Chapter of Dissolution

B. Supersaturation from ASD dissolution

What happens to the supersaturation that a neat amorphous drug or an amorphous solid dispersion produces when it dissolves under non-sink conditions.

What this chapter covers

the two crystallization routes that remove it (crystallization of the wetted solid and crystallization from the supersaturated solution) and how temperature, the placement of the polymer (in the medium or in the dispersion) and the polymer content of the dispersion change them, the metastable crystal form that can appear first, the ranking of PVP, HPMC, HPMCAS, PAA and EPO for holding supersaturation and the solution tests used to screen them, polymers and drug–polymer complexes that raise the solubility in solution, the ceiling on dissolved drug at the amorphous solubility (also for marketed tacrolimus capsules) and the methods that see it (membrane flux, NMR, ultracentrifugation) or overread it (in situ UV, 0.45 µm filtration), the colloid of drug-rich droplets or particles that fast-releasing dispersions form, drug loading and release speed, a second amorphous drug or an undissolved polymer mixed with the drug that lowers the ceiling, additives that decide the size and lifetime of drug-rich droplets, surfactants that promote or slow crystallization and dissolve an enteric polymer from suspended particles, leaching of drug from enteric-polymer suspensions in acid, dispersions with a fast-releasing polymer and a minor crystallization inhibitor, the redissolution of what separated in acid after a rise in pH, seed crystals and crystals left from preparation and how their growth area and origin decide the loss of supersaturation, salt formation inside the dispersion against a fast crystallizer, crystallization of the wetted dispersion during a gastric stage and what the gastric pH, the polymer grade and an enteric coating on the tablet then do to release, the dose relative to the amorphous solubility and the reservoir of undissolved dispersion and droplets, fasted and fed biorelevant media, and the difference between a single enantiomer and its racemate. The papers and their findings are in sources.md and findings.md. The twenty-two papers run from 2008 to 2025 and study felodipine, indomethacin, ritonavir, nifedipine, celecoxib, danazol, lopinavir, resveratrol, tacrolimus, paclitaxel, posaconazole, delamanid and praziquantel with PVP, PVPVA, HPMC, HPMCAS, HPMCP, PAA, EPO, CMCAB, PVA, HPC, Eudragit L100 and L 100-55, cellulose esters and other insoluble polymers (CA, CAP, EC, Eudragit RL).

22 papers2008–202529 findings

01Findings map

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

02Which paper supports which finding

Show the table of papers and findings
Crystallization routes during amorphous dissolutionPolymers and the duration of supersaturationCeiling and the colloid it leavesDrug loading and components mixed with the drugSeed crystals and residual crystallinityAdditives and surfactants at drug-rich dropletsPolymer combinations and pH-shift releaseGastric stage and biorelevant media
paperF1F2F3F16F4F5F6F29F7F8F9F17F10F11F18F22F23F12F13F14F15F19F20F21F24F25F26F27F28
2008konno2008apolymer type and felodipine dispersion dissolution
2010alonzo2010two crystallization routes during amorphous dissolution
2011alonzo2011drug loading, nanoparticles and the dissolved-drug ceiling
2013ilevbare2013dritonavir nanodroplets and additives
2014raina2014bnifedipine polymorphs during dissolution
2015chen2015asurfactants in celecoxib–HPMCAS suspensions
2015jackson2015danazol dispersions, LLPS, drug loading and polymer
2015trasi2015bbinary amorphous drug combinations
2015wegiel2015resveratrol dispersions in aqueous media
2015xie2015celecoxib dispersions with polymer combinations
2016li2016blopinavir dispersions leaching in acid
2016trasi2016commercial tacrolimus capsules
2016xie2016acelecoxib with PAA and cellulose derivatives
2017xie2017indomethacin with EPO and HPMC
2018li2018lopinavir with insoluble polymers
2018que2018paclitaxel seed crystals and HPMCAS
2019elkhabaz2019aposaconazole dispersions through a gastric stage
2022duong2022adelamanid salts formed inside the dispersion
2023nguyen2023benteric coating on a delamanid dispersion tablet
2023nguyen2023cgastric pH, polymer grade and drug form
2024polyzois2024praziquantel dispersions, racemate and enantiomer
2025alvarenga2025praziquantel dispersions across media
other library papers41 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: the LLPS concentration of ritonavir and its solvent-shift measurement (Ilevbare 2013 on LLPS) ilevbare2013d R18, LLPS onset near the estimated amorphous solubility (Almeida e Sousa 2015) jackson2015 C3, and the lowering of the amorphous solubility by a second drug in antisolvent tests (Trasi 2015 on a second drug) trasi2015b C7. Taken in 2016–2018: the amorphous solubility as the ceiling of supersaturation, its measurement, also by UV scattering, and the range of solubility ratios of 5 to 65 (Almeida e Sousa 2015, Ilevbare 2013 on LLPS) trasi2016 C25, R17; li2018 C8, and the thermodynamic basis of a reduced maximum supersaturation with a miscible second component (Trasi 2015 on a second drug) li2018 C9. Given: the ceiling seen from dissolving dispersions, where flux and NMR put the free drug at the amorphous solubility, also for six marketed tacrolimus capsules (F7), the colloid of a dissolving dispersion as a drug-rich liquid formed at the LLPS concentration (F9), the second-drug drop in dissolving films and dispersions (F11), polymers that raise the solubility in solution (F17) and undissolved polymers that lower the ceiling (F18). A later salt and cocrystal study there cites the ASD dissolution studies for the free-drug ceiling almeidaesousa2016 C9. See Amorphous solubility and LLPS F8, F11, F12, F13, F19, F20, F22 and F23.

Takes from

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

Taken: seeds grown in different environments differing in their ability to grow (Schram 2016) que2018 C2; schram2016 C39, the separation of nucleation and growth for felodipine with HPMC (Alonzo 2012) alonzo2012 R18, the medium effects on nucleation of posaconazole and atazanavir, cited for the fed-state failure of praziquantel elkhabaz2021 C24; alvarenga2025 C18, and the HPMCAS-grade trade-off between inhibition and release at low pH; the induction-time method with its 120 min ritonavir baseline, used for the ritonavir additive screen and the celecoxib surfactant tests (Ilevbare 2013 on induction times) ilevbare2013d R17; chen2015a P9, danazol crystalline solubility and polymer effects (Jackson 2014) jackson2015 R11, and HPMC slowing felodipine nucleation and growth (Alonzo 2012), which places the main effect of HPMC on nucleation alonzo2012 R17 against the growth reading of the 2008 felodipine solutions (F5). Taken in 2015–2016: the seeded-growth method and the nucleation-rate estimate (Alonzo 2012) for celecoxib with HPMCAS xie2016a E6, R13, PAA as a poor nucleation inhibitor and the amphiphilic cellulose derivatives as the best inhibitors (Ilevbare 2013 on induction times) xie2016a C19; xie2015 C47, polymers with minimal impact on the amorphous solubility (Jackson 2016) trasi2016 C32, and a polymer that fails as a solution inhibitor, which motivated the polymer combinations (Trasi 2015 on acetaminophen, builds_on). Given: the felodipine crystalline solubility with HPMC and the solubility advantage of amorphous felodipine that set the supersaturation range of Alonzo 2012 (builds_on), and the celecoxib surfactant results, cited by the bile-salt studies for STC inhibiting celecoxib nucleation and for chain-tailed surfactants promoting crystallization chen2015 R9; lu2017 C30. See Crystallization from solution F6, F13, F17, F18, F19, F20, F28, F35, F37 and F44.

Takes from

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

Taken: the dry and humid solid-state rankings of PVP, HPMC and HPMCAS with felodipine (Konno 2006, Konno 2008 on moisture), the comparison for the dissolution ranking konno2008a R18; felodipine thermodynamic data for the Hoffman estimate (Marsac 2006) konno2008a R20; nifedipine crystallizing faster than felodipine at similar Tg and moisture sorption (Marsac 2006 and 2008) raina2014b R17; the storage stability of the same resveratrol dispersions (Wegiel 2013) wegiel2015 R21; and PAA as a solid-state growth inhibitor (Trasi 2012, builds_on of Xie 2015). Given: PVP as a poor inhibitor of felodipine crystallization from solution and PVP in the medium preventing immediate crystallization of amorphous felodipine, cited in a particle-size study of felodipine–PVP kestur2013b R29, C7; the PVP plus HPMC or HPMCAS celecoxib dispersions and their solution-inhibition rationale, cited by the storage study of the same binary and ternary dispersions, which found the PVP-major ternaries as stable as the PVP binary xie2016b R27, C3, C43; and the tacrolimus amorphous and crystalline solubility (50 and 1.4 µg/mL), the non-sink design and the HPMC induction time, cited by the crystallization study of commercial amorphous tacrolimus trasi2017 M1. See F2, F4, F16, F20.

Takes from

[Crystallization tendency](../../solid-state-stability/crystallization-tendency/index.md)

The counterion changing the crystallization tendency of amorphous salts (Towler 2008), taken as the basis of the delamanid salts duong2022a C5; nifedipine as a fast crystallizer (Baird 2010) raina2014b C26 and resveratrol as a rapid crystallizer (Van Eerdenbrugh 2010) wegiel2015 R22. See Crystallization tendency F18, F1 and F16.

Takes from

and gives to Dissolution / A. Release mechanism and LoC

Given: nanodroplets from dissolution of low-loading dispersions and the dependence of LLPS on polymer and drug loading (Alonzo 2011, Jackson 2015) are cited there as the background of the first of two proposed origins of nanodroplets indulkar2017b C6, C7; the same links run to the ritonavir hydration and copovidone release papers and to a study of nanodroplet release and polymer selection (builds_on, as listed in the evidence index of this subcategory). Taken (evidence table, not builds_on): the affinity of HPMC for precipitated HPMCAS, set beside the polymer pairs of the celecoxib ternaries hiew2025 C16. See F9, F10, F20.

Takes from

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

Taken: seeded desupersaturation of tacrolimus products with an absorptive sink and the discriminating power of small-volume non-sink tests hate2019 R17, C49; purohit2018 C57, the fed- and fasted-state behaviour of a pretomanid dispersion with an enteric polymer, with surface crystals in acid and a negative food effect nguyen2023a R22, C53, and the stronger solubilization of the crystal than of the amorphous form in micellar media elkhabaz2019b C35; the diffusion-cell flux method, the free drug as the quantity that sets supersaturation and membrane transport, and the amorphous solubility as its limit (Raina 2014 on LLPS) jackson2015 C26; trasi2015b C4; trasi2016 C34, no nifedipine solubility gain with 1 mg/mL polymer raina2014b P6, M2, micellar surfactants that raise the amorphous solubility and the apparent supersaturation C/Ceq in solubilizing media (Raina 2015) trasi2016 C32; li2016b C7, the UV extinction method for the amorphous solubility and no gain in activity above it (Raina 2014, builds_on of Xie 2017), and drug-rich nanodroplets as a reservoir (Indulkar 2016) xie2017 C42. Given: fast nanodroplet-forming release at 10% drug and slower release without nanodroplets at 50% drug from felodipine–HPMC dispersions, cited in the nanodroplet reservoir study indulkar2016 R14; the same links run to the coupled dissolution–permeation and ezetimibe papers and, for the mutual lowering of two drugs, to the darunavir–atazanavir study (builds_on, as listed in the evidence index of this subcategory). Given in 2018–2020: soluble resveratrol–HPMCAS complexes that lower free drug and mass flow, cited by a telaprevir dispersion study mosqueragiraldo2018b C5; the tacrolimus amorphous solubility of about 50 µg/mL and its ratio to the crystalline solubility, cited by three tacrolimus crystallinity and absorption studies purohit2018 R4; hate2019 M1; purohit2019 M3; and poorly soluble polymers that limit release and supersaturation, cited by an enzalutamide polysaccharide study wilson2020 C6. See Bioperformance F6, Bioperformance F8, F7, F10, F11, F17, F18.

Takes from

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

Taken: HPMCAS inhibiting the growth of two enantiomers of a chiral compound to different extents in a melt (Sato 2015), cited for the weaker protection of R-praziquantel polyzois2024 C28.

Gives to

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

The seed work of 2018 is cited there for percent crystallinity being a crude specification and for residual crystals growing better than bulk seeds moseson2020a C4, C41; a posaconazole study found 0.3% residual crystallinity deciding the outcome after a pH shift and matrix crystallization rising only where crystals were already present shah2024 C56, C36, and an aluminium oxide nanocoating of dispersion particles delayed matrix crystallization during release moseson2023 C40. Lower concentrations from ritonavir–lopinavir co-granules are explained there by mixing of the two drugs in the amorphous solid, which lowers each amorphous solubility trasi2019 C38, and crystal growth within dispersion particles by matrix crystallization is reported there moseson2021 C27; both papers cite the work here (builds_on). Lopinavir as a poorly soluble drug of low crystallization propensity, with its amorphous solubility and Tg, is taken from the lopinavir papers of 2016 and 2018 by a study of HPMC dispersion microstructure li2019 C7. See F2, F11, F18.

Takes from

and gives to [Solution methods](../../characterization-methods/solution-methods/index.md)

Taken: the UV overestimate from particles (Van Eerdenbrugh 2011) alonzo2011 R25; jackson2015 C12. Given: the longer supersaturation with HPMCAS than with PVP from 10% danazol dispersions, cited in a fluorescence-lifetime study of ritonavir and lopinavir dispersions tres2018 R26; the UV extinction onset of a disordered phase and the polymer inhibition of nifedipine crystallization are cited by the fluorescent-probe study (builds_on). See F8, F9.

Left to other subcategories: the amorphous solubility itself, the phase that separates above it and its calculation (Amorphous solubility and LLPS, written before this chapter); how fast crystals nucleate and grow from supersaturated solutions with polymers, surfactants and bile salts (Crystallization from solution, written before this chapter); the release mechanism of dispersions and the limit of congruency (Dissolution / A. Release mechanism and LoC, written after this chapter and named without a link); membrane transport and absorption (Bioperformance); crystallization of the amorphous solid in storage and the crystallization classes of neat drugs and their salts (Crystallization tendency) and the storage stability of binary and ternary dispersions (Physical stability); and the probe, UV and light-scattering techniques as 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 8 · 4 findings · F1–F3, F16

Crystallization routes during amorphous dissolution

F1

Topic 1Crystallization routes during amorphous dissolution1 of 4

A wetted amorphous drug loses its supersaturation either by crystallizing in the solid or by crystallizing from the solution.

Amorphous felodipine at 37 °C, nifedipine and celecoxib crystallized in the wetted solid within minutes and dissolved no higher than the crystal. Amorphous indomethacin at 25 °C stayed amorphous while crystals grew in the liquid and the concentration fell alonzo2010 R2, R1, R11, R19, R7; raina2014b R6; xie2015 R8, R7.

moderateModerate to strong where in situ Raman and polarized light separate the two routes directly; weaker where the route was inferred, as for felodipine at 25 °C and resveratrol at pH 6.8 alonzo2010 K1, X6; raina2014b K1; wegiel2015 K6.

felodipine 37 °C · ≈54% crystallinenifedipine glass · no glass leftfelodipine 25 °C · ≈46% crystallinecelecoxib · widely crystallineindomethacin 25 °C · still amorphous1101001000time after wetting, min (log scale)

Wetted neat amorphous drugs followed by Raman or polarized light; only indomethacin kept its amorphous solid, while needles grew in the liquid. alonzo2010 R2, R11, R19; raina2014b R6; xie2015 R8

Crystallized in the wetted solid
felodipine at 37 °Cnifedipinecelecoxibresveratrol in HPMCASposaconazole in HPMCAS
Solid amorphous, crystals in the liquid
indomethacin at 25 °Cnifedipine

Nifedipine is in both lists: the neat glass crystallized in the solid, its 50:50 dispersions from the solution. alonzo2010 R2, R11, R19; raina2014b R2, R13; xie2015 R8; wegiel2015 R18; elkhabaz2019a R16

For your drug

  1. Wet the neat amorphous drug with the dissolution medium at 37 °C and follow the solid by Raman, PXRD or polarized light for 15–30 min while the concentration is read in a non-sink test.
  2. If the solid crystallizes within minutes, the polymer has to be in the dispersion; if the solid stays amorphous while the concentration falls, a solution crystallization inhibitor is the lever.

alonzo2010 P5, P8, C33, C40; raina2014b P4

How it works and key numbers
  1. Water lowers the Tg of the wetted solid: dry felodipine has a Tg of about 45 °C and just below 35 °C after exposure to 75% RH (cited), so at 37 °C the hydrated solid is above its Tg alonzo2010 C34, M1.
  2. A solid that "crystallizes more rapidly than it can dissolve" gives the solubility of the crystal, and no supersaturation forms (felodipine at 37 °C) alonzo2010 C8, C33.
  3. A solid that stays amorphous dissolves past the crystalline solubility, and the crystals then form in the liquid, which limits the concentration (indomethacin at 25 °C) alonzo2010 C31, C40.
  4. A polymer mixed into the dispersion keeps the hydrated matrix amorphous, so for nifedipine the route "has changed from the matrix to the solution phase" raina2014b C21, C24.
  5. In gastric fluid, where HPMCAS stays undissolved and the solution is subsaturated, "Solution-phase crystallization cannot occur", so crystals form in the matrix (F24) elkhabaz2019a C34.
≈54% at 1 mincrystallinity of wetted amorphous felodipine at 37 °Calonzo2010 R2
≈14.9 → ≈2.7 µg/mLindomethacin in solution at 25 °C while its solid stayed amorphousalonzo2010 R7, R11
≈1.70 vs ≈1.85 µg/mLneat amorphous against crystalline celecoxib at 16 hxie2015 R7
Evidence: data, conditions and papers

Finding F1. An amorphous drug can lose its supersaturation during dissolution by crystallizing in the wetted solid or from the solution, and which route acts depends on the drug, the temperature, and which polymer is present and where it sits

In short. Neat amorphous felodipine slurried in pH 6.8 buffer at 37 °C was ≈54% crystalline at the first Raman reading (1 min) and dissolved no higher than the crystal (≈0.9–1.1 µg/mL); at 25 °C it took about 8 min to reach 50% crystallinity and its solution peaked at ≈2.45 µg/mL alonzo2010 R2, R1. Amorphous indomethacin at 25 °C stayed amorphous for at least 4 h while needles grew in the liquid and the concentration fell from ≈14.9 to ≈2.7 µg/mL alonzo2010 R11, R19, R7. Neat amorphous nifedipine crystallized inside the particles within minutes, with or without polymer in the buffer, whereas in 50:50 dispersions the particles stayed non-birefringent and crystals below 2 µm formed in the solution raina2014b R2, R6, R13. Amorphous celecoxib behaved like nifedipine: it was crystalline in a slurry within an hour, mostly on the particles, and dissolved no higher than the crystal (≈1.70 against ≈1.85 µg/mL at 16 h) xie2015 R4, R8, R7; a 25% resveratrol–HPMCAS dispersion crystallized about equally at pH 6.8 and at pH 1.2, where the polymer does not dissolve, with crystals inside intact particles at pH 1.2 wegiel2015 R17, R18. The authors conclude that the rates of these two transformations relative to dissolution "in large part shape" the concentration–time profile alonzo2010 C32, C47.

Type. observation in 7 drugs (felodipine, indomethacin, nifedipine, celecoxib, resveratrol, posaconazole, delamanid) Strength. to strong for the routes, which in situ Raman and polarized light separate directly for felodipine at 37 °C, indomethacin at 25 °C, neat nifedipine and neat celecoxib, and SHG for posaconazole dispersions in gastric fluid alonzo2010 K1: strong, K5: moderate to strong; raina2014b K1: strong; xie2015 K2: moderate; elkhabaz2019a K2: moderate to strong; weaker where the route was inferred rather than seen (felodipine at 25 °C and with dissolved polymer, the nifedipine dispersions, resveratrol at pH 6.8, where only the similarity to pH 1.2 points to the matrix) alonzo2010 X6, X7; raina2014b K5: moderate, X10; wegiel2015 K6: weak to moderate.

How it was shown

Alonzo and co-workers (2010) followed slurries of melt-quenched felodipine (pH 6.8, 25 and 37 °C) and indomethacin (pH 2) by in situ Raman spectroscopy and polarized light, beside non-sink dissolution with fibre-optic UV alonzo2010 P1, P2, P3, P5. Raina and co-workers (2014) did so for nifedipine glass and 50:50 dispersions, Xie and Taylor (2015) for neat amorphous celecoxib, and Wegiel and co-workers (2015) a 25% resveratrol–HPMCAS dispersion at pH 6.8 and at pH 1.2, where HPMCAS does not dissolve raina2014b P6, P4; xie2015 P3, P7; wegiel2015 P7, A3.

What the data show

Felodipine at 37 °C, nifedipine glass and neat celecoxib crystallized in the wetted solid within minutes, while indomethacin at 25 °C stayed amorphous as needles grew in the liquid alonzo2010 R2, R11, R19; raina2014b R6; xie2015 R8.

drug and formconditionssolidsolutionids
felodipine, neat amorphouspH 6.8, 37 °C≈54% crystalline at 1 minplateau ≈0.9–1.1 µg/mL, like the crystalalonzo2010 R2, R1
felodipine, neat amorphouspH 6.8, 25 °C≈46% crystalline at 8 minpeak ≈2.45 µg/mL at ≈16 minalonzo2010 R2, R1
indomethacin, neat amorphouspH 2, 25 °Camorphous band kept at 120–240 min; needles in the liquid within 60 min≈14.9 → ≈2.7 µg/mLalonzo2010 R11, R19, R7
nifedipine glass; 50:50 PVP dispersionpH 6.8, 25 °Cglass fraction zero from 6 min; dispersion particles not birefringentcrystals below 2 µm in the solution around the dispersionraina2014b R6, R13
celecoxib, neat amorphouspH 6.8, 37 °Ccrystallization complete within an hour≈1.70 against ≈1.85 µg/mL for the crystal at 16 hxie2015 R4, R7
resveratrol–HPMCAS 25:75pH 6.8 and pH 1.2, 37 °CRaman ratio ≈0.96 and ≈0.93 (crystal 0.76); crystals inside intact particles at pH 1.2not measuredwegiel2015 R17, R18, R8
Fig. 3 of alonzo2010: Raman crystallinity of amorphous felodipine slurries at 25 and 37 °C
Fig. 3 · alonzo2010Raman crystallinity of amorphous felodipine slurries at 25 and 37 °C

At 37 °C the slurry is above 50% crystalline at the first reading, at 25 °C only after about 8 min alonzo2010 R2.

Why

For felodipine at 37 °C the amorphous solid "crystallizes more rapidly than it can dissolve", which the authors explain by the glass transition: the hydrated solid at 37 °C is above Tg and "presumably" crystallizes faster alonzo2010 C8, C33, C34. For indomethacin at 25 °C crystallization from solution is the limiting factor alonzo2010 C40. In the nifedipine dispersions the polymer keeps the hydrated matrix amorphous, so the route "has changed from the matrix to the solution phase" raina2014b C21, C24.

Limits and transfer

The slurries held about 250–375 mg/mL felodipine against 500 µg/mL in dissolution, so their timings rank systems rather than give the time scale in a dissolution vessel alonzo2010 X5; raina2014b X9. Wet the neat amorphous drug with the medium at 37 °C and follow the solid for 15–30 min beside a non-sink test: a solid that crystallizes within minutes needs the polymer in the dispersion, and an amorphous solid with a falling concentration needs a solution inhibitor alonzo2010 P5, C33, C40.

How it was shown

Alonzo and co-workers (2010) asked which crystallization route limits the concentration reached from an amorphous drug alonzo2010 C5. They melt-quenched felodipine and indomethacin, cryomilled them and kept the 100–300 µm fraction alonzo2010 P1. Felodipine was dissolved at 100, 500 or 1,000 µg solid per mL in 20 mL of 50 mM pH 6.8 phosphate buffer at 37 °C, and at 500 µg/mL at 25 °C, with fibre-optic UV every minute at 500 rpm; indomethacin at 300 µg/mL in 50 mL of 50 mM pH 2 phosphate buffer at 25 and 37 °C alonzo2010 P2, P3. Slurries of about 500–750 mg solid in 2 mL (felodipine) or 5 mL (indomethacin) of the same media were followed by in situ Raman spectroscopy, with a PLS model for felodipine crystallinity and, for indomethacin, the α band at 1,648 cm−1 and an amorphous-only band at 753 cm−1; wetted indomethacin was watched under polarized light alonzo2010 P5, P6, P7, P9. Raina and co-workers (2014) slurried about 500 mg of melt-quenched nifedipine in 2 mL of 50 mM pH 6.8 phosphate buffer, with or without 1 mg/mL PVP, HPMC or HPMCAS dissolved in it, or 1 g of 50:50 dispersions in 4 mL, at 25 and 37 °C; Raman spectra were taken every minute for 15 min and every 5 min up to 3 h and split into glass, γ and α by multivariate curve resolution (MCR), and particles were watched under crossed polarizers raina2014b P6, P7, P10, P4. A dissolution test of the neat glass and of the HPMC dispersion at 5 mg/mL solids and 37 °C gave the solution concentration raina2014b P11. Xie and Taylor (2015) melt-quenched celecoxib, sieved it to 106–250 µm, wetted particles with 3–4 drops of pH 6.8, 100 mM phosphate buffer, with or without 5 µg/mL HPMC or HPMCAS, under polarized light, slurried it in the same buffer at 37 °C with in situ Raman, and dissolved 8.8 mg in 400 mL at 37 °C and 300 rpm with in situ UV for 16 h, in triplicate, against the same mass of crystal xie2015 P2, P7, P3, P5. Wegiel and co-workers (2015) slurried about 300–500 mg of a 25% resveratrol–HPMCAS dispersion in 5 mL of pH 6.8 phosphate buffer, where HPMCAS dissolves, and of pH 1.2 HCl solution, where it does not, at 37 °C, followed the 1630/1605 cm−1 Raman ratio (0.76 for the crystal, about 1.1 for the amorphous dispersions; n = 3) and imaged the particles under polarized light after 24 h wegiel2015 P7, A3, R8, P9.

What the data show

Felodipine at 37 °C. The slurry was ≈54, ≈83 and ≈96% crystalline at 1, 5 and 24 min alonzo2010 R2. 100 µg/mL of amorphous solid followed almost the curve of the same mass of crystal (≈0.85 against ≈1.0 µg/mL near 120 min), and 500 and 1,000 µg/mL dissolved faster but plateaued at only ≈1.1 and ≈0.95–1.0 µg/mL, from ≈30 and ≈10 min alonzo2010 R1. Felodipine at 25 °C. The slurry was ≈10% crystalline at 1 min, ≈46% at 8 min and ≈89% at 29 min, and the solution peaked at ≈2.45 µg/mL at ≈16 min before falling to ≈0.8 µg/mL at 90 min alonzo2010 R2, R1. Indomethacin at 25 °C. Spectra after 120–240 min kept the amorphous band; dendritic needles appeared in the liquid between the particles within 60 min while the particles themselves did not crystallize; the solution peaked at ≈14.9 µg/mL at ≈25 min and was ≈2.7 µg/mL at 130 min alonzo2010 R11, R19, R7. Indomethacin at 37 °C. The slurry was largely amorphous at 20 min, clearly α at 90 min and like pure α at 120 min; the solution peaked at ≈11.2 µg/mL at ≈30 min, near the onset of conversion, and the powder agglomerated into a few large particles alonzo2010 R12, R13, R7, R10. Nifedipine. Particles were covered with birefringent crystals 15 min after wetting at 25 °C, in buffer and with each dissolved polymer; by MCR the glass fraction was ≈0.95, ≈0.61 and ≈0.35 at 3, 4 and 5 min and zero from 6 min; the neat glass gave ≈6 µg/mL in the dissolution test, on the crystalline-solubility line raina2014b R2, R6, R14. In the 50:50 PVP dispersion the particles shrank without turning birefringent and small plate-shaped crystals appeared in the surrounding solution within minutes; the authors state the same for the HPMC and HPMCAS dispersions without images raina2014b R13, X18. The HPMC dispersion reached ≈100 µg/mL at ≈22 min and fell to ≈41 µg/mL by 150 min raina2014b R14. Celecoxib. Wetted particles showed birefringent spots after 2 min and were widely crystalline at 10 min, with needles also in the surrounding liquid; in the slurry crystallization was complete within an hour xie2015 R8, R4. The amorphous solid dissolved faster at first (≈0.49 against ≈0.13 µg/mL at 20 min) but then followed the crystal, ending at ≈1.70 against ≈1.85 µg/mL at 16 h xie2015 R7. Resveratrol. The Raman ratio of the 25% HPMCAS dispersion fell from ≈1.05 to ≈0.96 at pH 6.8 and from ≈1.05–1.08 to ≈0.93 at pH 1.2 over about 1440 min, the curves overlapping within their error bars; at pH 1.2 the particles (≈200–300 µm) stayed intact with birefringent regions inside, at pH 6.8 they dispersed and left small crystalline particles wegiel2015 R17, R18. Posaconazole and delamanid in acid. Posaconazole–HPMCAS dispersions crystallized within 30 min in FaSSGF although the medium stayed below the crystalline solubility, at about 68% of the undissolved drug at 50% drug, and delamanid dispersions crystallized at their surfaces at pH 3.0 and 5.0 while the drug concentration in the acid hardly fell (F24) elkhabaz2019a R16, R20, R1; nguyen2023c R19, R23.

papersystemmethod and conditionsresultids
alonzo2010felodipine, neat amorphous, pH 6.8Raman slurry and dissolution (100–1,000 µg/mL), 37 °C≈54% crystalline at 1 min; plateau ≈0.9–1.1 µg/mL, like the crystalR2, R1
alonzo2010felodipine, 25 °Csame, 500 µg/mL50% crystalline after about 8 min; peak ≈2.45 µg/mL at ≈16 minR2, R1
alonzo2010indomethacin, pH 2, 25 °CRaman, polarized light, dissolution 300 µg/mLsolid amorphous for at least 4 h; needles in the liquid by 60 min; ≈14.9 → ≈2.7 µg/mLR11, R19, R7
alonzo2010indomethacin, 37 °Csameα by 90 min; peak ≈11.2 µg/mL near the onset of conversionR12, R13, R7
raina2014bnifedipine glass, buffer ± 1 mg/mL PVP, HPMC, HPMCASpolarized light, Raman–MCR, 25 °Cbirefringent at 15 min in every medium; glass gone by ≈6 minR2, R6
raina2014bnifedipine–PVP 50:50polarized lightparticles stay dark; crystals below 2 µm form in the solutionR13
raina2014bneat glass; nifedipine–HPMC 50:50dissolution 5 mg/mL, 37 °C≈6 µg/mL; peak ≈100 µg/mL, ≈41 µg/mL at 150 minR14
ilevbare2013c (Crystallization from solution)amorphous ritonavir, efavirenz, celecoxibdissolution, pH 6.8, 37 °C19.8 of 20.6, 12.3 of 19.8 and 2.5 of 22.6 µg/mL calculatedR2
chen2015acelecoxib–HPMCAS spray-dried particles, pH 3, Triton X100suspension, polarized light, 7 daysbirefringence on the particles, no free needlesR20
xie2015celecoxib, neat amorphous, pH 6.8polarized light; Raman slurry, 37 °Cspots at 2 min, widely crystalline at 10 min; complete within an hourR8, R4
xie2015same; crystaldissolution 8.8 mg in 400 mL, 37 °C, 16 h≈1.70 against ≈1.85 µg/mLR7
wegiel2015resveratrol–HPMCAS 25:75, pH 6.8 and pH 1.2Raman ratio, polarized light, 37 °C, 24 h≈0.96 and ≈0.93 (crystal 0.76); crystals inside intact particles at pH 1.2R17, R18, R8
ilevbare2013c (Crystallization from solution)amorphous celecoxib; efavirenzpolarized light, pH 6.8celecoxib birefringent at ≈1 min; efavirenz shrank without birefringence for 3 hR4, R5
elkhabaz2019aposaconazole–HPMCAS 10 / 25 / 50% and Noxafil powder in FaSSGF, solution subsaturatedSHG and TPE-UVF after 30 min, 37 °Ccrystals in every system; estimated matrix crystallization ≈0.026 / ≈0.050 / ≈68 / ≈0.047%R16, R20
nguyen2023cdelamanid salt dispersions, five enteric grades, 1 h at pH 1.6–5.0PLM and SEM of films and powders; concentration in acid; PVPVA in the mediumcrystals on the dispersion surfaces; concentration held and PVPVA changed nothingR19, R23, R22

Figure

Fig. 3 of alonzo2010: Raman crystallinity of amorphous felodipine slurries at 25 and 37 °C
Fig. 3 · alonzo2010Raman crystallinity of amorphous felodipine slurries at 25 and 37 °C

At 37 °C (open circles) the slurry is already above 50% crystalline at the first reading; at 25 °C (triangles) 50% takes about 8 min, the window in which some supersaturation could form alonzo2010 R2.

Fig. 10 of raina2014b: a nifedipine–PVP dispersion dissolving while crystals form in the solution
Fig. 10 · raina2014ba nifedipine–PVP dispersion dissolving while crystals form in the solution

The dispersion particles shrink without birefringence while fine crystals multiply in the liquid around them between 1 and 10 min raina2014b R13.

Fig. 8 of wegiel2015: Raman ratio of a 25% resveratrol–HPMCAS dispersion at pH 6.8 and pH 1.2
Fig. 8 · wegiel2015Raman ratio of a 25% resveratrol–HPMCAS dispersion at pH 6.8 and pH 1.2

The two curves overlap within their error bars although HPMCAS dissolves only at pH 6.8: the crystals form in or at the matrix whether or not the polymer leaves it wegiel2015 R17, C15.

Why

For felodipine at 37 °C the authors state that the amorphous solid "crystallizes more rapidly than it can dissolve", so that the crystal is what dissolves and no amorphous advantage appears alonzo2010 C8, C33. They explain the difference between 25 and 37 °C by the glass transition: dry felodipine has a Tg of about 45 °C and just below 35 °C after exposure to 75% RH (cited), so the hydrated solid at 37 °C is above Tg and "presumably" crystallizes faster alonzo2010 C34, M1. Indomethacin crystallized much more slowly although its Tg also falls with water and its driving force is larger, which they take as "an indication" that a single parameter such as Tg "will not fully explain" the behaviour alonzo2010 C42. For the falling indomethacin concentration at 25 °C they point to the needles in the liquid: crystallization from solution is the limiting factor there ("These observations indicate") alonzo2010 C31, C40. At 37 °C they combine agglomeration (less surface), conversion of the solid to α and weaker solution inhibition ("Presumably") alonzo2010 C41, C21. Fig. 16 of the paper sets the competition out as a scheme in which dissolution scales with surface area and a concentration difference and nucleation and growth rise with supersaturation alonzo2010 C43, E3, E4, E5. For nifedipine, a relatively fast crystallizer, Raina and co-workers find the matrix route "primarily" for the neat glass and argue that its inherent faster crystallization "appears" to carry over from earlier solid-state work raina2014b C10, C28, R17; in the dispersions the polymer keeps the hydrated matrix amorphous, so the route "has changed from the matrix to the solution phase" ("strongly suggest") raina2014b C21, C24. An alternative reading for felodipine at 25 °C is that the fall after the peak comes partly from loss of the dissolving amorphous phase, since the slurry was ≈70% crystalline at 15 min; the routes were not separated there alonzo2010 X6. For celecoxib, Xie and Taylor conclude that the neat amorphous drug "appears to undergo rapid crystallization", "primarily via the matrix route", which they relate to water lowering the Tg (not measured); the low concentration "indicates either" rapid complete matrix crystallization or rapid growth of seed crystals from the residual amorphous material xie2015 C26, C1, C32, C34. For resveratrol, a rapid crystallizer in the cited classification, Wegiel and co-workers infer from the alike kinetics at pH 6.8 and 1.2 that the route "may also be analogous", the crystals at pH 6.8 "most likely" forming from the matrix rather than from a supersaturated solution wegiel2015 R22, C14, C15; crystallization "appeared to occur in or at the surface of the matrix" wegiel2015 C16. (synthesis: in all five drugs the outcome follows from one comparison, how fast the wetted solid crystallizes against how fast it dissolves; the temperature effect for felodipine and the polymer placement for nifedipine both act through that comparison, and which polymer forms the dispersion decides the solid side of it, see F16.) For posaconazole in gastric fluid the authors argue that "Solution-phase crystallization cannot occur" in a subsaturated medium, so the crystals formed in the matrix elkhabaz2019a C34, and for delamanid the solution route was ruled out by a constant concentration in the acid and an ineffective solution inhibitor nguyen2023c C37, C39.

Conditions and limits

Neat melt-quenched powders and 50:50 dispersions; felodipine and nifedipine in pH 6.8 buffer, indomethacin in pH 2 buffer; 25 and 37 °C; up to 4 h alonzo2010 A1, A2; raina2014b A2, A3. The Raman slurries held about 250–375 mg/mL felodipine against 500 µg/mL in dissolution, so the polymer-to-solid ratio differed about 500–750-fold, and the nifedipine slurries held 125–250 mg/mL drug; slurry timings therefore rank systems rather than give the time scale in a dissolution vessel alonzo2010 X5; raina2014b X9. Replicates are not stated for any slurry run alonzo2010 X8; raina2014b X14. The two drugs of Alonzo were tested in different media and set-ups, so their comparison is qualitative alonzo2010 X9. The celecoxib micrographs do not always show one field, and the amount of neat amorphous celecoxib slurried is not stated xie2015 X13, X11; the resveratrol Raman ratio is uncalibrated, and the pH comparison has no statistical test wegiel2015 X13, C14.

Counterexamples and conflicts

Not every neat amorphous drug loses its advantage on wetting: in the crystallization-from-solution chapter amorphous ritonavir dissolved to 19.8 of a calculated 20.6 µg/mL, while celecoxib reached only 2.5 of 22.6 µg/mL, and amorphous efavirenz dissolved slowly without birefringence for 3 h ilevbare2013c R2, R5, C23, and in the LLPS chapter amorphous films of three weak bases reached 69–110% of their LLPS concentration (Amorphous solubility and LLPS F13). In acidified suspensions of celecoxib–HPMCAS particles, where the polymer barely dissolves, the particles stayed crystal-free for 48 h without surfactant and crystallized on or in the particles only after about 7 days chen2015a R14, R20, C33. No paper in the library contradicts the two-route frame itself.

Transfer check

Wet the neat amorphous drug with the dissolution medium at 37 °C and follow the solid (Raman, PXRD or polarized light) during the first 15–30 min while the concentration is read in a non-sink test alonzo2010 P5, P8; raina2014b P4. Above about 50% crystallinity within minutes, as for felodipine at 37 °C and nifedipine, the neat glass dissolves like the crystal and the polymer has to be in the solid; if the solid stays amorphous while the concentration falls, as for indomethacin at 25 °C, crystallization from solution is the problem and a solution inhibitor is the lever alonzo2010 C33, C40. Test at 37 °C: felodipine supersaturated at 25 °C but not at 37 °C alonzo2010 C6. For a dispersion of an enteric polymer, a slurry at a pH where the polymer stays undissolved (pH 1.2 for HPMCAS) shows matrix crystallization without the solution route wegiel2015 A3, C16.

History

The two ways in which an amorphous form loses its advantage were proposed in cited work alonzo2010 C2. Alonzo and co-workers (2010) were the first in the library to separate them in situ, for felodipine and indomethacin alonzo2010 C47. Raina and co-workers (2014) added nifedipine, the switch from the matrix route of the neat glass to the solution route of the dispersion, and a metastable crystal form on both routes (F3) raina2014b C21, C29. Wegiel and co-workers (2015) added resveratrol and used an undissolving medium to show the matrix route in a dispersion wegiel2015 C16; Xie and Taylor (2015) added celecoxib, whose neat glass crystallized mainly on its particles xie2015 C1. The title was widened from "where the polymer sits" to "which polymer is present and where it sits" when the papers of 2015–2018 showed that the dispersion polymer itself decides whether the wetted matrix crystallizes (F16). Later papers of the library cite Alonzo 2010 for matrix against solution crystallization during dissolution, among them work on celecoxib dispersions, on ezetimibe and posaconazole dispersions and on residual crystallinity (builds_on, as listed in the evidence index of this subcategory). Elkhabaz and co-workers (2019) and Nguyen and co-workers (2023) found the matrix route in gastric media, where an enteric polymer stays undissolved and the solution cannot be the source (F24) elkhabaz2019a C23; nguyen2023c C43.

F2

Topic 1Crystallization routes during amorphous dissolution2 of 4

Polymer dissolved in the medium protected wetted amorphous felodipine; nifedipine and celecoxib needed the polymer inside the dispersion.

With 500 µg/mL PVP, HPMC or HPMC-AS in the buffer, wetted felodipine took ≈13.5–20.5 min instead of less than 1 min to reach 50% crystallinity alonzo2010 R6. The same polymers in the medium did not delay nifedipine or celecoxib, whose particles crystallized within minutes, but in 50:50 nifedipine dispersions the wetted matrix stayed amorphous raina2014b C11, R2, R13; xie2015 R9, R10.

moderateModerate: Raman and PXRD agree for felodipine and the micrographs are direct for nifedipine and celecoxib, but the slurries held 500–750 times less polymer per unit of solid than the dissolution tests, and replicates are not stated alonzo2010 K3, X5, X8; raina2014b K1.

Wetted amorphous felodipine, 37 °C: minutes to 50% crystallinityno polymerbelow 1 minHPMC-AS in medium≈13.5HPMC in medium≈18.5PVP in medium≈20.5

Each polymer at 500 µg/mL in pH 6.8 buffer; crystallinity by Raman. alonzo2010 R6

Felodipine dissolution peak with the polymer in the medium, µg/mLcrystalline felodipine≈1.1amorphous, PVP≈7.3amorphous, HPMC≈8.9amorphous, HPMC-AS≈12.0

The estimated amorphous solubility is about 9 µg/mL; with PVP the peak fell to ≈2.1 µg/mL by 130 min. alonzo2010 R4, R3

For your drug

  1. Wet the neat amorphous drug with medium that holds the candidate polymer at the concentration the dispersion would release, and follow crystallinity for 15–30 min at 37 °C.
  2. A lag of several minutes means the polymer can act from solution; no lag means it must be molecularly mixed with the drug, and the wetted dispersion particles should then be checked for birefringence at the intended drug loading.

alonzo2010 P5, P8; raina2014b C11, C24; moseson2021 C27

How it works and key numbers
  1. The authors "speculate" that crystallization starts at the surface of the amorphous particle, is made worse by water plasticization, and that dissolved polymer interacts with that surface and delays surface crystallization; adsorption was not measured alonzo2010 C36, R22, R23.
  2. (synthesis) A polymer in the medium can act only on a surface it reaches before nuclei form: the nifedipine glass was unchanged for only about 2 min before γ appeared, while felodipine with polymer stayed below about 30% crystalline for 10 min raina2014b R6; alonzo2010 R6.
  3. Nifedipine and felodipine have similar Tg and moisture sorption (cited), so the difference "appears" to come from the faster inherent crystallization of nifedipine raina2014b C27, C28.
  4. Inside a dispersion the polymer prevents crystallization of the hydrated matrix, and crystals then form only in the solution raina2014b C24, C21.
≈13.5–20.5 vs below 1 mintime to 50% crystallinity of wetted felodipine with and without dissolved polymeralonzo2010 R6
≈12.0 µg/mLfelodipine peak with HPMC-AS in the medium, above the estimated amorphous solubility of about 9alonzo2010 R4, R3
5–20 minwhen crystals appeared on celecoxib particles despite 5 µg/mL HPMC or HPMCAS in the bufferxie2015 R9, R10
Evidence: data, conditions and papers

Finding F2. Polymer dissolved in the medium delayed crystallization of wetted amorphous felodipine but not of nifedipine or celecoxib, or of indomethacin at 37 °C; the same polymers mixed into a dispersion kept the nifedipine matrix amorphous

In short. With 500 µg/mL PVP, HPMC or HPMC-AS in the medium, the felodipine slurry reached 50% crystallinity only after ≈20.5, ≈18.5 and ≈13.5 min instead of within 1 min, wetted powder with 1 mg/mL PVP showed no crystal peaks after 15 min, and felodipine then peaked at ≈7.3, ≈8.9 and ≈12.0 µg/mL against an estimated amorphous solubility of about 9 µg/mL alonzo2010 R6, R5, R4, R3. The same three polymers at 1 mg/mL changed neither the onset nor the route of nifedipine crystallization, and PVP or HPMC at 250 µg/mL did not substantially delay crystallization of the indomethacin solid at 37 °C raina2014b C11, R2; alonzo2010 C26. With 5 µg/mL HPMC or HPMCAS in the buffer, wetted amorphous celecoxib formed no crystals in the liquid but crystallized on its particles within 5–20 min and dissolved only to ≈3.05–3.50 µg/mL, against ≈1.85 µg/mL for the crystal xie2015 R9, R10, R7. In 50:50 nifedipine dispersions the wetted matrix stayed amorphous, and at pH 2, where HPMCAS barely dissolves, the HPMCAS dispersion stayed amorphous for 3 h raina2014b R13, R15.

Type. observation in 4 drugs Strength. : Raman and PXRD agree for felodipine and the micrographs are direct for nifedipine and celecoxib, but the slurries held 500–750 times less polymer per unit of solid than the dissolution tests, replicates are not stated, the indomethacin result is "data not shown", and the celecoxib slurry with dissolved polymer is described two ways and not shown alonzo2010 K3: moderate to strong, X5, X8, R16; raina2014b K1: strong, K5: moderate; xie2015 K2: moderate, X7.

How it was shown

Alonzo and co-workers (2010) slurried amorphous felodipine at 37 °C in pH 6.8 buffer holding 500 µg/mL PVP, HPMC or HPMC-AS, followed crystallinity by Raman and dissolved the solid in the same media alonzo2010 P5, P6, P2. Raina and co-workers (2014) watched nifedipine glass with 1 mg/mL dissolved polymer and 50:50 dispersions under crossed polarizers and by Raman, and Xie and Taylor (2015) wetted amorphous celecoxib with buffer holding 5 µg/mL HPMC or HPMCAS raina2014b P4, P6; xie2015 P7.

What the data show

Dissolved polymers put a lag before felodipine crystallized but did not protect nifedipine or celecoxib, whose particles crystallized in every medium alonzo2010 R6; raina2014b C11; xie2015 R9, R10.

systempolymer and placementresultids
felodipine, 37 °C500 µg/mL PVP / HPMC / HPMC-AS in the medium50% crystalline at ≈20.5 / ≈18.5 / ≈13.5 min against below 1 min; dissolution peaks ≈7.3 / ≈8.9 / ≈12.0 µg/mLalonzo2010 R6, R4
indomethacin, 37 °C250 µg/mL PVP or HPMC in the mediumno substantial delay of the solid (data not shown)alonzo2010 C26, R16
nifedipine glass1 mg/mL PVP / HPMC / HPMCAS in the mediumonset and route unchanged; γ majority at the first readingraina2014b C11, R7
nifedipine 50:50 dispersionspolymer in the dispersionmatrix not birefringent; γ at 1 min (solution route)raina2014b R13, R11
nifedipine–HPMCAS 50:50, pH 2undissolved polymer in the dispersionmatrix amorphous for 3 h; few small crystals in the solutionraina2014b R15
celecoxib glass, 37 °C5 µg/mL HPMC or HPMCAS in the mediumcrystals on the particles within 5–20 min, none in the liquid; ≈3.05 / ≈3.50 µg/mL at 16 h against ≈1.70 without polymerxie2015 R9, R10, R7
Fig. 6 of alonzo2010: dissolved polymers put a lag before amorphous felodipine crystallizes in the slurry
Fig. 6 · alonzo2010dissolved polymers put a lag before amorphous felodipine crystallizes in the slurry

Without polymer the solid is crystalline at once; with each polymer the curve is sigmoidal with a lag of roughly 10–20 min alonzo2010 R6, C14.

Why

Alonzo and co-workers "speculate" that crystallization starts at the surface of the amorphous particle and that the dissolved polymer interacts with that surface and delays surface crystallization; adsorption was not measured alonzo2010 C36, R22, R23. Raina and co-workers note that nifedipine and felodipine have similar Tg and moisture sorption (cited), so the difference "appears" to come from the faster inherent crystallization of nifedipine raina2014b C27, C28. Xie and Taylor conclude that dissolved polymers are "clearly unable" to inhibit crystal formation in the celecoxib matrix xie2015 C35.

Limits and transfer

Early crystallinity values with polymer lie within the Raman model error, and the amorphous matrix of the HPMC and HPMCAS nifedipine dispersions at pH 6.8 is stated, not shown alonzo2010 X8; raina2014b X18. Wet the amorphous drug with medium holding the candidate polymer and follow crystallinity for 15–30 min at 37 °C: a lag of several minutes means the polymer can act from solution, and no lag means it must be molecularly mixed with the drug alonzo2010 P5, P8; raina2014b C11, C24.

How it was shown

Alonzo and co-workers (2010) slurried amorphous felodipine at 37 °C in pH 6.8 buffer containing 500 µg/mL PVP K29/32, HPMC 606 or HPMC-AS MF and quantified crystallinity by Raman PLS; wetted powder with 1 mg/mL PVP or HPMC-AS was examined by PXRD after 15 min; dissolution of 500 µg/mL amorphous felodipine was run with the same polymers predissolved at 500 µg/mL alonzo2010 P5, P6, P8, P2. Indomethacin slurries at 37 °C with 250 µg/mL PVP or HPMC were followed by Raman (data not shown) alonzo2010 R16. Raina and co-workers (2014) watched neat nifedipine glass in buffer with 1 mg/mL dissolved PVP, HPMC or HPMCAS under crossed polarizers and in Raman slurries at 25 and 37 °C, compared it with 50:50 dispersions of the same polymers in plain buffer, and placed the HPMCAS dispersion in pH 2 buffer to hold its matrix undissolved raina2014b P4, P6, P7, P5. Xie and Taylor (2015) watched amorphous celecoxib particles wetted with buffer containing 5 µg/mL HPMC or HPMCAS under polarized light for 60 min, slurried amorphous celecoxib with 22 µg/mL of a polymer, and dissolved 8.8 mg of it in 400 mL of buffer holding 5 µg/mL HPMCAS or HPMC at 37 °C for 16 h xie2015 P7, P3, P5, A5.

What the data show

Felodipine. Every polymer turned the crystallization curve sigmoidal: at 10 min the solid was ≈8% crystalline with PVP, ≈20% with HPMC and ≈32% with HPMC-AS against ≈90% without polymer, and all were ≈92–95% crystalline by ≈22–25 min alonzo2010 R6. By PXRD the wetted powder without polymer showed sharp felodipine peaks, with PVP none, and with HPMC-AS a largely amorphous pattern with a small peak at 10° 2θ alonzo2010 R5. In dissolution, PVP gave a peak of ≈7.3 µg/mL at ≈15 min that fell to ≈2.1 µg/mL at 130 min, HPMC ≈8.9 µg/mL at 40–50 min and ≈7.1 at 240 min, and HPMC-AS ≈12.0 µg/mL at ≈100 min and ≈10.2 at 240 min, while crystalline felodipine reached ≈1.1 µg/mL alonzo2010 R4. Indomethacin at 37 °C. Neither polymer substantially delayed the onset of crystallization of the slurried solid alonzo2010 C26, R16, although both held solvent-shift solutions far longer than buffer (F4) alonzo2010 R17. Nifedipine. With dissolved polymer, γ was the majority form at the first measurement at both temperatures and the γ profiles reached their maximum within ≈2–11 min, as in buffer raina2014b R7, R9. In the dispersions the particles did not become birefringent, and γ was detected in the slurry at 1 min with every polymer, which the authors read as crystallization from the solution raina2014b R13, R11, C21. At pH 2 the HPMCAS dispersion did not dissolve quickly, stayed non-birefringent and amorphous by Raman for 3 h, and only a few small crystals that did not grow substantially appeared in the solution after about 1 min raina2014b R15. Celecoxib. With 5 µg/mL HPMC a few small birefringent spots appeared on the particles at 20 and 60 min and none in the liquid; with HPMCAS spots at 5 min and birefringent regions on several particles at 60 min, again none in the liquid xie2015 R9, R10. In dissolution the concentration rose to ≈3.05 (HPMCAS) and ≈3.50 µg/mL (HPMC) at 16 h, against ≈1.70 µg/mL without polymer xie2015 R7. With 22 µg/mL of a polymer in the slurry, crystallization was "not substantially retarded" according to the results and lasted longer according to the discussion; neither is shown xie2015 R4, X7.

papersystemmethod and conditionsresultids
alonzo2010felodipine slurry, 500 µg/mL PVP / HPMC / HPMC-AS in mediumRaman PLS, 37 °C50% crystalline at ≈20.5 / ≈18.5 / ≈13.5 min, against below 1 minR6
alonzo2010wetted felodipine, 1 mg/mL PVP or HPMC-ASPXRD at 15 minno peaks (PVP); small peak at 10° (HPMC-AS); sharp peaks without polymerR5
alonzo2010felodipine dissolution, same polymersin situ UV, 37 °Cpeaks ≈7.3 / ≈8.9 / ≈12.0 µg/mL; estimate about 9 µg/mLR4, R3
alonzo2010indomethacin slurry, 250 µg/mL PVP or HPMCRaman, 37 °Cno substantial delay (data not shown)C26, R16
raina2014bnifedipine glass, 1 mg/mL PVP / HPMC / HPMCAS in mediumpolarized light, Raman–MCRonset and route unchanged; γ majority at the first readingC11, R7
raina2014bnifedipine 50:50 dispersionspolarized light, Ramanmatrix not birefringent; γ at 1 min (solution route)R13, R11
raina2014bnifedipine–HPMCAS 50:50 at pH 2polarized light, Raman, 3 hmatrix amorphous; few small crystals in the solutionR15
xie2015celecoxib glass, 5 µg/mL HPMC or HPMCAS in bufferpolarized light, 60 mincrystals on the particles within 5–20 min; none in the liquidR9, R10
xie2015samedissolution, 37 °C, 16 h≈3.05 / ≈3.50 µg/mL against ≈1.70 without polymerR7
xie2016acelecoxib–PAA 5:5 and 1:9, 5 µg/mL HPMCAS in mediumdissolution, 37 °C, 16 hrelease stopped at ≈9.7–11.6 of 22 µg/mL; needle crystals in the residueR9, R10
moseson2021 (ASD process)bicalutamide–PVPVA particlestime-lapse polarized light, 37 °Ccrystals grow by matrix crystallization within the particlesC27
mosqueragiraldo2018b (Bioperformance)telaprevir 50% HPMCAS dispersiondissolution, micrographsslow release and matrix crystallization, no phase separationC40
nguyen2023cdelamanid salt dispersions, 1 mg/mL PVPVA in the medium, pH 3.0 → 6.5in situ UV≈44 against ≈41, ≈82 against ≈80.5, ≈7 against ≈10% without PVPVAR22

Figure

Fig. 6 of alonzo2010: dissolved polymers put a lag before amorphous felodipine crystallizes in the slurry
Fig. 6 · alonzo2010dissolved polymers put a lag before amorphous felodipine crystallizes in the slurry

Without polymer (filled circles) the solid is crystalline at once; with PVP, HPMC or HPMC-AS the curves are sigmoidal with a lag of roughly 10–20 min, the window in which a supersaturated solution forms alonzo2010 R6, C14.

Fig. 3 of raina2014b: nifedipine glass after 15 min in buffer with and without dissolved polymer
Fig. 3 · raina2014bnifedipine glass after 15 min in buffer with and without dissolved polymer

All four media (B–E) give birefringent particles: polymer in the medium does not protect the nifedipine glass raina2014b R2.

Why

Alonzo and co-workers "speculate" that crystallization starts at the surface of the amorphous particle, is made worse by water plasticization, and that the small amount of dissolved polymer interacts with that surface and delays surface crystallization, as a thin polymer film is known to do (cited); adsorption on the amorphous surface was not measured alonzo2010 C36, R22, R23. The felodipine result is "consistent with" an earlier report of HPMC in the medium protecting an amorphous macrolide during dissolution alonzo2010 C35, R21. Raina and co-workers note that amorphous nifedipine and felodipine have similar Tg and moisture sorption (cited), so the difference that appears only with polymers present "appears" to come from the faster inherent crystallization of nifedipine raina2014b C27, C28, R17. Inside a dispersion the polymer prevents crystallization of the hydrated matrix, and at pH 2 the slow dissolution of HPMCAS means low supersaturation and slow nucleation and growth from solution raina2014b C24, C25, C37. (synthesis: a polymer in the medium can act only on a surface it reaches before nuclei form; the nifedipine glass was unchanged for only about 2 min before MCR showed γ raina2014b R6, whereas the felodipine solid with polymer stayed below about 30% crystalline for 10 min alonzo2010 R6. This reading uses the authors' surface hypothesis, which neither paper tested.) For celecoxib, Xie and Taylor conclude that polymers dissolved in solution are "clearly unable" to inhibit crystal formation in the amorphous matrix, which "confirm[s] the need to prevent matrix crystallization", and that the polymer must be present in the dispersion to act xie2015 C35, C36, C16. A later celecoxib paper of this chapter reached the same conclusion for PAA dispersions in a medium holding HPMCAS: the dissolved drug stayed supersaturated but the drug left in the particles crystallized ("It therefore appears") xie2016a C31 (F16).

Conditions and limits

Polymer in the medium at 250, 500 or 1,000 µg/mL; no dispersion of felodipine or indomethacin was dissolved in this paper, and nifedipine dispersions were 50:50 only alonzo2010 A4; raina2014b A3. The PXRD check is one time point at twice the polymer level of the slurries and dissolution tests alonzo2010 X13. Early crystallinity values with polymer (about 5–12%) lie within the Raman model error (RMSEE 7.21) alonzo2010 X8. For the HPMC and HPMCAS dispersions at pH 6.8 the amorphous matrix is stated, not shown raina2014b X18.

Counterexamples and conflicts

A polymer in the dispersion does not always keep the matrix amorphous: bicalutamide–PVPVA particles crystallized within the particles during dissolution, and a telaprevir dispersion with 50% HPMCAS crystallized in the matrix and never phase separated moseson2021 C27; mosqueragiraldo2018b C40. Among the ritonavir dispersions of this chapter, HPMC in the dispersion gave no crystallization in 2 h of dissolution (F12) ilevbare2013d C15. At 35% drug the cellulosic dispersions of resveratrol crystallized in the matrix within the first hour, and only 80–95% polymer prevented it (F16) wegiel2015 R9, R14. No paper of the library reports a polymer in the medium protecting wetted nifedipine or celecoxib; in an ASD process study, polymeric additives in the medium were "largely ineffective" against matrix crystallization of bicalutamide dispersions, at best slightly delaying nucleation moseson2021 C72.

