime; can turn into a drug-rich barrier layer.

Formulas

none.

How it is measured or obtained

SEM-EDX of cross-sections of compacts exposed face down (fluorine of the drug as F/F0) and confocal fluorescence with a drug-rich dye (Nile red) and a polymer- and water-rich dye (Alexa Fluor 488); confocal imaging of the hydrating edge of 100 mg tablets at 37 °C moseson2022b P14, P15, P16, P17; benson2025 P5, P13. In the release-mechanism papers: not characterized directly in these papers; inferred from release rates, from micro-CT of tablets after 10 min of dissolution and from films exposed to about 100% RH, whose contiguous drug-rich network "likely also forms" in the transient gel layer saboo2021 C39, R19, R21. Thickness of the gel in confocal cross-sections of surfactant-containing compacts after 5–20 min (ImageJ, unit not printed) yang2023 P9, R15, X8; position of the glass–gel and gel–solution boundaries on the ternary diagram deac2024b R26, R27.

Values in the library
materialvalue or classconditionspaper ids
30% BCL–PVPVA compact, 1 hporous gel layer F/F0 0.93 ± 0.06 under a 94 ± 8 µm drug-rich layerSEM-EDXmoseson2022b R15
same, confocalgel layer 440 ± 6 µm; compact swelled from 2092 ± 24 to 2696 ± 50 µm in 60 minNile red, Alexa Fluor 488moseson2022b R16, R17
50% BCL–PVPVA compactno gel layer distinguished; swelled from 1988 ± 11 to 2441 ± 12 µmsamemoseson2022b R17
uncoated ritonavir–PVPVA tablet edgesmall discrete red droplets throughout a green gel layer that moves into solutionconfocal, 37 °Cbenson2025 R14, R16
coated ritonavir–PVPVA tablet edgegreen and red networks along particle boundaries within 2 min; connected red regions remain outside the receding tablet at 4 minsamebenson2025 R14, R16
felodipine–PVPVA 30% with 0, 2% TPGS; 5, 10% TPGSporous surface layer with voids at the dissolution front; homogeneous sectionmicro-CT after 10 minsaboo2021 R19
PVPVAat least 11% water to start chain disentanglement at 37 °Cestimatedhiew2022b R21
ritonavir–PVPVA 10–40%gel layer with a sharp boundary to the glassy core at every loading; no grain boundaries in the gelconfocal cross-sections, pH 6.8yang2022a R7, C42
ritonavir–PVPVA 0–20%; 30%, 40%gel–glass front through ≈100% of the compact at 20 min; ≈29 and 17% with a plateaureal-time imagingyang2022a R8
neat HPMCAS-MF in pH 6.8 phosphate 5; 13; 51 mM/ΔpHno gel; 3 ± 1 µm; 19 ± 5 µmconfocal with prodan, 60 minbapat2023 R14
neat HPMCAS-MF gel, pH 6.8 phosphate 13–51 mM/ΔpHapparent pH 5.6–6.2gel scraped after the rotating-disk testbapat2023 R15
MePHPH–PVPVA 5–50%; PHPH–PVPVA 5–20%gel layer on every compact; 5% PHPH gel 356 ± 18 µmgravimetric and cross-sectional, steady statedeac2023a R4, C44, C31
ritonavir–PVPVA + Tween 80, 30%≈147.6 → 279.6 (5 → 20 min)confocal cross-sections, unit not printedyang2023 R15, X8
ritonavir–PVPVA + Span 20, 40%≈90.7 → 50.7 (5 → 20 min)sameyang2023 R15
neat PVPVA; 5% PHPH; 5 and 20% MePHPHgel–solution boundary from a linear water gradientternary diagram, 37 °Cdeac2024b R27, E4
Pitfalls and disagreements

Layer thicknesses come from compacts, whereas the authors say polymer loss is much faster from particles than from compacts moseson2022b C39, X20. Dye assignments and the polymer-depleted state of the crust are inferred moseson2022b X16. The confocal tablet images come from a different compaction and size than the release tablets, and the large red blobs of the uncoated row at 2–3 min are a mounting artefact benson2025 X5, R15, C29. That croscarmellose and starch glycolate raise the viscosity of the PVPVA gel is a speculation benson2025 C50. Hydrophilic surfactants "would reasonably be expected" to draw more water into the gel–water interface and so speed polymer dissolution, an argument without data correasoto2022b C42. Yang and co-workers read thickness as the balance of water penetration and disentanglement, but water ingress was not measured on the compacts yang2023 C26, C27. The gel-layer region of the 2024 diagrams rests on a fitted water Tg and on gel water contents cited from 2023 deac2024b X11, R40.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

Gibbs-Duhem equation

The relation between the changes of chemical potential of the components of a mixture; integrated with the measured water activity against composition from a sorption isotherm, it gives the activity of the drug in the water-saturated amorphous phase, the term e^{-I(a_2)} of the amorphous solubility estimate (the Murdande method) [almeidaesousa2015 E16, P7; ilevbare2013a P2]. In the solution-crystallization papers the factor lowers the Hoffman estimate of the amorphous solubility, and I(a2) is the sum of a Henry's-law term from zero water to the limit of linearity and a numerical integral \sum \langle (n_1/n_2)(1/a_1)\rangle\,\Delta a_1 over the sorption isotherm up to unit water activity [hsieh2012 E5, E6, P13; ilevbare2013c E6].

Findings

Amorphous solubility and LLPS: F5. Crystallization from solution: F2, F21.

Related concepts

yields the water sorption correction of amorphous solubility; input is water sorption; related to thermodynamic activity; corrects the Hoffman equation; used for the amorphous solubility advantage.

Formulas

Gibbs-Duhem equation, amorphous solubility advantage with water-sorption correction.

How it is measured or obtained

Numerical integration of moles of water per mole of drug against 1/a_1 over the sorption isotherm [hsieh2012 E5]. The papers of this chapter only name the method. The crystallization-from-solution papers measured the isotherm by dynamic vapour sorption of the amorphous solid at the test temperature (37 °C, 5–95% RH in 10% steps, three samples; 25 °C for danazol), with the water content extrapolated to water activity 1 [hsieh2012 P8, P13; jackson2014 P3, P4].

Values in the library

The resulting factors are listed under water sorption correction of amorphous solubility [ilevbare2013a M1; almeidaesousa2015 M6]. Values printed in the crystallization-from-solution papers:

materialvalue or classconditionspaper ids
danazol\exp[-I(a_2)] = 0.935DVS 5–95% RH, 25 °C[jackson2014 E1, R2]
five weak baseswater correction lowers the estimate for every base, for ketoconazole from 202 to 56.6 µg/mLDVS, 37 °C[hsieh2012 R10.d]
ritonavir, efavirenz, celecoxibI(a2) values not printed; theoretical amorphous solubilities 20.6, 19.8, 22.6 µg/mL37 °C[ilevbare2012b E8; ilevbare2013c E6, R2]
six dihydropyridinese^(−I(a2)) 0.74–0.91moisture sorption, TA Q5000[raina2015b M1–M6]
Pitfalls and disagreements

The expression is not printed in the 2015 and 2016 papers (named only) and the integral is not shown in any paper of 2013–2016 [almeidaesousa2015 E16; almeidaesousa2016 E4]. The sorption isotherms, the values of I(a2) and the preparation of the amorphous samples are not printed in the 2012 paper, so the estimates cannot be recomputed [hsieh2012 X14]. The amorphous solids for sorption (melt-quenched) and for dissolution (solvent-evaporated) differ in preparation [ilevbare2013c X17]. The sorption conditions and water contents are not printed [raina2015b P3].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

glass-forming ability

In the library, glass-forming ability (GFA) is the ease with which a melt vitrifies on cooling instead of crystallizing; a compound that crystallizes during a controlled DSC cooling (class I) has a low GFA [baird2010 C8; trasi2014a R14]. It is kept apart from glass stability, the resistance of the glass to crystallization on reheating or storage [baird2010 C4, C47; trasi2014a R14]. The definition above comes from the crystallization-tendency papers, where GFA is measured on neat drugs from the melt. New aspect (ASD process): in the thermogravimetry study of 2020, indomethacin, posaconazole and bicalutamide were chosen as class III molecules of high glass-forming ability so that degradation could be tested in both the crystalline and the amorphous state; the class comes from the cooling and reheating classification of the library [moseson2020 C5; baird2010 C8]. Class III glass formers can still nucleate when held for an hour between Tg and Tm.

Findings

Crystallization tendency: F3, F9, F10, F11, F12, F15, F17. ASD process: F31. Physical stability: F17, F24, F34. Supersaturation from ASD dissolution: F7, F23.

Related concepts

contrasts with glass stability; measured by crystallization tendency classification and critical cooling rate; depends on nucleation temperature zone; related to melt viscosity and reduced glass transition temperature; see crystallization tendency; related to crystallization inhibition by polymers and nucleation and crystal growth; related to physical stability.

Formulas

Barandiaran-Colmenero critical cooling rate, Cabral critical cooling rate, critical cooling rate to avoid nucleation, reduced glass transition temperature.

How it is measured or obtained

By whether the melt crystallizes on DSC cooling at 20 °C/min, with liquid-N2 quenching to separate class I-A (still crystallizes) from I-B (vitrifies) [baird2010 P1, P6, R3]; by slow cooling at 1 °C/min [baird2010 R7]; by the critical cooling rate from rapid heat–cool DSC [baird2013 R5, R9]; and, as a proxy, by the melt viscosity at Tm [baird2012 C31]. A drug's GFA is also reported from DSC cooling in later formulation papers trasi2020 R5; duong2022a R3. In the 2020 thermogravimetry study the class was cited, not measured; what was measured is nucleation of the neat undercooled melt during isothermal holds below Tm: posaconazole (130–160 °C, 1 h) and bicalutamide (130–180 °C, 1 h) melted on reheating, indomethacin (130–150 °C, 4 h) showed only a glass transition [moseson2020 P7, R7]. When the melt route is excluded by degradation, by attempting amorphization by spin coating, rotary evaporation and cryomilling [wegiel2013b P2, R1]. In the study of commercial tacrolimus capsules: DSC of crystalline tacrolimus monohydrate, with a first heating (broad endotherm between 60 and 120 °C, then melting of the anhydrate), cooling of the melt to an amorphous solid, and reheating through the glass transition without crystallization; the high Tg and the absence of recrystallization on reheating "suggest" good glass-forming ability and stability [trasi2016 R3, M1, C13].

Values in the library
materialvalue or classconditionspaper ids
51 drug-like molecules23 crystallize on cooling (low GFA)DSC, 20 °C/min[baird2010 R1]
23 class I molecules8 vitrify on liquid-N2 quench (I-B)melt plunged into liquid N2[baird2010 R3]
antipyrin, chlorpropamide, flufenamic acid, tolbutamideglass already at 25 °C/minrapid heat–cool DSC[baird2013 R5]
8 class I-A moleculescrystallize even at 800–1100 °C/minrapid heat–cool DSC[baird2013 R1, R3]
acetaminophenforms a glass even at slow coolingcited DSC data[trasi2012a R1]
nilutamidegood glass former; attributed to low nucleationDSC at 15 °C/min[trasi2014b R2, C9]
vemurafenib"relatively poor glass former", about 25 °C supercoolingDSC at 10 °C/min[lu2016 R1, C5]
tacrolimusgood GFA and stability; melting onset 121 °C, Tg onset 75 °C, no crystallization on reheatingDSC heat–cool–reheat[trasi2016 R3, C13, M1]
lumefantrine; artemetherclass 3 (Tg ≈18 °C, no crystallization on reheating); class 1 (crystallized on cooling from about 60 °C)DSC heat–cool–heattrasi2020 R5, R6, C7
acetaminophenglass because nucleation (50–60 °C) and growth barely overlapDSC cool–reheat, hot stage[trasi2012a C39, R12.a, R8.a]
resveratrolnot made amorphous by spin coating from four solvents, rotary evaporation or 6 h of cryomillingneat drug[wegiel2013b R1, C6]
curcuminamorphous by spin coating, not in larger amounts by rotary evaporation; cryomilling gave a larger amorphous massneat drug[wegiel2014 C9]
celecoxibeasily made amorphous by cooling the melthot stage[mosqueragiraldo2014 R15]
delamanidno glass at up to 50 °C/min; class I; a glass quenched in liquid nitrogen recrystallized just above its Tg of 43.3 °CDSC; liquid-N2 quenchduong2022a R3, C44
bicalutamidehigh GFA but rapid crystallization above Tgcitedmoseson2022b R26
posaconazole, indomethacin, bicalutamideclass III (high glass-forming ability)cited[moseson2020 C5]
posaconazole, bicalutamide neat meltsnucleated within 1 h between Tg and TmDSC holds[moseson2020 R7]
Pitfalls and disagreements

A high GFA says nothing about stability on reheating: class II and some class III drugs form glasses easily yet crystallize on reheating or grow fast once nucleated [baird2013 C24; trasi2014a C14]. The judgement depends on the cooling rate and on the unknown liquid-N2 quench rate [baird2010 C17, C21]. Standard predictors (Tg/Tm, glass-stability parameters, fragility) did not rank GFA of organic molecules [baird2010 C38; baird2012 C43]. The amount of polymer needed for a stable dispersion is expected to depend on GFA and glass stability [trasi2012a C4]. A high glass-forming ability also says nothing about stability of the glass on holding near Tm; the dispersion, not the neat glass, was used for isothermal degradation tests for that reason [moseson2020 C17, C55]. Easy glass formation said nothing about growth once nucleated: celecoxib forms a glass easily yet grows fast [mosqueragiraldo2014 R15, R16]. Good glass-forming ability of lumefantrine, read as making it "a good candidate" for a stable dispersion, did not keep its PVPVA dispersion amorphous beyond 1 week at 40 °C/75% RH trasi2020 C27, R3. The tacrolimus result rests on one cooling run, at 15 °C/min with reheating at 10 °C/min [trasi2016 P1]; the class is inferred from it, not measured by the cooling-rate criteria of the crystallization-tendency papers [trasi2016 C13]. Rotary evaporation was too slow to trap delamanid, a poor glass former, above about 10–15% drug, whereas spray drying gave an amorphous dispersion at 25% drug [duong2022a C45; nguyen2023c R5].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

glass-gel interface

Evidence table: glass-gel interface (names merged there: glass-gel boundary, glass-gel interface). Content from the release-mechanism chapter (2022–2025).

The boundary between the dry glassy core of a dissolving compact and the swollen, rubbery gel layer. Plasticization by water turns the glassy matrix into a rubbery gel with a sharp glass–gel interface (cited) yang2022a C41; solvent plasticizes the glass at this interface while entangled chains there diffuse slowly (cited) deac2023a C42. Its movement "indicates" how fast water penetrates the dispersion yang2022a C28. Below the limit water penetration of ritonavir–PVPVA was not slowed by the drug, and above it penetration became slower as loading rose yang2022a C29. In the 2024 PVP paper the glass–gel boundary appeared as a sharp colour change between dry dispersion and gel at the edge of dissolving compacts deac2024a C32; the 2024 phase-diagram paper places it at the water content at which Tg equals 37 °C deac2024b C36, R26.

Findings

Release mechanism and LoC: F25, F29, F30.

Related concepts

inner boundary of the gel layer; moves by plasticization by water; followed by polymer chain disentanglement at the outer gel surface; related to polymer chain entanglement and polymer swelling.

Formulas

none.

How it is measured or obtained

Time-lapse confocal imaging of a compact between slides, the boundary between the unchanged dry compact and the gel layer marked in each frame, and the depth reached given as % of the initial compact thickness yang2022a R8, R9; the onset of phase separation is given as a distance from this boundary deac2023a R8.

Values in the library
materialvalue or classconditionspaper ids
neat PVPVA; ritonavir–PVPVA 10, 20%same rate; about half the compact at 10 min, all of it at 20 minreal-time confocal, pH 6.8yang2022a R8
ritonavir–PVPVA 30; 40%≈29 and 17% at 20 min, then a plateausameyang2022a R8, C29
MePHPH–PVPVA 5–50%onset of phase separation closer to the glass/gel boundary as loading rosein situ confocaldeac2023a R6, R8
Pitfalls and disagreements

The penetration depth comes from a compact edge imaged between slides with the medium added by pipette, not from the rotating-disk release test yang2022a R9; deac2023a X10.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

glass–liquid phase separation

Phase separation of a supersaturated solution into a water-rich phase and a drug-rich phase that is a glass at the test temperature, because its water-plasticized Tg lies above that temperature; the term was judged "more appropriate" than LLPS for atazanavir (Tg of the precipitate about 51 °C at 37 °C) [indulkar2015 C38]. It is the title phenomenon for telaprevir (pellet Tg 52 °C) [mosqueragiraldo2015 C13, C21]. Griseofulvin and sorafenib were also treated as GLPS drugs [almeidaesousa2015 C40]. The papers of 2017–2022 add pazopanib: the colloids formed after a pH shift were called glass–liquid phase separation from a Tg of about 83 °C measured on the dried precipitate [sugihara2018 R17, C27, C28], and telaprevir with bile salts (GLPS onset 146–149 µg/mL in buffer) [lu2017b R2]. New aspect (Bioperformance): telaprevir with a dry Tg of 103 °C and a wet precipitate Tg of 52 °C mosqueragiraldo2018b M1, C8; enzalutamide, whose water-saturated amorphous Tg by Fox estimate lies above 37 °C, forms a glassy precipitate, and its colloidal aggregates are called products of GLPS [wilson2018 R4, C7, C14]. New aspect (Crystallization from solution): telaprevir above its amorphous solubility (about 90–100 µg/mL) separates into glassy drug-rich particles of 200–400 nm, which the authors think may provide interfaces for nucleation; in solutions that contain them the apparent concentration drops twice, the first drop being assigned to the aggregates [mosqueragiraldo2016 R1, R3, C7, C11; lu2017 R12].

Findings

Amorphous solubility and LLPS: F2, F7, F5, F4, F17, F23. Bioperformance: F1, F7, F23. Crystallization from solution: F25, F32, F37, F43.

Related concepts

special case of liquid-liquid phase separation; depends on plasticization by water and structural relaxation; contrasts with supercooled liquid; gives a drug-rich phase; related to heterogeneous nucleation (the glassy particles as possible nucleation interfaces).

Formulas

amorphous-crystalline free energy difference from heat capacity.

How it is measured or obtained

As LLPS (extinction, probe, NMR, flux), with the glassy state read from the Tg of the isolated phase, from storage at high humidity, or from the free-energy match (F2) [mosqueragiraldo2015 P4; indulkar2015 P16; almeidaesousa2015 P8]. The GLPS concentration of telaprevir is about 90–100 µg/mL mosqueragiraldo2018b M1, R1, R2. Cryo-SEM of a 150 µg/mL solution and the double fall of the 270 nm signal; zeta potential of droplets formed at 180 µg/mL [mosqueragiraldo2016 R2, R3; lu2017 R8].

Values in the library
materialvalue or classconditionspaper ids
telaprevir phaseTg 52 °C (dry 103 °C); redissolves in about 2 min on dilutionpH 6.8, 37 °C[mosqueragiraldo2015 R2, R8]
atazanavir phaseTg about 51 °C (dry 104 °C)water, 37 °C[indulkar2015 R22]
griseofulvin; sorafenibwet Tg 88 and 49 °C at 97% RH; onset matches the supercooled-liquid estimate25 °C[almeidaesousa2015 R9, R5, R6, R11]
pazopanib precipitateTg about 83 °C (dried); wet Tg not measuredpH 6.5, 37 °C[sugihara2018 R17, X5]
telaprevironset 146–149 (buffer), 311–360 (12 mM STDC, SGDC), 238–290 µg/mL (12 mM STCDC)50 mM pH 6.5, 37 °C[lu2017b R2]
telaprevironset 92 ± 2 µg/mL; precipitate Tg 52 °CpH 6.8, 37 °C[mosqueragiraldo2015 R4, C13]
telaprevir, bile salts149 / 146 µg/mL (pH 6.5, 50 mM); 104 / 102 µg/mL (pH 6.8, 100 mM)ultracentrifugation / UV[lu2017b R9]
enzalutamideonset about 42.5 µg/mL; amorphous precipitate glassy under cross-polarized lightpH 6.5, 37 °C[wilson2018 R2, R4]
telaprevir 150 µg/mL, no polymerconcentration about 162 → 100 µg/mL by about 12 min, then a steep fall at 15–25 minpH 6.8, 37 °C[mosqueragiraldo2016 R3]
telaprevir δ 28.8, 1.86 mM bile saltinduction time SGDC >960, STDC 550, STC 60, SGC 30 minpH 6.5, 37 °C[lu2017 R4]
telaprevir at δ 28.8 with 150 µg/mL HPMCAS-MFturbid in all media (glassy drug-rich phase)five media, 37 °C[lu2018 R8, C35]
enzalutamide above 42 µg/mLglassy droplets of about 100–200 nm; agglomeration without polymer "most likely"pH 6.5[wilson2021 R11, C29]
Pitfalls and disagreements

The glassy phase behaves like a liquid one in onset, probe uptake and redissolution; the phase was never isolated for griseofulvin and sorafenib, and "relaxed" is inferred [almeidaesousa2015 C37, C38; mosqueragiraldo2015 C30]. The state depends on temperature: loratadine droplets are glassy at 5 °C and liquid at 37 °C yang2021 C16. The glassy state of the pazopanib phase rests on a dry Tg; with a water uptake of about 4.6% the rule of about 10 °C per 1% would bring 83 °C close to 37 °C (synthesis) [sugihara2018 X5; ilevbare2013a E15; mosqueragiraldo2015 M1]. The onset of telaprevir depends on buffer strength and pH [lu2017b R9]. Neither HPMCAS dispersion of enzalutamide showed GLPS: the 10% one crystallized and the 50% one did not dissolve above the ceiling (F23) [wilson2018 C23]. For telaprevir the dihydroxy bile salts STCDC and SGCDC cap the activity at δ 21–24, so they could not be tested at δ 28.8 [lu2017 R1].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

glass stability

The resistance of a glass, or of the liquid formed when it is reheated above Tg, to crystallization; the authors of the 2010 classification call the term "somewhat of a misnomer" because it is usually judged by reheating rather than by the glass itself [baird2010 C4]. In the classification, glass stability means no crystallization on reheating [trasi2014a R14].

Findings

F9, F15, F16, F17.

Related concepts

contrasts with glass-forming ability; measured by glass-stability parameters and critical heating rate; depends on quenched-in nuclei; part of physical stability.

Formulas

critical cooling rate to avoid nucleation.

How it is measured or obtained

By DSC reheating after cooling (class II against III) [baird2010 R1]; by glass-stability parameters from crystallization onsets on reheating [baird2010 E5]; by critical heating rates [baird2013 R9]; by storage of glasses below Tg [baird2010 P7].

Values in the library
materialvalue or classconditionspaper ids
class IImuch lower glass stability than class IIIDSC reheating and storage[baird2010 C47]
class IIIhigh glass-forming ability and high stability on reheatingDSC[baird2010 C34]
indoprofen glassfully crystalline after 1 day30 °C, 0% RH[baird2010 R23]
class II glassesRcrit,heat 12.5 to above 1910 °C/minrapid heat–cool DSC[baird2013 R9]
acetaminophenquenched-in nuclei may matter for stability over longer timesargument[trasi2012a C41]
Pitfalls and disagreements

The storage evidence for a link between glass-forming ability and glass stability rests on one or two glasses per class [baird2010 X16]. Glass-stability parameters ranked class II molecules inconsistently [baird2010 X15].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

glass transition temperature

The temperature that separates the glass from the supercooled liquid [lu2016 C2]; it is a kinetic transition where the system falls out of equilibrium [trasi2014b C2]. Tg is called "probably" one of the most important properties of an amorphous solid, because storage temperature relative to Tg affects stability [towler2008 C20]. This draft is written from the crystallization-tendency chapter; the evidence table covers far more papers that later chapters will add. New aspect (PEG dispersions): the Tg of the drug relative to the solidification temperature as a possible determinant of whether an amorphous drug is excluded from the crystalline carrier. In polymer blends the additive's mobility, through the blend Tg, is one of three factors that decide exclusion [zhu2011 C2]. In the drug/PEG study a drug Tg above the 25 °C solidification temperature (nilutamide about 33 °C, ketoconazole 44 °C) did not change the pattern [zhu2011 C28, C31]. For water in PEO, Tg describes plasticization (water −136 °C, PEO about −67 °C) [marsac2008b M12, M7, C26].

Findings

Crystallization tendency: F4, F12, F20. PEG dispersions: F6, F11.

Related concepts

used in reduced glass transition temperature and Tm − Tg temperature gap; bounds the supercooled liquid; related to fragility, amorphous salt, plasticization and interlamellar incorporation.

Formulas

reduced glass transition temperature, Vogel-Tammann-Fulcher equation.

How it is measured or obtained

By DSC on reheating a melt-quenched or freeze-dried sample, as onset or midpoint [baird2010 P1; trasi2014b M1; towler2008 P6]; for fast crystallizers that give no Tg, estimated from a Tg/Tm ratio or a Trg–molecular-weight fit [vaneerdenbrugh2010a E7; baird2010 E27]. In the PEG papers the Tg values of the drugs were cited from the crystallization-tendency classification, or measured by DSC (acetaminophen) or estimated with a Tg/Tm ratio (naproxen) [zhu2011 M5, M6; marsac2008b M1, M3, E5].

Values in the library
materialvalue or classconditionspaper ids
propranolol base; hydrochloride−9.3; 35.9 °CDSC[towler2008 R4]
nicardipine base; hydrochloride3.2; 81.0 °CDSC[towler2008 R5]
nilutamide32 °C (onset)DSC[trasi2014b M1]
vemurafenib108 °CDSC at 10 °C/min[lu2016 M1]
felodipine; nifedipine; indomethacin45 °C eachDSC midpoint[baird2010 M37, M32, M40]
lumefantrineabout 18 °C; 19.7 °C (onset)DSCtrasi2020 R5; hiew2022a R3
five drugs with 10 mol% PVPraised by about 2–3 °CDSC[trasi2014a R7]
nilutamide; ketoconazoleabout 33 °C; 44 °Ccited[zhu2011 M5, M6]
benzocaine−31 °Ccited[zhu2012 M3]
acetaminophen; ketoprofen; naproxen; ibuprofen; felodipine; ketoconazole22.1; −3.0; 24 (estimated); −43.6; 43.1; 44.4 °CDSC and cited[marsac2008b M1, M2, M3, M4, M5, M6]
amorphous PEO; waterabout −67 °C (reported −67 to −55 °C); −136 °Ccited[marsac2008b M7, M12]
Pitfalls and disagreements

Whether a Tg is onset or midpoint is not always stated [towler2008 X7]; Tg of 16 class I molecules is an estimate [baird2010 X17]. Crystallization tendency cannot be predicted from relaxation times and Tg alone marsac2010 C29, and a high Tg did not prevent a propranolol salt from crystallizing [towler2008 R4.a, R12]. In the solvent screen the Tg contribution separates the classes partly because the storage criterion selects high-Tg compounds [vaneerdenbrugh2010a C41]. The Tg conclusion in the drug/PEG study rests on two drugs whose Tg lie 8 and 19 °C above 25 °C and that also differ in interaction and crystallization tendency [zhu2011 X13]. The Tg of haloperidol is given as below 25 °C in the card of Zhu and co-workers and as 33 °C (calculated from the molecular weight) in the classification paper [zhu2011 M1; baird2010 M17]. The naproxen Tg of 24 °C does not follow from the Tg/Tm rule it cites: the Table 1 melting point gives 26.7 °C [marsac2008b E5, X4]. (synthesis: papers also give different Tg for the same drug, nilutamide 32 °C (onset) against about 33 °C, and felodipine 45 °C (midpoint) against 43.1 °C [trasi2014b M1; zhu2011 M5; baird2010 M37; marsac2008b M5].)

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

Gordon-Taylor equation

The relation T_g=(w_1T_{g1}+Kw_2T_{g2})/(w_1+Kw_2) for the Tg of a miscible binary blend from the weight fractions and Tgs of its components, with K either from true densities and Tgs (Simha–Boyer form, K=\rho_1T_{g1}/\rho_2T_{g2}) or fitted [moseson2018 E3; li2019 E1; konno2006 E3]. In the ASD process chapter it gives the formulation Tg line of the phase diagram and, with K = 0.628 fitted to nanoTA softening temperatures, inverts a local Tg into a local drug content [moseson2018 R5; li2019 R13, R16]. Two later papers print it with the density-based constant: bicalutamide–PVPVA and posaconazole–HPMCAS [moseson2022c E6; shah2024 E2]. New aspects (Physical stability): a measured dispersion Tg below the Gordon–Taylor line was read as non-ideal mixing with weak hetero-interactions (felodipine with HPMCAS and HPMC) [konno2006 C16, C32]. New aspect (Release mechanism and LoC): Saboo and co-workers (2020) use the equation in reverse to follow the composition of a dissolving surface: the constant k = 0.91 was fitted by partial least squares to nanoTA Tgs of homogeneous indomethacin–PVPVA films (indomethacin 53 °C, PVPVA 130 °C), and the local Tg of a 25% film after immersion and drying was converted into its drug content saboo2020 R27, R28, E3. In 2024 dry MePHPH–PVPVA dispersions followed the Gordon–Taylor equation with K = 0.65, while PHPH–PVPVA had Tgs above both components and could not be described by it deac2024b E14, R32, R31.

Findings

ASD process: F7, F8, F15, F41. Physical stability: F5. Release mechanism and LoC: F7, F17, F30.

Related concepts

gives the Tg line of the temperature-composition phase diagram; used to read composition by nanoTA (see glass transition temperature, which it predicts for a blend); alternative to Couchman-Karasz equation. Reads surface drug enrichment from a local glass transition temperature.

Formulas

Gordon–Taylor equation.

How it is measured or obtained

Tg of the blend by modulated DSC against the predicted line [moseson2018 P3]; for nanoTA a calibration of miscible films from 0 to 100% DL fitted with K = 0.628, Tg1 = 367 K, Tg2 = 482 K and inverted to compute local LPV content li2019 P10, R13, E1. In the 2006 physical-stability papers, compared with DSC onset Tgs of rotary-evaporated dispersions at 0–100 wt% polymer [konno2006 P4, P5; marsac2006a R17]. In the release-mechanism papers: local Tg by AFM-nanoTA on films immersed for 5, 10 and 20 min and dried saboo2020 R28.

Values in the library
materialvalue or classconditionspaper ids
IDM–PVPVA 50/5072.2 ± 0.5 °C measured, 72.9 °C predicted (K = 0.932 with Tg in K)DSC[moseson2018 R5.f, E3]
LPV–HPMC E5 filmsK = 0.628; local Tg from about 209 °C (HPMC) to about 94 °C (LPV)nanoTAli2019 R13, E1
felodipine and nifedipine with PVPclose to Gordon–Taylor and Couchman–Karasz predictions ("relatively ideal")DSC, 0–100 wt%[marsac2006a R17, C21]
felodipine with HPMCAS and HPMC at 50 wt%Tg ≈50 and 49 °C against plotted lines ≈63 and 68 °CDSC 20 K/min[konno2006 R6.d, R7]
felodipine–PVP 50 wt%≈83 °C above its plotted line (≈70 °C)same[konno2006 R6.d, R7]
IND:PVPVA filmsnanoTA Tg and drug content by Gordon–Taylor10–90% DLsaboo2020 R27, E3
BCL–PVPVA 30%K = 0.987 (Tg in K, densities 1.35 and 1.18 g/mL); Tg 88.5 °C against about 89.6 °C read from the figureDSC[moseson2022c E6, R9]
PCZ–HPMCAS 50/50printed line about 81.5 °C; recomputed 89.1 °C with K = 0.852 (Tg in K) and 81.4 °C with K = 0.504 (Tg in °C)DSC[shah2024 E2, R6]
indomethacin–PVPVA 25% film at 0, 5, 10, 20 minlocal Tg 111, 95, 88, 82 °C; 23, 44, 52, 60 wt% drugnanoTA, immersed and driedsaboo2020 R28
MePHPH–PVPVA dry dispersionsK = 0.65DSC, midpointdeac2024b R32, E14
Pitfalls and disagreements

The unit of K matters: with Tg in °C the 50/50 IDM–PVPVA prediction would be 62.9 °C instead of 72.9 °C [moseson2018 E3]. A miscible 33% DL lopinavir film reads as about 40% LPV on the fitted curve, so local contents carry about ±10% DL uncertainty li2019 X17. In the posaconazole paper the printed line matches K computed from Tg in °C, whereas in the indomethacin paper it matches K computed from Tg in K; neither paper states the unit [shah2024 E2; moseson2018 E3]. The plotted lines of the 2006 felodipine paper reproduce only with Tg entered in °C in the density-based constant; in kelvin PVP too falls about 14 °C below its line [konno2006 X3]. HPMC deviates more than HPMCAS although HPMCAS bonds more weakly [konno2006 X10]. The nanoTA probe is about 50 nm deep and worked on films, while FTIR and EDX of the same chapter worked on tablets, so the surface drug content at 20 min is best quoted as about 60–72 wt% saboo2020 X15.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

halogen bonding

Evidence table: halogen bonding. Content from the release-mechanism chapter (2021–2025), with rows from the Miscibility and drug-polymer interactions chapter.

A non-covalent interaction between a halogen atom (Cl, Br, I) of a drug and an electron donor, in PVP and PVPVA the amide carbonyl oxygen of the vinylpyrrolidone unit (I···O=C) que2020 C1; que2021 C15. On combined XPS, NMR and IR evidence four model compounds with halogens and no hydrogen-bond donors are proposed to form such bonds in PVPVA dispersions que2020 C1. Que and co-workers (2021) find that the methyl ether of the iodinated phenol TIPP can form only halogen bonds with the VP carbonyl, and its smaller carbonyl shift "suggests" this halogen bond is weaker than the hydrogen bond formed by the phenolic group que2021 C7. Yang and co-workers (2021) note that their two low-Tg drugs lack hydrogen-bond donors but contain chlorine and can halogen-bond with polymer carbonyls (not measured) yang2021 C8. Of the four analogues TIPP forms hydrogen and halogen bonds and MeTIPP halogen bonds only; the halogen-bonded MeTIPP took about 9 wt% PVPVA into its drug-rich phase against about 36.5 for TIPP deac2023b C2, R3. The 2024 phase-diagram paper treats the halogen bonding of the iodinated analogues TIPP and MeTIPP as weak hydrogen bonding in PC-SAFT, with fitted association sites and energy deac2024b P19.

Findings

Release mechanism and LoC: F17, F27, F30.

Related concepts

the weaker alternative to drug-polymer hydrogen bonding in donor-free analogues; a kind of drug-polymer interactions; went with a higher limit of congruency than hydrogen bonding in the analogue pairs.

Formulas

molar amount of halogen at the lower XPS binding energy.

How it is measured or obtained

XPS of the halogen core level, where a second doublet at lower binding energy marks more electron-rich halogen atoms, and the shift of the VP carbonyl IR band que2021 R9, R7; que2020 R7, R11; the share of halogen atoms at the lower binding energy converted to a molar amount per 100 mg dispersion que2021 R11, R12, E4.

Values in the library
materialvalue or classconditionspaper ids
TIPP, Me-TIPP neat; in PVPVAI 3d5/2 620.7 eV; additional doublet at 618.1 eVXPS, compactsque2021 R9
Me-TIPP–PVPVA 10, 20, 30, 40%60.8, 53.3, 29.9, 22.2% of iodine at the lower binding energyXPSque2021 R11
TIPP–PVPVA 10, 20, 30, 40%55.9, 26.5, 15.6, 8.9%XPSque2021 R11
TIPP; Me-TIPP in PVPVA, 10–40%≈0.017–0.027; ≈0.029–0.050 mmol lower-binding-energy iodine per 100 mgderivedque2021 R12
Me-TIPP–PVPVAVP carbonyl shift at most 7 cm⁻¹IR, filmsque2021 R7
clotrimazole, brotrimazole; Me-DIBF in PVPVA (Miscibility chapter)VP carbonyl 1684 → 1682 cm⁻¹ from 10 to 90%; 6 cm⁻¹ downshiftIR, filmsque2020 R11
Pitfalls and disagreements

Bond energies or association constants were not measured; the weaker strength is read from the size of the IR shift que2021 C7. The XPS share of Me-TIPP is cited from the authors' earlier study que2021 R11.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

Henderson-Hasselbalch equation

The relation between pH, pKa and the ratio of un-ionized to ionized drug, \mathrm{pH} = \mathrm{p}K_a + \log_{10}([\mathrm{B}]/[\mathrm{BH}^+]) for a weak base [indulkar2015 E1]. It is used in this chapter in three ways: to split a measured total concentration into its un-ionized part, C_U = \frac{X}{1+X}C_T with X = 10^{\mathrm{pH}-\mathrm{p}K_a} [indulkar2015 E6]; to predict the total solubility at any pH from the free-base solubility [indulkar2015 E8]; and to express concentrations at pH 4.6, equal to the pKa, as un-ionized drug [almeidaesousa2016 E3, C13]. The pH-shift titration uses modified forms before and after precipitation [indulkar2015 E4, E5]. The papers of 2017–2022 add the total-solubility form C_T = \frac{1+X}{X}C_U with X = 10^{\mathrm{pH}-\mathrm{p}K_a}, used for pazopanib with the pH 8.4 solubility as C_U and pKa 6.4 [sugihara2018 E1, C9].

Findings

F10, F14, F23.

Related concepts

quantifies ionization; uses pKa; gives pH-dependent solubility.

Formulas

Henderson-Hasselbalch equation, pH-solubility profile.

How it is measured or obtained

Calculated from the measured pH and the pKa [indulkar2015 E6].

Values in the library

Clotrimazole at pH 6 with total crystalline solubility 1.08 µg/mL and pKa 5.89 gives an un-ionized 0.61 µg/mL (recomputed); atazanavir at pH 1.5, free-base solubility 1.04 µg/mL, pKa 4.52, gives 1090 µg/mL against 1.1 mg/mL printed [indulkar2015 E6, E8].

Pitfalls and disagreements

The printed percentage ionized of nicardipine at pH 9 (0.9%) differs from the recomputed value (1.6%) [indulkar2015 X4]. Eqs. 4 and 5 print the denominator in a way that subtracts a concentration from 1 [indulkar2015 X18].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

heterogeneous nucleation

Nucleation at an interface (a foreign particle, a container wall, a second phase), which lowers the nucleation barrier, so nucleation there proceeds more readily [wilson2021 C44]. New aspect (PEG dispersions): a crystalline carrier as the nucleating surface. Zhu and co-workers conclude that crystalline PEG acts as a favourable heterogeneous nucleation site for the slowly crystallizing ibuprofen and fenofibrate, which explains why the drugs began to crystallize in the dispersion (after about 100 and 120–180 min) earlier than most neat samples, despite a smaller thermodynamic driving force ("it appears") [zhu2012 C4, C34, R23.a]. New aspect (Crystallization from solution): In solution, impurities in large volumes at high supersaturation may induce heterogeneous nucleation, which the authors give as a reason for the small scatter (below 15%) of induction times ("it is reasonable to expect") [ilevbare2013c R17, C16]. For danazol the interface of the drug-rich droplets is a candidate site: crystals could form from the drug-rich or the drug-lean phase, the change to a two-phase solution can alter nucleation, and polymer at the droplet–water interface is "likely" to disrupt nucleation there [jackson2014 C45, C53]. Micelles of dihydroxy bile salts "may" offer interfaces for heterogeneous nucleation, and the surfaces of drug-rich telaprevir particles are expected to enable it; adsorbed bile salt is expected to modify it [lu2017 C34, C36, C39]. New aspect (Supersaturation from ASD dissolution): the ASD dissolution papers invoke it three times: polymer adsorbed on parent γ nifedipine crystals could reduce heterogeneous nucleation of α on them, and many small solution-grown crystals offer more surface for it [raina2014b C31, C36]; the interfaces of a drug-rich phase "may" act as heterogeneous nucleation sites [trasi2015b C31]; surfactants promoted ritonavir crystallization only when the ritonavir–water interface of droplets was present [ilevbare2013d C43].

Findings

Crystallization tendency: F10, F17. PEG dispersions: F9. Crystallization from solution: F14, F15, F25, F32, F34, F37, F38. Supersaturation from ASD dissolution: F3, F11, F13.

Related concepts

part of nucleation; contrasts with classical nucleation theory (homogeneous form); related to surface crystallization, stochastic nucleation, nucleation induction time and semicrystalline solid dispersion; related to secondary nucleation and polymer adsorption to drug-rich droplets; related to drug-rich nanodroplets and surfactant-induced crystallization.

Formulas

classical nucleation theory.

How it is measured or obtained

Rarely measured directly; inferred from scatter of crystallization temperatures in DSC pans [baird2010 C19], from crystals forming at a seeded interface [zhu2012 R15, R19], from the effect of shear in a rheometer [baird2012 C8] or from the change of slope of induction time against supersaturation [duong2022b C28]. In the seeding test a small piece of crystalline PEG is placed in the supercooled neat drug at 25 °C and observed by polarized light microscopy for where the first crystals form; crystals formed at the PEG edge within minutes and none in the bulk [zhu2012 P7, R15, R19]. In the crystallization-from-solution papers it is not measured; the site of nucleation (droplet, interface or bulk) was not determined [jackson2014 X15]. Seeds added on purpose test the related seeded growth (F5, F20) [alonzo2012 P4]. In the ASD dissolution papers it is not measured either, but argued from conversion kinetics and induction times [raina2014b C32; ilevbare2013d R16].

Values in the library
materialvalue or classconditionspaper ids
ibuprofen; fenofibratecrystals form at a crystalline PEG interface within minutes, none in the bulk25 °C[zhu2012 R15, R19, C4]
neat ibuprofen; fenofibrate0.20 and 0.34 of 50 samples crystallized after 3 weeks25 °C, no carrier[zhu2012 R2, R3]
ibuprofen; fenofibrate in 20/80 PEG 3350onset about 100 min; 120–180 min25 °C[zhu2012 R23.a]
class I-A meltscrystallization temperatures higher in the rheometer than in DSC, ascribed to the upper plateshear 30 s⁻¹[baird2012 R5, C8]
class I moleculesscatter of crystallization temperatures ascribed to stochastic and heterogeneous nucleationDSC pans[baird2010 C19; baird2013 C18]
felodipine filmsnucleation "most likely heterogeneous"spin-coated films[konno2006 C33]
posaconazolehomogeneous at high supersaturation, heterogeneous at low; shallow slope of log t against 1/log²S below S about 12 read as heterogeneous ("has been attributed")PBS pH 6.5, 37 °C[duong2022b R10, C28]
enzalutamide with drug-rich dropletsdroplets enhance crystallization; droplet/water interface "likely" a favourable site; induction times fall on crossing 42 µg/mLpH 6.5, 2.5–100 µg/mL polymer[wilson2021 C45, C46, R3]
bicalutamidefractures of mechanically activated samples favour heterogeneous nucleationdispersionsmoseson2022b C45
induction-time replicates, 50–80 mL, S 2.4–15.4scatter below 15%triplicate[ilevbare2013c R17]
danazol, HPMC-ASinduction time 516 → 277 min as drug concentration rises from 10 to 20 µg/mL25 °C[jackson2014 R17]
telaprevir δ 28.8, buffercrystallizes immediately with a drug-rich phase presentpH 6.5, 37 °C[lu2017 R4]
atazanavir ASD particlesdissolving ASD did not seed nucleation (about 300 against 350 min)PVPVA + SDS, pH 6.8[indulkar2019b R5, C25]
ritonavir with SDS; Tween 80, below and above LLPSabout 262 against 34.7 min; about 289 against 23.6 min37 °C[ilevbare2013d R16, R12]
nifedipine dispersions against glassγ → α complete in ≈5–40 min against ≈40–145 min with dissolved polymer25 °C[raina2014b R12, R10]
Pitfalls and disagreements

Heterogeneous nucleation by a carrier breaks the link between the crystallization of the pure drug and of the drug in the dispersion [zhu2012 C41]. Homogeneous classical theory is applied to systems that are most likely heterogeneous [konno2006 C33; marsac2006a C32]. The PEG seeding was done in pure supercooled drug, not in the dispersion, and enrichment of the drug in the remaining non-crystalline fraction after PEG crystallizes is an alternative that the experiments cannot separate [zhu2012 X13]. Whether other slowly crystallizing drugs (nilutamide, ketoconazole) are nucleated by crystalline PEG was not tested; in the same PEG at the same ratio neither was fully crystalline at 24 h [zhu2011 R18.e, R18.f]. Nucleation by polymers in solution has been reported, outside the library, and most reports of drugs in polymers find retardation of crystallization [zhu2012 C35, C36]. The attribution to nucleation at the droplet interface is an inference; solutions at 10 µg/mL with HPMC or HPMC-AS are already above their measured onsets [jackson2014 X3, X15]. Impurity-induced nucleation was expected, not tested [ilevbare2013c C16]. Neither micelles as nucleation sites nor the nucleation site in the two-phase solutions were observed [lu2017 C34, C40]. Neither the enzalutamide nor the posaconazole paper located the nucleation site; the homogeneous–heterogeneous assignment rests on a slope change [wilson2021 C45; duong2022b X11]. None of the three proposals of the ASD dissolution papers was tested directly [raina2014b C36; trasi2015b C31; ilevbare2013d C43].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

hierarchical particle approach

Evidence table: hierarchical particle approach (names merged there: hierarchical particle, hierarchical particle approach). Content from the release-mechanism chapter (2023–2025).

A core amorphous dispersion particle with an additional water-soluble component coating its surface. For co-precipitated amorphous dispersions (cPAD) it was made by pre-dissolving a secondary polymer in the anti-solvent, which deposits on the particle surfaces during isolation and drying hiew2023 C7. Diluting the surface drug in this way shifts the release of a high-loading dispersion toward that of a lower loading hiew2023 C57. Earlier, incorporating co-precipitated particles into a water-soluble HPMC matrix had managed poor wettability at loadings similar to spray-dried dispersions, leaving open whether it could remedy the slowdown at high loading (cited) hiew2023 C5. The 2025 study screened seven secondary excipients in the anti-solvent on 75% grazoprevir–HPMCAS particles and applied HPMC or SDS by high shear to a solvent-evaporated dispersion; only excipients that made the surface wettable helped, and HPMC had to be dissolved, not dispersed, in the anti-solvent hiew2025 P6, P7, C27, C40. The authors call the approach "promising" for high loading hiew2025 C11.

Findings

Release mechanism and LoC: F14, F28, F35.

Related concepts

lowers surface drug enrichment; improves wettability; allows a higher drug loading; acts on particles with a large specific surface area; tested for oral bioavailability.

Formulas

none.

How it is measured or obtained

Co-precipitation of grazoprevir–HPMCAS with HPMC or HPC dissolved or suspended in the anti-solvent, isolation by filtration or rotary evaporation; surface drug by XPS; two-stage dissolution (SGF then FaSSIF); exposure in dogs hiew2023 R10, R11, R12, R14, P14, R15.

Values in the library
materialvalue or classconditionspaper ids
binary grazoprevir–HPMCAS cPADs, 60; 75%≈37.5; 17% (acidified water), 8% (MTBE) released at 90 mintwo-stage dissolutionhiew2023 R10, R14
hierarchical cPADs, HPMC or HPC dissolved in the anti-solvent≈56–72%samehiew2023 R10, R12
washed binary cPAD; HPMC suspended in MTBE≈47%; ≈8–15%samehiew2023 R10, R11
eight materialssurface drug ≤34% with ≈47–72% release; ≥53% with ≈8–17%XPShiew2023 R14
hierarchical against binary cPAD, ≈73% drugAUC 135 against 73 µM·hdogs, n = 6hiew2023 R15
grazoprevir–HPMCAS 75:25 with 5 mg/mL SDS, TPGS, PEG, HPMC, PVP, gelatin, poloxamer 407≈37 / 31 / 31 / 23 / 21 / 14 / 13% at 90 mintwo-stage SGF → FaSSIFhiew2025 R9
same with 10 mg/mL HPMC≈47–52%samehiew2025 R9
Pitfalls and disagreements

The best hierarchical particle is called a 60% material in the discussion but assays 73.4% drug with about 1.6 wt% HPMC retained hiew2023 X1. Wetting was judged by eye only hiew2023 X12. A recomputation from the plasma profile gives AUCs about 1.3-fold lower than the table, possibly a unit issue; the table values are used hiew2023 X4.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

Higuchi two-component dissolution model

Evidence table: Higuchi two-component dissolution model. Content from the release-mechanism chapter (2019–2020), with a comparison row from the ASD dissolution chapter.

The diffusion-controlled model of Higuchi and co-workers (cited) for a non-interacting, non-disintegrating mixture of two components: the composition of the dissolving interface stays constant only at one critical mixture ratio; at any other ratio the surface enriches in one component, which then controls dissolution, and for components of very different solubility the drug fraction that gives polymer control is very low indulkar2019a C23; saboo2020a C35. Corrigan (cited) noted that such models "appear to" describe high-loading dispersions controlled by a drug-rich surface layer but not low-loading ones, where drug and polymer are released together over a range of compositions indulkar2019a C24.

Findings

Release mechanism and LoC: F2.

Related concepts

contradicted by congruent release at low loading; predicts a drug-rich surface layer at high loading; related to polymer-controlled release.

Formulas

Higuchi-Corrigan critical mixture ratio.

How it is measured or obtained

Applied by calculation: for felodipine–PVPVA with an amorphous solubility of 8 µg/mL, a PVPVA solubility of 46 mg/mL and a diffusion-coefficient ratio of 10, the critical ratio is about 1.7 × 10⁻³ (printed 1.7 × 10⁻⁶) saboo2020a R27, X1.

Values in the library
materialvalue or classconditionspaper ids
felodipine–PVPVAcritical drug:polymer ratio ≈1.7 × 10⁻³, far below the 5–50% testedcalculatedsaboo2020a R27, C36
ritonavir–PVPVAcongruent at 10–25%, contrary to the single-ratio predictiontabletsindulkar2019a C24, C25
celecoxib (ASD dissolution chapter)Corrigan's condition as the basis of polymer control at low and drug control at high loadingcitedxie2016a E2, C4
Pitfalls and disagreements

The model "may adequately describe" high-loading dispersions but fails for congruent release at 10–15% loading saboo2020a C37; judging release by the drug:polymer ratio alone is "clearly an over simplification", since the PVPVA limit varies with the drug and HPMCAS and EUDS stay congruent to 50% saboo2020a C38.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

Hoffman equation

An approximation for the free-energy difference between the supercooled liquid and the crystal at a temperature T below Tm, needing only Tm and the heat of fusion [vaneerdenbrugh2010a E2; lu2016 E1]. It assumes that the enthalpies of crystal and supercooled liquid vary linearly with temperature, that is a constant heat-capacity difference, and applies above Tg [marsac2006b C37; ilevbare2013a C58]. In this chapter it supplies the crystallization driving force; most other library papers use it to estimate the amorphous solubility advantage. New aspect (solution methods): in the solution-methods papers the Hoffman equation supplies the free-energy advantage of the amorphous form in the amorphous solubility estimate, printed with a positive sign and \Delta T = T_m - T: \Delta G = \frac{\Delta H_f\,\Delta T}{T_m}\cdot\frac{T}{T_m} [raina2015a E2]. New aspect (C. Amorphous solubility and LLPS): those papers print it as the free-energy term of Eq. 1, \Delta G = \Delta H_f\,(T_m - T)\,T/T_m^{2}, and list its assumptions: a constant, temperature-independent ΔCp, small undercooling and Tg close to T∞; it also does not address the crystal-to-glass conversion [ilevbare2013a E2, C58; almeidaesousa2015 E2, C8; mosqueragiraldo2015 E2; almeidaesousa2016 E2]. For atazanavir Eq. 2 is printed with DSC Tm 208 °C and ΔHf 90.1 J/g, and the paper's own ratio of 62 follows from them when 0.22 is read as exp[−I(a)], although Table I heads that column I(a) (synthesis) [indulkar2017a E2, E3, X1; indulkar2015 M2]. New aspect (Bioperformance): the equation estimates the amorphous-to-crystalline solubility ratio \sigma_a/\sigma_c = e^{\Delta G/RT} and is combined with a water-sorption correction [raina2014a E3, E5; raina2015c E1, E2]. New aspect (Crystallization from solution): in the solution-crystallization papers \exp(\Delta G_c/RT) is the activity ratio taken as the solubility ratio before a water-sorption correction, evaluated at 25 or 37 °C, and the ratio times the measured crystalline solubility is compared with plateaus after pH shifts and with onsets of phase separation (F2) [hsieh2012 E3, E4, R10; hsieh2014 E2, E3; jackson2014 E2, R5]. New aspect (Supersaturation from ASD dissolution): the ASD dissolution papers use it to estimate the amorphous solubility advantage of felodipine and indomethacin; the felodipine inputs of 2008 come from earlier work, which found the equation estimated felodipine's free-energy difference well (cited) [konno2008a E2, R20].

Findings

Crystallization tendency: F6, F7, F13. Solution methods: F5. C. Amorphous solubility and LLPS: F5, F7. Bioperformance: F1, F23. Crystallization from solution: F2, F16, F21. Supersaturation from ASD dissolution: F5, F7.

Related concepts

measures thermodynamic driving force for crystallization; depends on enthalpy of fusion and degree of supercooling; related to entropy of fusion, amorphous-crystalline free energy difference and amorphous solubility; compared with the heat-capacity route in amorphous-crystalline free energy difference; accuracy set by degree of supercooling. Related to amorphous solubility advantage; corrected by the Gibbs-Duhem equation route.

Formulas

Hoffman equation, amorphous solubility advantage from free energy difference.

How it is measured or obtained

Calculated from DSC Tm and ΔHfus at the temperature of interest, per mole, per gram or, with the crystal density, per volume [baird2010 E25; vaneerdenbrugh2010a P11]. Its agreement with MDSC-based free energies was checked for felodipine and nifedipine [marsac2006a C14]. In solution work it enters \exp\left(\frac{\Delta G}{RT}\right) as the amorphous-to-crystalline solubility ratio [alonzo2010 R3; duong2022a R27]. ΔHf and Tm were measured by DSC at 10 °C/min in pinhole aluminum pans; the values are not printed [raina2015a P4, E2]. With a heat-capacity term it becomes \frac{\Delta G_{a\to c}}{RT} = \frac{\Delta H_f}{RT}\left(1 - \frac{T}{T_m}\right) + \frac{1}{RT}\int_{T_m}^{T}\Delta C_p\,dT - \frac{1}{R}\int_{T_m}^{T}\frac{\Delta C_p}{T}\,dT [mosqueragiraldo2015 E3]. In the amorphous solubility papers ΔHf and Tm are DSC values at 10 °C/min (5 °C/min in one paper), evaluated at 25 or 37 °C [almeidaesousa2015 P5; indulkar2015 P6, P5; almeidaesousa2016 P9]. In the Bioperformance papers ΔHf and Tm come from DSC melting onset and enthalpy, and the water sorption from gravimetric moisture sorption [raina2014a P3, P4]. The DSC method is not given in the 2014 pH-shift paper and the heats of fusion are not printed in the 2012 paper [hsieh2012 P13, X14; hsieh2014 X11]. In the ASD dissolution papers: from the DSC enthalpy of fusion and melting temperature (felodipine 30.12 kJ/mol, 143.41 °C; indomethacin 32.48 kJ/mol, 153.4 °C) and the crystalline solubility [alonzo2010 P10, P12, M1, M2]; inputs not printed in the 2008 and 2011 papers [konno2008a E2; alonzo2011 E3].

Values in the library
materialvalue or classconditionspaper ids
felodipine; nifedipine6.2 and 8.8 kJ/mol25 °C[marsac2006a E3, R4]
34 drugsΔGv −8.6 (lidocaine) to −54.7 J/cm³ (acetaminophen)298 K[baird2012 M5, M12]
vemurafenib α against βα lower in free energy up to a virtual transition at 319 °CTm and ΔHm of both forms[lu2016 R22, E1]
felodipineestimated amorphous solubility about 9 µg/mL37 °C[alonzo2010 R3]
delamanidsolubility ratio 31.8 calculated against 42.3 measured37 °Cduong2022a R27
ritonavir, efavirenz, celecoxib≈10.2, ≈2.70, ≈7.74 kJ/mol (extractor calculation)37 °C[ilevbare2013c E7]
six dihydropyridinesused for the yardstick of F5; no ΔG value printed25 and 37 °C[raina2015a E2, R11]
diverse drugsCp method closer to the measured LLPS onsets than the Hoffman equation25 °C[almeidaesousa2015 R11, C43]
ritonavir10.1 kJ/mol (extractor recomputation from Table 2 inputs)37 °Cilevbare2013a E2
ibuprofen to griseofulvin3.24, 4.84, 5.69, 8.51, 10.33, 9.69 kJ/mol25 °C[almeidaesousa2015 R11]
telaprevir13.31 kJ/mol (recomputed); amorphous solubility 245 ± 5 µg/mL, 2.7 times the onset37 °C[mosqueragiraldo2015 E1, R13, R17]
clotrimazole6.26 kJ/mol with a molar mass not printed in the paper (extractor)310 K[indulkar2015 E3]
CRH15.68 kJ/mol; estimate 11.2 µg/mL at pH 4.625 °C[almeidaesousa2016 M1, R2]
atazanavir14.55 kJ/mol (recomputed from Table I); ratio about 62, as printed, with 0.22 read as exp[−I(a)]; about 228 read as I(a)310 K[indulkar2017a E2, X1; indulkar2015 M2]
felodipineHoffman ratio 10.92 (25 °C), 8.64 (37 °C); water factor 0.74, 0.83Tm 147 °C, ΔHf 28.67 kJ/mol[raina2014a R7]
nifedipineprinted ratio 8.78; recomputed 14.45Tm 173 °C, ΔHf 32.5 kJ/mol[raina2014a R7, X3]
atazanavirratio 62, predicted 68 µg/mL310 Kindulkar2017a R5
indomethacin17–25 µg/mL (25 °C), about 37 µg/mL (37 °C)Hoffman estimate[alonzo2010 R8]
enzalutamideprinted estimate about 39 µg/mL (13-fold); the printed inputs give 27.737 °C, Tm 470 K[wilson2018 E1, R3, X1]
ritonavirΔHf 60.4 kJ/mol, Tm 121 °C, 37 °C: ΔG = 10.1 kJ/mol and exp(ΔG/RT) = 50.8 (extractor calculation); calculated amorphous solubility 20.6 µg/mL with the water term37 °C[ilevbare2012b E8, E9, R1]
glyburide; warfarinabout 60-fold and 48-fold (59.9 and 47.7 recomputed) from Tm 175.6 °C, ΔHf 45.5 kJ/mol and Tm 169.2 °C, 43.6 kJ/mol25 °C (assumed)[hsieh2014 R16, E3, M3, M4]
danazolTm 225.4 °C, ΔHf 28.9 kJ/mol: ΔG = 6.95 kJ/mol; ratio with the 0.935 water factor 15.4 recomputed against 19.6 printed25 °C[jackson2014 E1, E2, X1]
five weak basesratios 22.2, 11.9, 20.4, 54.6, 7.0 without water correction (carvedilol, clotrimazole, clozapine, ketoconazole, loratadine)37 °C[hsieh2012 R10]
felodipine (six-dihydropyridine study)e^(ΔG/RT) recomputed 10.84 at 298.15 K from 74.6 J/g and 147 °CDSC data of the paper[raina2015b E1, R1.b]
posaconazoleTm 169.1 °C, ΔHf 76.95 J/g; printed amorphous/crystalline ratio 37.9 with water factor 0.33, estimate 10.22 against 9.08 µg/mL measured310 K; the extractor obtains ΔG = 16.13 J/g and a ratio of about 26.5[duong2022b R7, E3, X2]
felodipineratio about 10; about 9.5 µg/mL37 °C[konno2008a R17]
felodipineΔG 5729 J/mol, ratio 9.22 (recomputed) against "around 9"37 °C[alonzo2010 E1]
felodipineabout 9.1 µg/mL (37 °C); 5–6 µg/mL (25 °C)pH 6.8alonzo2011 M1
Pitfalls and disagreements

The approximation "can lack accuracy": it assumes a constant ΔCp and small undercooling [almeidaesousa2015 C8, C34], and was judged inappropriate for telaprevir, far below its melting point [mosqueragiraldo2015 C24]. It ignores ionization and water sorption [raina2014a C10]. Printed values are sometimes not reproducible from the printed inputs [baird2012 X2; raina2014a X3]. Sign conventions differ: some papers plot crystal minus liquid [lu2016 X17] or print a leading minus sign duong2022a E2. In the solution-methods papers the Hoffman-based estimate was above the measured danazol onset (16 against 13 µg/mL) and cannot follow polymer effects [jackson2014 R5]. In the amorphous solubility papers, for telaprevir (Tm 238 °C, 37 °C test) the authors judge it inappropriate for large undercooling [mosqueragiraldo2015 C24, M1]. In the 2013 paper four of eight predictions cannot be reproduced from the printed Table 2 inputs ilevbare2013a X1. Eq. 2 of the weak-base paper is printed with a sign that does not give its stated ratios [indulkar2015 X1]. Eq. 3 of the atazanavir paper is printed with an inverted sign indulkar2017a X1. The nifedipine ratio of raina2014a does not follow from the printed inputs [raina2014a X3]. The enzalutamide estimate cannot be reproduced from its printed inputs, and the stated S of "approximately 13" matches the estimate rather than the measured 42/2.9 = 14.5 [wilson2018 X1, X2]. The danazol ratio cannot be reproduced from the printed inputs, and the weak-base estimates cannot be recomputed from the 2012 paper [jackson2014 X1; hsieh2012 X14]. The equation neglects water mixed into the amorphous phase, which can lower the amorphous solubility by up to a factor of 2 [hsieh2014 R17]. Its use for warfarin assumed 25 °C because the temperature is not printed [hsieh2014 E2]. For posaconazole the printed ratio of 37.9 does not follow from the printed melting data, and the exponent of the printed amorphous-solubility equation has the wrong sign [duong2022b X2]. The indomethacin estimate at 25 °C does not reproduce from the printed inputs [alonzo2010 X2]. The estimate becomes increasingly approximate far below Tg, and a configurational heat-capacity estimate is more rigorous (cited) alonzo2011 C5.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

hydrogen-bond basicity

The strength of a group as a hydrogen-bond acceptor

In this chapter it is used qualitatively to rank polymer groups and drug groups: the more basic PVP amide is said to explain why PVP takes the OH from carboxylic acid dimers [taylor1997 C36]; PVP carries a better acceptor than the drug's own groups [marsac2009 C39]; the pyrrolidone groups of PVP and PVP/VA are stronger acceptors than the acetate groups of PVAc [kestur2010a C24, C25; kestur2011 C26]; and the imidazole nitrogen of bifonazole "would be expected" to be a better acceptor than the PAA carbonyl [kestur2011 C16]. A numerical scale (pKBHX) with classes weak < 0.75 < medium < 1.5 < strong < 2.25 < very strong is applied to polymer groups in another paper of the library [wegiel2013b E2, R17, C30]. The numerical pKBHX scale (weak < 0.75 < medium < 1.5 < strong < 2.25 < very strong, from the association of a model compound with 4-fluorophenol) is applied to all donor and acceptor groups of 15 drugs and 7 polymers, with the carbonyl of a COOH group taken as an ester because no value exists [vaneerdenbrugh2011a C14, R1, R2]; the polyphenol paper reuses it for its six polymers [wegiel2013a R12, P8].

Findings

F1, F12, F13, F24, F25.

Related concepts

part of hydrogen bonding; related to pKa and drug-polymer interactions.

Formulas

none.

How it is measured or obtained

Not measured in this chapter's papers; assigned from chemistry, from the drug NH shift in films with different polymers [kestur2010a R9] and from the cited scale [kestur2011 C26].

Values in the library
materialvalue or classconditionspaper ids
PVP, PVP/VA against PVAcstronger acceptor (pyrrolidone against acetate); PVP/VA has 40% acetate side chainspolymer chemistry[kestur2010a C24, M3; kestur2011 C26]
PVP amide against carboxylic acidthe amide is the more basiccited[taylor1997 C36]
polymer groups on the pKBHX scale (other chapter)classes from weak to very strongcited values[wegiel2013b R17, E2]
PVP, PVPVA pyrrolidonevery strong acceptor, 1-methyl-2-pyrrolidone 2.38, no donorpKBHX classes[vaneerdenbrugh2011a R2; wegiel2013a R12]
E100 amine; imidazole of bifonazolestrong 1.98 (triethylamine); very strong 2.72 (1-methylimidazole)same[vaneerdenbrugh2011a R1, R2]
ester, COOH carbonyl, ether, alcoholmedium: 1.07, 1.07, 1.01, 1.02same[vaneerdenbrugh2011a R2; wegiel2013a R12]
amide carbonyl of benzamide, phenacetinstrong 1.81, 1.69same[vaneerdenbrugh2011a R1]
PSSA sulfonic acidlow 0.71 (acceptor); very strong donorsame[vaneerdenbrugh2011a R2]

Evidence table: hydrogen-bond basicity.

Pitfalls and disagreements

The acceptor-strength explanation of the small edge of PVP and PVP/VA over PVAc for nimesulide is not resolved by the NH maxima, which move as far with PVAc as with PVP [kestur2011 X16]. PVP/VA is compared at equal weight, not at equal numbers of pyrrolidone groups, and the 40% acetate figure is not defined as mass or mole [kestur2010a X11]. The group tables call the acceptor classes "donor strength" in a footnote and cite two different references for the values [vaneerdenbrugh2011a X2]; the HPMCAS COOH acceptor mark is missing in the polyphenol paper's table [wegiel2013a X13]. The pKBHX predicted the PVP and E100 as best acceptors, but E100 formed no strong hydrogen bonds because its amine is ionized [wegiel2013a C32, C33].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

hydrogen-bond donor and acceptor groups

The groups of a drug or polymer that can give a hydrogen bond (NH, OH, COOH) or take one (carbonyl, ether or hydroxyl oxygen, amine nitrogen), and their relative strengths; used to choose a polymer whose strongest group complements a free group of the drug [trasi2012b C20, C8; wegiel2013b C30].

Findings

F18, F24.

Related concepts

part of hydrogen bonding; measured by hydrogen-bond basicity; limited by intramolecular hydrogen bonding and self-association; related to Etter's hydrogen-bond rules.

Formulas

none.

How it is measured or obtained

From structure, with acceptor strength classed on the pKBHX scale [wegiel2013b E2, R17]:

\text{weak} < 0.75 < \text{medium} < 1.5 < \text{strong} < 2.25 < \text{very strong}

from computed partial charges on the polymer carbonyl oxygen [trasi2012b R25]; and from IR shifts of drug and polymer bands in films [trasi2012b R14; trasi2012a R16, R17].

Values in the library
materialvalue or classconditionspaper ids
PVP amide; E100 amine; ester, ether and hydroxyl groups of cellulosics and PAAvery strong (2.38); strong (1.98); medium (1.01–1.07) acceptorspKBHX of model compounds[wegiel2013b R17.d, R17.b, R17.a, R17.f, R17.g]
PVP, PIPA, PDMA, PAA, PVAc carbonyl oxygen−0.65, −0.647, −0.64, −0.606, −0.598NBO charge, DFT in vacuum[trasi2012b R25]
flutamideone NH donor; carbonyl and nitro acceptorsstructure[trasi2012b C20]
acetaminophenphenol OH the stronger donor; amide carbonyl the much better acceptorstructure[trasi2012a C32]
curcumin with PVP against cellulosicsacceptor-only polymer against donor-and-acceptor polymersstorage stability[wegiel2014 C31, C34]
Pitfalls and disagreements

A group present in the structure may not be available: the flutamide carbonyl and curcumin's keto–enol group are held in intramolecular bonds [trasi2012b C34, C35; wegiel2014 C3]. A donor polymer can prefer itself (PAA dimers) [trasi2012b C37]. The size of an IR shift did not rank storage stability for curcumin [wegiel2014 X7], and the charge ranking of four carbonyl polymers fails for PAA [trasi2012b X8].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

hydrogen bonding

In the papers of this chapter, a bond between a donor group of the drug (the carboxylic acid OH of indomethacin, the NH of felodipine and nimesulide, hydroxyl groups of sucrose) and an acceptor group of the polymer (the lactam carbonyl of PVP, the acetate groups of PVAc and PVP/VA, the carboxyl of PAA, the groups of HPMCAS), or between molecules of the same kind (acid dimers of the drug, self-association of PAA) [taylor1997 C25, C35; kestur2010a C18; rumondor2009a C45]. A lower NH wavenumber means a stronger bond [kestur2010a C18]. PVP carries a better acceptor than the drug's own groups, so its bonds replace weaker drug–drug bonds [marsac2009 C39]; the more acidic carboxyl of indomethacin is expected to bond more strongly than the NH of felodipine or nifedipine or the OH of sucrose [marsac2009 C42]. A drug donor can also be bound within its own molecule (see intramolecular hydrogen bonding), which leaves little to bond to a polymer [kestur2011 C27]. Later papers add polyphenol OH groups bonding to the PVP carbonyl (a lower OH wavenumber and a larger carbonyl shift mean a stronger bond: OH band at 3138 and 3135 cm⁻¹ with PVP against 3329–3399 cm⁻¹ with the other polymers) [wegiel2013a C8, C9, C11, R2, R4]; dextran hydroxyls bonding to the PVP carbonyl in a polymer–polymer pair, where dextran–dextran bonds are assumed to be stronger or more numerous [vaneerdenbrugh2012a C10, C36]; and a donor and acceptor classification of the groups of 15 drugs and 7 polymers by bonding atom, acidity and the pKBHX scale [vaneerdenbrugh2011a C13, C14, C19]. Lumefantrine did not hydrogen-bond to PVPVA in dried films hiew2022a C20, R17.

Findings

F1, F2, F3, F4, F12, F13, F14, F17, F20, F22, F24, F25.

Related concepts

part of drug-polymer interactions; includes intramolecular hydrogen bonding and self-association; contrasts with dipole-dipole interactions; related to hydrogen-bond basicity, pKa and binding constant; contrasts with halogen bonding and acid-base interaction; classified by Etter's hydrogen-bond rules.

Formulas

fraction of hydrogen-bonded carbonyl groups from band areas.

How it is measured or obtained

By IR and Raman. Cyclic acid dimers are found by the mutual exclusion rule: an acid band present in the IR and absent in the Raman [taylor1997 C14]. Drug–polymer bonds are read from shifts of the drug NH or acid C=O band and of the polymer carbonyl band, in spin-coated or solvent-cast films at one donor per polymer carbonyl or at 20–50 wt% polymer, always against the amorphous drug and a physical mix, not against the crystal [marsac2009 P4; kestur2010a P6, P7; taylor1997 C7, C24]. A dilution series in a non-polar solvent tests for intramolecular bonds [kestur2011 P9]. In dispersions, a second principal component of the IR spectra beyond a calculated physical mixture is read as "presumably" hydrogen bonding [rumondor2009a C20]. DFT gives the geometry of single molecules [kestur2011 P11]. Further methods: the fraction of PVP carbonyls bonded, from a free and a maximally bonded band fitted to the carbonyl region (fraction of hydrogen-bonded carbonyl groups from band areas) [vaneerdenbrugh2012a P5, E1]; the polyphenol OH band and the polymer C=O shift at 30% polyphenol [wegiel2013a P4]; crystal-structure statistics of competition between groups [vaneerdenbrugh2011a P5, R14]; DFT for intramolecular bonds [vaneerdenbrugh2011a P6].

Values in the library
materialvalue or classconditionspaper ids
indomethacin–PVP-K90PVP C=O at 1636 against 1679 cm⁻¹; drug acid C=O at 1726 cm⁻¹5–70 wt% PVP, solvent-evaporated[taylor1997 R5.l, R11, R12]
amorphous indomethacinacid dimer at 1710 cm⁻¹ (IR) with no Raman bandquench-cooled melt[taylor1997 R5.h, R6]
indomethacin, felodipine, sucrose, ketoconazole with PVP K12PVP C=O shift 45, 25, 25 and 0 cm⁻¹one donor per carbonyl, spin-coated[marsac2009 R12]
felodipine with PVP, PVP/VA, HPMCAS, PVAcNH at 3294, 3298, 3348, 3354 cm⁻¹ against 3341 cm⁻¹50 wt% polymer films[kestur2010a R9]
nimesulideNH at 3345 cm⁻¹ at every concentrationdichloromethane, 1–100 mg/ml[kestur2011 R11]
nimesulide with PVPPVP C=O ≈1684 → ≈1680 cm⁻¹, shoulder ≈1657 cm⁻¹20–50 wt% PVP[kestur2011 R14]
felodipine–PVP, nifedipine–PVPsecond PC with NH and carbonyl loadings10–90% and 25–70% PVP[rumondor2009a R7, R9]
naringenin, quercetin with PVPpolyphenol OH band 3138 and 3135 cm⁻¹; PVP C=O shift 21 and 24 cm⁻¹spin-coated films, 30% polyphenol[wegiel2013a R2, R4]
dextran–PVPPVP C=O 1680 → 1661 cm⁻¹; hydrogen-bonded fraction 1.00 (DEX1–PVP12) to about 0.09 (DEX450–PVP90) at 0.8 dextranspin-coated films[vaneerdenbrugh2012a R2, R14]
benzamide, phenacetin crystalsamide–amide only 100 and 94% alone; 0% with a COOH partner; 14 and 33% with C(O)NC2CSD survey[vaneerdenbrugh2011a R14]
lumefantrine–PVPVAcarbonyl bands fixed at 1736 and 1684 cm⁻¹ at 10, 25 and 50% drugdried spin-coated filmshiew2022a R17

Evidence table: hydrogen bonding.

Pitfalls and disagreements

Assignments rest on analogy with liquid models: the same non-bonded acid C=O is assigned at 1735 cm⁻¹ (chain ends) and 1726 cm⁻¹ (PVP-bonded molecule), and how one turns into the other is not shown [taylor1997 C32, X4]. IR bonds were recorded at 20–50 wt% polymer, whereas the growth effects were measured at 0.5–5 wt% and 70–110 °C [kestur2010a X5; kestur2011 X10]. The felodipine–PVP carbonyl shift is 25 cm⁻¹ in one paper and about 20 cm⁻¹ in a cited study [marsac2009 R12.b; kestur2011 R20]. A drug without a donor (ketoconazole) shows no shift yet mixes about athermally [marsac2009 R7.c, R12.h]. For bifonazole the donor–acceptor picture rests on crystal-structure reasoning and was not measured [kestur2011 X9]. The bond between indomethacin and PVP is proposed as the reason PVP inhibits crystallization, but no crystallization was measured in that paper [taylor1997 X8]. The PVP shoulder at 1661 cm⁻¹ with naringenin overlaps the drug's own band, and HPMC and PAA are placed on the IR trend line by projection [wegiel2013a X9, X12]. The bonded fraction of dextran–PVP rests on references set by one system and on films prepared differently from the DSC samples [vaneerdenbrugh2012a X12, X8]. No hydrogen bond was measured in the 15-drug screen, and its melt spectra are not shown [vaneerdenbrugh2011a X13].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

hydrophilic-lipophilic balance

Evidence table: hydrophilic-lipophilic balance. Content from the release-mechanism chapter (2019–2025), with rows from the Physical stability chapter.

The balance of hydrophilic and lipophilic parts of a surfactant, used in the library to rank surfactants from hydrophobic (Span 85) to hydrophilic (SDS). Que and co-workers (2019) screened five surfactants at 5 parts per 100 parts drug plus polymer in ledipasvir–PVPVA and found that the more hydrophilic poloxamer 407 and SDS raised the limit of congruency to 7.5 and 30% que2019 A2, C12. For clopidogrel SDS (HLB 40) was the only surfactant that raised release, and its higher effective level for droplet stability "most likely" reflects its high HLB correasoto2022a R1, C42, C55; for atazanavir, charge and hydrophilicity did "not appear" to affect release substantially among the low-molecular-weight additives correasoto2022b C50. In ritonavir–PVPVA at 30% the outcome did not follow HLB: SDS (40) and Span 85 (1.8) released fast or fully, Tween 80 (15) and Span 20 (8.6) stalled, and the authors saw no correlation between surfactant properties and performance indulkar2022 M4, M5, M7, M8, C64. In the 2023 surfactant study the most hydrophilic surfactant (SDS) raised the water needed for separation and the most lipophilic (Span 85) softened the drug-rich layer; at 40% only SDS and Tween 80 kept partial release yang2023 R21, C18, R2.

Findings

Release mechanism and LoC: F13, F16, F21, F31.

Related concepts

related to critical micelle concentration and polymer-surfactant interaction; raises the limit of congruency.

Formulas

none.

How it is measured or obtained

Not measured; the surfactants are ranked by name, and no HLB values are printed que2019 X19. HLB values are cited correasoto2022a R1; correasoto2022b M3.

Values in the library
materialvalue or classconditionspaper ids
Span 85, Tween 80, vitamin E TPGS in ledipasvir–PVPVA 7.5%no rescue of release (≤ ≈4% drug at 60 min)pH 6.8, 37 °Cque2019 R6
poloxamer 407; SDSLoC 7.5%; 30%sameque2019 C12
SDS, Tween 80, Span 20, Span 85 in ritonavir–PVPVA (Physical stability)hydrophilic SDS mainly in the polymer-rich phase, the more hydrophobic surfactants preferentially in drug-rich domainshumidified filmsyang2022b C61, C35
SDS, CTAB, TPGS, Tween 80HLB 40, 22, 13.2, 15citedcorreasoto2022a R1
Span 20, Span 80, Span 85HLB 8.6, 15 (as printed), 11citedcorreasoto2022b M7, M8, M9
SDS, Tween 80, TPGS, Span 20, Span 85 in ritonavir–PVPVA 30:70HLB 40, 15, 13.2, 8.6, 1.8 (cited); ritonavir ≈78, ≈25, ≈89, ≈41, ≈87% at 90 minpH 6.8, 37 °Cindulkar2022 M4, M5, M6, M7, M8, R5, R6, R9, R7, R8
SDS, Tween 80, Span 20, Span 85 in ritonavir–PVPVAHLB 40, 15.0, 8.6, 1.8 (cited)10 parts per 100 parts drug and polymeryang2023 M3, M4, M5, M6
Pitfalls and disagreements

Why SDS works was not tested; the authors offer that the surfactants "possibly" reduce the rate or tendency of phase separation que2019 C53. Surfactant location was not measured in the ledipasvir dispersions que2019 C53. Span 80 is printed with the same HLB as Tween 80 (15) correasoto2022b X8. Span 85 is given HLB 11 in the atazanavir paper against 1.8 in the two ritonavir surfactant papers (synthesis: comparison of the cited values) correasoto2022b M9; indulkar2022 M8; yang2023 M6. For ledipasvir the 2019 study gives the gain with SDS as 5 → 30% (F13) que2019 C12, while the 2023 surfactant paper cites it as 7.5 → 30% yang2023 R27.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

hydrophobic effect

The release of the ordered, "iceberg-like" water around apolar groups when a solute leaves the water, which costs enthalpy and gains entropy. Ueda and co-workers invoke it for the transfer of a polymer from water into the ibuprofen-rich phase, which has positive ΔH and ΔS for most of the range, and for the vinyl acetate units of PVP-VA and the methyl groups of HPMC ("should be considered", "are expected") ueda2022 C49, C50, C54. The same reasoning is offered for the stronger partitioning of PVP-VA than PVP (entropy cost of hydrating apolar groups) [ueda2021 C30].

Findings

F20, F21.

Related concepts

related to hydrophobic interactions (association of apolar molecules); drives polymer partitioning into the drug-rich phase.

Formulas

van't Hoff equation.

How it is measured or obtained

Not measured; it is inferred from the signs of ΔH and ΔS of transfer and from the negative enthalpies of solution of PVP and HPMC (cited) ueda2022 R23, R29, C50.

Values in the library
materialvalue or classconditionspaper ids
polymer transfer into the ibuprofen-rich phaseΔH of HPMC 58 → 12, PVP-VA 25 → 5, PVP 30 → 1 kJ/mol; −TΔS −71 → −31 (HPMC)15–60 °Cueda2022 R23
Pitfalls and disagreements

Water structure around the polymers and the hydration of HPMC with temperature were not measured, and polymer hydrophobicity was not measured [ueda2022 C50, C57; ueda2021 X8]. The explanation of HPMC's temperature dependence by dehydration ("likely reflecting") is untested in these solutions ueda2022 C57.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

hydrophobic interactions

The association of non-polar drug molecules to minimize contact with water; Ilevbare and Taylor call it "intuitive" that LLPS of drugs with Log P 2.24–5.98 is driven by hydrophobic interactions and attribute the lower LLPS concentration at higher ionic strength to salting-out, which strengthens them ("may be attributed") ilevbare2013a C37, C38, C41. The papers of 2017–2022 add that the lower GLPS onset of telaprevir in 100 mM than in 50 mM phosphate (104/102 against 149/146 µg/mL) is also attributed to hydrophobic aggregation promoted by ionic strength, again untested [lu2017b R9, C20]; and that the signs of the transfer of polymer into a drug-rich phase (positive ΔH and ΔS) are related to the hydrophobic effect ueda2022 C50 (see hydrophobic effect). New aspect (Crystallization from solution): in the crystallization-inhibition papers hydrophobic interaction is the proposed driver of polymer adsorption on drug crystals and of polymer–polymer association; salts make water a poorer solvent for hydrophobic groups, so if hydrophobic forces drive the polymer to the crystal, a higher buffer concentration should strengthen the interaction and the inhibition [ilevbare2013b C27, C28]. The cellulose polymers gained from 50 to 100 mM phosphate, which the authors read as hydrophobic interaction "verified"; PVPVA did not and is explained by a hydrogen bond [ilevbare2013b R10, C48, C51]. Polymer pairs were also more effective in 100 mM, taken as support for hydrophobic interpolymer complexes ilevbare2012a C43. New aspect (Mesoporous silica): the possible binding of lipophilic drugs to the hydrophobic siloxane part of a silica surface, expected for drugs of log P above 4 ("considered feasible") but not found: adsorption of ritonavir (log P 5.98), indomethacin (4.27) and its methyl ester (4.6) did not change with ionic strength [dening2019 C51, C22, M1; mccarthy2020 C6, C31, M1, M2]. A second sense appears for loaded silica: as hydrophobic drug fills the pores the formulation becomes more hydrophobic and water enters more slowly, which "may contribute" to low release at high loading [hate2020a C44, C45; hate2020b C43].

Findings

Amorphous solubility and LLPS: F1, F9, F18, F21. Crystallization from solution: F8, F11, F17, F36, F44. Mesoporous silica: F5, F11.

Related concepts

proposed driver of liquid-liquid phase separation; related to the critical micelle concentration analogy for the temperature profile; related to polymer hydrophobicity, interpolymer complex and polymer adsorption; contrasts with drug-silanol hydrogen bonding as a mechanism of drug adsorption onto silica.

Formulas

none.

How it is measured or obtained

Not measured: neither solvent polarity nor drug association was tested ilevbare2013a C41. In the crystallization-inhibition papers it is inferred by comparing effectiveness ratios at two buffer concentrations (50 and 100 mM phosphate, pH 6.8), with buffer molarity standing in for ionic strength [ilevbare2013b P13, X11; ilevbare2012a P12]. In the Mesoporous silica papers the same salting-out logic is applied to adsorption: adsorption in distilled water, 0.1 M and 0.5 M NaCl, where a hydrophobic contribution should raise adsorption at higher ionic strength [dening2019 P4, C16; mccarthy2020 P10, C30].

Values in the library

None printed in the amorphous solubility and LLPS papers beyond the telaprevir onsets; the crystallization-from-solution and Mesoporous silica papers give the following.

materialvalue or classconditionspaper ids
HPMC on celecoxib; efavirenz6.45 → 10.15; 1.1 → 2.55 (50 → 100 mM)S 6.6; S 1.2[ilevbare2013b R10]
PVPVA on celecoxib; efavirenz7.6 → 7.4; 4.5 → 4.9same[ilevbare2013b R10]
eight polymer pairs on ritonavir1.1–2.6 → 1.7–4.8S 4.3 against 7.7ilevbare2012a R14
telaprevir GLPS onset (amorphous solubility chapter)lower in 100 than in 50 mM phosphate, attributed to hydrophobic aggregation37 °C[lu2017b R9, C20]
A5a, ECB, ECD with telaprevir and atazanavirdrug–CH3 RDF peaks about 25–36 at 0.4–0.5 nm against carboxylate peaks 10–23 at 1.6–2.6 nmMD, 10 ns[mosqueragiraldo2018a R11, C35]
HPMCAS grades with posaconazolehydrophobic drug–polymer interaction proposed to rise with acetyl content and lower pHnot measuredshah2025 C6, C48
ritonavir on SBA-15about 91–95, 162–182, 249–294 mg/g at initial 2.5, 7, 14 µg/mL; no significant salt effectwater, 0.1 and 0.5 M NaCl[dening2019 R9]
indomethacin; methyl ester on SBA-15about 0.8–0.9 and 8–9; about 11 and 65–76 mg/g at 2 and 8 µg/mL; no significant salt effectsame[mccarthy2020 R15]
Pitfalls and disagreements

The Log P of ritonavir is 5.6 in the table and 5.98 in the text ilevbare2013a X2. Buffer molarity, solubility and supersaturation change together in the pair test, and the growth rate without polymer at 50 mM is not reported [ilevbare2012a X12; ilevbare2013b X11]. The hydrophobic contribution for ritonavir rests on the SP trend alone [ilevbare2013b X14]. Mesoporous silica: the ritonavir salt series was run in unbuffered water, where adsorption was higher than in buffer [dening2019 X5]; the indomethacin series used equal concentrations, not equal activities, and an unstated pH [mccarthy2020 X9]. The formulation hydrophobicity invoked for high loadings was not measured [hate2020a C44]. The same salting-out test reads as a hydrophobic contribution for cellulose polymers on drug crystals [ilevbare2013b R10, C48] but finds none for drug on silica [dening2019 R9; mccarthy2020 R15]; the chapters agree on the test and differ in its outcome for the two surfaces.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

hydrophobic ion pairing

Evidence table: hydrophobic ion pairing. Content from the release-mechanism chapter (2024–2025), with rows from the Miscibility chapter.

The pairing of an ion with an oppositely charged amphiphile into a poorly soluble complex, driven by electrostatic attraction and hydrophobic interaction; ionic polymers form such insoluble complexes with oppositely charged amphiphiles bapat2024 C33, C34. In the release papers a lipophilic drug cation pairs with the ionized succinoyl groups of HPMCAS, and the pair reduces polymer hydration and release bapat2025a C5, C34. In the lumefantrine study of the Miscibility chapter the ion pair reduces the number of carboxylates available for hydration, so a polymer needing a high critical ionization cannot dissolve once part of its acid groups is paired hiew2022a C53, C57.

Findings

Release mechanism and LoC: F32, F33.

Related concepts

a form of drug-polymer ionic interactions; gives an insoluble drug-polymer complex; acts against the critical ionization for polymer dissolution.

Formulas

none.

How it is measured or obtained

Inferred from insoluble complex formation in buffer and from drug protonation by XPS; not measured directly in a gel bapat2024 P9, R8; bapat2025a C5.

Values in the library
materialvalue or classconditionspaper ids
cinnarizine, loratadine, clotrimazole with HPMCAS-MF70–90% of the polymer complexed at about 1:1pH 6.0bapat2024 R12
lumefantrine with CAP, HPMCP (Miscibility chapter)CAP needs ≈0.94 of its groups ionized against 0.88 left free; HPMCP slightly below 0.8325% loading, calculatedhiew2022a C57
Pitfalls and disagreements

Cinnarizine complexed beyond the 1:1 ratio expected for electrostatic pairing (plateau near 1.5:1), which the authors attribute "likely" to shielding by buffer ions bapat2024 C36. The neutral phenolphthalein also complexed HPMCAS, by hydrogen bonding in the authors' "conjecture", so not every complex is an ion pair bapat2024 C41.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

hydrophobicity

The tendency of a drug to avoid water, read in the library from its calculated log P; for the moisture-separation papers a hydrophobic drug is expected to have a positive water–drug interaction parameter, so that sorbed water makes the dispersion less favourable for it rumondor2010c C30, M1, M2, M3, M4. The same papers treat it as one of three factors, with dispersion hygroscopicity and drug–polymer interaction strength, behind moisture-induced amorphous–amorphous phase separation rumondor2011 C1, C28.

Findings

F13, F23.

Related concepts

related to hygroscopicity (the two together set the water–drug term); part of the argument for moisture-induced phase separation; enters Flory-Huggins interaction parameter (\chi_{WD}); related to lipophilicity.

Formulas

multicomponent Flory-Huggins free energy of mixing, through the water–drug parameter \chi_{WD} rumondor2010c E1, C30.

How it is measured or obtained

Calculated log P (ChemBioDraw Ultra) for the drugs rumondor2010c M1; rumondor2011 P9; cited log P for resveratrol and felodipine [wegiel2013b R20]. The water uptake of the hydrophobic films themselves was not measured rumondor2011 X6.

Values in the library
materialvalue or classconditionspaper ids
felodipine, quinidine, indomethacin, pimozidecalculated log P 2.24, 2.48, 3.58, 5.34drugs of PVP, PVPVA and HPMCAS dispersionsrumondor2010c M1, M2, M4, M3
indoprofen, nilutamide, loratadine, clofoctol, probucollog P 2.84, 2.14, 4.13, 8.19, 10.0drugs of PVP filmsrumondor2011 R15.e, R15.s, R15.t, R15.f, R15.g
resveratrol against felodipinelog P 3.1 against 4.5 (cited)contrast of PVP dispersions in humid storage[wegiel2013b R20]
pimozide with HPMCASthe only HPMCAS dispersion that separated; attributed to hydrophobicity94% RH, driedrumondor2010c C35, R3.e
clofoctol–PVP (≥ 70% drug), probucol–PVP (90% drug)no separation up to 94% RH; "it is thought" too little water sorbed22 °C filmsrumondor2011 C36, R14
Pitfalls and disagreements

The direction of the effect is disputed within the library: pimozide's high log P is used to explain separation even with HPMCAS rumondor2010c C35, while in the 20-system study the two most hydrophobic drugs were the only ones that resisted at some compositions and log P was dropped from the discriminant model as insignificant rumondor2011 X14, R16. Calculated and cited log P values differ between papers for the same drug: felodipine 2.24 rumondor2010c M1 against 4.5 [wegiel2013b R20].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

hygroscopicity

How much water a material takes up at a given humidity

For HPMC grades at 21 °C: E3 3.22, E6 3.56, E50 3.43 and AFFINISOL 2.03% w/w at 40% RH; the polymer's hygroscopicity is held to set how much water a film takes up during formation and so the size of drug-rich domains [mugheirbi2017 R2, C23]. Solvents can be hygroscopic too: methanol takes up almost an equimolar amount of water at 50% RH [li2017 R26, C39]. In the coating papers hygroscopicity is a powder-level property read from dynamic vapour sorption of coated and uncoated particles; the abstract of the ezetimibe paper generalizes lower hygroscopicity to all coated powders, which only the thick coatings show [duong2022c C59, X6]. New aspect (Physical stability): for drug–polymer dispersions the polymer sets the hygroscopicity, because the drug is hydrophobic, so a dispersion takes up more water than the amorphous drug, the amount depending on polymer type and content [konno2008 C6, C18]. Nifedipine and its dispersions are more hygroscopic than felodipine's [marsac2008a C12]. New aspect (Release mechanism and LoC): since water-induced AAPS depends on the water absorbed, polymer hygroscopicity "likely" also matters for the limit of congruency; the congruent release of high-loading HPMCAS and EUDS dispersions "conceivably" reflects water uptake too low to induce AAPS saboo2020a C44.

Findings

ASD process: F4, F2, F44, F45, F49. Physical stability: F6, F11, F16, F23, F33, F35. Release mechanism and LoC: F8, F11, F12.

Related concepts

measured as water sorption and by water sorption isotherm; sets moisture-induced phase separation; drives plasticization by water; acts with hydrophobicity in the water–drug term. Ranks with wettability; drives amorphous-amorphous phase separation on hydration; related to polymer hydrophobicity.

Formulas

Flory-Huggins water sorption isotherm.

How it is measured or obtained

Gravimetric moisture sorption (SGA-100; 42–44 mg of as-received powder dried at 60 °C, equilibrated at 21 °C at 5, 7, 20 and 40% RH, n = 3) [mugheirbi2017 P14]. Gravimetric sorption isotherms of bulk dispersions at 25 °C [konno2008 P7; marsac2008a P6]. In the release-mechanism papers: gravimetric water sorption of neat polymers and amorphous felodipine at 37 °C from 5 to 95% RH, single runs; uptake of 40% HPMCAS dispersions at 100% RH extrapolated from isotherms saboo2020a R3, R18.

Values in the library
materialvalue or classconditionspaper ids
HPMC E33.22, 1.517, 0.48% w/w40, 20, 7% RH[mugheirbi2017 R2.a]
AFFINISOL2.03, 0.89, 0.19% w/w; about 63% of E3 at 40% RHsame[mugheirbi2017 R2.d, C21]
PVP, HPMC, HPMCAS (outside)PVP absorbs more water than HPMC, HPMC more than HPMCAS, at the same RH and temperature25 °C[rumondor2010a C6, R1]
ritonavir ASDs (outside)PVP and PVPVA are more hygroscopic than HPMCAS, so their ASDs are expected to be more prone to moisture-induced AAPSargumentpurohit2017b C45
polymer hygroscopicity and AAPS (outside)the water–drug contribution to the free energy of mixing depends on the water sorbed, which depends on polymer hygroscopicityfelodipine, indomethacin and others in PVP, PVPVA, HPMCASrumondor2010c C30
PVP, HPMC, HPMCAS, felodipine≈33.5, 10.9, 6.2, 0.7 g/100 g75% RH, 25 °C[konno2008 R8]
felodipine with 25% PVP, HPMC, HPMCAS≈4.7, 2.3, 1.7 g/100 g75% RH[konno2008 R9.d]
nifedipine vs felodipine with 25% PVP≈5.5 vs 4.6 g/100 g75% RH[marsac2008a R2]
felodipine–PVP vs HPMCAS dispersionsPVP dispersions more hygroscopic (cited)93% RH[rumondor2009b R25]
75:25 felodipine and quinidine with PVP, PVPVA, HPMCAS6.4/3.6/2.4 and 5.3/3.4/2.4 g per 100 g25 °C/85% RHrumondor2010c R18
PVP, PVPVA, HPMCAS alone≈50, ≈24, ≈8 g per 100 g at ≈85% RHcited isotherms, 25 °Crumondor2010c R19
40% resveratrol–PVP dispersion against its physical mixture≈12.8 against ≈36.5% at 95% RH25 °C[wegiel2013b R19]
PVP K29/32, K12, PVPVA, HPMC, HPMCAS; amorphous celecoxib≈68, 67, 48, 31, 12; ≈2.2 g/100 g at 95% RHDVS, 25 °Cxie2016b R12
six tacrolimus capsule fills1.6–12.8% at 95% RH, most with the most croscarmelloseDVS, 25 °C[trasi2017 R4, C16]
PVP, PVPVA, HPMC, EUDS, HPMCAS≈34, ≈20, ≈9, ≈7.8, ≈5.9% at 75% RH; ≈71, ≈47, ≈28, ≈12.7, ≈10.2% at 95% RH37 °Csaboo2020a R3
amorphous felodipine≈1.3% at 75% RH37 °Csaboo2020a R3
40% HPMCAS dispersions of nilvadipine, felodipine, cilnidipine≈5.83, ≈5.67, ≈5.45% at 100% RH (extrapolated)37 °Csaboo2020a R18
Pitfalls and disagreements

Sorption of dry powders at equilibrium is a proxy for uptake during a seconds-long coating; no water was measured during coating [mugheirbi2017 X4]. Plotted against water content the polymers' nucleation rates fell together within scatter, but at similar water content 7% PVP still nucleated faster than 7% cellulose polymer [konno2008 C30, X4]. The uptake used to explain the polymer order was measured on 75:25 powders at 85% RH, not on the 50:50 test samples rumondor2010c X7. Hygroscopicity is not a variable of the 20-system model rumondor2011 X5. Water uptake did not rank celecoxib dispersions at 94% RH: PVPVA, with about twice the uptake of HPMCAS, lasted longer xie2016b R13, R23, C50. In tacrolimus capsules extra croscarmellose raised sorption but did not destabilize the innovator product [trasi2017 C30]. Water uptake separated the hydrophilic from the hydrophobic polymers but did not rank the limits within the hydrophilic group: HPMC takes up less water than PVPVA yet had the lower limit saboo2020a X7. The uptake was measured on neat polymers saboo2020a X7.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

in situ salt formation

Evidence table: in situ salt formation. Content from the ASD dissolution chapter (delamanid 2022–2023).

Forming the drug salt in the same solution and evaporation or drying step that forms the dispersion, so that drug, counterion and polymer are processed together and the dispersion contains the protonated drug. It was used to keep a fast-crystallizing weak base amorphous at a drug loading at which the free base left crystals behind: the salts have a much higher Tg, and the authors "speculate" that protonating the piperidine ring keeps the long, thin molecules from lining up into a crystal duong2022a P8, C50. Salts inside dispersions were rare before, with meloxicam–meglumine and naproxen–meglumine formed during melt extrusion duong2022a C6. The counterion is added at a 1:1 molar ratio to the spray-drying or evaporation solution, and alcohols are avoided with sulfonic acids to prevent sulfonate esters [nguyen2023b P1, C13; duong2022a C8].

Findings

F23, F25, F27.

Related concepts

raises the Tg of an amorphous salt; prevents residual crystallinity from preparation; limited by salt disproportionation and plasticization by water; read with crystallization tendency.

Formulas

none.

How it is measured or obtained

Salt formation is confirmed by the downfield shift of the protons at the basic nitrogen in the proton NMR spectrum and by a broad N+–H band in the infrared spectrum, with the free-base band gone; the solid is then characterized by PXRD, DSC and water sorption, and stored at 40 °C/75% RH duong2022a R16, R17, P6, P13.

Values in the library
materialvalue or classconditionspaper ids
eight delamanid sulfonate salts, neatseven amorphous, Tg 83.7–117.8 °C against 43.3 °C for the free base; water uptake 5.8–21.1% at 95% RH; four liquefied on storage2 weeks at 40 °C/75% RHduong2022a R20
delamanid edisylate 1:1 with excess acidTg 53.9 °C and 59% water uptake, against 117.8 °C and 11.6% for the 2:1 salt95% RHduong2022a R21
salt dispersions at 20% drug with HPMCASTg 100.4–117.0 °C against 86.7 °C for the free base; water uptake ≈10–13.6% against ≈8.2%95% RHduong2022a R23, R22
four salt dispersions at 25% drug with HPMCP against the free base≈95–97 against ≈20 µg/mL at pH 6.5; ≈85–91 against ≈55 µg/mL after a pH shifttablets, 100 µg/mL = completeduong2022a R26
delamanid edisylate dispersions with HPMCP, 10–40% drug≈99 / ≈98 / ≈95 / ≈59 / ≈21 µg/mL of 100PBS pH 6.5, 37 °Cduong2022a R24
chloride and edisylate dispersions with HPMCP-50, uncoated tablets≈86 and ≈93 µg/mL after a pH 1.6 stage against ≈62 µg/mL for the free basepH 1.6 → 6.5[nguyen2023b R2]
Pitfalls and disagreements

No PXRD of any salt dispersion and no storage data for salt dispersions appear in the main text, so the crystal-free state is asserted rather than shown, and the free-base and salt dispersions were cast from different solvents with an unstated drug-loading basis duong2022a X8, X7, X6. The salt does not stop crystallization where the polymer stays undissolved: salt dispersion films crystallized at pH 3.0 like the free base, and the salt "only partially remediated" the pH dependence [nguyen2023b C17; nguyen2023c C20]. Three of the four salts chosen for their stability liquefied at 40 °C/75% RH, and release of several salt dispersions was lower after an acid stage than in a single stage duong2022a X19, C63.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

in vitro–in vivo correlation

The relation between an in vitro test and in vivo performance. The papers up to 2018 state expectations only [raina2015c C44; elkhabaz2017 C2, C60; purohit2018 C58, C65]. Four later papers set an in vitro measure against exposure in rats, dogs or monkeys; they rank formulations and do not give a quantitative relation (F25, F26, F30) [wilson2018 C51, C57; wilson2020 C44; purohit2019 C40; nguyen2023a C57, C73].

Findings

F11, F17, F25, F26, F27, F30, F31.

Related concepts

relates biorelevant media and oral bioavailability to virtual bioequivalence.

Formulas

non-compartmental AUC, relative bioavailability, absolute bioavailability.

How it is measured or obtained

(1) The mass flow of the dissolved formulation across a dialysis membrane plotted against Cmax and AUC in rats [wilson2018 R17; wilson2020 R8, R6]. (2) A comparison of the same formulations in compendial or low-volume dissolution, an absorptive test and dogs (F31) [purohit2019 C40]. (3) Release in biorelevant media against monkey exposure, fasted and fed (F26, F27) nguyen2023a R17, R19, R23. (4) The PBPK route, with the dissolution profile as release input [purohit2018 P10, P12].

Values in the library
materialvalue or classconditionspaper ids
tacrolimus capsulessimulated bioequivalence lost from 20% (100 mL input) or 40% (900 mL input)virtual trials[purohit2018 R17]
posaconazole, atazanavir (Elkhabaz 2021)in vitro onset about 80 min against 93 min in human jejunum; atazanavir about 2 h against 1.25 hFaHIF[elkhabaz2021 C34, C36]
enzalutamide, five ASD and slurry formulationsmass flow 0.632 to 0.063 µg/min in the order of rat Cmax and AUC0–48, except the crystallizing 10% HPMCAS ASDrats, 10 mL/kg[wilson2018 R15, R17, C51]
enzalutamide, four formulationsmass flow about 0.53, 0.49, 0.068, 0.063 µg/min against AUC0–inf 516, 305, 45, 43.1 µg·h/mLrats, 50 mg/kgwilson2020 R8, R6
tacrolimus capsulefully crystalline capsule 51% of the fresh generic's AUC in dogs; 17–22% in the absorptive test; 8% or 55% in simulation (100 or 900 mL input)dogs, 1 mg[purohit2019 R9, C40; hate2019 R13; purohit2018 R14, R16]
pretomanid HPMCAS-HF ASDin vitro release to the crystalline solubility below FeSSIF pH 5.8; monkey fed exposure 72.2% of fasted (crystalline reference 163%; printed, dose-normalized)cynomolgus monkeys, 30 mgnguyen2023a R19, R23, C73, C85
Pitfalls and disagreements

Solubilizing components of biorelevant media, if ignored, "may explain" poor correlations [raina2015c C44]. The tacrolimus human study was pending [purohit2018 C58]. Non-sink closed dissolution did not rank the rat exposures, and the dissolution AUC ranked the ASDs differently over 0–2 h and 0–4 h (F25) [wilson2018 C57, R7]. In vitro gains from a surfactant or a base did not carry over to monkeys, and standard media missed the food effect on an enteric-polymer ASD (F26, F27) nguyen2023a C57, C73, C85. The in vivo dose-to-fluid volume ratio is unknown, so the choice among the low-volume and large-volume in vitro results decides how a dog result is read (F31) [purohit2019 C40].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

incongruent release

Polymer and drug leave the dispersion at different rates; above the limit of congruency the polymer leaves first, the undissolved solid becomes drug-rich and release slows [moseson2021 C34, C58]. For bicalutamide–PVPVA at 30% DL, PVPVA reached about 90% of its dose within 20 min while only about 30–60% of the drug dissolved in 4 h, and the undissolved solid went from PVPVA:BCL 7:3 to 1:1 within 5 min (computed from solution data) [moseson2021 R25, R26, R17]. Incongruent release can also come from a coating: in tablets of coated ritonavir–PVPVA particles slower hydration let phase separation outpace dissolution, which the authors describe as a lower effective limit of congruency benson2025 C34. New aspect (Release mechanism and LoC): above the limit of congruency the polymer leaves faster than the drug, and the ritonavir tablets show a transition loading (30%) that starts congruent and turns incongruent after about 40 min indulkar2019a R5, C3, C32. Humidity can make a congruent dispersion incongruent saboo2019 R9, C41. The papers of 2020–2022 add drug release that starts only after a lag while PVPVA dissolves from the start: from 30% lumefantrine benzoate about 20% of the polymer and almost no drug had been released at 30 min, "indicative of" incongruent release hiew2022b R13, C18; and incongruent release that develops after minutes when crystals cover the surface of a congruent compact saboo2020 R8, C17. Partly connected drug-rich domains at 40% MePHPH gave release that was not fully congruent: drug lagged polymer by 30 min and accumulated in the gel deac2023a C61, R1, R3.

Findings

ASD process: F27, F38, F40, F48. Release mechanism and LoC: F3, F6, F7, F8, F12, F19, F22, F25.

Related concepts

above the limit of congruency; produces surface drug enrichment; precedes matrix crystallization; with a drug-rich barrier layer.

Formulas

surface-normalized release rate.

How it is measured or obtained

Polymer by size-exclusion chromatography and drug by UV or HPLC against time; surface by SEM, IR, XPS or EDX after short exposures [moseson2021 P14, R24; indulkar2019a R16, R17]. In the release-mechanism papers: as for congruent release, from separately assayed drug and polymer saboo2019 R8.

Values in the library
materialvalue or classconditionspaper ids
BCL–PVPVA S/180 (crystal-free)PVPVA about 36 µg/mL at 2.5 min, about 58.8 µg/mL at 60 min (of 70)30 µg/mL BCL dose[moseson2021 R25]
BCL–PVPVA M/155 (3.5% crystals)PVPVA about 54.6 µg/mL at 2.5 min, levelling at about 64same[moseson2021 R25]
undissolved solid after 5 minPVPVA:BCL 1:1 (crystal-free), 1:2 (with residual crystals)computed[moseson2021 R26]
ritonavir–PVPVA 50% DL tablet (outside)surface drug-rich after 5 minIR, SEMindulkar2019a C18, C41
nilvadipine and cilnidipine–PVPVA compacts (outside)XPS shows surface drug enrichment of incongruently releasing compacts, none for congruent ones10 minsaboo2019 C25
BCL–PVPVA 20 / 30% DLpolymer about 82 / 68% against drug about 33 / 18% at 10 min; ends about 88 / 86%dose of at most 30 µg/mLmoseson2022b R6, R7
BCL–PVPVA 50% DLpolymer about 18% at 10 min and 80% at 2 h; drug plateau about 73% from about 120 minsamemoseson2022b R6, R7
BCL–PVPVA 30% DL with 1.5% TPGSincongruent; about 54% (106–250 µm) at 30 min, about 93–94% at 4 hsamemoseson2022b R11, R13
coated RTV–PVPVA 20% DL tabletsconnected drug-rich regions along particle boundaries; about 35–75% at 60 min at pH 6.8tabletsbenson2025 R10, R14
ritonavir–PVPVA 30%lag ~15 min; together to ~40 min; then PVPVA ≈96 against drug ≈48.5% at 120 minpH 6.8, 37 °Cindulkar2019a R5, R3
ritonavir–PVPVA 35%PVPVA ≈49 against drug ≈11% at 300 minsameindulkar2019a R6
nilvadipine 15:85, 20:80; cilnidipine 20:80, 25:75 in PVPVApolymer/drug rate ratio about 20, 40, 40, 105samesaboo2019 R5, R6
nilvadipine 10:90 compact after 12 h at 97% RH≈0.34% drug against ≈2.6% polymer in 15 minsamesaboo2019 R9
felodipine 15–30% in PVPdrug ≈0.005–0.020 against PVP ≈1.7–1.9 mg/min/cm²samesaboo2020a R14
indomethacin–PVPVA 15, 20, 25%drug ≈0.04, 0.02, 0.01 against PVPVA ≈0.72, 0.64, 0.50 mg/min/cm²5-min rates, pH 2.1, 37 °Csaboo2020 R3, M5
clopidogrel–PVPVA 60%drug ≈0.2 against PVPVA ≈4.1 mg/min/cm²compactscorreasoto2022a R18
atazanavir–PVPVA 10%drug ≈0.07 against PVPVA ≈0.24 mg/min/cm²pH 6.8, 37 °Ccorreasoto2022b R3, P5
lumefantrine benzoate–PVPVA 30%≈0 drug and ≈20% PVPVA released at 30 min; ≈8.5 and ≈50% at 90 mincompacts, 37 °Chiew2022b R13
Pitfalls and disagreements

The drug-rich layer is inferred from the shape of the PVPVA release curve and pitted surfaces, "presumably drug-rich"; its composition was not measured [moseson2021 C32, C58]. Incongruent release does not by itself doom a dispersion: a TPGS dispersion released incongruently yet completely because little solid was left when nucleation began moseson2022b C50. Polymer release was not measured in the ritonavir tablets, so the shift of the limit is inferred benson2025 X18. The 35% ritonavir tablet is placed with 30% in one passage and with 40–50% in another indulkar2019a X13.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

insoluble drug-polymer complex

Evidence table: insoluble drug-polymer complex. Content from the release-mechanism chapter (2024–2025), with a row from the Physical stability chapter.

A precipitate of drug and dissolved polymer that forms when both meet in buffer at a pH where the polymer alone stays dissolved, so that polymer in the pellet marks a complex bapat2025a C9; bapat2024 C8. With HPMCAS it forms from lipophilic weak bases ionized at the gel pH, and from the neutral phenol phenolphthalein, and its low solubility is read as lowering the polymer's interfacial solubility and hence release ("likely largely accounts") bapat2024 C19, C32, C47. Bedaquiline complexes formed from pH 6.0–7.0 held the polymer's carbonyl band and disordered drug, and the drug in them was about half protonated, so the authors call them ionic rather than free base kaur2025 R11, C14, C35. The phenolphthalein–PVPVA drug-rich phase of the 2023 PVPVA work is read as an insoluble complex of the same kind (F27) deac2023b C43.

Findings

Release mechanism and LoC: F32, F33, F34, F17, F23.

Related concepts

formed by drug-polymer ionic interactions as a hydrophobic ion pairing product, or by hydrogen bonding of a phenol; a case of drug-polymer complexation; suppressed by micellar solubilization of the drug; lowers pH-dependent polymer solubility at the gel surface.

Formulas

percent polymer complexed.

How it is measured or obtained

Drug and polymer are dissolved together in THF and spiked into stirred buffer (0.5–1.0 mg/mL polymer, drug above its amorphous solubility), the pellet is removed by ultracentrifugation and the polymer left in the supernatant is assayed by HPLC or the phenol–sulfuric acid method; controls are drug alone (precipitates as drug) and polymer alone (stays clear) bapat2024 P9, R10; bapat2025a P9, R17; kaur2025 P7.