Transfer check

Wet the neat amorphous drug with medium that holds the candidate polymer at the concentration the dispersion would release, and follow crystallinity for 15–30 min at 37 °C alonzo2010 P5, P8. A lag of several minutes, as for felodipine, means the polymer can act from solution; no lag, as for nifedipine, means it must be molecularly mixed with the drug raina2014b C11, C24. For the dispersion itself, check the wetted particles for birefringence at the intended drug loading, since high loadings can crystallize in the matrix moseson2021 C27.

History

HPMC in the medium protecting an amorphous solid during dissolution was reported in earlier cited work alonzo2010 R21. Alonzo and co-workers (2010) showed it in the library for felodipine with three polymers and two methods alonzo2010 C13, C14. Raina and co-workers (2014) found that it fails for nifedipine and that the polymer has to sit in the dispersion, and checked this with an HPMCAS dispersion at pH 2 raina2014b C11, C24. Xie and Taylor (2015) found the same for celecoxib and added that the dissolved polymer still stops crystallization in the liquid xie2015 C26, C35; the title gained celecoxib then. Papers of the ASD process and Bioperformance chapters later describe matrix crystallization of high-loading dispersions (bicalutamide, telaprevir) moseson2021 C27; mosqueragiraldo2018b C40, and F16 collects what the dispersion polymer itself does. Nguyen and co-workers (2023) found that 1 mg/mL PVPVA in the medium, a known solution inhibitor of delamanid, left release after a pH 3.0 stage unchanged where the dispersions crystallized at their surfaces (F24) nguyen2023c R22, P16.

F3

Topic 1Crystallization routes during amorphous dissolution3 of 4

Wetted nifedipine glass crystallized first as the metastable γ form and then converted to α; dissolved polymers delayed the conversion.

Raman spectra separated by multivariate curve resolution (MCR, a calibration-free split of mixed spectra) showed the glass in buffer becoming pure γ by about 6 min and pure α by 40 min at 25 °C raina2014b R6, P10. With 1 mg/mL dissolved PVP, HPMC or HPMCAS, γ stayed pure for about 20, 60 and 110 min raina2014b R9.

moderateModerate: the γ-before-α sequence holds in every medium and in both analyses, but no replicates are stated and the two analyses date the same events up to about 15 min apart raina2014b K2, K3, X5, X14.

last reading with pure γα completebuffer1340PVP in medium2060HPMC in medium60105HPMCAS in medium11014550:50 dispersionsMCR; γ detected at 1 minPVP ≈5HPMC, HPMCAS 400306090120150time after wetting at 25 °C, min

Neat glass with 1 mg/mL dissolved polymer, and 50:50 dispersions; at 37 °C the order of the polymers is the same. raina2014b R6, R9, R10, R11, R12, R7

For your drug

  1. For a drug with a known metastable form, follow the solid by in situ Raman during dissolution with and without the candidate polymer, and resolve the forms by MCR if the metastable form cannot be isolated.
  2. Weigh the result by the solubility ratio of the forms: nifedipine's estimated 2.4 makes the life of γ matter, whereas a ratio of 1.2 (mefenamic acid, cited) gave about equal plasma levels.

raina2014b C5, C43, C39, C40, R20

How it works and key numbers
  1. The glass first crystallizes as γ in a step "complete within about 10 min", and γ then converts to α through the solution raina2014b C13.
  2. A polymer could slow the conversion by adsorbing on γ crystals, by inhibiting α nucleation from solution or by inhibiting α growth (cited) raina2014b C31.
  3. The lag before α lengthened with polymer while the slope after onset stayed similar, so the authors judge it "most likely" that the polymers interfere with nucleation of α raina2014b C32.
  4. Dispersions dissolve faster, "may" reach a higher supersaturation and give many small crystals with more sites for heterogeneous nucleation, so they converted quickly raina2014b C33, C36.
To feel the numbers. With HPMCAS in the buffer γ was still pure at 110 min, against 13 min without polymer: 110 ÷ 13 ≈ 8.5 times longer.
13 → 110 minlast reading with pure γ: buffer against 1 mg/mL HPMCAS, 25 °Craina2014b R6, R9
≈5 vs 40 minα complete in the PVP against the cellulose 50:50 dispersionsraina2014b R12
2.4estimated solubility ratio of the metastable to the stable formraina2014b C40, M1
Evidence: data, conditions and papers

Finding F3. Amorphous nifedipine crystallized first as the metastable γ form and then converted to α; dissolved polymers lengthened the life of γ (HPMCAS > HPMC > PVP), while dispersions converted at least as fast as the neat glass in buffer

In short. By MCR of in situ Raman spectra at 25 °C, the nifedipine glass in buffer became pure γ from ≈6 to ≈13 min, and α replaced it completely by ≈40 min (by ≈30 min at 37 °C) raina2014b R6, R8. With 1 mg/mL PVP, HPMC or HPMCAS in the buffer, γ stayed intact for ≈20, ≈60 and ≈110 min, and α was complete at ≈60, ≈105 and ≈145 min raina2014b R9, R10. In 50:50 dispersions γ appeared at 1 min and α was complete at ≈5 min (PVP) and ≈35–40 min (HPMC, HPMCAS) at 25 °C raina2014b R11, R12. The authors estimate the metastable form at 2.4 times the solubility of α, so that its lifetime "could be of biological significance" raina2014b C40, M1.

Type. single-system observation (nifedipine, three polymers, two temperatures) Strength. : the γ-before-α sequence holds in every medium and both analyses, and the polymer ranking is large, but no replicates are stated, timings differ between peak ratios and MCR by up to about 15 min, and three 25 °C profiles repeat the same values shifted in time raina2014b K2: strong, K3: moderate, X5, X11, X14.

How it was shown

Raina and co-workers (2014) followed nifedipine glass in pH 6.8 buffer, with or without 1 mg/mL dissolved polymer, and 50:50 dispersions by Raman spectroscopy for up to 3 h at 25 and 37 °C raina2014b P6, P7. Multivariate curve resolution (MCR) split each series into glass, γ and α without calibration mixtures raina2014b P10, C6.

What the data show

In buffer, with each dissolved polymer and in each dispersion, γ appeared before α raina2014b R6, R9, R11. The dissolved polymers lengthened the γ plateau, while the dispersions converted fast raina2014b R9, R12.

systemγ intact until, 25 °C; 37 °Cα complete at, 25 °C; 37 °Cids
neat glass in buffer≈13 min; ≈9 min40 min; 30 minraina2014b R6, R8
neat glass, 1 mg/mL PVP≈20 min; ≈12 min60 min; 80 minraina2014b R9, R10
neat glass, 1 mg/mL HPMC≈60 min; ≈35 min105 min; 135 minraina2014b R9, R10
neat glass, 1 mg/mL HPMCAS≈110 min; ≈60 min145 min; 135 minraina2014b R9, R10
50:50 dispersions PVP / HPMC / HPMCASγ detected at 1 min≈5 / 40 / 40 min by MCR at 25 °Craina2014b R11, R12
Fig. 7 of raina2014b: γ nifedipine against time with buffer, PVP, HPMC and HPMCAS at 25 and 37 °C
Fig. 7 · raina2014bγ nifedipine against time with buffer, PVP, HPMC and HPMCAS at 25 and 37 °C

The γ plateau lengthens from buffer to PVP, HPMC and HPMCAS, while the decline after it is similarly steep at 25 °C raina2014b R9, X11.

Why

Because the lag before α lengthens while the slopes after onset are similar, the authors judge it "most likely" that the polymers interfere with nucleation of α; slower growth would have flattened the curves raina2014b C32. For the dispersions they propose that faster dissolution "may" reach a higher supersaturation and give many small crystals with more sites for heterogeneous nucleation raina2014b C33, C36.

Limits and transfer

The slurries were concentrated (125–250 mg/mL drug), their supersaturation was not measured, and the two analyses date the same events up to ≈15 min apart raina2014b X9, X10, X5. The authors' "stabilized the metastable polymorph" holds only relative to the PVP dispersion: γ was gone by ≈35 min in the cellulose dispersions, against ≈40 min for the neat glass in buffer raina2014b C41, X8, R12, R6. For a drug with a metastable form, follow the solid by in situ Raman with and without the candidate polymer and weigh the result by the solubility ratio of the forms, since nifedipine's estimated 2.4 makes the lifetime of γ matter raina2014b C5, C39, C40.

How it was shown

Raina and co-workers (2014) followed neat nifedipine glass (about 500 mg in 2 mL of pH 6.8 phosphate buffer, with or without 1 mg/mL dissolved polymer) and 50:50 dispersions (1 g in 4 mL) by Raman spectroscopy every minute for 15 min and every 5 min up to 3 h, at 25 and 37 °C raina2014b P6, P7. Forms were identified by the C−C−O band (glass 1214, α 1224, γ 1205 cm−1) raina2014b P8, M1. PCA showed that three components explained close to 96% of the variance, and MCR with non-negativity and closure split each series into the spectra of glass, γ and α and their relative amounts over time, without calibration mixtures; the γ reference was a time point at which only γ was present raina2014b R3, P10, C6, C7, E1. The resolved spectra matched measured reference spectra of the pure forms raina2014b R4, C9.

What the data show

Neat glass in buffer. At 25 °C γ was 1.0 from 6 to 13 min, then ≈0.88, ≈0.69, ≈0.47, ≈0.30 and ≈0.16 at 14, 15, 20, 25 and 30 min, and 0 from 40 min, mirrored by α (≈0.12 at 14 min, ≈0.53 at 20 min, 1.0 from 40 min); the authors read a crystallization step "complete within about 10 min" followed by conversion, with a γ half-life of about 20 min raina2014b R6, R7, C13. At 37 °C the γ plateau ended at ≈9 min and α was complete by 30 min raina2014b R8. The β form and form IV were never seen raina2014b R16. With dissolved polymer. At 25 °C the last time γ was still 1.0 was ≈13 min in buffer, ≈20 min with PVP, ≈60 min with HPMC and ≈110 min with HPMCAS; α reached 1.0 at 40, 60, 105 and 145 min raina2014b R9, R10. At 37 °C the plateau ended earlier (≈9, ≈12, ≈35 and ≈60 min), but α was complete only at 30, 80, 135 and 135 min raina2014b R9, R10. The peak-ratio summary gives the same order raina2014b R7. Dispersions. By peak ratios γ was detected at 1 min in every dispersion and α at 3, 25 and 30 min (25 °C) or 4, 7 and 9 min (37 °C) for PVP, HPMC and HPMCAS raina2014b R11. By MCR at 25 °C, γ vanished at 4 min in the PVP dispersion with α ≈0.99 at 5 min, and in the HPMC and HPMCAS dispersions γ declined from ≈5–7 min to 0 at 35 min while α rose to 1.0 at 40 min raina2014b R12. Solution-grown crystals were below 2 µm, against 1−300 µm for the crystallized glass raina2014b R13, R2.

papersystemmethod and conditionsγ intact until; α complete atids
raina2014bneat glass in bufferRaman–MCR, 25 °C; 37 °C≈13 min, 40 min; ≈9 min, 30 minR6, R8
raina2014bneat glass, 1 mg/mL PVPsame≈20 min, 60 min; ≈12 min, 80 minR9, R10
raina2014bneat glass, 1 mg/mL HPMCsame≈60 min, 105 min; ≈35 min, 135 minR9, R10
raina2014bneat glass, 1 mg/mL HPMCASsame≈110 min, 145 min; ≈60 min, 135 minR9, R10
raina2014b50:50 dispersions PVP / HPMC / HPMCASpeak ratios, first α; MCR at 25 °C3 / 25 / 30 min (25 °C), 4 / 7 / 9 min (37 °C); α complete ≈5 / 40 / 40 minR11, R12
alonzo2010indomethacin glass, pH 2, 37 °CRaman α bandα present at 90 min, like pure α at 120 minR12
xie2017indomethacin precipitate from an EPO 3:7 dispersion, pH 2.2SHG of the suspension; Raman, PXRD; SEMmetastable α form, mostly under 10 µmR23, R24, R25

Figure

Fig. 7 of raina2014b: γ nifedipine against time with buffer, PVP, HPMC and HPMCAS at 25 and 37 °C
Fig. 7 · raina2014bγ nifedipine against time with buffer, PVP, HPMC and HPMCAS at 25 and 37 °C

The flat γ plateau lengthens from buffer to PVP, HPMC and HPMCAS, while the decline after it is similarly steep at 25 °C (A); at 37 °C (B) the plateau is shorter but the cellulose curves decline more slowly raina2014b R9, X11.

Why

The authors list three ways in which a polymer could slow the conversion: adsorption on the parent γ crystals that reduces heterogeneous nucleation of α on them, inhibition of α nucleation from solution, and inhibition of α growth (cited) raina2014b C31. Because the lag before α appears lengthens while the slopes after onset are similar, "particularly at 25 °C", they judge it "most likely" that the polymers interfere with nucleation of α; slower growth would have flattened the curves, as polymers do for anhydrate-to-hydrate conversions (cited) raina2014b C32, R19. For the faster conversion of the dispersions they propose that the dispersion dissolves faster and "may" reach a higher supersaturation, which "would" give faster nucleation and many small crystals whose larger surface dissolves faster and offers more sites for heterogeneous nucleation, "which may explain" the faster conversion ("most likely explained by the faster dissolution rate") raina2014b C33, C36. When nucleation and growth are fast, as they "appear to be" for nifedipine, dissolution controls the solution-mediated transformation raina2014b C35, C34. Metastable forms are common in melt crystallization because conversion is slow in a viscous melt and hard to catch in solvents where it is fast; the one-minute Raman sampling caught γ raina2014b C30. Supersaturation in the slurries was not measured: the only dissolution test used the HPMC dispersion at a 50-fold lower solid loading raina2014b X10. (synthesis: the nucleation reading rests on curve shapes alone, and the repeated values in three 25 °C profiles call for the original data before slopes are compared raina2014b X11.)

Conditions and limits

One drug, 1 mg/mL dissolved polymer, 50:50 dispersions only, 25 and 37 °C, pH 6.8, concentrated slurries (125–250 mg/mL drug) raina2014b A1, A2, A3, X9. MCR gives relative amounts under a closure constraint, checked only against peak ratios; γ and α do not always add up to 1, and the two analyses date the same events up to ≈15 min apart raina2014b X15, X6, X5. No MCR profiles of the dispersions at 37 °C are shown raina2014b X3. "Faster at 37 °C" holds for the onset of conversion, not for its completion with HPMC raina2014b X7.

Counterexamples and conflicts

The authors write that the dispersions "stabilized the metastable polymorph" raina2014b C41; at 25 °C γ was gone by ≈35 min in the cellulose dispersions, no later than for the neat glass in plain buffer (≈40 min), so the stabilization holds only relative to the PVP dispersion raina2014b X8, R12, R6. Indomethacin in this chapter crystallized in the wetted solid at 37 °C as the α form, with no other form reported alonzo2010 R12; a later indomethacin paper of the chapter describes α as the slightly less stable monotrope of the stable γ form (cited) xie2017 M1, so indomethacin too crystallized first as a metastable form, and it was again α, of 5–10 µm, that precipitated from the highly supersaturated solution of an EPO dispersion at pH 2.2, identified by SHG, Raman and PXRD xie2017 R23, R24, R25, C46 (F21). None found in the library against the γ-first pattern for nifedipine.

Transfer check

For a drug with a known metastable form, follow the solid by in situ Raman during dissolution with and without the candidate polymer, and use MCR or another calibration-free resolution if the metastable form cannot be isolated raina2014b C5, C43. Compare the solubility ratio of the forms: nifedipine's estimated 2.4 makes the lifetime of γ matter, whereas a ratio of 1.2 (mefenamic acid, cited) gave about equal plasma levels raina2014b C39, C40, R20. A lag before the stable form appears that lengthens with polymer, at unchanged slope, points to nucleation inhibition of the stable form raina2014b C32.

History

The scheme of two routes, each through a metastable form I to a stable form II, was adapted by Raina and co-workers (2014) from Alonzo and co-workers (2010) raina2014b C4. Polymer delay of an anhydrate-to-hydrate conversion in slurries (cited) was the model for the slope argument raina2014b R19, C32. None of the other papers of this chapter revisits nifedipine polymorphs; the dihydropyridine series of the crystallization-from-solution chapter found nifedipine precipitating within 0.25 h from a solvent shift raina2015b R6. Xie and co-workers (2017) found the metastable α form of indomethacin precipitating from a dissolving EPO dispersion, "expected" from the high supersaturation (cited), and showed that these small crystals redissolved faster than sieved α crystals when the pH rose xie2017 C45, C46, C4. The earlier wording of this finding, that indomethacin formed no metastable form, overlooked that α is the metastable indomethacin form and was corrected then.

F16

Topic 1Crystallization routes during amorphous dissolution4 of 4

Whether a wetted dispersion crystallizes in its particles depends on the polymer in the particle and its share, not on polymer in the medium.

Resveratrol dispersions with 35% drug stayed amorphous in buffer with PVP or E100 but partly crystallized with the cellulosic polymers, and only 80–95% cellulosic polymer prevented it wegiel2015 R9, R14. Celecoxib–PAA dispersions released only about half their drug although HPMCAS in the medium kept the dissolved drug supersaturated, and needle crystals were found in the residue xie2016a R9, R10, C31.

moderateModerate: Raman, XRPD and polarized light show matrix crystallization directly for resveratrol, celecoxib and lopinavir, but for the PAA dispersions the route is inferred, and the resveratrol Raman ratio is uncalibrated wegiel2015 K5, X13; xie2015 K2; li2018 K5; xie2016a K3, X6.

Resveratrol: % polymer at which the wetted matrix stayed amorphousPVPonly 65% tested65 or lessE100only 65% tested65 or lessHPMC80HPMCAS85CMCAB95

Slurries in pH 6.8 buffer at 37 °C followed by Raman; lower contents of the cellulosic polymers crystallized, mostly within the first hour. wegiel2015 R14, R13, R9, X7

Posaconazole–HPMCAS in FaSSGF: estimated matrix crystallization, %10% drug≈0.02625% drug≈0.05050% drug≈68

Ratio of SHG to TPE-UVF volume fractions after 30 min, with the polymer undissolved (F24). elkhabaz2019a R20

For your drug

  1. Slurry the dispersion in the medium at 37 °C at the intended drug loading and at one or two higher polymer contents, and follow crystallinity by Raman, XRPD or polarized light for several hours.
  2. Dissolve it with a solution inhibitor predissolved: if release stops well below the dose while the dissolved drug holds, the matrix has crystallized; treat a very hydrophilic, fast-dissolving carrier such as PAA as a poor matrix inhibitor until shown otherwise.

wegiel2015 P7, A2; xie2016a R9, R10, C33; elkhabaz2017 C34

How it works and key numbers
  1. Matrix crystallization, which HPMCAS in solution cannot influence, competes with release, and once the matrix has crystallized no further drug can dissolve from it xie2016a C31.
  2. For resveratrol the authors think "insufficiently strong" drug–polymer interactions let the cellulosic dispersions crystallize, the dependence on polymer content "most probably" reflecting the limited number of polymer groups able to hydrogen-bond with the drug wegiel2015 C36, C37.
  3. The inhibitor therefore has to stay in close contact with the drug during hydration and be released with it xie2016a C54.
  4. (synthesis) Crystals in the particle can seed the solution; in the PAA case HPMCAS in the medium slowed growth enough to hold the dissolved drug xie2016a C36.
80 / 85 / 95%HPMC, HPMCAS and CMCAB content needed to stop resveratrol matrix crystallizationwegiel2015 R14
≈9.7–11.6 of 22 µg/mLrelease from celecoxib–PAA dispersions with HPMCAS in the mediumxie2016a R9, R10
≈0.026 vs ≈68%estimated matrix crystallization of 10% against 50% posaconazole–HPMCAS in FaSSGFelkhabaz2019a R20
Evidence: data, conditions and papers

Finding F16. Whether a wetted dispersion crystallizes in its matrix depends on the dispersion polymer and its content: resveratrol needed 80–95% cellulosic polymer, celecoxib crystallized in PAA particles but not in PVP-K29/32 or HPMCAS ones at 50% drug, and an inhibitor dissolved in the medium did not prevent it

In short. Resveratrol dispersions with 35% drug stayed amorphous in pH 6.8 buffer with PVP or E100 but partly crystallized within the first hour with HPMC, HPMCAS or CMCAB (Raman ratio ≈0.87, ≈0.84 and ≈0.81 against 0.76 for the crystal), and only 80% HPMC, 85% HPMCAS or 95% CMCAB stopped it wegiel2015 R9, R14. Celecoxib dispersions at 50% drug stayed amorphous in a slurry for 7 h with PVP-K29/32, HPMCAS or the HPMCAS ternaries, but the PVP-K12 one crystallized within 4 h xie2015 R4; PAA dispersions released only about half their drug even when 5 µg/mL HPMCAS in the medium held the dissolved drug for 16 h, and needle crystals were retrieved from the residue, which the authors read as crystallization in the matrix ("It therefore appears") xie2016a R9, R10, C31. Lopinavir dispersions at 50% drug showed crystals in the particles after 8–16 h with Eudragit RL (EUD) or CAP and none after 48 h with HPMCP li2018 R7. In gastric fluid, where HPMCAS stays undissolved, matrix crystallization of posaconazole–HPMCAS rose from about 0.03–0.05% of the undissolved drug at 10–25% drug to about 68% at 50% elkhabaz2019a R20, and delamanid dispersions crystallized at their surfaces more with HPMCAS grades than with HPMCP (F24) nguyen2023c C4.

Type. observation in 5 drugs (resveratrol, celecoxib, lopinavir, posaconazole, delamanid) Strength. : Raman, XRPD and polarized light show matrix crystallization directly for resveratrol, slurry Raman for celecoxib and micrographs for lopinavir wegiel2015 K5: moderate, K6: weak to moderate; xie2015 K2: moderate; li2018 K5: moderate; for the PAA dispersions the matrix route is inferred from incomplete release and retrieved crystals xie2016a K3: moderate, X6; the slurries held far more solid than the dissolution tests, and the resveratrol Raman ratio is uncalibrated wegiel2015 X6, X13.

How it was shown

Wegiel and co-workers (2015) slurried resveratrol dispersions with five polymers at 35% drug, and with the cellulosic polymers at 60–95% polymer, in pH 6.8 buffer at 37 °C and followed the 1630/1605 cm−1 Raman ratio (n = 3) wegiel2015 P5, P7, A1, A2. Xie and Taylor (2015, 2016) slurried 50% celecoxib dispersions with Raman for 7 h and dissolved PAA dispersions in buffer holding 5 µg/mL HPMCAS xie2015 P3; xie2016a P6. Li and Taylor (2018) imaged 50% lopinavir films with seven polymers under polarized light in pH 3 buffer li2018 P6, P7.

What the data show

Matrix crystallization followed the polymer in the particle and its share wegiel2015 R13; xie2015 R4; xie2016a R9; li2018 R7.

systemmethodresultids
resveratrol 35% with PVP / E100 / HPMC / HPMCAS / CMCABRaman slurry, pH 6.8, 37 °C≈1.13 / ≈1.13 / ≈0.87 / ≈0.84 / ≈0.81 (crystal 0.76)wegiel2015 R9
resveratrol with HPMC, HPMCAS, CMCAB at 60–95% polymersameno crystallization from 80% / 85% / 95% polymerwegiel2015 R13, R14
celecoxib 50% with PVP-K12; PVP-K29/32, HPMCAS, HPMCAS ternariesRaman slurry, 37 °C, 7 hcrystalline within 4 h; amorphous for 7 hxie2015 R4
celecoxib–PAA 5:5 and 1:9, 5 µg/mL HPMCAS in the mediumdissolution, 22 µg/mL nominal, 16 h≈9.7–11.6 µg/mL held; needle crystals in the residuexie2016a R9, R10
lopinavir 50% with EUD, CAP; HPMCAS; HPMCPpolarized light, pH 3, 25 °Ccrystals by 8–16 h; faint at 16 h; none at 48 hli2018 R7
posaconazole–HPMCAS 10 / 25 / 50% in FaSSGFSHG/TPE-UVF ratio after 30 min≈0.026 / ≈0.050 / ≈68%elkhabaz2019a R20
Fig. 6 of wegiel2015: Raman ratio against time for resveratrol dispersions at several HPMCAS, CMCAB and HPMC levels
Fig. 6 · wegiel2015Raman ratio against time for resveratrol dispersions at several HPMCAS, CMCAB and HPMC levels

The highest level of each polymer stays flat and every lower level falls within hours wegiel2015 R13.

Why

Wegiel and co-workers think the cellulosic dispersions crystallized because of "insufficiently strong" drug–polymer interactions, the dependence on polymer content "most probably" reflecting the limited number of polymer groups able to hydrogen-bond with the drug wegiel2015 C36, C37. For the PAA dispersions Xie and Taylor conclude that matrix crystallization, which HPMCAS in solution cannot influence, competes with release, PAA being "a very poor inhibitor of matrix crystallization, irrespective of the drug loading" xie2016a C31, C33. The inhibitor therefore has to stay in close contact with the drug during hydration xie2016a C54.

Limits and transfer

The PVP-K12 celecoxib dispersion that crystallized in the slurry released completely in dissolution, so a slurry result need not carry over to a dilute dissolution test xie2015 R4, R6, C39. Slurry the dispersion at the intended drug loading and at one or two higher polymer contents at 37 °C for several hours; if release into a medium holding a solution inhibitor stops well below the dose while the dissolved drug holds, the matrix has crystallized wegiel2015 P7, A2; xie2016a R9, R10.

How it was shown

Wegiel and co-workers (2015) made resveratrol dispersions by rotary evaporation (53–250 µm) with PVP, E100, HPMC, HPMCAS or CMCAB at 35% drug, and with the three cellulosic polymers at 60–95% polymer, slurried about 300–500 mg in 5 mL of pH 6.8 phosphate buffer at 37 °C, followed the 1630/1605 cm−1 Raman ratio every 5 min in the first hour and then less often up to 24–48 h (n = 3), checked the dried residues by XRPD and measured dissolved drug and polymer after about 24 h wegiel2015 P5, P7, A1, A2, P8. Xie and Taylor (2015) slurried 200 mg of 50% drug celecoxib dispersions (106–250 µm) in 2 mL of pH 6.8 buffer at 37 °C and followed the amorphous Raman shoulder near 1598 cm−1 every 15 min for 7 h xie2015 P1, P3, R3. Xie and Taylor (2016) dissolved PAA dispersions at 50% and 10% drug (dose 22 µg/mL in 400 mL, 37 °C) in buffer holding 5 µg/mL predissolved HPMCAS, retrieved the undissolved solid soon after the peak for polarized light, and watched wetted particles under polarized light from 20 s to 30 min xie2016a P6, P8. Li and Taylor (2018) suspended 50% drug lopinavir films with CA, CAP, EC, EUD, HPMCAS, HPMCP or HPMC in pH 3 citrate buffer at 25 °C without a crystallization inhibitor, imaged the particles under polarized light at 8–48 h and assayed the solution by HPLC at 2–48 h li2018 P6, P7.

What the data show

Resveratrol. The PVP dispersion stayed at a Raman ratio of ≈1.12–1.13 and E100 at ≈1.13, while HPMC fell from ≈1.07 to ≈0.87, HPMCAS from ≈1.05 to ≈0.84 and CMCAB from ≈1.03 to ≈0.81, mostly within the first hour, never reaching the crystal's 0.76; XRPD of the residues agreed wegiel2015 R9, R10. More polymer meant less crystallization: 85% HPMCAS stayed at ≈1.10 while 75% and 65% fell to ≈0.96 and ≈0.84; 95% CMCAB stayed flat while 90%, 85% and 65% fell to ≈0.99, ≈0.86 and ≈0.80; 80% HPMC stayed flat while 70% and 60% fell to ≈0.92 and ≈0.83 wegiel2015 R13. The minimum levels that stopped crystallization were 95% (CMCAB), 85% (HPMCAS) and 80% (HPMC); E100 and PVP were tested only at 65%, so their entries are upper bounds wegiel2015 R14, X7. The more the dispersion crystallized, the less it raised the concentration: the HPMCAS dispersions at 85, 75 and 65% polymer gave ≈1250, ≈885 and ≈460 µg/mL at 24 h wegiel2015 R15, C12. Celecoxib. The PVP-K12 dispersion lost its amorphous band between 2.5 and 4 h and showed a sharp band near 1550 cm−1 like the crystal; PVP-K29/32, HPMCAS and both HPMCAS ternaries kept the amorphous pattern for 7 h; the HPMC-containing dispersions were not reported xie2015 R4, X11. Wetted PAA 5:5 particles dissolved from 20 s and showed needle crystals at 5 and 10 min, too fast to tell matrix from solution crystallization, whereas HPMCAS 3:7 particles dissolved slowly and stayed crystal-free for 30 min xie2016a R7, C28, R8. With HPMCAS in the medium the PAA 5:5 dispersion peaked at ≈9.7 µg/mL within ≈5 min and still held ≈8.8 µg/mL at 16 h, the 1:9 one ≈11.6 and ≈10.8 µg/mL, of a possible 22 µg/mL; the residue retrieved after the peak was birefringent needles xie2016a R9, R10. PAA dispersions with 10% HPMCAS at 40–50% drug levelled at ≈15.9–16.8 µg/mL, which the authors take as continuing matrix crystallization ("it is apparent") xie2016a R14, C41. Lopinavir. EUD and CAP particles had marked regions at 8 h and coloured crystals at 16 h, CA and EC marked regions at 16 h, HPMCAS faint birefringence at 16 h, and HPMCP particles none at 48 h; amorphous lopinavir was a fibrous crystalline mass at 8 h li2018 R7. In solution EUD and CAP lost their supersaturation within about 10–12 h, like amorphous lopinavir, HPMCAS, CA and EC after about 12 h, and HPMCP stayed at ≈2.5–3.0 µg/mL, at or below its crystalline solubility, for 24 h li2018 R6, C25, X6.

papersystemmethod and conditionsresultids
wegiel2015resveratrol 35% with PVP / E100 / HPMC / HPMCAS / CMCABRaman slurry, pH 6.8, 37 °C≈1.13 / ≈1.13 / ≈0.87 / ≈0.84 / ≈0.81 (crystal 0.76)R9
wegiel2015resveratrol with HPMC, HPMCAS, CMCAB at 60–95% polymersameno crystallization from 80% / 85% / 95% polymerR13, R14
xie2015celecoxib 50% with PVP-K12; PVP-K29/32, HPMCAS, HPMCAS ternariesRaman slurry, 200 mg in 2 mL, 37 °C, 7 hcrystalline within 4 h; amorphous for 7 hR4
xie2016acelecoxib–PAA 5:5 and 1:9, 5 µg/mL HPMCAS in mediumdissolution, 22 µg/mL nominal, 16 h≈9.7–11.6 µg/mL held; needle crystals in the residueR9, R10
xie2016acelecoxib–PAA–HPMCAS 5:4:1, 4:5:1same, no polymer in mediumplateau ≈15.9–16.8 µg/mLR14
li2018lopinavir 50% with EUD, CAP; CA, EC; HPMCAS; HPMCPpolarized light, pH 3, 25 °Ccrystals by 8–16 h; at 16 h; faint at 16 h; none at 48 hR7
elkhabaz2017 (Bioperformance)ezetimibe–PAA dispersionspolarized light in two mediacrystallization from the solid matrix dominant, birefringent domains within minutesC34
mosqueragiraldo2018b (Bioperformance)telaprevir 50% HPMCAS dispersiondissolution, micrographsmatrix crystallization; HPMCAS left the matrix about twice as fast as the drugC40, C43
wilson2018 (Bioperformance)enzalutamide–HPMCAS 10:90 against 50:50dissolutionpoor performance attributed to rapid matrix crystallization of the 10:90 dispersion onlyC56
moseson2021 (ASD process)bicalutamide–PVPVA particlesslurry Raman with HPMCAS in the mediumpolymeric additives in the medium "largely ineffective" against matrix crystallizationC72
moseson2022b (ASD process)bicalutamide–PVPVA dispersionsrelease, SEMhighest risk with high drug loading, mechanical activation or surfactantC67
elkhabaz2019aposaconazole–HPMCAS 10 / 25 / 50% suspended in FaSSGFSHG/TPE-UVF ratio after 30 min≈0.026 / ≈0.050 / ≈68%R20
nguyen2023cdelamanid salt dispersions with HPMCP-50 / -55 and HPMCAS-LF / -MF / -HFfilms and powders after 1 h in acidmore crystals with HPMCAS; HPMCAS-HF even at pH 1.6R18, R19, C4

Figure

Fig. 6 of wegiel2015: Raman ratio against time for resveratrol dispersions at several HPMCAS, CMCAB and HPMC levels
Fig. 6 · wegiel2015Raman ratio against time for resveratrol dispersions at several HPMCAS, CMCAB and HPMC levels

The highest level of each polymer stays flat; every lower level falls within hours: the polymer content, not only the polymer, decides whether the wetted matrix crystallizes wegiel2015 R13.

Fig. 7 of xie2016a: PAA dispersions dissolved in buffer holding 5 µg/mL HPMCAS
Fig. 7 · xie2016aPAA dispersions dissolved in buffer holding 5 µg/mL HPMCAS

Release stops at about half the dose and then does not fall for 16 h: the dissolved drug is protected, the drug left in the particles is not xie2016a R9, C31.

Why

For resveratrol, a rapid crystallizer whose dispersions had already differed in storage (PVP with strong hydrogen bonds and E100 with an ionic interaction stable, the cellulosics not; cited), Wegiel and co-workers think crystallization of the cellulosic dispersions is due to "insufficiently strong" drug–polymer interactions, its dependence on polymer content "most probably" reflecting the limited number of polymer groups able to hydrogen-bond with the drug, and a finer dispersion at low drug loading "will also" hinder it; none of these was measured in the wet state wegiel2015 R21, R22, C36, C37, C38. For celecoxib, Xie and Taylor find the drug in a dispersion "considerably more stable" on contact with buffer than the neat glass, with a higher PVP grade more resistant, but note that Raman alone does not identify the route by which the PVP-K12 dispersion crystallized xie2015 C37, C15, C38. For the PAA dispersions they conclude that matrix crystallization, which HPMCAS in solution cannot influence, competes with release and that once the matrix has crystallized no further drug can dissolve; since 10% drug did not help, PAA is "a very poor inhibitor of matrix crystallization, irrespective of the drug loading" xie2016a C31, C33. The inhibitor therefore has to stay in close contact with the drug during hydration and be released with it; in PAA–HPMCAS ternaries the two polymers "presumably" separated, leaving part of the drug without it (F20) xie2016a C54, C62. The extractor notes that the needles could also have nucleated in the concentrated layer around the dissolving particles xie2016a X6. For lopinavir, matrix crystallization followed the solution trends, and the authors expect crystallization of suspended dispersions to depend on the supersaturation, the solubility of the polymer and its inhibition in solution and matrix li2018 C26, C60. (synthesis: in the three drugs the protection of the wetted matrix followed the polymer in the particle and its share, not the polymer in the medium (F2); once crystals form in the particle they cap what the particle can release (F1) and seed the solution, and the crystallization-from-solution chapter finds that dissolved polymers at µg/mL levels rarely stop growth on seeds (Crystallization from solution F20); in the PAA case HPMCAS in the medium did slow growth enough to hold the dissolved drug xie2016a C36.)

Conditions and limits

Resveratrol at pH 6.8 (and 1.2, F1), 37 °C; celecoxib at pH 6.8, 37 °C; lopinavir at pH 3, 25 °C and only at 50% drug wegiel2015 A1; xie2015 P3; li2018 P6. The resveratrol and celecoxib slurries held about 60–100 and 100 mg/mL solids, and the solids loading of the resveratrol comparison is unresolved wegiel2015 X6; xie2015 P3. The HPMC-containing celecoxib dispersions were not checked in the slurry xie2015 X11. The amount and location of the crystals in the PAA dispersions were not determined xie2016a X6.

Counterexamples and conflicts

Polymer in the medium did delay crystallization of wetted amorphous felodipine (F2) alonzo2010 R6. The PVP-K12 celecoxib dispersion that crystallized in the slurry within 4 h released completely in dissolution, desupersaturated only from solution, and was fully protected by 5 µg/mL HPMCAS or HPMC in the medium, so a slurry result need not carry over to a dilute dissolution test xie2015 R4, R6, C39. Stopping matrix crystallization did not by itself give supersaturation: PVP and E100 kept resveratrol amorphous but gave no more dissolved drug than the crystal (F17) wegiel2015 C9. More polymer is not always safer: an enzalutamide dispersion with 90% HPMCAS was read as crystallizing in the matrix where a 50:50 one did not, an interpretation the extractor flags because no wetted solid was analysed wilson2018 C56.

Transfer check

Slurry the dispersion at the intended drug loading and at one or two higher polymer contents in the medium at 37 °C, and follow crystallinity by Raman, XRPD or polarized light for several hours wegiel2015 P7, A2. Dissolve it with a solution inhibitor predissolved: if release stops well below the dose while the dissolved drug holds, the matrix has crystallized, and the residue should be birefringent xie2016a R9, R10. Treat a very hydrophilic, fast-dissolving carrier (PAA) as a poor matrix inhibitor until shown otherwise xie2016a C33; elkhabaz2017 C34.

History

Alonzo and co-workers (2010) separated the two routes and Raina and co-workers (2014) showed that a dispersion moves nifedipine from the matrix to the solution route (F1, F2) alonzo2010 C47; raina2014b C21. Wegiel and co-workers (2015) were the first in the library to measure the polymer content needed to stop matrix crystallization during dissolution wegiel2015 C11. Xie and Taylor (2015, 2016) ranked celecoxib dispersions in slurries and showed that an inhibitor in the medium cannot replace the dispersion polymer against matrix crystallization xie2015 C37; xie2016a C31. Li and Taylor (2018) added lopinavir with six insoluble polymers at 50% drug li2018 C26. Later papers of the Bioperformance and ASD process chapters made matrix crystallization a main risk of high-loading dispersions mosqueragiraldo2018b C40; moseson2021 C72; moseson2022b C67. Elkhabaz and co-workers (2019) measured the loading dependence of matrix crystallization in gastric fluid for posaconazole–HPMCAS, and Nguyen and co-workers (2023) its polymer dependence for delamanid (F24) elkhabaz2019a C36; nguyen2023c C4.

Topic 2 of 8 · 4 findings · F4–F6, F29

Polymers and the duration of supersaturation

F4

Topic 2Polymers and the duration of supersaturation1 of 4

No single polymer ranking held across drugs; the best crystallization inhibitor had to be found for each drug.

Each drug was tested near its amorphous solubility with several polymers. Cellulosic polymers held felodipine, danazol, celecoxib and praziquantel longest, but PVP held amorphous indomethacin at 25 °C, had no effect on ritonavir, and PVPVA held delamanid as long as HPMCAS and HPMCP konno2008a R10; jackson2015 R5; xie2015 R2; polyzois2024 R3; alonzo2010 R14; ilevbare2013d R12; duong2022a R4.

strongStrong for praziquantel, delamanid, felodipine and celecoxib, where screens are replicated or two papers agree; single tests for indomethacin, ritonavir and tacrolimus polyzois2024 K1; duong2022a K7; konno2008a K1; xie2015 K1; alonzo2010 K6; ilevbare2013d K6; trasi2016 K5.

Racemic praziquantel: minutes before crystallizationno polymer5.5PVPVA10.9HPC14.3PVA15.7HPMC 60324.5HPMCAS-LF50.5HPMCAS-MF83 or moreHPMC E5 LV83 or more

At the amorphous solubility in PBS pH 6.5 with 300 µg/mL polymer; the run ended at 83 min. polyzois2024 R3

Delamanid: minutes before crystallization (log scale)Eudragit L10010.2no polymer10.7HPMC≈50PVPVAmore than 1000HPMCPmore than 1000HPMCASmore than 1000

At the amorphous solubility (0.76 µg/mL) in PBS pH 6.5 with 300 µg/mL polymer; PVPVA, weak for praziquantel, matched the enteric cellulose esters here. duong2022a R4, R2, P4, P7

For your drug

  1. Rank the polymers for your own drug in a non-sink test at 37 °C, at the polymer concentration that complete release would give, after checking that the polymer leaves the crystalline solubility unchanged.
  2. Treat the felodipine order HPMCAS > HPMC > PVP as a hypothesis, and expect very hydrophilic, fast-dissolving polymers (PAA, EPO in acid) to give no solution inhibition until tested.

konno2008a P4, C6; alonzo2010 R14; ilevbare2013d R12; xie2016a C14; xie2017 C2

How it works and key numbers
  1. None of the polymers changed the crystalline solubility of felodipine at 1 mg/mL (0.98–1.01 against 0.94 µg/mL), so the gain is a maintained supersaturation, not solubilization konno2008a R1, C17, C22.
  2. For ritonavir, the more hydrophobic, negatively charged cellulose polymers were effective and the more hydrophilic uncharged ones ineffective or less effective ilevbare2013d C30.
  3. For celecoxib the cellulose derivatives "may" interact more with dense liquid clusters of the drug than hydrophilic PVP, and the very hydrophilic PAA "is expected" to interact more with water than with the drug xie2015 C46; xie2016a C18.
  4. Grades of one polymer also differed: HPMCAS-LF and HPMC 603 were weaker than the MF and E5 LV grades for praziquantel, attributed "likely" to functional group content and amphiphilicity, not measured polyzois2024 C25.
14.1 / 4.9 / 2.3 µg/mLfelodipine maximum from 75% HPMCAS, HPMC and PVP dispersionskonno2008a R7, R10
120.0 vs 119.3 minritonavir induction time with 5 µg/mL PVP against no additiveilevbare2013d R12
10.9 vs more than 1000 minPVPVA with praziquantel against PVPVA with delamanidpolyzois2024 R3; duong2022a R4
Evidence: data, conditions and papers

Finding F4. Which polymer sustains supersaturation best depends on the drug: for felodipine, danazol, celecoxib and praziquantel the cellulosic polymers held it far longer than PVP or PVPVA, and PAA, EPO and Eudragit L100 did not slow crystallization of celecoxib, indomethacin and delamanid, whereas PVP held amorphous indomethacin at 25 °C and did nothing for ritonavir, and PVPVA held delamanid as long as HPMCAS and HPMCP while HPMC did not

In short. Felodipine dispersions with 75% polymer reached 14.1 (HPMCAS), 4.9 (HPMC) and 2.3 µg/mL (PVP), the gap grew with polymer content, and 1 mg/mL of each polymer left the crystalline solubility at 0.98–1.01 against 0.94 µg/mL konno2008a R7, R10, R1. With the polymer dissolved in the medium, amorphous felodipine peaked at ≈7.3 µg/mL with PVP and lost most of it within an hour, while HPMC and HPMC-AS held it above 7 and 10 µg/mL for 4 h alonzo2010 R4. In danazol dispersions crystallization began after ≈56–70 min with PVP, ≈188–200 min with HPMC and ≈284–319 min with HPMCAS jackson2015 R5. At 22 µg/mL celecoxib with 5 µg/mL polymer, crystallization began within 5 min without polymer and with PAA, after about 1 h with PVP-K12 and about 2 h with PVP-K29/32, and not within 8–16 h with HPMCAS or HPMC xie2015 R1; xie2016a R3. At pH 2.2, HPMC held indomethacin at its amorphous solubility for about 1.5 h while EPO let it crystallize during the titration, and 50 µg/mL HPMC moved the onset of tacrolimus crystallization at 50 µg/mL from within 3 h to 6–8 h xie2017 R5, R8; trasi2016 R9. But 250 µg/mL PVP held amorphous indomethacin at ≈23.8 µg/mL for 4 h at 25 °C, and 5 µg/mL PVP left the ritonavir induction time at 120.0 against 119.3 min alonzo2010 R14; ilevbare2013d R12. For racemic praziquantel at its amorphous solubility, HPMCAS-MF and HPMC E5 LV prevented crystallization for the 83-min run against 10.9–50.5 min for PVPVA, HPC, PVA, HPMC 603 and HPMCAS-LF, and for delamanid PVPVA, HPMCP and HPMCAS held more than 1000 min while HPMC gave about 50 min and Eudragit L100 none (10.2 against 10.7 min without polymer) polyzois2024 R3; duong2022a R4, R2.

Type. observation in 9 drugs (felodipine, danazol, celecoxib, indomethacin, ritonavir, tacrolimus, paclitaxel, delamanid, praziquantel) Strength. for praziquantel and delamanid, whose screens are replicated with standard deviations polyzois2024 K1: strong; duong2022a K7: strong; strong for felodipine, where two papers and a particle-growth test agree konno2008a K1: strong; alonzo2010 K4: moderate; alonzo2011 K6: moderate, and for celecoxib, where two papers agree in triplicate time courses xie2015 K1: strong; xie2016a K1: strong; moderate for danazol (one example run per system behind the profiles, replicates of the summary not stated) jackson2015 K3: moderate, X11; single tests for indomethacin, ritonavir and tacrolimus alonzo2010 K6: moderate; ilevbare2013d K6: moderate; xie2017 K1: strong; trasi2016 K5: moderate.

How it was shown

Konno and co-workers (2008) dissolved felodipine dispersions with PVP, HPMC and HPMCAS at 10–75% polymer under non-sink conditions, and Jackson and co-workers (2015) timed crystallization from dissolving danazol films konno2008a P1, P3; jackson2015 P1, P3. Solvent-shift tests near the amorphous solubility timed celecoxib, ritonavir, delamanid and racemic praziquantel with each polymer in the medium xie2015 P4; ilevbare2013d P6; duong2022a P4; polyzois2024 P3.

What the data show

The cellulosic polymers held felodipine, danazol, celecoxib and praziquantel longest, but PVP held indomethacin, did nothing for ritonavir, and PVPVA matched the enteric polymers for delamanid konno2008a R10; jackson2015 R5; xie2015 R2; polyzois2024 R3; alonzo2010 R14; ilevbare2013d R12; duong2022a R4.

drug and testconditionsresult by polymerids
felodipine dispersions, 75% polymernon-sink dissolution, pH 6.8, 37 °Cmaximum 14.1 (HPMCAS), 4.9 (HPMC), 2.3 µg/mL (PVP)konno2008a R7, R10
danazol dispersions, 90:10 and 70:30film dissolution, pH 6.8, 25 °Cinduction ≈56–70 (PVP), ≈188–200 (HPMC), ≈284–319 min (HPMCAS)jackson2015 R5
celecoxib 22 µg/mL, 5 µg/mL polymersolvent shift, pH 6.8, 37 °Conset below 5 min without polymer and PAA as no polymer, ≈1 h (PVP-K12), ≈2 h (PVP-K29/32), more than 8 h (HPMCAS, HPMC)xie2015 R1, R2; xie2016a R3
amorphous indomethacin, 250 µg/mL PVPdissolution, pH 2, 25 °C≈23.8 µg/mL for 4 halonzo2010 R14
ritonavir 20 µg/mL, 5 µg/mL polymersolvent shift, 37 °Cinduction 120.0 (PVP), 146.0 (HPMCAS), 242.8 min (CAAdB 0.81) against 119.3 minilevbare2013d R12
delamanid 0.76 µg/mL; racemic praziquantel at its amorphous solubility300 µg/mL polymer, PBS pH 6.5, 37 °Cdelamanid more than 1000 min (PVPVA, HPMCP, HPMCAS), ≈50 min (HPMC), 10.2 against 10.7 min (Eudragit L100); praziquantel at least 83 min (HPMCAS-MF, HPMC E5 LV), 10.9–50.5 min (five others)duong2022a R4, R2; polyzois2024 R3
Fig. 2 of xie2015: 22 µg/mL celecoxib with and without 5 µg/mL polymer over 8 h
Fig. 2 · xie201522 µg/mL celecoxib with and without 5 µg/mL polymer over 8 h

The polymer-free solution crashes within minutes, PVP-K12 falls after about 1 h and PVP-K29/32 after about 2 h, while HPMCAS and HPMC stay near 21 µg/mL xie2015 R1, R2.

Why

The crystalline felodipine solubility was unchanged by 1 mg/mL of each polymer (0.98–1.01 against 0.94 µg/mL), so solubilization "can be discounted" and the polymers maintain the supersaturation konno2008a R1, C17, C22. For ritonavir the more hydrophobic, negatively charged cellulose polymers were effective and the more hydrophilic uncharged ones ineffective or less effective ilevbare2013d C30. For celecoxib the very hydrophilic PAA "is expected" to interact more with water than with the drug xie2016a C18.

Limits and transfer

Felodipine maxima above about 9.5 µg/mL and danazol UV peaks above 8 µg/mL include drug in particles (F8) konno2008a X5; jackson2015 C12. Rank the polymers for the new drug itself in a non-sink test at the polymer concentration that complete release would give; the felodipine order HPMCAS > HPMC > PVP is a hypothesis for another drug, not a rule konno2008a P4, C6; alonzo2010 R14; ilevbare2013d R12.

How it was shown

Konno and co-workers (2008) made felodipine dispersions with PVP K30, HPMC 606 and HPMCAS AS-MF at 10–75% w/w polymer by solvent evaporation, dissolved powder holding 30 mg felodipine in 600 mL of pH 6.8 test fluid at 37 °C and 50 rpm (50 µg/mL if all dissolved), read UV through a 70-µm filter for 6 h in triplicate, and measured crystalline solubility with 1 mg/mL polymer over 24 h konno2008a P1, P3, P4, X15. Alonzo and co-workers (2010) dissolved amorphous felodipine (500 µg/mL) with 500 µg/mL polymer in pH 6.8 buffer at 37 °C, and amorphous indomethacin (300 µg/mL) with 250 µg/mL PVP or HPMC in pH 2 buffer at 25 and 37 °C alonzo2010 P2, P3. Alonzo and co-workers (2011) followed felodipine particle growth by light scattering after a methanol shift without polymer and during dissolution of 90:10 PVP and HPMC dispersions at 25 °C alonzo2011 P5, R10. Jackson and co-workers (2015) spin-coated danazol films with PVP K29/32, HPMC 606 or HPMCAS MF at 90:10, 70:30 and 50:50 polymer:drug and dissolved them in 50 mL of 10 mM pH 6.8 phosphate buffer with pyrene at 25 °C and 300 rpm, 20–30 µg/mL if all dissolved; the induction time was read where the UV concentration fell and the pyrene ratio rose jackson2015 P1, P2, P3. Ilevbare and co-workers (2013) added a ritonavir stock to 100 mM pH 6.8 buffer at 37 °C to 20 µg/mL with 15 additives at 5 µg/mL (F12) ilevbare2013d P6. Xie and Taylor (2015, 2016) pipetted a celecoxib methanol stock into 50 mL of 100 mM pH 6.8 phosphate buffer at 37 °C and 300 rpm to 22 µg/mL, about the cited amorphous solubility, with 5 µg/mL of PVP-K12, PVP-K29/32, HPMCAS, HPMC, PAA or pairs, and read the onset as a rise of extinction at 350 nm with a fall of absorbance at 249 nm, in triplicate for 8–16 h xie2015 P4, C11; xie2016a P3. Xie and co-workers (2017) pumped an indomethacin ethanol stock into pH 2.2 McIlvaine buffer at 37 °C with 100 µg/mL HPMC or EPO and followed absorbance and extinction for 4 h xie2017 P4. Trasi and co-workers (2016) followed a 50 µg/mL tacrolimus solution in 5 mM pH 4.5 phosphate buffer at 37 °C without and with 50 µg/mL HPMC, in triplicate trasi2016 P10. Que and co-workers (2018) timed unseeded paclitaxel at S ≈88 with and without 20 µg/mL HPMCAS que2018 P5. Duong and co-workers (2022) timed delamanid at its amorphous solubility (0.76 µg/mL) in PBS pH 6.5 with 300 µg/mL HPMC, PVPVA, Eudragit L100, HPMCP or HPMCAS duong2022a P4, P7. Polyzois and co-workers (2024) timed racemic and R-praziquantel at their amorphous solubilities in PBS pH 6.5 with 300 µg/mL of seven polymers over an 83-min run polyzois2024 P3.

What the data show

Felodipine dispersions. Maxima rose with polymer content, steeply for HPMCAS (≈1.7, 2.3, 4.4, 6.8 and 14.1 µg/mL at 10, 20, 50, 60 and 75%), little for PVP (≈0.8 to 2.3) and in between for HPMC (≈1.7 to 5.0); 10–50% PVP did not exceed the crystalline solubility konno2008a R10, R8. The 75% PVP dispersion dissolved fastest at first (≈0.272 against ≈0.092–0.115 µg/mL·min for the cellulosic ones) but gave the lowest supersaturation konno2008a R11. Felodipine with polymer in the medium. PVP ≈7.3 µg/mL at ≈15 min, ≈2.7 at 60 and ≈2.1 at 130 min; HPMC ≈8.9 at 40–50 min and ≈7.1 at 240 min; HPMC-AS ≈12.0 at ≈100 min and ≈10.2 at 240 min alonzo2010 R4. Felodipine particles. Without polymer the particles measured 450 nm at once and 936 nm at 7 min; from a 90:10 PVP dispersion they grew from ≈218 to ≈459 nm between 10 and 90 min, from HPMC dispersions to ≈280–307 nm alonzo2011 R10, R8. The 90:10 PVP apparent concentration fell from ≈36.5 to ≈9.2 µg/mL within an hour at 25 °C, the 90:10 HPMC one from ≈26.8 to ≈20.7 µg/mL alonzo2011 R5. Danazol. Induction times were ≈70, ≈56 and ≈60 min for the 90:10, 70:30 and 50:50 PVP dispersions, ≈200 and ≈188 min for 90:10 and 70:30 HPMC and ≈284 and ≈319 min for 90:10 and 70:30 HPMCAS; the 50:50 HPMC and HPMCAS dispersions did not crystallize within 1440 min, but they also dissolved slowly (F10) jackson2015 R5, R4. Indomethacin. With PVP the concentration was ≈23.7 µg/mL at 30 min and ≈23.8 at 240 min at 25 °C, and at 37 °C reached the same ≈23.7 at ≈80 min before falling to ≈13.7 µg/mL; with HPMC it rose slowly to ≈24.3 µg/mL at 240 min at 25 °C and reached only ≈14.5 at 37 °C, against ≈14.9 and ≈11.2 µg/mL peaks without polymer alonzo2010 R14, R15, R7. The crystalline α solubility was not changed by either polymer alonzo2010 R9. Ritonavir. With 5 µg/mL PVP, PVPVA, HPMC, HPMCAS and CAAdB 0.81 the induction times were 120.0, 119.2, 134.0, 146.0 and 242.8 min, against 119.3 min without additive ilevbare2013d R12. Celecoxib. Without polymer the concentration peaked at ≈20.8 µg/mL and fell to ≈4.1 µg/mL within 1 h; with PVP-K12 it held ≈20.9 µg/mL to 60 min and fell to ≈4.4 µg/mL by 8 h, with PVP-K29/32 it began to fall at about 2 h and was ≈9.1 µg/mL at 8 h, and with HPMCAS or HPMC, alone or HPMCAS with either PVP, it was ≈20.2–21.2 µg/mL at 8 h xie2015 R2. PAA left the curve unchanged (≈3.6 µg/mL at 60 min), whereas HPMCAS and HPMC kept ≈19.0 and ≈20.0 µg/mL at 16 h, also with PAA present xie2016a R3. Indomethacin at pH 2.2. With 100 µg/mL HPMC the absorbance plateau held from ≈16 to ≈110 min and then fell; with 100 µg/mL EPO the absorbance bent down and many small crystals appeared during the addition xie2017 R5, R8. Tacrolimus. Without HPMC the 50 µg/mL solution held for about 150 min and fell to ≈8 µg/mL by ≈680 min; with HPMC it held to ≈400 min and was ≈40 µg/mL at 800 min trasi2016 R9. Paclitaxel. Without polymer the unseeded solution crystallized within 6 min, with HPMCAS not within 16 h (F22) que2018 R3. Delamanid. PVPVA, HPMCP and HPMCAS prevented crystallization for the 1000 min observed, HPMC delayed it to about 50 min and Eudragit L100 had no effect (10.2 ± 3.1 against 10.7 ± 1.2 min) duong2022a R4, R2. Praziquantel. Induction times were 5.5 (none), 10.9 (PVPVA), 14.3 (HPC), 15.7 (PVA), 24.5 (HPMC 603) and 50.5 min (HPMCAS-LF), and HPMCAS-MF and HPMC E5 LV reached the end of the 83-min run; with R-praziquantel the same two gave 37 and 15.5 min (F29) polyzois2024 R3, R4. Posaconazole. A 10% HPMCAS dispersion dissolved directly in FaSSIF held about 21 µg/mL, near its amorphous solubility, for 180 min elkhabaz2019a R6.

papersystemmethod and conditionsresultids
konno2008afelodipine dispersions, 75% HPMCAS / HPMC / PVPnon-sink dissolution, pH 6.8, 37 °Cmaximum 14.1 / 4.9 / 2.3 µg/mLR7, R10
konno2008acrystalline felodipine, 1 mg/mL polymer24 h, 37 °C0.98–1.01 against 0.94 µg/mLR1
alonzo2010amorphous felodipine, 500 µg/mL PVP / HPMC / HPMC-AS in mediumdissolution, 37 °C≈7.3 → ≈2.1 µg/mL (130 min); ≈8.9 → ≈7.1; ≈12.0 → ≈10.2 (240 min)R4
alonzo2011felodipine particles: none; 90:10 PVP; 90:10 HPMClight scattering, 25 °C936 nm at 7 min; ≈459 nm at 90 min; ≈280–307 nm at 90 minR10, R8
jackson2015danazol dispersions PVP / HPMC / HPMCAS, 90:10 and 70:30film dissolution, pH 6.8, 25 °Cinduction ≈56–70 / ≈188–200 / ≈284–319 minR5
alonzo2010amorphous indomethacin, 250 µg/mL PVPdissolution, pH 2, 25 °C; 37 °C≈23.8 µg/mL for 4 h; ≈23.7 → ≈13.7 µg/mLR14
ilevbare2013dritonavir 20 µg/mL, 5 µg/mL PVP / HPMCAS / CAAdB 0.81solvent shift, 37 °Cinduction 120.0 / 146.0 / 242.8 against 119.3 minR12
ilevbare2013b (Crystallization from solution)ritonavir, celecoxib, efavirenz seeds, 5 µg/mL PVP or PVPVAseeded growth, 37 °CPVP and PVPVA slowed celecoxib and efavirenz but not ritonavir growthR9
xie2015celecoxib 22 µg/mL, 5 µg/mL PVP-K12 / PVP-K29/32 / HPMCAS / HPMCsolvent shift, pH 6.8, 37 °Conset ≈1 h / ≈2 h / >8 h / >8 h (none: <5 min)R1, R2
xie2016acelecoxib 22 µg/mL, 5 µg/mL PAA / HPMCAS / HPMCsame, 16 hPAA as no polymer; ≈19.0 and ≈20.0 µg/mL at 16 hR3
xie2017indomethacin, pH 2.2, 100 µg/mL HPMC; EPOsolvent-shift titration to 80 µg/mL, 37 °Csupersaturation held ≈1.5 h; crystals during the additionR5, R8
trasi2016tacrolimus 50 µg/mL, 50 µg/mL HPMCpH 4.5, 37 °Conset within 3 h against 6–8 hR9
que2018paclitaxel at S ≈88, 20 µg/mL HPMCAS, unseededinduction time, pH 6.8, 37 °Cwithin 6 min without polymer against more than 16 hR3
duong2022adelamanid at 0.76 µg/mL, 300 µg/mL PVPVA / HPMCP / HPMCAS / HPMC / Eudragit L100induction time, PBS pH 6.5, 37 °Cmore than 1000 min for the first three; ≈50 min; 10.2 against 10.7 min without polymerR4, R2
polyzois2024racemic praziquantel at 1.1 mg/mL, 300 µg/mL of seven polymersinduction time, PBS pH 6.5, 37 °C, 83-min run10.9–50.5 min for five polymers; at least 83 min for HPMCAS-MF and HPMC E5 LV (none: 5.5 min)R3
elkhabaz2019aposaconazole–HPMCAS 10% directly in FaSSIFdissolution, HPLC, 37 °Cabout 21 µg/mL held to 180 minR6

Figure

Fig. 3 of konno2008a: maximum felodipine concentration against polymer content for the three polymers
Fig. 3 · konno2008amaximum felodipine concentration against polymer content for the three polymers

The HPMCAS curve climbs steeply to 14.1 µg/mL at 75% polymer while PVP stays near the crystalline solubility up to 50% polymer konno2008a R10. Values above about 9.5 µg/mL lie above the paper's own amorphous-solubility estimate and are total UV-detected drug (F8) konno2008a X5.

Fig. 4 of jackson2015: crystallization induction times and LLPS onset concentrations of the danazol dispersions
Fig. 4 · jackson2015crystallization induction times and LLPS onset concentrations of the danazol dispersions

PVP bars are shortest and HPMCAS longest at every loading; the onset concentrations on the right lie near 8 µg/mL whatever the polymer jackson2015 R5.

Fig. 2 of xie2015: 22 µg/mL celecoxib with and without 5 µg/mL polymer over 8 h
Fig. 2 · xie201522 µg/mL celecoxib with and without 5 µg/mL polymer over 8 h

The polymer-free solution crashes within minutes, PVP-K12 falls after about 1 h and PVP-K29/32 after about 2 h, while HPMCAS, HPMC and the PVP plus HPMCAS pairs stay near 21 µg/mL xie2015 R1, R2.

Why

Konno and co-workers found that none of the polymers changed the crystalline solubility at 1 mg/mL, so that solubilization by complexation "can be discounted" and "it can be inferred" that the dispersions generate supersaturated solutions that the polymers maintain konno2008a C17, C22; they attribute the maintenance to slower crystal growth, which "most likely contributes" (F5) konno2008a C37. Alonzo and co-workers (2010) conclude that PVP is a poor inhibitor of felodipine crystallization from solution while HPMC and HPMC-AS inhibit it, "in excellent agreement" with Konno and co-workers alonzo2010 C11, C38; for indomethacin PVP "appears" to be an effective inhibitor of solution crystallization "at this temperature and supersaturation", and HPMC holding the 37 °C level better than PVP "could" reflect a lower driving force at its lower supersaturation alonzo2010 C22, C24, C25. Alonzo and co-workers (2011) read the faster growth of particles from PVP dispersions as HPMC inhibiting felodipine growth better alonzo2011 C18, C51. Jackson and co-workers conclude that the duration of supersaturation depends on the polymer and on the drug loading jackson2015 C15. For ritonavir the more hydrophobic, negatively charged cellulose polymers were effective and the more hydrophilic uncharged ones ineffective or less effective ilevbare2013d C30. For celecoxib, Xie and Taylor argue from classical nucleation theory that the polymer differences come neither from supersaturation, which they take as similar in all polymer solutions, nor from interfacial tension, which adsorbed polymer would lower, and suggest that the cellulose derivatives "may" interact more with dense liquid clusters of celecoxib than hydrophilic PVP, which also interacts with the solvent xie2015 C43, C44, C46; the effect "must be due to subtle molecular level interactions", and PAA's failure is "perhaps not particularly surprising" because the very hydrophilic polymer "is expected" to interact more with water than with celecoxib xie2016a C17, C18. For indomethacin HPMC's general effectiveness is attributed to its amphiphilic structure (cited), while EPO did not inhibit crystallization although it solubilizes the drug (F17) xie2017 C11, C2. For tacrolimus the induction times "suggest" that HPMC holds the supersaturation for a biologically relevant time trasi2016 C17. (synthesis: the six drugs were never compared on one scale; the crystallization-from-solution chapter relates growth and nucleation inhibition to the hydrophobicity of the polymer relative to the drug (Crystallization from solution F8, Crystallization from solution F13), which fits the failure of the very hydrophilic PAA and may be why the felodipine ranking does not carry over to indomethacin or ritonavir.) Duong and co-workers call PVPVA, HPMCP and HPMCAS "highly effective" for delamanid but find that PVPVA "shows disadvantages" because its drug-rich droplets grow (F12) duong2022a C12, C52. Polyzois and co-workers attribute the weaker effect of HPMCAS-LF and HPMC 603 than of the MF and E5 LV grades "likely" to functional group content and amphiphilicity, not measured polyzois2024 C25. Elkhabaz and co-workers judge HPMCAS "potentially an effective solution-crystallization inhibitor" for posaconazole when no matrix crystals are present elkhabaz2019a C52.

Conditions and limits

Felodipine at pH 6.8 and 37 °C (one dose, 30 mg in 600 mL), indomethacin at pH 2, danazol at 25 °C, ritonavir at 20 µg/mL with 5 µg/mL additive konno2008a X15; alonzo2010 P3; jackson2015 P2; ilevbare2013d P6. Polymer grades: PVP K29/32 or K30, HPMC 606, HPMCAS MF; molecular weights and substitution are not printed konno2008a M2, M3, M4; alonzo2010 M3, M4, M5. The felodipine maxima above about 9.5 µg/mL and the danazol UV peaks above 8 µg/mL include drug in particles (F8) konno2008a X5; jackson2015 C12. Celecoxib was tested at one polymer level (5 µg/mL) and one starting supersaturation, indomethacin at pH 2.2 only, tacrolimus at pH 4.5 with HPMC only xie2015 X8; xie2017 P4; trasi2016 P10; the crystalline solubility of celecoxib was measured with 22 µg/mL polymer, not the 5 µg/mL of the induction tests xie2015 X9.

Counterexamples and conflicts

For danazol the polymer changed how long supersaturation lasted, not how high the free drug went: every dispersion that formed a drug-rich phase gave 7.1–9.1 µg/mL by flux whatever the polymer (F7) jackson2015 R9. PVP in the medium delayed crystallization of the wetted felodipine solid at least as well as the cellulosics (F2) alonzo2010 C38. Among the 75% felodipine dispersions, PVP dissolved fastest at first konno2008a R11. In seeded growth PVP and PVPVA slowed celecoxib and efavirenz but not ritonavir growth, which agrees with the ritonavir result here ilevbare2013b R9. PVP is not without effect on celecoxib: it delayed nucleation by 1–2 h, longer for the higher molecular weight grade, and slowed the fall after nucleation xie2015 R1, C12. The enteric methacrylate Eudragit L100 had no effect on delamanid, and HPMC, effective for several drugs here, delayed delamanid only to about 50 min duong2022a R4. Even HPMCAS, which stopped paclitaxel nucleation for 16 h, only slowed growth on seeds (F22) que2018 C30. A ranking made with racemic praziquantel did not hold for its R-enantiomer (F29) polyzois2024 R4.

Transfer check

Rank the polymers for the new drug itself in a non-sink test at 37 °C, at the polymer concentration that complete release would give, after checking that the polymer leaves the crystalline solubility unchanged konno2008a P4, C6. Read the duration of supersaturation against the estimated amorphous solubility and check concentrations above it by a free-drug method (F7, F8). The felodipine order HPMCAS > HPMC > PVP is a hypothesis for another drug, not a rule: indomethacin and ritonavir gave other orders alonzo2010 R14; ilevbare2013d R12. Very hydrophilic polymers chosen for fast release (PAA, EPO in acid) should be expected to give no solution inhibition until tested xie2016a C14; xie2017 C2.

History

Before 2008 the same three polymers had been ranked for felodipine only in the solid state: alike when dry, HPMCAS and HPMC ahead of PVP with moisture (cited) konno2008a R18. Konno and co-workers (2008) ranked them first in the library by dispersion dissolution konno2008a C35. Alonzo and co-workers (2010) confirmed the felodipine ranking with the polymer in the medium and found PVP effective for indomethacin alonzo2010 C11, C22; Alonzo and co-workers (2011) added faster particle growth with PVP alonzo2011 C18; Ilevbare and co-workers (2013) found PVP without effect on ritonavir ilevbare2013d R12; Jackson and co-workers (2015) found the same order of duration for danazol at three loadings jackson2015 C19. Xie and Taylor (2015, 2016) found the cellulosic polymers far ahead of PVP and PAA for celecoxib, Trasi and co-workers (2016) found HPMC prolonging tacrolimus supersaturation, and Xie and co-workers (2017) found HPMC effective and EPO ineffective for indomethacin at pH 2.2 xie2015 C3; xie2016a C14, C15; trasi2016 C17; xie2017 C1, C2; the title gained celecoxib, PAA and EPO then. Que and co-workers (2018) found HPMCAS a "highly effective" nucleation inhibitor for paclitaxel, Duong and co-workers (2022) found PVPVA as good as the enteric cellulose esters and HPMC and Eudragit L100 poor for delamanid, and Polyzois and co-workers (2024) ranked seven polymers for praziquantel que2018 C13; duong2022a C12; polyzois2024 C7; the title gained praziquantel, PVPVA, Eudragit L100 and delamanid then.

F5

Topic 2Polymers and the duration of supersaturation2 of 4

Cellulosic polymers held supersaturated felodipine flat for hours; tests that separate the steps found nucleation inhibited far more than growth.

After a solvent shift to a nominal 50 µg/mL, felodipine with HPMC or HPMCAS read ≈6.8 µg/mL at 5 min and still ≈6.35 µg/mL at 240 min, while PVP and buffer solutions kept falling konno2008a R12. The 2008 authors read this as inhibited crystal growth konno2008a C26. Later tests that separated growth on seed crystals from nucleation (formation of new crystal nuclei) found HPMC and HPMCAS acting mainly on nucleation alonzo2012 R5, R17; xie2016a C40.

strongStrong for the concentration profiles and the paclitaxel contrast; weak to moderate for the 2008 growth reading, since no precipitate was examined and equal crystal surface areas were assumed konno2008a K3, K4, X4; que2018 K3.

Felodipine left at 240 min, µg/mL (nominal 50 µg/mL start)HPMCAS≈6.35HPMC≈6.35PVP≈1.9no polymer≈1.05

Solvent shift into pH 6.8 test fluid with 150 µg/mL polymer, 37 °C; every solution first dropped steeply within 5 min. konno2008a R12

Slowing of each step: polymer-free rate ÷ rate with polymerfelodipine growth1 µg/mL HPMC≈1.6×felodipine nucleation1 µg/mL HPMC≈1,400×celecoxib growth5 µg/mL HPMCAS≈70×celecoxib nucleation5 µg/mL HPMCAS~4000×

Felodipine ratios computed in the synthesis from 0.607 and 7.05 × 10⁻⁴ of the polymer-free rates; celecoxib nucleation from an induction time capped at 960 min. alonzo2012 R5, R17; xie2016a R12, R13

For your drug

  1. Run a seeded desupersaturation test and an unseeded induction-time test at the same supersaturation, below the amorphous solubility, and identify the precipitate by microscopy or diffraction.
  2. Do not read a flat plateau after an initial drop as growth inhibition by itself.

konno2008a X4; alonzo2012 R18

How it works and key numbers
  1. The authors "rationalize" the immediate drop as rapid nucleation, which the polymers "do not appear" to have prevented konno2008a C24, C25.
  2. After the drop the solution has, "it appears", moved into the metastable zone, where only growth could lower the concentration, so the flat plateau "strongly suggests" growth inhibition konno2008a C27, C26.
  3. The separating test compares growth on seeds with unseeded induction times: J_0/J_p = (R_p/R_0)^3 (t_{u,p}/t_{u,0})^4 xie2016a E6.
  4. With it, HPMC left felodipine growth on seeds at 0.607 of the polymer-free rate, and HPMCAS slowed celecoxib growth about 70-fold but nucleation about 4000-fold alonzo2012 R5; xie2016a R12, R13.
  5. (synthesis) The nominal 50 µg/mL start lies about five times above the estimated amorphous solubility of about 9.5 µg/mL, so the first drop need not be crystal nucleation konno2008a R17.
To feel the numbers. With a growth ratio of 70 and induction times of 5 min without and 960 min with HPMCAS, (1/70)^3 \times (960/5)^4 = 192^4 / 343{,}000 \approx 1.36 \times 10^9 / 343{,}000 \approx 3962, about 4000.
≈6.35 vs ≈1.05 µg/mLfelodipine at 240 min with HPMCAS against no polymerkonno2008a R12
0.607felodipine growth rate on seeds with 1 µg/mL HPMC, relative to no polymeralonzo2012 R5
6 min vs more than 16 hunseeded paclitaxel at S ≈88 without and with 20 µg/mL HPMCASque2018 R3
Evidence: data, conditions and papers

Finding F5. In supersaturated felodipine solutions the cellulose polymers held the concentration near its early level for hours after an initial drop, which the authors read as inhibited crystal growth; later felodipine, celecoxib and paclitaxel studies placed the main effect of HPMC and HPMCAS on nucleation

In short. After a solvent shift to a nominal 50 µg/mL every solution read about 6 µg/mL at 5 min; with 150 µg/mL HPMC or HPMCAS it was still ≈6.35 µg/mL at 240 min, with PVP ≈1.9 and without polymer ≈1.05 µg/mL konno2008a R12. Started at 9.5 and 15 µg/mL, the cellulose solutions held about 8–9 and about 11 µg/mL for the whole run konno2008a R14, R15. Initial slopes of the 9.5 µg/mL curves were ~0.1399 (buffer), ~0.0398 (PVP), ~0.0044 (HPMC) and ~0.0021 µg/mL-min (HPMCAS), read as growth rates on the assumption of equal crystal surface areas, and the authors conclude that the polymers "appeared to reduce" growth and "do not appear" to have prevented nucleation konno2008a R16, C28, C36, C25. With seeded and unseeded runs separated, 1 µg/mL HPMC left felodipine growth at 0.607 of the polymer-free rate but cut the estimated nucleation rate to 7.05 × 10⁻⁴ of it (synthesis: about 1.6-fold and 1,400-fold; Crystallization from solution F6) alonzo2012 R5, R17. For celecoxib at 22 µg/mL, 5 µg/mL HPMCAS slowed growth on seed crystals about 70-fold but nucleation an estimated ~4000-fold, and the authors conclude ("it can be surmised") that HPMCAS acts much more on nucleation than on growth xie2016a R12, R13, C40. For paclitaxel at S ≈88, 20 µg/mL HPMCAS held an unseeded solution for more than 16 h against 6 min without polymer, whereas seeded dispersions lost much of their supersaturation over 16 h, which the authors read as HPMCAS being "unable to completely block crystal growth" (F22) que2018 R3, R14, C30.

Type. observation in 3 drugs (felodipine with three polymers; celecoxib and paclitaxel with HPMCAS) Strength. for the concentration profiles (four runs, n = 3) and for the paclitaxel contrast between nucleation and growth konno2008a K3: strong; que2018 K3: strong; weak to moderate for the growth reading, since no precipitate was examined, surface areas were assumed equal and the slopes come from one panel konno2008a K4: weak to moderate, X4, X7; moderate for the celecoxib growth and nucleation ratios, which cannot be reproduced from the printed data and use an induction time capped at 960 min xie2016a K2: moderate, X8.

How it was shown

Konno and co-workers (2008) made felodipine solutions by solvent shift to nominal 50, 15 or 9.5 µg/mL in pH 6.8 test fluid with 150 or 50 µg/mL polymer or none, and ranked growth rates from initial slopes, assuming similar crystal surface areas konno2008a P5, P6, C28. Xie and Taylor (2016) compared seeded desupersaturation of celecoxib with unseeded induction times to separate growth from nucleation xie2016a P4, P11, P12.

What the data show

After an initial drop HPMC and HPMCAS held felodipine near its 5-min level while PVP and buffer declined; tests that separated the steps found nucleation inhibited more than growth konno2008a R12, R14; alonzo2012 R5, R17; xie2016a R12, R13.

systemtestresultids
felodipine nominal 50 µg/mL, 150 µg/mL polymersolvent shift, 5 → 240 min≈6.8 → ≈6.35 (HPMCAS, HPMC), ≈6.3 → ≈1.9 (PVP), ≈2.7 → ≈1.05 µg/mL (none)konno2008a R12
felodipine 9.5 µg/mL startinitial slopes, equal surface areas assumed~0.1399 (buffer), ~0.0398 (PVP), ~0.0044 (HPMC), ~0.0021 µg/mL-min (HPMCAS)konno2008a R16
felodipine S 10, 1 µg/mL HPMC (Crystallization from solution)seeded growth; unseeded induction timegrowth at 0.607 of the polymer-free rate; induction 15.3 → 136.5 minalonzo2012 R5, R16
celecoxib 22 µg/mL, 5 or 22 µg/mL HPMCASseeded desupersaturation; unseeded induction capped at 960 minR_0/R_p ≈70 and 158; J_0/J_p ~4000xie2016a R12, R13
paclitaxel at S ≈88, 20 µg/mL HPMCASunseeded induction time; seeded dissolution over 16 hmore than 16 h unseeded; ≈7.9–25.3 µg/mL left at 16 h with seedsque2018 R3, R14
Fig. 6 of konno2008a: supersaturated felodipine solutions started at 9.5 and 15 µg/mL with 150 µg/mL polymer
Fig. 6 · konno2008asupersaturated felodipine solutions started at 9.5 and 15 µg/mL with 150 µg/mL polymer

The cellulose polymers stay almost flat while PVP and buffer decline konno2008a R14, R15.

Why

Konno and co-workers read the immediate drop as rapid nucleation and the later plateau, in the metastable zone, as growth inhibition ("strongly suggests"); no precipitate was isolated or examined konno2008a C24, C27, C26, X4. For celecoxib the nucleation ratio follows from J_0/J_p = (R_p/R_0)^3 (t_{u,p}/t_{u,0})^4, and HPMCAS inhibited both steps, nucleation more xie2016a E6, R12, C40. (synthesis: the nominal 50 µg/mL start lies about five times above the estimated amorphous solubility of about 9.5 µg/mL konno2008a R17, so the immediate drop need not be crystal nucleation.)

Limits and transfer

The felodipine slopes come from one panel without uncertainty, and the celecoxib ratio uses an induction time taken as 960 min konno2008a X7; xie2016a R13. To locate the effect for a new drug, run a seeded desupersaturation test and an unseeded induction-time test at the same supersaturation, below the amorphous solubility, and identify the precipitate konno2008a X4; alonzo2012 R18.

How it was shown

Konno and co-workers (2008) added a small volume of felodipine in ethanol or methanol to 600 mL of pH 6.8 test fluid containing 150 or 50 µg/mL polymer (the levels that complete dissolution of 75% and 50% polymer dispersions would give) or none, to nominal 50, 15 or 9.5 µg/mL, at 37 °C and 100 rpm, with UV through a 70-µm filter or with second-derivative correction for scattering, n = 3 konno2008a P5, C6. From the initial linear part of each 9.5 µg/mL curve they took dMc/dt and, by Eq. 5, ranked growth rates assuming similar crystal surface areas konno2008a E5, P6, C28. The amorphous solubility was estimated at about 9.5 µg/mL (about 10 times the crystal) from the Hoffman equation with literature data konno2008a R17, E1, E2. Xie and Taylor (2016) suspended 7 mg of celecoxib seed crystals in 50 mL of pH 6.8 buffer at 37 °C with 0, 5, 11 or 22 µg/mL HPMCAS, added a methanol stock to 11 or 22 µg/mL and followed the fall in concentration by UV; the growth ratio R_0/R_p came from the initial slope without polymer and the slope over 16 h with polymer, and the nucleation ratio from these and the unseeded induction times xie2016a P4, P11, P12, E5, E6.

What the data show

50 µg/mL with 150 µg/mL polymer. HPMCAS ≈6.8 → ≈6.35 and HPMC ≈6.8 → ≈6.35 µg/mL over 240 min; PVP ≈6.3 → ≈1.9; no polymer ≈2.7 at 5 min → ≈1.05 konno2008a R12. 50 µg/mL with 50 µg/mL polymer. HPMCAS ≈6.4 → 6.0, HPMC ≈6.2 → 5.5, PVP ≈5.3 → 1.35 µg/mL konno2008a R13. 9.5 µg/mL. HPMCAS ≈9.1 → ≈8.5 and HPMC ≈8.95 → ≈7.8 µg/mL at about 210 min; PVP ≈8.1 → ≈2.8; no polymer ≈7.8 at 5 min, ≈4.3 at 30 min and ≈1.95 at the end konno2008a R14. 15 µg/mL. HPMCAS ≈11.1 → ≈10.45, HPMC ≈11.1 → ≈10.85, PVP ≈9.6 → ≈3.5, no polymer ≈3.1 → ≈1.8 µg/mL over 240 min konno2008a R15. The higher the start, the larger the drop by 5 min: about 86% of the nominal 50 µg/mL, 26% of 15 µg/mL and 4% of 9.5 µg/mL with HPMCAS (synthesis: (50 − 6.8)/50, (15 − 11.1)/15 and (9.5 − 9.1)/9.5 from the 5-min readings) konno2008a R12, R15, R14. The plotted buffer slope (≈7.8 → ≈4.3 µg/mL between 5 and 30 min) reproduces the printed ~0.14 µg/mL-min konno2008a E5. In the 2011 felodipine work, particles in methanol-shift solutions with HPMC grew from ≈183–203 nm at 5 min to ≈280–307 nm at 90 min at 25 °C, and precipitation at a supersaturation ratio of about 60 occurred even with HPMC present, which the authors read as nucleation not completely suppressed alonzo2011 R8, C30. Celecoxib. Without polymer seeded solutions fell from ≈22.5 to ≈4.0 µg/mL in 30 min with no lag; with HPMCAS they fell from ≈12.4 to ≈10.9 µg/mL in 4 h (11/11 µg/mL drug/polymer), to ≈19.8 (22/22) and to ≈16.0 µg/mL (22/5) xie2016a R11. The growth ratios were approximately 130, 158 and 70, less inhibition at the higher supersaturation and lower polymer level, and with no induction time seen in 16 h (taken as 960 min) the nucleation ratio J_0/J_p came to ~4000 xie2016a R12, R13, C37, by

\frac{J_0}{J_p} = \left(\frac{R_p}{R_0}\right)^{3}\left(\frac{t_{u,p}}{t_{u,0}}\right)^{4} xie2016a E6

which reproduces with an unseeded induction time of 5 min without polymer: (1/70)^3 \times (960/5)^4 \approx 3962 xie2016a E6.

papersystemmethod and conditionsresultids
konno2008afelodipine 50 µg/mL, 150 µg/mL HPMCAS / HPMC / PVP / nonesolvent shift, pH 6.8, 37 °C≈6.35 / ≈6.35 / ≈1.9 / ≈1.05 µg/mL at 240 minR12
konno2008afelodipine 9.5 µg/mL, 150 µg/mL polymersame7.8–8.9 (HPMC), 8.5–9.1 µg/mL (HPMCAS) for the run; PVP ≈2.8R14
konno2008afelodipine 15 µg/mL, 150 µg/mL polymersameabout 11 µg/mL held with both cellulosics; PVP ≈3.5 at 240 minR15
konno2008ainitial slopes, 9.5 µg/mL startE5, equal surface areas assumed~0.1399 / ~0.0398 / ~0.0044 / ~0.0021 µg/mL-minR16
alonzo2011felodipine methanol shift with HPMC, S about 60light scattering, 25 °Cparticles ≈183–203 → ≈280–307 nm in 90 minR8, C30
alonzo2012 (Crystallization from solution)felodipine S 10, 1 µg/mL HPMCseeded growth; unseeded induction timegrowth at 0.607 of the polymer-free rate; induction 15.3 → 136.5 minR5, R16
alonzo2012 (Crystallization from solution)felodipine, 1 µg/mL HPMC, seeded and unseededconcentration over 200 minunseeded ≈5.4 → 5.0 µg/mL; seeded ≈5.1 → 2.2 µg/mL in 58 minR18
xie2016acelecoxib 22 µg/mL seeded, 5 or 22 µg/mL HPMCAS; 11/11 µg/mLseeded desupersaturation, pH 6.8, 37 °CR_0/R_p ≈70 and 158; ≈130R11, R12
xie2016acelecoxib 22 µg/mL, 5 µg/mL HPMCASunseeded induction time capped at 960 min with growth ratioJ_0/J_p ~4000R13
que2018paclitaxel at S ≈88, 20 µg/mL HPMCAS; 49/51 dispersion with 18 wt% seedsunseeded induction time; seeded dissolution over 16 hmore than 16 h unseeded; ≈7.9–25.3 µg/mL left at 16 h with seedsR3, R14

Figure

Fig. 6 of konno2008a: supersaturated felodipine solutions started at 9.5 and 15 µg/mL with 150 µg/mL polymer
Fig. 6 · konno2008asupersaturated felodipine solutions started at 9.5 and 15 µg/mL with 150 µg/mL polymer

The cellulose polymers stay almost flat while PVP and buffer decline; the initial slopes of panel (a) are the growth estimates of R16, from curves that start at different 5-min levels konno2008a R14, R15, X7.

Why

The authors "rationalize" the immediate drop as rapid nucleation, faster and giving more particles at higher concentration, which the polymers "do not appear" to have prevented konno2008a C24, C25. After the drop the solution has, "it appears", moved from the labile into the metastable zone, where nucleation is no longer spontaneous and only crystal growth could lower the concentration further; that the concentration stays up "strongly suggests" that the cellulose polymers inhibit growth konno2008a C27, C26. They add that a high theoretical solubility ratio, by classical nucleation theory, means easy nucleation, so that amorphous felodipine dissolving alone "will be accompanied by rapid crystallization" ("These data suggest") konno2008a C20, C21. The mechanism rests on concentration curves alone: no precipitate was isolated or examined konno2008a X4. The crystallization-from-solution chapter separates the two steps for felodipine with HPMC: an unseeded solution at S 10 with 1 µg/mL HPMC barely changed over 200 min while a seeded one fell from about 5.1 to 2.2 µg/mL in 58 min, so HPMC acted mainly by delaying nucleation (Crystallization from solution F6, Crystallization from solution F20) alonzo2012 R18, R17. (synthesis: the nominal 50 µg/mL start lies about five times above the estimated amorphous solubility of about 9.5 µg/mL konno2008a R17, the range in which later papers find a non-crystalline drug-rich phase separating before crystals (Amorphous solubility and LLPS F1); the immediate drop therefore need not be crystal nucleation, and the long flat plateaus with HPMC and HPMCAS fit nucleation inhibition at least as well as growth inhibition.) For celecoxib, Xie and Taylor find HPMCAS "a less effective inhibitor of growth at a higher supersaturation", in agreement with the models cited, and use the slow seeded growth to explain why crystals formed in dissolving PAA particles did not empty a medium holding HPMCAS (F16) xie2016a C37, C36; because growth from seeds is harder to stop than nucleation, they call it "critical" to prevent crystals forming in the dissolving matrix xie2016a C70.

Conditions and limits

One drug, pH 6.8 test fluid, 37 °C, 100 rpm against 50 rpm in the dissolution tests, two UV set-ups without saying which run used which konno2008a X6. The slopes come from one panel without uncertainty, from curves that start at ≈9.0, ≈8.1 and ≈7.8 µg/mL konno2008a X7. PVP and buffer solutions declined toward but did not reach the crystalline solubility in 4 h, and the 9.5 µg/mL run ended at about 210 min konno2008a X10, X16. Statements that buffer solutions precipitated "within 5 min" hold for the 15 µg/mL run only konno2008a X11.

Counterexamples and conflicts

The growth reading is contradicted for HPMC by the seeded and unseeded felodipine tests of the crystallization-from-solution chapter (growth at 0.607 of the polymer-free rate, estimated nucleation-rate ratio 7.05 × 10⁻⁴) alonzo2012 R5, R17. For celecoxib the growth effect was not small: HPMCAS slowed seeded growth 70- to 158-fold, so here both steps were inhibited, nucleation more xie2016a R12, C40. That chapter also finds growth inhibition weakening as supersaturation rises (HPMC's Kubota–Mullin factor on felodipine falling from 0.7 at S 3 to 0.2 at S 12), in line with the larger losses here from the higher starts (Crystallization from solution F9) alonzo2012 R9. The abstract's lead of HPMCAS in the solution tests holds only at 50 µg/mL polymer and from 9.5 µg/mL; at 150 µg/mL HPMC matched HPMCAS konno2008a X3.

Transfer check

To learn whether a polymer acts on nucleation or on growth for a new drug, run a seeded desupersaturation test and an unseeded induction-time test at the same supersaturation, below the amorphous solubility so that no drug-rich phase forms, and identify the precipitate by microscopy or diffraction (Crystallization from solution F5) konno2008a X4; alonzo2012 R18. A flat plateau after an initial drop does not by itself locate the effect.

History

Similar solution profiles of nifedipine with HPMCAS and HPMC had been reported (cited) konno2008a R19. Konno and co-workers (2008) gave the library's first solvent-shift profiles of felodipine with the three polymers and the growth reading konno2008a C36. Alonzo and co-workers (2011) showed particles forming and growing in such solutions alonzo2011 R8. Alonzo and co-workers (2012), in the crystallization-from-solution chapter, revised the mechanism for HPMC by separating nucleation from growth alonzo2012 R17. Xie and Taylor (2016) applied the same seeded and unseeded comparison to celecoxib with HPMCAS within this chapter and found nucleation affected far more than growth xie2016a C40; the title gained celecoxib and HPMCAS then. Que and co-workers (2018) found the same split for paclitaxel with HPMCAS, a nucleation inhibitor that only slowed growth on seeds, and related the remaining growth to a critical two-dimensional nucleus smaller than the spacing of adsorbed polymer (F22) que2018 C36, C38; the title gained paclitaxel then.

F6

Topic 2Polymers and the duration of supersaturation3 of 4

A solution test with the polymer predissolved ranked polymers as dispersion dissolution did, but missed some polymers and additives.

Induction times measured with the polymer predissolved put PVP below the cellulosic polymers for felodipine, danazol and celecoxib, as dissolution of the dispersions did konno2008a C31; jackson2015 R5; xie2015 C48. The test missed HPMC for felodipine, a surfactant whose effect changed when the dispersion polymer leached, and crystallization inside dissolving PAA particles konno2008a R7; chen2015a R19, R14; xie2016a C31.

moderateModerate: the rank order agreed in four of five systems, but absolute times differed, the danazol comparator comes from a thesis, and the celecoxib comparisons have no statistical test konno2008a K6; jackson2015 K3, X16; chen2015a K5, X18.

solution with predissolved polymerdispersions 90:10 and 70:30PVP≈56–70≈111HPMC≈173≈188–200HPMCAS≈284–319≈3650100200300400danazol induction time, min

Same order in both tests, but the PVP dispersions crystallized after about half the solution time. jackson2015 R5, X8

Predicted by the solution test
felodipine PVP vs HPMCASdanazol ordercelecoxib 50% dispersionsPAA dispersions
Missed by the solution test
felodipine HPMCcelecoxib with Poloxamer 188PAA dispersionsdelamanid with PVPVA

PAA dispersions are in both lists: the test predicted their crash but not the crystals that formed in the particles. konno2008a C31, R7; jackson2015 C20; xie2015 C48; xie2016a C25, C31; chen2015a R19, C28; duong2022a C52

For your drug

  1. Screen polymers at the concentration the dispersion would release, and when screening surfactants include the dispersion polymer at the level that leaches from the particles.
  2. Use the screen to rank, then confirm the top two or three candidates by non-sink dissolution of the dispersion, with induction times expressed as ratios to a control in the same protocol.

konno2008a C6; chen2015a C26; jackson2015 X8

How it works and key numbers
  1. A polymer acts on two routes, the solution and the wetted solid, and a solution test covers only the first alonzo2010 C38, C45.
  2. Leached dispersion polymer changes the medium: with 3 µg/mL HPMCAS the Poloxamer 188 induction time rose from ≈12 to ≈50 min, which "most likely explains" the crystal-free suspension chen2015a R19, C28.
  3. Crystallization inside dissolving PAA particles stopped release at ≈9.7–11.6 of 22 µg/mL, even with an inhibitor in the medium xie2016a R9, C31.
  4. Droplet growth with PVPVA, which an induction time does not show, led the delamanid authors to prefer the enteric polymers duong2022a C52.
≈111 vs ≈56–70 mindanazol with PVP: solution test against dispersionsjackson2015 R5
4.9 vs 14.1 µg/mL75% HPMC against 75% HPMCAS felodipine dispersions, equal in solutionkonno2008a R7, R12
12 → ≈50 minPoloxamer 188 induction time without and with 3 µg/mL HPMCASchen2015a R12, R19
Evidence: data, conditions and papers

Finding F6. A solution test with the polymer predissolved predicted the polymer ranking during dispersion dissolution only as a rank order, and not for every polymer or additive

In short. For felodipine, the solvent-shift test agreed with dispersion dissolution for PVP and HPMCAS but not for HPMC, which matched HPMCAS in solution (≈6.35 µg/mL each at 240 min) yet reached 4.9 against 14.1 µg/mL from 75% dispersions; the authors call the reasons "not clear" konno2008a C31, C32, R12, R7. For danazol, dispersion induction times ranked PVP < HPMC < HPMCAS as antisolvent solutions did (≈111, ≈173 and ≈365 min), but the PVP dispersions crystallized after ≈56–70 min, about half the antisolvent value jackson2015 R5, X8. For celecoxib, Poloxamer 188 shortened the solution induction time to 12 min (88 min without surfactant), yet its suspension stayed crystal-free for 48 h; with 3 µg/mL HPMCAS added the induction time was ≈50 min chen2015a R12, R14, R19. For 50% celecoxib dispersions the solution test ranked the polymers as dissolution did (PVP-K12 failed first, then PVP-K29/32, the cellulosics not within the test), which the authors call "quite predictive" xie2015 C48, and it predicted the crash of PAA dispersions, but not that the drug of PAA dispersions crystallized in the particles even when an inhibitor was in the medium xie2016a C25, C31. For praziquantel the screen picked HPMCAS-MF and HPMC E5 LV, both beyond the 83-min run, but at 1.5 mg/mL their 30% dispersions released ≈94 and ≈74–77% polyzois2024 R3, R9; for delamanid PVPVA held the solution as long as the enteric polymers (more than 1000 min), but its drug-rich droplets grew duong2022a R4, R5.

Type. method comparison in 6 drugs (felodipine, danazol, celecoxib, indomethacin, praziquantel, delamanid) Strength. : the rank order agrees in four of the five systems, the absolute times differ, the danazol comparator comes from a thesis, and the celecoxib comparisons have no statistical test and use different polymer levels in the two tests konno2008a K6: moderate; jackson2015 K3: moderate, X16; chen2015a K5: weak to moderate, X18; xie2015 K7: moderate, X8.

How it was shown

Each paper set a solution test with the polymer or surfactant predissolved beside dissolution of the solid: felodipine solvent shifts against dispersion powder, danazol antisolvent solutions from a thesis against films, and celecoxib induction times against suspensions of spray-dried particles and against 50% dispersions konno2008a P5, P3; jackson2015 P7; chen2015a P9, P10; xie2015 P4, P5.

What the data show

The rank order mostly agreed, but HPMC with felodipine, Poloxamer 188 and the PAA matrix escaped the solution test konno2008a C31; chen2015a R14; xie2016a C31.

systemsolution testdispersion or suspensionids
felodipine, HPMC against HPMCASequal at 150 µg/mL (≈6.35 µg/mL each at 240 min)4.9 against 14.1 µg/mL from 75% dispersionskonno2008a R12, R7
danazol, PVP / HPMC / HPMCAS≈111 / ≈173 / ≈365 min (cited)≈56–70 / ≈188–200 / ≈284–319 minjackson2015 R5
celecoxib, Poloxamer 18812 min (88 min without surfactant); ≈50 min with 3 µg/mL HPMCASno crystals in 48 h in suspensionchen2015a R12, R19, R14
celecoxib, PVP-K12 / PVP-K29/32 / HPMCASonset ≈1 h / ≈2 h / more than 8 h50% dispersions ≈6.5 / ≈19.7 / ≈21.1 µg/mL at 16 hxie2015 R1, R6
celecoxib–PAA dispersionsPAA as no polymer; HPMCAS holds the solution 16 hcrash to ≈2.7 µg/mL; with HPMCAS in the medium release stops at ≈9.7–11.6 of 22 µg/mLxie2016a R3, R4, R9
praziquantel, HPMCAS-MF against HPMC E5 LVboth at least 83 min (run capped)30% dispersions at 1.5 mg/mL: ≈94 against ≈74–77%polyzois2024 R3, R9
Fig. 9 of chen2015a: celecoxib induction times with and without 3 µg/mL HPMCAS in three surfactant media
Fig. 9 · chen2015acelecoxib induction times with and without 3 µg/mL HPMCAS in three surfactant media

Only the Poloxamer 188 bars separate clearly: a trace of the ASD polymer changes the ranking a surfactant screen gives chen2015a R19.

Why

Konno and co-workers call HPMC "less predictable" konno2008a C31. The longer induction time with leached HPMCAS "most likely explains" the stable Poloxamer 188 suspension chen2015a C28. A polymer acts on two routes, so a test of the solution route can misrank it on the solid route, and the test cannot see crystallization inside PAA particles alonzo2010 C45; xie2016a C31. Droplet growth with PVPVA, which the induction time does not show, led the delamanid authors to prefer the enteric polymers duong2022a C52.

Limits and transfer

The tests differ in volume, stirring, polymer level and temperature from the dissolution runs they are compared with konno2008a X6; jackson2015 X2; chen2015a X13. Screen with the polymer at the concentration the dispersion would release, include the dispersion polymer when screening surfactants, and confirm the top candidates by non-sink dissolution of the dispersion konno2008a C6; chen2015a C26; jackson2015 X8.

How it was shown

Konno and co-workers (2008) compared solvent-shift solutions with 150 or 50 µg/mL predissolved polymer at 100 rpm against powder dissolution of the dispersions at 50 rpm, both at 37 °C in pH 6.8 test fluid konno2008a P5, P3, X6. Jackson and co-workers (2015) compared their film dissolution runs with antisolvent solutions of 15 µg/mL danazol with predissolved polymer taken from a thesis (100 µg/mL polymer in the tables, 10 µg/mL in the Fig. 4 legend) jackson2015 P7, X2, X16. Chen and co-workers (2015) measured celecoxib induction times after a methanol shift to S = 5 in 50 mL at 300 rpm and 25 °C in eight media, and compared them with 10 mg/mL suspensions of celecoxib–HPMCAS spray-dried particles in 10 mL at 150 rpm, then repeated the solution test in three media with 3 µg/mL HPMCAS, the lowest level expected to leach from the particles chen2015a P9, P10, A3, C26, X13. Alonzo and co-workers (2010) ran solvent-shift tests of indomethacin at 25 and 37 °C with PVP or HPMC alongside dissolution of the amorphous solid alonzo2010 P4. Xie and Taylor (2015, 2016) set induction-time tests of 22 µg/mL celecoxib with 5 µg/mL polymer beside non-sink dissolution of 50% (and 30%) drug dispersions dosed to 22 µg/mL in 400 mL, both in pH 6.8 buffer at 37 °C xie2015 P4, P5; xie2016a P3, P5. Xie and co-workers (2017) measured the amorphous solubility of indomethacin with HPMC or EPO by titration at pH 2.2 and dissolved the matching dispersions in the same buffer xie2017 P4, P7.

What the data show

Felodipine. At 150 µg/mL polymer HPMC and HPMCAS held the solution equally; at 50 µg/mL HPMC was slightly lower (≈5.5 against ≈6.0 µg/mL at 240 min) konno2008a R12, R13, C14. From the dispersions, 75% HPMC gave 4.9 µg/mL and 75% HPMCAS 14.1 µg/mL konno2008a R7. Danazol. ASD induction times (90:10, 70:30) were ≈70 and ≈56 min (PVP), ≈200 and ≈188 min (HPMC) and ≈284 and ≈319 min (HPMCAS), against ≈111, ≈173 and ≈365 min with predissolved polymer; the 50:50 HPMC and HPMCAS dispersions did not crystallize within 1440 min jackson2015 R5. Celecoxib. Solution induction times at S = 5 were 7 min (Polysorbate 80), 12 (Poloxamer 188), 41 (SDS 0.25%), 88 (no surfactant), 273 (Triton X100) and more than 960 min (STC 0.75%) chen2015a R12. In the suspensions crystals appeared at 0.5 h with SDS and 1 h with Polysorbate 80 and not within 48 h in the other four media, including Poloxamer 188 chen2015a R14. With 3 µg/mL HPMCAS the induction time went from ≈12 to ≈50 min with Poloxamer 188, from ≈41 to ≈26 min with SDS and from ≈7 to ≈5.3 min with Polysorbate 80 chen2015a R19. The surfactant-free suspension held S ≈4.3–6.7 for 48 h without crystals, although the solution test in the same medium crystallized after 88 min at S = 5 chen2015a R17, R12, X6. Indomethacin. The solvent-shift tests predicted that both polymers would largely inhibit solution crystallization at the levels reached by dissolving the amorphous solid; at 25 °C dissolution with PVP held ≈23.8 µg/mL for 4 h, but at 37 °C it fell to ≈13.7 µg/mL by 240 min alonzo2010 C29, R14. Celecoxib dispersions. The PVP-K12 dispersion peaked at ≈21.0 µg/mL near 6 h and fell to ≈6.5 µg/mL at 16 h, PVP-K29/32 held ≈19.7 µg/mL at 16 h, and the HPMCAS dispersion reached ≈21.1 µg/mL without falling, in the order of the induction times (≈1 h, ≈2 h, more than 8 h) xie2015 R6, R1. The PAA dispersions peaked at ≈9–11 µg/mL within 3 min and fell to ≈2.7 µg/mL, "in excellent agreement" with PAA's lack of effect in solution; with 5 µg/mL HPMCAS in the medium, which holds the solution for 16 h, release still stopped at ≈9.7–11.6 µg/mL of 22 xie2016a R4, C25, R9. Indomethacin at pH 2.2. EPO let the drug crystallize during the titration and the EPO dispersion crystallized within about 20 min (8.8 µg/mL in the filtered supernatant at 1 h); HPMC held the solution about 1.5 h and the HPMC 3:7 dispersion did not crystallize in the acid stage xie2017 R8, R11, R5, R13.

papersystemsolution testdispersion or solid dissolutionids
konno2008afelodipine, HPMC against HPMCASequal at 150 µg/mL (≈6.35 each at 240 min)4.9 against 14.1 µg/mL from 75% dispersionsR12, R7
jackson2015danazol PVP / HPMC / HPMCAS≈111 / ≈173 / ≈365 min (cited)≈56–70 / ≈188–200 / ≈284–319 min (90:10, 70:30)R5
chen2015acelecoxib, Poloxamer 18812 min; ≈50 min with 3 µg/mL HPMCASno crystals in 48 h in suspensionR12, R19, R14
chen2015acelecoxib, no surfactant88 min at S = 5S ≈4.3–6.7 for 48 h, no crystalsR12, R17, R14
alonzo2010indomethacin, PVPsolution held at both temperaturesheld 4 h at 25 °C; fell to ≈13.7 µg/mL at 37 °CC29, R14
xie2015celecoxib, PVP-K12 / PVP-K29/32 / HPMCASonset ≈1 h / ≈2 h / >8 h50% dispersions: ≈6.5 / ≈19.7 / ≈21.1 µg/mL at 16 hR1, R6
xie2016acelecoxib, PAA; PAA dispersion with HPMCAS in the mediumPAA as no polymer; HPMCAS holds 16 hcrash to ≈2.7 µg/mL; release stops at ≈9.7–11.6 of 22 µg/mLR3, R4, R9
xie2017indomethacin pH 2.2, EPO; HPMCcrystals during titration; ≈1.5 hEPO dispersion 8.8 µg/mL at 1 h (HPLC); HPMC 3:7 no crystallization in 1 hR8, R5, R11, R13
polyzois2024praziquantel, HPMCAS-MF against HPMC E5 LVboth at least 83 min (run capped)30% dispersions at 1.5 mg/mL: ≈94 against ≈74–77%R3, R9
duong2022adelamanid, PVPVA against HPMCP and HPMCASall more than 1000 min; PVPVA droplets ≈455 → ≈900 nmenteric polymers gave much more release than two neutral polymers (SI)R4, R5, R28

Figure

Fig. 9 of chen2015a: celecoxib induction times with and without 3 µg/mL HPMCAS in three surfactant media
Fig. 9 · chen2015acelecoxib induction times with and without 3 µg/mL HPMCAS in three surfactant media

Only the Poloxamer 188 bars (blue without, red with polymer) separate clearly: a trace of the ASD polymer changes the ranking a surfactant screen gives chen2015a R19.

Why

Konno and co-workers suggest a solution test "could be used" to screen polymers for a drug, find "a reasonable correlation" for PVP and HPMCAS, call HPMC "less predictable" and note the same behaviour of HPMC for nifedipine in earlier work konno2008a C30, C31, R19. Jackson and co-workers conclude that screening predicts the relative stability to crystallization "quite well" jackson2015 C20. Chen and co-workers suspected that leached HPMCAS would change the surfactant effect and conclude that the longer induction time "most likely explains" the stable Poloxamer 188 suspension, the real polymer level being "likely to be higher" chen2015a C25, C28. Alonzo and co-workers (2010) add that a polymer acts on two routes, so a test of one route (the solution) can misrank it on the other (the solid) (F2) alonzo2010 C38, C45. (synthesis: a solution test isolates what dissolved polymer or surfactant does to nucleation and growth at a fixed supersaturation; it leaves out how fast the dispersion releases drug, the supersaturation actually reached, and what dissolves out of the particles, which are where the HPMC, PVP and Poloxamer 188 discrepancies arise.) Xie and Taylor infer that, since the PVP and HPMCAS dispersions released completely, matrix crystallization was suppressed and the dissolution differences reflect solution crystallization, which the induction time measures ("it is apparent"); the HPMC-containing dispersions neither released fully nor were checked in the slurry xie2015 C39, X3. (synthesis: the PAA dispersions show the other blind spot of the solution test, crystallization of the wetted matrix, which no solution test can rank; see F16.) Polyzois and co-workers could not rank their two best polymers against each other because both reached the end of the 83-min run polyzois2024 K1. For delamanid, droplet growth with PVPVA, which the induction time does not show, led the authors to prefer the enteric polymers duong2022a C52.

Conditions and limits

The tests differ in volume, stirring, polymer level and temperature from the dissolution runs they are compared with konno2008a X6; jackson2015 X2; chen2015a X13. Error-bar type and replicates of the danazol induction times are not stated jackson2015 X8. The celecoxib HPMCAS comparison is one test per medium without statistics, and the SDS whiskers differ between two figures of the same mean chen2015a X18.

Counterexamples and conflicts

The crystallization-from-solution chapter finds induction times of one drug near its amorphous solubility differing up to about sixfold between protocols of the same group, so that inhibitor effects transfer only as ratios to a control run in the same protocol (Crystallization from solution F35). None found in the library in which a solution screen reversed the order of two polymers that the dispersion test separated widely, apart from HPMC against HPMCAS for felodipine and nifedipine konno2008a R19. A solid-state screen misled in the other direction: for resveratrol, PVP and E100, which had kept the dispersions amorphous at high humidity, kept them amorphous in buffer but gave no more dissolved drug than the crystal (42 and 46 against 42 µg/mL) wegiel2015 R21, R11, C9 (F17).

Transfer check

Screen with the polymer at the concentration the dispersion would release and, when screening surfactants or other excipients, include the dispersion polymer at the level that leaches from the particles konno2008a C6; chen2015a C26. Use the screen to rank, then confirm the top two or three candidates by dissolving the dispersion under non-sink conditions; express induction times as ratios to a control in the same protocol jackson2015 X8.

History

Konno and co-workers (2008) proposed the solution screen and found it imperfect for HPMC konno2008a C30, C32. Alonzo and co-workers (2010) showed that it covers only the solution route alonzo2010 C45. Jackson and co-workers (2015) confirmed the rank order for danazol and three loadings jackson2015 C20. Chen and co-workers (2015) showed that a surfactant screen without the ASD polymer misranks Poloxamer 188 chen2015a C28. Xie and Taylor (2015) found the induction times "quite predictive" for 50% celecoxib dispersions, and in 2016 that the test cannot see crystallization inside PAA particles xie2015 C48; xie2016a C31; Wegiel and co-workers (2015) found that a storage-stability ranking did not predict the concentration reached wegiel2015 C9, C35. Duong and co-workers (2022) added droplet size to the induction-time screen for delamanid duong2022a C13, and Polyzois and co-workers (2024) chose the praziquantel carriers by induction time and then found them far apart in release at the higher dose polyzois2024 C7, C17.

F29

Topic 2Polymers and the duration of supersaturation4 of 4

The polymers that held racemic praziquantel longest held its R-enantiomer far shorter; the inhibitor ranking did not carry over.

At their own amorphous solubilities with 300 µg/mL polymer, racemic praziquantel did not crystallize within the 83-min run with HPMCAS-MF or HPMC E5 LV, whereas R-praziquantel crystallized after 37 and 15.5 min polyzois2024 R3, R4. R-praziquantel released as well as or better than the racemate from HPMCAS-MF but lost dissolved drug from HPMC E5 LV polyzois2024 R12, R13; alvarenga2025 R8, C36.

moderateModerate for the loss of inhibition with the enantiomer, which is large but rests on n = 2 without a statistical test; weak to moderate for every proposed mechanism polyzois2024 K2, K6, X12; alvarenga2025 K5, K6.

racemateR-praziquantelno polymer≈55.5HPMC E5 LV15.583 or moreHPMCAS-MF3783 or more0153045607590praziquantel: minutes before crystallization

Each form at its own amorphous solubility (1.1 and 1.4 mg/mL) in PBS pH 6.5 with 300 µg/mL polymer; the run ended at 83 min. polyzois2024 R3, R4, R2

Released at 1.5 mg/mL from 30% dispersions, %R-praziquantel–HPMCAS-MF94racemate–HPMCAS-MF94R-praziquantel–HPMC E5 LVpeak, then fell to 6277 → 62racemate–HPMC E5 LV≈74–77

PBS pH 6.5; in 2025 R-praziquantel–HPMC also lost dissolved drug in every medium tested. polyzois2024 R12, R9; alvarenga2025 C36

For your drug

  1. For an enantiopure product, screen crystallization inhibitors with the enantiomer itself at its own amorphous solubility, not with the racemate.
  2. Measure crystalline and amorphous solubility of both forms in the test media, identify the solid form that crystallizes during release by PXRD and polarized light, and match the purity of the two forms before attributing differences to chirality.

polyzois2024 R4, C8, R1, C26; alvarenga2025 R3, C43, R25, R26, X17

How it works and key numbers
  1. The racemate crystallizes as an anhydrate with syn conformation and R-praziquantel as hydrates with anti conformation, which "may be attributed" to a different drug–polymer interaction polyzois2024 C26.
  2. It is "not unreasonable to speculate" that the chiral cellulose polymers bind S-praziquantel more polyzois2024 C28.
  3. Molecules of one handedness "can" pack more efficiently and nucleate faster, while in the racemate the counter-enantiomer acts as an "impurity" alvarenga2025 C40.
  4. (synthesis) R-praziquantel crystallized sooner although it was less supersaturated against its own crystal, about 5.0 against 5.6 for the racemate, so the difference does not come from a larger driving force on the crystal side polyzois2024 R1, R2.
  5. The better release of R-praziquantel from HPMCAS in PBS pH 6.5 "is likely attributable" to its higher amorphous solubility there (1.39 against 1.17 mg/mL) alvarenga2025 C42, R3.
83 or more vs 37 minHPMCAS-MF: racemate against R-praziquantel, time before crystallizationpolyzois2024 R3, R4
83 or more vs 15.5 minHPMC E5 LV: racemate against R-praziquantelpolyzois2024 R3, R4
77 → 62%R-praziquantel released from a 30% HPMC E5 LV dispersion, peak and endpolyzois2024 R12
Evidence: data, conditions and papers

Finding F29. The two polymers that held racemic praziquantel at its amorphous solubility beyond the 83-min test held the R-enantiomer only 37 and 15.5 min; R-praziquantel released as well as or better than the racemate from HPMCAS-MF but lost dissolved drug from HPMC E5 LV, so an inhibitor ranking made with the racemate did not carry over to the enantiomer

In short. At their amorphous solubilities (1.1 and 1.4 mg/mL in PBS pH 6.5) with 300 µg/mL polymer, racemic praziquantel did not crystallize within the 83-min run with HPMCAS-MF or HPMC E5 LV, whereas R-praziquantel crystallized after 37 ± 11 and 15.5 ± 1.6 min; without polymer both crystallized in about 5 min polyzois2024 R2, R3, R4. From 30% HPMCAS-MF dispersions at 1.5 mg/mL both forms released 94%, and at 40% R-praziquantel about 92.5 against 82.5% polyzois2024 R12, R9, R13; in 2025, R-praziquantel–HPMCAS reached about 88% (≈1.4 mg/mL) against 71% (≈1.1 mg/mL) for the racemate in PBS pH 6.5, but the two performed alike in fasted media alvarenga2025 R8, C43. From HPMC E5 LV, R-praziquantel peaked at 77% and fell to 62% in 2024 and lost dissolved drug in every medium at 1.5 mg/mL in 2025, the racemate only in biorelevant media polyzois2024 R12; alvarenga2025 C36. The authors call the inhibition of R-praziquantel "significantly less potent" and identify HPMCAS-MF as "the preferred polymer system" for it polyzois2024 C8, C40.

Type. single-system observation (praziquantel enantiomer against racemate, HPMCAS-MF and HPMC E5 LV), with a chiral melt-growth comparator Strength. for the loss of inhibition with the enantiomer (large, but n = 2 and no test) and for the better release of R-praziquantel from HPMCAS-MF (within the error bars at 40% drug); weak to moderate for the faster crystallization of R-praziquantel from HPMC dispersions, inferred from release curves, and for every proposed mechanism polyzois2024 K2: moderate, K4: moderate, K6: weak to moderate, X12, X13; alvarenga2025 K5: weak to moderate, K6: weak to moderate, X17.

How it was shown

Polyzois and co-workers (2024) timed crystallization of R- and racemic praziquantel, each at its own amorphous solubility in PBS pH 6.5, with 300 µg/mL of seven polymers over an 83-min run, and released HPMCAS-MF and HPMC E5 LV dispersions of both forms polyzois2024 P2, P3, P8. Alvarenga and co-workers (2025) extended the release tests to fasted and fed media with PLM and PXRD alvarenga2025 P9, P6, P5.

What the data show

The two best polymers for the racemate were much weaker for R-praziquantel, which released well from HPMCAS-MF but lost dissolved drug from HPMC E5 LV polyzois2024 R3, R4, R12; alvarenga2025 C36.

systemconditionsresultids
racemic praziquantel at 1.1 mg/mL, 300 µg/mL polymerinduction time, PBS pH 6.5, 37 °C, 83-min runnone 5.5; PVPVA 10.9 to HPMCAS-LF 50.5 min; HPMCAS-MF and HPMC E5 LV at least 83 minpolyzois2024 R3
R-praziquantel at 1.4 mg/mLsame, n = 2none ≈5; HPMC E5 LV 15.5; HPMCAS-MF 37 minpolyzois2024 R4
crystalline solubility, R- against racemicshake flask, PBS pH 6.5282.6 against 196.4 µg/mLpolyzois2024 R1
R- against racemic, HPMCAS-MF 30 / 40%release at 1.5 mg/mL94 against 94%; ≈92.5 against ≈82.5%polyzois2024 R12, R9, R13
same with HPMC E5 LV 30%samepeak 77% → 62% against ≈74–77%polyzois2024 R12, R9
R- against racemic, HPMCAS-MF 30% (2025)PBS pH 6.5, 1.5 mg/mL≈88 against 71% (≈1.4 against ≈1.1 mg/mL)alvarenga2025 R8
Fig. 2 of polyzois2024: induction times of racemic praziquantel with seven polymers and of R- against racemic praziquantel with the two best
Fig. 2 · polyzois2024induction times of racemic praziquantel with seven polymers and of R- against racemic praziquantel with the two best

With the racemate HPMC E5 LV and HPMCAS-MF reach the 83-min end of the run; with R-praziquantel the same two give only 15.5 and 37 min polyzois2024 R3, R4.

Why

Polyzois and co-workers give hedged reasons: the racemate crystallizes as an anhydrate with syn conformation and R-praziquantel as hydrates with anti conformation, which "may be attributed" to a different drug–polymer interaction, and it is "not unreasonable to speculate" that the chiral cellulose polymers bind S-praziquantel more polyzois2024 C26, C28. Alvarenga and co-workers propose that molecules of one handedness "can" pack more efficiently and nucleate faster, while in the racemate the counter-enantiomer acts as an "impurity" alvarenga2025 C40. (synthesis: R-praziquantel crystallized sooner although it was less supersaturated against its own crystal, about 1400/282.6 ≈ 5.0 against 1100/196.4 ≈ 5.6 for the racemate polyzois2024 R1, R2.)

Limits and transfer

The R-praziquantel induction times rest on n = 2, no statistical test was applied to release, and the two forms differ in purity polyzois2024 X12; alvarenga2025 X11, X17. For an enantiopure product, screen crystallization inhibitors with the enantiomer itself at its own amorphous solubility, measure both solubilities of both forms in the test media, and identify the solid form that crystallizes during release polyzois2024 R4, C8, R1, C26; alvarenga2025 R25, R26.