Values in the library
materialvalue or classconditionspaper ids
IND, INDester, RTV, CIL / PHPH, LOR, CNZ with HPMCAS-MF at 1:15–17% / 60, 70, 90% complexedpH 6.0, 50 mM phosphatebapat2024 R12
cinnarizine with HPMCAS-MF12% (0.125:1) to ≈99–100% (≥1.5:1)pH 6.0bapat2024 R11, R12
cinnarizine with HPMCAS LF; HF30 → 95%; 70 → 98% (0.25:1 → 2:1)pH 6.0bapat2025a R9
bedaquiline with HPMCAS LF; MF, highest ratio≈96 / 94.5% (pH 6.0) to ≈7 / 5.5% (pH 10.5)bufferskaur2025 R5, R7
bedaquiline with HPMCAS LF in FaSSIF-V1; FeSSIF-V2≈25; 17% against ≈58.5 and 90% in the blank buffersbiorelevant fluidskaur2025 R6, R5
lumefantrine–polymer granules (Physical stability chapter)complex "could conceivably" explain low release, set aside because 20% loading dissolved much betterreleasetrasi2020 C43
Pitfalls and disagreements

The complex is measured in dilute buffer spiked from THF, at an unstated temperature or at 25 °C, not in a dissolving gel, so its link to release is a correlation across drugs and media bapat2024 X10, X13; kaur2025 X14. Complexation also fell in a stronger phosphate buffer at equal pH (about 70 to 48% for loratadine), which the authors take as a sign that the complex survives physiological ionic strength bapat2024 R16, C37, X11. The extent of complexation does not equal the loss of release: a "relatively low extent" can be "extremely detrimental" kaur2025 C45.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

interfacial free energy

The free energy per unit area (or length of a step edge) of the interface between a crystal or nucleus and the solution; a lower value gives a smaller critical nucleus and faster nucleation or growth, and the authors use it to explain why SDS speeds felodipine growth [schram2016 E3, C36]. New aspect (Physical stability): more generally, the free energy cost per area of creating an interface between a new phase (a nucleus or crystal) and its surroundings; in classical nucleation theory the thermodynamic barrier to nucleation grows with its cube [konno2006 E8, C33; baird2012 E2]. Additives can raise it (a polymer layer at a nucleus) or lower it (surfactants) [konno2006 C39; schram2016 C36]. Crystal–solution interface (formerly the page "crystal-solution interfacial free energy", from Crystallization from solution): the free energy per unit area of the boundary between a crystal or a crystal nucleus and the surrounding solution, written γ; in classical nucleation theory it enters the nucleation rate as \gamma^{3} in the exponent, so a small change in γ changes the rate steeply [duong2022b E6; indulkar2018 E6]. In the solution-crystallization papers it is the quantity through which surface-active additives are proposed to speed nucleation: lecithin adsorbing on the growing nucleus ("possibly"), SDS hemimicelles on the crystal surface ("is hypothesized to play a role") and phospholipid digests ("it is postulated") [indulkar2018 C40; indulkar2019b C33; enright2020 C26]. This content comes from the papers of 2018–2022 in Dissolution / D. Crystallization from solution; the free energy per area of a three-dimensional nucleus is distinct from the edge free energy per length of a two-dimensional nucleus used for step pinning (the felodipine edge value below). Interfacial tension (formerly the page "interfacial tension", from Crystallization from solution and Supersaturation from ASD dissolution), the name several papers use for the same quantity: the free energy per area of the interface between a crystal (or a crystal nucleus) and the solution, γ. It enters classical nucleation theory through the barrier \Delta G^{*} and the Kubota–Mullin effectiveness factor α through the surface excess energy [alonzo2012 E7; ilevbare2013c E4]. A surfactant that adsorbs at the crystal–solution interface lowers it, which can speed growth when this outweighs blocking of kink sites ilevbare2012a C51. The polymer is said to lower the surface tension needed to form the drug-rich phase of danazol, and SDS to lower the interfacial energy of felodipine; neither was measured [jackson2016 C36; schram2016 C36]. The danazol statement concerns the boundary of a liquid drug-rich phase, not of a crystal (synthesis: the drug-rich phase forms by liquid–liquid phase separation). New aspect (Supersaturation from ASD dissolution): the interfacial tension between an embryonic crystal and a water-saturated supercooled drug liquid is expected to be lower than against dilute aqueous solution, which together with the higher drug concentration favours nucleation in drug-rich droplets ("not unreasonable") [ilevbare2013d C40]. It enters the printed nucleation rate of the felodipine study as γ [konno2008a E3].

Findings

Crystallization from solution: F18, F22, F24, F34, F38, F39, F42. Physical stability: F4, F17. Supersaturation from ASD dissolution: F4, F13.

Related concepts

related to critical radius of a two-dimensional nucleus; general form of crystal-melt interfacial free energy; part of classical nucleation theory; sets the critical nucleus; related to kinetic barrier to nucleation, hemimicelle, mixed micelles, polymer-surfactant interaction, heterogeneous nucleation and drug-rich phase.

Formulas

critical radius of a two-dimensional nucleus (formula table only); classical nucleation theory, classical nucleation barrier, pre-exponential factor of classical nucleation theory, Kubota-Mullin impurity effectiveness factor. The critical nucleus radius r^{*} = 2\gamma\nu/(kT\ln S) follows from γ [duong2022b E9].

How it is measured or obtained

For felodipine the edge free energy γ = 3.9 × 10⁻²⁰ J/nm came from water and ethylene glycol contact angles (Wu harmonic mean, angles not printed) [schram2016 P9, R13, X10]. Not measured in the solid-state physical-stability papers, where it enters arguments only [konno2006 C39]. In solution, values follow from linearized nucleation-rate data [duong2022b E7]. The crystal–solution value is not measured directly in the library. One paper obtained it from the slope of \ln(J/S) against 1/\ln^{2}S fitted to induction times converted into nucleation rates, with a molecular volume of 920 ų and T = 310 K, for posaconazole in buffer and three intestinal media [duong2022b P15, E7]. The other papers infer a change of γ from shorter induction times, from pyrene signals of adsorbed surfactant, or from a cited surface tension of a medium (32.6 against 54.4 mN/m) [indulkar2019b R6, R7; enright2020 R32]. Not measured in the crystallization-from-solution papers that call it interfacial tension. For paclitaxel the crystal–water value could not be determined and literature values of representative compounds were used [que2018 C37]. Surface tension measurements were used only to find polymer adsorption on seeds [alonzo2012 P6]. Not measured in the ASD dissolution papers either [ilevbare2013d C40].

Values in the library
materialvalue or classconditionspaper ids
felodipine crystal edgeγ 3.9 × 10⁻²⁰ J/nm (contact angles, not printed); ρc 3.98 nm at S 425 °C[schram2016 R13, R14, X10]
atazanavir in lecithin media; with lecithin, lyso-PC and oleatelecithin "possibly" lowers the interfacial energy between solute and emerging crystal; proposed to be lowered, more by the digests; not measured3 mM STC, pH 6.5; bile salt media, pH 6.5[indulkar2018 C40, E6; enright2020 C26]
felodipine with polymera polymer-rich layer at the nucleus "may also increase" the surface penaltyargument[konno2006 C39]
felodipine solution with SDSfaster growth explained by a lower interfacial energyS = 4[schram2016 C36]
felodipine–PVPVA–TPGSTPGS lowering the energy between separated phases slows coarseningASD hydrationsaboo2021 C40
flutamide prenucleiunfavourable interfacial term outweighs the volume term below a critical radiusframework[trasi2012b C46]
posaconazole, PBS pH 6.53.52 mJ/m²37 °C, fit of the high-supersaturation induction times[duong2022b R16]
posaconazole, FaSSIF V1, FaSSIF V2, FeSSIF V12.61, 2.73, 3.24 mJ/m²; FeSSIF V2 not fittableas above[duong2022b R16, R15]
naproxen, acetaminophen, tolazamide, lovastatin, cefodizime sodium, prasugrel hydrochloride, spironolactone (cited)0.60–2.80 mJ/m²literature[duong2022b R18]
atazanavir with SDS hemimicellesproposed to be lowered; not measured0.075–0.3 mg/mL SDS[indulkar2019b C33, X4]
felodipine–HPMCγ, a and L of eq 7 not givenKubota–Mullin[alonzo2012 C27]
surfactants on ritonavirgrowth about twice as fast with TPGS or Tween 80 at 5 µg/mLseeded, S 7.6ilevbare2012a R17, C51
paclitaxel critical radius 5–7 nmfrom literature surrogates of γS 88[que2018 R15, C37]
supersaturated drugs in surfactant mediasurfactants should lower γ and speed nucleation; human fluid slowed it insteadclassical nucleation theory, 37 °C[elkhabaz2021 C20, C21]
Pitfalls and disagreements

The interfacial energy in SDS or HPMCAS solution was not measured [schram2016 X8]. The solid-state papers use homogeneous theory although nucleation in the films is "most likely heterogeneous" [konno2006 C33]. The papers disagree on whether γ carries the medium effect: the posaconazole fits find no trend of induction time with γ and assign the effect to the pre-exponential factor, whereas the lecithin, SDS and digest papers assume a lower γ [duong2022b C51, C52; indulkar2018 C40; indulkar2019b C33]. The fits rest on 3–9 points per medium, and γ also falls in the induction-time order for three of four media, so a γ contribution is not excluded [duong2022b X11, X12]. The human-fluid paper notes that surfactants that lower γ should speed nucleation, while human fluid slowed it, and adds an attachment-rate term [elkhabaz2021 C20, C22]. In the celecoxib work on polymer combinations the differences between polymers were not attributed to interfacial tension, because polymer adsorption on the nucleus would lower it and raise the nucleation rate, the opposite of what was observed; the point is argued, not measured [xie2015 C43]. This is opposite in sign to the felodipine argument that a polymer-rich layer at the nucleus "may also increase" the surface penalty [konno2006 C39] (synthesis: two papers assume opposite effects of polymer on γ; neither measured it). The lower interfacial tension in droplets is an expectation, not a measurement [ilevbare2013d C40]. Interfacial tension with and without polymer was not measured, and the text cites the wrong equation for it [xie2015 C43, X1]. The same γ is reported per area (mJ/m²) for three-dimensional nuclei and per length (J/nm) for the step edge of a two-dimensional nucleus, so the two kinds of value are not comparable [schram2016 R13; duong2022b R16] (synthesis: different units and geometry).

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

intramolecular hydrogen bonding

A hydrogen bond between two groups of the same molecule

It matters for polymer selection because it removes a donor or acceptor from the pool available to the polymer: the sulfonamide NH of nimesulide bonds to its own ether oxygen, which the authors say "considerably diminished" its capacity to bond to polymers and "most likely" explains why the polymers differ less than anticipated [kestur2011 C20, C27, C28]. Flufenamic acid holds its aniline N–H in a resonance-assisted hydrogen bond (N···O 2.682 Å in form III and 2.646 Å in form I, against a range of 2.66–2.74 Å for such bonds) and is therefore regarded as interacting only through its acid group [vaneerdenbrugh2010b R12, C12]. Further cases: the 5-OH and keto group of naringenin and the 5-OH and 3-OH of quercetin, which leave two and three phenolic OH groups free for the polymer [wegiel2013a M1, M2, C30]; the aniline N–H of flufenamic acid (DFT) and the energy profile of anthranilic acid, where one aniline hydrogen stays free [vaneerdenbrugh2011a R5, R6, C18]; and the OH of lumefantrine, bonded to its own nitrogen in the crystal hiew2022a R33, C61.

Findings

Miscibility and drug-polymer interactions: F14, F15, F17, F24, F25, F26. Physical stability: F18, F24.

Related concepts

part of hydrogen bonding; limits drug-polymer interactions and hydrogen-bond donor and acceptor groups; contrasts with self-association; makes acid-base interaction the alternative [wegiel2014 C44].

Formulas

none.

How it is measured or obtained

By a donor band that stays at the same wavenumber on a 100-fold dilution in a non-polar solvent (nimesulide NH at 3345 cm⁻¹, 1–100 mg/ml); by no change on adding a strong acceptor or donor (1-ethyl-2-pyrrolidinone, acetic acid); by comparing the band of the amorphous and crystalline forms; by crystal structure and DFT geometry [kestur2011 R10, R11, R12, R17, R19]. For flufenamic acid, from N···O distances in two crystal structures [vaneerdenbrugh2010b P11, R12]. By a conformer energy profile of the single molecule in vacuum [trasi2012b P9, R24]; by an IR band of the amorphous drug that matches the intramolecularly bonded form of the crystal [wegiel2014 R2, C11].

Values in the library
materialvalue or classconditionspaper ids
nimesulideNH 3345 cm⁻¹ at 1–100 mg/ml in dichloromethane; unchanged with added acid or lactamIR, 100 µm cell[kestur2011 R11, R17]
nimesulideNH ≈3288 (crystal), ≈3276 cm⁻¹ (amorphous)KBr; spin-coated film[kestur2011 R12]
flufenamic acidN···O 2.682 Å (form III), 2.646 Å (form I)crystal structures[vaneerdenbrugh2010b R12]
flutamide; curcumin (other chapters)intramolecular CH···O leaves a poor acceptor; intramolecular bond limits polymer bondingcalculation; IR, stability[trasi2012b C35; wegiel2014 C3]
naringenin, quercetin5-OH to keto O (both); 3-OH to keto O (quercetin); PVP still bonds the free OH (OH band 3138 and 3135 cm⁻¹)structure; IR[wegiel2013a M1, M2, R2]
anthranilic acidenergy about 31–33 kJ/mol up to 30° (acid O–H to N), about 50 at 80–90°, about 0 at 180° (N–H to carbonyl O); no bifurcated bondDFT dihedral scan[vaneerdenbrugh2011a R6, C18]
lumefantrineOH···N bond in the crystal; no PVPVA carbonyl shiftcrystal structures (cited); IRhiew2022a R33, R17
flutamideplanar lowest-energy conformer with the carbonyl next to C(5)–H; second minimum ≈2.7 kJ/mol higher; barriers ≈23 kJ/molDFT, vacuum[trasi2012b R23, R24]
flutamide crystalamide carbonyl in a bifurcated bond, one contact intramolecularcited structure[trasi2012b R26]
amorphous curcuminketo–enol band at 1626 cm⁻¹ as in the crystal; no carbonyl band near 1700 cm⁻¹IR[wegiel2014 R2, C11]
curcumin against resveratrol with PVPbonded PVP carbonyl dominant only at 60% curcumin, already at 50% resveratrolIR of films[wegiel2014 R8, R9, C32]

Evidence table: intramolecular hydrogen bonding.

Pitfalls and disagreements

For the amorphous state the evidence is that a broad band lies near the crystal's, and the crystal contains an intermolecular NH bond too [kestur2011 R19, R12]. The NH maximum shifts as much with PVAc as with PVP in the films, which weakens the argument that the intramolecular bond alone sets the polymer ranking [kestur2011 X16]. The treatment of flufenamic acid as purely acidic is an assumption supported by crystal geometry, not by a spectrum in the films [vaneerdenbrugh2010b C12]. An intramolecular bond limits but does not exclude polymer bonding when other donors remain (naringenin and quercetin bonded PVP strongly) [wegiel2013a R2, R4]. Whether the lumefantrine OH bond persists in the dispersion was not measured hiew2022a C61. No curcumin analogue without the intramolecular bond was tested, and within the curcumin paper PVP still gave the largest shifts [wegiel2014 X13]. For flutamide the bond in the glass is inferred from a vacuum calculation, and PAA's failure may reflect poor mixing instead [trasi2012b C35, X12].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

intrinsic dissolution rate

Evidence table: intrinsic dissolution rate. Content from the release-mechanism chapter (2018–2022) and two papers of the ASD process and Peptide permeability chapters.

The dissolution rate per unit area of a compact of one pure material, with one face of fixed area exposed; for a dispersion each component's rate divided by its weight fraction gives the rate per area "as if it were the pure material" bhardwaj2018 R4; saboo2020a E3. Bhardwaj and co-workers equate the ratio of the intrinsic dissolution rates of two solid forms with the ratio of their solubilities, carried over from polymorphs to amorphous against crystalline ITZ ("should be the same") bhardwaj2018 E3, C45.

Findings

Release mechanism and LoC: F1, F2, F11, F15, F18, F24.

Related concepts

basis of congruent release read-outs; related to the Noyes-Whitney equation; sets the ceiling of polymer-controlled release.

Formulas

surface-normalized release rate, ratio of intrinsic dissolution rates and of solubilities.

How it is measured or obtained

Compacts of 25–100 mg in an 8 mm die (face ~0.5 cm²), Wood's apparatus or a backed die, rate from the initial linear slope bhardwaj2018 P6, P7; saboo2019 P9, E4; saboo2020a P6. In the papers of 2020–2022 the neat PVPVA compact is run beside every series as the reference rate saboo2020 R3; correasoto2022a R18; correasoto2022b R3. The same surface-normalized rotating-disk method gave the dissolution rates of the enteric polymer HP-50, its salts and its miconazole dispersions qi2022 P10.

Values in the library
materialvalue or classconditionspaper ids
crystalline ITZ; melt-quenched ITZ2.8 ± 0.2; 51 ± 2 µg/min/cm² (ratio ≈18)0.1 N HCl, 37 °C, 300 rpmbhardwaj2018 R4, R5
PVPVA as received10.4 mg/min/cm² over 4.5 min (8.1 cited)samebhardwaj2018 R9, R10
PVPVA; amorphous nilvadipine3.49 ± 0.07; 0.002 mg/min/cm²pH 6.8, 100 rpm, 37 °Csaboo2019 R5
PVP, PVPVA, HPMC, HPMCAS, EUDS; amorphous felodipine≈3.6, ≈3.4, ≈0.37, ≈0.77, ≈0.23; ≈0.0008 mg/min/cm²pH 6.8 (EUDS 7.4)saboo2020a R13
OCA, SNAC, PVPVA (Peptide permeability)OCA about twice SNAC; neat OCA above neat PVPVApH 6.8, 0.5 cm²bapat2025b C2, C12
amorphous ritonavir against 20% ritonavir–PVPVA (ASD process, cited)amorphous drug significantly sloweras citedbenson2025 R24
neat PVPVA (indomethacin; ester series)≈3.4; ≈3.8 mg/min/cm²5-min rates, 37 °Csaboo2020 R3
neat PVPVA≈2.6–2.7 mg/min/cm²compactscorreasoto2022a R18
neat PVPVA at 37 and 55 °C≈2.7; ≈3.7 mg/min/cm²compactscorreasoto2022b R7
neat PVPVA at 37 and 5 °C≈3.45; ≈1.68 mg/min/cm²compactsyang2021 X16, R21
HP-50; nine HP-50 salts≈0.92; ≈2.35–3.09 mg/min/cm²compacts, 50 mM pH 6.8 phosphate, 37 °Cqi2022 R10
HP-50-BIS-TRIS, 20–100 mol% base≈1.22 → 2.93 mg/min/cm²sameqi2022 R13, X9
Pitfalls and disagreements

The neat PVPVA values differ with medium, paddle speed and compact mass (10.4, 3.49 and ≈3.4 mg/min/cm²), and an extractor check of the 2020 curve gives ≈1.7 bhardwaj2018 R9; saboo2019 R5; saboo2020a X10. The visible part of the 2018 PVPVA curve corresponds to about 8 mg/min/cm² bhardwaj2018 X8. The amorphous-to-crystalline ITZ solubility ratio behind the rate ratio was not measured bhardwaj2018 C45. Packed particles present a renewed surface, so the rate reflects layers of particles bhardwaj2018 C64. Ueda 2024 (p. 44) exclude these rate methods from measuring the amorphous solubility: intrinsic dissolution rates of multicomponent systems do not reflect it, because of their phase behavior, and those of crystalline poorly soluble drugs are typically inaccessible.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

ionization

The fraction of a drug that carries a charge at the pH of the medium, set by the pKa through the Henderson–Hasselbalch equation. In this chapter the un-ionized concentration is what the amorphous solubility limits: "LLPS cannot occur until the concentration of the un-ionized form is exceeded", so more total drug is needed at lower pH for a base [indulkar2015 C47]. An ionized second solute does not mix into a hydrophobic drug-rich phase [trasi2015a C44]. The papers of 2017–2022 add pazopanib (strongest basic group pKa 6.4): fully ionized in gastric fluid and essentially un-ionized at pH 8.4, with a crystalline solubility that falls by more than four orders of magnitude between pH 1.2 and 6.5 [sugihara2018 M1, C9, C19]. New aspect (Bioperformance): only the unionized free drug is thought to cross a membrane passively [raina2015c C49]. In a PAMPA receiver at pH 3 atazanavir (pKa 4.48) ionizes on crossing and keeps the receiver free drug near zero hate2022 C52. Most model drugs of the Bioperformance papers were unionized or nearly so at the pH used (synthesis: from the table rows below). New aspect (Crystallization from solution): In the pH-shift studies the ionization of a weak acid or base sets the supersaturation: raising the pH of a base (or lowering that of an acid) beyond the pKa leaves the less soluble neutral form above its crystalline solubility; the final pH was at least two units beyond the pKa [hsieh2012 C1; hsieh2014 P2]. In the growth and nucleation papers the ionization of the polymer matters instead: the carboxylated cellulose esters are nearly fully ionized at pH 6.8 and less than 25% ionized at pH 3.8, whereas the drugs are un-ionized at both (see polymer ionization) [ilevbare2013b R18, C33]. Media were chosen to keep 11 drugs un-ionized (naproxen about 18%, indomethacin about 9% and compound 1 about 20% still ionized by the card's arithmetic); celecoxib is about 7.5% ionized at pH 10 and flibanserin 80% un-ionized at pH 6.5 [chen2015 C6, X3; li2016a R3]. New aspect (Release mechanism and LoC): ionization of the dispersion polymer rather than the drug. For the enteric polymer HP-50, partially neutralized BIS-TRIS salts dissolved more slowly as ionization fell from 100 to 20%, with the largest drop, almost 2-fold, from 100 to 80% qi2022 C21, R13; the series "confirms" the importance of the ionized form, and the critical ionization of about 83% estimated for HP-50 "may explain" the drop qi2022 C36. Polymer solubilization via ionization, linked to transport of protons across the boundary layer, is called the rate-limiting step of HP-50 dissolution qi2022 C2. For weak bases with HPMCAS the 2024–2025 papers compute ionization at the gel pH from pKa: at pH 6.0 HPMCAS about 96% (printed), cinnarizine above 99%, clotrimazole 46% and loratadine 14%; loratadine complexation fell with its calculated ionization from about 20% (pH 5.8) to 0.5% (pH 7.5) bapat2024 R19, X4; bapat2025a R13, C32. Bedaquiline was about half protonated (55 ± 4%) in its complex with HPMCAS and in a dry dispersion (52 ± 7%) by XPS kaur2025 R20.

Findings

Amorphous solubility and LLPS: F10, F11, F13, F14, F23. Bioperformance: F1, F11, F22, F26. Crystallization from solution: F1, F2, F11, F16, F28, F29, F44. Release mechanism and LoC: F24, F32, F33.

Related concepts

quantified by pKa; gives pH-dependent solubility; calculated with the Henderson-Hasselbalch equation; sets the amorphous solubility in total-concentration terms. Related to pH-shift dissolution and polymer dissolution pH threshold. Related to polymer ionization and pH-induced precipitation; of the polymer: critical ionization for polymer dissolution. Of the polymer: critical ionization for polymer dissolution, polymer salt formation, microenvironmental pH.

Formulas

Henderson-Hasselbalch equation, pH-solubility profile. Amorphous solubility advantage with water-sorption correction (ionization term).

How it is measured or obtained

Calculated from the pKa and the pH; the pKa of atazanavir was measured by UV-metric titration in 0.15 M NaCl at 37 °C, the others were taken from the literature or predicted [indulkar2015 P2, E1]. In the Bioperformance papers the ionization is taken from the pKa and not measured: felodipine pKa below 2 and nifedipine below 3.5 at pH 6.8 [raina2014a C9, E4]; ezetimibe phenol 9.72 [elkhabaz2017 C6]; nevirapine 2.8 [hate2017 C8]; clotrimazole about 6, 99% unionized at pH 8 [indulkar2016 C8]; atazanavir 4.52 or 4.42 hate2018 C15, X1. In the pH-shift studies: pKa by UV-metric titration (and cosolvent extrapolation for the poorly soluble bases) at 37 °C and 0.15 M KCl; the neutral-species concentration by mass and charge balance [hsieh2012 P1, P2, P3, P4]. In the release-mechanism papers: degree of ionization set by the amount of base used to make the partial salt, not measured qi2022 X9. Henderson–Hasselbalch from pKa kaur2025 E2; bapat2025a P11; XPS N 1s with a protonated component near 402 eV kaur2025 R19; bapat2024 R8.

Values in the library
materialvalue or classconditionspaper ids
clotrimazole98.7% ionized at pH 4; 0.8% at pH 8pKa 5.89[indulkar2015 R18]
atazanavir90.9% ionized at pH 3.5 (91.3% recalculated); 0.0% at pH 9pKa 4.52[indulkar2015 R18, X4]
nicardipine94.1% at pH 6; 0.9% at pH 9 (1.6% recalculated)pKa 7.2[indulkar2015 R18, X4]
ritonavirun-ionized at pH above 7.0pKa 1.8 and 2.6ilevbare2013a C13
diclofenacionized at pH 6.8; did not mix with the ritonavir-rich phasepKa 4.2[trasi2015a M5, R11]
CRH1un-ionized and ionized equal at equilibrium at pH 4.6pKa 4.6[almeidaesousa2016 C13]
pazopanibdissolves in SGF (pH 1.2); essentially un-ionized at pH 8.4pKa 6.4[sugihara2018 C9, C19]
felodipine, nifedipineionization term set to 1pH 6.8[raina2014a C9]
clotrimazoleabout 99% unionizedpH 8[indulkar2016 C8]
ezetimibebuffer solubility measured at pH 2 because of degradation at neutral pH[elkhabaz2017 C9, X5]
atazanavir, clotrimazoleamorphous solubility rises as pH falls toward the pKa; ratio constant[indulkar2015 C46]
atazanavirpH 3 receiver acts as a sink like 2% SDSPAMPA, pKa 4.48hate2022 C52, R15
bifonazole; carvedilol; clotrimazole; clozapine; dipyridamolepKa 6.22; 7.75; 5.89; 3.83 and 7.54; below 1 and 6.0837 °C, 0.15 M KCl[hsieh2012 M1–M5]
droperidol; ketoconazole; loratadine; papaverine; pyrimethaminepKa below 2, 7.38 and 10.96; 3.16 and 6.13; 5.26; 6.29; 7.07same[hsieh2012 M6–M10]
papaverine; dipyridamole; glyburide; warfarinpKa 6.4; 6.2 and 0.8; 4.9; 5.325 °C[hsieh2014 M1–M4]
final pH of the 2014 pH shifts8.4–9.0 (papaverine), 8.2–9.0 (dipyridamole), 1.9–2.9 (glyburide), 2.2–3.3 (warfarin)1 mg/mL polymer[hsieh2014 R4]
naproxen, indomethacin, compound 118%, 9%, 20% ionized (extractor arithmetic)pH 3.5, 3.5, 4[chen2015 X3]
posaconazolepKa 3.6 and 4.6 (cited); unionized at pH 5.5–7.5; crystalline 0.31–0.34 µg/mLFaSSIF-V2 buffer, 37 °Cshah2025 M1, R1, C9
posaconazolefitted pKa 3.53 and 1.24 at 37 °C, 0.14 M; crystalline 0.27 (pH 7.0) to 347 µg/mL (pH 1.0)phosphate buffers pH 1.0–7.0[duong2022b R2, R1]
HP-50-BIS-TRIS, 20–100 mol% baserate ≈1.22 → 2.93 mg/min/cm²50 mM pH 6.8 phosphate, 37 °Cqi2022 R13
cinnarizine in HPMCAS-MF 25%protonated 0 (neat), 20 (dry dispersion), 11% (after partial dissolution)XPS N 1sbapat2024 R8
bedaquiline: free base, complex, dry 40% dispersion4, 55, 52% protonatedXPS N 1skaur2025 R20
HPMCAS and bedaquiline at pH 6.0 and 5.891.5 / 88.1% and above 99% ionizedHenderson–Hasselbalchkaur2025 R21, X18
Pitfalls and disagreements

Loratadine (pKa 5.0) may be partly ionized at the final pH 4–6 of the pH-shift runs, although the paper calls it un-ionized ilevbare2013a C13, X9. Two printed percentages in the weak-base table do not match their pKa [indulkar2015 X4]. The atazanavir pKa is printed as 4.52 or 4.42 in one card and as 4.48 in the PAMPA study hate2018 X1; hate2022 C52. Dipyridamole's pKa is "<1" in one table and 0.8 in the model inputs [hsieh2012 X10]. The charge of the polymer at the final pH (cationic Eudragit E100 at pH 2–3, anionic polymers at pH 8–9 with the bases) was not varied independently [hsieh2014 R4]. The plotted quantity is mol% BIS-TRIS added, read as % ionization, and the 0% point is HP-50 in sodium phosphate buffer, not a salt qi2022 X9. Several printed ionization values do not reproduce from the stated pKa (HPMCAS 96% printed against about 93%; 88.1% for HPMCAS at pH 5.8) bapat2024 X4; kaur2025 X18.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

kinetic barrier to nucleation

The activation energy for moving molecules across the nucleus–matrix interface, \Delta G_a in classical nucleation theory, related to diffusivity or reciprocal viscosity; distinct from the thermodynamic barrier set by interfacial energy and driving force [konno2006 E8, C33; marsac2006a E9, C31]. Experimentally the Arrhenius activation energy of the nucleation rate is used as its measure [marsac2006a R3, E2].

Findings

F1, F2, F4.

Related concepts

part of classical nucleation theory; contrasts with thermodynamic driving force for crystallization; related to molecular mobility and polymer rejection at the crystal growth front.

Formulas

classical nucleation theory, Arrhenius equation.

How it is measured or obtained

Not measured directly; nucleation rates at several temperatures give an Arrhenius slope, taken separately above and below Tg [marsac2006a P5, R2, R3]; otherwise argued from the size of a polymer effect at low content [konno2006 C40, C41].

Values in the library
materialvalue or classconditionspaper ids
nifedipine, felodipineactivation energy below Tg 122 (11) and 145 (3) kJ/mol; above Tg 78 and 95Arrhenius, ≈25–75 °C[marsac2006a R3]
with 3 wt% PVPbelow Tg 127 and 201; above Tg 103 and 111 kJ/molsame[marsac2006a R3.c, R3.d]
felodipine with 3–25% PVP, HPMCAS, HPMCspeculated rise of ΔGa, set by amount rather than type of polymer22 °C, dry[konno2006 C40, C41]

Evidence table: kinetic barrier to nucleation.

Pitfalls and disagreements

The Arrhenius plot carries no rate unit and its temperatures are given only by the axis; the activation-energy difference between the two drugs is significant only below Tg, a restriction the abstract drops [marsac2006a X2, X6]. The polymer-raised barrier is speculation ("it seems reasonable to speculate") [konno2006 C40].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

kinetic trapping

A state that persists because molecular mobility is too low for the system to reach its equilibrium state; here, a glassy dispersion whose phase state, mixed or separated, was fixed by how it was made. After solvent removal both phases of an itraconazole–HPMC film are glassy at room temperature (Tg 60 °C for amorphous itraconazole, 140 °C for HPMC), so a phase-separated film "would be expected to persist" even if mixing were favoured, and a miscible glass made by heating and cooling would "very likely" be trapped in the same way [purohit2015a C46, C47, M1, M2]. The authors say it is "very hard to determine" whether the separation is kinetic (solvent-induced) or thermodynamic [purohit2015a C48]. Outside the subcategory, itraconazole–HPMC was thermodynamically miscible as a dry binary but became trapped in a phase-separated state when made from a water-containing solvent [mugheirbi2017 C39, C41]; drug droplets in evacetrapib–HPMC films stay trapped after the water has gone, and the apparent miscibility of other films "may be" a trapped metastable state [li2017 C38, C43]; and a dry PVP dispersion would be a trapped one-phase glass if its moisture-induced separation were purely kinetic rumondor2009c C36. In telaprevir films the authors prefer spectral mixing to a trapped, non-equilibrium composition as the reason why the dispersed-phase spectra look richer in drug at higher loading ("a more likely explanation") [li2016c C21]. New aspect (ASD process): drug droplets that separate while the solvent is present cannot remix when the solvent has gone and stay as drug-rich domains [li2017 C38; mugheirbi2017 C39, C41]. The converse reading, that a dry "miscible" film is itself a trapped state that water unlocks, was judged "less likely" [li2017 C43]. For delamanid free-base ASDs the solvent evaporation rate decides whether material is trapped before nucleation and growth duong2022a C45.

Findings

Miscibility and drug-polymer interactions: F18, F19. ASD process: F1, F2, F6.

Related concepts

contrasts with equilibrium drug-polymer miscibility; acts in amorphous-amorphous phase separation; related to kinetic stabilization and to the glass transition temperature. Follows solvent-induced phase separation and moisture-induced phase separation.

Formulas

none.

How it is measured or obtained

It is not measured. It is inferred from the glass transition temperatures against the preparation and storage temperatures, from remixing on heating above Tg (films made transparent and uniform after 2 min at 165 °C), and from the dependence of the phase state on solvent, water content and drying rate [purohit2015a C46, R1, R5, R12; mugheirbi2017 C39]. In the 2017 film paper, persistence of domains after drying and remixing on heating were used (170 °C for 1 min removed ECP domains, data not shown) [li2017 R10, C12].

Values in the library
materialvalue or classconditionspaper ids
itraconazole, HPMCTg 60 and 140 °C, both glassy at room temperatureDSC, midpoint[purohit2015a M1, M2, C46]
itraconazole–HPMC 10:90 to 50:50domains removed by 2 min at 165 °C; pyrene I/III 1.39–1.42 → 1.50–1.53spin-coated films[purohit2015a R1, R12, C38]
itraconazole–HPMC, dry against water-containing solventmiscible as a dry binary; trapped separated state with waterfilms, spray-dried particles[mugheirbi2017 C39]
evacetrapib–HPMCdrug droplets stay trapped when the water has goneternary diagram argument[li2017 C38]
felodipine–PVPdry glass as a trapped one-phase mixture that water plasticises enough to separateargumentrumondor2009c C36
delamanid free-base ASDssolvent evaporation rate decides whether material is trapped before nucleation and growthrotary evaporationduong2022a C45

Evidence table: kinetic trapping.

Pitfalls and disagreements

No χ, phase diagram or drying-solvent composition was measured to separate the kinetic from the thermodynamic reading, and a methanol–tetrahydrofuran film separated like the methanol–dichloromethane one [purohit2015a C47, C45, R2]. The dry-binary result of the later water study suggests that the separation of itraconazole–HPMC films belongs to the preparation rather than to limited miscibility [mugheirbi2017 C39]. The statement that a heated and cooled film is a trapped miscible glass was not tested by a long-term storage experiment [purohit2015a C46]. In the evacetrapib films the reading that apparent miscibility is a trapped state ("may be") and the converse reading, a dry film that water unlocks ("less likely"), are both given by the same paper [li2017 C43]. No phase diagram of the drying path was measured, so what is trapped is inferred [mugheirbi2017 C41, X4]. Heating-induced remixing is "data not shown" [li2017 X13].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

kinetic versus thermodynamic control of crystal growth

Growth of a crystal from a supercooled liquid needs both mobility and a driving force: near Tm mobility is high and the driving force low (thermodynamic control), and on cooling the driving force rises while mobility falls (kinetic control) [mosqueragiraldo2014 C25]. Felodipine growth that slowed on cooling over 70–110 °C was read as transport-limited [kestur2010b C22, C23]. In the indomethacin polymorph paper mobility limits growth below the temperature of fastest growth and the driving force above it, and the steep rise of polymer inhibition above that temperature is placed in the second region [tian2017 C22, C35, C36].

Findings

F3, F22, F29.

Related concepts

depends on thermodynamic driving force for crystallization and molecular mobility; related to melting point depression and degree of supercooling; contrasts with Tg-scaled crystal growth rate.

Formulas

temperature of maximum crystal growth rate.

How it is measured or obtained

From where growth peaks between Tg and Tm and from how an additive's effect changes with temperature [trasi2012a C35; mosqueragiraldo2014 C36].

Values in the library
materialvalue or classconditionspaper ids
celecoxib with 10% TPGS and 10% PVPcelecoxib Tm 151.49 °C (12 °C depressed); growth about 0.03 of PVP alone at 120 °C, 0.6 at 70 °Cseeded melt growth[mosqueragiraldo2014 R5.f, R2.b, X5]
celecoxib with 3, 5, 7% PVP, with and without TPGSpaired curves cross at 110, 100, 90 °Csame[mosqueragiraldo2014 R3, R4, C14]
felodipine form IIgrowth falls on cooling from 105 to 70 °C although the driving force risesmelt films[kestur2010b C22, C23]
acetaminophengrowth maximum closer to Tm, nucleation at larger supercoolingclassical picture[trasi2012a C35]
indomethacin α with 10% HPMCfastest growth moved from 135 to 100 °C; ratio without/with polymer ≈11 (100 °C) → ≈2900 (120 °C)melt growth[tian2017 R15, R12]
Pitfalls and disagreements

The driving force was not calculated for the celecoxib mixtures, and melting-point depression alone does not order them [mosqueragiraldo2014 C33, X13]. The celecoxib growth temperatures were assumed to lie in the mobility-controlled range [mosqueragiraldo2014 C26].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

lever rule

Evidence table: lever rule. Content from the release-mechanism chapter (2023–2025), with rows from the Physical stability chapter.

The rule that gives the relative amounts of two coexisting phases from the position of the overall composition on the tie line joining them: the ratio of the amount of phase A to phase B equals the ratio of the lengths BX to AX yang2022b E1. In the Physical stability chapter it was used on a schematic ritonavir–PVPVA–water diagram to argue that relative phase amounts set bicontinuous or discrete morphology along different hydration paths yang2022b C50. In the 2023 phenolphthalein-analogue paper the majority phase after separation is the binode closer to the initial composition: a polymer/drug ratio above the plait point gives a majority hydrophilic phase with discrete hydrophobic domains, one below it a majority hydrophobic phase, and the hydrophobic-phase volume against drug load is "approximately" a step function with the step at the plait point deac2023b C34, C36. Used quantitatively in 2024: along a hydration path at constant drug-to-polymer ratio the lever rule at the spinodal gives the mass fraction of drug-rich phase, W^{\alpha} = (W_i^T - W_i^{\beta})/(W_i^{\alpha} - W_i^{\beta}), taken as continuous above 0.5 deac2024b E12, P20, C51; in 2023 it was used on a schematic ritonavir diagram with and without SDS yang2023 E2, C41.

Findings

Release mechanism and LoC: F27, F30, F31.

Related concepts

needs a tie line on the ternary phase diagram; its step lies at the critical point; decides phase inversion.

Formulas

lever rule.

How it is measured or obtained

Applied in 2022 and 2023 to schematic ternary diagrams only; no tie line was measured in those papers deac2023b E5, X14; yang2022b E1. In 2024 applied to computed PC-SAFT diagrams deac2024b E12, P20.

Values in the library
materialvalue or classconditionspaper ids
ritonavir–PVPVA–water, schematic (Physical stability chapter)relative phase amounts set bicontinuous against discrete morphologyargument onlyyang2022b C50
phenolphthalein analogue–PVPVA–water, schematichydrophobic-phase volume steps at the plait pointargument onlydeac2023b C36
MePHPH–PVPVAW^{\alpha} ≈0.15 at 27% → ≈0.82 at 39.5%PC-SAFT diagram, spinodal onsetdeac2024b R35
PHPH–PVPVA≈0.16 at 3.0% → ≈0.82 at 4.5%samedeac2024b R35
Pitfalls and disagreements

The 2023 use assumes complete separation to the binodal compositions as soon as the hydration path enters the two-phase region deac2023b E5, and on phases reaching equilibrium as fast as water penetrates, the local equilibrium assumption deac2023b C38. No computed MePHPH point lies between 27 and 39.5% except the critical point, and the fraction comes from the model only deac2024b X8, X16.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

limit of congruency

The highest drug loading at which a dispersion still releases drug and polymer congruently; for ritonavir–PVPVA it is 25% DL indulkar2019a C2; li2020 R23. The ritonavir spray-drying paper uses it as the reference point: phase separation has its largest effect on release at or below the limit, and above it release is already as slow as the neat amorphous drug li2020 C67, C66. For bicalutamide–PVPVA the limit was not located; drug and polymer released together at 5 and 10% DL and apart at 20% moseson2022b R6, R7, X15. Benson (2025) studied 10 and 20% DL ritonavir–PVPVA coated powders and tablets below the limit of 25% and describes coated tablets as having a lower effective limit benson2025 C34. New aspect (Release mechanism and LoC): defined by Indulkar and co-workers (2019) as the highest drug loading at which congruent release is observed, 25% for ritonavir–PVPVA indulkar2019a C2. Each value is the last congruent loading tested, so the switch lies inside the next step indulkar2019a X7; saboo2020a X11. The 2019 dihydropyridine study calls it the "drop-off" loading below which formulations must stay if rapid release is required saboo2019 C33. Across the papers of 2018–2020 it was not set by drug log P or molecular weight saboo2019 C35; que2019 C48, was raised by a surfactant in the dispersion que2019 C12, was absent up to 50% felodipine with HPMCAS and Eudragit S 100 saboo2020a R15, and coincided with water-induced phase separation of films, which the authors read as its cause ("likely") saboo2020a C43; indulkar2019a C33. Papers of 2020–2022 relate it to drug–polymer hydrogen bonding (analogues with donors 5–10% against 25–40% without) saboo2020 C14, C48; que2021 R19, C33 and to the drug's Tg against the dissolution temperature (cooling below the wet Tg lowered it) saboo2020 C51; yang2021 C35, raise it with surfactants inside the dispersion saboo2021 C16; correasoto2022a C55; correasoto2022b C12, and find that salt formation raising the Tg of lumefantrine lowered it hiew2022b C42. It is also expressed per mole que2021 E3. The 2022 ritonavir surfactant paper calls strategies to raise the limit "essential" for all but the most potent compounds, and showed rescue at one loading above it (30%) without locating a new limit indulkar2022 C5, A1. Yang and co-workers (2022) tied the ritonavir limit (cited 25%) to the loading at which the drug-rich phase at the gel surface becomes continuous yang2022a C15, C58. Plasticizers raised the limit of the high-Tg drugs atazanavir and ledipasvir three- to fivefold and that of low-Tg ritonavir 1.2-fold correasoto2023 R16, C12, C17. For MePHPH–PVPVA the drug content of the gel rose at 40 and 50%, which suggests a true limit below the cited 40% although at least 80% release is still reached at 40% deac2023a C14, R3, R14. For four phenolphthalein analogues the limit trends with the PVPVA content of the hydrophobic phase formed by water-induced separation, and strong drug–polymer interactions are proposed to lower it by shifting the plait point to a lower drug/polymer ratio deac2023b C67, C63. The papers of 2023–2025 add two causes beside drug–polymer interactions and drug Tg: the polymer's molecular weight (clotrimazole–PVP below 5% with K12 and K17, 20% with K25 and about 33–38% from K29/32, near the entanglement weight) and the critical point of the drug–polymer–water phase diagram, whose loading followed the cited limits of four phenolphthalein analogues within 7% deac2024a R12, C37; deac2024b R37, C59. The PVP paper defines the limit operationally as the highest loading releasing more than 80% of the drug deac2024a C36.

Findings

ASD process: F21, F38, F48. Release mechanism and LoC: F6, F7, F8, F9, F10, F11, F13, F14, F17, F18, F19, F21, F22, F25, F26, F27, F29, F30, F31.

Related concepts

ends congruent release; above it release is incongruent and drug-controlled. Marked by the falling-off-the-cliff effect; proposed to follow from phase separation kinetics of the hydrating surface; above it a drug-rich barrier layer forms; not ranked by lipophilicity; lowered by drug-polymer hydrogen bonding; depends on the wet glass transition temperature against the test temperature; set by phase inversion near the critical point, or lower by nanodroplet agglomeration when chains are below the critical entanglement molecular weight.

Formulas

molar drug loading, surface-normalized release rate, mole-based limit of congruency.

How it is measured or obtained

From the last drug loading in a series with congruent release of drug and polymer; the criterion varies (simultaneous release; at least 80% of drug released) and each value is the last loading tested, so the threshold lies between it and the next loading deac2024a C36; saboo2020a X11; hiew2022a X17. In the release-mechanism papers: from a loading series dissolved as constant-area compacts with drug and polymer assayed (see F1); an earlier film study read the same switch from LLPS in the medium indulkar2019a A1; saboo2019 A2; purohit2017b R11. Loadings can be expressed in mol% saboo2019 E1. Later criteria: last congruent loading by 5-min rates saboo2020 C14; congruent with at least 80% of the drug in 90 min que2021 P9; highest loading without a significant drug–polymer difference by t-test yang2021 P17; highest loading with good drug release, no stated criterion hiew2022b X6.

Values in the library
materialvalue or classconditionspaper ids
ritonavir–PVPVA25% DL; 30% initially congruent then incongruenttablets, pH 6.8, 37 °Cindulkar2019a C2, C32
felodipine, five polymersPVP 10, PVPVA 15, HPMC 10% DL; HPMCAS and EUDS no limit to 50%30% DL test setsaboo2020a R15
ledipasvir–PVPVA5% DL (between 5 and 7.5%); 30% with 5 wt% SDS (5 parts per 100 parts drug and polymer); 7.5% with poloxamer 407compactsque2019 C10, R9, C12
atazanavir–PVPVA5% DL; 10–15% with surfactants (10% with SDS or CTAB, 15% with Span 80)compactscorreasoto2022b C12
clopidogrel–PVPVAabout 40% DL; 50% with SDScompactscorreasoto2022a C46, C55
lumefantrine–PVPVA35% DLcompactshiew2022a C31
loratadineHPMCAS 20% at 37 °C, 5% at 5 °C; PVPVA 30% and 2%compactsyang2021 R22
BCL–PVPVAbetween 10 and 20% DL (not located)powders, polymer by size-exclusion chromatographymoseson2022b R6, R7, X15
coated RTV–PVPVA tabletseffective limit described as below the 10 and 20% DL studiedconfocal, tabletsbenson2025 C34
ITZ–PVPVAswitch between 25 and 20% (spray-dried), 20 and 10% (melt-extruded)0.1 N HCl, compactsbhardwaj2018 X6, R4
ritonavir films with PVP; PVPVALLPS up to 20%; only at 10%25 °C, 100 mM pH 6.8purohit2017b R10, R11
nilvadipine; cilnidipine in PVPVA10% (6 mol%); 15% (7 mol%); switch at about 6–9 and 7–9 mol%pH 6.8, 37 °Csaboo2019 R5, R6, C14
indomethacin; its methyl ester in PVPVA10%; at least 25% (5-min rates)37 °Csaboo2020 C14, P5
indomethacin–PVPVA10% (25–57 °C), 5% (17 °C), below 5% (10 °C)temperature seriessaboo2020 R29
PHPH, TIPP, Me-TIPP, Me-PHPH in PVPVA5, 10, 30, 40%; 0.016, 0.012, 0.035, 0.115 mol per 100 gpH 6.8 (TIPP 2.5)que2021 R19, R20, P9
felodipine–PVPVA with 0, 2, 5, 10% TPGS15, 25, 35, 45%pH 6.8saboo2021 R12, P6
lumefantrine free base; eight salts in PVPVAat least 35%; 2–25%drug release onlyhiew2022b R20, X7
atazanavir–PVPVA with 5 g plasticizer per 100 g5 → 7.5–25% (citrate esters 20–25%)compacts, pH 6.8, 37 °Ccorreasoto2023 R1, C12
ledipasvir–PVPVA with 10 g TEAC, TBC; GTB5 → 15; 20%samecorreasoto2023 R11, C17
ritonavir–PVPVA with 5 g GTB or TBCcomplete release at 30%, not at 35% (cited limit 25%)samecorreasoto2023 R14, R16
MePHPH–PVPVA 40%; 50%gel drug content 40 → 49%; 50 → 59.5% over 30 minscraped gel, dry basisdeac2023a R3
PHPH, TIPP, MeTIPP, MePHPH–PVPVAlimit 5 / 10 / 30 / 40% (cited) against PVPVA in nanoparticles ≈77 / 36.5 / 9 / 5 wt%nanoparticles at 60 °Cdeac2023b R8, R3
clotrimazole–PVP K12, K17, K25, K29/32, K60, K90<5, <5, 20, ≈33, 35, ≈38%compacts, pH 8.0, >80% drug in 90–120 mindeac2024a R12, X5
PHPH, TIPP, MeTIPP, MePHPH in PVPVAcited 5, 10, 30, 40% against critical-point loadings ≈3.7, 13.7, 32.6, 33.2%PC-SAFT phase diagrams, 37 °Cdeac2024b R37
ritonavir–PVPVA + 10 parts Span 20 or Span 85between 30 and 40% (cited 25% without)compacts, pH 6.8yang2023 R2, R1
Pitfalls and disagreements

The limit depends on temperature, drug, polymer and additives, and on how it is defined; the lopinavir–HPMC films of F14 show that phase separation can raise release above a loading at which the miscible film is already drug-controlled li2019 R2. For ritonavir–PVPVA the next loading above 25% was 30% in the later release studies yang2022a C15. For coated ritonavir–PVPVA tablets the shift is inferred because polymer release was not measured benson2025 X18. The ritonavir release at the first failing loading (30%) differed about 1.6-fold between two series indulkar2019a X3. The molar loadings of the dihydropyridine study cannot be reproduced with one convention saboo2019 X2. The coincidence of interaction saturation with the ledipasvir limit "may be coincidental" que2019 C45. The link to water-induced phase separation rests on films and humidified compacts, not on dissolving tablets indulkar2019a X6; saboo2019 X10. The same pair gave different limits by LLPS in films at 25 °C and by congruency in tablets at 37 °C (ritonavir–PVPVA, 10–20% against 25%) purohit2017b R11; indulkar2019a C2. Limits from 5-min rates and from 30-min release differ for a fast crystallizer saboo2020 X7, R8; hydrogen bonding and Tg go together across drugs and are hard to separate yang2021 C25; correasoto2022a C49. In the 2022 ritonavir imaging paper release below 30% was measured only at 20%; the 25% limit is cited yang2022a X7. The MePHPH limit is given as 40% from an earlier paper, while the methods of the 2023 interface paper call 30% "at the LoC" deac2023a X1. The plait-point mechanism is drawn on schematic diagrams; no ternary diagram, tie line or plait point was measured deac2023b X14. The phase-diagram paper did not measure release: its limits are cited, and the MePHPH data it shows place the limit only between 30 and 50% deac2024b X9. In the PVP paper the 80% criterion is applied at an unstated time in tests of 90 or 120 min, with some profiles still rising deac2024a X6. For ledipasvir with SDS the 2019 study gives 5 → 30% que2019 C10, C12, while the 2023 surfactant paper cites the gain as 7.5 → 30% yang2023 R27. The PHPH critical-point loading is 3.7% as the paper states; read from its PHPH–PVPVA–water diagram (about 2.6 wt% PHPH, 59.5 wt% PVPVA) it is about 4.2% (synthesis: 2.6/(2.6 + 59.5) ≈ 0.042), see critical point deac2024b R37.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

lipophilicity

The affinity of a drug for lipid over water, written as log P of the neutral species. In these papers it is a descriptor used to explain solubility, membrane partitioning and transport, and it is quoted or calculated rather than measured [hate2022 C36, C53; alkalla2026 C18, C33]. In a membrane cell a high log P means a large membrane partition coefficient, so that the unstirred water layer rather than the membrane limits transport (F21) hate2022 C44, C53. For polymers the corresponding idea is polymer hydrophobicity. In the growth-inhibition papers of 2012–2013 it places three model drugs on a hydrophobicity scale that is then compared with the solubility parameters of the polymers [ilevbare2013b M1–M3; ilevbare2013c M1–M3]. New aspect (Release mechanism and LoC): drug lipophilicity was tested as a predictor of the limit of congruency. Saboo and co-workers (2019) hypothesized that the more hydrophobic drug lowers the hydrophilicity of the drug–polymer blend faster with composition and so releases congruently over a smaller loading range saboo2019 C6; for nilvadipine and cilnidipine in PVPVA the hypothesis was "incorrect for the systems evaluated" saboo2019 C35. Que and co-workers (2019) found that the limit "does not appear to depend" on hydrophobicity or molecular weight que2019 C48. Within congruent release at 40% in HPMCAS, by contrast, drug and polymer release fell with drug log P, which the authors read as support that hydrophobicity influences release "at least" in such systems saboo2020a C19, C32. Papers of 2021–2022 found no log P trend across four phenolphthalein analogues and six drugs, and conclude that log P "shows little indication" of dispersion performance que2021 C29; yang2021 C19, C42. Lipophilic plasticizers (log P around 2.5) "appear" more effective at higher loading than hydrophilic ones, and TBC or GTB lowered the water sorption of PVPVA more than dilution would correasoto2023 C44, C26. The fall in release rate of MePHPH (log P ~4) dispersions above 20% "may" come from lipophilicity lowering the thermodynamic driving force for water penetration deac2023a C53. In HPMCAS the 2024 paper found drugs of "somewhat comparable" log P (4.1–5.9) losing release with loading very differently, which "strongly" suggests drug–polymer interactions, and attributes the slower release of non-complexing drugs at high loading "likely" to lipophilicity through less hydration bapat2024 C26, C28, C42; the 2025 grade paper reads the faster release of loratadine than of cinnarizine from HPMCAS-LF as due to less complexation, not lipophilicity (log P 5.2 against 5.8) bapat2025a C30.

Findings

Bioperformance: F20, F21, F22, F24. Crystallization from solution: F8, F13, F30, F44. Release mechanism and LoC: F9, F25, F26, F32, F33.

Related concepts

sets the partition into the membrane in membrane asymmetry; limits transport through the unstirred water layer; related to micellar solubilization and crystalline solubility; related to solubility parameter and polymer hydrophobicity. Measured as the octanol-water partition coefficient; tested against the limit of congruency.

Formulas

octanol-water partition coefficient.

How it is measured or obtained

Taken from the literature or calculated: a cited cLogP for enzalutamide in one paper and a MarvinSketch value in the next; log P of atazanavir, posaconazole and darunavir cited from reviews [wilson2018 M1; wilson2020 M1, P4; elkhabaz2019b M1, M2; alkalla2026 M1, M2; hate2022 M1, M6]. Calculated with ChemBioDraw (version 11.0 or 12.0, both named) or taken from the literature [ilevbare2013b X16]. In the release-mechanism papers: calculated (ClogP), cited, or measured by shake flask saboo2019 A1; que2019 R28; saboo2020a E5.

Values in the library
materialvalue or classconditionspaper ids
enzalutamide2.98 (cLogP, cited from a regulatory report) and 4.75 (MarvinSketch)neutral species[wilson2018 M1; wilson2020 M1, P4]
atazanavirabout 4.5pKa 4.3–4.52[elkhabaz2019b M1; alkalla2026 M1; hate2022 M1]
posaconazole4.6pKa 3.6 and 4.6[elkhabaz2019b M2]
darunavir2.8pKa 2.4[alkalla2026 M2]
acetaminophen0.46 and 0.51 as printedhydrophilic comparatorhate2022 M6, X5
lumefantrine8.34; good release to 35% in PVPVAbase form, citedhiew2022b C35, M1, R20
ritonavir; efavirenz; celecoxibLog P 5.6 (5.98 in the 2012 paper); 4.7; 3.5SP 20.03; 21.89; 23.38 MPa^1/2[ilevbare2013b M1–M3; ilevbare2012c M1]
growth-inhibiting windowcellulose polymers of SP 20.56–23.28 for drugs of Log P 3.5–5.65 µg/mL[ilevbare2013b C43]
13 bile saltsLogP'A of the ionized acid from 2.65 (SDC) to −0.50 (STC); none for STDC, STCDC, SLCliterature[li2016a M4–M16]
posaconazolelog P 4.6 (cited); phase-separates at about 10 µg/mLpH 6.5shah2025 M1, C48
nifedipinelog P 3.17 (cited)model drugindulkar2017b M1
nilvadipine; cilnidipineClogP 3.04; 5.54; LoC in PVPVA 10 and 15% (about 6–9 and 7–9 mol%)pH 6.8, 37 °Csaboo2019 A1, C35
ritonavir; ledipasvirlog P 4.3, LoC 25%; LoC 5% for ledipasvircited; PVPVAque2019 R28, R27, C10
nilvadipine, felodipine, cilnidipine at 40% in HPMCASlog P 4.06, 4.46, 5.40; rates 0.42, 0.34, 0.26 mg/min/cm²pH 6.8saboo2020a R16
TIPP, Me-TIPP, PHPH, Me-PHPHlog P 6.39, 7.60, 2.63, 3.93 (ACD); limits 10, 30, 5, 40%calculatedque2021 M1, M2, M3, M4, R19
loratadine, miconazole, danazol, elbasvir, paclitaxel, ivacaftorlog P 4.4, 5.69, 3.8, 5.33, 3.96, 5.68; PVPVA drops at 25, 40, 5, 10, 5–10, 5–10%citedyang2021 M1, M2, M3, M4, M5, M6, R7, R8, R9, R10, R11, R12
clopidogrelcLogP 3.8; limit about 40%citedcorreasoto2022a M1, C46
ritonavir (log P 5.7) against loratadine (4.55) in HPMCAS-MF, 25%0.45 against 0.17 mg/min/cm² (table values)compacts, pH 6.8bapat2024 X18, R2
Pitfalls and disagreements

The same drug carries two log P values 1.8 units apart in two papers of one group [wilson2018 M1; wilson2020 M1] (synthesis: 4.75 − 2.98). The large crystalline solubility gap between atazanavir (1.6 µg/mL) and darunavir hydrate (265.6 µg/mL) is attributed to crystal packing and the lower log P of darunavir, an attribution that was not tested [alkalla2026 C33, R3]. The higher PAMPA mass flow of atazanavir and nifedipine than of acetaminophen is credited to lipophilicity although the drugs also differ in dose, pKa and concentration (F21) hate2022 C36, R16. The Log P source is given as version 12.0 in the text and 11.0 in the table footnote; Log P values are calculated estimates [ilevbare2013b X16]. The papers use Log P only to describe the drugs; the polymer match is made on SP, not on Log P [ilevbare2013c C37]. The two log P sets for nilvadipine and cilnidipine differ (ClogP 3.04 and 5.54 against measured 4.06 and 5.40) saboo2019 A1; saboo2020a R16. Two drugs per comparison cannot separate log P from other differences such as the glass transition que2019 C49. Miconazole log P is printed as 5.69 and 5.22 yang2021 X1, and two programs give TIPP 6.39 and 8.08 que2021 M1. The printed log P values refer to the neutral species; indomethacin is ionized at pH 6.8, so its lipophilicity in the gel is lower than its log P bapat2024 X18.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

liquid-liquid phase separation

The splitting of a highly supersaturated aqueous drug solution into a water-rich continuous phase and a dispersed, non-crystalline drug-rich phase, before crystals form; the authors call it glass–liquid phase separation when the drug-rich phase is a glass [ilevbare2013a C2; indulkar2015 C38]. The concentration at which it starts is called the LLPS concentration, CL-L or coexistence concentration, and in this chapter equals the amorphous solubility within the accuracy of the methods ilevbare2013a C14, C3. It was earlier discussed as "promiscuous aggregation" in screening assays and as "oiling out" in crystallization ilevbare2013a C7, C9, C35. The papers of 2017–2022 add a weak base shifted from simulated gastric fluid to pH 6.5: pazopanib gave a milky, bluish solution at once, with particles of 495.9 nm (145.4 nm with 50 µg/mL HPMC) and no particles at a dose below its amorphous solubility [sugihara2018 R14, R15, R20], and ibuprofen droplets that measured 3182–5313 nm in buffer and 268–345 nm with HPMC or PVP-VA ueda2020b R5. New aspect (Bioperformance): the two phases are in metastable equilibrium with equal activity [raina2014a C3, C4, C33; indulkar2016 C1; hate2018 C5]. For high-Tg drugs such as telaprevir the term glass–liquid phase separation is used mosqueragiraldo2018b M1. Drug-rich spheres were also found by SEM in pooled human intestinal fluid, the first such demonstration according to the authors [elkhabaz2019b R4, C24]; a crystalline co-drug lowers the concentration at which atazanavir separates [alkalla2026 C2]. New aspect (Supersaturation from ASD dissolution): dispersion dissolution, unlike dissolution of a neat amorphous drug, can push the concentration past the amorphous solubility, so that LLPS follows dissolution and precedes crystallization jackson2015 C7, C29; the colloids of rapidly dissolving ritonavir dispersions "highly likely" originate from LLPS [ilevbare2013d C33].

Findings

Amorphous solubility and LLPS: F1, F2, F3, F4, F5, F8, F9, F11, F13, F15, F16, F22, F23. Bioperformance: F1, F2, F4, F5, F10, F18, F19, F27. Supersaturation from ASD dissolution: F7, F9, F10.

Related concepts

produces the drug-rich phase; special case glass-liquid phase separation; sets the amorphous solubility; described by the binodal and spinodal decomposition; grows by droplet coalescence; precedes crystallization (a precursor, F3). Produces drug-rich nanodroplets; related to metastable equilibrium.

Formulas

binodal condition, amorphous solubility advantage with water-sorption correction, ideal-mixing reduction of amorphous solubility.

How it is measured or obtained

By extinction at a non-absorbing wavelength during slow addition of a drug stock, by a polarity-sensitive probe or the drug's own fluorescence, by DLS or NTA sizing of the droplets, by ultracentrifugation of the phases, by NMR of dissolved drug, by a flux break, and by a solvent-free pH-shift titration for weak bases [ilevbare2013a P5, P10, P11; almeidaesousa2015 P1, P2; mosqueragiraldo2015 P10; trasi2015a P6; indulkar2015 P10] (F4). In the Bioperformance papers: rise of extinction on solvent shift; turbidity without birefringence under polarized light [raina2014a R4, C12]; droplet size and number by NTA or DLS [indulkar2016 P4; hate2018 R6, R7]; the 369 nm fluorescence band of atazanavir hate2018 P6, C18; the flux plateau; antisolvent titration read by 450 nm extinction [alkalla2026 P7, C16]; the drug's own fluorescence intensity and SEM of the centrifuged pellet [elkhabaz2019b R3, R4, C17]. During dispersion dissolution: the pyrene ratio, with the onset read as the UV concentration at the pyrene drop; stepwise dissolution with dilution; turbidity titration with polymer present [jackson2015 P3; ilevbare2013d P4, P2].

Values in the library
materialvalue or classconditionspaper ids
ritonavir dropletsabout 345 nm at 1 min, about 842 nm at 64 minwater, 37 °C, single addition at the onsetilevbare2013a R3
ritonavir drug-rich phase94.85–95.97% drug, 4.03–5.15% water, Tg 0.4 °C10–50 °C, ultracentrifugedilevbare2013a R5, R6
weak-base dropletsZ-average about 116–387 nmclotrimazole, atazanavir, nicardipine, 37 °C[indulkar2015 R14]
telaprevirspecies about 300 nmpH 6.8, 37 °C[mosqueragiraldo2015 R5]
ritonavir dropletsabout 360 nm at 30 µg/mL100 mM pH 6.8, 25 °C[trasi2015a R15]
pazopanib colloids495.9 nm without, 145.4 nm with 50 µg/mL HPMC (DLS); NTA about 50–650 nmpH 6.5 after pH shift, 37 °C[sugihara2018 R15, R16]
ibuprofen droplets3182–5313 nm (buffer); 272–345 (HPMC); 268–320 (PVP-VA); 472–808 nm (EUD-E)pH 2.0 (D2O), 37 °C, freshueda2020b R5
felodipineonset 5.70–13.4 µg/mL20–45 °C, buffer[raina2014a R1]
nifedipineLLPS only with 1 mg/mL HPMC: 30.86–88.89 µg/mL20–45 °C[raina2014a R1, R5]
clotrimazoleonset 7.5 µg/mL; droplets 111–257 nmpH 8[indulkar2016 R2, R4]
atazanavir78 µg/mL; droplets 204–226 nmpH 6.8hate2018 R2, R6
ritonavironset about 38 µg/mL in waterUV extinctionilevbare2013a R2
enzalutamideonset about 42 µg/mLpH 6.5, 37 °C[wilson2018 R2, C16]
atazanavir, darunavir93.1 and 363.8 µg/mL (antisolvent, 450 nm)pH 6.8, 37 °C[alkalla2026 R3, C16]
pretomanidabout 166 µg/mL in buffer, 308 in FaSSIFpH 6.5, 37 °Cnguyen2023a P2, R2
danazol dispersions (eight)onset about 6.0–10.4 µg/mL against 8 µg/mLpH 6.8, 25 °Cjackson2015 R5, M1
ritonavir–PVP dispersion, stepwiseonset between 10 and 20 µg/mL37 °C[ilevbare2013d R1, X8]
ritonavir, 180 µg/mL PVP / PAA / HPMC / HPMCAS / CAAdP 0.8518.3 / 18.3 / 18.7 / 18.2 / 21.3 µg/mL (18.2 without)titration, 37 °C[ilevbare2013d R10]
Pitfalls and disagreements

Extinction alone cannot tell droplets from crystals, and a fast crystallizer may crystallize before it phase separates (griseofulvin without polymer) [almeidaesousa2015 C16, C18]. The ritonavir phase diagram rests on four binodal points between about 11 and 29 °C ilevbare2013a X17. Droplet size grows with time by coalescence and varies with drug and technique ilevbare2013a R3, C18. In SDS the 369 nm band that marks the atazanavir drug-rich phase in buffer appears from about 200 µg/mL, far below the amorphous solubility of about 1450 µg/mL, so a spectral marker has to be checked in the micellar medium indulkar2017a R17, R18, C27; extinction rose on the first addition to STCDC and SGCDC without visible turbidity [lu2017b R4]. LLPS is seen only if nucleation is slow compared with phase separation; the metastable zone for LLPS is "small" by the authors' reading [raina2014a C30, C32]. Turbidity does not tell LLPS from crystallization without a crystal-specific method [elkhabaz2017 C30]. Above the onset an inhibitor can still fail: pretomanid with HPMCAS-HF crystallized within minutes in the presence of droplets (F27) nguyen2023a R7, C13. A polymer in the droplets lowers the onset (F19) ueda2020a R1, C13. In the danazol dispersion study the overshoot above the amorphous solubility before LLPS was inferred from UV, which is unreliable there jackson2015 X12; a slowly releasing dispersion (50:50 HPMCAS danazol) never reached it jackson2015 C33.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

local equilibrium

Evidence table: local equilibrium. Content from the release-mechanism chapter (2023–2025).

The assumption that phase separation in a hydrating dispersion is at least as fast as water penetration, so that the phases at each depth of the gel layer are in pseudo-equilibrium with the local water content and their compositions can be read from the equilibrium ternary diagram deac2023b C38; deac2023a C70. The gel surface, with water activity near unity, can equilibrate with the solution and resemble the dilute nanoparticle composition, while deeper layers with less water reach other regions of the diagram deac2023b C61. Compacts above the limit formed a surface barrier "in pseudo-equilibrium" with the aqueous phase deac2023b C3. The 2024 phase-diagram paper assumes that the separated phases reach local equilibrium at once along the hydration path, "likely" valid for MePHPH and PHPH because both drug-rich phases are rubbery at 37 °C, and expects high-Tg drugs "may not" conform deac2024b C48, C49, C50, C54.

Findings

Release mechanism and LoC: F25, F27, F30.

Related concepts

lets the ternary phase diagram, its binodal and tie lines describe the gel layer; needs a mobile phase, related to the wet glass transition temperature.

Formulas

none.

How it is measured or obtained

Indirectly: time for nanoparticle composition to settle and for compact surfaces to reach a constant composition deac2023b C38, R2, R6, R7, and comparison of the released hydrophobic phase with equilibrated nanoparticles, with its Tg against the test temperature deac2023a C39, R12.

Values in the library
materialvalue or classconditionspaper ids
PHPH and MePHPH nanoparticles with PVPVAcomposition settled within 5 min37 °Cdeac2023b C38, R2
PHPH and MePHPH compact surfaces above the limitpseudo-equilibrium within 10 minATR-FTIRdeac2023b C38, R6, R7
hydrophobic phase released from 30% MePHPH; 5% PHPHTg 16.8; −5.8 °C, both below 37 °CDSCdeac2023a R12, C39
Pitfalls and disagreements

The assumption "may be valid" when the hydrophobic phase is mobile; dispersions whose hydrophobic phase has a high Tg need further work deac2023a C70.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

matrix crystallization

Crystallisation of the amorphous solid itself while it is in contact with the medium, before the drug has dissolved (also called solid-mediated crystallisation), in competition with dissolution and with crystallisation from solution [moseson2021 C1, C27]. Bicalutamide–PVPVA is the case in point of the ASD process papers: a hydrated, polymer-depleted, drug-rich solid that is "likely" below its Tg at 37 °C becomes mobile enough to crystallise in place, a surface-driven reaction triggered by hydration and polymer loss [moseson2021 C55, C56, C59]. Moseson (2022) tested the route across loadings: bicalutamide–PVPVA at 5 and 10% loading released drug and polymer together and escaped it, whereas 20–50% loading, cryomilling and cryomilled surfactant-containing powders raised the risk. The authors call it surface-mediated: a polymer-depleted, drug-rich boundary layer forms, crystallizes and "could prevent release" moseson2022b C36, C39, C43, R6, R7. In posaconazole–HPMCAS at 50% loading a 12 nm coating went with a much lower SHG signal after 3 h and higher release, which the authors suggest is a delay of matrix crystallization moseson2023 R15, R18, C40. New aspect (Bioperformance): crystallization inside the undissolved ASD particle during dissolution, as against crystallization from solution [mosqueragiraldo2018b C40; elkhabaz2017 C34]. The poor exposure of the 10% enzalutamide–HPMCAS dispersion was attributed to rapid matrix crystallization on contact with water; the printed evidence is crystals in the medium and a 10 µg/mL maximum [wilson2018 C56, X11]. New aspect (Supersaturation from ASD dissolution): in the first study of the two routes it is called "crystallization from matrix": the amorphous particle converts to crystal on contact with the medium, against nucleation and growth from the supersaturated solution [alonzo2010 C43, C47]. If it is faster than dissolution, no concentration above that of the crystal can be reached, because the crystal is what dissolves [alonzo2010 C33]. The papers of 2015–2018 show that the dispersion polymer and its share decide it: resveratrol dispersions needed 80–95% cellulosic polymer to stay amorphous in buffer, PAA failed for celecoxib "irrespective of the drug loading", and an inhibitor dissolved in the medium cannot reach it [wegiel2015 R14; xie2016a C33, C31; xie2015 C35].

Findings

ASD process: F27, F28, F29, F38, F39, F40, F41, F46. Bioperformance: F9, F11, F12, F23, F26, F27, F30. Supersaturation from ASD dissolution: F1, F2, F3, F16, F24, F27.

Related concepts

contrasts with desupersaturation; accelerated by residual crystallinity; not blocked by crystallization inhibition by polymers in solution; accompanies incongruent release and surface drug enrichment; related to surface crystallization; avoided by congruent release; fed by the drug-rich surface layer; delayed by an atomic layer coating in one posaconazole system. Contrasts with solution crystallization; favoured by drug loading; part of crystallization during dissolution; related to plasticization by water.

Formulas

None specific; the competition with dissolution is set out with the Noyes-Whitney equation [alonzo2010 E3].

How it is measured or obtained

Time-lapse polarised light microscopy of particles in buffer, in-line Raman of a slurry resolved by MCR-ALS, XRPD and SEM of recovered solids, polymer release by size-exclusion chromatography, and dissolution at several doses read for plateaus below the amorphous solubility and a falling fraction dissolved [moseson2021 P14, P15, P16, R17, R18, R19]. SEM, SEM-EDX (fluorine occurs only in the drug, F/F0) and confocal fluorescence of compacts exposed face down to medium for 5–60 min; Raman slurries resolved by MCR-ALS for the form 2 time course moseson2022b P12, P14, P15, P16, P17. SHG of particles after 3 h in buffer moseson2023 R18. Polarized light microscopy of particles in buffer mosqueragiraldo2018b R18; SHG [elkhabaz2017 P10]; indirectly, a flux ceiling not reached mosqueragiraldo2018b R16. In the ASD dissolution papers: in situ Raman of aqueous slurries with a PLS model for crystallinity or marker bands, PXRD of wetted powder after 15 min, and polarized light microscopy of wetted particles [alonzo2010 P5, P6, P8; raina2014b P4, P6, P10]; the 1630/1605 cm−1 Raman ratio of resveratrol slurries, also in a medium where the enteric polymer does not dissolve (pH 1.2) [wegiel2015 P7, A3]; the amorphous Raman shoulder near 1598 cm−1 of celecoxib slurries [xie2015 P3, R3]; polarized light of residues retrieved after the release peak xie2016a P6.

Values in the library
materialvalue or classconditionspaper ids
BCL–PVPVA 30:70, crystal-freeform 2 begins at 20–30 min (half conversion about 36 min); plateau about 37–38 µg/mL against an amorphous solubility of 150 µg/mL60 and 150 µg/mL doses, pH 6.8[moseson2021 R12, R13, R19]
BCL–PVPVA with residual or added form 1 crystalsform 1 first detectable at about 15 min (S/155), 7 min (M/155), from the first spectrum (10% seeds)Raman slurry, 10 mg/mL[moseson2021 R21]
amorphous nifedipine (outside)crystallises mainly by the matrix route within about 10 min; PVP, HPMC or HPMCAS in solution do not change onset or routebuffer, 25 °C[raina2014b C10, C11]
celecoxib dispersions (outside)polymers dissolved in solution cannot inhibit crystal formation in the matrixhigh drug loading[xie2015 C35]
telaprevir 50% HPMCAS (outside)slow, incongruent release; HPMCAS leaves about twice as fast as the drug, leaving a drug-rich layeroptical micrographsmosqueragiraldo2018b C40, C43
enzalutamide 10:90 HPMCAS (outside)rapid matrix crystallisation on contact with waterdissolution[wilson2018 C56]
posaconazole ASDs in acid (outside)matrix crystallisation about 68% at 50% DL, about 0.05% at 25% DLSHG over TPE-UVF, 30 min[elkhabaz2019a R20, C38]
BCL–PVPVA 5 / 10 / 20 / 30 / 50% DL powdersend level about 91 / 96 / 88 / 86 / 73% of the dose; polymer ahead of drug from 20% DLdose of at most 30 µg/mL, pH 6.8moseson2022b R6, R7
30% and 50% DL compacts, 1 hdrug-rich boundary layer of 94 ± 8 µm with crystals (F/F0 1.41 ± 0.10); 5–10 µm crust of crystalsSEM-EDXmoseson2022b R15
30% DL cryomilled 2 and 5 minabout 50 and 49% of the dose, plateau about 15 µg/mLsamemoseson2022b R4
10% DL after 10 min of cryomilling or extrusion and 30 s of millingabout 93% of the dosesamemoseson2022b R8
30% DL with 3% TPGS, cryomilled 5 minstops at about 60% (about 18 µg/mL)samemoseson2022b R12
50% PCZ–HPMCAS, small particles, uncoated against 12 nm Al2O3SHG 126.7 against 3.7; about 3.35 against 5.1 µg/mL at 3 hsingle stage, pH 6.5moseson2023 R18, R15
telaprevir 50% HPMCAS ASDbirefringent domains in the particle at 20 min; 0.65 µg/minpH 6.8mosqueragiraldo2018b R16, R18
telaprevir 47.5:47.5:5 SDS ASDnone visible; 1.07 µg/minsamemosqueragiraldo2018b R16, R18
ezetimibe PAA ASDcrystals within minutes, inferred from the matrixbuffer, FeSSIF[elkhabaz2017 C34, R12, R16]
posaconazole ASDs 10 / 25 / 50%SHG crystallinity 0.3–0.4 / 3–4 / 19–26%60 min FaSSGF[shah2024 R21]
posaconazole ASDs50% DL final crystallinity about 250 times that of 25% DL[elkhabaz2019a R18]
enzalutamide 10:90 HPMCAS-MF ASDpeak about 10 µg/mL, crystals in the mediumpH 6.5, 100 µg/mL total[wilson2018 R6, C56]
pretomanid HPMCAS-HF ASD tabletscrystalline drug in the particles after FeSSIF at pH 5.5 and below, and after a 1 h gastric stagePXRD and SEM, 30 mg in 150 mLnguyen2023a R20, R22
neat amorphous felodipine≈54% crystalline at 1 min (37 °C); 50% after about 8 min (25 °C)pH 6.8 slurry[alonzo2010 R2]
felodipine with 500 µg/mL PVP, HPMC, HPMC-AS in the medium50% crystalline at ≈20.5, ≈18.5, ≈13.5 min37 °C[alonzo2010 R6]
neat amorphous indomethacinα form present at 90 min, like pure α at 120 minpH 2, 37 °C[alonzo2010 R12]
nifedipine 50:50 dispersions (PVP shown)particles not birefringent; crystals form in the solutionpH 6.8[raina2014b R13, X18]
nifedipine–HPMCAS 50:50 at pH 2matrix amorphous for 3 hpolymer barely soluble[raina2014b R15]
celecoxib–HPMCAS 33.3% particles in pH 3 suspensioncrystals on or in particles after about 7 days (Triton X100), none in 48 h25 °Cchen2015a R20, R14
resveratrol 35% with HPMC / HPMCAS / CMCABRaman ratio ≈0.87 / ≈0.84 / ≈0.81 (crystal 0.76) within hourspH 6.8, 37 °C[wegiel2015 R9]
resveratrol, minimum polymer to prevent it80% HPMC, 85% HPMCAS, 95% CMCABpH 6.8, 37 °C[wegiel2015 R14]
neat amorphous celecoxibcomplete within an hour; crystals on the particles from 2 minpH 6.8, 37 °C[xie2015 R4, R8]
celecoxib–PVP-K12 50%crystalline within 4 h in a slurrypH 6.8, 37 °C[xie2015 R4]
celecoxib–PAA 5:5 and 1:9, HPMCAS in the mediumrelease stopped at about half; needles in the residuepH 6.8, 37 °Cxie2016a R9, R10
lopinavir 50% with EUD, CAP / HPMCPcrystals by 8–16 h / none at 48 hpH 3, 25 °C[li2018 R7]
delamanid salt dispersions, films after 1 h in acidclear at pH 1.6 (HPMCP); crystals at pH 3.0 on all but HPMCP-55; small crystals on every film at pH 5.025% drug, 37 °C[nguyen2023c R19]
same, powderspitted, porous HPMCAS surfaces with agglomerates increasing with pH; HPMCP-50 covered at pH 5.01 h in acid[nguyen2023c R18]
delamanid dispersions in HPMCP, films with and without a 2 µm Eudragit L 100-55 layerstar- and needle-shaped crystals on every uncoated film; none under the layerpH 3.0, 1 h[nguyen2023b R3, R6]
posaconazole–HPMCAS dispersionscrystals by SHG in every system after 30 min in FaSSGF, more numerous after transfer37 °C[elkhabaz2019a R16]
Pitfalls and disagreements

The hydrated-solid mobility mechanism was not measured (the wet Tg of amorphous bicalutamide could not be determined) and the kinetics come from slurries far above the dose concentrations [moseson2021 R27, X8, X11]. Attribution to the matrix route is often inferred: crystals could instead nucleate in the concentrated boundary layer around the dissolving particles, or the evidence is crystals in the medium and a low maximum without a solid-state analysis [xie2016a X6; wilson2018 X11]. Solution-mediated growth is not absent at high dose [moseson2021 X4]. The results and the discussion of the 2022 study disagree on whether 20–30% loading crystallized, the crystals of the compacts were identified by shape and not by diffraction, and the polymer-depleted state of the crust is inferred from a dye moseson2022b X14, X16, X18. The Tg and composition of the hydrated layer were not measured moseson2022b C60. One micrograph without XRPD supports the telaprevir case mosqueragiraldo2018b X13. Matrix and solution crystallization were not separated for enzalutamide: no solid-state analysis of the wetted dispersion is shown (F9) [wilson2018 X11]. In the ASD dissolution papers, slurries held far more solid per unit of polymer than dissolution vessels (about 500–750-fold for felodipine), so their lag times rank systems but do not give the time scale in dissolution [alonzo2010 X5]. The proposal that crystallization starts at the particle surface and that dissolved polymer delays it there was not tested [alonzo2010 C36]. For felodipine at 25 °C the fall after the peak may come from the matrix as well as from solution [alonzo2010 X6]. The PVP-K12 celecoxib dispersion crystallized in a slurry yet released fully in dissolution [xie2015 R4, R6]. PXRD found no crystals in delamanid dispersion powders after 1 h in acid, a method that detects about 1–5% crystallinity, so the crystal mass that harmed release was small [nguyen2023c R15, R16, C46].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

melt viscosity

The steady-shear viscosity of a drug melt at Tm (ηmelt) and below it in the undercooled range; its rise on cooling is expressed as the ratio \eta/\eta_{melt} [baird2012 P1, E7]. It stands for the molecular mobility that nucleation and growth need [baird2012 C4].

Findings

F5, F12.

Related concepts

measures molecular mobility for crystal growth rate and nucleation; used to obtain fragility; related to Tm − Tg temperature gap and glass-forming ability.

Formulas

Vogel-Tammann-Fulcher equation, linear fit of melt viscosity on Tm − Tg.

How it is measured or obtained

Parallel-plate rheometry at 30 s⁻¹, stepwise from Tm downward with remelting between steps [baird2012 P1]; fitted with the VTF equation [baird2012 P5]; in drug–polymer melts by the same method [tian2017 R13].

Values in the library
materialvalue or classconditionspaper ids
benzamide2.86 × 10⁻³ Pa·s, the lowestat Tm[baird2012 R1.b]
ritonavir1.99 Pa·s, the highestat Tm[baird2012 R1.ah]
felodipine; nifedipine154.0 and 36.20 × 10⁻³ Pa·sat Tm[baird2012 R1.u, R1.q]
class I-A; class III averages≈0.005 and ≈0.11 Pa·s at Tm; ≈0.014 and ≈0.53 Pa·s at 20 °C undercoolingclass averages[baird2012 R8]
17 drugs\eta(T_m) falls linearly with Tm − Tg, R^2 = 0.7368data of baird2012[trasi2014a R9]
indomethacin with 10% PVPhigher viscosity than with HPMC or HPMCAS at 80–105 °C; pure indomethacin crystallized during measurementrheometry[tian2017 R13, C19]
indomethacin in a polymermatrix viscosity falls quickly as the drug plasticizes the polymerhot melt extrusion[moseson2018 C45]
Pitfalls and disagreements

Single runs at one shear rate; shear itself promoted nucleation at the plate [baird2012 X12, C8]. The link to crystallization is an association across classes, not shown within classes [baird2012 X15]. Viscosity does not fully describe felodipine mobility in PVP dispersions [kestur2010b C24].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

melting point depression

The lowering of the melting temperature of a crystalline component by the second component of a miscible mixture. Marsac and co-workers describe it as a manifestation of the reduced thermodynamic activity of the drug in the polymer: the dispersed drug reaches the chemical potential of the crystal at a lower temperature [marsac2006b C39]. In drug–PEG dispersions both branches of the liquidus are depressed, the drug's by dissolving in molten PEG and PEG's by dissolved drug, until they meet at the eutectic [baird2011 E1, E2]. Whether a pair shows depression separates miscible from immiscible pairs [marsac2009 C12]. New aspects (Miscibility and drug-polymer interactions): For drugs in amorphous polymers the depression is the visible sign of a miscible pair and the route to χ: pairs reported miscible lower the melting point of the drug, immiscible or partially miscible pairs show little or none, and a depression beyond the entropy-only (athermal) prediction means negative χ [marsac2009 C5, C12]. The offset of the melting endotherm is used because it gives the melting point at the final composition if mixing is complete [marsac2009 C16]. New aspect (ASD process): for an amorphous polymer the depressed melting point at a fixed composition is called the critical temperature Tc (the temperature at which the last drug crystal has dissolved in the polymer); it is the crystalline solubility temperature of that composition and the lowest product melt temperature at which a crystal-free extrudate is possible in theory, but it is not an upper or lower critical solution temperature [moseson2018 P2, C43]. A negative Flory–Huggins \chi adds depression beyond the combinatorial entropy [moseson2018 C9]. New aspect (Physical stability): used as the test of whether a few percent of polymer lowers the driving force for crystallization: no depression means no thermodynamic route [kestur2010b C25, C26].

Findings

PEG dispersions: F1, F2, F3, F4, F8, F10. Miscibility and drug-polymer interactions: F6, F7, F8, F9, F11. ASD process: F8, F9, F17, F19, F35, F36, F41. Physical stability: F4, F18, F22, F28, F29.

Related concepts

part of temperature-composition phase diagram; measured by liquidus temperature; depends on enthalpy of mixing and Flory-Huggins interaction parameter; reduces degree of supercooling; related to eutectic; measures Flory-Huggins interaction parameter through the Flory–Huggins relation; depends on drug-polymer miscibility and on the glass transition temperature of the polymer; related to thermodynamic driving force for crystallization. Measured to give formulation critical temperature; sets the lower bound of the HME operating design space.

Formulas

Flory-Huggins melting point depression, Lacoulonche liquidus model.

How it is measured or obtained

By hot-stage polarized light microscopy as the temperature at which the last crystal melts (1 °C/min) and by DSC offset melting (1 °C/min), on fused or physical mixtures that are ground and stored dry [baird2011 P2, P3; zhu2011 P3, P4; zhu2012 P9, P10]. For amorphous polymers the offset is extrapolated to 0 °C/min [moseson2018 R5]. An interaction parameter follows from the slope of the Flory–Huggins relation at 50–80% drug [zhu2011 P5]. In the PVP studies: physical mixtures of sieved crystalline drug and polymer (45–75 µm or 45–90 µm), dried for a week over phosphorus pentoxide or nitrogen, geometric mixing, modulated DSC at 1 °C/min under nitrogen, onset (marsac2006b) or offset (marsac2009) of the melting endotherm [marsac2006b P1; marsac2009 P1]. Only polymers that are liquid-like at the drug melting point work: PVP K12 (Tg 100 °C) gave depression, PVP K29/30 (Tg 168 °C) at 10 °C/min essentially none [marsac2006b C29, R11, M3, M4]. The fit uses data over 0–0.25 polymer fraction [marsac2006b R8]. In the extrusion work: cryomilled physical mixtures at 40–90% drug loading (DL), triplicate preparations, 3–5 mg scanned from 25 to 180 °C at six heating rates (0.5, 1, 2, 3, 5, 10 °C/min); the melting point offset temperature is fitted with a second-order polynomial against heating rate and extrapolated to 0 °C/min to give Tc [moseson2018 P1, P2, E7]. The offset rises with heating rate, for 50/50 IDM:PVPVA from about 133.2 °C at 0.5 °C/min to about 146.1 °C at 10 °C/min [moseson2018 R3.f]. In the felodipine growth work: DSC offset of the bulk melting endotherm at 1 °C/min of crystalline felodipine cryomilled with 3% PVP K-12; not possible for higher PVP grades, whose Tg lies above the drug melting point [kestur2010b P6].

Values in the library
materialvalue or classconditionspaper ids
benzocaine in PEG 3350melting around 89 °C neat, eutectic around 48 °C; text of the other paper: 92 °C neat and about 55 °C for the 20/80 blendfused dispersions[zhu2012 C32, M3; zhu2011 R1]
ibuprofen; fenofibrate in PEG 3350about 30 °C; about 20 °C by the text, about 24 °C by the ploteutectic depression[zhu2012 C34, X11, R24]
chlorpropamide, aceclofenac in PEG 3350liquidus at 40 wt% drug about 55–56 and 86–88 °C against about 98 and 135.5 °C predictedDSC and hot stage[baird2011 R5.e, R6.e]
nifedipine, felodipine in PVP K12decreased linearly over 0–25 wt% polymer; \chi −3.8 and −4.21 °C/min, small particles[marsac2006b R7, R9]
indomethacin in PVP K12\chi −6.16 (onset), −1.94 (midpoint), −0.82 (offset)1 °C/min[marsac2009 R6]
indomethacin in PVPVAabout 30 °C at 50% drug loading; 1–4 °C below 30% polymerDSC offsets[moseson2018 R6]
probucol in PEOmelting point 101 °C, Form II only, "may be due to" depressioncompression-moulded dispersion[broman2001 R4.f, C20]
nifedipine in PVP K12onset ≈171 → ≈156.5 °C; ≈144.5 °C at Φ ≈ 0.3831 °C/min[marsac2006b R6]
felodipine in PVP K12onset ≈141 → ≈122 °C; ≈115.5 °C at Φ ≈ 0.3831 °C/min[marsac2006b R6]
indomethacin in PVP K12offset ≈161.5 → ≈155 °C; onset ≈160 → ≈135.5 °CΦ ≈ 0.23[marsac2009 R2]
ketoconazole in PVP K12offset ≈150.0 → ≈147.5 °CΦ ≈ 0.23[marsac2009 R3]
itraconazole with Eudragit E100offset ≈168.0 → ≈167.4 °Cpolymer fraction up to ≈0.54[marsac2009 R4]
felodipine with 3% PVP, PVP/VA, HPMCAS, PVAc140.7, 142.9, 141.4, 142.6 °C against 141.5 °C: noneoffset, 1 °C/min[kestur2010a R1]
indomethacin (IDM) with PVPVA, 90/10 to 40/60Tc 159.9 ± 0.3, 157.2 ± 0.4, 151 ± 3, 141 ± 3, 132.3 ± 0.8, 129 ± 6 °C; IDM 160.64 °C; depressions 0.7, 3.4, 9.6, 19.6, 28.3, 31.6 °Coffset extrapolated to 0 °C/min[moseson2018 R5, R6]
probucol with PAA (solvent / moulded)melting 110 / 116 °C against 116 °C for pure Form II; read as depression "can be explained by"DSC 20 °C/min for dispersions, 10 °C/min for references[broman2001 R4.c, R4.d, C17, X5]
polymers and surfactants with celecoxib (10% additive)3–4 °C with one additive; 12 °C for TPGS–PVPDSC[mosqueragiraldo2014 C18]
IDM with copovidone (1:5)solubility temperature about 78 °C (cited)phase diagram[moseson2019 R21]
bicalutamide with PVPVA, 30–90% BCLTc 145 °C at 30% BCL to about 192.3 °C at 90%; drug about 193.8 °Coffset extrapolated to 0 °C/min[moseson2022c R8, R9]
posaconazole with HPMCAS MF, PCZ fractions 0.4–1.0Tc about 161.7 °C at 0.4 to about 168.6 °C for neat PCZ; calculated 135 / 155 / 165 °C at 10 / 25 / 50% DLsame[shah2024 R1, R4, R5, X7]
felodipine with 3 wt% PVP K-12140.7 vs 141.5 °C, within the ±1 °C SD1 °C/min[kestur2010b R1.e, M1, X11]
indomethacin–PVP (cited)χ23 from melting point depression used as input to the ternary sorption modelliterature[rumondor2010a P5]
acetaminophen with 10% w/w polymers166.7–168.6 against 169 °Cphysical mixtures, DSC[trasi2012a R9]
flutamide with 10 mol% polymers108–110 °CDSC[trasi2012b R7]
six compounds with 1–20% PHB0–2 °C (1–10% PHB), up to 4 °C (20%)DSC of physical mixtures[sato2016 R7, X11]
indomethacin with 10% polymernamed as a possible reason for the steep inhibition above the growth maximum; not measuredargument[tian2017 C36]
Pitfalls and disagreements

Onset, midpoint and offset of the melting event give different depressions and different \chi [marsac2009 R6]. DSC and hot-stage values differ by up to about 16 °C at some compositions [baird2011 X7]. The low-temperature endotherm of the chlorpropamide and aceclofenac dispersions drifts to 39–49 °C in drug-rich traces, which a simple eutectic would not show [baird2011 R4, X8]. Very slow scans and controlled particle size were needed to see substantial depression with PVP K12, and with PVP K29/32 at 10 °C/min there was essentially none [marsac2006b C30, R11]. For PEG, the depression of the drug is the cited reason for a smaller driving force and delayed crystallization of benzocaine, but the supercooling in the dispersion was not measured [zhu2012 C32, C33]. The felodipine premix test read as slow mixing has an unverified direction [marsac2009 X6, R8]. The linear plot has a small non-zero intercept and the fit range is stated two ways [marsac2006b X4]. At 3 wt% polymer no depression is measured, and the melting point used there is that of form I in physical mixtures while form II grows [kestur2010a R1, X7]. Sucrose degrades on melting [marsac2009 C14]. A polymer with Tg near the drug melting point can hide the depression [marsac2009 C22]. In the extrusion work, mixtures with little polymer show only 1–4 °C of depression and the extent depends on interaction strength [moseson2018 C16, C42]. The 40/60 mixture scattered by about ±6 °C and lay above the model line, attributed to viscosity, and was left out of the fit [moseson2018 R5.g, C17]. In the probucol study depressions of a few °C compare dispersion melts at 20 °C/min with reference melts at 10 °C/min, and the table does not say whether values are onsets or peaks [broman2001 X4, X5]. The same low melting of probucol in moulded PEO is read as depression "may be due to" [broman2001 C20]. The depression of bicalutamide at 30% loading is large (about 49 °C from 193.8 °C to 145 °C, arithmetic on the cited values); that of posaconazole measured at 40% PCZ is about 7 °C (168.6 against 161.7 °C), and the values at 10–25% loading are extrapolations from the fitted line [moseson2022c R8, R9; shah2024 R1, X7]. The felodipine growth test used one composition and one grade only; the conclusion that the driving force is unchanged rests on a 0.8 °C difference inside the error [kestur2010b X11]. The celecoxib text gives 3–4 °C for one additive while the table gives 1.68–4.49 °C [mosqueragiraldo2014 X3], and the depression does not order the celecoxib ternaries [mosqueragiraldo2014 X13].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

membrane flux

The rate at which drug crosses a membrane in a side-by-side diffusion cell, taken as the slope of the receiver concentration against time; with diffusion coefficient, area, thickness and membrane activity coefficient constant, it is proportional to the donor activity [mosqueragiraldo2015 E4, C10; trasi2015a P6]. It rises linearly with concentration up to the amorphous solubility and then plateaus (F8). The papers of 2017–2022 add atazanavir (flux per area, 7.07 cm²) and telaprevir (mass flow rate), both linear up to the amorphous solubility in buffer and flat above it, and flux in micellar media as a free-drug read-out [indulkar2017a E7, R10, R11; lu2017b E1, R6]. New aspect (Bioperformance): the mass of drug crossing a membrane per time (and per area), proportional to the solute activity in the donor when area, diffusion coefficient, membrane thickness and membrane activity coefficient are fixed [raina2014a C11, E6; raina2015c C14]. It is reported as µg/min from receiver slope × volume, as mass flow, or per area (F2). In rats the mass flow of the dissolved formulation across a dialysis membrane ranked formulations by exposure (F25) [wilson2018 R15, R17; wilson2020 R8, C27, C44]. New aspect (Crystallization from solution): it serves as an activity read-out in micellar and polymer media, where a flux plateau marks the maximum free-drug concentration and equal flux means equal activity [jackson2016 E1, E2, C9, C16; li2016a E2, C14]. New aspect (Supersaturation from ASD dissolution): flux used as a particle-blind measure of dissolved drug while dispersions dissolve: across a dialysis membrane, relative to the crystal alonzo2011 E1, C9, and in a side-by-side cell, converted to free drug with a standard curve jackson2015 E1, E3, P4.

Findings

Amorphous solubility and LLPS: F4, F8, F11, F16, F17. Bioperformance: F2, F3, F4, F5, F7, F15, F18, F19, F20, F21, F22, F24, F25. Crystallization from solution: F22, F31, F32, F38, F40. Supersaturation from ASD dissolution: F7, F8, F17.

Related concepts

reads thermodynamic activity; plateau marks the amorphous solubility; basis of the claimed nanodroplet reservoir effect. Described by Fick's first law; requires sink conditions; part of membrane transport and membrane asymmetry; measures free drug concentration.

Formulas

membrane flux in terms of solute activity. Flux definition, mass flow rate from receiver concentration slope, membrane flux from permeability and concentration, supersaturation from membrane flux ratio, membrane flux from concentration difference.

How it is measured or obtained

Regenerated cellulose membrane (6–8 kDa cut-off), 30–32 mL per side, 25 or 37 °C, receiver measured by UV probe or HPLC, sink conditions [mosqueragiraldo2015 P11; trasi2015a P6]. In the Bioperformance papers: side-by-side diffusion cell with UV dip probes and a receiver under sink conditions [raina2014a P8, P9]; flow-through cell with fresh receiver buffer [indulkar2016 P5, P10]; hollow-fibre module [hate2017 P4]; Caco-2 monolayers [alhalaweh2016 P17]; side-by-side cell with a dialysis membrane and a donor taken from a dissolved formulation [wilson2018 P15, P16; wilson2020 R8]; side-by-side cell with a regenerated cellulose membrane in simulated and pooled human intestinal fluids [elkhabaz2019b R7]; lipid-impregnated PVDF (PAMPA) cell with a buffer or surfactant receiver hate2022 R1, R19; Caco-2 monolayers with a crystalline co-drug present [alkalla2026 R13]. The flux is normalized by membrane area as J = dm/(dt\,A) [wilson2018 E3; alkalla2026 E2]. In the crystallization-from-solution papers: side-by-side diffusion cell with a regenerated cellulose membrane (6–8 kDa), the same medium on both sides, a donor concentration series and the receiver read by UV dip probe below sink limits [jackson2016 P9; li2016a P8; lu2017 E2]. In the ASD dissolution papers: dialysis bag (6–8 kDa in the text, 10 kDa on the figure) with 500 µg/mL HPMC in the receptor, slope over 10–40 min alonzo2011 P4, X1; regenerated cellulose membrane (6–8 kDa), 200 mL per side, 30 mm opening, 25 °C jackson2015 P4; PermeGear side-by-side cells, 7.065 cm², regenerated cellulose 6–8 kDa (resveratrol) or 12–14 kDa (tacrolimus), receiver kept below a third of the crystalline solubility [wegiel2015 P10; trasi2016 P9].

Values in the library
materialvalue or classconditionspaper ids
telaprevirabout 0.068 µg/min at 5 µg/mL; about 0.97 at 90; about 1.07 at 130 µg/mL donor37 °C[mosqueragiraldo2015 R12]
ritonavir; lopinavir; paclitaxelplateaus about 0.21–0.22; 0.13–0.14; 0.25–0.27 µg/min25 °C[trasi2015a R2]
ritonavir, lopinavir, paclitaxel in 30 + 30 µg/mL mixturesflux of each drug lower than from the single-drug donor25 °C[trasi2015a R12]
atazanavirabout 0.003 µg/min·cm² at 1 µg/mL, 0.106 at 70, 0.121 at 100, 0.114 at 200 µg/mL; slope 0.0017 mL/min·cm²buffer, 37 °Cindulkar2017a R10
telaprevirslope 0.009 µg/min per µg/mL; about 1.32 µg/min at 150 µg/mL; plateau 1.25–1.2750 mM pH 6.5, 37 °C[lu2017b R6]
telaprevir with 12 mM STDCabout 0.43 against 0.83 µg/min at 90 µg/mL37 °C[lu2017b R12, R6]
felodipineplateau 63–71 (25 °C) and 136–149 × 10⁻³ µg/min (37 °C)buffer + HPMC[raina2014a R11, R12]
nifedipineabout 1.7–1.9 µg/min37 °C, 1 mg/mL HPMC[raina2014a R14]
clotrimazoleJmax 0.686–0.693 µg/(h·cm²)flow-through, pH 8[indulkar2016 R9]
telaprevir1.05–1.18 µg/min above 90 µg/mLASD dose seriesmosqueragiraldo2018b R1
atazanavir, ritonavir(10.5 / 9.1) × 10⁻⁵ mg/min/cm² alone; about half in 1:1Caco-2[alhalaweh2016 R17]
telaprevir, antisolventplateau about 18-fold the saturated solutionside-by-side[mosqueragiraldo2015 R12, C40]
tacrolimusabout 0.0050–0.0053 µg/min above 50 µg/mL; pure-drug solutions 20 / 50 / 60–100 µg/mL: ≈0.0027 / ≈0.0047 / ≈0.0050–0.0055 µg/minpH 4.5, 37 °C[trasi2016 R14]
danazol, no polymer, 25 °Cflux rises linearly to 8 µg/mL (about 0.0152) and plateaus (about 0.0156–0.0159, units as printed)donor 2–12 µg/mL[jackson2016 R10]
enzalutamideabout 0.18 µg/min at 10 µg/mL, about 0.87 at 50 and 0.81–0.91 up to 100; 10:90 ASD solution and drug with 900 µg/mL polymer both about 0.76side-by-side, 5 µg/mL HPMCAS[wilson2018 R13, R14]
enzalutamide formulations after 1 h of dissolution0.632, 0.456, 0.437, 0.147, 0.063 µg/min (10% and 50% copovidone, 50% HPMCAS, 10% HPMCAS ASDs, slurry)dialysis membrane[wilson2018 R15]
enzalutamide, four formulationsabout 0.53, 0.49, 0.068, 0.063 µg/min (10:90 and 50:50 CPHPC-106 ASDs, CA Sub ASD, slurry)dialysis membranewilson2020 R8
atazanavir, posaconazoleJ_{eq} 2.08–2.48 × 10⁻³ and 5.79–6.97 × 10⁻⁴; J_{amph} 0.105–0.139 and 0.0191–0.0239 µg/(min·cm²)six media, 37 °C[elkhabaz2019b R7]
atazanavir, PAMPAabout 0.33 µg/min at 10 µg/mL, about 1.95 at 70 and 2.0–2.3 above; with 2% SDS receiver about 5.0 at 80 to 8.8 at 1000 µg/mLlipid-impregnated PVDFhate2022 R1, R19
atazanavir alone and with darunavir hydrateplateau about 9.5 × 10⁻⁵ against 2.9 × 10⁻⁵ µg/(min·cm²); Caco-2 about 0.083 against 0.053pH 6.8, 400 µg/mL HPMCAS[alkalla2026 R9, R13]
danazol, PVP, HPMC, HPMC-AS 1–1000 µg/mLmaximum flux about 0.0126–0.0175 against about 0.0153donor 15 µg/mL[jackson2016 R11]
celecoxib, nevirapine, 0.1% STC or SGC0.44, 0.46, 0.41 and 20.9, 23.4, 21.0 µg/min (no additive, STC, SGC)pH 6.5, 37 °C[li2016a R15]
tacrolimus, cilnidipine at the amorphous solubility0.027–0.031 and 0.0014–0.0018 µg/min·cm² in buffer, FaSSIF-V1, Composite-SIF; flux at the crystalline solubility not measurable37 °C, 7.07 cm², regenerated cellulose 6–8 kD[indulkar2018 R12, R13]
telaprevir, bile salt mixturesmass flow unchanged at 1.86 mM, lower at 3.72 and 5.58 mM50 mM phosphate pH 6.5[lu2018 R2, X2]
felodipine controls 10 and 5 µg/mLratios 10.0 ± 3.4 and 4.8 ± 0.39 to the crystal37 °Calonzo2011 R14
felodipine 90:10, 50:50, pure amorphous10.5 ± 1.2, 9.5 ± 1.8, 8.5 ± 1.837 °Calonzo2011 R14
danazol dispersions PVP, HPMC, HPMCAS14.0–18.3 × 10⁻⁵ µg/(min·mm²) with LLPS; 10.3 × 10⁻⁵ without (50:50 HPMCAS)25 °Cjackson2015 R9
tacrolimus products dissolved in 30 mL0.0048–0.0054 µg/minpH 4.5, 37 °C[trasi2016 R15]
resveratrol–HPMCAS solutions; saturated crystal≈4.4 → ≈2.6 µg/min; 2.0 µg/minpH 6.8, 37 °C[wegiel2015 R20]
Pitfalls and disagreements

The plateau still rises by about 10% from 90 to 130 µg/mL [mosqueragiraldo2015 X6]; the low-donor flux traces are curved and the slope window is not stated [mosqueragiraldo2015 X13]. The membrane is described as regenerated cellulose and, once, cellulose acetate [mosqueragiraldo2015 X1]. Whether micelles or drug-loaded aggregates cross the 6–8 kDa membrane is not stated, so lower activity and slower diffusion are not separated; replicates are not stated [lu2017b X8, X4; indulkar2017a X9, X12]. In the Bioperformance papers units are not comparable between papers (µg/min, µg/(h·cm²), mg/min/cm²), and replicates and error definitions are often not stated [raina2015c X12; indulkar2016 X8]. A plateau needs a sink receiver and a stable donor [raina2014a C20]; the hollow-fibre module shows a continuing rise hate2018 R9. The plateau is not universal: with a sink receiver the PAMPA mass flow of atazanavir keeps rising above the amorphous solubility (F22) hate2022 R19. The position of the break is known only to within the spacing of the concentrations tested hate2022 X13. The area behind a printed µg/min is not always stated [elkhabaz2019b X6; wilson2018 R15]. The flux axes of the danazol paper carry no time unit, replicates are not stated and the crystalline reference flux differs between figures (about 0.0011 and 0.0008) [jackson2016 X9, X10, X11]. In the SDS study the flux values behind the stated supersaturation of about 65 are not printed [indulkar2019b X6]. In the ASD dissolution papers all felodipine ratios share one unreplicated crystalline slope, and no statistical test supports their equality alonzo2011 X4, X5. The danazol absolute fluxes do not reproduce from the example profile and the flux window per formulation is not stated jackson2015 X4, X6. Below 50 µg/mL the tacrolimus flux rose but did not extrapolate to zero, and the product donors' conditions are unclear [trasi2016 X8, X7]; flux was measured only for one resveratrol series [wegiel2015 C10]. The upper tacrolimus plateau is read as about 0.0053 µg/min in one chapter and ≈0.0055 µg/min in the ASD dissolution chapter, from the same result [trasi2016 R14].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

membrane mass transfer coefficient

The overall coefficient K_in (cm/s) of a hollow-fibre module, the sum of three resistances in series; independent of the donor concentration in theory [hate2017 C11, E3]. For tacrolimus the fitted coefficient of the absorption profiles was 1.09 × 10⁻⁴ cm/s [hate2019 R16, E3].

Findings

F13, F14, F15, F28, F29.

Related concepts

composed of the resistance-in-series permeability model; affected by the unstirred water layer.

Formulas

hollow-fibre donor depletion, resistances-in-series model.

How it is measured or obtained

Fitting the donor-depletion equation to donor profiles [hate2017 P10, E9].

Values in the library
materialvalue or classconditionspaper ids
nevirapine(9.07 ± 1.06) × 10⁻⁵ cm/s mean; 4.9 × 10⁻⁵ to 1.54 × 10⁻⁴ over 0.5–4 mL/minhollow fibre[hate2017 R12, R14]
atazanavira changed coefficient above the amorphous solubility is inferred, not measuredhate2018 C25, X11
tacrolimus1.09 × 10⁻⁴ cm/shollow fibre, 2 mL/min inside and outside[hate2019 R16, E3]
Pitfalls and disagreements

The model curve used a value above the mean [hate2017 X8]. The absorption line of the absorption-versus-growth model cannot be reproduced from the printed coefficient, area and flow rates (F29) [hate2019 X4].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

metastable equilibrium

The state in which the drug-rich and the drug-lean phases coexist with equal activity while both remain supersaturated with respect to the crystal [raina2014a C33; alhalaweh2016 C1; indulkar2016 C23]. The Crystallization from solution papers extend it to amorphous precipitates and add cases: type 2 bases precipitate when the concentration is close to the amorphous solubility and keep a metastable equilibrium between solution and amorphous precipitate [hsieh2012 C29]; after danazol separates, the supersaturation stays constant because the drug-lean solution is in equilibrium with the droplets [jackson2014 C28]; the dihydropyridine precipitates are taken to be in metastable equilibrium with a supersaturated water-rich phase, so that crystallization can start in either, and for danazol the binodal compositions are x = 4.27 × 10⁻⁷ (water-rich) and 0.92 (droplet) mole fraction [raina2015b C24, C39; jackson2016 R22].

Findings

Bioperformance: F1, F5, F10. Crystallization from solution: F1, F2, F4, F21, F22.

Related concepts

the state of liquid-liquid phase separation; related to chemical potential; characterizes amorphous precipitation; related to amorphous solubility.

Formulas

none.

How it is measured or obtained

Not measured as such; concentration or flux staying constant while two phases coexist [raina2014a C36]. In the pH-shift and danazol papers it is inferred from a concentration plateau at the amorphous solubility while the precipitate remains amorphous (Bjerrum data following the curve for the supernatant concentration, a pyrene ratio held at about 1.5), and by the later fall to the crystalline solubility [hsieh2012 R8, R9; jackson2014 R8, R15].

Values in the library
materialvalue or classconditionspaper ids
telaprevira 130 µg/mL solution has the same flux as a 90 µg/mL solution; added drug increases the amount of drug-rich phase while the drug-lean concentration stays constant37 °C[mosqueragiraldo2015 C35, C36]
danazol ASDsall except 50:50 HPMCAS exceed the amorphous solubility only brieflyjackson2015 C31
felodipineamorphous precipitates are probably viscous supercooled liquids in metastable equilibrium[raina2015b C24]
loratadineplateau 9.6–10.3 µg/mL to about 91 min against crystalline 1.6 µg/mLpH shift, 37 °C[hsieh2012 R8, R10]
danazol above 13 µg/mLpyrene about 1.5 for 9 min, then crystallization25 °C[jackson2014 R15]
atazanavir (Bioperformance)metastable equilibrium until crystal nucleation, drug activity equal in both phasesASD-coupled dissolution and membrane transferhate2018 C5
danazol–water, 25 °Cbinodal 4.27 × 10⁻⁷ and 0.92 mole fraction danazolfrom the onset and moisture sorption[jackson2016 R22]
Pitfalls and disagreements

It lasts only until crystals nucleate (F10). The phase was not observed or analysed in the type 2 bases, and phase separation was "believed" to explain them [hsieh2012 C34]. For danazol, how LLPS affects subsequent crystallization is "not well understood" [jackson2014 C45].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

micellar solubilization

Increase of the apparent solubility of a drug by incorporation into surfactant micelles; with Tween 80 above its CMC, ritonavir's crystalline solubility rose 2.7-fold and its LLPS concentration about 2.5-fold (synthesis: 46.1 ÷ 18.8 = 2.45), leaving their ratio about unchanged ilevbare2013a R16, X5. The papers of 2017–2022 add two cases. In 3.6 mg/mL SDS atazanavir's crystalline solubility rose from 1.1 to about 45.6 µg/mL and its amorphous solubility to about 1450 µg/mL, so the concentration ratio fell from about 65 to about 33 while the flux-derived activity ratio stayed at about 65 (molar solubilization ratio κ 0.006, 0.183 and 0.351 for crystal, measured and predicted amorphous) indulkar2017a R7, R9, R13. With 12 mM bile salts, STDC, STCDC, SGDC and SGCDC raised telaprevir's crystalline solubility 1.8–2.4 times and its GLPS onset about twofold, while STC and SGC did not [lu2017b R1, R2, X9]. New aspect (Bioperformance): uptake of drug into surfactant or bile-salt micelles raises the equilibrium solubility and the total concentration but not the free drug [raina2015c C30]. In simulated and pooled human intestinal fluids bile salts and lecithin raised the crystalline solubility proportionally more than the amorphous solubility (F18) [elkhabaz2019b C35]; high log P drugs are expected to show a positive food effect for this reason nguyen2023a C77, C78. New aspect (Crystallization from solution): In the bile-salt and surfactant papers the question is whether the surfactant raises the dissolved drug without raising its activity: STC at 0.1% raised the crystalline solubility only 1.1- to 3.5-fold across 11 drugs, whereas SDS at 0.1% raised it up to about 266-fold, and 12 mM dihydroxy bile salts needed about twice the telaprevir for the same activity [chen2015 R1, R2; lu2017 R1]. The 2018–2025 papers carry the question into bile salt–lecithin media and above the CMC of SDS, where micelles raise both the crystalline and the amorphous solubility but not the activity-based supersaturation at the amorphous solubility [indulkar2018 R8, R12; indulkar2019b R1, R2; duong2022b R8]. New aspect (Mesoporous silica): with drug-loaded silica, micelles act in two ways at once, by solubilizing released drug and, for a surfactant that competes for the silica surface, by displacing adsorbed drug; the authors write a three-way metastable equilibrium, drug adsorbed to silica ⇌ drug in solution ⇌ drug solubilized in micelles [dening2019 E11, C57]. They call micellar solubilization "therefore advantageous" for silica systems because it raises release and micellar drug replenishes free drug as it permeates, while cautioning that micelles "may actually reduce" the free fraction and the flux [dening2019 C60, C58, C59]. New aspect (Supersaturation from ASD dissolution): in the celecoxib suspension study each surfactant raised the Form III solubility steeply above its CMC, and supersaturation was referred to the solubility in each medium so that solubilization alone would not raise S chen2015a R5, C2, C3. In suspensions of enteric lopinavir dispersions at pH 3, drug leaching followed the solubilization of the crystalline drug by each surfactant, so that the leached concentration rose with the crystalline solubility in the same medium and their ratio stayed nearly constant for a given polymer [li2016b C39, C40]. With a polymer present STC at least doubled the crystalline solubility given by STC alone, and PVPVA with SDS raised it from 3.3 to 11.4 µg/mL [li2016b R5, C43]. A marketed tacrolimus product containing sodium lauryl sulfate reached the same maximal flux as the others, so no solubilization was seen at its level [trasi2016 C38]. New aspect (Release mechanism and LoC): two surfactant papers of 2021–2022 ask whether micelles explain the higher limit of congruency of surfactant-containing dispersions. Monomeric TPGS did not raise the crystalline solubility of felodipine (about 1.3 µg/mL, as in buffer), so no significant solubilization occurs without micelles saboo2021 C8, R2; since 2% TPGS raised the limit to 25% with TPGS below its CMC, and at 30% both 5% TPGS (below the CMC) and 10% TPGS (above it) released congruently, micellar solubilization plays "a negligible role" in the limit saboo2021 C33. For clopidogrel the effect on the LLPS concentration depended on the surfactant: SDS raised it only above its CMC, while TPGS and Tween 80 raised it at 50 but not at 5 µg/mL correasoto2022a C9, R3; up-field NMR shifts with 50 µg/mL TPGS below and above the LLPS concentration are read as solubilization of clopidogrel in the less polar micelles correasoto2022a C16, R11. The micellar content of FaSSIF did not raise HPMCAS-MF dissolution or release from 10% indomethacin–HPMCAS, consistent with polymer-controlled release bapat2023 C11, C20. In the 2025 bedaquiline study simulated intestinal fluids raised the crystalline solubility from undetected (pH 6.5) to 7.8 µg/mL (FaSSIF-V1), from below 0.1 to 258.8 µg/mL (FeSSIF-V2) and to 628 µg/mL (FeSSIF-V1), and cut drug–HPMCAS complexation from up to about 90% to at most about 29%; the authors read the micelle affinity of the drug cation as the reason the complex does not form ("explains") kaur2025 R2, R6, R8, C36, C39.

Findings

Amorphous solubility and LLPS: F12, F16, F17, F18. Bioperformance: F3, F4, F16, F18. Crystallization from solution: F19, F28, F29, F31, F32, F34, F38. Mesoporous silica: F12. Supersaturation from ASD dissolution: F7, F14, F15, F19, F28. Release mechanism and LoC: F21, F23, F34.

Related concepts

surfactant above the critical micelle concentration; leaves thermodynamic activity unchanged; raises crystalline solubility. Papers of 2017–2022: described by the micelle/water partition coefficient; cost for transport: solubility-permeability interplay; measured on the activity scale by activity-based supersaturation. Contrasts with nanodroplet reservoir effect; lowers free drug concentration; measured by membrane flux; related to mixed micelles. Competes with drug adsorption onto silica together with competitive adsorption of the surfactant; related to supersaturation. Distinct from surfactant partitioning into the drug-rich phase; ruled out as the cause of a higher limit of congruency with TPGS.

Formulas

solid-liquid equilibrium solubility equation. Activity from concentration, micelle-water partition coefficient, membrane flux from permeability and concentration, membrane flux in terms of solute activity, supersaturation from membrane flux ratio, supersaturation ratio.

How it is measured or obtained

Crystalline solubility and LLPS concentration with and without the surfactant, 500 µg/mL Tween 80 in 100 mM phosphate pH 6.8 at 37 °C ilevbare2013a P1, P5, A6. In the Bioperformance papers crystalline solubility is measured against surfactant concentration and free drug by flux or ultracentrifugation [raina2015c P1; indulkar2017a R11]. In the bile-salt and surfactant papers: 48 h shake-flask solubility with and without the surfactant, a membrane mass flow that follows the activity, and an activity-based supersaturation calibrated from the flux [chen2015 P1; li2016a P8, R15; lu2017 E1, E2]. In the Mesoporous silica papers: crystalline and amorphous solubility of ritonavir with SDS (28 µg/mL) and Vit E TPGS (28 and 500 µg/mL; cited CMC 212 µg/mL) in pH 6.8 phosphate at 37 °C, and release from ritonavir–SBA-15 dosed at the amorphous solubility of each medium [dening2019 P1, P2, P9, M3]; release in FaSSIF dosed at its amorphous solubility [dening2018 P6, R21]. In the ASD dissolution papers: excess Form III stirred 48 h at 25 °C in pH 3 HCl with the surfactant, ultracentrifuged and assayed by HPLC chen2015a P6; crystalline solubility in every leaching medium, with excess polymer, 48 h at 25 °C, ultracentrifuged [li2016b P5]; break of crystalline solubility against surfactant concentration as the CMC [li2016b P3]. In the release-mechanism papers: crystalline solubility against surfactant concentration with and without 900 µg/mL PVPVA saboo2021 R2; LLPS concentration by UV extinction, centrifugation and diffusion cell with 5 and 50 µg/mL surfactant correasoto2022a R3.

Values in the library
materialvalue or classconditionspaper ids
ritonavir with 500 µg/mL Tween 80crystalline 1.3 → 3.5 µg/mL; LLPS 18.8 → 46.1 µg/mL37 °Cilevbare2013a R16
felodipine with 0.04% vitamin E TPGScrystalline solubility up almost 40-fold; concentration ratio 9.2 → 4.537 °C[raina2015c C29]
atazanavir with SDScrystalline 1.1 → 45.6 µg/mL; κ 0.006 (crystal), 0.183 (amorphous), 0.351 (predicted)0–3.6 mg/mL SDS, pH 6.8, 37 °Cindulkar2017a R7, R9
telaprevir with 12 mM bile saltscrystalline 5.2 → 11.1 (STDC), 12.2 (STCDC), 12.4 (SGDC), 9.6 (SGCDC), 6.7 (STC), 6.2 µg/mL (SGC)50 mM pH 6.5, 37 °C[lu2017b R1]
felodipine1.1 to 35.3–49.0 µg/mL with six additives above CMC / 0.1–1%37 °C[raina2015c R2]
nifedipine10.3 to 53.4–90.7 µg/mL37 °C[raina2015c R3]
atazanavir + SDSconstant about 1 µg/mL to 0.5 mg/mL SDS, then 2.6 / 22.2 / 45.6 µg/mL at 0.6 / 2.0 / 3.6 mg/mLpH 6.8indulkar2017a R7, R8
celecoxib Form IIISDS 0.25% 14.5, STC 0.75% 5.8 µg/mL25 °Cchen2015a R5
posaconazolecrystalline 0.23 (buffer) to 3.2 µg/mL (FaSSIF-V1); amorphous 8.1 to 43.3six media, 37 °C[elkhabaz2019b R1, R2]
atazanavircrystalline 1.4 to 7.1 µg/mL; amorphous 79 to about 99–102six media, 37 °C[elkhabaz2019b R1, R2]
pretomanidequilibrium solubility about 3-fold (FaSSIF V1) and 6-fold (FeSSIF V2) the buffer value37 °Cnguyen2023a R1, C33
11 drugs, 0.1% STC and SDSSTC 1.1–3.5-fold; SDS 1.2–266-fold25 °C (telaprevir 37 °C)[chen2015 R1]
celecoxib, 0.1% STC, SGC, HPMCASsolubility 1.2 → 2.9, 2.4, 2.4 µg/mL; mass flow unchanged (0.44–0.46 µg/min)pH 6.5, 37 °C[li2016a R15]
telaprevir, 12 mM STDC, SGDC, STCDCabout 140 against 60 µg/mL for the same δ 11.5pH 6.5, 37 °C[lu2017 R1]
ritonavir, cilnidipine; buffer, FaSSIF-V1, Composite-SIFamorphous/crystalline ratio 12 → 8.4, 7.8 and 36.5 → 12.9, 13.7; ritonavir SRamorph 9.2–10 throughoutpH 6.5, 37 °C, 3 mM bile salt[indulkar2018 R8, R12]
telaprevir, 3.72 and 5.58 mM bile salt mixturesδ 11.5 at about 72–77 against 60 µg/mL in buffer50 mM phosphate pH 6.5, 37 °C[lu2018 R1.h, R2]
atazanavir, SDS above the CMC (0.5 mg/mL)crystalline about 46 and amorphous about 1480 µg/mL at 3.6 mg/mL; concentration ratio about 35–38 against SRamorph stated about 6550 mM phosphate pH 6.8, 37 °C[indulkar2019b R1, R2, X6]
posaconazole, five biorelevant mediaconcentration ratio 17.9–20.7 against 28.3–33.7 in buffers; Km/w about 635–1820 at the amorphous and about 1440–3240 at the crystalline solubility37 °C, pH 1.6–6.5[duong2022b R8, R14]
atazanavir, posaconazole in aspirated human fluidconcentration ratio about 15 and 5.4 against cited activity ratios 54 and 30pH 7.3, 37 °C[elkhabaz2021 R1, R4, X14]
ritonavir, 28 µg/mL SDS; 28 and 500 µg/mL Vit E TPGScrystalline 3.6 → 6.6; 11.8; 14.9 µg/mL; amorphous 27.9 → 26.8; 27.7; 76.6 µg/mLpH 6.8, 37 °C[dening2019 R1]
ritonavir–SBA-15 in micellar Vit E TPGS69% at 30 min against 50% in buffer; bound drug 72 against 146 mg/g; crystallized about 45 mindose 77 µg/mL[dening2019 R18, R19]
ritonavir in FaSSIFcrystalline 8.8, amorphous 42.7 µg/mL; release from SBA-15 about 71% against about 50%dose 43 µg/mL[dening2018 M1, R21]
celecoxib Form III, SDS 0 → 0.40%1.1 → 92.6 µg/mLpH 3, 25 °Cchen2015a R6
STC 0.10 → 1.50%1.8 → 26.0 µg/mLpH 3chen2015a R7
polysorbate 80 0 → 1%1.2 → 198.4 µg/mLpH 3chen2015a R8
Triton X100 0 → 0.15%1.2 → 59.6 µg/mLpH 3chen2015a R9
Poloxamer 188 0.002 → 3%1.4 → 2.5 µg/mLpH 3chen2015a R10
lopinavir with HPMCAS-HF, + SDS / Poloxamer 188 / polysorbate 80 / STC3.3 / 3.0 / 4.5 / 7.2 against 1.9 µg/mLpH 3, 25 °C[li2016b R5]
lopinavir with HPMCAS-HF, PVPVA and SDS11.4 µg/mLpH 3, 25 °C[li2016b R5]
lopinavir with HPMCAS-HF and SDS at pH 56.3 µg/mL25 °C[li2016b R5]
delamanid, crystalline0.52 (FaSSIF V1), 2.30 (FeSSIF V2), 13.10 (FEDGAS pH 4.5) and 57.97 µg/mL (FEDGAS pH 3.0) against below 0.02 µg/mL in buffer above pH 5.537 °C[nguyen2023b R13, R18]
praziquantel, amorphous and crystallineamorphous 1.74 and 1.70, crystalline 0.31 and 0.43 mg/mL in FeSSIF-V2 (racemate, R-enantiomer) against 1.17/1.39 and 0.16/0.23 mg/mL in PBS pH 6.537 °C[alvarenga2025 R1]
delamanid, amorphous69.9 (FaSSGF), 7.93 (FaSSIF V1), 3.11 (FaSSIF V2) and 0.76 µg/mL (PBS pH 6.5)37 °Cduong2022a R1
felodipine with monomeric TPGScrystalline solubility ≈1.3 µg/mL, as in buffer; slope change near 48 (buffer) and 40 µg/mL TPGS (with PVPVA)37 °Csaboo2021 R2, C8, P1
clopidogrel in buffer; with 50 µg/mL TPGS; with 50 µg/mL Tween 80LLPS concentration 23 ± 3; 29 ± 2; 30 ± 2 µg/mL37 °Ccorreasoto2022a R3
clopidogrel with 5 µg/mL TPGS, CTAB or 50 µg/mL SDS20 ± 1 µg/mL37 °Ccorreasoto2022a R3
neat HPMCAS-MF in FaSSIF; in blank FaSSIF buffer≈0.56; ≈0.57 mg/min/cm²pH 6.5, 12 mM/ΔpHbapat2023 R7
bedaquiline in FaSSIF-V1, FeSSIF-V2, FeSSIF-V1crystalline solubility 7.8, 258.8, 628 µg/mL37 °Ckaur2025 R2
Pitfalls and disagreements

Whether the surfactant enters the drug-rich phase and the activity in the micellar solution were not measured ilevbare2013a C54. Total concentration in micelles overstates the driving force (F12). Total concentration in micelles overstates the driving force; the micelle/water partition coefficient depends on the drug concentration, so a prediction from the crystalline solubility overshoots about twofold for atazanavir in SDS indulkar2017a C46, C48. Whether micelles cross the 6–8 kDa membrane was not tested [indulkar2017a X9; lu2017b X8]. In the Bioperformance papers the micelle capacity changes with drug load, so a single partition coefficient is wrong [raina2015c C37]; it was not measured there. In human fluid the micelles added proportionally less drug at the amorphous than at the crystalline solubility; the printed partition coefficients are total-to-buffer ratios, one higher than the defining equation gives (F18) [elkhabaz2019b R11, X2]. A ratio of concentration to solubility understates the supersaturation when the solubilizer raises the solubility but not the activity (celecoxib with STC, SGC and HPMCAS) [li2016a X18]; at matched ratio the SDS runs held up to 36 times more drug [chen2015 X4]. In micellar media the partition coefficient falls with drug concentration, so a concentration ratio near 20 can correspond to an activity ratio near 34; the posaconazole paper converts by assuming a linear fall between the two solubilities [duong2022b C9, C26, E11]. Mesoporous silica: both Vit E TPGS media crystallized between 30 and 45 min, so it is "not clear" whether release had finished [dening2019 C34]; the release gain was not shown as a flux gain [dening2019 C58]. The FaSSIF gain is attributed "likely" to micellar solubilization and better wetting, neither measured [dening2018 C48]. The silica papers' view that micellar drug replenishes free drug as it permeates [dening2019 C60, C58] sits against the Bioperformance statement that micelles raise the total concentration but not the free drug [raina2015c C30]; the silica authors themselves caution that micelles may reduce the free fraction and the flux [dening2019 C59]. In the celecoxib suspensions the solubility used to normalize S in SDS was measured without the leached HPMCAS present chen2015a X10, and two test-level solubilities are not in the supplementary tables chen2015a X14. The surfactant-titration curves of the lopinavir study give lower solubilities than its table for the same media, and the reading that polymers weaken Poloxamer 188 rests on them [li2016b X3, X4]; leached HPMCP shifted the SDS break to about 0.1% [li2016b R11]. A modest gain in a fed medium leaves room for the medium to act on crystallization instead: praziquantel release fell to about 34–52% in FeSSIF-V2 at 1.5 mg/mL [alvarenga2025 R18, C29], whereas the several-hundredfold gain for delamanid raised the release of the marketed tablet [nguyen2023b R14, C29]. The TPGS concentrations listed for the felodipine runs assume complete release into 100 mL; only about half the TPGS had been released at 60 min, so the bulk concentration was about half the listed value saboo2021 X14. Micellar solubilization and disruption of the complex were not separated in FaSSIF-V1 kaur2025 X13.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

microenvironmental pH

Evidence table: microenvironmental pH (names merged there: diffusion layer pH, microenvironmental pH, surface pH). Content from the release-mechanism chapter (2022–2025), with rows from the Bioperformance and Peptide permeability chapters.

The pH at a dissolving surface, in its gel layer or in the adjacent boundary layer, which can differ from the bulk pH. When an acidic polymer dissolves above its pKa, ionization releases protons and lowers the interfacial pH, which can lower solubility and dissolution; the protons leave by diffusion, by neutralization with hydroxyl ions from the bulk or through proton carriers (buffer species), and finite diffusion times give a surface-to-bulk gradient set by hydrodynamics, the pKa and solubility of the solute and the pKa and concentration of the buffer (cited) qi2022 C24. HP-50 is extensively ionized at pH 6.8 given its pKa of 4.2, "but the pH at the dissolving surface may differ" qi2022 C23. For HPMCAS-MF a lower pH at the polymer–solution interface, set up by the protons the ionizing polymer releases, is called "probable" and is "strongly supported" by the gel measurements; more buffer species carry more protons to the bulk and lessen the drop bapat2023 C38, C39. Polymer release rate was highly correlated with gel-layer pH, which was substantially lower than bulk pH bapat2023 C51. In the Bioperformance chapter a base was added to pretomanid–HPMCAS-HF dispersions in the expectation that it raises the microenvironmental pH and so speeds polymer dissolution nguyen2023a C26. In the Peptide permeability chapter a high local concentration of permeation enhancer at the tablet surface raised the surface pH and changed insulin release fagan2025 C33. The papers of 2024–2025 use the HPMCAS gel pH of 6.0 in 50 mM pH 6.8 phosphate (measured in 2023) as the pH at which a weak base meets the ionized polymer, so complexation was measured at pH 6.0, and weak bases are more ionized there than in the bulk bapat2024 C9, C48, R20; bapat2025a C28, R15; kaur2025 C44, R22. The 2025 grade paper measured the pH of polymer slurries in water, taken as the lowest possible surface pH: 4.52 (LF), 4.61 (MF) and 4.73 (HF) bapat2025a C10, M3, M4, M5.

Findings

Release mechanism and LoC: F23, F24, F32, F33.

Related concepts

set by buffer capacity and buffer pKa; decides whether the polymer reaches its critical ionization for polymer dissolution; avoided by polymer salt formation; located in the gel layer and the unstirred water layer; related to polymer ionization.

Formulas

boundary-layer diffusion flux (film model).

How it is measured or obtained

Gel-layer apparent pH by indicator absorbance: HPMCAS made with chlorophenol red or bromothymol blue, compacted, exposed in the rotating-disk apparatus, the gel removed and its spectrum read bapat2023 P10. In the HP-50 paper surface pH was not measured; a cited gradient for HP-50 films was used qi2022 R18, X16. In the Peptide permeability chapter, the pH of saturated enhancer suspensions and the colour of a pH indicator drop on the tablet surface fagan2025 R5, R19.

Values in the library
materialvalue or classconditionspaper ids
HP-50 films (cited)surface pH ≈0.4 units below bulkphosphate of similar capacityqi2022 R18
HPMCAS-MF gel at 13, 26, 51 mM/ΔpH; pH 7.5 phosphateapparent pH 5.6, 6.0, 6.2; 6.3, against rates ≈0.60–1.09 mg/min/cm²bulk pH 6.8 or 7.5bapat2023 R15, R16
HPMCAS-TEA gelapparent pH 6.7, rate ≈1.62 mg/min/cm²50 mM pH 6.8 phosphatebapat2023 R16, C41
C10 and SNAC minitablets (Peptide permeability chapter)surface pH near 8 and near 7 by indicator; suspensions pH 8.8–9.2 and 7.6–7.9biorelevant mediafagan2025 C36, C8
HPMCAS LF, MF, HF slurries in waterpH 4.52, 4.61, 4.73overnight stirringbapat2025a M3, M4, M5
25% loratadine–HPMCAS-MF on a cited gel-pH axis 6.0, 6.2, 6.3release ≈0.12, 0.29, 0.68 mg/min/cm²three buffersbapat2024 R15, X6
Pitfalls and disagreements

The HP-50 paper calls polymer ionization the rate-limiting step in the abstract but "likely" in the discussion; surface pH, proton flux and gel hydration were not measured, and the proton-carrier argument uses calculated buffer pKa values and a cited gradient qi2022 X16. The HPMCAS values are apparent pH of gel removed from the compact, not an in situ profile bapat2023 P10. Only the gel pH of 6.0 has a stated source; the 6.2 and 6.3 values of the 2024 plot do not bapat2024 X6. The MF slurry pH has no stated source bapat2025a X4.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

mixed micelles

Aggregates of bile salts with phospholipids and their hydrolysis products, the good drug solubilizers of intestinal fluid; the bile-salt papers worked with single bile salts and name mixed micelles with lecithin as the next, more biorelevant step [chen2015 C4; lu2017 C42]. From 2018 the library measures mixed micelles of bile salt and lecithin directly in crystallization tests: lecithin shortens induction times and raises the amorphous solubility of atazanavir, its digests accelerate more, and the bile salt to phospholipid ratio sets the induction time in volunteer media [indulkar2018 R16, R6; enright2020 R10, R18].

Findings

F28, F32, F39, F40, F41, F43.

Related concepts

related to bile salt micelles and biorelevant media.

Formulas

none.

How it is measured or obtained

Not measured in these papers.

Values in the library
materialvalue or classconditionspaper ids
telaprevir, single bile saltssystems with micelles and a drug-rich phase are called probably the most relevant in vivo and need lecithin mixed micellespH 6.5, 37 °C[lu2017 C42]
FaSSIF-V1, Composite-SIFunimodal 49 ± 4 nm; bimodal 63 ± 4 nm (56%) and 3.9 ± 0.4 nm (44%)DLS, 173°[indulkar2018 R5]
atazanavir, 3 mM STC with 0–0.75 mM lecithininduction time about 595 → 43 min; amorphous solubility 38 → about 82 µg/mLpH 6.5, 37 °C[indulkar2018 R16, R6]
atazanavir, volunteer media with 350 µM phospholipidbile salt:phospholipid 1.6–14.7; 23–33 against 112–144 minpH 6.5, 37 °C[enright2020 R18, E2]
posaconazole, FaSSIF-V1 against FaSSIF-V2more lecithin gives higher amorphous solubility and Km/w for posaconazole, not for atazanavirbiorelevant and human fluids[elkhabaz2019b C38]
Pitfalls and disagreements

Lecithin was absent from all the bile-salt studies of this chapter's papers up to 2017, and may alter solubility and kinetics [li2016a C64]. The two proposed lecithin routes (taurocholate drawn into mixed micelles; lecithin lowering the interfacial energy of the nucleus) were not measured [indulkar2018 C40; elkhabaz2021 C25].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

moisture barrier effect

Reduction of the uptake of water, or of its rate, by a particle coating. It was offered as one of two reasons why an alumina shell stabilizes an ASD powder, the other, "perhaps more importantly", being lower surface molecular mobility [duong2022c C53, C54]; alumina nanoshells blocked water uptake of amorphous lactose in earlier work (cited) [duong2022c C6]. In the ASD process papers it is measured as equilibrium uptake and as uptake kinetics, and the two do not agree: thin coatings leave equilibrium uptake unchanged, thick or slow-deposited coatings lower or slow it [moseson2022a C20; duong2022c C59; moseson2023 C13].

Findings

F43, F45, F47.

Related concepts

measured as water sorption and hygroscopicity; set by coating defect density and thickness; proposed beside surface molecular mobility as a stabilizing mechanism of the atomic layer coating.

Formulas

none.

How it is measured or obtained

Dynamic vapour sorption of coated and uncoated powder: isotherms at 40 °C (0–95% RH) or 37 °C (5–95% RH in 5% steps, n = 3), or kinetics after drying at 0% RH and a step to 90% RH for 2–3 h [moseson2022a P12, R8, R9; duong2022c P9, R9; moseson2023 P10, R7, R8; benson2025 P8, R3].

Values in the library
materialvalue or classconditionspaper ids
erlotinib–HPMCAS, 5–25 nmabout 5.7% uncoated against about 5.4% coatedDVS 40 °C, 75% RHmoseson2022a R8, R9, C20
ezetimibe–HPMCAS 50% DL, uncoated / thin / thickabout 5.65 / 5.83 / 3.17%DVS 37 °C, 95% RH[duong2022c R9]
ezetimibe–HPMCAS 70% DL, uncoated / thin / thickabout 4.88 / 5.21 / 4.35%same[duong2022c R9]
posaconazole–HPMCAS 25% DL, 0 / 11 / 23 / 39 nmabout 4.7 / 4.3 / 3.7 / 1.2% at 30 minDVS 37 °C, 90% RHmoseson2023 R7
posaconazole–HPMCAS 50% DL, slow-deposited 26 nmabout 0.33% at 2 h against about 4.2–4.5%samemoseson2023 R8
ritonavir–PVPVA 20% DL, slow-coated 20.5 nmabout 15.1% against about 20% at 3 hsamebenson2025 R3
Pitfalls and disagreements

The thin 50% ezetimibe coating protected for two years without lowering uptake, so equilibrium uptake is not a measure of protection [duong2022c X7; moseson2023 C52]. The abstract of the ezetimibe paper generalizes lower hygroscopicity to all coated powders, which only the thick coatings show [duong2022c C59, X6]. Sorption was measured on dry powders, not on powders in storage, and the slow-sorbing posaconazole samples had not levelled off within 2 h moseson2023 X17. Moseson (2022) read the unchanged bulk uptake as a coating that "would block water adsorption to the particle surface", which was not measured moseson2022a C42, C43.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

moisture-induced crystallization

Crystallization of an amorphous drug, alone or in a dispersion, that sorbed water starts or speeds up. In the library it is measured as a nucleation rate, a crystal growth rate or a crystallized fraction that rises with storage relative humidity [konno2008 C11; rumondor2010 C8, C9; rumondor2009b C7]. Two routes are distinguished: water raises molecular mobility (plasticization) and may raise the drug's chemical potential, or water first splits a dispersion into drug-rich and polymer-rich amorphous phases, from which the drug-rich phase crystallizes [marsac2008a C1, C26; rumondor2009c C5; marsac2010 C25]. New aspect (Supersaturation from ASD dissolution): it serves as the solid-state comparison for the polymer ranking in dissolution: dry felodipine dispersions with PVP, HPMC and HPMCAS nucleated alike, whereas with moisture HPMCAS and HPMC inhibited crystallization better than PVP (cited) [konno2008a R18]. The resveratrol dispersions that resisted crystallization at high humidity (PVP, E100) also stayed amorphous in buffer but gave no concentration gain, and those that crystallized at high humidity (HPMC, HPMCAS, CMCAB) also crystallized in buffer at 35% drug [wegiel2015 R21, C7, C9]. Indomethacin dispersions at 60% drug with HPMC or EPO crystallized within 5 days at 40 °C/75% RH, the EPO–HPMC ternary not within 100 days [xie2017 R26].

Findings

Physical stability: F9, F11, F15, F24, F25, F33, F34. Supersaturation from ASD dissolution: F4, F6, F16, F20.

Related concepts

depends on plasticization by water and water sorption; can follow moisture-induced phase separation; part of solid-state crystallization of amorphous drugs; related to hygroscopicity; related to physical stability and crystallization inhibition by polymers.

Formulas

none specific; the water uptake that drives it is described by Flory-Huggins water sorption isotherm.

How it is measured or obtained

Storage over saturated salt solutions at fixed RH and counting of birefringent nucleation sites in spin-coated films [konno2008 P3, P4]; growth of existing crystals in films at fixed RH [rumondor2010 P3, P4, P5]; PXRD crystallinity of stored powders with PLS calibration [rumondor2009b P5]; AFM and polarized light on films after 1–16 h at 94% RH marsac2010 P14, R19. Outside the subcategory, SHG imaging of spray-dried dispersions at 40 °C and 75–82% RH [correasoto2017 R4, C15].

Values in the library
materialvalue or classconditionspaper ids
amorphous felodipine filmnucleation ≈1.4 × 10⁵ → 2.9 × 10⁶ m⁻³ s⁻¹0 → 75% RH, 22 °C[konno2008 R1.a, R3.a]
amorphous nifedipine filmnucleation ≈4.7 × 10⁵ → 6.8 × 10⁶ m⁻³ s⁻¹0 → 75% RH[marsac2008a R1.a]
amorphous felodipine filmgrowth ≈0.030 → 0.066 mm/min (13–80% RH), 2.3–2.8 mm/min at 87–93% RH, with needleshumidity stage, 25 °C[rumondor2010 R1, C9]
felodipine–PVP 25% powder1.2% (0% RH) to 82.1% (93% RH) crystallized after ≈494 days22–25 °C[rumondor2009b R9.a, R9.g]
felodipine–HPMCAS 50% powder9.2–16.6% at every RH after ≈490 days22–25 °C[rumondor2009b R9]
felodipine–PVP 50% filmcrystals by 4 h at 94% RH, after phase separationAFM, polarized lightmarsac2010 R19, C24
FTM–HPMCAS spray-dried dispersion (outside)faster crystallization at 82% than at 75% RH40 °C, SHG[correasoto2017 C15]
Accord tacrolimus capsules (outside)rapid crystallization in the powder blend40 °C/75% RH[purohit2019 C33]
resveratrol with HPMC, HPMCAS, CMCAB, PAAcrystalline at the first sampling at 84% RH, then fully; PVP and E100 not25 °C[wegiel2013b R12, R14, R16]
curcumin dispersionsat 84% RH: E100 > 350, cellulosics 75, PVP 22, neat 14 days25 °C[wegiel2014 R13]
indoprofen–PVPseparation at 54% RH, crystals from 75% (30% PVP) or 84% RH (50% PVP)22 °C filmsrumondor2011 R11, R14
lumefantrine–CAP 40:60 precipitated into water (9% water)crystalline from the first day at 40 °C/75% RH; amorphous 3 months under vacuumPXRDbhujbal2021 R4.a, R5, R10, C17
tacrolimus generic capsule contents≈36, 68 and 84.5% at 30, 35 and 40 °C/75% RH, ≈11% at 40 °C/54% RH, 4 weeksopen dish[trasi2017 R14]
felodipine dispersions with PVP, HPMC, HPMCAS (cited)no difference dry; HPMCAS ≈ HPMC > PVP at high RHstorage[konno2008a R18]
flutamide and ezetimibe HPMCAS dispersions (Solid-state methods)first storage time with detected crystallinity, by methodstorage[correasoto2017 R1]
tacrolimus capsules (Bioperformance)% crystallized against storage timestorage[purohit2019 R1]
resveratrol dispersions (storage, cited)PVP, E100 stable; HPMC, HPMCAS, CMCAB crystallized at high RHstorage[wegiel2015 R21]
indomethacin 60% with HPMC; EPO; EPO–HPMCcrystals within 5 days; within 5 days; amorphous beyond 100 days40 °C/75% RH[xie2017 R26]

Evidence table: moisture-induced crystallization.

Pitfalls and disagreements

The growth jump of felodipine above 80% RH has no counterpart in water uptake or Tg, and its cause is "currently unknown" [rumondor2010 C31, C33]. Bulk powder of pure amorphous felodipine crystallized within 12 days at 0% as well as at 93% RH, so at that resolution water made no difference [rumondor2009b R12, X8]. Whether crystallization follows the wet one-phase route or the phase-separated route changes how polymer content acts (no effect of PVP level at 93% RH) [rumondor2009b C20, C21]. For resveratrol the authors "do not fully understand" why humidity acted more than heat, and the contrast fails at 120 °C [wegiel2013b C40, X8]. In the precipitated lumefantrine series water content varies with the polymer, so the water effect is inferred bhujbal2021 C51, C56. A solid-state ranking under moisture need not hold in dissolution: HPMCAS and HPMC were alike in humid solids but HPMCAS dispersions gave far more supersaturation, and the authors suggest the inhibition mechanisms "may vary" with the amount of water [konno2008a C33, C34].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

moisture-induced phase separation

Splitting of an initially miscible drug–polymer dispersion into drug-rich and polymer-rich amorphous phases because of water, either taken up during storage or present during preparation. Two routes are distinguished: water carried into a drying solution, which gives drug-rich spheres in a polymer-rich matrix, and water absorbed by a dry film, which gives a drug-rich network with polymer-rich holes (evacetrapib) [li2017 C24, C28, C32]. Water acts as an antisolvent for hydrophobic drugs [li2017 C32; saboo2017 C42]. New aspect (Physical stability): in the physical-stability papers, sorbed water splits an initially one-phase drug–PVP dispersion into drug-rich and polymer-rich amorphous phases before crystals appear; the authors hold it to be thermodynamically driven, with mobility setting its rate rumondor2009c C2, C35, C41; marsac2010 C14.

Findings

ASD process: F1, F2, F4, F6. Physical stability: F12, F13, F14, F15, F16, F23, F31, F32.

Related concepts

a case of solvent-induced phase separation; a form of amorphous-amorphous phase separation; depends on hygroscopicity and water sorption; trapped by kinetic trapping; explained by Δχ effect; followed by moisture-induced crystallization; reversed by remixing of separated amorphous phases; driven also by hydrophobicity.

Formulas

Δχ effect, multicomponent Flory-Huggins free energy of mixing.

How it is measured or obtained

AFM topography and roughness, TEM with EDX, AFM-LCR and nanoTA, fluorescence microscopy and, for powders, modulated DSC for the number of Tgs [li2017 P8, P10, P13; mugheirbi2017 P8, P9, P11; li2019 P9, P10]. In the drug–PVP storage papers: IR of re-dried films against a calculated physical-mixture spectrum, DSC for two Tgs wet and re-dried, near-additive water uptake, AFM phase contrast and TEM without diffraction rings rumondor2009c P7, P9, R22; marsac2010 R19, R20.

Values in the library
materialvalue or classconditionspaper ids
ECP–HPMC / PVPVA filmsfeatureless at 18% RH; domains at 35–50% RH; 20 µL water per mL of stock splits a 50% filmspin coated[li2017 R3, R5, R12]
ECP–PVPVA after 97% RH, 7 daysnet-like structures at 10–80% DL; F/N 0.10 (continuous) against 0.06TEM-EDX[li2017 R19, R22]
ECP–PVPVA powders after 24 h at 97% RHtwo Tgs at 10–50% DL, one at 60–90%modulated DSC[li2017 R24]
ITZ–HPMC E3 filmsdomains at 40% and 20% RH, none at 7% RH; network after 24 h at 40 °C/75% RHspin coated[mugheirbi2017 P13, R1, R3, R17]
LPV–HPMC E5 films after 97% RHirregular discrete and semi-continuous domains; continuous phase 173 ± 13 °CnanoTAli2019 R8, R14
felodipine–PVP at about 75% RH and abovedrug-rich and polymer-rich amorphous phasescited[rumondor2009b R24]
telaprevir ASD filmsdry nitrogen (RH below 18%) eliminates water-vapour-induced separationcitedmosqueragiraldo2018b C11
LPV ASD powders with EC, HPMCAS, HPMCPstayed one phase after 48 h at 97% RHTg[li2018 R9, C40]
nifedipine-, pimozide-, droperidol–PVPseparated within 1 h at 94% RH; pimozide from 54% RHdried filmsrumondor2009c R7, R9, R10, R12
indomethacin-, ketoprofen–PVPone phase for 40 and 68 days at 94% RHsamerumondor2009c R14, R16
felodipine–PVPsmall change at 33–58% RH, distinct at 75% RH, amorphous-felodipine-like after 94% RH1 day–1 weekmarsac2010 R7, R11
felodipine with 25% HPMCAS or HPMCno change after 7 weeks at 75% RHdried films[konno2008 R11]
same drugs with PVP, PVPVA, HPMCASextent follows polymer hygroscopicity, PVP > PVPVA > HPMCASIR band loss, DSCrumondor2010c C38, C33
20 drug–polymer systemsHPMCAS dispersions less susceptible in general; PVP highly vulnerableclassesrumondor2011 C29
miconazole–PVPVA 50:501–3 µm drug-rich domains after 7 days at 75% RH; 4–25 µm domains within 5–30 min in bufferconfocal, AFM-IR[saboo2017 R15, R18, R19]
celecoxib–PVP 6:4two Tg events after 3 days at 94% RH, not after 75% RHDSCxie2016b R18, R19
ritonavir–PVPVA 30:70 with surfactantsSDS and Tween 80 delay visible separation; Spans speed it and coarsen the domainsconfocal at high RH, 37 °Cyang2022b R5, R6, R7, R8, C7
Pitfalls and disagreements

The water content of films and solutions was not measured in the film studies, so "moisture" is inferred from humidity and added water [li2017 X14; mugheirbi2017 X4]. The water-uptake explanation of the DL effect on storage separation rests on powders after 24 h, not on films [li2017 X8]. Whether a dry film is miscible or kinetically trapped is open [li2017 C43]. The effect of water reverses with PrOH and BuOH [mugheirbi2018 C12]. In the drug–PVP storage study, two-phase evidence in the wet state exists only for pimozide; for nifedipine and droperidol it rests on IR of re-dried films and sorption rumondor2009c X10. Donor type, carbonyl red shift and drug–water χ split the drugs the same way rumondor2009c X13. Class labels per system ignore that resistance depended on drug loading rumondor2011 X13, C38. The pattern depends on how water arrives: humid air gives drug-rich droplets in a polymer-rich matrix, bulk water a coarser connected structure [saboo2017 C46].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

molecular mobility

How fast molecules of an amorphous solid move and rearrange, the kinetic side of crystallization next to the driving force [marsac2006a C4; vaneerdenbrugh2010a C3]. In the library it is read from Tg (higher Tg, lower mobility at a given temperature), from enthalpy relaxation times, from melt viscosity and from model relaxation times, and water raises it by plasticization [konno2006 C2; marsac2006a R4.n; kestur2010b R10; rumondor2010 E1; marsac2008a C1].

Findings

F5, F9, F13, F14, F21, F22.

Related concepts

indicated by glass transition temperature; measured by enthalpy relaxation and structural relaxation time; raised by plasticization by water; related to kinetic barrier to nucleation.

Formulas

Kohlrausch-Williams-Watts equation, Stokes-Einstein equation; the AGV equation is listed on the chapter page as table only.

How it is measured or obtained

Enthalpy recovery after ageing fitted with the KWW function [konno2006 P6; marsac2006a P9]; zero-shear melt viscosity [kestur2010b P4]; Adam–Gibbs–Vogel relaxation time from Tg [rumondor2010 P8]; Tg and Tg − T as indicators [marsac2008a R8].

Values in the library
materialvalue or classconditionspaper ids
amorphous nifedipine, felodipineτ 6.3 and 4.2 h at 23.5 °C; nucleation 2–4 times faster for nifedipinedry[marsac2006a R4.n, C13]
felodipine with 3 wt% PVP K-12, K-29/32, K-90melt viscosity ≈58, 156, 690 Pa·s vs ≈44 Pa·s alone100 °C[kestur2010b R10.c]
amorphous felodipine filmsgrowth follows AGV mobility to the power 0.513–75% RH[rumondor2010 R7, C27]
pimozide–PVPmoisture-induced separation much slower at 4 °C than at 22 °C75% RHrumondor2009c R11, C41
ketoprofen–PVPwet Tg −23 °C, mobile, yet no separation94% RHrumondor2009c R25, C38
coated ASD powders (outside)crystallization onset linked to Tg − T at the storage condition40 °Cmoseson2022a C24, C25
ritonavir ASDs (outside)Tg only a crude indicator of mobilitydegradation study[alvarenga2022 C21]
celecoxib with miscible surfactantsmain effect "most likely" on mobilityTg-scaled growth[mosqueragiraldo2014 C30]
felodipine free surfacefaster growth "may be attributed" to mobile surface moleculesfilms[kestur2013a C16]

Evidence table: molecular mobility.

Pitfalls and disagreements

Bulk mobility measures did not rank crystallization: DSC relaxation may not describe "the motion involved in nucleation", viscosity "cannot be used as a precise measure" of drug mobility, and growth outran AGV mobility [marsac2006a C37; kestur2010b C24; rumondor2010 C26]. Mobility sets the rate of moisture-induced separation but does not cause it [rumondor2009c C35, C41; li2017 C44]. Tg did not rank polymers for acetaminophen, flutamide, resveratrol or curcumin [trasi2012a C18; trasi2012b C33; wegiel2013b C33; wegiel2014 C22].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

molecular recognition

The specific fit between molecules that lets them assemble in a given arrangement; in crystal engineering hydrogen bonding is the most reliable directional interaction for it [vaneerdenbrugh2011a C2]. In the physical-stability papers it is the name for how an additive may order the drug locally or enter its pre-nuclei, an effect that classical nucleation theory does not directly contain [trasi2012a C48, C49].

Findings

F17.

Related concepts

part of nucleation; contrasts with classical nucleation theory; related to hydrogen-bond donor and acceptor groups and self-association.

Formulas

classical nucleation theory (which does not contain it) [trasi2012a C49].

How it is measured or obtained

Not measured directly in these papers; it is inferred when an additive changes nucleation in a way that growth inhibition, Tg or hydrogen bonding do not explain [trasi2012a C50, C52; trasi2012b C47].

Values in the library
materialvalue or classconditionspaper ids
acetaminophen with 10% w/w PAA26 nuclei per cycle against 10.8; PAA "may" exert a local ordering effecthot-stage cycle to −30 °C[trasi2012a R12.e, C50]
flutamide with 10 mol% nilutamide (structural analogue)one nucleus in the imaged region; nilutamide "may" enter prenuclei and block themfilm cooled to −30 °C and reheated[trasi2012b R12, C47]
15 drugs with 7 polymers (other chapter)hydrogen-bond recognition rules applied to choose polymers that prevent crystallizationspin-coated films[vaneerdenbrugh2011a C51]
Pitfalls and disagreements

Both physical-stability uses are hypotheses: local ordering of acetaminophen near PAA and nilutamide inside flutamide prenuclei were not observed [trasi2012a C50; trasi2012b C47]. The acetaminophen counts behind the PAA reading add up nucleation over zones of different width, so PAA need not raise the rate per unit time [trasi2012a X8].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

monolayer coverage

The amount of adsorbate that covers a surface with one layer

Two meanings are used in the library, and the papers say they must be told apart [dening2019 C44]. The geometric (theoretical) monolayer is the drug that would cover the whole specific surface area of a carrier with flat-lying molecules, each occupying the area of its two largest dimensions [dening2018 E3, C17; hate2020a E2, C20; mccarthy2020 E3, P11]. The BET monolayer Q_m is the first-layer capacity fitted to an isotherm measured from water; Dening and co-workers read it as the silanol sites occupied in the presence of co-adsorbed water ("it is feasible") [dening2019 R6, C41]. Outside silica the same geometric idea gives the surfactant needed to cover the surface of drug-rich nanodroplets correasoto2022a E2.

Findings

F2, F1, F10, F11.

Related concepts

obtained from an adsorption isotherm through the BET isotherm; contrasts with multilayer adsorption; sets the scale for drug loading of silica; related to nanoconfinement.

Formulas

theoretical monolayer adsorption capacity, liquid-phase BET isotherm.

How it is measured or obtained

Geometric: specific surface area (586 m²/g for SBA-15, as supplied) times 10^{20} times the molar mass, divided by the contact area and Avogadro's number, with the contact area from molecular dimensions measured with Mercury on a crystal structure [dening2018 E3, P3, M3; hate2020a P15; mccarthy2020 P11]. BET: nonlinear fit of a liquid-phase BET equation to an isotherm by solution depletion [dening2019 P12; mccarthy2020 P17; hate2020a P16].

Values in the library
materialvalue or classconditionspaper ids
ritonavir on SBA-15geometric 0.253 g/g (printed "25.3% w/w"); BET 103 mg/g18.2 × 15.2 Å; pH 6.8 phosphate, 37 °C[dening2018 R4; dening2019 R6]
atazanavir on SBA-15geometric 278 mg/g (about 28% w/w); BET 4.5 mg/g17.53 × 14.07 Å; 300 µg/mL silica, HPMC[hate2020a R1, R3]
indomethacin on SBA-15geometric 0.287 g/g; BET 29 mg/g13.0 × 9.4 Å; pH 2.2, HPMC[mccarthy2020 R16, R10]
indomethacin methyl ester on SBA-15geometric 0.269 g/g (0.260 recomputed); BET 31 mg/g13.9 × 10.0 Å[mccarthy2020 R16, R10, X19]
ketoconazole, clozapine, atazanavir on SBA-15BET Qm 0.006–0.275, unit printed "mg/mol"pH 1–6.8, HPMC[hate2020b R21, X9]
clopidogrel nanodroplets, nonionic surfactantscalculated monolayer agrees reasonably with the effective concentrationphosphate buffer, 37 °Ccorreasoto2022a R24, C41

Evidence table: monolayer coverage.

Pitfalls and disagreements

The BET values from water are 2.5 to about 60 times below the geometric values (synthesis: 253/103 and 278/4.5) [dening2018 R4; dening2019 R6; hate2020a R1, R3]. Whether adsorption is "multilayer" depends on which monolayer is meant: indomethacin exceeded its BET value tenfold but its geometric value only at the top points [mccarthy2020 X10]. The geometric value is quoted in g/g silica and as % w/w of the formulation as if equal; 0.253 g/g is about 20.2% w/w on a drug-plus-silica basis [dening2018 X4; mccarthy2020 X4; hate2020a X4]. The geometric value assumes the whole surface accessible and a flat orientation; no paper measured coverage directly [dening2018 C17, C38]. The BET form assumes a homogeneous surface without lateral interactions, which silica is not [dening2019 C14, C15]. The geometric monolayer marked where ritonavir flux fell with loading, and the BET value matched the ritonavir release floor [dening2018 C38; dening2019 C32].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

multilayer adsorption

Adsorption beyond one layer of adsorbate on the surface

In the mesoporous-silica papers it is inferred when the isotherm exceeds a monolayer and models that allow more than one layer fit better than Langmuir; it is read as driven by supersaturation and as ending in partial pore filling near the amorphous solubility [dening2019 C11, C13, C45; mccarthy2020 C43, C44; hate2020a C25].

Findings

F2, F3.

Related concepts

contrasts with monolayer coverage; modelled by the BET isotherm and Freundlich isotherm; read from an adsorption isotherm; related to nanoconfinement through pore filling near the amorphous solubility.

Formulas

liquid-phase BET isotherm, Freundlich isotherm.

How it is measured or obtained

Comparison of the isotherm with the geometric or BET monolayer; fit quality of BET and Freundlich against Langmuir; the pyrene I_1/I_3 ratio of a solution in contact with silica below the LLPS concentration [dening2019 R2, R3, R6, R7; mccarthy2020 R7, R8, R10, R6].

Values in the library
materialvalue or classconditionspaper ids
ritonavir on SBA-15up to 424 mg/g against 253 (geometric) and 103 mg/g (BET)pH 6.8, 37 °C[dening2019 R2, R3, R6]
ritonavir + SBA-15pyrene I_1/I_3 1.83 against 1.91 in buffer (p = 0.054)30 µg/mL drug, 12.5 µg/mL silica[dening2019 R7]
indomethacin; methyl ester on SBA-15about 289; 342 mg/g against 287; 269 (geometric) and 29; 31 mg/g (BET)pH 2.2, HPMC[mccarthy2020 R7, R8, R16, R10]
indomethacin; methyl ester + SBA-15pyrene I_1/I_3 1.72; 1.88 against 2.00 with silica alonesub-LLPS drug[mccarthy2020 R6]
atazanavir on SBA-15"possibly" beyond the 4.5 mg/g BET monolayer300 µg/mL silica[hate2020a C25, R3]

Evidence table: multilayer adsorption.

Pitfalls and disagreements

Whether the top points are multilayers depends on the monolayer used: against the geometric value indomethacin and its ester are at or only modestly above one layer [mccarthy2020 X10]. The pyrene test was not significant and would also give a drop if pyrene entered a single adsorbed layer [dening2019 X11]; the indomethacin test lacks drug-alone controls at the same concentrations [mccarthy2020 X11]. The proposed change of mechanism at Q_m is not supported by the adsorbed fraction, which is already constant below it [dening2019 C31, X10].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

nanoconfinement

The state of drug held in pores a few nanometres wide, where in the literature view it resists crystallization, especially below the critical nucleus size, has a lower melting temperature and is held by the pore wall [hate2020a C38; hate2020b C2; dening2018 C7]. In the papers it is inferred from the absence of a glass transition, melting and diffraction in drug-loaded SBA-15 (7.1 nm pores) [hate2020a C4; hate2020b C15]. Dening and co-workers also invoke confinement for adsorption from solution: by analogy with capillary condensation, filling the pores is expected to be more favourable than LLPS in the bulk ("we believe") [dening2019 C45].

Findings

F1, F3, F11.

Related concepts

limited by drug loading relative to monolayer coverage; read from the absence of a glass transition temperature and of crystallization; related to drug-silanol hydrogen bonding at the pore wall.

Formulas

theoretical monolayer adsorption capacity (sets the loadings).

How it is measured or obtained

PXRD of loaded silica against a crystalline physical-mixture control; modulated DSC for a glass transition and melting; TGA degradation temperature; ATR-FTIR of carbonyl and isolated-silanol bands; a series of loadings around the calculated monolayer [hate2020a P3, P4, P5, P6, M10; mccarthy2020 P12, P13; dening2018 P4, P5].

Values in the library
materialvalue or classconditionspaper ids
atazanavir in SBA-15, 5–20% w/wno glass transition or meltingMDSC 2 °C/min[hate2020a R9]
atazanavir in SBA-15, 30 and 50% w/wglass transition near 105 °C and melting near 208 °C; 50% crystalline after 1 weekMDSC; storage dry, room temperature[hate2020a R9, R8]
ketoconazole, clozapine, atazanavir, 20% w/wX-ray halo, no thermal eventsPXRD, DSC[hate2020b R6]
ritonavir in SBA-15, up to 38.1% w/wno crystalline peaksXRPD[dening2018 R26]
indomethacin; methyl ester in SBA-15amorphous at 25–50% of monolayer; peaks from 75% and 100%PXRD[mccarthy2020 R19]

Evidence table: nanoconfinement.

Pitfalls and disagreements

Confinement is inferred from absences: the location of the drug inside or outside the pores was not measured [hate2020a C39]. The XRPD control with 5% crystalline drug showed only one weak peak, so low levels of crystals are missed [hate2020a X5]. The degradation temperatures did not fall in order of loading [hate2020a X6]. Broad DSC rises near 100 °C in two 20% w/w traces were not discussed [hate2020b X13]. Atazanavir at 30 and 50% w/w was X-ray amorphous but showed a glass transition and melting [hate2020a R7, R9].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

nanodroplet agglomeration

Evidence table: nanodroplet agglomeration (names merged there: droplet agglomeration, nanodroplet agglomeration). Content from the release-mechanism chapter (2023–2024), with a row from the Bioperformance chapter.

The joining of drug-rich droplets into clusters or networks

In the 2024 PVP molecular-weight paper droplets that formed in the gel of short-chain PVP dispersions joined into strands anchored in the gel near the gel–solution boundary and stayed there while the polymer left, a release failure the authors name "Failure Mode I", distinct from phase inversion deac2024a R10, C26, C38. In the 2023 surfactant study Tween 80 let ritonavir droplets agglomerate at the gel surface and leave as chunks, which "could potentially explain" slower release yang2023 R10, C20. In the Bioperformance chapter atazanavir droplets with PVPVA agglomerated in solution during a dissolution–absorption run hate2018 C27.

Findings

Release mechanism and LoC: F29, F31, F16, F20, F25.

Related concepts

prevented, in the authors' hypothesis, by polymer chain entanglement above the critical entanglement molecular weight; not prevented by steric stabilization in dilute solution; contrasts with phase inversion as a cause of the limit of congruency; acts on drug-rich nanodroplets.

Formulas

none.

How it is measured or obtained

Confocal imaging of dye-labelled humid films and of the edge of dissolving compacts deac2024a P10, P8; yang2023 P7, P8; DLS size and PDI in solution hate2018 R20.

Values in the library
materialvalue or classconditionspaper ids
clotrimazole–PVP K12 10%droplet strands by 11 h; network at the gel–solution boundary within 2 min100% RH films; in situ compact edgedeac2024a R7, R10
clotrimazole–PVP K29/32 10%no agglomeration (films, 11 h; compact, >7 min)samedeac2024a R7, R10
ritonavir–PVPVA + Tween 80, 30%droplets agglomerated in the gel, released as chunkscompacts, confocalyang2023 R10
atazanavir solution with PVPVA (Bioperformance chapter)≈245 nm to ≈10000 nm over 105 minDLShate2018 R20
Pitfalls and disagreements

Agglomeration in the gel was imaged for one short grade, at a loading other than the one released, and inferred for two others deac2024a X7, X11. Droplet growth in dilute solution did not differ with the PVP grade, so solution tests do not predict agglomeration in the gel deac2024a R5, C44.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

nanodroplet reservoir effect

The proposal that the drug-rich phase replenishes drug absorbed from the water phase, keeping the activity and flux at their maximum for as long as it lasts [mosqueragiraldo2015 C39; indulkar2015 C54, C55]. In the Amorphous solubility papers of 2013–2016 it is argued from the flux plateau and from earlier work: none of them depleted the dissolved drug and followed resupply [mosqueragiraldo2015 C39]. The flow-through experiments of 2016 test it, by the length of the steady receiver period against the excess over the onset [indulkar2016 R5, R6]. The papers of 2017–2022 add that Sugihara and Taylor expect the amorphous particles to maintain supersaturation by replenishing absorbed drug ("is expected"), and Indulkar and co-workers that an LLPS system sustains maximum flux while a micellar system at the same total concentration gives lower flux; neither flux with and without particles nor resupply was measured in these papers [sugihara2018 C43; indulkar2017a C61, C62]. New aspect (Bioperformance): replenishment of absorbed free drug by dissolution of drug-rich droplets, which keeps the solution at the amorphous solubility and the flux at its maximum until the droplets are used up [indulkar2016 C25, C31; raina2014a C38]. Micelle-solubilized drug is not an equivalent reservoir [indulkar2016 C26]. A depot role was proposed for amorphous aggregates in vivo, with little in vivo data [wilson2018 C8, C40]; in a PAMPA cell nanodroplets are said to raise the concentration at the donor-side membrane surface and remove the unstirred-layer gradient hate2022 C58, C61, C76. New aspect (Mesoporous silica): silica formulations are the library's case where the reservoir is absent. Released drug approached but did not exceed the amorphous solubility, so no drug-rich phase formed to replenish absorbed drug [dening2018 C32, C44], and an acid-first atazanavir–silica run reached the amorphous solubility without LLPS, from which the authors infer that the reservoir "may not occur" with silica [hate2020a R23, C54]. New aspect (Supersaturation from ASD dissolution): in the dispersion-dissolution papers the reservoir idea is cited, not tested: a drug-rich phase in metastable equilibrium with the water "has been suggested" to keep supersaturation constant while drug is absorbed jackson2015 C8, and a polymer that promotes LLPS "may be preferable" for that reason [trasi2015b C46]. For indomethacin, the droplets that a fast-releasing EPO–HPMC dispersion formed in acid redissolved within minutes when the pH rose to 5, which the authors call a reservoir that becomes available on dilution to higher pH; here the reservoir means redissolution, not replenishment during membrane transport [xie2017 C42, X9]. New aspect (Release mechanism and LoC): Que and co-workers (2019) take as their starting point "an emerging opinion" that drug-rich colloids act as a reservoir sustaining maximum flux, so that the optimal outcome of ASD dissolution is to exceed the amorphous solubility with colloid formation que2019 C3. They add that the smaller colloids formed with surfactants have a larger specific surface area, which "can potentially" improve absorption through faster replenishment, so colloid size should be considered when formulations release alike que2019 C54. Papers of 2021–2022 use it as the reason to keep released droplets small: smaller colloids "can potentially" improve absorption by faster replenishment, and surfactants that coarsen droplets "would be a poor choice" que2021 C37; correasoto2022a C1, C43.

Findings

Amorphous solubility and LLPS: F8, F16, F23. Bioperformance: F5, F8, F19, F22, F23. Mesoporous silica: F8, F15. Supersaturation from ASD dissolution: F7, F9, F21, F26. Release mechanism and LoC: F4, F13, F16.

Related concepts

depends on the drug-rich phase; inferred from membrane flux; related to thermodynamic activity. Needs drug-rich nanodroplets; contrasts with micellar solubilization. Absent where drug adsorption onto silica keeps the solution below the amorphous solubility; related to free drug concentration; the droplets form under congruent release.

Formulas

Receiver concentration-time profile with flow washout, membrane flux in terms of solute activity.

How it is measured or obtained

Not measured in the Amorphous solubility papers of 2013–2016; later papers use donors with and without nanodroplets and a membrane [indulkar2016 R7]. In the Bioperformance papers: a flow-through cell with a sink receiver, taking the length of the steady receiver period against the excess over the onset [indulkar2016 R5, R6] and a comparison with coarse amorphous particles [indulkar2016 R7]; a hollow-fibre receiver above the amorphous-solubility level and a fluorescence ratio falling to the amorphous-solubility level hate2018 R13, R16; hollow-fibre receiver Cmax against donor concentration above the amorphous solubility ueda2020a R10, C26; and PAMPA mass flow against donor concentration with a sink receiver, with an interface concentration estimated from it hate2022 R19, C61. In the Mesoporous silica papers: dissolution of ritonavir–SBA-15 at 200–1000% of the amorphous solubility with 1 µm filtration to count nanodroplets, against membrane flux [dening2018 P10, R8]; side-by-side comparison of atazanavir–SBA-15 with an HPMC dispersion of the same loading at 200 µg/mL in an absorptive apparatus [hate2020a P12]. Not measured in the ASD dissolution papers; the danazol work shows only that the free drug plateau is the same for all dispersions with a drug-rich phase jackson2015 R9. In the release-mechanism papers: not measured in these papers; colloid size by DLS que2019 R12.

Values in the library

None in the Amorphous solubility papers of 2013–2016; the Bioperformance, Mesoporous silica and ASD dissolution papers give the following.

materialvalue or classconditionspaper ids
clotrimazole 10 / 15 / 20 µg/mLsteady period 1 / 5 / at least 13 h16 h flow-through[indulkar2016 R6, X5]
clotrimazole + 7.5 mg/mL 150–250 µm particlesno reservoir (0.63 to 0.42 µg/mL)5 h[indulkar2016 R7]
atazanavir 90:10 ASDsreceiver above AS level 120 min; 4 h: about 200 minhollow fibrehate2018 R13, R21
posaconazole ASDs (FaSSGF)longer supersaturation at higher dose, "most likely" reservoirtwo doses[elkhabaz2019a C48]
ritonavir on SBA-15no reservoir at the amorphous solubility without excess drug[dening2018 C44]
ritonavir–SBA-15, 400 and 1000% doseabout 24 µg/mL, about 85% of the amorphous solubility; no drug-rich phase by dissolutionpH 6.8[dening2018 R22, C32]
10% atazanavir–SBA-15 against 10% HPMC ASDdonor about 48–57 against up to about 207 µg/mL with LLPS; receiver about 4.3–5.2 against 10.2–11.6 µg/mL200 µg/mL, absorptive[hate2020a R24, R25]
atazanavir, clozapine, two HPMCAS gradesCmax keeps rising above the amorphous solubility with approximately parallel slopeshollow fibre, 37 °Cueda2020a R10, C26, C27
atazanavir, PAMPA with 2% SDS receivermass flow 5.0 to 8.8 µg/min between 80 and 1000 µg/mL; estimated interface concentration near a plateau at 400 µg/mLlipid-impregnated hydrophobic PVDFhate2022 R19, C61
enzalutamide in ratsaggregate-forming ASD about 30% more AUC than two ASDs that only reached the ceiling (no statistical test)10 mL/kg[wilson2018 R17, C46, X6]
danazol dispersions with LLPSsame maximum flux, read as the maximum transport rate25 °Cjackson2015 C39, C32
indomethacin EPO–HPMC 3:5:2 dispersionapparent ≈93.5 → ≈43 µg/mL within ≈2 min of the shift; 39.1 of 40 µg/mL at 3 hpH 2.2 → 5, 37 °C[xie2017 R10, R20]
posaconazole–HPMCAS 10% dispersion, two dosesthe same peak near 20 µg/mL; desupersaturation about an hour earlier at one-fifth of the dose, with fewer dropletsFaSSGF → FaSSIF, 37 °C[elkhabaz2019a R12, R6, R14]
delamanid salt dispersions during releasestable drug-rich nanodroplets, smaller with HPMCP than with HPMCASPBS pH 6.5, 37 °Cduong2022a R25
ledipasvir–PVPVA 5%; with poloxamer 407; 7.5% with SDS≈225–257; ≈96–130; ≈60–63 nmDLS, 10–60 minque2019 R12
TIPP, Me-TIPP; PHPH, Me-PHPHcolloids 179–193; 348–364 nmDLS, 30 minque2021 R22
clopidogrel dropletsstable with 4–50 µg/mL SDS, TPGS or Tween 80 for 4 hDLScorreasoto2022a R6
Pitfalls and disagreements

The claim that a colloidal drug-rich phase is favourable for absorption rests on literature and argument ("likely") [indulkar2015 C55, X15]. A plateau of flux shows constant activity but not resupply [trasi2015a C14]. The Amorphous solubility papers of 2013–2016 treat the effect as untested, whereas the flow-through experiments of indulkar2016 follow resupply by the length of the steady receiver period [indulkar2016 R5, R6]; so it is untested only in the former. In the Bioperformance papers depletion times were back-calculated in a way that does not match a mass balance [indulkar2016 X3]; droplet dissolution speed was estimated, not measured [indulkar2016 R18]; with mesoporous silica the effect "may not occur" [hate2020a C54]. The interface concentration of the PAMPA study is derived from mass flow anchored at 75 µg/mL, so the 1000 µg/mL point equals 75 by construction and the plotted values still rise from about 64 at 400 to 75 at 1000; no interface concentration, layer thickness or droplet dissolution rate was measured, so the mechanism is an interpretation (F22) hate2022 X7, X8. The rat difference rests on one aggregate-forming ASD that also dissolved fastest (F23) [wilson2018 X14]. Mesoporous silica: at the tenfold ritonavir dose, flux equalled that of amorphous ritonavir while dissolution through a filter that passes the droplets gave about 85% of the amorphous solubility, so whether the LLPS concentration was reached is unresolved [dening2018 X14, C33]. The method used to look for nanodroplets in the acid-first atazanavir run is not described and its data are not shown [hate2020a C54, R23]. In the ASD dissolution papers, for ritonavir the droplets "appear" to promote crystallization, the opposite of a stabilizing role [ilevbare2013d C41]. Danazol transport was measured across a dialysis-type membrane only, without absorption data jackson2015 X12. The posaconazole reservoir was inferred from the dose effect; neither the undissolved amorphous drug nor the droplet mass was measured over time [elkhabaz2019a X8]. The three colloid-forming formulations differ in loading and release rate, so the size difference cannot be assigned to the surfactant alone que2019 X11. No flux or absorption was measured in these papers que2019 C54; que2021 C37.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

Nernst-Brunner equation

Evidence table: Nernst-Brunner equation. Content from the release-mechanism chapter (2019–2022).

The diffusion-layer form of the dissolution rate, dC/dt = (DA/Vh)(C_s - C), with diffusion coefficient D, surface area A, medium volume V, diffusion-layer thickness h and the solubility C_s of the solid form at the dissolving surface indulkar2019a E2, C22. For an amorphous drug-rich surface C_s is the amorphous solubility, so the rate approaches zero as the bulk concentration approaches it indulkar2019a C22. The ledipasvir study prints the same relation as the Noyes–Whitney equation with a Nernst–Brunner diffusion layer, dM/dt = (DA/h)(C_s - C), and concludes that dissolving an amorphous drug cannot raise the free concentration above its amorphous solubility que2019 E1, C2. Printed again in the 2022 ritonavir surfactant study for drug-controlled release at high loading, with C_s the amorphous solubility; release halts when the bulk concentration reaches it indulkar2022 E2, C21.

Findings

Release mechanism and LoC: F1, F3.

Related concepts

a form of the Noyes-Whitney equation; uses the diffusion boundary layer; separates drug-controlled release from polymer-controlled release.

Formulas

Noyes-Whitney equation, saturated-medium condition.

How it is measured or obtained

Used as an argument, not fitted: release from a drug-rich surface into medium presaturated at the amorphous solubility should be zero indulkar2019a C42.

Values in the library
materialvalue or classconditionspaper ids
ritonavir–PVPVA 50%no release into ritonavir-saturated medium, "in agreement with" the equationpH 6.8, 37 °Cindulkar2019a R12, C42
ritonavir–PVPVA 10%unchanged release into saturated medium, read as polymer controlsameindulkar2019a R12, C43
Pitfalls and disagreements

D and h were not given and no rate was computed indulkar2019a E2; the equation does not apply to dispersions whose release exceeds the amorphous solubility que2019 E1.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

NMR chemical exchange broadening

The widening of the NMR peaks of a species that moves between two environments, here ibuprofen exchanging between the aqueous phase and the drug-rich phase. The dissolved-ibuprofen peaks stay sharp in saturated polymer solutions and in buffer with droplets, and broaden only when a drug-rich phase that contains polymer is present [ueda2021 R1, R9, C9]. The authors attribute this to lifetime broadening by exchange with a mobility-suppressed, polymer-loaded phase with faster spin–spin relaxation, and not to solution viscosity [ueda2020b C24; ueda2021 C9; ueda2022 C14].

Findings

F15.

Related concepts

used to read the drug-rich phase and polymer partitioning into the drug-rich phase.

Formulas

none.

How it is measured or obtained

Line shape of the aqueous-phase peaks of the drug (H4, H5 or H5, H6) after Lorentzian decomposition at 37 °C or at 15–60 °C; widths are described qualitatively and were not tabulated [ueda2020b P4; ueda2021 P3; ueda2022 P4].

Values in the library
materialvalue or classconditionspaper ids
dissolved ibuprofen with HPMC, PVP-VAsharp below the amorphous solubility, broad above it; narrower and resolved again during stirring as PVP-VA droplets leavepH 2.0 (D2O), 37 °Cueda2020b R3, R10, R14
dissolved ibuprofen with six polymersbroadened most with HPMC and PVP-VA; positions unchanged1000 µg/mL polymer, 400 µg/mL drug[ueda2021 R3]
dissolved ibuprofen, 15–60 °Cbroader in PVP-VA and HPMC solutions than in PVP solution1000 µg/mL polymerueda2022 R5
Pitfalls and disagreements

The exchange rate and the relaxation rates were not measured; the authors say the mobility suppression "also appears to contribute" [ueda2020b C24; ueda2021 C17]. The polymer-induced downfield shift of the drug-rich peaks reduces the shift difference, and mobility suppression in the drug-rich phase strengthens the lifetime broadening, so both enter the explanation [ueda2021 C9].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

non-sink dissolution

Dissolution at a dose that would exceed the crystalline solubility if it all dissolved, so that supersaturation can build up and the competing kinetics of dissolution, nucleation and crystal growth can be seen; non-sink testing is called essential for supersaturating systems and more sensitive to crystals than most solid-state methods [moseson2021 C3]. In the ASD process papers it is a statement about the dose against the solubility of each solid form, not one apparatus: ritonavir and lopinavir granules at pH 6.8 were "highly non-sink" against crystalline solubilities of 1.8 and 2.9 µg/mL [trasi2019 C10, M1, M2], and a bicalutamide dose of 3 µg/mL, the lowest that could be weighed and below the form 1 solubility, still "does not meet the traditional definition of sink conditions" [moseson2021 C24]. Further non-sink designs in the later papers: bicalutamide–PVPVA powder at a dose giving at most 30 µg/mL, chosen so that nucleation from solution does not interfere moseson2022b P10, C7; posaconazole coated powders at a dose equal to the amorphous solubility (8 µg/mL) moseson2023 P13; posaconazole after a gastric-to-intestinal pH shift at about 10 times the amorphous solubility (about 200 µg/mL) [shah2024 P11]; ritonavir powders and tablets at up to 25 µg/mL benson2025 P11; and 10 mg ezetimibe in 50 mL [duong2022c P15]. New aspect (Bioperformance): the dose is larger than the medium can dissolve at the (crystalline or amorphous) solubility, so that supersaturation and its loss can be seen [elkhabaz2017 P7; purohit2018 C30; alhalaweh2016 P10]. Absorptive tests combine non-sink dissolution with a membrane at three volumes, 5 mg of tacrolimus in 240, 100 and 40 mL [hate2019 R7, C39]. New aspect (Supersaturation from ASD dissolution): in the ASD dissolution papers of 2008–2015 the dose is set against both reference solubilities: non-sink with respect to the crystal so that supersaturation can show, and, in the danazol work, also above the amorphous solubility so that a drug-rich phase can form; danazol films were dosed at 20–30 µg/mL against 8 µg/mL amorphous and about 1 µg/mL crystalline solubility jackson2015 C10, P1. Only part of the dose may dissolve: the highest felodipine value, 14.1 µg/mL, was about 28% of a 50 µg/mL nominal dose [konno2008a X15]. The papers of 2015–2018 add two dose designs: a dose equal to the amorphous solubility (celecoxib, 8.8 mg in 400 mL, 22 µg/mL), at which a dispersion that stays amorphous should release completely while any drug crystallized in the matrix cannot dissolve [xie2015 C17; xie2016a C8], and the whole contents of a marketed capsule in 40 mL, the baseline gastric volume (tacrolimus, 125 µg/mL nominal against an amorphous solubility of about 50 µg/mL) [trasi2016 P11, C29].

Findings

ASD process: F14, F21, F23, F26, F27, F28, F29, F38, F39, F40, F41, F46, F47, F48. Bioperformance: F8, F10, F14, F16, F17, F25, F28, F30, F31. Supersaturation from ASD dissolution: F1, F4, F6, F7, F8, F10, F16, F20, F21, F22, F24, F25, F26.

Related concepts

reads desupersaturation; detects residual crystallinity and matrix crystallization; uses the amorphous solubility advantage; also the setting for the release of coated particles (see atomic layer coating) and for the effect of wettability. Contrasts with sink conditions; related to pH-shift dissolution and absorptive sink; measured by free drug concentration; related to supersaturation and amorphous solubility.

Formulas

supersaturation ratio. Sink index, Noyes-Whitney equation.

How it is measured or obtained

IDM: 200 mL of 50 mM pH 4.5 acetate buffer at 37 °C stirred at 300 rpm, a UV dip probe with a scattering-corrected calibration (absorbance at 317 nm minus 450 nm), n = 3, 12 h, maximum 50 µg/mL, S = 6 [moseson2020a P9]. BCL: 3, 30, 60 and 150 µg/mL for 4 h at 37 °C, triplicate [moseson2021 P13]. Ritonavir granules: 250 mL, 150 rpm, 0.45 µm PTFE filtrate assayed by HPLC [trasi2019 P8, P15]. Two-stage pH-shift tests: 60 min in 40 mL fasted-state simulated gastric fluid (pH 1.6), then double-strength intestinal medium added to pH 6.5, samples centrifuged and assayed by HPLC (n = 3), with SHG, two-photon UV fluorescence and focused beam reflectance giving the solid [shah2024 P11, P12, P13, P14, P15]; posaconazole–HPMCAS powders held 30 min to 4 h at pH 1.6 or 4.0 and then moved to pH 6.5 moseson2023 P13. In the Bioperformance papers powder or capsule contents are dissolved in a small volume with in situ UV or sampled HPLC [elkhabaz2017 P7; purohit2018 P8; hate2018 P8]. In the ASD dissolution papers: paddle dissolution of powder with UV sampling through a 70-µm filter [konno2008a P3]; small-volume vessels with fibre-optic UV probes read every minute [alonzo2010 P2; alonzo2011 P2]; film dissolution with pyrene aliquots jackson2015 P2; filtered sampling for clear PVP solutions and ultracentrifugation for turbid HPMCAS ones [trasi2015b P5, P9]. Two-stage tests of indomethacin dispersions, 1 h in pH 2.2 buffer and then pH 5 or 6.8 by adding phosphate [xie2017 P7, P8]; suspensions of enteric dispersions in acid as non-sink leaching tests [li2016b P4]; films cast in vials and stirred 48 h at pH 3 [li2018 P4, P5].

Values in the library
materialvalue or classconditionspaper ids
IDM–PVPVA extrudatesC720 about 43.1 → 28.8 µg/mL with 0 → 25% crystalline drug50 µg/mL total dose, pH 4.5, 12 h[moseson2020a P9, R6]
BCL–PVPVA 30:70fraction dissolved at 4 h about 0.82 → 0.23 as the dose rises 3 → 150 µg/mL (crystal-free)pH 6.8, 37 °C[moseson2021 P13, R17]
RTV and LPV granulesRTV about 4 µg/mL in the co-granule against about 30 alone250 mL, pH 6.8, 0.45 µm filtrate[trasi2019 P8, R4]
tacrolimus capsules (outside)100 mL gives 50 µg/mL at complete dissolution, equal to the amorphous solubilitypH 4.5, 37 °C, 300 rpm[trasi2017 R3, C12]
tacrolimus generic capsules (outside)the more non-sink tests (100 and 40 mL) discriminate crystallinity better than larger volumesUSP and non-pharmacopeial media[purohit2018 C57]
BCL–PVPVA 5 / 10 / 20 / 30 / 50% DL powdersend level about 91 / 96 / 88 / 86 / 73% of the dosedose of at most 30 µg/mL, pH 6.8, 4 hmoseson2022b R6
BCL–PVPVA 30% DL, cryomilled 2 and 5 minabout 50 and 49% of the dose (about 15 µg/mL, the form 2 solubility)samemoseson2022b R4, M1
PCZ–HPMCAS 10% DL, extruded at 175 °C (no crystals) against 125 °C (0.3% crystals)peak about 172.5 against 178 µg/mL; about 125 against 14.5 µg/mL at 300 minpH shift at 60 min, dose about 200 µg/mL[shah2024 R12, R14]
PCZ–HPMCAS 25% DL coated 11–39 nm, pH 6.5about 90% of the dose in 10–20 mindose 8 µg/mLmoseson2023 R9
ezetimibe–HPMCAS 50% DL, uncoated / thin / thickpeak about 14.0 / 12.5 / 10.1 µg/mL fresh; at 12 months about 5.6 against 12.4 and 11.1 µg/mL10 mg in 50 mL, pH 6.5[duong2022c R13, R23]
ezetimibe ASDs7.5 mg in 15 mL, about 500 µg/mLbuffer, FeSSIF, Ensure Plus[elkhabaz2017 P7]
ritonavir, atazanavir PVP ASDs150 mg in 15 mL, 120 minpH 6.8[alhalaweh2016 P10]
atazanavir ASDs200 µg/mL in 50 mLclosed vesselhate2018 P8
tacrolimus capsules5 mg in 900 / 450 / 100 / 40 mLmedium I[purohit2018 P7, P8]
tacrolimus (Accord)maximum 45 µg/mL within 40 min, about 25 µg/mL at 2 hone capsule in 100 mL[trasi2017 R3, C12]
tacrolimus 5 mg in 240 / 100 / 40 mLmaximum donor concentration about 21 / 50 / 125 µg/mL; sink index against the amorphous solubility 2.4 / 1 / 0.4absorptive hollow-fibre test[hate2019 R7]
tacrolimus capsule contents5 mg in 100 mL, pH 4.5, 50 µg/mL HPC, 300 rpmUSP-type test 1 medium[purohit2019 P5, E3, C35]
enzalutamide ASDs100 µg/mL total in 12.5 mL, pH 6.5, 300 rpmclosed vessel[wilson2018 R6]
felodipine dispersions, 10–75% PVP, HPMC or HPMCAS30 mg in 600 mL (50 µg/mL nominal); maxima 0.8–14.1 µg/mLpH 6.8, 37 °C, 50 rpm[konno2008a P3, R10, X15]
neat amorphous felodipine100, 500 and 1,000 µg/mL; plateau ≈0.9–1.1 µg/mL, like the crystalpH 6.8, 37 °C[alonzo2010 P2, R1]
neat amorphous indomethacin300 µg/mL; peak ≈14.9 (25 °C) and ≈11.2 µg/mL (37 °C)pH 2[alonzo2010 P3, R7]
HPMC–felodipine 90:10 and 50:5030 and 150 µg/mL nominal; UV ≈27 and ≈8.9 µg/mL18 mL, 37 °Calonzo2011 R1
danazol films, three polymers, three loadings20–30 µg/mL nominal; free drug 5.4–9.1 µg/mLpH 6.8, 25 °Cjackson2015 P1, R9
ritonavir and lopinavir 20% dispersions20 mg in 40 mLpH 6.8, 25 °C[trasi2015b P5]
celecoxib dispersions with PVP, HPMCAS, HPMC, PAA, 10–60% drug22 µg/mL nominal (= amorphous solubility) in 400 mLpH 6.8, 37 °C, 16 h[xie2015 P5; xie2016a P5]
six marketed tacrolimus capsules5 mg in 40 mL (125 µg/mL nominal); plateau ≈46–50 µg/mLpH 4.5, 37 °C[trasi2016 P11, R10]
indomethacin dispersions and crystals4 mg in 50 mL (80 µg/mL), then 100 mL (40 µg/mL)pH 2.2 → 5[xie2017 P7]
lopinavir films, 15–85% drug2 mg solids in 10 mL, 48 hpH 3, 25 °C[li2018 P4, P5]
paclitaxel–HPMCAS 49/51 dispersiondose set to reach the amorphous solubility (31.6 µg/mL) in 15 mLpH 6.8, 37 °C, 16 h[que2018 P8, R1]
posaconazole–HPMCAS dispersions and Noxafil powder400 µg/mL in the gastric stage, 200 µg/mL after transfer, ten times the amorphous solubilityFaSSGF pH 1.6 → FaSSIF pH 6.5, 37 °C[elkhabaz2019a P6]
delamanid dispersions and tablets100 µg/mL at full release, about 100 times the amorphous solubility at pH 6.5PBS pH 6.5 or pH 1.6 → 6.5, 37 °Cduong2022a P16
praziquantel dispersions667 µg/mL and 1.5 mg/mL against an amorphous solubility of 1.1–1.4 mg/mLPBS pH 6.5, 37 °Cpolyzois2024 P8, R2
Pitfalls and disagreements

Filtering through 0.45 µm removes colloids above that size, and the authors treat the filtrate as molecularly dissolved drug even though material that formed at pH 6.8 passed larger-pore filters [trasi2019 C11, X13]. The dose per fluid volume decides how much supersaturation seeds can consume: seeds are expected to be a greater risk in a small fluid volume in vivo, and the apparent potency of the seeds rose with dose in the bicalutamide tests [moseson2020a C56; moseson2021 C76]; results "should be put in perspective of the minimum and maximum fluid volumes expected in vivo" [hate2019 C39]. The 12 h window is longer than gastrointestinal transit but lets dissolution and growth both be seen [moseson2020a C32]. At 30 µg/mL bicalutamide with PVPVA does not nucleate from solution, so a fall at that dose is read as the solid route moseson2022b C7, R22. In the posaconazole pH-shift test "desupersaturation" means a fall below the LLPS concentration (about 19 µg/mL), not a return to the crystalline solubility of 1.2 µg/mL [shah2024 R11, X15]. For the coated powders the replicate numbers and the meaning of the error bars are not printed moseson2023 X17; benson2025 X20. In the Bioperformance papers a closed vessel overstates supersaturation over time (F14), and most absorption is not modelled in such tests. The volume decides the result: the same 20% crystalline capsule passed the virtual check at 100 mL and failed at 40 mL (F28) [hate2019 R13, C41], and closed dissolution did not rank the rat exposures (F25) [wilson2018 C57]. In the ASD dissolution papers, above the amorphous solubility UV readings include particles, so the apparent maximum of a non-sink test overstates dissolved drug alonzo2011 C27; jackson2015 C12. Results compare only at similar dose-to-volume ratios [konno2008a X15]. The two drugs of the 2010 study were tested at different pH, volume, stirring and solid amounts [alonzo2010 X9]. With the dose at the amorphous solubility a test asks whether a dispersion reaches the ceiling, not whether it can stay above it xie2016a X11. A shift to pH 6.8 let three indomethacin dispersions look alike that a shift to pH 5 separated [xie2017 C66]. In the tacrolimus test the 100 mL control called sink is nominally at the amorphous solubility [trasi2016 X5]. Where the dose equals the amorphous solubility, complete release and the ceiling cannot be told apart [que2018 P8; xie2016a X11]; where it is ten to a hundred times higher, the test asks instead how long the drug stays at the ceiling [elkhabaz2019a P6; duong2022a P16].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

Noyes-Whitney equation

The dissolution-rate relation dC/dt = (DA/hV)(C_s-C) (diffusion coefficient D, surface area A, boundary-layer thickness h, liquid volume V, solubility C_s): in the ASD process chapter it is applied to crystals dissolving in a polymer melt, where higher temperature and plasticisation by dissolved drug raise D, smaller particles raise A and shear thins h [moseson2018 E5, C52; moseson2019 E2, C39]. In the bicalutamide model the Noyes–Whitney form is carried by a size-dependent shrinkage rate with one fitted rate constant that lumps viscosity, plasticization by dissolved drug, viscous heating and the absence of sink conditions [moseson2022c E18, E9, C38]. New aspect (Supersaturation from ASD dissolution): in aqueous dissolution of dispersions it appears as the dissolution arm of the two-route scheme, dissolution rate proportional to surface area and a concentration difference ("modified Noyes and Whitney", cited) [alonzo2010 E3, C43], and in a carrier-controlled form in which the drug dissolves at the polymer rate scaled by the drug:polymer ratio alonzo2011 E4, C37. For indomethacin precipitates, a higher crystalline solubility from dissolved EPO speeds dissolution by the Noyes–Whitney relation, but "this effect alone cannot explain" the fast redissolution of the small crystals, which the authors attribute mainly to their size [xie2017 E1, C47, C48]. New aspect (Release mechanism and LoC): in the release-mechanism papers of 2017–2020 the equation describes drug-controlled release, with the solubility term set to the amorphous solubility of the drug-rich surface indulkar2017b E4; indulkar2019a E1, C22. Two consequences are drawn from it: dissolving an amorphous drug cannot raise the free concentration above its amorphous solubility que2019 E1, C2; purohit2017b C50, and a dispersion that keeps releasing into a medium already at the amorphous solubility cannot be drug-controlled, since the equation then gives a zero rate indulkar2017b E5, C35. Saboo and co-workers (2020) use it to argue that an amorphous form gives a dissolution-rate advantage similar to its 2–20-fold solubility advantage, which for exceptionally insoluble drugs is "likely" still insufficient saboo2020a E1, C1.

Findings

ASD process: F9, F11, F12, F31, F36, F37. Supersaturation from ASD dissolution: F1, F10, F21. Release mechanism and LoC: F1, F3.

Related concepts

uses the diffusion boundary layer; with Stokes–Einstein equation; related to polymer-controlled release and crystallization during dissolution. Written with the Nernst-Brunner equation diffusion layer; describes drug-controlled release; related to the intrinsic dissolution rate.

Formulas

Noyes–Whitney equation, congruent release relation, saturated-medium condition.

How it is measured or obtained

Used in words, not fitted, in the ASD process papers; its parameters (viscosity, boundary-layer thickness, local temperature) were not measured [moseson2018 C52, X15; moseson2019 E3]. Also used qualitatively in the ASD dissolution papers; no rate constant was fitted [alonzo2010 E3; alonzo2011 E4]. In the release-mechanism papers: used as an argument, with no rate constant fitted; the test is release into medium presaturated with drug indulkar2017b C35; indulkar2019a R12.

Values in the library
materialvalue or classconditionspaper ids
crystals in a polymer meltframework for the diffusion-only model that the fragmentation mechanism extendsIDM in copovidone[moseson2019 E2, C40]
amorphous drug dissolution into mediumdriving force vanishes at the amorphous solubilityritonavir ASDspurohit2017b C50
congruent and incongruent releasedissolution rate follows Noyes–Whitney and Nernst–Brunner with the solubility of the surface formritonavir–copovidoneindulkar2019a C22
crystals in a polymer melt, physical mixtures against a dispersionthe lag of a mixture with 93 µm crystals (about 10 °C in TGA) is explained by crystal dissolution at a rate set by particle sizeBCL–PVPVA[moseson2020 E1, C33, R13]
BCL crystals in PVPVA at Tc, population balance modelfitted dissolution rate constant 0.1002 ± 0.0511 µm/s against assumed 0.5 and 4 µm/s30% BCL, 145 °C[moseson2022c R16, A4]
felodipine, indomethacin (scheme)dissolution competes with matrix and solution crystallizationFig. 16[alonzo2010 C43]
felodipine and indomethacin 90:10 dispersionsdissolution "appears" polymer-controlled, much faster than 50:50pH 6.8 and 2.0alonzo2011 C38
indomethacin α precipitate (5–10 µm) against sieved α (106–250 µm) with matched EPO32.1 µg/mL at 3 h against 24.6 µg/mL at 8 hpH 5, 37 °C[xie2017 R19, R17, R25]
nifedipine 10, 20% with HPMC-E5 or PVPVArelease continued into water saturated at the amorphous solubility (110 µg/mL), so not drug-controlled5 °C, D2Oindulkar2017b C35, R8, R9
ledipasvir–PVPVAthe highest free drug from dissolving amorphous drug is its amorphous solubilityargumentque2019 C2
felodipineamorphous solubility only about 6 times the crystalline; intrinsic rate extremely low, so amorphization alone gives little rate advantage ("unlikely")pH 6.8saboo2020a C26
Pitfalls and disagreements

The equation neglects crystal defects and mechanical breakage, which is the gap the 2019 paper addresses [moseson2019 C2]; the particle number is taken as constant in a published HME model [moseson2019 R25, C55]. The equation is named in the thermogravimetry paper without inputs [moseson2020 E1]. In the aqueous scheme of 2010 the printed form A(C − Ceq) is negative while a solid dissolves below Ceq, so it gives directions only [alonzo2010 X3]. The ledipasvir study restricts the equation to dispersions whose release stays at or below the amorphous solubility que2019 E1. The 2017 ritonavir paper prints the equation with the same label as its Flory–Huggins equation and calls it eq. 3 in the text purohit2017b X2.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

nucleation induction time

The time from creating a supersaturation until crystals are first detected, t_{ind} = t_n + t_g: the time to form stable nuclei plus the time for them to grow to a detectable size; if growth is quick, t_{ind} \propto J^{-1} and a longer time means a slower nucleation rate [ilevbare2013c E2, E3, C14]. It depends on the detection method, since crystals are seen earlier by SHG than by a probe ratio or light scattering [jackson2014 R25, R17].

Findings

F3, F4, F5, F6, F13, F14, F15, F25, F27, F28, F29, F32, F34, F35, F37, F38, F39, F40, F41, F42, F43, F44.

Related concepts

part of nucleation; gives nucleation rate; modified by nucleation inhibition; measured on supersaturation.

Formulas

induction time decomposition, relative nucleation rate from seeded and unseeded induction times, classical nucleation theory.

How it is measured or obtained

A methanol stock of drug is pumped or injected into stirred buffer with or without predissolved polymer and the signal is followed: extinction at a wavelength where the drug does not absorb (280 or 350 nm) or the fall in UV absorbance, taking the crossing of regression lines through the flat and rising (or falling) parts as the time; pyrene fluorescence and SHG as second read-outs; triplicate [alonzo2012 P5; ilevbare2013c P9, P10; jackson2014 P8]. The stated supersaturation uses a methanol-free solubility; the methanol fraction is about 0.5% v/v [ilevbare2013c X16].

Values in the library
materialvalue or classconditionspaper ids
celecoxib; efavirenz; ritonavir, no polymerabout 2.4; 5.1; 120 minat the calculated amorphous solubility, 37 °C[ilevbare2013c R8, R9.a]
ritonavir, CAB Adp 0.81; efavirenz, CAB Adp 0.81; celecoxib, HPMCabout 244; 28.0; 12.6 min5 µg/mL polymer[ilevbare2013c R9]
celecoxib at 11 µg/mL, none against HPMC27.5 ± 0.7 against 855.5 ± 6.0 minS 7.3[ilevbare2013c R15]
felodipine, none against 1 µg/mL HPMC15.3 against 136.5 minS 10, 25 °C[alonzo2012 R16]
danazol, none; PVP; HPMC; HPMC-AS6–10; 88–162; 111–285; 250–516 min10–20 µg/mL, 25 °C[jackson2014 R17]
celecoxib 22 µg/mL, 5 µg/mL HPMCAS (ASD dissolution chapter)held for 16 h; J_0/J_p about 4,00037 °Cxie2016a R3, R13
paclitaxel 30.7 µg/mL (S 88) (ASD dissolution chapter)within 6 min; more than 16 h with 20 µg/mL HPMCAS37 °C[que2018 R3]
indomethacin S 6 (ASD process chapter)about 40 min; more than 12 h with 5–50 µg/mL PVPVApH 4.5, 37 °C[moseson2020a R3]
11 drugs, 0.1% STC and SDS, matched C/Ceqbuffer 7–87 min; STC 15 to >1000; SDS shorter for 7 of 925 °C, telaprevir 37 °C[chen2015 R3]
acetaminophen, S 1.595% of vials 26 min; first crystals 150–785 s20 °C[trasi2015 R1, R10]
celecoxib, nevirapine, flibanserin, 13 bile salts3 min to >16 h (celecoxib); 0–577 (nevirapine); 0–623 min (flibanserin)pH 6.5, 37 °C[li2016a R6]
telaprevir, 80 and 150 µg/mL, 26 polymersHPMC >700 and 243; none 14–15 minpH 6.8, 37 °C[mosqueragiraldo2016 R4]
telaprevir δ 11.5 and 28.8, six bile salts30 min and immediate in buffer; >960 min with 1.86 mMpH 6.5, 37 °C[lu2017 R3, R4]
danazol 15 µg/mL, PVP, HPMC, HPMC-AS 1–1000 µg/mLabout 5 min; 26–412 min25 °C[jackson2016 R17]
atazanavir without additive, five protocolsabout 40, 92–102, 170, 200, 253 ± 65 minnear the amorphous solubility, 37 °C[mosqueragiraldo2018a R1; elkhabaz2021 R6; indulkar2018 R19; indulkar2019b R3; enright2020 R2]
posaconazole without additive, three protocolsabout 5–8, 8.4, 29 ± 5 minpH 6.5, 37 °C[elkhabaz2021 R7; duong2022b R10; shah2025 R3]
enzalutamide without polymerabout 5–15 min, 30–120 µg/mLpH 6.5[wilson2021 R1]
Pitfalls and disagreements

The assumption t_n \gg t_g was not tested; strong inhibitors give gradual onsets whose fitted times depend on where the lines are drawn (rise above baseline at about 25 min against a fitted 31.5 min; about 180 against 260 min) [ilevbare2013c C14, X14]. Methods differ by up to about 40% for single conditions [jackson2014 X5]. The same polymer, drug and concentration gave 10–13 min in one laboratory and more than 8–16 h in another [ilevbare2013c R9; xie2015 R1; xie2016a R3]. The efavirenz run was at S about 2.3, not 15 [ilevbare2013c X4]. Replicate scatter is below 15% [ilevbare2013c R17]. Values above 960 or 720 min are lower bounds set by the run length [lu2017 X16; chen2015 X7]. The control induction time of one drug differs up to about sixfold between protocols, so effects compare only as ratios to a control in the same protocol [mosqueragiraldo2018a R1.b; enright2020 R2]. Several papers do not identify the scattering particles at the induction time [indulkar2018 X14; enright2020 X15].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

nucleation rate

The number of stable crystal nuclei formed per unit volume and time, J. Classical nucleation theory gives J = A\exp(-\Delta G_{crit}/kT) with a barrier that falls steeply with supersaturation, \Delta G^{*} \propto 1/(\ln S)^{2}; where the induction time is dominated by nucleation, t_{ind} \propto J^{-1} [ilevbare2013c E3, E4; hsieh2012 E7, E8]. The nucleation-rate ratio with and without a polymer is estimated from seeded and unseeded induction times [alonzo2012 E10]. New aspect (Physical stability): in the solid-state papers of the library it is the slope of the volume density of birefringent sites against time in amorphous films, in m⁻³ s⁻¹ [konno2006 C12, R3; marsac2008a E4]; in solution papers it is derived from induction times or counts of particles or SHG signals per time [alonzo2012 E10; elkhabaz2021 E5].

Findings

Crystallization from solution: F6, F14, F27, F32, F33, F34, F42. Physical stability: F1, F2, F9, F10, F11.

Related concepts

inverse of nucleation induction time; modified by nucleation inhibition; described by classical nucleation theory; measures nucleation; set by kinetic barrier to nucleation and thermodynamic driving force for crystallization; related to crystal growth rate.

Formulas

relative nucleation rate from seeded and unseeded induction times, classical nucleation theory, induction time decomposition, depth of field of a microscope objective, Arrhenius equation.

How it is measured or obtained

Not measured as an absolute rate in the papers of the crystallization-from-solution chapter. The ratio is J/J_0 = (t_s/t_{s,0})^{3}(t_{u,0}/t_u)^{4}, with the seeded induction-time ratio replaced by the growth-rate ratio R/R_0 at the same supersaturation and polymer level [alonzo2012 P10, E9, E10]. In the ASD dissolution chapter the same relation was applied to celecoxib xie2016a R13. In the solid-state papers: spin-coated films stored at a fixed RH and temperature; sites counted under polarized light in 12 areas per film, converted from area to volume with the depth of field of the objective (0.0144 mm at 10×), triplicate, film edges excluded [konno2006 P2, E1; marsac2006a P4; konno2008 P4]. Sites are counted once they reach about 1 µm [konno2008 C38]. In SHG images of griseofulvin the number density of crystal sites was followed over time with a 60 µm depth of field [wanapun2010 R17].

Values in the library
materialvalue or classconditionspaper ids
felodipine, 1 µg/mL HPMCJ/J_0 7.05 × 10⁻⁴ (text: more than thousand-fold; conclusions: factor of 1000)S 10, 25 °C[alonzo2012 R17, C38, C46]
celecoxib, 5 µg/mL HPMCASJ_0/J_p about 4,000 (unseeded time taken as 960 min)22 µg/mL drug, 37 °Cxie2016a R13
acetaminophen, S 1.5J 1465 (none), 3820 (PAA), 81.86 (HPMCAS), 40.68 (HPMC) # m⁻³ s⁻¹1.2 mL vials, 20 °C[trasi2015 R3]
telaprevir with STC, SGCJ/J₀ 2.5 × 10⁻³, 2.9 × 10⁻⁶δ 11.5[lu2017 R10]
atazanavir, posaconazole, six mediaSHG count rate about 0.1–1.6 and 0.05–48 counts/min37 °C, relative per field[elkhabaz2021 R14, E5, X13]
posaconazole, PBS and three mediaJ from induction times, fitted for A and γ37 °C, S above about 7–13[duong2022b R15, X10]
amorphous felodipine≈1.3 × 10⁵ m⁻³ s⁻¹; ≈2–3 × 10³ with 3% PVP, HPMCAS or HPMC0% RH, 22 °C[konno2006 R4]
amorphous nifedipine vs felodipine0.39 vs 0.17 × 10¹⁰ m⁻³ day⁻¹0% RH, 22 °C[marsac2006a R4.a]
nifedipine and felodipine with 7% PVP≈1.4 × 10³ and ≈2.7 × 10² m⁻³ s⁻¹0% RH[marsac2006a R16.b]
felodipine with 3% PVP vs HPMCAS≈8.6 × 10⁵ vs ≈1.3 × 10⁴ m⁻³ s⁻¹75% RH, 22 °C[konno2008 R3.b]
nifedipine vs felodipine with 25% PVP≈4.3 × 10⁵ vs ≈2.3 × 10³ m⁻³ s⁻¹75% RH[marsac2008a R1.f, R1.l]
felodipine (activation energy)145 kJ/mol below Tg; 201 with 3% PVPArrhenius, ≈25–75 °C[marsac2006a R3]
griseofulvin melt (SHG imaging)number density ≈45 → ≈600 mm⁻³ over ≈62–285 min125 °C, SHG[wanapun2010 R17]
Pitfalls and disagreements

The ratio rests on one pair of induction times without uncertainty and on a seeded ratio standing in for a seeded induction-time ratio; a 10% change in the polymer-case time changes J/J_0 about 1.5-fold [alonzo2012 X7, C11]. The printed inverse of 0.607 is 1.643 against 1.647, with J/J_0 7.05 or 7.06 × 10⁻⁴ [alonzo2012 X6]. The celecoxib value is a lower bound because no desupersaturation occurred within the experiment xie2016a R13. In the film papers absolute rates are per depth-of-field volume and comparable only within one counting method; in one paper Table II and two figures disagree about fourfold, and the felodipine-alone rate of that paper's Fig. 9 (≈3 × 10⁴) is about fourfold below the other papers' ≈1.3–1.4 × 10⁵ (synthesis) [marsac2006a X1; konno2006 R4.a]. The 2006 methods describe the area-to-volume conversion as multiplication where division is meant [konno2006 X6]. Site density rose roughly linearly, but early points can lie below the fitted line, so a short lag is not excluded [konno2006 X8].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

nucleation

Nucleation is the formation of crystal nuclei, the first of two dependent steps of crystallization, each with its own rate and temperature dependence [baird2013 C32; kestur2010a C27]. In classical nucleation theory the barrier to a critical nucleus grows with the cube of the interfacial free energy and falls with the square of the driving force [vaneerdenbrugh2010a E3]; the library adds molecular recognition as a further factor [trasi2012a C48; konno2006 C33]. This draft comes from the crystallization-tendency chapter (supercooled melts and glasses); nucleation from solution is covered by other chapters. New aspects (Miscibility and drug-polymer interactions): For indomethacin and PVP the proposal is that a critical γ nucleus is built of acid dimers, so that "the formation of a critical nucleus of indomethacin would require the breaking of the PVP-indomethacin hydrogen bond"; the same logic is expected to hold for α, which hydrogen-bonds in chains [taylor1997 C43, C44]. During solvent removal nucleation and growth can occur once the drug's solubility in the drying solution is exceeded, and a polymer may alter the supersaturation reached [vaneerdenbrugh2010b C29]. Pure nifedipine and felodipine nucleate much faster than dispersions with even small amounts of polymer, which is the main argument that the polymer acts through kinetics [marsac2006b R16, C42]. New aspect (Crystallization from solution): nucleation from supersaturated aqueous solution differs from nucleation in a supercooled melt in that the driving force is the supersaturation S and the read-out is the induction time at fixed S; it is "energetically more demanding" than growth, so at some supersaturations crystals grow while new nuclei do not form [ilevbare2013c C10, E3]. Polymers can slow it several-fold at the supersaturation of amorphous dissolution and by much more at lower supersaturation (F13, F14), and for felodipine far more than they slow growth (F6) [alonzo2012 C46; ilevbare2013c R12, R15]. In a two-phase solution the droplet interface is a candidate site (see heterogeneous nucleation) [jackson2014 C45, C53]. New aspect (Physical stability): the physical-stability papers treat nucleation as the initiating event that a dispersion must suppress, framed by classical nucleation theory with a thermodynamic barrier and a kinetic barrier, while noting that nucleation in films is "most likely heterogeneous" [marsac2006a C5; konno2006 C33]. New aspect (Supersaturation from ASD dissolution): three readings from dissolving dispersions: a fast initial drop of a highly supersaturated felodipine solution as rapid nucleation, faster and giving more particles at higher concentration [konno2008a C24]; immediate crystallization of drug released at very high local supersaturation from a 10% drug dispersion alonzo2011 C29; and nucleation inside drug-rich droplets, favoured by the high drug concentration and an expected low crystal–liquid interfacial tension [ilevbare2013d C39, C40].

Findings

Crystallization tendency: F3, F4, F7, F15, F16, F18, F19, F21. Miscibility and drug-polymer interactions: F1, F9, F10, F15. Crystallization from solution: F3, F6, F13, F14, F20, F34, F36. Physical stability: F1, F2, F9, F10, F16, F17, F20, F29. Supersaturation from ASD dissolution: F3, F5, F13.

Related concepts

part of the process together with crystal growth rate (contrasts with); measured by nucleation temperature zone; modelled by classical nucleation theory; includes heterogeneous nucleation and sub-Tg nucleation; related to quenched-in nuclei and prenucleation clusters; depends on thermodynamic driving force for crystallization; related to crystallization inhibition and kinetic stabilization; includes secondary nucleation; inhibited by nucleation inhibition; quantified as nucleation rate; controlled by kinetic barrier to nucleation; see molecular recognition and nucleation and crystal growth; related to nucleation induction time and metastable zone.

Formulas

classical nucleation barrier, critical cooling rate to avoid nucleation, classical nucleation theory, induction time decomposition, relative nucleation rate from seeded and unseeded induction times, Arrhenius equation, depth of field of a microscope objective.

How it is measured or obtained

Directly, by the number of nuclei grown to visible size after a hold (two-step method) [trasi2014b P7] or by nucleation-site density over time in films [marsac2006a R1]; by locating a nucleation zone with DSC cooling to successive end points and reheating [trasi2014b P1; trasi2012a R12]; indirectly, from critical heating rates after slow and fast cooling [baird2013 C38] or from the absence of crystallization on reheating [trasi2014b C39]. In solution, induction times are used, which include a growth time [chen2015 C5]. In the felodipine, bifonazole and nimesulide growth studies nuclei are only formed and then grown: films are stored over P2O5 at 40 °C (or at ambient temperature) before the hot-stage growth runs, and nucleation with the polymers is not quantified [kestur2010a P3, X10; kestur2011 P2]. The spin-coating screen of vaneerdenbrugh2010b scores the crystalline area over 7 days, which mixes nucleation and growth [vaneerdenbrugh2010b P2, C29]. In the crystallization-from-solution papers by unseeded induction times (see nucleation induction time) and by the nucleation-rate ratio from seeded and unseeded runs [alonzo2012 P5, P10; ilevbare2013c P9]. In the physical-stability papers, by counting birefringent sites in films at fixed RH and temperature, and by the Arrhenius slope of the rate above and below Tg [konno2008 P4; marsac2006a P5]. A lag before detectable crystals in stored powders was read as delayed nucleation [rumondor2009b R17, C29]. In the ASD dissolution papers it is not measured directly but inferred from concentration curves, induction times, particle appearance and Raman lag times [konno2008a X4; ilevbare2013d R16; raina2014b C32].

Values in the library
materialvalue or classconditionspaper ids
nilutamide glass≈12.6 nuclei per sample at −30 °C; ≈0.8–2.5 at −20 to 40 °C30-min hold, open surface, 1 min growth at 65 °C[trasi2014b R9]
acetaminophennucleation zone 50–60 °CDSC cool–reheat[trasi2012a C22]
acetaminophen with polymersHPMCAS reduces nuclei to about a third; PAA gives nearly three times more10% w/w[trasi2012a C23]
flutamidenucleation zone 10–40 °CDSC cool–reheat[trasi2012b R10]
nifedipine against felodipinefaster nucleation for nifedipinepure films, 22 °C, 0% RH[marsac2006a R1]
felodipine filmsrate rises with storage RH; drug alone fastest22 °C, with polymers[konno2008 C11]
indomethacin polymorphsδ fastest at 60 °C; α favoured at 80 °C; γ not readily (only from seeds); polymers retarded nucleationamorphous films, storage at 60 and 80 °C[tian2017 R1, R5, C7]
celecoxibsamples "quite hard to nucleate"hot stage[mosqueragiraldo2014 R15]
vemurafenib βnucleation the limiting step above 150 °C (qualitative)hot stage[lu2016 C46]
pure nifedipine, felodipine against dispersionsnucleation much faster for the pure drugscited from a companion study[marsac2006b R16]
indomethacin–PVPnucleus requires breaking the PVP–drug bond (proposed, untested)no crystallization data[taylor1997 C43, X8]
flufenamic acid–PSSA, chlorpropamide–PSSA, lidocaine–PVP filmsfully crystalline within 30 min of coatingspin coating[vaneerdenbrugh2010b R2.an, R2.s, R2.as]
celecoxib; efavirenz; ritonavirinduction time about 2.4; 5.1; 120 minat the calculated amorphous solubility[ilevbare2013c R8]
felodipine, HPMC 1 µg/mLJ/J_0 7.05 × 10⁻⁴S 10[alonzo2012 R17]
danazol6–10 min without polymer; 88–516 min with 10 µg/mL polymer25 °C[jackson2014 R17]
nine drugs with carboxylated cellulose derivativescontact with the emerging nucleus "clearly a prerequisite" for disruption5 µg/mL, pH 6.8[mosqueragiraldo2018a C44]
amorphous felodipinerate ≈1.4 × 10⁵ → 2.9 × 10⁶ m⁻³ s⁻¹0 → 75% RH, 22 °C[konno2008 R1.a, R3.a]
nifedipine vs felodipinefaster at every PVP level and RH0–75% RH[marsac2008a R1, C7]
felodipine with 50% HPMCASnegligible crystals for 35–120 days at 52–93% RH, read as delayed nucleationPXRD of powders[rumondor2009b R17, C29]
flutamide with 10 mol% PVAc, PIPAgrowth rate at the DSC exotherm maximum 7.7 and 7.0 against 4.4 µm/s, read as fewer nucleiDSC and growth curve[trasi2012b R11.b, R11.d, R11.f, C18]
flutamide with 10 mol% nilutamideone nucleus in the imaged regioncooled to −30 °C, reheated[trasi2012b R12, C16]
felodipine with 3% PVP≈150-fold lower rate (cited)30 °C[kestur2013b R22, C35]
ritonavir 17 against 20 µg/mL (below and above LLPS)induction about 284 against 119.3 minpH 6.8, 37 °C[ilevbare2013d R16, R12]
felodipine methanol shift with HPMC, S about 60precipitation not completely suppressed25 °Calonzo2011 C30
nifedipine α in γ slurries with polymerlag lengthened at similar slopes, read as α nucleation inhibition25 °C[raina2014b C32]
Pitfalls and disagreements

Nucleation is stochastic and often heterogeneous, which scatters crystallization temperatures [baird2010 C19; baird2013 C18]. Nuclei counts are not rates unless area and time are controlled [trasi2014b X7]. Polymers can act oppositely on nucleation and growth: HPMCAS was the best nucleation inhibitor but the weakest growth inhibitor for acetaminophen [trasi2012a C46], and drug–additive hydrogen bonding correlated with growth inhibition but not with nucleation for flutamide [trasi2012b C45]. Classical nucleation theory does not capture molecular recognition or polymer effects [trasi2012a C49]. The role of the hydrogen bond in nucleation is argued, not tested [taylor1997 X8]. The growth-rate ranking of polymers says nothing about nucleation, which was not measured [kestur2010a X10; kestur2011 P3]. The film screen cannot separate crystallization during coating from crystallization during storage except through the day-0 score [vaneerdenbrugh2010b R2]. In solution, how additives slow nucleation is "more speculative" than how they slow growth, because the molecular events cannot be observed [ilevbare2013c C9]; the papers do not separate nucleation from early growth inside the induction time [ilevbare2013c X14]. The delayed-nucleation reading of the HPMCAS lag in stored felodipine powders assumes that growth below and above the detection limit follows the same factors [rumondor2009b C28]. Nucleation counts separated polymers at 33% RH that PXRD crystallinity could not separate within 490 days (synthesis) [konno2008 R2.b; rumondor2009b R19]. The flutamide nucleation verdicts rest on two Tmax values per sample and an unnamed test [trasi2012b X4]. Nuclei per cycle are not rates when the zones differ in width [trasi2012a X8]. The felodipine "nucleation then growth" reading rests on curves alone [konno2008a X4]; the ritonavir 17 µg/mL comparison has no n or SD and mixes droplets with a higher bulk supersaturation [ilevbare2013d X18].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

octanol-water partition coefficient

Evidence table: octanol-water partition coefficient. Content from the release-mechanism chapter (2019–2022), with rows from the Solid-state methods and Bioperformance chapters.

The ratio of drug concentrations in octanol and in an aqueous buffer at equilibrium, given as log P; it measures drug lipophilicity saboo2020a E5. In the release-mechanism papers it was the variable tested against the limit of congruency and against congruent release rates saboo2019 A1, C6; saboo2020a C32.

Findings

Release mechanism and LoC: F9.

Related concepts

measures lipophilicity; tested against the limit of congruency.

Formulas

octanol-water partition coefficient.

How it is measured or obtained

Shake flask with octanol-saturated pH 6.5 buffer, compounds predominantly un-ionized, concentrations by LC-MS saboo2020a E5; calculated (ClogP) saboo2019 A1; cited indulkar2017b M1; que2019 R28. Shake flask with LC-MS of both phases at pH 2.0 (indomethacin) and pH 6.5 (its methyl ester) saboo2020 P21, E4; two calculation programs for the phenolphthalein analogues que2021 M1.

Values in the library
materialvalue or classconditionspaper ids
nifedipine3.17 (cited)indulkar2017b M1
nilvadipine; cilnidipineClogP 3.04; 5.54calculatedsaboo2019 A1
nilvadipine; felodipine; cilnidipine4.06; 4.46; 5.40shake flask (felodipine from the literature)saboo2020a R16
ritonavir4.3 (cited)que2019 R28
probucol; procaine (Solid-state methods)10; 1.3citedpurohit2015b C5
enzalutamide (Bioperformance)4.75 (calculated)wilson2020 C18
indomethacin; its methyl ester4.07; 4.53shake flasksaboo2020 M1, M2
four phenolphthalein analogues2.63–7.60 (ACD), 4.11–8.14 (MarvinSketch)calculatedque2021 M1, M2, M3, M4
loratadine, miconazole, danazol, elbasvir, paclitaxel, ivacaftor4.4, 5.69, 3.8, 5.33, 3.96, 5.68citedyang2021 M1, M2, M3, M4, M5, M6
lumefantrine8.34citedhiew2022b M1
Pitfalls and disagreements

Calculated and measured values for the same drugs differ by up to about 1 log unit (nilvadipine 3.04 against 4.06) saboo2019 A1; saboo2020a R16. A log P difference of about 2.5 units did not change the molar limit of congruency saboo2019 C35. Within the analogue series none of the log P values tracked the limit que2021 C29.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

oral bioavailability

The fraction of the dose reaching the circulation, F = F_a F_{gut} F_H [purohit2018 E6]. The papers up to 2018 measured none; the claims were expectations [alhalaweh2016 C37; indulkar2016 C47; mosqueragiraldo2018b C58]. Later papers give exposure in animals as AUC and Cmax (dogs, rats, monkeys) and, for pretomanid, a bioavailability relative to a reference product (F23, F26, F30) [purohit2019 R9; wilson2018 R16; nguyen2023a R23].

Findings

F17, F23, F24, F25, F26, F30, F31.

Related concepts

assessed by virtual bioequivalence; related to in vitro–in vivo correlation. Also related to food effect (fed and fasted exposure) and endogenous crystallization (exposure of crystals formed in the product).

Formulas

F = F_a F_{gut} F_H is printed in words [purohit2018 E6]; see non-compartmental AUC, relative bioavailability and absolute bioavailability.

How it is measured or obtained

Simulated by a PBPK model for tacrolimus [purohit2018 R12]. Measured as AUC0–24 and Cmax in six beagle dogs after 1 mg of tacrolimus, with whole-blood LC-MS/MS [purohit2019 R9]; as AUC0–48 in rats [wilson2018 R16]; and in cynomolgus monkeys, fasted and fed, after 30 mg of pretomanid nguyen2023a R23.

Values in the library
materialvalue or classconditionspaper ids
tacrolimussimulated F 20.2% (observed 14.4–25%); Fa·Fgut 20.8% (14%); FH 97.1% (96.8%)GastroPlus[purohit2018 R12]
grazoprevirabout 1.8-fold AUC with hierarchical cPAD in dogshiew2023 R16, C32
tacrolimus capsules, dogsAUC0–24 42.1 (fresh generic), 22.9 (50% crystalline), 21.6 (100%), 5.29 (reference crystals) ng·h/mL1 mg, n = 6[purohit2019 R9, R11, C56]
enzalutamide, ratsAUC0–48 about 770, 575, 575, 61, 91 µg·h/mL (10% copovidone, 50% copovidone, 50% HPMCAS, 10% HPMCAS ASDs, crystalline)10 mL/kg gavage[wilson2018 R16]
pretomanid, monkeysrelative bioavailability of the 20% HPMCAS-HF tablet 155% (fasted); fed exposure 72.2% of fasted for the ASD and 163% for the crystalline product (printed, dose-normalized)30 mg, n = 4, crossovernguyen2023a R23, R33, C50, C53
Pitfalls and disagreements

The simulated Fa·Fgut exceeds the observed value [purohit2018 X3]. The dog Cmax unit is printed as "(ng)" and the whole-blood concentration is not a plasma concentration [purohit2019 R9]. The exposure of the endogenously crystallized drug lay about four times above that of purchased reference crystals, so exposure depends on how the crystals were made (F30) [purohit2019 R11, C56].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

peptide-enhancer co-release

The release of an oral peptide and its permeation enhancer from one dosage form at the same rate, so that the two reach the epithelium together and at the same relative amounts as in the solid. Two names are used for it in the library: congruent or synchronous release, borrowed from amorphous dispersion work and judged by equal surface-normalized release rates of every component bapat2025b C3, C15, E1, and corelease or temporal synchronicity, judged by the times at which peptide and enhancer reach their maximum release from a tablet fagan2025 C44, C46, R20. The motive is cited rather than measured in both papers: a high local enhancer concentration is needed, the absorption window after the enhancer acts is short, and co-localization of peptide and enhancer at the absorption site is considered important and hard to achieve with a solid oral form, especially in the small intestine bapat2025b C8, C10. Co-release is a release property only; neither paper that measures it measured permeability, transport or absorption, so the benefit remains an expectation ("may improve co-localization at the epithelial membrane", "would likely result in incongruous presentation") bapat2025b C6; fagan2025 C45. Evidence table: peptide-enhancer co-release.

Findings

F4, F5, F6, F1.

Related concepts

the same criterion as congruent release applied to three components; ends at the loading boundary of limit of congruency and its failure is incongruent release; achieved here through polymer-controlled release from an eroding gel layer; depends on drug loading and on pH-dependent solubility of the peptide; intended to serve membrane transport and oral bioavailability, neither of which was measured.

Formulas

surface-normalized release rate is the test for co-release in the compact route; equal values for every component are the criterion bapat2025b E1, C15.