How it was shown

Polyzois and co-workers (2024) measured the crystalline solubility of R- and racemic praziquantel by shake flask in PBS pH 6.5 at 37 °C and the amorphous solubility by pumping a DMSO stock into PBS pH 6.5 or HCl pH 1.6 until light scattering rose polyzois2024 P1, P2. For the induction time they added the drug to its own amorphous solubility in PBS holding 300 µg/mL of one of seven polymers, and timed the appearance of scattering from crystals over an 83-min run (n = 3 for the racemate, n = 2 for R-praziquantel) polyzois2024 P3, X14. Solvent-evaporated dispersions of racemic praziquantel (20–50%) and R-praziquantel (30–40%) with HPMCAS-MF or HPMC E5 LV were released in 50 mL of PBS pH 6.5 at 667 µg/mL or 1.5 mg/mL with in situ UV (n = 3) polyzois2024 P4, P8. Alvarenga and co-workers (2025) made 30% dispersions of each form with each polymer by solvent evaporation and with HPMCAS by hot-melt extrusion, released them in buffers, fasted and fed media at 0.667 and 1.5 mg/mL in single- and two-stage tests, and looked for crystals by PLM and PXRD alvarenga2025 P3, P4, P9, P10, P6, P5. The racemate had a purity of 95%+ and R-praziquantel 99.9% alvarenga2025 M2, M1.

What the data show

Solubilities. Crystalline solubility in PBS pH 6.5 was 282.6 ± 3.3 µg/mL for R-praziquantel and 196.4 ± 0.3 µg/mL for the racemate, and amorphous solubility 1.4 ± 0.1 and 1.1 ± 0.1 mg/mL; at pH 1.6 both were 1.4 mg/mL polyzois2024 R1, R2. In the nine media of 2025 the amorphous-to-crystalline ratio was 4.0–5.8 for R-praziquantel and 5.6–7.7 for the racemate, lower because crystalline R-praziquantel is more soluble, and the amorphous solubilities differed significantly only in PBS pH 6.5 (1.39 against 1.17 mg/mL) alvarenga2025 R1, R3. Induction times. Racemate: none 5.5, PVPVA 10.9, HPC 14.3, PVA 15.7, HPMC 603 24.5, HPMCAS-LF 50.5 min, and HPMCAS-MF and HPMC E5 LV at least 83 min; R-praziquantel: about 5 min without polymer, 15.5 min with HPMC E5 LV, 37 min with HPMCAS-MF polyzois2024 R3, R4. Release from HPMCAS-MF. At 1.5 mg/mL both forms released 94% at 30% drug; at 40% drug R-praziquantel reached about 92.5% and the racemate about 82.5%, with racemate error bars of about ±11 polyzois2024 R12, R9, R13, X13. In 2025, at 1.5 mg/mL in PBS pH 6.5, R-praziquantel reached about 88% (maximum ≈1.4 mg/mL) against 71% (≈1.1 mg/mL) for the racemate, and after the pH 1.6 shift 91% against 73%; at 0.667 mg/mL and in fasted media the two released alike alvarenga2025 R8, R9, C43. After the pH 3.0 shift at 1.5 mg/mL R-praziquantel also ended higher (about 58 against 46%) alvarenga2025 R11, X13. Release from HPMC E5 LV. In 2024, R-praziquantel at 30% drug peaked at 77% at about 25 min and fell to 62%, while the racemate stayed at about 74–77% polyzois2024 R12, R9. In 2025, R-praziquantel–HPMC fell from 65 to 60% in PBS pH 6.5, from maxima of about 68% and 72% to about 58% after pH 3.0 and 5.0 starts, by 30% after 75% in FaSSIF, and from about 47 to 34% in FeSSIF-V2, whereas the racemate stayed level or rose in aqueous media alvarenga2025 R8, R11, R14, R18, C36. PLM showed birefringent needles and aggregates in R-praziquantel–HPMC samples at 60 and 120 min in all four aqueous protocols, and PXRD of HPMC residues gave clear R-praziquantel peaks against weak racemate peaks alvarenga2025 R20, R25, R26.

papersystemmethod and conditionsresultids
polyzois2024racemic praziquantel at 1.1 mg/mL, 300 µg/mL polymerinduction time, PBS pH 6.5, 37 °C, 83-min runnone 5.5; PVPVA 10.9 to HPMCAS-LF 50.5 min; HPMCAS-MF and HPMC E5 LV at least 83 minR3
polyzois2024R-praziquantel at 1.4 mg/mLsame, n = 2none ≈5; HPMC E5 LV 15.5; HPMCAS-MF 37 minR4
polyzois2024R- against racemic praziquantel, HPMCAS-MF 30 / 40%release at 1.5 mg/mL94 against 94%; ≈92.5 against ≈82.5%R12, R9, R13
polyzois2024same with HPMC E5 LV 30%samepeak 77% → 62% against ≈74–77%R12, R9
alvarenga2025R- against racemic praziquantel, HPMCAS-MF 30%PBS pH 6.5, 1.5 mg/mL; pH 1.6 → 6.5≈88 against 71% (≈1.4 against ≈1.1 mg/mL); 91 against 73%R8, R9
alvarenga2025same with HPMC E5 LVall media, 1.5 mg/mLR-praziquantel lost dissolved drug in every medium; the racemate only in biorelevant mediaC36, R8, R14
alvarenga2025both formssolubility in nine mediaamorphous-to-crystalline ratio 4.0–5.8 (R) against 5.6–7.7 (racemate)R1
sato2015 (Physical stability)R- and S-enantiomers of a chiral amino alcohol with 5% polymerspherulite growth from the melt, 60 °CHPMCAS slowed one enantiomer about twice as much as the other, the favoured one switching between LF and HF grades; PVP and HPMCP slowed both alikeC10, C11

Figure

Fig. 2 of polyzois2024: induction times of racemic praziquantel with seven polymers and of R- against racemic praziquantel with the two best
Fig. 2 · polyzois2024induction times of racemic praziquantel with seven polymers and of R- against racemic praziquantel with the two best

In (a) HPMC E5 LV and HPMCAS-MF reach the 83-min end of the run with the racemate; in (b) the same two polymers give only 15.5 and 37 min with R-praziquantel polyzois2024 R3, R4.

Fig. 5 of alvarenga2025: polarized light images of R-praziquantel–HPMC during aqueous release
Fig. 5 · alvarenga2025polarized light images of R-praziquantel–HPMC during aqueous release

Few particles at 5 min and birefringent needles and aggregates at 60 and 120 min in all four protocols alvarenga2025 R20.

Why

Polyzois and co-workers give hedged reasons for the weaker inhibition of R-praziquantel: the racemate crystallizes as an anhydrate with syn conformation and R-praziquantel as hydrates with anti conformation, which "may be attributed" to a different drug–polymer interaction; water bound to an R-praziquantel carbonyl "may" reduce interaction with the polymer; and it is "not unreasonable to speculate" that the chiral cellulose polymers bind S-praziquantel more polyzois2024 C26, C27, C28. The fall of R-praziquantel release from HPMC E5 LV is attributed "likely" to crystallization, consistent with its short induction time with that polymer; no crystals were looked for in 2024 polyzois2024 C20. Alvarenga and co-workers read the HPMC curves as indicating that R-praziquantel crystallizes more readily from highly supersaturated solution ("indicate"), propose that molecules of one handedness "can" pack more efficiently and nucleate faster while in the racemate the counter-enantiomer acts as an "impurity", and that the driving force "likely" differs between the solid forms that crystallize alvarenga2025 C25, C40, C39. Bile salts "may" also have sped R-praziquantel crystallization in FaSSIF alvarenga2025 C37. The better release of R-praziquantel from HPMCAS in PBS pH 6.5 "is likely attributable" to its higher amorphous solubility there, and the two forms behaved alike in fasted media because bile salts raise the solubility of both alvarenga2025 C42, C43. Nucleation and growth rates were not measured, the crystal forms in the residues were not identified, and the two drugs differ in purity alvarenga2025 X14, X17. (synthesis: R-praziquantel crystallized sooner although it was less supersaturated against its own crystal at the amorphous solubility, about 1400/282.6 ≈ 5.0 against 1100/196.4 ≈ 5.6 for the racemate polyzois2024 R1, R2, so the difference does not come from a larger driving force on the crystal side. A polymer that discriminates between enantiomers in crystal growth was already shown for HPMCAS in a melt sato2015 C11, and the ranking of polymers depends on the drug as it does across drugs in Crystallization from solution F13; an enantiomer is, for this purpose, another drug.)

Conditions and limits

One drug pair, two cellulose polymers for the dispersions, one 83-min induction run per system; the two forms were tested at their own amorphous solubilities, so at different concentrations polyzois2024 X14. R-praziquantel induction times rest on n = 2 and no statistical test was applied to release polyzois2024 X12; alvarenga2025 X11. The 1.5 mg/mL aqueous and fasted curves of 2025 are given only in the text alvarenga2025 X1. Long-term physical stability of the R-praziquantel dispersions was not determined, and the 20% HPMCAS-MF racemate dispersion showed small crystalline peaks after 21 weeks at 40 °C/75% RH polyzois2024 C41, R7. R-praziquantel was not extruded in 2024 and only in two conditions in 2025 polyzois2024 C32; alvarenga2025 A3.

Counterexamples and conflicts

The R-praziquantel advantage from HPMCAS-MF at 40% drug lies within the racemate error bars polyzois2024 X13. In FeSSIF-V2 the authors report no significant difference between the forms, without a test, beside an HPMC pair at about 34 against 48% (F28) alvarenga2025 C38, X11. In the melt study of the Physical stability chapter the racemate grew more slowly than either enantiomer and each polymer inhibited the racemate less than the enantiomer sato2015 C12, whereas in solution here the polymers protected the racemate far longer polyzois2024 R3, R4.

Transfer check

For an enantiopure product, screen crystallization inhibitors with the enantiomer itself at its own amorphous solubility, not with the racemate polyzois2024 R4, C8. Measure crystalline and amorphous solubility of both forms in the test media, since the enantiomer's crystal may be more soluble and its gain may appear only in simple buffer polyzois2024 R1; alvarenga2025 R3, C43. Identify the solid form that crystallizes during release (PXRD of residues, polarized light), since hydrate and anhydrate forms differ between enantiomer and racemate polyzois2024 C26; alvarenga2025 R25, R26. Match the purity of the two forms before attributing differences to chirality alvarenga2025 X17.

History

In the Physical stability chapter, Sato and co-workers (2015) found HPMCAS discriminating between the enantiomers of a chiral compound in melt growth while PVP and HPMCP did not sato2015 C10, C11. Polyzois and co-workers (2024) were the first in the library to compare polymer inhibition and dispersion release for an enantiomer and its racemate, and found both best polymers much weaker for the enantiomer polyzois2024 C8, C39. Alvarenga and co-workers (2025) confirmed the HPMC failure with R-praziquantel by PLM and PXRD in all aqueous protocols and found the HPMCAS advantage of R-praziquantel limited to simple buffer and the pH 1.6 and 3.0 shifts alvarenga2025 C25, C42, C43, R11.

Topic 3 of 8 · 4 findings · F7–F9, F17

Ceiling and the colloid it leaves

F7

Topic 3Ceiling and the colloid it leaves1 of 4

A dispersion that dissolves past the amorphous solubility does not raise the free drug above it.

Methods that detect only dissolved drug (membrane flux, solution NMR, ultracentrifugation) put dispersions of felodipine, danazol, ritonavir and lopinavir, and six marketed tacrolimus capsules, at about their amorphous solubility, the concentration above which a drug-rich liquid phase separates alonzo2011 R14; jackson2015 R9; trasi2015b R13; li2018 R3; trasi2016 R10.

moderateModerate: several particle-blind methods agree, but no statistical test supports "the same", the felodipine reference is a single run, and the tacrolimus product flux is given only as a range alonzo2011 K1, X4; jackson2015 K2; trasi2016 K3, X7.

free or dissolved drug from the dispersionsdanazolPVP, HPMC, HPMCAS dispersions87.1–9.1lopinavir–HPMC15–85% drug17.417.5–18.9ritonavir–HPMCAS20% drug25≈26.9tacrolimus capsulessix products465046–500102030405060concentration, µg/mL

Dashed ticks: the amorphous solubility of each drug in the same medium (for tacrolimus the range of five methods). jackson2015 R9, M1; li2018 R3, R1; trasi2015b R13, M1; trasi2016 R10, R4

Felodipine: membrane flux relative to the crystal90:10 HPMC dispersion10.550:50 HPMC dispersion9.5pure amorphous felodipine8.5predicted amorphous advantageabout 9

UV read the 90:10 dispersion about three times higher than the 50:50 one (F8); the flux did not. alonzo2011 R14, M1, X2

For your drug

  1. Above the estimated amorphous solubility, measure free drug by flux across a membrane that excludes droplets, by solution NMR or by ultracentrifugation, and expect a plateau at the amorphous solubility.
  2. Read a plateau clearly below it as slow release, a second drug or a polymer mixed into the drug-rich phase, and one above it as counted particles or a solubilizing polymer; do not design for free drug above the amorphous solubility.

alonzo2011 P4; jackson2015 P4; trasi2015b P9; trasi2016 C46

How it works and key numbers
  1. A dispersion can dissolve to above the amorphous solubility, but only briefly: a drug-rich phase forms rapidly, in metastable equilibrium with the water-rich phase jackson2015 C27, C31.
  2. That equilibrium fixes the free drug at the amorphous solubility, so above it added drug only forms more drug-rich phase jackson2015 C31; trasi2016 C37.
  3. Membrane transport follows the activity of the free drug, so the flux levels off at the same concentration trasi2016 C36.
  4. A polymer that does not dissolve and stays mixed with the drug lowered the lopinavir cap, to ≈0.3–0.6 µg/mL at 15% drug (F18) li2018 R3.
To feel the numbers. Each tacrolimus capsule put 5 mg into 40 mL, 125 µg/mL if all dissolved, which is 125 ÷ 50 = 2.5 times the ceiling; at least (125 − 50) ÷ 125 = 60% of the dose therefore stayed outside the free solution.
7.1–9.1 vs 8 µg/mLfree danazol by flux from every dispersion with a drug-rich phase, against its amorphous solubilityjackson2015 R9, M1
≈46–50 µg/mLplateau of six marketed tacrolimus capsules, equal to the amorphous solubilitytrasi2016 R10, R4
10.5 / 9.5 / 8.5felodipine flux ratios (90:10, 50:50, pure amorphous) against a predicted 9alonzo2011 R14, M1
Evidence: data, conditions and papers

Finding F7. Dissolving a dispersion past the amorphous solubility did not raise the free drug above it: flux, NMR and ultracentrifugation put felodipine, danazol, ritonavir, lopinavir and the tacrolimus of six marketed capsules at about their amorphous solubility, whatever the drug loading or the dissolving polymer

In short. Receiver slopes relative to crystalline felodipine were 10.5 ± 1.2 for a 90:10 HPMC dispersion, 9.5 ± 1.8 for a 50:50 dispersion and 8.5 ± 1.8 for pure amorphous felodipine, against a predicted amorphous advantage of about 9, although UV read the 90:10 dispersion about three times higher alonzo2011 R14, M1, R1, X2. Every danazol dispersion that formed a drug-rich phase gave 7.1–9.1 µg/mL free drug by flux, like antisolvent solutions (7.2–8.2), against an amorphous solubility of 8 µg/mL, even where UV read ≈16.2 µg/mL jackson2015 R9, R2, M1. Ultracentrifuged ritonavir and lopinavir dispersions plateaued at ≈26.9 and ≈17.8 µg/mL (HPMCAS) against cited amorphous solubilities of 25 and 17 µg/mL trasi2015b R13, M1, M2; lopinavir–HPMC dispersions gave ≈17.5–19 µg/mL at every loading from 15 to 85% against 17.4 µg/mL at pH 3 li2018 R3, R1. Six marketed 5-mg tacrolimus capsules, the innovator and five generics, all levelled off at ≈46–50 µg/mL in 40 mL against an amorphous solubility of 46–50 µg/mL measured four ways, and their solutions crossed a membrane at 0.0048–0.0054 µg/min, on the plateau of the pure drug trasi2016 R10, R4, R15, R14. The authors conclude that the maximum achievable supersaturation of an ASD "is dictated by the LLPS concentration" jackson2015 C38, and that "at least in the case of tacrolimus" the maximum concentration of marketed formulations can be predicted from the amorphous solubility trasi2016 C45.

Type. observation in 5 drugs (felodipine, danazol, ritonavir, lopinavir, tacrolimus), with total concentrations at about the same limit for paclitaxel, posaconazole and praziquantel Strength. : two particle-blind methods agree for felodipine, the danazol fluxes are triplicates and five methods agree on the tacrolimus ceiling, but no statistical test supports "the same", the felodipine normaliser is a single run, the danazol PVP and HPMC dispersions sit at 7.1–7.3 against 8.7–9.1 µg/mL, and the tacrolimus product flux is given only as a range across six products alonzo2011 K1: moderate, X4, X5; jackson2015 K2: moderate, X7; trasi2015b K2: strong; trasi2016 K2: strong, K3: moderate to strong, X7.

How it was shown

Free drug was measured by dialysis flux and solution ¹H NMR for felodipine, by side-by-side flux for danazol and by ultracentrifugation for ritonavir and lopinavir alonzo2011 P4, P7; jackson2015 P4; trasi2015b P9; li2018 P5. Trasi and co-workers (2016) dissolved the contents of six marketed 5-mg tacrolimus capsules in 40 mL of pH 4.5 buffer at 37 °C and measured membrane mass flow trasi2016 P11, P9.

What the data show

Each dispersion with a dissolving polymer settled at about its amorphous solubility, whatever the drug loading or the polymer jackson2015 R9; trasi2015b R13; li2018 R3; trasi2016 R10.

drug and systemmethodfree drug against limitids
felodipine 90:10 and 50:50 HPMC dispersions; pure amorphousdialysis flux ratio to the crystal, 37 °C10.5 / 9.5 / 8.5 against about 9alonzo2011 R14, M1
danazol dispersions with LLPS (PVP, HPMC, HPMCAS)side-by-side flux, 25 °C7.1–9.1 against 8 µg/mLjackson2015 R9, M1
ritonavir; lopinavir, HPMCAS / PVP dispersionsultracentrifuged, 2 h≈26.9 / ≈22.0 against 25; ≈17.8 / ≈15.9 against 17 µg/mLtrasi2015b R13, M1, M2
six marketed tacrolimus capsules0.45-µm filtrate HPLC; membrane flux≈46–50 against 46–50 µg/mL; 0.0048–0.0054 µg/min against a pure-drug plateau of ≈0.0050–0.0055trasi2016 R10, R4, R15, R14
lopinavir–HPMC films, 15–85% drugultracentrifuged, pH 3, 48 h≈17.5–18.9 against 17.4 µg/mLli2018 R3, R1
Fig. 8 of trasi2016: membrane mass flow of tacrolimus solutions against concentration, with the band of the six dissolved products
Fig. 8 · trasi2016membrane mass flow of tacrolimus solutions against concentration, with the band of the six dissolved products

Pure-drug flux rises up to 50 µg/mL and then levels off; the band of the dissolved products lies on that plateau trasi2016 R14, R15.

Why

A drug-rich phase in metastable equilibrium with the water-rich phase forms rapidly and fixes the free drug at the amorphous solubility, so all dispersions that undergo LLPS "should" give the same flux jackson2015 C27, C31. Membrane transport follows the activity of the free drug, so drug added above the amorphous solubility only forms more drug-rich phase trasi2016 C36, C37. For felodipine the authors add that the equality "may be purely coincidental" alonzo2011 C48.

Limits and transfer

The danazol fluxes are relative, and the tacrolimus products were tested in one buffer with unknown drug loadings jackson2015 X4; trasi2016 P11, X4. A polymer that does not dissolve and is mixed with the drug lowers the cap (F18) li2018 R3. Above the estimated amorphous solubility, measure free drug by flux, solution NMR or ultracentrifugation, and do not design for free drug above it alonzo2011 P4; jackson2015 P4; trasi2015b P9.

How it was shown

Alonzo and co-workers (2011) dissolved 90:10 and 50:50 HPMC–felodipine dispersions, pure amorphous felodipine and crystalline felodipine in a 300 mL donor at 37 °C; after the donor UV plateau (about 40 min for amorphous solids) a dialysis bag with 10 mL buffer containing 500 µg/mL HPMC and a second UV probe was immersed, and the receptor slope over 10–40 min was divided by the crystalline slope; methanol-shift solutions at nominal 5 and 10 µg/mL checked that flux scales with concentration alonzo2011 P4, C9. Solution ¹H NMR of 50-min samples, which sees only mobile dissolved molecules, compared the aromatic felodipine signal of the two dispersions alonzo2011 P7, C27. Jackson and co-workers (2015) dissolved danazol dispersions in the 200 mL donor of a side-by-side diffusion cell with a regenerated cellulose membrane (6–8 kDa) at 25 °C, took the flux from the receiver slope after the donor peaked and before crystallization, and converted it to free drug with a standard curve of solutions of known supersaturation jackson2015 P4. Trasi and Taylor (2015) dissolved 20% ritonavir and lopinavir dispersions in PVP and HPMCAS in 100 mM pH 6.8 buffer and assayed the supernatant after ultracentrifugation at 40,000 rpm for 20 min, at 20 min and 2 h trasi2015b P9, P5. Ilevbare and co-workers (2013) measured the ritonavir LLPS concentration by turbidity titration with 180 µg/mL polymer, the level a dissolved 10:90 dispersion would give ilevbare2013d P2. Trasi and co-workers (2016) measured the amorphous solubility of tacrolimus in 5 mM pH 4.5 phosphate buffer at 37 °C by UV scattering, pyrene fluorescence, 0.22-µm filtration, ultracentrifugation and film dissolution, dissolved the whole contents of each of six 5-mg capsules in 40 mL of the same buffer (125 µg/mL if all dissolved) with HPLC of 0.45-µm filtrates, and measured the mass flow rate across a regenerated cellulose membrane (12–14 kDa) from pure-drug solutions of 20–100 µg/mL and from capsule contents dissolved for an hour in 30 mL trasi2016 P3–P8, P11, P9. Li and Taylor (2018) cast lopinavir–HPMC films at 15–85% drug in vials and stirred them in 10 mL of pH 3 citrate buffer holding 20 µg/mL HPMC at 25 °C for 48 h, ultracentrifuging the samples, against an amorphous solubility from an HPMC film and from the LLPS onset li2018 P4, P5, P2, P3.

What the data show

Felodipine. The controls behaved as the flux equation requires: 10 and 5 µg/mL gave ratios of 10.0 ± 3.4 and 4.8 ± 0.39, slopes in the ratio 2.07 alonzo2011 R14, E1. The slopes were 0.0858 ± 0.0094 (90:10), 0.0782 ± 0.015 (50:50) and 0.0698 ± 0.015 (pure amorphous) against 0.0082 for the crystal (n = 1) alonzo2011 R14. In UV the 90:10 donor read ≈27.0 µg/mL and the 50:50 donor ≈8.9 µg/mL at 60 min, and the pure amorphous donor ≈8.6 µg/mL alonzo2011 R12. The NMR integrals were 1370 and 1014, a difference of about 26%, not threefold alonzo2011 R15. Danazol. Free drug was 7.3 ± 1.0 and 7.1 ± 1.1 µg/mL for 90:10 and 50:50 PVP, 8.7 ± 1.2 and 9.1 ± 1.6 for 90:10 and 50:50 HPMC and 8.2 ± 1.2 for 90:10 HPMCAS; antisolvent solutions gave 8.1 ± 1.2 without and 7.2–8.2 µg/mL with polymer; crystalline danazol 1.0 ± 0.1 µg/mL jackson2015 R9. The 50:50 HPMCAS dispersion, which did not form a drug-rich phase, gave 5.4 ± 0.8 µg/mL (F10) jackson2015 R9. Ritonavir and lopinavir. At 2 h the single-drug dispersions gave ritonavir ≈26.9 (HPMCAS) and ≈22.0 µg/mL (PVP) and lopinavir ≈17.8 and ≈15.9 µg/mL; drug-only films reached 22.9 and 15.6 µg/mL after 60 min trasi2015b R13, R5. The RTV–PVP dispersion was the one that stayed below its amorphous solubility, at about 22 µg/mL even after 2 h trasi2015b C29. Polymers and the ritonavir limit. With 180 µg/mL PVP, PAA, HPMC or HPMCAS the LLPS concentration was 18.3, 18.3, 18.7 and 18.2 µg/mL against 18.2 ± 0.35 µg/mL without polymer; CAAdP 0.85 gave 21.3 ± 1.22 µg/mL ilevbare2013d R10. In the LLPS chapter, a 1:9 ritonavir–PVP dispersion added in portions stalled at 18.3 and 18.0 µg/mL with 24.0 µg/mL added ilevbare2013a R17. Tacrolimus. The crystalline solubility was 1.4 µg/mL and the amorphous solubility 46 (scattering), 40–50 (pyrene), 50 (filtration), 49 (ultracentrifugation) and 48 µg/mL (film), a ratio of about 35, which the authors place near the middle of the 5–65 range of other drugs (cited) trasi2016 R4, R16, R17; the LLPS chapter finds the ratio running from about 2 to about 600 across drugs (Amorphous solubility and LLPS F6). At 5 min the products ranged from ≈26 (Prograf) to ≈41 µg/mL (Accord); all reached their maximum within about 45 min, read ≈46–50 µg/mL from 45 to 120 min and did not fall trasi2016 R10, C18, C30. The product containing sodium lauryl sulfate reached the same plateau trasi2016 M10, R10. Pure-drug flux rose from ≈0.0027 µg/min at 20 µg/mL to ≈0.0047 at 50 µg/mL and stayed at ≈0.0050–0.0055 µg/min from 60 to 100 µg/mL trasi2016 R14. Lopinavir with a dissolving polymer. HPMC dispersions gave ≈18.1–19.0 µg/mL at 3 h and ≈17.5–18.9 µg/mL at 48 h at 15–85% drug, against 17.4 ± 0.3 (HPMC film) and 18 ± 2 µg/mL (LLPS onset); a physical mixture of amorphous lopinavir and HPMCAS also reached ≈17–18.5 µg/mL li2018 R2, R3, R1, R14. Later papers. A paclitaxel–HPMCAS dispersion reached ≈31–33 µg/mL with or without seeds against an amorphous solubility of 31.6 µg/mL que2018 R13, R1, posaconazole–HPMCAS dispersions ≈21–24 µg/mL against an LLPS onset of about 20 µg/mL in FaSSIF elkhabaz2019a R6, R7, R2, and R- and racemic praziquantel–HPMCAS dispersions maxima of about 1.4 and 1.1 mg/mL against 1.39 and 1.17 mg/mL in PBS pH 6.5 alvarenga2025 R8, R1; these are total concentrations by UV or after moderate centrifugation, not free drug (F8).

papersystemmethod and conditionsfree drug against limitids
alonzo2011felodipine 90:10 and 50:50 HPMC dispersions; pure amorphousdialysis flux ratio to crystal, 37 °C10.5 / 9.5 / 8.5 against about 9R14, M1
alonzo2011the same two dispersions¹H NMR at 50 min1370 against 1014 (about 26% apart)R15
jackson2015danazol dispersions with LLPS (PVP, HPMC, HPMCAS)side-by-side flux, 25 °C7.1–9.1 against 8 µg/mLR9, M1
jackson2015danazol antisolvent solutions (cited)same7.2–8.2 µg/mL with polymer, 8.1 withoutR9
trasi2015britonavir; lopinavir single-drug dispersions, HPMCAS / PVPultracentrifuged, 2 h≈26.9 / ≈22.0 against 25; ≈17.8 / ≈15.9 against 17 µg/mLR13, M1, M2
ilevbare2013dritonavir LLPS concentration with 180 µg/mL polymerturbidity titration, 37 °C18.2–18.7 µg/mL (21.3 with CAAdP 0.85) against 18.2R10
ilevbare2013a (Amorphous solubility and LLPS)ritonavir–PVP 1:9, added in portionsin situ UV, 37 °C18.3 and 18.0 µg/mL with 24.0 µg/mL addedR17
ueda2020b (Amorphous solubility and LLPS)ibuprofen with 300 µg/mL HPMC or PVP-VANMR, 37 °Camorphous solubility 177.1 lowered to 96.9 and 90.7 µg/mLR1
trasi2016six marketed tacrolimus capsules, 5 mg in 40 mL0.45-µm filtrate HPLC, pH 4.5, 37 °C, 2 h≈46–50 µg/mL against 46–50 µg/mLR10, R4
trasi2016same, dissolved in 30 mL; pure-drug solutions 20–100 µg/mLside-by-side flux0.0048–0.0054 µg/min against a pure-drug plateau of ≈0.0050–0.0055R15, R14
li2018lopinavir–HPMC films 15–85% drugpH 3, 25 °C, 48 h, ultracentrifuged≈17.5–18.9 against 17.4 µg/mLR3, R1
que2018paclitaxel–HPMCAS 49/51, with and without 18 wt% seedsin situ UV, 15 mL, 37 °C (total drug)≈31–33 µg/mL reached against 31.6 µg/mLR13, R1
elkhabaz2019aposaconazole–HPMCAS 10% and 25% after transfer to FaSSIFmicro-centrifuged supernatant, HPLC (may include droplets)≈22–24 and ≈21–22 against an LLPS onset of about 20 µg/mLR6, R7, R2
alvarenga2025R- and racemic praziquantel–HPMCAS 30%, 1.5 mg/mL, PBS pH 6.5in situ UV (total drug)maxima ≈1.4 and ≈1.1 against 1.39 and 1.17 mg/mLR8, R1

Figure

Table 1 of alonzo2011: receptor slopes and their ratios to crystalline felodipine
Table 1 · alonzo2011receptor slopes and their ratios to crystalline felodipine

The two controls show that the cell separates 5 from 10 µg/mL; the 90:10, 50:50 and pure amorphous ratios sit together near the predicted factor of 9 alonzo2011 R14.

Table 2 of jackson2015: flux and free drug concentration of danazol dispersions and antisolvent solutions
Table 2 · jackson2015flux and free drug concentration of danazol dispersions and antisolvent solutions

Every row with a drug-rich phase lands at 7.1–9.1 µg/mL; only 50:50 HPMCAS, which never reached the amorphous solubility, is lower jackson2015 R9.

Fig. 8 of trasi2016: membrane mass flow of tacrolimus solutions against concentration, with the band of the six dissolved products
Fig. 8 · trasi2016membrane mass flow of tacrolimus solutions against concentration, with the band of the six dissolved products

Pure-drug flux rises up to 50 µg/mL and then levels off; the band of the dissolved products lies on that plateau trasi2016 R14, R15.

Why

Jackson and co-workers state that the dispersions dissolve to a concentration above the amorphous solubility, but only briefly: a drug-rich phase in metastable equilibrium with the water-rich phase forms rapidly and fixes the free drug at the amorphous solubility, so that all dispersions that undergo LLPS "should" give the same flux and the extra solubility a dispersion might offer "cannot be realized" jackson2015 C27, C31, C32. Ilevbare and co-workers conclude that "it appears" there is an upper concentration of free drug that ASD dissolution can reach, and that the LLPS concentration "represents the upper limit of supersaturation" ilevbare2013d C35; the unchanged LLPS concentration with four polymers "suggests" that these polymers are not substantially incorporated into the ritonavir-rich phase ilevbare2013d C22. Alonzo and co-workers (2011) find the three felodipine activities "remarkably close" to the estimate, but add that "there is no reason to expect" a dispersion to give the same solution activity as the pure amorphous drug and that the equality "may be purely coincidental" alonzo2011 C22, C45, C48. Trasi and Taylor conclude that the maximum after 2 h is "not dependent on the polymer type" trasi2015b C28. The LLPS chapter frames the same cap as the amorphous solubility, reached but not exceeded by any solid form whose crystallization is slow enough (Amorphous solubility and LLPS F13), with free drug, activity and flux levelling off at that concentration (Amorphous solubility and LLPS F8). For tacrolimus, Trasi and co-workers state that membrane transport into a sink follows the activity of the free drug, not the total concentration, so that above the amorphous solubility added drug only forms more drug-rich phase and the mass flow reaches a maximum, "as observed for other drugs" trasi2016 C36, C37; the products reaching that maximum means that "the amorphous solubility advantage is achieved" and that the formulation components neither solubilize the drug nor change its amorphous solubility, "at least not at the concentrations present" trasi2016 C38, C31. They recall that polymers have little effect on the amorphous solubility, that small molecules mixing into the drug-rich phase lower it and micellar surfactants raise it, and that lactose, the main excipient, is "not anticipated" to do either trasi2016 C32, C33. For lopinavir, Li and Taylor read the unchanged ceiling with HPMC as the polymer dissolving and "not substantially mixed with the drug droplets due to its high aqueous solubility" li2018 C48. (synthesis: here the cap holds for dispersions and products of five drugs, at 10–85% drug, with polymers that dissolve; it is lowered by something that stays mixed with the drug, a second drug (F11), a polymer that enters the drug-rich phase, as for ibuprofen in the LLPS chapter, or a polymer that does not dissolve (F18); the measured total can rise above it with a polymer that solubilizes the drug (F17); and it is not reached when release is too slow (F10).)

Conditions and limits

The felodipine particle-blind test was run for HPMC dispersions at 37 °C only, and the claims for PVP–felodipine and both indomethacin systems rest on UV and light scattering alonzo2011 X16. The danazol fluxes are relative: the absolute values do not reproduce from the example profile, the flux and concentration columns are not proportional, and the flux window per formulation is not stated jackson2015 X4, X5, X6. The ritonavir and lopinavir values are plot readings with undefined error bars, and the cited amorphous solubilities come from an earlier paper trasi2015b X5, X14. Temperatures: felodipine 37 °C, danazol and the RTV/LPV dispersions 25 °C alonzo2011 P4; jackson2015 P4; trasi2015b P5. The tacrolimus products were tested in one buffer (pH 4.5) and 40 mL only; their drug loadings were not known, and the plateau was read on 0.45-µm PTFE filtrates whose retention of droplets was not tested trasi2016 P11, X4, X10; the 100 mL control the authors call sink is nominally 50 µg/mL, at the amorphous solubility trasi2016 X5. The lopinavir HPMC result is at pH 3 and 25 °C, with HPMC also in the medium li2018 P5.

Counterexamples and conflicts

CAAdP 0.85 at 180 µg/mL raised the ritonavir LLPS concentration by about 17%, unlike the other four polymers ilevbare2013d X7. In the LLPS chapter, dissolved HPMC and PVP-VA lowered the amorphous solubility of ibuprofen by about half by entering its drug-rich phase (Amorphous solubility and LLPS F19) ueda2020b R1; the ritonavir titrations here found no such lowering at 180 µg/mL ilevbare2013d R10. Konno's 75% HPMCAS felodipine dispersion reached 14.1 µg/mL against an estimate of about 9.5 µg/mL, unexplained in that paper and measured by UV (F8) konno2008a X5. The 2018 lopinavir study found the cap lowered when the polymer does not dissolve and is mixed with the drug: HPMCAS, CAP, HPMCP and EC dispersions stayed below 17.4 µg/mL at pH 3, down to ≈0.3–0.6 µg/mL at 15% drug (F18) li2018 R3; the title was narrowed to the dissolving polymer then. With a polymer that solubilizes the drug, the measured concentration can exceed the cap while free drug does not: HPMCAS–resveratrol solutions held up to ≈1610 µg/mL with at most about twice the crystal's flux (F17) wegiel2015 R19, R20, C41.

Transfer check

Above the estimated amorphous solubility, measure free drug by flux across a membrane that excludes droplets, by solution NMR or by ultracentrifugation; expect a plateau at the amorphous solubility alonzo2011 P4; jackson2015 P4; trasi2015b P9. A plateau clearly below it means slow release (F10), a second drug (F11) or a polymer that mixes into the drug-rich phase (LLPS chapter); a plateau above it means the method is counting particles (F8) or that a polymer solubilizes the drug (F17). Do not design for free drug above the amorphous solubility. For a marketed or multi-excipient product, compare its plateau and its maximal flux with the amorphous solubility and the flux plateau of the pure drug in the same medium, as the authors recommend for baseline metrics trasi2016 C46.

History

The LLPS chapter traces the cap to earlier dispersion work and to the ritonavir–PVP dispersion of 2013 (Amorphous solubility and LLPS F13). Within this chapter, Alonzo and co-workers (2011) gave the first particle-blind test of dispersions, which Ilevbare and co-workers (2013) cite as diffusion from dissolved ASDs being capped at the amorphous drug level (builds_on) ilevbare2013d R19. Ilevbare and co-workers (2013) named the LLPS concentration as the upper limit ilevbare2013d C35; Jackson and co-workers (2015) confirmed it by flux for three polymers and two loadings ("is confirmed here") jackson2015 C30; Trasi and Taylor (2015) by ultracentrifugation for two drugs and two polymers trasi2015b C28. Trasi and co-workers (2016) carried it to marketed multicomponent products, six tacrolimus capsules, by plateau and flux trasi2016 C42, C43; later tacrolimus papers of the library take the ≈50 µg/mL amorphous solubility as the design value of their non-sink and absorptive tests purohit2018 R4; trasi2017 M1; hate2019 M1. Li and Taylor (2018) confirmed the cap for lopinavir with HPMC and showed that undissolved polymers lower it (F18) li2018 C18, C67. Que and co-workers (2018), Elkhabaz and co-workers (2019) and Alvarenga and co-workers (2025) found dispersions reaching, not exceeding, the amorphous solubility measured in the same medium, by methods that do not exclude particles que2018 C20; elkhabaz2019a C7; alvarenga2025 R8.

F8

Topic 3Ceiling and the colloid it leaves2 of 4

In situ UV counts drug inside submicron particles, so readings above the amorphous solubility need a method that excludes particles.

A 90:10 felodipine dispersion read about 27 µg/mL by UV, three times a 50:50 one, yet membrane flux and NMR found similar dissolved drug in both alonzo2011 R1, R14, R15. Colloids from HPMCAS dispersions of ritonavir and lopinavir passed 0.45 µm filters, so the dissolved drug had to be measured after ultracentrifugation trasi2015b R6, R7, C22.

moderateModerate: two particle-blind methods, a summed spectrum and the tracking of filtrates agree, but the particle absorbance at the probe was not quantified and the nanosuspension reference comes from a thesis alonzo2011 K3, X7; trasi2015b K4.

Reading with particles present against dissolved drug, µg/mLfelodipine 90:10 · UV≈27.0felodipine 50:50 · UV≈8.9danazol 90:10 HPMCAS · UV≈16.2danazol 90:10 HPMCAS · flux8.2indomethacin EPO · in situ UV≈29.5indomethacin EPO · HPLC8.8

The two felodipine dispersions gave similar flux and NMR values; the indomethacin HPLC value is from the filtered supernatant. alonzo2011 R12, R14, R15; jackson2015 R2, R9; xie2017 R11

dissolved felodipine · 29490:10 dispersion solution · 312solution + nanosuspension · ≈316crystal nanosuspension · 325290300310320330position of the UV valley, nm

The 90:10 spectrum lies between solution and particles, close to their sum: the probe records both. alonzo2011 R19, R21

For your drug

  1. If the medium turns cloudy or extinction rises at a wavelength where the drug does not absorb, treat UV values as total drug.
  2. Confirm the dissolved level by ultracentrifugation (for example 40,000 rpm for 20 min), by membrane flux or by solution NMR; if a filter is used, test which pore size retains the drug's droplets and close the mass balance with a filter rinse.

ilevbare2013d P3; trasi2015b R6, P9; alonzo2011 P4; trasi2016 R8, R13

How it works and key numbers
  1. Particles of 200–400 nm absorb light like the dissolved drug alonzo2011 C27.
  2. Second-derivative processing does not remove this absorbance, so UV counts drug inside particles ("The most likely explanation") alonzo2011 C27.
  3. Diffusion across a membrane and solution NMR detect only highly mobile, dissolved molecules alonzo2011 C27.
  4. A 0.45 µm filter passed the HPMCAS colloids (about 160–500 nm), and filtration "may" itself induce crystallization (cited) trasi2015b R7; jackson2015 C12.
  5. For tacrolimus a 0.7-µm glass filter passed 220 nm droplets, while a 0.22-µm glass fiber filter held them trasi2016 R8, R11.
≈27.0 vs ≈8.9 µg/mLUV of 90:10 against 50:50 felodipine dispersions with similar dissolved drugalonzo2011 R12, R14
≈16.2 vs 8.2 µg/mLdanazol 90:10 HPMCAS dispersion by UV against by fluxjackson2015 R2, R9
0.22 µmpore size that retained tacrolimus droplets where 0.7 µm did nottrasi2016 R8
Evidence: data, conditions and papers

Finding F8. In situ UV overreads the dissolved drug once submicron particles form, and 0.45 µm filters do not remove the colloid of fast-dissolving HPMCAS dispersions; flux, NMR or ultracentrifugation give the dissolved concentration

In short. UV read ≈27 µg/mL for a 90:10 HPMC–felodipine dispersion against ≈8.9 µg/mL for a 50:50 one, while flux and NMR gave similar dissolved levels; the 90:10 spectrum peaked at 367 nm with a valley at 312 nm, between dissolved felodipine (360 and 294 nm) and a crystalline nanosuspension (373 and 325 nm) alonzo2011 R1, R14, R15, R19. The 90:10 HPMCAS danazol dispersion read ≈16.2 µg/mL by UV but 8.2 ± 1.2 µg/mL by flux jackson2015 R2, R9. Colloids from HPMCAS dispersions of ritonavir and lopinavir passed 0.45 µm filters (about 500 and 160 nm by tracking), so that ultracentrifugation had to be used trasi2015b R6, R7, C22, C27. Konno's felodipine maxima of 14.1 µg/mL lie above that paper's own estimate of about 9.5 µg/mL and were read through a 70-µm filter konno2008a R7, R17, X5. A suspension of small indomethacin crystals from an EPO dispersion read ≈29.5 µg/mL by in situ UV against 8.8 µg/mL by HPLC of the filtered supernatant, and a dispersion that formed nanodroplets read ≈93.5 µg/mL against a nominal maximum of 80 µg/mL xie2017 R11, R15, X7. Tacrolimus droplets passed a 0.7-µm glass filter but were held by a 0.22-µm glass fiber filter trasi2016 R8. In later papers, UV readings of seeded paclitaxel dispersions lay ≈2–10 µg/mL above HPLC values of filtrates at 16 h, praziquantel release plateaus reached up to about 117% of the dose and the racemate exceeded its amorphous solubility at 1.5 mg/mL, and delamanid dispersions read up to ≈80–101 µg/mL at pH 5.0 and 6.5 against amorphous solubilities near 1 µg/mL, none of which was resolved que2018 X4; polyzois2024 X3, X4; nguyen2023c X9.

Type. method comparison in 6 drugs (felodipine, danazol, ritonavir, lopinavir, indomethacin, tacrolimus), with readings above the limit unresolved for paclitaxel, posaconazole, praziquantel and delamanid Strength. : two particle-blind methods for felodipine, a spectral sum that reproduces the mixed spectrum, flux for danazol, tracking of filtrates for ritonavir and lopinavir and HPLC checks for indomethacin; the particle absorbance at the probe was not quantified and the reference nanosuspension spectrum comes from a thesis alonzo2011 K3: moderate, X7; trasi2015b K4: moderate; xie2017 X7.

How it was shown

Alonzo and co-workers (2011) compared the UV spectrum of a dissolving 90:10 HPMC–felodipine dispersion with a solution, a crystalline nanosuspension and their sum, and Jackson and co-workers (2015) compared UV with flux for danazol alonzo2011 P2, P10; jackson2015 P2, P4. Filtrates were examined by nanoparticle tracking or HPLC, and tacrolimus solutions were passed through 0.22-µm and 0.7-µm glass filters trasi2015b P8; xie2017 P9; trasi2016 P6.

What the data show

Wherever submicron particles formed, UV or filtrate readings lay above the particle-blind value alonzo2011 R12, R14; jackson2015 R2, R9; xie2017 R11.

systemUV or filtrateparticle-blind valueids
felodipine 90:10 against 50:50 HPMC dispersion≈27.0 against ≈8.9 µg/mLflux ratios 10.5 against 9.5; NMR 1370 against 1014alonzo2011 R12, R14, R15
felodipine 90:10 solution spectrumpeak 367, valley 312 nmsum of solution and nanosuspension: ≈370 and ≈316 nmalonzo2011 R19, R21
danazol 90:10 HPMCAS dispersion≈16.2 µg/mL8.2 ± 1.2 µg/mL by fluxjackson2015 R2, R9
ritonavir and lopinavir HPMCAS dispersions0.45 µm filtrates turbid; ≈500 and ≈160 nmultracentrifuged values (F7)trasi2015b R6, R7, R13
indomethacin EPO 3:7 dispersion with α crystals, pH 2.2≈29.5 µg/mL by in situ UV8.8 µg/mL by HPLC of the filtered supernatantxie2017 R11
tacrolimus 60 µg/mL0.7 µm passes 220 nm droplets0.22 µm retains the dropletstrasi2016 R8, R11
Fig. 13 of alonzo2011: UV spectra of dissolved felodipine, a crystalline nanosuspension and the 90:10 dispersion solution
Fig. 13 · alonzo2011UV spectra of dissolved felodipine, a crystalline nanosuspension and the 90:10 dispersion solution

The 90:10 spectrum has its valley at 312 nm, between the solution (294 nm) and the nanosuspension (325 nm): the probe sees dissolved drug plus particles alonzo2011 R19.

Why

"The most likely explanation" is that submicron particles absorb light like the solution and are not corrected by second-derivative processing, so UV counts drug inside particles, whereas diffusion and NMR detect only highly mobile species alonzo2011 C27. The drug-rich phase may pass a filter, and filtration may induce crystallization (cited) jackson2015 C12. Trasi and Taylor call ultracentrifugation "the optimum way" to determine dissolved drug for turbid dispersions trasi2015b C27.

Limits and transfer

The particle absorbance at the probe was not quantified alonzo2011 K3. Later papers report readings above the amorphous solubility without a particle-blind check que2018 X4; elkhabaz2019a X3; polyzois2024 X3; nguyen2023c X9. If the medium turns cloudy, treat UV values as total drug, confirm the dissolved level by ultracentrifugation, flux or solution NMR, and test which pore size retains the drug's droplets (0.22 µm for tacrolimus) trasi2015b R6, P9; alonzo2011 P4; trasi2016 R8.

How it was shown

Alonzo and co-workers (2011) followed dissolution with fibre-optic UV probes (270–450 nm every minute, second-derivative spectra calibrated in methanol) in 18 mL of buffer at 300 rpm, and compared the 90:10 solution spectrum at 60 min with a 10 µg/mL methanol solution, a 25 µg/mL crystalline felodipine nanosuspension and their sum scaled by 0.9 alonzo2011 P2, P10. Jackson and co-workers (2015) read UV at 288 nm with 350 nm as a no-absorption reference and compared it with free drug from flux jackson2015 P2, P4. Trasi and Taylor (2015) sampled through 0.45 µm glass syringe filters, examined filtrates by nanoparticle tracking, and switched to ultracentrifugation for the HPMCAS dispersions trasi2015b P5, P8, P9. Konno and co-workers (2008) sampled through a 70-µm filter on the dissolution tester and, in solvent-shift runs, either the same filter or second-derivative correction konno2008a P3, P5. Ilevbare and co-workers (2013) used extinction at non-absorbing wavelengths (280–450 nm) as the signal of a second phase ilevbare2013d P3. Xie and co-workers (2017) read indomethacin as the 319 nm absorbance minus the 450 nm extinction with a dip probe and checked selected runs by HPLC of filtered samples at 1, 3 and 8 h xie2017 E4, P9. Trasi and co-workers (2016) filtered a 60 µg/mL tacrolimus solution through 0.22-µm and 0.7-µm glass filters, examined 0.7-µm filtrates by nanoparticle tracking, and rinsed the filter of a dissolved capsule with acetonitrile to recover the undissolved drug trasi2016 P6, P13, P14.

What the data show

Felodipine. With more 90:10 dispersion the apparent peaks rose with the dose (≈75, ≈53 and ≈28 µg/mL for 90, 60 and 30 µg/mL added, 80–100% of the drug added) alonzo2011 R2. The summed reference spectrum gave a valley at ≈316 against ≈313 nm and a peak at ≈370 against ≈367 nm, and the shift appeared within 5 min of the start, not at any time for the 50:50 dispersion, pure amorphous felodipine or the controls alonzo2011 R21, R20. Particles of 200–400 nm absorb like the solution, and the cited work showed that this absorbance is not removed by the second derivative and grows relative to scattering as particles get smaller alonzo2011 C27, R25. The methanol-shift controls read ≈4.3 and ≈9.0 µg/mL against nominal 5 and 10 µg/mL even without particles alonzo2011 R12, X18. Indomethacin. The 90:10 PVP dispersion read ≈55.5 µg/mL against ≈22 µg/mL for 50:50 and a predicted 21 µg/mL; 90:10 HPMC–indomethacin fluctuated between 80 and 120 µg/mL near the linear limit of the probe; neither was checked by a particle-blind method alonzo2011 R16, R18, X16. Danazol. UV peaks above 8 µg/mL (≈9.4–16.2 µg/mL) contrast with flux values of 7.1–9.1 µg/mL jackson2015 R2, R9. Ritonavir and lopinavir. HPMCAS dispersions gave uniformly turbid solutions within minutes and turbid filtrates with many scattering species, of mean size about 500 nm (RTV–HPMCAS) and about 160 nm (both drugs); PVP filtrates were clear trasi2015b R6, R7, R8. Felodipine maxima of 2008. 14.1 µg/mL from the 75% HPMCAS dispersion and about 11 µg/mL held from a 15 µg/mL solvent shift, against an estimate of about 9.5 µg/mL konno2008a R7, R15, R17. Indomethacin. The EPO dispersion read ≈29.5 µg/mL by UV at 1 h while the filtered supernatant held 8.8 ± 0.6 µg/mL; after the pH rise UV and HPLC agreed better (≈33 against 32.1 µg/mL) xie2017 R11, R19, R10. The EPO–HPMC dispersion read ≈93.5 µg/mL at pH 2.2 against 80 µg/mL nominal, which the authors attribute to a changed extinction coefficient with nanodroplets xie2017 R15, C36. Tacrolimus. The 0.22-µm glass filter retained the droplets of a 60 µg/mL solution; 0.7-µm filtrates held 220 nm droplets trasi2016 R8, R11. The filtrates of dissolved capsules held particles of 210 nm both in 40 mL and in 100 mL, which the authors attribute to croscarmellose passing the filter, so tracking could not decide whether drug particles formed; the 0.7-µm filtrates held 45–50 µg/mL and the filter rinse ≈70 against 75 µg/mL expected trasi2016 R12, C39, R13, E3. Celecoxib. After crystallization the UV readings settled at ≈2.6–2.9 µg/mL, above the 1.5 µg/mL measured by HPLC after ultracentrifugation, and the crystal itself read ≈1.85 µg/mL at 16 h xie2016a R4, R1, X4; xie2015 R7, X12.

papersystemUV or filtrateparticle-blind valueids
alonzo2011felodipine 90:10 against 50:50 HPMC, 37 °C≈27.0 against ≈8.9 µg/mLflux ratios 10.5 against 9.5; NMR 1370 against 1014R12, R14, R15
alonzo201190:10 solution spectrumpeak 367, valley 312 nmsum of solution and nanosuspension: ≈370 and ≈316 nmR19, R21
jackson2015danazol 90:10 HPMCAS, 25 °C≈16.2 µg/mL8.2 ± 1.2 µg/mL by fluxR2, R9
trasi2015britonavir and lopinavir HPMCAS dispersions0.45 µm filtrate turbid; ≈500 and ≈160 nmultracentrifuged values (F7)R6, R7, R13
konno2008afelodipine 75% HPMCAS14.1 µg/mL through a 70-µm filternone; estimate about 9.5 µg/mLR7, R17, X5
ilevbare2013a (Amorphous solubility and LLPS)ritonavir drug-rich phaseextinction onset 37.2 µg/mL in water36.0 µg/mL left in the supernatantR8, R6
xie2017indomethacin, EPO 3:7 dispersion with α crystals, pH 2.2≈29.5 µg/mL by in situ UV8.8 µg/mL by HPLC of the filtered supernatantR11
xie2017indomethacin, EPO–HPMC 3:5:2 dispersion with nanodroplets≈93.5 µg/mL against 80 nominalnot measured in the acid stageR15, X7
trasi2016tacrolimus 60 µg/mL; dissolved capsules0.22 µm retains droplets, 0.7 µm passes 220 nm dropletscapsule filtrates 45–50 µg/mL; filter rinse ≈70 against 75 µg/mLR8, R11, R13
que2018paclitaxel–HPMCAS with seeds, 16 hin situ UV ≈2–10 µg/mL above HPLCHPLC of 0.45-µm filtrates; unseeded ≈31.3 against ≈31.6 µg/mLX4, R13, R14
elkhabaz2019aposaconazole–HPMCAS after transfer to FaSSIFsupernatant after 14,800 rpm, 15 minnone; may include nanodropletsX3
polyzois2024praziquantel dispersions, PBS pH 6.5in situ UV plateaus up to ≈117%; racemate above 1.1 mg/mL at 1.5 mg/mLnoneX3, X4
nguyen2023cdelamanid dispersions at pH 5.0 and 6.5second-derivative UV up to ≈80–101 µg/mLnone; amorphous solubility ≈1 and 0.76 µg/mLX9, R11, R1

Figure

Fig. 13 of alonzo2011: UV spectra of dissolved felodipine, a crystalline nanosuspension and the 90:10 dispersion solution
Fig. 13 · alonzo2011UV spectra of dissolved felodipine, a crystalline nanosuspension and the 90:10 dispersion solution

The black 90:10 spectrum has its valley at 312 nm, between the red solution (294 nm) and the blue nanosuspension (325 nm): the probe sees dissolved drug plus particles alonzo2011 R19.

Fig. 2 of alonzo2011: apparent felodipine concentration from 90:10 and 50:50 HPMC dispersions at 37 °C
Fig. 2 · alonzo2011apparent felodipine concentration from 90:10 and 50:50 HPMC dispersions at 37 °C

The black 90:10 curve near 27 µg/mL is not all dissolved drug; flux and NMR put both dispersions at about the same dissolved level alonzo2011 R1, R14.

Why

Alonzo and co-workers give "The most likely explanation" for the contradiction between UV and the particle-blind methods: the submicron particles absorb light like the solution and are not corrected by second-derivative processing, so UV counts drug inside particles, whereas diffusion and NMR detect only highly mobile species alonzo2011 C27. Because absorption is additive, a spectrum that sums solution and nanosuspension "if our speculation is correct" should match, and it does alonzo2011 C35, C34. Jackson and co-workers warn that above the amorphous solubility nanospecies both absorb and scatter, and that filtering "may not be particularly useful" because the drug-rich phase may pass the filter and filtration may induce crystallization (cited) jackson2015 C12. Trasi and Taylor note that the failure of 0.45 µm filtration has "important analytical implications" and call ultracentrifugation "the optimum way" to determine dissolved drug for turbid dispersions trasi2015b C22, C27. Xie and co-workers note that the turbid suspension of tiny crystals interfered with the in situ UV, and that the very small crystals absorb light, which kept the absorbance well above that of a solution at the crystalline solubility xie2017 R11, C26. Trasi and co-workers caution that the concentration measured after dissolving a multicomponent formulation can include drug held in micelles or in a drug-rich phase, and rely on flux for the free drug trasi2016 C35, C36. (synthesis: the six papers point to one rule; any reading above the amorphous solubility estimate, or a plateau above the crystalline solubility after crystallization, is suspect until a method that excludes particles confirms it, because the excess is where the colloid or the fine crystals sit; and the filter that separates droplets has to be checked for the drug, since 0.7 µm passed and 0.22 µm held the tacrolimus droplets.) (synthesis: four later papers report readings above the amorphous solubility, or above 100% of the dose, without a particle-blind check: the paclitaxel UV excess, the posaconazole supernatants, the praziquantel plateaus and the delamanid values far above 1 µg/mL que2018 X4; elkhabaz2019a X3; polyzois2024 X3; nguyen2023c X9; by the reasoning above they are total drug, part of it in droplets or particles.)

Conditions and limits

The particle absorbance at the probe was not quantified; the nanosuspension reference comes from a thesis alonzo2011 K3, X7. The NMR comparison is a single pair of integrals alonzo2011 X6. Tracking sizes are given without the type of mean or distribution trasi2015b X13. The danazol UV readings were not corrected for the 2 mL withdrawn and replaced at each fluorescence time point jackson2015 X14. Replicate numbers of the indomethacin dissolution runs and HPLC checks are not stated xie2017 X6; the product(s) and replicates behind the tacrolimus filtration and tracking tests are not stated, and no croscarmellose-only control was run trasi2016 X6, X5.

Counterexamples and conflicts

Where no particles formed, UV agreed with the expected level: the 50:50 felodipine dispersion and pure amorphous felodipine read ≈8.9 and ≈8.6 µg/mL, near the predicted 9 µg/mL alonzo2011 R12, M1. In acidified celecoxib–HPMCAS suspensions, where the polymer barely dissolves, drug in the liquid was assayed after a 0.45 µm nylon filter without a colloid check chen2015a P11. The LLPS chapter compares onset methods and finds that absorbance alone and scattering alone can mislead (Amorphous solubility and LLPS F4).

Transfer check

If the medium turns cloudy or bluish, or extinction rises at a wavelength where the drug does not absorb, treat UV values as total drug ilevbare2013d P3; trasi2015b R6. Confirm the dissolved level by ultracentrifugation (for example 40,000 rpm for 20 min), by flux across a membrane that excludes droplets, or by solution NMR, and check the UV spectrum for a shift of peak or valley trasi2015b P9; alonzo2011 P4, R20. Do not rely on 0.45 µm filtration to separate nanodroplets trasi2015b C22; if a filter is used, test which pore size retains the drug's droplets in the medium (0.22 µm for tacrolimus) and close the mass balance with a filter rinse trasi2016 R8, R13. After crystallization in a turbid suspension, take the dissolved concentration from a filtered or centrifuged sample xie2017 R11.

History

Particle absorption by felodipine nanosuspensions had been described in work the 2011 paper cites, among it a paper of the library's Solution methods chapter (builds_on, as listed in the evidence index) alonzo2011 R25. Alonzo and co-workers (2011) were the first in this chapter to show the artefact for dispersions and to resolve it by flux and NMR alonzo2011 C27. Jackson and co-workers (2015) repeated the warning and used flux jackson2015 C12; Trasi and Taylor (2015) showed that 0.45 µm filters pass the HPMCAS colloid trasi2015b C22. Trasi and co-workers (2016) found the pore size that separates tacrolimus droplets and met the limit of particle tracking in a product with an insoluble excipient trasi2016 R8, C39; Xie and co-workers (2017) showed the overreading for a suspension of small crystals and checked it by HPLC xie2017 R11. Later papers of the chapter used in situ UV or moderate centrifugation without a particle-blind check, and their extractors flag the excesses que2018 X4; elkhabaz2019a X3; polyzois2024 X4; nguyen2023c X9.

F9

Topic 3Ceiling and the colloid it leaves3 of 4

Fast-releasing dispersions put the excess drug into submicron droplets within minutes; for felodipine the particles were read as crystals.

When a 10:90 ritonavir–PVP dispersion was added stepwise to 20 µg/mL, droplets of about 350 nm appeared, and they vanished again on dilution to 10 µg/mL ilevbare2013d R1. Danazol and indomethacin dispersions formed droplets of 246–284 nm and 70–100 nm at the LLPS concentration (where liquid–liquid phase separation starts), while 90:10 felodipine dispersions shed particles that grew from about 185 to about 300 nm jackson2015 R6; xie2017 R6; alonzo2011 R8.

moderateModerate to strong that a submicron phase forms; four methods agree for ritonavir, but the crystallinity of the felodipine particles was inferred, without diffraction ilevbare2013d K1, K2; alonzo2011 K4, X7.

Ritonavir–PVP dispersion: light-scattering count rate, kcps10 µg/mL≈150–23020 µg/mL≈4700diluted back to 10 µg/mL≈190–260

The scattering switches on between 10 and 20 µg/mL and off again after dilution, which crystals at about ten times their solubility could not do. ilevbare2013d R1, C6

non-crystalline drug-rich dropletsparticles read as crystallineritonavir≈350danazol246–284indomethacin70–100posaconazole≈304–339delamanid≈440–600felodipinegrew over 90 min≈183 → ≈3070100200300400500600700particle size, nm

Sizes by DLS or nanoparticle tracking in each paper's own medium; delamanid droplets held with HPMCP and HPMCAS. ilevbare2013d R1; jackson2015 R6; xie2017 R6; elkhabaz2019a R13; duong2022a R5; alonzo2011 R8

For your drug

  1. Add the dispersion stepwise and then dilute below the onset: a scattering signal that disappears means droplets, not crystals.
  2. Isolate the dispersed phase by ultracentrifugation for DSC, follow a polarity probe such as pyrene, and for a fast crystallizer check the colloid by diffraction or polarized light within the first minutes.

ilevbare2013d P4, C6, P9, P7; alonzo2011 X7

How it works and key numbers
  1. Drug released above the LLPS concentration forms a drug-rich phase; an LLPS origin of the colloids of rapidly dissolving dispersions is "highly likely" ilevbare2013d C33.
  2. Crystals would not dissolve at 10 µg/mL, far above the 1.3 µg/mL crystalline solubility, so scattering that disappears on dilution "strongly support[s]" liquid droplets ilevbare2013d C6.
  3. The isolated ritonavir phase had a Tg of 1.05 °C against 50 °C for dry amorphous ritonavir, "consistent with" a supercooled liquid holding a few percent of water ilevbare2013d R2, M1, C7.
  4. For felodipine the authors "speculate" that a 90:10 dispersion puts almost all its drug into a highly supersaturated state that immediately crystallizes, and conclude that the particles were crystalline ("it would be reasonable to conclude") alonzo2011 C29, C33.
≈350 nmritonavir droplets at 20 µg/mL, gone after dilution to 10 µg/mLilevbare2013d R1
1.05 °CTg of the isolated ritonavir-rich phase (dry amorphous ritonavir 50 °C)ilevbare2013d R2, M1
4.1–4.5 × 10⁹ per mLnumber of danazol droplets at the concentration maximumjackson2015 R6
Evidence: data, conditions and papers

Finding F9. Fast-releasing dispersions put the excess drug into a submicron colloid within minutes: for ritonavir, danazol and indomethacin a non-crystalline drug-rich phase that appears at the LLPS concentration, for felodipine particles that the authors read as crystalline

In short. A ritonavir–PVP dispersion added stepwise gave no scattering at 10 µg/mL, ≈350 nm droplets and a count rate of ≈4700 kcps at 20 µg/mL, and a return to baseline on dilution back to 10 µg/mL ilevbare2013d R1. The isolated phase had a glass transition at about 1 °C, the pyrene ratio fell from ≈1.91 to ≈1.43–1.46, and SEM showed spherical droplets that turned into needles by 90–120 min ilevbare2013d R2, R3, R4. Danazol dispersions lowered the pyrene ratio once the UV concentration passed about 6–10 µg/mL and held droplets of 246–284 nm at 4.1–4.5 × 10⁹ per mL jackson2015 R2, R5, R6. 90:10 HPMC–felodipine dispersions shed particles of ≈185 nm at 5 min that grew to ≈300 nm by 90 min, none from 50:50 even at 250 µg/mL, and the authors conclude from spectra and birefringence at about 1 µm (not shown) that they "were indeed crystalline" alonzo2011 R8, R7, C33, X7. Indomethacin with HPMC at pH 2.2 separated 70–100 nm droplets from 36–40 µg/mL, and an EPO–HPMC dispersion that released fast gave ≈75 nm drug-rich nanospecies in its filtrates at 30 and 60 min xie2017 R4, R6, R15.

Type. observation in 7 drugs (ritonavir, danazol, indomethacin, felodipine, lopinavir, posaconazole, delamanid) Strength. to strong that a submicron phase forms; for its nature moderate to strong for ritonavir, where four methods agree ilevbare2013d K1, K2: moderate to strong, moderate for danazol (probe and tracking) jackson2015 K1: moderate and indomethacin (extinction, DLS and the drug's own fluorescence; no solid-state check of the droplets) xie2017 K3: moderate to strong, X18, weak to moderate for the crystallinity of the felodipine particles, which was inferred alonzo2011 K4: weak to moderate.

How it was shown

Ilevbare and co-workers (2013) added a 10:90 ritonavir–PVP dispersion in portions to pH 6.8 buffer at 37 °C up to about 20 µg/mL, then diluted it to 10 µg/mL while following light scattering and extinction, and scanned the isolated dispersed phase by DSC ilevbare2013d P4, P3, P9. The danazol, felodipine and indomethacin colloids were followed by a pyrene probe, nanoparticle tracking, light scattering or the drug's own fluorescence jackson2015 P3, P5; alonzo2011 P5; xie2017 P6.

What the data show

Ritonavir, danazol and indomethacin formed a phase with the properties of a drug-rich liquid, while the felodipine particles grew continuously ilevbare2013d R1, R2; jackson2015 R6; xie2017 R6; alonzo2011 R8.

drug and systemmethodresultids
ritonavir–PVP 10:90, stepwise to 20 µg/mL, then 10 µg/mLDLS and extinction, 37 °Cdroplets ≈350 nm at 20 µg/mL; signals back to baseline after dilutionilevbare2013d R1
ritonavir, isolated dispersed phaseDSCTg inflection 1.05 °C (amorphous ritonavir 50 °C)ilevbare2013d R2, M1
danazol 90:10 dispersions PVP / HPMC / HPMCASNTA at the maximum, 25 °C256 / 284 / 246 nm; 4.1–4.5 × 10⁹ per mLjackson2015 R6
indomethacin with 100 µg/mL HPMC, pH 2.2extinction, DLS, fluorescence, 37 °Conset 36 µg/mL; droplets 70–100 nm from 40 µg/mLxie2017 R4, R6, R7
felodipine 90:10 HPMC; 50:50light scattering, 25 °C≈183–203 → ≈280–307 nm in 90 min; none detected from 50:50alonzo2011 R8, R7
posaconazole–HPMCAS 10% and 25%, after transfer to FaSSIFNTA of supernatants≈304–339 and ≈328 nmelkhabaz2019a R13
Fig. 4 of ilevbare2013d: count rate and extinction while a ritonavir–PVP dispersion is added and then diluted
Fig. 4 · ilevbare2013dcount rate and extinction while a ritonavir–PVP dispersion is added and then diluted

Both signals switch on between the 10 and 20 µg/mL plateaus and off again after dilution to 10 µg/mL ilevbare2013d R1, C6.

Why

Crystals would not dissolve at 10 µg/mL, far above the 1.3 µg/mL crystalline solubility, so the reversible scattering "strongly support[s]" liquid droplets, and the low Tg is "consistent with" a ritonavir-rich phase holding a few percent of water ilevbare2013d C6, C7. For indomethacin an extinction rise with the absorbance staying high is read as a liquid droplet phase rather than crystals xie2017 C16. For felodipine, continuous growth, birefringence at about 1 µm and the spectra lead the authors to conclude ("it would be reasonable to conclude") that the particles were crystalline alonzo2011 C33.

Limits and transfer

No diffraction of the felodipine particles was made, and tracking cannot tell droplets from crystals alonzo2011 X7; jackson2015 X13. Add the dispersion stepwise and then dilute below the onset: a scattering signal that disappears means droplets, not crystals; for a fast crystallizer, check the colloid by diffraction or polarized light within the first minutes ilevbare2013d P4, C6; alonzo2011 X7.

How it was shown

Ilevbare and co-workers (2013) added a 10:90 ritonavir–PVP dispersion in about 3 mg portions to 25 mL of 100 mM pH 6.8 phosphate buffer at 37 °C, up to about 20 µg/mL, and diluted it to 10 µg/mL after about 60 min, following count rate and size by dynamic light scattering in a flow-through cell and extinction at non-absorbing wavelengths ilevbare2013d P4, P3. The dispersed phase from a dispersion dissolved in water was ultracentrifuged (274356g, 15 min) and scanned by DSC, a pyrene probe was followed after dispersion dissolution, and dried samples were imaged by SEM over 480 min ilevbare2013d P9, P7, P8. Jackson and co-workers (2015) read the pyrene I1/I3 ratio on aliquots during film dissolution and sized the scattering phase by nanoparticle tracking at the concentration maximum of the 90:10 dispersions jackson2015 P2, P3, P5. Alonzo and co-workers (2011) watched dispersion particles under crossed polars and sized the colloid by light scattering in dissolving dispersions and in methanol-shift solutions at 25 and 37 °C alonzo2011 P6, P5. Trasi and Taylor (2015) noted turbidity and tracked particles in filtrates of 20% ritonavir and lopinavir dispersions trasi2015b R6, P8. Xie and co-workers (2017) followed extinction at 450 nm, where indomethacin does not absorb, the drug's own fluorescence near 378 nm and DLS during titration with 100 µg/mL HPMC at pH 2.2, and filtered (0.45 µm) samples of dissolving dispersions for DLS and fluorescence xie2017 P4, P5, P6, P10. Trasi and co-workers (2016) tracked particles in a 60 µg/mL tacrolimus solution and in filtrates of dissolved capsules trasi2016 P13.

What the data show

Ritonavir. Count rate ≈150–230 kcps at 0 and 10 µg/mL, ≈4700 kcps at the first 20 µg/mL point, falling to ≈3550 kcps over 20 min; after dilution ≈190–260 kcps ilevbare2013d R1. The data bracket the onset between 10 and 20 µg/mL; the 18.3 µg/mL quoted for it is the separately titrated LLPS concentration with PVP ilevbare2013d X8, R10. The isolated phase showed a glass transition with onset −2.69 °C, inflection 1.05 °C and end 3.64 °C, against 50 °C for amorphous ritonavir ilevbare2013d R2, M1. I1/I3 fell from ≈1.91 to ≈1.50 within ≈8 min, stayed at ≈1.43–1.46 to 105 min and rose to ≈1.77 at 120 min ilevbare2013d R3. SEM showed smooth spheres mostly below 1 µm at 30 min, merging droplets at 60 min and needle clusters at 120 and 480 min; droplets from a solvent shift with 180 µg/mL PVP looked the same ilevbare2013d R4, R11. Danazol. The 90:10 PVP dispersion passed 8 µg/mL after ≈27 min and peaked at ≈9.4 µg/mL at ≈60 min as I1/I3 fell from ≈1.95 to ≈1.56; HPMC peaked at ≈9.9 µg/mL with I1/I3 ≈1.44–1.46, HPMCAS at ≈16.2 µg/mL with ≈1.39–1.57 jackson2015 R2. Onsets read from the probe were ≈6.0–10.4 µg/mL for eight dispersions against ≈8.1–8.3 µg/mL for antisolvent solutions jackson2015 R5. Tracking gave 256 ± 75 (PVP), 284 ± 81 (HPMC) and 246 ± 54 nm (HPMCAS) at 4.1–4.5 × 10⁹ per mL, against 205–267 nm and 2.9–3.2 × 10⁹ per mL for antisolvent solutions jackson2015 R6. Felodipine. The 90:10 HPMC particle had dissipated within 5 min and the medium turned uniformly cloudy, whereas a 50:50 particle kept its shape for at least 30 min alonzo2011 R4, R3. Particles from the 90:10 dispersion and from methanol-shift solutions with HPMC started at ≈183–203 nm and reached ≈280–307 nm by 90 min at 25 °C, and grew to ≈720 nm near 10 h; at 37 °C the dispersion-born particles started larger (≈259–274 against ≈194–219 nm) alonzo2011 R8, R6, R11, X19. 90:10 PVP–indomethacin gave 210 nm at 30 min; 50:50 PVP–indomethacin no correlation function alonzo2011 R17. Ritonavir and lopinavir, HPMCAS. Uniform turbidity within minutes, colloids of about 500 and 160 nm passing 0.45 µm filters; PVP dispersions dissolved more slowly with clear filtrates trasi2015b R6, R7. Indomethacin. With HPMC the 319 nm absorbance lost linearity and the 450 nm extinction rose from 36 µg/mL, DLS found droplets of 70–100 nm (PDI below 0.1) at or above 40 µg/mL, and the fluorescence band near 378 nm, negligible below 40 µg/mL, grew from ≈88 at 40 to ≈445 at 80 µg/mL xie2017 R4, R6, R7. Among dispersions, only the 10% HPMC one held droplets (65–80 nm, PDI about 0.24) in its 60-min filtrate, and the EPO–HPMC dispersion gave ≈75 nm species (PDI about 0.1) at 30 and 60 min, which crystallized after 3 h if the pH stayed at 2.2 xie2017 R14, R15. Tacrolimus. A 60 µg/mL solution held a second phase of 220 nm mean size after 0.7-µm filtration; for the dissolved capsules no drug colloid could be shown (F8) trasi2016 R11, C39. Posaconazole. After transfer to FaSSIF, 10% and 25% HPMCAS dispersions gave nanodroplets of about 304–339 and 328 nm and the tablet powder about 218 nm; the 10% droplets grew while their number fell (F26) elkhabaz2019a R13, R14. Delamanid. Drug-rich droplets formed at 50 µg/mL crystallized at once without polymer but stayed at about 440 (HPMCP) and 600 nm (HPMCAS) for 3 h, and salt dispersions produced stable nanodroplets during release duong2022a R7, R5, R25.

papersystemmethod and conditionsresultids
ilevbare2013dritonavir–PVP 10:90, stepwise to 20 µg/mL then 10 µg/mLDLS and extinction, 37 °Cdroplets ≈350 nm at 20 µg/mL; signals back to baseline after dilutionR1
ilevbare2013disolated dispersed phaseDSC, 20 °C/minTg inflection 1.05 °C (amorphous ritonavir 50 °C)R2, M1
ilevbare2013ddissolved dispersion with pyrenefluorescenceI1/I3 ≈1.91 → ≈1.43–1.46, then ≈1.77 at 120 minR3
jackson2015danazol 90:10 dispersions PVP / HPMC / HPMCASNTA at the maximum, 25 °C256 / 284 / 246 nm; 4.1–4.5 × 10⁹ per mLR6
jackson2015eight danazol dispersionspyrene onset≈6.0–10.4 against ≈8.1–8.3 µg/mL (antisolvent)R5
alonzo2011felodipine 90:10 HPMC; 50:50light scattering, 25 °C≈183–203 → ≈280–307 nm in 90 min; none detectedR8, R7
trasi2015britonavir, lopinavir HPMCAS dispersionsNTA of filtratesabout 500 nm (RTV) and 160 nm (both drugs)R7
ilevbare2013a (Amorphous solubility and LLPS)ritonavir drug-rich phase from a solvent shiftDSCTg 0.4 °C against 50.4 °C dryR5
xie2017indomethacin with 100 µg/mL HPMC, pH 2.2titration; extinction, DLS, fluorescence, 37 °Conset 36 µg/mL; droplets 70–100 nm from 40 µg/mLR4, R6, R7
xie2017indomethacin EPO–HPMC 3:5:2; HPMC 1:9 dispersions0.45-µm filtrates, DLS≈75 nm; 65–80 nmR15, R14
trasi2016tacrolimus 60 µg/mL, pH 4.50.7-µm filtrate, NTA220 nm second phaseR11
elkhabaz2019aposaconazole–HPMCAS 10% and 25%; Noxafil powder, after transfer to FaSSIFNTA of supernatants≈304–339 and ≈328 nm; ≈218 nmR13
duong2022adelamanid 50 µg/mL with 300 µg/mL HPMCP or HPMCAS; edisylate dispersionsDLS, 3 h; during release≈430–440 and ≈595–600 nm held; stable droplets, smaller with HPMCPR5, R25

Figure

Fig. 4 of ilevbare2013d: count rate and extinction while a ritonavir–PVP dispersion is added and then diluted
Fig. 4 · ilevbare2013dcount rate and extinction while a ritonavir–PVP dispersion is added and then diluted

Both signals switch on between the 10 and 20 µg/mL plateaus and off again after dilution to 10 µg/mL, which crystals at ten times their solubility could not do ilevbare2013d R1, C6.

Fig. 2a of jackson2015: dissolution of the 90:10 PVP danazol dispersion with the pyrene ratio
Fig. 2a · jackson2015dissolution of the 90:10 PVP danazol dispersion with the pyrene ratio

The pyrene ratio (blue) falls as the UV curve crosses the 8 µg/mL line and rises again when crystallization depletes the drug-rich phase jackson2015 R12.

Why

For ritonavir the authors argue that crystals would not dissolve at 10 µg/mL, far above the 1.3 µg/mL crystalline solubility, so the reversible scattering "strongly support[s]" liquid droplets; the low Tg is "consistent with" a ritonavir-rich phase holding a few percent of water, a supercooled liquid at 37 °C ("indicating"); and an LLPS origin of the colloids of rapidly dissolving dispersions is "highly likely" ilevbare2013d C6, C7, C8, C33. For danazol the pyrene drop is "consistent with" the probe entering a newly formed disordered drug-rich phase, and the scattering phase gives "additional support" for amorphous precipitation without loss of the amorphous advantage jackson2015 C13, C25. For felodipine the authors "speculate" that a 90:10 dispersion puts almost all its drug into a highly supersaturated state that immediately crystallizes; continuous growth, birefringence at about 1 µm, the spectra and the fast crystallization of amorphous felodipine in water lead them to conclude ("it would be reasonable to conclude") that the particles were crystalline, an origin in amorphous nanodomains "seems unlikely" alonzo2011 C29, C33, C36. No diffraction of the 200–300 nm particles was made alonzo2011 X7. Later papers of the library cite the 2011 work for nanodroplets formed by fast ASD dissolution at low drug loading (builds_on, as listed in the evidence index of this subcategory). For indomethacin, Xie and co-workers read the extinction rise with absorbance staying high as a liquid droplet phase rather than crystals, which would drop the absorbance, and the drug's fluorescence as "further evidence", its quantum yield being "anticipated" to rise when molecules are close together; the onset is "nearly identical" to the calculated amorphous solubility at 37 °C (cited) xie2017 C16, C17, C25, C23. In the EPO–HPMC dispersion, fast release by the ionized EPO carried the drug past the amorphous solubility and HPMC kept the excess from crystallizing ("attributed to") xie2017 C34, C36. Trasi and co-workers link the absence of a demonstrable colloid from the tacrolimus capsules to a 50% drug loading reported for the innovator, which they "believe" makes dissolution drug controlled (F10) trasi2016 C41. (synthesis: felodipine was the neat amorphous drug that crystallized fastest in water in this chapter (F1), which fits a crystalline colloid, but the evidence is indirect, and for ritonavir, danazol and indomethacin the same kind of colloid was read as non-crystalline.)

Conditions and limits

Ritonavir at 37 °C in 100 mM buffer or water; danazol at 25 °C in 10 mM buffer; felodipine at 25 and 37 °C ilevbare2013d P4, P9; jackson2015 P2; alonzo2011 A4. Tracking cannot tell droplets from crystals and was run on 90:10 danazol dispersions only jackson2015 X13. The ritonavir probe run is described in two media ilevbare2013d X1. Droplet sizes differ by method (SEM of dried samples about 500 nm where DLS in water starts at ≈240 nm) ilevbare2013d X12. Indomethacin at pH 2.2 and 37 °C; the non-crystalline state of its droplets rests on optical methods, valid within the first hour xie2017 X18. Tacrolimus at pH 4.5 and 37 °C trasi2016 P13.

Counterexamples and conflicts

The 50:50 dispersions of felodipine and indomethacin formed no detectable colloid, and slower PVP dispersions of ritonavir and lopinavir gave clear filtrates alonzo2011 R7, R17; trasi2015b R6. The ritonavir phase of the LLPS chapter, made by a solvent shift, had a Tg of 0.4 °C, close to the 1.05 °C here (Amorphous solubility and LLPS F2) ilevbare2013a R5. None found in the library that shows the 2011 felodipine particles to be amorphous by a direct measurement. Slowly releasing indomethacin dispersions (30% and 50% HPMC) formed no droplets in acid, and the six tacrolimus products, at a high drug loading, gave no sign of drug beyond the amorphous solubility xie2017 R14; trasi2016 C40; the indomethacin droplets of the EPO–HPMC dispersion crystallized after 3 h at pH 2.2 xie2017 R15.

Transfer check

Add the dispersion stepwise, then dilute below the onset: a scattering signal that disappears means droplets, not crystals ilevbare2013d P4, C6. Isolate the dispersed phase by ultracentrifugation for DSC, follow a polarity probe such as pyrene, and compare the onset with the LLPS concentration from a solvent shift in the same medium (Amorphous solubility and LLPS F4) ilevbare2013d P9, P7. For a fast crystallizer, check the colloid by diffraction or polarized light within the first minutes alonzo2011 X7.

History

Colloids from a β-carotene–PVP dispersion were reported in 1965 (cited) ilevbare2013d R22. Alonzo and co-workers (2011) reported submicron particles from 90:10 dispersions alonzo2011 C13. Ilevbare and co-workers (2013) were the first in the library to show that a dispersion colloid is a drug-rich liquid formed at the LLPS concentration ilevbare2013d C59. Jackson and co-workers (2015) extended it to danazol with three polymers and three loadings, and Trasi and Taylor (2015) to HPMCAS dispersions of ritonavir and lopinavir jackson2015 C29; trasi2015b C45. Xie and co-workers (2017) added indomethacin, detected without a probe by the drug's own fluorescence, and the redissolution of the droplets when the pH rose (F21) xie2017 C17, C5; the title gained indomethacin then. Elkhabaz and co-workers (2019) found nanodroplets after a pH shift from posaconazole dispersions that already held crystals from the acid stage (F26), and Duong and co-workers (2022) stable droplets from delamanid salt dispersions elkhabaz2019a C46; duong2022a C39.

F17

Topic 3Ceiling and the colloid it leaves4 of 4

Some dissolved polymers raised the drug's own solubility, so a high measured concentration was not a high supersaturation.

Dissolved HPMCAS raised the solubility of crystalline resveratrol from 42 to 414 µg/mL at 10 mg/mL, and a resveratrol–HPMCAS dispersion reached about 1610 µg/mL while its membrane flux stayed close to that of the crystal wegiel2015 R2, R3, R19, R20. EPO raised both solubilities of indomethacin, while felodipine, celecoxib and lopinavir kept their crystalline solubility at the polymer levels tested xie2017 R1, R3; konno2008a R1; xie2015 R11; li2018 R1.

moderateModerate: the solubilities were measured directly and the flux series has a crystal control, but most resveratrol values are read from plots and no complex was detected directly wegiel2015 K1, K7, X5; xie2017 K2.

Crystalline resveratrol solubility with dissolved HPMCAS, µg/mLbuffer425 mg/mL HPMCAS≈14110 mg/mL HPMCAS41420 mg/mL HPMCAS≈1230

pH 6.8, 37 °C, 24 h; HPMC raised it only to ≈85 µg/mL at 20 mg/mL. wegiel2015 R2, R3

Resveratrol membrane flux, µg/mincrystal suspension2.0dispersion, ≈530 µg/mL dissolved≈4.4dispersion, ≈1610 µg/mL dissolved≈2.6

15:85 resveratrol–HPMCAS dispersion at rising loadings: the dissolved amount tripled while the flux fell toward that of the crystal. wegiel2015 R19, R20

For your drug

  1. Measure the crystalline solubility at the dissolved-polymer level that the dispersion actually releases, and refer the supersaturation to it.
  2. Measure free drug by flux: a flux that falls while the concentration rises means drug bound in solution; for phenolic drugs with PVP watch for a precipitate, and for acidic drugs with a cationic polymer expect solubilization.

wegiel2015 P8, E2, P10, C19, C31; xie2017 C55

How it works and key numbers
  1. The authors equate solubilization by a polymer with drug–polymer complex formation: complexed drug raises the total concentration but not the free drug, so membrane transport is not faster wegiel2015 C25, C23.
  2. On the rising branch of the loading series more dispersion gave more total but less free resveratrol ("indicating"), and the gain from HPMCAS is "mainly due to" a soluble complex wegiel2015 C19, C41.
  3. With PVP, complexation of the three-phenol resveratrol "can be readily rationalized" and gave a non-crystalline precipitate, and the PVP dispersion gave only the crystal's 42 µg/mL wegiel2015 C31, R7, R11.
  4. For indomethacin, drug–polymer interactions in solution "presumably" lower the thermodynamic activity of the drug, so LLPS begins at a higher concentration xie2017 C55, C56.
  5. (synthesis) Solubilization grew with the polymer level, so a polymer without effect at a screening level may solubilize at the mg/mL that a high-polymer dispersion releases, 3.7–4.7 mg/mL in the resveratrol slurries wegiel2015 R11.
42 → 414 µg/mLcrystalline resveratrol solubility without and with 10 mg/mL HPMCASwegiel2015 R2, R3
≈2.6 vs 2.0 µg/minresveratrol flux at ≈1610 µg/mL dissolved against the crystalwegiel2015 R19, R20
1.61 → 6.2 µg/mLγ indomethacin solubility without and with 1000 µg/mL EPO at pH 2.2xie2017 R1
Evidence: data, conditions and papers

Finding F17. Some polymers raised the drug's solubility in solution: dissolved HPMCAS raised crystalline resveratrol about tenfold at 10 mg/mL and EPO raised both solubilities of indomethacin, so the measured concentration overstated the supersaturation, whereas felodipine, celecoxib and lopinavir kept their crystalline solubility within about 1.4-fold at the polymer levels tested

In short. Dissolved HPMCAS raised the crystalline solubility of resveratrol from 42 to ≈141, 414 and ≈1230 µg/mL at 5, 10 and 20 mg/mL (HPMC to ≈85 µg/mL at 20 mg/mL), and a 15:85 resveratrol–HPMCAS dispersion gave up to ≈1610 µg/mL while the membrane flux fell from ≈4.4 to ≈2.6 µg/min against 2.0 µg/min for the crystal; the authors attribute the gain "mainly" to a soluble resveratrol–HPMCAS complex, with free drug at most about twice saturation wegiel2015 R2, R3, R19, R20, C41. In PVP solution resveratrol formed a non-crystalline precipitate with the polymer, and PVP dispersions gave only the crystal's 42 µg/mL wegiel2015 R6, R7, R11. At pH 2.2, 1000 µg/mL EPO raised the crystalline solubility of indomethacin from 1.61 to 6.2 µg/mL (γ form), and adding EPO to HPMC raised its amorphous solubility from 36 to 41–56 µg/mL xie2017 R1, R3. With 22 µg/mL to 1 mg/mL of polymer the crystalline solubility of felodipine, celecoxib and lopinavir changed by 0.84–1.43 times (synthesis: ratios of the printed values) konno2008a R1; xie2015 R11; xie2016a R1; li2018 R1.

Type. observation in 2 drugs (resveratrol, indomethacin) set against 3 others Strength. : the solubilities were measured directly and the flux series has a crystal control, but most resveratrol values are read from plots, the 20 mg/mL HPMCAS point exceeds the drug added, no complex was detected directly, and the amorphous solubility with EPO alone could not be measured wegiel2015 K1: moderate to strong, K7: moderate, X5; xie2017 K2: moderate.

How it was shown

Wegiel and co-workers (2015) stirred crystalline resveratrol for 24 h at 37 °C in pH 6.8 buffer holding 5, 10 or 20 mg/mL HPMC or HPMCAS, and used solutions of a 15:85 resveratrol–HPMCAS dispersion as donors in a side-by-side diffusion cell wegiel2015 P2, P10, A4. Xie and co-workers (2017) measured both solubilities of indomethacin at pH 2.2 with HPMC, EPO or both xie2017 P2, P4.

What the data show

HPMCAS raised the resveratrol solubility steeply and EPO raised both indomethacin solubilities, while three other drugs kept their crystalline solubility at the polymer levels tested wegiel2015 R2, R3; xie2017 R1, R3; konno2008a R1; xie2015 R11; li2018 R1.

drug and polymermethodresultids
crystalline resveratrol, 5 / 10 / 20 mg/mL HPMCAS; HPMCshake flask, pH 6.8, 37 °C, 24 h≈141 / 414 / ≈1230 against 42 µg/mL; HPMC ≈38 / ≈51 / ≈85wegiel2015 R2, R3
15:85 resveratrol–HPMCAS, 6–35 mg/mL24 h; side-by-side fluxup to ≈1610 µg/mL; flux ≈4.4 → ≈2.6 against 2.0 µg/min for the crystalwegiel2015 R19, R20
indomethacin γ / α, 1000 µg/mL EPO, pH 2.2shake flask, 37 °C, 48 h6.2 against 1.61; 8.9 against 2.8 µg/mLxie2017 R1
indomethacin, HPMC with EPO, pH 2.2titration, extinctionamorphous solubility 41–56 against 36 µg/mLxie2017 R3
felodipine, 1 mg/mL polymer; celecoxib, 22 µg/mL polymer; lopinavir, excess polymercrystalline solubility0.98–1.01 against 0.94; 1.89–2.14 against 1.5; 2.6–3.6 against 3.1 µg/mLkonno2008a R1; xie2015 R11; li2018 R1
Fig. 10 of wegiel2015: resveratrol and polymer in solution and membrane flux against loading of a 15:85 HPMCAS dispersion
Fig. 10 · wegiel2015resveratrol and polymer in solution and membrane flux against loading of a 15:85 HPMCAS dispersion

Concentration peaks near 18.8 mg/mL loading where flux is lowest, not far above the crystal flux of 2.0 µg/min: most of the dissolved resveratrol is not free wegiel2015 R19, R20.

Why

Wegiel and co-workers equate solubilization by polymers with drug–polymer complex formation, which raises the total concentration but not the free drug, so that membrane transport is not faster wegiel2015 C25, C23. On the rising branch of the loading series more dispersion gave more total but less free resveratrol ("indicating"), and the gain from HPMCAS is "mainly due to" a soluble complex wegiel2015 C19, C41. For indomethacin the higher solubilities are attributed "presumably" to drug–polymer interactions in solution that lower the thermodynamic activity of the drug xie2017 C55.

Limits and transfer

Flux was measured only for the 15:85 HPMCAS series, and the 20 mg/mL HPMCAS point exceeds the drug stated as added wegiel2015 C10, X5. Measure the crystalline solubility at the dissolved-polymer level the dispersion actually releases, refer the supersaturation to it and measure free drug by flux; a flux that falls while the concentration rises means drug bound in solution wegiel2015 P8, E2, P10, C19.

How it was shown

Wegiel and co-workers (2015) stirred 20 mg of crystalline resveratrol in 20 mL of pH 6.8 buffer holding 5, 10 or 20 mg/mL HPMC or HPMCAS (or saturated E100 or CMCAB) for 24 h at 37 °C and measured the supernatant by UV; they added rising amounts of crystal (658–11,037 µg/mL nominal) to 20 mg/mL PVP and examined the precipitate by PXRD and IR; and they stirred 6–35 mg/mL of a 15:85 resveratrol–HPMCAS dispersion for 24 h and used the solutions as donors in a side-by-side diffusion cell (6–8 kDa membrane), against a saturated crystal suspension wegiel2015 P2, P3, P10, A4. The apparent supersaturation was the excess over the crystal solubility at the dissolved-polymer level, and supersaturation was taken as proportional to flux wegiel2015 E2, E3. Xie and co-workers (2017) shook γ and α indomethacin for 48 h at 37 °C in pH 2.2 McIlvaine buffer with 50–1000 µg/mL HPMC, EPO or both, and α at pH 5 with 100 µg/mL, and located the amorphous solubility by titration with extinction at 450 nm xie2017 P2, P4. The comparators measured crystalline solubility with 1 mg/mL polymer (felodipine), 22 µg/mL polymer (celecoxib, 48 h, ultracentrifuged) or an excess of each polymer (lopinavir) konno2008a P4; xie2015 P6; xie2016a P7; li2018 P1.

What the data show

Resveratrol with HPMCAS. Crystal solubility was 42 ± 6 µg/mL in buffer and ≈141, 414 and ≈1230 µg/mL with 5, 10 and 20 mg/mL HPMCAS; with HPMC ≈38, ≈51 and ≈85 µg/mL wegiel2015 R2, R3. The 65% HPMCAS dispersion gave 458 µg/mL with 4.7 mg/mL dissolved polymer, the 85% one ≈1250 µg/mL against ≈82 µg/mL crystal solubility at its polymer level; the polymer-corrected excess values (155 and about 1166 µg/mL) conflict between table, figure and text wegiel2015 R11, R15, X2, X3. In the loading series dissolved resveratrol rose from ≈530 to ≈1610 µg/mL (6.4 to 18.8 mg/mL loading) and then fell with a gelatinous precipitate, while flux fell from ≈4.4 to ≈2.6 µg/min and stayed at ≈2.8–3.1 µg/min beyond; the crystal gave 2.0 µg/min wegiel2015 R19, R20, X9. Resveratrol with PVP. Added at 658, 1795, 4231, 6744 and 11,037 µg/mL, it gave 709, 1610, 1193, 706 and 99 µg/mL in solution, with a growing non-crystalline precipitate containing resveratrol and PVP wegiel2015 R6, R7. The PVP dispersion "did not readily dissolve" and gave 42 µg/mL; E100, which does not dissolve at pH 6.8, gave 46 µg/mL wegiel2015 R12, R11, C28. Indomethacin with EPO. Crystalline solubility rose from 1.61 to 1.9, 2.3 and 6.2 µg/mL (γ) and from 2.8 to 2.8, 3.4 and 8.9 µg/mL (α) at 50, 150 and 1000 µg/mL EPO; HPMC left it at 1.35–1.5 (γ) and 2.47–2.9 µg/mL (α); at pH 5 the α solubility was 15 alone, 17 with HPMC and 27 µg/mL with EPO xie2017 R1, R2. The amorphous solubility was 36 µg/mL with 100 µg/mL HPMC, 41, 50 and 56 µg/mL at HPMC/EPO 150/50, 100/100 and 50/150, and above 80 µg/mL with 1000 µg/mL EPO; with EPO alone the drug crystallized during the titration xie2017 R3, R8. Predissolved EPO lifted the plateau of a 10% HPMC dispersion from ≈41 to ≈53, ≈69 and ≈77.5 µg/mL at 150, 500 and 1000 µg/mL, but only the highest level held to 300 min xie2017 R18, X19. Other pairs. Felodipine 0.98–1.01 against 0.94 µg/mL with 1 mg/mL polymer; celecoxib 1.72–2.14 against 1.5 µg/mL with 22 µg/mL polymer; lopinavir 2.6–3.6 against 3.1 µg/mL with excess polymer konno2008a R1; xie2015 R11; xie2016a R1; li2018 R1.

papersystemmethod and conditionsresultids
wegiel2015crystalline resveratrol, 5 / 10 / 20 mg/mL HPMCAS; HPMCshake flask, pH 6.8, 37 °C, 24 h≈141 / 414 / ≈1230 against 42 µg/mL; HPMC ≈38 / ≈51 / ≈85R2, R3
wegiel201515:85 resveratrol–HPMCAS, 6–35 mg/mL24 h; side-by-side fluxup to ≈1610 µg/mL; flux ≈4.4 → ≈2.6 against 2.0 µg/minR19, R20
wegiel2015crystalline resveratrol in 20 mg/mL PVP24 h1610 µg/mL at 1795 added; 99 at 11,037 added; amorphous drug–PVP precipitateR6, R7
xie2017indomethacin γ / α, 1000 µg/mL EPO, pH 2.2shake flask, 37 °C, 48 h6.2 against 1.61; 8.9 against 2.8 µg/mLR1
xie2017indomethacin, HPMC with EPO, pH 2.2titration, extinctionamorphous solubility 41–56 against 36 µg/mLR3
konno2008acrystalline felodipine, 1 mg/mL PVP / HPMC / HPMCAS24 h, 37 °C0.98–1.01 against 0.94 µg/mLR1
xie2015crystalline celecoxib, 22 µg/mL polymer48 h, 37 °C1.89–2.14 against 1.5 µg/mLR11
li2018crystalline lopinavir, excess of six polymerspH 3, 25 °C, 48 h2.6–3.6 against 3.1 µg/mLR1
jackson2014 (Crystallization from solution)crystalline danazol, 10 µg/mL HPMCshake flask0.9 → 2.2 µg/mLR1
ueda2020b (Amorphous solubility and LLPS)ibuprofen, 300 µg/mL EUD-E, pH 2.0NMR, 37 °Camorphous 177.1 → 256.3, crystalline 29.8 → 42.1 µg/mL; complexes in the bulkR1, C34
hate2018 (Bioperformance)atazanavir, 1.8 mg/mL PVPVApH 6.8, 37 °Camorphous solubility raised to 94 µg/mLR3, C33
jackson2016 (Crystallization from solution)danazol with three polymersfour methodspolymers neither solubilize nor mix with the dropletsC42

Figure

Fig. 10 of wegiel2015: resveratrol and polymer in solution and membrane flux against loading of a 15:85 HPMCAS dispersion
Fig. 10 · wegiel2015resveratrol and polymer in solution and membrane flux against loading of a 15:85 HPMCAS dispersion

Concentration peaks near 18.8 mg/mL loading where flux is lowest; the dashed crystal flux of 2.0 µg/min lies not far below: most of the dissolved resveratrol is not free wegiel2015 R19, R20.

Fig. 2 of wegiel2015: crystalline resveratrol solubility against dissolved HPMC and HPMCAS
Fig. 2 · wegiel2015crystalline resveratrol solubility against dissolved HPMC and HPMCAS

HPMCAS raises the solubility steeply above a few mg/mL, HPMC only modestly; the 20 mg/mL HPMCAS point exceeds the drug stated as added wegiel2015 R3, X5.

Why

Wegiel and co-workers equate solubilization by polymers with drug–polymer complex formation, and recall that complexed drug raises the total concentration but not the free drug, so that membrane transport is not faster and complexed solutions are thermodynamically "quite different" from supersaturated ones wegiel2015 C25, C23, C44. On the rising branch of the loading series more dispersion gave more total but less free resveratrol ("indicating"), and the gain from HPMCAS is "mainly due to" a soluble complex wegiel2015 C19, C41. PVP is known to form insoluble complexes with phenols above a critical ratio (cited), so the complexation with three-phenol resveratrol "can be readily rationalized"; the PVP dispersion's insolubility "appears" to arise from it, and such a complex "would be expected" to hinder crystallization wegiel2015 C31, C32, C29, C34. The authors suggest that soluble complexes "might explain" very high concentrations reported for other polyphenol dispersions wegiel2015 C43. For indomethacin, Xie and co-workers attribute the higher solubilities "presumably" to drug–polymer interactions in solution that lower the thermodynamic activity of the drug, so that LLPS begins at a higher concentration; where the crystalline solubility rises, the amorphous solubility "typically" rises too (cited) xie2017 C55, C56, C27; in the solid, EPO is expected to form a salt with the drug's carboxylic acid (cited) xie2017 C49. (synthesis: in both cases the solubilization grew with the polymer level, resveratrol from ≈141 to ≈1230 µg/mL between 5 and 20 mg/mL HPMCAS and indomethacin from 1.9 to 6.2 µg/mL between 50 and 1000 µg/mL EPO, while the near-unchanged values of the other drugs were measured at 22 µg/mL to 1 mg/mL; a polymer that does not solubilize at a screening level may do so at the mg/mL a high-polymer dispersion releases, 3.7–4.7 mg/mL in the resveratrol slurries wegiel2015 R11. The LLPS chapter shows the same pattern for a micellar solubilizer, which raises both solubilities together (Amorphous solubility and LLPS F12), and for the cationic EUD-E with ibuprofen (Amorphous solubility and LLPS F19).)

Conditions and limits

Resveratrol at pH 6.8 and 37 °C with mg/mL levels of dissolved polymer; flux was measured only for the 15:85 HPMCAS series, not for the 65% slurry, HPMC or PVP wegiel2015 C10. Indomethacin at pH 2.2 and 5 xie2017 P2. UV values in PVP solutions carry at least about 8% error wegiel2015 X12.

Counterexamples and conflicts

E100 gave no gain for resveratrol because it does not dissolve at pH 6.8, although the abstract names complexation wegiel2015 C28, X8. HPMC at 10 µg/mL raised the danazol crystalline solubility 2.4-fold (synthesis: 2.2/0.9) at a low level jackson2014 R1 (Crystallization from solution F19). For the six tacrolimus products the maximal flux showed no solubilization by the excipients, including sodium lauryl sulfate trasi2016 C38. A solubilizing excipient added to a supersaturated solution consumes supersaturation by the factor of its solubilizing effect, a Bioperformance paper finds raina2015c C33.

Transfer check

Measure the crystalline solubility at the dissolved-polymer level the dispersion actually releases (measure that level, as for resveratrol by HPLC with an aerosol detector), refer the supersaturation to it, and measure free drug by flux wegiel2015 P8, E2, P10. A flux that falls while the concentration rises means drug bound in solution wegiel2015 C19. For phenolic drugs with PVP watch for a precipitate as the drug-to-polymer ratio rises; for acidic drugs with a cationic polymer expect solubilization wherever the polymer dissolves wegiel2015 C31; xie2017 C55.

History

Konno and co-workers (2008) ruled out complexation of felodipine at 1 mg/mL polymer, and Alonzo and co-workers (2011) found no felodipine–HPMC complex by flux (F4, F7) konno2008a C17; alonzo2011 C23. Wegiel and co-workers (2015) were the first in the library to show soluble and insoluble drug–polymer complexes during dispersion dissolution wegiel2015 C49; Xie and co-workers (2017) found EPO raising both solubilities of indomethacin xie2017 C2. Later papers cite the resveratrol work for concentration not being free drug mosqueragiraldo2018b C5; jackson2016 C43, and the LLPS chapter measured how a cationic Eudragit raises ibuprofen solubility by complexes in the bulk ueda2020b C34.

Topic 4 of 8 · 3 findings · F10–F11, F18

Drug loading and components mixed with the drug

F10

Topic 4Drug loading and components mixed with the drug1 of 3

Low-loading dispersions released within minutes and overshot into a colloid; at 50% drug, cellulosic dispersions released slowly and could miss the ceiling.

A 90:10 HPMC–felodipine particle dissipated within 5 min, while a 50:50 particle kept its shape for at least 30 min alonzo2011 R4. At 50% drug the HPMCAS danazol dispersion levelled near 6 µg/mL, below the amorphous solubility of 8 µg/mL, and celecoxib–HPMCAS dispersions needed 16 h to release what the 10% drug dispersion released within 4 h jackson2015 R2, R13; xie2016a R4.

moderateModerate: particle disintegration and the loading series are direct, but the release regimes are read from concentration curves without measuring polymer release, and the 50:50 danazol films were about 10% crystalline before dissolution alonzo2011 K2; xie2016a K4; jackson2015 K4, X10.

at 1 hat 16 h10% drugdose 2218.321.830% drug2210.520.450% drug225.021.160% drug222.015.80510152025celecoxib released from HPMCAS dispersions, µg/mL

Dose equal to the amorphous solubility (22 µg/mL), pH 6.8, 37 °C; none of these curves fell. xie2016a R4, X11

Delamanid edisylate–HPMCP tablets: released at pH 6.5, µg/mL of 10010% drug≈9920% drug≈9825% drug≈9530% drug≈5940% drug≈21

A release cliff between 25 and 30% drug; praziquantel–HPMCAS-MF dispersions showed none (≈100, ≈94 and ≈83% at 20, 30 and 40% drug). duong2022a R24; polyzois2024 R9

For your drug

  1. Watch the dispersion particles in the medium for the first 5–30 min and follow the drug under non-sink conditions at two or three loadings.
  2. Check the starting dispersion for crystals before ranking loadings, and read the early part of the curve as well as the plateau, since products may differ only in rate.

alonzo2011 P6; jackson2015 A2, R1; trasi2016 R10

How it works and key numbers
  1. At high polymer loading there is too little drug to form a layer that limits dissolution, and the drug dissolves at a fraction of the polymer rate (cited) alonzo2011 C37, E4.
  2. At moderate to high drug loading the polymer leaves the surface faster, and a drug-rich interface, "possibly in the amorphous state", regulates dissolution alonzo2011 C38.
  3. Fast release at 10% drug gives "very high local supersaturations", which rapid precipitation into a colloid depletes (F9) alonzo2011 C39.
  4. At 50% drug release can be too slow to reach the amorphous solubility: the 50:50 HPMCAS danazol dispersion gave 5.4 ± 0.8 µg/mL free drug and no drug-rich phase jackson2015 R9, R2.
  5. The fastest carriers were ionized or very hydrophilic at the test pH, PAA at pH 6.8 and EPO at pH 2.2 xie2016a C24; xie2017 C29.
5 vs 30 min90:10 HPMC–felodipine particle gone, against a 50:50 particle still intactalonzo2011 R4
5.4 ± 0.8 µg/mLfree danazol from the 50:50 HPMCAS dispersion, below the amorphous solubilityjackson2015 R9
≈95 → ≈59 µg/mLdelamanid edisylate–HPMCP release at 25% against 30% drug (of 100)duong2022a R24
Evidence: data, conditions and papers

Finding F10. Drug loading and polymer set how fast a dispersion releases and whether it reaches the ceiling: 10% drug dispersions released within minutes and overshot into a colloid, while at 50% drug HPMC and HPMCAS dispersions of danazol, celecoxib and indomethacin released slowly and 50:50 HPMCAS danazol never reached the amorphous solubility

In short. A 90:10 HPMC–felodipine particle dissipated within 5 min and 80–100% of the drug appeared within about 10 min, while a 50:50 particle kept its shape for at least 30 min and its solution rose slowly to ≈8.9 µg/mL alonzo2011 R4, R2, R1. Danazol dispersions still formed a drug-rich phase at 30% drug with all three polymers, but at 50% drug the HPMC dispersion passed 8 µg/mL only after ≈270 min and the HPMCAS dispersion levelled at ≈6 µg/mL without a drug-rich phase, with 5.4 ± 0.8 µg/mL free drug jackson2015 C36, R2, R9. The 50:50 PVP danazol dispersion dissolved as fast as the 90:10 one (≈9.3 µg/mL at ≈62 min) jackson2015 R2, X9. HPMCAS dispersions of ritonavir and lopinavir reached their maximum within 20 min and PVP dispersions in about 2 h trasi2015b R14. Celecoxib–HPMCAS dispersions released completely within 4 h at 10% drug but only after 16 h at 50% and to ≈15.8 of 22 µg/mL at 60%, HPMC dispersions more slowly still, while PVP and PAA dispersions at 50% released within 2–4 h and minutes xie2016a R4, R17; xie2015 R6; indomethacin–HPMC dispersions reached ≈39.5, ≈24.5 and ≈18.5 µg/mL at 60 min at 10, 30 and 50% drug, only the 10% one approaching the amorphous solubility and forming droplets xie2017 R10, R13, R14. Praziquantel dispersions showed no release cliff: with HPMCAS-MF they released completely at 20–50% drug at 667 µg/mL and about 100, 94 and 83% at 20, 30 and 40% drug at 1.5 mg/mL, which the authors read as polymer-controlled ("suggests") polyzois2024 R8, R9, C17, and delamanid edisylate dispersions with HPMCP released ≈95–99 µg/mL of 100 up to 25% drug and ≈59 and ≈21 at 30 and 40% duong2022a R24; a 50% posaconazole–HPMCAS dispersion never reached the amorphous solubility, with or without an acid stage elkhabaz2019a R8, C44.

Type. observation in 10 drugs (felodipine, danazol, ritonavir, lopinavir, celecoxib, indomethacin, tacrolimus, posaconazole, delamanid, praziquantel) Strength. : the disintegration and colloid formation of 10% drug dispersions are direct alonzo2011 K2: strong, and the celecoxib and indomethacin loading series are triplicate time courses in one test each xie2016a K4: strong; xie2017 K3: moderate to strong, but the release regimes are read from concentration curves, the drug-rich surface layer, local supersaturation and polymer release were not measured, and the 50:50 danazol films were about 10% crystalline before dissolution alonzo2011 K5: weak to moderate; jackson2015 K4: moderate, K6: weak, X10; trasi2016 K7: weak.

How it was shown

Alonzo and co-workers (2011) watched 90:10 and 50:50 HPMC–felodipine dispersion particles under crossed polars and dissolved them under non-sink conditions with in situ UV alonzo2011 P1, P6, P2. Jackson and co-workers (2015) dissolved danazol films at 90:10, 70:30 and 50:50 polymer:drug, Xie and Taylor (2016) celecoxib dispersions at 10–60% drug at a dose of 22 µg/mL, about the amorphous solubility, and Xie and co-workers (2017) indomethacin–HPMC dispersions at 10, 30 and 50% drug at pH 2.2 jackson2015 P1, P2; xie2016a P5; xie2017 P7.

What the data show

Release slowed as the drug loading rose, and at 50% drug the cellulosic dispersions stayed below the ceiling for hours or for good alonzo2011 R4, R1; jackson2015 R2; xie2016a R4; xie2017 R10.

systemconditionsresultids
felodipine HPMC 90:10 against 50:50polarized light; UV, 37 °C90:10 gone within 5 min, ≈23.4 µg/mL at 10 min; 50:50 intact at 30 min, ≈5.5 µg/mL at 10 minalonzo2011 R4, R1
danazol 50:50 PVP / HPMC / HPMCASfilm dissolution, 25 °C≈9.3 µg/mL at 60 min / past 8 µg/mL at ≈270 min / ≈6.0 µg/mL plateau without LLPS, 5.4 ± 0.8 µg/mL by fluxjackson2015 R13, R2, R9
celecoxib–HPMCAS 10 / 30 / 50 / 60% drug22 µg/mL nominal, pH 6.8, 37 °C≈18.3 / ≈10.5 / ≈5.0 / ≈2.0 µg/mL at 1 h; ≈21.8 / ≈20.4 / ≈21.1 / ≈15.8 at 16 hxie2016a R4
indomethacin–HPMC 10 / 30 / 50% drugpH 2.2, 80 µg/mL nominal, 37 °C≈39.5 / ≈24.5 / ≈18.5 µg/mL at 60 min; droplets only at 10%xie2017 R10, R14
praziquantel–HPMCAS-MF 20 / 30 / 40% drugPBS pH 6.5, 1.5 mg/mL≈100 / ≈94 / ≈83% releasedpolyzois2024 R9
delamanid edisylate–HPMCP 10 / 20 / 25 / 30 / 40%tablets, PBS pH 6.5≈99 / ≈98 / ≈95 / ≈59 / ≈21 µg/mL of 100duong2022a R24
Fig. 4 of alonzo2011: 50:50 and 90:10 HPMC–felodipine particles in buffer under crossed polars
Fig. 4 · alonzo201150:50 and 90:10 HPMC–felodipine particles in buffer under crossed polars

The 50:50 particle keeps its shape for 30 min; the 90:10 particle has dissipated within 5 min alonzo2011 R4.

Why

Following cited work, Alonzo and co-workers distinguish two regimes: at high polymer loading the drug dissolves at a fraction of the polymer rate, while at moderate to high drug loading the polymer leaves the surface faster and a drug-rich interface, "possibly in the amorphous state", regulates dissolution alonzo2011 C37, C38, E4. At 10% drug this gives "very high local supersaturations" that rapid precipitation depletes alonzo2011 C39. Jackson and co-workers cannot determine whether the missing drug-rich phase of the 50:50 HPMCAS danazol dispersion comes from a lower solubility, a much slower release or crystallization during dissolution jackson2015 C34.

Limits and transfer

The release regimes were not checked by measuring polymer release, and the 50:50 danazol films were partly crystalline before dissolution alonzo2011 A1; jackson2015 X10. Watch the dispersion particles in the medium for the first 5–30 min, follow the drug under non-sink conditions at two or three loadings, and check the starting dispersion for crystals before ranking loadings alonzo2011 P6; jackson2015 A2, R1.

How it was shown

Alonzo and co-workers (2011) made 90:10 and 50:50 polymer:drug dispersions of felodipine and indomethacin with HPMC or PVP by rotary evaporation, watched particles disintegrate under crossed polars, dissolved them under non-sink conditions with in situ UV, and dissolved three amounts of the 90:10 HPMC–felodipine dispersion alonzo2011 P1, P6, P2, A5. Jackson and co-workers (2015) dissolved spin-coated danazol films at 90:10, 70:30 and 50:50 with PVP, HPMC and HPMCAS at 25 °C, set to give 20–30 µg/mL if all dissolved, and measured free drug by flux for 90:10 and 50:50 jackson2015 P1, P2, P4. Trasi and Taylor (2015) followed 20% total-drug dispersions in PVP and HPMCAS by ultracentrifugation at 20 min and 2 h trasi2015b P9. Raina and co-workers (2014) dissolved neat amorphous nifedipine and a 50:50 HPMC dispersion at 5 mg/mL solids, 37 °C raina2014b P11. Chen and co-workers (2015) suspended 33.3% drug celecoxib–HPMCAS spray-dried particles at pH 3, where the polymer barely dissolves chen2015a P2, P10. Xie and Taylor (2015, 2016) dissolved celecoxib dispersions with PVP-K12, PVP-K29/32, HPMCAS, HPMC or PAA at 10–60% drug (106–250 µm) at a dose giving 22 µg/mL, about the amorphous solubility, in 400 mL of pH 6.8 buffer at 37 °C for 16 h xie2015 P5; xie2016a P5. Xie and co-workers (2017) dissolved indomethacin–HPMC dispersions at 10, 30 and 50% drug and an EPO dispersion, each holding 4 mg drug, in 50 mL of pH 2.2 buffer (80 µg/mL nominal) xie2017 P7. Trasi and co-workers (2016) compared the early dissolution of six tacrolimus products of unstated loading trasi2016 P11, X4; Li and Taylor (2018) sampled lopinavir films at 3 and 48 h li2018 P5.

What the data show

Felodipine. The 90:10 dispersion read ≈18.6 µg/mL at 5 min and ≈23.4 µg/mL at 10 min, the 50:50 dispersion ≈3.3 and ≈5.5 µg/mL alonzo2011 R1. Three amounts of 90:10 dispersion (90, 60 and 30 µg/mL of felodipine) peaked at ≈75, ≈53 and ≈28 µg/mL within about 10 min; at 90 µg/mL the reading then fell to ≈22.6 µg/mL by 50 min alonzo2011 R2. At 25 °C 90% PVP particles disappeared almost instantly, and 50% PVP particles stayed intact alonzo2011 R4. Only the 90% polymer media turned uniformly cloudy, with felodipine or indomethacin alonzo2011 R3. Danazol. Read from the 50:50 profiles, PVP gave ≈9.3 µg/mL at 60 min, HPMC ≈4.6 µg/mL at 60 min, ≈8.3 at 300 min and ≈9.85 at 1200 min, and HPMCAS ≈2.2, ≈5.3 and ≈6.1 µg/mL at 60, 300 and 990 min jackson2015 R13. The pyrene ratio of 50:50 HPMCAS drifted only from ≈1.93 to ≈1.82–1.89 and ≈1.745 at ≈890 min jackson2015 R2. By flux, 50:50 HPMC gave the highest value measured (9.1 ± 1.6 µg/mL) and 50:50 HPMCAS the lowest (5.4 ± 0.8 µg/mL) jackson2015 R9. Ritonavir and lopinavir. At 20 min the single-drug dispersions gave ritonavir ≈26.5 µg/mL from HPMCAS and ≈16.5 µg/mL from PVP; by 2 h ≈26.9 and ≈22.0 µg/mL trasi2015b R12, R13. Nifedipine. The 50:50 HPMC dispersion reached ≈100 µg/mL at ≈22 min against ≈6 µg/mL for the neat glass raina2014b R14. Celecoxib at pH 3. Without surfactant the liquid held only about 1.5–3.5 µg/mL HPMCAS over 24 h, and drug in the liquid rose slowly from S ≈4.3 to ≈6.7 over 48 h chen2015a R18, R17. Celecoxib at pH 6.8. HPMCAS dispersions reached ≈18.3, ≈10.5, ≈5.0 and ≈2.0 µg/mL at 1 h and ≈21.8, ≈20.4, ≈21.1 and ≈15.8 µg/mL at 16 h at 10, 30, 50 and 60% drug, without any fall; HPMC dispersions reached only ≈16.5 (50%) and ≈18.2 µg/mL (30%) at 16 h xie2016a R4, R17. At 50% drug the PVP dispersions gave ≈16–17 µg/mL at 2 h and ≈20 µg/mL by 4 h, the HPMCAS one ≈9.0 at 2 h and the HPMC one ≈5.8 µg/mL at 2 h xie2015 R6; the PAA dispersions peaked at ≈9–11 µg/mL within 3 min xie2016a R4. Indomethacin at pH 2.2. The HPMC dispersions read ≈5.5, ≈9 and ≈30.5 µg/mL at 10 min for 50, 30 and 10% drug, and ≈18.5, ≈24.5 and ≈39.5 µg/mL at 60 min; the 10% one was biphasic, fast to ≈30.5 µg/mL in 10 min and then slow, and "appeared to just reach" the amorphous solubility; the EPO dispersion peaked near ≈77 µg/mL at about 5 min xie2017 R10, R13. Tacrolimus. At 5 min the products ranged from ≈26 (Prograf) to ≈41 µg/mL (Accord) and by 20 min from ≈41 to ≈49 µg/mL, all at the same plateau later (F7) trasi2016 R10. Lopinavir at pH 3. From 3 to 48 h the HPMCAS, CAP and HPMCP films kept rising (for example HPMCAS at 33% drug ≈5.0 → ≈9.3 µg/mL), while HPMC, EC and CA films released fast li2018 R2, R3, C22.

papersystemmethod and conditionsresultids
alonzo2011felodipine HPMC 90:10 against 50:50polarized light; UV, 37 °C90:10 gone within 5 min, ≈23.4 µg/mL at 10 min; 50:50 intact at 30 min, ≈5.5 µg/mL at 10 minR4, R1
alonzo2011felodipine 90:10 HPMC, 90 / 60 / 30 µg/mL addedUV, 37 °C, single runspeaks ≈75 / ≈53 / ≈28 µg/mL within about 10 minR2
jackson2015danazol 50:50 PVP / HPMC / HPMCASfilm dissolution, 25 °C≈9.3 µg/mL at 60 min / past 8 µg/mL at ≈270 min / ≈6.0 µg/mL plateau, no LLPSR13, R2
jackson2015danazol 50:50 HPMC; 50:50 HPMCASflux9.1 ± 1.6; 5.4 ± 0.8 µg/mLR9
trasi2015britonavir 20% HPMCAS against PVPultracentrifuged at 20 min; 2 h≈26.5 against ≈16.5; ≈26.9 against ≈22.0 µg/mLR12, R13
raina2014bnifedipine–HPMC 50:50 against neat glassdissolution 5 mg/mL, 37 °C≈100 against ≈6 µg/mLR14
indulkar2019a (Release mechanism and LoC)ritonavir–copovidone 10% and 30% drugrelease into drug-saturated mediumsimilar release, read as polymer-controlledC43
saboo2020a (Release mechanism and LoC)PVP, PVPVA and HPMC dispersionsnormalized release ratesat low drug loading drug and polymer release together at about the neat polymer rateC16
xie2016acelecoxib–HPMCAS 10 / 30 / 50 / 60% drugdissolution to 22 µg/mL nominal, pH 6.8, 37 °C≈18.3 / ≈10.5 / ≈5.0 / ≈2.0 µg/mL at 1 h; ≈21.8 / ≈20.4 / ≈21.1 / ≈15.8 at 16 hR4
xie2015celecoxib 50%, PVP-K12 / PVP-K29/32 / HPMCAS / HPMCsame≈16.1 / ≈16.9 / ≈9.0 / ≈5.8 µg/mL at 2 hR6
xie2017indomethacin–HPMC 10 / 30 / 50% drugpH 2.2, 80 µg/mL nominal, 37 °C≈39.5 / ≈24.5 / ≈18.5 µg/mL at 60 min; droplets only at 10%R10, R14
trasi2016six marketed tacrolimus capsules40 mL, pH 4.5, 37 °C≈26–41 µg/mL at 5 min, same plateau after 45 minR10
elkhabaz2019aposaconazole–HPMCAS 50% drugtwo-stage and FaSSIF only, 37 °Cfell to ≈6 µg/mL within 30 min in both; amorphous solubility never reachedR8, C44
duong2022adelamanid edisylate 10 / 20 / 25 / 30 / 40%, HPMCP; HPMCAStablets, PBS pH 6.5≈99 / ≈98 / ≈95 / ≈59 / ≈21; ≈95 / ≈87 / ≈87 / ≈85 / ≈48 µg/mL of 100R24
nguyen2023cdelamanid salt with HPMCAS-HF, pH 6.5drug by UV; polymer by HPLC-ELSDdrug ≈0% while ≈29.5% of the polymer dissolved in 60 minR11, R12
polyzois2024praziquantel–HPMCAS-MF 20–50%; HPMC E5 LVPBS pH 6.5, 667 µg/mL and 1.5 mg/mLcomplete at 20–50% (667 µg/mL); ≈100 / ≈94 / ≈83% at 20 / 30 / 40% (1.5 mg/mL); HPMC E5 LV slower, 86% at 50% (667 µg/mL)R8, R9
polyzois2024praziquantel–HPMCAS-MF 20 and 30%, hot-melt extruded against solvent-evaporated1.5 mg/mL≈106 against ≈100%; ≈100 against ≈94%R11, R9

Figure

Fig. 4 of alonzo2011: 50:50 and 90:10 HPMC–felodipine particles in buffer under crossed polars
Fig. 4 · alonzo201150:50 and 90:10 HPMC–felodipine particles in buffer under crossed polars

The 50:50 particle (a, b) keeps its shape for 30 min; the 90:10 particle (c, d) has dissipated within 5 min alonzo2011 R4.