How it is measured or obtained

Two routes, one per paper. (1) Surface-normalized release from a constant-area compact in a Wood's rotating die (100 mg, 0.5 cm² exposed face, 100 rpm, 100 mL of 50 mM pH 6.8 phosphate buffer, 37 °C, n = 3), with each component assayed in the same run by reversed-phase HPLC or aqueous size-exclusion chromatography and each profile converted to a rate per unit area and per weight fraction by surface-normalized release rate; equal rates mean the dissolved mixture has the composition of the solid bapat2025b P4, P2, E1. (2) Paddle dissolution of minitablets (40 mL, 75 rpm, samples to 120 min, n = 3) with peptide and enhancer assayed in the same samples by size-exclusion HPLC, compared by their times to maximum release fagan2025 P4, P7, R20. Both routes need every component to be assayable: sodium decanoate could not be quantified in the first study, so its co-release is inferred, and in the second the same enhancer was below detection in the two gastric media until the vessel was made basic bapat2025b R6, C19, X1; fagan2025 R14, R16.

Values in the library
materialvalue or classconditionspaper ids
octreotide : SNAC : copovidone, 1.6% peptideco-release; ≈8.1 / ≈8.4 / ≈8.9 mg min⁻¹ cm⁻²; complete 25–30 minpH 6.8, 0.5 cm² compact, 37 °Cbapat2025b R2.f–h, R5
octreotide : sodium decanoate : copovidone, 1.6% peptideco-release of the two assayable components; ≈23 / ≈25 mg min⁻¹ cm⁻²; complete in about 10 min; enhancer inferredsamebapat2025b R2.j–k, R9, C19
SNAC : copovidone 50:50 (no peptide)≈7.9 / ≈8.7 mg min⁻¹ cm⁻², about 4.4 and 2.7 times the neat ratessamebapat2025b R2.d–e, X18
cyclosporine : copovidone ± enhancer, 1.6% peptidepeptide follows the polymer: complete in about 50 min (binary), about 10 min (decanoate), ≈95% at 60 min (SNAC)samebapat2025b R10, C21
cyclosporine ternaries, 5–20% peptideco-release lost: polymer complete while peptide stalls at ≈54.5% and ≈16% (decanoate), all components slowed (SNAC)samebapat2025b R11.i, R12.i, R13.i
insulin with 72% sodium caprate or SNAC, minitabletstaggered: enhancer maximum at about 10–20 min, insulin at about 30 minsix simulated fluids, 40 mL, 75 rpmfagan2025 R20, R14, R15
neat peptide and neat enhancer, no release-controlling excipientrates differ: ≈4.5 (octreotide) against ≈1.8 (SNAC) mg min⁻¹ cm⁻²; amorphous cyclosporine below 0.1% in 6 hpH 6.8, 0.5 cm² compactbapat2025b R2.a–c, R14
Pitfalls and disagreements

The criterion is only as good as the assay: a component that cannot be quantified turns co-release into an inference, as for sodium decanoate in every dispersion of the first study, which also carries its extension "to different types of PEs" bapat2025b X1, C43. Overlapping profiles are not the same as equal rates: the cyclosporine dispersions are called congruent although no normalized rate was computed for any of them, and at 1.6% loading with SNAC the peptide in fact lagged the enhancer and polymer (≈75.5% against ≈85% and ≈89.5% at 30 min) bapat2025b X2, R10.f, C21. In the minitablet study the enhancer's apparent incompleteness is partly an artefact of the centrifugation step, since almost all of it was recovered once the medium was made basic, which makes the measured stagger an upper bound fagan2025 C28, R16, X9. Release above 100% in both papers bounds the precision to a few percentage points bapat2025b X9; fagan2025 X11. Co-release says nothing about the state of the released enhancer: it may sit in colloidal self-assemblies or a second phase rather than as free monomers or micelles, "which may restrict their efficacies", and SNAC quenched the octreotide fluorescence in solution, an interaction that was not followed up fagan2025 C43, C32; bapat2025b C31. No paper in the library relates any co-release measurement to a permeability, cell, tissue or in vivo result; the optimal release timeframe "remains to be elucidated" bapat2025b C37, C6; fagan2025 C45.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

pH-dependent polymer solubility

Evidence table: pH-dependent polymer solubility. Content from the ASD dissolution chapter (2014, 2015) and from papers of the release-mechanism and crystallization-from-solution chapters.

The change of a polymer's aqueous solubility with pH through ionization of its acidic or basic groups. HPMCAS, an enteric polymer, is a weak acid (pKa about 5), insoluble when un-ionized and soluble when sufficiently ionized kaur2025 C27. In the ASD dissolution chapter this is used twice: an HPMCAS dispersion of nifedipine placed at pH 2 keeps its matrix in place because the polymer is not very soluble there (cited) [raina2014b C25], and celecoxib–HPMCAS particles are dosed as an acidified suspension because the polymer stays largely undissolved at pH 3 chen2015a R18. The papers of 2015–2018 add further uses: a resveratrol–HPMCAS dispersion crystallized about equally at pH 6.8 and at pH 1.2, where HPMCAS is "essentially insoluble", which placed the crystallization in the matrix [wegiel2015 M4, C16]; enteric dispersions of lopinavir at pH 3 leached less than 5 µg/mL of polymer [li2016b R3, C8]; at pH 3 HPMCAS, HPMCP and CAP stay undissolved, which keeps a mixed dispersion's composition and lets the polymer lower the drug's maximum concentration [li2018 C12, C45]; and the cationic EPO dissolves by ionization at pH 2.2 but is "soluble up to pH 5" [xie2017 M3, C29]. New aspect (Release mechanism and LoC, 2024–2025): the HPMCAS grades differ in how much they need to ionize: the more succinoylated LF dissolved about three times faster than HF at pH 6.8 and 7.5, and the authors propose that it needs less ionization to dissolve bapat2025a R1, C25. HPMCAS alone stays dissolved at pH 5.8 and above at 0.5 mg/mL, while about 77% ionization is estimated to be needed for it to start dissolving kaur2025 C11, R3, C28. A drug that complexes the polymer lowers its solubility at a pH where it would otherwise dissolve (insoluble drug-polymer complex) bapat2024 C29. Co-precipitation into acidified water uses the low solubility of HPMCAS at low pH to make high-loading particles hiew2025 C6.

Findings

Supersaturation from ASD dissolution: F2, F15, F1, F15, F16, F18, F19, F21, F24, F25, F27. Release mechanism and LoC: F23, F33, F34, F35.

Related concepts

related to polymer ionization, drug leaching and polymer-controlled release. Set by critical ionization for polymer dissolution; lowered at the surface by microenvironmental pH and by an insoluble drug-polymer complex.

Formulas

Henderson-Hasselbalch equation.

How it is measured or obtained

By polarized light of the undissolved matrix [raina2014b P5], by colorimetric assay of dissolved polymer chen2015a P12, or by polymer solubility at fixed pH kaur2025 R4.

Values in the library
materialvalue or classconditionspaper ids
nifedipine–HPMCAS 50:50 at pH 2matrix undissolved and amorphous for 3 hpolarized light, Raman[raina2014b R15]
HPMCAS-LF from celecoxib particles at pH 3about 1.5–3.5 µg/mL in the liquid over 24 h without surfactant25 °Cchen2015a R18
HPMCAS LF and MF at pH 5.0 (Release mechanism and LoC)about 250 and 110 µg/mLblank FeSSIF-V1 pHkaur2025 R4
HPMCAS grades with posaconazole (Crystallization from solution)incomplete release where the grade is less solublepH 5.5–7.5shah2025 C16
HPMCAS at gastric pH (Release mechanism and LoC)insoluble, so exposed surface area mattered only in the FaSSIF stagetwo-stage releasehiew2025 C32
HPMCAS LF / MF / HF / HPMCP, spray-dried alone≈15 / ≈19 / ≈68 / below 5 µg/mLpH 3, 25 °C, 1–3 h[li2016b R2]
the same from 33% lopinavir dispersionsbelow 5 µg/mLpH 3[li2016b R3]
HPMCAS-HF from lopinavir dispersions with SDS at pH 5≈74.5–134 µg/mL25 °C[li2016b R13]
cellulosic polymers in lopinavir release testsmostly below detection, estimated 3–25 µg/mLpH 3, 25 °C[li2018 R5]
HPMCP-50; HPMCP-55893 ± 95 and 189 ± 18 µg/mL at pH 5.0; insoluble below pH 4.548 h, 37 °C[nguyen2023c R4]
HPMCAS-LF; -MF; -HF1687 ± 47 and 1401 ± 69 µg/mL at pH 5.5; HF only from about pH 6.048 h, 37 °C[nguyen2023c R4]
Eudragit L 100-55 coat on tabletsintact 15 to more than 17 h at pH 1.6–3.0; failed after ≈130 min at pH 4.5 and ≈150 min at pH 5.0; dissolved within 10–15 min at pH 6.0500 mL, 37 °C[nguyen2023b R7]
neat HPMCAS LF, MF, HF≈1.50 / 0.90 / 0.45 (pH 6.8) and ≈1.73 / 1.09 / 0.63 mg/min/cm² (pH 7.5)compacts, 50 mM phosphate, 37 °Cbapat2025a R1
HPMCAS LF, MF slurries in waterpH 4.52, 4.61 (HF 4.73)overnight stirringbapat2025a M3, M4, M5
HPMCAS with ≈5 mg/mL solubility at pH 6.0lowered by lipophilic weak bases through complexationspike testbapat2024 C29
bedaquiline–HPMCAS 20% in FeSSIF-V1 (pH 5.0)≈22.5–25% releasedpowder, 120 minkaur2025 R16, C51
Pitfalls and disagreements

A surfactant can dissolve the polymer at low pH and undo the effect (SDS raised dissolved HPMCAS to about 860 µg/mL at pH 3) chen2015a R18. The low dissolved levels at pH 3 lie far below the printed calibration range of the assay chen2015a X8. HPMCAS-HF, the grade with the highest pKa, leached most of the three grades at pH 3, "somewhat counterintuitive", perhaps from a small low-pH-soluble fraction ("may") [li2016b C9, C10]; the dispersion polymer values lie below the detection limit or near the quantitation limit [li2016b X7]. Dissolved polymer does not guarantee released drug: delamanid release from an HPMCAS-HF dispersion stayed near zero at pH 6.5 while about 30% of the polymer dissolved [nguyen2023c R11, R12]. The printed polymer solubilities above about 3.3 mg/mL exceed what the stated amounts allow [nguyen2023c X1]. The MF slurry pH has no stated source bapat2025a X4; raising the bulk pH speeds the neat polymer as well as reducing drug ionization, so the two effects are not separated in the grade comparison bapat2025a K2.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

pH-dependent solubility

The rise of the solubility of an ionizable drug as pH moves toward and past the pKa; for a weak base the total solubility is the free-base solubility times (1 + 10^{\mathrm{p}K_a-\mathrm{pH}}) [indulkar2015 E8]. The amorphous solubility follows the same shape with the amorphous free-base solubility in place of the crystalline one, so the un-ionized concentration at the LLPS onset is constant across pH (F10) [indulkar2015 C46, R9]. The papers of 2017–2022 add pazopanib, for which the crystalline free base follows the curve from pH 5 to 8.4 and the amorphous solubility follows its curve from pH 6 upward but lies below it at pH 5 and 5.5 [sugihara2018 R2, R3, C10, C11]. New aspect (Crystallization from solution): in the pH-shift studies the shift itself generates supersaturation, since weak bases with pKa 5–8 dissolve at gastric pH 1.5–3.5 and can precipitate at duodenal pH 5–7 [hsieh2012 C1]; the Bjerrum plot ties the pH, the total concentration and the solubility of whatever solid is present, and the curve moves by \log_{10}(S_0'/S_0) pH units when the solid's solubility changes (0.85 units for 11.3 against 1.6 µg/mL) [hsieh2012 E2, R9]. New aspect (Supersaturation from ASD dissolution): a weak acid. Indomethacin (pKa 4.42, cited) has an aqueous solubility of 1.5 µg/mL at pH 1.2 and 105 µg/mL at pH 7.4 (cited) [xie2017 M1]; the measured solubility of the α crystals rose from 2.8 µg/mL at pH 2.2 to 15 µg/mL at pH 5 [xie2017 R1, R2]. In a two-stage test the rise of pH after the acid stage therefore turns what separated in acid into a solid that can dissolve again: the drug-rich droplets of an EPO–HPMC dispersion disappeared within minutes of a rise to pH 5, "consistent with" an increase in the amorphous solubility on ionization [xie2017 C40, R20]. Weak bases (formerly the page "pH-dependent solubility of weak bases", from ASD process and Supersaturation from ASD dissolution): the solubility of a weakly basic drug rises when it is ionised at low pH and falls when the pH rises. Ritonavir (pKa 1.8 and 2.6) is "highly, not completely" ionised at pH 1.2, with a crystalline solubility of about 0.4 mg/mL there against 1.8 µg/mL at pH 6.8, so dissolution in 0.1 N HCl is at sink and at pH 6.8 strongly non-sink; lopinavir is not ionised at either pH [trasi2019 M1, M2, C14]. On a pH rise the ionised drug becomes supersaturated and, above its amorphous solubility, forms a drug-rich phase [trasi2019 C40]. For posaconazole the acid stage releases drug that becomes supersaturated at pH 6.5; extruded dispersions release more in acid than amorphous ones because crystalline drug sits apart from HPMCAS, which does not dissolve in acid [shah2024 C41, R12]. Coated posaconazole powders were held 30 min to 4 h at pH 1.6 or 4.0 and then moved to pH 6.5 moseson2023 R10, R12, R13; coated and uncoated ritonavir tablets released alike in 0.1 N HCl, where the drug is far more soluble benson2025 R12. For a weak base formulated with an enteric polymer, the drug and the polymer change their solubility in opposite directions across the gastric-to-intestinal range, and the window in which neither dissolves well decides the outcome. Delamanid, with a fitted pKa of 3.94 ± 0.04 against a reported 4.3, loses about 500-fold of its crystalline solubility and about 200-fold of its amorphous solubility between pH 1.6 and 6.5, while the enteric polymers dissolve only from about pH 5–6; the authors summarize that at pH 1.6 the drug dissolves and the polymers do not, at pH 3.0 and 5.0 both are poorly soluble, and at pH 6.5 the polymers dissolve and the drug hardly at all [nguyen2023c R1, R2, R3, R4, C14, C15]. Posaconazole shows the same pattern between gastric and intestinal fluid, which the authors attribute to nearly complete ionization in acid [elkhabaz2019a R1, C11].

Findings

Amorphous solubility and LLPS: F10, F23. Crystallization from solution: F1, F2, F34. Supersaturation from ASD dissolution: F21, F24, F25. ASD process: F23, F24, F41, F46, F48.

Related concepts

depends on ionization and pKa; applies to crystalline solubility and amorphous solubility; related to intrinsic solubility and pH-induced precipitation; related to pH-shift dissolution, precipitate redissolution and polymorphism; produces supersaturation read in non-sink dissolution; mixing in the drug-rich phase gives mutual amorphous solubility reduction; sets the window with pH-dependent polymer solubility; drives salt disproportionation; read with gastric pH variability and drug leaching.

Formulas

pH-solubility profile, Henderson-Hasselbalch equation, Bjerrum function, amorphous-to-crystalline solubility ratio.

How it is measured or obtained

Shake-flask crystalline solubility in 0.1 M buffers over about ±2 pH units of the pKa; LLPS onset by antisolvent addition, fluorescence and solvent-free pH-shift titration at each pH [indulkar2015 P3, P8, P9, P10]. In the pH-shift studies the crystalline solubility of the neutral form is measured at a pH at least two units above the pKa for bases (pH 10 buffer) or below it for acids (pH 2 buffer) [hsieh2012 P11; hsieh2014 P5]; potentiometric (CheqSol) titration of the neutral concentration and 72 h shake-flask solubility at fixed pH [hsieh2012 P4, P11]. For indomethacin: shake-flask solubility of the γ and α forms in pH 2.2 McIlvaine buffer (37 °C, 48 h) and of the α form at pH 5, with and without dissolved polymer [xie2017 P2, R1, R2]. For weak bases in the ASD process papers: dissolution in 0.1 N HCl and pH 6.8 phosphate buffer, and an acid-to-pH 6.8 shift with ultracentrifugation of the supernatant [trasi2019 P8, P9, P11, P12]. In the ASD dissolution papers: crystalline solubility by shake flask in each buffer and amorphous solubility by the onset of light scattering during slow addition of a stock, with a Henderson–Hasselbalch fit over the measured values to give the pKa [nguyen2023c P1, P2, E1]; the same measurements in simulated gastric and intestinal fluids [elkhabaz2019a P2, P4; duong2022a P1, P2].

Values in the library
materialvalue or classconditionspaper ids
clotrimazolecrystalline 0.55 (pH 8) to about 62 µg/mL (pH 4); LLPS 7.7 to 490.2 µg/mL37 °C[indulkar2015 R4, R5, R18]
atazanavircrystalline 1.04 (pH 9) to about 40 µg/mL (pH 3); LLPS about 65 to about 1970 µg/mL37 °C[indulkar2015 R4, R6]
nicardipineLLPS 5.5 (pH 9) to about 355 µg/mL (pH 5.5); no crystalline value37 °C[indulkar2015 R7, R1]
CRH1un-ionized onset about 12 µg/mL at pH 6.8 and pH 4.625 °C[almeidaesousa2016 R24]
pazopanibcrystalline about 0.60 → 0.018 µg/mL; amorphous 60 → 9.2 µg/mL (pH 5 → 8.4); ratio about 103 at pH 5, 500–600 from pH 6.437 °C, 0.1 M buffers + 5 µg/mL HPMC[sugihara2018 R1, R2, R4]
loratadineBjerrum data on the curve for S0 = 11.3 µg/mL, 0.85 pH units from the curve for the crystal (1.6 µg/mL)37 °C[hsieh2012 R9, E2]
dipyridamoledata left the ionization curve at pH about 5.1 and met the crystal curve at pH about 4.037 °C[hsieh2012 R4]
papaverine, dipyridamole, glyburide, warfarincrystalline solubility in pH 10 or pH 2 buffer: 12.2, 5.4, 0.2 (titration), 3.7 µg/mL25 °C, no polymer[hsieh2014 R4]
posaconazolecrystalline 0.27 (pH 5.5–7.0) to 347.03 µg/mL (pH 1.0); amorphous 8.92–9.20 to 7761.96 µg/mL; diprotic HH fitphosphate buffers, 0.14 M, 37 °C[duong2022b R1, R2, E4]
indomethacin (cited)1.5 µg/mL at pH 1.2 to 105 µg/mL at pH 7.4; pKa 4.42literature[xie2017 M1]
indomethacin γ; α1.61; 2.8 µg/mL at pH 2.2; α 15 µg/mL at pH 537 °C, no polymer[xie2017 R1, R2]
delamanid, amorphous and crystalline154.5 → 0.76 and 10.2 → 0.018 µg/mL between pH 1.6 and 6.5, a ratio of 42; fitted pKa 3.94 ± 0.04 against a reported 4.3 (Henderson–Hasselbalch fit)37 °C[nguyen2023c R1, R2, R3]
praziquantelamorphous 1.17–1.43 mg/mL across six buffers; calculated pKa 1.14, so the drug is neutral above about pH 337 °C[alvarenga2025 R1, R4]
ritonavir from the marketed tabletabout 84 µg/mL in acid falling to about 4.6 after the shift to pH 6.8200 mL acid, 30 min, then NaOH and buffer[trasi2019 R8]
ritonavir solution without excipientsabout 97 → 16 µg/mL after neutralisation; precipitate not birefringentultracentrifuged supernatant[trasi2019 R9, R10]
posaconazole (outside)solubility much higher in the gastric than in the intestinal medium because the drug is nearly completely ionised in acidbiorelevant media[elkhabaz2019a C11, C40]
delamanid (outside)pH-solubility profile of a weak base by the Henderson–Hasselbalch equationbuffers and media[nguyen2023b E1, R13]
posaconazole form Icrystalline solubility 86.5 µg/mL at pH 1.6 (FaSSGF) and 1.2 µg/mL at pH 6.5 (FaSSIF V2); LLPS concentration 2326 and 19.1 µg/mL37 °C[shah2024 R11, C14]
PCZ–HPMCAS extruded at 125 °C against 175 °C, 10 / 25 / 50% DLabout 38 / 43 / 73.5 against 30 / 28.5 / 39.5 µg/mL after 60 min at pH 1.6two-stage test[shah2024 R12, R15, R18]
coated and uncoated 20% DL RTV–PVPVA tablets in 0.1 N HClabout 87–91% at 60 mintabletsbenson2025 R12
delamanid in biorelevant media, crystalline; amorphous17.6 / 0.52 / 0.086 / 0.018 and 69.9 / 7.93 / 3.11 / 0.76 µg/mL (FaSSGF, FaSSIF V1, FaSSIF V2, PBS pH 6.5)37 °Cduong2022a R1
posaconazole, crystalline115.1 ± 9.4 µg/mL in FaSSGF against 1.69 ± 0.06 µg/mL in FaSSIF48 h, 37 °C[elkhabaz2019a R1]
posaconazole, amorphousabout 20 µg/mL in FaSSIF with 20 µg/mL HPMCAS; 8 µg/mL in plain buffer pH 6.537 °C[elkhabaz2019a R2, R4]
Pitfalls and disagreements

The predicted amorphous curve is the crystalline curve times one factor, so it is not an independent test of the shape [indulkar2015 X14]. The relation holds where the solution is in equilibrium with the neutral form and not the salt [indulkar2015 E8]. Below pH 6 the amorphous boundary of the pazopanib diagram is a model curve, not a measurement [sugihara2018 X12]. Solubility was measured in other buffers than the precipitation, and buffer compositions are not given [hsieh2014 X8]. The legend of the loratadine Bjerrum figure names the predicted amorphous solubility, the text the supernatant value (11.0 against 11.3 µg/mL) [hsieh2012 X6]. The plotted Henderson–Hasselbalch fit of the posaconazole paper lies far below the data at pH 2.5–3.0 for one assignment of the two pKa values [duong2022b X3]. The pH profile of indomethacin is cited, not measured, and its amorphous solubility was measured at pH 2.2 only, so the ionization explanation of the droplet disappearance at pH 5 is an inference [xie2017 M1, R3, C40]. Ionization does not explain the whole pH dependence of release: praziquantel, neutral above about pH 3, still lost release after gastric stages at pH 3.0 and 5.0, so the pH dependence of release need not come from the drug [alvarenga2025 R4, R10]. Acid-stage release does not rule out the problem: the neutral partner drug still lowered ritonavir release in acid, and the fall after the pH shift reflects loss of ionisation, dilution and mixing with the partner (not separated) [trasi2019 C41, C47]. The final pH after the shift was not measured and the acid volume is printed as 250 mL in the caption and 200 mL in the methods [trasi2019 X4, X5]. The fitted curve for delamanid follows the amorphous data but gives about 3.7 instead of the measured 10.2 µg/mL for the crystal at pH 1.6 [nguyen2023c R3]. The gastric supersaturation that the drug's own pH dependence creates did not order the final release of delamanid dispersions [nguyen2023c C39].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

pH-induced precipitation

The precipitation of an ionizable drug when a change of pH makes its neutral, less soluble form exceed the crystalline solubility: a weak base dissolved in the stomach can precipitate at duodenal pH 5–7 [hsieh2012 C1]; the 2014 series also shifted two weak acids to a final pH of 1.9–3.3 [hsieh2014 P2]. Precipitation of a base releases protons and lowers the pH, dissolution consumes them [hsieh2012 C6].

Findings

F1, F2, F16.

Related concepts

produces amorphous precipitation; classified by chaser and non-chaser behaviour; related to ionization and ph-dependent solubility.

Formulas

Bjerrum function, supersaturation factor, scattering vector.

How it is measured or obtained

By potentiometric (CheqSol) titration in a Sirius GLpKa titrator: drug dissolved at low pH, titrated with KOH to the turbidity point, then alternating acid and base aliquots; neutral concentration from mass and charge balance, with the solid examined by polarized light, DSC and PXRD or synchrotron WAXS and the supernatant by HPLC [hsieh2012 P4–P6, P9–P12; hsieh2014 P1–P7]. For the 2014 polymer series the drug was dissolved in its ionized form with or without 1 mg/mL polymer and the pH moved two units beyond the pKa [hsieh2014 P2].

Values in the library
materialvalue or classconditionspaper ids
ten weak basesfive crystalline (supersaturation 3.1–14.7 min) and five amorphous (7.2–20.7 times crystalline solubility)37 °C, 0.15 M KCl[hsieh2012 R1, R5, R10]
papaverine, dipyridamole, glyburide, warfarin, no polymerpeaks about 240, 84, 6.5 and 165 µg/mL; crystallized25 °C[hsieh2014 R1]
glyburide, warfarin with six to eight polymersamorphous precipitate for at least 6 h; warfarin 103–224 µg/mL1 mg/mL polymer[hsieh2014 R4]
pazopanib HCl shifted from simulated gastric to pH 6.5 (amorphous solubility chapter)supersaturation 5 ± 2 min without HPMC, about 39 min with 50 µg/mL37 °C[sugihara2018 R22]
Pitfalls and disagreements

The titration amounts and replicate numbers are not printed, the duration of supersaturation has no criterion, and the degree of supersaturation is defined differently for the two types [hsieh2012 X13, X5, X3]. In 2014 solubility was measured in other buffers over 72 h and concentration in KCl within 1 h [hsieh2014 X8]. No in vivo data test the link to absorption [hsieh2012 C28].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

pH-shift dissolution

Two-stage dissolution in which the dose dissolves in acid and the pH is raised, creating supersaturation of a weak base [hate2017 C8, C41]. Two-stage tests were also used for the enteric-polymer pretomanid ASD: a gastric stage, then fasted or fed intestinal medium nguyen2023a P11, P12, C63.

Findings

F10, F14, F26, F27.

Related concepts

related to non-sink dissolution and ionization.

Formulas

none.

How it is measured or obtained

30 min in 0.1 N HCl, then an equal volume of 0.17 M Na2HPO4, giving pH 6.5 [hate2017 P7].

Values in the library
materialvalue or classconditionspaper ids
nevirapine powder (100 mL) and tablet (400 mL)nominal S 3.9; donor 475–500 µg/mL after the shift37 °C[hate2017 R7, R18]
ketoconazole, clozapine on silicadissolved amount decreased by 30–35% on shiftingpH 1 to 5.5/6.8[hate2020b R10, R11]
pretomanid ASD tablets1 h gastric stage, then intestinal medium: all three tablets crystallized30 mg in 150 mLnguyen2023a R22, P12
Pitfalls and disagreements

The PVPVA run used another route to supersaturation [hate2017 X15].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

phase inversion

Evidence table: phase inversion. Content from the release-mechanism chapter (2022–2025), with rows from the Solid-state methods chapter.

The change of which of two separated phases is continuous and which forms discrete domains, as their relative amounts change. In dissolving PVPVA dispersions the lower-volume phase forms the discrete phase and the higher-volume phase the continuous one, so inversion from a discrete to a continuous drug-rich phase "is anticipated" as drug loading rises; the low-composition component tends to form the discrete phase, which gives a discrete drug-rich phase and fast congruent release at low loading (cited) yang2022a C46, C59. In MePHPH–PVPVA compacts the morphology inverted at 50% (hydrophobic continuous, hydrophilic discrete), persisted and coarsened deac2023a C26. In the Solid-state methods chapter dry dextran–PVP blends with distinct phases had a dextran-rich continuous phase with PVP-rich domains at high dextran molecular weight and inverted morphology for DEX40-PVP90 and DEX6-PVP90 vaneerdenbrugh2012c C43. The 2024 papers locate it: clotrimazole films with PVP K12 and K29/32 held drug-rich droplets to 30% and a continuous drug-rich phase at 40% after 1 h at 100% RH, named "Failure Mode II" deac2024a R8, C23, C40; MePHPH films kept droplets to 30% and were continuous from 50%, PHPH films switched between 10 and 15%, and the lever-rule fraction of drug-rich phase jumps from about 0.15 to 0.82 across the critical point, taken as a surrogate for inversion deac2024b R18, R19, R35, C64.

Findings

Release mechanism and LoC: F20, F25, F27, F29, F30.

Related concepts

part of phase separation morphology; its loading is shifted by associative phase separation and segregative phase separation; relative phase amounts from the lever rule; gives the drug-rich barrier layer when the drug-rich phase becomes continuous.

Formulas

lever rule (relative phase amounts).

How it is measured or obtained

Fluorescence confocal imaging of the edge of a dissolving compact with two dyes that partition into the two phases, and imaging of compact surfaces after partial dissolution deac2023a R6, R9; in dry blends local AFM-IR spectra of the continuous phase and the domains vaneerdenbrugh2012c R15, R17.

Values in the library
materialvalue or classconditionspaper ids
MePHPH–PVPVA 5–30%; 40%; 50%discrete particles below 1 µm; networks; inverted, hydrophobic continuousin situ confocal of the dissolving compact edgedeac2023a R6, C26
MePHPH–PVPVA 30%; 50% compact surfaces50% surface the inverse of the 30% surfaceafter partial dissolutiondeac2023a R9, C35
dextran–PVP blends DEX450-PVP12, DEX40-PVP12; DEX40-PVP90, DEX6-PVP90 (Solid-state methods chapter)dextran-rich continuous phase; phase inversionAFM-IR, dry filmsvaneerdenbrugh2012c C43, R15, R17
clotrimazole–PVP K12, K29/32 filmsdroplets at 20–30%, inverted at 40%100% RH, 1 h, confocaldeac2024a R8
MePHPH–PVPVA films 10–60%droplets to 30%; co-continuous 1 h, droplets 6 h at 40%; continuous 50–60%100% RH, confocaldeac2024b R18
PHPH–PVPVA films 5–20%droplets 5–10%; continuous 15–20%samedeac2024b R19
Pitfalls and disagreements

For ritonavir the inversion is an expectation argued from phase volumes, not located at a measured loading yang2022a C46. In the dissolving compacts the continuous drug-rich phase appeared at 40% as networks before full inversion at 50%, so the change was gradual over loading deac2023a C26. The loading at which MePHPH becomes continuous is stated as above 40%, 40% or higher, and 35–40% in different parts of the 2024 paper deac2024b X4; for PHPH the computed critical point (3.7% as the paper states; about 4.2% read from its diagram, see critical point) lies below the film switch deac2024b X5. Inversion was imaged for two PVP grades only deac2024a X8.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

phase-separated domain size

The lateral size of the drug-rich (or polymer-rich) regions in a phase-separated dispersion. It decides which methods can see the separation: DSC is said to miss domains below about 15–30 nm or 10–50 nm [rumondor2009a C6; vaneerdenbrugh2012a R18], diffraction-limited fluorescence imaging cannot resolve domains below about 300–500 nm [tian2016 C44], and AFM-IR resolves about 100 nm (best about 20 nm) in films of a few hundred nanometres [li2016c R24]. In the papers of this chapter the domains are submicron to a few microns, and the authors expect their size to matter for dissolution ("is likely to") and for crystallization, because less polymer surrounds the drug in a drug-rich domain [li2016c C42, C41; purohit2015a C51].

Findings

F18, F19.

Related concepts

characterizes amorphous-amorphous phase separation; limits spectral mixing and the detection by the single-Tg miscibility criterion; related to drug-polymer miscibility.

Formulas

none.

How it is measured or obtained

From AFM height images with the software ruler, the diameter read from fluorescence images and from nanoIR maps [li2016c P2; purohit2015a P4, P9]; by image analysis (ImageJ) of confocal images [purohit2017a R18]; by solid-state NMR spin diffusion as a bracket [purohit2017a R21, R22]. The papers give no size distributions in this chapter [purohit2015a X8].

Values in the library
materialvalue or classconditionspaper ids
itraconazole–HPMC 10:90 to 50:50, solvent-cast filmsdomains 500–1000 nm (authors); about 0.4–1.4 µm in the images; 1.5–2.5 µm in the chemical map of 30:70AFM-nanoIR, spin-coated[purohit2015a C37, R10, R14, X8]
telaprevir–HPMCbelow 50 nm at 10:90; around 100–200 nm in the other filmsAFM height[li2016c R7]
telaprevir–HPMCASabout 120 nm wide and 50 nm high at 40% drug; 122 × 13 nm at 50:50, gaps 21 and 25 nmAFM height[li2016c R5, R7]
telaprevir–PVPVAabout 280 nm wide and 20 nm high at 10%; about 380 nm and 100 nm at 50%AFM height[li2016c R6]
itraconazole–HPMC 40:60, outside the subcategoryabout 3–5 µm in slowly cast films; about 0.4–1 µm, D50 0.9 µm, in spin-coated filmsconfocal fluorescence[purohit2017a R16, R17, R18]

Evidence table: phase-separated domain size.

Pitfalls and disagreements

The domain sizes quoted in the text are not borne out in every image (up to about 1.4 µm in Fig. 6d, about 2.5 µm in the chemical map), and no distribution was measured [purohit2015a X8]. In crowded films (gaps of 21–25 nm) the domains are below the AFM-IR resolution and the spectra of the two phases coincide [li2016c C15, R11]. Size depends on how the film was made: it fell from 3–5 µm in slowly cast films to about 1 µm in spin-coated films of the same itraconazole–HPMC composition [purohit2017a C43]. Domain widths of different figures and films must not be combined [li2016c X13].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

phase separation kinetics

Evidence table: phase separation kinetics. Content from the release-mechanism chapter (2017–2022).

The rate at which a hydrating dispersion undergoes water-induced amorphous–amorphous phase separation, set against the rate at which it dissolves. Saboo and co-workers (2020) state that the thermodynamic favourability of water-induced AAPS depends on drug loading, polymer type, the relative affinity of drug and polymer for water and the water absorbed, and that its kinetics compete with dissolution ("it has been suggested") saboo2020a C39. The competition "may be key": if dissolution is faster, drug and polymer release congruently and the surface keeps its composition; if AAPS is faster, the polymer-rich domains dissolve first, the surface turns drug-rich and drug release slows saboo2020a C41. The ritonavir and ledipasvir papers explain the steep drop of release over a small loading step the same way, by a faster rate of AAPS relative to dissolution at high loading ("can be attributed"; "may") indulkar2019a C33; que2019 C35. Saboo and co-workers (2021) assume separation in the hydrated matrix to be faster than polymer dissolution and propose that TPGS may slow it or slow coarsening saboo2021 C38, C41, C51; Correa Soto and co-workers (2022) find the kinetics and morphology changed by the surfactant, with a significance for release "if any" unknown correasoto2022a C61, and in the atazanavir study separation needs mobility that the surfactants supply correasoto2022b C41.

Findings

Release mechanism and LoC: F8, F20.

Related concepts

the rate of amorphous-amorphous phase separation; proposed cause of the limit of congruency; depends on drug-polymer-water miscibility.

Formulas

none.

How it is measured or obtained

Not measured as a rate in the release papers: inferred from films dipped in water for seconds or held at high humidity, together with the release data indulkar2019a X6; saboo2020a C41. The time course was followed only by the pyrene ratio of ritonavir films at 97% RH, where all PVP and PVPVA films began to separate as early as 1 h purohit2017b R2, C22.

Values in the library
materialvalue or classconditionspaper ids
ritonavir 50:50 PVP, PVPVA filmsseparated within 10 s in buffer; 10:90 did not25 °Cpurohit2017b R4, R9
ritonavir PVP, PVPVA filmsAAPS from about 1 h at 97% RHpyrene I/IIIpurohit2017b C22
felodipine dispersions ≤ 10%dissolution thought to outpace AAPS with every polymerargumentsaboo2020a C41
atazanavir–PVPVA 10% filmsbinary uniform for 3 h at 37 °C, separated within 10 min at 50 °C; surfactant films within 10 min100% RHcorreasoto2022b R9, R12, R10, R11
Pitfalls and disagreements

Neither the rate of AAPS nor that of dissolution was measured on the same sample; the competition is the authors' inference from films plus release data indulkar2019a X6. At low loading too little drug for a contiguous layer may keep release congruent as well as slower AAPS saboo2020a C42.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

phase separation morphology

Evidence table: phase separation morphology. Content from the release-mechanism chapter (2021–2023), with rows from the Physical stability chapter.

The shape and connectivity of the drug-rich and polymer-rich phases that form when water separates a drug–polymer dispersion: discrete (circular, separated) drug-rich domains in a continuous polymer-rich phase, bicontinuous structures, or a continuous drug-rich phase with discrete polymer-rich domains saboo2021 R21, R23; correasoto2022a R20. Saboo and co-workers (2021) propose that at high loading whether release is drug- or polymer-controlled "depends largely" on the architecture of the drug-rich phase formed in the hydrated matrix saboo2021 C37; in the abstract discrete spherical drug-rich domains with surfactant "appeared to be linked" to congruent, rapid release and a contiguous drug-rich phase to its loss saboo2021 C53. For clopidogrel the binary films matched the release profiles and "earlier reports" that continuous drug-rich phases go with poor release correasoto2022a C32. Domain size and interconnectivity of the drug-rich domains "appear" critical for release of ritonavir–PVPVA, and a continuous drug-rich phase is called catastrophic for drug release yang2022a C4, C58.

Findings

Release mechanism and LoC: F20, F21, F25.

Related concepts

the outcome of amorphous-amorphous phase separation; kept discrete when drug-rich phase coarsening is slowed; a continuous drug-rich phase acts as a drug-rich barrier layer; set within the gel layer; changed by surfactant partitioning into the drug-rich phase.

Formulas

none.

How it is measured or obtained

AFM topography and deflection and AFM-nanoIR ratio images of 30% felodipine films after 12 h at about 100% RH saboo2021 R21, R23; micro-CT of tablets after 10 min of dissolution saboo2021 R19; fluorescence confocal imaging with Nile red (drug) and Alexa 488 (polymer) of films before and after 5 min at 100% RH, with a detection limit of about 500 nm correasoto2022a R20, R21; time-lapse fluorescence and O-PTIR of ritonavir films (Physical stability chapter) yang2022b R4, R22.

Values in the library
materialvalue or classconditionspaper ids
felodipine–PVPVA 30% with 0, 2% TPGS; 5, 10% TPGSirregular semi-continuous domains; circular, discrete domainsAFM, 12 h at ≈100% RHsaboo2021 R21
felodipine–PVPVA 30% with 0; 10% TPGScontiguous, elongated drug-rich regions; round, separated drug-rich domains in a continuous drug-lean phaseAFM-nanoIRsaboo2021 R23
clopidogrel–PVPVA 40, 50, 60%uniform; bicontinuous; continuous drug-rich phase with discrete polymer-rich domains5 min at 100% RHcorreasoto2022a R20
clopidogrel–PVPVA with 5 g SDS per 100 g at 50%homogeneous within the ≈500 nm detection limitsamecorreasoto2022a R21
clopidogrel–PVPVA with TPGS; with Tween 80, at 50 and 60%bicontinuous, then large irregular structures; fine-scale heterogeneous patternsamecorreasoto2022a R22, R23
ritonavir–PVPVA 30% binary; with SDS or Tween 80; with Span 85 (Physical stability chapter)bicontinuous; discrete circular drug-rich domains; continuous drug-rich phasefilms, time-lapseyang2022b R4, R22, C9
ritonavir–PVPVA 10–20%; 30%; 40%discrete droplets 0.5–2 µm; porous continuous layer; continuous layerconfocal of dissolving compactsyang2022a R6, R10, R12, R13
MePHPH–PVPVA 5–30%; 40%; 50%discrete particles below 1 µm; networks; inverted morphologyin situ confocal of the dissolving edgedeac2023a R6, C26
PHPH–PVPVA 10–20%networksamedeac2023a R7
Pitfalls and disagreements

Morphology was imaged in films or humidified compacts, not in the dissolving gel layer; the contiguous network "likely also forms" there saboo2021 C39. Morphology and release did not track in every system: with TPGS the 50% clopidogrel film was bicontinuous correasoto2022a R22, and Correa Soto and co-workers (2022) find kinetics and morphology changed by the surfactant with a significance for release "if any" unknown correasoto2022a C61.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

physical stability

The ability of an amorphous drug or dispersion to stay amorphous, and unseparated, during manufacture and storage [vaneerdenbrugh2010a C19; kestur2013b C46]. In this chapter it is approached through the crystallization tendency of the neat drug; dispersion stability is treated in other chapters. New aspects (Miscibility and drug-polymer interactions): For polymer dispersions, physical stability is read as the time to the first crystalline peaks under a stress condition, and it depends on whether the polymer bonds the drug. Naringenin and quercetin dispersions with E100 or PVP showed no crystals for more than 200 to more than 450 days at each of five storage conditions, whereas dispersions with HPMCAS, HPMC, CMCAB or PAA crystallized within 1–3 days at 84% RH/25 °C and at 75% RH/40 °C [wegiel2013a R9, C22]. Lumefantrine–PVPVA dispersions crystallized after 1 to 8 weeks at 40 °C/75% RH, while enteric-polymer dispersions showed drug crystals only at 50% drug loading hiew2022a R6, C10. Phase separation is expected to lower stability: a phase-separated dispersion "would be expected" to crystallize faster in storage and dissolution [purohit2015a C2, C35; li2016c C1, C41]. Dry storage, humidity and polymer content each change the ranking of polymers [wegiel2013a R9, X3; vaneerdenbrugh2011a C50]. New aspect (Physical stability): for the resveratrol and curcumin dispersions it is likewise read as days before crystals appear at a set storage condition, and it depended "greatly" on polymer and condition [wegiel2013b C23; wegiel2014 C21]. New aspect (Supersaturation from ASD dissolution): two settings in which physical stability decides dissolution performance. For dispersions with two polymers: at 60% indomethacin and 40 °C/75% RH the HPMC and the EPO binaries both crystallized within 5 days (growth much slower with EPO), whereas the EPO–HPMC ternary stayed amorphous for more than 100 days, contrary to the expectation that partly replacing EPO with HPMC would make it similar or slightly worse ("unexpected"); at 30% drug the ternary was also more stable than the HPMC binary [xie2017 R26, C51, R27]. For suspensions of dispersions dosed preclinically, the crystallization tendency "is expected" to depend on the extent of supersaturation, the polymer solubility in the medium and the polymer's ability to inhibit crystallization in solution and matrix [li2018 C60]. Lopinavir–HPMCP dispersions, with the strongest solubility suppression, were the most stable against crystallization ("correlates"), and where suppression brought the concentration to or below the crystalline solubility the authors see no driving force for crystallization, so that such dispersions "should remain" physically stable, dry and as suspensions [li2018 C61, C62, C63, C64].

Findings

Crystallization tendency: F17, F20, F21. Miscibility and drug-polymer interactions: F15, F17, F23, F24, F26. Physical stability: F24, F25, F26, F30, F33, F34, F35. Supersaturation from ASD dissolution: F18, F20, F23.

Related concepts

includes glass stability and surface crystallization; depends on crystallization tendency; related to amorphous salt; depends on drug-polymer interactions, acid-base interaction and amorphous-amorphous phase separation; includes crystallization inhibition; tested by accelerated stability testing; lost through moisture-induced crystallization; depends on solubility suppression in suspensions; related to ternary amorphous solid dispersion and matrix crystallization.

Formulas

none.

How it is measured or obtained

By storage at set temperature and humidity followed by PLM, XRPD or fluorescence [baird2010 P7; tian2016 R17; hiew2022b R7]; by Raman or PXRD crystallinity against time [kestur2013b R3]. For the lumefantrine and polyphenol dispersions: open-dish storage at 40 °C/75% RH with PXRD at times from 1 to 76 weeks hiew2022a P8; five conditions (22–25 °C over P2O5, 22–25 °C at 84% RH over potassium chloride, 40 °C at 75% RH over sodium chloride, 50 °C and 90 °C over Drierite) with PXRD for the first sharp peaks [wegiel2013a P3]; for thin films, polarized-light scoring of the crystalline area over 7 days of dry storage, expressed as an amorphicity index [vaneerdenbrugh2011a P2, P3, E1]. For resveratrol and curcumin, storage tables of first sampling times with crystals by XRPD at five or six temperature–humidity conditions [wegiel2013b P3, P4, R12; wegiel2014 P5, R13]. In the ASD dissolution papers: open-vial storage of 60% and 30% dispersions at 40 °C/75% RH with PXRD up to 100 days [xie2017 P16, R26]; in suspension, concentration over 48 h and polarized light microscopy of 50% dispersions in pH 3 buffer without a dissolved inhibitor [li2018 P6, P7].

Values in the library
materialvalue or classconditionspaper ids
indoprofen; droperidol, nifedipine; clotrimazole, felodipinecrystalline in 1 day; by 3 months; edges only at 3 monthsquenched glasses, 0% RH, 14–20 °C below Tg[baird2010 R23, R24, R25]
felodipine with 3% PVPnot completely crystallized after 24 weeks30 °C, dry[kestur2013b C11]
indomethacin–PVP dispersions, 10–90% drugamorphous over 3 months (all compositions)40 °C, desiccant[tian2016 R16, C35]
indomethacin with HPMC or HPMCAS, 10–90% drugabove the miscibility limit crystalline in 2–15 days; at or below it amorphous 13–14 months40 °C, desiccant[tian2016 R17, C53]
pretomanid–HPMCAS dispersionsstable several months; neat glass crystallized within minutesambientnguyen2023a C62
lumefantrine HCl and sulfate saltsno recrystallization for at least 16 weeks40 °C/75% RHhiew2022b R7
delamanid saltsno PXRD peaks after 2 weeks40 °C/75% RHduong2022a C32
naringenin, quercetin with E100 and PVPno crystals for >200 to >450 daysfive conditions, 40–50% polymer[wegiel2013a R9]
naringenin, quercetin with HPMCAS, HPMC, CMCAB, PAAfirst crystals after 1–3 days84% RH/25 °C and 75% RH/40 °C, 30–80% polymer[wegiel2013a R9]
lumefantrine–PVPVA at 50, 25, 10 and 5% drug loadingfirst crystals after 1, 2, 4 and 8 weeks40 °C/75% RH, open dishhiew2022a R6
lumefantrine at 50% drug loading with HPMCAS, Eudragit L 100, HPMCP, CAPfirst drug crystals after 1, 8, 32 and 40 weekssamehiew2022a R6
resveratrol with PVP K29/32, E100, HPMC, HPMCAS, CMCAB, PAAPVP never crystallized (> 400 days); E100 > 400 days at 84% RH; the others crystalline at day 1 at 84% RH25 °C[wegiel2013b R12]
curcumin with E100, cellulosics, PVP; neat> 350, 75, 22 and 14 days at 84% RH25 °C[wegiel2014 R13]
curcumin dispersionsall > 350 days at 0% RH/25 °C; all crystalline within 1 day at 90 °C/0% RH and 60 °C/98% RHstorage[wegiel2014 R13, C23]
indomethacin 60% with HPMC; EPO; EPO–HPMC 6:2.9:1.1crystals within 5 days; within 5 days, slower growth; amorphous beyond 100 days40 °C/75% RH, open vials[xie2017 R26]
indomethacin 30%, EPO–HPMC against HPMCternary more stable (text only)40 °C/75% RH[xie2017 R27]
lopinavir 50% HPMCP dispersion in suspension≈2.5–3.0 µg/mL over 48 h; no crystals at 48 hpH 3, 25 °C, no inhibitor[li2018 R6, R7]
lopinavir 50% EC; CA dispersions in suspension≈4.3–5.0 µg/mL to 12 h, then ≈1.6–3.4; ≈10.5–11.2 µg/mL to 12 h, then ≈2.3–3.9same[li2018 R6]
delamanid sulfonate salts, neatseven of eight amorphous with Tg 83.7–117.8 °C against 43.3 °C for the free base; all amorphous after 2 weeks at 40 °C/75% RH, four liquefiedopen dishduong2022a R20
delamanid salt dispersions at 20% drug with HPMCASTg 100.4–117.0 °C against 86.7 °C; water uptake ≈10–13.6% against ≈8.2% at 95% RH37 °Cduong2022a R23, R22
praziquantel dispersions at 20% drugHPMC E5 LV amorphous at 23 weeks; HPMCAS-MF small crystalline peaks by 21 weeks40 °C/75% RHpolyzois2024 R7
Pitfalls and disagreements

Miscible dispersions were stable while phase-separated ones crystallized quickly [tian2016 C53]. Extrapolation of high-temperature growth data can overestimate stability [kestur2013a C7]. The class of the neat drug is only a first flag (see F17). The storage time reached by dispersions without crystals is not stated for lumefantrine, so the ranking is relative and no shelf life follows hiew2022a X9. Some dispersions crystallize only partly and then stop, which the authors do not fully understand [wegiel2013a C23, C43]. Peaks in stored CAP dispersions came from crystalline material in the polymer itself, not from the drug hiew2022a C11, R7. Small unexplained peaks appear in low-loading HPMCP traces after 64–76 weeks hiew2022a X10. The polyphenol dispersions differ in polymer content (30–80%) and in storage protocol from the lumefantrine ones, so the two sets are compared only in direction [wegiel2013a X3; hiew2022a X9]. In the resveratrol and curcumin tables, day values are first sampling times with unstated intervals and a 5–10% detection limit [wegiel2014 X10; wegiel2013b X16]. The mildest and the harshest conditions did not separate any polymer [wegiel2014 C23]. Long-term stability of the EC and HPMCP dispersions at 15 and 33% drug is inferred from 48-h concentrations; suspension and matrix stability were tested only at 50% drug, where the EC dispersion lost supersaturation after 12 h [li2018 X8]. The 30% indomethacin comparison is stated in the text only [xie2017 R27]. The praziquantel statement that both dispersions stayed stable for several months is not borne out by the peaks in the HPMCAS-MF sample polyzois2024 X1.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

pKa

The pH at which half of an ionizable drug is protonated; two pH units above the pKa a weak base is almost fully un-ionized and two units below almost fully ionized, which set the pH range of the weak-base solubility studies [indulkar2015 C16]. New aspects (Miscibility and drug-polymer interactions): The acid dissociation constant is also used to classify the drugs of a polymer screen as acidic, weakly acidic or basic, and as a proxy of donor strength: a lower pKa means a stronger acid and a better hydrogen-bond donor [vaneerdenbrugh2010b M3, M4, M5, M6, M7, M8; rumondor2011 C30]. The values are computed, not measured. In the later papers the pKa decides whether a proton can move between drug and polymer: PSSA (−1.5) with the basic pKa of anthranilic acid (2.0), lidocaine (amine 7.8) and dibucaine (amine 9.8), and not PAA (4.5) or flufenamic acid (basic −2.1) [vaneerdenbrugh2011a R1, R2, R9, C22, C23]; lumefantrine (amine 8.73, cited) with enteric polymers of pKa 4.32–6.21 hiew2022a M1, R22. New aspect (Release mechanism and LoC): the pKa of the buffer species, relative to the surface and bulk pH, decides whether a buffer carries protons away from a dissolving enteric polymer. BIS-TRIS (pKa 6.5) and phosphate (7.2) bind protons at the lower surface pH and release them at the bulk pH, BIS-TRIS better because more of it is in the base form at a surface about 0.4 units below bulk; Tris (8.1) and TEA (10.2) are mostly protonated at both and cannot act as proton carriers, which slows HP-50 dissolution qi2022 C27. For HPMCAS-MF, pH 7.5 phosphate gave faster dissolution than pH 9.0 phosphate because the latter has a low buffer capacity bapat2023 C15. The polymer pKa values used were 4.2 for HP-50 and 4.92 or 5.0 for HPMCAS-MF, both cited qi2022 C23; bapat2023 M3. The 2025 grade paper titrated HPMCAS LF and HF, giving pKa 4.91 and 5.06 at the half-neutralization point against a cited 4.97 for MF bapat2025a R8, C11, M3, M4, M5; the 2024–2025 papers flag weak bases with pKa above about 5 as at risk of complexing HPMCAS at the gel pH bapat2024 C45.

Findings

C. Amorphous solubility and LLPS: F10, F23. Miscibility and drug-polymer interactions: F15, F17, F21, F24, F26. Physical stability: F13, F24. Release mechanism and LoC: F23, F32, F33.

Related concepts

sets ionization and pH-dependent solubility; indicates donor strength in hydrogen bonding; related to drug-polymer interactions, hydrogen-bond basicity, acid-base interaction and hydrogen-bond donor and acceptor groups. Of buffer species, sets buffer capacity at a given pH and the microenvironmental pH; of the polymer, sets the critical ionization for polymer dissolution.

Formulas

Henderson-Hasselbalch equation.

How it is measured or obtained

UV-metric titration at 37 °C in 0.15 M NaCl (atazanavir), or taken from the literature or predicted by software (the other drugs) [indulkar2015 P2, M1, M3; almeidaesousa2015 M3]. In the polymer screens, calculated with the ChemAxon plugins of MarvinSketch 5.2.0 from the structures [vaneerdenbrugh2010b P9]. Functional-group densities of the polymers (mmol/g of COOH, amide, amine) were calculated from the structures in the same way [vaneerdenbrugh2010b P10]. For the enteric polymers the pKa was measured by potentiometric base-to-acid titration, as the pH at 50% neutralization, with the carboxylic acid content between the two end points (HPMCAS 1.19 mmol/g, pKa 4.97; HPMCP 1.69, 4.32; CAP 2.94, 4.57; Eudragit L 100 4.48, 6.21), giving 99, >99, >99 and 80% ionization at pH 6.8 hiew2022a P17, R22. In the 20-system moisture study, calculated with MarvinSketch unless marked otherwise in the table rumondor2011 P9. In the release-mechanism papers: buffer pKa values calculated or stated (table in the HP-50 paper) qi2022 C27, X16; polymer pKa cited qi2022 C23; bapat2023 M3.

Values in the library
materialvalue or classconditionspaper ids
clotrimazole; atazanavir; nicardipine5.89 (cited); 4.52 (measured); 7.2 (cited)37 °C[indulkar2015 M1, M2, M3]
ritonavir1.8 and 2.6citedilevbare2013a M1
loratadine; efavirenz5.0; 10.2citedilevbare2013a M3, M2
telapreviracid 11.8; base 0.31cited[mosqueragiraldo2015 M1]
CRH14.6 (base)method not printed[almeidaesousa2016 M1]
ibuprofen; phenylbutazone; diclofenac4.35; 4.35; 4.03 (acids)cited[almeidaesousa2015 M1, M2, M4]
pazopanib6.4 (strongest basic group)stated without a source; used for the 37 °C curves[sugihara2018 M1, C9]
flurbiprofen; flufenamic acid; chlorpropamide4.37; 3.88; 4.33 (acidic)computed[vaneerdenbrugh2010b M3, M4, M5]
chlorzoxazone9.39 (weakly acidic)computed[vaneerdenbrugh2010b M6]
bifonazole; lidocaine6.69; 7.75 (basic)computed[vaneerdenbrugh2010b M7, M8]
indoprofen against other carboxylic acids (other chapter)a somewhat weaker acid, with the smallest phase separationPVP dispersions with moisturerumondor2011 C33
PAA; PSSA; E100 amine4.5; −1.5; 8.5computed[vaneerdenbrugh2011a R2]
anthranilic acid; flufenamic acid (basic pKa)2.0; −2.1computed[vaneerdenbrugh2011a R1, R9]
HPMCAS, HPMCP, CAP, Eudragit L 1004.97, 4.32, 4.57, 6.21 (acid content 1.19, 1.69, 2.94, 4.48 mmol/g)titration, n = 2hiew2022a R22
lumefantrine (tertiary amine)8.73citedhiew2022a M1
indomethacin, ketoprofen, indoprofen in PVPpKa 4.5, 5.02, 5.8; resist, resist, separate slightly20-system tablerumondor2011 R15.a, R15.d, R15.e
20 drug–polymer systemsOPLS-DA loading of pKa ≈ −0.35: lower pKa goes with no separationdiscriminant modelrumondor2011 R17, C40
curcumin against E100pKa 10.51, 9.88, 8.38 against an average 8.4 for the basic monomeracid–base pairing[wegiel2014 M1, M5, C16]
HP-50 in BIS-TRIS, phosphate, Tris, TEA buffersbuffer pKa 6.5, 7.2, 8.1, 10.2; ≈44.8, 28.4, 6.6, 1.8% HP-50 dissolved at 60 min50 mM, pH 6.8qi2022 R2, C27
HP-50; HPMCAS-MFpKa 4.2; 4.92 or 5.0 (cited)qi2022 C23; bapat2023 M3
HPMCAS LF, MF, HF4.91, 4.97 (cited), 5.06back-titration, half-neutralizationbapat2025a M3, M4, M5
bedaquiline8.5 (measured)SI, not suppliedkaur2025 M1
Pitfalls and disagreements

Several pKa values are predicted, not measured (tolnaftate, sorafenib, griseofulvin) [almeidaesousa2015 M3, M5, M6]. The pKa values of the polymer screens are calculated and rest on one program [vaneerdenbrugh2010b P9]. Flufenamic acid is treated as purely acidic because its aniline N–H is in an intramolecular bond [vaneerdenbrugh2010b C12]. The acid–base reading of the PAA/PSSA reversal is the authors' hypothesis; interactions in the films were not measured [vaneerdenbrugh2010b C33]. The pKa values of the moisture discriminant model are calculated and correlate with donor type and carbonyl shift, so their separate weight is not established rumondor2011 P9, X10. The proton-carrier argument uses calculated buffer pKa values and a cited surface-to-bulk gradient; surface pH was not measured in the HP-50 paper qi2022 X16. The pKa of HPMCAS-MF is used as 4.92 or 5.0 (cited) in the 2023 HPMCAS dissolution paper, against 4.97 measured by titration in the lumefantrine study and cited in the 2025 grade paper (synthesis: comparison of the values on this page) bapat2023 M3; hiew2022a R22; bapat2025a M4.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

plasticization by water

The lowering of the glass transition temperature of an amorphous drug by absorbed water, taken in these papers as about 10 °C per 1% water [ilevbare2013a C23, E15; indulkar2015 C39]. A water-saturated drug-rich phase therefore has a wet Tg far below that of the dry amorphous drug, and its state at the test temperature (supercooled liquid or glass) follows from it (F2). New aspect (ASD process): in the coating study of four drug–polymer systems, water sorbed at the storage humidity lowers the glass transition of the powder, and the wet Tg onset minus the storage temperature (Tg − T, negative when stored above Tg) is the number compared with crystallization onset moseson2022a P6, E2, R12. Nucleation and growth speed up with humidity because sorbed water raises mobility and lowers the wet Tg, so a coating that works on the surface cannot rescue a powder whose bulk is mobile moseson2022a C41, C25. In dissolution, hydration lowers the Tg of a drug-rich bicalutamide layer, and the authors list mobility above the wet Tg among the reasons why not every ASD is susceptible to matrix crystallization moseson2022b C63. For hydrating posaconazole–HPMCAS the gastric stage lets crystals grow inside the wetted matrix after water uptake and plasticization (the authors' reading) [shah2024 C45]. New aspect (Physical stability): in drug–polymer dispersions water erases the Tg gain of a high-Tg polymer: at 75–76% RH felodipine and nifedipine dispersions with up to 25% PVP fell below the Tg of the dry drug [konno2008 C16; marsac2008a C17]. Plasticization is "directly related to the hygroscopicity of polymer", yet per gram of water it lowers the Tg of the pure drug most [konno2008 C20; marsac2008a C19]. New aspect (Supersaturation from ASD dissolution): the ASD dissolution papers use it in two places: to explain why wetted amorphous felodipine crystallizes faster at 37 than at 25 °C (dry Tg about 45 °C, just below 35 °C at 75% RH, cited) [alonzo2010 M1, C34], and to read the low Tg of an isolated ritonavir drug-rich phase as a ritonavir-rich phase holding a few percent of water [ilevbare2013d C8]. New aspect (Release mechanism and LoC): the wet Tg of the drug-rich phase decides whether nanodroplets are glassy or liquid at the test temperature. Indulkar and co-workers (2017) estimate that water-saturated amorphous nifedipine droplets have a Tg near 17 °C (dry 42 °C, 2.5% water), which makes drug exchange between droplets and solution slow at 5 °C, the premise of their isotope test indulkar2017b C16, M1, C13. Ritonavir, with a wet Tg around 0 °C, is a supercooled liquid under release conditions que2019 R28, C49; indulkar2019a M1. For indomethacin the relevant wet Tg is "plausibly" that of the drug-enriched surface (a 70% dispersion with about 6% water, onset 18 °C) rather than that of the neat drug (estimated 29 °C) saboo2020 C52, R30, M1; by the same 10 °C per 1% rule every lumefantrine dispersion's wet Tg would lie below 37 °C hiew2022b C44.

Findings

Amorphous solubility and LLPS: F2. ASD process: F44, F38, F41. Physical stability: F5, F6, F9, F12, F33, F34. Supersaturation from ASD dissolution: F1, F9. Release mechanism and LoC: F5, F9, F18.

Related concepts

lowers the glass transition temperature; measured with water sorption; decides glass-liquid phase separation against LLPS; related to supercooled liquid. Raises surface molecular mobility; lowers the Tg that decides surface crystallization; sets how long an atomic layer coating protects a powder. Special case of plasticization; set by hygroscopicity; raises molecular mobility; related to matrix crystallization, drug-rich phase and moisture-induced crystallization. Gives the wet glass transition temperature.

Formulas

water plasticization rule of thumb, Tg − T, Gordon-Taylor equation.

How it is measured or obtained

DSC of the isolated drug-rich phase or of amorphous drug stored at high humidity, with water from gravimetric sorption or from drying the pellet [ilevbare2013a P8, P9, P15; mosqueragiraldo2015 P4, P5; almeidaesousa2015 P8]. For stored ASD powders the wet Tg onset was read in hermetically sealed DSC pans after 24 h at the storage humidity, 5 °C/min, triplicate preparations moseson2022a P6. The Tg of hydrated bicalutamide could not be determined [moseson2021 R27, X8]. In the felodipine and nifedipine moisture papers, DSC of bulk samples equilibrated at each RH and sealed [konno2008 P6; marsac2008a P7], reported as ΔTg dry minus 75% RH [konno2008 R9]. In the ASD dissolution papers: by DSC of the phase isolated by ultracentrifugation [ilevbare2013d P9]; for felodipine the humid Tg is cited, not measured in the medium [alonzo2010 C34]. In the release-mechanism papers: dry Tg by DSC, water content extrapolated from a 25 °C sorption profile to 100% RH, and a rule of about 10 °C Tg depression per 1% water indulkar2017b P3, P4, E6. DSC of a 70% dispersion after 4 h at 100% RH saboo2020 P23; sorption at 37 °C extrapolated to 100% RH with the rule yang2021 P9.

Values in the library
materialvalue or classconditionspaper ids
ritonavirTg 50.4 → 0.4 °C with 4.03–5.15% waterisolated phase, 10–50 °Cilevbare2013a R5, R6
clotrimazole; atazanavirTg 28 → about 14 °C (1.4% water); 104 → about 51 °C (5.2%)precipitates, 37 °C[indulkar2015 R22, M1, M2]
telaprevirTg 103 → 52 °C; 4.31% water at 95% RHpellet, 37 °C[mosqueragiraldo2015 R2, M1]
sorafenib; griseofulvinTg 88.2 → 49 °C; 90.8 → 88 °C at 97% RHamorphous drug[almeidaesousa2015 M5, M6, R9]
erlotinib–HPMCAS 60% DLwet Tg − T about −8.8 °C (75% RH) and −2.3 ± 1.1 °C (43% RH)24 h at RH, T = 40 °Cmoseson2022a R12
erlotinib–PVPVA 50% DL−0.5 ± 1.2 °C43% RHmoseson2022a R12
naproxen–HPMCAS 10% DL; lumefantrine–PVPVA 40% DLabout +11.3 °C (75% RH); +10.7, +14.3, +11.3 and +11.4 °C (43% and 31% RH)samemoseson2022a R12
rule of thumb for stabilitymore than 50 °C between storage temperature and Tg (cited); the authors state the benefit of the coating holds at about 0 to +15 °Cmoseson2022a E3, C45, R17
felodipine with 25% PVP, HPMCAS, HPMCTg 54.9 → 31.1, 44.2 → 35.6, 43.1 → 34.4 °C0 → 75% RH[konno2008 R5]
felodipine dispersions ≤ 25% polymerTg ≈30–35 °C after 75% RH, below dry felodipine ≈43 °C25 °C[konno2008 R7, C16]
nifedipine pure; 25% PVP≈43 → 26 °C; ≈54 → 29 °C0 → 76% RH[marsac2008a R6]
amorphous felodipine (cited)Tg ≈45.7 → 29.6 °C, smooth0 → 94% RH[rumondor2010 R10]
pimozide–PVP 50:50wet Tgs −21 and 44 °C94% RHrumondor2009c R17
ketoprofen–PVP 70:30wet Tg −23 °C94% RHrumondor2009c R25
celecoxib 6:4 dispersionsTg 64–103 → 22–42.1 °C after 3 days at 94% RHDSCxie2016b R17, R20
tacrolimus; tacrolimus–HPMC 1:163.6 → 51.4 °C; 77.2 → 49.0 °C after 3 days at 75% RHDSC[trasi2017 R15]
lumefantrine dispersions precipitated into water4–6% water (HPMCP, HPMCAS), 9% (CAP); Tg 45–112 °CTGA; DSCbhujbal2021 R10
felodipine (cited)Tg about 45 °C dry, just below 35 °C after 75% RHstorage data[alonzo2010 M1]
ritonavir drug-rich phase from a PVP dispersionTg inflection 1.05 °C against 50 °C for the amorphous drugwater, 37 °C, DSC at 20 °C/min[ilevbare2013d R2, M1]
indomethacin (cited)Tg falls rapidly with water content, as for felodipineliterature[alonzo2010 R24]
nifedipinedry Tg 42 °C; wet Tg approximately 17 °C (estimated)2.5% water (estimated)indulkar2017b M1, C16
ritonavirTg 50 °C; wet Tg around 0 °C (cited)release conditionsque2019 R28
indomethacin; indomethacin–PVPVA 70%wet Tg 29 °C (estimated); onset 62.64 → 18.48 °C with ≈6% water37 °C, 100% RHsaboo2020 M1, R30
loratadine, miconazole, danazol, elbasvirwet Tg 13.8 (DSC), −4.7, 73.3, 129.1 °C (rule)37 °Cyang2021 M1, M2, M3, M4
atazanavirdry 105 °C, wet 55 °Ccitedcorreasoto2022b M1
Pitfalls and disagreements

The griseofulvin Tg falls only 2.8 °C with an estimated 2.7% water, against 39 °C for sorafenib with 1.8%, and storage time and water content are not stated [almeidaesousa2015 X11]. The water content of the telaprevir pellet was not measured [mosqueragiraldo2015 X3]. For the coated powders the wet Tg values are not printed, only Tg − T bars, and the definition in words is the reverse of the sign used moseson2022a R12, X24, E2. Uncoated powders failed in about 1–2 weeks across the whole range of Tg − T, so Tg − T orders the coated failures only in part moseson2022a X15. The 0 to +15 °C statement applies to coated powders only moseson2022a C45, R11. The rule of 10 °C per 1% water given in the Definition fits the pure drugs but not the 25% polymer dispersions of the felodipine study, which drop about 5 °C per 1% (synthesis: 23.7 °C with 4.68% water [konno2008 R6]). Plasticization did not by itself cause phase separation or rank nucleation [rumondor2009c C38; konno2008 C26]. Plasticization by water did not rank celecoxib dispersions at 94% RH: four Tgs within about 5 °C, very different stability xie2016b C46. The water content of the ritonavir phase was not measured [ilevbare2013d C8]. Plasticization does not rank crystallization: indomethacin, with a similar Tg drop, crystallized much more slowly than felodipine during dissolution [alonzo2010 C42]. The 17 °C nifedipine value is an estimate from a rule taken from indomethacin; no Tg of water-saturated nifedipine was measured indulkar2017b X8. The 70% indomethacin dispersion is a model of the surface layer saboo2020 X16, and most wet Tgs are rule estimates yang2021 P9.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

plasticization

Lowering of the glass transition temperature of a mixture by a component with a lower Tg; in the library water is the usual plasticizer of drugs, polymers and dispersions, and drugs, surfactants and plasticizers lower the Tg of polymers [konno2008 C2, C14; marsac2008a C1; correasoto2022b C39]. The opposite, a higher-Tg component raising the Tg, is antiplasticization [konno2008 C16]. New aspect (Supersaturation from ASD dissolution): plasticization by water acts during dissolution as well as during storage. For delamanid salts, four of eight liquefied at 40 °C/75% RH, which the authors attribute "presumably" to plasticization by water, and the salts took up 5.8–21.1% water against far less for the free base duong2022a R20, C27. In the undissolved matrix of an enteric dispersion in acid, absorbed water lowers the Tg and raises molecular mobility, which the authors give as the reason why the drug can crystallize there although the medium is subsaturated; water content and Tg were not measured in that state [nguyen2023c C43]. In hot-melt extrusion the drug itself plasticizes the polymer, which the authors use to justify extruding a drug at the polymer's Tg ("would") [alvarenga2025 C46]. New aspect (Release mechanism and LoC): in the release papers of 2021–2022 plasticization of the dispersion by the drug or by an added surfactant is used to explain faster polymer release. Clopidogrel (Tg −9 °C) lowered the dispersion Tg, and the faster PVPVA release from its binary dispersions is called a plasticization effect, as for PMMA with 20 wt% PEO, whose dissolution rate rose by a factor of two (cited) correasoto2022a C48, R30. TPGS lowered the Tg of 30% felodipine–PVPVA dispersions and "could" raise the limit of congruency through higher molecular mobility saboo2021 R5, C43. Surfactants and VP lowered the Tg of 10% atazanavir–PVPVA dispersions, and improved release is "due, at least in part," to plasticization raising polymer-chain mobility correasoto2022b R20, C40. In the other direction, more low-polarity drug "would be anticipated" to reduce water penetration and water plasticization and so lower the polymer rate yang2021 C32, and a drug–polymer interaction that persists in water is proposed to do the same que2021 C44. Surfactants can also promote crystallization by plasticizing the matrix (cited), and Tween 80 and TPGS "could possibly" plasticize ritonavir droplets so that they coalesce indulkar2022 C40, C48; except for SDS every surfactant lowered the single Tg of 30:70 ritonavir–PVPVA (midpoints 70.90–77.51 against 82.24 °C) indulkar2022 R18. Built into PVPVA dispersions of high-Tg drugs, plasticizers lowered the Tg and raised release and the limit; the authors suggest increased polymer chain mobility, that is a faster disentanglement rate, as one mechanism correasoto2023 C30, C39. Faster initial water entry from drug plasticization, together with phase separation moving most water into the hydrophilic phase, is a "possible explanation" for polymer release rising faster than water penetration in MePHPH–PVPVA up to 20% deac2023a C51, C50. The 2023 surfactant study attributes barrier disruption by non-ionic surfactants to plasticization: Span 20 and Span 85 lowered the Tg of amorphous ritonavir from 46.8 °C to 7.7–27.8 °C and, partitioning into the drug-rich phase, are taken to soften the drug-rich layer so that flow removes it yang2023 R22, C11, C18, C35. The 2025 high-loading particle study warns that SDS, also a plasticizer, may predispose amorphous formulations to phase separation and recrystallization hiew2025 C58.

Findings

Physical stability: F6, F9, F22, F28, F32. Supersaturation from ASD dissolution: F23, F24. Release mechanism and LoC: F15, F18, F21, F26, F31.

Related concepts

special case plasticization by water; contrasts with antiplasticization; measured by glass transition temperature; raises molecular mobility; tested by Tg-scaled crystal growth rate; lowers physical stability and matrix crystallization; limits in situ salt formation. Speeds polymer chain disentanglement.

Formulas

Gordon-Taylor equation gives the ideal-mixing Tg that plasticization lowers.

How it is measured or obtained

DSC of samples equilibrated at a given RH and sealed hermetically, onset or midpoint Tg [konno2008 P6; marsac2008a P7]; the drop in Tg between the dry state and storage at 75% RH, ΔTg [konno2008 R9]. Outside the subcategory, Tg of drug–polymer–surfactant or plasticizer blends by DSC correasoto2023 R17, C30; nguyen2023a R13. In the ASD dissolution papers: water sorption at rising relative humidity with DSC of the same materials for Tg, and open-dish storage at 40 °C/75% RH with visual inspection and PXRD duong2022a P12, P10, P13; in extrusion, the drug Tg and the polymer Tg set the processing window [alvarenga2025 M1, M2, M3, E2]. In the release-mechanism papers: DSC of dispersions with and without the additive saboo2021 R5; correasoto2022b R13.

Values in the library
materialvalue or classconditionspaper ids
felodipine with 25% PVP, HPMCAS, HPMCTg 54.9 → 31.1, 44.2 → 35.6, 43.1 → 34.4 °C0 → 75% RH, 25 °C[konno2008 R5]
felodipine–PVP 0–100%ΔTg ≈15 °C (7% PVP) to ≈158 °C (pure PVP)dry minus 75% RH[konno2008 R9]
25% polymer dispersionsTg drop ≈13.3 °C at ≈1.1% water (PVP) vs ≈6.2 °C (HPMCAS)25 °C[konno2008 R6, C14]
nifedipine, pure and 25% PVP≈43 → 31 °C with ≈1.15 g/100 g water; ≈54 → 43 °C with ≈2 g/100 g25 °C[marsac2008a R7, C19]
pimozide–PVP 50:50two Tgs −21 and 44 °C wet against one at 94 °C dry94% RHrumondor2009c R17
PTM–HPMCAS–TPGS (outside)Tg ≈79 → 63 °C with TPGS at 20% loadingDSCnguyen2023a R13, C22
atazanavir and ledipasvir ASDs with plasticizers (outside)lower Tg than the binary ASDDSCcorreasoto2023 C30
celecoxib with 10% TPGS or sucrose palmitateTg 55.34 → 44.81 and 44.46 °C; growth fasterDSC[mosqueragiraldo2014 R5, C16]
pretomanid–HPMCAS with TPGS (other chapter)Tg falls as TPGS risesDSCnguyen2023a R13, C22
ritonavir–PVPVA with Span 20 or Span 85Spans in the drug-rich phase, read as plasticizing it and speeding separation ("likely")O-PTIR, NMR, confocalyang2022b C58, X13
griseofulvin, DPB, celecoxib with 5% PHBTg −5 to −12 °C; growth up to ≈10-fold fasterDSC; melt growth[sato2016 R7, R11, X6]
delamanid sulfonate salts, neatwater 5.8–7.1% (aromatic), 8.1–11.6% (camsylate, edisylate), 16.2–21.1% (esylate, mesylate); four liquefied95% RH; 2 weeks at 40 °C/75% RHduong2022a R20
delamanid edisylate 1:1 with excess acid59% water uptake and Tg 53.9 °C against 11.6% and 117.8 °C for the 2:1 salt95% RHduong2022a R21
delamanid salt dispersions at 20% drug with HPMCASwater ≈10–13.6% against ≈8.2% for the free-base dispersion; Tg 100.4–117.0 against 86.7 °C95% RHduong2022a R22, R23
delamanid free-base dispersions, 0 to 20% drugTg 121.0 → 86.7 °C (HPMCAS) and 120.1 → 82.0 °C (HPMCP); water at 95% RH ≈10.8–11.6% → ≈7.9–8.2%DSC, sorptionduong2022a R9, R10
praziquantel, racemate and R-enantiomerTg about 37 and 34 °C, used to place the extrusion temperatures at 150 and 120 °CDSC[alvarenga2025 M2, M1]
felodipine–PVPVA 30% with 0, 2, 5, 10% TPGSTg 89.2, 86.0, 80.8, 71.1 °C (felodipine 44.7, PVPVA 105.4 °C)DSC, drysaboo2021 R5
atazanavir–PVPVA 10% with SDS, CTAB, TPGS, Tween 80, Span 20, Span 80, Span 85, VPTg lowered by 16, 9, 14, 14, 11, 13, 7, 16 °C from the binaryDSC, drycorreasoto2022b R20
clopidogrel–PVPVA 40–60%PVPVA ≈4.1–6.7 against ≈2.6–2.7 mg/min/cm² for neat PVPVAcompacts, 37 °Ccorreasoto2022a R18, C48
loratadine–HPMCAS 5%HPMCAS released faster than from neat HPMCAS, "feasible" plasticization by a low-Tg drugcompactsyang2021 C31, R18
ritonavir–PVPVA 30:70 with 5 parts Tween 80, TPGS, Span 20, Span 85, SDSTg midpoint 70.90, 72.84, 73.24, 77.51, 84.93 °C against 82.24 °CDSC, dryindulkar2022 R18
8:1 atazanavir and ledipasvir glasses with nine plasticizersTg lowered by 30.4–43.3 and 47.6–53.1 °Cmodulated DSCcorreasoto2023 R17, R18
ledipasvir–PVPVA 10% with 5 and 10 g TEACTg 99.1 → 85.8 °C; release 20 → 94% by 90 minDSC; compacts, pH 6.8correasoto2023 R9
amorphous ritonavir with Span 20 (80–20, 60–40)onset Tg 14.8, 7.7 °C (46.8 °C neat)DSCyang2023 R22
amorphous ritonavir with Span 85 (80–20, 60–40)27.8, 12.7 °CDSCyang2023 R22

Evidence table: plasticization.

Pitfalls and disagreements

Two framings coexist: water is the more efficient plasticizer of PVP dispersions at equal water content (compared with cellulose dispersions) and the more efficient plasticizer of the drug alone per gram of water (compared with PVP dispersions); both hold, for different comparisons [konno2008 C14; marsac2008a C19]. A rule of thumb in the library puts the Tg drop at about 10 °C per 1% water yang2021 E3, which fits pure drugs but overestimates the drop of the 25% polymer dispersions, about 5 °C per 1% (synthesis: 23.7 °C with 4.68% water for 25% PVP [konno2008 R6]). Plasticization alone does not cause moisture-induced phase separation rumondor2009c C38. Lower plasticization by water is offered as an alternative to the thermodynamic reading for HPMCAS dispersions rumondor2010c C32, X12. The Span plasticization rests on Tgs given only in the supplement yang2022b X13. Liquefaction was reported for four salts while the text and the table disagree on which, and the photograph of one looks unliquefied duong2022a X1, X11. The water content and Tg of the wetted matrix in acid, on which the mobility argument rests, were not measured [nguyen2023c C43]. For the extrusion window no Tg of a drug–polymer blend was measured [alvarenga2025 C46]. The dispersion Tg of the clopidogrel study is in the SI and not in the main text correasoto2022a R26, and the loratadine–HPMCAS dispersion Tg was not measured yang2021 C31. Among the atazanavir additives the Tg depression and the release enhancement did not rank together (TPGS lowered the Tg by 14 °C and raised release only 4-fold, Span 80 by 13 °C and 35-fold) correasoto2022b R20. The Tg of the drug-rich layer formed in situ was not measured; plasticization is inferred from drug–Span mixtures yang2023 X17.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

polymer adsorption to drug-rich droplets

The accumulation of a dissolved polymer at the interface of the drug-rich droplets of a phase-separated solution, where it is thought to reduce droplet coalescence and to disturb heterogeneous nucleation at the droplet–water interface ("likely"); with the cellulosic polymers it is accompanied by some polymer mixing into the droplets [jackson2014 C33, C50, C53, C48]. The zeta potential of danazol droplets moved with the charge of the polymer over 1–1000 µg/mL (PVP −7.1 to −3.5, HPMC −2.9 to −2.2, HPMC-AS −8.9 to −18.6 mV against −8.1), and bile salts made telaprevir droplets about −40 to −53 mV against −9.2 mV [jackson2016 R18; lu2017 R8].

Findings

F15, F32.

Related concepts

part of liquid-liquid phase separation; related to droplet coalescence, zeta potential and polymer adsorption.

Formulas

none.

How it is measured or obtained

Indirectly: droplet size by DLS over hours, zeta potential of the droplets, and the lowered onset of phase separation; preliminary NMR gave the polymer content of the droplets (not shown) [jackson2014 R22, R23, R5, R26].

Values in the library
materialvalue or classconditionspaper ids
danazol droplets aloneabout 490 nm at once, about 9800 nm after 1 h25 °C[jackson2014 R22]
danazol droplets with HPMC; HPMC-ASabout 305–345 nm up to 2 h; about 230–250 nm up to 4 h10 µg/mL polymer[jackson2014 R22]
zeta potential: alone; PVP; HPMC; HPMC-AS−8.1; −5.3; −2.3; −13.7 mV25 °C[jackson2014 R23]
polymer in the dropletsaround 10–20% for HPMC, below about 10% for PVP, none for HPMC-ASpreliminary NMR[jackson2014 R26]
ritonavir nanodroplets (ASD dissolution chapter)charge repulsion between polymers adsorbed at the ritonavir–water interface "likely" stabilizes against coalescence37 °C[ilevbare2013d C38]
telaprevir droplets, 1.86 mM six bile saltszeta about −40 (SGC) to −53 mV (STCDC)180 µg/mL, pH 6.5[lu2017 R8]
Pitfalls and disagreements

The NMR is preliminary and not shown, with no value for HPMC-AS; the site of nucleation was not measured [jackson2014 X15]. The coalescence claim has no droplet size in the first minutes for danazol alone [jackson2014 X6]. Zeta potential was measured at 180 µg/mL, not in the induction-time solutions [lu2017 X6].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

polymer adsorption

The attachment of a dissolved polymer to a surface, here the drug crystal (and, for danazol, the droplet interface). Every explanation of crystal growth inhibition in these papers assumes that the polymer must adsorb on the crystal to act, and "there is a general consensus" that it must (Mullin 2001, outside the library) [ilevbare2012c C3, C35; ilevbare2013b C47]. Adsorption can be physical (van der Waals, electrostatic, usually reversible) or chemical, and is driven by hydrophobic interaction, electrostatic attraction and hydrogen bonding [ilevbare2012c C4]. On crystal surfaces (formerly the page "polymer adsorption on crystal surfaces", from Crystallization from solution): the binding of a dissolved polymer to the faces of a growing drug crystal, which blocks growth sites and slows or shapes growth; it is usually face-selective, because molecular crystals are anisotropic, and changes habit when it slows the fast faces [ilevbare2012c C3, C5, R18]. It is the central assumed mechanism of crystal growth inhibition: the polymer occupies growth sites as a mechanical barrier and pins advancing steps [alonzo2012 C9; ilevbare2012c R19]. HPMCAS-LF was seen by AFM on three faces of felodipine, (1 1 −1), (1 −2 −2) and (1 −1 1), with no visible difference in density, taken as nonspecific adsorption, and AFM-IR identified the adsorbed material on a dried film [schram2015 R23, R25, R20, R21].

Findings

Crystallization from solution: F7, F8, F10, F11, F12, F23, F24, F27, F36, F38, F42, F44.

Related concepts

related to surface coverage, step pinning, polymer conformation, crystal habit and BFDH morphology prediction; mechanism of crystal growth inhibition.

Formulas

adsorbed amount by solution depletion, Langmuir-Freundlich isotherm, Kubota-Mullin model, Cabrera-Vermilyea step pinning.

How it is measured or obtained

By depletion: seeds equilibrated with polymer solution for 16–24 h, the amount adsorbed per area from the polymer lost from the supernatant, C_a = (C_i - C_f)\,V/(m \times A), with the polymer assayed by the phenol–sulfuric acid method at 490 nm, or by surface tension for HPMC [ilevbare2012b P9, E10; alonzo2012 P6]. In the ritonavir screen and the 2013 growth paper adsorption was not measured [ilevbare2012c C35; ilevbare2013b X14]. Adsorption on crystal faces is also read indirectly by growth-rate ratios against polymer concentration, by crystal habit and PXRD of the grown crystals, and by FTIR shifts of the drug bands after exposure to polymer [alonzo2012 R8; ilevbare2012c R4, R6; ilevbare2013b R12].

Values in the library
materialvalue or classconditionspaper ids
HPMC on felodipine seedsabout 60–167 µg/mL/m² up to 0.38 µg/mL equilibrium; 285–534 at 0.62–1.12 µg/mLsurface tension, 16–24 h[alonzo2012 R6]
CAP Adp 0.85 on ritonavir seedsplateau about 41 mg/m² (pH 3.8); about 27 mg/m² (pH 6.8)depletion, 4.0 mg seeds in 20 mL[ilevbare2012b R9, R10]
PVPVA on indomethacin crystalsglobule spacing 160 ± 50 nm (5 µg/mL); 70 ± 20 nm (50 µg/mL)AFM[moseson2020a R12]
HPMCAS on paclitaxel dendritesadsorption-site spacing about 10–16.8 nmSEM finger width[que2018 R12]
HPMCAS-LF pre-adsorbed on felodipine seedsovergrown by fresh drug in polymer-free solution (growth ratio about 1.8, then 1.08 in a second run)S 4, 25 °C[schram2016 R2, R3]
A5a, A5b, ECA, ECB, ECD on amorphous atazanavirA5a even, no globules; ECA, ECB small even globules; ECD larger; A5b large uneven globules5 µg/mL, 1 h, tapping-mode AFM in buffer[mosqueragiraldo2018a R4]
HPMCAS L, M, H on posaconazole dropletspolymer on every droplet surface from the ζ-potential ("is expected to delay surface crystallization")pH 6.5shah2025 R15, C43, C44
HPMC, felodipine seedsinhibition plateau (ratio about 0.55) where fitted coverage reaches about 1 (1 µg/mL)S 8, 25 °C[alonzo2012 R7, R8]
Pn-IPAAmd, ritonaviraspect ratio 4.4 against 8.8; (200) PXRD peak about 245 against 150 countsS 7.6, 37 °C[ilevbare2012c R4, R6]
PVPVA, celecoxib and efavirenz seedsN–H bands 3331 → 3321, 3225 → 3217; 3316 → 3308 cm⁻¹overnight in 100 µg/mL[ilevbare2013b R12]
HPMCAS on paclitaxel seedspolymer slows but does not block growth at S 88seeded ASD dissolution[que2018 C30, C38]
HPMCAS, earlier felodipine work"may adsorb at the crystal surface and block growth sites"dilute supersaturated solution[rumondor2010 C38]
felodipine, HPMCAS-LF, pH 3adsorption on three faces exposing methyl/oxygen, chlorine/methyl and methyl/amine/oxygen groupsAFM in liquid[schram2015 R23, R25]
HPMC-606, HPMCAS-MF on atazanavir with SDSstrong adsorption keeps SDS off the crystal ("we can speculate"), not measured1 mg/mL polymer, 0.1 mg/mL SDS[indulkar2019b C43]
bile salts on atazanavir needlesblocking of the needle sides "hypothesized" from aspect ratios 41–83 against 12.4biorelevant media[elkhabaz2021 C47, R21]
Pitfalls and disagreements

Adsorption by depletion has no crystal-free control, so loss by aggregation or on vessel walls would count as adsorption [ilevbare2012b X15]. The amount adsorbed did not predict the effect: more adsorbed at pH 3.8 and less inhibition [ilevbare2012b R9, R7]. Maximal adsorption did not stop growth at S 7.6 with 100 µg/mL polymer [ilevbare2012b R17]. Isotherm fits missed adsorption at low concentration [alonzo2012 C21]. The adsorbed amount was not measured in either felodipine–HPMCAS paper [schram2015 X7]. The AFM coverage ranking is qualitative, one image per polymer [mosqueragiraldo2018a X16]. The face-specific binding of Pn-IPAAmd rests on means of 50 crystals with overlapping spreads and PXRD relative intensities, with no adsorption or face-specific rate measured [ilevbare2012c X12]. The BFDH fast faces are assumed to be the fast faces of the real crystals [ilevbare2012c C45]. The PVPVA hydrogen bond is proposed from N–H shifts alone [ilevbare2013b X13]. Nonspecific adsorption is a visual judgement and the (1 −1 1) region shows streaks [schram2015 X8]. Face-selective adsorption is the stated general case for ritonavir [ilevbare2012c C5], whereas HPMCAS-LF on felodipine showed no visible difference in density between three faces [schram2015 R23, R25]; neither paper measured face-specific adsorbed amounts (synthesis: contrast between papers).

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

polymer chain disentanglement

Evidence table: polymer chain disentanglement. Content from the release-mechanism chapter (2020–2025), with rows from the Miscibility and drug-polymer interactions and ASD process chapters.

The step in which polymer chains leave the swollen, plasticized gel layer for the medium. A glassy polymer dissolves by solvent ingress, swelling, plasticization and gel-layer formation, chain disentanglement by reptation over a characteristic time and diffusion of the free chains; for high-molecular-weight neutral polymers such as PVPVA under stirring, solvent ingress or disentanglement is typically rate-limiting (cited) correasoto2022b C33. Polymer dissolution as a whole is controlled by water diffusion into the matrix, chain disentanglement from the plasticized gel and chain diffusion in the boundary layer; a polymer with Tg above the test temperature must take up a critical amount of solvent before its chains can disentangle, and the further the temperature lies below Tg, the more solvent is needed hiew2022b C38, C39, E1. Que and co-workers (2021) add from the literature that solvent quality (Flory–Huggins χ) matters, and that neat PVPVA at high water activity has its Tg below room temperature and gels and dissolves rapidly que2021 C42. Disentanglement is faster above Tg; below Tg the gel layer thins and dissolution changes from disentanglement to cracking (cited) saboo2020 C54. Enteric polymers must also ionize, which increases hydration and chain mobility and enables reptative disentanglement qi2022 C10; the higher hydration of HP-50 salts "likely" offsets the effect of a lipophilic drug on the water fraction of the gel qi2022 C40. A neat PVPVA compact first swelled and then shrank, read as chains that had not yet had time to disentangle and later disentangled and dissolved yang2022a C32, R9. Correa Soto and co-workers (2023) cite the Devotta free-volume model, in which the maximum chain mobility rises with the fractional free volume of the gel, and take the disengagement rate as proportional to chain mobility correasoto2023 E2, E3, C39. In low-loading MePHPH gels about as much water per polymer was needed to disentangle as in neat PVPVA, as expected if the hydrophilic phase controls gel erosion, and the congruent release rate is proposed to be controlled by water penetration and by disentanglement at the gel/solution surface deac2023a C52, C73. The 2024 phase-diagram paper takes the gel–solution boundary as the polymer concentration at which chains disentangle, which a strongly interacting drug such as phenolphthalein "may impact" deac2024b C39; below the limit droplets leave when the chains disentangle, above it a continuous drug-rich phase cannot deac2024b C47.

Findings

Release mechanism and LoC: F15, F18, F22, F23, F24, F25, F26, F29, F30.

Related concepts

takes place in the gel layer; needs plasticization by water below the wet glass transition temperature; sets the rate of polymer-controlled release; faster with plasticization by the drug or a surfactant; needs chains above the critical entanglement molecular weight to be entangled in the first place.

Formulas

critical polymer volume fraction for glassy polymer dissolution; the disentanglement rate expression above is named and printed only by Hiew and Taylor (2022) hiew2022b E2. free-volume chain mobility (Devotta model).

How it is measured or obtained

Not measured directly in the library. It is inferred from polymer release rates of compacts saboo2020 C55; correasoto2022b C40 and estimated through the critical polymer volume fraction and the Narasimhan–Peppas disentanglement rate k_d = B/(1 - v_p)^{1.9} hiew2022b E1, E2.

Values in the library
materialvalue or classconditionspaper ids
PVPVA (Tg 102.9 °C, density 1.19 g/cm3)critical polymer volume fraction 0.89, so at least 11% water to start disentangling37 °C, estimatedhiew2022b R21
lumefantrine salt–PVPVA dispersions35–55% water at 95% RH, more at lower loading40 °Chiew2022b R5
lumefantrine–PVPVA 5–35%; 40–50% (Miscibility chapter)PVPVA ≈4.49–4.91 against 4.58 neat; 0.21–0.004 mg/min/cm²pH 6.8, 37 °Chiew2022a R13, C59
ritonavir–PVPVA tablets (ASD process chapter)discrete drug-rich nanodroplets in the gel layer move into solution as the polymer disentanglesuncoated tablets, 37 °Cbenson2025 C28
Pitfalls and disagreements

The papers propose but do not measure how the drug changes disentanglement: a drug–polymer interaction that persists in water is proposed to occupy polymer solvation sites and so slow plasticization and disentanglement que2021 C44, interaction of the hydrophobic drug with the polymer "is expected to" retard chain hydration hiew2022a C49, and above a critical loading dilution by the drug "likely" prevents enough water uptake for disentanglement hiew2022a C59. A lower Tg from TPGS "should theoretically" let disentanglement start with less water saboo2021 C43. With 10 °C per 1% water, the wet Tg of every lumefantrine dispersion should lie below 37 °C, so the authors find release "difficult to rationalize" by wet Tg and the disentanglement model alone hiew2022b C44. PVPVA dissolves when a critical water concentration is reached at the gel–solution interface, at a steady state between water penetration and disentanglement benson2025 C61. For HPMCAS-MF (about 18 kDa, below the critical values estimated for other polysaccharides) the authors judge molecular entanglement "unlikely" and dissolution diffusion- rather than disentanglement-controlled, since the rate stayed linear in the square root of rotation speed with no plateau bapat2023 C45, C30, R27.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

polymer chain entanglement

Evidence table: polymer chain entanglement (names merged there: polymer chain entanglement, polymer entanglement). Content from the release-mechanism chapter (2023–2025).

The topological constraint between long polymer chains that slows their diffusion. Linear, nonionic, glassy polymers above the entanglement molecular weight, such as PVPVA, dissolve through a rubbery gel layer: solvent plasticizes the glass at the glass/gel interface, entangled chains there diffuse slowly while their segments are mobile, the gel grows and swells as solvent enters and its viscosity falls, and at a critical solvent concentration the chains disentangle and dissolve (cited) deac2023a C42. Polymers above the critical molecular weight for entanglement form a gel layer in a good solvent because solvent penetrates faster than chains disentangle (cited) bapat2023 C34. HPMCAS-MF is "unlikely" to form molecular entanglements, so its dissolution is diffusion- rather than disentanglement-controlled bapat2023 C45. The 2024 PVP paper estimates entanglement from M_c \approx 30\,C_\infty M_0 and c_e = \rho M_c/M_w: only K29/32, K60 and K90 exceed M_c, entangling above 0.80, 0.12 and 0.04 v/v, with a mesh of at most 10, 36 and 80 nm at c_e; entanglement "may be contributing" to keeping drug-rich droplets apart in the gel deac2024a E1, E2, E4, C16, C45.

Findings

Release mechanism and LoC: F23, F25, F29.

Related concepts

undone by polymer chain disentanglement; requires the critical entanglement molecular weight; gives the gel layer and polymer swelling.

Formulas

Levich boundary-layer thickness (used for the rotation argument).

How it is measured or obtained

Not measured in these papers: inferred from molecular weight against cited critical values and from the rotation-speed dependence of the dissolution rate bapat2023 C45, R27, R19.

Values in the library
materialvalue or classconditionspaper ids
PVPVAabove the entanglement molecular weight (cited)deac2023a C42
HPMCAS-MF≈18,000 Da, below estimated critical values; rate linear in √rpm, no plateaurotating disk, 100–700 rpmbapat2023 C45, R19
PVP K29/32, K60, K90c_e 0.80, 0.12, 0.04 v/v; d_T(c_e) 10, 36, 80 nmcalculateddeac2024a M5, M6, M7
Pitfalls and disagreements

HPMCAS-MF still formed a thin, removable gel layer in some media; polymers near or below the critical value may form a swollen gel through viscosity effects (cited) bapat2023 C45, C34. Entanglement in the gel was not measured, and K29/32 entangles only above 0.80 v/v polymer deac2024a X10.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

polymer chain stiffness

How rigid a polymer backbone is

The authors attribute the advantage of cellulose derivatives over most synthetic polymers of similar hydrophobicity "most likely" to their semirigid, bulky backbones, which adsorb flat with more contact, against flexible chains that adsorb in loops with little contact [ilevbare2012c C39]. For nucleation the same property is given as a "perhaps" reason why bulky cellulose esters disrupt solute packing more than flexible chains [ilevbare2013c C39].

Findings

F8, F13.

Related concepts

related to polymer conformation, conformational flexibility, polymer hydrophobicity and polymer adsorption.

Formulas

none.

How it is measured or obtained

Not measured. The argument rests on the classification of the polymer chemistry (cellulose against vinyl-type chains) and on a molecular-dynamics result from the literature that stiffer chains adsorb more easily [ilevbare2012c R16, C39].

Values in the library
materialvalue or classconditionspaper ids
synthetic polymers on ritonavir growthabout 0.9–1.4 except Pn-IPAAmd (3.25)5 µg/mL[ilevbare2012c R9]
cellulose-based polymers on ritonavir growthup to 2.985 µg/mL[ilevbare2012c R9]
PAlAmn (SP 20.70) and Pn-IPAAmd (22.64) on ritonavir and efavirenz induction timesabout 112 and 119 min (ritonavir), 4.4 and 5.0 min (efavirenz), against 172–244 and 21.6–28.0 min for adipate esters of similar SPinduction time[ilevbare2013c R9, K4]
Pitfalls and disagreements

Only two synthetic polymers fall in the matching SP range for the nucleation argument, and for celecoxib the synthetic Pn-IPAAmd was among the best [ilevbare2013c K4, X11]. Rigidity was not measured, and the SP values of the synthetic polymers are not printed in the growth paper [ilevbare2012c X11]. Pn-IPAAmd is flexible yet the best growth inhibitor, attributed to a specific interaction [ilevbare2012c C44, C47].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

polymer conformation

The spatial arrangement of a polymer chain in solution and when adsorbed on a crystal: extended or condensed (globular), and, on a surface, trains lying on it, loops bulging into solution and tails [ilevbare2012c C39]. In these papers conformation is invoked to explain why the amount of polymer adsorbed does not predict how well it inhibits growth [ilevbare2012b C29, C30]. Simulated conformations of cellulose oligomers: short-spacer side chains stay extended (Rg 1.12–1.14 nm) and long-spacer charged ones fold (A5b Rg 0.92 nm); in-liquid AFM shows HPMCAS as globules at pH 3 and a flat layer at pH 6.8 [mosqueragiraldo2016 R18, R19; schram2015 R12, R10].

Findings

F8, F10, F11, F23, F25, F36, F37.

Related concepts

related to adsorbed polymer conformation, polymer chain stiffness, polymer ionization, polymer adsorption and conformational flexibility.

Formulas

Kubota-Mullin model, Langmuir-Freundlich isotherm.

How it is measured or obtained

It was not measured in any of these papers. It is inferred from the pH dependence of the growth ratio, adsorption isotherms, the zeta potential of seeds with polymer, and the Kubota–Mullin factor α, and by analogy with poly(acrylic acid), whose chains stretch as pH and ionization rise (pyrene-labelled chains, mean square radius of gyration) [ilevbare2012b R7, R9, R8, R16, R20].

Values in the library
materialvalue or classconditionspaper ids
CAP Adp 0.85 on ritonavirextended at pH 6.8 (α 4.35, plateau about 27 mg/m²); condensed at pH 3.8 (α 1.25, plateau about 41 mg/m²)σ 0.99[ilevbare2012b R9, R16, C46]
seeds with CAP Adp 0.85zeta potential −52.6 mV (pH 6.8); −27.2 mV (pH 3.8)10 mM citrate[ilevbare2012b R8]
cellulose esters against synthetic polymerssemirigid backbones lie flat in trains; flexible chains form loops, which fits the synthetic polymers' ratios of about 0.9–1.4ritonavir growth[ilevbare2012c C39, R9]
ionized adipate estersextended adsorbed chains block drug attachment bettercelecoxib, pH 6.8 against 3.8[ilevbare2013b C59, R13]
PVPVA on indomethacinadsorbed chains described as a flatter train at lower concentration, a thicker layer at higherAFM[moseson2020a C51]
cellulose oligomers A5a and A5bRg 1.12 and 0.92 nm; SASA 0.088 and 0.0705 nm² per atomMD 40 ns[mosqueragiraldo2016 R19]
A5a, A5b chains, alone and next to 25 telaprevir or atazanavir moleculesRg 3.58 and 3.16 nm alone; A5b 2.86 and 2.64 nm next to the drugMD, 310 K, 10 ns[mosqueragiraldo2018a R7]
HPMCAS against Eudragit E PO beside 10 enzalutamide moleculesRg about 1.38 against 0.69 nm (extended against globular)MD, 15 ns[wilson2021 R21]
Pitfalls and disagreements

The extended-against-condensed reading rests on the pH effect, higher depletion at pH 3.8 (which includes any loss other than adsorption) and α derived from a single point [ilevbare2012b X15, X8]. Other "plausible" explanations are a changed interaction with incoming drug molecules or with the surface energy of the crystal face [ilevbare2012b C32]. The cellulose-against-synthetic rigidity argument cannot be checked from the paper because the SP and rigidity of the synthetic polymers are not printed [ilevbare2012c X11]. Each simulation was run once and the chains are idealized (fully ionized, average substitution) [mosqueragiraldo2018a X9, X10; wilson2021 X14].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

polymer-controlled release

Dissolution paced by the dissolving polymer, fast and typical of low drug loading, at which the drug can exceed its amorphous solubility and form drug-rich droplets li2019 C48. In a phase-separated film the polymer-rich phase plays this role as "glue" that dissolves quickly and frees drug-rich domains li2019 C50. For ritonavir–PVPVA below 25% DL the polymer controls release; a single-phase spray-dried powder at 25% DL dissolved at about 3.5 mg·min⁻¹·cm⁻¹, and phase separation by water in the spray solvent lowered it to about 2.27 and 0.90 li2020 C63, R10. The marketed lopinavir–ritonavir tablet "appears" polymer-controlled because it forms a milky dispersion at pH 6.8 [trasi2019 C44]. New aspect (Supersaturation from ASD dissolution): the polymer-controlled regime (cited) is connected with what happens in solution: at 10% drug there is too little drug to form a dissolution-limiting layer, the drug dissolves at a fraction of the polymer rate, and it can reach "very high local supersaturations", "most likely local", that are depleted by rapid precipitation alonzo2011 C37, C39, C47, E4. In acid, where HPMCAS barely dissolves, release of celecoxib from a 33.3% drug dispersion "appears" to follow the polymer chen2015a C31. Release from HPMC dispersions of indomethacin and HPMCAS or HPMC dispersions of celecoxib became faster as drug loading fell, "indicative of" polymer-controlled dissolution, HPMC gelling and releasing "probably" by matrix-regulated diffusion [xie2017 C31, C64; xie2016a C20]; a carrier that dissolves fast by ionization (PAA at pH 6.8, EPO at pH 2.2) releases a burst that crystallizes unless an inhibitor is present [xie2016a C24; xie2017 C29]. New aspect (Release mechanism and LoC): the polymer carries the drug into the medium because there is too little drug to form an intact surface layer ("is thought to occur"), so drug and polymer leave at the polymer's normalized rate and drug release can far exceed that of the neat amorphous drug indulkar2019a C25, C26. Release that continues into a medium already at the amorphous solubility is the authors' test of it indulkar2017b C35; indulkar2019a C43. The two-component Higuchi model does not predict it: its critical mixture ratio is far below any practical loading, about 1.7 × 10⁻³ for felodipine–PVPVA saboo2020a R27, C36, C37. The polymer itself is slowed by the drug, "most likely" by the hydrophobicity of the formulation or by drug–polymer interactions saboo2019 C13; bhardwaj2018 C49. At the limit four phenolphthalein analogues released at the neat-polymer rate, so the system is "agnostic" to the compound and drug release "can be predicted" from polymer release que2021 C39, C41. The polymer rate in a dispersion need not be the neat rate: clopidogrel made PVPVA dissolve about twice as fast, which the authors attribute to plasticization ("is thought to") correasoto2022a C30, C48. For a binary dispersion of non-interacting components at low loading the soluble polymer carries the drug at the same relative rate, and congruent, complete release is "generally" observed indulkar2022 C20, E1. For HPMCAS-MF dispersions of indomethacin and its methyl ester at 10%, drug and polymer followed each other across buffer capacities and media, and the authors conclude that drug release from HPMCAS dispersions of model acidic or neutral drugs is controlled by polymer release bapat2023 C16, C49; in this regime Noyes–Whitney type equations "fail" to describe drug release bapat2023 C2. Hiew and co-workers (2023) restate the transition for copovidone dispersions and found release of grazoprevir particles drug-dominated once the surface drug reached about 50% hiew2023 C35, C53. For HPMCAS the 2024–2025 papers take polymer solubility at the gel–solution interface as the rate-limiting step, through the flux J_p = (D_p/\delta)\,C_p, so that a drug that lowers this solubility by forming an insoluble complex slows both components bapat2024 C31, E3, C32; kaur2025 C41. Kaur and co-workers support polymer control by low release at acidic pH and in FeSSIF-V1, where the drug is far more soluble but HPMCAS does not dissolve kaur2025 C40, C51. For PVP, congruent dispersions released like the neat polymer and more slowly with higher molecular weight deac2024a C19, C31.

Findings

ASD process: F14, F15, F21, F23, F38, F48. Supersaturation from ASD dissolution: F9, F10, F15, F20, F25. Release mechanism and LoC: F1, F2, F4, F11, F14, F15, F23, F28, F29, F32, F34.

Related concepts

contrasts with drug-controlled release; related to drug-rich nanodroplets, drug leaching and congruent release. Contradicts the Higuchi two-component dissolution model at low loading; tested with the Nernst-Brunner equation; capped by the polymer's intrinsic dissolution rate; its rate is set by polymer chain disentanglement in the gel layer; slowed by insoluble drug-polymer complex formation with enteric polymers.

Formulas

congruent release relation, Noyes-Whitney equation, Higuchi-Corrigan critical mixture ratio, saturated-medium condition.

How it is measured or obtained

Release against drug loading: LPV concentration at 10 min fell from about 16.9 µg/mL at 15% DL to about 1.2 µg/mL at 100% DL for miscible films li2019 R2. In the ASD dissolution papers: by particle disintegration under polarized light, by the speed of release in UV and by dissolved polymer measured by colorimetry alonzo2011 P6, P2; chen2015a P12. In the release-mechanism papers: equal normalized drug and polymer rates from constant-area compacts, and release into presaturated medium saboo2019 R8; indulkar2019a R12; integrated over time, (dC/dt)_{drug} = (dC/dt)_{polymer}\,m_{drug}/m_{polymer} gave ≈7.4 against ≈7.6 mg ritonavir at 20 min from a 10% tablet indulkar2019a E3, R1, R2.

Values in the library
materialvalue or classconditionspaper ids
LPV–HPMC E5 miscible, 15% DLabout 25 µg/(mL·min) peak rate; about 16.9 µg/mL at 10 min30 µg/mL doseli2019 R2.a
ritonavir ASDshigh-DL PVP and PVPVA lose polymer-controlled release by rapid AAPSoutsidepurohit2017b C3, C54
ritonavir ASDsLLPS was seen only for ASDs whose release was polymer-controlled and that stayed miscible during the initial phaseoutsidepurohit2017b C6
ledipasvir–PVPVA at 2 and 5% DLrelease polymer-controlled and congruentoutsideque2019 C9
indomethacin–PVPVA at 10% DL or lessdrug and polymer release rates resemble the neat polymer rateoutsidesaboo2020 C11
10% DL ritonavir and lopinavir ASDsdissolution polymer-controlled, driven by the polymer's aqueous solubilityoutsidetres2018 C23
ritonavir–PVPVA, spray-dried, 25% DLabout 3.5 mg·min⁻¹·cm⁻¹ from methanol; about 2.27 from 10:90 and about 0.90 from 60:40 water:methanolpH 6.5, 100 rpmli2020 R10
marketed lopinavir/ritonavir tablet (Aluvia)milky dispersion at pH 6.8, read as nanodroplets; drug loading inferred at 25% or lowernot measured[trasi2019 R20, C44, C45]
BCL–PVPVA 5 and 10% DLdrug and polymer released together; about 91 and 96% of the dose within 10 mindose of at most 30 µg/mLmoseson2022b R6, R7, C17
felodipine 90:10 HPMC dispersionparticle gone within 5 min; 80–100% of the drug in solution within about 10 min37 °Calonzo2011 R4, R2
ritonavir and lopinavir 20% HPMCAS against PVP dispersionsmaximum within 20 min against about 2 hpH 6.8, 25 °C[trasi2015b R14]
celecoxib–HPMCAS 33.3% particles, pH 3HPMCAS ≈3.5 (none) to ≈860 µg/mL (SDS) at 24 h, drug following it in absolute termssuspension, 25 °Cchen2015a R18, X9
celecoxib–HPMCAS 10 / 30 / 50 / 60% drug≈18.3 / ≈10.5 / ≈5.0 / ≈2.0 µg/mL at 1 h (22 nominal)pH 6.8, 37 °Cxie2016a R4
celecoxib 50%, PVP-K12 against HPMCAS≈16.1 against ≈9.0 µg/mL at 2 hpH 6.8, 37 °C[xie2015 R6]
indomethacin–HPMC 10 / 30 / 50% drug≈39.5 / ≈24.5 / ≈18.5 µg/mL at 60 min (80 nominal)pH 2.2, 37 °C[xie2017 R10]
delamanid salt dispersions, polymer release against drug releaseat pH 5.0 HPMCP-55 released ≈65% of its polymer and no drug; HPMCAS-LF released ≈92% of its polymer after pH 1.6 with ≈47.5% drug25% drug, 37 °C[nguyen2023c R12, R11]
praziquantel–HPMCAS-MF 20 / 30 / 40% drug≈100 / ≈94 / ≈83% released at 1.5 mg/mL, a gradual decline without a release cliffPBS pH 6.5, 37 °Cpolyzois2024 R9
nifedipine 10, 20% with HPMC-E5 or PVPVArelease continued to ≈214–218 µg/mL in medium presaturated at 110 µg/mL5 °C, D2Oindulkar2017b R8, R9
ITZ–PVPVA 10%199 µg/min/cm², about 4 times amorphous ITZ; polymer at 0.22–0.29 of neat PVPVA0.1 N HCl, 37 °Cbhardwaj2018 R4, R12
ritonavir–PVPVA 10% tablet≈67 mg PVPVA by 20 min against ≈46 mg for neat PVPVApH 6.8, 37 °Cindulkar2019a R2
nilvadipine 10% in PVPVA2.13 mg/min/cm² against 0.002 for amorphous nilvadipine (synthesis: about 1100-fold)pH 6.8, 37 °Csaboo2019 R5
felodipine 10% in PVP, PVPVA, HPMC, HPMCAS, EUDS≈3.8, ≈2.4, ≈0.14, ≈0.82, ≈0.16 mg/min/cm² (amorphous drug ≈0.0008)pH 6.8; EUDS 7.4saboo2020a R14, R13
four phenolphthalein analogues at their limitsdrug and PVPVA ≈2.8–3.7 against neat ≈3.0 mg/min/cm²compactsque2021 R21
clopidogrel–PVPVA 40–60%PVPVA ≈4.1–6.7 against neat ≈2.6–2.7 mg/min/cm²compactscorreasoto2022a R18
lumefantrine free base 5–35%drug ≈3.15–3.9 mg/min/cm²compactshiew2022b R12
indomethacin–HPMCAS-MF 10%drug = polymer, ≈0.12 → 0.82 mg/min/cm², following the neat polymerpH 6.8 phosphate 3–51 mM/ΔpHbapat2023 R9, R10
bedaquiline–HPMCAS 20% in FeSSIF-V1 (pH 5.0)≈22.5–25% in 120 min despite 628 µg/mL crystalline solubilitypowder, in situ UVkaur2025 R16, R2, C51
clotrimazole–PVP congruent dispersionsslower with higher PVP grade, like neat PVPcompacts, pH 8.0deac2024a C19, R3
Pitfalls and disagreements

The boundary between polymer- and drug-control was not located for LPV–HPMC here li2019 C48. Phase separation can lower as well as raise polymer-controlled release depending on where the drug-rich phase ends up li2020 C64. Polymer release was not measured in the 2011 felodipine study, and the local supersaturation at the dissolving particles "cannot be discounted" but was not measured alonzo2011 C28. In the celecoxib suspensions the polymer–drug link holds for absolute concentration in four media, not for supersaturation chen2015a X9. Polymer release was not measured in the celecoxib and indomethacin papers either, so the regime is inferred from drug release [xie2015 C50; xie2017 C31]. For praziquantel the gradual decline with loading is read as polymer-controlled release, although polymer release was not measured polyzois2024 C17. Polymer-controlled does not mean fast, against the general description of the regime as fast in the Definition: 10% felodipine–HPMC released at ≈0.14 mg/min/cm², about a sixth of HPMCAS saboo2020a R14. The persisting drug–polymer interaction proposed for low-loading ritonavir was not measured indulkar2019a C36. The 10% ITZ profiles were non-linear (R² 0.957–0.983), which "might" reflect polymer hydration and swelling bhardwaj2018 R4, C20. Drugs and surfactants change the polymer rate itself, so the neat-polymer rate bounds polymer-controlled release only roughly correasoto2022a R18; correasoto2022b R22. Kaur and co-workers did not measure polymer release, so polymer control is inferred from the pH dependence of drug release kaur2025 X14. In PVP the coupled rates of different grades were compared at different loadings deac2024a R1.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

polymer hydration

Evidence table: polymer hydration. Content from the release-mechanism chapter (2024–2025).