Fig. 3c of jackson2015: dissolution of the 50:50 HPMCAS danazol dispersion with the pyrene ratio
Fig. 3c · jackson2015dissolution of the 50:50 HPMCAS danazol dispersion with the pyrene ratio

The UV curve levels near 6 µg/mL, below the red amorphous-solubility line, and the pyrene ratio barely moves: no drug-rich phase forms jackson2015 R2, R13.

Fig. 4 of xie2016a: release of celecoxib from PAA and HPMCAS dispersions at several drug loadings
Fig. 4 · xie2016arelease of celecoxib from PAA and HPMCAS dispersions at several drug loadings

The PAA dispersions spike and crash within the first hour; the HPMCAS dispersions rise more slowly the higher the drug loading, and the 60% one stays below the dose at 16 h xie2016a R4.

Why

Following cited work, Alonzo and co-workers distinguish two regimes: at high polymer loading there is too little drug to form a layer that limits dissolution, and the drug dissolves at a fraction of the polymer rate (Eq. 4); at moderate to high drug loading the polymer leaves the surface faster and a drug-rich interface, "possibly in the amorphous state", regulates dissolution; their data "appear to agree" alonzo2011 C37, C38, E4. At 10% drug this gives "very high local supersaturations", which they hold to be "most likely local" and depleted by rapid precipitation, while at 50% drug the drug-rich layer, if it stays amorphous, "would presumably" cap the concentration at the pure amorphous level alonzo2011 C39, C47, C46. Jackson and co-workers cannot tell whether the missing drug-rich phase of the 50:50 HPMCAS dispersion comes from a lower drug solubility in this formulation, a much slower release, or crystallization during dissolution ("it is not possible to determine"), and judge that 50% loadings "might not be expected" to perform comparably in membrane transport in vivo jackson2015 C34, C37. Trasi and Taylor conclude that the polymer influenced the tendency to undergo LLPS on dissolution trasi2015b C45. Chen and co-workers state that at this "relatively low" drug loading drug release "appears to be" controlled by the polymer chen2015a C31. Xie and Taylor recall the cited analyses in which drug and polymer dissolve together at low loading while at high loading the polymer may dissolve faster and leave a drug-rich layer xie2016a C4, E1; they attribute the fast start of PAA dispersions "presumably" to PAA being fully ionized (pKa 4.28) and very hydrophilic at pH 6.8 xie2016a C24. For indomethacin the faster release at lower loading is "indicative of" polymer-controlled dissolution, HPMC gelling and releasing "probably through a matrix-regulated diffusion mechanism", while EPO, ionized at pH 2.2, dissolves fast xie2017 C31, C64, C29. Trasi and co-workers "believe" that the high (50%) drug loading reported for the tacrolimus innovator makes its dissolution drug controlled, which would explain why no drug colloid formed; the loading is unreferenced and unknown for the generics trasi2016 C41, X4. (synthesis: the polymer that dissolves fastest in the medium carries the drug fastest, and its speed depends on the pH: PAA at pH 6.8 and EPO at pH 2.2 are ionized; HPMCAS at pH 6.8 dissolved fastest in the ritonavir and lopinavir work but slowest of the three in the 50:50 danazol films, so the polymer ranking for release speed is not fixed either and depends on drug loading. A fast polymer that does not inhibit crystallization loses the gain within minutes, see F16 and F20.) For praziquantel the gradual decline with loading "suggests that the release is polymer controlled", and no "falling-of-the-cliff" effect appeared; polymer release was not measured polyzois2024 C17, C16. For delamanid, HPMCAS-HF released almost no drug at pH 6.5 while about 30% of the polymer dissolved, so dissolved polymer did not guarantee released drug nguyen2023c R11, R12. Elkhabaz and co-workers read the poor 50% posaconazole dispersion as competitive crystallization during release, "highlighting" its susceptibility elkhabaz2019a C44.

Conditions and limits

Only 10, 30 and 50% drug were tested (no 30% felodipine), the release regimes were not checked by measuring polymer release (except HPMCAS leaching in acid), and the 70:30 danazol profiles were not shown alonzo2011 A1; jackson2015 R4; chen2015a P12. The 50:50 danazol films were partly crystalline before dissolution, so the high-loading results mix a loading effect with residual crystals jackson2015 X10. The felodipine runs at three amounts were single runs and rose faster than the triplicate run at the same dose alonzo2011 X15. In the celecoxib series the dose equalled the amorphous solubility, so "complete" means reaching about 22 µg/mL, and the 10% HPMCAS dispersion was cryo-milled, not sieved xie2016a X11, X10; the indomethacin series ran at pH 2.2 only xie2017 P7.

Counterexamples and conflicts

The 50:50 PVP danazol dispersion released like the 90:10 one and gave the same free drug jackson2015 X9, R9. The release-mechanism chapter of the library (written later) tests the polymer-controlled regime with normalized drug and polymer release rates saboo2020a C16; indulkar2019a C43. The Bioperformance chapter finds that a lower loading is not always better for reaching the amorphous solubility (Bioperformance F8).

Transfer check

Watch dispersion particles in the medium for the first 5–30 min and follow the drug under non-sink conditions at two or three loadings alonzo2011 P6; jackson2015 A2. A dispersion that disintegrates within minutes and overshoots the amorphous solubility will form a colloid (F9); one that dissolves slowly and stays below it, as 50:50 HPMCAS danazol did, gives less free drug (F7). Check the starting dispersion for crystals before ranking loadings jackson2015 R1. When comparing products of one drug (for example a brand and generics), read the early part of a non-sink test as well as the plateau, since the products may differ only in rate trasi2016 R10.

History

Polymer-controlled and drug-controlled dissolution were described in cited work on PVP coprecipitates alonzo2011 R26. Alonzo and co-workers (2011) linked the two regimes to colloid formation in ASD dissolution alonzo2011 C39. Jackson and co-workers (2015) found LLPS up to 30% danazol with three polymers and slow release at 50% jackson2015 C36, C37; Trasi and Taylor (2015) found HPMCAS faster than PVP for ritonavir and lopinavir trasi2015b R14. Xie and Taylor (2015, 2016) and Xie and co-workers (2017) found the same loading dependence for celecoxib and indomethacin with HPMCAS and HPMC and contrasted it with fast-dissolving PVP, PAA and EPO xie2016a C20; xie2015 C19; xie2017 C31; the title gained celecoxib and indomethacin then. Later papers of the library cite the 2011 and 2015 work for the dependence of LLPS on drug loading and polymer (builds_on, as listed in the evidence index of this subcategory), and an enzalutamide study cites the 2016 and 2018 work for soluble polymers releasing fast but letting the drug crystallize and poorly soluble polymers limiting release wilson2020 C6. Polyzois and co-workers (2024) found no release cliff for praziquantel up to 40–50% drug and hot-melt extruded dispersions releasing at least as well as solvent-evaporated ones, and Alvarenga and co-workers (2025) found release "minimally affected" by the process polyzois2024 C16, C31; alvarenga2025 C48.

F11

Topic 4Drug loading and components mixed with the drug2 of 3

Two amorphous drugs that mix in the drug-rich phase lower each other's ceiling in proportion to their mole fractions.

Films of ritonavir (RTV) and lopinavir (LPV) mixed at 7:3, 5:5 and 3:7 gave lower concentrations of each drug the smaller its share; five of six values lay within 0.5 µg/mL of the ideal-mixing ceiling C_{max} = S_a x_d, the amorphous solubility S_a times the mole fraction x_d trasi2015b R5, E1. Two single-drug dispersions added together gave the same kind of drop trasi2015b R11.

strongStrong for the drop and its fit to ideal mixing; moderate for the separate-addition result; weak to moderate for the slower crystallization, which was followed for 5 h trasi2015b K1, K2, K5, K6.

measured, 60 minritonavir alone2522.9RTV:LPV 7:316.715.2RTV:LPV 5:511.611.4RTV:LPV 3:76.86.3051015202530ritonavir from films, µg/mL

Dashed ticks: amorphous solubility (alone, cited) or ideal-mixing ceiling (blends). trasi2015b R5, E1, M1

measured, 60 minlopinavir alone1715.6RTV:LPV 3:712.312.7RTV:LPV 5:59.09.1RTV:LPV 7:35.65.9051015202530lopinavir from films, µg/mL

Films in pH 6.8 buffer with 10 µg/mL HPMCAS; dashed ticks as above. trasi2015b R5, E1, M2

For your drug

  1. For two amorphous drugs in one product, or two products taken together, check that the pair is miscible (one Tg of the blend) and un-ionized at the intestinal pH, and compute each ceiling as amorphous solubility times mole fraction.
  2. Confirm the ceilings by dissolving films or the dispersion with ultracentrifugation, and weigh the lower ceiling against slower crystallization of the mixed phase.

trasi2015b R2, E1, P9, C49

How it works and key numbers
  1. Above the LLPS concentration each drug forms a disordered drug-rich phase, and two miscible drugs mix in that phase trasi2015b C36.
  2. Mixing lowers the chemical potential of each drug, and with it the concentration of each in the water, "as long as the two components are miscible in the drug-rich phase" trasi2015b C36.
  3. For ideal mixing (cited) each ceiling is C_{max} = S_a x_d; the agreement "indicat[es]" a close to ideal mixture, and each blend had a single Tg trasi2015b C38, C39, E1, R2.
  4. The lower supersaturation of each drug is the authors' reading, "at least in part", of why the mixed drug-rich phase did not crystallize within 5 h while lopinavir alone did after 1–2 h trasi2015b C51, R15.
To feel the numbers. In the 3:7 RTV:LPV film ritonavir reached 6.3 µg/mL against 22.9 µg/mL alone: 6.3 ÷ 22.9 ≈ 0.28, about a quarter of its own ceiling.
15.2 / 11.4 / 6.3 µg/mLritonavir from 7:3, 5:5 and 3:7 RTV:LPV films (22.9 alone)trasi2015b R5
11.2 and 9.1 µg/mLritonavir and lopinavir after two single-drug HPMCAS dispersions were added togethertrasi2015b R11
1–2 h vs none in 5 hcrystallization of lopinavir's drug-rich phase alone against the mixed phasetrasi2015b R15
Evidence: data, conditions and papers

Finding F11. A second amorphous drug that mixes with the first lowered each drug's ceiling to about its amorphous solubility times its mole fraction, whether the two were co-formulated or dissolved from separate dispersions, and the mixed drug-rich phase crystallized later

In short. In drug-only films ritonavir reached 22.9 µg/mL alone and 15.2, 11.4 and 6.3 µg/mL at 7:3, 5:5 and 3:7 RTV:LPV, and lopinavir 15.6 alone and 12.7, 9.1 and 5.9 µg/mL at 3:7, 5:5 and 7:3; five of the six mixed values lay within 0.5 µg/mL of the ideal-mixing ceiling C_{max} = S_a\,x_d, the exception being ritonavir from 7:3 (15.2 against 16.7) trasi2015b R5, E1. PVP and HPMCAS dispersions with 20% total drug gave the same ratio-dependent drop after 2 h, and two single-drug HPMCAS dispersions added together gave 11.2 µg/mL ritonavir and 9.1 µg/mL lopinavir after 60 min, close to the 5:5 dispersion trasi2015b R13, R11, R9. Drug-rich phases holding both drugs showed no crystallization within 5 h, whereas lopinavir alone crystallized between 1 and 2 h trasi2015b R15, C33, C34. The authors advise that "the potential for decreased bioavailability due to lowered effective drug concentrations should be considered" trasi2015b C52.

Type. single-system observation (ritonavir–lopinavir; films and two polymers) Strength. for the drop and its fit to ideal mixing trasi2015b K1: strong, K2: strong; moderate for the separate-addition result and the agreement of dispersion data with the ideal-mixing lines trasi2015b K5: moderate, K3: moderate; weak to moderate for the crystallization benefit, followed for 5 h trasi2015b K6: weak to moderate.

How it was shown

Trasi and Taylor (2015) dissolved drug-only films of ritonavir (RTV), lopinavir (LPV) or RTV:LPV 7:3, 5:5 and 3:7, and 20% total-drug dispersions in PVP and HPMCAS, in pH 6.8 buffer, assaying filtered samples or ultracentrifuged supernatants trasi2015b P2, P6, P1, P9. Two single-drug dispersions were also added together, and drug-rich phases made above the LLPS concentration were followed with pyrene for 5 h trasi2015b P7, P11.

What the data show

Each drug's ceiling fell with its share in the mixture, close to the ideal-mixing ceiling C_{max} = S_a x_d computed with amorphous solubilities of 25 (RTV) and 17 µg/mL (LPV) trasi2015b R5, E1, M1, M2.

systemmethodresultids
RTV:LPV films 7:3 / 5:5 / 3:7, ritonavirfilm dissolution, filtered, 60 min15.2 / 11.4 / 6.3 against 16.7 / 11.6 / 6.8 µg/mL predictedtrasi2015b R5
same films, lopinavirsame5.9 / 9.1 / 12.7 against 5.6 / 9.0 / 12.3 µg/mL predictedtrasi2015b R5
20% HPMCAS dispersions 7:3 / 5:5 / 3:7, ritonavirultracentrifuged, 2 h≈17.0 / ≈12.0 / ≈7.0 µg/mLtrasi2015b R13
two single-drug HPMCAS dispersions added togetherultracentrifuged, 60 minRTV 11.2, LPV 9.1 µg/mLtrasi2015b R11
drug-rich phases: LPV alone; RTV + LPVpyrene, supernatant, 5 hLPV crystallized at 1–2 h (4.3 µg/mL at 5 h); mixtures unchangedtrasi2015b R15, R16
Fig. 3 of trasi2015b: ritonavir (a) and lopinavir (b) dissolving from pure and mixed amorphous films
Fig. 3 · trasi2015britonavir (a) and lopinavir (b) dissolving from pure and mixed amorphous films

The pure film reaches close to the amorphous-solubility line; each step toward a larger share of the other drug lowers the plateau trasi2015b R3, R4.

Why

The authors trace the drop to mixing of the two drugs in the disordered drug-rich phase, which lowers the chemical potential of each and with it the concentration of each in the water, "as long as the two components are miscible in the drug-rich phase" trasi2015b C36. The agreement with ideal mixing "indicat[es]" a close to ideal mixture, and each blend had a single Tg trasi2015b C38, C13. The later crystallization of the mixed phases is attributed "at least in part" to the lower supersaturation trasi2015b C51.

Limits and transfer

One drug pair that mixes almost ideally was followed for 5 h only, and no drug-rich phase was analysed after separate addition trasi2015b X5, X11, X9. For two amorphous drugs in one product, or two products taken together, check miscibility (one Tg of the blend), compute each ceiling as amorphous solubility times mole fraction and confirm it by dissolution with ultracentrifugation; the minor drug loses most (synthesis: 6.3/22.9 = 0.28 for ritonavir in the 3:7 film) trasi2015b R2, E1, P9, R5.

How it was shown

Trasi and Taylor (2015) coated 5 mg of drug (RTV only, LPV only, or RTV:LPV 7:3, 5:5, 3:7 by weight) inside vials by rotary evaporation, dissolved the films in 10 mL of 100 mM pH 6.8 buffer with 10 µg/mL HPMCAS as crystallization inhibitor at 300 rpm, filtered samples through 0.45 µm glass filters and assayed them by HPLC up to 60 min trasi2015b P2, P6, P10. They made 20% total-drug dispersions in PVP K-29/32 and HPMCAS-MF by rotary evaporation, dissolved 20 mg in 40 mL at 25 °C, and assayed filtered samples (PVP) or ultracentrifuged supernatants (both polymers) at 20 min and 2 h trasi2015b P1, P5, P9. For separate addition, equal weights of RTV and LPV were added as two single-drug PVP dispersions (filtered sampling) or two HPMCAS dispersions (ultracentrifuged at 60 min) trasi2015b P7. DSC gave one Tg for every drug mixture and dispersion trasi2015b R2. Drug-rich phase suspensions were made by adding methanol stocks above the LLPS concentration (RTV 50, LPV 35, RTV 25 + LPV 17, RTV 50 + LPV 35 µg/mL) with pyrene, followed by the I3/I1 ratio for 5 h, and the supernatant was assayed at 0 and 5 h trasi2015b P11, P12. The ceiling was computed from Eq. 1 with amorphous solubilities of 25 (RTV) and 17 µg/mL (LPV) cited from the group's antisolvent study trasi2015b E1, M1, M2.

What the data show

Films. Each film released drug quickly over the first 20–30 min and then rose slowly; the predicted ceilings were 16.7, 11.6 and 6.8 µg/mL for RTV and 5.6, 9.0 and 12.3 µg/mL for LPV at 7:3, 5:5 and 3:7 trasi2015b R3, R4, R5. PVP dispersions, filtered, 60 min. RTV ≈20.4 µg/mL from the RTV dispersion against ≈12.2, ≈10.8 and ≈6.0 from 7:3, 5:5 and 3:7; LPV ≈18.0 against ≈12.0, ≈9.1 and ≈5.9 from 3:7, 5:5 and 7:3 trasi2015b R9. Ultracentrifuged, 2 h, HPMCAS / PVP. RTV ≈17.0 / ≈14.9 (7:3), ≈12.0 / ≈11.4 (5:5), ≈7.0 / ≈6.4 (3:7); LPV ≈13.0 / ≈12.0 (3:7), ≈8.0 / ≈8.4 (5:5), ≈5.2 / ≈5.6 (7:3) trasi2015b R13. Plotted against RTV mole fraction in the drug-rich phase, the HPMCAS RTV points (≈7.0, ≈12.0, ≈17.0 µg/mL) lie on the Eq. 1 line (≈7.0, ≈11.7, ≈16.9), and the LPV points (≈13.0, ≈8.0, ≈5.0) on or up to about 15% below it (≈12.2, ≈9.2, ≈5.9) trasi2015b R17, X8. Separate addition. With two PVP dispersions RTV rose to ≈15.2 µg/mL at 20 min and fell to ≈12.2 µg/mL at 60 min as LPV climbed to ≈9.7 µg/mL trasi2015b R10. Miscibility. Tg 46 °C (RTV), 77 °C (LPV), 66, 60.5 and 54 °C for 3:7, 5:5 and 7:3 trasi2015b R2. Crystallization of drug-rich phases. LPV alone: I3/I1 ≈0.645 at 0 h, ≈0.640 at 1 h, ≈0.565 at 2 h and ≈0.510 at 5 h, with 4.3 µg/mL free LPV at 5 h; RTV alone ≈0.62–0.63 with 25.4 µg/mL at 5 h; both mixtures ≈0.63–0.66, with free RTV 14.2–15.8 and LPV 7.0–7.5 µg/mL unchanged from 0 to 5 h, at nearly the same values for twice the total drug trasi2015b R15, R16.

papersystemmethod and conditionsresultids
trasi2015bRTV:LPV films 7:3 / 5:5 / 3:7film dissolution, filtered, 60 minRTV 15.2 / 11.4 / 6.3 against 16.7 / 11.6 / 6.8 µg/mL predictedR5
trasi2015bsame films, LPVsame5.9 / 9.1 / 12.7 against 5.6 / 9.0 / 12.3 µg/mLR5
trasi2015b20% dispersions, HPMCAS and PVPultracentrifuged, 2 h, 25 °Cratio-dependent drop for both drugs and both polymersR13
trasi2015btwo HPMCAS single-drug dispersions added togetherultracentrifuged, 60 minRTV 11.2, LPV 9.1 µg/mLR11
trasi2015bdrug-rich phases: LPV alone; RTV + LPVpyrene, supernatant, 5 hLPV crystallized at 1–2 h (4.3 µg/mL at 5 h); mixtures unchangedR15, R16
trasi2015a (Amorphous solubility and LLPS)ritonavir with 10 µM lopinavir, paclitaxel or felodipineantisolvent LLPS onsetabout 14, 10 and 12 against about 26 µg/mLR7
alhalaweh2016 (Bioperformance)ritonavir–atazanavir dispersionCaco-2 fluxbinary flux about half that of each drug aloneR17
trasi2019 (ASD process)ritonavir and lopinavir co-granulesdissolution, pH 6.8lower concentrations attributed to mixing of the two drugsC38

Figure

Fig. 3 of trasi2015b: ritonavir (a) and lopinavir (b) dissolving from pure and mixed amorphous films
Fig. 3 · trasi2015britonavir (a) and lopinavir (b) dissolving from pure and mixed amorphous films

The pure film (diamonds) reaches close to the blue amorphous-solubility line; each step toward a larger share of the other drug lowers the plateau trasi2015b R3, R4.

Fig. 8 of trasi2015b: ideal-mixing lines against the mole fraction of ritonavir in the drug-rich phase, with HPMCAS dispersion data
Fig. 8 · trasi2015bideal-mixing lines against the mole fraction of ritonavir in the drug-rich phase, with HPMCAS dispersion data

The RTV diamonds sit on the blue line; the LPV circles sit on or slightly below the orange line trasi2015b R17, X8.

Why

The authors trace the drop to mixing of the two drugs in the disordered drug-rich phase, which lowers the chemical potential of each and with it the concentration of each in the water, "as long as the two components are miscible in the drug-rich phase" trasi2015b C36. Assuming ideal mixing (cited), the ceiling is C_{max} = S_a x_d; the good agreement "indicat[es]" a close to ideal mixture, and the single Tg of each blend is read as miscibility trasi2015b C38, C39, C13. In the LLPS chapter the same relation is written from the ideal-mixing chemical potentials \mu_1 = \mu_1^{\circ} + RT\ln x_1 trasi2015a E2, E4. The solution phase behaviour is the same whether supersaturation comes from antisolvent addition or from dissolving a dispersion trasi2015b C44. After separate addition, the authors read the drop as mixing in solution followed by LLPS, so that intimate contact in the formulation is not needed ("can also potentially occur"); no colloid or drug-rich phase was analysed in those runs trasi2015b C47, X9. The later crystallization of the mixed phases is attributed "at least in part" to the lower supersaturation that follows from the lower amorphous solubility, presented as "one potential advantage" trasi2015b C51, C49. (synthesis: the polymer sets only how fast the lowered ceiling is reached (HPMCAS within 20 min, PVP in about 2 h); the composition of the drug-rich phase sets its height.) Li and Taylor (2018) apply the same reasoning to a polymer that does not dissolve: mixing with it lowers the chemical potential of the drug, and the lopinavir ceiling fell below the amorphous solubility, near or below the line of the amorphous solubility scaled by drug weight fraction for several polymers (F18) li2018 C9, C43, E7.

Conditions and limits

One drug pair that mixes almost ideally, 20% total drug, a simple buffer, 25 °C for powder dissolution and unstated temperatures for films, ultracentrifugation and pyrene runs trasi2015b X5. The Eq. 1 check uses cited amorphous solubilities; the pure films reached about 8% less trasi2015b X14. The mole fractions need molecular weights that the paper does not print trasi2015b E1. Crystallization was followed for 5 h only, and the attribution to lower supersaturation is not separated from other effects of ritonavir trasi2015b X11.

Counterexamples and conflicts

The LPV points of the dispersions lie up to about 15% below the ideal-mixing line trasi2015b X8. In the LLPS chapter an ionized partner (diclofenac) did not lower the ritonavir ceiling, because it stayed in the water (Amorphous solubility and LLPS F11) trasi2015a R11. None found in the library in which a miscible un-ionized second drug failed to lower the ceiling.

Transfer check

For two amorphous drugs in one product, or two amorphous products taken together, check that the pair is miscible (one Tg of the blend) and both un-ionized at the intestinal pH, compute each ceiling as amorphous solubility times mole fraction, and confirm it by dissolving films or the dispersion with ultracentrifugation trasi2015b R2, E1, P9. The minor drug loses most: in the 3:7 film ritonavir reached about a quarter of its pure-film value (synthesis: 6.3/22.9 = 0.28) trasi2015b R5. Weigh the lower ceiling against the slower crystallization of the mixed phase trasi2015b C49.

History

The group's antisolvent study, in the LLPS chapter, first showed that a second drug lowers the amorphous solubility of each trasi2015b C7; trasi2015a R7. Trasi and Taylor (2015) carried it to dissolving films and dispersions and to separate products taken together trasi2015b C9, C47. Later papers of the library cite it for the lower maximum supersaturation of binary amorphous combinations, for co-granules of ritonavir and lopinavir and for atazanavir with darunavir (builds_on, as listed in the evidence index of this subcategory) trasi2019 C38. Within this chapter, a lopinavir leaching study took the mutual lowering of amorphous solubility as the precedent for drug and polymer holding each other back in a dispersion li2016b C33, C34, and Li and Taylor (2018) cite it as the basis for an undissolved polymer lowering the ceiling (F18) li2018 C9.

F18

Topic 4Drug loading and components mixed with the drug3 of 3

A polymer that stays undissolved and mixed with the drug held lopinavir below its amorphous solubility, most at low drug loading.

At pH 3, where the enteric and insoluble polymers stay undissolved, lopinavir films with HPMCAS, CAP, EC or HPMCP gave 48-h concentrations of only ≈0.3–4.3 µg/mL at 15% drug and ≈10.5–15.7 µg/mL at 85% drug, against an amorphous solubility of 17.4 µg/mL li2018 R3, R1. HPMC films, which dissolve, and a physical mixture of amorphous lopinavir with HPMCAS reached the amorphous solubility li2018 R3, R14.

moderateModerate: direct triplicate concentrations with a soluble-polymer and a physical-mixture control, but several curves were still rising at 48 h and the interaction ranking rests on indirect evidence li2018 K1, K2, K3, X4, X5.

dissolving polymertwo Tgs (phase-separated)one phase, undissolved: 15% to 85% drugHPMC17.417.5–18.9CA and EUD17.412.8–17.0HPMCAS17.44.3 → 15.7EC17.40.3 → 15.3HPMCP17.40.6 → 10.505101520lopinavir at 48 h, pH 3, µg/mL

Cast films in citrate buffer with 20 µg/mL HPMC, 25 °C, ultracentrifuged; dashed tick: amorphous solubility. li2018 R3, R1, R8

Lopinavir with HPMCAS at 48 h, µg/mLdispersion, 15% drug≈4.3dispersion, 85% drug≈15.7physical mixture, any loading≈17–18.5

Only the molecularly mixed dispersion held the drug back; the physical mixture reached the amorphous solubility. li2018 R3, R14

For your drug

  1. For a dispersion with an enteric or insoluble polymer, measure the drug concentration at two or three loadings in the medium where the polymer stays undissolved, for 48 h with a solution inhibitor, and compare it with a physical mixture of amorphous drug and polymer.
  2. Count glass transitions: two Tgs predict little suppression, one Tg with evidence of interaction predicts suppression that grows as loading falls; then check release once the polymer dissolves at intestinal pH.

li2018 P5, P14, C56, C35, C62, C64

How it works and key numbers
  1. Mixing with a polymer and taking up water lower the chemical potential of the drug relative to the pure amorphous phase li2018 C43.
  2. A lower drug loading and a more negative interaction parameter χ lower the solubility further, as in the cited Flory–Huggins term \Delta\mu_{drug}/RT = \ln\Phi_{drug} + (1 - 1/r)\Phi_{poly} + \chi\Phi_{poly}^{2} li2018 C44, E4.
  3. This holds only while the dispersion is one phase, stays one phase on hydration, and the polymer is insoluble enough to keep the composition, as for an enteric polymer at low pH li2018 C45.
  4. In phase-separated dispersions and the physical mixture the components "behave independently", and a soluble polymer is not substantially mixed with the drug droplets li2018 C49, C48.
  5. The authors give the "approximate trend" HPMCP > EC > HPMCAS and relate it to functional groups, for example about 31% phthalyl groups in HPMCP that hydrogen-bond strongly li2018 C54, C55.
≈0.3–4.3 vs 17.4 µg/mLlopinavir from 15% drug films with HPMCAS, CAP, EC or HPMCP, against the amorphous solubilityli2018 R3, R1
≈17–18.5 µg/mLphysical mixture of amorphous lopinavir and HPMCAS at every loadingli2018 R14
7.5–11.5%posaconazole released from HPMCAS dispersions in FaSSGF, below the crystalline solubilityelkhabaz2019a R10, R1
Evidence: data, conditions and papers

Finding F18. A polymer that stays undissolved and is mixed with the drug lowered the maximum lopinavir concentration below the amorphous solubility, most at low drug loading and with HPMCP and EC, whereas phase-separated dispersions, a physical mixture and a dissolving polymer reached it

In short. At pH 3 and 25 °C, lopinavir films with HPMCAS, CAP, EC or HPMCP gave 48-h concentrations that rose with drug loading and stayed below the 17.4 µg/mL amorphous solubility: at 15% drug ≈4.3, ≈3.1, ≈0.3 and ≈0.6 µg/mL, at 85% drug ≈15.7, ≈11.4, ≈15.3 and ≈10.5 µg/mL, against a crystalline solubility of 3.1 µg/mL li2018 R3, R1. CA and EUD films, which showed two glass transitions, gave ≈12.8–17.0 µg/mL, a physical mixture of amorphous lopinavir with HPMCAS ≈17–18.5 µg/mL and HPMC films ≈17.5–19 µg/mL li2018 R3, R8, R14. The authors rationalize the extent of suppression by "ASD composition, mixing state and the extent and strength of drug-polymer interactions", and the most suppressed dispersion (HPMCP) was also the slowest to crystallize li2018 C68, C61.

Type. single-system observation (lopinavir, seven polymers, 15–85% drug) Strength. : the concentrations are direct triplicates with a soluble-polymer and a physical-mixture control, but several curves were still rising at 48 h, dissolved polymer was not measured, χ was not measured and the interaction ranking rests on indirect evidence li2018 K1: moderate to strong, K2: moderate to strong, K3: weak to moderate, X4, X5, X3.

How it was shown

Li and Taylor (2018) cast lopinavir films with seven polymers at 15–85% drug, stirred them in pH 3 citrate buffer holding 20 µg/mL HPMC at 25 °C, and assayed lopinavir at 3 h and, after ultracentrifugation, at 48 h li2018 P4, P5. The mixing state came from modulated DSC, IR and water sorption, and a physical mixture of amorphous lopinavir and HPMCAS served as control li2018 P9, P10, P11, P14.

What the data show

Molecularly mixed, undissolved polymers held lopinavir below its amorphous solubility, the more so the lower the drug loading li2018 R3.

systemconditionsresult at 48 hids
lopinavir 15% / 85% drug with HPMCAS, CAP, EC, HPMCPfilms, pH 3, 25 °C, ultracentrifuged≈4.3, ≈3.1, ≈0.3, ≈0.6 / ≈15.7, ≈11.4, ≈15.3, ≈10.5 against 17.4 µg/mLli2018 R3
same with CA, EUD (two Tgs)same≈12.8–17.0 µg/mLli2018 R3, R8
HPMCAS physical mixture against dispersionsame≈17–18.5 against ≈4.3–15.7 µg/mLli2018 R14
HPMC films, 15–85% drugsame≈17.5–18.9 µg/mLli2018 R3
50% dispersions at 90% RHwater sorption against additive predictionHPMCAS ≈5.4 against 6.8%, HPMCP ≈5.1 against 7.3%; CA, EUD on the predictionli2018 R12
posaconazole–HPMCAS 10 / 25 / 50% in FaSSGF, polymer undissolvedHPLC after 60 min7.5 / 10 / 11.5% of a 400 µg/mL dose, below the 115.1 µg/mL crystalline solubilityelkhabaz2019a R10, R1
Fig. 2 of li2018: lopinavir concentration against drug loading for seven polymers after 3 and 48 h
Fig. 2 · li2018lopinavir concentration against drug loading for seven polymers after 3 and 48 h

HPMC sits at the amorphous-solubility band at every loading, while the insoluble polymers lie below it and rise with loading, HPMCP lowest li2018 R3, E7.

Why

Mixing with a polymer and taking up water lower the chemical potential of the drug relative to the pure amorphous phase, so a low drug loading and a more negative χ lower its solubility, as long as the dispersion stays one phase and the polymer is insoluble enough to keep the composition li2018 C43, C44, C45. The cited Flory–Huggins term, \Delta\mu_{drug}/RT = \ln\Phi_{drug} + (1 - 1/r)\Phi_{poly} + \chi\Phi_{poly}^{2}, is "probably best applied in a qualitative manner" li2018 E4, C46. In phase-separated dispersions and the physical mixture the components "behave independently" li2018 C49. The authors relate the "approximate trend" HPMCP > EC > HPMCAS to functional groups li2018 C54, C55.

Limits and transfer

Several curves were still rising between 3 and 48 h, so part of the suppression could be slow release li2018 X4, X5. For a dispersion with an enteric or insoluble polymer, measure the drug concentration at two or three loadings in the medium where the polymer stays undissolved, for 48 h with a solution inhibitor and against a physical mixture; one Tg with evidence of interaction predicts suppression that grows as loading falls li2018 P5, P14, C56, C35.

How it was shown

Li and Taylor (2018) cast films of 2 mg solids (15, 33, 50, 70 and 85% drug) inside vials from methanol–dichloromethane, added 10 mL of 50 mM pH 3 citrate buffer holding 20 µg/mL HPMC to block crystallization, stirred at 25 °C and 300 rpm, and assayed lopinavir at 3 h and, after ultracentrifugation, at 48 h, with release followed to 7 days (not shown) li2018 P4, P5, R4. Crystalline solubility was measured with an excess of each polymer, and the amorphous solubility from a 10% HPMC film and from the LLPS onset by UV scattering li2018 P1, P2, P3. Mixing state came from modulated DSC of dry and 97% RH samples, IR of spin-coated films and water sorption against an additive prediction; a physical mixture of amorphous lopinavir and HPMCAS was tested at 48 h; 50% drug films were also followed without inhibitor li2018 P9, P10, P11, P12, E1, P14, P6. In 2016 the same group had measured lopinavir leaching from spray-dried 33% dispersions of three HPMCAS grades and HPMCP at pH 3 li2016b P1, P4.

What the data show

At 48 h: HPMCAS ≈4.3, 9.3, 12.3, 14.2 and 15.7 µg/mL from 15 to 85% drug; CAP ≈3.1, 6.7, 8.2, 9.9 and 11.4; EC ≈0.3, 3.1, 8.8, 13.2 and 15.3; HPMCP ≈0.6, 2.5, 4.6, 7.8 and 10.5; CA ≈13.8–17.0; EUD ≈12.8–16.8; HPMC ≈17.5–18.9 µg/mL li2018 R3. EC and HPMCP at 15 and 33% drug sat below or close to the crystalline solubility measured with those polymers (3.6 and 3.4 µg/mL), which the authors call "extreme solubility suppression" li2018 R3, R1, C63. At 3 h the same pattern held with lower values for HPMCAS, CAP and HPMCP (HPMCAS at 33% ≈5.0 against ≈9.3 µg/mL) li2018 R2. CA showed two Tgs at every loading, EUD at 15–50% and CAP at 15–33%; EC, HPMCAS and HPMCP one Tg falling from ≈90–92 °C at 15% to ≈69–79 °C at 50–85% drug li2018 R8. At 50% drug and 90% RH, HPMCAS and HPMCP dispersions took up ≈5.4% and ≈5.1% water against ≈6.8% and ≈7.3% predicted, CA and EUD followed the prediction li2018 R12. IR changed for CAP, EC, HPMCAS and HPMCP and not for CA and EUD li2018 R10, R11. The physical mixture gave ≈17.0–18.5 µg/mL at all loadings against ≈4.3–15.7 µg/mL for the HPMCAS dispersion li2018 R14. In the 2016 leaching study the dispersions reached about 7 µg/mL (HPMCAS) and about 5 µg/mL (HPMCP) against an amorphous solubility of ≈16.6 µg/mL, while leaching less polymer than the pure polymers, which the authors find "consistent with a miscible solid dispersion" li2016b R4, R6, R2, R3, C35.

The authors frame the suppression with the cited Flory–Huggins term for the drug's chemical potential in the polymer,

\frac{\Delta\mu_{drug}}{RT} = \ln\Phi_{drug} + \left(1 - \frac{1}{r}\right)\Phi_{poly} + \chi\Phi_{poly}^{2} li2018 E4

combined with a Gibbs–Duhem term for absorbed water in a model of drug solubility in a one-phase dispersion li2018 E5, E6; no term was evaluated. The dashed "ideal" line of their figure is the amorphous solubility scaled by drug weight fraction (17.4 × 0.50 = 8.7 µg/mL at 50%), which the extractor notes is not the χ = 0 case of the equation li2018 E7, X2.

papersystemmethod and conditionsresultids
li2018lopinavir 15% / 85% with HPMCAS, CAP, EC, HPMCPfilms, pH 3, 25 °C, 48 h, ultracentrifuged≈0.3–4.3 / ≈10.5–15.7 against 17.4 µg/mLR3
li2018same with CA, EUD (two Tgs)same≈12.8–17.0 µg/mLR3, R8
li2018HPMCAS physical mixture against dispersionsame≈17–18.5 against ≈4.3–15.7 µg/mLR14
li201850% dispersions, 90% RHwater sorption against additive predictionHPMCAS ≈5.4 / 6.8, HPMCP ≈5.1 / 7.3 %; CA, EUD on the predictionR12
li2016blopinavir 33% with HPMCAS grades; HPMCPspray-dried suspensions, pH 3, 25 °C, 3 h≈7; ≈5 against ≈16.6 µg/mLR4, R6
ueda2021 (Amorphous solubility and LLPS)ibuprofen with six dissolved polymers at 1000 µg/mLNMRdissolved ibuprofen lowered from 154 to ≈89–131 µg/mLR5
deac2023b (Release mechanism and LoC)phenylhydrazone drug with PVPVAamorphous solubilitylower with PVPVA, "likely" insoluble complexesC15
elkhabaz2019aposaconazole–HPMCAS 10 / 25 / 50% in FaSSGF, polymer undissolvedHPLC after 60 min7.5 / 10 / 11.5% of a 400 µg/mL dose, below the 115.1 µg/mL crystalline solubilityR10, R1
nguyen2023cdelamanid edisylate with HPMCP-55 against HPMCP-50, pH 1.6release in acid; polymer release≈9% against ≈30%; supersaturation ratio ≈0.9; polymer ≈1–2%R11, R13, R12

Figure

Fig. 2 of li2018: lopinavir concentration against drug loading for seven polymers after 3 and 48 h
Fig. 2 · li2018lopinavir concentration against drug loading for seven polymers after 3 and 48 h

Panel B is the main result: HPMC at the amorphous-solubility band at every loading, the insoluble polymers below it and rising with loading, HPMCP lowest, CA and EUD near the top; the diagonal is proportional dilution li2018 R3, E7.

Fig. 9 of li2018: HPMCAS dispersion against a physical mixture of amorphous lopinavir and HPMCAS
Fig. 9 · li2018HPMCAS dispersion against a physical mixture of amorphous lopinavir and HPMCAS

The physical mixture sits at the amorphous solubility; only the molecularly mixed dispersion is suppressed li2018 R14, C50.

Why

Mixing with a polymer and taking up water lower the chemical potential of the drug relative to the pure amorphous phase; a low drug loading and a more negative χ lower its solubility, as long as the dispersion is one phase, stays one phase on hydration and the polymer is insoluble enough to keep the composition, as for an enteric polymer at low pH li2018 C43, C44, C45. The model ignores the change of χ with water and is "probably best applied in a qualitative manner" li2018 C46. In phase-separated dispersions and the physical mixture the components "behave independently", and a soluble polymer is not substantially mixed with the drug droplets li2018 C49, C48. The authors give the "approximate trend" HPMCP > EC > HPMCAS and relate it to functional groups, about 31% phthalyl groups in HPMCP that hydrogen-bond strongly and "may also" stack with the drug's phenyl rings, against about 7% succinoyl groups in HPMCAS-HF and about 50% free hydroxyls in EC; EUD lacks a hydrogen-bond donor, "likely the cause" of weak interaction li2018 C54, C55, C57. Water content does not explain the ranking li2018 C59. Lower supersaturation is expected to lower the crystallization tendency of suspensions, which the authors see in the HPMCP dispersion ("correlates") li2018 C60, C61. (synthesis: this is the thermodynamics of F11 with a polymer in place of a second drug, and of the polymers that enter the drug-rich phase of ibuprofen in the LLPS chapter (Amorphous solubility and LLPS F19); what matters is that the polymer stays mixed with the drug, which an undissolved polymer does by construction.) In gastric media the same holding back appeared for weak bases: posaconazole released more from HPMCAS dispersions at higher drug loading, the trend reported for lopinavir, but stayed below even its crystalline solubility elkhabaz2019a R10, C29, and delamanid with HPMCP-55 released only ≈9% at pH 1.6 (supersaturation ratio ≈0.9) against ≈30% with HPMCP-50, which the authors relate ("may") to stronger drug–polymer interactions lowering the chemical potential of the drug, not measured nguyen2023c R11, R13, C41, C42.

Conditions and limits

One drug, pH 3, 25 °C, cast films with high surface area and 20 µg/mL HPMC in the medium li2018 P4, P5. Concentrations from HPMCAS, CAP, HPMCP and EUD films were still rising between 3 and 48 h, so part of the suppression could be slow release; the 3 h deficit is attributed to release kinetics ("can be attributed") li2018 X4, X5, C21. The polymer dissolved was mostly below detection (estimated 3–25 µg/mL), and the ± 2% composition estimate holds only at the low end li2018 R5, X3. The order is given as approximate, CAP is left out of it, and at 15% drug EC and HPMCP cannot be told apart li2018 X9.

Counterexamples and conflicts

Dissolved polymers can also lower an amorphous solubility, by entering the drug-rich phase (ibuprofen) or, "likely", by insoluble complexes ueda2021 R5; deac2023b C15; the lopinavir HPMC control showed neither. The HPMCAS curve lies slightly above the proportional-dilution line, and CAP and EC cross it with loading li2018 C20. The prediction that EC and HPMCP dispersions at 15–33% drug "should remain physically stable for long periods" was not tested li2018 C64, X8.

Transfer check

For a dispersion with an enteric or insoluble polymer, measure the drug concentration from films or particles at two or three loadings in the medium where the polymer stays undissolved, for 48 h with a solution inhibitor, and compare it with a physical mixture of amorphous drug and polymer li2018 P5, P14. Count glass transitions: two Tgs predict little suppression, one Tg with evidence of interaction (IR change, water sorption below the additive line) predicts suppression that grows as loading falls li2018 C56, C35. Expect less gastric supersaturation and less crystallization of a suspension, but check release once the polymer dissolves at intestinal pH li2018 C62, C64.

History

A second miscible drug had been shown to lower the maximum supersaturation, and a cited thermodynamic analysis predicted the same for drug–polymer blends li2018 C9. Li and co-workers (2016) found lopinavir leaching from enteric dispersions below its amorphous solubility li2016b C16. Li and Taylor (2018) were the first in the library to measure the suppression against drug loading, mixing state and polymer li2018 C67. A later ASD process paper takes its 17 µg/mL amorphous solubility as the design value li2019 C7, and an enzalutamide study cites it for poorly soluble polymers limiting release wilson2020 C6. Elkhabaz and co-workers (2019) cite it for more release from insoluble-polymer dispersions at higher drug loading elkhabaz2019a C29, and Nguyen and co-workers (2023) invoked a lowered chemical potential for delamanid in HPMCP-55 nguyen2023c C42.

Topic 5 of 8 · 2 findings · F22–F23

Seed crystals and residual crystallinity

F22

Topic 5Seed crystals and residual crystallinity1 of 2

Seed crystals of equal mass lowered paclitaxel supersaturation according to their growth area, never down to the crystalline solubility.

A paclitaxel–HPMCAS dispersion reached the amorphous solubility (about 31.6 µg/mL, 88 times the crystalline solubility) with or without 18 wt% seed crystals que2018 R1, R13. After 16 h, short sonicated needles had pulled it down to ≈7.9–9.0 µg/mL and long needles grown at low supersaturation only to ≈19.2 µg/mL, while the unseeded run stayed at ≈31.6 µg/mL que2018 R14.

moderateModerate for the contrast between seeds at equal mass and strong for nucleation against growth; weak to moderate for the explanation by nucleus size and polymer spacing, which uses interfacial tensions of other compounds que2018 K1, K3, K4, X7.

Paclitaxel left after 16 h, µg/mL (HPLC)no seeds≈31.6bulk API seeds≈25.3long needles grown at S 16≈19.2needles grown at S 80≈10.4S 80 needles, sonicated≈9.0S 16 needles, sonicated≈7.9

49/51 paclitaxel–HPMCAS dispersion with 18 wt% seeds, pH 6.8, 37 °C; the crystalline solubility is 0.36 µg/mL. que2018 R14, R13, R1

critical two-dimensional nucleusspacing of adsorbed HPMCAS (finger width)nucleus at S = 885.4–7.0nucleus at the residual SS ≈22–54 after 16 h≈6.8–8.8polymer spacing≈10.5–16.805101520length scale on the crystal surface, nm

A nucleus smaller than the spacing fits between the adsorbed chains, so growth continues; interfacial tensions of other compounds were used. que2018 R15, R17, R12, X7

For your drug

  1. Characterize any residual crystals by habit and size as well as by weight percent, and seed with crystals of the same origin as those in the product where possible.
  2. Run an unseeded induction-time test and a seeded dissolution of the dispersion at the target dose, read the residual concentration by HPLC rather than UV, and do not assume a return to the crystalline solubility in absorption models.

que2018 R6, C6, R3, C30, X4, C42; moseson2020a C41; schram2016 C39

How it works and key numbers
  1. HPMCAS is a "highly effective" nucleation inhibitor, so the unseeded dispersion held S = 88 for 16 h que2018 C13, C29.
  2. On seeds the polymer adsorbs and pins the growth steps, so the crystal grows only between adsorption sites, and the finger width is taken as their spacing ("can be explained") que2018 C26, C27.
  3. A new layer needs a two-dimensional nucleus of critical radius \rho_c = \gamma a/(kT\ln S); at S = 88 it is 5–7 nm, small enough to fit between the adsorbed chains, so growth continues que2018 E2, C38.
  4. As the concentration falls ρc grows, and "we can predict" that growth stops when it equals the spacing, which leaves a residual supersaturation que2018 C39, C40.
  5. Per unit mass, long needles offer less growth area than short crystals, "the most likely explanation" of the modest effect of some seeds que2018 C48.
To feel the numbers. With the step-pinning relation v/v_0 = 1 - \rho_c/l, a nucleus of 6 nm between chains 14 nm apart lets a step move at about 1 − 6/14 ≈ 0.57 of its unhindered speed; growth stops only when \rho_c reaches l.
≈31.6 µg/mLamorphous solubility reached by every run, about 88 times the crystalline solubility of 0.36que2018 R1, R13
≈7.9 vs ≈19.2 µg/mLpaclitaxel left at 16 h with sonicated against long S 16 needlesque2018 R14
7–9-foldrise of the needle-end area per gram on sonicationque2018 R6
Evidence: data, conditions and papers

Finding F22. At equal mass, seed crystals lowered the supersaturation produced by a dispersion according to their growth area and origin: HPMCAS held an unseeded paclitaxel solution at the amorphous solubility for 16 h but only slowed growth on seeds, and a residual supersaturation far above the crystalline solubility remained

In short. A paclitaxel–HPMCAS 49/51 dispersion reached the amorphous solubility (≈31–33 µg/mL, about 88 times the crystalline solubility of 0.36 µg/mL) with or without 18 wt% seed crystals in the medium; at 16 h the unseeded run still held ≈31.6 µg/mL, while seeds left ≈25.3 (bulk API), ≈19.2 (long needles grown at S 16), ≈10.4 (needles grown at S 80), ≈9.0 and ≈7.9 µg/mL (sonicated needles) que2018 R1, R2, R13, R14. Sonication raised the needle-end area per gram about 7–9-fold, and the needles grown at S 16 and S 80 had the same end area but different tips que2018 R6, R18. HPMCAS held unseeded paclitaxel at S ≈88 for more than 16 h against crystallization within 6 min without polymer, yet could not stop growth on seeds, which the authors explain by a critical two-dimensional nucleus (5.4–7.0 nm) smaller than the spacing of adsorbed polymer (≈10.5–16.8 nm) que2018 R3, R15, R12, C38. The authors conclude that the mass of seeds "is not the relevant parameter" and that percent crystallinity "per se is not a predictive indicator" que2018 C5, C54.

Type. single-system observation (paclitaxel–HPMCAS, five seed types), set against seeding studies of felodipine, indomethacin, bicalutamide, posaconazole and tacrolimus Strength. for the main contrast, sonicated against long needles at equal mass, which is large and agrees between UV and HPLC, and strong for nucleation against growth; weak to moderate for the nucleus-spacing explanation, which uses interfacial tensions of other compounds, and weak for the stop of growth at the residual supersaturation que2018 K1: moderate, K3: strong, K4: weak to moderate, K5: weak, X9, X4, X7.

How it was shown

Que and co-workers (2018) measured the crystalline and amorphous solubility of paclitaxel in pH 6.8 buffer at 37 °C and its unseeded induction time with or without 20 µg/mL HPMCAS que2018 P1, P2, P5. Seeds were grown at S = 16 or 80, half of each batch was sonicated, and as-received crystals served as bulk API seeds que2018 P6. A 49/51 paclitaxel–HPMCAS film was dissolved in buffer or in a seed suspension at 18 wt%, with UV for 16 h and HPLC of filtrates at 16 h que2018 P8, P9.

What the data show

Every run first reached the amorphous solubility, and the seeds then lowered the concentration according to their type que2018 R13, R14.

systemconditionsresultids
paclitaxel at S ≈88, without and with 20 µg/mL HPMCAS, unseededinduction time, pH 6.8, 37 °Cwithin 6 min against more than 16 hque2018 R3
seed end area per gram: S16, S80, S16 sonicated, S80 sonicatedSEM, cuboid crystals assumed≈0.00024, ≈0.00023, ≈0.0021, ≈0.0017 m²/gque2018 R6
paclitaxel–HPMCAS 49/51, no seeds or 18 wt% seedsdissolution, HPLC at 16 h≈31.6 (none), ≈25.3 (bulk API), ≈19.2 (S16), ≈10.4 (S80), ≈9.0 and ≈7.9 µg/mL (sonicated)que2018 R13, R14
seeds grown with HPMCAS at S 88TEM finger width; Eq. 2≈10.5–16.8 nm against ρc 5.4–7.0 nmque2018 R12, R15
posaconazole 10% dispersions, amorphous against 0.3% crystals (ASD process)two-stage release, SHG≈125 µg/mL at 300 min against a fall to ≈18.5 µg/mL by 150 minshah2024 R11, R12
Fig. 12 of que2018: residual paclitaxel concentration after 16 h by HPLC for each seed type
Fig. 12 · que2018residual paclitaxel concentration after 16 h by HPLC for each seed type

The bars run from ≈8–10 µg/mL (sonicated and S80 seeds) to ≈25 µg/mL (bulk API), all far above the crystalline-solubility line que2018 R14.

Why

Per unit mass, high-aspect-ratio needles offer less growth area than shorter crystals, "the most likely explanation" of the modest effect of some seeds, and sonicated needles "presumably" have more ends que2018 C48, C15, C21. HPMCAS is a "highly effective" nucleation inhibitor, but on seeds a two-dimensional nucleus of critical radius \rho_c = \gamma a/(kT\ln S), 5–7 nm at S = 88, fits between the adsorbed chains, so that growth continues que2018 C13, E2, C38. As the concentration falls ρc grows, and "we can predict" that growth stops when it equals the spacing que2018 C39.

Limits and transfer

One drug and one polymer were tested, with an 18 wt% seed load added to the medium and ρc computed from interfacial tensions of other compounds que2018 P8, P9, X7. Characterize residual crystals by habit and size as well as by weight percent, read the residual concentration by HPLC rather than UV, and do not assume a return to the crystalline solubility in absorption models que2018 R6, C6, X4, C42.

How it was shown

Que and co-workers (2018) tested the hypothesis that seed crystals of different morphology, compared at the same initial weight percent crystallinity, change the dissolution of a dispersion differently que2018 C9. The crystalline solubility of paclitaxel dihydrate was measured by shake flask in 50 mM pH 6.8 phosphate buffer at 37 °C over 48 h with ultracentrifugation, and the amorphous solubility, with 20 µg/mL HPMCAS-MF, by the onset of light scattering at 400 nm, by pyrene fluorescence and by the supernatant of an ultracentrifuged drug-rich phase, each in triplicate que2018 P1, P2, P3, P4. The induction time of unseeded paclitaxel at 30.7 µg/mL was read from the extinction rise in 50 mL of buffer with or without 20 µg/mL HPMCAS que2018 P5. Seeds were grown from methanol stocks at 5.8 µg/mL (S = 16) or 28.8 µg/mL (S = 80) for 5.5 h; half of each batch was probe-sonicated for 10 min, and as-received crystals slurried for 5.5 h served as bulk API seeds que2018 P6. SEM of 100 crystals per sample gave length and width distributions, from which the end area per gram was estimated assuming cuboid crystals, and TEM and SEM imaged the tips que2018 P10, C18, P13. Seeded growth at 18 wt% seeds was followed by in situ UV from 31.6 µg/mL without polymer, and crystals grown with HPMCAS were imaged by TEM, the width of their fingers being measured 20 times per sample que2018 P7, P11. A 49/51 paclitaxel–HPMCAS film made by rotary evaporation, holding enough drug to reach the amorphous solubility in 15 mL, was dissolved in 15 mL of paclitaxel-saturated buffer or of a seed suspension at 18 wt%, with UV for 16 h and HPLC of 0.45-µm filtrates at 16 h que2018 P8, P9. The radius of the critical two-dimensional nucleus was computed with interfacial tensions of methylene iodide, octane and felodipine, since that of paclitaxel could not be measured que2018 P15, C37.

What the data show

Solubilities and nucleation. The amorphous solubility was 31.5 ± 0.8, 30.9 ± 1.8 and 32.3 ± 0.4 µg/mL by the three methods, about 31.6 µg/mL on average, against 0.36 ± 0.01 µg/mL for the crystal que2018 R1, R2, C12. Unseeded paclitaxel crystallized within 6 min without polymer and stayed supersaturated for more than 16 h with 20 µg/mL HPMCAS que2018 R3. Seeds. The end area per gram was ≈0.00024 (S16), ≈0.00023 (S80), ≈0.0021 (S16 sonicated) and ≈0.0017 m²/g (S80 sonicated), and the mean aspect ratios ≈23.6, ≈20.1, ≈7.3 and ≈4.7 que2018 R6, R9. S16 tips were pointed and smooth, S80 tips flat and rough que2018 R18. Without polymer. From 31.6 µg/mL, sonicated seeds brought the concentration to ≈12–13 µg/mL within 2 min against ≈21.6 (S16) and ≈26.1 µg/mL (S80); by 10 min S16 had fallen lowest (≈3.3 µg/mL) and S80 still held ≈11.5 µg/mL que2018 R7. After this growth the S16 aspect ratio fell from ≈23.6 to ≈17.7 while those of the other seeds rose, which the authors explain by fine crystals from secondary nucleation ("can be explained") que2018 R9, C43. With HPMCAS. Seeds grown with the polymer split at their ends into fingers ≈16.8 (S16), ≈16.0 (S80), ≈10.5 (S16 sonicated) and ≈14.3 nm wide (S80 sonicated) que2018 R11, R12. Dispersion dissolution. The unseeded dispersion rose to ≈31 µg/mL within ≈1.5 h and stayed there for 16 h; every seeded run also first reached ≈32–33 µg/mL at ≈2–4 h que2018 R13, C29, C47. The sonicated seeds then pulled the concentration down from ≈3.5–4 h, fast at first and then more slowly, S80 later but steadily, while S16 and bulk API declined only slightly que2018 R13, C31. By HPLC at 16 h the residual concentrations were ≈25.3 (bulk API), ≈19.2 (S16), ≈10.4 (S80), ≈9.0 (S80 sonicated) and ≈7.9 µg/mL (S16 sonicated), against ≈31.6 µg/mL without seeds que2018 R14. The UV readings of the seeded runs lay ≈2–10 µg/mL above the HPLC values at 16 h (F8) que2018 X4. Critical nucleus. With the three interfacial tensions, Eq. 2 gave ρc = 5.7, 7.0 and 5.4 nm at S = 88, and at the residual supersaturation after 16 h (S ≈22–54) the curve reads ≈6.8–8.8 nm que2018 R15, R17.

papersystemmethod and conditionsresultids
que2018paclitaxel at S ≈88, without and with 20 µg/mL HPMCAS, unseededinduction time, pH 6.8, 37 °Cwithin 6 min against more than 16 hR3
que2018four seed types, 18 wt%, no polymerseeded desupersaturation from 31.6 µg/mL≈12–13 µg/mL at 2 min (sonicated) against ≈21.6 (S16) and ≈26.1 (S80); ≈3.3 (S16) and ≈11.5 µg/mL (S80) at 10 minR7
que2018paclitaxel–HPMCAS 49/51, no seeds or 18 wt% of five seed typesdissolution in 15 mL, UV; HPLC at 16 hall reach ≈31–33 µg/mL; at 16 h ≈31.6 (none), ≈25.3 (bulk API), ≈19.2 (S16), ≈10.4 (S80), ≈9.0 and ≈7.9 µg/mL (sonicated)R13, R14
que2018seeds grown with HPMCAS at S 88TEM finger width; Eq. 2≈10.5–16.8 nm against ρc 5.4–7.0 nmR12, R15
alonzo2012 (Crystallization from solution)felodipine at S 10, 1 µg/mL HPMC, unseeded against seededdesupersaturation≈5.38 → ≈5.03 µg/mL in 198 min against ≈5.10 → ≈2.17 µg/mL in 58 minR18
schram2016 (Crystallization from solution)felodipine seeds made four ways, 5 µg/mL HPMCASseeded growth at S 4growth slowed ≈2.7-fold (method i) to ≈12-fold (method iv)R2
moseson2020a (ASD process)indomethacin–PVPVA extrudates with 3–25% residual crystals against bulk seeds at the same amorphous dosenon-sink dissolution, concentration at 720 minextrudates well below the line of bulk-seed blendsR19, C39
moseson2021 (ASD process)bicalutamide dispersions with residual crystals against 10% external seedsRaman–MCRrelative growth rate ≈0.071–0.088 against ≈0.044R22, C65
shah2024 (ASD process)posaconazole 20 µg/mL with 5 or 10 µg/mL seeds, 0–180 µg/mL HPMCASseeded desupersaturation, FaSSIF V2≈46.5 and ≈25% left at 30 min without polymer; ≈96 and ≈74.5% with 180 µg/mL HPMCASR22, C37
shah2024 (ASD process)posaconazole 10% dispersions, amorphous against 0.3% crystalstwo-stage release, SHG≈125 µg/mL at 300 min against a fall to ≈18.5 µg/mL by 150 minR11, R12
hate2019 (Bioperformance)tacrolimus with seeds from a crystallized generic, from 50 and 20 µg/mLseeded desupersaturationinitial rate ≈0.39 against ≈0.075 on the axis of µg s⁻¹ mL⁻¹R17

Figure

Fig. 11 of que2018: dissolution of the paclitaxel–HPMCAS dispersion with and without seed crystals over 16 h
Fig. 11 · que2018dissolution of the paclitaxel–HPMCAS dispersion with and without seed crystals over 16 h

All runs reach ≈31–33 µg/mL; the sonicated seeds and later the S80 seeds pull the concentration down, while S16, bulk API and the unseeded run stay high que2018 R13.

Fig. 12 of que2018: residual paclitaxel concentration after 16 h by HPLC for each seed type
Fig. 12 · que2018residual paclitaxel concentration after 16 h by HPLC for each seed type

The bars run from ≈8–10 µg/mL (sonicated and S80 seeds) to ≈25 µg/mL (bulk API), all far above the dashed crystalline-solubility line que2018 R14.

Why

The authors read the needle habit as fast growth at the needle ends ("indicating") and give as "the most likely explanation" of the modest effect of some seeds that, per unit mass, high-aspect-ratio needles offer less growth area than shorter or more equant crystals que2018 C14, C48. Sonication breaks the needles into shorter crystals that "presumably" have more ends, and the faster early loss with sonicated seeds is attributed to their larger end area ("presumably") que2018 C15, C21. S16 and S80 seeds had equal end areas, and the authors take their different tips as "most likely" a sign of different growth mechanisms at the two generation supersaturations, giving different numbers of active sites for growth and for polymer adsorption; the active sites were not measured que2018 C52, K7. That every seeded run still reached the amorphous solubility is read as dissolution being much faster than growth, "quite a remarkable observation" que2018 C47. HPMCAS is a "highly effective" nucleation inhibitor, which is why the unseeded dispersion held S = 88 for 16 h que2018 C13, C29. On seeds the polymer adsorbs and pins the growth steps, so that crystal grows only between adsorption sites ("can be explained"), and the finger width is taken as the spacing of the sites que2018 C26, C27. In adsorption layer theory a new layer needs a two-dimensional nucleus of critical radius

\rho_c = \frac{\gamma\, a}{k T \ln S} que2018 E2

and the step velocity with adsorbed polymer at spacing l is

\frac{\upsilon}{\upsilon_0} = 1 - \frac{\rho_c}{l} \quad (l > \rho_c), \qquad \upsilon = 0 \quad (l < \rho_c) que2018 E3

so that at S = 88 the nucleus (5–7 nm) fits between the adsorbed chains (10–20 nm) and HPMCAS cannot prevent growth, "presumably" because of the very high supersaturation, though it still poisons the interface que2018 C38. As the concentration falls, ρc grows, and "we can predict" that growth stops when it equals the spacing, which for the sonicated seeds "explain[s]" the almost zero growth at 16 h que2018 C39, C40. The extractor notes that by Eq. 3 the S80 sonicated seeds would still grow at about 40% of the unhindered step speed (synthesis: 1 − 8.4/14.3 ≈ 0.41) que2018 X5, R17, R12. The authors present the comparison as the theoretical underpinning of residual supersaturation seen in earlier seeded studies, and as a reason to revise PBPK models that assume a return to the crystalline solubility que2018 C41, C42. (synthesis: this is the dispersion counterpart of Crystallization from solution F20, where polymers at µg/mL hold crystal-free solutions but not seeded ones, and of the weakening of growth inhibition with supersaturation in Crystallization from solution F9; the step-pinning account is the one fitted for HPMCAS on felodipine in Crystallization from solution F10, and seed origin deciding the inhibition is the felodipine result of Crystallization from solution F24.)

Conditions and limits

One drug, one polymer, one drug loading (49 wt%) and one seed load (18 wt%), far above typical crystallinity limits; the seeds were added to the medium, not formed inside the dispersion, and equant crystals, which the authors expect to be most harmful, were not tested que2018 P8, P9, C56. Replicate numbers and error-bar meanings are not stated, and the HPMCAS level and the supersaturation of the seeded tests are given inconsistently (33 against 31.6 µg/mL; S 80 against 88) que2018 X9, X1, X2. The bulk API seeds were not characterised que2018 X17. ρc uses interfacial tensions of other compounds, and with the printed units Eq. 2 gives a dimensionless number que2018 X7. No seeded-growth curve with HPMCAS alone is shown, so growth and dissolution are not separated in the polymer case que2018 X15.

Counterexamples and conflicts

The aspect-ratio ranking does not hold everywhere: S80 needles, with the end area and nearly the aspect ratio of S16, left ≈10 µg/mL with HPMCAS like the sonicated seeds, and without polymer S16 went lowest by 10 min que2018 X11, R7, R14. By HPLC bulk API retained the most, by UV S16, so the order at the top depends on the method que2018 X4. A small seed load is not always harmless: in posaconazole dispersions of the ASD process chapter, 0.3% residual crystals turned a supersaturation that lasted beyond 300 min into a fall to ≈18.5 µg/mL by 150 min shah2024 R11, R12. For indomethacin–PVPVA at S = 6, PVPVA cut growth on bulk seeds 18- to 56-fold and residual crystals mostly cost potency, with only slight desupersaturation moseson2020a C12, C13. Seeds made outside the dispersion understate the damage of residual crystals: extrudate crystals grew better with PVPVA than bulk seeds, so bulk seeds are "not an equivalent surrogate" moseson2020a C39, C41, and seeds crystallized from a felodipine dispersion with HPMCAS were, on the contrary, slowed 12-fold against about 2.7-fold for buffer-grown seeds schram2016 R2 (Crystallization from solution F24).

Transfer check

Characterize any residual crystals by habit and size as well as by weight percent: needles cut into short pieces multiplied the growth area per gram 7–9-fold que2018 R6, C6. Run an unseeded induction-time test and a seeded dissolution of the dispersion at the target dose: a polymer that blocks nucleation (6 min against more than 16 h for paclitaxel) can still let existing crystals grow que2018 R3, C30. Seed with crystals of the same origin as those in the product where possible (crystals from the dispersion or the process), since seeds from another environment may grow faster or slower moseson2020a C41; schram2016 C39. Read the residual concentration by HPLC after filtration or ultracentrifugation rather than by UV (F8) que2018 X4. Expect a residual supersaturation above the crystalline solubility when a growth inhibitor is present, and do not assume a return to the crystalline solubility in absorption models que2018 C33, C42.

History

Alonzo and co-workers (2012), in the crystallization-from-solution chapter, found that seeds removed felodipine supersaturation even with HPMC and advised minimizing residual crystallinity alonzo2012 R18, C45. Schram and co-workers (2016) showed that seeds made in different environments grow at different rates schram2016 C39. Que and co-workers (2018) were the first in this chapter to compare seeds of different morphology at equal mass in the dissolution of a dispersion and to relate the residual supersaturation to the critical nucleus and the spacing of adsorbed polymer que2018 C3, C41. Later papers of the ASD process chapter cite it for percent crystallinity being a crude specification, compared residual with bulk seeds for indomethacin and bicalutamide, and traced the effect of external seeds to their surface area rather than their mass moseson2020a C4, C41; moseson2021 C65; a posaconazole study found low residual crystallinity, detectable only by SHG, deciding the outcome after a pH shift shah2024 R11, R12. The delamanid papers of 2022–2023 met the same problem with residual crystals from preparation (F23).

F23

Topic 5Seed crystals and residual crystallinity2 of 2

Rotary-evaporated delamanid dispersions held crystals above 10–15% drug and released incompletely; a sulfonate salt formed in situ restored release.

Delamanid, a weak base that could not be vitrified at 50 °C/min, gave free-base dispersions with crystalline peaks from 15% (HPMCAS) and 20% drug (HPMCP), and at 25% drug these released only ≈2 and ≈20 µg/mL of 100 at pH 6.5 duong2022a R3, R8, R14. Four sulfonate salt dispersions with HPMCP at 25% drug released ≈95–97 µg/mL duong2022a R26.

moderateModerate for the residual crystals and their effect on release, strong for the salt against free-base contrast at 25% drug, weak to moderate for the crystal-free state of the salt dispersions, which is asserted but not shown in the main text duong2022a K1, K4, K3, X8.

25% delamanid with HPMCP: released at pH 6.5, of 100free base, rotary-evaporated≈20marketed tablet, spray-driedestimated 20–25% drug≈20free base, spray-driedmore than 80four sulfonate salts, in situ≈95–97

Single-stage release; 100 µg/mL is complete release, about 100 times the amorphous solubility at pH 6.5. duong2022a R14, R15, M26, R26, P16; nguyen2023c R5, R6

Glass transition of amorphous delamanid forms, °Cfree base43.3esylate, besylate, mesylate83.7–86.2edisylate 2:1117.8

Seven of eight sulfonate salts were amorphous; four of them liquefied at high humidity. duong2022a R20, M1

For your drug

  1. Classify the neat drug by glass-forming ability and by its induction time at the amorphous solubility; a drug that cannot be vitrified at 50 °C/min and crystallizes within minutes needs fast solvent removal or a higher-Tg form.
  2. Check every dispersion for residual crystals by a sensitive method before release testing; for a weak base, screen salts by Tg and water uptake together, then confirm that the salt survives in the dispersion and through an acid stage.

duong2022a R3, R2, C46, C56, R29, R20, C63; shah2024 C56

How it works and key numbers
  1. Delamanid is a poor glass former (Class I) with a high tendency to crystallize in the solid state and from solution duong2022a C10, C44.
  2. Rotary evaporation was "not fast enough", even with polymer, to trap the drug before nucleation and growth above about 10% drug; spray drying "It is likely" could avoid this duong2022a C45, C46.
  3. The residual crystals grow, in the hydrated matrix or after release ("Presumably"), and their growth competes with dissolution of the surrounding amorphous drug ("can be explained") duong2022a C56, C57.
  4. In the salt, drug–counterion electrostatic interactions "likely" raise Tg and lower mobility, and the authors "speculate" that protonating the piperidine ring keeps the long, thin molecules from lining up into a crystal duong2022a C5, C50.
  5. Spray drying the free base at 25% drug gave an amorphous dispersion, which Nguyen and co-workers attribute to faster drying nguyen2023c R5, C17.
2.4 and 10.7 mininduction time of delamanid at its amorphous solubility at pH 1.6 and 6.5duong2022a R2
≈20 vs ≈95–97 µg/mLrelease at pH 6.5 from 25% free-base against salt dispersions with HPMCP (of 100)duong2022a R26
43.3 vs 83.7–117.8 °CTg of the free base against seven amorphous sulfonate saltsduong2022a R20, M1
Evidence: data, conditions and papers

Finding F23. A fast-crystallizing drug left crystals in rotary-evaporated dispersions above 10–15% drug, and once any crystallinity could be detected release stayed incomplete; a sulfonate salt formed in the same step raised the Tg and gave near-complete release of delamanid at 25% drug

In short. Delamanid, a weak base with a Tg of 43.3 °C that could not be vitrified at 50 °C/min and crystallized within 2.4–10.7 min at its amorphous solubility, gave rotary-evaporated free-base dispersions with drug PXRD peaks from 15% drug (HPMCAS) and 20% drug (HPMCP) duong2022a M1, R2, R3, R8. At pH 6.5 the 10% dispersions released ≈92–100 µg/mL of 100, the 20% ones ≈6 and ≈53 and the 25% ones ≈2 and ≈20 µg/mL (HPMCAS, HPMCP), and the marketed spray-dried HPMCP product plateaued at ≈20 µg/mL duong2022a R14, R15. Seven of eight sulfonate salts were amorphous with Tg of 83.7–117.8 °C, and four salt dispersions at 25% drug with HPMCP released ≈95–97 µg/mL against ≈20 for the free base duong2022a R20, R26. The authors conclude that release was incomplete "once any level of residual crystallinity could be detected", and that salt formation combined with ASD formation "is a promising approach" duong2022a C56, C67; spray-drying the free base at 25% drug in a later paper gave an amorphous dispersion that released more than 80% at pH 6.5 nguyen2023c R5, R6.

Type. single-system observation (delamanid free base and four sulfonate salts, HPMCAS and HPMCP, 5–40% drug), set against lumefantrine and pretomanid Strength. for the residual crystals of the free-base dispersions and their release, strong for the salt-against-free-base release contrast at 25% drug, weak to moderate for the crystal-free state of the salt dispersions, which is asserted but not shown in the main text duong2022a K1: moderate, K4: strong, K3: weak to moderate, X8.

How it was shown

Duong and co-workers (2022) measured the crystalline and amorphous solubility, induction time and glass-forming ability of delamanid, made free-base dispersions with HPMCAS-LF (5–40% drug) and HPMCP (5–25%) by rotary evaporation, and checked them by PXRD and DSC duong2022a P1, P2, P3, P4, P18, P8, P9. Eight sulfonate salts were made, and in the salt dispersions the salt formed in situ from drug, polymer and acid duong2022a P5, P6. Tablets holding 5 mg drug were dissolved in PBS pH 6.5, where 100 µg/mL equals complete release duong2022a P14, P16.

What the data show

The free-base dispersions held crystals from 15–20% drug and then released poorly, whereas the salt dispersions at 25% drug released almost completely duong2022a R8, R14, R26.

systemconditionsresultids
delamanid, no polymerinduction time at the amorphous solubility; melt cooling2.4 min (pH 1.6), 10.7 min (pH 6.5); no glass at 50 °C/minduong2022a R2, R3
free-base dispersions, rotary evaporationPXRDdrug peaks from 15% (HPMCAS) and 20% (HPMCP)duong2022a R8
free-base dispersions 10 / 20 / 25% drug, HPMCAS; HPMCPtablets, PBS pH 6.5, 37 °C≈92 / ≈6 / ≈2; ≈98–100 / ≈53 / ≈20 µg/mLduong2022a R14
seven amorphous sulfonate saltsDSCTg 83.7–117.8 against 43.3 °Cduong2022a R20, M1
four salt dispersions against the free base, 25% drug, HPMCPPBS pH 6.5; pH shift≈95–97 against ≈20; ≈85–91 against ≈55 µg/mLduong2022a R26
free-base HPMCP 25%, spray-dried against rotary-evaporatedPXRD; release at pH 6.5amorphous; more than 80% against 20%nguyen2023c R5, R6
Fig. 9 of duong2022a: four sulfonate salt dispersions against the free-base dispersion at 25% drug with HPMCP
Fig. 9 · duong2022afour sulfonate salt dispersions against the free-base dispersion at 25% drug with HPMCP

All four salt dispersions reach ≈95–97 µg/mL at pH 6.5 against ≈20 for the free base duong2022a R26.

Why

The authors class delamanid as a poor glass former (Class I) and argue that rotary evaporation was "not fast enough", even with polymer, to trap it before nucleation and growth duong2022a C10, C44, C45. The residual crystals grow, in the hydrated matrix or after release ("Presumably"), and their growth competes with dissolution of the surrounding amorphous drug ("can be explained") duong2022a C56, C57. For the salts, drug–counterion electrostatic interactions "likely" raise Tg and lower mobility duong2022a C5, C50. Nguyen and co-workers attribute the better release of the spray-dried free base to the absence of crystals from faster drying nguyen2023c C17.

Limits and transfer

Crystallinity was not quantified, no PXRD of any salt dispersion appears in the main text, and crystal growth during release was not measured duong2022a X10, X8, C56. Classify the neat drug by glass-forming ability and induction time, check every dispersion for residual crystals by a sensitive method before release testing, and for a weak base rank salts by Tg and water uptake together, since several high-Tg salts liquefied duong2022a R3, R2, C46, C56, R29, R20.

How it was shown

Duong and co-workers (2022) measured the crystalline solubility of delamanid by shake flask and its amorphous solubility by the onset of light scattering in FaSSGF, FaSSIF V1, FaSSIF V2 and PBS pH 6.5, its induction time at the amorphous solubility at pH 1.6 and 6.5, and the glass-forming ability of the melt cooled at up to 50 °C/min or quenched in liquid nitrogen duong2022a P1, P2, P3, P4, P18. Free-base dispersions with HPMCAS-LF (5–40% drug) and HPMCP HP-50 (5–25% drug) were made by rotary evaporation from DCM:MeOH, cryo-milled and sieved, and characterized by PXRD, DSC and water sorption duong2022a P8, P9, P10, P12. Eight sulfonate salts were made by rotary evaporation from DCM:acetone and checked by NMR, IR, PXRD, DSC, water sorption and two weeks at 40 °C/75% RH; in the salt dispersions drug, polymer and acid were dissolved together so that the salt formed in situ duong2022a P5, P6, P8. Tablets holding 5 mg delamanid were dissolved in 50 mL of PBS pH 6.5 (single stage) or for 1 h in 45 mL of HCl pH 1.6 and then at pH 6.5 (two stage), at 37 °C with in situ UV; 100 µg/mL equals complete release, about 100 times the amorphous solubility at pH 6.5 duong2022a P14, P15, P16. Nguyen and co-workers (2023) later spray-dried free-base delamanid with HPMCP at 25% drug and compared it with the rotary-evaporated dispersion nguyen2023c R5, R6.

What the data show

The drug. Crystalline solubility was 17.6 µg/mL in FaSSGF and 0.018 µg/mL at pH 6.5, amorphous solubility 69.9 and 0.76 µg/mL; crystals appeared after 2.4 ± 0.5 min at pH 1.6 and 10.7 ± 1.2 min at pH 6.5 without polymer duong2022a R1, R2. The melt could not be made amorphous at 50 °C/min, and a glass quenched in liquid nitrogen recrystallized just above its Tg duong2022a R3. The measured amorphous-to-crystalline ratio at pH 6.5 was 42.3; from the free energy difference,

\Delta G = -RT\ln\left(\frac{C_a}{C_s}\right) duong2022a E1

with the Hoffman approximation

\Delta G = -\frac{\Delta H_f\,(T_m - T)\,T}{T_m^{2}} duong2022a E2

the authors estimate 31.8 at 37 °C, in "reasonable agreement" duong2022a R27, C43. (synthesis: the Hoffman estimate lies about a quarter below the measured ratio, (42.3 − 31.8)/42.3 ≈ 0.25, whereas for high-melting drugs the LLPS chapter finds it overshooting (Amorphous solubility and LLPS F7).) Free-base dispersions. HPMCAS dispersions showed a weak drug peak at 15% drug and clear peaks at 20 and 40%; HPMCP dispersions weak features at 20% and clear peaks at 25%; 5 and 10% were amorphous with both duong2022a R8. In the single-stage test the 10% dispersions reached ≈92 (HPMCAS) and ≈98–100 µg/mL (HPMCP), the 20% ones ≈6 and ≈53 and the 25% ones ≈2 and ≈20 µg/mL; after the pH shift they ended at ≈95 and ≈100, ≈35 and ≈87, and ≈30 and ≈55 µg/mL duong2022a R14. Marketed product. Deltyba, a spray-dried HPMCP dispersion of an estimated 20–25% drug, plateaued at ≈20 µg/mL at pH 6.5 and ≈58.5–60.5 µg/mL after the shift duong2022a R15, M26. Salts. Seven of eight salts were amorphous, with Tg of 117.8 °C (edisylate 2:1) down to 83.7–86.2 °C (esylate, besylate, mesylate), against 43.3 °C for the free base, and stayed amorphous for two weeks at 40 °C/75% RH; they took up 5.8–21.1% water at 95% RH and four liquefied duong2022a R20, M1. At 20% drug with HPMCAS the salt dispersions had Tg of 100.4–117.0 °C against 86.7 °C for the free base duong2022a R23. Salt dispersions. Edisylate dispersions with HPMCP released ≈99, ≈98 and ≈95 µg/mL at 10, 20 and 25% drug and ≈59 and ≈21 µg/mL at 30 and 40% at pH 6.5; at 25% drug the besylate, edisylate, mesylate and tosylate dispersions released ≈95–97 µg/mL against ≈20 for the free base, and ≈85–91 against ≈55 µg/mL after the pH shift duong2022a R24, R26. Spray drying. The spray-dried free-base HPMCP dispersion at 25% drug was amorphous and released more than 80% at pH 6.5, against 20% for the rotary-evaporated one nguyen2023c R5, R6, C17.

papersystemmethod and conditionsresultids
duong2022adelamanid, no polymerinduction time at the amorphous solubility; melt cooling2.4 min (pH 1.6), 10.7 min (pH 6.5); no glass at 50 °C/minR2, R3
duong2022afree-base dispersions, HPMCAS 5–40%, HPMCP 5–25% drug, rotary evaporationPXRD after preparationdrug peaks from 15% (HPMCAS) and 20% (HPMCP)R8
duong2022afree-base dispersions 10 / 20 / 25% drug, HPMCAS; HPMCPtablets, PBS pH 6.5, 37 °C, 100 µg/mL = complete≈92 / ≈6 / ≈2; ≈98–100 / ≈53 / ≈20 µg/mLR14
duong2022aDeltyba (spray-dried HPMCP dispersion)same; pH shift≈20 µg/mL; ≈58.5–60.5 µg/mLR15
duong2022aseven amorphous sulfonate saltsDSC; 2 weeks at 40 °C/75% RHTg 83.7–117.8 against 43.3 °C; all amorphous, four liquefiedR20
duong2022afour salt dispersions against the free base, 25% drug, HPMCPsingle stage; pH shift≈95–97 against ≈20; ≈85–91 against ≈55 µg/mLR26
nguyen2023cfree-base HPMCP dispersion 25% drug, spray-dried against rotary-evaporatedPXRD; release at pH 6.5amorphous; more than 80% against 20%R5, R6
hiew2022b (Release mechanism and LoC)lumefantrine salt–PVPVA dispersions40 °C/75% RH, PXRDbenzoate and PEG 250 diacid salt dispersions crystalline within a week; camsylate after 12 weeksR8
towler2008 (Crystallization tendency)amorphous propranolol and nicardipine saltscrystallization of the neat saltsdifferent salts of one drug crystallized to different extentsC32
nguyen2023a (Bioperformance)pretomanid and delamanidTg, reduced Tg, induction timeclass I rapid crystallizers, Tg about 10 and 43 °C, crystals within minutes from solutionC59
shah2024 (ASD process)posaconazole extrudates with residual crystals down to 0.3%release at 10–50% drugreduced extent or duration of supersaturation at every loadingC56

Figure

Fig. 4 of duong2022a: release of free-base delamanid dispersions at pH 6.5 and after a pH shift
Fig. 4 · duong2022arelease of free-base delamanid dispersions at pH 6.5 and after a pH shift

At pH 6.5 (A) the 10% dispersions approach complete release, the 20 and 25% dispersions stay far lower; after a pH shift (B) the end values are higher but still incomplete duong2022a R14.

Fig. 9 of duong2022a: four sulfonate salt dispersions against the free-base dispersion at 25% drug with HPMCP
Fig. 9 · duong2022afour sulfonate salt dispersions against the free-base dispersion at 25% drug with HPMCP

All four salt dispersions reach ≈95–97 µg/mL at pH 6.5 (A) against ≈20 for the free base; after the pH shift (B) they end at ≈85–91 against ≈55 µg/mL duong2022a R26.

Why

The authors class delamanid as a poor glass former (Class I) with a high tendency to crystallize in the solid state and from solution duong2022a C10, C44. They argue that the solvent evaporation rate decides whether a drug is trapped before nucleation and growth, and that rotary evaporation was "not fast enough", even with polymer, so that free-base dispersions above about 10% drug held crystals; spray drying "It is likely" could avoid this duong2022a C45, C46. The residual crystals keep part of the drug from its amorphous solubility advantage and grow, in the hydrated matrix or after release ("Presumably"); their growth competes with dissolution of the surrounding amorphous drug ("can be explained"), and the polymers cannot substantially delay crystal growth under hydrated conditions ("indicates") duong2022a C19, C56, C57. Delamanid in this respect behaves like tacrolimus and bicalutamide, not like indomethacin, whose residual crystals the polymer poisons duong2022a C58. For the salts, drug–counterion electrostatic interactions "likely" raise Tg and lower mobility, and the authors "speculate" that protonating the piperidine ring keeps the long, thin molecules from lining up into a crystal; this low crystallization tendency carried over to the dispersions ("highly successful", "no detectable residual crystallinity") duong2022a C5, C50, C48. No PXRD of any salt dispersion appears in the main text duong2022a X8. The spray-dried free base of 2023 fits the evaporation-rate argument: Nguyen and co-workers attribute the better release to the absence of crystals from faster drying nguyen2023c C17. (synthesis: this is the residual-crystal problem of F22 with crystals made during preparation rather than added; the paclitaxel dispersion reached its amorphous solubility with 18 wt% seeds and lost it over hours, whereas the delamanid free-base dispersions with crystals never approached complete release, which fits growth inhibition failing at the very high supersaturation of release, 100 times the amorphous solubility here duong2022a P16.) The Tg gain of the salts is the dispersion counterpart of Crystallization tendency F20, where salt formation raised the Tg of an amorphous base for every counterion tested while crystallization did not follow the counterion, and the role of the evaporation rate that of Crystallization tendency F14.

Conditions and limits

One drug, rotary evaporation for all dispersions except the spray-dried comparison, tablets of 5 mg, buffer media (biorelevant media gave the same profiles) duong2022a P8, P14, R13. Crystallinity was not quantified, and the PXRD and release loadings only partly overlap duong2022a X10, X16. Free-base and salt dispersions were cast from different solvents, and the drug-loading basis of the salt dispersions (free base or salt) is not stated duong2022a X7, X6. Three of the four salts chosen for their stability liquefied at 40 °C/75% RH, and storage of the salt dispersions is not shown duong2022a X19, X8. Crystal growth during release, the stated cause of the poor free-base release, was not measured duong2022a C56.

Counterexamples and conflicts

Salt formation did not protect every dispersion: lumefantrine dispersions of lower-Tg salts (benzoate, PEG 250 diacid) crystallized within a week at 40 °C/75% RH, and the Tg of the drug or salt "appears" to be the predictor of stability hiew2022b R8, C34, C37. Residual crystals are not always fatal: indomethacin–PVPVA extrudates with up to 25% residual crystals mostly lost potency, with only slight desupersaturation (F22) moseson2020a C13, whereas posaconazole extrudates with as little as 0.3% residual crystals lost extent or duration of supersaturation shah2024 C56. Edisylate dispersions with HPMCP still lost release at 30–40% drug (≈59 and ≈21 µg/mL), which the paper does not explain duong2022a R24, X8. After the acid stage, release from several salt dispersions was lower than in the single-stage test, which "may suggest" physical instability of the drug left in the undissolved matrix (F24) duong2022a C63.

Transfer check

Classify the neat drug by glass-forming ability and its induction time at the amorphous solubility: a drug that cannot be vitrified at 50 °C/min and crystallizes within minutes needs a fast solvent removal process or a higher-Tg form duong2022a R3, R2, C46. Check every dispersion for residual crystals by a sensitive method before release testing, since detectable crystallinity predicted incomplete release here and 0.3% did so for posaconazole duong2022a C56; shah2024 C56. For a weak base, screen salts with counterions whose pKa is low enough for proton transfer, and rank them by Tg and by water uptake together, since several high-Tg salts liquefied duong2022a R29, R20. Confirm that the salt survives in the dispersion and through an acid stage, which was not measured here duong2022a C63.

History

In the Crystallization tendency chapter, Towler and co-workers (2008) found that the counterion changes the crystallization tendency of amorphous salts towler2008 C32, C34, and residual crystals in commercial products were the starting point of the seeding work of 2018 (F22) que2018 C7. Duong and co-workers (2022) were the first in the library to form a drug salt in situ during preparation of a polymer dispersion of a fast crystallizer and to tie incomplete release to residual crystallinity from rotary evaporation duong2022a C6, C56. Hiew and co-workers (2022), in the Release mechanism and LoC chapter, found salts in dispersions "a double edged sword" for lumefantrine hiew2022b C34, C37. Nguyen and co-workers (2023) showed that spray drying removes the residual crystals of the free base, and used the in situ salts of 2022 to study gastric pH and enteric coating (F25, F27) nguyen2023c C17.

Topic 6 of 8 · 5 findings · F12–F15, F19

Additives and surfactants at drug-rich droplets

F12

Topic 6Additives and surfactants at drug-rich droplets1 of 5

Additives set droplet size and droplet life separately: some kept ritonavir droplets small but made them crystallize sooner.

In ritonavir solutions just above the LLPS concentration, 5 µg/mL of 15 additives fell into four groups ilevbare2013d R14. Hydrophobic anionic cellulose esters and HPMCAS kept droplets at about 200–350 nm and lengthened the induction time from 119.3 to 146.0–242.8 min, while Tween 80 and several cellulose and pullulan ethers kept droplets small but cut it to 23.6–59.5 min ilevbare2013d R12.

strongModerate for the ritonavir groups, whose triplicate induction times vary far less than the spread between additives; strong for the delamanid screen; weak to moderate for the charge mechanism, which was not measured ilevbare2013d K6, K5, X5; duong2022a K7.

small droplets, crystallization delayedsmall droplets, crystallization soonerno size stabilizationlarge droplets, slight delaygroup IVHPMCAS, cellulose esters · 203−352 nmnone 119.3146.0–242.8group IITween 80, ethers, pullulan · 178−395 nm119.323.6–59.5group IPVP, PVPVA, PAA, SDS · up to 511–922 nm119.334.7–120.0group IIIHPMC · 203−714 nm119.3134.0050100150200250ritonavir induction time at 20 µg/mL, min

5 µg/mL additive, solvent shift at 37 °C; sizes are the range before crystallization; dashed tick: no additive. ilevbare2013d R12, R14

Delamanid droplets with 300 µg/mL polymer, size, nmHPMCPheld for 3 h≈430–440HPMCASheld for 3 h≈595–600PVPVAgrew from ≈455≈900HPMC, Eudragit L100crystals within 30–60 minup to ≈6200

Droplets formed at 50 µg/mL in PBS pH 6.5; without polymer they crystallized at once. duong2022a R5, R7

For your drug

  1. Screen candidate additives at the concentration the dispersion releases, just above the LLPS concentration, and measure both the droplet size over 2–3 h and the induction time.
  2. Select only additives that pass both tests, check the ionic strength of the medium, and treat a charged polymer as a lead, not a guarantee.

ilevbare2013d P6, R14, R9, X5

How it works and key numbers
  1. Uncharged polymers were "largely ineffective" against coalescence of the droplets; the authors propose that a major stabilization mechanism is "likely" charge repulsion between polymers adsorbed at the ritonavir–water interface ilevbare2013d C37, C38.
  2. Cellulose ω-carboxyalkanoates, whose side chains end in carboxyl groups, are plausibly displayed on the droplet exterior ("It is not difficult to imagine") ilevbare2013d C49.
  3. The hydrophobically modified ethers may sit partly inside the droplets ("it is certainly possible"), which the authors offer for their promotion of crystallization ilevbare2013d C47.
  4. Except HPMC, every effective crystallization inhibitor was also an effective size stabilizer, but not the reverse ilevbare2013d C51; (synthesis) a small, stable droplet is therefore not a stable supersaturation.
119.3 → 242.8 minritonavir induction time without additive against CAAdB 0.81ilevbare2013d R12
23.6 mininduction time with Tween 80, although its droplets stayed at 178−182 nmilevbare2013d R12
≈430–440 nm for 3 hdelamanid droplets with HPMCP; with HPMC and Eudragit L100 they grew and crystallizedduong2022a R5
Evidence: data, conditions and papers

Finding F12. Additives decided the size and the life of drug-rich droplets: for ritonavir hydrophobic anionic cellulose esters and HPMCAS kept them small and delayed crystallization, surfactants and several cellulose and pullulan ethers kept them small but made them crystallize sooner, and PVP, PVPVA and PAA did neither; for delamanid HPMCP and HPMCAS kept droplets at about 440 and 600 nm for 3 h, PVPVA droplets grew, and HPMC and Eudragit L100 droplets crystallized

In short. In ritonavir solutions at 20 µg/mL, just above the LLPS concentration, with 5 µg/mL additive, HPMCAS and four new cellulose esters kept droplets at about 200–350 nm and lengthened the induction time from 119.3 to 146.0–242.8 min; Tween 80, PQ-10, a butyl pullulan and two hydrophobically modified cellulose ethers kept droplets at 178–395 nm but cut the induction time to 23.6–59.5 min; PVP, PVPVA, PAA and SDS stabilized neither; HPMC only delayed crystallization (134.0 min) ilevbare2013d R12, R14. In dissolving dispersions, PVP alone gave droplets growing from ≈360 to ≈5590 nm in 120 min, HPMC droplets above 1000 nm without crystallization in 2 h, CAAdP 0.33 and 0.85 droplets of ≈290–400 nm throughout, and Tween 80 droplets of ≈210–240 nm that crystallized at about 30 min ilevbare2013d R5, R6, R7. The authors see charged additives "in general" slowing coalescence, "likely" by charge repulsion between adsorbed polymers ilevbare2013d C37, C38. Delamanid droplets formed at 50 µg/mL crystallized at once without polymer; with 300 µg/mL polymer they started at ≈440 (HPMCP), ≈455 (PVPVA), ≈560 (HPMCAS), ≈630 (HPMC) and ≈770 nm (Eudragit L100), stayed at ≈430–440 and ≈595–600 nm with HPMCP and HPMCAS for 3 h, grew slowly to ≈900 nm with PVPVA, and grew to ≈1050–6200 nm within 30–60 min with HPMC and Eudragit L100 as crystals formed duong2022a R7, R5.

Type. observation in 2 drugs (ritonavir, 15 additives in solution, 7 dispersions; delamanid, 5 polymers) Strength. for the delamanid screen duong2022a K7: strong; moderate for the ritonavir classes, whose induction times are triplicates with standard deviations far smaller than the spread ilevbare2013d K6: moderate; weak to moderate for the charge mechanism, which has exceptions in the paper's own table and was not measured ilevbare2013d K5: weak to moderate, X5, X6.

How it was shown

Ilevbare and co-workers (2013) shifted ritonavir to 20 µg/mL in pH 6.8 buffer at 37 °C with one of 15 additives at 5 µg/mL, in triplicate, and read the induction time from extinction at 280 nm and droplet size by light scattering ilevbare2013d P6, P3. Duong and co-workers (2022) formed delamanid droplets at 50 µg/mL in PBS pH 6.5 with 300 µg/mL of five polymers and followed their size by DLS for 3 h duong2022a P7, A2.

What the data show

The additives fell into groups by droplet size and by induction time, and the two properties did not always go together ilevbare2013d R12, R14; duong2022a R5.

systemadditivessize before crystallization; induction time or outcomeids
ritonavir 20 µg/mLno additive188−830 nm; 119.3 minilevbare2013d R12
ritonavir, group IVHPMCAS, CAAdP 0.85, CA Sub 0.90, CAAdP 0.33, CAAdB 0.81203−352 nm; 146.0–242.8 minilevbare2013d R12, R14
ritonavir, group IITween 80, butyl pullulan, PQ-10, HM-HEC, HM-HPMC178−395 nm; 23.6–59.5 minilevbare2013d R12, R14
ritonavir, group IPVP, PVPVA, PAA, SDSup to 511–922 nm; 34.7–120.0 minilevbare2013d R12, R14
ritonavir, group IIIHPMC203−714 nm; 134.0 minilevbare2013d R12
delamanid 50 µg/mL300 µg/mL HPMCP / PVPVA / HPMCAS / HPMC and Eudragit L100≈430–440 nm held; ≈455 → ≈900 nm; ≈560 → ≈595–600 nm held; ≈1050–6200 nm within 30–60 min with crystalsduong2022a R5
Table 5 of ilevbare2013d: four classes of additive by size stabilization and crystallization inhibition
Table 5 · ilevbare2013dfour classes of additive by size stabilization and crystallization inhibition

Group IV holds both properties; group II stabilizes size but every member is marked as a crystallization promoter ilevbare2013d R14.

Why

The authors find uncharged polymers "largely ineffective" against coalescence and propose that a major stabilization mechanism is "likely" charge repulsion between polymers adsorbed at the ritonavir–water interface ilevbare2013d C37, C38. The hydrophobically modified ethers may sit partly inside the droplets ("it is certainly possible"), which they offer for their promotion of crystallization ilevbare2013d C47. Except HPMC, every effective crystallization inhibitor was also an effective size stabilizer, but not the reverse ilevbare2013d C51. For delamanid the authors chose HPMCP and HPMCAS by both properties duong2022a C13.

Limits and transfer

Adsorption, droplet charge and composition were not measured, and the charge rule has exceptions in the paper's own classification: PAA is a poor size stabilizer, while the uncharged HM-HEC, HM-HPMC and Tween 80 are good ones ilevbare2013d X5. Screen candidate additives at the concentration the dispersion releases, just above the LLPS concentration, measure both droplet size over 2–3 h and the induction time, and select only additives that pass both ilevbare2013d P6, R14.

How it was shown

Ilevbare and co-workers (2013) added a 4 mg/mL methanol solution of ritonavir to 50 mL of 100 mM pH 6.8 phosphate buffer at 37 °C and 300 rpm to 20 µg/mL, with one of 15 additives predissolved at 5 µg/mL (the butyl pullulan at 2 µg/mL), in triplicate; the induction time was the onset of the extinction rise at 280 nm, where ritonavir does not absorb, and droplet size was followed by light scattering in a flow-through cell ilevbare2013d P6, P3. The solvent shift removes the dissolution kinetics of the dispersion from the comparison ilevbare2013d C23. They also dissolved about 20 mg of dispersions holding 10% ritonavir (10:90 with PVP; 10:80:10 with HPMC, HPMCAS, CAAdP 0.33, CAAdP 0.85 or Tween 80; 10:70:10:10 with Tween 80 and CAAdP 0.33) in 50 mL at 37 °C and followed droplet size, and compared water with 100 mM buffer ilevbare2013d P1, P5, A4. Duong and co-workers (2022) formed delamanid droplets at 50 µg/mL in PBS pH 6.5 with 300 µg/mL of five polymers and followed their size by DLS for 3 h duong2022a P7, A2.

What the data show

Solvent shift (size range before crystallization; induction time). No additive 188−830 nm, 119.3 ± 8.14 min. Group I: PVP 188−631 nm, 120.0 min; PVPVA 215−913 nm, 119.2 min; PAA 213−922 nm, 93.0 min; SDS 268−511 nm, 34.7 min. Group II: Tween 80 178−182 nm, 23.6 min; butyl pullulan 189−208 nm, 28.0 min; PQ-10 183−303 nm, 34.5 min; HM-HEC 292−385 nm, 53.3 min; HM-HPMC 331−395 nm, 59.5 min. Group III: HPMC 203−714 nm, 134.0 min. Group IV: HPMCAS 235−352 nm, 146.0 min; CAAdP 0.85 203−248 nm, 171.4 min; CA Sub 0.90 220−276 nm, 181.5 min; CAAdP 0.33 210−214 nm, 238.0 min; CAAdB 0.81 204−210 nm, 242.8 min ilevbare2013d R12, R14. Over 3 h, droplets without additive grew from ≈250 to ≈1200 nm, SDS droplets fastest (≈1540 nm at 96 min), while CAAdP 0.85 and 0.33 stayed at ≈200–260 nm; abrupt size changes at about 100 (PAA), 130 (PVP) and 40 min (SDS) matched their induction times ilevbare2013d R13, C26. Dispersions. RTV/PVP ≈360 nm at the first reading, ≈1090 nm at 50 min, ≈5590 nm at 120 min, with crystallization at about 80–90 min by the methods used ilevbare2013d R5, X11. With HPMC ≈1240–1990 nm without crystallization in 2 h; with HPMCAS ≈340 rising to ≈640–670 nm; with CAAdP 0.33 or 0.85 ≈290–400 nm ilevbare2013d R5, C15, C16. With Tween 80 ≈210–240 nm for 30 min, then ≈730–840 nm after needles formed; with Tween 80 and CAAdP 0.33 the step came at about 90 min ilevbare2013d R6, R7. Crystals formed with Tween 80 had an aspect ratio of ≈22.4 against ≈3.9 with PVP alone ilevbare2013d R8. Medium. Droplets were smaller and grew more slowly in water than in 100 mM buffer (first readings ≈240 against ≈360 nm; ≈810 against ≈5590 nm at 120 min) ilevbare2013d R9.

papersystemmethod and conditionssize before crystallization; induction timeids
ilevbare2013dritonavir 20 µg/mL, no additivesolvent shift, 37 °C188−830 nm; 119.3 minR12
ilevbare2013dgroup IV: HPMCAS, CAAdP 0.85, CA Sub 0.90, CAAdP 0.33, CAAdB 0.81 (5 µg/mL)same203−352 nm; 146.0–242.8 minR12, R14
ilevbare2013dgroup II: Tween 80, butyl pullulan, PQ-10, HM-HEC, HM-HPMCsame178−395 nm; 23.6–59.5 minR12, R14
ilevbare2013dgroup I: PVP, PVPVA, PAA, SDSsameup to 511–922 nm; 34.7–120.0 minR12, R14
ilevbare2013d10% ritonavir dispersions with PVP; HPMC; CAAdP; Tween 80dissolution, DLS, 37 °C≈360 → ≈5590 nm; >1000 nm; ≈290–400 nm; ≈210–240 nm then crystals at about 30 minR5, R6
jackson2014 (Crystallization from solution)danazol droplets with HPMC or HPMC-ASDLS, 25 °Cabout 230–345 nm for 2–4 h against about 9800 nm in 1 h without polymerR22
ueda2020b (Amorphous solubility and LLPS)ibuprofen droplets, 300 µg/mL HPMC; PVP-VADLS, 37 °C272–345; 268–320 nm against 3182–5313 nm in bufferR5
duong2022adelamanid 50 µg/mL, 300 µg/mL HPMCP / PVPVA / HPMCAS / HPMC / Eudragit L100DLS, 3 h, PBS pH 6.5, 37 °C≈430–440 nm held; ≈455 → ≈900 nm; ≈560 → ≈595–600 nm held; HPMC and Eudragit L100 ≈1050–6200 nm within 30–60 min with crystalsR5

Figure

Table 5 of ilevbare2013d: four classes of additive by size stabilization and crystallization inhibition
Table 5 · ilevbare2013dfour classes of additive by size stabilization and crystallization inhibition

Group IV holds both properties; group II stabilizes size but every member is marked as a crystallization promoter ilevbare2013d R14.

Fig. 7 of ilevbare2013d: droplet size during dissolution of five ritonavir dispersions
Fig. 7 · ilevbare2013ddroplet size during dissolution of five ritonavir dispersions

PVP alone (black) grows to micrometres within 2 h; the CAAdP dispersions stay low throughout ilevbare2013d R5.

Why

The authors find uncharged polymers "largely ineffective" against coalescence and the charged additives except SDS effective, and propose that a major stabilization mechanism is "likely" charge repulsion between polymers adsorbed at the ritonavir–water interface ilevbare2013d C37, C38. The randomly substituted cellulose ω-carboxyalkanoates, with ester-linked side chains ending in carboxyl groups, are plausibly displayed on the droplet exterior ("It is not difficult to imagine"), which "could help to explain" their effect ilevbare2013d C49. The hydrophobically modified ethers may sit partly inside the droplets ("it is certainly possible"), and the regioselectively substituted pullulan may bury its ether chains ("it may be"), which the authors offer for their promotion of crystallization ilevbare2013d C47, C48. They summarize that, except HPMC, every effective crystallization inhibitor was also an effective size stabilizer but not the reverse, and that within their limited data set cellulose esters "tend to" inhibit crystallization better than polysaccharide ethers ilevbare2013d C51, C46; with too few structures they cannot yet rationalize which polysaccharides promote crystallization ilevbare2013d C45. Larger droplets at higher ionic strength are "in line with expectations", since water-structuring salts enhance hydrophobic interactions ilevbare2013d C58. Adsorption, droplet charge and droplet composition were not measured ilevbare2013d X5. (synthesis: size and crystallization are separate properties of an additive here; a small, stable droplet is not a stable supersaturation, as Tween 80 and PQ-10 show.) For delamanid the authors chose HPMCP and HPMCAS by both properties, long induction times and small, stable droplets, and found PVPVA, which also held the solution beyond 1000 min, at a disadvantage because its droplets grow duong2022a C13, C52. (synthesis: as for ritonavir, the two properties came apart: PVPVA delayed delamanid crystallization like the enteric esters but did not hold the droplet size duong2022a R4, R5.)

Conditions and limits

One drug, 37 °C, 100 mM buffer, one additive level (5 µg/mL) in the solvent shift and 10% of the dispersion in dissolution ilevbare2013d A6, A3, X9. The charge rule has exceptions in the paper's own classification: PAA is a poor size stabilizer, while the uncharged HM-HEC, HM-HPMC and Tween 80 are good ones ilevbare2013d X5. HPMC's gain in induction time is about 12% ilevbare2013d X15, and CAAdB 0.81 equals CAAdP 0.33 ilevbare2013d X17. Several text sizes do not match the tables ilevbare2013d X14, X2.

Counterexamples and conflicts

PVP-VA, ineffective for ritonavir at 5 µg/mL, gave small fresh ibuprofen droplets at 300 µg/mL in the LLPS chapter (but did not keep them dispersed) (Amorphous solubility and LLPS F22) ueda2020b R5; the polymer concentrations differ about 60-fold (synthesis: 300/5). In danazol solutions HPMC and HPMC-AS kept droplets at about 230–345 nm for hours (Crystallization from solution F15) jackson2014 R22, whereas HPMC gave large ritonavir droplets here ilevbare2013d R5.

Transfer check

For a drug that forms droplets, screen candidate additives at the concentration the dispersion releases, just above the LLPS concentration, and measure both droplet size over 2–3 h and the induction time; select only additives that pass both ilevbare2013d P6, R14. Check the medium's ionic strength, since droplets grew faster in 100 mM buffer than in water ilevbare2013d R9. A charged polymer is a lead, not a guarantee ilevbare2013d X5.

History

Surfactants had been found to stabilize aggregates of other drugs against coalescence (cited) ilevbare2013d R20. Ilevbare and co-workers (2013) gave the library's first screen of additives on droplets formed by ASD dissolution ilevbare2013d C59. Later papers took up the droplet-size effect of polymers for danazol and ibuprofen and cite this work for polymer adsorption at the amorphous surface (builds_on, as listed in the evidence index of this subcategory). Duong and co-workers (2022) applied the size-and-life screen to delamanid and chose HPMCP and HPMCAS by it duong2022a C13; the title gained delamanid then.

F13

Topic 6Additives and surfactants at drug-rich droplets2 of 5

Ritonavir crystallized sooner just above its LLPS concentration than just below it, and surfactants acted only when droplets were present.

At 17 µg/mL, just below the LLPS concentration, ritonavir crystallized after about 284 min; at 20 µg/mL, with droplets present, after 119.3 min ilevbare2013d R16, R12. SDS and Tween 80 cut the induction time to 34.7 and 23.6 min at 20 µg/mL, but had little effect at 17 µg/mL ilevbare2013d R16, R12.

weakWeak to moderate: the 17 µg/mL values are single reported values without n or SD, and the site of nucleation was not observed ilevbare2013d K7, X18.

17 µg/mL, no droplets20 µg/mL, droplets presentno additive119.3∼284SDS34.7∼262Tween 8023.6∼289050100150200250300ritonavir induction time, min

Solvent shift into pH 6.8 buffer at 37 °C, 5 µg/mL surfactant; the 17 µg/mL values are single reported values. ilevbare2013d R16, R12, X18

For your drug

  1. Measure the induction time just below and just above the LLPS concentration in the same medium, with and without the surfactant or additive of the formulation.
  2. An additive that promotes crystallization only above the onset puts its risk in the droplet regime that fast-dissolving dispersions create (F9).

ilevbare2013d A7, C43

How it works and key numbers
  1. If the droplets and the surrounding water are in equilibrium, the supersaturation is the same in both phases ilevbare2013d C40.
  2. Inside the droplets the drug concentration is much higher, and the interfacial tension between an embryonic crystal and the water-saturated supercooled liquid is expected to be lower, so by classical nucleation theory nucleation should be favoured there ("not unreasonable") ilevbare2013d C40, E1.
  3. SDS and Tween 80 had no appreciable effect at 17 µg/mL but strong effects at 20 µg/mL, so "it is apparent" that they need the ritonavir–water interface, as in amphiphile-directed nucleation in emulsions (cited) ilevbare2013d C43, C42, R21.
  4. (synthesis) The bulk supersaturation also rose, from about 13 to about 15 relative to the 1.3 µg/mL crystalline solubility, so part of the shorter induction time could come from the higher supersaturation ilevbare2013d M1.
To feel the numbers. Against the 1.3 µg/mL crystalline solubility, 17 µg/mL is a supersaturation of 17 ÷ 1.3 ≈ 13 and 20 µg/mL one of 20 ÷ 1.3 ≈ 15.4, about a fifth higher, while the induction time fell by 284 ÷ 119.3 ≈ 2.4 times.
∼284 vs 119.3 mininduction time just below (17 µg/mL) and just above (20 µg/mL) the LLPS concentrationilevbare2013d R16, R12
∼289 vs 23.6 minthe same comparison with Tween 80ilevbare2013d R16, R12
30 minfirst needles among the droplets of a dispersion with Tween 80, against about 90 min withoutilevbare2013d R7, R4
Evidence: data, conditions and papers

Finding F13. Ritonavir crystallization appeared to start in the drug-rich droplets: just below the LLPS concentration the induction time was about 284 min against about 120 min just above it, and SDS and Tween 80 promoted crystallization only when droplets were present

In short. At 17 µg/mL ritonavir, below the LLPS concentration of 18.2 µg/mL, the induction time was given as ">280 min" and "∼284 min", against 119.3 min at 20 µg/mL; with SDS it was ∼262 min and with Tween 80 ∼289 min at 17 µg/mL, against 34.7 and 23.6 min at 20 µg/mL ilevbare2013d R16, R12, R10. Needles appeared among the droplets in SEM, from about 90 min with PVP alone and from 30 min with Tween 80 ilevbare2013d R4, R7. The authors conclude that crystallization "appears" to start in the drug-rich phase and that, for ritonavir, the droplets "appear to promote" crystallization, contrary to the suggestion that a colloidal phase stabilizes against it ilevbare2013d C39, C41.

Type. single-system observation (ritonavir) Strength. to moderate: the 17 µg/mL values are single reported values without n or SD, and the nucleation site was not observed directly ilevbare2013d K7: weak to moderate, X18.

How it was shown

Ilevbare and co-workers (2013) ran the solvent-shift induction-time test (extinction at 280 nm, 37 °C, pH 6.8 buffer) at 17 µg/mL ritonavir, below the LLPS concentration, without additive and with SDS or Tween 80, and compared it with runs at 20 µg/mL ilevbare2013d P6, A7. Dried samples of dissolving dispersions were imaged by SEM over time ilevbare2013d P8.

What the data show

Below the LLPS concentration the induction time was more than twice as long, and the two surfactants lost their effect ilevbare2013d R16, R12.

systemtestresultids
ritonavir, no additivesolvent shift, 17 against 20 µg/mL, 37 °C">280 min" and "∼284 min" against 119.3 ± 8.14 minilevbare2013d R16, R12, X18
ritonavir, SDSsame∼262 against 34.7 ± 1.04 minilevbare2013d R16, R12
ritonavir, Tween 80same∼289 against 23.6 ± 1.59 minilevbare2013d R16, R12
RTV/PVP and RTV/PVP/Tween 80 dispersionsSEM, water, 37 °Cneedles among droplets from about 90 min; from 30 min with Tween 80ilevbare2013d R4, R7
lopinavir drug-rich phase, 35 µg/mLpyrene I3/I1crystallization between 1 and 2 htrasi2015b R15
Fig. 6 of ilevbare2013d: SEM of the dispersed phase from a ritonavir–PVP dispersion between 5 and 480 min
Fig. 6 · ilevbare2013dSEM of the dispersed phase from a ritonavir–PVP dispersion between 5 and 480 min

Smooth droplets give way to an aggregate at 90 min and needle clusters at 120 and 480 min, which the authors read as crystals forming from the droplets ilevbare2013d R4, C11.

Why

If droplets and water are in equilibrium, the supersaturation is the same in both phases, and by classical nucleation theory nucleation should then be favoured inside the droplets, where the drug concentration is much higher and the interfacial tension with an embryonic crystal is expected to be lower ("not unreasonable") ilevbare2013d C40, E1. Because SDS and Tween 80 had no appreciable effect at 17 µg/mL, "it is apparent" that they need the ritonavir–water interface to promote crystallization ilevbare2013d C43, C42. (synthesis: the bulk supersaturation also rose from about 13 to about 15 relative to the 1.3 µg/mL crystalline solubility ilevbare2013d M1, so part of the shorter induction time could come from it.)

Limits and transfer

The 17 µg/mL runs have no figure, table, n or SD, and the site of nucleation was not observed ilevbare2013d X18, K7. Mixed ritonavir–lopinavir drug-rich phases did not crystallize within 5 h, so more droplets did not by themselves bring crystallization (F11) trasi2015b R15, C51. Measure the induction time just below and just above the LLPS concentration in the same medium, with and without the surfactant or additive of the formulation ilevbare2013d A7.

How it was shown

Ilevbare and co-workers (2013) ran the solvent-shift induction-time test (extinction at 280 nm, 37 °C, 100 mM pH 6.8 buffer) at 17 µg/mL, below the LLPS concentration, without additive and with SDS or Tween 80, and compared it with the 20 µg/mL runs ilevbare2013d P6, A7. Dried samples of dissolving dispersions were imaged by SEM over time ilevbare2013d P8.

What the data show

Without additive: ">280 min" and "∼284 min" at 17 µg/mL (both printed), 119.3 ± 8.14 min at 20 µg/mL ilevbare2013d R16, R12, X18. SDS: ∼262 against 34.7 ± 1.04 min; Tween 80: ∼289 against 23.6 ± 1.59 min ilevbare2013d R16, R12. In SEM of the RTV/PVP dispersion, spherical droplets at 5–60 min were followed by an irregular aggregate among flattened droplets at 90 min and needle clusters at 120 and 480 min; with Tween 80, needles radiated from a centre among droplets at 30 min ilevbare2013d R4, R7. The pyrene ratio rose from ≈1.46 to ≈1.77 at about 120 min, read as crystals expelling the probe ilevbare2013d R3, C10. In the lopinavir work of 2015, a drug-rich phase of lopinavir alone (35 µg/mL, above its LLPS concentration) crystallized between 1 and 2 h trasi2015b R15.

papersystemmethod and conditionsresultids
ilevbare2013dritonavir 17 against 20 µg/mL, no additivesolvent shift, 37 °Cabout 284 against 119.3 minR16, R12
ilevbare2013dsame with SDS; Tween 80sameabout 262 against 34.7 min; about 289 against 23.6 minR16, R12
ilevbare2013dRTV/PVP and RTV/PVP/Tween 80 dispersionsSEM, water, 37 °Cneedles among droplets from about 90 min; from 30 min with Tween 80R4, R7
trasi2015blopinavir drug-rich phase, 35 µg/mLpyrene I3/I1crystallization between 1 and 2 hR15
wilson2021 (Crystallization from solution)enzalutamide above its amorphous solubilityinduction time with polymersdroplet–solvent interface proposed as a favourable site for heterogeneous nucleationC45

Figure

Fig. 6 of ilevbare2013d: SEM of the dispersed phase from a ritonavir–PVP dispersion between 5 and 480 min
Fig. 6 · ilevbare2013dSEM of the dispersed phase from a ritonavir–PVP dispersion between 5 and 480 min

Smooth droplets (a–c) give way to an aggregate at 90 min (d) and needle clusters at 120 and 480 min (e, f), which the authors read as crystals forming from the droplets ilevbare2013d R4, C11.