The uptake of water by the ionized polymer chains that plasticizes and dilutes them so that they can dissolve. For HPMCAS the release papers of 2024–2025 hold that protonated HPMCAS interacts little with water, that ionization to the carboxylate brings hydration, plasticization and dilution, and that hydration resulting from ionization, rather than ionization itself, solubilizes the chains bapat2024 C24; bapat2025a C2; kaur2025 C46. Anything that hinders hydration "can impact" polymer solubility and rate: a lipophilic drug lowers the rate and extent of hydration as loading rises, and a drug cation bound to the carboxylate blocks it (F32) bapat2025a C3; bapat2024 C25; kaur2025 C3.

Findings

Release mechanism and LoC: F32, F33, F15.

Related concepts

follows critical ionization for polymer dissolution; lowered by drug-polymer ionic interactions and drug lipophilicity; precedes polymer chain disentanglement.

Formulas

none.

How it is measured or obtained

Not measured in these papers; it is the step through which loading, complexation and grade are proposed to act bapat2025a X11; kaur2025 C46.

Values in the library
materialvalue or classconditionspaper ids
HPMCAS-MF dispersions of non-complexing drugs, 5–60%slower release at higher loading attributed "likely" to less hydrationcompacts, pH 6.8bapat2024 C28, R2
HPMCAS LF against HF at 25% weak base"spare" carboxylates of LF proposed to keep hydratingproposedbapat2025a C26
Pitfalls and disagreements

Hydration of the polymer in a dissolving dispersion was not measured; the grade argument rests on an analogy with maleic anhydride copolymers bapat2025a X11, C25.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

polymer hydrophobicity

Water affinity of a polymer, judged here by aqueous solubility and by a calculated solubility parameter; the two rank cellulose acetate suberate and HPMCAS differently mosqueragiraldo2018b C13, X6. HPMCAS grade AS-HF is more hydrophobic than AS-LF (more acetate, less succinate) and goes more into the drug-rich phase ueda2020a C34, C35; for the enzalutamide polysaccharides the polymer needs a balance of hydrophobic and hydrophilic substituents wilson2020 C28, C30. New aspect (Crystallization from solution): in the growth and nucleation papers it is judged by the Fedors solubility parameter \delta (lower means more hydrophobic; water 49.01 MPa^1/2) relative to that of the drug [ilevbare2012c E1; ilevbare2013c E5, M29], and the working claim is that a polymer must have a moderate hydrophobicity relative to the drug to inhibit crystallization: a very hydrophilic polymer stays solvated, a very hydrophobic one collapses on itself [ilevbare2012c C36; ilevbare2013c C4]. For six dihydropyridines PVPVA, HPMC and HPMCAS (moderately hydrophobic) delayed crystallization of the precipitate most, the very hydrophilic PAA and the hydrophobic P2VP not at all, with hydrophobicity not measured; for telaprevir the calculated SP did not predict the order across chemistries [raina2015b C41, C42, X9; mosqueragiraldo2016 C25].

Findings

Bioperformance: F7, F8, F10, F19, F24, F27. Crystallization from solution: F8, F13, F16, F17, F25, F26, F36, F37, F44.

Related concepts

governs polymer partitioning into the drug-rich phase, polymer dissolution pH threshold; measured by solubility parameter; related to amphiphilicity, polymer chain stiffness, degree of substitution, hydrophobic interactions and polymer adsorption.

Formulas

Fedors group-contribution solubility parameter.

How it is measured or obtained

Gravimetric aqueous solubility at pH 6.8; Fedors solubility parameter mosqueragiraldo2018b P11, P21. In the crystallization-from-solution papers calculated by the Fedors group-contribution method from the repeat unit (with a molar-volume correction for glassy polymers) [ilevbare2012c E1, E2, E3], and used in a multivariate model with the other polymer descriptors (SP, DP, Mn, monomer Mw, hydrogen-bond donors and acceptors, Tg) [ilevbare2012c R12, R14].

Values in the library
materialvalue or classconditionspaper ids
CA Sub / HPMCAS / HPMC / PVPVA3.3 / 20.5 / 37.1 / 45.9 mg/mL; 23.18 / 21.47 / 23.93 / 23.59 MPa^1/2pH 6.8mosqueragiraldo2018b M2, M3, M4, M5
ezetimibe in Ensure Plusopposite polymer ranking in the aqueous and oily phases "raises questions" about hydrophilicity[elkhabaz2017 C52]
ritonavir, cellulose esterssolubility parameter 20.56–23.28 inhibited growth; more hydrophobic ones did not[ilevbare2012c C25, C30]
PVP / HPMCAS filmscontact angle 11.8° / 45°spin-coatedsaboo2020a R4
CPHPC-106 / cellulose acetate suberatedissolves (cited 43.5 mg/mL) / does not (3.0 mg/mL); the better solution inhibitor was the insoluble oneenzalutamidewilson2020 M2, M3, C35
14 new cellulose estersSP 19.62–23.28 MPa^1/2; effective (ratio 1.64–2.98) at 20.56–23.28, ineffective (0.83–1.01) at 19.62–20.41ritonavir growth, 5 µg/mL[ilevbare2012c R10]
OPLS-DA of 19 cellulose-based polymersSP loading about 0.70, R²Ycum 0.713, Q²Y 0.512ritonavir growth[ilevbare2012c R12, R14]
effective polymers, ritonavir; efavirenz; celecoxibmean SP 20.87; 21.73; 24.28 against drug SP 20.03; 21.89; 23.38induction time at 5 µg/mL[ilevbare2013c R13]
16 polymers on three drugswindow 20.56–23.28 for drugs of SP 20.03–23.38seeded growth[ilevbare2013b R9, M1–M3]
pH-shift precipitation, nine polymersPAA (very hydrophilic) and CMCAB failed for warfarin; CAP-adipate (most hydrophobic) failed for both acids1 mg/mL[hsieh2014 R4, C39]
celecoxib, HPMCAS; PAAHPMCAS and HPMC effective, very hydrophilic PAA not22 µg/mL drugxie2016a C18
PVPVA, HPMC, HPMCAS; PAA, P2VPbeyond 24 h for four drugs; as buffernominal 10 mg/mL, 4.5 mg/mL polymer[raina2015b R9]
six carboxylated cellulose derivatives (neutral structures)Fedors SP 25.5 (A5a), 24.3 (A5b), 19.9–22.2 MPa^1/2 (ethers); ECA (19.9) the most broadly effective5 µg/mL, nine drugs[mosqueragiraldo2018a R6, R2]
HPMCAS L, M, Hmore acetyl, less succinoyl: longer posaconazole induction times, more polymer in dropletspH 5.5–7.5shah2025 R3, R17, C48
Pitfalls and disagreements

CA Sub is "more hydrophobic" than HPMCAS by aqueous solubility but not by solubility parameter mosqueragiraldo2018b X6. Hydrophobicity cuts both ways: it improved inhibition of crystallization and lowered the ceiling (F19, F24); HPMCAS-HF, the most hydrophobic grade, was the only effective pretomanid inhibitor (F27) ueda2020a C35; wilson2020 C35; nguyen2023a R5. SP and the carboxyl content of the new esters co-vary, so their effects are not separated [ilevbare2012c X10]. The SP values of the commercial and synthetic polymers are not printed in the 2012 paper [ilevbare2012c X11]. The 2013 text misstates the failing range as SP "greater than 20.56" [ilevbare2013b X2]. The rule predicts the best polymer for ritonavir and efavirenz but the synthetic Pn-IPAAmd and PAA are exceptions for celecoxib, and PVPVA works for celecoxib and efavirenz through a proposed hydrogen bond [ilevbare2013c X11; ilevbare2013b C51]. The rule was reached from three drugs [ilevbare2013c K3]. The cellulose ether with the lowest calculated SP was the best inhibitor for fast crystallizers, so the SP window does not carry across chemistries [mosqueragiraldo2018a R2, R6].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

polymer ionization

The degree to which the acid or base groups of a polymer are ionized at the test pH. The ω-carboxyalkanoate substituents (adipate, suberate, sebacate) of the new cellulose esters have a pKa of about 4.43, so they are nearly fully ionized at pH 6.8 and less than 25% ionized at pH 3.8; the ritonavir and celecoxib in the growth tests are un-ionized at both pH [ilevbare2012c R15; ilevbare2013b R18, C33]. HPMCAS-LF (pKa 5.5) is taken as nearly fully ionized at pH 6.8 and un-ionized at pH 3; two carboxylated cellulose esters lost their whole effect on telaprevir at pH 3.0; PAA failing for acetaminophen is attributed to its ionization at pH 6.8 [schram2015 C4; mosqueragiraldo2016 R7; trasi2015 C27]. Above the polymer pKa the degree of ionization still matters: for HPMCAS (pKa about 4.9) a rise from pH 5.5 to 7.5 weakened every grade against posaconazole nucleation, and the grade with the least succinoyl was the best inhibitor shah2025 R3, C14, M2. New aspect (Supersaturation from ASD dissolution): in the dissolution of dispersions, ionization decides whether the polymer dissolves and so how fast the drug is released: EPO is highly soluble at pH 2.2 "due to ionization", which gave rapid and complete dissolution of the indomethacin–EPO dispersion above the amorphous solubility, followed by crystallization [xie2017 C29]. In leaching from suspended lopinavir dispersions, a small extent of HPMCAS ionization from pH 3 to pH 5 "significantly enhanced" leaching in media with an ionic surfactant (with SDS drug from about 13 to about 36 µg/mL and polymer from about 21 to about 120 µg/mL), lopinavir itself not ionizing over this range [li2016b C24]. HPMCAS LF, with a lower pKa than HF, is taken as more ionized at pH 5 [li2016b C27]. The authors "can only speculate" that ionized chains become less coiled and expose less polar, uncharged groups to SDS [li2016b C49].

Findings

Crystallization from solution: F11, F13, F16, F23, F25, F27, F36, F44. Supersaturation from ASD dissolution: F10, F15, F20.

Related concepts

related to ionization, degree of substitution, polymer conformation and polymer self-association; related to polymer-surfactant complexation, pH-dependent polymer solubility and drug leaching.

Formulas

none.

How it is measured or obtained

Not measured: the degree of ionization is taken from the pKa of the substituent (literature) and the pH of the medium [ilevbare2012c R15; ilevbare2013c R18]. The effect is read from growth ratios or induction times at two pH, with non-ionizable HPMC as the control [ilevbare2012b R7; ilevbare2013c R14]. In the dispersion-dissolution papers it is likewise not measured but inferred from the medium pH and cited pKa values [li2016b C27, C24].

Values in the library
materialvalue or classconditionspaper ids
adipate, suberate, sebacate substituentspKa about 4.43; about 100% ionized at pH 6.8; less than 25% at pH 3.8literature[ilevbare2012c R15; ilevbare2013c R18]
CAP Adp 0.85; HPMC on ritonavirgrowth ratio 2.98 → 1.12; 2.19 → 2.31 from pH 6.8 to 3.8S 7.6[ilevbare2012b R7]
CA 320S Sub 0.63 on celecoxib6.1 → 1.5 (75% lower)S 6.6[ilevbare2013b R13]
CAP Adp 0.85 on efavirenzinduction time 24.9 → 12.6 min19 µg/mL[ilevbare2013c R14]
HPMCAS, Eudragit E100 in the pH-shift studyHPMCAS unionized at the acidic final pH 1.9–3.3; E100 cationic1 mg/mL[hsieh2014 C36, R4]
PAA in celecoxib dispersions (ASD dissolution chapter)pKa 4.28, completely ionized at pH 6.8pH 6.8xie2016a C24
CAP-Adp-085, CA-Sub-090, telaprevir68 → 9 and 105 → 8 min (pH 6.8 → 3.0)150 µg/mL, 5 µg/mL polymer[mosqueragiraldo2016 R7]
HPMCAS L, M, H (A/S about 0.28–0.64, 0.5–1.1, 1.25–3.5)posaconazole induction time M >240, 208, 136 min at pH 5.5, 6.5, 7.5; ζ of droplets −12.9, −10.8, −7.4 mV (L, M, H, pH 6.5)FaSSIF-V2 buffer, 37 °Cshah2025 R3, R15, M2
carboxylated ethyl cellulose ECD (two acids)modelled fully ionized; partial protonation "possible"MD, 310 K[mosqueragiraldo2018a C32, X9]
HPMCAS-HF lopinavir dispersions with SDS, pH 3 → pH 5drug about 13 → about 36 µg/mL; polymer about 21 → about 120 µg/mL25 °C[li2016b C24]
EPO in indomethacin dispersionshighly soluble at pH 2.2 owing to ionization37 °C[xie2017 C29]
Pitfalls and disagreements

The pH arm changes the buffer species (acetate against phosphate) and sometimes the polymer-free rate or time [ilevbare2013b X11; ilevbare2013c X9]. The size of the loss at pH 3.8 does not follow the carboxyl content in the middle of the ranking [ilevbare2012b X17]. PAA, fully ionized at pH 6.8, did not inhibit any of the three drugs [ilevbare2013b R9.b]. The degree of ionization was not measured in these papers [schram2015 C4; mosqueragiraldo2016 X24]. Ionization and hydrophobicity of HPMCAS change together with pH and were not measured; the pH effect on the induction time is measured, its route is not shah2025 X8. The degree of ionization of the HPMCAS grades at pH 3 and pH 5 was not measured, and how a small degree of ionization raises SDS-driven leaching is "currently unclear" [li2016b C24, C27, C49].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

polymer partitioning into the drug-rich phase

The distribution of a dissolved polymer between the aqueous phase and the drug-rich phase that forms above the amorphous solubility, expressed as the polymer:drug weight ratio in the drug-rich phase or as the partition coefficient K = C_p/C_q (polymer in the drug-rich phase over polymer in water) [ueda2021 P4; ueda2022 E3]. For ibuprofen it is seen as the polymer that disappears from the solution NMR spectrum when droplets form, because polymer in the viscous droplets reorients too slowly to give a signal [ueda2020b C22; ueda2021 C7]. Polymer in the drug-rich phase lowers the chemical potential of the drug there and so the amorphous solubility (F19–F21) [ueda2021 C11]. New aspect (Bioperformance): a large share of polymer in the drug-rich phase lowers the chemical potential of the drug there and may lower the flux plateau mosqueragiraldo2018b C34, C35, C37. HPMCAS grade AS-HF distributed much more into the drug-rich phase than AS-LF for four drugs, which the authors say accounts for its lower amorphous solubility ueda2020a C20, C33; HPMCAS and PVP are not expected to enter the atazanavir–darunavir phase [alkalla2026 C38]. New aspect (Crystallization from solution): the share of a dissolved polymer found in the drug-rich precipitate against the solution, with PVPVA and HPMCAS in both (about 7% of the felodipine precipitate), PAA almost only in the water and P2VP in the precipitate [raina2015b R12, C20]; from 2021 the polymer share in the droplets was set against crystallization inhibition, and it did not rank HPMCAS against Eudragit E PO for enzalutamide but did rank three HPMCAS grades for posaconazole [wilson2021 C38; shah2025 C51].

Findings

Amorphous solubility and LLPS: F15, F19, F20, F21, F22. Bioperformance: F7, F19. Crystallization from solution: F19, F26, F37, F44.

Related concepts

lowers the amorphous solubility through the chemical potential of the drug in the drug-rich phase; driven by the hydrophobic effect and drug–polymer interaction (Flory-Huggins interaction parameter); measured with the help of NMR chemical exchange broadening; affects colloidal stability. Depends on polymer hydrophobicity. Related to amorphous precipitation.

Formulas

van't Hoff equation, Flory-Huggins reduction of amorphous solubility, ideal-mixing reduction of amorphous solubility. Drug-rich phase composition, polymer partitioning into the drug-rich phase by depletion.

How it is measured or obtained

Quantitative ¹H NMR of the dissolved polymer (peak at 2.0 ppm for PVP and PVP-VA, 3.1 ppm for HPMC) against TSP and a calibration line, compared with the polymer concentration before drug is added; the missing part is taken as being in the drug-rich phase and divided by the phase-separated drug [ueda2021 P3, P4]. Variable-temperature NMR gives K and, from a van't Hoff analysis, ΔG, ΔH and ΔS of transfer ueda2022 P12. Other methods in the library assay the polymer in the ultracentrifuged pellet or supernatant mosqueragiraldo2018b R14; shah2025 R16. Colorimetric assay of polymer in the centrifuged pellet and Nile red fluorescence for drug mosqueragiraldo2018b P12–P14. Solution NMR of the polymer with and without droplets (acetyl or hydroxypropyl peak), the lost signal being read as polymer in the droplets ueda2020a R7, R8. Ultracentrifugation of the suspension and ¹H NMR of precipitate and supernatant in d6-DMSO, masses scaled to 10 mL [raina2015b P8].

Values in the library
materialvalue or classconditionspaper ids
ibuprofen with six polymerspolymer:drug ratio 0.40 (PVP K12), 0.52 (K25, K90), 0.87 (PVP-VA), 0.95 (HPMC 603), 1.14 (HPMC 615); dissolved drug 131–89 µg/mL1000 µg/mL polymer, 400 µg/mL drug, pH 2.0 (D2O), 37 °C[ueda2021 R5]
ibuprofen with PVP K25, PVP-VA, HPMC 603ratio stops rising above 200 (K25) and 500 µg/mL polymer (PVP-VA); HPMC 603 keeps rising (about 0.08 → 0.95)25–1000 µg/mL polymer[ueda2021 R8]
ibuprofen with HPMC, PVP-VA, EUD-Epolymer still in solution at S_a + 300 µg/mL: about 141, 85, 289 of 300 µg/mL37 °Cueda2020b R13
ibuprofen, 15–60 °Cratio 0.24 → 0.62 (PVP), 0.46 → 1.32 (PVP-VA), 0.20 → 1.46 (HPMC, to 55 °C)1000 µg/mL polymerueda2022 R10
polymer transfer into the ibuprofen-rich phaseΔG −12 to −19 kJ/mol; ΔH of HPMC 58 → 12, PVP-VA 25 → 5 kJ/mol15–60 °C, quadratic van't Hoff fitueda2022 R22, R23
telaprevir ASDs, 150 µg/mL drugpolymer fraction of the pellet about 0.9 (cellulose acetate suberate), below 0.3 (PVPVA, HPMCAS)pH 6.8, 37 °Cmosqueragiraldo2018b R14, C35
posaconazole with HPMCAS grades L, M, Hpolymer weight fraction in the phase about 0.05, 0.14, 0.31, water ignored100 µg/mL drug, 900 µg/mL polymer, pH 6.5, 37 °Cshah2025 R16, R17, C30, E3
enzalutamide dropletsEudragit E PO associates with the droplets more than HPMCASpH 6.5, 37 °C[wilson2021 R7, C19]
telaprevir, CA Sub / HPMCAS / 70% HPMCAS / PVPVApolymer fraction 0.90 / 0.21 / 0.27 / 0.22150 µg/mLmosqueragiraldo2018b R14
felodipinePVPVA and HPMCAS distributed; PAA in the supernatant; P2VP with the drugprecipitates[raina2015b C20, R12]
ibuprofen, polymerspolymer ratio falls with total drug37 °C[ueda2021 R10]
atazanavir, nifedipine, clozapine, ketoconazole droplets with 1000 µg/mL AS-LF / AS-HFNMR-detected polymer about 975 / 880, 955 / 480, 920 / 415, 990 / 600 µg/mL37 °Cueda2020a R8, C20
felodipine 100 mg, PVPVA 45 mgprecipitate 6.8 mg, supernatant 36.7 mg10% DMSO, pH 6.8[raina2015b R12]
felodipine, HPMCAS7.1 mg and 34.2 mgsame[raina2015b R12]
felodipine, PAA; P2VP (18 mg)0.9 and 46.6 mg; 17.7 mg and not detectedsame[raina2015b R12]
enzalutamide droplets, HPMCAS, Eudragit E PO12.7–24.7 and 40.8–41.0 w/w% (NMR); about 19–23 w/w% both (colorimetry)120 and 70 µg/mL drug, pH 6.5[wilson2021 R7, R9, X4, X5]
Pitfalls and disagreements

The "polymer in the drug-rich phase" is the NMR-invisible polymer and would include polymer adsorbed at droplet surfaces; the droplet composition and the activity of the drug in it were not measured [ueda2021 X4; ueda2020b X4]. The molecular-weight rule fails between PVP K25 and K90, polymer hydrophobicity was not measured, and the ranking of HPMC 603 against PVP-VA reverses with polymer concentration [ueda2021 X7, X8]. Two papers state that polymers used in ASDs have minimal impact on the amorphous solubility or do not take part in the drug-rich phase, which the ibuprofen data contradict for PVP K25 (154 → 121 µg/mL) [trasi2016 C32; alkalla2026 C38; ueda2021 R5]. The transfer enthalpy is per polymer species of different molar masses and has no stated uncertainty ueda2022 X9, X8. In the telaprevir study HPMCAS and PVPVA fractions are equal although their solubilities differ twofold mosqueragiraldo2018b X7. For atazanavir only about 12% of AS-HF disappeared from the solution signal although the ceiling fell by more than half, and the signal does not separate polymer mixed into the droplet from polymer adsorbed at its surface (F19) ueda2020a X4, X10. The felodipine precipitate study used four polymers, one drug and single determinations, and its totals deviate from the stated amounts by up to about 8% [raina2015b X9, X12].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

polymer salt formation

Evidence table: polymer salt formation. Content from the release-mechanism chapter (2022–2023), with rows from the Bioperformance chapter.

Pre-ionizing an acidic dispersion polymer by reacting its acid groups with a base (sodium or an amine) before the dispersion is made. Pre-ionization removes the generation and transport of protons during dissolution; the comparisons of HP-50 with HP-50-Na (faster in 50 mM phosphate, independent of buffer capacity, soluble in water) "confirm" that proton generation and removal hinder dissolution of the protonated polymer qi2022 C31. Polymer salts dissolved about 3-fold faster than HP-50 at pH 6.8, and pre-ionization via salt formation is called a successful strategy for designing polymers for better dispersion performance qi2022 C3, C6. The triethylamine salt of HPMCAS, which releases no protons, had a gel pH close to the bulk and released faster than protonated HPMCAS bapat2023 C41. In the Bioperformance chapter base was added at one mole per mole of HPMCAS-HF acid groups to pretomanid dispersions, which "likely" forms a polymer salt nguyen2023a E7, C67.

Findings

Release mechanism and LoC: F23, F24.

Related concepts

removes the dependence on buffer capacity and on the microenvironmental pH; exceeds the critical ionization for polymer dissolution before dissolution; a form of polymer ionization of enteric polymers.

Formulas

none.

How it is measured or obtained

Acid–base reaction of the polymer with the base, then dispersion preparation bapat2023 P4, M4; the sodium content of HP-50-Na by ICP-OES and ¹H NMR qi2022 R3; rotating-disk dissolution of neat and drug-loaded compacts qi2022 R10, R15.

Values in the library
materialvalue or classconditionspaper ids
HP-50-Na3.38–3.52 wt% sodium, 91–95% of acid groupsICP-OES, ¹H NMRqi2022 R3
HP-50 and nine salts≈0.92 against ≈2.35–3.09 mg/min/cm²50 mM pH 6.8 phosphate, 37 °Cqi2022 R10
HP-50-Na; HP-50≈2.80 → 2.45; ≈0.92 → 0.14 mg/min/cm² from 29 to 3 mM/ΔpHpH 6.8 phosphateqi2022 R12
miconazole 20% on HP-50, HP-50-Na, PTEAdrug ≈0.22 / 3.15 / 2.70 mg/min/cm²50 mM pH 6.8 phosphateqi2022 R15
HPMCAS-TEA against HPMCAS-MF≈1.62 against ≈0.89 mg/min/cm²; gel pH 6.7 against 6.050 mM pH 6.8 phosphatebapat2023 R16, R15
Pitfalls and disagreements

Water uptake does not rank the salts: the sodium salt took up most water without dissolving faster than the amine salts qi2022 X17, C35. The amounts used to prepare the partial salts are not printed qi2022 X9. The salts change the dry dispersion as well: Tg ranged from 55 °C for the tris salt to 231 °C for the sodium salt qi2022 R8.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

polymer self-association

The association of polymer chains with one another in solution, which frees them less to interact with the drug or to adsorb on the crystal. Ilevbare and co-workers propose it for two cases: a very hydrophobic polymer that "is likely" to interact more favourably with other polymer molecules than with the drug, and un-ionized carboxylic acid polymers at pH 3.8, whose loss of effect "may be attributed to increased self-association" [ilevbare2013b C50; ilevbare2013c C4, C43]. The long-spacer charged cellulose oligomers (A5b, A6) fold onto their backbone in simulation and are said to self-aggregate; A7 was not simulated [mosqueragiraldo2016 R18, C62, X9].

Findings

F11, F13, F25, F36.

Related concepts

related to polymer ionization, polymer hydrophobicity and polymer conformation.

Formulas

none.

How it is measured or obtained

Not measured in either paper; it is inferred from the effect of pH and of polymer hydrophobicity on growth ratios and induction times [ilevbare2013c C5, C43; ilevbare2013b X14].

Values in the library
materialvalue or classconditionspaper ids
efavirenz with CAP Adp 0.85; CAB Adp 0.81induction time 24.9 → 12.6 min; 27.9 → 13.6 min from pH 6.8 to 3.819 µg/mL drug, 5 µg/mL polymer[ilevbare2013c R14]
the most hydrophobic esters (CAB Adp 0.25, CAP Seb, CAB Seb)growth ratios about 0.85–1.3 on celecoxib, efavirenz and ritonavir5 µg/mL[ilevbare2013b R9]
A5b; A6 oligomersRg 0.92 and 1.02 nm; SASA 0.0705 and 0.077 nm² per atomMD 40 ns[mosqueragiraldo2016 R19]
A5b ((CH2)8 tether)most compact chain, shrinking next to the drug; RDF peak only at 6–7 nm; large uneven globules on amorphous atazanavirMD and AFM[mosqueragiraldo2018a R7, R9, R4, C27]
Pitfalls and disagreements

The pH arm changes the buffer species and the polymer-free induction time (5.1 against 6.6 min) as well as the ionization [ilevbare2013c X9]. For growth, the same pH loss is explained by a condensed adsorbed conformation, not by self-association in solution (F11) [ilevbare2012b C46].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

polymer-surfactant complexation

Evidence table: polymer-surfactant complexation. Content from the ASD dissolution chapter (celecoxib, 2015).

Association of surfactant molecules with polymer chains in solution, which can raise the solubility of the polymer. SDS is proposed to raise the solubility of HPMCAS at pH 3 "most likely" by forming polymer–surfactant complexes, as reported for HPMC with SDS and during release from solid dispersions (cited) chen2015a C32. With lopinavir, PVPVA and SDS "may be able to form a complex" with a higher solubilizing capacity than either alone, and slight ionization of HPMCAS at pH 5 raised SDS-driven leaching of drug and polymer by a mechanism the authors call "currently unclear" [li2016b C31, C42, C24, C49]; surfactant–polymer complexation "can also enhance" polymer solubility [li2016b C44].

Findings

F15, F19.

Related concepts

related to polymer-surfactant interaction, micellar solubilization and drug leaching.

Formulas

None.

How it is measured or obtained

Not detected directly; inferred from dissolved polymer in suspension liquids chen2015a P12, R18.

Values in the library
materialvalue or classconditionspaper ids
HPMCAS-LF from celecoxib particles, 0.25% SDS≈73 µg/mL at 0.5 h, ≈420 at 4 h, ≈860 at 24 hpH 3, 25 °Cchen2015a R18
same, 0.75% STC; no surfactant≈43 and ≈3.5 µg/mL at 24 hpH 3chen2015a R18
HPMCAS-HF from lopinavir dispersions, SDS at pH 3 / pH 5≈19–24 / ≈105–134 µg/mL25 °C[li2016b R8, R13]
lopinavir with HF, PVPVA and SDScrystalline solubility 11.4 against 3.3 µg/mL with HF and SDSpH 3[li2016b R5]
Pitfalls and disagreements

No complex was detected in this system; the mechanism is by analogy with HPMC–SDS chen2015a C32. Polymer was not measured in the polysorbate 80 and Poloxamer 188 media chen2015a X9. Neither complex was characterized [li2016b C31, C44].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

polymer-surfactant interaction

The association of a polymer with a surfactant in solution, which changes the properties of both and, for a hydrophobic polymer, can reduce the polymer's adsorption on the crystal and so its crystallization inhibition ilevbare2012a C53, C54. Pharmaceutical examples named are PEG with polysorbate 80, HPMC with poloxamer and polysorbate 80, and PVP with SLS ilevbare2012a C3. For felodipine, 100 µg/mL SDS cancelled most of the effect of 5 µg/mL HPMCAS on growth (2.7 → 1.07) although HPMCAS still adsorbed [schram2016 R16, R17]. New aspect (Release mechanism and LoC): for TPGS with dissolved PVPVA, the CMC and the critical aggregation concentration differ minimally and insignificantly relative to the TPGS levels used, which "suggests" little-to-no TPGS–PVPVA interaction affecting the CMC saboo2021 C7, R1. The authors conclude that the surfactant should be incorporated into the dispersion rather than added as an external excipient, since TPGS pre-dissolved in the medium did not help saboo2021 C35, R15. For ritonavir–PVPVA Indulkar and co-workers (2022) suggest that SDS forms micellar aggregates on the PVPVA chain and that this complex "may" dissolve faster than the polymer alone, about doubling early polymer release, and that a surfactant interacting strongly with the polymer "can" make a crystallization-inhibiting polymer ineffective indulkar2022 C33, R20, C42; complexation was not measured there indulkar2022 C33.

Findings

Crystallization from solution: F18, F24, F38. Release mechanism and LoC: F13, F15, F21.

Related concepts

related to competitive adsorption and interfacial tension. Measured through the critical micelle concentration.

Formulas

none.

How it is measured or obtained

Not measured in the binary-additive paper: the effect is read from the growth-rate ratio of surfactant–polymer pairs against the components ilevbare2012a R17, X15. In the ASD dissolution chapter, the CMC of TPGS with and without PVPVA gave about 50 µg/mL against 40 µg/mL (a critical aggregation concentration) saboo2021 R1. In the release-mechanism papers: CMC by drug solubility against surfactant level and by the pyrene I1/I3 ratio, without and with 900 µg/mL PVPVA saboo2021 P1, P2, R1.

Values in the library
materialvalue or classconditionspaper ids
Tween 80 with CAP Adp 0.33; 0.85growth ratio 0.70; 0.83 against 1.64; 2.97 for the esters alone5 µg/mL each, ritonavir, S 7.6ilevbare2012a R17
TPGS with and without 900 µg/mL PVPVACMC about 50 µg/mL; about 40 µg/mL with PVPVA, "little-to-no" interactionpH 6.8, 37 °Csaboo2021 R1, C7
surfactants with a crystallization-inhibiting polymerthe polymer can be rendered fully or partly ineffective, particularly when surfactant and polymer interact extensivelyritonavir–PVPVA ASD (argued)indulkar2022 C42
felodipine, HPMCAS + SDSgrowth ratio 1.07 against 2.7 (HPMCAS)S 4, 25 °C[schram2016 R16]
SDS with PVPVA, HPMC-606, HPMCAS-MFCAC 0.1, 0.2, 0.2 mg/mL; with 0.1 mg/mL SDS atazanavir induction time 350, >1000, >1000 min1 mg/mL polymer, pH 6.8[indulkar2019b R8, R4]
ritonavir–PVPVA 30:70:5 with SDS against binary 25:75PVPVA ≈35.4 against ≈14.0 units at 10 min (unnormalized)compacts, pH 6.8indulkar2022 R20, X6
Pitfalls and disagreements

Polymer–surfactant aggregates, polymer adsorption and surfactant adsorption were not measured in the ritonavir study ilevbare2012a X15. Surfactants were only tested below their CMC and only Tween 80 with two related esters ilevbare2012a R17. The SDS–polymer correlation rests on two CAC values and one SDS level equal to the PVPVA CAC, with censored times [indulkar2019b X8].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

polymer swelling

Evidence table: polymer swelling. Content from the release-mechanism chapter (2018–2025).

The uptake of water by the polymer of a dissolving compact, with an increase in volume before the chains dissolve. Bhardwaj and co-workers (2018) suggest that the deviation of the 10% ITZ–PVPVA release from linearity "might" come from initial hydration and swelling of the polymer bhardwaj2018 C20. Que and co-workers (2019) report that the drug-rich layer of ledipasvir–PVPVA compacts above the limit "appears" to stop release of drug and of PVPVA, leading to swelling que2019 C32. At 40% MePHPH the drug-rich network was weaker than at 50% and intermittently ruptured, "possibly" through swelling pressure, and water entering through the pores of the barrier moves the glass/gel boundary deac2023a C60, C58. The 2024 PVP paper proposes that entangled, high-molecular-weight PVP swells more, which "is expected to" space drug-rich droplets apart before the chains disentangle deac2024a C46.

Findings

Release mechanism and LoC: F2, F25, F29.

Related concepts

part of polymer-controlled release; behind a drug-rich barrier layer.

Formulas

none.

How it is measured or obtained

Not measured: inferred from the shape of release profiles and from micro-CT of dried compacts bhardwaj2018 R4; que2019 R13.

Values in the library
materialvalue or classconditionspaper ids
ITZ–PVPVA 10%non-linear profiles (R² 0.957–0.983)0.1 N HCl, 37 °Cbhardwaj2018 R4, C20
ledipasvir–PVPVA 10%bulging, porous top layer by 30 minmicro-CT, driedque2019 R13
Pitfalls and disagreements

Neither swelling nor gel thickness was measured in these papers bhardwaj2018 C20.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

reduced glass transition temperature

T_{rg} = \frac{T_g}{T_m} with both temperatures in kelvin [baird2010 E4]. Assuming equal viscosity at Tg, a higher Trg means a more viscous liquid between Tg and Tm and so, it was expected, a better glass former; a typical value of 0.66 had been proposed [baird2010 C1, R29].

Findings

F5, F12.

Related concepts

depends on glass transition temperature; related to Tm − Tg temperature gap; proposed predictor of glass-forming ability; contrasts with melt viscosity as a predictor.

Formulas

reduced glass transition temperature.

How it is measured or obtained

From DSC Tg (midpoint) and melting peak [baird2010 P1]; where Tg cannot be measured, Tg is estimated from a Trg–molecular-weight fit or a fixed Tg/Tm ratio [baird2010 E27; vaneerdenbrugh2010a E7].

Values in the library
materialvalue or classconditionspaper ids
class I (23 molecules)0.69 ± 0.02DSC[baird2010 R14]
class III (17 molecules)0.73 ± 0.04, not significantly different from class IDSC[baird2010 R14]
classes II and III0.65–0.76 and 0.65–0.81DSC[baird2010 F5]
ritonavir0.81DSC[baird2010 R18.ab]
class II compounds0.65–0.76, not the constant 2/3DSC[baird2012 R14]
pretomanid; delamanid0.67; 0.64, both class IDSCnguyen2023a C59
35 compoundsT_{rg} = 0.00021\,\mathrm{MW} + 0.64433,\quad R^2 = 0.44regression[baird2010 E27, R19]
Pitfalls and disagreements

Trg did not separate the classes, nor class I-A from I-B [baird2010 C23, C37], and compounds with similar Tm − Tg had very different tendencies [baird2012 C36]. Trg of the 16 class I molecules without measured Tg is a function of molecular weight alone [baird2010 X17]. A small Tm − Tg (high Trg) did go with slow growth [trasi2014a R8.h].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

remixing of separated amorphous phases

The return of a phase-separated amorphous dispersion to one phase once the cause of separation (here sorbed water) is removed and molecular mobility is high enough; below Tg the separated phases stay apart because both are glassy marsac2010 C45, C46, C47.

Findings

F12, F14, F30.

Related concepts

reverse of amorphous-amorphous phase separation; blocked by kinetic trapping; depends on molecular mobility.

Formulas

the peak-height ratio of hydrogen-bonded NH bands is listed on the chapter page as table only.

How it is measured or obtained

Isothermal IR at 125 °C of a film separated at 94% RH, following the ratio of the drug–polymer (3290 cm⁻¹) to drug–drug (3345 cm⁻¹) NH bands against a never-exposed film; DSC heat–cool cycles to rising temperatures marsac2010 P13, E2, P12.

Values in the library
materialvalue or classconditionspaper ids
felodipine–PVP 50% film after 94% RHband ratio ≈0.70 (5 min) → ≈1.41 (1500 min) vs ≈1.47 never exposed125 °Cmarsac2010 R17
felodipine–PVP 46.5 wt% powderthermal event moves up with each DSC cycle; single Tg ≈80 °C on second scansDSC to 60–110 °Cmarsac2010 R15, R14
felodipine–PVP film at room temperatureno remixing after 1 week of drying0% RHmarsac2010 R8
celecoxib–PVP 6:4 after 94% RHtwo Tg events on first heating, one on reheating; remixing during the scan a "possible explanation"DSCxie2016b R18, C34
indomethacin–HPMC, 50–90% drugsingle Tg above the miscibility limit, which remixing during heating "might" explainDSC[tian2016 C31]
miconazole–PVPVA 50:50 powderone Tg after 60 min at 100 °CDSC[saboo2017 R22]

Evidence table: remixing of separated amorphous phases.

Pitfalls and disagreements

Remixing was still incomplete after 25 h, and the extrapolated 39 h has no stated method; a straight extension of the last points gives about 2.5–3 days marsac2010 X8.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

resistance-in-series permeability model

The overall resistance of a membrane module as the sum of inner boundary layer, membrane and outer boundary layer, 1/K_{in} = 1/k_{in} + 1/k_m + 1/k_{out} [hate2017 E3]. In a PAMPA cell the same sum has two unstirred water layers and the lipid membrane, 1/P_{eff} = 1/P_{UWL} + 1/P_m + 1/P_{UWL} hate2022 E1, C10.

Findings

F13, F21.

Related concepts

part of the membrane mass transfer coefficient.

Formulas

resistances-in-series model.

How it is measured or obtained

The three coefficients were not given; only K_in was fitted [hate2017 E3, R12].

Values in the library
materialvalue or classconditionspaper ids
nevirapine, hollow fibreK_in (9.07 ± 1.06) × 10⁻⁵ cm/s2 mL/min[hate2017 R12]
atazanavir, nifedipine, PAMPAtransport limited by the unstirred layer (high P_m, low P_{UWL})log P about 4.5 for atazanavirhate2022 C44, C32
Pitfalls and disagreements

Inputs k_in, k_m and k_out not given [hate2017 E3].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

segregative phase separation

Evidence table: segregative phase separation. Content from the release-mechanism chapter (2023–2025).

Phase separation in which drug and polymer go to different phases: an insoluble phase rich in drug and poor in polymer, with the polymer in the aqueous phase; the contrast is associative separation, in which both enrich the insoluble phase (terms cited from polymer solution work) deac2023b C47. MePHPH–PVPVA separates segregatively, and in the conclusions MeTIPP is grouped with it deac2023b C47. In dissolving MePHPH–PVPVA gels the separation of the two dyes "indicates" segregative separation into a hydrophobic and a hydrophilic phase deac2023a C25. Segregative separation gives negatively sloped tie lines with the plait point on the high-drug side of the diagram and a higher maximum limit of congruency deac2023b C48; deac2023a C69. Measured in 2024: in MePHPH–PVPVA–water the drug-rich phase held 82.9–94.1 wt% drug and its PVPVA fell from about 13.7 to 2.5 wt% as total water rose, with tie lines sloping down deac2024b R15, R17, C18, C19; clotrimazole–PVP separated segregatively into a drug-rich phase of about 83–84 wt% drug and a water-rich phase of about 39–41 wt% PVP, the same for two grades deac2024a R11, C28.

Findings

Release mechanism and LoC: F25, F27, F29, F30.

Related concepts

contrasts with associative phase separation; low polymer partitioning into the drug-rich phase; drawn on the ternary phase diagram with sloped tie lines and a critical point; a kind of amorphous-amorphous phase separation.

Formulas

drug-rich phase composition.

How it is measured or obtained

Polymer content of drug-rich nanoparticles by depletion mass balance from aqueous-phase concentrations (¹H NMR or HPLC) deac2023b R2, R3; dye partitioning between the phases in confocal images of dissolving compacts deac2023a R6; drug content and Tg of the released hydrophobic phase deac2023a R12.

Values in the library
materialvalue or classconditionspaper ids
MePHPH nanoparticles with PVPVA0.5–7.5 wt% PVPVA37 °C, two preparation routesdeac2023b R2
MePHPH; MeTIPP nanoparticles≈5; ≈9 wt% PVPVA60 °C, NMRdeac2023b R3
hydrophobic phase released from 30% MePHPH–PVPVA98.8 wt% drug, Tg 16.8 °CHPLC, DSCdeac2023a R12
MePHPH; MeTIPP–PVPVAlimit 40; 30% (cited)deac2023b R8
MePHPH–PVPVA–water, 25–99 wt% waterPVPVA in the drug-rich phase ≈13.7 → 2.5 wt%equilibrated, NMR, 37 °Cdeac2024b R17
clotrimazole–PVP K12, K29/32, 40:60 with bufferdrug-rich phase ≈83–84 wt% drug; water-rich ≈39–41 wt% PVPNMR after 90 °C protocoldeac2024a R11
Pitfalls and disagreements

In the 2023 paper the tie-line slopes and plait-point positions are drawn on schematic diagrams; no ternary diagram was measured there deac2023b X14. TIPP was measured in pH 2.5 buffer and the others at pH 6.8 deac2023b R3.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

self-association

Association of a molecule with its own kind, by hydrogen bonds between drug molecules or between polymer molecules. In the papers of this chapter: the cyclic carboxylic acid dimers that hold most of amorphous indomethacin, as in the γ crystal, with a few chain ends [taylor1997 C20]; the NH-to-carbonyl bond between neighbouring felodipine molecules [kestur2010a R15]; the weak C–H···N chains of crystalline bifonazole [kestur2011 R18]; and the multiple intra-species hydrogen bonds of PAA, which can compete with a drug [rumondor2009a R24, C45]. A polymer is thought to slow crystallization when it breaks the self-association needed for attachment to the crystal, for example by taking the acid OH of indomethacin or by bonding the imidazole nitrogen of bifonazole, and PAA self-association "is easily disrupted" by a better acceptor [taylor1997 C43, C45; kestur2011 C16, C19]. Further cases: dextran–dextran hydrogen bonds, assumed to be stronger or more numerous than dextran–PVP ones [vaneerdenbrugh2012a C36, C37]; amide self-association in benzamide and phenacetin crystals, broken more often by a carboxylic acid partner than by a tertiary amide [vaneerdenbrugh2011a C34, C35]; hydrogen-bonded sheets of naringenin and quercetin with a strong lattice energy [wegiel2013a C26]; and Br···C contacts of 3.373 and 3.425 Å in the brotrimazole crystal, which may compete with the polymer que2020 R5, C27. The bile-salt simulations of 2016 add a solution aspect, the tendency of a bile salt to contact itself instead of the drug: SUDC paired with itself during 73% of the trajectory of a nevirapine–SUDC tetramer and SDC during 5%, which the authors say "may indicate a lower tendency to interact with a nevirapine nucleus" for SUDC [li2016a R26, C60].

Findings

Miscibility and drug-polymer interactions: F1, F13, F14, F17, F20, F22, F24, F25. Crystallization from solution: F2, F30. Physical stability: F18, F24, F30.

Related concepts

part of hydrogen bonding; contrasts with drug-polymer interactions; related to intramolecular hydrogen bonding and binding constant; related to bile salt micelles and polymer self-association; competes with hydrogen-bond donor and acceptor groups; related to molecular recognition.

Formulas

none.

How it is measured or obtained

By IR and Raman of the amorphous drug against the crystal, with the dimer found by the mutual exclusion rule [taylor1997 C14, C15]; by the felodipine NH and carbonyl bands (3341 cm⁻¹, 1701 and 1682 cm⁻¹) [kestur2010a R10, R15]; from crystal structures [kestur2011 R18, R19]. In solution, by cluster analysis of 100 ns molecular-dynamics runs (molecules within 3.0 Å form one cluster) [li2016a P9, P10].

Values in the library
materialvalue or classconditionspaper ids
amorphous indomethacinacid dimers (IR 1710 cm⁻¹, no Raman band); chain-end shoulder 1735 cm⁻¹quench-cooled melt[taylor1997 R5.g, R5.h, R6, C20]
α-indomethacinacid bands in both IR and Raman, read as chainspolymorph reference[taylor1997 R5.e, R5.f, C16, C17]
amorphous felodipineNH 3341 cm⁻¹ bonded to a neighbouring carbonyl; carbonyls 1701 and 1682 cm⁻¹spin-coated film[kestur2010a R9.a, R10, R15]
bifonazoleweak C–H···N chains along the b axis; no traditional donorcrystal structure[kestur2011 R18]
PAAdimers and other self-associations, easily disruptedcited[kestur2011 R22]
felodipine–PAAPAA self-association "speculated" to limit mixing at 30–70% PAADSC, IR, PXRD[rumondor2009a C45, R24]
resveratrol, ledipasvir, itraconazole (other chapters)disrupting self-assembly by a polymer thought critical; drug–drug interactions seen by NMR; ITZ aggregates by fluorescencevarious[wegiel2013b C5; que2019 C23; mugheirbi2017 C31]
dextran–PVPdextran–dextran bonds assumed stronger or more numerous than dextran–PVP; OH band 3356–3358 → 3370–3383 cm⁻¹ with more PVPFTIR, DEX1–PVP12[vaneerdenbrugh2012a C36, C37, R16]
carboxylic acid drugs; benzamide, phenacetinacid dimers in crystals; amide–amide only 100 and 94% alone, 0% with COOHcrystal structures, CSD[vaneerdenbrugh2011a R7, R14]
naringenin, quercetinhydrogen-bonded sheets; two and three free OH after intramolecular bondsstructure[wegiel2013a C26, C30]
brotrimazoleBr···C 3.373 and 3.425 Å inside the 3.55 Å van der Waals sum150 K crystalque2020 R5, C29
SUDC-SUDC; SDC-SDC in NVP tetramerscontact 73%; 5% of 2000 snapshotsMD, 310 K[li2016a R26]
NVP-SUDC; NVP-SDC tetramersone cluster in 86% of snapshots; mostly two or three clustersMD, 310 K[li2016a R24]
posaconazole, ionized, below pH 2.5solubility above the calculated values, "probably" self-associationphosphate buffers, 37 °C[duong2022b C13, C14]
PAA with flutamidePAA forms hydrogen-bonded dimers and "very likely" prefers itself; no IR shift with the drug1:1 films[trasi2012b R28, C37, R18]
resveratrolthree OH groups in an extended network with flip-flop bonding; high crystallization tendencycrystal structure, cited[wegiel2013b C27, C28]
curcumin with donor-and-acceptor polymerscellulosics "may" disrupt curcumin self-association better than acceptor-only PVPstorage[wegiel2014 C31]
celecoxib with PVP, PVPVAstrong drug–polymer hydrogen bonds "may restrict" diffusion and self-associationargument from IRxie2016b C44
indomethacin in HPMC from 60% drug1709 cm⁻¹ acid-dimer band returns; an emission band near 480 nm "could be due to" dimersIR; fluorescence[tian2016 R10, C27, C46]

Evidence table: self-association.

Pitfalls and disagreements

The 1735 cm⁻¹ chain-end assignment rests on analogy with liquid acetic acid and α-indomethacin, and the evidence for dimers is the absence of a Raman band [taylor1997 K2, X4]. The α chain model depends on unpublished unit-cell data [taylor1997 X10]. PAA self-association is cited from the literature and was not measured in the felodipine dispersions [rumondor2009a C39, R24]. For bifonazole the statement that the imidazole nitrogen breaks PAA dimers is reasoning, not measurement [kestur2011 X9, C16]. The bile-salt simulations used one trajectory per system, nevirapine only, tetramers for SDC and SUDC only [li2016a X24]. In the physical-stability papers self-association in the dispersions was not measured either; the readings come from crystal structures, cited data and missing IR shifts [trasi2012b R28; wegiel2014 X7].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

single-Tg miscibility criterion

The rule of thumb that a single glass transition, lying between those of the components, shows one amorphous phase, and more than one Tg more than one phase; DSC is called the "golden standard" [rumondor2009a C5]. Taylor and Zografi used a single Tg reported earlier for indomethacin–PVP as support of one phase [taylor1997 C39, R17]. The criterion is not infallible and gives no information on the thermodynamics of mixing [marsac2009 C2]. In the dextran–PVP blends one Tg after heating to 200–250 °C was read as miscible and two as phase separated, and the verdict agreed with the FTIR bonding trend [vaneerdenbrugh2012a P3, C13]. The criterion failed for itraconazole–HPMC, where powders gave one broad Tg at every loading while films held itraconazole-rich domains, and the authors explain the single Tg by mixing during the scan [purohit2015a C36, C39]; it cannot readily resolve telaprevir and PVPVA, whose Tg differ by about 5 °C [li2016c C26, M1, M4].

Findings

F3, F4, F18, F19, F22.

Related concepts

measures drug-polymer miscibility; depends on glass transition temperature; contrasts with the structure-sensitive IR and PXRD methods of drug-polymer interactions.

Formulas

Couchman-Karasz equation.

How it is measured or obtained

By DSC on dry ground powders at 20 °C/min, cycled, with the midpoint Tg compared with the Couchman–Karasz prediction [rumondor2009a P2, P10, E1].

Values in the library
materialvalue or classconditionspaper ids
ketoconazole–PVPone Tg at every composition, ≈7–10 °C below Couchman–Karasz at 10–30% PVP0–100% PVP, 20 °C/min[rumondor2009a R3, R4, X9]
felodipine–PAAtwo Tgs at 10 and 30% PAA in both regimens; single Tgs 121/86 and 114/84 °C at 70 and 90% PAAtwo heating regimens[rumondor2009a R1]
felodipine–PVP, nifedipine–PVPone Tg in earlier studiescited[rumondor2009a R5]
itraconazole–HPMC (other chapter)one broad Tg (87 °C) although fluorescence found phase separationmDSC[purohit2017a R3, C26]
itraconazole–HPMC 10:90 to 50:50, powdersone Tg per composition, first-run midpoint 131 → 77 °C, step width 11–25 °C; second run 115 → 64 °C, width 6–16 °CmDSC 2 °C/min, hold 2 min at 170 °C[purohit2015a R7, C25, C26]
dextran–PVP, 20 pairsnone of the maltodextrin pairs phase separated; DEX450–PVP90 phase separated at all nine compositionsDSC 10 °C/min to 200–250 °C, second heating[vaneerdenbrugh2012a R13]
telaprevir 102.7, PVPVA 108, HPMCAS 122, HPMC 140 °CTg of the pure components; no blend run by DSCDSC midpoint, 20 °C/min[li2016c M1, M2, M3, M4, X8]

Evidence table: single-Tg miscibility criterion.

Pitfalls and disagreements

Domains smaller than 15–30 nm may give one Tg; heating during the scan can change miscibility; a single Tg above the lowest component Tg may not show the number of phases at room temperature [rumondor2009a C6, R25]. Ketoconazole–PVP shows one Tg while PXRD suggests partial miscibility; the authors offer heating-driven mixing or poor detection [rumondor2009a C42]. Which of the three DSC cycles is reported, the sample mass and the number of replicates are not stated, and each Tg is a single determination [rumondor2009a X10]. The agreement with Couchman–Karasz is called "reasonable" but is approximate [rumondor2009a X9]. The first scan changes the sample: the itraconazole–HPMC step narrows and its midpoint falls by 13–26 °C on reheating, an effect the paper reports but does not explain [purohit2015a R7, X14]. A pair classed miscible by DSC showed domains of about 0.3–0.6 µm in films (DEX6–PVP90) vaneerdenbrugh2012c R16.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

sink conditions

Two senses occur

In membrane cells the receiver stays far below saturation so that it does not slow transport; in dissolution the medium can dissolve the whole dose (sink index above 1) [raina2014a C20; purohit2018 E1]. A receiver can be made a sink for a lipophilic weak base by solubilizing it, with 2% SDS or at pH 3, which raised PAMPA mass flow by partitioning rather than by micelles as such hate2022 C30, C52. In diffusion cells it is the condition under which the flux depends only on the donor activity; in the danazol cell the receiver stayed below 0.3 µg/mL [jackson2016 P9, C9]. New aspect (Mesoporous silica): in the silica papers "sink" also means a total dose diluted to about the crystalline solubility, a test of whether drug held by the silica comes out when nothing in solution holds it back; release still stopped at 60–65% [dening2018 P7, R18, C27, X7]. In desorption tests, adsorbed drug was diluted to "33% of the crystalline saturated solubility" [mccarthy2020 P8]. In the diffusion cell, sink means receiver concentrations below the crystalline solubility [dening2018 C12, R11].

Findings

Bioperformance: F2, F5, F13, F16, F21, F22. Crystallization from solution: F22, F31. Mesoporous silica: F8, F9, F14.

Related concepts

contrasts with non-sink dissolution; quantified by sink index; condition for membrane flux, absorptive sink (a membrane sink during dissolution), membrane asymmetry (a solubilizing receiver); reveals the partly irreversible part of the dynamic adsorption-desorption equilibrium; provided during release by absorptive dissolution testing.

Formulas

sink index, membrane flux from concentration difference, membrane flux in terms of solute activity.

How it is measured or obtained

Receiver concentration kept under one third of the crystalline solubility [raina2014a P8; raina2015c P7]; fresh receiver buffer flow [indulkar2016 P5; hate2017 P4]; sink index from solubility, volume and dose [purohit2018 R4]. Receiver with SDS at, below and above its CMC, or at pH 3 hate2022 R7, R13, R15; the sink effect is said to be available at 0.15% SDS, above the CMC of 0.05% hate2022 R13, X6. Receiver concentration followed with a UV dip probe and checked to stay far below the donor [jackson2016 P9]. Sequential dilution with fresh buffer every 30 min until the theoretical supersaturation reaches 1 [dening2018 P7]; dilution of an equilibrated suspension for 24 h [mccarthy2020 P8]; an absorptive receiver after a pH shift [hate2020b P8].

Values in the library
materialvalue or classconditionspaper ids
felodipine, 25 °Creceiver about 0.024–0.155 µg/mL at 60 minunder one third of crystalline solubility[raina2014a R10, C20]
tacrolimus, 900 / 450 / 100 / 40 mLSI amorphous 9 / 4.5 / 1 / 0.4USP medium I[purohit2018 R4]
tacrolimus40 mL non-sink relative to the amorphous solubility; 100 mL needed for exact sink5 mg dose[trasi2016 C29]
telaprevir, bile saltsreceiver always under one half of crystalline solubilitydiffusion runs[lu2017b R25, C11]
atazanavir, PAMPAreceiver with 2% SDS or pH 3 raised mass flow from about 0.65 to about 2 µg/min at 20 µg/mL and from about 3.2 to 8.6–9.0 at 1000 µg/mLlipid-impregnated hydrophobic PVDFhate2022 R15, C30
tacrolimus 5 mg in 240 / 100 / 40 mLsink index against the amorphous solubility 2.4 / 1 / 0.4dose-to-volume[hate2019 R7]
danazol diffusion cellreceiver maximum below 0.3 µg/mLregenerated cellulose 6–8 kDa, 25 °C[jackson2016 P9]
four drugs in three mediareceiver sink assumed so that flux tracks donor activityside-by-side cell, 37 °C[indulkar2018 C9, E2]
ritonavir–SBA-15, diluted to S about 1release about 40 → 60–66%; 2.1 µg/mL against 3.6 µg/mL crystalline solubility50 mL, 180 min[dening2018 R18]
indomethacin; methyl ester on SBA-15, diluted to sink73%; 57% desorbed; 0.98; 4.16 mg/g left24 h, pH 2.2[mccarthy2020 R13]
ritonavir diffusion cellreceiver linear (R² > 0.99) and below the crystalline solubility30–120 min[dening2018 R11]
ketoconazole–SBA-15 with absorptive sinkabout 54–60.5% → 69.5% over 4 hpH 1 → 6.8[hate2020b R17]
Pitfalls and disagreements

"Sink" is relative to the crystalline or the amorphous solubility; a medium can be a sink for one and not the other [purohit2018 C20]. About 20% of the dose stayed in the hollow-fibre module [hate2017 X12]. A solubilizing receiver also changes membrane partitioning, so the same donor gives a different mass flow with and without it (F22) hate2022 C52, C53. The flux estimate also assumes a constant donor concentration [jackson2016 C9]. Mesoporous silica: "drug release was always incomplete, even under sink conditions" refers to a total dose equal to the crystalline solubility, not to excess dissolution capacity [dening2018 C2, X7], which differs from the dissolution sense above (a medium that can dissolve the whole dose). The supersaturation assigned to the last dilution samples is uncertain [dening2018 X6].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

sink index

SI = C_s V/\text{dose}: solubility times medium volume over dose; above 1 the medium can dissolve the dose [purohit2018 E1].

Findings

F16, F17, F28, F31.

Related concepts

quantifies sink conditions and non-sink dissolution.

Formulas

sink index.

How it is measured or obtained

Computed from measured crystalline solubility and cited amorphous solubility [purohit2018 P9, R4].

Values in the library
materialvalue or classconditionspaper ids
tacrolimus, medium I, 900 / 450 / 100 / 40 mLSI crystalline 0.32 / 0.16 / 0.04 / 0.01; SI amorphous 9 / 4.5 / 1 / 0.45 mg[purohit2018 R4]
tacrolimus, medium II 900 mLSI crystalline 2.6814.9 µg/mL[purohit2018 R4]
tacrolimus 5 mg in 240 / 100 / 40 mLSI against the amorphous solubility 2.4 / 1 / 0.4absorptive hollow-fibre test[hate2019 E1, R7]
Pitfalls and disagreements

The amorphous solubility is cited and approximate [purohit2018 R4]. A crystalline fraction does not dissolve unless the sink index against the crystalline solubility is at least 1, which none of the three volumes reached (synthesis: 2.5 µg/mL × 240 mL / 5 mg = 0.12 at most) [hate2019 C32, R7].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

solubility parameter

The square root of the cohesive energy density, \delta = \sqrt{\sum_i \Delta e_i / \sum_i \Delta v_i} = \sqrt{\Delta E_v / V} in MPa^1/2, estimated by the Fedors group-contribution method from the structural formula alone; a lower value means a more hydrophobic compound, and water is 49.01 MPa^1/2 [ilevbare2012c E1; ilevbare2013c E5, P1]. In these papers it is the scale on which a polymer's hydrophobicity is compared with the drug's [ilevbare2013c C37, C3]. Fedors SP of the telaprevir polymers: effective acids 22.46–23.18 MPa^1/2, CAP-Seb-024 23.04 (fails), A5a 25.54 (works), A5b 24.29 (fails); no correlation across the chemically diverse set [mosqueragiraldo2016 M12–M14, M24, M25, C25].

Findings

F8, F13, F17, F25, F36.

Related concepts

measures polymer hydrophobicity; related to lipophilicity and degree of substitution.

Formulas

Fedors group-contribution solubility parameter.

How it is measured or obtained

Calculated, not measured: group contributions at 25 °C (Fedors 1974, outside the library) are summed over the repeat unit; for glassy polymers (Tg above 25 °C) an extra molar volume of 4n (n < 3) or 2n (n ≥ 3) is added, n being the number of main-chain atoms in the repeat unit [ilevbare2012c E2, E3, P11]. No uncertainty is stated.

Values in the library
materialvalue or classconditionspaper ids
ritonavir; efavirenz; celecoxib20.03; 21.89; 23.38 MPa^1/2 (Log P 5.6, 4.7, 3.5)Fedors[ilevbare2013c M1–M3; ilevbare2013b M1–M3]
14 new cellulose esters19.62 (CAB Seb) to 23.28 (CP Adp)Fedors with correction[ilevbare2012c R10, M23–M36]
CAB Adp 0.25; CAP Adp 0.33; CAB Adp 0.81; CAP Adp 0.8520.05; 20.56; 20.86; 21.27Fedors[ilevbare2013c R10]
CA 320S Seb; HPMCAS; CAPh; CA 320S Sub; HPMC; CA 320S Adp; CMCAB; CP Adp22.36; 22.44; 22.48; 22.62; 22.68; 22.95; 23.18; 23.28Fedors[ilevbare2013c R10]
Pn-IPAAmd; PAlAmn22.64; 20.70Fedors[ilevbare2013c R10]
PVPVA; PAA; HPC; PVP; PVPdn-O25.77; 25.92; 25.98; 28.39; 32.24Fedors[ilevbare2013c R10]
effective polymers, mean SP20.87 (ritonavir); 21.73 (efavirenz); 24.28 (celecoxib)induction time[ilevbare2013c R13]
CAP-Adp-085, CA-Sub-090, CAP-Seb-02422.46, 23.18, 23.04Fedors, no ionization[mosqueragiraldo2016 M12–M14]
A5a, A5b, ECA, ECB, ECC, ECD25.5, 24.3, 19.9, 22.2, 22.0, 21.4 MPa^1/2 (neutral structures)Fedors method[mosqueragiraldo2018a R6, P12]
Pitfalls and disagreements

The SP values of the commercial and synthetic polymers are not printed in the 2012 paper, so the 20.56–25.98 range and the "similar hydrophobicity" of synthetic polymers cannot be checked there [ilevbare2012c X11]. The mean SP of the effective polymers in Table 6 is over every polymer in each SP window including those coded ineffective [ilevbare2013c X3]. The 2013 growth paper prints the failing range as SP "greater than 20.56", the reverse of its own convention [ilevbare2013b X2]. SP did not predict PVPVA and PVP on ritonavir, PAA, or Pn-IPAAmd [ilevbare2013c X11]. The A5a/A5b difference of 1.25 exceeds the 0.72 spread of the effective acids [mosqueragiraldo2016 X8].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

solubility-permeability interplay

The loss of membrane transport that accompanies a rise of apparent solubility when the rise comes from a solubilizer that lowers the free drug and its activity, in contrast to supersaturation from an amorphous formulation, which raises apparent solubility without lowering permeability [indulkar2017a C1, C2; lu2017b C4]. The same total concentration therefore gives a lower flux in micellar solution than in buffer (F16).

Findings

F16, F17.

Related concepts

consequence of micellar solubilization; read on the activity scale as thermodynamic activity and activity-based supersaturation; measured by membrane flux.

Formulas

membrane flux in terms of solute activity.

How it is measured or obtained

Flux across a 6–8 kDa membrane against donor concentration in buffer and in the surfactant or bile-salt medium, and apparent permeability with the donor concentration taken as activity or as total concentration [indulkar2017a P7, P15; lu2017b P4].

Values in the library
materialvalue or classconditionspaper ids
atazanavir in 3.6 mg/mL SDSapparent permeability equal to buffer on an activity basis, 20-fold lower on a total basis (1/0.047 = 21, synthesis)pH 6.8, 37 °Cindulkar2017a R27, E12
telaprevir with 12 mM STDC, SGDCflux about half at a given concentration (0.43 against 0.83 µg/min at 90 µg/mL for STDC)50 mM pH 6.5, 37 °C[lu2017b R12, R6]
progesterone with cyclodextrins, surfactants, cosolvents (cited)apparent permeability fell with higher apparent solubility; an ASD did notcited workindulkar2017a R30
Pitfalls and disagreements

Permeability calculated from total concentration is "implausible" because it is a property of the molecule for a given membrane, and permeability models that assume a constant micelle–drug association (the reciprocal permeability approach) "must be used with caution" if Km/w depends on concentration indulkar2017a C58, C59. The authors argue, without in vivo or permeation data for such formulations, that surfactant-containing ASDs ranked by dissolution may mislead indulkar2017a C57.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

solution crystallization

Nucleation and growth of crystals from the supersaturated solution, as against crystallization inside the undissolved ASD (matrix crystallization) [elkhabaz2017 C38; mosqueragiraldo2018b C52]. Crystallization from solution decided the enzalutamide-PVPVA dispersions (fall after the maximum) and the pretomanid case, in which droplets present above the amorphous solubility defeated HPMCAS-HF within minutes [wilson2018 C18, C42; nguyen2023a C13]. New aspect (Supersaturation from ASD dissolution): crystals nucleate and grow in the supersaturated liquid after the amorphous solid has dissolved, the second route by which an amorphous solid loses its advantage [alonzo2010 C47]. Polymer in a dispersion can move crystallization from the matrix to this route (nifedipine) [raina2014b C21]. When dispersions release completely, the authors of a celecoxib study take matrix crystallization as suppressed and attribute the differences between polymers to crystallization from solution, which the induction time measures [xie2015 C39, C40].

Findings

Bioperformance: F9, F10, F11, F12, F14, F23, F27. Supersaturation from ASD dissolution: F1, F3, F4, F6, F14, F21, F24.

Related concepts

part of desupersaturation; contrasts with matrix crystallization; related to crystal growth and crystallization tendency; part of crystallization during dissolution; measured by nucleation induction time.

Formulas

supersaturation ratio, classical nucleation theory.

How it is measured or obtained

Fall of concentration with SHG, PLM or PXRD for the crystals; induction time by UV extinction [elkhabaz2017 P5, P8, P9, P10; hate2017 P2]. In the ASD dissolution papers: by a fall of the solution concentration together with crystals seen in the liquid rather than in the solid: needles between amorphous particles under polarized light [alonzo2010 R19], fine plate-shaped crystals in the solution around dissolving dispersion particles [raina2014b R13], free-floating needles in suspensions chen2015a R15, or a rise of a pyrene ratio as crystals expel the probe jackson2015 C14.

Values in the library
materialvalue or classconditionspaper ids
ezetimibe, buffer 21 µg/mLinduction about 1 min; PVP 100 µg/mL about 71 min; HPMC-AS about 50 min37 °C[elkhabaz2017 R6]
ezetimibe, FeSSIF 123 µg/mLHPMC-AS 50 µg/mL more than 360 min; PVP about 10 min37 °C[elkhabaz2017 R7]
nevirapine 500 µg/mLabout 5 min; PVPVA about 60 min; HPMC-AS over 4 hpH 6.5[hate2017 R2]
telaprevir 90% PVPVA ASDbelow 90 µg/mL from about 43 min; about 20 µg/mL at 100 minmosqueragiraldo2018b R5
atazanavir 50:50 PVPVA ASDcrystals from about 80 minhollow fibrehate2018 R14
indomethacin–Eudragit EPO ASDcrystallization after 15–20 min; small α crystals within about 20 minacid stage, pH 2.2, 37 °C[xie2017 R11, R23]
celecoxib, no polymer or PAAwithin 5 min at 22 µg/mL; ≈3.6 µg/mL at 1 hpH 6.8, 37 °Cxie2016a R2, R3
enzalutamide 70 µg/mLcrystallized in about 15 min without polymer; held more than 16 h by four of 24 polymers added at 50 µg/mLpH 6.5wilson2020 R1, C32
pretomanid 80 µg/mL1.6–3.1 min with most enteric polymers, 22–24 min with HPMCAS-MF or HPMC, over 1000 min with HPMCAS-HF100 µg/mL polymer, pH 6.5nguyen2023a R5
amorphous indomethacinneedles in the liquid within 60 min, solid amorphous ≥4 h; ≈14.9 → ≈2.7 µg/mLpH 2, 25 °C[alonzo2010 R19, R11, R7]
nifedipine 50:50 dispersionscrystals below 2 µm in solution against 1–300 µm by the matrix routepH 6.8[raina2014b R13, R2]
danazol dispersions PVP / HPMC / HPMCASinduction ≈56–70 / ≈188–200 / ≈284–319 minpH 6.8, 25 °Cjackson2015 R5
celecoxib–HPMCAS suspension with SDS; polysorbate 80free needles at 0.5 h; 1 hpH 3, 25 °Cchen2015a R14, R15
celecoxib–PVP-K12 50% dispersiondesupersaturation about 2 h after complete releasepH 6.8, 37 °C[xie2015 C20]
tacrolimus 50 µg/mLonset within 3 h; 6–8 h with HPMCpH 4.5, 37 °C[trasi2016 R9]
delamanid salt dispersions in acidconcentration did not generally fall during the acid stage, and 1 mg/mL predissolved PVPVA left release after a pH 3.0 stage unchangedpH 1.6–5.0, 37 °C[nguyen2023c R23, R22]
Pitfalls and disagreements

In the telaprevir and nevirapine solutions crystallization is inferred from concentration, without solid-state analysis [mosqueragiraldo2018b X13; hate2017 C42]. Crystallization of the enzalutamide-PVPVA solutions is inferred from concentration, without a solid-state analysis [wilson2018 X12]. For felodipine with dissolved polymers this route was named dominant without monitoring the solid in the vessel [alonzo2010 X7]. In the felodipine solvent-shift tests of 2008 no precipitate was examined [konno2008a X4]. The danazol crystallization is inferred from UV and pyrene, without solid-state identification jackson2015 C14. Complete release was taken to exclude matrix crystallization although the HPMC-containing celecoxib dispersions neither released fully nor were checked [xie2015 X3]. Where the medium is subsaturated, as in the gastric stage of an enteric dispersion, the solution route is excluded and crystals must have formed in the wetted solid [elkhabaz2019a C34; nguyen2023c C39].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

solution-mediated phase transformation

Evidence table: solution-mediated phase transformation. Content from the ASD dissolution chapter (papers of 2010 and 2014) and two papers of the solid-state chapters.

Conversion of a metastable solid into a more stable one through the solution, in three stages: the metastable phase dissolves to a supersaturated solution, the new phase nucleates driven by that supersaturation, and its growth depletes the solution so that more metastable phase dissolves [raina2014b C34]. Alonzo and co-workers use the term for the loss of supersaturation by crystallization from solution after an amorphous solid dissolves [alonzo2010 C44]. When nucleation and growth are fast, dissolution controls the transformation [raina2014b C35].

Findings

F1, F3.

Related concepts

related to polymorphic transformation, solution crystallization and heterogeneous nucleation; contrasts with matrix crystallization.

Formulas

multivariate curve resolution bilinear model.

How it is measured or obtained

In situ Raman of slurries resolved into the fractions of each form (MCR) [raina2014b P10]; solution concentration with crystals seen in the liquid [alonzo2010 R19]; elsewhere by solid-form analysis after slurrying [lu2016 R23].

Values in the library
materialvalue or classconditionspaper ids
nifedipine γ → α, glass in bufferγ half-life about 20 min; α complete at ≈40 min (25 °C), 30 min (37 °C)pH 6.8 slurry[raina2014b R7, R6, R8]
nifedipine γ → α, 1 mg/mL HPMCAS in bufferγ intact to ≈110 min, α complete at 145 min25 °C[raina2014b R9, R10]
nifedipine 50:50 dispersionsα complete at ≈5 min (PVP), ≈40 min (HPMC, HPMCAS)25 °C[raina2014b R12]
amorphous indomethacindominant route of supersaturation loss; needles in the liquidpH 2, 25 °C[alonzo2010 C44, R19]
vemurafenib β → α (Crystallization tendency)solvent-mediated conversion at room temperature, data not shownslurry[lu2016 R23]
hollow organic crystals (Solid-state methods)reported cases arise from solvent-mediated phase transformationliterature[correasoto2017 C39]
Pitfalls and disagreements

Whether a polymer slows the transformation by blocking nucleation of the new phase on the parent crystal, nucleation from solution or growth was not separated; the nucleation reading rests on curve shapes [raina2014b C31, C32, X11]. The faster conversion in dispersions is attributed to faster dissolution and higher supersaturation, neither measured in the slurries [raina2014b C33, X10].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

solvent-induced phase separation

Kinetic phase separation of a drug–polymer system caused by the changing solvent composition as the solvent leaves, even where the dry components would mix; the system crosses a miscibility gap during drying and the dry glass traps the result [mugheirbi2017 C3, C41]. In mixed solvents of different volatility and solvency the drug may exceed its miscibility limit when the better solvent leaves first [purohit2015a C45]. Moisture-induced separation is treated as a case in which the polymer prefers water and the drug does not purohit2015b C24; purohit2017b C44. In a spray droplet of ritonavir, PVPVA, methanol and water the faster loss of methanol raises the water fraction (15 → about 26% for a 15:85 feed) and the path crosses the two-phase region; a feed with 60% water had already separated before spraying li2020 C49, R21, R13.

Findings

F1, F2, F3, F5, F20, F21.

Related concepts

includes moisture-induced phase separation; ends in kinetic trapping; related to polymer aggregation in solution.

Formulas

Raoult's law.

How it is measured or obtained

By comparing films or particles made from different solvent compositions, humidities and water contents, and by following the evaporating solution (fluorescence, DLS, TEM), the evaporation of the pure solvent mixture (TGA) and the polymer in drug-free solution (DLS) [mugheirbi2017 P6, P15; mugheirbi2018 P5, P12, P13].

Values in the library
materialvalue or classconditionspaper ids
ITZ alone in DCM–MeOHturbid by 120 min; DLS radius 168 ± 5 nmevaporating solution[mugheirbi2017 R19, R20]
ITZ–HPMC spray driedhomogeneous from dry solvents; domains with 1–12% water in methanolBüchi B-290[mugheirbi2017 P3, R26, R27]
ITZ–HPMC in five alcohol–DCM solventsMeOH, EtOH, IPA separate at 50% RH; PrOH, BuOH mixed at 50% RH and separate at 20% and 7% RHspin coated[mugheirbi2018 R1, R2, R4]
pure DCM:MeOH with 4% waterevaporation about 12 → 40 minTGA[mugheirbi2018 R9]
ritonavir–PVPVA spray-dried from methanol, 10:90, 60:40 water:methanol25% DL surface RTV by XPS 21% / 43% / 70%; aged DSC second phase at 50% DL from 10:90; pyrene ratio lower for 60:40BLD-35 dryer, 4% solidsli2020 R4, R6, R7
same pair, droplet modelthreshold about 12.5:87.5 at 25% DL; peak C/S about 2.4 and about 320 at 12.5:87.5 and 15:8530 µm dropletli2020 R17, R20
Pitfalls and disagreements

The composition path of the drying film was not measured; the azeotrope analysis ignores DCM and the solutes [mugheirbi2018 C35, X8]. Dried solvent at 20% RH reduced but did not remove the ITZ–HPMC domains [mugheirbi2017 X21]. The model keeps the 10:90 path single-phase although the powders show separation; its threshold "may move higher or lower" li2020 X12, C51.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

specific surface area

The surface area of a powder per gram, here from nitrogen adsorption (BET) at 0.05–0.25 relative pressure moseson2022a E4; moseson2023 E1. Two uses in the ASD process papers: as the area that drives dissolution of drug crystals in a polymer melt (Noyes–Whitney), and as the area over which the oxide mass of a coating is spread to give a thickness label (see coating thickness from oxide content and specific surface area) [moseson2022c R1, C44; benson2025 X19].

Findings

F36, F39, F42.

Related concepts

drives crystal dissolution into a polymer melt; the denominator in the thickness of an atomic layer coating; related to surface roughness.

Formulas

coating thickness from oxide content and specific surface area.

How it is measured or obtained

Nitrogen adsorption isotherm, BET analysis, n = 3 for the bicalutamide lots [moseson2022c P5, R1]; for coated powders the BET area of the uncoated powder enters the thickness conversion benson2025 R1, E1. Surface area of cryomilled dispersions was ranked from SEM images and not measured moseson2022b X9.

Values in the library
materialvalue or classconditionspaper ids
bicalutamide lots L3 / L37 / L38 / L42 / L931.91 / 0.142 / 0.156 / 0.236 / 0.112 m²/g (D50 3.51 / 37.0 / 38.0 / 42.2 / 92.7 µm)BET[moseson2022c R1]
ritonavir–PVPVA, uncoated large and small fractions0.22–0.76 m²/gBETbenson2025 R1
ritonavir–PVPVA, 3.75% oxide at 0.56 m²/g22.3 nm (arithmetic on cited values)thickness conversionbenson2025 X19, R1
Pitfalls and disagreements

BET area did not rank the bicalutamide lots by amorphization time: L42 had the highest BET area of the recrystallized lots and was the slowest of the three lots of 37–42 µm, and the authors conclude that D50 and surface area alone are not indicative of the dissolution rate [moseson2022c R1, R10, C44]. Surface area explains the extrusion route only partly because the small ground fraction still exceeded the extrudate moseson2022b C52. Thickness labels from a mass balance are not comparable between size fractions of one powder, and the inner surfaces of hollow spray-dried particles may not be reached by the coating benson2025 R1, E1; moseson2022a C40.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

spectral mixing

A local AFM-IR spectrum that contains bands of the neighbouring phase or of material below or beside the probed spot, so that both components appear in both phases even if the phases are fully separated: "some prudency is in order" [vaneerdenbrugh2012b C22]. It can occur through the film thickness or laterally below the spatial resolution [li2016c C14]. New aspects (Miscibility and drug-polymer interactions): In AFM-IR the volume probed is larger than the domain, laterally or through the film thickness, which explains why bands of both drug and polymer appear in both the dispersed and the continuous phase of telaprevir films ("can be caused either" by partial miscibility or by spectral mixing), why the dispersed-phase spectra look richer in drug at higher loading ("a more likely explanation" than a trapped composition), and why the spectra of the two phases of a 50:50 telaprevir–HPMCAS film coincide [li2016c C14, C21, C46, R11]. The same caveat is stated for earlier AFM-IR work: "some spectral mixing … cannot be excluded, even for a completely phase-separated system" [vaneerdenbrugh2012b C22]. In dextran–PVP blends spectra near a phase boundary were intermediate, and spectral mixing is named among the reasons why the phases of DEX6–PVP90 could not be told apart chemically vaneerdenbrugh2012c C23, C38.

Findings

Solid-state methods: F12, F13, F14, F15. Miscibility and drug-polymer interactions: F19.

Related concepts

degrades spatial resolution; depends on photothermal expansion; related to drug-polymer miscibility; limits the reading of amorphous-amorphous phase separation; depends on phase-separated domain size; contrasts with kinetic trapping as an explanation of changing phase spectra.

Formulas

none.

How it is measured or obtained

Seen as intermediate spectra at phase boundaries, as identical spectra from different positions and as composition trends that depend on domain size [vaneerdenbrugh2012c R15, R20; li2016c C21]. Not separated experimentally from partial miscibility in any paper of the chapter [vaneerdenbrugh2012b C20, C22]. It is not measured. It is inferred from the size of the domains against the resolution of the method (typical AFM-IR resolution about 100 nm, best about 20 nm, integrating absorption through film thickness) and from spectra that vary with position or loading; ratio images and band ratios reduce the thickness effect [li2016c R24, C12, C22, C50].

Values in the library
materialvalue or classconditionspaper ids
DEX450–PVP12boundary spectrum intermediate between domain and matrix spectrasingle positionsvaneerdenbrugh2012c R15, C23
DEX6–PVP90six spectra alike, pattern of pure PVP90domains 0.3–0.6 µmvaneerdenbrugh2012c R20, C38, R19
felodipine–PAA 50:50other component's bands in both phasesfour spectra per phase[vaneerdenbrugh2012b R9, R10, C20]
telaprevir dispersionsapparent drug enrichment of the dispersed phase with loading judged more likely spectral mixingAFM-IR[li2016c C21]
telaprevir–HPMC 60:40, HPMCAS 80:20, PVPVA 50:50bands of both components in both phaseslocal AFM-IR, 4–5 points per phase[li2016c R8, R9, R10, C14]
telaprevir–HPMCAS 50:50spectra of the two phases identical; IR imaging faileddomains 122 × 13 nm, gaps 21–25 nm[li2016c R7, R11, C46]
telaprevir dispersed-phase spectradrug band grows relative to polymer bands as loading risesHPMC 2:8 → 5:5, HPMCAS 5:5 → 8:2, PVPVA 1:9 → 5:5[li2016c R12, C21]
Pitfalls and disagreements

The stronger absorber (PVP against dextran) dominates mixed spectra; a strong PVP band in a dextran-rich spectrum does not show much PVP vaneerdenbrugh2012c R6, C16. The explanation was not tested: domain thickness and the composition of either phase were not measured, so spectral mixing and a kinetically trapped composition are not separated [li2016c X10]. A band in both phases cannot by itself give a phase composition, only a ranking of which phase is richer [li2016c C14, X3].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

spinodal decomposition

Spontaneous demixing of a solution beyond the spinodal curve, with no nucleation barrier; between the binodal and the spinodal a new liquid phase must nucleate, and the "metastable zone for LLPS" is the distance between them [ilevbare2013a C32, C34; jackson2016 C33]. The papers of 2017–2022 add that continual addition of the drug stock with extinction detection "might approach one of the spinodal decomposition points" for telaprevir [lu2017b C15]. New aspect (ASD process): in solvent-cast films it is described as spontaneous separation of a mixture without a nucleation barrier, giving an interconnected, network-like structure instead of discrete droplets [mugheirbi2017 C48]; network-like or worm-like textures are read as spinodal-like, discrete round domains as nucleation and growth [mugheirbi2018 C9, C45; purohit2017a C34]. New aspect (Release mechanism and LoC): in a hydrating dispersion water penetrates fast, so phase separation is "assumed" to occur mainly by spinodal decomposition where the hydration path crosses the spinodal; the authors state that the same conclusions hold for nucleation and growth from the metastable region deac2023b C33. In 2024 MePHPH–PVPVA films became co-continuous at every loading within 8–15 min at 100% RH and broke into droplets at 14–31 min, read as the signature of spinodal decomposition; the hydration path is taken to reach the spinodal deac2024b R18, C23, C48, E19.

Findings

Amorphous solubility and LLPS: F3, F4. ASD process: F5, F7. Release mechanism and LoC: F27, F30.

Related concepts

inside the binodal; mechanism of liquid-liquid phase separation. In films it contrasts with discrete-domain separation by nucleation and growth at the binodal; a mode of amorphous-amorphous phase separation. Along the hydration path on the ternary phase diagram; read with the lever rule and local equilibrium.

Formulas

binodal condition.

How it is measured or obtained

The spinodal temperature at each concentration is where the linear extrapolation of the reciprocal 90° scattering intensity against temperature reaches zero ilevbare2013a E13, P12. In the film papers (2017, 2018) it is not measured as a mechanism; it is inferred from FLOM and TEM morphology of the continuous phase [mugheirbi2017 R7, R8; mugheirbi2018 R1, R2].

Values in the library
materialvalue or classconditionspaper ids
ritonavirTsp about 17.6, 23.4, 25.2, 29.2 °C at about 58, 50, 46.5, 42.7 µg/mL; 4.5–7.7 K above TL-L (synthesis)scattering, 0.5 °C/minilevbare2013a R11
ITZ–HPMC E3 film, 40% RHinterconnected network of drug-rich and polymer-rich regions in the continuous phase; light HAADF regions about 2.9% N against 2.3%HAADF, EDX[mugheirbi2017 R7, R8, C48]
ITZ–HPMC from IPA–DCM above 30 °Cinhomogeneous fluorescence with spinodal-like microstructureFLOM[mugheirbi2018 R1, C9]
ritonavir–PVPVA filmsbinary and Span films may separate by spinodal decomposition, Tween 80 and SDS films by nucleation and growthcited from outsideyang2022b C55
phenolphthalein analogue–PVPVA–waterseparation assumed spinodal along the hydration pathargument onlydeac2023b C33
Pitfalls and disagreements

Binodal and spinodal exist for four concentrations between about 11 and 29 °C only; the authors read the small gap as a low energy barrier to LLPS ilevbare2013a X17, C31. In the film papers the time-resolved evolution of the structure was not followed ("may have occurred") [mugheirbi2017 C48]; network-like textures with PrOH and BuOH are read as solvent incompatibility with HPMC instead [mugheirbi2018 C45]. In the 2023 phenolphthalein-analogue paper the mode of separation was not observed; the conclusions are stated not to depend on it deac2023b C33.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

steric stabilization

Evidence table: steric stabilization. Content from the release-mechanism chapter (2022–2025), with rows from the Amorphous solubility and LLPS chapter.

Stabilization of droplets or particles against coalescence by repulsion between adsorbed layers of polymer or surfactant at their surfaces. For ritonavir droplets released from 30% ritonavir–PVPVA, Span 20 and Span 85 built into the dispersion "may" inhibit coalescence by steric repulsion indulkar2022 C50. In the Amorphous solubility and LLPS chapter HPMC adsorbed at the surface of ibuprofen-rich droplets is said to suppress coalescence by steric repulsion, as HPMC is reported to stabilize emulsions sterically, while uncharged PVPVA gave neither charge repulsion nor sufficient steric repulsion ueda2020b C51, C50. The 2024 PVP paper set it aside for clotrimazole droplets in the gel ("not the likely mechanism"), because 1 mg/mL PVP K12 or K29/32 did not slow droplet growth in dilute suspension deac2024a C44, R5.

Findings

Release mechanism and LoC: F16, F29.

Related concepts

slows drug-rich phase coarsening of drug-rich nanodroplets; related to surfactant partitioning into the drug-rich phase.

Formulas

none.

How it is measured or obtained

Inferred from droplet size over time by DLS; adsorption and repulsion were not measured in either paper indulkar2022 R11; ueda2020b X3.

Values in the library
materialvalue or classconditionspaper ids
ritonavir droplets with built-in Span 85; Span 20; no surfactant≈330 → 960; ≈550 → 1410; ≈940 → 2200 nmDLS of the release medium, 5–90 minindulkar2022 R11
ibuprofen-rich droplets with HPMC; with PVPVA (Amorphous solubility and LLPS chapter)coarsening suppressed; ineffective against coarsening and creamingueda2020b C51, C50
clotrimazole droplets ± 1 mg/mL PVP K12, K29/32≈540 → 1000; ≈340 → 610; ≈290 → 630 nm, same relative growthDLS, 37 °Cdeac2024a R5
Pitfalls and disagreements

In both papers the steric mechanism is proposed, not shown: for HPMC the zeta potential was close to that in buffer and no adsorption was measured ueda2020b X3, and for the Spans it is one of two alternatives indulkar2022 C50.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

Stokes-Einstein equation

The relation between the diffusion coefficient of a particle and its hydrodynamic radius, D = k_B T/(6\pi\eta r) indulkar2017a E5. In the amorphous solubility and LLPS papers it converts the self-diffusion coefficient of SDS micelles from pulsed-gradient NMR into a radius, and it is invoked qualitatively to explain why drug carried in larger bile-salt aggregates diffuses more slowly [indulkar2017a R25; lu2017b E8, C46]. New aspect (ASD process): it also estimates solute diffusivity in a viscous polymer melt and is used to explain why dissolution of crystals in the melt took hours and fragments stayed in place [moseson2019 E3, C39, C51]; the 2022 bicalutamide paper uses it as the framework for the low fitted dissolution rate in the viscous melt, again without inputs [moseson2022c E19, C37]. New aspect (Bioperformance): it is used for particle sizing of drug-rich nanodroplets by NTA and to argue that the effective diffusion coefficient in a membrane is constant [indulkar2016 E18, C21]. New aspect (Release mechanism and LoC): besides sizing nanodroplets by NTA, where it converts Brownian motion of tracked particles into size indulkar2017b E7; saboo2019 E5, it supplies the ratio of drug and polymer diffusion coefficients in the Higuchi critical-mixture calculation: with a drug of about 1 nm, a polymer of about 10 nm hydrodynamic radius and similar viscosity, D_{drug}/D_{polymer} = 10 saboo2020a E6, R27. The 2024 PVP molecular-weight paper uses it to argue that entanglement slows the diffusion of particles larger than the tube diameter while water and drug molecules move freely, so droplets of a few hundred nanometres are held in a mesh of at most 80 nm deac2024a C14, C45.

Findings

Amorphous solubility and LLPS: F17, F18. ASD process: F11, F36, F37. Bioperformance: F5, F15, F22. Release mechanism and LoC: F4, F5, F29.

Related concepts

used for the micelle size in the micelle/water partition coefficient mechanism; related to micellar solubilization and membrane flux; related to the Noyes–Whitney equation; sets the diffusion boundary layer. Used to size drug-rich nanodroplets. Feeds the Higuchi two-component dissolution model.

Formulas

Stokes-Einstein equation, Higuchi-Corrigan critical mixture ratio.

How it is measured or obtained

PGSE-NMR self-diffusion of 40 mg/mL SDS in D2O at 25 °C with 0, 0.4 and 7 mg/mL atazanavir, with the viscosity of water at 25 °C indulkar2017a P12, C9. In the bile-salt paper the relation is stated in words only [lu2017b E8]. In the melt papers of 2019 and 2022 it was not evaluated numerically, because the viscosity and radius are not given [moseson2019 E3]. NTA sizing of Brownian motion [indulkar2016 P4]; named only, not computed hate2018 E7. In the release-mechanism papers: applied by the NTA software indulkar2017b E7; at equal viscosity the diffusion coefficient falls with the radius saboo2020a E6.

Values in the library
materialvalue or classconditionspaper ids
SDS micellesD 10^−10.3 m²/s, radius 4.61 nm (0 and 0.4 mg/mL drug); D 10^−10.42 m²/s, radius 6.08 nm (7 mg/mL drug)40 mg/mL SDS in D2O, 25 °Cindulkar2017a R25
telaprevir in bile-salt micelleslower flux read as slower diffusion of drug-loaded aggregates (not quantified)12 mM STDC, SGDC[lu2017b C46, R12]
nanodroplets in other chaptersthe same relation is used for NTA sizingtacrolimus, ritonavir[trasi2016 E4; purohit2017b E1]
IDM in copovidone at 130 °Cslow diffusion in the viscous matrix gives gradients of about 8 µm after 1 hEDX[moseson2019 R9, C41, C51]
clotrimazole droplets111–257 nmNTA[indulkar2016 R4]
ritonavir ASD films200 (PVPVA), 250 (HPMCAS), 315 nm (PVP)NTApurohit2017b R8, E1
tacrolimus second phase220 nmNTA[trasi2016 R11, E4]
nifedipine dispersions, HPMC-E5 and PVPVA≈190–222 nmNTA, 5 °C, D2Oindulkar2017b R7
nilvadipine; cilnidipine in PVPVANTA scattering only at congruent loadings; sizes in the DLS rangepH 6.8, 37 °Csaboo2019 R12, E5
felodipine and PVPVAdiffusion-coefficient ratio 10 from radii 1 and 10 nmcalculatedsaboo2020a R27, E6
Pitfalls and disagreements

The viscosity of water is used although the solvent is D2O, and the printed exponent gives 4.90 nm rather than the printed 4.61 nm within rounding of the exponent (extractor recomputation) indulkar2017a E5, X7. The NMR samples differ in temperature, solvent and SDS concentration from the flux experiments indulkar2017a X7. In the bile-salt paper the relation is used to explain the same flux drop that is elsewhere read as lower activity, and the two are not separated [lu2017b X8]. In the melt papers the relation is only a framework: the paper gives no melt viscosity [moseson2019 E3, X6]. In indulkar2016 and hate2018 it is not used quantitatively. In the PAMPA study of hate2022 colloids of very different size gave the same mass flow, contrary to the Stokes-Einstein expectation that smaller particles move faster (F22) hate2022 C56, E3, R17. In the NTA papers the equation is named only, and the viscosity and temperature of the runs are not given indulkar2017b E7; saboo2019 E5. The radii of the 2020 calculation are estimates saboo2020a E6.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

structural relaxation time

The mean time for molecular rearrangement in a glass or supercooled liquid; in this chapter it is calculated with the Adam–Gibbs–Vogel equation from Tg and fictive temperature and compared with crystal growth [rumondor2010 E1, P8].

Findings

F5, F19.

Related concepts

measure of molecular mobility; related to structural relaxation and enthalpy relaxation.

Formulas

the AGV equation and the coupling exponent are listed on the chapter page as table only; Kohlrausch-Williams-Watts equation gives the enthalpy-relaxation time.

How it is measured or obtained

From the AGV equation with cited constants for felodipine (D 9.2, T0 253.4 K, fictive temperature 310 K) and the Tg at each storage RH, assuming that only Tg changes with water [rumondor2010 M1, C25]; outside the subcategory from viscosity and growth rate [trasi2014a E4].

Values in the library
materialvalue or classconditionspaper ids
amorphous felodipinelog(τTg/τ) ≈−1.73 at T/Tg 0.91, ≈−0.92 at 0.95AGV, Tg 317 K[rumondor2010 R7.j, E1]
amorphous felodipine growthfollows (τTg/τ) to the power 0.5 between T/Tg 0.94 and 0.9713–75% RH[rumondor2010 R7, C27]
amorphous nifedipine (cited)coupling constant 0.75 between relaxation and crystallizationcited[rumondor2010 R11]
nine compounds (outside)normalized growth against melting entropy, R² 0.61viscosity-based τ[trasi2014a R11]
felodipine at 45 °Ctaken as 100 s to count layers added per relaxation timeassumed[kestur2013a R18, X1]

Evidence table: structural relaxation time.

Pitfalls and disagreements

The fit with an exponent of 0.5 has no statistic and leaves out the high-RH points; the cited Tg sets differ by about 2 K [rumondor2010 X9, X11].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

structural relaxation

The approach of a glass toward the equilibrium supercooled liquid, with loss of excess enthalpy and entropy. In the amorphous solubility papers a phase formed in water is argued to be "much more relaxed" than a melt-quenched glass, with a heat capacity close to that of the supercooled liquid, because water raises molecular mobility and speeds relaxation [almeidaesousa2015 C37]; telaprevir's glass formed in water is likewise assumed "highly relaxed" [mosqueragiraldo2015 C26, C25].

Findings

F2, F7.

Related concepts

concerns the supercooled liquid and glass-liquid phase separation; influenced by plasticization by water; enters the amorphous-crystalline free energy difference.

Formulas

amorphous-crystalline free energy difference from heat capacity.

How it is measured or obtained

Not measured in these papers; inferred from the match between the onset and the supercooled-liquid free-energy estimate, which was lower than the glass estimate for griseofulvin, sorafenib and telaprevir [almeidaesousa2015 R6, R11; mosqueragiraldo2015 R13].

Values in the library
materialvalue or classconditionspaper ids
sorafenibonset 0.532 µg/mL; supercooled-liquid estimate 0.479; glass estimate 0.72525 °C[almeidaesousa2015 R6, R11]
griseofulvinonset 355.96 µg/mL; supercooled-liquid 356.44; glass 531.4125 °C, HPMCAS-HF[almeidaesousa2015 R5, R11]
telaprevironset 90–92 µg/mL; supercooled-liquid Cp 97 ± 8; crystal-to-glass Cp 189 ± 1637 °C[mosqueragiraldo2015 R13]
Pitfalls and disagreements

The new phase could not be isolated, so its relaxation state is an inference; the reference state is justified by the agreement it produces [almeidaesousa2015 C38, X4; mosqueragiraldo2015 X11].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

supercooled liquid

The amorphous state between Tg and Tm: mobile, but below the melting point; below Tg the same material is a glass [lu2016 C2]. "Undercooled melt" is used as a synonym [baird2012 A1]. A glass of a drug–polymer mixture can be regarded as a non-equilibrium supercooled liquid of high viscosity [taylor1997 C6]. New aspect (C. Amorphous solubility and LLPS): the amorphous reference state of the solubility calculation is the water-saturated supercooled liquid [ilevbare2013a C58; almeidaesousa2015 C39], and the drug-rich phase counts as one when its water-plasticized Tg lies below the experimental temperature [ilevbare2013a C22; indulkar2015 C38]. Ibuprofen, whose Tg of −45 °C makes its drug-rich phase a supercooled liquid at 37 °C, can be treated as an emulsion and seen by solution NMR ueda2020b C38, M1, C7. New aspects (Miscibility and drug-polymer interactions): The growth studies measure crystal growth into the supercooled liquid of drug or drug–polymer mixtures, 27–67 °C above the Tg of felodipine (70–110 °C against 43.3 °C), 3–85 °C above that of bifonazole (18–100 °C against 15.2 °C) and up to 61 °C above that of nimesulide (18–80 °C against 19.5 °C) (synthesis: temperature minus Tg) [kestur2010a P4, M1; kestur2011 P3, M1, M2]. Its lowest point, 18 °C, is at or just below the nimesulide onset Tg [kestur2011 X13]. Below Tg a binary drug–polymer glass can be regarded as a non-equilibrium, highly viscous supercooled liquid of "solvent" and "solute" molecules with homo- and hetero-associations, which makes the "solution" picture of the indomethacin–PVP dispersion reasonable "at least in terms of molecular interactions if not kinetics" [taylor1997 C6, C41, C42]. New aspect (Physical stability): in the physical-stability growth studies the supercooled liquid is the melt film, quenched and held between Tg and Tm, from which seeded crystals grow; the polymer effect on growth is placed in this liquid rather than at the crystal faces [kestur2013a C1, C6]. New aspect (Release mechanism and LoC): whether the drug-rich phase is a supercooled liquid or a glass at the release temperature is offered as a drug property that could matter for the limit of congruency. Que and co-workers (2019) name it "One interesting difference" between ritonavir (supercooled liquid under release conditions, LoC 25%) and ledipasvir (a glass, LoC 5%), and state that further investigation is "clearly" needed que2019 C49, R28. For ritonavir Indulkar and co-workers (2019) add that drug-rich nanodomains "can" coalesce into contiguous regions because the drug is a supercooled liquid at 37 °C indulkar2019a C40. Saboo and co-workers (2020) place the water-saturated indomethacin-rich phase in the supercooled-liquid state at 25–57 °C and in the glassy state at 10 °C, and find most PVPVA drugs studied "most likely" supercooled liquids at 37 °C in water (all but ledipasvir) saboo2020 C32, C58; at 5 °C loratadine behaves as a high-Tg compound yang2021 C16.

Findings

Crystallization tendency: F1, F7. C. Amorphous solubility and LLPS: F2, F7, F15, F22. Miscibility and drug-polymer interactions: F1, F10, F13. Physical stability: F3, F18, F19, F27, F28. Release mechanism and LoC: F7, F9, F18.

Related concepts

bounded by glass transition temperature; property melt viscosity; process cold crystallization and crystallization from the supercooled melt; related to crystal growth rate, structural relaxation and plasticization by water; medium for crystal growth inhibition by polymers; related to amorphous solid dispersion; site of glass-crystal growth mode near Tg; related to kinetic versus thermodynamic control of crystal growth. Set by plasticization by water and the glass transition temperature; allows a contiguous drug-rich surface layer to form.

Formulas

Vogel-Tammann-Fulcher equation, Jackson interface-kinetics growth rate, amorphous-crystalline free energy difference from heat capacity; viscosity-limited normal growth law.

How it is measured or obtained

Made by melting and cooling (quench or controlled), then studied isothermally above Tg on a hot stage or in a rheometer [lu2016 P1, P2; baird2012 P1]. In solution work, a drug-rich phase is a supercooled liquid when its water-plasticized Tg lies below the experimental temperature [ilevbare2013a C22; indulkar2015 C38]. The drug-rich phase is examined by DSC of the isolated phase, and the free energy of conversion from the crystal to the supercooled liquid is obtained by the Hoffman or heat-capacity cycle [ilevbare2013a P9; almeidaesousa2015 E9, E10, E11]. In the kestur2010a and kestur2011 growth studies, films of 30–50 µm were made by melting 3–5 mg between cover glasses and cooling rapidly to about 50 K below Tg, with the absence of birefringence checked under crossed polarizers, then nucleated at 40 °C or at ambient temperature and grown on a hot stage [kestur2010a P2, P3, P4; kestur2011 P2, R1]. Melt-quenched films between cover slips, held on a hot stage, in the physical-stability growth papers [trasi2012a P2; trasi2012b P2; mosqueragiraldo2014 P3; kestur2013a P1]. In the release-mechanism papers: from the dry or wet Tg against the test temperature, cited or measured que2019 R28, M1.

Values in the library
materialvalue or classconditionspaper ids
vemurafenibsupercooled liquid between Tg 108 °C and Tm 271 °Cmelt-quenched glass[lu2016 M1, R19.a]
34 drugsviscosities at Tm from 2.86 × 10⁻³ to 1.99 Pa·srheometry[baird2012 R1]
felodipine with 3% polymersgrowth from the supercooled liquid substantially reducedhot stage[kestur2010a C28]
bifonazole, nimesulidegrowth strongly temperature dependentsupercooled liquid[kestur2011 C6]
ritonavir drug-rich phaseTg 0.4 °C, so a supercooled liquid at 37 °Caqueous LLPSilevbare2013a C22
clotrimazole; atazanavir precipitatesTg ~14 °C (supercooled liquid at 37 °C); ~51 °C (glass)water at 37 °C[indulkar2015 R22, C38]
nicardipine drug-rich phasesupercooled liquid at 37 °C (dry Tg 15 °C); more viscous after 4 h at 2 °Cwater[indulkar2015 M3, R23]
griseofulvin; sorafenib new phaseonset matches the supercooled-liquid estimate although the dry drugs are glasses at 25 °C25 °C[almeidaesousa2015 R11, C36]
telaprevircrystal-to-supercooled-liquid Cp estimate 97 ± 8 µg/mL against 90–92 µg/mL onset37 °C[mosqueragiraldo2015 R13]
felodipinegrowth into the supercooled liquid peaks near 105 °C; 70–110 °C studiedform II, hot stage[kestur2010a R5, C10]
bifonazolegrowth falls by about 6.4 orders from 100 to 18 °C (plot)melt-quenched films[kestur2011 R7, X6]
nimesulidegrowth falls by about 5.4 orders from 80 to 18 °C (plot)melt-quenched films[kestur2011 R9, X6]
indomethacin–PVP glassnon-equilibrium supercooled liquid; single Tg citedsolvent-evaporated[taylor1997 C6, R17]
acetaminophenTg 21.2 °C, Tm 169 °CDSC, 10 °C/min[trasi2012a R9.a]
flutamideTg −3.1 °C; Tm 108–110 °C with 10 mol% additivesDSC[trasi2012b R7]
celecoxibTg 55.34 °C, Tm 163.46 °CDSC[mosqueragiraldo2014 R5.a]
ATP enantiomers (Tg 16–17 °C)growth from the supercooled liquid at 40–90 °Cmelt films[sato2015 R1, R5]
six compounds (Tg −1 to 90 °C) with PHBgrowth from the supercooled liquid at 30–150 °Cmelt films[sato2016 A4, M1, M2, M3, M4, M5, M6]
ritonavirwet Tg around 0 °C; supercooled liquid at 37 °Crelease conditionsque2019 R28; indulkar2019a M1
ledipasvirglass under release conditions37 °Cque2019 C49, M1
indomethacin-rich phase (70% dispersion)supercooled liquid at 25–57 °C, slightly below its onset at 17 °C, glass at 10 °Cwet Tg onset 18 °Csaboo2020 C32, R30
loratadinesupercooled liquid at 37 °C, glass at 5 °Cwet Tg 13.8 °Cyang2021 C16, M1
Pitfalls and disagreements

Near Tg diffusion decouples from viscosity, so viscosity-based growth laws fail there [trasi2014a C21]. Polymer effects on growth from the supercooled liquid act on the liquid phase rather than at the crystal surface for felodipine [kestur2013a C6]. In the amorphous solubility papers a glass formed in water may behave as a supercooled liquid, which is inferred and not measured [almeidaesousa2015 C37, C38]. The text orders of magnitude (5.5 and 6 for bifonazole) are smaller than the plot readings (6.4 and 6.9) [kestur2011 X6]. Whether dilute dispersions made by cryomilling are molecularly mixed in the melt is assumed [kestur2010a C5]. In the acetaminophen and flutamide growth papers, interactions in the liquid were judged from spin-coated films at other compositions, not from the growth samples [trasi2012b X9; trasi2012a X15]. Two drugs only; the idea was not tested que2019 C49.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

supersaturation

A solution concentration above the crystalline solubility of the drug [almeidaesousa2016 C2; ilevbare2013a C21]. In this chapter the highest supersaturation a solution can hold without crystals is set by the amorphous solubility: above it the excess forms a drug-rich phase, and the concentration and activity of the continuous phase stay at that ceiling [mosqueragiraldo2015 C34, C35]. Taylor and Zhang 2016 (p. 10) add that the strict upper limit is the spinodal point: a one-phase solution can persist for a time between the binodal and the spinodal, and after phase separation the level is the binodal, which is the amorphous solubility (synthesis). Supersaturation can be generated by solvent shift, pH shift, or dissolution of a high-energy solid form (amorphous drug, dispersion, salt, co-crystal) [almeidaesousa2015 C4, C5; almeidaesousa2016 C2]. The papers of 2017–2022 add that in a micellar medium the supersaturation that matters is the activity ratio a/a^{*} and not the concentration ratio, the two differing about twofold for atazanavir in SDS at the amorphous solubility (65–70 against 33–38) indulkar2017a R13, C21, and that after a pH shift of a weak-base salt the apparent concentration is held near the amorphous solubility if the dose exceeds it [sugihara2018 R8, R12]. New aspect (Bioperformance): a dissolved drug concentration above the crystalline solubility, with a solute activity above that of a solution saturated with the crystal; the supersaturation ratio is activity over crystal activity, and equals the concentration ratio c/c^* only if the activity coefficients are equal [raina2015c C7, E5, E6, C32]. The highest supersaturation a solution can hold as one phase is set by the amorphous solubility; above it LLPS or crystallization takes over [raina2014a C27, C30]. Its highest concentration-based value is the ratio of amorphous to crystalline solubility, and that ratio falls when a polymer, a second drug or micelles enter the drug-rich phase or the medium (F18, F19, F20) [ueda2020a E1, C17; alkalla2026 C1, C37; elkhabaz2019b C21, C25]. New aspect (Crystallization from solution): in the crystallization papers supersaturation is the ratio S = C/C_{eq} of the concentration to the crystalline solubility (concentration used in place of activity because the solutions are very dilute), with \sigma = \ln S for growth analyses; the amorphous solubility of ritonavir is S 15.3–15.4 and σ 2.7 [ilevbare2013b E4, C14; ilevbare2012b E1, E2, R3]. The reference solubility is that of the stable crystal, measured without methanol and, to be consistent, with the polymer present (F19) [hsieh2012 P4; ilevbare2013c P9, X16; hsieh2014 C18]. Other scales in these papers: C/Ceq in the medium of interest (1.5–15), S' = C/Cs with the solubility with additive, the activity ratio δ from membrane flux (2.4–28.8), S 1.5 for acetaminophen, and a nominal 10 mg/mL solvent shift [chen2015 E2; li2016a E1; lu2017 E1; trasi2015 P2; raina2015b P1].

Findings

Amorphous solubility and LLPS: F1, F5, F6, F8, F13, F14, F9, F10, F15, F16, F17, F19, F23. Bioperformance: F3, F10, F13, F14, F18, F19, F20, F28, F29. Crystallization from solution: F1, F2, F9, F14, F19, F21, F22, F27, F31, F34.

Related concepts

capped by amorphous solubility; measured against crystalline solubility; expressed as supersaturation ratio or via thermodynamic activity; relieved by crystallization. Papers of 2017–2022: activity-based supersaturation, maximum achievable supersaturation. Lost by desupersaturation; contrasts with solubilization; summarized by supersaturation factor.

Formulas

supersaturation ratio. Activity-based supersaturation ratio, supersaturation from membrane flux ratio, supersaturation factor, power-law crystal growth rate.

How it is measured or obtained

As concentration divided by the crystalline solubility in the same medium (the supersaturation ratio), or in terms of activity from the flux ratio; the concentration-based ratio at the ceiling is the amorphous-to-crystalline ratio (F6) [almeidaesousa2015 E15; mosqueragiraldo2015 R12]. In the Bioperformance papers: concentration ratio by UV or HPLC; activity-based ratio from membrane flux relative to the flux at the crystalline solubility [raina2015c E9, R13]; receiver-derived "effective" supersaturation from a Cmax calibration [hate2017 C49, R18]; generated by solvent shift, pH shift or ASD dissolution [raina2014a P7; hate2017 P7; hate2018 P9]. The activity-based maximum is the ratio of the flux from a solution at the amorphous solubility to the flux from a crystalline suspension in the same medium, J_{amph}/J_{eq} [elkhabaz2019b E2, R8, R9]. A dose is described by its ratio to the crystalline solubility: 5 mg of tacrolimus in 100 mL gives S = 20 and in 240 mL S = 8 [hate2019 R7, R14, E2]; pretomanid nucleation is compared at S = 5 nguyen2023a E1, R5. In the crystallization-from-solution papers: concentration by fibre-optic UV on second-derivative spectra or by HPLC; S from the crystalline solubility measured in the same buffer (48–72 h at 37 or 25 °C); the supersaturation factor integrates S over time [ilevbare2012a E2; ilevbare2013c E8].

Values in the library
materialvalue or classconditionspaper ids
ibuprofen to sorafenibmaximum ratio 4.3 to 54.025 °C, fluorescence onset[almeidaesousa2015 R5]
telaprevirmaximum ratio about 18 (stated); flux gain about 18pH 6.8, 37 °C[mosqueragiraldo2015 R14, R15]
clotrimazole; atazanavirabout 13; about 6337 °C[indulkar2015 R10]
CRH1about 10pH 6.8 and pH 4.6[almeidaesousa2016 R24]
atazanavir in 0–3.6 mg/mL SDSconcentration-based 64.8 → 33.0; activity-based 66.0 → 65.0 at the amorphous solubility37 °Cindulkar2017a R13
telaprevir in bile saltsconcentration-based value 3.9–6.7 at an activity-based 5.050 mM pH 6.5, 37 °C[lu2017b R17]
felodipine, 25 °C2.7–6.8 at 2–5 µg/mL; about 8 at the amorphous solubilitybuffer[raina2014a R17]
felodipine with BSAS 1.3 and 1.1 by concentration ratio; 7.3 and 4.2 from flux50 µg/mL[raina2015c R13]
nevirapinenominal S 3.9; receiver-derived 2.8 (powder), 4.10 (powder + HPMC-AS)pH shift, 128 µg/mL crystalline[hate2017 R18]
ritonavir (mesoporous-silica study)S 7.8; 3.93.6 µg/mL crystalline[dening2018 E6]
atazanavir, six mediaactivity-based maximum about 50–56; concentration-based 56 in buffer to 14 in pooled human intestinal fluid37 °C, side-by-side cell[elkhabaz2019b R8]
posaconazole, six mediaactivity-based maximum about 29–37; concentration-based about 35–37 in buffer to 5 in human fluid37 °C[elkhabaz2019b R9]
tacrolimusS 20 (5 mg in 100 mL) and S 8 (240 mL); maximum ratio about 33solvent-shift solutions, hollow-fibre module[hate2019 R7, R14; purohit2019 C30]
tacrolimus, fully crystalline capsule contentsconcentration 2.5 times the crystalline solubility during 2 h5 mg in 100 mL, pH 4.5[purohit2019 R5]
atazanavir with darunaviratazanavir in the drug-lean phase about 61–63 instead of 91–96 µg/mL150 µg/mL atazanavir, about 196 µg/mL darunavir added[alkalla2026 R11, C1]
felodipineS 3–12; amorphous benchmark about 10solubility about 0.5 µg/mL, 25 °C[alonzo2012 E1, C42]
ritonavirS 3.8, 7.6 (7.7), 15.3 (15.4) at 5, 10, 20 µg/mL; 4.3 in 50 mM buffersolubility 1.3 µg/mL (100 mM), 2.3 µg/mL (50 mM), 37 °C[ilevbare2012a R3; ilevbare2012b R3]
celecoxib; efavirenzS 6.6, 14.7 at 10 and 22 µg/mL; 1.2 at 10 µg/mLsolubility 1.5 and 8.2 µg/mL[ilevbare2013b R7]
type 1 weak basespeak 1.4–26.7 times the titration solubility, lasting 3.1–14.7 minpH shift, 37 °C[hsieh2012 R5]
type 2 weak bases7.2–20.7 times the crystalline solubilitypH shift[hsieh2012 R10]
telaprevir with six bile saltsδ 11.5 and 28.8 need 60 and 150 µg/mL in buffer, 140 and 300–330 with 12 mM STDC/SGDCpH 6.5, 37 °C[lu2017 R1]
atazanavir, ritonavir in buffer, FaSSIF-V1, Composite-SIFflux-based supersaturation at the amorphous solubility 63–65 and 9.2–10pH 6.5, 37 °C[indulkar2018 R12]
posaconazoleamorphous/crystalline about 34 from pH 2 to 7phosphate buffers, 37 °C[duong2022b R1, C19]
Pitfalls and disagreements

The ratio depends on the crystal form (a hydrate for paclitaxel) and the medium [trasi2015a X12]. A solubilizer raises total concentration without raising supersaturation in activity terms, and the concentration-based ratio can fall [ilevbare2013a C54; raina2015c C29]. Total UV concentration is not free drug once a drug-rich phase exists (F4) [almeidaesousa2016 R12]. Concentration ratios understate supersaturation where micelles solubilize the drug, and flux-based values assume that micelles do not cross the membrane [indulkar2017a C42, X9; lu2017b X8]. In the Bioperformance papers, with solubilizers the concentration ratio under-reads the activity-based supersaturation (F3) [raina2015c C38]. Concentration ratios are not valid above the amorphous solubility, where two phases coexist [dening2018 E6]. UV readings above the amorphous solubility include scattered light hate2018 X15. In six media of rising solubilizing capacity the concentration ratio fell several-fold while the flux ratio stayed about the same (F18) [elkhabaz2019b R8, R9, C21]. Which dose-to-volume ratio a test imposes decides whether absorption or growth on seeds dominates: S of 8 and S of 20 gave different results in the same module (F28, F29) [hate2019 R14, R17]. Polymer in the drug-rich phase lowers the achievable supersaturation although it inhibits crystallization (F19) ueda2020a C37. S for 10 µg/mL ritonavir is printed as 7.6 and 7.7, and for 20 µg/mL as 15.3 and 15.4, depending on rounding (10/1.3 = 7.69; 20/1.3 = 15.38) ilevbare2012a X1. The efavirenz induction-time runs state S 2.4, the ratio of the calculated amorphous solubility to the crystalline solubility, while the concentration used gives 2.3 [ilevbare2013c X4]. A polymer that raises the solubility lowers S for the same concentration (F19) [ilevbare2013c X7]. C/Cs understates the supersaturation of celecoxib in media where the mass flow does not change [li2016a X18].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

surface crystallization

Nucleation and growth of crystals at a free surface of an amorphous solid, reported to be faster than in the bulk by orders of magnitude because surface molecules are more mobile [duong2022c C2; trasi2014a C4]. It is a failure mechanism of amorphous solid dispersions in storage and during dissolution [duong2022c C2; saboo2020 C36]. New aspect (ASD process): in the coating papers the surface route is the target of the treatment, since crystal growth at the free surface of an amorphous solid is orders of magnitude faster than in the bulk, so a thin shell is expected to act where crystals start [duong2022c C2, C3; moseson2022a C6]. Uncoated powders stored open at 40 °C showed crystals by SEM within 1–2 weeks (ezetimibe–HPMCAS 12–19 days), coated ones later or not at all [moseson2022a R11; duong2022c R16, R17]. In a coated particle that did crystallize, crystals lay above an intact coating, "as is common for amorphous materials" moseson2022a C26, R15. In dissolution, a hydrated, drug-rich surface layer of bicalutamide–PVPVA crystallizes on the compact surface within 30–60 min (see drug-rich surface layer) moseson2022b R14, R15. New aspect (Supersaturation from ASD dissolution): a proposal for wetted amorphous particles: crystallization "probably" starts at the particle surface, is made worse by water plasticization, and dissolved polymer delays it by interacting with that surface, as a thin polymer film does for amorphous indomethacin (cited) ("reasonable to speculate") [alonzo2010 C36, R22, R23]. New aspect (Release mechanism and LoC): for indomethacin methyl ester–PVPVA, congruency was lost at a later time point above 5% loading: drug release ceased and polymer release slowed, which the authors attribute to drug crystallization at the compact surface, supported by XRD and PLM saboo2020 C17, R8, R9. A congruency read-out over the first minutes therefore misses this failure. A surfactant built into the dispersion can bring the same failure to a drug that does not crystallize on the binary tablet: ritonavir–PVPVA at 30% with SDS released fast and congruently, then stopped near 80% when needle crystals covered the tablet surface by 15 min, which "likely served as a barrier" indulkar2022 R5, R15, R16, C38. With 10 parts of SDS in ritonavir–PVPVA, needle crystals covered the 30% compact surface at 30 min, to which the authors attribute the release plateau ("can be attributed"); SDS covered about 98 wt% of the dissolved surface, which "conceivably" promotes crystallization through higher surface mobility yang2023 R16, C24, R17, C50.

Findings

Crystallization tendency: F4, F21. ASD process: F43, F44, F38, F40. Supersaturation from ASD dissolution: F1, F2, F14, F24, F27. Release mechanism and LoC: F19, F31.

Related concepts

part of physical stability; related to crystal growth rate and nucleation; contrasts with bulk crystallization in crystallization from the supercooled melt. Targeted by the atomic layer coating through surface molecular mobility; sped up by plasticization by water; in dissolution follows the drug-rich surface layer and leads to matrix crystallization; related to crystallization inhibition by polymers. Ends congruent release after a delay; a form of crystallization during dissolution.

Formulas

none.

How it is measured or obtained

Growth on films with the top coverslip removed [trasi2014a P2]; nuclei counted on an exposed glass surface [trasi2014b P7]; SEM, SHG or PLM of particle and tablet surfaces in storage or dissolution [duong2022c R16; correasoto2017 R16; saboo2020 R9]. SEM was the primary detector of surface crystals on stored coated powder, with XRPD, DSC and SEM agreeing for ezetimibe and XRPD missing several arms of the four-system study [moseson2022a C22, X14; duong2022c R16, R18, R20]; SEM and SEM-EDX of exposed compacts moseson2022b P14, P15. In the ASD dissolution papers: by polarized light of suspended particles over days chen2015a P10, R20 and indirectly by the lag in slurry crystallinity with polymer in the medium [alonzo2010 R6]. In the release-mechanism papers: SEM of the tablet surface at 5, 10 and 20 min, besides XRD, PLM and the 1607 cm⁻¹ IR band of crystalline ester saboo2020 R22, R18, C23. SEM of dried tablets and ATR-IR of blotted wet tablets against the crystalline drug indulkar2022 P9, P11.

Values in the library
materialvalue or classconditionspaper ids
felodipine form Iabout 6 times faster at the surface than in the bulk; about 23 times with 3% PVP30 °C, 0% RH[kestur2013b R12]
felodipine≈0.06–0.42 µm/s at the surfaceT/Tg ≈1.04–1.11[trasi2014a R4.g]
loratadine≈0.00005 µm/s at the surface, slowest of 14near Tg[trasi2014a R4.n]
nilutamidemuch higher nucleation at the surface than in the bulkmelt-cooled films[trasi2014b R1]
ezetimibe spray-dried dispersionscrystals after 19 days (50% DL) and 12 days (70% DL) uncoated40 °C/75% RH[duong2022c C33]
uncoated amorphous powders (erlotinib, naproxen and lumefantrine ASDs)crystallization onset within 1–2 weeks40 °C, open dish; 31–75% RHmoseson2022a R11
flutamide spray-dried dispersionneedle crystals growing from particle surfaces40 °C/75% RH[correasoto2017 C26]
indomethacin methyl ester compactssurface crystals within 10 min of dissolutionPVPVA, 25% DLsaboo2020 R9
ritonavir–PVPVA–SDS compactsneedle-shaped surface crystals during dissolution30% DLindulkar2022 R15; yang2023 R16
delamanid dispersion filmsrapid surface crystallization at pH 3.01 h[nguyen2023b R3, C37]
ezetimibe–HPMCAS 50% DL, uncoatedneedle-like crystals at 19 days; about 26% crystalline at 270 days40 °C/75% RH[duong2022c R16, R19]
ezetimibe–HPMCAS 70% DL, uncoatedplate-like crystals at 12 days; about 50% crystalline at 270 dayssame[duong2022c R16, R19]
ezetimibe–HPMCAS coated (50% thin and thick, 70% thick; about 12–40 nm)no crystals by SEM, PXRD or DSC for 24 monthssame[duong2022c R16, R17, R18, R20]
ezetimibe–HPMCAS 70% thin coating (11.7–15.0 nm)first crystals at 7 months; about 1.5% at 270 dayssame[duong2022c R17, R19]
erlotinib, naproxen and lumefantrine ASD powders, 13 coated arms3–24 weeks, or none within 48 weeks in 7 arms40 °C, 31–75% RHmoseson2022a R11
extruded and milled 30% and 50% DL BCL–PVPVA compactsneedle-like crystals on the surface at 30 min; a 5–10 µm crystal crust on the 50% compact at 1 hpH 6.8, 37 °Cmoseson2022b R14, R15
amorphous felodipine, polymer in the mediumlag of about 13–20 min before 50% crystallinitypH 6.8, 37 °C slurry[alonzo2010 R6]
celecoxib–HPMCAS spray-dried particles, Triton X100birefringent regions on or in the particles after about 7 days, no free needlespH 3, 25 °Cchen2015a R20, C37
same, no surfactantcrystallization only after more than 7 days, apparently from matrix or surfacepH 3chen2015a C33
delamanid salt dispersions, five enteric gradescrystals on films and powders after 1 h in acid, more with HPMCAS and at higher pH; HPMCAS-HF also at pH 1.625% drug, 37 °C[nguyen2023c R19, R18]
delamanid dispersions after the pH shiftundissolved particles covered with small crystals within 30 minpH 6.5[nguyen2023c R21]
indomethacin methyl ester–PVPVA 25%smooth at 5 min; scattered needle-like crystals at 10 min; surface extensively covered at 20 minSEM, pH 6.8saboo2020 R22, M6
indomethacin methyl ester–PVPVA 10–25%drug release levelled off after 7.5–20 min30 min runssaboo2020 R8
ritonavir–PVPVA 30:70:5 with SDSsmooth at 2 min; needle crystals and crystalline-ritonavir IR bands at 15 min; release flat near 80%SEM, ATR-IR, pH 6.8indulkar2022 R15, R16, R5
ritonavir–PVPVA–SDS 30–70–10birefringent needles at 30 minPLM, SEM of the compact surfaceyang2023 R16
Pitfalls and disagreements

Screens with films sandwiched between cover glasses assume surface crystallization is minimized, which was not tested [baird2010 C45]. Surface and bulk data are often taken at different temperatures [trasi2014a X16]. Where surface growth exceeds bulk growth, extrapolating bulk data may overpredict stability [kestur2013a C18]. The coating delays surface crystallization but does not stop it: coated arms failed at 3, 6 and 24 weeks and at 7 months, and the benefit depends on humidity through the wet glass transition, on the polymer and, for a fast crystallizer at high loading, on thickness (see F44) [moseson2022a R11, R12; duong2022c R17]. Neither surface mobility nor water uptake during storage was measured [moseson2022a C4; duong2022c X7]. XRPD shows no crystals through 48 weeks for uncoated extruded lumefantrine powders that SEM scored at 1 week moseson2022a X14. Where crystallization starts on the wetted felodipine particles and whether polymer adsorbs there were not measured [alonzo2010 C36]. The 7-day observations of the celecoxib suspensions appear only in the discussion and are imaged for Triton X100 only chen2015a X17. The authors read the crystals as forming mainly at the surface of the wetted matrix, where water lowers the Tg and raises mobility, and as acting as seeds once the polymer dissolves [nguyen2023c C43, C44]. The 5-min rates used to set the limit of congruency did not show the later stop of release saboo2020 X7. Crystals were imaged only at 30% and not identified yang2023 X12.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

surface drug enrichment

A drug-rich layer at the surface of a dispersion or at the dissolving interface. In the lopinavir films, with 50–100% water in the casting solvent the continuous phase softened at 142 ± 11, 116 ± 16 and 124 ± 7 °C (37–92% LPV), which the authors read as drug enrichment at the surface ("suggesting"), lowering release li2019 R15, R16, C30. In spray-dried ritonavir–PVPVA powders XPS gave the outer 0–10 nm composition and the surface drug content rose with the water in the spray solvent; in granules of two drugs a lopinavir-rich surface is proposed to form in acid as ritonavir dissolves first [li2020 R7, R24; trasi2019 C29, C47]. Fluorine EDX (F/F0; fluorine occurs only in the drug) quantified it on bicalutamide–PVPVA compacts: the surface of a 30% compact reached F/F0 = 1.23 ± 0.07 after 30 min in buffer moseson2022b R14, E1. New aspect (Release mechanism and LoC): two kinds appear. During dissolution the surface of compacts above the limit of congruency turns drug-rich within minutes, read by IR, XPS and EDX, while congruent compacts keep their composition indulkar2019a R16, R15; que2019 R15; saboo2019 R18; saboo2020a R22. Before dissolution the surface of spray-dried particles can already differ from the bulk, set by the spray solvent bhardwaj2018 R20, C57. For indomethacin–PVPVA the dissolving surface was followed in time by three methods of different probe depth, whose agreement the authors call "compelling evidence" saboo2020 C44. In ritonavir–PVPVA at 40% the surface became enriched in drug during incongruent release by preferential polymer release, in agreement with the drug-rich layer seen in cross-section yang2022a C39, C40. Hiew and co-workers (2023) lowered the surface drug of high-loading co-precipitated particles on purpose, by depositing a water-soluble polymer from the anti-solvent; a surface drug of 50% or more appeared to make release drug-dominated hiew2023 C45, C53. In 2023–2025 surface composition was followed during dissolution: SDS kept the ritonavir surface of a 40% compact at its bulk composition (about 41 and 40% before and after 30 min) while covering it itself yang2023 R19, R17, C33, and a 40% bedaquiline–HPMCAS dispersion went from about 32 to 55 wt% surface drug after 1 h at pH 6.5, read as preferential loss of polymer and a second cause of poor release kaur2025 R20, C26, C43. For 75% grazoprevir particles, surface drug contents of 32–50% did not separate good from poor secondary excipients hiew2025 R14, C35.

Findings

ASD process: F15, F3, F21, F23, F27, F38. Release mechanism and LoC: F7, F14, F17, F28, F31, F32, F35.

Related concepts

promotes drug-controlled release; a drug-rich layer follows incongruent release; in dissolution becomes the drug-rich surface layer. Forms the drug-rich barrier layer.

Formulas

molar amount of halogen at the lower XPS binding energy, Gordon-Taylor equation.

How it is measured or obtained

Not measured in depth for the lopinavir films; inferred from nanoTA and a mass balance that is not shown li2019 C30, X18. For other dispersions the drug-rich surface was read from IR, SEM, EDX and XPS of tablet or particle surfaces indulkar2019a C18, C41; saboo2020a C22; bhardwaj2018 C40. In the release-mechanism papers: ATR-IR of blotted tablets against reference spectra indulkar2019a P7; XPS of the top ~10 nm with pure-component fits que2019 P7; saboo2019 P17; bhardwaj2018 P11; EDX of an element carried only by the drug (N/O ratio, chlorine) saboo2019 P16, E2; saboo2020a P9. SEM-EDX of the Cl/N ratio (one Cl and one N per indomethacin, one N per PVPVA unit) and AFM-nanoTA local Tg converted to composition by the Gordon–Taylor equation saboo2020 E2, E3, P14, P18.

Values in the library
materialvalue or classconditionspaper ids
LPV–HPMC E5 33% DL, 50 / 70 / 100% watercontinuous-phase local Tg 142 / 116 / 124 °CnanoTAli2019 R15, R16
ritonavir–PVPVA 50% DL tabletsurface enriched in drug after 5 minIR, SEM (outside)indulkar2019a C18, C41
felodipine ASDs 30% DLincongruent PVP, PVPVA and HPMC enrich the interface; congruent HPMCAS and EUDS do not: chlorine ≈3.0 → 6.7, 4.6 → 6.4, 2.6 → 7.3 (PVP, PVPVA, HPMC); ≈2.9 → 3.1 and ≈3.0 → 2.7 (HPMCAS, EUDS; ns)EDX, 10 min (outside)saboo2020a C22, C28, R22
spray-dried ITZ–PVPVA, 20%n-hexane batches drug-rich at the surface; water lowered surface drug: 4.2% (water in solvent), 28.1% (DCM–methanol), 31.8–35.7% (n-hexane), bulk 20%XPS N 1s, before dissolution (outside)bhardwaj2018 C40, C41, R20
ritonavir–PVPVA spray-dried, 25% DLsurface RTV by XPS (C 1s) about 21% (methanol), 43% (10:90), 70% (60:40); at 50% DL 85–91% from 60:40XPS, at least 4 spotsli2020 R7, R11
polymer-free 200:50 lopinavir:ritonavir melt after 1 h in 0.1 N HCl1630/1718 cm⁻¹ band ratio 7.7 → 11.2, read as ritonavir loss from the surfaceATR-FTIR[trasi2019 R16, C29]
BCL–PVPVA 30:70PVPVA:BCL of the undissolved solid 7:3 → 1:1 within 5 min (computed); surfaces rough and pitted after 20 minSEC, SEM[moseson2021 R24, R26, C32]
30% BCL–PVPVA compact surfaceF/F0 = 1.23 ± 0.07 (about 20% enrichment)30 min in buffer, SEM-EDXmoseson2022b R14
same, cross-sectionboundary layer F/F0 = 1.41 ± 0.10 over a gel layer of 0.93 ± 0.061 hmoseson2022b R15
ritonavir 50:50 PVP and PVPVA filmsporous or granular surface after 10 s in bufferSEMpurohit2017b R9
ledipasvir–PVPVA 20, 50%17 → 54 and 40 → 61 wt% drug in 10 minXPSque2019 R15
nilvadipine 15:85; cilnidipine 20:802 → 32% and 20 → 60% in 10 min; rim N/O ≈0.50 against ≈0.35 inside a pitXPS, EDXsaboo2019 R18, R16
indomethacin–PVPVA 25%25 → 41 → 55 → 72 wt% (EDX), 23 → 44 → 52 → 60 wt% (nanoTA), ≈40–50 → ≈60% (FTIR) over 0–20 mintablets and films, pH 2.1saboo2020 R21, R28, R17, M5
ritonavir–PVPVA 40% compactsurface ritonavir ≈35 → 72 wt% after 30 minXPS, pH 6.8yang2022a R14
grazoprevir–HPMCAS co-precipitates and one solvent-evaporated dispersion, eight materialssurface drug ≤34% with ≈47–72% release; ≥53% with ≈8–17%XPS; two-stage release at 90 minhiew2023 R14
ritonavir–PVPVA–SDS 40–60–10surface SDS ≈60 → 98 wt%; ritonavir ≈41 → 40% on a drug-plus-polymer basisXPS; ATR-FTIR, before and after 30 minyang2023 R17, R19
bedaquiline–HPMCAS-MF 40%surface drug 32 ± 2 → 55 ± 2 wt%XPS, 1 h in pH 6.5 bufferkaur2025 R20
grazoprevir–HPMCAS 75:25 particles with five excipients≈32–50% before SGF, ≈46–69% afterXPShiew2025 R14
Pitfalls and disagreements

Surface and bulk composition may differ, and surface enrichment retards release li2019 C52. XPS and pyrene fluorescence see only the near-surface region, and the ATR-FTIR evidence for the lopinavir-rich barrier comes from a drug-drug melt without polymer, not from the granules [li2020 C34, R24; trasi2019 X7]. The 15:85 nilvadipine surface started polymer-rich (2% drug against 15% nominal) saboo2019 X13. No XPS was done at the first failing ledipasvir loading (7.5%) que2019 X21. The PVPVA felodipine tablet started with more surface chlorine than the other four saboo2020a X16. For the spray-dried ITZ particles surface composition and morphology change together bhardwaj2018 X12. The indomethacin methods probe about 50 nm to 1 µm, on tablets and films, so the value at 20 min is best quoted as about 60–72 wt% saboo2020 X15; the EDX conversion factor is unstated saboo2020 X3. The drop in cinnarizine protonation after partial dissolution was linked to surface drug enrichment that the 2024 paper did not show bapat2024 X7. The bedaquiline enrichment comes from a 40% dispersion that was not release-tested kaur2025 X9, X10.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

surface molecular mobility

The mobility of molecules at the free surface of an amorphous solid, which is taken to be much higher than in the bulk and to be the reason why crystals nucleate and grow faster at a surface (see surface crystallization) [duong2022c C2]. In the coating papers it is the mechanism proposed for the protection by an atomic layer coating: the shell lowers surface mobility, "attributed primarily" in the study of four systems and "perhaps more importantly" than a moisture barrier in the ezetimibe study [moseson2022a C4, C44; duong2022c C53, C54]. Water raises mobility and lowers the wet glass transition temperature, so a coating that acts on the surface cannot rescue a powder whose bulk is mobile moseson2022a C41, C25.

Findings

F43, F44.

Related concepts

reduced by the atomic layer coating; raised by plasticization by water; drives surface crystallization; the alternative explanation is the moisture barrier effect.

Formulas

Tg − T.

How it is measured or obtained

Not measured in any ASD process paper [moseson2022a C4; duong2022c X7]. It is inferred from crystallization onset in coated and uncoated powders and from the wet Tg minus the storage temperature, computed with the onset Tg after 24 h at the storage humidity (see Tg − T) moseson2022a P6, E2, R11, R12.

Values in the library
materialvalue or classconditionspaper ids
erlotinib–HPMCAS, 75% RHwet Tg − T about −8.8 °C; coated onset about 3 weeks (uncoated about 2)40 °Cmoseson2022a R12, R11
erlotinib–HPMCAS, 43% RH−2.3 ± 1.1 °C; coated none at 48 weeks40 °Cmoseson2022a R12, R11
erlotinib–PVPVA, 43% RH−0.5 ± 1.2 °C; coated onset about 6 weeks40 °Cmoseson2022a R12, R11
naproxen–HPMCAS 75% RH; lumefantrine–PVPVA 43% and 31% RHabout +11.3, +10.7 and +14.3 °C; coated 24 weeks, 24 weeks and none at 48 weeks40 °Cmoseson2022a R12, R11
uncoated powders of all four systemscrystals within about 1–2 weeks whatever Tg − T40 °C, 31–75% RHmoseson2022a R11, X15
Pitfalls and disagreements

The authors write that "this confirms that the mobility of the sample was the primary mechanism" of the coated failures moseson2022a C25; uncoated powders failed in 1–2 weeks across the whole range of Tg − T, the stable erlotinib–HPMCAS arm at −2.3 °C lies outside the range of about 0–15 °C that the discussion gives, and whether the wet Tg was measured on coated or uncoated powder is not stated moseson2022a X15, C45. The ezetimibe study offers both mobility and a moisture barrier and could not separate them [duong2022c C53, C54, X7].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

surface-normalized dissolution rate

Evidence table: surface-normalized dissolution rate. Content from the release-mechanism chapter (2020–2022), with rows from the ASD process and Miscibility and drug-polymer interactions chapters.

The release rate of one component of a compact of constant exposed area, per unit area and normalized to the component's weight fraction, so that drug and polymer of a dispersion can be compared with each other and with the neat components; it is the intrinsic dissolution rate per component saboo2020 E1, P5; correasoto2022b E1. Equal drug and polymer values mean congruent release saboo2020 R3. Hiew and Taylor (2022) found that all lumefantrine formulations with near-complete drug release had drug rates above 3 mg/min/cm² hiew2022b C17.

Findings

Release mechanism and LoC: F1, F15.

Related concepts

the per-component form of the intrinsic dissolution rate; equal values for drug and polymer define congruent release.

Formulas

surface-normalized release rate.

How it is measured or obtained

Compacts in a die, one face exposed, rotated at 100 rpm in buffer at 37 °C; drug and polymer assayed separately and the slope of the initial linear part taken saboo2020 P5, R3; hiew2022b P8. In the ASD process chapter the slope of drug concentration against time is normalized by the area of the dissolving front and the drug loading li2020 E13.

Values in the library
materialvalue or classconditionspaper ids
indomethacin–PVPVA 5, 10%; 15–25%drug ≈3.44, 3.14; ≈0.04–0.01 mg/min/cm² (amorphous drug alone 0.002)0–5 min, 37 °Csaboo2020 R3
atazanavir–PVPVA 10%; with eight additives≈0.07; ≈1.0–5.6 mg/min/cm² (neat PVPVA ≈2.7)37 °Ccorreasoto2022b R3
lumefantrine free base 5–35%; sulfate 2%≈3.15–3.9; ≈4.5 mg/min/cm²37 °Chiew2022b R12
lumefantrine–PVPVA 5–35% (Miscibility chapter)drug 3.15–3.92, PVPVA 4.49–4.91 mg/min/cm²pH 6.8, 37 °Chiew2022a R13
ritonavir–PVPVA 25% spray-dried from methanol; 10:90 and 60:40 water:methanol (ASD process chapter)≈3.5; ≈2.27; ≈0.90per the paper's unitsli2020 R10
Pitfalls and disagreements

How the lumefantrine rates were calculated is not printed, and a 5% PVPVA dispersion delivering 3.68 mg/min/cm² of drug is far above what a compact of that loading could deliver by mass, which the extractor reads as each rate being normalized to that component's weight fraction hiew2022a X7. The unit of the ritonavir rates is printed as mg/min/cm li2020 R10.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

surface roughness

The arithmetic mean roughness Ra of an AFM height image (Gwyddion 2.47), used as a single number for whether a spin-coated or cast film is featureless or carries domains [li2017 E3, P8; li2019 P14]. In the HME particle-engineering study the roughness of drug crystal surfaces was described qualitatively from SEM (L38 tabular with rough surfaces, L93 smooth) and not quantified [moseson2022c R3].

Findings

F1, F4, F15, F36.

Related concepts

reports moisture-induced phase separation and microstructure.

Formulas

none.

How it is measured or obtained

Contact-mode AFM, 5 × 5 µm images (ECP) or 10 × 10 µm (lopinavir), Ra from the height image [li2017 P8; li2019 P9].

Values in the library
materialvalue or classconditionspaper ids
ECP–HPMC E3, 10–90% DLRa about 0.7–1.7 nm at 18% RH; up to about 45.8 nm at 50% RHspin coated[li2017 R5]
50% ECP–HPMC with waterabout 1.0 nm at 10 µL, about 35 nm at 20 µL, about 166 nm at 100 µL per mL of stock18% RH[li2017 R15]
LPV–HPMC E5, 33% DLabout 0.8–2.5 nm without water; tens to hundreds of nm at 2–10% watercast filmsli2019 R7
Pitfalls and disagreements

Ra falls at high DL when domains crowd (ECP) [li2017 C9]; Ra values of one film vary by more than two orders of magnitude between images (2% water, lopinavir) li2019 R9, R7.b; it cannot explain the release gain alone li2019 C21. The Fig. 3 caption names the quantity "Rg" and the legend "0% RH" [li2017 X1].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

surfactant partitioning into the drug-rich phase

Evidence table: surfactant partitioning into the drug-rich phase. Content from the release-mechanism chapter (2022–2025), with rows from the Physical stability chapter.

The uptake of a surfactant into the drug-rich phase, nanodroplets in solution or drug-rich domains in a hydrated dispersion, read from its depletion from the aqueous phase or from its spectral bands in the drug-rich phase. TPGS was depleted from the aqueous phase by clopidogrel nanodroplets, and the droplets hold about 50:17 w/w drug:TPGS correasoto2022a C19, R12; non-ionic surfactants partition into the clopidogrel-rich phase while ionic ones act at the nanodroplet–water interface correasoto2022a C60. For atazanavir, PVPVA and VP did not partition into the nanodroplets within detection limits, TPGS solution concentration was only minimally affected, and Span 20, Span 80 and Span 85 "seemed to" partition into them correasoto2022b C26, R17. In ritonavir films (Physical stability chapter) the most hydrophilic surfactant, SDS, resides mainly in the polymer-rich phase and the more hydrophobic ones preferentially in drug-rich domains yang2022b C61. The 2023 surfactant study builds on the vapour-sorption finding that Span 20 and Span 85 partition into the ritonavir-rich phase: a continuous drug-rich layer containing Span 85 "is expected to be more liquid-like" and is removed by shear yang2023 R24, C18, C35.

Findings

Release mechanism and LoC: F16, F21, F31.

Related concepts

distinct from micellar solubilization; may slow drug-rich phase coarsening; changes the phase separation morphology of surfactant-containing dispersions; related to the hydrophilic-lipophilic balance of the surfactant.

Formulas

none.

How it is measured or obtained

Quantitative ¹H NMR of the surfactant left in solution with and without nanodroplets, with HPLC after pelleting the droplets correasoto2022a R12; correasoto2022b R17; NMR peak shifts of drug and surfactant at 50 °C correasoto2022a R13, C18; O-PTIR spectra of the separated phases of films (Physical stability chapter) yang2022b C46.

Values in the library
materialvalue or classconditionspaper ids
70 µg/mL clopidogrel with 50 µg/mL TPGSaqueous TPGS 50 → 33 ± 5.4 µg/mL; droplets ≈50:17 w/w drug:TPGSqNMRcorreasoto2022a R12
200 µg/mL atazanavir with PVPVA, VP, SDS, TPGSadditive in solution reduced by 1, 0, 7, 13%¹H NMR, 37 °Ccorreasoto2022b R17
200 µg/mL atazanavir with 20 µg/mL Span 20, Span 85, Span 80reduced by 65, 25, 68%; droplets ≈29:3, 60:4, 62:5 drug:Span by weightsamecorreasoto2022b R17, R19
ritonavir–PVPVA films with SDS; Tween 80 and Spans (Physical stability chapter)SDS only in the polymer-rich phase; Tween 80 and the Spans in the ritonavir-rich phaseO-PTIRyang2022b C46
Pitfalls and disagreements

Partitioning did not predict release enhancement for atazanavir: SDS shows little affinity for the drug and Span 80 partitions into the droplets, and both enhance release correasoto2022b C45. With the Spans the amorphous solubility of atazanavir fell by about 28% (64 to 46 µg/mL) correasoto2022b R18. The temperature of the TPGS depletion measurement is not stated correasoto2022a R12.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

temperature-composition phase diagram

A plot of the liquidus temperature, the temperature at which the last crystal melts, against the composition of a drug–polymer mixture. For a crystalline polymer such as PEG the diagram has a drug-rich and a PEG-rich branch that meet at the eutectic, or, for a monotectic system, only a steep drug branch [baird2011 R5, R8; zhu2011 R4]. Outside the PEG papers the same construction gives the solubility line of a drug in an amorphous polymer, whose crossing with the formulation Tg and the polymer's minimum melt temperature sets a minimum processing temperature [moseson2018 R8, C22]. New aspect (ASD process): for IDM:PVPVA the diagram plots the experimental and predicted critical (solubility) temperature Tc, falling from 160.6 °C for the pure drug to 131 °C at a drug weight fraction of 0.5, together with the formulation Tg line (Gordon–Taylor), the drug melting point, the polymer Tg and a dotted minimum processing temperature Tmin of 117 °C [moseson2018 R5, R8, R9]. Above the solubility line all crystals can dissolve at equilibrium; below it at 50% DL they cannot [moseson2018 C43]. The diagram guided the choice of the extrusion temperature for posaconazole–HPMCAS: 125 °C, below, and 175 °C, above the calculated solubility temperature at each loading [shah2024 R5, R10, C21].

Findings

PEG dispersions: F1, F2, F4. ASD process: F8, F9, F35, F36, F41.

Related concepts

consists of liquidus temperature; contains eutectic or monotectic system; depends on melting point depression; related to drug solubility in polymer. In extrusion work it consists of formulation critical temperature and is used in the HME operating design space.

Formulas

Lacoulonche liquidus model, Flory-Huggins melting point depression, Gordon–Taylor equation.

How it is measured or obtained

Physical mixtures or fused dispersions are heated at 1 °C/min on a hot stage under polarized light, and the temperature at which the last crystal or particle melts is recorded; DSC offset melting at 1 °C/min is used as a second method [baird2011 P2, P3; zhu2011 P3, P4; zhu2012 P9, P10]. For amorphous polymers the offset temperature is extrapolated to 0 °C/min [moseson2018 R5]. For IDM:PVPVA the model line comes from the Flory–Huggins equation with one \chi, and the Tg line from Gordon–Taylor with a density-based constant [moseson2018 P2, E2, E3]. Extrusion outcome is then placed on a plane of product melt temperature against residence time, coloured by the most sensitive method that still called a run amorphous [moseson2018 R15].

Values in the library
materialvalue or classconditionspaper ids
chlorpropamide, aceclofenac, loratadine, haloperidol with PEG 3350predicted line against DSC and hot-stage points; two systems far below the line at 20–60 wt%0–100 wt%, 1 °C/min[baird2011 R5, R6, R7, R8]
benzocaine, ibuprofen, nilutamide, ketoconazole with PEG 3350eutectic (30, 40, 10 wt%) or monotectichot stage, 1 °C/min[zhu2011 R1, R2, R3, R4, R5]
fenofibrate with PEG 3350eutectic minimum about 58 °C at 15–20 wt%CPOM and DSC[zhu2012 R24]
indomethacin–PVPVATc 131 °C ± 2 °C at 50% drug loadingoffset extrapolated to 0 °C/min[moseson2018 C22, R8]
IDM–PVPVApredicted solubility line crosses Tmin near drug weight fraction 0.39 and the Tg line near 0.23 (about 88 °C); 50% DL point marked 131 ± 2 °CFig. 2, readings[moseson2018 R8, X3]
IDM–PVPVA process mapboundary of "amorphous by all techniques" from about 148 °C at 2 min to about 131 °C at 20 min; "X-ray and DSC amorphous" from about 136 °C at 2 min to about 131 °C at about 6 min15 extrusions[moseson2018 R15]
BCL–PVPVA, 30% DLTc = 145 °C and Tm = 195 °C bound the dissolution regime of the extrusion mapFlory–Huggins model, Fig. S2b not supplied[moseson2021 M1, P1]
BCL–PVPVA 30–90% BCLsolubility line from Tc 145 °C (30%) to about 192.3 °C (90%) with χ = −1.57DSC, Flory–Huggins[moseson2022c R8, R9]
PCZ–HPMCAS MFcalculated Tc 135 / 155 / 165 °C at 10 / 25 / 50% DL; extrusion at 125 °C left 0.3 / 3.2 / 19.3 wt% crystals, at 175 °C none2 min, SHG[shah2024 R5, R10, X7]
Pitfalls and disagreements

DSC and hot-stage liquidus values differ by up to about 16 °C at some compositions [baird2011 X7]. The PEG 3350 liquidus is about 61 °C in the diagrams and 55 °C in the model [baird2011 R5, M5, X10]. The diagram describes melting equilibria, not the state of the stored dispersion: a stored 20/80 dispersion has most of its PEG crystalline within minutes (see semicrystalline solid dispersion) [zhu2012 R4]. For amorphous polymers the experimental points depend on heating rate and the 40% drug-loading point deviated from the model line [moseson2018 R3, C19]. For IDM:PVPVA the 131 °C used is the predicted value, the experimental one is 132.3 ± 0.8 °C, and the origin of the "± 2 °C" is not stated [moseson2018 X2]. The switch from Tc to the polymer's Tmin as the lower bound is placed by the authors at 50% DL although the predicted line crosses Tmin near 39% DL [moseson2018 C22, X3]. The diagram gives thermodynamics only; the process map adds kinetics for one micro-extruder [moseson2018 X15]. The BCL diagram is known only through the two temperatures and χ = −1.57 in the text of the 2021 paper [moseson2021 M1].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

ternary phase diagram

A phase diagram of three components

In the ASD process chapter the authors sketch drug–solvent–water for the preparation route and drug–water–polymer for storage, with the phase boundaries only (kinetics not considered) to show how trace water moves the system across the binodal [li2017 C38, C42]. New aspect (Release mechanism and LoC): Yang and co-workers (2021) use the drug–polymer–water diagram as "an alternative explanation" for the fall of the loratadine limit of congruency at 5 °C: because the diagram changes with temperature (cited), drug–polymer miscibility in the presence of water may fall at low temperature, giving a drug-rich phase at lower loading yang2021 C36. They expect drug Tg to act on kinetics and hydrogen-bonding ability on thermodynamics and the ternary diagram, and call for work to separate the two yang2021 C38. Deac and co-workers (2023) drew schematic hydration paths in the type I drug–PVPVA–water diagram: straight toward the water vertex for congruent dispersions, deviating within the two-phase region for incongruent ones, and the side of the plait point at which the path enters decides whether the hydrophobic phase is continuous deac2023a C66, C67, C68. Drug–PVPVA–water systems typically form type I diagrams with PVPVA acting as cosolvent, and real systems are likely to have sloped tie lines; associative separation gives positively sloped tie lines with the plait point on the low-drug side, segregative separation negatively sloped ones with the plait point on the high-drug side deac2023b C31, C48. The 2024 phase-diagram paper measured the drug–PVPVA–water diagrams of phenolphthalein (PHPH) and its methyl ether (MePHPH) at 37 °C from dispersion–buffer mixtures equilibrated for up to 147 days and computed all four analogue diagrams with PC-SAFT, each fitted to one dilute tie line; all share fully miscible polymer–water and drug–polymer binaries and a drug–water gap that closes as PVPVA increases deac2024b P4, P19, R22, R23, R24. The 2023 surfactant study argues on a schematic ritonavir–PVPVA–water diagram that SDS enlarges the miscible region yang2023 C42.

Findings

ASD process: F2, F6, F20. Release mechanism and LoC: F18, F27, F30, F31.

Related concepts

shows the binodal; used with moisture-induced phase separation. The thermodynamic alternative to the wet glass transition temperature as the cause of a lower limit of congruency at low temperature; shifted by drug-polymer hydrogen bonding.

Formulas

none.

How it is measured or obtained

Not measured in the ASD process papers; the schematic uses the Raoult's-law uptake of water by methanol and the observed thresholds [li2017 C39]. In the release-mechanism papers: not measured in the 2021 loratadine study, where it is argued from the temperature dependence of the limit yang2021 C36. In 2024: equilibrated mixtures separated by centrifugation and analysed by quantitative ¹H NMR and HPLC (binodes and tie lines), films at stepped RH for the onset at low water, and PC-SAFT computation of binodal, spinodal and critical point deac2024b P4, P7, P8, P19.

Values in the library
materialvalue or classconditionspaper ids
ECP–methanol–watertrace water moves the system from A to B (still miscible); spin coating carries it along B → D across the binodal at C; water spiking along A → B → E separates at Eschematic[li2017 C38]
ritonavir–PVPVA–waterhydration paths from different DLs enter the two-phase regionschematic from outsideyang2022b C50
MePHPH–PVPVA–waterPC-SAFT binodal, spinodal and tie lines at 37 °Ccomputed and measureddeac2024b R22
drug–PVPVA–water systemstypically type I diagrams (drug–water immiscible, PVPVA a cosolvent)outsidedeac2023b C31
ritonavir–PVPVA–solvent (pseudo-ternary, solvent = methanol + water)at 11.5:88.5 the 25% DL path bypasses the two-phase region and the 50% DL path runs along its edge; at 15:85 and 30:70 both lie inside for most of their lengthcomputedli2020 R18, C55
loratadine–PVPVA; –HPMCASlimit 30 → 2%; 20 → 5% from 37 to 5 °Ccompactsyang2021 R22, C36
MePHPH–PVPVA–watersegregative; critical point ≈29 wt% drug, 59 wt% PVPVA, 12 wt% watermeasured and PC-SAFT, 37 °Cdeac2024b R22
PHPH–PVPVA–waterassociative; critical point ≈2.6 wt% drug, 59.5 wt% PVPVA, 38 wt% watersamedeac2024b R23
TIPP, MeTIPP–PVPVA–waterplait point ≈10 and ≈23 wt% drugPC-SAFT from one tie-line slopedeac2024b R25
Pitfalls and disagreements

The diagram is much more complex with polymer and with both volatile solvents (quaternary or higher) [li2017 C36]. The pseudo-ternary treats total solvent as one corner, so the water to methanol ratio is not shown on the axes li2020 P12. The kinetic reading (loratadine glassy below its wet Tg of 13.8 °C) and the thermodynamic reading (lower miscibility at 5 °C) were not separated yang2021 C16, M1, C36, C38. No ternary diagram was measured for the phenolphthalein analogues in 2023; the diagrams are schematic deac2023b X14. For PHPH the measured gap is smaller than computed, and the TIPP slope was measured at pH 2.5 deac2024b C34, X10.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

Tg-scaled crystal growth rate

Crystal growth rate plotted against the distance from each system's own glass transition, T - T_g, so that the part of an additive's effect that comes from shifting Tg is removed and the remainder can be compared [mosqueragiraldo2014 P7, R12].

Findings

F5, F22, F28.

Related concepts

depends on glass transition temperature; used to test plasticization; contrasts with kinetic versus thermodynamic control of crystal growth; part of crystal growth rate.

Formulas

none.

How it is measured or obtained

Growth rates measured at fixed temperatures are shifted by the DSC Tg of each mixture [mosqueragiraldo2014 P7, R5, R12].

Values in the library
materialvalue or classconditionspaper ids
celecoxib alone and with 10% sucrose palmitate, SLS, TPGS≈0.020, ≈0.014, ≈0.039, ≈0.17 µm/s at T - T_g ≈25 °Cseeded melt growth[mosqueragiraldo2014 R12]
same≈12, ≈3.2, ≈13, ≈7.4 µm/s at T - T_g ≈65 °Csame[mosqueragiraldo2014 R12]
celecoxib with 10% PVP and with PVP plus TPGSTPGS–PVP about two orders of magnitude below PVP at T - T_g ≈26–28 °Csame[mosqueragiraldo2014 X4, R12]
DPB, griseofulvin, celecoxib with 5–10% PHBrates against T − Tg close to the pure compounds; 20% PHB and 5% PVAc belowmelt films[sato2016 R10, C21]
Pitfalls and disagreements

The authors call the corrected surfactant curves "fairly close", but they still span about 12-fold at 25 °C above Tg, against about 85-fold at equal temperature (70 °C), so the correction removes about half of the spread on a log scale (synthesis) [mosqueragiraldo2014 X4, C30, R1]. Tg differences below about 1 °C are unresolved [mosqueragiraldo2014 X7]. The scaling ignores the driving force, which falls with melting-point depression [mosqueragiraldo2014 C33].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

thermodynamic activity

The activity of the drug in a phase, the product of its mole fraction and activity coefficient, a_i = x_i\gamma_i, or of concentration and activity coefficient, a = C\gamma; at phase equilibrium it is equal in all phases [ilevbare2013a E6, E7; mosqueragiraldo2015 E5]. In the LLPS picture the drug has the same activity in the water phase and in the drug-rich phase, which is why the water-phase concentration is capped and why added drug raises the amount of drug-rich phase and not the activity [ilevbare2013a C36, C48; mosqueragiraldo2015 C35]. Membrane flux is proportional to activity (F8) [mosqueragiraldo2015 C10]. The papers of 2017–2022 add that with micelles present the free drug sets the activity: in 3.6 mg/mL SDS the free atazanavir at the amorphous solubility was 65–70 µg/mL, the same as in buffer, although the total was about 1450 µg/mL (slope of free against total 0.047) indulkar2017a R11, and that bile salts change the telaprevir activity at a given concentration (flux about halved with 12 mM STDC) while the activity at the phase boundaries stays [lu2017b R12, C49]. New aspect (Bioperformance): membrane flux is proportional to the activity, a = \gamma C, so equal concentrations need not give equal flux when additives change the activity coefficient [raina2015c C14, E4]. Relative to the crystal, the activity in a one-phase supersaturated solution is C/C_S and is about 8 for felodipine at 25 °C at the amorphous solubility; above it the activity stays constant [raina2014a E10, R17, C35]. The enzalutamide, posaconazole, atazanavir and darunavir papers use the same relation to infer activity from flux: with area, diffusion coefficient, thickness and membrane activity coefficient fixed, J = D a/(h\gamma_m) [wilson2018 E4, E5, C12; elkhabaz2019b E3; alkalla2026 E2, C10].

Findings

Amorphous solubility and LLPS: F5, F8, F11, F12, F16, F17, F18. Bioperformance: F2, F3, F4, F6, F15, F18, F19, F20, F22, F25.

Related concepts

defined with the activity coefficient; related to chemical potential; read from membrane flux; capped by the amorphous solubility. Papers of 2017–2022: expressed as activity-based supersaturation; partition between phases in micelles: micelle/water partition coefficient. Related to free drug concentration.

Formulas

activity from concentration, membrane flux in terms of solute activity, activity-based supersaturation ratio.

How it is measured or obtained

Not measured directly in these papers: it is inferred from the flux across a membrane when diffusion coefficient, area, thickness and membrane activity coefficient are constant, or argued from the phase equilibrium [mosqueragiraldo2015 C10; trasi2015a C14; ilevbare2013a X15]. Flux across a 6–8 kDa regenerated cellulose membrane calibrated in buffer, up to the amorphous solubility, where the activity coefficient is taken as one; flux of a crystal-saturated solution F° gives δ = F/F° [indulkar2017a P8, R10; lu2017b P6, E6]. In the Bioperformance papers it is not measured directly: it is inferred from flux (plateau = constant activity) [raina2014a C36], from flux relative to a reference [raina2015c E9], or from free drug after ultracentrifugation [alhalaweh2016 P10]. The activity-based maximum supersaturation is the ratio of the flux from a solution at the amorphous solubility to the flux from a crystalline suspension, J_{amph}/J_{eq} [elkhabaz2019b E4, R7]; the mass flow of a dissolved formulation gives its donor activity [wilson2018 C12]. Free monomeric drug is taken as the permeating species ueda2020a C24; hate2022 C41.

Values in the library

None printed in this chapter; the activity of the water-saturated amorphous drug appears as the factor exp[−I(a2)] (0.22 for atazanavir to 0.999 for ibuprofen) [indulkar2015 M2; almeidaesousa2015 M1]. The papers of 2017–2022 add activity read from flux: free atazanavir 65–70 µg/mL at about 1450 µg/mL total in 3.6 mg/mL SDS (slopes of free against total 0.998, 0.181, 0.086 and 0.047 at 0, 1, 2 and 3.6 mg/mL SDS) at 37 °C indulkar2017a R11, and telaprevir with δ = C/C° in buffer (slope 1.011) and bile-salt media off the 1:1 line in 50 mM pH 6.5 buffer at 37 °C [lu2017b R16, R17].

In the Bioperformance papers:

materialvalue or classconditionspaper ids
felodipineactivity relative to crystal about 8 (5.99/0.74 = 8.09)25 °C[raina2014a E10, R17]
felodipine suspensionssame low flux at about 1 and 40 µg/mL dissolvedcrystal fixes activity[raina2015c R4, C20]
atazanavir + SDSfree drug about 1 to about 65 µg/mL with and without SDS37 °Cindulkar2017a C19, R11
telaprevir, bile saltsdeviation from the buffer slope gives the activity coefficient changeflux[lu2017b C41]
atazanavir, posaconazole, six mediaJ_{amph}/J_{eq} about 50–56 and 29–37 while the concentration ratio fell to 14 and 537 °C, side-by-side cell[elkhabaz2019b R7, R8, R9]
enzalutamidemass flow rises up to about the amorphous solubility (42 µg/mL), then is roughly constant5 µg/mL HPMCAS, side-by-side cell[wilson2018 R13, C25]
atazanavir, nifedipine and three other drugs, PAMPAbreak from a linear rise at about the amorphous solubilitylipid-impregnated PVDFhate2022 R1, C11, X13
Pitfalls and disagreements

Total concentration with micelles or with a second drug present is not activity; the maximum extent of supersaturation in activity terms is not raised by a solubilizer, whereas the concentration ratio can fall [ilevbare2013a C54; raina2015c C29]. The activity coefficient in the dilute solution is assumed constant between the crystalline and the amorphous concentration ilevbare2013a C55. The free-drug and δ read-outs assume that only dissolved drug crosses the membrane and that the additive does not change it [indulkar2017a X9; lu2017b X8]. Constant activity above the amorphous solubility is an inference from flux [raina2014a X12]; it fails in the hollow-fibre module, where transfer keeps rising (F15) hate2018 C25. With a sink receiver the PAMPA mass flow of atazanavir kept rising above the amorphous solubility, so a plateau is not guaranteed (F22) hate2022 R19, X8. A crystalline co-drug or a polymer mixed into the drug-rich phase lowers the activity of the drug in it, and with it flux (F19, F20) [alkalla2026 C37; ueda2020a C24].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

thermodynamic driving force for crystallization

The free-energy difference between the supercooled liquid (amorphous form) and the crystal, written ΔGv per unit volume or ΔG per mole or gram; it is zero at Tm and grows on cooling [baird2012 C32; vaneerdenbrugh2010a E2]. A larger driving force lowers the classical nucleation barrier [vaneerdenbrugh2010a E3, C39]. This draft comes from the crystallization-tendency chapter; for drugs in polymers the same quantity is lowered by mixing [konno2006 C34]. New aspect (PEG dispersions): in a dispersion in a crystalline polymer the driving force of the drug is lowered by melting point depression, because the supercooling at the storage temperature falls. Zhu and co-workers attribute the delayed crystallization of benzocaine in PEG to entropic mixing and favourable benzocaine–PEG interactions that depress its melting point (around 48 °C at the eutectic against around 89 °C for the neat drug), so that supercooling and driving force at 25 °C are much smaller; with a Tg of −31 °C they consider a thermodynamic rather than a kinetic cause "reasonable" [zhu2012 C32, C33]. New aspects (Miscibility and drug-polymer interactions): In a miscible dispersion the chemical potential of the drug, and so the driving force for crystallization, must be lower than for the pure amorphous drug, through the entropy of mixing and, if adhesive interactions exceed cohesive ones, the enthalpy; melting point depression is its visible sign [marsac2006b C38, C39]. In the PVP dispersions the predicted reduction is small: the Hoffman estimate "does not forecast a large reduction", especially at lower temperature, and is "most likely underestimated" because equilibrium depression is hard to reach at high polymer content [marsac2006b C41, C40]. At low polymer levels, where the melting point and Tg of the drug are unchanged, there "does not appear" to be a macroscopic effect on ΔG, so polymer effects on growth are not read as thermodynamic [kestur2010a C36, C41]. New aspect (Physical stability): for dispersions holding water, the driving force is framed as the degree of supersaturation of the drug in the polymer–water co-solvent, \sigma = (\mu^{1} - \mu^{0})/RT, which water raises as an anti-solvent; it was reasoned, not computed [marsac2008a E1, C26, C49, X4].

Findings

Crystallization tendency: F2, F6, F7, F13. PEG dispersions: F8, F9. Miscibility and drug-polymer interactions: F9, F10, F11. Physical stability: F2, F4, F18, F22, F28, F29.

Related concepts

measured by Hoffman equation; depends on enthalpy of fusion, entropy of fusion and degree of supercooling, which is reduced in a dispersion via melting point depression; part of classical nucleation theory; related to nucleation, crystal growth rate and heterogeneous nucleation; lowered by entropy of mixing; contrasts with kinetic stabilization; related to crystal growth inhibition by polymers, supersaturation, cosolvency and kinetic barrier to nucleation; balanced against mobility in kinetic versus thermodynamic control of crystal growth.

Formulas

Hoffman equation, classical nucleation barrier, entropy of fusion, solid-liquid equilibrium solubility equation, Flory-Huggins activity equation.

How it is measured or obtained

Mostly estimated with the Hoffman equation from Tm and ΔHfus [vaneerdenbrugh2010a E2; baird2010 E25; lu2016 E1]; from MDSC heat capacities, which agreed with the Hoffman estimate for felodipine and nifedipine [marsac2006a R11, C14]; as \Delta G \approx \Delta S_m\,\Delta T for growth analysis [trasi2014a E3]; for dispersions, from melting-point depression and Flory–Huggins mixing [marsac2006b C41; marsac2009 C34]. In the PEG dispersions it was not measured: the melting points are cited and the driving force is inferred from the phase diagram [zhu2012 C32, M3]. For the PVP dispersions, estimated with the Hoffman equation, for pure nifedipine from 0 to 180 °C and, with the depressed melting temperature, for 30 and 40% PVP [marsac2006b P8, E4, R12]; for the dispersions the melting temperature of the 40% PVP curve is not shown in the paper's own melting data [marsac2006b X5]. The unchanged offset melting point of physical mixtures with 3% polymer is taken as an unchanged driving force at a given temperature [kestur2010a R1, C36]. In the moisture papers: Hoffman estimates from Tm and heat of fusion for six drugs at 25 °C rumondor2009c E3, M1; crystal solubility in NMP and NMP–water as stand-ins for PVP and PVP–water [marsac2008a P8].

Values in the library
materialvalue or classconditionspaper ids
nifedipineΔG ≈−30, ≈−24, ≈−16 J/g at 0, 50, 100 °CMDSC and Hoffman[marsac2006a R11]
felodipineΔG ≈−18, ≈−13, ≈−7 J/g at 0, 50, 100 °CMDSC and Hoffman[marsac2006a R11]
34 drugsΔGv from −8.6 (lidocaine) to −54.7 J/cm³ (acetaminophen)Hoffman, 298 K[baird2012 M5, M12]
class I against class IIIΔGv ≈−0.40 against ≈+0.57 SD from the meanper volume, 293.15 K[baird2010 R22.g]
spin-coat classes I, II, III≈−0.29, ≈+0.29, ≈+0.13 SDper volume[vaneerdenbrugh2010a R20.e]
vemurafenib α; β≈−11.0; ≈−6.3 kJ/mol at about 115 °CHoffman, plotted as crystal minus liquid[lu2016 R22, X17]
nifedipine with 40% PVPreduction smaller than the nifedipine–felodipine differencemelting-point depression[marsac2006b C41]
drugs in PVPdriving force remains at most practical polymer contentsinteraction parameters[marsac2009 C34]
benzocaine in PEG 3350melting point depression from around 89 to around 48 °C at the eutecticcited[zhu2012 C32, M3]
ibuprofen; fenofibrate in PEG 3350melting point depression of about 30 °C; about 20 °C (text), about 24 °C (plot)eutectic[zhu2012 C34, X11]
nifedipine, pure; 30% PVP; 40% PVP−9.0, −8.4, −7.95 kJ/mol at 20 °C (zero at ≈171, ≈148, ≈128 °C)Hoffman, plot readings[marsac2006b R12]
nifedipine, pure; 30% PVP; 40% PVP−5.45, −4.1, −2.7 kJ/mol at 100 °Cas above[marsac2006b R12]
felodipine with 3% PVP, PVP/VA, HPMCAS, PVAcmelting point of physical mixtures unchanged (140.7–142.9 °C against 141.5 °C)offset, 1 °C/min[kestur2010a R1]
bifonazole, nimesulide with 5% polymersTg rise 0.4–2.2 °CDSC onset[kestur2011 R6, C12]
nifedipine, felodipine, droperidol, pimozide, indomethacin, ketoprofenHoffman ΔGc 8.2, 6.1, 9.2, 11.0, 8.1, 4.1 kJ/mol25 °Crumondor2009c M1, M6, M3, M2, M4, M5
nifedipine vs felodipine crystalsmole-fraction solubility 0.05 vs 0.10 in NMP: larger lattice term for nifedipine25 °C[marsac2008a R10, C35]
nifedipine and felodipine in PVPFlory–Huggins activity ≈0.84 and ≈0.83 at Φ 0.2χ −3.8, −4.2[marsac2006a R19]
acetaminophen and flutamide with 10% polymerTm barely changed, so the driving force is similar for all polymersDSC[trasi2012a R9, C19; trasi2012b R7, C33]
celecoxib with TPGS and PVPTm 12 °C lower; a smaller driving force "could contribute" to slower growth near TmDSC, melt growth[mosqueragiraldo2014 R5.f, C33]
six compounds with PHBdriving force inferred unchanged from Tm and IR ("can be inferred")DSC; IR[sato2016 C18, X11]
indomethacin polymorphsdifferences in growth persist after a driving-force normalizationmelt growth[tian2017 R11, C24]
Pitfalls and disagreements

The class trend is not monotonic: class II, not class III, had the least negative ΔGv in the solvent screen [vaneerdenbrugh2010a X10]. Pair comparisons of viscosity can be confounded by driving force [baird2012 X9]. Indomethacin has a larger driving force than felodipine yet crystallizes more slowly during dissolution [alonzo2010 C42], and metastable vemurafenib β outgrows α despite α's larger driving force [lu2016 C52]. Low polymer levels barely change it, so polymer effects on growth are read as kinetic [kestur2010b C28]; thermodynamically stable dispersions are hard to achieve [marsac2009 C34]. For ibuprofen and fenofibrate in PEG the depression should lower the driving force, yet the onset in the dispersion is earlier than for the neat drug; the authors explain it by nucleation on crystalline PEG, not by the driving force [zhu2012 C34, C41]. The estimated solubilities of benzocaine (28%) and ibuprofen (25%) exceed the 20% loading, which the card's extractor notes as not discussed [zhu2012 X13, M3, M4]. The 40% PVP curve rests on a melting temperature not shown among the measured data [marsac2006b X5]. The unchanged-driving-force conclusion for 3% polymer uses the melting point of form I in physical mixtures while form II grows [kestur2010a X7]. The size of the lowering differs between the polymers (synthesis: contrast between papers): in PEG 3350 the melting point depression (benzocaine from around 89 to around 48 °C at the eutectic) is taken to make supercooling and driving force much smaller [zhu2012 C32, C33], whereas for PVP the predicted reduction is small [marsac2006b C41]. The driving force did not sort drugs by moisture-induced phase separation rumondor2009c C32. The supersaturation explanation of the nifedipine–felodipine ranking with water rests on NMP data and printed cosolvency fits that do not reproduce their points [marsac2008a X2, X4]. The celecoxib driving force was argued from Tm and not calculated [mosqueragiraldo2014 C33].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

tie line

Evidence table: tie line. Content from the release-mechanism chapter (2023–2025).

The line on a ternary phase diagram joining the compositions of two phases in equilibrium; every overall composition on it separates into the same two phases. Real drug–PVPVA–water systems are "likely" to have sloped tie lines deac2023b C31; associative separation gives positively sloped tie lines and segregative separation negatively sloped ones deac2023b C48. Hydrating a dispersion to the binodal gives a hydrophobic phase that is not in equilibrium with a dilute aqueous phase, and PVPVA diffuses out of it until the polymer/drug ratio reaches that of the dilute-solution binode on the tie line deac2023b C53. Measured in 2024 for MePHPH–PVPVA (sloping down) and PHPH–PVPVA (sloping up) from equilibrated mixtures; each drug's PC-SAFT binary parameter was fitted to its most dilute tie line deac2024b R22, R23, P19.

Findings

Release mechanism and LoC: F27, F30.

Related concepts

joins two points of the binodal and ends at the critical point of the ternary phase diagram; used by the lever rule; its slope distinguishes associative phase separation from segregative phase separation.

Formulas

lever rule.

How it is measured or obtained

Not measured in the 2023 paper, where the slopes are drawn on schematic diagrams deac2023b X14; measured from equilibrated mixtures in 2024 deac2024b R22, R23. The binode compositions in dilute water are estimated from the polymer content of nanoparticles and of particles held in buffer deac2023b C52, R4, R5.

Values in the library
materialvalue or classconditionspaper ids
PHPH–PVPVA; MePHPH–PVPVA particlespolymer diffused out until about 72% and below 5% PVPVA, the hydrophobic binodal compositions48 h in buffer with PVPVAdeac2023b C52, R4, R5
MePHPH–PVPVA–waternegatively slopedmeasured and PC-SAFTdeac2024b R22
PHPH–PVPVA–waterpositively slopedsamedeac2024b R23
Pitfalls and disagreements

One schematic diagram of the 2023 paper uses horizontal tie lines although the text expects sloped ones deac2023b X14, C31. The binode drug loads stated in the text do not exactly match the nanoparticle data (PHPH "roughly 30" against about 22–30%) deac2023b X18. The tie line of the driest MePHPH mixture misses its total composition deac2024b C31, X3.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

Tm − Tg temperature gap

The span between the melting point and the glass transition, the range a melt must cross to become a glass [trasi2014a C27]. If viscosity at Tg is similar for all compounds, a small Tm − Tg with a high viscosity at Tm means a high viscosity at the temperature of fastest growth and so a low maximum growth rate [trasi2014a C27].

Findings

F5, F12.

Related concepts

related to reduced glass transition temperature; related to melt viscosity and crystal growth rate.

Formulas

linear fit of melt viscosity on Tm − Tg.

How it is measured or obtained

From DSC Tm and Tg [trasi2014a M1; baird2012 M1].

Values in the library
materialvalue or classconditionspaper ids
ritonavir; tolazamide77; 154 °CDSC[baird2012 M34, M18]
chlorpropamide; celecoxib; ketoconazole108; 105; 105 °C, in classes I-B, II, IIIDSC[baird2012 M9, M14, M26]
slow and fast growth groups85–117 and 121–146 for drugs with viscosity dataDSC[trasi2014a R9]
class means I-A, I-B, II, III123 ± 11, 119 ± 11, 126 ± 20, 108 ± 16 °C, not significantly differentDSC[baird2012 R10]
Pitfalls and disagreements

The celecoxib Tm − Tg of 125 in one table conflicts with its own Tm and Tg (108) [trasi2014a X1], and the dibucaine row of another table repeats lidocaine [baird2012 X1]. The gap tracked growth groups but not the DSC classes (synthesis: compare R9 of trasi2014a with R10 of baird2012).

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

unstirred water layer

The aqueous boundary layer next to a membrane or solid surface that adds a diffusion resistance; thinner under flow [hate2017 C2, C35, C15]. In a lipid-impregnated PVDF cell the layer, not the membrane, limited the transport of atazanavir and nifedipine; steady diffusion across it is C_b - C_{m1} = J\,\delta_{UWL}/D hate2022 C32, C44, E6. New aspect (Release mechanism and LoC): the aqueous boundary layer at a dissolving enteric polymer compact. For HP-50, polymer solubilization via ionization, linked to the transport of protons and other ionic species across the boundary layer, is called the rate-limiting step qi2022 C2. A carboxylic acid polymer must ionize before it dissolves: without a gel layer the steps are transport of water and base to the polymer, acid–base reaction, release of polymer from the matrix and transport of polymer and protons through the aqueous boundary layer (cited) bapat2023 C33. Faster rotation thins the layer and increases HPMCAS dissolution, and the slope of the stirring dependence differs between media because the interfacial polymer solubility differs bapat2023 C44. In the 2025 grade paper polymer solubility at the interface sets how fast the polymer diffuses across the aqueous boundary layer, and the drug follows bapat2025a C29.

Findings

Bioperformance: F13, F15, F19, F21, F22. Release mechanism and LoC: F23, F33.

Related concepts

part of resistance-in-series permeability model; related to membrane mass transfer coefficient, lipophilicity and membrane asymmetry. Carries the protons that set the microenvironmental pH; its capacity depends on buffer capacity; same layer as the diffusion boundary layer of the dissolving compact.

Formulas

resistances-in-series model, boundary-layer diffusion flux (film model), Levich boundary-layer thickness.

How it is measured or obtained

Not measured directly in the first papers; invoked to explain the higher transfer of a hollow-fibre module (continuous flow thins the layer) and its dependence on flow rate [hate2017 C15, C35]. Drug-rich colloids are suggested to thin it in vivo hate2018 C7; Brownian convection of nanoparticles in the boundary layer is one of three untested explanations for the continuing rise above the amorphous solubility hate2018 C56. A PAMPA study inferred it from the insensitivity of mass flow to filter, pore size and lipid and from the rise with a solubilizing receiver, and estimated the donor-side interface concentration from mass flow hate2022 R5, R16, C32, C44. In the release-mechanism papers: rotation speed of the rotating disk, with the layer thickness from the Levich expression bapat2023 E3, R18, R19.

Values in the library
materialvalue or classconditionspaper ids
nevirapinetransfer rises with flow rate then falls0.5–9 mL/min, hollow fibre[hate2017 R10, C15]
HPMCAS (polymer dissolution)Levich thickness \delta = 1.612\,D^{1/3}\nu^{1/6}\omega^{-1/2}rotating discbapat2023 E3, C44
atazanavir, nifedipine, acetaminophenatazanavir and nifedipine mass flow changed little with filter or lipid; acetaminophen (log P about 0.5) rose from about 0.19 to 0.50 µg/min with lipidPAMPA, buffer receiverhate2022 R5, R16
Caco-2 and donor stirring300 rpm donor and 500 rpm insert shaking to minimise the layerside-by-side and Caco-2[alkalla2026 C15]
neat HPMCAS-MF and HPMCAS-TEArate linear in √rpm, ≈2.9–3.3 times the 100 rpm rate at 700 rpm, no plateaurotating disk, 100–700 rpmbapat2023 R18, R19, X10
Pitfalls and disagreements

Boundary-layer effects were not tested by varying stirring in the side-by-side or Caco-2 work [alhalaweh2016 C3]. Smaller nanodroplets "would be expected" to help by diffusing into the layer, but droplets of about 280 and 1000 nm gave the same PAMPA mass flow (F22) ueda2020a C30, C39; hate2022 R17. The rate rises above the \omega^{1/2} proportionality at 700 rpm (≈2.88–3.34 against 2.65) bapat2023 X10.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

virtual bioequivalence

A simulated crossover study in a population of virtual subjects; a level passes when the 90% confidence interval of the test-to-reference ratio of Cmax, AUCt and AUC lies within 80.00–125.00% [purohit2018 E10, P12]. An absorptive dissolution test gives a second route: the test-to-reference ratio of receiver AUC with the 80–125% limits, at three volumes [hate2019 R13, E6, C25].

Findings

F17, F28, F31.

Related concepts

assesses oral bioavailability; input from non-sink dissolution, residual crystallinity and absorptive sink.

Formulas

none.

How it is measured or obtained

24 virtual healthy fasted subjects, 5 mg, 50% CV on CYP3A parameters, Phoenix average bioequivalence [purohit2018 P12].

Values in the library
materialvalue or classconditionspaper ids
generic vs Prograf, 100 mL inputfails from 20% crystallinity (AUC ratio about 70%)[purohit2018 R13, R17]
generic vs fresh generic, 100 mL inputfails from 10% (about 79.5%)[purohit2018 R14, R17]
generic vs both, 900 mL inputfails from 40% (about 69% and 74.5%)[purohit2018 R15, R16, R17]
tacrolimus (generic with residual crystallinity against Prograf), absorptive test20% crystallinity bioequivalent at 100 mL, not at 40 mL; 50% and 100% not at any volume; fresh generic above the limit at 240 mLhollow-fibre module, 240, 100, 40 mL[hate2019 R13, C25]
Pitfalls and disagreements

Two-way crossover with fixed limits, not the replicated reference-scaled design now required for narrow-therapeutic-index drugs [purohit2018 C13, X14]. Only the mean ratio was evaluated in the absorptive test, and the outcome depends on the volume, so a pass at one volume is not a pass at all (F28) [hate2019 R13, C41].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

water sorption correction of amorphous solubility

The factor e^{-I(a_2)} in Eq. 1, the activity of the amorphous drug once it has absorbed water to saturation; it is below 1 because water dilutes the amorphous drug, and lowers the predicted amorphous solubility ilevbare2013a C59, E1. The water-saturated supercooled liquid and the drug-rich phase made by LLPS have the same activity ilevbare2013a C61. The papers of 2017–2022 add that the water content of the ibuprofen-rich phase without polymer is negligible and has little impact on its amorphous solubility, and that the ibuprofen inputs of Eq. 1 come from H2O work while the measurements were in D2O [ueda2021 R20; ueda2022 X6].

Findings

F5, F6.

Related concepts

computed with the Gibbs-Duhem equation from water sorption; enters the amorphous solubility; related to plasticization by water.

Formulas

amorphous solubility advantage with water-sorption correction, Gibbs-Duhem equation.

How it is measured or obtained

From a gravimetric water sorption isotherm of the amorphous drug (0–95% RH at the test temperature) by integrating the Gibbs–Duhem equation (the Murdande method) [ilevbare2013a P2, P15; almeidaesousa2015 P7; indulkar2015 P7; mosqueragiraldo2015 P5; almeidaesousa2016 P8; hsieh2012 E5].

Values in the library
materialvalue or classconditionspaper ids
ritonavir; efavirenz; loratadine0.27; 0.44; 0.6037 °Cilevbare2013a M1, M2, M3
ketoconazole; indomethacin; felodipine0.28; 0.73; 0.8537 °Cilevbare2013a M8, M7, M9
ibuprofen to griseofulvin0.999, 0.997, 0.985, 0.932, 0.750, 0.69925 °C[almeidaesousa2015 M1, M2, M3, M4, M5, M6]
clotrimazole; atazanavir0.82; 0.2237 °C[indulkar2015 M1, M2]
telaprevir; CRH10.30; 0.75537 °C; 25 °C[mosqueragiraldo2015 M1; almeidaesousa2016 M1]
atazanavirexp[−I(a)] 0.22; 5.2% moisture37 °Cindulkar2017a M2
Pitfalls and disagreements

The sorption isotherms and the integration are not shown, so the factor cannot be reproduced from the papers; only the ritonavir isotherm of the 2013 paper is shown [ilevbare2013a M1, R7; mosqueragiraldo2015 X3]. The griseofulvin and sorafenib water contents at water activity 1 are estimates with an unstated basis [almeidaesousa2015 R8]. For ibuprofen the predicted S0a/S0c lies below the measured one at every temperature, with D2O named as one possible reason ueda2022 R16, C37.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

water sorption isotherm

Equilibrium water content of a solid against relative humidity (water activity) at fixed temperature; for amorphous solids it can be treated as dissolution of water and fitted with Flory–Huggins theory [rumondor2010a C16, E1].

Findings

F6, F7, F8, F23.

Related concepts

measures water sorption and hygroscopicity; analysed with Flory-Huggins interaction parameter.

Formulas

Flory-Huggins water sorption isotherm, ternary Flory-Huggins water sorption isotherm, additive moisture sorption.

How it is measured or obtained

Gravimetric vapour sorption (VTI SGA-100) at 25 °C, either stepwise 5–95% RH with a weight criterion or a fixed time per step (PVP 1000 min), or one RH per experiment held to a plateau (about 600 min for amorphous drugs, about 1000 min for dispersions) [konno2008 P7; marsac2008a P6, R3; rumondor2010a P2; marsac2010 P10].

Values in the library
materialvalue or classconditionspaper ids
PVP K29/32≈33 (75% RH), ≈75 g/100 g (95% RH)25 °C[konno2008 R8.a; rumondor2010a R1]
HPMC, HPMCAS≈10.4–10.9 and ≈6.2–6.3 g/100 g at 75% RH25 °C[konno2008 R8; rumondor2010a R1]
amorphous felodipine, indomethacin≈1.1 and ≈1.55 g/100 g at 75% RH25 °C[rumondor2010a R1.h]
felodipine–PVP 70 wt% PVP≈10.3 (65% RH) turning up to ≈55.5 wt% (95% RH)25 °Cmarsac2010 R9
amorphous ritonavir (outside)≈1.55% at 50% RH, rising, extrapolated linearly to 100% RH37 °Cilevbare2013a R7, E14
PVP, PVPVA, HPMCASisotherms at 25 °C, PVP far above the others at high RHcitedrumondor2010c R19
resveratrol–PVP dispersion and physical mixture0–95% RH, mixture above dispersion at every step25 °C[wegiel2013b R19]

Evidence table: water sorption isotherm.

Pitfalls and disagreements

Equilibration protocols differ between polymers and papers (5 h at fixed RH gives about half the plateau value for 50% PVP; synthesis from 4.8 against ≈9.4 g/100 g [marsac2010 R10.b; rumondor2010a R2.d]). One paper reports different PVP water contents in two figures [konno2008 X2]. Isotherms appear to be single runs [rumondor2010a X12].

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

water sorption

The uptake of water vapor by an amorphous drug as a function of relative humidity; amorphous solids sorb more than their crystals, and the uptake sets both the activity of the water-saturated amorphous drug and the wet Tg ilevbare2013a C23, C59. The papers of 2017–2022 add dynamic vapor sorption of melt-made ibuprofen/PVP-VA and ibuprofen/HPMC 603 ASDs at 99% RH, used to test whether extra water explains the stronger effect of PVP-VA [ueda2021 P6, R17]. New aspect (ASD process): in the evacetrapib papers of 2017, low-DL dispersions are held to absorb more water because they contain more polymer, which is why they separate on storage while high-DL films stay miscible [li2017 C42, C52]. In the coating papers it is the uptake of coated and uncoated ASD powders in dynamic vapour sorption, as isotherms at 40 or 37 °C and as kinetics at 90% RH over 2–3 h (see moisture barrier effect) [moseson2022a R8, R9; duong2022c R9; moseson2023 R7, R8; benson2025 R3]. PVPVA ASDs sorb over three times as much water as HPMCAS ASDs benson2025 C42, R23. New aspect (Physical stability): one-phase drug–polymer blends sorb less water than the weighted sum of their components, while blends that have separated sorb close to additively [rumondor2010a C10; rumondor2009c C24]. New aspect (Release mechanism and LoC): in the release papers of 2021–2022 water sorption of the dispersion is read as a proxy for the water that enters the hydrating compact. Neat PVPVA sorbs much water at high water activity, its Tg falls below room temperature and it gels and dissolves rapidly (cited) que2021 C42; a drug–polymer interaction that persists in water is proposed to lower the water uptake and so the polymer dissolution rate que2021 C44. Surfactants slightly raised the water uptake of atazanavir–PVPVA correasoto2022b C25, and salt formation changed the uptake of amorphous lumefantrine by counterion hiew2022b C10. For HPMCAS-MF dispersions the drug was proposed to lower polymer release at higher buffer capacity by reducing the amount and rate of water the polymer absorbs, leaving a more viscous gel bapat2023 C46. Plasticizers changed the rate and extent of water vapour uptake of atazanavir–PVPVA dispersions only slightly, against suggestions that additives act through solvent ingress correasoto2023 C34, C35.

Findings

Amorphous solubility and LLPS: F2, F5, F20. ASD process: F6, F4, F43, F45, F47. Physical stability: F6, F7, F23. Release mechanism and LoC: F15, F22, F24, F26.

Related concepts

input to the Gibbs-Duhem equation and to plasticization by water; determines the water sorption correction of amorphous solubility. Governed by hygroscopicity; drives moisture-induced phase separation. Measured by water sorption isotherm; marker of amorphous-amorphous phase separation. Sets plasticization by water and so the wet glass transition temperature; needed for polymer chain disentanglement.

Formulas

Gibbs-Duhem equation, water plasticization rule of thumb, additive moisture sorption, Flory-Huggins water sorption isotherm.

How it is measured or obtained

Gravimetric vapor sorption (SGA-100) at the test temperature, 0–95% RH, equilibrium criterion about 0.01% weight change; the isotherm of ritonavir was extrapolated linearly from the high-water region to 100% RH [ilevbare2013a P15, E14; almeidaesousa2015 P7; mosqueragiraldo2015 P5]. In the ASD process papers: water absorbed by ASD powder in DSC pans after 24 h over saturated K2SO4 (procedure not printed), % w/w dry basis [li2017 P14]; equilibrium sorption of polymer powders by dynamic gravimetric sorption (see hygroscopicity) [mugheirbi2017 P14]. In the moisture-induced separation papers: plateau uptake at fixed RH (about 600 min for amorphous drugs, about 1000 min for dispersions) or isotherms at 25 °C [marsac2008a R3; rumondor2010a P2; rumondor2009c P11]. In the release-mechanism papers: dynamic vapour sorption at 37 °C up to 95% RH correasoto2022b R16 and at 5–95% RH for the neat amorphous salts hiew2022b R4.

Values in the library
materialvalue or classconditionspaper ids
ritonavirabout 4.98% at 95% RH; 5.21% extrapolated to 100% RH (slope 0.075, intercept −2.290)37 °C, melt-quenchedilevbare2013a R7, E14
telaprevir4.31% at 95% RH; about 4.6% estimated at 100% RHmelt-quenched glass[mosqueragiraldo2015 M1]
clotrimazole; atazanavir1.4%; 5.2%amorphous, 37 °C[indulkar2015 M1, M2]
griseofulvin; sorafenib2.7%; 1.8% at water activity 1 (estimated, basis not stated)25 °C[almeidaesousa2015 R8]
atazanavir5.2% moisture, exp[−I(a)] 0.22amorphous, 37 °Cindulkar2017a M2
ibuprofen/HPMC 603 and ibuprofen/PVP-VA ASDs13.9 and 13.0% (1/1); 6.5 and 4.2% (4/1) after 200 min99% RH, 37 °C[ueda2021 R17]
ECP–PVPVA powdersabout 61% (PVPVA), 35% (10% DL), 4–7% (20–50% DL), 0.5–3.6% (60–100% DL)24 h, 97–98% RH[li2017 R25, X3]
felodipine, indomethacin, PVP, HPMC, HPMCASFlory–Huggins water parameters from isotherms25 °C[rumondor2010a R11]
clofoctol–PVP with 70% API or more; probucol–PVPresistance to moisture-induced separation attributed to too little moisture sorbed by the hydrophobic systems; no water content or sorption was reported for those filmsoutsiderumondor2011 C36, X6
70 wt% PVP felodipine dispersionwater vapour sorption isotherm at 25 °Coutsidemarsac2010 R9, R10
erlotinib–HPMCAS 60% DL, uncoated against 5–25 nm coatedabout 5.7 against 5.4%DVS 40 °C, 75% RHmoseson2022a R8, R9
ezetimibe–HPMCAS 50% DL, uncoated / thin / thickabout 5.65 / 5.83 / 3.17%DVS 37 °C, 95% RH[duong2022c R9]
PCZ–HPMCAS 25% DL, uncoated and coated 11 / 23 / 39 nmabout 4.7 / 4.3 / 3.7 / 1.2% at 30 minDVS 37 °C, 90% RHmoseson2023 R7
PCZ–HPMCAS 50% DL, slow-deposited 26 nmabout 0.33% at 2 h against about 4.2–4.5%samemoseson2023 R8
RTV–PVPVA 20% DL powdersabout 18.8–20.8% at 3 h; slow-coated 20.5 nm about 15.1%90% RHbenson2025 R3
nifedipine; felodipine; with 25% PVP≈1.8; 1.1; 5.5; 4.6 g/100 g75% RH, 25 °C[marsac2008a R2]
felodipine–PVP 25%43–64% below additivity15–85% RH[rumondor2010a R7.b]
nifedipine-, pimozide-, droperidol–PVP5.9, 7.4, 0.2% from additivity (phase separated)95% RHrumondor2009c R22
indomethacin–PVP 75:254.9 vs 21.7 g/100 g predicted95% RHrumondor2009c R22.g
40% resveratrol–PVP dispersion≈1.8, ≈5.9, ≈8.7, ≈12.8% at 20, 60, 80, 95% RH, below its physical mixture at every step25 °C[wegiel2013b R19]
atazanavir–PVPVA 10%; with SDS or Span 8044%; 49% waterDVS, 37 °C, up to 95% RHcorreasoto2022b R16
amorphous lumefantrine salts≈6.6 (PEG 250 diacid 1:1), 3.3 (sulfate), below 2% (benzoate, besylate, tosylate, camsylate, HCl) at 95% RHDVShiew2022b R4
lumefantrine salt–PVPVA dispersions35–55% water, higher at lower loading95% RH, 40 °Chiew2022b R5
HP-50-Na; amine salts of HP-50; HP-50≈42.4; ≈24.6–30.1; ≈9.7% water at 96 hpowders, 100% RH, 37 °Cqi2022 R11
neat HPMCAS-MF; indomethacin and its methyl ester dispersionshighest extent and rate for the neat polymer; lower with indomethacin, lowest with the esterpowders, 95% RH, 37 °C, 12 hbapat2023 R20, C31
PVPVA; with 10% TBC; with 10% GTB≈41.8; ≈34.4; ≈32.0% water at 300 min95% RH, 37 °Ccorreasoto2023 R22
Pitfalls and disagreements

The relative humidity to which the % moisture of the weak-base table refers is not stated [indulkar2015 M1, M2]. Linear extrapolation to 100% RH is an approximation ilevbare2013a E14. In the film papers, uptake was measured on bulk powders, not on the films imaged by TEM, and the values at 20–50% and 60–80% DL differ by only a few per cent although separation was seen to 80% DL [li2017 X8, R19]. The same explanation (too little moisture sorbed at high loading) is given for other hydrophobic drug–PVP systems without sorption data rumondor2011 C36, X6. The thin 50% ezetimibe coating protected for two years without lowering uptake [duong2022c X7]. The slow-sorbing posaconazole samples had not levelled off within 2 h moseson2023 X17. The two moisture papers normalise the deviation from additivity differently (against the prediction, against the measured value) [rumondor2010a E6; rumondor2009c E6]. No sorption was measured on the films in which nucleation and growth were counted [marsac2008a X12]. The lower uptake of the resveratrol dispersion is read as hydrogen bonds suppressing sorption, but bonding in the wet dispersion was not measured [wegiel2013b C37, X18]. The dispersion sorption curves of both papers are in SI not supplied correasoto2022b R16; hiew2022b R5. The excess-acid PEG 250 diacid (1:1) salt liquified at 95% RH hiew2022b C10. Among the HP-50 salts the sodium salt took up the most water without dissolving faster, which weakens hydration as the explanation of the salt effect qi2022 X17, C35.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

wettability

How readily a medium spreads on a solid

In the earliest chapter paper the authors suggest that the PEO gel's longer contact with the drug "may" improve wetting, give the medium access to the drug surface and prevent aggregation, but wetting was not measured [broman2001 C40, C5]. In the later papers wetting is inferred, not measured: uncoated 70% ezetimibe–HPMCAS powder floated on the medium whereas coated powder was wetted and released faster [duong2022c R14, C30]; a coating that keeps water out leaves particles dry benson2025 R7, R8; SDS in the medium raised the release of the binary bicalutamide powder only slightly, so SDS improves wetting moseson2022b R9, R13, C24; agglomerated fines delayed the first minutes of a cryomilled 10% dispersion moseson2022b R8, C20. New aspect (Release mechanism and LoC): in the five-polymer study a higher contact angle of dissolution buffer means poorer wetting and higher surface hydrophobicity of the polymer, and the contact angles ranked the polymers in the same order as water sorption saboo2020a C11. Saboo and co-workers (2021) conclude that TPGS acts beyond any wetting benefit, without measuring wetting saboo2021 C34, X13. In the 2022 ritonavir surfactant study 50 µg/mL SDS in the medium, the amount a dissolved tablet delivers, did not change release of the binary dispersion, which the authors read as poor wetting being "unlikely" to explain the effects, although the same paper suggests that Tween 80 and Span 20 "may" improve initial wetting indulkar2022 R10, C13, C44. Poor wetting "could have" caused the poor release of binary grazoprevir–HPMCAS co-precipitates, whose larger specific surface area could predispose them to it hiew2023 C20, C39. The 2025 high-loading particle study measured wettability as the FaSSIF contact angle of drops on powder beds over 10 s: 75% grazoprevir–HPMCAS particles with SDS (0°) or 10 mg/mL HPMC (about 30–52°) released about 37–52% at 90 min, those with PVP, poloxamer 407, HPMC dispersed in heptane or an MTBE treatment (about 119–137°) about 8–20%; the authors call proper wetting "pivotal" hiew2025 R15, R17, C40, C59.

Findings

ASD process: F18, F39, F40, F46, F48, F49. Release mechanism and LoC: F11, F21, F28, F35.

Related concepts

related to polymer-controlled release. Measures polymer hydrophobicity; ranks with hygroscopicity.

Formulas

None.

How it is measured or obtained

Not measured in the earliest chapter paper. Elsewhere by static contact angle on spin-coated polymer films or powder beds and by visual observation of floating powder saboo2020a R4; hiew2025 R15; hiew2023 R9. Visual observation of floating powder [duong2022c R13, R14]; confocal imaging of particle hydration with a drug-rich and a polymer- and water-rich dye benson2025 P12, R7, R8, R9; medium controls containing SDS or TPGS at the level the dispersion delivers moseson2022b P10, X12. In the release-mechanism papers: static contact angle of buffer (pH 6.8; pH 7.4 for EUDS) on spin-coated polymer films, triplicate saboo2020a R4, P4. Contact angle of 4 µL SGF or FaSSIF drops on powder beds stuck to tape, followed for 10 s, n = 4 hiew2025 P17.

Values in the library
materialvalue or classconditionspaper ids
probucol–PEO tabletsgel formation in the medium; highest release29 h[broman2001 R15, R12]
polymer films (outside)higher contact angle means poorer wetting: HPMCAS = EUDS > HPMC > PVPVA > PVP (46.8 ± 5.7°, 45.9 ± 1.6°, 26 ± 1°, 14.6 ± 0.4°, 11.9 ± 0.9°)pH 6.8 buffersaboo2020a R4, C11
binary cPADs (outside)floating and aggregating; poor wetting may have caused poor release; hierarchical co-precipitates wetted betterdissolution mediumhiew2023 R9, C20
uncoated 70% ezetimibe–HPMCAS powderfloated; peak about 7.6 µg/mL against about 11.9 and 10.9 for the coated powders10 mg in 50 mL, pH 6.5[duong2022c R13, R14]
slow-coated 20.5 nm ritonavir–PVPVA particlespart unhydrated after 10 min; almost no further hydration after 3 h in acid; sonic sieving restores itconfocalbenson2025 R7, R8, R9
30% BCL–PVPVA, binary powder with 3 µg/mL SDS in the mediumabout 46% at 30 min against about 42% withoutdose of at most 30 µg/mLmoseson2022b R9
PVPVA; HPMCAS (cited)water contact angle 30.6°; 58.6°literatureyang2021 M7, M8
grazoprevir–HPMCAS 75:25 particles with SDS; with 10 mg/mL HPMC0° from 1 s; ≈30° and 51–52° at 10 sFaSSIF, powder bedhiew2025 R15
same with PVP, poloxamer 407; heptane particles; MTBE-treated dispersion≈121°, 131°; 137 ± 5°; ≈119°samehiew2025 R15
Pitfalls and disagreements

SDS dissolved in the medium did not change dissolution of a ritonavir ASD, so poor wetting is unlikely to explain that case (outside) indulkar2022 R10, C13. The contact angles are of neat polymer films, not of the dispersions saboo2020a R4. The two most hydrophobic polymers by contact angle released felodipine congruently to 50%, the most hydrophilic had the lowest limits saboo2020a R15. Wetting was not measured in the surfactant study that excluded it saboo2021 X13. Wetting was not measured in the ritonavir surfactant study, and its control used SDS only, at one level indulkar2022 X8. In the grazoprevir particle study wetting was judged by eye only hiew2023 X12. The relation is two clusters of seven materials, not a graded trend; the fully wetting SDS particles released less than the HPMC ones, and HPMC was compared at twice the concentration of the others hiew2025 X11, X8.

← Concepts and formulas

concept · as used in A. Release mechanism and LoC

zeta potential

The electrical potential at the slipping plane of a particle or droplet in liquid; here a read-out of the charge that an adsorbed or ionized polymer gives a drug crystal or a drug-rich droplet [ilevbare2012b C25; jackson2014 C34].

Findings

F11, F15, F32, F33, F37, F44.

Related concepts

reports polymer adsorption to drug-rich droplets and polymer ionization; related to droplet coalescence.

Formulas

none.

How it is measured or obtained

Electrophoretic light scattering: ritonavir seeds (4.0 mg in 20 mL, 10 mM citrate, overnight at 37 °C) with 5 µg/mL CAP Adp 0.85; danazol droplets formed above the onset of phase separation with and without 10 µg/mL polymer [ilevbare2012b P8; jackson2014 P9]. n and the danazol concentration are not printed [jackson2014 X11].

Values in the library
materialvalue or classconditionspaper ids
ritonavir seeds with CAP Adp 0.85−27.2 mV (pH 3.8); −52.6 mV (pH 6.8)10 mM citrate, no polymer-free control[ilevbare2012b R8, X14]
danazol droplets: alone; PVP; HPMC; HPMC-AS−8.1; −5.3; −2.3; −13.7 mVpH 6.8 buffer, 25 °C[jackson2014 R23]
atazanavir nanodroplets (Bioperformance)HPMCAS and Eudragit L100 give a negative charge; HPMC and PVPVA neutral droplets; SDS negative, CTAB positivedonor additives, 37 °Chate2022 R17, C38
lumefantrine ASD filtrate (Physical stability)high particle charge, "most likely" from ionized polymer or drug at the interface50 mM pH 6.8 phosphatetrasi2020 R15, C20
danazol droplets−8.1 mV alone; −3.5 (PVP), −2.2 (HPMC), −18.6 mV (HPMC-AS) at 1000 µg/mL25 °C[jackson2016 R18]
telaprevir droplets, 1.86 mM bile salts−9.2 mV alone; about −40 to −53 mV180 µg/mL[lu2017 R8]
telaprevir seeds, 1.86 mM bile salts−7.7 mV alone; about −38 to −50 mV; no correlation with inhibitionpH 6.5[lu2017a R13, C25]
enzalutamide droplets, 45–120 µg/mL−9 to −18 mV alone; about −15.5 to −30 with HPMCAS; +9.5 to +15 with Eudragit E PO50 mM phosphate pH 6.5, 37 °C[wilson2021 R13]
posaconazole droplets, 100 µg/mLabout −1 mV alone; −12.9, −10.8, −7.4 mV with HPMCAS L, M, HpH 6.5, 900 µg/mL polymershah2025 R15
Pitfalls and disagreements

The ritonavir zeta potentials were measured in citrate, not the 100 mM acetate and phosphate of the growth tests, and without a polymer-free control [ilevbare2012b X14]. The danazol shifts are read as polymer at the droplet surface ("indicating") but no polymer-free droplet charge by another method is given beyond the alone value [jackson2014 C34, R23]. Values within ±30 mV were read as steric rather than electrostatic stabilization ("most likely"), without following ripening over time [wilson2021 C28].

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

activity-based supersaturation ratio

Expression

SR = \frac{a}{a^{*}} = \frac{\gamma\,c}{\gamma^{*}\,c^{*}} indulkar2017a E9;

\ln\delta = \frac{\mu - \mu^{\circ}}{RT} = \ln\frac{a}{a^{\circ}} [lu2017b E3];

from flux,

\frac{F}{F^{\circ}} = \frac{a}{a^{\circ}} = \delta [lu2017b E6];

the ratio of flux slopes below the plateau gives the activity-coefficient ratio,

\frac{dF/dC}{\left(dF/dC\right)_{\mathrm{buffer}}} = \frac{\gamma}{\gamma_{\mathrm{buffer}}} [lu2017b E7];

and the maximum value in a simple dilute solution,

\ln\delta_{\mathrm{Max}} = \ln\frac{C_{\mathrm{amorphous}}}{C_{\mathrm{crystalline}}} [lu2017b E5].

In the Bioperformance papers the ratio is printed as

\ln S = \frac{\mu - \mu^{*}}{RT} = \ln\frac{a}{a^{*}} = \ln\frac{\gamma c}{\gamma^{*} c^{*}} [raina2015c E5];

below the amorphous solubility, with a constant activity coefficient, it reduces to \alpha = C_i/C_S [raina2014a E10].

In the bile-salt papers of 2016–2017 it is printed as

S = \frac{a}{a_{s^*}} = \frac{C\,\gamma}{C_{s^*}\,\gamma_{s^*}} [li2016a E3]

and again as \ln\delta = (\mu - \mu^{\circ})/RT = \ln(a/a^{\circ}) [lu2017 E1].

In the Mesoporous silica papers it is printed as

\ln S = \frac{\mu - \mu^{*}}{RT} = \ln\frac{a}{a^{*}} = \ln\frac{\gamma C}{\gamma^{*} C^{*}} [dening2018 E5],

and in the same form [dening2019 E5].

In the ASD dissolution papers the activity is printed as the free drug concentration over the crystalline solubility,

a = \frac{C_i}{C_S} = S_i jackson2015 E2,

and the ratio as \ln S = \frac{\mu - \mu^{*}}{RT} [xie2015 E4].

Variables and units

symbolmeaningunits
a, a^{*} (or a^{\circ})activity of the drug in the solution and in a solution saturated with the crystaldimensionless [indulkar2017a E9; lu2017b E3; dening2019 E5]
\gamma, \gamma^{*}activity coefficients at the two statesdimensionless [indulkar2017a E9; dening2019 E5]
c, c^{*} (or C, C^{*})concentrations at the two statesµg/mL [indulkar2017a E9; dening2019 E5]
F, F^{\circ}mass flow rate of the solution and of the crystal-saturated solutionµg/min [lu2017b E6]
\deltafundamental (activity-based) supersaturationdimensionless [lu2017b E3]
\mu, \mu^*chemical potential in the solution and at saturation with the crystalJ/mol [raina2015c E5; dening2018 E5]
C_i, C_Sconcentration and crystalline solubilityµg/mL [raina2014a E10]
S; a_{s^*}, C_{s^*}, \gamma_{s^*}supersaturation as an activity ratio; activity, concentration and activity coefficient at crystalline saturation (2016 notation)dimensionless; µg mL⁻¹ for C_{s^*} [li2016a E3]
C_i (danazol notation), S_ifree drug concentration (from flux); supersaturation, equal to aµg/mL; dimensionless jackson2015 E2
R, Tgas constant, temperatureJ/(mol K), K [xie2015 E4]

Assumptions and valid domain

The concentration ratio equals SR only if γ/γ* = 1; flux is proportional to activity with D, S, h and γm constant and sink conditions; F° is the same with and without the additive; the buffer series (γ = 1 up to the amorphous solubility) calibrates media with unknown activity coefficient [indulkar2017a C20, C37; lu2017b C11, C36, C37]. Tested for atazanavir in SDS at 37 °C and for telaprevir with six bile salts at 37 °C [indulkar2017a A1; lu2017b A1]. The activity coefficient is constant between the crystalline and the amorphous solubility ("a reasonable assumption for these highly dilute solutions") [raina2014a C34]. Reduces to C/C_s only when the activity coefficients of the supersaturated and the saturated solution are equal, which surfactants can upset; the activity is taken from the membrane flux [li2016a E3, R39; lu2017 E1, E2]. In the Mesoporous silica papers the relation is used as an argument about adsorption rather than to compute a number. Because the chemical potential of dissolved drug equals that of drug in any phase in equilibrium with it, adsorption to silica is taken to lower the achievable chemical potential, so the driving force for desorption falls as S rises ("it appears", "it is clear") [dening2018 C56]. Conversely a higher S raises the drug's activity and the driving force for adsorption onto the high-energy silica surface ("can be proposed") [dening2019 C39]. In the ASD dissolution papers the activity is estimated as free concentration over crystalline solubility (cited) jackson2015 E2; the ratio is printed together with S = c/c^{*} for dilute solutions, without a stated assumption [xie2015 E4, E5].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
indulkar2017aSRactivity and SRconc of atazanavir in 0–3.6 mg/mL SDSSRactivity about 65–70 at the amorphous solubility; SRconc 33–38 in SDSreproduces (1450 ÷ 45.6 = 31.8 against about 31.0 and 33.0 in Figs. 7a, 7b) indulkar2017a E9, R12, R13
lu2017bδ of telaprevir from fluxbuffer slope 1.011, R² 0.9928; δ about 28 at the boundary (22 with STCDC, SGCDC)reproduces (F° = 0.009 × 5.2 = 0.0468 µg/min; F ≈ 1.24 µg/min at 140 µg/mL gives δ ≈ 26.5; 148 ÷ 5.2 = 28.5) [lu2017b E5, E6, R16, R18]
lu2017bactivity-coefficient ratio from flux slopesslopes not printedinputs not printed [lu2017b E7]
other chaptersthe same relation printed as an activity ratio or a chemical-potential differencenoneprinted; not recomputed here [raina2014a E10; raina2015c E5; jackson2015 E2; lu2017 E1; wilson2018 E7; elkhabaz2019b E2; indulkar2019b E1]
raina2014aactivity of felodipine5.99/0.74 = 8.09 (text about 8); 2/0.74 = 2.70reproduces [raina2014a E10]
raina2015cdefining Snonenot applicable [raina2015c E5]
jackson2015danazol activity8.1/0.9 = 9.0 against about 8.9reproduces jackson2015 E2
wilson2018enzalutamideS printed "approximately 13" from the Table 2 ratiomismatch: 42/2.9 = 14.5; 13 matches the theoretical 39/2.9 [wilson2018 E7, X2]
elkhabaz2019batazanavir and posaconazole in six mediaread as J_{amph}/J_{eq}; \gamma not determinedinputs not printed [elkhabaz2019b E2, C28]
li2016aapparent S' = C/C_s with γ ratio set to 1, tested against mass flownevirapine S' 7.1–8.7; celecoxib printed 13.6 against 16.7 recomputedinputs not printed for γ; mismatch for celecoxib [li2016a E1, X1, X18]
lu2017δ 11.5 and 28.8 for telaprevir with six bile saltssee the flux-ratio formulacalibrated from flux [lu2017 E1, R1]
indulkar2018supersaturation in lecithin and SIF mediaSR = a/a^{*}, crystalline standard stateinputs not printed [indulkar2018 E1]
indulkar2019batazanavir in SDSas abovestated about 65, flux not shown [indulkar2019b E1, X6]
elkhabaz2021cited for atazanavir and posaconazole in six medianamed only54; 36 and 30 [elkhabaz2021 E8, R4]
duong2022bposaconazole in micellar mediaestimated from the concentration ratio with Km/w falling linearlyinputs not printed [duong2022b E11]
dening2018falling released fraction with dose from silicanoneinputs not printed [dening2018 E5]
dening2019adsorption onto silica rising with supersaturationnoneinputs not printed [dening2019 E5]
jackson2015maximum supersaturation of danazol dispersionseight bars equal free drug over 0.9 µg/mL; 90:10 HPMCAS and 50:50 HPMC do notreproduces in part jackson2015 R10, X3
xie2015definition of the driving force for celecoxib nucleationnonenot applicable [xie2015 E4, C43]

Where it fails or is disputed

F° is not shown and for SGCDC cannot be the same at 1.86 and 12 mM, so part of the offset between δ and C/C° reflects the solubility–flux mismatch [lu2017b X7]. The conversion needs a membrane that passes only dissolved drug [indulkar2017a X9; lu2017b X8]. Free-drug and SRactivity values at intermediate totals differ by up to about 40% between the two figures of the atazanavir paper indulkar2017a X12. Activity coefficients are not printed in the Bioperformance papers; with micelles or complexes \gamma/\gamma^* \ne 1 [raina2015c C36]. In the media study the gap between this ratio (read from flux) and the concentration ratio is the only access to \gamma/\gamma_{eq} (F18) [elkhabaz2019b C21, C28]. The concentration ratio fails for celecoxib with bile salts and HPMCAS, where the solubility rises but the mass flow does not; the activity coefficients are not printed [li2016a X18, E3]. The formula is also printed by ten papers outside the crystallization-from-solution chapter (see the evidence table). In the silica papers the chemical potential or activity of adsorbed drug and of drug in the adsorption samples was not measured, so both uses are arguments [dening2018 C56; dening2019 C39]. For the danazol dispersions the result depends on the crystalline solubility used, 0.9 or 1.0 µg/mL (about 10%) jackson2015 X15.

Concepts

activity-based supersaturation, supersaturation, maximum achievable supersaturation, chemical potential, thermodynamic activity, drug adsorption onto silica, free drug concentration. Findings. Amorphous solubility and LLPS: F16, F17. Bioperformance: F2, F3, F18. Crystallization from solution: F31, F32, F34, F40, F43. Mesoporous silica: F4, F8. Supersaturation from ASD dissolution: F4, F7.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

activity from concentration

Expression

a_{i1} = x_i\,\gamma_{i1} ilevbare2013a E7;

a = C\,\gamma [mosqueragiraldo2015 E5].

The papers of 2017–2022 print the same relation as

a = \gamma\,c indulkar2017a E8

and as

a = C\,\gamma [lu2017b E2].

In the Bioperformance papers of 2014–2016 it is printed as

a = \gamma\,C [raina2014a E7; raina2015c E4; alhalaweh2016 E2].

Variables and units

symbolmeaningunits
athermodynamic activity of the drugdimensionless [mosqueragiraldo2015 E5]
x_imole fraction of the componentdimensionless ilevbare2013a E7
Cconcentration of the drug in the donor solutionµg/mL [mosqueragiraldo2015 E5]
\gammaactivity coefficient in the bulk (donor) solutiondimensionless [mosqueragiraldo2015 E5]

Assumptions and valid domain

None stated for the definition; the amorphous solubility treatment assumes a constant activity coefficient in the dilute solution between the crystalline and the amorphous concentration [ilevbare2013a C55; mosqueragiraldo2015 C10]. In the Bioperformance papers γ equals 1 in a dilute solution without solubilizers; with micelles or protein it does not [raina2015c C32, C36].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
ilevbare2013aactivity of a species equal in all phases at equilibriumnonenot applicable (no numerical output) ilevbare2013a E6, E7
mosqueragiraldo2015donor activity in the flux equationnone printedinputs not printed (γ) [mosqueragiraldo2015 E5]
indulkar2017afree atazanavir in SDS from the slope γ of free against total drugγ 0.998, 0.181, 0.086, 0.047 at 0, 1, 2, 3.6 mg/mL SDSreproduces (0.047 × 1450 µg/mL = 68 against about 70 plotted free) indulkar2017a E8, R11
lu2017bactivity of telaprevir in bile-salt medianone printedinputs not printed (γ) [lu2017b E2]
raina2014aflux proportional to activityγ not printednot applicable [raina2014a E7]
raina2015cwhy equal concentrations give different fluxγ not printednot applicable [raina2015c E4]
alhalaweh2016Caco-2 flux of ritonavir–atazanavir mixturesγ not printedinputs not printed [alhalaweh2016 E2]

Where it fails or is disputed

γ was not measured in either paper, so activity is only inferred, from the flux plateau [mosqueragiraldo2015 C10; ilevbare2013a X15]. γ in the micellar solutions is estimated with the ideal dilute solution as standard state and from a buffer calibration, not measured independently indulkar2017a R11, C18. In the Bioperformance papers γ was never measured directly. In the media study the activity-based and concentration-based supersaturation ratios agreed in buffers and diverged in micellar media, so γ/γ_eq departs from 1 there (F18) [elkhabaz2019b C28, C42].

Concepts

thermodynamic activity, activity coefficient, membrane flux, micellar solubilization. Findings. Amorphous solubility and LLPS: F8, F12, F16. Bioperformance: F3, F18.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

additive moisture sorption

Expression

Printed in words in the two moisture papers (weight-averaged sum of the pure-component uptakes); written here in symbols:

\text{uptake}_{blend} = w_D\,\text{uptake}_D + w_P\,\text{uptake}_P [rumondor2009c E6; rumondor2010a E5]

as printed outside the subcategory:

M_{additive} = M_D w_D + M_P w_P [li2018 E1]

Variables and units

symbolmeaningunits
w_D, w_Pdry-basis weight fractions of drug and polymer– rumondor2009c E6
uptake, Mwater sorbed at the same RHg/100 g dry solid [rumondor2010a E5]

Assumptions and valid domain

The blend behaves like a physical mixture, every water-binding group keeping its ability [rumondor2010a C9]; components sorb independently rumondor2009c E6.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
rumondor2009cmarker of moisture-induced separationwithin 0.2–7.4% of measured for separating dispersions; 121.7% and 341.5% off for mixed onesreproduces within 0.1 rumondor2009c E6, R22
rumondor2010ashortfall of one-phase blendsup to ≈64% (felodipine–PVP) below the sumreproduces from Fig. 1 readings [rumondor2010a E5, R7]
li2018 (outside)lopinavir dispersions with six polymersCA, EUD, CAP near additive; HPMCAS, HPMCP belowreproduces [li2018 E1, C33]

Where it fails or is disputed

It overestimates the uptake of one-phase blends by up to about two-thirds [rumondor2010a R7]. The two Rumondor papers express the deviation against different references (measured value, prediction) [rumondor2009c E6; rumondor2010a E6].

Concepts

water sorption, water sorption isotherm, amorphous-amorphous phase separation. Findings. F7.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

amorphicity index

Expression

A score for a spin-coated film or a drug–polymer pair, built from the category codes assigned by polarized light microscopy at four time points. Each sample gets a four-letter code (AAAA completely amorphous to CCCC fully crystalline), and the amorphicity index counts its amorphous letters:

\mathrm{AI}\ (\%) = \frac{\text{number of A letters in the four category codes of a sample}}{16}\times 100 [vaneerdenbrugh2010b E1]

(printed in words; 16 is the number of A letters of a sample that is AAAA at all four time points). The scores are then averaged over the seven drug/polymer weight ratios of a pair, over all drugs for one polymer, and over all polymers for one drug (all printed in words):

\overline{\mathrm{AI}}_{\mathrm{pair}} = \frac{1}{7}\sum_{i=1}^{7}\mathrm{AI}_i [vaneerdenbrugh2010b E2];

\overline{\mathrm{AI}}_{\mathrm{polymer}} = \frac{1}{N_{\mathrm{drugs}}}\sum_{\mathrm{drugs}}\overline{\mathrm{AI}}_{\mathrm{pair}} [vaneerdenbrugh2010b E3];

\overline{\mathrm{AI}}_{\mathrm{drug}} = \frac{1}{N_{\mathrm{polymers}}}\sum_{\mathrm{polymers}}\overline{\mathrm{AI}}_{\mathrm{pair}} [vaneerdenbrugh2010b E4].

The 2011 paper prints the same definition, with the index of a drug–polymer pair as the mean of the indices of its weight ratios [vaneerdenbrugh2011a E1, P3].

Variables and units

symbolmeaningunits
AIamorphicity index of one sample% [vaneerdenbrugh2010b E1]
A letteramorphous letter in the four-letter category, one for each of day 0, 1, 3 and 7count, 0 to 4 per sample [vaneerdenbrugh2010b P2, E1]
\overline{\mathrm{AI}}_{\mathrm{pair}}mean AI over the 7 drug/polymer ratios (90/10 to 10/90 w/w)% [vaneerdenbrugh2010b E2, P1]
N_{drugs}, N_{polymers}8 drugs and 7 polymerscount [vaneerdenbrugh2010b R2]

Assumptions and valid domain

The categories are semiquantitative and come from the extent of birefringence under polarized light, which is assumed to follow the amount of crystalline drug because the films are thin and crystallization extends over the full film height [vaneerdenbrugh2010b C11, P2]. The same weight is given to the four time points and to each ratio [vaneerdenbrugh2010b E1, E2]. Defined for dry-stored spin-coated films from ethanol, or from ethanol/dichloromethane for HPMC and HPMCAS [vaneerdenbrugh2010b P1].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
vaneerdenbrugh2010bamorphicity of 392 spin-coated drug–polymer films (synthesis: 8 drugs × 7 polymers × 7 ratios)BD-E100 25/75 = 44; FFA-PAA mean 13; PVP mean 70; BD mean 48reproduces (4 + 1 + 1 + 1 = 7 A letters, 7/16 = 43.75%; FFA-PAA mean 12.5; PVP mean 70.0; BD mean 47.6) [vaneerdenbrugh2010b E1, E2, E3, E4]
vaneerdenbrugh2010bper-drug rankingPH 47, CZ 47, BD 48, LI 55, FFA 59, FB 68, CP 73, BI 97derived [vaneerdenbrugh2010b R4]
vaneerdenbrugh2010bper-polymer rankingPVP 70, PVPVA 70, E100 67, HPMC 66, HPMCAS 62, PAA 49, PSSA 48derived [vaneerdenbrugh2010b R5]
vaneerdenbrugh2011aamorphicity of 105 spin-coated pairs (15 drugs × 7 polymers; ratios 75/25, 50/50, 25/75 and five more for the drugs of the first screen)PH–PSSA 78; FFA–PAA 13; the 8 repeated drugs equal the first screenreproduces: a sample scored AAAA at all four time points has 4 × 4 = 16 A letters, AI 100%; per-sample categories not printed [vaneerdenbrugh2011a E1, R3, X9]

Where it fails or is disputed

One entry of the supplementary table (FFA–PSSA 60/40, printed 94 where the category codes give 6) does not reproduce, and the averages for FFA–PSSA, FFA and PSSA reproduce only with the printed value [vaneerdenbrugh2010b X1]. The averages hide the drug-by-drug reversal of the acidic polymers: PAA and PSSA are the best polymers for basic drugs and the worst for acidic drugs, yet their polymer means (49, 48) are the lowest of the seven [vaneerdenbrugh2010b R5, C3]. Film thickness, total solids concentration and storage temperature are not stated, so scores can be compared with other papers only qualitatively [vaneerdenbrugh2010b X10]. The cellulosic polymers were cast from a different solvent, which confounds their scores with solvent [vaneerdenbrugh2010b X12]. The paper reports only averaged scores, not the polymer fraction needed for each drug [vaneerdenbrugh2010b X13]. In the 2011 screen the number of ratios averaged per drug is not stated, there are no error bars, and one changed letter moves a three-ratio mean by about 2.1% [vaneerdenbrugh2011a X9, X10].

Concepts

crystallization inhibition, crystal growth inhibition by polymers, drug-polymer interactions, crystallization tendency. Findings. F15, F16, F24.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

amorphous-crystalline free energy difference from heat capacity

Expression

With linear reversing heat capacities C_p^{sl} = aT + b and C_p^{c} = cT + d [almeidaesousa2015 E6, E7], the crystal-to-supercooled-liquid change at T is

\Delta H_{c\to sl} = \Delta_{fus}H + \frac{aT^2 + 2bT}{2} - \frac{aT_m^2 + 2bT_m}{2} + \frac{cT_m^2 + 2dT_m}{2} - \frac{cT^2 + 2dT}{2} [almeidaesousa2015 E9],

\Delta S_{c\to sl} = \frac{\Delta_{fus}H}{T_m} + (T_m - T)(c - a) + \ln\left(\frac{T_m}{T}\right)(d - b) [almeidaesousa2015 E10],

\Delta G_{c\to sl} = \Delta H_{c\to sl} - T\,\Delta S_{c\to sl} [almeidaesousa2015 E11].

A glass version uses C_p^{g} = eT + f below Tg [almeidaesousa2015 E8, E12, E13, E14]. The integral form printed for telaprevir is

\frac{\Delta G_{a\to c}}{RT} = \frac{\Delta H_f}{RT}\left(1 - \frac{T}{T_m}\right) + \frac{1}{RT}\int_{T_m}^{T}\Delta C_p\,dT - \frac{1}{R}\int_{T_m}^{T}\frac{\Delta C_p}{T}\,dT [mosqueragiraldo2015 E3].

Variables and units

symbolmeaningunits
a, b; c, d; e, flinear fit parameters of the reversing Cp of supercooled liquid, crystal, glassJ mol⁻¹ K⁻¹ and J mol⁻¹ K⁻² [almeidaesousa2015 E6, E7, E8]
\Delta_{fus}H, T_menthalpy of fusion, melting temperaturekJ/mol, K [almeidaesousa2015 E9]
\Delta H, \Delta S, \Delta Gconversion enthalpy, entropy, free energy at TkJ/mol, J mol⁻¹ K⁻¹, kJ/mol [almeidaesousa2015 R12]

Assumptions and valid domain

Cp linear in temperature over the range of interest (shown for tolnaftate only); un-ionized, non-solvated crystal that melts without degradation; only the reversing Cp is used because the entropy change is the reversibly exchanged heat divided by T [almeidaesousa2015 C10, C11, E17]. For much larger undercooling the form with a 1/T^2 term is better [almeidaesousa2015 E5, C10].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
almeidaesousa2015six drugs at 25 °C; sorafenib and griseofulvin also to the glassΔG 3.56–10.34 kJ/mol (to supercooled liquid); 11.37 and 10.38 kJ/mol (to glass)ΔG = ΔH − TΔS reproduces from Table 7 (9.39 kJ/mol for griseofulvin); parameters a–f not printed [almeidaesousa2015 E11, R11, R12]
mosqueragiraldo2015telaprevir at 37 °C97 ± 8 and 189 ± 16 µg/mL through Eq. 1ΔCp values not printed [mosqueragiraldo2015 E3, R13]
almeidaesousa2016CRH15.85 and 5.95 kJ/molmethod named only, parameters not printed [almeidaesousa2016 E5, M1]

Where it fails or is disputed

The method's superiority is concluded on the hypothesis that the onset is governed by the supercooled liquid, and neither ΔG nor the amorphous solubility was determined independently [almeidaesousa2015 X4]. Eq. 4 is printed with a symbol clash with Eqs. 5–7 and is not used [almeidaesousa2015 X13].

Concepts

amorphous-crystalline free energy difference, supercooled liquid, structural relaxation. Findings. F7.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

amorphous solubility advantage from free energy difference

Expression

\ln x_{SL,L_1} = \ln x_{C,L_1} + \frac{\Delta G_{a\to c}}{RT} ilevbare2013a E5;

\frac{\mu_1^{\circ} - \mu_{1c}^{\circ}}{RT} = \ln\frac{S_a}{S_c} [trasi2015a E1];

\frac{S_{amorphous}}{S_{crystalline}} \approx \frac{a_{amorphous}}{a_{crystalline}} = \exp\left[\frac{\Delta G_c}{RT}\right] [hsieh2012 E4; hsieh2014 E3].

The ASD dissolution papers print it as

\Delta G_c = RT\ln\frac{a_{\mathrm{amorphous}}}{a_{\mathrm{crystalline}}} \approx RT\ln\frac{S_{\mathrm{amorphous}}}{S_{\mathrm{crystalline}}} [konno2008a E1];

\frac{\sigma^{\mathrm{amorph}}}{\sigma^{\mathrm{crystal}}} = e^{\Delta G/RT} alonzo2011 E2;

\frac{S_A}{S_C} = \exp\left(\frac{\mu_A - \mu_C}{RT}\right) [li2018 E2];

\Delta G = -RT\ln\left(\frac{C_a}{C_s}\right) duong2022a E1.

Variables and units

symbolmeaningunits
x_{SL,L_1}, x_{C,L_1}mole-fraction solubility of the supercooled liquid and of the crystal in waterdimensionless ilevbare2013a E3, E4
\Delta G_{a\to c}free-energy difference amorphous–crystalilevbare2013a E2
\mu_1^{\circ}, \mu_{1c}^{\circ}chemical potential of pure amorphous (supercooled liquid) and crystalline drug[trasi2015a E1]
S_a, S_camorphous and crystalline solubilityµg/mL [trasi2015a E1, R1]
S_{amorphous}, S_{crystalline}solubility of the amorphous and crystalline formsµg/mL [hsieh2012 E4]
a_{amorphous}, a_{crystalline}thermodynamic activity of the solid formdimensionless [hsieh2012 E4]
\Delta G_cfree-energy difference between the forms (Hoffman equation)kJ/mol [hsieh2014 E3]
R, Tgas constant; temperatureJ mol⁻¹ K⁻¹; K
\sigma^{\mathrm{amorph}}, \sigma^{\mathrm{crystal}}solubility of each form (2011 notation)µg/mL alonzo2011 E2
S_A, S_Camorphous and crystalline solubility (2018 notation)µg/mL [li2018 E2]
\mu_A, \mu_Cchemical potential of the drug in the amorphous and the crystalline solidJ/mol [li2018 E2]
\Delta G; C_a, C_sfree-energy difference; amorphous and crystalline solubility (2022 notation)J/mol; µg/mL duong2022a E1

Assumptions and valid domain

The activity coefficient is constant between the crystalline and amorphous concentration; the amorphous phase is a supercooled liquid; the first form omits the water term, which amorphous solubility advantage with water-sorption correction adds [ilevbare2013a C55, C58; trasi2015a C36]. In the activity form the ratio of solubilities equals the ratio of activities; water mixing into the amorphous phase is neglected, which can lower the amorphous solubility by up to 2-fold [hsieh2014 R17]. Used at 25 and 37 °C. In the ASD dissolution papers the activity ratio is approximated by the solubility ratio [konno2008a E1]; solute–solvent interactions are taken as equal for both solid forms, which the 2011 authors call "unlikely to be true" for a dispersion alonzo2011 C6, C41. The drug activity coefficient in solution varies little between the crystalline and the amorphous solubility, and the amorphous form and the solution equilibrate; crystallization, water ingress and glass relaxation hamper that equilibrium [li2018 C41].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
ilevbare2013afirst approximation of the amorphous solubility, ritonavirnone printednot applicable (no numerical output) ilevbare2013a E5
trasi2015adefines the amorphous-to-crystalline solubility ratioritonavir 15–16, lopinavir 6.0–6.4, paclitaxel hydrate 85–94, felodipine 7–8 (extractor arithmetic)not applicable; ratios from Table 1 [trasi2015a E1, X12]
hsieh2012uncorrected amorphous solubility of five basesratios 22.2, 11.9, 20.4, 54.6, 7.0ratios reproduce from printed solubilities (24.4/1.1 = 22.2) [hsieh2012 E4, R10]
hsieh2014glyburide and warfarinabout 60 and 48reproduces 59.9 and 47.7 at 25 °C [hsieh2014 E3, R16]
konno2008afelodipine at 37 °Cratio about 10: 10 × 0.94 = 9.4 against printed about 9.5 µg/mLreproduces within rounding [konno2008a E1]
alonzo2011felodipine at 37 °Cratio about 9 implies ΔG = RT ln 9 ≈ 5.67 kJ/molinputs not printed alonzo2011 E2
alonzo2011flux of pure amorphous felodipine against crystalratio 8.5close to the estimate alonzo2011 R14, C40
li2018lopinavir, pH 3, 25 °Cmeasured S_A/S_C = 17.4/3.1 = 5.6; \mu_A - \mu_C not printedinputs not printed [li2018 E2, R1] (synthesis: RT\ln 5.6 ≈ 4.3 kJ/mol at 298 K)
duong2022aturning a Hoffman free-energy estimate into a delamanid solubility ratiomeasured ratio 42.3 at pH 6.5 against 31.8 estimatedthe two equations are used together; no ΔG value is printed duong2022a E1, E2, R27

Where it fails or is disputed

The paclitaxel ratio lies outside the 5–50-fold range quoted in the introduction and rests on a hydrate [trasi2015a X12, R18]. The ketoconazole estimate (54.6-fold) is 2.6 times the measured supernatant, and the water correction brings it to 15.3-fold [hsieh2012 X2, R10.d]. For warfarin with Eudragit E100 the polymer-free supersaturation of 60.5 exceeds the 48-fold ceiling [hsieh2014 X4]. A dispersion and the pure amorphous drug need not give the same solution activity; their measured equality for felodipine "may be purely coincidental" alonzo2011 C45, C48. For lopinavir the measured ratio is used; the free-energy difference from thermal data is printed but not applied to data [li2018 E3, C43]. The delamanid ratio was measured in PBS pH 6.5, where both solubilities are very low (0.76 and 0.018 µg/mL), so small absolute errors move the ratio duong2022a R1.

Concepts

amorphous solubility advantage, chemical potential, amorphous solubility, Hoffman equation. Findings. Amorphous solubility and LLPS: F6, F11. Crystallization from solution: F2. Supersaturation from ASD dissolution: F7, F18, F23.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

amorphous solubility advantage with water-sorption correction

Expression

C_{\mathrm{amorphous}} = C_{\mathrm{eq}}\,\exp\left(-I(a_2)\right)\,\exp\left(\frac{\Delta G_{a \to c}}{RT}\right) ilevbare2013a E1;

the same relation is printed with \Delta G_{c\to a} and the activity term written e^{-I(a_2)} [almeidaesousa2015 E1; mosqueragiraldo2015 E1; almeidaesousa2016 E1]. For weak bases it is printed as

C_A = \exp\left[-\frac{\Delta G}{RT}\right]\exp\left[-I(a)\right]C_T [indulkar2015 E2],

where C_T is the crystalline solubility at the pH of interest. The free energy factor must exceed 1 in every form on this page: \Delta G_{a\to c} and \Delta G_{c\to a} are positive magnitudes, as in Ueda 2024 (Eq. 2), and the forms printed with -\Delta G/RT give the reported ratios only with \Delta G taken as negative. The mole-fraction form of the 2013 appendix is

\ln x_{SL,L_1} = \ln x_{C,L_1} + \frac{\Delta G_{a\to c}}{RT} + \ln\left(x_{SL,L_2}\,\gamma_{SL,L_2}\right) ilevbare2013a E11.

The papers of 2017–2022 print the relation in the same form for atazanavir,

S_{\mathrm{pred}} = \exp\left(\frac{-\Delta G}{RT}\right)\exp\left(-I(a)\right)S_{\mathrm{xtal}} indulkar2017a E3,

for ibuprofen as

C_{\mathrm{amorphous}} = C_{\mathrm{eq}}\,e^{-I(a_2)}\,e^{\Delta G_{c\to a}/RT} [ueda2021 E1],

and as a ratio

\frac{S_a^{0}}{S_c^{0}} = e^{-I(a_2)}\,e^{\Delta G_{c\to a}/RT} ueda2022 E1.

In the Bioperformance papers the ratio form for an unionized solute is

\frac{\sigma_a}{\sigma_c} = e^{-I(a_2)}\, e^{\Delta G/RT} [raina2014a E5; raina2015c E2].

With ionization terms the general form is \sigma_a/\sigma_c = [(1-\alpha^x)/(1-\alpha^a)]\,e^{-I(a_2)}\,e^{(\mu_2^a - \mu_2^x)/RT} [raina2014a E4]. The clotrimazole paper prints C_{amorph} = \exp(-\Delta G/RT)\exp(-I(a))\,C_{crystal} with an unstated sign convention for ΔG [indulkar2016 E15, X11].

The crystallization-from-solution papers print it as

\frac{S_{amorphous}}{S_{crystalline}} = \exp[-I(a_2)]\cdot\exp\left[\frac{\Delta G_c}{RT}\right] [hsieh2012 E6];

C_{amorphous} = C_{eq}\,\exp[-I(a_2)]\,\exp\left[\frac{\Delta G_{a\to c}}{RT}\right] [ilevbare2012b E8; ilevbare2013b E2; ilevbare2013c E6];

\frac{\sigma^{amorph}}{\sigma^{crystal}} = e^{-I(a_2)}\,e^{\Delta G/RT} [jackson2014 E1].

Variables and units

symbolmeaningunits
C_{amorphous}predicted amorphous solubilityµg/mL ilevbare2013a E1
C_{eq}, C_Tcrystalline solubility in the test mediumµg/mL [ilevbare2013a E1; indulkar2015 E2]
e^{-I(a_2)}activity of the amorphous drug saturated with water, from the Gibbs–Duhem treatment of the sorption isothermdimensionless, 0.22–0.999 [indulkar2015 M2; almeidaesousa2015 M1]
\Delta Gfree-energy difference between amorphous (supercooled liquid or glass) and crystalkJ/mol, from the Hoffman or heat-capacity route [almeidaesousa2015 E2, E11, E14]
R, Tgas constant (8.314 J mol⁻¹ K⁻¹ in the checks), temperature298.15 or 310.15 K [almeidaesousa2015 E1; ilevbare2013a E1]
\sigma_a, \sigma_camorphous and crystalline solubilityµg/mL [raina2014a E5]
e^{-I(a_2)} for felodipine, nifedipinefactor for the activity lowered by absorbed water0.74–0.83 [raina2014a R7]
S_{amorphous}, S_{crystalline}; \sigma^{amorph}, \sigma^{crystal}amorphous and crystalline solubility (2012 and 2014 notation)µg/mL [hsieh2012 E6; jackson2014 E1]
I(a_2)Gibbs–Duhem integral from the water sorption isotherm of the amorphous soliddimensionless [hsieh2012 E5]

Assumptions and valid domain

The amorphous drug is treated as a supercooled liquid (or a relaxed glass), the drug activity coefficient in the dilute solution is the same at the crystalline and the amorphous concentration, and water absorption is accounted for by the Murdande correction [ilevbare2013a C55, C58, C59; indulkar2015 C43]. It was tested for un-ionized drug at 25 and 37 °C in buffers and water without solubilizers, and for CRH1 with 20 µg/mL HPMC at pH 4.6 [ilevbare2013a R8; almeidaesousa2015 R11; almeidaesousa2016 R2]. In raina2014a the solute is unionized, ΔG is the Hoffman estimate, and the water uptake from gravimetric sorption is extrapolated to water activity 1 [raina2014a C9, C10, P4]. In the crystallization-from-solution papers the activity ratio of the two solid forms is taken as the solubility ratio, water taken up by the amorphous solid lowers its activity, and ΔG comes from the Hoffman approximation [hsieh2012 E4, E5, E6; jackson2014 E1, E2]; tested at 25 and 37 °C for drugs with Tm 117–242 °C.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
ilevbare2013aeight drugs, 37 °C4.0–133.3 µg/mL; ritonavir 39.2 in water, 20.6 in bufferreproduces within about 5% for ketoconazole, clotrimazole, felodipine, clozapine, not for ritonavir (32.9 against 39.2), efavirenz, loratadine, indomethacin ilevbare2013a E1, X1
almeidaesousa2015six drugs, 25 °CHoffman 0.272–402.29, Cp supercooled liquid 0.325–356.44 µg/mLreproduces (ibuprofen, Hoffman: 29.29 × 0.999 × exp(3240/(8.314 × 298.15)) = 108.1 against 108.16) [almeidaesousa2015 E1, R11]
indulkar2015clotrimazole, atazanavirratios about 9.2 and 62; 4.9 and 64.9 µg/mLprinted sign mismatch: exp[−ΔG/RT] gives 0.072 for clotrimazole; exp[+ΔG/RT] gives 9.30 and 62.2 [indulkar2015 E2, X1]
mosqueragiraldo2015telaprevir, 37 °C245 ± 5 (Hoffman), 189 ± 16 (Cp glass), 97 ± 8 µg/mL (Cp supercooled liquid)Hoffman route reproduces (about 241–246 µg/mL); Cp routes cannot be checked [mosqueragiraldo2015 E1, E3]
almeidaesousa2016CRH1, pH 6.8 and pH 4.6 + HPMC9.0–10.0 and 11.2–12.5 µg/mLreproduces for all six values [almeidaesousa2016 E1, R2]
indulkar2017aatazanavir, 37 °Cratio 62 and 68 µg/mL printed; Table I inputs give about 62 with 0.22 read as exp[−I(a)], about 228 read as I(a) (synthesis)reproduces with that reading; the printed sign is inverted [indulkar2017a E3, X1; indulkar2015 M2]
ueda2021ibuprofen, pH 2.0 (D2O), 37 °C151 µg/mL against 154 µg/mL measuredinputs not printed (ΔG and I(a2) are in ref 20); a combined factor of 3.50 follows from 43.1 µg/mL (synthesis: 151 ÷ 43.1) [ueda2021 E1, R6, R2]
ueda2022ibuprofen in buffer, 25–60 °Cpredicted ratio about 3.7 → 1.3 (20 → 65 °C); measured 5.8 → 2.5inputs not printed; predicted below measured at every temperature ueda2022 E1, R16
raina2014afelodipine, nifedipine0.74 × 10.92 × 0.74 = 5.98 (printed 5.99); 10.00 × 8.78 × 0.82 = 72.0reproduces [raina2014a E5]
raina2015csame drugs, FaSSIFFaSSIF estimate assumes the buffer ratioinputs not printed [raina2015c E2]
indulkar2016clotrimazolefactor in square brackets in the paperinputs not printed [indulkar2016 E15]
wilson2018enzalutamideprinted about 39 µg/mL (C_eq 2.9, I(a2) 0.69, ΔG 7594 J/mol from ΔH_f 33,820 J/mol, Tm 470 K, T 310 K)mismatch: recomputed 27.7 µg/mL [wilson2018 E2, X1]
hsieh2012five type 2 basesratios 12.3, 9.8, 16.7, 15.3, 4.3inputs not printed; ratios reproduce from printed solubilities [hsieh2012 E6]
ilevbare2012britonavir20.6 µg/mL from Ceq 1.3, ΔHf 60.4 kJ/mol, Tm 121 °Cinputs not printed (I(a2)) [ilevbare2012b E8, R1]
ilevbare2013bcelecoxib, efavirenz, ritonavir22.6, 19.8, 20.6 µg/mLinputs not printed [ilevbare2013b E2]
ilevbare2013csame, starting concentrationssameinputs not printed [ilevbare2013c E6, R2]
jackson2014danazolexp[−I(a2)] 0.935; ratio 19.6 printedmismatch: 15.4 recomputed [jackson2014 E1, X1]
raina2015be^(−I(a2)) e^(ΔG/RT) for six dihydropyridinese^(−I(a2)) 0.74–0.91; estimates 0.5–48 µg/mL in buffermismatch: felodipine 5.93 recomputed against 6.68 µg/mL [raina2015b E2, X2]
jackson2016amorphous solubility of danazol from crystalline solubility, DSC data with heat capacity and moisture sorption7.8 µg/mL (earlier 16)named only; thermal inputs not printed [jackson2016 E3, R3]
duong2022bposaconazole at pH 7.0C_A = \exp[-\Delta G/RT]\exp(-I_a)C_T as printed; ratio 37.9 with activity factor 0.33estimate 10.22 against 9.08 µg/mL measured; exponent sign and ratio not reproducible (extractor: about 26.5) [duong2022b E2, R7, X2]

Where it fails or is disputed

Tolnaftate's onset is 1.72 times its prediction and clotrimazole's about 1.6 times [almeidaesousa2015 X5; indulkar2015 X6]. The Hoffman route overshoots for telaprevir [mosqueragiraldo2015 C23]. The inputs of the 2013 predictions are not stated unambiguously ilevbare2013a X3. The atazanavir ratio of 62 follows from the printed inputs only with 0.22 read as exp[−I(a)], although Table I heads it I(a) [indulkar2017a X1; indulkar2015 M2]; the ibuprofen prediction rests on H2O inputs while the measurements are in D2O ueda2022 X6; the calculation cannot be made for pazopanib, which degrades on melting [sugihara2018 C17]. The sign convention of ΔG differs between papers [indulkar2016 X11; indulkar2015 E2]. The estimate failed in FaSSIF [raina2015c C18] and for telaprevir [mosqueragiraldo2015 C24]. The enzalutamide estimate cannot be reproduced from its printed inputs (F1) [wilson2018 X1]. The danazol ratio does not follow from the printed inputs, and for the five weak bases the matching estimate changes with the compound (uncorrected for clotrimazole and loratadine, corrected for clozapine) [jackson2014 X1; hsieh2012 X2]. The measured value is lower than the calculated one when the drug crystallizes first (celecoxib 2.5 against 22.6 µg/mL) [ilevbare2013c R2]. The amorphous samples for sorption and for dissolution were prepared differently [ilevbare2013c X17]. The dihydropyridine ratios differ between media in ways the equation does not allow, and the Fig. 9 bars differ from Table 3 for felodipine and nifedipine [raina2015b X1, X2]. The posaconazole paper prints the exponent with a minus sign, which would give an amorphous solubility below the crystalline one [duong2022b X2].

Concepts

amorphous solubility advantage, amorphous solubility, water sorption correction of amorphous solubility, amorphous-crystalline free energy difference, Hoffman equation, ionization, Gibbs-Duhem equation. Findings. Amorphous solubility and LLPS: F5, F6, F7, F10, F16, F18, F21. Bioperformance: F1, F23. Crystallization from solution: F2, F21, F22.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

amorphous-to-crystalline solubility ratio

Expression

\frac{\sigma_a}{\sigma_c} = \frac{\text{LLPS onset concentration}}{\text{crystalline solubility in the same medium}} [raina2015c E8], printed in words.

The ASD dissolution papers print it from the free-energy difference,

\frac{\sigma^{\mathrm{amorph}}}{\sigma^{\mathrm{crystal}}} = e^{\Delta G/RT} [alonzo2010 E1],

and in words as the measured ratio, \mathrm{ratio} = S_{\mathrm{amorphous}}/S_{\mathrm{crystalline}} [trasi2016 E1] and \mathrm{A/C} = S_{\mathrm{amorphous}}/S_{\mathrm{crystalline}} [alvarenga2025 E1]; [nguyen2023c E2] uses the same ratio as the supersaturation at the amorphous solubility.

Variables and units

symbolmeaningunits
LLPS onsetconcentration of the extinction rise (the amorphous solubility)µg/mL
crystalline solubilityshake-flask value in the same mediumµg/mL
\sigma^{\mathrm{amorph}}, \sigma^{\mathrm{crystal}}solubility of amorphous and stable crystalline formµg/mL [alonzo2010 E1]
\Delta Gfree-energy difference, from the Hoffman equationJ/mol [alonzo2010 E1]

Assumptions and valid domain

The onset represents the amorphous solubility [raina2015c C13]. The ratio is not a constant of the drug but depends on medium and polymer (F4). In the 2010 dissolution paper it is used as printed, with \Delta G from the Hoffman equation and the measured crystalline solubility [alonzo2010 P12]. For tacrolimus the amorphous solubility is the value after ultracentrifugation [trasi2016 E1].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
raina2015cfelodipine in three media177.3/39.3 = 4.51; 214.6/42.8 = 5.01; 10.4/1.1 = 9.45 (printed 9.2)reproduces except buffer [raina2015c E8, X2]
alonzo2010felodipine 37 °CΔG 5729 J/mol, ratio 9.22reproduces [alonzo2010 E1]
trasi2016tacrolimus monohydrate49/1.4 = 35.0reproduces: 35.0 against printed approximately 35 [trasi2016 E1, R16]
lu2017btelaprevir148/5.2 = 28.5reproduces [lu2017b E5]
purohit2019tacrolimus, maximum supersaturationprinted about 33mismatch: 50/1.4 = 35.7 with the text value, 50/1.5 = 33.3 with the figure-caption value [purohit2019 E2, X1]
ueda2020aatazanavir, nifedipine, clozapine, ketoconazole with HPMCAS gradestwelve ratios in Table 1eleven reproduce; clozapine with AS-LF printed 5.9, recomputed 219.0/22.0 = 9.95 ueda2020a E1, X1
nguyen2023apretomanid in seven mediaprinted 6.0 in FaSSIF V1mismatch: 308/53.8 = 5.72; buffer pH 6.5 reproduces (166.1/16.2 = 10.25, printed 10.2) nguyen2023a E3
alonzo2010indomethacin, 37 °Cratio 12.17 × 3 µg/mL = 36.5 against about 37 µg/mLreproduces [alonzo2010 E2]
alonzo2010indomethacin, 25 °Cratio 15.75 gives 15.8–23.6 against printed 17–25 µg/mLmismatch [alonzo2010 X2]
que2018paclitaxel, pH 6.8, 37 °C31.6/0.36reproduces: 87.8 against printed 88 [que2018 R1, R2]
duong2022adelamanid at pH 6.50.76/0.018reproduces: 42.2 against printed 42.3 duong2022a R1, R27
nguyen2023cdelamanid at pH 1.6 and 6.5154.5/10.2 and 0.76/0.018reproduces: 15.1 and 42.2 against printed 42 at pH 6.5 [nguyen2023c R1, R2]
alvarenga2025praziquantel in nine media, racemate and R-enantiomer5.6–7.7 and 4.0–5.8reproduces for PBS pH 6.5: 1.17/0.16 ≈ 7.3 and 1.39/0.23 ≈ 6.0 [alvarenga2025 R1, E1]
polyzois2024praziquantel at pH 6.51.4/0.2826 and 1.1/0.1964reproduces: ≈5.0 and ≈5.6 against the authors' "around fivefold" polyzois2024 R1, R2, R17

Where it fails or is disputed

The text writes the ratio as σc/σa in two places [raina2015c X3]. The buffer value follows only from an unrounded solubility of about 1.13 µg/mL [raina2015c X2]. The ratio fell with HPMCAS-HF and with micelles in the medium, although the flux advantage did not (F18, F19) [ueda2020a C17; elkhabaz2019b R8, R9]. The 25 °C indomethacin range of the 2010 paper does not reproduce; the comparisons drawn from it keep their direction [alonzo2010 X2]. The ratio is lower for the praziquantel enantiomer than for the racemate because its crystal is more soluble, not because its amorphous solubility is lower, so a larger ratio does not mean more dissolved drug [alvarenga2025 R1]. The text of the praziquantel paper of 2025 gives "approximately 8- and 6-fold", above every tabulated value for the enantiomer [alvarenga2025 X4]. For delamanid the ratio holds only at the pH at which both solubilities were measured; it falls to about 15 at pH 1.6 [nguyen2023c R1, R2].

Concepts

amorphous solubility advantage, amorphous solubility, Hoffman equation. Findings. Bioperformance: F1, F4, F18, F19. Supersaturation from ASD dissolution: F1, F4, F22, F23, F25, F28, F29.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

boundary-layer diffusion flux (film model)

Evidence table: boundary-layer diffusion flux (film model). Content from the release-mechanism chapter (2023–2025), with a row from the Bioperformance chapter.

Expression

J_p = \frac{D_p}{\delta}\,C_p bapat2023 E2

The Bioperformance chapter printed the steady-state form across an unstirred water layer:

C_b - C_{m1} = \frac{J \times d_{UWL}}{D} hate2022 E6

J_p = \frac{D_p}{\delta}\, C_p bapat2024 E3

J_p = \frac{D_p}{\delta}\, C_p kaur2025 E1

Variables and units

symbolmeaningunit
J_ppolymer fluxnot printed
D_ppolymer diffusion coefficientnot printed
\deltaboundary-layer thicknessnot printed
C_ppolymer solubility at the polymer–solution interfacenot printed
C_b, C_{m1}bulk donor concentration; aqueous concentration at the layer–membrane interface (Bioperformance form)not printed
J, d_{UWL}, Dmass flow rate; layer thickness; solute diffusion coefficient (Bioperformance form)not printed

Assumptions and valid domain

Diffusion-controlled regime at a rotating disk under laminar flow (cited) bapat2023 E2; in the Bioperformance form, steady state with mass flow across the layer equal to that across the membrane (cited) hate2022 E6.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
bapat2023HPMCAS-MF release across media, gel pH and rotation speednoneinputs not printed (D_p, C_p) bapat2023 E2, R5, R16, R18
hate2022 (Bioperformance)transport of supersaturated solutions across PAMPA membranesnoneinputs not printed hate2022 E6, R19
bapat2024lower interfacial HPMCAS solubility from an insoluble drug complex slows polymer and drug releasenoneused in argument bapat2024 E3, C32
kaur2025the same for bedaquiline–HPMCASnoneused in argument kaur2025 E1, C41

Where it fails or is disputed

The interfacial polymer solubility C_p is not measured; a lower interfacial pH, inferred from gel measurements, stands in for it bapat2023 C38. The rate rose above the \omega^{1/2} proportionality expected with the Levich thickness at 700 rpm bapat2023 X10. The interfacial polymer solubility was not measured in either paper bapat2024 X10; kaur2025 X14.

Concepts

unstirred water layer, microenvironmental pH, buffer capacity, diffusion boundary layer. Findings. Release mechanism and LoC: F23, F32, F34.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

classical nucleation barrier

Expression

W^* = \frac{16\pi\gamma^3}{3\,\Delta G_v^2} [baird2010 E24; vaneerdenbrugh2010a E3];

W^* = \frac{16\pi\,\sigma_{cm}^3}{3\,\Delta G_v^2} [baird2012 E2], which enters the steady-state rate I_{SS} = I_0 \exp\left[-\frac{W^* + \Delta G_\eta}{k_B T}\right] [baird2012 E1].

\Delta G^{*} \propto \frac{1}{(\ln S)^{2}} [hsieh2012 E8]. The same dependence appears in the nucleation-rate expression used for celecoxib, J = A\exp[-16\pi\gamma^{3}v^{2}/(3k^{3}T^{3}(\ln S)^{2})] [xie2015 E3].

Variables and units

symbolmeaningunits
W^*free energy to form a nucleus of critical sizenot stated [baird2010 E24]
\gamma, \sigma_{cm}interfacial free energy of the nucleus–liquid (or nucleus–matrix) interface per areanot stated [vaneerdenbrugh2010a E3; baird2012 E2]
\Delta G_vfree energy difference per volume between crystal and liquidJ/cm³ [vaneerdenbrugh2010a E2, E5]
\Delta G^{*}free energy of forming the critical nucleusJ [hsieh2012 E8]
Ssupersaturation ratiodimensionless
\gamma, vinterfacial tension and molecular volume (in the full expression)J/m²; m³ [xie2015 E3]

Assumptions and valid domain

Homogeneous nucleation and a similar interfacial energy for the compared classes [baird2010 E24]; spherical nuclei [baird2012 E2]. Neither γ nor σcm was measured or estimated in any of the three papers [baird2010 E24; vaneerdenbrugh2010a E3; baird2012 E2]. In the supersaturation form the barrier falls steeply as S rises, so crystals nucleate only above a certain supersaturation, which depends on compound and conditions [hsieh2012 C3]; no numerical output is stated in the pH-shift paper.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
baird2010argument that a more negative ΔGv of class I lowers the barriernoneinputs not printed [baird2010 E24, C61]
vaneerdenbrugh2010areading the ΔGv–class linknoneinputs not printed [vaneerdenbrugh2010a E3, C39]
baird2012argument that viscosity enters nucleation and growthnoneinputs not printed [baird2012 E2, C4, C32]
duong2022bposaconazole barrier in buffer and nucleus size from fitted γ\Delta G^{*} = 16\pi\gamma^{3}\nu^{2}/(3k^{2}T^{2}\ln^{2}S); 2.73 × 10⁻²¹ J against ≈2.72 × 10⁻²¹ J read from the figure; PBS 2.72 × 10⁻²¹ J at S 33.6reproduces [duong2022b E8, R17]
hsieh2012why type 1 bases precipitate only after reaching a supersaturation of 1.4–26.7 times the titration solubilitynonenot applicable (no numerical output) [hsieh2012 E8, R5]
xie2015reading polymer effects on celecoxib induction times (ASD dissolution chapter)γ, v not fittedprinted [xie2015 E3]

Where it fails or is disputed

W* depends on γ³ but only on ΔGv²; the authors read the ΔGv–class correlation as suggesting that γ differences between compounds are small [vaneerdenbrugh2010a C39], an inference that rests on a ΔGv ranking that is not monotonic across classes [vaneerdenbrugh2010a X10]. In the pans and films used, nucleation may be heterogeneous [baird2010 C19; baird2012 C8], which the homogeneous form does not cover. Precipitation was seen at widely different supersaturations (1.4 for pyrimethamine to 26.7 for droperidol) [hsieh2012 R5, C22]. (synthesis: the barrier expression alone does not predict this spread without the interfacial energies of the compounds, which the paper does not give.)

Concepts

classical nucleation theory, nucleation, thermodynamic driving force for crystallization, heterogeneous nucleation. Findings. Crystallization tendency: F3, F6. Crystallization from solution: F1, F14, F34.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

classical nucleation theory

Expression

J \propto \exp\left(-\frac{\Delta G^{*}}{k_B T}\right) [hsieh2012 E7]

J = A\exp\left(\frac{-\Delta G_{crit}}{kT}\right) [ilevbare2013c E4]

J_{N} = v^{*} z n \exp\left(\frac{-16\pi\gamma^{3}v^{2}}{3k_{B}^{3}T^{3}(\ln S)^{2}}\right) [indulkar2018 E6]

J = A\exp\left(\frac{16\pi \nu_o^{2} \gamma^{3}}{3 (k_B T)^{3} (\ln S)^{2}}\right) [elkhabaz2021 E2] (printed without the minus sign)

J = A\,S\,\exp\left(\frac{-16\pi\gamma^{3}\nu^{2}}{3k^{3}T^{3}\ln^{2}S}\right) [duong2022b E6]

\ln(J/S) = \ln A - \frac{B}{\ln^{2}S}, \qquad B = \frac{16\pi\gamma^{3}\nu^{2}}{3k^{3}T^{3}} [duong2022b E7]

J = A\exp\left(-\frac{16\pi\gamma^{3}v^{2}}{3k^{3}T^{3}(\ln S)^{2}}\right) [trasi2015 E6; xie2015 E3]

Nucleation rate with a thermodynamic and a kinetic barrier, as printed in the solid-state papers of the physical-stability chapter:

I = A\exp\left(\frac{-\left(\Delta G^{*} + \Delta G_{a}\right)}{kT}\right) [konno2006 E8]

I = A\exp\frac{-\left(\Delta G^{*} + \Delta G_{a}\right)}{kT} [marsac2006a E9]

and for the undercooled melt:

I_{SS} = I_0\exp\left(-\frac{W^{*} + \Delta G_{\eta}}{k_B T}\right) [baird2012 E1]

In the reduced-temperature form printed for acetaminophen, with its typesetting as printed:

J = A\exp\left[-\frac{16\pi r^{3}}{3kT_m\Delta H_f^{2}T_r(\Delta T_r)^{2}} + \frac{\Delta G'}{KT}\right] [trasi2012a E1]

where the card reads r as the interfacial energy \gamma and the kinetic term as -\Delta G'/kT, as the text describes [trasi2012a X1].

The ASD dissolution papers of 2008 and 2010 print it with ln S unsquared,

J = A\exp\left(-\frac{16\pi\gamma^{3}v^{2}}{3k^{3}T^{3}\,(\ln S)}\right) [konno2008a E3],

J \propto \exp\left[-\frac{1}{\ln S}\right] [alonzo2010 E4];

the ritonavir dispersion paper states the dependence in words only: the relative nucleation rate rises with the drug concentration in a phase and falls with the crystal–solution interfacial tension [ilevbare2013d E1].

Variables and units

symbolmeaningunit
Jnucleation ratem⁻³ s⁻¹
Apre-exponential kinetic factor, depends on molecular mobilitym⁻³ s⁻¹
ΔG*, ΔG_critfree energy of forming a critical nucleusJ
k, k_BBoltzmann constantJ/K
Tabsolute temperatureK
γinterfacial tension (free energy) between nucleus and solutionJ/m² (mJ/m² in the posaconazole fits)
ν, v, ν_omolecular volumem³ (920 ų for posaconazole)
Ssupersaturationdimensionless
v*, z, nmonomer attachment rate, Zeldovich factor, number density of moleculesas printed
Inucleation rate in the film papersm⁻³ s⁻¹ [konno2006 R4]
\Delta G^{*}, W^{*}thermodynamic barrier, from interfacial term against bulk driving forceJ [konno2006 E8]
\Delta G_{a}, \Delta G_{\eta}kinetic barrier for transport onto the nucleusJ [konno2006 E8]
T_r, \Delta T_rreduced temperature T/T_m and 1 - T_r– [trasi2012a E1]
\Delta H_f; \Delta G'heat of fusion; activation energy for molecular motionnot given [trasi2012a E1]

Assumptions and valid domain

Clusters grow by sequential molecular additions; the barrier rises with the cube of the interfacial energy and falls with (\ln S)^{2} (see classical nucleation barrier) [ilevbare2013c E4, C14; hsieh2012 E8]. Used qualitatively; no fit to induction times is printed. The solid-state papers assume homogeneous nucleation, although nucleation in the films is "most likely heterogeneous"; stresses from the volume change are ignored [konno2006 C33; marsac2006a C32]. In the ASD dissolution papers of 2008–2013 it is used only qualitatively: higher supersaturation, faster nucleation [konno2008a C20; alonzo2010 C43; ilevbare2013d C40]. The 2015 celecoxib paper prints the classical form with (\ln S)^{2} and uses it to argue that neither supersaturation nor interfacial tension explains the polymer differences in induction time [xie2015 E3, C43].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
hsieh2012why type 1 bases precipitate only above a certain supersaturationnonenot applicable (no numerical output) [hsieh2012 E7]
ilevbare2013cwhy a polymer gains more at lower supersaturation (celecoxib 31-fold at S 7.3)noneinputs not printed [ilevbare2013c E4, C45]
xie2015celecoxib dispersions: J = A\exp[-16\pi\gamma^{3}v^{2}/(3k^{3}T^{3}(\ln S)^{2})]; longer induction times with polymers read as lower nucleation rate; why HPMCAS and HPMC lengthen celecoxib induction times more than PVPγ, v not fitted; γ, v, A not printedprinted; inputs not printed [xie2015 E3, C42, C43]
trasi2015J = A exp[−16πγ³v²/(3k³T³(ln S)²)] to state that T, S and γ set Jacetaminophen S 1.5, 20 °Cinputs (A, γ, v) not printed [trasi2015 E6]
li2016anamed only: nucleation rate depends highly on supersaturationbile-salt seriesnamed only [li2016a E5]
indulkar2018why lecithin might accelerate nucleation through γnoneinputs not printed [indulkar2018 E6, C40]
elkhabaz2021why surfactants should lower γ, and why human fluid does not fitnoneprinted without minus sign [elkhabaz2021 E2, X1]
duong2022blinearized fit of posaconazole induction times in buffer and three mediaγ 3.52, 2.61, 2.73, 3.24 mJ/m²; A 2.44, 5.14, 4.98, 9.87reproduces from the printed slopes and intercepts [duong2022b E7, R16]
konno2006sorting polymer effects into driving force and kinetic barriernoneinputs not printed [konno2006 E8]
marsac2006aframework for the nifedipine–felodipine comparisonnoneframework only [marsac2006a E9]
baird2012role of viscosity in class differencesnoneinputs not printed [baird2012 E1]
trasi2012aframework for polymer effects on acetaminophen nucleationnoneinputs not printed; printed form has misprints [trasi2012a E1, X1]
konno2008afelodipine nucleates readily at a high solubility rationonenot applicable [konno2008a E3]
alonzo2010scheme of dissolution against crystallizationnonenot applicable [alonzo2010 E4]
ilevbare2013dnucleation favoured in drug-rich dropletsnoneprinted in words [ilevbare2013d E1]

Where it fails or is disputed

Induction times include growth to detectable size, so a rate from them is nucleation plus early growth [ilevbare2013c X14]. The two-step picture (disordered cluster, then reorganization) is assumed to be rate-limiting but not shown [ilevbare2013c C5, C15]. The critical supersaturation at which precipitation is seen depends on compound and conditions [hsieh2012 C3]. The Poisson fit uses the printed volume 0.0012 m³ and a positive exponent, both misprints (V = 1.2 mL and a minus sign reproduce the 95% times within about 12%) [trasi2015 X1, X2, E5]. In the posaconazole fits the high-supersaturation sets hold 3–9 points (R² 0.84–0.97, FeSSIF V2 not fittable), and the conversion of induction time into J is not stated [duong2022b X10, X11]. No parameter was fitted in the solid-state papers; the theory serves to exclude a driving-force route and to frame a kinetic one [konno2006 C35, C40]. The polymer effects on acetaminophen nucleation were "not particularly straightforward" to explain with it, and it does not contain molecular recognition [trasi2012a C49]. The 2008 and 2010 dissolution papers print ln S without the square of the classical expression; use the squared form to compute rates [konno2008a X8; alonzo2010 X3]. The 2015 celecoxib form carries the square; in its argument the supersaturation is not the same with and without polymer (about 14.7 against 10.3–11.6), and the text refers to Eq. 2 where interfacial tension appears in Eq. 3 [xie2015 X9, X1].

Concepts

classical nucleation theory, nucleation rate, crystal-solution interfacial free energy, kinetic barrier to nucleation, interfacial free energy, nucleation, interfacial tension. Findings. Crystallization from solution: F1, F14, F27, F29, F5, F34, F39, F42. Physical stability: F1, F4, F17. Supersaturation from ASD dissolution: F1, F4, F5, F13.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

coating thickness from oxide content and specific surface area

Expression

No paper prints the formula; three describe it in words: the estimated thickness is obtained from the residual oxide content (TGA) and the specific surface area of the sample moseson2022a E1; moseson2023 E2; benson2025 E1. The extractor's back-calculation for ritonavir–PVPVA reproduces all nine thickness labels within 0.1 nm with

d\approx\frac{w_{ox}}{\rho_{ox}\,A_{BET}}

where w_{ox} is the oxide mass fraction, \rho_{ox} = 3.0 g/cm³ and A_{BET} the BET area of the uncoated powder; for 3.75% oxide and 0.56 m²/g this gives 22.3 nm (arithmetic on the cited values) benson2025 X19, R1.

Variables and units

symbolmeaningunitids
destimated mean thickness of the oxide shellnmmoseson2022a E1; benson2025 E1
w_{ox}residual weight after heating in dry air to 800–850 °C, taken as the metal oxide contentmass fraction (printed in %)[moseson2022a E1, P9; duong2022c P10; benson2025 E1]
A_{BET}specific surface area of the powder by nitrogen adsorption at 0.05–0.25 relative pressurem²/gmoseson2022a E4; moseson2023 E1
\rho_{ox}oxide density, not printed; about 3.0 g/cm³ by back-calculationg/cm³benson2025 X19; moseson2023 X6

Assumptions and valid domain

The residue is aluminium oxide (or zinc oxide) and the organic matter burns off; the shell is uniform over the BET area of the uncoated powder moseson2022a E1; benson2025 E1. Tested against cross-sectional TEM in two papers, where the two methods differ by up to a factor of two moseson2022a X10; moseson2023 R1, R2.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
moseson2022athickness labels of four systems, oxide 0.50–5.60%7.4–24 nm; TEM 4.4–37.7 nminputs not printed (conversion formula and oxide density) moseson2022a E1, R2
moseson2023thickness labels of twelve posaconazole–HPMCAS samples, oxide 0.40–3.68%11–39 nm; implied oxide density 2.95–3.08 g/cm³ for seven samples, 2.47 g/cm³ for PH25/S/C11inputs not printed; implied density from extractor check moseson2023 E2, R1, X6
benson2025thickness labels of nine coated ritonavir–PVPVA samples, oxide 0.92–5.30%, BET 0.22–0.76 m²/g9.3–28.3 nmreproduced within 0.1 nm with 3.0 g/cm³ benson2025 E1, R1, X19

Where it fails or is disputed

TGA and TEM disagree: TEM/TGA about 0.6–2.0 in four systems, and for posaconazole–HPMCAS about 12, 29, 8 and 40 nm by TEM against 12, 26, 13 and 36 nm by TGA moseson2022a R2, X10; moseson2023 R1, R2. Two lumefantrine–PVPVA coatings labelled 8.0 and 11 nm share the same oxide content (3.47%) and surface area moseson2022a R2, X2. The label is an average over the BET area of the uncoated powder, so it ignores surfaces the precursor does not reach and cannot show cracks or pinholes; labels of two size fractions of one powder are not comparable benson2025 R1, E1; moseson2022a C40. For ezetimibe the drug-content drop of coated powders was about twice the TGA residue, so the coating mass is uncertain there [duong2022c R12, X5].

Concepts

atomic layer coating, specific surface area, coating conformality, coating defect density. Findings. F42, F47.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

congruent release relation

Evidence table: congruent release relation. Content from the ASD dissolution chapter (2011) and from papers of the release-mechanism chapter.

Expression

G_D = \frac{G_C\,A_D}{A_C} alonzo2011 E4

\left(\frac{dC}{dt}\right)_{drug} = \left(\frac{dC}{dt}\right)_{polymer}\frac{m_{drug}}{m_{polymer}} indulkar2019a E3

G_B = \frac{N_B}{N_A}\,G_A xie2016a E1

Printed with weight fractions in the 2020 felodipine study:

\left(\frac{dC}{dt}\right)_{drug} = \left(\frac{dC}{dt}\right)_{polymer}\frac{N_{drug}}{N_{polymer}} saboo2020a E2

Printed in the 2022 ritonavir surfactant study:

\left(\frac{dC}{dt}\right)_{\mathrm{drug}} = \frac{\left(\frac{dC}{dt}\right)_{\mathrm{polymer}} m_{\mathrm{drug}}}{m_{\mathrm{polymer}}} indulkar2022 E1

Variables and units

symbolmeaningunit
G_D, G_Cdissolution rate of drug and of carrieras measured
A_D, A_Cproportion of drug and of carrier in the solidw/w
(dC/dt)_{drug}, (dC/dt)_{polymer}release rates of drug and polymerµg/(mL min)
m_{drug}, m_{polymer}masses in the dispersionmg
G_A, G_Bdissolution rates of components A and Bas measured
N_A, N_Bproportion of each componentw/w
N_{drug}, N_{polymer}weight fractions of drug and polymer–

Assumptions and valid domain

High polymer loading, so that no drug-rich layer limits dissolution alonzo2011 C37. Holds when Corrigan's condition N_A/N_B > D_A C_{SA}/(D_B C_{SB}) is met (cited), which the 2016 paper takes as the basis of polymer-controlled release at low and drug-controlled release at moderate to high drug loading xie2016a E2, C4. Release controlled by polymer dissolution saboo2020a E2; the polymer dissolves and brings the drug into solution because there is too little drug to form an intact surface layer indulkar2019a E3. In the normalized form of the surface-normalized release rate it predicts equal drug and polymer rates saboo2020a E2, E3.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
alonzo2011why 90:10 dispersions dissolve much faster than 50:50noneinputs not printed alonzo2011 E4
indulkar2019aritonavir–copovidone release at low drug loading (10% ritonavir–PVPVA at 20 min)integrated over time at 10% drug: ≈67 mg PVPVA × 10/90 = ≈7.4 mg ritonavir against ≈7.6 mg read from the release curvereproduces (inputs read from plots) indulkar2019a E3, R1, R2
saboo2020anormalized drug and polymer release rates; nilvadipine, felodipine, cilnidipine at 40% in HPMCASequal normalized rates predicted; drug/polymer 0.42/0.42, 0.34/0.32, 0.26/0.24 mg/min/cm²reproduces in the normalized form, equal within SD saboo2020a E2, R16
indulkar2022cited regime, the good regime for 30:70 ritonavir–PVPVA with surfactantsnonenot applicable (not fitted) indulkar2022 E1
xie2016awhy celecoxib release slows at high drug loadingnonenot applicable xie2016a E1, C4

Where it fails or is disputed

In the 2011 study neither rate was measured, so the regime is inferred from particle disintegration and UV speed alonzo2011 C38, C28. Above the limit of congruency the polymer leaves first and the relation no longer holds saboo2020a R14; indulkar2019a R5. It fixes the ratio of the two rates, not their size: in congruent dispersions the polymer rate itself was below that of a neat polymer compact saboo2019 R8; saboo2020a C19.

Concepts

polymer-controlled release, congruent release. Findings. Supersaturation from ASD dissolution: F10, F20. Release mechanism and LoC: F1, F2.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

Δχ effect

Evidence table: Δχ effect. Content from the release-mechanism chapter (2017–2021), with a row from the Physical stability chapter.

Expression

\left|\Delta\chi\right| = \left|\chi_{12} - \chi_{13}\right| marsac2010 E1

Stated in words as the magnitude of the difference between the water–drug and water–polymer parameters; the larger it is, the higher the tendency to phase separate purohit2017b E4. Written in that paper's symbols (synthesis: transcription of the words):

\Delta\chi = \left|\chi_{WD} - \chi_{WP}\right|

Printed with absolute-value bars in the drug-property study yang2021 E2:

\left|\Delta\chi\right| = \left|\chi_{12} - \chi_{13}\right| yang2021 E2

Variables and units

symbolmeaningunit
\chi_{12}, \chi_{WD}Flory–Huggins interaction parameter water–drug–
\chi_{13}, \chi_{WP}Flory–Huggins interaction parameter water–polymer–

Assumptions and valid domain

Phase separation is promoted when the two components interact asymmetrically with the solvent (cited) marsac2010 E1; the named effect of a cited paper purohit2017b E4.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
marsac2010 (Physical stability)felodipine–PVP–waterχ water–felodipine ≈3.3, water–PVP ≈0.5no Δχ printed; the inputs give 3.3 − 0.5 = 2.8 marsac2010 E1, R22
purohit2017bwhy ritonavir–PVP and –PVPVA separate with waternonenot applicable (no χ values) purohit2017b E4, C43
yang2021why log P does not predict water-induced separation of six drugsnoneinputs not printed yang2021 E2, C21

Where it fails or is disputed

No χ values were stated for the ritonavir systems, so the argument is qualitative purohit2017b E4.

Concepts

Δχ effect, Flory-Huggins interaction parameter, amorphous-amorphous phase separation. Findings. Release mechanism and LoC: F8, F9.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

Fedors group-contribution solubility parameter

Expression

\delta = \sqrt{\frac{\sum_i \Delta e_i}{\sum_i \Delta v_i}} = \sqrt{\frac{\Delta E_v}{V}} [ilevbare2012c E1; ilevbare2013c E5; ilevbare2013b E1; ilevbare2012a E1]

Molar-volume correction for glassy polymers (Tg above 25 °C):

\Delta v_i = 4n \quad (n < 3), \qquad \Delta v_i = 2n \quad (n \geq 3) [ilevbare2012c E2, E3]

Variables and units

symbolmeaningunit
δsolubility parameter; lower means more hydrophobicMPa^1/2
Δe_igroup contribution to the energy of vaporizationJ/mol
Δv_igroup contribution to the molar volumecm³/mol
ΔE_v, Venergy of vaporization and molar volumeJ/mol; cm³/mol
nnumber of main-chain skeletal atoms in the smallest repeating unitinteger

Assumptions and valid domain

Group contributions at 25 °C; only the structural formula is needed; for glassy polymers the estimated molar volume deviates from the measured one, hence the correction [ilevbare2012c E1, E2]. Applied to drugs and to cellulosic, vinyl and acrylic polymers; no uncertainty is stated.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
ilevbare2012c14 new cellulose esters19.62–23.28 MPa^1/2inputs not printed (group contributions are in the reference) [ilevbare2012c E1]
ilevbare2012a14 polymers20.05–32.24 MPa^1/2inputs not printed ilevbare2012a E1
ilevbare2013b16 polymers and 3 drugsdrugs 20.03, 21.89, 23.38inputs not printed [ilevbare2013b E1]
ilevbare2013c21 polymers and 3 drugs19.62–32.24; drugs as aboveinputs not printed [ilevbare2013c E5]
mosqueragiraldo2016Fedors SP of 18 new cellulose derivatives (ionization not allowed for)SP 22.08–25.54 MPa^1/2 for the telaprevir polymersnot recomputed [mosqueragiraldo2016 P5, M10–M27]
mosqueragiraldo2018asix carboxylated cellulose derivatives, neutral structuresnamed only19.9–25.5 MPa^1/2 [mosqueragiraldo2018a E2, R6]

Where it fails or is disputed

The SP values of the commercial and synthetic polymers are not printed in the 2012 growth paper [ilevbare2012c X11]. The SP window explains ritonavir and efavirenz but not PVPVA on celecoxib and efavirenz or Pn-IPAAmd and PAA on celecoxib [ilevbare2013c X11; ilevbare2013b C51]. Hydrophobicity (SP) and carboxyl content are confounded in the new esters [ilevbare2012c X10]. The SP of A5a (25.54) and A5b (24.29) differ by more than the span of the effective acids, and the calculated SP did not predict effectiveness across chemistries [mosqueragiraldo2016 X8, C25]. The method cannot include ionized substituents, while the simulations of the same paper treat the chains as fully ionized [mosqueragiraldo2018a P12, X9].

Concepts

solubility parameter, polymer hydrophobicity. Findings. F8, F13, F25, F36.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

Flory-Huggins activity equation

Expression

Activity coefficient of the drug in a polymer, with the amorphous drug as the solvent (2006):

\ln\gamma_{\mathrm{drug}} = \ln\frac{\Phi_{\mathrm{drug}}}{x_{\mathrm{drug}}} + \left(1-\frac{1}{m}\right)\Phi_{\mathrm{polymer}} + \chi\,\Phi_{\mathrm{polymer}}^{2} [marsac2006b E6];

the same quantity scaled from a liquid analogue (1-ethyl-2-pyrrolidone, EP) to PVP (2009):

\ln\gamma_{\mathrm{drug}}^{PVP} = \frac{MV_{\mathrm{drug}}}{MV_{\mathrm{lattice}}}\left[\frac{1}{m_{\mathrm{drug}}}\ln\frac{\Phi_{\mathrm{drug}}}{x_{\mathrm{drug}}} + \left(\frac{1}{m_{\mathrm{drug}}}-\frac{1}{m_{PVP}}\right)\Phi_{PVP}\right] + \ln\gamma_{\mathrm{drug}}^{EP} [marsac2009 E8];

\ln\gamma_{\mathrm{drug}}^{PVP} = \frac{MV_{\mathrm{drug}}}{MV_{\mathrm{lattice}}}\left[\frac{1}{m_{\mathrm{drug}}}\ln\frac{\Phi_{\mathrm{drug}}}{x_{\mathrm{drug}}} + \left(\frac{1}{m_{\mathrm{drug}}}-\frac{1}{m_{PVP}}\right)\Phi_{PVP} + \chi\,\Phi_{PVP}^{2}\right] [marsac2009 E9].

As the activity of the drug in the library's other papers:

\ln a = \ln\Phi_1 + \left(1-\frac{1}{x_{12}}\right)\Phi_2 + \chi\,\Phi_2^{2} [konno2006 E9];

\ln a_{\mathrm{drug}} = \ln\Phi_{\mathrm{drug}} + \left(1-\frac{1}{m}\right)\Phi_{PVP} + \chi\,\Phi_{PVP}^{2} [marsac2006a E10].

The ASD dissolution papers print it as the change of the drug chemical potential in an undissolved polymer:

\frac{\Delta\mu_{\mathrm{drug}}}{RT} = \ln\Phi_{\mathrm{drug}} + \left(1-\frac{1}{r}\right)\Phi_{\mathrm{poly}} + \chi\,\Phi_{\mathrm{poly}}^{2} [li2018 E4]

Variables and units

symbolmeaningunits
\gamma_{drug}, aactivity coefficient and activity of the drugdimensionless [marsac2006b E6; konno2006 E9]
\Phivolume fractiondimensionless [marsac2006b E6]
x_{drug}mole fraction of the drugdimensionless; mole-fraction basis in PVP not printed [marsac2009 X13]
mratio of polymer to lattice-site volumedimensionless [marsac2006b E6]
MVmolar volumecm³/mol (e.g. 288.62 for nifedipine) [marsac2006b M1; marsac2009 E8]
\chiinteraction parameterdimensionless [marsac2006b E6]
\Delta\mu_{\mathrm{drug}}change of the drug chemical potential on mixingJ/mol [li2018 E4]
\Phi_{\mathrm{drug}}, \Phi_{\mathrm{poly}}volume fractions of drug and polymer (2018 notation)dimensionless [li2018 E4]
rV_{\mathrm{poly}}/V_{\mathrm{drug}}, volume ratio of polymer to drug (2018 notation for m)dimensionless [li2018 E4]

Assumptions and valid domain

In the analogue liquid the first two terms vanish when the mixing entropy is ideal (minimal size difference) [marsac2006b C46]. The 2009 scaling assumes ideal mixing entropy with EP, identical contacts of the drug with EP and with the PVP repeat unit, Flory–Huggins combinatorial entropy for PVP, and equal γ at the solubility limits in EP and in PVP [marsac2009 E6, E7, C11]. In the ASD dissolution use: a drug–polymer dispersion that is one phase and stays one phase on hydration, with a polymer largely insoluble in the medium; the change of χ with water is not included [li2018 C45, C46].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
marsac2006bsolubility of the crystalline drug in PVP and methyl pyrrolidonewith χ −3.8 and −4.2reproduces for felodipine in PVP K12 with m = 7.50 (Φ_drug 0.210, 0.31 g/g against 0.31); felodipine in K29/32 gives 0.29 against 0.25 [marsac2006b E6, R17]
marsac2009γ of five compounds in PVP K12, K29/32, K90 from γ in EPγ in PVP 0.50–5.97inputs not printed (lattice volume of EP, mole-fraction basis) [marsac2009 E8, E9, R9]
marsac2006adrug activity against PVP content with χ of the melting routeactivity ≈0.84 (nifedipine) and ≈0.83 (felodipine) at Φ_PVP 0.2reproduces approximately (0.839, 0.826 with 1/m ≈ 0) [marsac2006a E10, R19]
marsac2006aargument that PVP lowers the driving force alike and little for nifedipine and felodipine, so the ranking persistsactivity ≈0.96, 0.84, 0.67 at Φ 0.1, 0.2, 0.3same calculation as the row above [marsac2006a R19, C47]
konno2006argument that Flory–Huggins gives little activity loweringnoneχ and x₁₂ for felodipine–polymer not given [konno2006 E9, C35]
li2018qualitative ranking of the suppression of lopinavir concentration by insoluble polymersχ and r not determinedinputs not printed [li2018 E4, C44, C51]

Where it fails or is disputed

The values in PVP are predictions under the stated assumptions; none was checked against a solubility measured in a polymer, and the one check (methyl pyrrolidone) is about 30% low for nifedipine [marsac2006b X10; marsac2009 X17]. The 2009 relation has no printed lattice volume, so it cannot be recomputed from the paper [marsac2009 X4, X13]. The combinatorial and residual parts are linked, because order imposed by exothermic interactions lowers the entropy of mixing [marsac2009 C10]. The conclusion drawn from it in the physical-stability papers, that a few percent of polymer acts kinetically, was not tested by any measured activity [konno2006 C35; marsac2006a C46]. For lopinavir, χ was not measured for any lopinavir–polymer pair, so the use is qualitative [li2018 C46, C51]. With χ = 0 and a large r the equation gives a drug activity of about 0.82 at a drug volume fraction of 0.5, above the proportional-dilution line that the paper calls ideal (extractor calculation) [li2018 X2].

Concepts

activity coefficient, combinatorial entropy of mixing, Flory-Huggins theory, drug solubility in polymer, thermodynamic driving force for crystallization, Flory-Huggins interaction parameter, chemical potential, solubility suppression. Findings. Miscibility and drug-polymer interactions: F8, F9. Physical stability: F4. Supersaturation from ASD dissolution: F18.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

Flory-Huggins free energy of mixing

Expression

In mole numbers, as printed in the 2006 paper:

\frac{\Delta G_M}{RT} = n_{\mathrm{drug}}\ln\Phi_{\mathrm{drug}} + n_{\mathrm{polymer}}\ln\Phi_{\mathrm{polymer}} + n_{\mathrm{drug}}\,\Phi_{\mathrm{polymer}}\,\chi [marsac2006b E1];

per lattice site, with the size ratios m of the 2009 paper:

\frac{\Delta G}{RT} = \frac{\Phi_{\mathrm{drug}}}{m_{\mathrm{drug}}}\ln\Phi_{\mathrm{drug}} + \frac{\Phi_{\mathrm{polymer}}}{m_{\mathrm{polymer}}}\ln\Phi_{\mathrm{polymer}} + \chi\,\Phi_{\mathrm{drug}}\Phi_{\mathrm{polymer}} [marsac2009 E10];

and for a drug (volume fraction \Phi) and a polymer of m lattice sites, as printed in two later papers of the library:

\Delta G_{mix} = RT\left[\Phi\ln\Phi + \frac{1-\Phi}{m}\ln(1-\Phi) + \chi\,\Phi\,(1-\Phi)\right] [tian2017 E2];

\Delta G = RT\left[\varphi\ln\varphi + \frac{1-\varphi}{m}\ln(1-\varphi) + \chi\,\varphi\,(1-\varphi)\right] [moseson2018 E1].

A form is named but not printed in [rumondor2009b E2].

The itraconazole–HPMC paper prints the same form for a drug D and a polymer P,

\frac{\Delta G_{mix}}{RT} = n_D\ln\phi_D + n_P\ln\phi_P + n_D\,\phi_P\,\chi [purohit2015a E1],

and uses it in words only.

Variables and units

symbolmeaningunits
\Delta G_M, \Delta Gfree energy of mixingdivided by RT in the 2006 and 2009 forms [marsac2006b E1; marsac2009 E10]
n_{drug}, n_{polymer}moles of drug and polymermol [marsac2006b E1]
\Phivolume fractiondimensionless; from weight fraction and true density [marsac2006b P5, E8]
m, m_{drug}, m_{polymer}ratio of the molecular volume to that of the lattice sitedimensionless [marsac2009 E10; moseson2018 E1]
\chiinteraction parameterdimensionless [marsac2006b E1]
R, Tgas constant, absolute temperature[marsac2006b E1]

Assumptions and valid domain

The amorphous drug is treated as a solvent and one lattice site equals the molecular volume of the drug [marsac2006b E1, C9]; χ is independent of composition [marsac2009 P8]; the entropy curves are computed with χ = 0 for nifedipine with methyl pyrrolidone and three PVP grades [marsac2006b R1]. The temperature and the PVP grade of the 2009 curves are not printed [marsac2009 X12]. The critical χ for miscibility depends on how the lattice is defined [marsac2006b C18]. The indomethacin polymorph paper uses it for drug–polymer melts at 80–135 °C, above Tg, with 10% w/w polymer, as an argument only [tian2017 E2, A2].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
marsac2006bentropy of mixing of nifedipine with methyl pyrrolidone and PVP; ΔG/RT for χ −4.2 to 2.0χ = 0, −4.2, −3.8, 0.5, 1.0, 2.0; miscibility needs about 0.6 or lessprinted; not applicable, curves carry no ordinate scale [marsac2006b E1, R1, R2, R3]
marsac2009ΔG/RT of five PVP pairs and sucrose–dextran from two sets of χindomethacin minimum ≈2.4 and ≈5 times the athermal oneprinted; not applicable, no numerical axis [marsac2009 E10, R10]
tian2017argument that stronger drug–polymer interactions lower the driving force, so that PVP acts "most likely" through both mobility and driving forcenoneprinted; Φ, m and χ not given; interactions cited from another paper [tian2017 E2, C30, C31, X13]
moseson2018framework for the melting depression of the drug in PVPVAnone directlyprinted; no numerical output [moseson2018 E1]
purohit2015aargument that, without hydrogen-bond donors, itraconazole–HPMC mixing is entropy-driven and may be limited at room temperaturenone (no χ, n or φ given)printed; not applicable [purohit2015a E1, C41, C42, C47]

Where it fails or is disputed

The notation differs between papers (mole numbers against size ratios against polymer segments), so a χ from one convention is not directly usable in another [marsac2006b E1; marsac2009 E10; moseson2018 E1]. The first two terms are the entropy of mixing and are small for a polymer; the curves depend on the lattice and on χ's constancy, while the melting-route χ refers to temperatures near the drug melting point [marsac2006b C11, C32]. The same function applied to a ternary water–drug–polymer system needs three χ values that cannot be transferred from the binary ones [alonzo2010 C44]. The driving-force argument of the indomethacin polymorph paper cannot explain why HPMC beat HPMCAS at high temperature, and χ was not measured for any of the three polymers [tian2017 C29, X13].

Concepts

free energy of mixing, entropy of mixing, Flory-Huggins theory, Flory-Huggins interaction parameter, drug-polymer miscibility, thermodynamic driving force for crystallization. Findings. Miscibility and drug-polymer interactions: F5, F6, F18. Physical stability: F4, F29.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

Flory-Huggins melting point depression

Expression

For a crystalline drug in an amorphous polymer, extended from polymer–solvent equations (2006):

\frac{1}{T_M^{mix}} - \frac{1}{T_M^{pure}} = \frac{-R}{\Delta H_{fus}}\left[\ln\Phi_{\mathrm{drug}} + \left(1-\frac{1}{m}\right)\Phi_{\mathrm{polymer}} + \chi\,\Phi_{\mathrm{polymer}}^{2}\right] [marsac2006b E3];

rearranged so that the slope of a plot against \Phi_{\mathrm{polymer}}^{2} is χ:

\left(\frac{1}{T_M^{mix}}-\frac{1}{T_M^{pure}}\right)\frac{\Delta H_{fus}}{-R} - \ln\Phi_{\mathrm{drug}} - \left(1-\frac{1}{m}\right)\Phi_{\mathrm{polymer}} = \chi\,\Phi_{\mathrm{polymer}}^{2} [marsac2006b E10];

with the lattice volume set by a liquid analogue (2009):

\left(\frac{1}{T_M^{mix}}-\frac{1}{T_M^{pure}}\right) = \frac{-R}{\Delta H_{fus}}\left(\frac{MV_{\mathrm{drug}}}{MV_{\mathrm{lattice}}}\right)\left[\frac{\ln\Phi_{\mathrm{drug}}}{m_{\mathrm{drug}}} + \left(\frac{1}{m_{\mathrm{drug}}}-\frac{1}{m_{\mathrm{polymer}}}\right)\Phi_{\mathrm{polymer}} + \chi\,\Phi_{\mathrm{polymer}}^{2}\right] [marsac2009 E2].

The relation is also printed for drugs in PEG 3350 and for PVPVA:

\frac{1}{T_M^{mix}} - \frac{1}{T_M^{pure}} = -\frac{R}{\Delta H_{fus}}\left[\ln\varphi_{API} + \left(1-\frac{1}{m}\right)\varphi_{\mathrm{polymer}} + \chi\,\varphi_{\mathrm{polymer}}^{2}\right] [zhu2011 E1];

\frac{1}{T_c} - \frac{1}{T_m} = -\frac{R}{\Delta H}\left[\ln\varphi + \left(1-\frac{1}{m}\right)(1-\varphi) + \chi\,(1-\varphi)^{2}\right] [moseson2018 E2].

In the extrusion work T_c is the depressed melting point of the mixture and T_m that of the pure drug [moseson2018 E2]. The linearised form used there to fit \chi as a slope (printed as A=\chi B with B=(1-\phi)^2):

\left(-\frac{\Delta H}{R}\right)\left(\frac{1}{T_c}-\frac{1}{T_m}\right)-\left[\ln\phi+\left(1-\frac{1}{m}\right)(1-\phi)\right]=\chi(1-\phi)^2

[moseson2018 E4].

Variables and units

symbolmeaningunits
T_M^{mix}, T_M^{pure}melting temperature of the drug with polymer and pure (onset in 2006, offset in 2009)K [marsac2006b E3, P1; marsac2009 C16]
\Delta H_{fus}heat of fusion of the pure drugkJ/mol (39.89 and 30.83 for nifedipine and felodipine) [marsac2006b M1, M2]
\Phi_{drug}, \Phi_{polymer}volume fractionsdimensionless [marsac2006b E8]
mratio of the polymer volume to the lattice-site (drug) volume7.80 for PVP K12 with nifedipine (synthesis: 2252.25/288.62) [marsac2006b M3, M1]
MV_{drug}/MV_{lattice}molar volume of the drug over that of the lattice site (EP)dimensionless; not printed [marsac2009 X4, P6]
\chiinteraction parameterdimensionless [marsac2006b R9]
T_c, T_mdepressed melting point of the mixture; melting point of the pure drug (extrusion papers)K [moseson2018 E2]
R, \Delta Hgas constant; enthalpy of fusion of the drug (IDM 37.8 ± 0.6 kJ/mol)J/(mol K); J/mol [moseson2018 E2, M1]
\phidrug volume fraction from true densitiesdimensionless [moseson2018 E2]
mratio of the polymer molecular volume to the drug's (170.7 at 50/50 IDM:PVPVA)dimensionless [moseson2018 E2]

Assumptions and valid domain

The drug and polymer must be chemically stable over the temperature range and interact enough for a depression to appear; the polymer must be liquid-like at the drug melting point, so Tg should lie well below it [marsac2006b C27; marsac2009 C6]. The equation is linear only at low polymer fractions (fit range 0–0.25) and gives χ at temperatures close to the drug melting point [marsac2006b R8, C32; marsac2009 C7]. The offset is used because it gives the melting point at the final composition, assuming complete mixing [marsac2009 C16]. In the extrusion work: one \chi independent of temperature and composition; the drug's molecular volume as lattice volume; offset temperature extrapolated to 0 °C/min; fitted through 90/10 to 50/50 IDM:PVPVA with 40/60 excluded for high variability [moseson2018 C18, P2, R4]. Later papers use the same form with the drug's molecular volume as lattice volume: bicalutamide–PVPVA with m = 46,610/319 = 146.1, φ from amorphous densities of 1.35 and 1.18 g/mL, ΔH = 45.9 kJ/mol and Tm = 467.25 K [moseson2022c E5, E21, R9]; posaconazole–HPMCAS with m = 25.95, ΔH = 50,323.87 J/mol and Tm = 441.78 K, φ from densities of 1.28 and 1.27 g/mL [shah2024 E1, E4].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
marsac2006bχ of nifedipine and felodipine with PVP K12−3.8 (r² 0.99); −4.2 (r² 0.92)reproduces (T_M^mix 430.2 K = 157.1 °C at Φ_polymer 0.278, against ≈157 °C on the curve) [marsac2006b E3, R9, R10]
marsac2009χ of five PVP pairs, three dextran pairs, itraconazole–Eudragit E100−0.82, −0.08, 0.00, −0.08, 0.02; 0.20, 0.38, 0.72, 0.11inputs not printed (depressed melting temperatures only plotted, lattice volume not printed) [marsac2009 E2, R7, X4]
marsac2009indomethacin–PVP K12 from three points of the peak−6.16, −1.94, −0.82as above [marsac2009 R6]
zhu2011χ of drugs with PEG 3350see the PEG chapterinputs not printed [zhu2011 E1]
moseson2018χ of indomethacin–PVPVA−1.97; Tc 131.0 °C predicted at 50/50 against 132.3 ± 0.8 °C measuredreproduces within 0.05 °C for all nine predicted Tc (φ = 0.4739, m = 170.7, Tm = 433.79 K) [moseson2018 E2, R4, R5]
moseson2022cχ of BCL–PVPVA from the heating-rate-extrapolated melting offset, 30–90% BCL−1.57 (R² 0.994); Tc 145 °C at 30% BCLreproduces (30 wt% BCL: 144.3 °C against 145 °C measured); the linearized form gives A/B = −1.53 against the fitted −1.57 [moseson2022c E5, E20, R8, R9]
shah2024χ of posaconazole–HPMCAS MF, PCZ fractions 0.4–1.0+0.43 (R² 0.991)reproduces within about 1 °C (135.9, 155.3 and 165.2 °C at 10, 25 and 50 wt% against printed 135, 155 and 165 °C) [shah2024 E1, E3, R4, R5]

Where it fails or is disputed

The nifedipine volume fractions of the 2006 fit appear to use felodipine's density, and the felodipine plot behind −4.2 is not shown [marsac2006b X2, X4]. The positive χ of non-depressing pairs are lower limits [marsac2009 C19, X11]. A high-Tg polymer hides the depression (PVP K29/30 at 10 °C/min) [marsac2006b R11, C29]. The choice of onset, midpoint or offset changes χ 7.5-fold (synthesis: 6.16/0.82) [marsac2009 R6]. Differences between laboratories for one pair are attributed to preparation, heating rate and onset against offset [moseson2018 C21]. In the extrusion work, written as A=\chi B (a line through the origin) the printed \chi is not reproduced: a fit through the origin gives −1.86 and only a free intercept of about +0.02 gives −1.97; using the drug weight fraction in place of \phi would give 133.9 °C instead of 131.0 °C [moseson2018 E2, E4, X7]. The 40/60 mixture lies well above the line (129 ± 6 against 118.5 °C) because viscosity hindered the offset [moseson2018 R5.g, C17]. Values of \chi for one pair differ between studies and with onset, midpoint or offset [moseson2018 R7, C21; marsac2009 R6]. The posaconazole line has a free intercept (it meets B = 0 at A of about −0.05) and its values below 40% PCZ are extrapolated [shah2024 R4, X7, X8]. The basis of φ (weight or volume fraction) is not stated in the bicalutamide paper [moseson2022c E5]; for posaconazole, setting φ equal to the weight fraction changes the result by only about 0.2 °C [shah2024 E1].

Concepts

melting point depression, Flory-Huggins interaction parameter, drug-polymer miscibility, enthalpy of mixing, Flory–Huggins theory, formulation critical temperature. Findings. Miscibility and drug-polymer interactions: F6, F7, F8. ASD process: F8, F35, F41.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

Flory-Huggins water sorption isotherm

Expression

Binary form, water (1) in one amorphous solid (2):

\ln\left(\frac{p}{p_0}\right) = \ln\phi_1 + \left(1 - \frac{1}{x_{12}}\right)\phi_2 + \chi_{12}\phi_2^{2} [rumondor2010a E1]

with the molar volume ratio written explicitly (outside the subcategory):

\ln(a_{1,g}) = \ln\phi_1 + \phi_2\left(1 - \frac{v_1}{v_2}\right) + \chi_{12}\phi_2^{2} li2020 E12

The 2009 and 2010 moisture papers name it for the drug–water parameter without printing it rumondor2009c E5; marsac2010 E3.

Variables and units

symbolmeaningunits
p/p_0water activity (RH/100)– [rumondor2010a E1]
\phi_1, \phi_2volume fractions of water and solid– [rumondor2010a E1]
x_{12}molecular volume of the solid relative to water16.7 (felodipine), 14.9 (indomethacin) [rumondor2010a P4]
\chi_{12}water–solid interaction parameter– [rumondor2010a E1]

Assumptions and valid domain

Water uptake by an amorphous solid treated as dissolution [rumondor2010a C16]; fitted at p/p0 0.15–0.85 or 0.95 at 25 °C [rumondor2010a P4].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
rumondor2010aχ with water of five amorphous solidsfelodipine 3.27, indomethacin 2.86, PVP 0.36, HPMC 1.33, HPMCAS 1.62point values bracket the stated averages except PVP (≈0.47–0.75 against 0.36) [rumondor2010a R11, E1, X5]
rumondor2009cdrug–water χ of six drugs from 95% RH uptake2.50–3.58extractor check reproduces 2.84, 3.58, 2.71 rumondor2009c R24, E5
marsac2010water–felodipine χ from the 2008 sorption dataabout 3.3named only marsac2010 R22, E3

Where it fails or is disputed

The stated water–PVP value cannot be recovered from the plotted PVP isotherm; the x12 for the polymers and the averaging are not stated [rumondor2010a X5]. The 2009 χ values rest on densities partly approximated as 0.9 × crystal density rumondor2009c X4.

Concepts

Flory-Huggins interaction parameter, water sorption isotherm, Δχ effect. Findings. F6, F8, F13.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

Fox equation

Expression

\frac{1}{T_g} = \frac{x_1}{T_{g,1}} + \frac{x_2}{T_{g,2}} [alhalaweh2016 E6].

As printed for curcumin dispersions:

\frac{1}{T_{g,mix}} = \frac{w_1}{T_{g1}} + \frac{w_2}{T_{g2}} [wegiel2014 E1]

Named without an expression in the 2021 phenolphthalein-analogue study que2021 E2. Printed for wet dispersions and separated phases in the 2024 phase-diagram study:

\frac{1}{T_{g,wet}} = \frac{w_{ASD}}{T_{g,ASD}} + \frac{w_{water}}{T_{g,water}} deac2024b E13

Variables and units

symbolmeaningunits
T_gglass transition of the mixtureK
T_{g,1}, T_{g,2}pure-component values (ritonavir 323 K, atazanavir 377 K)K [alhalaweh2016 M1, M2]
x_1, x_2weight fractions–
w_1, w_2; T_{g1}, T_{g2}weight fractions and component Tg in the curcumin formunits not stated; Table 4 lists °C [wegiel2014 E1]
T_{g,wet}Tg of the wet dispersion or separated phase (2024 form)K deac2024b E13
w_{ASD}, w_{water}weight fractions of dry dispersion and water– deac2024b E13
T_{g,ASD}, T_{g,water}Tg of the dry dispersion; Tg of water, 135 KK deac2024b E13

Assumptions and valid domain

Miscible blend, free-volume additivity; specific interactions violate it [wegiel2014 E1]. None stated in the 2021 phenolphthalein-analogue study que2021 E2.

Use in the library

In the phenolphthalein-analogue study the estimate for neat TIPP (84 °C) shows that the Tg measured for TIPP with 10% PVPVA (86.1 °C) is "likely" slightly above that of neat TIPP, so it can stand for the drug in the comparison of the four analogues' Tgs que2021 C3, R1, M1.

paperused forvalues or fitted parametersstatus / recomputed
alhalaweh2016ritonavir–atazanavir melt-quenched mixturesw_RTV 0.2: 364.8 K against about 365 Kreproduces the line; data 3–8 K below [alhalaweh2016 E6, X7]
que2021neat TIPP Tg357.4 K = 84.2 °Creproduces que2021 E2
wilson2018wet Tg of amorphous enzalutamide352 K printed; water Tg and fraction not printednamed only; inputs not printed [wilson2018 E8, C14]
wegiel2014deviation of the dispersion Tg as a marker of drug–polymer interactionprinted predictions 42 (E100), 96 (PVP), 92 (HPMC), 80 (HPMCAS), 89 °C (CMCAB)mismatch: computed in °C at 25% curcumin; with kelvin and the stored 75% curcumin 43.2, 66.6, 64.4, 58.5, 63.1 °C, deviations +18.8, −3.6, +3.6, +6.5, −1.1 °C [wegiel2014 E1, R18, X1]
deac2024bTg of wet miscible dispersions and of the separated phasesT_{g,water} = 135 Kreproduces ≈51 °C for 5% PHPH at 0.10 water deac2024b E13

Where it fails or is disputed

The measured Tg lie below the line [alhalaweh2016 X7]. In the curcumin paper, after recalculation only the E100 deviation survives, which the authors read as consistent with an ionic interaction; the negative deviations they read as a net loss of interactions disappear [wegiel2014 C41, C42, X1].

Concepts

Fox equation, drug–drug miscibility, acid-base interaction, plasticization. Findings. Bioperformance: F6. Physical stability: F5, F24. Release mechanism and LoC: F17, F30.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

Gibbs-Duhem equation

Expression

I(a_2) = \left(\frac{n_1}{n_2}\right)_{Henry} + \int_{\bar{a}_1^{H}}^{\bar{a}_1^{S}} \frac{n_1}{n_2}\,\frac{1}{a_1}\,da_1 [hsieh2012 E5]

The integral is evaluated numerically as \sum \langle (n_1/n_2)(1/a_1)\rangle (a_1^{i+1} - a_1^{i}) over the sorption isotherm [hsieh2012 E5]. The other chapter papers name the Gibbs–Duhem equation without printing it [ilevbare2013b E7; jackson2014 E3].

Variables and units

symbolmeaningunit
n_1, n_2moles of water and of solute in the amorphous solidmol
a_1water activitydimensionless
ā_1^Hwater activity at the limit of Henry's-law linearitydimensionless
ā_1^Swater activity of the solid in equilibrium with a dilute solution (extrapolated to unit water activity)dimensionless
I(a_2)integral entering \exp[-I(a_2)], the activity of the water-saturated amorphous drugdimensionless

Assumptions and valid domain

A Henry's-law region from zero water up to the limit of linearity plus a "high water" region from the sorption isotherm (Murdande 2010, outside the library) [hsieh2012 E5, P13]. Applied to amorphous drugs at 37 °C (5–95% RH) and 25 °C (danazol).

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
hsieh2012water correction of five amorphous basesI(a2) not printedinputs not printed [hsieh2012 E5]
ilevbare2013bamorphous solubility of three drugs−I(a2) not printednamed only [ilevbare2013b E7]
jackson2014danazolexp[−I(a2)] = 0.935named only [jackson2014 E3, E1]

Where it fails or is disputed

The sorption isotherms and I(a2) values are not printed, so the corrected amorphous solubilities cannot be recomputed [hsieh2012 X14].

Concepts

Gibbs-Duhem equation, water sorption correction of amorphous solubility. Findings. F2.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

Gibbs free energy of mixing

Expression

The general relation between the free energy, enthalpy and entropy of mixing, as printed in the 2009 study of drug–polymer miscibility:

\Delta G_{mix} = \Delta H_{mix} - T\,\Delta S_{mix} [rumondor2009a E5];

with the ideal (combinatorial) entropy of mixing, printed without the leading minus sign:

\Delta S_{mix} = R\,(X_u\ln X_u + X_v\ln X_v) [rumondor2009a E3];

the form that is positive for all compositions, as the text requires (synthesis: the minus sign restored, as the card's note X7 reads it):

\Delta S_{mix} = -R\,(X_u\ln X_u + X_v\ln X_v) [rumondor2009a E3, X7];

and the enthalpy of mixing, written as the pure-component enthalpies minus the mixture enthalpy:

\Delta H_{mix} = (H_{ii}+H_{jj}) - H_{ij} [rumondor2009a E4].

For a drug (A) and a buffer solution (B) in a partially miscible system, the free energy of mixing is written with chemical potentials:

\Delta G_{mix} = x_A(\mu_A - \mu_A^{*}) + x_B(\mu_B - \mu_B^{*}) [raina2014a E8].

The conditions for the two points of phase separation are given in words only: the binodal points are the two minima of \Delta G_{mix} against composition, and the spinodal points are the inflection points, found by setting the second derivative to zero [rumondor2009a E6, E7].

The dextran–PVP paper prints the same relation for a polymer blend,

\Delta G_{mix} = \Delta H_{mix} - T\,\Delta S_{mix} [vaneerdenbrugh2012a E3],

and splits it into a Flory–Huggins enthalpy \Delta H_{mix} = kT\chi\phi_1\phi_2 per lattice site [vaneerdenbrugh2012a E4] and the combinatorial entropy of Flory-Huggins combinatorial entropy of mixing.

Variables and units

symbolmeaningunits
\Delta G_{mix}, \Delta H_{mix}, \Delta S_{mix}free energy, enthalpy and entropy of mixingnot printed [rumondor2009a E3, E4, E5]
X_u, X_vmole fractions of the two componentsdimensionless [rumondor2009a E3]
H_{ii}, H_{jj}, H_{ij}enthalpies of the pure components and of the mixturenot printed [rumondor2009a E4]
x_A, x_Bmole fractions of drug and buffer solutiondimensionless [raina2014a E8]
\mu, \mu^{*}chemical potential and its standard-state value[raina2014a E8]
T, Rtemperature and gas constant[rumondor2009a E3, E5]

Assumptions and valid domain

Ideal mixing entropy with mole fractions is assumed in the 2009 form [rumondor2009a E3]. Positive \Delta G_{mix} is read as unfavourable mixing and negative as favourable; one minimum is read as a single phase, two minima as partial miscibility, and a positive curve as immiscibility [rumondor2009a C35, C37]. The scheme is liquid-mixture theory extended to amorphous solids [rumondor2009a C35]. The drug–buffer form is used for a partially miscible system at constant temperature [raina2014a E8].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
rumondor2009aframework for the three miscibility behaviours of felodipine, nifedipine and ketoconazole dispersionsnoneprinted; not applicable, no numerical output (E3 is a misprint of sign) [rumondor2009a E3, E4, E5, C35]
rumondor2009aargument that a favourable drug–polymer interaction gives one minimum and a one-phase dispersion; competition with intra-polymer hydrogen bonds makes mixing less favourablenonenot applicable [rumondor2009a C37, C39, C45]
raina2014aframework for the onset of liquid–liquid phase separation as binodal pointsnoneprinted; not applicable [raina2014a E8, C27]
vaneerdenbrugh2012aargument that a blend mixes only if the combinatorial entropy outweighs a positive enthalpynone (χ not determined)printed; not applicable, no numerical output [vaneerdenbrugh2012a E3, E4, C32]

Where it fails or is disputed

Equation 3 of the 2009 paper is printed without the minus sign and as printed would give a negative entropy of mixing [rumondor2009a X7]. The sign convention of \Delta H_{mix} in E4 is the reverse of the conventional one, and the text mixes the two conventions [rumondor2009a X8]. Taking the binodal points as the minima of \Delta G_{mix} holds only for a symmetric curve, so E6 cannot locate the binodal compositions of an asymmetric drug–polymer system [rumondor2009a X15]. The paper applies none of the relations to data. The Flory–Huggins form of the same quantity, with its size-ratio terms, is a separate page: Flory-Huggins free energy of mixing.

Concepts

free energy of mixing, enthalpy of mixing, entropy of mixing, drug-polymer miscibility. Findings. F3, F4, F22.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

Gordon-Taylor equation

Expression

As printed with a density-based constant:

T_g=\frac{w_1T_{g1}+Kw_2T_{g2}}{w_1+Kw_2},\qquad K=\frac{\rho_1T_{g1}}{\rho_2T_{g2}}

[moseson2018 E3]. As printed with the drug weight fraction w_1 and a fitted constant:

T_g=\frac{w_1T_{g1}+K(1-w_1)T_{g2}}{w_1+K(1-w_1)}

li2019 E1.

As printed in the felodipine nucleation paper:

T_{g12} = \frac{w_1 T_{g1} + K w_2 T_{g2}}{w_1 + K w_2} [konno2006 E2]

K = \frac{T_{g1}\rho_1}{T_{g2}\rho_2} [konno2006 E3]

with a Couchman–Karasz constant:

K = \frac{\Delta C_{P1}}{\Delta C_{P2}} [konno2006 E4]

In the acetaminophen paper the Gordon–Taylor-type rule is cited in words only: the Tg of a miscible blend varies with the weight fraction and Tg of each component [trasi2012a E2].

As printed in the indomethacin release study, with a fitted constant:

T_{g,mix} = \frac{w_1 T_{g1} + k\,w_2 T_{g2}}{w_1 + k\,w_2} saboo2020 E3

As printed in the 2024 phase-diagram study of the phenolphthalein analogues:

T_{g,ASD} = \frac{w_d T_{g,d} + K\,w_p T_{g,p}}{w_d + K\,w_p} deac2024b E14

Variables and units

symbolmeaningunitids
T_gglass transition temperature of the miscible blendK[moseson2018 E3]
w_1, w_2weight fractions of drug and polymer–[moseson2018 E3]
T_{g1}, T_{g2}Tg of drug (IDM 43.7 °C) and polymer (PVPVA 104.2 °C); nanoTA: 367 K and 482 KK[moseson2018 M1, M2; li2019 E1]
Kconstant from true densities (0.932 with Tg in K) or fitted (0.628)–[moseson2018 E3; li2019 E1]
\rho, \Delta C_Pdensities 1.33 (felodipine), 1.25 (PVP), 1.29 (HPMCAS), 1.19 g/cm³ (HPMC); heat capacity steps 0.33, 0.20, 0.31, 0.25 J/g/Kg/cm³; J/g/K[konno2006 M1, M2, M3, M4]
T_{g,mix}Tg of the homogeneous film (indomethacin release study)°Csaboo2020 E3
w_1, T_{g1}weight fraction and Tg of indomethacin (53 °C by nanoTA)–, °Csaboo2020 E3
w_2, T_{g2}weight fraction and Tg of PVPVA (130 °C by nanoTA)–, °Csaboo2020 E3
kfitted constant, 0.91–saboo2020 E3

Assumptions and valid domain

A miscible, ideally mixing blend; K from the Simha–Boyer rule with Tg in kelvin (the temperature unit of K is not stated in the paper); for nanoTA the fit to softening temperatures of miscible rotary-evaporated films from 0 to 100% DL [moseson2018 E3; li2019 P10, R13]. The felodipine paper states that the components are miscible and their free volumes additive [konno2006 E2]. In the indomethacin release study: homogeneous films; Tg from nanoTA; k by partial least squares to films of 10–90% drug saboo2020 E3, R27.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
moseson2018formulation Tg line of IDM–PVPVA72.9 °C predicted against 72.2 ± 0.5 °C at 50/50reproduces within 0.05 °C for all predicted Tg (K = 0.932 with Tg in K) [moseson2018 E3, R5]
li2019local drug content from nanoTA softeningK = 0.628, Tg1 = 367 K, Tg2 = 482 Kreproduces (110 °C → 0.794; 180 °C → 0.174; 150 and 105 °C → 0.40 and 0.85) li2019 E1, R16
moseson2022cTg line of BCL–PVPVAK = 0.987 with Tg in K (BCL 52.3 °C, 1.35 g/mL; PVPVA 104.2 °C, 1.18 g/mL)reproduces: 88.5 °C at 30% BCL against about 89.6 °C read from the figure; the density choice is not stated [moseson2022c E6, R9]
shah2024Tg line of PCZ–HPMCASTg of PCZ 61 °C and HPMCAS 122 °C, densities 1.28 and 1.27 g/mLmismatch: printed line about 81.5 °C at 0.5 PCZ; 89.1 °C with K = 0.852 (Tg in K); 81.4 °C with K = 0.504 (Tg in °C), which matches the line at 0.1–0.9 within about 0.5 °C [shah2024 E2, R6]
konno2006ideal-mixing Tg lines for felodipine with PVP, HPMCAS, HPMCK 0.280, 0.398, 0.351 (Tg in °C)reproduces the plotted lines only with Tg in °C; with kelvin K 0.767, 0.845, 0.858 and all systems fall below [konno2006 E3, X3]
trasi2012aTg rises of 1.7–4.2 °C with 10% polymer read as miscibilitynoneprinted in words; polymer Tg values not printed [trasi2012a E2, R9, C17]
trasi2017context for the Tg drop of amorphous tacrolimus and its HPMC dispersion after 75% RHnonenamed only [trasi2017 E7, R15]
saboo2020inverting the local Tg of a dissolving 25% indomethacin–PVPVA film into its drug content111, 95, 88, 82 °C → 23, 44, 52, 60 wt% at 0–20 minreproduces: at 82 °C w_1 = k(T_{g2} - T_g)/(T_g(1 - k) - T_{g1} + k T_{g2}) = 0.601 against 60 ± 5; 111 °C gives 23 wt% saboo2020 E3, R28
deac2024bdry MePHPH–PVPVA Tg; Tg against water for the glass–gel boundaryK = 0.65; fitted water Tg 197.6–297.1 Kreproduces 349.3 against 349.1 K deac2024b E14, X11

Where it fails or is disputed

With Tg in °C, K = 0.466 and 50/50 would give 62.9 °C [moseson2018 E3]. nanoTA softening temperatures lie 20–60 °C above DSC Tg, so a nanoTA calibration is a separate fit, and a miscible 33% DL film (about 145–154 °C) reads as about 40% LPV on the curve li2019 C25, X17. Some drug-rich values lie below the pure-LPV calibration point li2019 X16. In the posaconazole paper the printed line matches K computed from Tg in °C, whereas in the indomethacin paper it matches K computed from Tg in K, and the unit of K is not stated in either [shah2024 E2; moseson2018 E3]. In the felodipine nucleation paper the temperature scale of the constant is not stated either and the plotted lines need °C [konno2006 X3]; the Couchman–Karasz constant as printed reproduces neither orientation [konno2006 X4]. The nanoTA method probes about 50 nm of a film, while FTIR and EDX of the same study probed tablets more deeply, so at 20 min the three estimates span about 60–72 wt% saboo2020 X15. Could not describe dry PHPH–PVPVA, whose Tg lay above both components deac2024b E14, R31.

Concepts

Gordon–Taylor equation, temperature-composition phase diagram, glass transition temperature, Couchman-Karasz equation, surface drug enrichment. Findings. ASD process: F7, F8, F15. Physical stability: F5, F18, F33. Release mechanism and LoC: F7, F30.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

Henderson-Hasselbalch equation

Expression

\mathrm{pH} = \mathrm{p}K_a + \log_{10}\frac{[\mathrm{B}]}{[\mathrm{BH}^+]} [indulkar2015 E1];

the un-ionized part of a measured total concentration:

C_U = \frac{X}{1+X}\,C_T,\qquad X = 10^{\mathrm{pH}-\mathrm{p}K_a} [indulkar2015 E6];

and the pH-shift titration curve before and after precipitation (E4, E5), printed with the denominator 1 - (\Delta vol_1/\Delta vol_2)\times[\mathrm{sample}] [indulkar2015 E4, E5, X18]. Almeida e Sousa and co-workers name the relation without printing it [almeidaesousa2016 E3].

The paper of 2018 prints the total-solubility form

C_T = \left(\frac{1 + X}{X}\right)C_U,\qquad X = 10^{\mathrm{pH} - \mathrm{p}K_a} [sugihara2018 E1].

The Mesoporous silica paper on electrostatics names the equation without printing it and uses it for the ionized fraction and for crystalline pH-solubility profiles [hate2020b E1, P10, P11].

Variables and units

symbolmeaningunits
[\mathrm{B}], [\mathrm{BH}^+]concentration of the un-ionized base and its conjugate acid[indulkar2015 E1]
C_U, C_Tun-ionized and total concentrationµg/mL [indulkar2015 E6]
\mathrm{p}K_apKa of the base; in the Mesoporous silica paper ketoconazole 2.9 and 6.5, clozapine 7.3 (7.5 in the introduction), atazanavir 4.49[indulkar2015 M1, M2, M3; hate2020b M1, M2, M3, X1]

Assumptions and valid domain

A weak base is almost fully un-ionized two pH units above its pKa and almost fully ionized two units below [indulkar2015 C16]. The Mesoporous silica paper states none [hate2020b E1].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
indulkar2015percent ionized; un-ionized LLPS concentration; titrationclotrimazole pH 4: 98.7% ionized; clotrimazole pH 6: C_U 0.61 µg/mLreproduces (nicardipine pH 9 printed 0.9%, recomputed 1.6%) [indulkar2015 E1, E6, X4]
almeidaesousa2016expresses CRH1 concentrations at pH 4.6 as un-ionized drugnone printednamed only [almeidaesousa2016 E3, C13]
sugihara2018predicted crystalline and amorphous solubility curves of pazopanibpKa 6.4; C_U from the pH 8.4 valuesreproduces (crystalline at pH 4: 252 × 0.018 µg/mL = 4.5 µg/mL against about 4.8 read from the curve) [sugihara2018 E1, R3]
hate2020bionized fraction at pH 1, 4.5, 5.5 and 6.8ketoconazole about 100, 99, 91, 33%; clozapine about 100, 100, 98, 76%; atazanavir about 100, 50, 9, 0.5%reproduces (synthesis: at pH 6.8, 1/(1 + 10^(6.8 − 6.5)) = 33%, 1/(1 + 10^(6.8 − 7.3)) = 76%, 1/(1 + 10^(6.8 − 4.49)) = 0.5%) [hate2020b R1]
hate2020bcrystalline pH-solubility profilescurves leave their plateau near pH 5 (atazanavir), 7 (ketoconazole), 8 (clozapine)intrinsic solubilities not printed [hate2020b R19, P11]

Where it fails or is disputed

The printed percentage for nicardipine at pH 9 and atazanavir at pH 3.5 differ slightly from the recomputed values [indulkar2015 X4]. The clozapine pKa is 7.5 in the introduction and 7.3 in the calculations [hate2020b X1].

Concepts

Henderson-Hasselbalch equation, ionization, pKa, re-adsorption after pH shift. Findings. Amorphous solubility and LLPS: F10, F14, F23. Mesoporous silica: F6, F13.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

Higuchi-Corrigan critical mixture ratio

Evidence table: Higuchi-Corrigan critical mixture ratio. Content from the release-mechanism chapter (2019–2020), with a row from the ASD dissolution chapter.

Expression

\frac{N_{drug}}{N_{polymer}} = \frac{D_{drug}\,C_{s(drug)}}{D_{polymer}\,C_{s(polymer)}} saboo2020a E4

\frac{N_A}{N_B} > \frac{D_A\,C_{SA}}{D_B\,C_{SB}} xie2016a E2

Named, without an expression, as the critical mixture ratio of the Higuchi two-component model, set by the relative solubilities and diffusivities of the components indulkar2019a E4.

Variables and units

symbolmeaningunit
Nweight fraction (proportion) of a component–
Ddiffusion coefficient–
C_s, C_Ssaturation solubility of a componentmg/mL

Assumptions and valid domain

Diffusion-controlled dissolution of a two-component system (cited) saboo2020a E4; physical mixture, non-interacting components, non-disintegrating surface indulkar2019a E4. For felodipine–PVPVA: amorphous solubility 8 µg/mL, PVPVA solubility 46 mg/mL (cited), D_{drug}/D_{polymer} = 10 saboo2020a R27.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
indulkar2019athe model fails for congruent release at 10–25% ritonavirnonenamed only indulkar2019a E4, C24
saboo2020acritical ratio of felodipine–PVPVAprinted 1.7 × 10⁻⁶mismatch: 10 × 0.008 / 46 = 1.7 × 10⁻³ saboo2020a X1, R27
xie2016a (ASD dissolution)basis of polymer control at low and drug control at high celecoxib loadingnonenot applicable xie2016a E2

Where it fails or is disputed

Both the printed and the recomputed ratio lie far below the 5–50% loadings tested, so the model predicts drug control where release was congruent saboo2020a X1, C36, C37. The SI calls the relation "equation 3" of the main article, which is Eq. (4) saboo2020a X1. Judging release by the drug:polymer ratio alone is "clearly an over simplification" saboo2020a C38.

Concepts

Higuchi two-component dissolution model, polymer-controlled release, Stokes-Einstein equation. Findings. Release mechanism and LoC: F2.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

Hoffman equation

Expression

\Delta G_v = -\frac{\Delta H_{fus}\,(T_{melt,ons} - T)\,T}{T_{melt,ons}^{2}} [baird2010 E25];

\Delta G_v = -\frac{\Delta H_{fus}\,(T_{m} - T)\,T}{T_{m}^{2}} [vaneerdenbrugh2010a E2];

\Delta G_v = \frac{\Delta H_{m}\,(T_{m} - T)\,T}{T_{m}^{2}} [lu2016 E1].

Named but not printed in [baird2012 E6]. The sign differs between papers: the two 2010 papers print a leading minus sign, the 2016 paper does not and plots the negative of its own expression [lu2016 X17].

Two more printed forms. In the PEG dispersions paper the expression is printed without a leading sign and used inside the simplified solubility equation \ln[\gamma_d x_d] = -\Delta G_{fus}/(R\,T) [baird2011 E5]:

\Delta G_{fus} = \frac{\Delta H_{fus,d}\,(T_{melt,d} - T)\,T}{T_{melt,d}^{2}} [baird2011 E6].

In the solution-methods paper it is printed with a positive sign and \Delta T = T_m - T:

\Delta G = \frac{\Delta H_f\,\Delta T}{T_m}\cdot\frac{T}{T_m} [raina2015a E2],

which equals \Delta H_f\,(T_m - T)\,T/T_m^{2} and is the amorphous-minus-crystal free energy that enters e^{\Delta G/RT} of the amorphous solubility estimate.

The papers of the amorphous solubility chapter print the relation with a positive sign, as the amorphous-minus-crystal free energy that enters e^{\Delta G/RT}:

\Delta G_{a\to c} = \frac{\Delta H_f\,(T_m - T)\,T}{T_m^{2}} [ilevbare2013a E2; indulkar2015 E3; mosqueragiraldo2015 E2; almeidaesousa2016 E2];

the 2015 Almeida e Sousa paper writes \Delta_{fus}H for the heat of fusion and \Delta G_{c\to a} for the direction [almeidaesousa2015 E2]. For atazanavir it is printed again,

\Delta G = \frac{\Delta H_f\,(T_m - T)\,T}{T_m^{2}} indulkar2017a E2.

The papers of the crystallization-from-solution chapter print it with a positive sign as well:

\Delta G_c = \Delta H_f\,\frac{(T_m - T)\,T}{T_m^{2}} [hsieh2012 E3; hsieh2014 E2];

\Delta G_{a \to c} = \frac{\Delta H_{fus}\,(T_m - T)\,T}{T_m^{2}} [ilevbare2012b E9; ilevbare2013c E7];

\Delta G_C = \frac{\Delta H_f\,(T_m - T)\,T}{T_m^{2}} [ilevbare2013b E3];

\Delta G = \frac{\Delta H_f\,\Delta T\,T}{T_m^{2}}, \qquad \Delta T = T_m - T [jackson2014 E2].

The moisture-induced separation paper of the physical-stability chapter prints it with a positive sign,

\Delta G_c = \Delta H_f\frac{\left(T_m - T\right)T}{T_m^{2}} rumondor2009c E3,

and the felodipine kinetics paper names it without an expression [rumondor2009b E1].

The ASD dissolution papers print it as

\Delta G_c = \Delta H_f\,\frac{(T_m - T)\,T}{T_m^{2}} [konno2008a E2],

\Delta G = \frac{\Delta H_f\,\Delta T\,T}{T_m^{2}} [alonzo2010 E2; alonzo2011 E3],

and, with the sign that makes \Delta G negative,

\Delta G = -\frac{\Delta H_f\,(T_m - T)\,T}{T_m^{2}} duong2022a E2.

Variables and units

symbolmeaningunits
\Delta G_vfree energy difference between crystal and amorphous or liquid stateJ/cm³ after conversion with crystalline density [vaneerdenbrugh2010a E2, E5; baird2010 E25]; kJ/mol [lu2016 E1]
\Delta H_{fus}, \Delta H_menthalpy of fusionkJ/mol or J/cm³ [baird2010 E26; vaneerdenbrugh2010a E1]
T_m, T_{melt,ons}melting temperature (onset)K [vaneerdenbrugh2010a E1; lu2016 E1]
Ttemperature of evaluation293.15 K [baird2010 E25; vaneerdenbrugh2010a E2], 298 K [baird2012 E6], crystallization temperature [lu2016 E1]; 25 or 37 °C [hsieh2014 E2; ilevbare2012b E9]
\Delta G_{fus}, \Delta H_{fus,d}, T_{melt,d}free energy difference between crystalline and liquid drug at T (298.15 K in the check); heat of fusion of the drug in kJ/mol; its melting temperature\Delta H_{fus,d} in kJ/mol; temperatures in K; unit of \Delta G_{fus} not printed [baird2011 E5, E7]
\Delta H_fmolar heat of fusionnot printed [raina2015a E2]
\Delta TT_m - TK [raina2015a E2]
\Delta G_{a\to c}amorphous-minus-crystal free energy that enters e^{\Delta G/RT} in the amorphous solubility papers (\Delta G_{c\to a} in the 2015 Almeida e Sousa paper)kJ/mol in the use table below [ilevbare2013a E2; almeidaesousa2015 E2]
\Delta G_c, \Delta G_Cfree-energy difference between amorphous (supercooled liquid) and crystalkJ/mol [hsieh2012 E3; ilevbare2013b E3]
\Delta H_f, T_m, T in the moisture paperheat of fusion; melting and evaluation temperatureskJ/mol; K rumondor2009c E3
\Delta G_c, \Delta G (ASD dissolution papers)free-energy difference between amorphous and crystalline drugJ/mol [konno2008a E2; alonzo2010 E2]

Assumptions and valid domain

Lu et al. call it an approximation [lu2016 E1]. Papers outside this chapter state that it assumes enthalpies of crystal and supercooled liquid linear in temperature and applies above Tg [marsac2006a E3; marsac2006b E4], that it assumes a constant heat-capacity difference and small undercooling [almeidaesousa2015 E2], and that it may not suit large undercoolings [mosqueragiraldo2015 E2]. In this chapter it is evaluated at room temperature, far below Tm and below Tg for many compounds [baird2010 E25; baird2012 E6]. In the PEG dispersions paper it is used as an estimate of \Delta G_{fus} from thermal properties, with the drug solubility in PEG 400 as a proxy for the polymer [baird2011 E6, C20, C21]. In the solution-methods paper no assumptions are stated beyond the reference; ΔHf and Tm come from DSC at 10 °C/min [raina2015a E2, P4]. In the amorphous solubility papers the assumptions are a constant, temperature-independent ΔCp, small undercooling and Tg close to T∞ [almeidaesousa2015 C8], and a temperature of interest "reasonably close to Tm", which is violated for telaprevir (Tm 238 °C, 37 °C) [mosqueragiraldo2015 C24, M1]. The pH-shift and crystal-growth papers state that the enthalpies of crystal and supercooled liquid vary linearly with temperature, "to a first approximation" [hsieh2014 E2; jackson2014 E2]; ΔHf and Tm come from DSC of the crystalline material and temperatures must be in kelvin [hsieh2012 E3]. The felodipine kinetics paper states that it applies to a pure amorphous drug; with polymer and sorbed water a reasonable estimate is "extremely difficult" [rumondor2009b C17]. In the ASD dissolution papers it is called increasingly approximate far below Tg (cited) alonzo2011 C5 and was judged a good estimate for felodipine in earlier work (cited) [konno2008a R20].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
baird2010ΔGv descriptor in the class PCAclass I contribution −0.40 (more negative ΔGv)inputs not printed [baird2010 E25, R22.g]
vaneerdenbrugh2010aΔGv descriptor in the class PCAcontributions −0.29, +0.29, +0.13 for classes I, II, IIIinputs not printed [vaneerdenbrugh2010a E2, R20.e]
baird2012ΔGv column at 298 K−8.6 (lidocaine) to −54.7 J/cm³ (acetaminophen)named only; the standard form reproduces the other 33 rows within about 0.6 J/cm³, ritonavir printed −37.6 against about −21.4 [baird2012 E6, M5, M12, X2]
lu2016driving force of α and β vemurafenib; virtual transitionα 11.0 kJ/mol at 115 °C; transition 319 °Creproduces [lu2016 E1, R22]
marsac2006afelodipine and nifedipine driving force6.22 and 8.83 kJ/mol at 25 °Creproduces [marsac2006a E3]
ilevbare2013cdriving force at 37 °C (extractor calculation)ritonavir ≈10.2, efavirenz ≈2.70, celecoxib ≈7.74 kJ/molinputs not printed for a stated output [ilevbare2013c E7]
baird2011\Delta G_{fus} inside the activity coefficient of four drugs in PEG 400 at 25 °Cno \Delta G_{fus} value printednot applicable; checked through the activity coefficient (0.614 for chlorpropamide, reproduces) [baird2011 E6, E7]
raina2015aΔG in the amorphous solubility estimate of six dihydropyridinesΔHf and Tm not printedinputs not printed [raina2015a E2]
ilevbare2013aΔG inside Eq. 1 for eight drugsritonavir 10.1 kJ/mol at 37 °C from Table 2 inputsno ΔG printed; recomputed ilevbare2013a E2
almeidaesousa2015comparator of the Cp method3.24–10.33 kJ/mol for six drugsreproduces (ibuprofen 3.25 against 3.24 kJ/mol) [almeidaesousa2015 E2, R11]
indulkar2015ΔG at 310 K for clotrimazole and atazanavir6.26 kJ/mol (clotrimazole, with an unprinted molar mass)inputs not printed [indulkar2015 E3]
mosqueragiraldo2015telaprevir13.31 kJ/mol; amorphous solubility 245 ± 5 µg/mLreproduces [mosqueragiraldo2015 E1, E2]
almeidaesousa2016CRH15.68 kJ/molreproduces (5.685) [almeidaesousa2016 E2]
indulkar2017aΔG of atazanavir inside Eq. 314.55 kJ/mol from Table I (ΔHf 90.1 J/g, Tm 208 °C, 310 K)not printed; with 0.22 read as exp[−I(a)] it gives the printed 62, and about 228 read as I(a) (synthesis) [indulkar2017a E2, X1; indulkar2015 M2]
hsieh2012amorphous solubility of five basesΔHf, Tm not printedinputs not printed [hsieh2012 E3]
ilevbare2012britonavirΔHf 60.4 kJ/mol, Tm 121 °C, 37 °CΔG 10.1 kJ/mol, exp(ΔG/RT) 50.8 (extractor) [ilevbare2012b E9]
hsieh2014glyburide, warfarin175.6 °C and 45.5 kJ/mol; 169.2 °C and 43.6 kJ/molreproduces: 59.9 and 47.7 at 25 °C [hsieh2014 E2, E3]
jackson2014danazolΔHf 28.9 kJ/mol, Tm 225.4 °CΔG 6.95 kJ/mol; ratio 15.4 against 19.6 printed [jackson2014 E1, E2]
duong2022bposaconazole, 310 K\Delta G = \Delta H_f(T_m - T)T/T_m^{2}Tm 442.25 K, ΔHf 76.95 J/g; ΔG 16.13 J/g by the extractor [duong2022b E3, X2]
rumondor2009cdriving force of six drugs tested as a predictor of moisture-induced separation4.1 (ketoprofen) to 11.0 kJ/mol (pimozide); nifedipine 8.2, felodipine 6.1reproduces (nifedipine 8.23, pimozide 10.97, ketoprofen 4.14) rumondor2009c E3, M1, M2, M5
rumondor2009bnamed as the pure-drug driving forcenonenamed only [rumondor2009b E1]
konno2008afelodipine amorphous solubility, 37 °Cratio about 10, about 9.5 µg/mLinputs not printed [konno2008a E2, R17]
alonzo2010felodipine, 37 °C30.12 kJ/mol, 143.41 °C: ΔG 5729 J/mol, ratio 9.22 against about 9reproduces [alonzo2010 E1]
alonzo2010indomethacin, 37 °C; 25 °C32.48 kJ/mol, 153.4 °C: ΔG 6445 J/mol, ratio 12.17, 36.5 against about 37 µg/mL; 15.8–23.6 against printed 17–25 µg/mLreproduces; mismatch at 25 °C [alonzo2010 E2, X2]
alonzo2011felodipine, 37 and 25 °Cabout 9.1 and 5–6 µg/mLinputs not printed alonzo2011 E3, M1
duong2022adelamanid amorphous-to-crystalline solubility ratio at 37 °C, against the measured 42.3ratio 31.8; Tm 196.1 °Cinputs partly printed; (synthesis: a ratio of 31.8 at 310 K needs ΔG ≈ 8.9 kJ/mol, so ΔHf ≈ 39.8 kJ/mol) duong2022a E2, R27, M1

Where it fails or is disputed

The ΔGv term does not rank the classes monotonically: class II, not class III, has the most positive contribution [vaneerdenbrugh2010a X10]. A printed ΔGv in one table does not follow from its own inputs [baird2012 X2]. Similar viscosity with a twofold different ΔGv weakens a viscosity-only comparison [baird2012 X9]. For vemurafenib the larger driving force of α did not make α dominate at 120–190 °C [lu2016 C52]. Outside this chapter, errors at large undercooling are reported [almeidaesousa2015 E2; mosqueragiraldo2015 E2]. In the PEG dispersions paper the relation is evaluated at 25 °C, far below the melting points of 126.7–151.7 °C, and the result is the activity coefficient of F3 of the PEG dispersions chapter [baird2011 E7, M1, M2, M3, M4]. In the solution-methods papers, for diverse drugs the heat-capacity method gave estimates much closer to measured LLPS onsets [almeidaesousa2015 C43]; the Hoffman-based danazol estimate (16 µg/mL) was above the measured 13 µg/mL [jackson2014 R5]. In the amorphous solubility papers it lacked accuracy for diclofenac (28.9 against 52.2 measured ratio) and telaprevir (2.7 times the onset) [almeidaesousa2015 R13, R5; mosqueragiraldo2015 R17]; Table 10 of the six-drug paper does not predict the size of the error [almeidaesousa2015 X8]. The DSC method and some inputs are not stated [hsieh2014 X11; hsieh2012 X14]. The danazol ratio of 19.6 cannot be reproduced [jackson2014 X1]. The temperature of the warfarin and glyburide calculation is not printed (25 °C assumed) [hsieh2014 E2]. In the physical-stability papers the driving force did not sort the six drugs by moisture-induced separation rumondor2009c C32; for nifedipine against felodipine it pointed the right way for nucleation (F2 of the physical stability chapter) [marsac2006a R4.l]. The 25 °C indomethacin range of the 2010 dissolution paper does not reproduce from its inputs [alonzo2010 X2]. Felodipine concentrations of 14.1 µg/mL measured by UV exceed the 9.5 µg/mL estimate of the same 2008 paper [konno2008a X5]. For delamanid the estimate lies about a quarter below the measured ratio (42.3), which the authors call "reasonable agreement" duong2022a R27, C43.

Concepts

Hoffman equation, thermodynamic driving force for crystallization, enthalpy of fusion, degree of supercooling, activity coefficient, amorphous-crystalline free energy difference, amorphous solubility advantage. Findings. Crystallization tendency: F6, F7, F13. PEG dispersions: F3. Solution methods: F5. C. Amorphous solubility and LLPS: F5, F7. Crystallization from solution: F2, F16. Physical stability: F2, F13. Supersaturation from ASD dissolution: F5, F7, F23.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

ideal-mixing reduction of amorphous solubility

Expression

S_a(x_1) = S_a^{\circ}\,x_1 [trasi2015a E4],

for the second drug S_a(x_2) = S_a^{\circ}(1 - x_1), from the ideal-mixing chemical potentials

\mu_1 = \mu_1^{\circ} + RT\ln x_1,\qquad \mu_2 = \mu_2^{\circ} + RT\ln(1 - x_1) [trasi2015a E2, E3].

The papers of 2017–2022 print the relation for a polymer as the second component,

S_a = S_a^{0}\,x_{drug} [ueda2021 E2]

and

\frac{S_a}{S_a^{0}} = x_{drug} ueda2022 E2.

For binary and ternary drug mixtures, applied to the free concentration and to the Caco-2 flux, the relation is printed as

S_1 = S_{A1}\,X_1, \qquad J_1 = J_{A1}\,X_1, \qquad X_1 = \frac{n_1}{n_1+n_2+n_3+\cdots} [alhalaweh2016 E7, E8, E9].

The ASD dissolution papers print it for one drug of a two-drug film or dispersion,

C_{max} = S_a\,x_d [trasi2015b E1],

and for a drug in an undissolved polymer by weight fraction,

C_{max} = S_a\,w_d [li2018 E7], printed in words as a straight line from 0 µg/mL at 0% to the amorphous solubility, 17.4 µg/mL, at 100% drug loading.

Variables and units

symbolmeaningunits
S_a(x_1)amorphous solubility of drug 1 at mole fraction x_1 in the drug-rich phaseµg/mL [trasi2015a E4]
S_a^{\circ}amorphous solubility of the pure drugµg/mL, ultracentrifuge values 26.2 and 17.1 [trasi2015a R1, X14]
x_1mole fraction of drug 1 among the drug molecules in the drug-rich phasedimensionless [trasi2015a E4]
S_1free concentration of drug 1 with a drug-rich phase containing other drugsM [alhalaweh2016 E7]
S_{A1}amorphous solubility of drug 1 aloneM [alhalaweh2016 E7]
X_1mole fraction of drug 1 in the drug-rich phase– [alhalaweh2016 E9]
J_1, J_{A1}flux with and without the other drugsmg/min/cm² [alhalaweh2016 E8]
C_{max}maximum bulk concentration of one drugµg/mL [trasi2015b E1; li2018 E7]
S_aamorphous solubility of that drug alone (25 µg/mL ritonavir, 17 µg/mL lopinavir)µg/mL [trasi2015b E1]
x_dmole fraction of the drug in the amorphous mixture or drug-rich phasedimensionless [trasi2015b E1]
w_ddrug weight fraction (drug loading) of the dispersiondimensionless [li2018 E7]

Assumptions and valid domain

Constant aqueous activity coefficients, droplets of about 350 nm too large to raise solubility, the same water content in single and mixed drug-rich phases, and the single-drug amorphous solubility as S_a^{\circ} [trasi2015a C38]. Tested for ritonavir–lopinavir at x = 0.06–0.70, 25 °C [trasi2015a R16]. Ideal mixing in the drug-rich phase and amorphous miscibility of the drugs [alhalaweh2016 C26]; tested for ritonavir, atazanavir and lopinavir in PVP. In the ASD dissolution papers the two amorphous drugs mix ideally (cited) [trasi2015b C38]; tested for ritonavir–lopinavir films and dispersions [trasi2015b R5, R17]. The 2018 line scales the amorphous solubility with the drug weight fraction ("ideal behavior") [li2018 E7].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
trasi2015abulk ritonavir and lopinavir against the ritonavir mole fractionlines 0 to about 20.8 µg/mL (ritonavir) and about 16.8 to about 3.4 µg/mL (lopinavir) for x = 0 to 0.8reproduces (26.2 × 0.8 = 20.96; 17.1 × 0.2 = 3.42) [trasi2015a E4, R16]
ueda2021dilution argument for polymer in the ibuprofen-rich phasenone (not evaluated numerically)not applicable [ueda2021 E2]
ueda2022qualitative link of Sa/Sa0 with the polymer contentno x_drug values printedthe per-chain mole fraction stays at 0.97 or more while Sa/Sa0 reaches 0.52–0.54 (extractor calculation) ueda2022 E2, X3, R17
other chaptersideal-mixing line for binary amorphous mixtures and polymer dispersionsnoneprinted; not recomputed here [trasi2015b E1; alhalaweh2016 E7; li2018 E7]
alhalaweh2016binary and ternary ceilings; Caco-2 fluxclinical 1:3 ratio: X_RTV = 0.246; 0.5 × 10.5 × 10⁻⁵ = 5.25 × 10⁻⁵reproduces [alhalaweh2016 E7, E8, E9]
li2018lopinavir ASD films17.4 × 0.50 = 8.7 µg/mLreproduces [li2018 E7]
trasi2015bfilm plateaus at 7:3, 5:5, 3:7five of six within 0.5 µg/mL; RTV 7:3 15.2 against 16.7 µg/mLprinted comparison [trasi2015b R5]
trasi2015b5:5 film with literature molecular weightsx_RTV 0.466: 11.6 and 9.1 µg/mL against printed 11.6 and 9.0reproduces [trasi2015b E1]
trasi2015bHPMCAS dispersions against the lineRTV on the line; LPV up to about 15% belowapproximate [trasi2015b R17, X8]
li2018positions of the polymers against the lineHPMCAS slightly above; CAP at 15–50% and EC at 50–85% drug near it; HPMCP belowprinted comparison [li2018 C20, R3]

Where it fails or is disputed

Ritonavir points lie 2–4 µg/mL above the line, no fit statistic is given, and which column of Table 1 supplied S_a^{\circ} is not stated [trasi2015a X9, X14]. Only one pair was modelled [trasi2015a C43]. For polymers the assumptions of similar molar volumes and adhesive interactions equal to cohesive ones fail, and the relation cannot reproduce the size of the solubility loss; it is used qualitatively [ueda2021 C28; ueda2022 X3]. In alhalaweh2016 the drug-rich phase composition was computed by mass balance and ideality was not measured [alhalaweh2016 C17]; the NTA count of the mixture does not show the phase below the single-drug limits [alhalaweh2016 X6]. The plotted RTV line ends at about 26 rather than 25 µg/mL; the mole fractions need molecular weights the paper does not print [trasi2015b X3, E1]. The authors read positions above or below the 2018 line as weaker or stronger interaction than ideal, but the line is proportional dilution by weight, whereas the 2015 relation uses mole fractions; with χ = 0 and a large polymer the Flory–Huggins drug activity at a drug volume fraction of 0.5 is about 0.82, above the line (extractor calculation) [li2018 X2, C20; trasi2015b E1].

Concepts

ideal mixing, chemical potential, drug-rich phase, drug–drug miscibility, amorphous solubility. Findings. Amorphous solubility and LLPS: F11, F19, F20, F21. Bioperformance: F6, F20. Supersaturation from ASD dissolution: F11, F18.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

Jackson interface-kinetics growth rate

Expression

U = \frac{2 k_B T}{\pi \lambda^2 \eta}\, f \left[1 - \exp\left(-\frac{\Delta H\,\Delta T}{k_B T\,T_m}\right)\right] \exp\left(-\frac{\Delta S}{k_B}\right) [trasi2014a E1].

Variables and units

symbolmeaningunits
Ucrystal growth ratenot stated [trasi2014a E1]
\lambdaaverage diffusion jump distancenot stated
\etaviscosityPa·s (cited data) [trasi2014a P7]
ffraction of interface sites that are active growth sitesdimensionless
\Delta H, \Delta Senthalpy and entropy difference between liquid and crystalnot stated
T, T_m, \Delta Ttemperature, melting temperature, undercoolingK

Assumptions and valid domain

Stokes–Einstein holds and viscosity describes diffusion at the interface in the studied range [trasi2014a C20]; not near Tg, where diffusion decouples from viscosity [trasi2014a C21]. The entropy term reflects the fraction of molecules with the right orientation to join the crystal [trasi2014a C31].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
trasi2014aframework for the driving-force correction and the entropy fitnone fitted directlyinputs not printed (λ, f and η(T) not given) [trasi2014a E1, R10, R11]

Where it fails or is disputed

At similar viscosity the drugs fell into two sets whose corrected growth rates differ by about 2–3 orders of magnitude, so factors beyond viscosity and driving force contribute [trasi2014a C30]. The 2012 viscosity study used a related screw-dislocation form without the entropy term [baird2012 E3].

Concepts

crystal growth rate, melt viscosity, entropy of fusion, thermodynamic driving force for crystallization. Findings. F2, F6.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

Kohlrausch-Williams-Watts equation

Expression

As printed:

1 - \phi(t) = \exp\left(\left(\frac{-t}{\tau}\right)^{\beta}\right) [konno2006 E7]

\frac{\Delta H_{t,T}}{\Delta H_{max,T}} = 1 - \exp\left(-\frac{t}{\tau}\right)^{\beta} [marsac2006a E7]

Both reproduce their data only in the standard stretched-exponential form, 1 - \phi(t) = \exp\left(-(t/\tau)^{\beta}\right) [konno2006 X5; marsac2006a X4].

Variables and units

symbolmeaningunits
\phi(t)fraction of the maximum enthalpy recovered after ageing time t– [konno2006 E5]
\taumean relaxation timeh [konno2006 R9]
\betastretch exponent– [konno2006 R9]

Assumptions and valid domain

Fitted to enthalpy recovery of glasses aged below Tg (2 °C, 23.5 °C), nonlinear regression [konno2006 P6; marsac2006a P9].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
konno20069:1 felodipine dispersions at 2 °Cτ 208 (PVP), 687 (HPMCAS), 319 h (HPMC); β 0.42–0.47reproduces Fig. 6 with the standard form [konno2006 E7, R9]
marsac2006aglasses and 10 wt% PVP dispersions at 23.5 °Cτ 6.3, 4.2 h (drugs); 42.1, 16.7 h (with PVP)reproduces Fig. 4 with the standard form [marsac2006a E7, R4.n, R7]

Where it fails or is disputed

Misprinted in both papers [konno2006 X5; marsac2006a X4]. The τ values did not rank nucleation [marsac2006a C37].

Concepts

enthalpy relaxation, Kohlrausch-Williams-Watts equation, molecular mobility. Findings. F5.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

lever rule

Evidence table: lever rule. Content from the release-mechanism chapter (2023–2025), with a row from the Physical stability chapter.

Expression

Printed in words: the ratio of the amount of phase A to that of phase B equals the ratio of the length BX to AX, X being the overall composition on the tie line joining A and B yang2022b E1. Written with these symbols (synthesis: no equation printed):

\frac{m_A}{m_B} = \frac{\overline{BX}}{\overline{AX}}

Named only in the 2023 phenolphthalein-analogue paper deac2023b E5.

Printed in 2024:

W^{\alpha} = \frac{m^{\alpha}}{m^{T}} = \frac{W_i^{T} - W_i^{\beta}}{W_i^{\alpha} - W_i^{\beta}} deac2024b E12

and stated in words for a ritonavir diagram in 2023 yang2023 E2.

Variables and units

symbolmeaningunit
m_A, m_Bamounts of the coexisting phases A and Bany consistent amount
\overline{AX}, \overline{BX}lengths on the tie line from the overall composition X to A and to B–

Assumptions and valid domain

Thermodynamic equilibrium, with the compositions joined by a tie line yang2022b E1; complete separation to the binodal compositions immediately on entering the unstable region deac2023b E5.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
yang2022b (Physical stability)phase amounts along hydration paths of a schematic ritonavir–PVPVA–water diagramnoneinputs not printed yang2022b E1, C50
deac2023bmajority phase and hydrophobic-phase volume against drug load, schematicnonenamed only deac2023b E5, C34, C36
yang2023amount of drug-rich phase on schematic ritonavir–PVPVA–water diagrams with and without SDSnoneschematic yang2023 E2, C41
deac2024bdrug-rich fraction at the spinodal against loading, from PC-SAFT diagramsW^{\alpha} ≈0.15 → 0.82 (MePHPH, 27 → 39.5%)inputs not printed; Table S1 row d fails the mass balance deac2024b E12, R35, X3

Where it fails or is disputed

In the 2023 paper used on schematic diagrams only; no ternary diagram or tie line was measured there deac2023b X14. The 2024 use assumes onset at the spinodal, immediate local equilibrium and inversion at 0.5 deac2024b E12, C51.

Concepts

lever rule, tie line, ternary phase diagram, phase inversion. Findings. Release mechanism and LoC: F27, F30, F31.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

liquid-phase BET isotherm

Expression

Q_a = \frac{Q_m K_S C_e}{\left(1 - K_L C_e\right)\left(1 - K_L C_e + K_S C_e\right)} [dening2019 E4].

\frac{1}{K_L} = C_0 (restated; printed in words) [dening2019 E7].

Q_a = Q_m \frac{K_S C_e}{(1 - K_L C_e)(1 - K_L C_e + K_S C_e)} [mccarthy2020 E8].

Q_a = Q_m \frac{K_{BET} X}{(1 - X)\left(1 + (K_{BET} - 1) X\right)}, \qquad X = \frac{C_e}{C_s} [hate2020a E1].

Variables and units

symbolmeaningunits
Q_aamount adsorbedmg/g [dening2019 E4]
Q_mfirst-layer (monolayer) capacitymg/g [dening2019 E4]
K_S, K_Lequilibrium constants of the first and upper layersprinted "µg/mL⁻¹", dimensionally mL/µg [dening2019 X1; mccarthy2020 E8]
C_eequilibrium concentrationµg/mL [dening2019 E4]
C_0saturation concentration of the liquid drug phase, proposed equal to the amorphous solubilityµg/mL [dening2019 E7]
K_{BET}, X, C_sconstant of adsorption and desorption; relative concentration; saturation concentration taken as the amorphous solubility[hate2020a E1]

Assumptions and valid domain

Multilayer adsorption with the strongest interaction in the first layer, no lateral interactions, a homogeneous surface and an infinite number of layers [dening2019 C14; hate2020a C23]. The form of Ebadi and co-workers is taken as suitable for liquid-phase data [mccarthy2020 E8]. Fitted to isotherms of ritonavir, indomethacin, its methyl ester and atazanavir on SBA-15 at 37 °C up to about 80–90% of the amorphous solubility [dening2019 R2; mccarthy2020 R7, R8; hate2020a R2].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
dening2019ritonavir isothermR² 0.94; Q_m 103 mg/g; K_S 1.169; K_L 0.031; 1/K_L 32.7 µg/mLreproduces: 430–436 mg/g at C_e about 24.6–24.7 against 424 measured; 1/0.031 = 32.3 [dening2019 E4, E7]
mccarthy2020indomethacin and methyl ester isothermsR² 0.94, 0.98; Q_m 29, 31 mg/g; K_L 0.025, 0.1181/K_L reproduces (40 and 8.47 µg/mL); K_S not printed [mccarthy2020 E8, R11]
hate2020aatazanavir isotherm, 300 µg/mL silicaQ_m 4.5 mg/ginputs not printed (K_{BET}) [hate2020a E1, R3]

Where it fails or is disputed

The heterogeneous silica surface is expected to cause deviations at low concentration, seen for atazanavir [dening2019 C15; hate2020a C24]. 1/K_L for ritonavir lies 17% above the measured amorphous solubility, from one fit without points at or above it [dening2019 X9, X8]. The Q_m values are far below the geometric monolayers [dening2019 R3; hate2020a R1; mccarthy2020 R16]. The electrostatics paper names a BET fit without printing its form and gives Q_m in "mg/mol" [hate2020b E2, X9].

Concepts

BET isotherm, multilayer adsorption, monolayer coverage, adsorption isotherm, amorphous solubility. Findings. F2, F3, F10.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

membrane flux from concentration difference

Expression

J = \frac{D_{eff}}{l}\left(C_d - C_r\right) [indulkar2016 E1]; with the receiver washed continuously, J = (D_{eff}/l)\,C_d [indulkar2016 E4]. A form with the membrane partition coefficient is printed for the PAMPA cell: C_{m1} - C_{m2} = \dfrac{J\,K\,d_m}{D}, with C_{m2} \ll C_{m1} under a receiver sink hate2022 E7.

For the dialysis membrane of the ASD dissolution papers it is printed with a sorption coefficient,

J_i = \frac{D_i K_i}{l}\,(c_{io} - c_{il}) alonzo2011 E1.

Variables and units

symbolmeaningunits
D_{eff}effective diffusion coefficient in the membranenot printed
ldiffusion path lengthnot printed
C_d, C_rdonor and receiver concentrationµg/mL
J_iflux of component i across the dialysis membraneas measured
D_i, K_idiffusion coefficient; sorption coefficient between liquid and membranenot given
c_{io} - c_{il}concentration difference across the membraneµg/mL

Assumptions and valid domain

Pseudo-steady state in the membrane [indulkar2016 C9]; receiver concentration neglected when washed [indulkar2016 C10]. For the dialysis set-up of the ASD dissolution papers the flux is taken as directly proportional to the concentration difference, so that a difference in dissolved drug between donors shows as a difference in receptor slope alonzo2011 C9; particles do not cross.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
indulkar2016flow-through model of clotrimazoleK = A D_eff/(V_d l) fittedinputs not printed [indulkar2016 E1, E4, E6]
hate2022donor-side interface concentration in a PAMPA cellK, membrane thickness and D not giveninputs not printed hate2022 E7, R19
alonzo2011dissolved felodipine from dispersionsslope ratios 10.5, 9.5, 8.5 (90:10, 50:50, pure amorphous)proportionality check 0.0816/0.0394 = 2.07 against 2.0 alonzo2011 R14, E1

Where it fails or is disputed

Droplets are assumed not to contribute to the flux [indulkar2016 C11, X4]. All ratios share one crystalline slope (n = 1), and the membrane cutoff is given as 6–8 kDa and as 10 kDa alonzo2011 X4, X1.

Concepts

membrane flux, sink conditions, free drug concentration. Findings. Bioperformance: F5. Supersaturation from ASD dissolution: F7, F8.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

membrane flux from permeability and concentration

Expression

J = P\,C [elkhabaz2019b E5], printed as J = pc in the enzalutamide study [wilson2018 E6]. In the supplement of the media study the apparent permeability is the normalized flux divided by the donor concentration, in cm/min [elkhabaz2019b E5].

Variables and units

symbolmeaningunits
Jflux across the membraneµg/(min·cm²) [elkhabaz2019b R7]
Pmembrane permeabilitycm/min [elkhabaz2019b E5]
Cconcentration available for permeationµg/mL, taken as µg/cm³ [elkhabaz2019b E5; wilson2018 E6]

Assumptions and valid domain

None stated in either paper; the concentration is meant to be the one available for permeation, that is the free drug [wilson2018 E6].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
wilson2018relation of flux to concentration for enzalutamidenot used numericallyprinted; no numerical output [wilson2018 E6]
elkhabaz2019bapparent permeability of atazanavir and posaconazole in six mediaatazanavir in buffer-V1 at J_{amph}: 1.19 × 10⁻¹/79 = 1.51 × 10⁻³ cm/minreproduces Table S2 [elkhabaz2019b E5, R12]

Where it fails or is disputed

With total concentration as C the apparent permeability fell in the micellar media, because only free drug crosses; multiplied by the ratio of total to buffer solubility it was the same at both solid phases in every medium (1.33–1.77 × 10⁻³ cm/min for atazanavir, 2.36–3.03 × 10⁻³ for posaconazole) (F18) [elkhabaz2019b R12, R13].

Concepts

membrane flux, Fick's first law, free drug concentration, micellar solubilization. Findings. F18, F25.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

membrane flux in terms of solute activity

Expression

J = \frac{dM}{dt} = \frac{D\,S\,a}{h\,\gamma_m} [mosqueragiraldo2015 E4].

The papers of 2017–2022 print the relation per unit area,

J = \frac{D\,a}{h\,\gamma_{m}} indulkar2017a E7,

with the flux defined as

J = \frac{dm}{A\,dt} indulkar2017a E4, and as the mass flow rate

F = \frac{dM}{dt} = \frac{D\,S\,a}{h\,\gamma_m} [lu2017b E1].

In the Bioperformance papers the relation is printed with the area outside the numerator,

J = \frac{dM}{dt\,S} = \frac{D\,a}{h\,\gamma_m} [alhalaweh2016 E1],

as J = dM/dt = D S a/(h \gamma_m) with the area S inside the numerator [raina2014a E6; raina2015c E3], and as J = (1/A)(dM/dt) = D a/(h \gamma_m) [hate2017 E1].

The crystallization-from-solution papers print it per area,

J = \frac{dM}{S\,dt} = \frac{D\,a}{h\,\gamma_m} [jackson2016 E1];

J = \frac{dM}{A\,dt} = \frac{D\,a}{h\,\gamma_m} [li2016a E2],

with the activity written as

a = C\,\gamma [jackson2016 E2].

In the Mesoporous silica papers it is printed as

J = \frac{dM}{A\,dt} = \frac{D\,a}{h\,y_{m}} [dening2018 E1],

with the membrane activity coefficient written y_m and the activity a = C\,y [dening2018 E2].

In the ASD dissolution papers it is printed per membrane area,

J = \frac{dM}{dt}\cdot\frac{1}{S} = \frac{D\,a}{h\,\gamma_m} jackson2015 E1,

and with the supersaturation as the activity,

J = S_i\,\frac{D}{h\,\gamma_m} jackson2015 E3;

the tacrolimus paper prints \frac{dM}{dt} \propto a in words: the rate of transport into sink conditions is proportional to the thermodynamic activity of the solute in the donor, not to its concentration [trasi2016 E2].

Variables and units

symbolmeaningunits
Jflux across the membraneµg/min in the telaprevir figure [mosqueragiraldo2015 E4, R12]
M, tmass transported, time[mosqueragiraldo2015 E4]
D, S, hdiffusion coefficient, membrane area, membrane thickness[mosqueragiraldo2015 E4]
asolute activity in the donor[mosqueragiraldo2015 E5]
\gamma_m (printed as italic y_m in the Mesoporous silica paper)activity coefficient of the drug in the membrane[mosqueragiraldo2015 E4; dening2018 E1]
J in the Bioperformance papersflux (or mass flow rate when S is inside)µg/min; µg/(h·cm²); mg/min/cm² [raina2014a E6; indulkar2016 E11; alhalaweh2016 R17]
S or Amembrane area7.065 cm² [raina2014a P8]; 1.77 cm² [indulkar2016 P5]; 115 cm² [hate2017 M10]; 7.07 cm² [dening2018 P12]
J in the crystallization-from-solution papersmass crossing the membrane per time and areaµg min⁻¹ cm⁻² (the printed danazol axis lacks the time) [jackson2016 E1]
S or A in the danazol cellmembrane area (orifice)7.065 cm²
D, hdiffusion coefficient of the solute in the membrane; membrane thicknesscm² s⁻¹; cm
C, \gammaconcentration and activity coefficient in solutionµg mL⁻¹, dimensionless [jackson2016 E2]
J in the ASD dissolution papersfluxµg/(min·mm²) jackson2015 E1
S in the danazol cell of 2015membrane cross-sectional area (not the supersaturation)mm² jackson2015 E1
S_isupersaturation, free drug over crystalline solubilitydimensionless jackson2015 E3
dM/dtmass flow rate into the receiverµg/min [trasi2016 E2]

Assumptions and valid domain

D, S, h and γm are constant across experiments, so differences in flux reflect differences in activity; sink conditions (receiver below half the crystalline solubility) [mosqueragiraldo2015 C10, R11]. In the Bioperformance papers: sink receiver, nearly constant donor concentration, and constant D, S, h and γm [raina2014a C11; alhalaweh2016 C2]. It was tested in a side-by-side cell with a regenerated cellulose membrane, a flow-through cell, a hollow-fibre module and Caco-2 monolayers. Sink conditions in the receiver, constant donor concentration, and S (or A), D, γ_m and h constant for a given set-up and solute, so that mass flow is proportional to the donor activity [jackson2016 C9; li2016a E2]. Tested for danazol (receiver below 0.3 µg/mL) and for celecoxib and nevirapine [jackson2016 P9; li2016a P8]. In the Mesoporous silica papers D, A, y_m and h are constant in all diffusion experiments, so mass flow follows donor activity; receiver concentrations stayed below the crystalline solubility [dening2018 C11, C12]. There it is used to read free drug released from drug-loaded silica, where dissolution sampling cannot tell free from held drug [dening2018 C22]. In the danazol dispersion study D, S, \gamma_m and h are constant in the cell, so flux is proportional to free drug, not total drug jackson2015 C11; in the tacrolimus study the receiver is under sink conditions and the relation is cited [trasi2016 E2].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
mosqueragiraldo2015telaprevir flux against donor concentrationabout 0.068 µg/min at 5 µg/mL, about 0.97 at 90, about 1.07 at 130inputs not printed (D, h, γm) [mosqueragiraldo2015 E4, R12]
trasi2015aflux of ritonavir, lopinavir, paclitaxel as a measure of activityplateaus 0.13–0.27 µg/minread-out, relation not printed [trasi2015a R2, C14]
indulkar2017aatazanavir flux in buffer, calibration of free drug in SDSslope 0.0017 mL/min·cm² (R² 0.998) up to the amorphous solubilityinputs not printed (D, h, γm) indulkar2017a E7, R10
lu2017btelaprevir mass flow rate against concentration0.009 µg/min per µg/mL (R² 0.9932)inputs not printed (D, h, γm; S not stated as a value) [lu2017b E1, R6]
raina2014afelodipine and nifedipine flux plateauD, h, γm not printedprinted; inputs not printed [raina2014a E6]
raina2015csolubilizer effect on fluxsameprinted [raina2015c E3]
alhalaweh2016Caco-2 flux of drug mixturesA, D, γm assumed constantprinted [alhalaweh2016 E1]
hate2017hollow-fibre transfernot applied numericallyprinted [hate2017 E1]
jackson2015danazol ASD flux; free danazol from dissolving dispersions17.5 × 10⁻⁵ µg/(min·mm²) printed; free drug 7.1–9.1 µg/mL with LLPS, 5.4 µg/mL withoutmismatch: recomputed 1.28 × 10⁻³ jackson2015 E1; flux and concentration columns not proportional jackson2015 R9, X5
trasi2016tacrolimus mass flow; solutions and dissolved marketed products, pH 4.5, 37 °Cstated in words; plateau ≈0.0050–0.0055 µg/min from 60–100 µg/mL, products 0.0048–0.0054 µg/minno constants printed [trasi2016 E2, R14, R15]
wilson2018enzalutamide, ASD solutions and drug with polymerD, h and γm constant; donor activity inferred from mass flowno numerical output [wilson2018 E4, E5, C12]
elkhabaz2019batazanavir, posaconazole in six mediaconstants not printedinputs not printed [elkhabaz2019b E3]
ueda2020aatazanavir, clozapine with two HPMCAS gradesflux proportional to the extent of supersaturation, in wordsnot applicable ueda2020a E2
alkalla2026atazanavir and darunavir in diffusion cells and Caco-2A, D, γm and h assumed constantinputs not printed [alkalla2026 E2]
jackson2016maximum free-drug concentration of danazol from the flux plateau at 8 µg/mL; maximum flux with 1–1000 µg/mL polymerflux about 0.0152–0.0159 (plateau); 0.0126–0.0175 with polymer (units as printed)plot readings [jackson2016 R10, R11, X9]
li2016acheck that 0.1% STC and SGC leave the activity of celecoxib and nevirapine unchanged0.44, 0.46, 0.41 and 20.9, 23.4, 21.0 µg/minmeasured [li2016a R15]
lu2017activity ratio δ = F/F° from the mass flow of telaprevir (calibration from an earlier study)δ 11.5 and 28.8 (concentrations 60–330 µg/mL)plot readings [lu2017 E2, R1]
indulkar2018flux as a measure of donor activity in micellar mediaJ = Da/(h\gamma_m)inputs not printed [indulkar2018 E2]
indulkar2019bsame, in SDSas aboveinputs not printed [indulkar2019b E2]
dening2018free ritonavir from SBA-15 at 50–1000% of the amorphous solubility3.80–9.12 ng/min against 9.20 for amorphous ritonavir; free drug about 19 and 23 µg/mL at 200 and 400%inputs not printed; printed "ng/min" equal receiver slopes in ng/mL per min [dening2018 E1, R8, R9, R10, X3]
dening2018ritonavir loadings 4.9–38.1% w/w; lopinavir5.1–5.4 against 4.37 and 4.10 ng/min; lopinavir 51.4 and 70.9%inputs not printed [dening2018 R27, R20]

Where it fails or is disputed

The plateau still rises by about 10% [mosqueragiraldo2015 X6]; replicates and the slope window are not stated [mosqueragiraldo2015 X13; trasi2015a X10]. The relation needs a membrane that passes only dissolved drug; the telaprevir paper explains the same flux drop with bile-salt micelles both by lower activity and by slower diffusion of drug-loaded aggregates, and does not separate them [lu2017b X8; indulkar2017a X9]. Flux of nifedipine at about 10 µg/mL, near its crystalline solubility, was about zero, which proportionality to activity does not predict [raina2014a X11]. In the hollow-fibre module transfer keeps rising above the amorphous solubility, where activity should be constant hate2018 C25. One paper uses γ for both the membrane and the donor coefficient [raina2015c X8]. With a sink receiver the PAMPA mass flow of atazanavir kept rising above the amorphous solubility, where activity should be constant (F22) hate2022 R19. A crystalline co-drug lowered the flux plateau by lowering the activity of the drug-rich phase (F20) [alkalla2026 C37], and flux and total concentration decouple in micellar media (F18) [elkhabaz2019b C25]. The flux axes of the danazol paper have no time unit and no replicates are stated; the crystalline reference flux differs between figures (0.0011 and 0.0008) and the plateau-to-crystal flux ratio (about 14 to 19) exceeds the concentration ratio (about 9), which is not discussed [jackson2016 X9, X10, X11]. For celecoxib the ratio of concentration to solubility disagrees with the unchanged flux [li2016a X18]. The formula is also printed by 14 papers outside the crystallization-from-solution chapter (see the evidence table). With ritonavir on SBA-15 at the 1000% dose the flux equalled that of amorphous ritonavir while filtered dissolution gave about 85% of the amorphous solubility, unresolved [dening2018 X14]. The membrane of that paper is regenerated cellulose in the methods and "cellulose acetate" in one section [dening2018 X2]. The percent of reference depends on whether the reference is dose-matched [dening2018 X15]. For one danazol system the example profile gives 128 × 10⁻⁵ against a printed 17.5 × 10⁻⁵ µg/(min·mm²), unresolved jackson2015 E1, X4; the standard curve has an intercept jackson2015 X5. Below 50 µg/mL the tacrolimus flux rose with concentration but did not extrapolate to zero [trasi2016 X8].

Concepts

membrane flux, thermodynamic activity, chemical potential, Fick's first law, sink conditions, incomplete drug release, free drug concentration. Findings. Amorphous solubility and LLPS: F8, F11, F16, F17. Bioperformance: F2, F3, F18, F19, F20, F22, F25. Crystallization from solution: F22, F31, F32, F38. Mesoporous silica: F8, F11, F15. Supersaturation from ASD dissolution: F7, F8.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

molar amount of halogen at the lower XPS binding energy

Evidence table: molar amount of halogen at the lower XPS binding energy. Content from the release-mechanism chapter (2019–2021).

Expression

n_{F,\mathrm{low}} = \frac{100\,\mathrm{mg} \times DL}{889\,\mathrm{g\,mol^{-1}}} \times 2 \times f_{\mathrm{low}} que2019 E4

Variables and units

symbolmeaningunit
n_{F,\mathrm{low}}moles of fluorine at the lower F 1s binding energy in a compactmmol
100 mgcompact massmg
DLdrug loading–
889 g/molmolecular weight of ledipasvirg/mol
2fluorine atoms per ledipasvir molecule–
f_{\mathrm{low}}share of F 1s at 684.0 eV (73.4% at 10% loading)–

Assumptions and valid domain

The composition of the whole compact is used que2019 E4. For iodine: four iodine atoms per molecule and the share of lower-binding-energy I 3d, homogeneous within the 10 nm XPS depth que2021 E4.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
que2019amount of drug–polymer-bonded fluorine against loading (secondary axis of Fig. 16)10% loading: printed 0.165 mmolmismatch: 10 mg / 889 g/mol × 2 × 0.734 = 0.0165 mmol, the value plotted que2019 E4, R25, X3
que2021halogen-bonded iodine of TIPP and Me-TIPP, 10–40%0.017–0.050 mmol per 100 mgreproduces: 10 mg / 821.91 × 4 × 0.559 = 0.0272 mmol; 20 mg / 849.97 × 4 × 0.533 = 0.0502 que2021 E4, R11, R12

Where it fails or is disputed

The printed example is a factor-10 misprint que2019 X3. XPS samples the top ~10 nm, so the whole-compact composition is an assumption que2019 P7, E4.

Concepts

drug-polymer interactions, surface drug enrichment. Findings. Release mechanism and LoC: F7, F10, F17.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

molar volume from molecular weight and density

Expression

Printed in words as "molecular volume = molecular weight / true density":

V_m=\frac{M}{\rho}

[moseson2018 E6].

Variables and units

symbolmeaningunitids
V_mmolecular (molar) volumecm³/mol[moseson2018 E6]
Mmolecular weightg/mol[moseson2018 E6]
\rhotrue densityg/mL[moseson2018 E6]

Assumptions and valid domain

None stated; densities of amorphous IDM (1.31 g/mL) and PVPVA (1.18 g/mL) were taken from the literature, and the PVPVA molecular weight (55,000 g/mol) is an estimate from the manufacturer's range [moseson2018 M1, M2].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
moseson2018volume fractions and the ratio m of the Flory–Huggins melting point depressionIDM 273 cm³/mol; PVPVA 46,610 cm³/molreproduces (357.8 / 1.31 = 273.1; 55,000 / 1.18 = 46,610) [moseson2018 E6, M1, M2]
moseson2022cm of bicalutamide–PVPVABCL 318.8 cm³/mol (printed 319); PVPVA 46,610; m = 146.1reproduces (430.37/1.35 = 318.8; 55,000/1.18 = 46,610) [moseson2022c E21, M1, M2]
shah2024m of posaconazole–HPMCASPCZ 546 and HPMCAS 14,164 cm³/mol; m = 25.95reproduces within rounding (701/1.28 = 547.7 against 546; 18,000/1.27 = 14,173 against 14,164; 14,164/546 = 25.94) [shah2024 E4, E1]

Where it fails or is disputed

The polymer molar volume depends on an estimated molecular weight, so m is approximate [moseson2018 M2].

Concepts

Flory–Huggins interaction parameter. Findings. F8, F41.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

multicomponent Flory-Huggins free energy of mixing

Expression

Water–drug–polymer system:

\frac{\Delta G_{mix}}{RT} = n_W\ln\phi_W + n_D\ln\phi_D + n_P\ln\phi_P + n_W\phi_D\chi_{WD} + n_W\phi_P\chi_{WP} + n_D\phi_P\chi_{DP} rumondor2009c E4; rumondor2010c E1; purohit2017b E2

Variables and units

symbolmeaningunits
n_W, n_D, n_Pamounts of water, drug, polymer (stated as mole fractions)– rumondor2009c E4
\phivolume fractions– rumondor2009c E4
\chi_{WD}, \chi_{WP}, \chi_{DP}pair interaction parameters, also holding non-ideal entropy– rumondor2009c E4

Assumptions and valid domain

First three terms the combinatorial entropy, last three the pair interactions rumondor2009c E4; purohit2017b E2. Used in words only: separation needs the interaction terms to outweigh the entropy, so a very unfavourable water–drug term next to a favourable water–polymer term can push the drug out rumondor2009c C42, C37.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
rumondor2009cthermodynamic origin of moisture-induced separationnoneargument only rumondor2009c E4
purohit2017b (outside)AAPS of ritonavir dispersions on hydrationnoneargument only purohit2017b E2
rumondor2010cwhy the same drugs separate more with PVP than with PVPVA and HPMCASnoneargument only; χ ranked by red shift and log P rumondor2010c E1, C26, C31, X13

Where it fails or is disputed

No χ values for the ternary systems were measured; the conclusion that separation needs a positive mixing enthalpy treats χ terms as purely enthalpic although they also carry entropy rumondor2009c X13, X14. The same data allow a mobility reading (less plasticized HPMCAS dispersions), which the free-energy argument does not exclude rumondor2010c C32, X12.

Concepts

Flory-Huggins theory, enthalpy of mixing, Δχ effect, moisture-induced phase separation. Findings. F8, F12, F13, F23.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

non-compartmental AUC

Expression

AUC_{0-\infty} = AUC_{0-t} + \frac{C_t}{\beta} [wilson2018 E9], with AUC_{0-t} by the linear trapezoidal rule. The rule is only named as the linear trapezoidal rule in the enzalutamide study of polysaccharide ASDs and as the linear-up/log-down trapezoidal rule in the pretomanid study wilson2020 E5; nguyen2023a E6.

Variables and units

symbolmeaningunits
AUC_{0-t}, AUC_{0-\infty}area under the plasma concentration–time curve to the last point and to infinityµg·h/mL (rats); ng·h/mL (monkeys) wilson2020 R6; nguyen2023a R23
C_tfinal measured plasma concentrationsame concentration unit [wilson2018 E9]
\betaterminal elimination rate constant1/h [wilson2018 E9]
ttime of the last measurable concentrationh

Assumptions and valid domain

Non-compartmental analysis with WinNonlin; nominal sampling times; values below the limit of quantification set to zero before the first quantifiable concentration and treated as missing thereafter wilson2020 E5; nguyen2023a E6.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
wilson2018rat Cmax and AUC0–48 against in vitro mass flowAUC0–∞ not reportedprinted in words; not applicable [wilson2018 E9, R17]
wilson2020rat AUC0–inf of four formulations516, 305, 45 and 43.1 µg·h/mLnamed only wilson2020 E5, R6
nguyen2023amonkey AUC0–inf, fasted and fedreference 7846 fasted and 11,663 fed ng·h/mLexpression not printed nguyen2023a E6, R23

Where it fails or is disputed

The window is not stated alike: the enzalutamide AUC is called AUC0–48 in the methods and AUC0–72 h on the mass-flow axis of the same paper, and AUC0–inf is used for bioavailability wilson2020 E5, R6, R8. The dog and monkey studies use few animals (six and four), and the sampling and the handling of values below quantification affect the area [nguyen2023a E6, R23; purohit2019 R9].

Concepts

oral bioavailability, in vitro–in vivo correlation. Findings. F23, F24, F25, F26, F30.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

Noyes-Whitney equation

Expression

As printed for crystals dissolving in a polymer melt (concentration C of dissolved drug in the liquid phase):

\frac{dC}{dt}=\frac{DA}{hV}\left(C_s-C\right)

[moseson2018 E5], and with a Nernst–Brunner diffusion layer in the same form [moseson2019 E2].

The ASD dissolution papers print a proportional form for aqueous dissolution,

\frac{dc}{dt} \propto A\,(C - C_{\mathrm{eq}}) [alonzo2010 E3],

and name the equation for indomethacin precipitates without an expression [xie2017 E1].

New printed forms (Release mechanism and LoC):

\frac{dm}{dt} = A\,\frac{D}{h}\left(C_s - C_b\right) indulkar2017b E4

\frac{dx}{dt} = C\left(S - x\right) purohit2017b E3

\frac{dC}{dt} = k\left(C_s - C\right) indulkar2019a E1

\frac{dC}{dt} = \frac{DA}{Vh}\left(C_s - C\right) indulkar2019a E2

\frac{dM}{dt} = \frac{DA}{h}\left(C_s - C\right) que2019 E1

\frac{dC}{dt} = k\left(C_s - C_t\right) saboo2020a E1

Stated in words as the Nernst–Brunner relation, the dissolution rate proportional to the saturation solubility under sink conditions correasoto2022b E4.

\left(\frac{dC}{dt}\right)_{\mathrm{drug}} = \frac{D A}{V h}\left(C_s - C\right) indulkar2022 E2

Variables and units

symbolmeaningunitids
C, C_sconcentration of dissolved drug; solubility of the crystalline drug in the molten polymer–[moseson2018 E5]
Ddiffusion coefficient–[moseson2018 E5]
Asurface area available for dissolution–[moseson2018 E5]
hboundary-layer thickness at the solid–liquid interface–[moseson2018 E5]
Vvolume of the liquid phase–[moseson2018 E5]
dc/dtdissolution rate in aqueous mediumµg/(mL min)[alonzo2010 E3]
C, C_{\mathrm{eq}}solution concentration; equilibrium concentration (aqueous form)µg/mL[alonzo2010 E3]
dm/dt, dM/dtmass of drug dissolved per unit time (release-mechanism forms)–indulkar2017b E4; que2019 E1
Asurface area exposed to the medium–indulkar2017b E4
D, hdrug diffusion coefficient; boundary or diffusion layer thickness–indulkar2019a E2
C_s, Ssolubility of the dissolving solid form (the amorphous solubility for an amorphous surface)µg/mLindulkar2019a E1, E2; purohit2017b E3
C_b, C, C_t, xdrug concentration in the bulk medium at time tµg/mLindulkar2017b E4; saboo2020a E1; purohit2017b E3
Vvolume of the dissolution mediummLindulkar2019a E2
k, C (purohit2017b)rate constant–indulkar2019a E1; purohit2017b E3

Assumptions and valid domain

Applied to crystal dissolution in the polymer melt, with viscosity not constant but falling as drug dissolves; no numerical output is stated in either paper [moseson2018 E5; moseson2019 E2]. Named the "modified Noyes and Whitney equation" (cited) and used as one arm of the scheme in which dissolution competes with crystallization of the solid and of the solution [alonzo2010 E3, C43]. Used to argue that EPO, by raising the crystalline solubility of indomethacin, "may" raise its dissolution rate [xie2017 C47]. Describes drug-controlled dissolution indulkar2017b E4; dissolution governed by the amorphous drug at high loading purohit2017b E3; C_s is the solubility of the solid form at the dissolving surface, and the rate approaches zero as C approaches it indulkar2019a E1, E2; D, A and h fixed, not applicable to dispersions whose release exceeds the amorphous solubility que2019 E1.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
moseson2018argument that temperature, plasticisation and shear speed up dissolutionnoneinputs not printed [moseson2018 C52]
moseson2019the diffusion-only model that fragmentation extendsnoneinputs not printed [moseson2019 C39, C40]
moseson2020why a physical mixture with large crystals lags a dispersion in thermogravimetry (crystal size sets dissolution in the molten polymer)nonenamed only [moseson2020 E1, C33]
moseson2022cframework for dissolution of bicalutamide crystals in PVPVA; the population balance model uses it through a size-dependent shrinkage rate with a fitted rate constantkd 0.1002 ± 0.0511 µm/s against assumed 0.5 and 4 µm/sinputs not printed (D, h and V not given) [moseson2022c E18, E9, R16]
alonzo2010scheme of Fig. 16nonenot applicable [alonzo2010 E3]
xie2017redissolution of indomethacin precipitates at pH 5α solubility 15 µg/mL, 27 µg/mL with 100 µg/mL EPOnamed only [xie2017 E1, R2, C47]
indulkar2017brelease into medium saturated at the amorphous solubilitynonenot applicable indulkar2017b E4, C35
purohit2017bwhy drug-controlled release cannot pass the amorphous solubilitynoneinputs not printed purohit2017b E3, C50
indulkar2019arelease from a drug-rich surface into saturated mediumnoneinputs not printed indulkar2019a E1, E2, C42
que2019the amorphous solubility as the ceiling of free drugnoneinputs not printed que2019 E1, C2
saboo2020arate advantage of an amorphous form similar to its solubility advantagenonenot applicable saboo2020a E1, C1
correasoto2022bintroduction: why the amorphous form dissolves fasternonenot applicable correasoto2022b E4
indulkar2022drug-controlled release of high-loading ritonavir–PVPVA (cited 50% result)noneinputs not printed indulkar2022 E2, R3
bapat2023named only, as the form that fails in the polymer-controlled regimenonenamed only bapat2023 E4, C2

Where it fails or is disputed

It neglects crystal defects, particle breakage and a changing particle number, which is the gap the 2019 paper addresses [moseson2019 C2, C55]. The 2022 paper replaces the diffusion-only picture by a model in which breakage is needed to finish within 20 min, and calls the equation a framework with unlikely sink conditions in HME [moseson2022c E18, R12]. As printed, A(C - C_{\mathrm{eq}}) is negative while a solid dissolves below C_{\mathrm{eq}}; read it as a direction only [alonzo2010 X3]. The solubility effect "alone cannot explain" the faster redissolution of the precipitate; crystal size, not tested with size-matched crystals, is the authors' main explanation [xie2017 C47, C48]. It does not describe polymer-controlled release, which continues into medium already at the amorphous solubility indulkar2017b C35; indulkar2019a C43. The 2017 ritonavir paper prints the label "(2)" for this equation, the same as for its Flory–Huggins equation, and calls it eq. 3 in the text purohit2017b X2.

Concepts

Noyes–Whitney equation, diffusion boundary layer, crystal dissolution into a polymer melt, crystallization during dissolution, Nernst-Brunner equation, drug-controlled release, amorphous solubility. Findings. ASD process: F9, F11, F12, F31, F36, F37. Supersaturation from ASD dissolution: F1, F10, F21. Release mechanism and LoC: F1, F2, F3, F4.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

octanol-water partition coefficient

Evidence table: octanol-water partition coefficient. Content from the release-mechanism chapter (2020).

Expression

\log P = \log\frac{[\mathrm{drug}]_{\mathrm{octanol}}}{[\mathrm{drug}]_{\mathrm{aqueous}}} saboo2020a E5

Variables and units

symbolmeaningunit
[\mathrm{drug}]_{\mathrm{octanol}}, [\mathrm{drug}]_{\mathrm{aqueous}}drug concentration in octanol and in the aqueous buffer, by LC-MSsame unit in both

Assumptions and valid domain

Compounds predominantly un-ionized; pH 6.5 buffer saturated with octanol saboo2020a E5.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
saboo2020alog P of nilvadipine and cilnidipine (felodipine from the literature)4.06, 5.40 (felodipine 4.46)inputs not printed saboo2020a E5, R16
saboo2020log P of indomethacin and its methyl ester4.07, 4.53inputs not printed saboo2020 E4, M1, M2

Where it fails or is disputed

The calculated ClogP values of the 2019 paper for the same two drugs (3.04 and 5.54) differ from the measured ones saboo2019 A1; saboo2020a R16.

Concepts

octanol-water partition coefficient, lipophilicity. Findings. Release mechanism and LoC: F9, F17.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

percent polymer complexed

Evidence table: percent polymer complexed. Content from the release-mechanism chapter (2024–2025).

Expression

\text{complexed}\ (\%) = \left(1 - \frac{\text{polymer in the supernatant}}{\text{total polymer in the solution}}\right) \times 100 bapat2024 E2

\%\ \text{complexed} = \left(1 - \frac{\text{polymer in supernatant}}{\text{total polymer}}\right) \times 100 bapat2025a E2

Variables and units

symbolmeaningunit
polymer in the supernatantdissolved polymer left after ultracentrifugation of the drug + polymer suspensionmg/mL
total polymerpolymer added to the buffer (0.5–1.0 mg/mL)mg/mL

Assumptions and valid domain

The polymer alone is fully soluble at the test pH, so any polymer that leaves the supernatant is counted as bound in an insoluble complex with the drug bapat2024 C8; bapat2025a C9. Tested at pH 5.8–7.5 for HPMCAS-MF and three grades, at drug:COOH ratios of 0.1:1 to 3:1 bapat2024 R12, R13; bapat2025a R9, R11. The bedaquiline study of 2025 used the same test, against a polymer-only control, without printing the expression kaur2025 P7.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
bapat2024complexation of HPMCAS-MF by eight drugs at pH 6.0 and by loratadine at pH 5.8–7.55–90% at 1:1; ≈85 → 2% with pHinputs not printed bapat2024 E2, R12, R13
bapat2025acomplexation of HPMCAS LF, MF, HF by cinnarizine and loratadineHF 70–99%, LF 30–70% (0.25:1 → 1:1, cinnarizine)inputs not printed bapat2025a E2, R9

Where it fails or is disputed

Measured in dilute buffer spiked from THF, with temperature, time and centrifugation conditions not stated in the 2024 paper, so values compare only within a paper bapat2024 X13. In the 2025 grade paper one equivalent loading in the conversion table (88% for LF at 2:1) is out of line bapat2025a X1.

Concepts

insoluble drug-polymer complex, drug-polymer complexation, drug-polymer ionic interactions. Findings. Release mechanism and LoC: F32, F33, F34.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

pH-solubility profile

Expression

C_T = C_B\left(1 + 10^{\,\mathrm{p}K_a - \mathrm{pH}}\right) [indulkar2015 E8].

The paper of 2018 prints the same relation as

C_T = \left(\frac{1 + X}{X}\right)C_U,\qquad X = 10^{\mathrm{pH} - \mathrm{p}K_a} [sugihara2018 E1],

which equals C_B\,(1 + 10^{\mathrm{p}K_a-\mathrm{pH}}) (synthesis: (1+X)/X = 1 + 1/X).

Two delamanid papers use the relation without printing it, one to fit the drug's pKa from measured solubilities and one to draw the predicted curve of a cited pKa [nguyen2023c E1; nguyen2023b E1]. The posaconazole paper prints it in the same form,

C_T = C_B\left(1 + 10^{\,\mathrm{p}K_a - \mathrm{pH}}\right) [duong2022b E1],

as cited by the delamanid work [nguyen2023c E1].

Variables and units

symbolmeaningunits
C_Ttotal solubility at the pHµg/mL [indulkar2015 E8]
C_Bcrystalline free-base solubility (the amorphous free-base solubility is substituted for the amorphous form)µg/mL [indulkar2015 E8, C46]
\mathrm{p}K_a, \mathrm{pH}pKa of the base, medium pH[indulkar2015 E8]
C_T (delamanid papers)total solubility of the drug at that pH, crystalline or amorphousµg/mL [nguyen2023c R1]
\mathrm{p}K_a (delamanid)pKa of the base: fitted 3.94 ± 0.04, 4.3 cited[nguyen2023c R3; nguyen2023b E1]

Assumptions and valid domain

The solution is in equilibrium with the neutral form, not the salt [indulkar2015 E8]. Tested for clotrimazole, atazanavir and nicardipine at 37 °C over about ±2 pH units of the pKa [indulkar2015 A2]. In the delamanid papers it is applied to a monoprotic weak base in equilibrium with the neutral form, over pH 1.6 to 6.5 at 37 °C, to the crystalline and to the amorphous solubility alike [nguyen2023c P1, P2, E1]. For the coated-tablet paper the intrinsic solubility behind the printed curve is not given, so the curve is a reference line rather than a fit [nguyen2023b E1].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
indulkar2015predicted crystalline and amorphous solubility at each pH; oral-dose scenariosatazanavir at pH 1.5: 1090 µg/mLreproduces (1.04 µg/mL, pKa 4.52; printed 1.1 mg/mL) [indulkar2015 E8, R26]
sugihara2018pazopanib crystalline and amorphous solubility against pHpKa 6.4; amorphous points fall below the curve at pH 5 and 5.5reproduces for the crystalline curve [sugihara2018 E1, R3, C11]
nguyen2023cfitting the delamanid pKa to crystalline and amorphous solubility between pH 1.6 and 6.5pKa 3.94 ± 0.04; crystalline 10.2 → 0.018 and amorphous 154.5 → 0.76 µg/mLthe fitted curve follows the amorphous data but gives about 3.7 instead of 10.2 µg/mL for the crystal at pH 1.6 [nguyen2023c R3, R1]
nguyen2023bdrawing the predicted buffer solubility of delamanid against the measured buffer and biorelevant valuespKa 4.3 cited; about 10.3 µg/mL at pH 1.6, below 0.02 µg/mL above pH 5.5inputs not printed; the biorelevant values lie far above the curve [nguyen2023b E1, R13, R18]

Where it fails or is disputed

The predicted amorphous curve is the crystalline curve times one factor, so its overlap with the LLPS data does not test the relation; the constancy of the un-ionized concentration does [indulkar2015 X14]. At the lowest pH a salt may limit solubility, not examined [indulkar2015 X7]. It covers the drug only: in the dispersions of the ASD dissolution papers the polymer's own pH-dependent solubility decides release, and the worst gastric pH for delamanid dispersions lay where neither drug nor polymer dissolved well [nguyen2023c C14, C15]. It does not apply to a neutral drug: praziquantel, with a calculated pKa of 1.14, kept an amorphous solubility of 1.17–1.43 mg/mL across six buffers and still lost release after gastric stages at pH 3.0 and 5.0 [alvarenga2025 R4, R1, R10]. Food components raised delamanid solubility far above the curve (13.10 and 57.97 µg/mL in a fed gastric medium) [nguyen2023b R13].

Concepts

pH-dependent solubility, ionization, pKa, pH-dependent solubility of weak bases, enteric polymer. Findings. Amorphous solubility and LLPS: F10, F23. Supersaturation from ASD dissolution: F24, F25, F28.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

polymer partitioning into the drug-rich phase by depletion

Expression

Printed in words in both papers; written here as the stated balances.

c_{p,\,\mathrm{droplets}} = c_{p,\,\mathrm{total}} - c_{p,\,\mathrm{solution}} [wilson2021 E3]

c_{p,\,\mathrm{droplets}} = c_{p,\,\mathrm{before}} - c_{p,\,\mathrm{supernatant}} shah2025 E2

w_{p} = \frac{c_{p,\,\mathrm{droplets}}}{c_{p,\,\mathrm{droplets}} + c_{d,\,\mathrm{droplets}}}, \qquad c_{d,\,\mathrm{droplets}} = c_{d,\,\mathrm{total}} - c_{d,\,\mathrm{solution}} [shah2025 E3; wilson2021 X4]

Variables and units

symbolmeaningunits
c_{p,\,\mathrm{total}}, c_{p,\,\mathrm{before}}polymer addedµg/mL
c_{p,\,\mathrm{solution}}, c_{p,\,\mathrm{supernatant}}polymer left dissolved (solution ¹H NMR, or HPLC–ELSD after ultracentrifugation)µg/mL
c_{d,\,\mathrm{solution}}drug left dissolved (NMR, or the LLPS concentration)µg/mL
w_{p}polymer weight fraction of the droplets, water ignoreddimensionless

Assumptions and valid domain

NMR sees only dissolved species, and the drug-rich phase is fully sedimented by ultracentrifugation; the water content of the droplets is ignored [wilson2021 C22; shah2025 E2, E3]. Tested for enzalutamide (25–100 µg/mL HPMCAS or Eudragit E PO, 70 or 120 µg/mL drug) and posaconazole (900 µg/mL HPMCAS L, M or H, 100 µg/mL drug) [wilson2021 R7; shah2025 R16].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
wilson2021share of HPMCAS and Eudragit E PO in enzalutamide dropletsHPMCAS 12.7–24.7, Eudragit E PO 40.8–41.0 w/w%reproduces with plot-read drug values (HPMCAS 100 µg/mL: 100 − 67.4 = 32.6 µg/mL in droplets) [wilson2021 E3, R7, X4]
shah2025share of HPMCAS L, M, H in posaconazole droplets895, 886, 861 µg/mL left of 900; fractions about 0.05, 0.14, 0.31reproduces (H: 39/(39 + 87.5) = 0.31) shah2025 E3, R16, R17
raina2015bpolymer in felodipine precipitate and supernatant (direct NMR of both phases, not depletion)PVPVA 6.8 and 36.7, HPMCAS 7.1 and 34.2 mgsingle determinations [raina2015b R12]

Where it fails or is disputed

The two enzalutamide polymers were compared at different drug totals (70 against 120 µg/mL), and a colorimetric pellet assay gave about 19–23 w/w% for both, so the ranking rests on NMR alone [wilson2021 X4, X5]. For posaconazole the L and M depletions (5 and 14 µg/mL) lie within one to two standard deviations of zero shah2025 X7.

Concepts

polymer partitioning into the drug-rich phase, drug-rich nanodroplets. Findings. F26, F37, F44.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

polynomial calibration curve

Evidence table: polynomial calibration curve. Content from the release-mechanism chapter (2018–2025).

Expression

Not printed: a second-degree polynomial calibration of PVPVA absorbance at 220 nm, solved for concentration bhardwaj2018 E7. Written as a generic second-degree form (synthesis: coefficients not printed):

A_{220} = a\,c^{2} + b\,c + d

Printed in 2023 for the drug load of PHPH compact surfaces by ATR-FTIR:

y = 5.1445x^{2} - 0.2064x + 4.1749 deac2023b E3

Variables and units

symbolmeaningunit
A_{220}absorbance at 220 nm after removal of the ITZ contribution–
cPVPVA concentrationµg/mL (2–140)
a, b, dfitted coefficientsnot printed
ydrug load of the surface (2023 form)%
xinverse of the PVPVA band intensity (1491 or 1492 cm⁻¹) normalized to the PHPH band at 1513 cm⁻¹–

Assumptions and valid domain

2–140 µg/mL, R² = 1.000; the ITZ contribution at 220 nm removed with the A253/A220 ratio of about 0.68 bhardwaj2018 E7, C10. The 2023 curve rests on standards of 5–50% drug measured in triplicate, R² = 0.9967 deac2023b E3.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
bhardwaj2018PVPVA release from ITZ–PVPVA compactscoefficients not printednamed only bhardwaj2018 E7, R8, R9, R14
deac2023bPHPH content of compact surfaces before and after exposurecoefficients printedreproduces: x ≈1.79 gives 20.3% for the 20% standard deac2023b E3, R6
yang2023ATR-FTIR peak ratio 1522/1369 cm⁻¹ against ritonavir loading, second ordercoefficients not printedinputs not printed yang2023 E3, R18

Where it fails or is disputed

No coefficients or residuals are printed, so PVPVA concentrations cannot be recomputed bhardwaj2018 E7.

Concepts

intrinsic dissolution rate, congruent release. Findings. Release mechanism and LoC: F1, F27, F31.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

reduced glass transition temperature

Expression

T_{rg} = \frac{T_g}{T_{melt}} [baird2010 E4].

Variables and units

symbolmeaningunits
T_{rg}reduced glass transition temperaturedimensionless [baird2010 E4]
T_g, T_{melt}glass transition and melting temperaturesK [baird2010 E4]

Assumptions and valid domain

Viscosity is taken as constant at Tg [baird2010 E4]; a value of 0.66 was proposed in the cited literature [baird2010 R29]. For 16 class I molecules without a measured Tg, Tg was estimated from a fit T_{rg} = 0.00021\,\mathrm{MW} + 0.64433 with R² 0.44 [baird2010 E27, X17].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
baird2010testing Trg against classI-A 0.69, I-B 0.7; class I 0.69 ± 0.02, class III 0.73 ± 0.04, not significantly differentreproduces: acetaminophen 297.15/443.15 = 0.671 [baird2010 E4, R14]
nguyen2023apretomanid0.67reproduces: (10 + 273.15)/(147.3 + 273.15) = 0.673 nguyen2023a E2

Where it fails or is disputed

Trg did not differ between class I-A and I-B, indicating no correlation with the ability to quench amorphous [baird2010 C23]. Tg/Tm was not a reliable indicator; class II alone spans Tg/Tm 0.65–0.76 [baird2012 C36, R14]. The class I values rest partly on estimated Tg [baird2010 X17].

Concepts

reduced glass transition temperature, glass transition temperature, glass-forming ability, Tm − Tg temperature gap. Findings. F12.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

resistances-in-series model

Expression

\frac{1}{K_{in}} = \frac{1}{k_{in}} + \frac{1}{k_m} + \frac{1}{k_{out}} [hate2017 E3]. A PAMPA form has two unstirred layers and the membrane: \dfrac{1}{P_{eff}} = \dfrac{1}{P_{UWL}} + \dfrac{1}{P_m} + \dfrac{1}{P_{UWL}} hate2022 E1.

Variables and units

symbolmeaningunits
K_{in}overall mass transfer coefficientcm/s
k_{in}, k_m, k_{out}inner boundary layer, membrane, outer boundary layercm/s; not given

Assumptions and valid domain

The three resistances act in series [hate2017 E3].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
hate2017structure of K_inonly K_in fittedinputs not printed [hate2017 E3, R12]
hate2022interpretation of PAMPA mass flow of atazanavir, nifedipine, acetaminophenP_m and P_{UWL} only in the SI tablesinputs not printed hate2022 E1, C44

Where it fails or is disputed

The split into the three terms was not determined [hate2017 E3].

Concepts

resistance-in-series permeability model. Findings. F13, F21, F22.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

sink index

Expression

\mathrm{SI} = \frac{C_s\,V}{\mathrm{Dose}} [purohit2018 E1].

Variables and units

symbolmeaningunits
C_ssolubility (crystalline or amorphous)µg/mL
Vmedium volumemL
Dosetotal drug5000 µg [purohit2018 R4]

Assumptions and valid domain

SI above 1: enough medium to dissolve the dose; sink in the compendial sense is three times the solubility needed [purohit2018 E1]. Ueda 2024 (Eqs. 15–16, p. 54) write the two forms separately, SI_{cr}=S_c/(Dose/V) and SI_{am}=S_a/(Dose/V): the criterion of 3 applies to SI_{cr}, and SI_{am}=1 marks the dose that just reaches the maximum activity.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
purohit2018five dissolution conditions1.8 × 900/5000 = 0.324; 14.9 × 900/5000 = 2.68reproduces [purohit2018 E1, R4]
hate2019tacrolimus 5 mg in 240, 100, 40 mL50 × 240/5000 = 2.4 (printed 2.4); 1 and 0.4reproduces [hate2019 E1, R7]

Where it fails or is disputed

The amorphous solubility is cited and approximate [purohit2018 R4].

Concepts

sink index, sink conditions. Findings. F16, F17, F28, F31.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

solid-liquid equilibrium solubility equation

Expression

\ln x_{C,L_1} = -\frac{\Delta G_{a\to c}}{RT} - \ln\gamma_{L_1} ilevbare2013a E3;

\ln C_B = -\frac{\Delta G}{RT} - \ln\gamma [indulkar2015 E7];

and for the supercooled liquid \ln x_{SL,L_1} = -\ln\gamma_{L_1} ilevbare2013a E4. As printed, \Delta G_{a\to c} and \Delta G are positive magnitudes; with the signed quantity \mu^{(c)}-\mu^{0(a)}, which is negative, the term carries a plus sign, as in Taylor and Zhang 2016 (Eqs. 2 and 6).

New forms (Miscibility and drug-polymer interactions). With the heat-capacity terms, as printed for the solubility of a crystalline drug in a polymer (2006):

\ln\gamma_{\mathrm{drug}}\,x_{\mathrm{drug}} = -\frac{\Delta H_{fus}}{RT}\left[1-\frac{T}{T_m}\right] - \frac{1}{RT}\int_{T_m}^{T}\Delta C_P^{\mathrm{config}}\,dT + \frac{1}{R}\int_{T_m}^{T}\frac{\Delta C_P^{\mathrm{config}}}{T}\,dT [marsac2006b E5];

and in the 2009 paper, where the left side is written as the free energy of fusion:

\ln\gamma_{\mathrm{drug}}\,x_{\mathrm{drug}} = \frac{-\Delta G_{fus}}{RT} = -\frac{\Delta H_{fus}(T_m)}{RT}\left[1-\frac{T}{T_m}\right] - \frac{1}{RT}\int_{T_m}^{T}\Delta C_P\,dT + \frac{1}{R}\int_{T_m}^{T}\frac{\Delta C_P}{T}\,dT [marsac2009 E1].

Simpler forms in other papers of the library:

\ln x_{actual} = -\frac{\Delta H_{fus}}{RT}\left(1-\frac{T}{T_M}\right) - \ln\gamma [marsac2008a E3];

\ln\left[\gamma_d\,x_d\right] = -\frac{\Delta G_{fus}}{RT} [baird2011 E5];

\ln x = -\frac{\Delta H_f}{R}\left(\frac{1}{T}-\frac{1}{T_m}\right) - \frac{\Delta C_p}{R}\left(1-\frac{T_m}{T}+\ln\frac{T_m}{T}\right) - \ln\gamma [raina2014a E1].

The ritonavir–atazanavir paper writes \log\chi = \log X_{ideal} - \log\gamma with \log X_{ideal} = -\frac{\Delta H_m}{2.303R}\frac{T_m - T}{T_m T} [alhalaweh2016 E4, E5].

Variables and units

symbolmeaningunits
x_{C,L_1}, C_Bsolubility of the crystalline drug in watermole fraction; µg/mL [ilevbare2013a E3; indulkar2015 E7]
\Delta Gfree-energy difference between supercooled liquid and crystal[indulkar2015 E7]
\gamma_{L_1}, \gammaactivity coefficient of the drug in the aqueous solutiondimensionless ilevbare2013a E3
\gamma_{drug}activity coefficient of the drug at the solubility limitdimensionless [marsac2009 E1]
\chi, X_{ideal}mole-fraction solubility and ideal solubility in the ritonavir–atazanavir paper– [alhalaweh2016 E4, E5]
x_{drug}mole-fraction solubilitydimensionless [marsac2009 E1]
\Delta H_{fus}, T_mheat of fusion and melting temperature of the drugkJ/mol, K (Table I and II values) [marsac2006b M1, M2; marsac2009 M1, M2]
\Delta C_P^{config}, \Delta C_Pheat-capacity difference between liquid and crystalvalues cited, not printed [marsac2006b X11; marsac2009 P7]
TtemperatureK; not stated for the Table II predictions [marsac2006b X11]

Assumptions and valid domain

The solvent is not present in the crystal; the first term is the lattice contribution and the second the solute–solvent interaction [indulkar2015 E7]; γ is constant over the crystalline and amorphous concentration range ilevbare2013a C55. For a drug in a polymer, the polymer assumes the role of a solvent, so the equation describes solubility of a crystalline drug in a polymer, with \gamma from Flory–Huggins theory [marsac2006b C45]. For the analogue liquid the entropy of mixing is assumed ideal [marsac2006b C46]. For ketoconazole the heat-capacity difference was approximated by its value at Tg, integrated between Tg and Tm [marsac2009 P7]. In the 2009 route the same γ is assumed at the solubility limits in the analogue and in PVP [marsac2009 C11]. The amorphous form removes the fusion terms, so \ln x = -\ln\gamma [raina2014a E2]. The ritonavir–atazanavir paper sets ΔCp to zero [alhalaweh2016 E5].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
ilevbare2013aappendix derivation of the amorphous solubilitynoneγ not printed ilevbare2013a E3, E4
indulkar2015argument that the un-ionized amorphous and crystalline solubility differ by a constant factornoneγ not printed [indulkar2015 E7, C42]
marsac2006bsolubility of nifedipine and felodipine in PVP K12, PVP K29/32 and methyl pyrrolidone0.06–0.07 g/g and 0.25–0.31 g/g in PVP; 0.15 and 0.48 g/g in methyl pyrrolidonereproduces with ΔC_P terms set to zero at 298.15 K for nifedipine in PVP K12 (0.071 against 0.07); one felodipine value in K29/32 does not match (≈0.29 against 0.25) [marsac2006b E5, E6, R17, X11]
marsac2009γ in EP from the measured solubility; ideal solubilityγ 0.15–0.89inputs not printed (heat capacities, ideal solubilities) [marsac2009 E1, R9, X4]
baird2011activity coefficient in PEG 400see the PEG chapterreproduces (through its E7) [baird2011 E5]
marsac2008aactivity coefficient of nifedipine and felodipine in water from the solubility in methyl pyrrolidoneγ in water 1.89 × 10³ and 2.43 × 10⁵reproduces within the stated SD with the lattice terms implied by the printed data (−5.40 and −3.51); ΔH_fus and T_M not printed [marsac2008a E3, R10, R11]
raina2014abackground to the amorphous solubility predictionnoneinputs not printed (ΔC_p and γ not printed) [raina2014a E1, R7]
alhalaweh2016crystal and solvation contributions to the solubility of ritonavir and atazanavir at 310 Klog γ about 4.45 and 3.88 (read)mismatch: recomputed 4.65 and 3.01 from the card's ideal solubility and the Table 2 crystalline solubility [alhalaweh2016 E4, R7]
alhalaweh2016ideal-solubility term of ritonavir and atazanavirplotted log X_ideal −1.07, −1.97; recomputed −2.59, −4.53mismatch [alhalaweh2016 E5, X1, X2]
marsac2008anifedipine and felodipine in methyl pyrrolidone and water (second reading)γ in water 1.73 × 10³ and 2.31 × 10⁵reproduces within SD [marsac2008a E3]

Where it fails or is disputed

The appendix prints its first equation as "(1)" but cites it as Eq. 3 ilevbare2013a X4. The temperature and the heat-capacity values of the 2006 Table II are not printed, the methyl pyrrolidone check is about 30% low for nifedipine, and the polymer-phase values are predictions, not measurements [marsac2006b X10, X11; marsac2009 X17]. Solubility measured in a small analogue overestimates solubility in the polymer unless corrected for the smaller mixing entropy [marsac2006b C51]. The plotted terms of the ritonavir–atazanavir paper mix concentration scales; the ordering of the terms survives the recomputation [alhalaweh2016 X2]. For marsac2008a the γ in water is given as 1.89 × 10³ and 2.43 × 10⁵ in one reading and as 1.73 × 10³ and 2.31 × 10⁵ in another; both are reported as reproducing within the stated SD [marsac2008a E3, R10, R11].

The ratio form of the same relation for liquid PEG is on the page activity coefficient from solubility.

Concepts

crystalline solubility, activity coefficient, ideal solubility, drug solubility in polymer, micellar solubilization, amorphous solubility. Findings. C. Amorphous solubility and LLPS: F5, F10, F12. Miscibility and drug-polymer interactions: F8, F9. Bioperformance: F1, F6.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

Stokes-Einstein equation

Expression

D_{NMR} = \frac{k_B T}{6\pi\eta r} indulkar2017a E5;

stated in words in the bile-salt paper, the diffusion coefficient of a particle falls with its radius,

D \propto \frac{1}{r} [lu2017b E8].

The same expression, D=k_BT/(6\pi\eta r), is printed for a solute in a polymer melt [moseson2019 E3]. In indulkar2016 and hate2018 the equation is named but not printed [indulkar2016 E18; hate2018 E7].

Printed in the 2017 ritonavir paper for NTA sizing:

D = \frac{k_B T}{6\pi\eta r} purohit2017b E1

Named without an expression in the nifedipine and dihydropyridine papers indulkar2017b E7; saboo2019 E5 and in the 2020 critical-ratio calculation saboo2020a E6.

Variables and units

symbolmeaningunits
D_{NMR}self-diffusion coefficient of the micellem²/s indulkar2017a E5
k_B, TBoltzmann constant; temperature (25 °C)indulkar2017a E5
\etaviscosity of water at 25 °Cindulkar2017a C9
rhydrodynamic radiusnm indulkar2017a R25
r in NTA sizinghydrodynamic radius of nanodropletsnm (111–257 nm) [indulkar2016 R4]
Ddiffusion coefficient–
k_B, TBoltzmann constant; absolute temperatureK
\etadynamic viscosity of the medium–
rparticle (hydrodynamic) radiusnm

Assumptions and valid domain

Surfactant and drug do not change the viscosity, and a high SDS concentration minimizes the monomer contribution to the diffusion coefficient indulkar2017a C9. Used for 40 mg/mL SDS in D2O at 25 °C indulkar2017a P12. In the melt papers it is used to estimate solute diffusivity in high-viscosity media such as a polymer melt; the viscosity and radius are not given [moseson2019 E3]. Spherical particles in a Newtonian medium; limited at high viscosity [moseson2022c E19]. Particles in Brownian motion in suspension purohit2017b E1; for the drug–polymer ratio, similar viscosity for both, drug about 1 nm and polymer about 10 nm hydrodynamic radius saboo2020a E6.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
indulkar2017aradius of SDS micelles with 0, 0.4 and 7 mg/mL atazanavirD 10^−10.3, 10^−10.3, 10^−10.42 m²/s; r 4.61, 4.61, 6.08 nmreproduces within the rounding of the printed exponent (r about 4.90 nm for 10^−10.3 m²/s, extractor; the radius ratio 6.08 ÷ 4.61 = 1.319 equals 10^0.12) indulkar2017a E5, R25
lu2017bexplanation of the lower flux of drug carried in bile-salt aggregatesnonenamed only, no numerical output [lu2017b E8, C46]
other chapterssizing of drug-rich nanodroplets by NTAnoneprinted; not recomputed here [trasi2016 E4; purohit2017b E1; indulkar2016 E18; hate2018 E7; tres2018 E3]
moseson2019explaining why dissolution of IDM crystals in copovidone took hours and fragments stayed in placenoneinputs not printed [moseson2019 C39, C51, E3]
moseson2022cframework for the low fitted dissolution rate of bicalutamide crystals in the viscous meltnoneinputs not printed [moseson2022c E19, C37]
indulkar2016NTA sizing of clotrimazole droplets; constancy of the effective diffusion coefficient in the membranenonenamed only [indulkar2016 E18]
hate2018NTA sizingnonenamed only hate2018 E7
hate2022colloid size against PAMPA mass flowdiffusion coefficient inversely proportional to particle size, in wordsnamed only hate2022 E3, C56
indulkar2017bNTA sizing of nifedipine nanodroplets≈190–222 nmnamed only indulkar2017b E7, R7
saboo2019NTA of nilvadipine and cilnidipine medianone printed from NTAnamed only saboo2019 E5, R12
saboo2020adiffusion-coefficient ratio of felodipine and PVPVAD_{drug}/D_{polymer} = 10reproduces (10 nm / 1 nm at equal viscosity) saboo2020a E6, R27
saboo2020NTA of indomethacin and ester media250–350 nm statednamed only saboo2020 E7, R7

Where it fails or is disputed

The viscosity of water is used for a D2O solvent indulkar2017a X7. In the bile-salt paper it is used to explain the same flux drop that is read elsewhere as lower activity, and the two readings are not separated [lu2017b X8]. In the melt papers it was not tested against the measured gradient of about 8 µm after 1 h at 130 °C [moseson2019 R9]; the authors note its limitations at high viscosity [moseson2022c E19]. In the PAMPA study of hate2022 colloids of very different size gave the same mass flow, contrary to the Stokes-Einstein expectation (F22) hate2022 C56, R17. The inputs of the NTA runs (temperature, viscosity, diffusion coefficients) are not printed purohit2017b E1. The radii of the 2020 calculation are estimates saboo2020a E6.

Concepts

Stokes-Einstein equation, micelle/water partition coefficient, membrane flux, diffusion boundary layer, drug-rich nanodroplets, Higuchi two-component dissolution model. Findings. Amorphous solubility and LLPS: F17, F18. ASD process: F11, F36, F37. Bioperformance: F5, F22. Release mechanism and LoC: F4, F5, F16.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

supersaturation from membrane flux ratio

Expression

In words: the supersaturation is directly proportional to flux, so S = J/J_{ref} with the flux of a reference solution at the crystalline solubility [raina2015c E9]; the activity form is F/F^\circ = a/a^\circ = \delta [lu2017b E6].

The activity form

\frac{F}{F^{\circ}} = \frac{a}{a^{\circ}} = \delta

is printed again in the telaprevir growth and bile-salt papers [lu2017a E1; lu2017 E2], and as SR = J/J^{*} for atazanavir and ritonavir [indulkar2018 E3; indulkar2019b E3].

Variables and units

symbolmeaningunits
Jflux of the test solutionµg/min
J_{ref}reference flux (felodipine 1 µg/mL in buffer, S = 1)µg/min; not stated [raina2015c X5]
F, F^{\circ}flux from the test solution and from a solution saturated with crystalline drugµg min⁻¹ cm⁻² [lu2017 E2]
a, a^{\circ}activity of the drug in the solution and at crystalline saturationdimensionless
\deltaactivity-based supersaturationdimensionless

Assumptions and valid domain

Flux proportional to activity (E3 of the same card) [raina2015c E9]. The flux is proportional to activity whatever the share of drug in micelles (a regenerated-cellulose membrane, 6–8 kDa, side-by-side cell); the calibration of δ against concentration comes from a companion study of the same group [lu2017 E1, E2, C6; lu2017a P2].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
raina2015cBSA solutionsS 7.3 and 4.2 from fluxinputs not printed; plot readings give about 16 and 9 [raina2015c E9, X5]
lu2017btelaprevir with bile saltsδ ≈ 26.5 at 140 µg/mLreproduces [lu2017b E6]
elkhabaz2019batazanavir and posaconazole in six mediaSR_{max} = J_{amph}/J_{eq}; atazanavir buffer-V1 0.119/0.00217 = 54.8 (figure about 55), six-medium mean 53.6reproduces [elkhabaz2019b E4, R8, R9]
lu2017set δ 11.5 and 28.8 in buffer and with six bile salts at 1.86 and 12 mMconcentration for δ 11.5: about 60 (most media), about 90 (SGCDC), about 140 µg/mL (12 mM STDC, SGDC, STCDC)plot readings [lu2017 R1, X12]
lu2017aset δ 2.4, 7.9, 12.5; read the free drug after 15 h of growthresidual 60.5 of 65.2 µg/mL (1.86 mM STCDC); 91.7 of 95.2 (SGCDC)measured; values are concentrations, not δ [lu2017a R12, X17]
indulkar2018atazanavir, ritonavir in buffer, FaSSIF-V1, Composite-SIF and the lecithin seriesSR = J/J^{*}; SR_{amorph} = J_{amorph}/J^{*}63–65; 9.2–10; about 40 in STC alone [indulkar2018 E3, R12, R10]
lu2018telaprevir in bile salt mixtures and complete mediaF/F^{\circ} = a/a^{\circ} = \delta with buffer calibrationδ 11.5 and 28.8 set per medium [lu2018 E1, R1]
indulkar2019batazanavir in SDSSR = J/J^{*}about 65 stated [indulkar2019b E3, R2]

Where it fails or is disputed

The reference flux behind the BSA values is not printed [raina2015c X5]. The flux ratio and the concentration ratio differ by up to about sixfold in pooled human fluid (posaconazole 29 against 5) (F18) [elkhabaz2019b R9]. Cell volumes, sampling times and replicates of the residual measurement are not printed; the starting concentration for SGCDC matches no δ of the calibration table; the error bars of the calibration curves are not defined [lu2017a P5, X4; lu2017 X12]. The formula is also printed by four papers outside the crystallization-from-solution chapter (see the evidence table). The flux at the crystalline solubility could not be measured for tacrolimus and cilnidipine, so their equal supersaturation is assumed [indulkar2018 R13, X4].

Concepts

free drug concentration, supersaturation, thermodynamic activity, membrane flux. Findings. Bioperformance: F3, F18. Crystallization from solution: F31, F32, F33, F38, F39, F40.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

supersaturation ratio

Expression

Printed in words: the supersaturation ratio is the LLPS concentration divided by the equilibrium solubility of the crystalline drug,

S = \frac{C_{\mathrm{LLPS}}}{C_{\mathrm{eq}}} (restated; printed in words) [almeidaesousa2015 E15].

The paper of 2018 prints it with the symbols C and C^{*} for the amorphous and the crystalline solubility at the same pH,

S_C = \frac{C}{C^{*}} [sugihara2018 E2].

In the ASD process papers the degree of supersaturation is the dissolved concentration over the crystalline solubility,

S=\frac{C}{C_{cryst}}

li2019 E2. The ritonavir granulation paper prints it in words as relative supersaturation, S=C/C^{*}, with C^{*} the crystal solubility [trasi2019 E1]; the residual-crystal paper prints it as the solution concentration over the equilibrium (crystalline) solubility [moseson2020a E3]. In the droplet-drying model the same ratio is C/S, the drug concentration over its solubility in the instantaneous droplet composition li2020 E14.

In the Bioperformance papers it is printed as

S = \frac{c}{c^{*}} [raina2015c E6],

with c^* the crystalline solubility in the same medium; it is also printed in words as experimental concentration over crystalline solubility [hate2017 E11].

The crystallization-from-solution papers print it as

S = \frac{C}{C_{eq}} [alonzo2012 E1; ilevbare2013c E1];

S = \frac{c}{c^{*}} [ilevbare2012c E4];

S = \frac{c}{c_{eq}}, \qquad \sigma = \ln S [ilevbare2012b E1, E2];

S = \frac{c}{c_0} ilevbare2012a E2;

S = \frac{C}{C_0} [ilevbare2013b E4; hsieh2012 E9].

In the Mesoporous silica papers it is printed as

S = \frac{C}{C^{*}} [dening2018 E6],

S = \frac{C}{C^{*}} [dening2019 E6], with the theoretical S of a dose given in words as the dose over volume divided by the crystalline solubility [dening2019 E6], and as

S \approx \frac{C}{C_{\mathrm{cry}}} (restated; printed in words) [mccarthy2020 E4].

In the ASD dissolution papers it is printed as

S = \frac{c}{c^{*}} [konno2008a E4; xie2015 E5; xie2016a E3],

S = \frac{C}{C_{\mathrm{eq}}} chen2015a E1; [li2016b E1], printed in words and called the apparent supersaturation ratio; and in the activity form

S = \frac{a}{a^{*}} = \frac{c\,\gamma^{\prime}}{c^{*}\,(\gamma^{\prime})^{*}} [que2018 E1], with the activity coefficients taken as equal in simple buffer [que2018 C10].

Variables and units

symbolmeaningunits
C_{LLPS}concentration at the onset of phase separationµg/mL [almeidaesousa2015 R5]
C_{eq}crystalline equilibrium solubility in the same mediumµg/mL [almeidaesousa2015 R5]
Sdegree of supersaturation (relative)dimensionless [li2019 E2; trasi2019 E1; moseson2020a E3]
Cmeasured, molecularly dissolved concentration (filtered or ultracentrifuged)µg/mL [trasi2019 E1, C11]
C_{cryst}, C^{*}, C_{cry}crystalline solubility of the stable form (equilibrium solubility in the same medium)µg/mL [trasi2019 E1; moseson2020a E3; mccarthy2020 E4]
theoretical Sconcentration if the whole dose dissolved, over the crystalline solubilitydimensionless [dening2019 E6; dening2018 P6]
C/Sdrug concentration over its solubility along the drying pathdimensionless li2020 E14
c, c^*solution concentration; crystalline solubility in the same mediumµg/mL; 128 µg/mL for nevirapine at pH 6.5 [hate2017 R1]
C_{eq}, c_{eq}, c^{*}, C_0, c_0equilibrium (crystalline) solubility at the test temperature and medium (crystallization-from-solution notation)µg/mL [ilevbare2012b E1; ilevbare2012a E2; ilevbare2013b E4]
\sigmanatural logarithm of S, used for growth analysesdimensionless [ilevbare2012b E2]
c, C; c^{*}, C_{\mathrm{eq}} (ASD dissolution notation)drug concentration in solution; equilibrium solubility of the crystal, for celecoxib Form III in the same mediumµg/mL [konno2008a E4; chen2015a E1]
C_{\mathrm{eq}} (lopinavir)crystalline solubility in a medium with the same excipients at the same temperatureµg/mL [li2016b E1]
a, a^{*}; \gamma^{\prime}, (\gamma^{\prime})^{*}activity and activity coefficient in the supersaturated and the saturated solution (paclitaxel)dimensionless [que2018 E1]

Assumptions and valid domain

None stated; it is a concentration ratio, not an activity ratio [almeidaesousa2015 E15; raina2015c C29]. In the process papers C is taken as the molecularly dissolved concentration, so colloids removed by 0.45 µm filtration are not counted [trasi2019 C11]. It is used against the crystalline solubility, not the amorphous one, so an S of 6 can lie below the amorphous solubility [moseson2020a R1, X17]. The Bioperformance papers state that it is valid only if the activity-coefficient ratio \gamma/\gamma^* is 1 (dilute solution, no solubilizer) and below the amorphous solubility [raina2015c C32; dening2018 E6]. In the crystallization-from-solution papers concentration replaces thermodynamic activity because the solutions are extremely dilute [ilevbare2013b C14]; the solubility is that of the stable crystal in the same buffer, measured without methanol [ilevbare2012a R1; ilevbare2013c X16]. In the pH-shift titration paper the degree of supersaturation is the peak concentration over the titration equilibrium solubility for type 1 bases but the supernatant over the HPLC crystalline solubility for type 2 bases [hsieh2012 E9, X3]. In the Mesoporous silica papers it states both the dose (theoretical S) and the result (achieved S) of release from silica, so their ratio is the fraction of the dose in solution [dening2018 P6, R6; mccarthy2020 R20, R21]. In the ASD dissolution papers, with surfactants, C_{\mathrm{eq}} is measured in each medium so that the same S gives the same driving force chen2015a C2; leached HPMCAS is assumed to leave C_{\mathrm{eq}} largely unchanged chen2015a C11. For lopinavir the ratio is called apparent because concentration ratios in complex media "may or may not" represent the driving force for crystallization [li2016b C7, E1]. The celecoxib papers print the form for dilute solutions [xie2015 E5].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
almeidaesousa2015six drugs4.3–54.0 (fluorescence), 4.7–64.5 (extinction)eleven of twelve ratios reproduce; diclofenac extinction printed 51.6, recomputed 54.3 [almeidaesousa2015 E15, R5]
indulkar2015weak basesabout 13 and about 63stated in words (amorphous over crystalline solubility) [indulkar2015 R10, C46]
sugihara2018pazopanib, pH 5.0 to 8.4about 103, 304, 379, 505, 603, 528, 501 (pH 5.0, 5.5, 6.0, 6.4, 6.5, 7.0, 8.4)reproduces (pH 6.5: 19.8 ÷ 0.033 = 600 against about 603) [sugihara2018 E2, R4]
li2019degree of supersaturation of lopinavir releasenone printedprinted li2019 E2
trasi2019compare single-drug and co-granulated dissolution at pH 6.8RTV about 17 alone and about 3 co-granulated; LPV about 7 and 5; C^{*} 1.8 and 2.9 µg/mLreproduces: 31 / 1.8 = 17.2 and 19 / 2.9 = 6.6; the figure values give about 2.0–2.2 for the co-granulated RTV [trasi2019 R5, E1, X3]
moseson2020athe test condition of 50 µg/mL indomethacinS = 6 (crystalline solubility about 8 µg/mL)reproduces: 50 / 8 = 6.25 [moseson2020a E3, R1]
li2020supersaturation of a drying dropletpeak about 2.4 (12.5:87.5 water:methanol) and about 320 (15:85) at 25% DLmodel output li2020 R20
raina2015ctest of c/c* against fluxBSA 0.1%: 50/39.0 = 1.28; 1%: 50/47.8 = 1.05reproduces [raina2015c E6]
hate2017nominal supersaturation after the pH shift500/128 = 3.91 (printed 3.9)reproduces [hate2017 E11]
alonzo2012felodipine S 3–12Ceq about 0.5 µg/mL; S 10 = 5 µg/mLreproduces [alonzo2012 E1]
ilevbare2013cinduction-time starts for celecoxib, ritonavir, efavirenzS 14.7, 15.4, 2.4; 22/1.5 = 14.67efavirenz printed 2.4 against recomputed 2.32 from 19/8.2 [ilevbare2013c E1, X4]
li2016aS' = C/Cs with the solubility measured with 0.1% bile saltnevirapine 7.1–8.7; celecoxib 13.6 printed, 16.7 recomputedmismatch for celecoxib [li2016a E1, X1]
elkhabaz2019bconcentration-based maximum in six mediaatazanavir buffer-V1 79/1.4 = 56.4; posaconazole human fluid 13.2/2.6 = 5.1reproduces [elkhabaz2019b E1, R8, R9]
hate2019tacrolimus dose levels5 mg in 100 mL: 50/2.5 = 20; in 240 mL: S 8reproduces [hate2019 E2, R7]
purohit2019crystallized capsule contents against the crystalline solubilityabout 3.7/1.5 = 2.5; with text values 4/1.4 = 2.9reproduces [purohit2019 E1, R5, X1]
nguyen2023apretomanid nucleation80/16.2 = 4.9 (stated 5); 160/16.2 = 9.9 (stated about 10)reproduces nguyen2023a E1, R5, R6
ilevbare2012critonavir S 7.610 µg/mL over 1.3 µg/mLprinted 7.6, recomputed 7.7 (10/1.3 = 7.69) [ilevbare2012c E4]
ilevbare2012britonavir S 3.8, 7.6, 15.3; σ_c 1.37c_eq about 1.31 µg/mL fits the printed setreproduces within rounding; σc 1.37 gives 5.13 µg/mL [ilevbare2012b E1, E2]
ilevbare2012aritonavir 100 and 50 mM bufferS 7.6/7.7 and 4.310/2.3 = 4.35 reproduces 4.3 ilevbare2012a E2
ilevbare2013bcelecoxib, efavirenz, ritonavirS 6.6, 1.2, 7.6, 14.7, 15.410/1.5 and 10/1.3 printed as 6.6 and 7.6 (truncated) [ilevbare2013b E4]
hsieh2012degree of supersaturationdipyridamole 71.3/5.7 = 12.5reproduces [hsieh2012 E9]
chen2015ratio of drug concentration to the crystalline solubility in the medium of interest, fixed per drug1.5–15 for 11 drugs; Ceq 0.2–81.3 µg/mLprinted in words; reproduces (13 × 19.0 = 247 µg/mL) [chen2015 E2, R1]
schram2015S = C/Ceq of felodipine, 4 µg/mL over about 0.5 µg/mLS 8reproduces [schram2015 E1]
schram2016same, 2 µg/mLS 4 (ln S 1.39)reproduces [schram2016 E1, R13]
dening2018ritonavir doses and the dilution scheduleS 7.8 (27.9/3.6) and 3.9; stepwise to 1reproduces (27.9/3.6 = 7.75; 14/3.6 = 3.9) [dening2018 E6, M1]
dening2019theoretical S of the dilution steps7.8, 3.9, 2.6, 1.9, 1.3, 1.0reproduces (28/3.6 = 7.8) [dening2019 E6, R16]
mccarthy2020theoretical and achieved S of indomethacin and methyl ester15.3 and 21.4 theoretical; 7.2 and 7.0 achievedreproduces (35.1/2.29 = 15.3; 9.0/0.42 = 21.4; 16.6/2.29 = 7.2) [mccarthy2020 E4, R21, R20]
konno2008aqualitative: nucleation rate rises with Snonenot applicable [konno2008a E4]
chen2015aS = 5 start in eight media; S of suspension liquidsSDS 107/14.5reproduces, 7.38 against printed 7.4 chen2015a E1, R17
alonzo2011supersaturation ratio about 60 of methanol-shift solutionscrystalline solubility at 25 °C not printedapproximate alonzo2011 C30, X9
li2016blopinavir leached from HPMCAS-HF and HPMCP suspensions into surfactant media, pH 3about 3.3–3.9 (HF) and 1.6–1.8 (HPMCP) across surfactantsreproduces nine of ten bars; HF without surfactant ≈7.3/1.9 = 3.8 against ≈3.9 [li2016b E1, R20, X2]
xie2015celecoxib 22 µg/mL with and without polymernone printedextractor calculation: 22/1.5 ≈ 14.7 without polymer, ≈10.3–11.6 with 22 µg/mL polymer [xie2015 E5, X9]
xie2016acelecoxib 22 µg/mLnone printedextractor calculation: 22/1.5 ≈ 15 without polymer xie2016a E3
que2018paclitaxel at the amorphous solubility31.6/0.36 ≈ 88reproduces, 87.8 against printed 88 [que2018 E1, R1, R2]
nguyen2023cdelamanid dispersions after 1 h in acid, against the crystalline solubility at that pH≈0.9–3.8 (pH 1.6), ≈3.3–11.4 (pH 3.0), ≈11–42 (pH 5.0); 42 at the amorphous solubilityreproduces at pH 6.5, 0.76/0.018 = 42.2 against printed 42 [nguyen2023c E2, R13, R2]

Where it fails or is disputed

The printed diclofenac extinction ratio is probably a misprint [almeidaesousa2015 X1]. The sorafenib ratio is stated as 54 and "between 50 and 60" and is 64.5 by extinction [almeidaesousa2015 X14]. The ratio is quoted as about 600 (abstract), 500–600 (results) and about 500 (conclusions) for the same data [sugihara2018 X1]; it is a concentration ratio, not an activity ratio (see activity-based supersaturation ratio). In the process papers the values of C^{*} at pH 6.8 for ritonavir and lopinavir are given without method or reference, so every S of that paper depends on them [trasi2019 X14]. A concentration-based ratio ignores that the driving force depends on the chemical potential, which is lowered when two drugs mix in one phase [trasi2019 C38]. With solubilizers c/c* under-reads the activity-based supersaturation [raina2015c C38]. It is not valid above the amorphous solubility [dening2018 E6]. In hate2019 the same dose gives S 8 or S 20 depending on volume, and the choice decides whether absorption or growth on seeds dominates (F28, F29) [hate2019 E2, R7]. A polymer can change the crystalline solubility, so S computed from the polymer-free value differs from S with the polymer (F19) [hsieh2014 C18; ilevbare2013c X7]. The printed values of S differ by rounding (7.6 and 7.7; 15.3 and 15.4) ilevbare2012a X1. Methanol (about 0.5% v/v) is present in the media but not in the solubility measurement [ilevbare2013c X16]. The ratio of concentration to solubility understates the supersaturation of celecoxib in bile-salt and HPMCAS media, where the mass flow does not change [li2016a X18]; the equilibrium concentration in the HPMCAS and SDS media was not reported for felodipine [schram2016 X9]. The supporting table of the indomethacin paper gives S values (8.2, 6.6, 7.4) that do not follow from the printed concentrations and solubilities [mccarthy2020 X6]. The dilution schedule of the ritonavir paper lists seven S values for six periods, so the S of the last samples is uncertain [dening2018 X6]. A misprint gives the lower ritonavir dose as S 3.6 instead of 3.9 [dening2018 X1]. In the celecoxib suspensions with SDS the normalization ignores about 860 µg/mL leached HPMCAS chen2015a X10; in polysorbate 80 S fell to ≈0.85, within the uncertainty of the solubility used chen2015a X14; the surfactant-free solubility is 1.1 or 1.2 µg/mL depending on the table chen2015a X16. For lopinavir with HPMCP and polysorbate 80 the plotted ratio ≈1.55 does not follow from the paper's own inputs, ≈7.45/3.2 = 2.3 [li2016b X2]. The celecoxib dispersion authors call the supersaturation the same for all polymer solutions, whereas the polymers raised the crystalline solubility by 26–43%, so S was about 1.3–1.4 times higher without polymer [xie2015 C43, X9]. For delamanid the ratios printed as 42 at pH 5.0 equal the amorphous-to-crystalline ratio, although the measured concentrations at that pH were far above the amorphous solubility, so the value looks capped [nguyen2023c X9]. The gastric ratio did not order the final release of the delamanid dispersions [nguyen2023c C39].

Concepts

supersaturation ratio, supersaturation, crystalline solubility, amorphous solubility advantage, non-sink dissolution, desupersaturation, incomplete drug release, micellar solubilization. Findings. Amorphous solubility and LLPS: F6, F16. ASD process: F20, F23, F25. Bioperformance: F3, F4, F10, F11, F14, F18, F23, F27, F28, F29, F30. Crystallization from solution: F1, F9, F14, F19, F23, F24, F28, F29, F31. Mesoporous silica: F7, F8, F15. Supersaturation from ASD dissolution: F4, F5, F6, F14, F15, F17, F19, F22, F24, F25.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

surface-normalized release rate

Evidence table: surface-normalized release rate. Content from the release-mechanism chapter (2018–2025), with rows from the ASD process and Peptide permeability chapters.

Expression

A = \frac{k \times V}{S \times N} saboo2020a E3

R = \frac{k \times V}{S \times x} bapat2025b E1

Stated in words: the release rate is "normalized (to account for differences in drug and polymer content)" bhardwaj2018 E4; the slope of the initial linear part of percent release against time, normalized to each component's content and to the exposed area saboo2019 E4; the slope of drug concentration against time normalized by the area of the dissolving front and by the drug loading li2020 E13.

Printed in the papers of 2020–2022:

R = \frac{k \times V}{S \times x} saboo2020 E1

R = \frac{k\,V}{A\,x} yang2021 E1

R = \frac{k}{S \times x} correasoto2022a E1

R = \frac{k}{S \times x} correasoto2022b E1

In the last two forms k is the slope of cumulative mg released, so the medium volume drops out correasoto2022a E1.

Printed in the papers of 2022–2023:

R = \frac{k\,V}{A\,x} yang2022a E1

R = \frac{k \times V}{S \times x} bapat2023 E1

R = \frac{k}{S \times x} correasoto2023 E1

Printed in the papers of 2023–2025:

R = \frac{k\,V}{A\,x} yang2023 E1

R = \frac{k \times V}{S \times x} bapat2024 E1

R = \frac{k \times V}{S \times x} bapat2025a E1

Variables and units

symbolmeaningunit
A, Rnormalized release rate of one componentmg/min/cm² (µg/min/cm² in the 2018 paper)
kslope of the regression line of concentration against time, not including the originmg/(mL min)
Vvolume of medium100 mL
Sexposed compact area0.5 cm²
N, xweight fraction of the component–
A (2022 ritonavir form)exposed surface area of the compactunits not printed

Assumptions and valid domain

The weight fraction is used on the assumption that the component densities are similar saboo2020a E3; the exposed area stays constant saboo2019 E4; the slope is taken from the linear part of the release curve bapat2025b E1. Used for compacts of 25–100 mg in an 8 mm die bhardwaj2018 P6; saboo2019 P9; saboo2020a P6. Slope from the linear region, the first 30 min when the profile is not linear yang2021 E1; from the initial linear points with the exposed area assumed constant correasoto2022a E1; slope window not stated correasoto2022b X19. The 2023 plasticizer paper took the slope after a lag time, from 30 to 60 min, where a lag occurred correasoto2023 E1, P6.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
bhardwaj2018loading-normalized ITZ and PVPVA rates of spray-dried compacts≈100, ≈250, ≈555, ≈2000 µg/min/cm² at 50, 25, 20, 10%reproduces if the rate is divided by the weight fraction: 106, 256, 565, 1990 bhardwaj2018 E4, R11
saboo2019nilvadipine, cilnidipine and PVPVA rates0.002–3.49 mg/min/cm²inputs not printed saboo2019 E4, R5, R6
saboo2020afelodipine and polymer rates, five polymers; 40% HPMCAS analogues≈0.0008–3.8 mg/min/cm²inputs not printed; plot-based check in X10 saboo2020a E3, R13, R14, R16
li2020 (ASD process)spray-dried ritonavir–PVPVAsurface-normalized dissolution rateinputs not printed li2020 E13
bapat2025b (Peptide permeability)release of OCA, SNAC and PVPVAneat PVPVA ≈3.2; OCA ≈8.1 mg/min/cm²reproduces within plot reading (≈3.1 and ≈8.6) bapat2025b E1, R2
saboo2020indomethacin and its methyl ester with PVPVA over 5 min≈0.01–4.2 mg/min/cm²; neat PVPVA ≈3.4plot check reproduces neat PVPVA ≈3.4 saboo2020 E1, R3
yang2021loratadine compacts with PVPVA and HPMCAS at 37 and 5 °C≈0–3.45 mg/min/cm²inputs not printed yang2021 E1, R18, R21
correasoto2022aclopidogrel and PVPVA, 40–60% ± surfactant≈0.2–6.7 mg/min/cm²inputs not printed correasoto2022a E1, R18
correasoto2022batazanavir and PVPVA with additives, 37 and 55 °C≈0.07–5.6 mg/min/cm²inputs not printed correasoto2022b E1, R3, R7
yang2022aritonavir and PVPVA rates, 10–50%congruency judged on normalized ratesinputs not printed yang2022a E1, R1, R2
bapat2023HPMCAS-MF, its salt, indomethacin and its methyl ester by medium and rotation speed≈0.12–1.62 mg/min/cm² at 100 rpminputs not printed bapat2023 E1, R5, R9, R10, R16
correasoto2023atazanavir, ledipasvir and PVPVA with plasticizersatazanavir ≈2.0–5.1; PVPVA with plasticizer ≈4.8–6.1; neat PVPVA ≈2.7 mg/min/cm²inputs not printed correasoto2023 E1, R6, R7, R13
yang2023PVPVA release from surfactant blends; Tween 80 dispersion at 30 against 40%≈3.6–6.9 mg/min/cm² (blends)inputs not printed yang2023 E1, R5
bapat2024drug and HPMCAS rates of eight drugs, 5–60%≈0.01–0.85 mg/min/cm²bapat2024 E1, R2
bapat2025aloratadine and cinnarizine in three HPMCAS grades≈0.01–0.73 mg/min/cm²bapat2025a E1, R2, R3

Where it fails or is disputed

For neat PVPVA an extractor check of the 2020 release curve gives ≈1.7 mg/min/cm² against ≈3.4 plotted, while the same check reproduces the other neat polymers; the compact mass of the neat polymers is not stated saboo2020a X10. The visible part of the 2018 PVPVA curve corresponds to about 8 against the stated 10.4 mg/min/cm² bhardwaj2018 X8. The neat PVPVA compact of the ledipasvir study weighed 250 mg against 100 mg for the dispersions que2019 X13. The basis of the felodipine–TPGS rates is not stated and they appear to be per total dispersion mass saboo2021 X4; the rates of the analogue study were derived in an unstated way que2021 X6; for ternary dispersions whether x uses the drug:polymer ratio or the weight fraction is not stated correasoto2022a X9. The basis of x (with or without surfactant) is not stated in the 2023 surfactant study yang2023 X10; in the 2025 grade paper the cinnarizine concentrations after 1 h do not match the plotted rates bapat2025a X8.

Concepts

intrinsic dissolution rate, congruent release, limit of congruency. Findings. Release mechanism and LoC: F1, F2, F3, F6, F11, F13, F14, F15, F17, F19, F21, F23, F26, F31, F32, F33.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

theoretical monolayer adsorption capacity

Expression

X_m = \frac{\mathrm{SSA} \times 10^{20} \times \mathrm{MW}}{S_c \times N_A} [dening2018 E3].

X_m = \frac{\mathrm{SSA}_{\mathrm{adsorbent}} \times 10^{20} \times MW_{\mathrm{adsorbate}}}{S_c \times N_A} [mccarthy2020 E3].

Q_{\mathrm{mono}} = \frac{\mathrm{SSA} \times M_{\mathrm{drug}}}{A_{\mathrm{molecule}} \times N_A} (restated; printed in words) [hate2020a E2].

Outside silica, the minimum surfactant to cover drug-rich nanodroplets is calculated in the same way from the droplet surface area and the surfactant's molecular area (printed in words) correasoto2022a E2.

Variables and units

symbolmeaningunits
X_m, Q_{mono}adsorbate needed for monolayer coverageg/g silica [dening2018 E3]
SSAspecific surface area of the adsorbentm²/g; 586 for SBA-15 [dening2018 M3]
10^{20}conversion of m² to Ų[dening2018 E3]
MW, M_{drug}molar mass of the adsorbateg/mol; not printed in the three papers [dening2018 E3; hate2020a E2; mccarthy2020 E3]
S_c, A_{molecule}contact area of one molecule, the product of its two largest dimensionsŲ [dening2018 P15; hate2020a P15; mccarthy2020 P11]
N_AAvogadro's numbermol⁻¹

Assumptions and valid domain

The whole surface is accessible and the drug adsorbs in the orientation that maximizes its contact with the surface, so the two largest dimensions give the contact area; the estimate is geometric only [dening2018 C17; hate2020a C20]. Applied to SBA-15 with 7.1 nm pores [dening2018 M3].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
dening2018ritonavir loadings at 25–150% of the monolayer0.253 g/g ("25.3% w/w"); 18.2 × 15.2 Åreproduces: 0.2536 g/g with molar mass 720.94 g/mol [dening2018 E3, R4]
hate2020aatazanavir278 mg/g (about 28% w/w); 17.53 × 14.07 Åinputs not printed; implies a molar mass of about 705 g/mol [hate2020a E2, R1]
mccarthy2020indomethacin and methyl ester loadings0.287 and 0.269 g/gindomethacin 0.285 against 0.287; methyl ester 0.260 against 0.269 g/g [mccarthy2020 E3, X19]
correasoto2022asurfactant on clopidogrel nanodropletsagrees reasonably for nonionic surfactantsinputs in the supporting information, not supplied correasoto2022a E2, C41

Where it fails or is disputed

The result is in g/g silica but is quoted and used as % w/w of the formulation; 0.253 g/g is about 20.2% w/w on a drug-plus-silica basis [dening2018 X4; mccarthy2020 X4; hate2020a X4]. BET monolayers fitted to adsorption from water are 2.5 to about 60 times lower (synthesis: 253/103; 278/4.5) [dening2019 R6; hate2020a R3]. The ritonavir flux drop placed at the calculated monolayer lies between 20.1 and 29.8% w/w, with no batch in between [dening2018 X16].

Concepts

monolayer coverage, drug loading, nanoconfinement. Findings. F2, F1, F11.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

van't Hoff equation

Expression

\frac{d\ln x}{dT} = \frac{\Delta H_f}{R\,T^{2}} [zhu2011 E3].

Zhu and co-workers (2012) name the van't Hoff equation for the same extrapolation without printing it [zhu2012 E3].

The amorphous solubility chapter uses the van't Hoff analysis for the partition coefficient of a polymer between the drug-rich phase (p) and water (q),

K_{p/q} = \frac{C_p}{C_q} ueda2022 E3,

\Delta G_{q\to p} = -RT\ln K_{p/q} ueda2022 E4,

\ln K_{p/q} = -\frac{\Delta H_{q\to p}}{RT} + \frac{\Delta S_{q\to p}}{R} ueda2022 E5,

and, when the straight line fits poorly, with a quadratic term that lets ΔH and ΔS vary with temperature,

\ln K_{p/q} = A + \frac{B}{T} + \frac{C}{T^{2}} ueda2022 E6,

\Delta H_{q\to p} = -R\left(B + \frac{2C}{T}\right),\qquad \Delta S_{q\to p} = R\left(A - \frac{C}{T^{2}}\right) ueda2022 E7, E8.

Variables and units

symbolmeaningunits
xmole-fraction solubility of the drug in liquid PEGdimensionless [zhu2011 E3]
\Delta H_fheat of solution (named "heat of solution" in the card)not printed [zhu2011 E3]
R, Tgas constant; temperatureK [zhu2011 E3]
K_{p/q}, C_p, C_qpartition coefficient of the polymer between the drug-rich phase (p) and water (q), and its concentrations in themdimensionless; C_p computed with 0.99 g/cm³ (amorphous ibuprofen) ueda2022 E3, X2
\Delta G_{q\to p}, \Delta H_{q\to p}, \Delta S_{q\to p}free energy, enthalpy and entropy of transfer from water into the drug-rich phasekJ/mol for ΔG and ΔH (see the use table); unit of ΔS not stated in the notes ueda2022 E4, E5
A, B, Cconstants of the quadratic fit of \ln K_{p/q} against 1/Tnot stated ueda2022 E6

Assumptions and valid domain

\ln x against 1/T along the drug liquidus (Figs. 2–5) is fitted by linear regression and extrapolated to 25 °C, below the PEG melting point, so the result refers to supercooled liquid PEG, and is converted to weight percent [zhu2011 E3, C8]. The second paper uses it to extrapolate solubilities from the binary phase diagrams to 25 °C [zhu2012 E3]. Tested on four liquidus series measured here (benzocaine, ibuprofen, nilutamide, ketoconazole) and on the cited chlorpropamide and haloperidol diagrams [zhu2011 R1, R2, R3, R4, R5]. In the amorphous solubility chapter the linear form assumes ΔH and ΔS independent of temperature; the linear fit gave R² of 0.817 (PVP), 0.962 (HPMC) and 0.961 (PVP-VA) and the quadratic fit 0.971 (PVP), 0.996 (HPMC) and 0.994 (PVP-VA) ueda2022 C47, R20, R21. The concentration in the drug-rich phase is computed with 0.99 g/cm³ (amorphous ibuprofen), a basis that ignores water in that phase and is not written out ueda2022 E3, X2. Valid at 15–60 °C (HPMC 15–55 °C), pH 2.0 in D2O ueda2022 P12, R3.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
zhu2011solubility of six drugs in PEG 3350 at 25 °C28, 26, 25, 11, 0, 0 wt% (benzocaine, chlorpropamide, ibuprofen, nilutamide, haloperidol, ketoconazole)printed; inputs not printed (liquidus points only plotted; regression lines and molar masses not printed) [zhu2011 E3, R5]
zhu2012solubility of haloperidol, benzocaine, ibuprofen, fenofibrate at 25 °Cbelow 1, 28, 25, 6 wt%named only [zhu2012 E3, M1, M2, M3, M4]
ueda2022ΔG, ΔH, ΔS of transfer of PVP, PVP-VA and HPMC from water into the ibuprofen-rich phaselinear: HPMC ln K = −4.23 × 10³ (1/T) + 19.9; PVP-VA −1.79 × 10³ (1/T) + 12.2; PVP −1.44 × 10³ (1/T) + 10.5; ΔG −12 to −19 kJ/mol; ΔH of HPMC 58 → 12 kJ/molreproduces (HPMC at 288.15 K: ΔH = −8.314 × (38700 − 45740) J/mol = 58.5 kJ/mol; −TΔS = −70.8 kJ/mol; ΔG = −RT ln K = −12.3 kJ/mol) ueda2022 E4, E5, E7, E8, R20, R21

Where it fails or is disputed

The nilutamide estimate (11 wt%) is above its eutectic content (10 wt% at 58.4 °C), whereas an extrapolation to a lower temperature would normally give a lower value [zhu2011 X4]. The regression lines and inputs are not printed in either paper, so the estimates cannot be recomputed [zhu2011 E3; zhu2012 E3]. The relation assumes a constant heat of solution over the extrapolated range (synthesis: the extrapolation runs from liquidus temperatures well above the PEG melting point down to 25 °C [zhu2011 R1, R2, R3, R4]). In the amorphous solubility chapter ΔH, ΔS and ΔG are derivatives of three-parameter fits to 9–10 points with no propagated uncertainty, so the temperature slopes of ΔH and ΔS rest on the curvature term; for PVP ΔH is negative at 55 and 60 °C ueda2022 X8, X1. The linear fits give temperature-independent ΔH of about 35 (HPMC), 15 (PVP-VA) and 12 kJ/mol (PVP) (extractor calculation), close to the quadratic values at mid-range ueda2022 X8. The two chapters apply the relation to different quantities (drug solubility along the liquidus in PEG; polymer partition coefficient between two liquid phases), so their values are not comparable.

Concepts

van't Hoff equation, drug solubility in polymer, liquidus temperature, polymer partitioning into the drug-rich phase, hydrophobic effect. Findings. PEG dispersions: F4. C. Amorphous solubility and LLPS: F21.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

Vogel-Tammann-Fulcher equation

Expression

\tau = \tau_0 \exp\left(\frac{D\,T_0}{T - T_0}\right) [baird2010 E12];

\eta = \eta_0 \exp\left(\frac{D\,T_0}{T - T_0}\right) [baird2012 E4].

Variables and units

symbolmeaningunits
\tau, \etamean molecular relaxation time, or viscositys; Pa·s [baird2010 E12; baird2012 E4]
\tau_0, \eta_0value for the unrestricted materialτ0 ≈ 10⁻¹⁴ s [baird2010 E12]
Dstrength parameterdimensionless [baird2012 E4]
T_0zero-mobility temperature, for some systems the Kauzmann temperatureK [baird2012 E4]

Assumptions and valid domain

For the strength parameter D^b: T_0 = T_K, τ(Tg) ≈ 10² s, τ0 ≈ 10⁻¹⁴ s [baird2010 E12]. Valid from Tm down to about 0.4 Tg on a scale with T_g = 0 and T_m = 1, with D and T0 fitted together [baird2012 E4]. Strong liquids have D above 30, fragile ones below 10 [baird2010 R30].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
baird2010D^b from Tg and Kauzmann temperature for class II and IIIindomethacin D^b 5reproduces: \ln(10^{16}) \times (318.15 - 282.15)/282.15 = 4.70 [baird2010 E12, R18]
baird2012fits of melt viscosity for 28 compoundsD 4.3–8.7, all below 10inputs not printed (η0 not reported) [baird2012 E4, R12]

Where it fails or is disputed

The fitted T0 and D do not satisfy the paper's own relation between T0, D and Tg [baird2012 X5]. The six class I-A compounds were not fitted, though the abstract calls all compounds fragile [baird2012 X7]. Whether a compound counts as strong or fragile depends on using m or D [baird2010 X14]. Good and poor glass formers showed the same non-Arrhenius behaviour, so kinetic fragility "may not accurately assess" glass-forming ability [baird2012 C43]; fragility was also invoked, untested, for two growth-rate outliers [trasi2014a C29, X18].

Concepts

fragility, melt viscosity, glass transition temperature, supercooled liquid. Findings. F5, F12.

← Concepts and formulas

formula · as used in A. Release mechanism and LoC

water plasticization rule of thumb

Evidence table: water plasticization rule of thumb. Content from the release-mechanism chapter (2017–2022), with a row from the amorphous solubility and LLPS chapter.

Expression

Stated in words: the wet Tg equals the dry Tg less about 10 °C for each 1% of water sorbed indulkar2017b E6; Tg falls by about 10 °C for each 1% of water sorbed ilevbare2013a E15. Written as an expression (synthesis: transcription of the words):

T_{g,\mathrm{wet}} \approx T_{g,\mathrm{dry}} - 10\,w

Variables and units

symbolmeaningunit
T_{g,\mathrm{wet}}, T_{g,\mathrm{dry}}glass transition temperature with and without sorbed water°C
wwater content% (w/w)

Assumptions and valid domain

A typical observation, taken from indomethacin (cited) indulkar2017b E6; cited from earlier work ilevbare2013a E15.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
indulkar2017bwet Tg of water-saturated nifedipine dropletsdry 42 °C, 2.5% water, approximately 17 °Creproduces: 42 − 10 × 2.5 = 17 indulkar2017b E6, M1, C16
ilevbare2013a (LLPS chapter)Tg of a water-saturated drug-rich phasedry 50.4 °C, 0.4 °C with 4.87% waterreproduces within rounding: 50.0 / 4.87 = 10.3 °C per 1% ilevbare2013a E15
saboo2020wet Tg of amorphous indomethacin from 37 °C sorption29 °Cinputs not printed saboo2020 E6, M1
yang2021wet Tg of miconazole, danazol, elbasvir from 37 °C sorption−4.7, 73.3, 129.1 °Cinputs not printed yang2021 E3, M2, M3, M4
hiew2022bwet Tg of lumefantrine dispersions with 35–55% waterall below 37 °Creproduces: 105.5 − 10 × 35 lies far below 37 hiew2022b E3, C44, R5

Where it fails or is disputed

The nifedipine water content was extrapolated from a 25 °C sorption profile to 100% RH and no Tg of water-saturated nifedipine was measured indulkar2017b X8. For lumefantrine dispersions the rule puts every wet Tg below 37 °C, so it cannot by itself explain release hiew2022b C44; a measured 70% indomethacin dispersion fell from 62.64 to 18.48 °C with about 6% water, about 7 °C per 1% (synthesis: 44.2/6) saboo2020 R30.

Concepts

plasticization by water, glass transition temperature, supercooled liquid. Findings. Release mechanism and LoC: F5, F18, F22.