Why

If the droplets and the surrounding water are in equilibrium, the supersaturation is the same in both phases; by classical nucleation theory nucleation should then be favoured inside the droplets, where the drug concentration is much higher and the interfacial tension between an embryonic crystal and the water-saturated supercooled liquid is expected to be lower ("not unreasonable") ilevbare2013d C40, E1. Because SDS and Tween 80 had no appreciable effect at 17 µg/mL but strong effects at 20 µg/mL, "it is apparent" that they need the ritonavir–water interface to promote crystallization, as in amphiphile-directed nucleation in emulsions (cited) ilevbare2013d C43, C42, R21. Trasi and Taylor (2015) add that a drug-rich phase "may" raise the crystallization tendency because its interfaces can act as heterogeneous nucleation sites trasi2015b C31. (synthesis: the comparison is not at equal driving force: the bulk supersaturation also rose from about 13 to about 15 relative to the 1.3 µg/mL crystalline solubility (17/1.3 and 20/1.3) ilevbare2013d M1, so part of the shorter induction time could come from the higher supersaturation; the surfactant result, which reverses with the appearance of droplets, is the stronger part of the argument.)

Conditions and limits

One drug, one temperature, solvent shift only; the 17 µg/mL runs have no figure, table, n or SD ilevbare2013d X18. The site of nucleation was not observed ilevbare2013d K7. The onset of RTV/PVP crystallization is placed between about 80 and 120 min depending on method and medium ilevbare2013d X11.

Counterexamples and conflicts

Mixed drug-rich phases of ritonavir and lopinavir, with up to twice the amount of drug-rich phase (RTV 50 + LPV 35 µg/mL), did not crystallize within 5 h, where the lower supersaturation of each drug is the authors' explanation (F11) trasi2015b R15, C51; more droplets therefore did not by themselves bring crystallization. The crystallization-from-solution chapter finds that above the amorphous solubility droplets make crystallization much harder to inhibit for enzalutamide and posaconazole (Crystallization from solution F37) wilson2021 C45, in line with the reading here.

Transfer check

Measure the induction time just below and just above the LLPS concentration in the same medium, with and without the surfactant or additive of the formulation ilevbare2013d A7. If an additive promotes crystallization only above the onset, its risk lies in the droplet regime that fast-dissolving dispersions create (F9).

History

A colloidal phase had been suggested to protect against crystallization (cited) ilevbare2013d C41. Ilevbare and co-workers (2013) reported the opposite for ritonavir and proposed nucleation in the droplets ilevbare2013d C39. Later papers of the crystallization-from-solution chapter proposed the droplet interface as a nucleation site for telaprevir and enzalutamide (Crystallization from solution F37).

F14

Topic 6Additives and surfactants at drug-rich droplets3 of 5

SDS and polysorbate 80 promoted crystallization of celecoxib and ritonavir; sodium taurocholate and Triton X100 slowed celecoxib nucleation.

At an initial supersaturation of 5, celecoxib crystallized after 7 min with polysorbate 80 and 41 min with SDS, against 88 min without surfactant, but after 273 min with Triton X100 and more than 960 min with sodium taurocholate (STC) chen2015a R12. Suspensions of celecoxib–HPMCAS particles at pH 3 showed crystals at 0.5 h with SDS and at 1 h with polysorbate 80, and none for 48 h in the other media chen2015a R14.

moderateModerate: the induction times are means of at least three runs and the suspension outcome agrees across microscopy, XRPD and drug concentrations, but suspension replicates are not stated and the tail-shape explanation rests on five surfactants chen2015a K1, K2, K3, X21.

Celecoxib at S = 5: minutes to crystallization (log scale)polysorbate 807Poloxamer 18812SDS41no surfactant88Triton X100273sodium taurocholatemore than 960

Each surfactant just above its CMC in pH 3 HCl, 25 °C; no ASD polymer in the solution. chen2015a R12

Crystals in the pH 3 suspension
SDSpolysorbate 80
No crystals for 48 h
no surfactantPoloxamer 188Triton X100sodium taurocholate

Poloxamer 188 shortened the solution induction time but not the life of the suspension, which the authors relate to leached HPMCAS (F6). chen2015a R14, R19, C28

For your drug

  1. Test the intended wetting agent at its formulation level in an induction-time test at fixed supersaturation with the ASD polymer present, and in the suspension or dispersion itself for the dosing period.
  2. Treat SDS and polysorbate 80 as suspects for promotion and STC and Triton X100 as alternatives to check ("should be assessed").

chen2015a P9, A3, P10, C36

How it works and key numbers
  1. The promoters SDS, polysorbate 80 and Poloxamer 188 have chain-like hydrophobic tails, the inhibitors STC and Triton X100 bulky groups chen2015a C20.
  2. The authors find it "conceivable" that flexible linear chains assemble at the many interfaces of a suspension and align with nucleating celecoxib, which rigid bulky groups would not allow chen2015a C21.
  3. Drug–surfactant interactions "may be" responsible for inhibition, and the effects held below the CMC ("Interestingly") chen2015a C22, C6.
  4. For ritonavir, SDS and Tween 80 need the ritonavir–water interface of the droplets to act (F13) ilevbare2013d C43.
7 / 41 vs 88 mincelecoxib induction time with polysorbate 80 and SDS against no surfactantchen2015a R12
more than 960 mincelecoxib induction time with 0.75% STCchen2015a R12
23.6 / 34.7 vs 119.3 minritonavir with 5 µg/mL Tween 80 and SDS against no additiveilevbare2013d R12
Evidence: data, conditions and papers

Finding F14. SDS and polysorbate 80 promoted crystallization of celecoxib from HPMCAS dispersion suspensions and of ritonavir drug-rich droplets, whereas sodium taurocholate and Triton X100 slowed celecoxib nucleation

In short. In pH 3 suspensions of celecoxib–HPMCAS spray-dried particles, crystals appeared at 0.5 h with 0.25% SDS and at 1 h with 0.0064% polysorbate 80, and not within 48 h without surfactant or with Poloxamer 188, Triton X100 or STC chen2015a R14. At S = 5 the induction time was 7 (polysorbate 80), 12 (Poloxamer 188) and 41 min (SDS) against 88 min without surfactant, and 273 (Triton X100) and more than 960 min (STC 0.75%); SDS below its CMC (0.175%) still gave 29 min chen2015a R12, C6. In ritonavir solutions with droplets, 5 µg/mL Tween 80 and SDS cut the induction time to 23.6 and 34.7 min from 119.3 min, and a dispersion with 10% Tween 80 crystallized at about 30 min ilevbare2013d R12, R6, R7. The authors link promotion to chain-like tails and inhibition to bulky groups ("conceivable") chen2015a C20, C21.

Type. observation in 2 drugs (celecoxib, ritonavir) Strength. : induction times are means of at least three runs and the suspension outcome agrees across microscopy, XRPD and drug concentrations, but replicates of the suspension tests are not stated and the tail-shape explanation rests on five surfactants without interfacial measurements chen2015a K1: moderate to strong, K2: strong, K3: weak, X21; ilevbare2013d K6: moderate.

How it was shown

Chen and co-workers (2015) measured celecoxib induction times at S = 5 in eight media at 25 °C, with each surfactant 6–14% above its CMC, and watched suspensions of 33.3% celecoxib–HPMCAS spray-dried particles in pH 3 acid under polarized light for up to 48 h chen2015a P2, X2, P9, P10. Ilevbare and co-workers (2013) used 5 µg/mL Tween 80 or SDS in the ritonavir solvent-shift test and 10% Tween 80 in a dispersion ilevbare2013d P6, P1.

What the data show

SDS and polysorbate 80 shortened the induction time and crystallized the suspensions, while Triton X100 and sodium taurocholate (STC) lengthened it chen2015a R12, R14.

systemtestresultids
celecoxib, S = 5induction time, 25 °C7 (polysorbate 80), 12 (Poloxamer 188), 41 (SDS) against 88 min; 273 (Triton X100) and more than 960 min (STC)chen2015a R12
celecoxib–HPMCAS particles, pH 3, 10 mg/mLsuspension, polarized light, 25 °Ccrystals at 0.5 h (SDS) and 1 h (polysorbate 80); none to 48 h in four other mediachen2015a R14
ritonavir 20 µg/mL, 5 µg/mL Tween 80; SDSsolvent shift, 37 °C23.6; 34.7 against 119.3 minilevbare2013d R12
ritonavir dispersion with 10% Tween 80dissolution, SEMcrystals from about 30 minilevbare2013d R6, R7
11 drugs, 0.1% STC; nine drugs, 0.1% SDS (Crystallization from solution)induction time at matched supersaturationSTC lengthened all eleven; SDS shortened seven of ninechen2015 R3
Fig. 4 of chen2015a: celecoxib induction times at S = 5 in eight media
Fig. 4 · chen2015acelecoxib induction times at S = 5 in eight media

Promoters on the left, the 88-min surfactant-free reference in the middle, inhibitors on the right; the STC bars are cut at the 400-min axis limit chen2015a R12, X3.

Why

Chen and co-workers note that the promoters have chain-like hydrophobic tails and the inhibitors bulky groups, and find it "conceivable" that flexible linear chains assemble at the interfaces of a suspension and align with nucleating celecoxib, which rigid bulky groups would not allow chen2015a C20, C21. The effects held below the CMC chen2015a C6. Ilevbare and co-workers conclude that SDS and Tween 80 need the ritonavir–water interface to act ilevbare2013d C43.

Limits and transfer

One level of each surfactant was tested, and the solution test differed from the suspension in volume, stirring and the absence of polymer chen2015a A1, X13. Lopinavir, a slow crystallizer, showed no crystals within 3 h in suspensions with SDS, STC, Poloxamer 188 or polysorbate 80 li2016b R21, C5. Test the intended wetting agent at its formulation level in an induction-time test with the ASD polymer present and in the suspension itself, treating SDS and polysorbate 80 as suspects and STC and Triton X100 as alternatives to check chen2015a P9, A3, P10, C36.

How it was shown

Chen and co-workers (2015) spray-dried celecoxib with HPMCAS-LF at 33.3% drug, read each surfactant's CMC in pH 3 HCl from the break in Form III solubility with celecoxib at saturation, and set test levels 6–14% above the printed CMCs chen2015a P2, P8, X2. They measured induction times at an initial S = 5 relative to Form III solubility in each medium (methanol stock into 50 mL, 300 rpm, 25 °C, extinction at 350 nm), and watched 10 mg/mL suspensions of the particles at 25 °C and 150 rpm under polarized light at 0.5–48 h, with XRPD of the SDS solids after 24 h chen2015a P9, P10, P4. Ilevbare and co-workers (2013) used 5 µg/mL Tween 80 or SDS in the ritonavir solvent-shift test and 10% Tween 80 in a dispersion (F12) ilevbare2013d P6, P1.

What the data show

Celecoxib. CMCs with celecoxib at saturation were 0.23% (SDS), 0.69% (STC), 0.0058% (polysorbate 80), 0.16% (Poloxamer 188) and 0.022% (Triton X100) chen2015a R4. Form III solubility at the test levels was 14.5 (SDS), 5.8 (STC), 3.7 (Triton X100), 2.0 (polysorbate 80), 1.4 (Poloxamer 188) and 1.1 µg/mL without surfactant chen2015a R5. In SDS, needle-like crystals floated in the liquid next to dark particle aggregates at 0.5 h, and the solids after 24 h gave Form III peaks on an amorphous halo; in polysorbate 80 many thin needles appeared at 1 h chen2015a R15, R16. STC at 0.4% (below its CMC) still lengthened the induction time, its value unresolved in the figure chen2015a C6, X3. After about 7 days in Triton X100, birefringence sat on or in the particles and no free needles were seen chen2015a R20. Ritonavir. Tween 80 droplets in solution stayed at 178−182 nm and crystallized after 23.6 min; SDS droplets grew fastest (≈1540 nm at 96 min) and crystallized after 34.7 min ilevbare2013d R12, R13. Below the LLPS concentration neither surfactant shortened the induction time (F13) ilevbare2013d R16. Crystals formed with Tween 80 were more needle-like (aspect ratio ≈22.4 against ≈3.9) ilevbare2013d R8.

papersystemmethod and conditionsresultids
chen2015acelecoxib–HPMCAS particles, pH 3, 10 mg/mLsuspension, polarized light, 25 °Ccrystals at 0.5 h (SDS), 1 h (polysorbate 80); none to 48 h in four other mediaR14
chen2015acelecoxib, S = 5, eight mediainduction time, 25 °C7 / 12 / 41 against 88 min; 273 and >960 min (Triton X100, STC)R12
ilevbare2013dritonavir 20 µg/mL, 5 µg/mL Tween 80; SDSsolvent shift, 37 °C23.6; 34.7 against 119.3 minR12
ilevbare2013dritonavir dispersion with 10% Tween 80dissolution, SEMcrystals from about 30 minR6, R7
chen2015 (Crystallization from solution)11 drugs, 0.1% STC; nine drugs, 0.1% SDSinduction time at matched supersaturationSTC lengthened all eleven; SDS shortened seven of nineR3
ilevbare2012a (Crystallization from solution)ritonavir seeds, 5 µg/mL TPGS and Tween 80seeded growthgrowth ratios about 0.49 and 0.53 (faster growth)R17
indulkar2019b (Crystallization from solution)atazanavir with SDSinduction time at equal activitySDS shortened it between about a seventh of its CMC and the CMCR3
yang2023 (Release mechanism and LoC)ritonavir–PVPVA–SDS compactsrelease, 30 minrelease plateau attributed to ritonavir crystallization on the compact surfacesC24

Figure

Fig. 4 of chen2015a: celecoxib induction times at S = 5 in eight media
Fig. 4 · chen2015acelecoxib induction times at S = 5 in eight media

Promoters on the left (7–41 min), the 88-min surfactant-free reference in the middle, inhibitors on the right; the STC bars are cut at the 400-min axis limit chen2015a R12, X3.

Fig. 5 of chen2015a: suspensions under polarized light
Fig. 5 · chen2015asuspensions under polarized light

Free needles in SDS at 0.5 h (a) and polysorbate 80 at 1 h (b); only particles and aggregates at 48 h in the other four media (c–f) chen2015a R15.

Why

Chen and co-workers note that the three promoters have chain-like hydrophobic tails and the two inhibitors bulky groups, and find it "conceivable" that flexible linear chains assemble at the many interfaces of a suspension, as Langmuir–Blodgett-type films (cited), and align with nucleating celecoxib, which rigid bulky groups would not allow; drug–surfactant interactions "may be" responsible for inhibition chen2015a C20, C21, C22. The effects held below the CMC ("Interestingly") chen2015a C6. In suspension, SDS and polysorbate 80 promote crystallization of drug dissolved in the liquid, "as evidenced by" free-floating needles chen2015a C35. Ilevbare and co-workers conclude that SDS and Tween 80 need the ritonavir–water interface to act, with amphiphile-directed nucleation as precedent ilevbare2013d C43, C42. In the crystallization-from-solution chapter, surfactants far below their CMC doubled the growth rate of ritonavir and cancelled growth inhibition by cellulose esters (Crystallization from solution F18) ilevbare2012a R17. (synthesis: two drugs and two settings, suspended dispersion particles in acid and droplets in neutral buffer, point the same way for SDS and polysorbate 80.)

Conditions and limits

One level of each surfactant, near its CMC for celecoxib and 5 µg/mL for ritonavir; 25 °C for celecoxib, 37 °C for ritonavir; pH 3 suspension against pH 6.8 solution chen2015a A1; ilevbare2013d P6. The solution test differed from the suspension in volume, stirring and the absence of polymer chen2015a X13. The stated polysorbate 80 tail length does not match the drawn structure, and the Poloxamer 188 CMC is weakly determined chen2015a X15, X20.

Counterexamples and conflicts

Poloxamer 188 promoted nucleation in solution but its suspension stayed crystal-free for 48 h, which the authors relate to leached HPMCAS (F6) chen2015a R19, C28. In the companion bile-salt study SDS did not shorten the induction time of griseofulvin and nevirapine (Crystallization from solution F28) chen2015 R3. The surfactant-free celecoxib suspension held S up to ≈6.7 for 48 h although its solution test crystallized after 88 min, which the nucleation-and-leaching account does not explain chen2015a X6. For lopinavir, a slow crystallizer chosen for that reason, suspensions of enteric dispersions with SDS, STC, Poloxamer 188 or polysorbate 80 showed no crystals within 3 h, and the authors warn that this "is unlikely" to hold for many other drugs li2016b R21, C5, C46; a marketed tacrolimus product containing sodium lauryl sulfate reached the same plateau as the others without falling over 2 h trasi2016 M10, R10, C30.

Transfer check

Test the intended wetting agent at its formulation level in an induction-time test at fixed supersaturation with the ASD polymer present, and in the suspension or dispersion itself for the dosing period chen2015a P9, A3, P10. Treat SDS and polysorbate 80 as suspects for promotion and STC and Triton X100 as alternatives to check, as the authors advise ("should be assessed") chen2015a C36. For drug-rich droplets, test above and below the LLPS concentration (F13).

History

Surfactants had been shown to enhance nucleation and polymorph conversion in other systems (cited) chen2015a C1. Ilevbare and co-workers (2013) first showed in the library that Tween 80 and SDS shorten the life of drug-rich droplets ilevbare2013d C42. Chen and co-workers (2015) extended the question to ASD suspensions and five surfactants chen2015a C38. Bile-salt and SDS studies of the crystallization-from-solution chapter cite this work for STC inhibition below and above its CMC and for chain surfactants promoting crystallization (builds_on, as listed in the evidence index of this subcategory). Li and co-workers (2016), within this chapter, took up the question of surfactants in ASD suspensions for lopinavir and measured how much drug they release rather than how fast it crystallizes (F19) li2016b C3, C45.

F15

Topic 6Additives and surfactants at drug-rich droplets4 of 5

In acidified suspensions of enteric-polymer dispersions, SDS dissolved more of the polymer and so released more drug.

After 24 h at pH 3, the liquid of a celecoxib–HPMCAS suspension held about 860 µg/mL HPMCAS with SDS against about 3.5 µg/mL without surfactant, about 250-fold more (synthesis) chen2015a R18. With SDS the celecoxib supersaturation peaked within 10 min and fell as crystals formed chen2015a R17. For lopinavir dispersions at pH 5, SDS raised dissolved HPMCAS-HF and lopinavir several-fold li2016b R13.

weakWeak to moderate: polymer was measured in a few media only, near its detection limit without surfactant, and polymer ionization and complexes were not measured chen2015a K4, X9; li2016b K5, X7.

HPMCAS dissolved from celecoxib–HPMCAS particles, pH 3, 24 h, µg/mLSDS≈860sodium taurocholate≈43Triton X100≈6.0no surfactant≈3.5

Colorimetric assay of the filtered liquid; polysorbate 80 and Poloxamer 188 media were not assayed. chen2015a R18, X9

pH 3, no surfactantpH 3 with SDSpH 5 with SDSHPMCAS-HF3–519–2474.5–134lopinavir71333–39110100in the liquid of lopinavir–HPMCAS-HF suspensions, µg/mL (log scale)

33% drug spray-dried dispersions in citrate buffer, 25 °C; drug and polymer rose together with SDS. li2016b R3, R8, R13

For your drug

  1. For an acidified suspension of an enteric-polymer dispersion, such as a toxicology vehicle, assay dissolved polymer and drug over the dosing window for each candidate wetting agent and check for crystals by polarized light at 0.5–6 h.
  2. Reject wetting agents that dissolve the polymer, and keep the vehicle pH well below the onset of HPMCAS ionization when an ionic surfactant is present.

chen2015a P10, P11, P12, C36; li2016b R13

How it works and key numbers
  1. At this "relatively low" drug loading, drug release "appears to be" controlled by the polymer, so a surfactant that dissolves more HPMCAS also releases more drug ("It is likely") chen2015a C31.
  2. SDS dissolves the polymer "most likely" through polymer–surfactant complexes, as reported for HPMC and SDS (cited); no complex was detected chen2015a C32.
  3. SDS combines this leaching with promoted nucleation (F14) and gave the least stable suspension, while STC and Triton X100 inhibit nucleation and leach little chen2015a C23, C29.
  4. For lopinavir the jump at pH 5 is related to slight ionization of HPMCAS, by a mechanism on which the authors "can only speculate" li2016b C24, C49.
≈860 vs ≈3.5 µg/mLHPMCAS in the pH 3 liquid at 24 h with SDS against no surfactantchen2015a R18
≈8.6 → ≈3.2celecoxib supersaturation with SDS between about 5 min and 1 h, as crystals formedchen2015a R17
≈33–39 vs ≈7.4 µg/mLlopinavir from HPMCAS-HF dispersions at pH 5 with and without SDSli2016b R13
Evidence: data, conditions and papers

Finding F15. In acidified suspensions of enteric-polymer dispersions, SDS dissolved more polymer and released more drug: about 250-fold more HPMCAS and the most celecoxib, which then crystallized, and at pH 5 more than 20-fold more HPMCAS-HF and about fivefold more lopinavir

In short. After 24 h at pH 3 the suspension liquid held about 860 µg/mL HPMCAS with SDS, about 43 with STC, about 6 with Triton X100 and about 3.5 µg/mL without surfactant (synthesis: 860/3.5 ≈ 250) chen2015a R18. With SDS the celecoxib supersaturation peaked within 10 min (7.4 in the text, ≈8.6 in the figure) and fell to ≈3.2 by 1 h as crystals formed, whereas with Triton X100 it stayed at ≈1.5–1.8 for 48 h chen2015a R17, X4. The authors propose that drug leaching "is likely" set by how much the surfactant dissolves HPMCAS, through polymer–surfactant complexes in the case of SDS ("most likely"), and that minimizing leaching is "clearly desirable" chen2015a C31, C32, C30. Without surfactant the supersaturation rose from ≈4.3 to ≈6.7 over 48 h without crystals chen2015a R17, R14. From 33% lopinavir dispersions at pH 3, SDS raised leached HPMCAS-HF from about 3–5 to about 19–24 µg/mL and lopinavir from about 7 to 13 µg/mL; at pH 5 with SDS they reached about 120 and 36 µg/mL, and HPMCAS-LF about 290–330 µg/mL with 23–30 µg/mL lopinavir, which the authors attribute to a "small extent" of polymer ionization by a mechanism "currently unclear" (synthesis: 120/5 > 20 and 36/7 ≈ 5) li2016b R3, R8, R7, R13, R16, C24, C49.

Type. observation in 2 drugs (celecoxib, lopinavir; HPMCAS grades and HPMCP, 33% drug, four to five surfactants) Strength. to moderate: polymer was measured in a few media only, near its detection limit without surfactant, the link holds for absolute drug concentration but not for supersaturation, the supersaturation in SDS assumes that about 860 µg/mL HPMCAS leaves the celecoxib solubility unchanged, and polymer ionization and complexes were not measured chen2015a K4: weak to moderate, X9, X10; li2016b K5: moderate, X7.

How it was shown

Chen and co-workers (2015) suspended a celecoxib–HPMCAS spray-dried dispersion in pH 3 HCl with or without one surfactant at 25 °C, assayed celecoxib in 0.45 µm filtrates by HPLC as supersaturation relative to Form III, and assayed dissolved HPMCAS by phenol–sulfuric acid colorimetry chen2015a P10, P11, P12. Li and co-workers (2016) did the same for 33.3% lopinavir dispersions in HPMCAS grades or HPMCP at pH 3 or 5 with four surfactants li2016b P1, P4, P7.

What the data show

SDS raised the dissolved polymer and the released drug together, and for celecoxib the extra drug crystallized chen2015a R17, R18; li2016b R8, R13.

systemmediumdissolved polymer; drugids
celecoxib–HPMCAS 33.3%, SDS 0.25%pH 3HPMCAS ≈860 µg/mL at 24 h; S ≈8.6 → ≈3.2 within 1 hchen2015a R17, R18
same, STC 0.75%; Triton X100 0.025%pH 3HPMCAS ≈43 and ≈6.0 µg/mL; S ≈3.5 → ≈4.9 and ≈1.6 → ≈1.8chen2015a R17, R18
same, no surfactantpH 3, 48 hHPMCAS ≈3.5 µg/mL; S ≈4.3 → ≈6.7chen2015a R17, R18
lopinavir–HPMCAS-HF 33%, SDS 0.055%; polysorbate 80pH 3HF ≈19–24 µg/mL, LPV ≈13; HF ≈3–4, LPV ≈14.5 µg/mLli2016b R8, R7
same, SDS; LPV–HPMCAS-LF, SDSpH 5HF ≈74.5–134, LPV ≈33–39 µg/mL; LF ≈216–326, LPV ≈23–30 µg/mLli2016b R13, R16
Fig. 8 of chen2015a: HPMCAS dissolved from the suspended particles in four media
Fig. 8 · chen2015aHPMCAS dissolved from the suspended particles in four media

On the log axis SDS lies more than two orders of magnitude above the surfactant-free and Triton X100 media, with STC between chen2015a R18, X7.

Why

At this "relatively low" drug loading release "appears to be" controlled by the polymer, so a surfactant that dissolves more HPMCAS also releases more drug ("It is likely") chen2015a C31. For SDS the polymer dissolves "most likely" through polymer–surfactant complexes (cited), none of which was detected here chen2015a C32. SDS combines this with promoted nucleation and gives the least stable suspension chen2015a C23, C29. For lopinavir the jump at pH 5 is related to slight ionization of HPMCAS, by a mechanism on which the authors "can only speculate" li2016b C24, C49.

Limits and transfer

Polymer was assayed in a few media only, and the surfactant-free medium had the lowest polymer level and the highest supersaturation from 1 h on, yet no crystals chen2015a X9, X5, X6. For an acidified suspension of an enteric-polymer dispersion, assay dissolved polymer and drug over the dosing window for each wetting agent, reject agents that dissolve the polymer, and keep the vehicle pH well below the onset of HPMCAS ionization when an ionic surfactant is present chen2015a P10, P11, C36; li2016b R13.

How it was shown

Chen and co-workers (2015) suspended 100 mg of the spray-dried dispersion in 10 mL of pH 3 HCl with or without one surfactant at 25 °C and 150 rpm, filtered the liquid through 0.45 µm nylon at each time point, assayed celecoxib by HPLC and divided it by the Form III solubility in that medium, and assayed HPMCAS by phenol–sulfuric acid colorimetry at 490 nm in the SDS, STC, Triton X100 and surfactant-free media chen2015a P10, P11, P12, E1. Crystals were checked by polarized light chen2015a P10. Li and co-workers (2016) suspended 100 mg of spray-dried lopinavir dispersions (33.3% drug in HPMCAS LF, MF, HF or HPMCP) in 10 mL of 50 mM citrate buffer at pH 3 or 5 at 25 °C and 300 rpm, with SDS, Poloxamer 188, polysorbate 80 or STC 10% above each CMC, or with 0.5% PVPVA, filtered samples (0.45 µm) up to 3 h and assayed lopinavir by HPLC and polymer by phenol–sulfuric acid colorimetry; Poloxamer 188, STC and PVPVA interfered with the polymer assay li2016b P1, P4, P7, P8.

What the data show

Supersaturation in the liquid. SDS ≈8.6 at about 5 min, ≈6.2 at 10 min, ≈4.3 at 0.5 h, ≈3.2 at 1 h, then ≈5.1 at 24 h; polysorbate 80 ≈3.35 at 0.5 h falling to ≈1.05 at 3 h; no surfactant ≈4.3 at 0.5 h rising to ≈6.7 at 48 h; STC ≈3.5 to ≈4.9; Poloxamer 188 ≈2.8, ≈4.2 at 4 h and ≈2.8 at 48 h; Triton X100 ≈1.6 to ≈1.8 chen2015a R17. Polymer in the liquid. SDS ≈35 µg/mL at about 0.1 h, ≈73 at 0.5 h, ≈420 at 4 h and ≈860 at 24 h; STC ≈5.5 at 0.5 h and ≈43 at 24 h; Triton X100 ≈2.9 to ≈6.0; no surfactant ≈1.5 to ≈3.5 chen2015a R18. In absolute terms the peak drug concentration was about 107–125 µg/mL in SDS, 28 in STC, 7.4 without surfactant and 6.7 µg/mL in Triton X100 (extractor arithmetic, maximum S times the solubility in each medium), which follows the polymer level except for Triton X100 against no surfactant chen2015a X9. Polysorbate 80 and Poloxamer 188 media were not assayed for polymer chen2015a X9. Lopinavir. The pure spray-dried polymers released about 15 (LF), 19 (MF), 68 (HF) and below 5 µg/mL (HPMCP) at pH 3, the dispersions below 5 µg/mL of each polymer li2016b R2, R3. With SDS at pH 3, HF from the HF dispersion rose to ≈19–24 µg/mL at 60–180 min and lopinavir to ≈13 µg/mL; polysorbate 80 left HF at ≈3–4 µg/mL but raised lopinavir to ≈14.5 µg/mL li2016b R8, R7. At pH 5 without surfactant neither lopinavir (≈7.4 µg/mL) nor HF changed, but with SDS HF rose to ≈74.5–134 µg/mL and lopinavir to ≈33–39 µg/mL; with the lower-pKa LF grade SDS gave ≈216–326 µg/mL polymer and ≈23–30 µg/mL lopinavir li2016b R13, R16, C27. PVPVA with SDS raised lopinavir to ≈50 µg/mL li2016b R17.

papersystemmethod and conditionsresultids
chen2015acelecoxib–HPMCAS 33.3%, pH 3, SDS 0.25%filtrate HPLC; colorimetry, 25 °CS ≈8.6 → ≈3.2 within 1 h; HPMCAS ≈860 µg/mL at 24 hR17, R18
chen2015asame, STC 0.75%; Triton X100 0.025%sameS ≈3.5 → ≈4.9 and ≈1.6 → ≈1.8; HPMCAS ≈43 and ≈6.0 µg/mLR17, R18
chen2015asame, no surfactantsameS ≈4.3 → ≈6.7 over 48 h; HPMCAS ≈3.5 µg/mLR17, R18
moseson2023 (ASD process)posaconazole–HPMCAS dispersions in acid, uncoated and coatedleached drug, 60 mina low amount of amorphous drug leaches in the gastric stage; a coating slows itC17, C20
kaur2025 (Release mechanism and LoC)HPMCASpH dependence of solubilityweak acid (pKa about 5), insoluble when un-ionizedC27
li2016blopinavir–HPMCAS-HF 33%, pH 3, SDS 0.055%; polysorbate 80filtrate HPLC; colorimetry, 25 °CHF ≈19–24 µg/mL, LPV ≈13; HF ≈3–4, LPV ≈14.5 µg/mLR8, R7
li2016bsame, pH 5, SDS; LPV–HPMCAS-LF, pH 5, SDSsameHF ≈74.5–134, LPV ≈33–39 µg/mL; LF ≈216–326, LPV ≈23–30 µg/mLR13, R16
li2016blopinavir–HPMCP 33%, pH 3, SDSsameHPMCP ≈9–14 µg/mL; LPV ≈4.4 against ≈4.8 without SDSR10, R9

Figure

Fig. 8 of chen2015a: HPMCAS dissolved from the suspended particles in four media
Fig. 8 · chen2015aHPMCAS dissolved from the suspended particles in four media

On the log axis SDS lies more than two orders of magnitude above the surfactant-free and Triton X100 media, with STC between chen2015a R18, X7.

Fig. 7 of chen2015a: celecoxib supersaturation in the suspension liquid over 48 h
Fig. 7 · chen2015acelecoxib supersaturation in the suspension liquid over 48 h

The SDS spike and fall within 1 h and the polysorbate 80 fall by 3 h match the crystals seen; the surfactant-free curve keeps rising without crystals chen2015a R17, R14.

Fig. 5 of li2016b: lopinavir and HPMCAS-HF leached at pH 3 and pH 5 with each surfactant
Fig. 5 · li2016blopinavir and HPMCAS-HF leached at pH 3 and pH 5 with each surfactant

With SDS at pH 5 both drug (a) and polymer (b) jump; STC rises a little, and the nonionic surfactants are unchanged by pH li2016b R13, R14, R15.

Why

The authors propose two factors behind a surfactant's effect on suspension stability: its effect on nucleation from the supersaturated liquid formed by leaching (F14), and its effect on drug leaching ("It is proposed"; "appear to play a critical role") chen2015a C19. At this "relatively low" drug loading release "appears to be" controlled by the polymer, so a surfactant that dissolves more HPMCAS also releases more drug ("It is likely") chen2015a C31. For SDS the polymer dissolves "most likely" through polymer–surfactant complexes, as reported for HPMC and SDS (cited); no complex was detected here chen2015a C32. SDS combines both effects and gives the least stable suspension; STC and Triton X100 inhibit nucleation and leach little chen2015a C23, C29. (synthesis: in acid, HPMCAS is meant to stay undissolved and hold the drug back; a surfactant that solubilizes the polymer removes that protection. It is the reverse of the incomplete release of HPMCAS dispersions at low pH found for posaconazole in the crystallization-from-solution chapter (Crystallization from solution F44).) For lopinavir, Li and co-workers relate the higher polymer leaching with SDS to surfactant–polymer complexation, which "can also enhance" polymer solubility, and the jump at pH 5 to slight ionization of HPMCAS; since polymer and SDS carry the same charge they "can only speculate" that ionized chains uncoil and expose less polar groups to SDS li2016b C44, C24, C49. With PVPVA in the vehicle, SDS "may" form a complex with a higher solubilizing capacity for lopinavir than either alone li2016b C31. Their main reading, however, is that lopinavir leaching follows how strongly the medium solubilizes the crystalline drug (F19) li2016b C39.

Conditions and limits

One drug, one polymer grade (LF), one drug loading, 25 °C, one level of each surfactant chen2015a A1. The HPMCAS calibration range is printed in mg/mL while the values reach down to about 1.5 µg/mL chen2015a X8. Replicates are not stated for the leaching data, and Fig. 7 has no error bars chen2015a X21. "More than 3 orders of magnitude" in the text corresponds to about 250-fold at 24 h and 50-fold at 0.5 h in the figure chen2015a X7. The lopinavir study ran 3 h at 25 °C with one loading; polymer values from the dispersions without surfactant lie below the detection limit or near the quantitation limit and differ between figures li2016b P4, X7, X6.

Counterexamples and conflicts

The surfactant-free medium had the lowest polymer level and the highest supersaturation from 1 h on, yet no crystals, so the two-factor account does not cover the control chen2015a X5, X6. With Poloxamer 188 the supersaturation fell slowly after 4 h without crystals by microscopy, which the authors suggest "could be" crystallization below detection chen2015a C15. The authors call the surfactant-free and STC supersaturation "relatively constant", whereas the figure shows both still rising at 48 h chen2015a X5. In the lopinavir suspensions polymer and drug did not always move together: polysorbate 80 raised lopinavir to ≈14.5 µg/mL without raising HPMCAS-HF, and SDS raised dissolved HPMCP to ≈9–14 µg/mL without raising lopinavir, which the authors explain by leached HPMCP lifting the SDS CMC above its level in the medium ("probably") li2016b R7, R8, R10, R9, C21.

Transfer check

For an acidified suspension of an enteric-polymer dispersion (for example a toxicology vehicle), assay dissolved polymer and drug in the vehicle over the dosing window for each candidate wetting agent, and check for crystals by polarized light at 0.5–6 h chen2015a P10, P11, P12. Reject wetting agents that dissolve the polymer; for celecoxib the authors propose STC and Triton X100 as alternatives chen2015a C36. A celecoxib suspension in plain pH 3 acid met the few-hour stability needed for dosing chen2015a C34. Keep the vehicle pH well below the onset of HPMCAS ionization when an ionic surfactant is present (pH 5 with SDS multiplied drug and polymer leaching), and test a suspending agent with the surfactant, since PVPVA with SDS raised dissolved lopinavir about sevenfold over the plain vehicle (synthesis: ≈50/7) li2016b R13, R17.

History

Polymer–surfactant complexes had been reported for HPMC with SDS and in release from solid dispersions (cited) chen2015a C32. Chen and co-workers (2015) were the first in the library to link surfactant, polymer leaching and crystallization of ASD suspensions chen2015a C38. Li and co-workers (2016) took up the question for lopinavir dispersions of three HPMCAS grades and HPMCP, adding pH and a suspending agent, and found SDS and polymer ionization raising polymer and drug leaching together li2016b C24, C29; the title was widened from one celecoxib system to enteric-polymer dispersions then.

F19

Topic 6Additives and surfactants at drug-rich droplets5 of 5

Drug leached from enteric dispersions in acid settled between its crystalline and amorphous solubility; surfactants raised lopinavir and its solubility alike.

At pH 3, 33% lopinavir dispersions leached about 7 µg/mL with HPMCAS and about 5 µg/mL with HPMCP, between the crystalline (≈1.5–2.7 µg/mL) and the amorphous solubility (≈16.6 µg/mL) li2016b R4, R5, R6. Surfactants raised the leached drug and the crystalline solubility together, so the ratio C/C_{\mathrm{eq}} stayed at ≈3.25–3.9 with HPMCAS-HF and ≈1.55–1.8 with HPMCP li2016b R19, R20.

moderateModerate: leaching and crystalline solubility were measured in matched media for ten lopinavir systems, but the constant ratio is shown at pH 3 only, without a statistical test, and three separation methods are combined li2016b K1, K2, X8.

lopinavir leachedno surfactant1.9≈7.3Poloxamer 1883.0≈10.0SDS3.3≈12.9polysorbate 804.5≈14.5STC7.2≈25.6110lopinavir–HPMCAS-HF suspensions, pH 3, µg/mL (log scale)

Dashed tick: crystalline solubility in the same medium; on the log axis the near-constant gap is the near-constant ratio C/Ceq. li2016b R19, R5, R20

lopinavir–HPMCAS-HFpH 3, five media3.25–3.9lopinavir–HPMCPpH 3, five media1.55–1.8celecoxib–HPMCAS-LFpH 3, five surfactants≈1.6–8.6delamanid dispersionspH 1.6≈0.9–3.8delamanid dispersionspH 5.0≈11–42110supersaturation ratio in acid, C/Ceq (log scale)

For lopinavir the polymer set the ratio whatever the surfactant; for celecoxib and delamanid it varied with surfactant or gastric pH. li2016b R20; chen2015a R17; nguyen2023c R13

For your drug

  1. For a suspension vehicle of an enteric-polymer dispersion, measure the crystalline solubility of the drug in the complete vehicle, the leached drug over the dosing window and the amorphous solubility in the same vehicle, and compute C/Ceq.
  2. A polymer that holds the ratio lower (HPMCP here) is the candidate for a fast-crystallizing drug, which must then be tested for crystallization at that ratio with the chosen surfactant.

li2016b P5, P4, E1, C38, C48

How it works and key numbers
  1. In a miscible dispersion drug and polymer lower each other's aqueous solubility (cited), so both leach less than from the pure components, which is "consistent with a miscible solid dispersion" li2016b C33, C34, C35.
  2. A surfactant solubilizes the crystalline drug in the medium, and leaching rose with it: the two "mirror each other very well" li2016b C39.
  3. The surfactants therefore changed the apparent solubility and the leaching "without affecting the supersaturation ratio", which the polymer set li2016b C40.
  4. HPMCAS-HF produced a higher supersaturation than HPMCP, so a lower crystallization risk with HPMCP "might be anticipated" li2016b C47, C48.
  5. For celecoxib the surfactants also acted on nucleation and on the amount of polymer dissolved (F14, F15), and the ratio varied with the surfactant chen2015a C19, C31, R17.
≈7 and ≈5 µg/mLlopinavir leached at pH 3 with HPMCAS grades and with HPMCPli2016b R4, R6
≈3.25–3.9 vs ≈1.55–1.8C/Ceq with HPMCAS-HF against HPMCP, with and without surfactantsli2016b R20
115.1 µg/mLposaconazole crystalline solubility in FaSSGF, above the ≈28–45.5 µg/mL its dispersions leachedelkhabaz2019a R1, R6, R7, R8
Evidence: data, conditions and papers

Finding F19. In acid, lopinavir and celecoxib leached from suspended enteric-polymer dispersions settled between the crystalline and the amorphous solubility, and surfactants raised it: for lopinavir in step with the crystalline solubility, so the supersaturation ratio stayed at about 3.3–3.9 with HPMCAS-HF and 1.6–1.8 with HPMCP, whereas for celecoxib it depended on the surfactant

In short. At pH 3 and 25 °C, 33% lopinavir dispersions leached about 7 µg/mL of drug with each HPMCAS grade and about 5 µg/mL with HPMCP within 1–3 h, above the crystalline solubility (≈1.5–2.7 µg/mL) and below the amorphous solubility (≈16.6 µg/mL), and less than 5 µg/mL of polymer li2016b R4, R5, R6, R3. Surfactants just above their CMC raised the leached lopinavir and its crystalline solubility in the same medium together (with HF: ≈7.3 → ≈10.0–25.6 µg/mL as the crystalline solubility rose from 1.9 to 3.0–7.2 µg/mL), so that C/Ceq stayed at ≈3.25–3.9 (HF) and ≈1.55–1.8 (HPMCP) li2016b R19, R20. For celecoxib–HPMCAS particles at pH 3 the supersaturation in the liquid ran from ≈1.6–1.8 with Triton X100 through ≈4.3–6.7 without surfactant to ≈8.6 at the SDS peak chen2015a R17. The authors conclude that lopinavir leaching "appears to be related to the extent of the solubilization" of the drug in the medium li2016b C39. Weak bases in gastric media did not always settle above the crystalline solubility: posaconazole–HPMCAS dispersions stayed below it in FaSSGF (≈28–45.5 against 115.1 µg/mL), and delamanid dispersions gave supersaturation ratios of ≈0.9–3.8 at pH 1.6 rising to ≈11–42 at pH 5.0 elkhabaz2019a R6, R7, R8, R1; nguyen2023c R13.

Type. observation in 2 drugs (lopinavir, celecoxib; HPMCAS grades and HPMCP, 33% drug) Strength. : leaching and crystalline solubility were measured in matched media for ten lopinavir systems and nine of ten ratios reproduce from the paper's inputs, but the constant ratio is shown at pH 3 only without a statistical test, three separation methods are combined, and the celecoxib values carry no error bars li2016b K1: moderate to strong, K2: moderate, X2, X5, X8; chen2015a X21.

How it was shown

Li and co-workers (2016) suspended 33.3% lopinavir dispersions with HPMCAS LF, MF, HF or HPMCP in pH 3 or 5 citrate buffer at 25 °C, with SDS, Poloxamer 188, polysorbate 80 or STC 10% above each CMC, and assayed 0.45-µm filtrates up to 3 h li2016b P1, P4. The crystalline solubility was measured in every medium with an excess of polymer, and the apparent supersaturation was S = C/C_{\mathrm{eq}} li2016b P5, E1. Chen and co-workers (2015) referred celecoxib leached from HPMCAS particles at pH 3 to the Form III solubility in each medium chen2015a P10, P11, E1.

What the data show

Lopinavir leached to between its crystalline and amorphous solubility, and the surfactants raised the leached drug and the crystalline solubility together li2016b R4, R6, R19, R20.

systemconditionsresultids
lopinavir 33% with HPMCAS LF / MF / HF; HPMCPsuspension, pH 3, 25 °C, 3 h≈7 µg/mL each; ≈5 µg/mL (crystalline 1.5–2.7, amorphous ≈16.6)li2016b R4, R5, R6
LPV–HF with four surfactantsleaching against Ceq in the same medium≈10.0–25.6 against 3.0–7.2 µg/mL; C/Ceq ≈3.25–3.9li2016b R19, R20
LPV–HPMCP with four surfactantssame≈4.4–10.1 against 2.7–6.0 µg/mL; C/Ceq ≈1.55–1.8li2016b R19, R20
celecoxib–HPMCAS-LF 33.3% with five surfactantssuspension, pH 3, 25 °C, 48 hS from ≈1.6 (Triton X100) to ≈8.6 (SDS peak)chen2015a R17
posaconazole–HPMCAS 10 / 25 / 50% in FaSSGFHPLC of supernatants, 60 min≈28 / ≈40 / ≈45.5 against a crystalline solubility of 115.1 µg/mLelkhabaz2019a R6, R7, R8, R1
delamanid dispersions, 1 h at pH 1.6 / 3.0 / 5.0maximum over crystalline solubility at that pH≈0.9–3.8 / ≈3.3–11.4 / ≈11–42nguyen2023c R13
Fig. 9 of li2016b: apparent supersaturation ratio for HPMCAS-HF and HPMCP lopinavir suspensions with each surfactant
Fig. 9 · li2016bapparent supersaturation ratio for HPMCAS-HF and HPMCP lopinavir suspensions with each surfactant

About 3.3–3.9 for every HF system and 1.6–1.8 for every HPMCP system li2016b R20, C40.

Why

Li and co-workers rationalize the surfactant effects by solubilization of the crystalline drug: leaching and crystalline solubility "mirror each other very well", and the surfactants changed both "without affecting the supersaturation ratio" li2016b C39, C40. In a miscible dispersion drug and polymer hold each other back, the lower leaching of both being "consistent with a miscible solid dispersion" li2016b C34, C35. HPMCAS-HF therefore produced a higher supersaturation than HPMCP, and a lower crystallization risk with HPMCP "might be anticipated" li2016b C47, C48.

Limits and transfer

The amorphous solubility was measured only in plain pH 3 buffer, three separation methods are combined, and at pH 5 or with PVPVA the ratios move to about 2.7–5.5 li2016b X15, X8, X5. For a suspension vehicle of an enteric-polymer dispersion, measure the crystalline solubility in the complete vehicle, the leached drug over the dosing window and the amorphous solubility in the same vehicle, and compute C/Ceq li2016b P5, P4, E1.

How it was shown

Li and co-workers (2016) spray-dried lopinavir with HPMCAS LF, MF, HF or HPMCP at 33.3% drug, suspended 100 mg in 10 mL of 50 mM citrate buffer (pH 3 or 5) at 25 °C and 300 rpm with SDS, Poloxamer 188, polysorbate 80 or STC at 10% above each CMC, and assayed 0.45-µm filtrates up to 3 h, taking the 60–180 min average as the plateau li2016b P1, P4. The CMCs were read from the break in crystalline lopinavir solubility against surfactant concentration, with and without polymer li2016b P3, R1. Crystalline solubility was measured in every medium with an excess of polymer after ultracentrifugation, and the amorphous solubility from an amorphous film in plain pH 3 buffer li2016b P5, P6. The ratio was

S = \frac{C}{C_{\mathrm{eq}}} li2016b E1

with C the leached concentration and Ceq the crystalline solubility in a medium of the same composition, called apparent because a concentration ratio may not represent the driving force in micellar media (cited) li2016b C7. Chen and co-workers (2015) suspended 100 mg of 33.3% celecoxib–HPMCAS-LF particles in 10 mL of pH 3 HCl at 25 °C with five surfactants and referred the drug in the 0.45-µm filtrate to the Form III solubility in each medium chen2015a P10, P11, E1.

What the data show

Lopinavir without surfactant. Leaching rose within 15 min and levelled over 1–3 h at about 7 µg/mL for LF, MF and HF ("not statistically different") and about 5 µg/mL for HPMCP; crystalline solubility was 2.5 µg/mL in buffer, 1.9 with HF, 2.7 with HPMCP and about 1.7 and 1.5 with LF and MF; the amorphous solubility ≈16.6 µg/mL; no crystals appeared in 3 h li2016b R4, R5, R19, R6, R21. The pure polymers leached about 15, 19, 68 and below 5 µg/mL, the dispersions below 5 µg/mL of each li2016b R2, R3. With surfactants. For HF, plateaus of ≈10.0 (Poloxamer 188), ≈12.9 (SDS), ≈14.5 (polysorbate 80) and ≈25.6 µg/mL (STC) against crystalline solubilities of 3.0, 3.3, 4.5 and 7.2 µg/mL; for HPMCP ≈4.9, ≈4.4, ≈7.45 and ≈10.1 µg/mL against 3.1, 2.7, 3.2 and 6.0 µg/mL li2016b R19, R5. The ratios were ≈3.9, 3.9, 3.35, 3.25 and 3.55 (HF, without and with each surfactant) and ≈1.8, 1.6, 1.55, 1.55 and 1.7 (HPMCP); the HPMCP–polysorbate 80 bar recomputes to ≈2.3 li2016b R20, X2. HPMCP moved the SDS break from about 0.05% to about 0.1%, so SDS was "probably" below its CMC in that medium, and both polymers flattened the Poloxamer 188 curve in the titrations, which conflict with the table values for the same media li2016b R11, R12, C21, X3. At pH 5 and with PVPVA the ratios recompute to about 2.7–5.5 li2016b X5. Celecoxib. Supersaturation (against Form III in each medium) was ≈8.6 at about 5 min with SDS, falling to ≈3.2 by 1 h as crystals formed; ≈3.35 at 0.5 h falling to ≈1.05 at 3 h with polysorbate 80; ≈4.3 rising to ≈6.7 over 48 h without surfactant; ≈3.5 to ≈4.9 with STC; ≈1.6 to ≈1.8 with Triton X100 chen2015a R17. The CMC of SDS read with the drug at saturation was 0.050% in the lopinavir medium and 0.23% in the celecoxib medium li2016b R1; chen2015a R4.

papersystemmethod and conditionsresultids
li2016blopinavir 33% with HPMCAS LF / MF / HF; HPMCPsuspension, pH 3, 25 °C, 3 h≈7 µg/mL each; ≈5 µg/mL (crystalline 1.5–2.7, amorphous ≈16.6)R4, R5, R6
li2016bsame, polymer leachedcolorimetrybelow 5 µg/mL against 15–68 µg/mL from the pure polymersR3, R2
li2016bLPV–HF with four surfactantsleaching against Ceq in the same medium≈10.0–25.6 against 3.0–7.2 µg/mL; C/Ceq ≈3.25–3.9R19, R20
li2016bLPV–HPMCP with four surfactantssame≈4.4–10.1 against 2.7–6.0 µg/mL; C/Ceq ≈1.55–1.8R19, R20
chen2015acelecoxib–HPMCAS-LF 33.3% with five surfactantssuspension, pH 3, 25 °C, 48 hS from ≈1.6 (Triton X100) to ≈8.6 (SDS peak)R17
ilevbare2013a (Amorphous solubility and LLPS)ritonavir with 500 µg/mL Tween 80crystalline solubility and LLPS concentrationboth raised about 2.6–2.7-fold; ratio ≈14.5 and ≈13.2R16
moseson2023 (ASD process)posaconazole–HPMCAS dispersions in acidleached druga low amount leaches in the gastric stage; more at 50% than 25% drugC17, C27
elkhabaz2019aposaconazole–HPMCAS 10 / 25 / 50% in FaSSGF, 37 °CHPLC of supernatants, 60 min≈28 / ≈40 / ≈45.5 µg/mL against a crystalline solubility of 115.1 µg/mLR6, R7, R8, R1
nguyen2023cdelamanid salt and free-base dispersions, 1 h at pH 1.6 / 3.0 / 5.0maximum concentration over crystalline solubility at that pH≈0.9–3.8 / ≈3.3–11.4 / ≈11–42R13
nguyen2023buncoated delamanid–HPMCP-50 tablets, HCl pH 1.6gastric stage, 60 min≈30–41 µg/mL against ≈10.3 µg/mL crystalline solubilityR2, R13

Figure

Fig. 9 of li2016b: apparent supersaturation ratio for HPMCAS-HF and HPMCP lopinavir suspensions with each surfactant
Fig. 9 · li2016bapparent supersaturation ratio for HPMCAS-HF and HPMCP lopinavir suspensions with each surfactant

About 3.3–3.9 for every HF system and 1.6–1.8 for every HPMCP system: the surfactant changes how much drug leaches, the polymer how supersaturated it is li2016b R20, C40.

Fig. 8 of li2016b: leached lopinavir against its crystalline solubility in the same medium
Fig. 8 · li2016bleached lopinavir against its crystalline solubility in the same medium

Blue (leaching) and red (crystalline solubility) bars rise together across the surfactants; the first blue bar of panel (a) is the amorphous solubility li2016b R19, R6.

Why

Li and co-workers rationalize the surfactant effects by solubilization of the crystalline drug: leaching and crystalline solubility "mirror each other very well", and the surfactants changed the apparent solubility and leaching "without affecting the supersaturation ratio", assuming the concentration ratio is a reasonable approximation li2016b C39, C40. They draw on the rule that components of a mixture lower each other's aqueous solubility (cited): in a miscible dispersion drug and polymer hold each other back, the lower leaching of both being "consistent with a miscible solid dispersion", with interactions "would be expected" to be similar across HPMCAS grades and "might suggest" more favourable ones with HPMCP li2016b C33, C34, C35, C36, C37. HPMCAS-HF therefore produced a higher supersaturation than HPMCP, and a lower crystallization risk with HPMCP "might be anticipated" li2016b C47, C48. For celecoxib, Chen and co-workers ascribe the surfactant effects to two factors, nucleation from the leached solution and the amount of polymer, and so drug, that the surfactant dissolves (F14, F15) chen2015a C19, C31. (synthesis: the constant lopinavir ratio is the leaching counterpart of the LLPS-chapter result that a micellar solubilizer raises the crystalline solubility and the LLPS concentration together, leaving their ratio near 14 for ritonavir (Amorphous solubility and LLPS F12); the celecoxib suspensions depart from it where a surfactant also dissolved much of the polymer (SDS, about 250-fold) or changed nucleation (polysorbate 80); the level below the amorphous solubility fits a drug held back by an undissolved polymer (F18).)

Conditions and limits

Lopinavir, a slow crystallizer chosen so that leaching could be measured without crystals, at pH 3 (and 5), 25 °C, 3 h, one loading li2016b C5, P4. The amorphous solubility was measured only in plain pH 3 buffer, so leaching with STC, SDS at pH 5 or PVPVA with SDS cannot be set against it li2016b X15. Leached drug (0.45-µm filtration), crystalline solubility (ultracentrifugation) and amorphous solubility (centrifugation, conditions not stated) come from three separation methods li2016b X8. The two papers used different acid media (citrate at pH 3 against HCl at pH 3), which may explain part of the difference in SDS CMC (synthesis) li2016b M11; chen2015a P10.

Counterexamples and conflicts

At pH 5 and with PVPVA the lopinavir ratios move to about 2.7–5.5, so the constancy holds for the pH 3 surfactant series li2016b X5. The celecoxib ratio varied about fivefold between surfactants (synthesis: 8.6/1.6) chen2015a R17. The concentration-based ratio understates the activity-based one in micellar media for atazanavir in the LLPS chapter (Amorphous solubility and LLPS F16), which is why the lopinavir ratio is called apparent li2016b C7.

Transfer check

For a suspension vehicle of an enteric-polymer dispersion, measure the crystalline solubility of the drug in the complete vehicle (surfactant, suspending agent, excess polymer), the leached drug over the dosing window, and the amorphous solubility in the same vehicle; compute C/Ceq li2016b P5, P4, E1. A polymer that holds the ratio lower (HPMCP here) is the candidate for a fast-crystallizing drug, which must then be tested for crystallization at that ratio with the chosen surfactant (F14) li2016b C38, C48.

History

Chen and co-workers (2015) first measured leaching and crystallization of an acidified HPMCAS dispersion suspension with surfactants chen2015a C38. Li and co-workers (2016) took over the spray-drying and CMC methods, added HPMCAS grades, HPMCP, pH and a suspending agent, and defined the apparent supersaturation as C/Ceq after a Bioperformance paper (builds_on) li2016b C3, C7. Li and Taylor (2018) then measured how far the undissolved polymer itself lowers the ceiling (F18) li2018 C4. In gastric media, Elkhabaz and co-workers (2019) found posaconazole leaching below its crystalline solubility, and Nguyen and co-workers (2023) delamanid ratios from below 1 up to the amorphous limit depending on the gastric pH (F24, F25) elkhabaz2019a C33; nguyen2023c C35; the title was narrowed to lopinavir and celecoxib then.

Topic 7 of 8 · 2 findings · F20–F21

Polymer combinations and pH-shift release

F20

Topic 7Polymer combinations and pH-shift release1 of 2

A minor cellulosic inhibitor added to a fast-releasing polymer kept released celecoxib and indomethacin supersaturated, at some cost in release rate.

A 50% celecoxib–PVP-K12 dispersion peaked at ≈21.0 µg/mL and fell to ≈6.5 µg/mL by 16 h, while ternaries in which a fifth of the PVP was replaced by HPMCAS or HPMC held ≈16.7–21.9 µg/mL but released more slowly at first xie2015 R6. An indomethacin dispersion with EPO and HPMC released fast at pH 2.2 into nanodroplets without crystallizing in the acid stage, while the EPO dispersion crystallized xie2017 R10, R15, R11.

moderateModerate to strong for the protection, which is large and seen in triplicate time courses; weak to moderate for the miscibility explanation, which rests on IR of spin-coated films xie2015 K4; xie2016a K4, K6, X13; xie2017 K3.

at 2 hat 16 hPVP-K12 5:56.516.1K12 / HPMCAS 5:4:110.121.8K29/32 / HPMCAS 5:4:111.321.9K12 / HPMC 5:4:16.716.7K29/32 / HPMC 5:4:112.420.8PVP-K12 5:5, HPMCAS in medium5 µg/mL predissolved13.622.50510152025celecoxib from 50% drug dispersions, µg/mL

Dose 22 µg/mL in pH 6.8 buffer at 37 °C; only the PVP-K12 binary fell, and the inhibitor in the medium cost less release rate. xie2015 R6

For your drug

  1. Choose a carrier that dissolves fast at the pH of interest and does not let the matrix crystallize at the target loading (slurry test), and add 10–20% of an inhibitor that holds the drug in a 5 µg/mL induction-time test.
  2. Check that the two polymers mix (IR band shifts, one Tg) and test release at the target loading and on storage, since the benefit fell between 30% and 50% drug.

xie2016a C33, C69, C68; xie2015 C53; xie2016b C29

How it works and key numbers
  1. The fast polymer releases the drug quickly: PVP is hydrophilic, PAA is fully ionized at pH 6.8 ("can presumably be attributed") and EPO is ionized at pH 2.2 xie2016a C24; xie2017 C29.
  2. HPMCAS or HPMC at about 5 µg/mL blocks nucleation in solution xie2015 C53, C42.
  3. The cellulose polymers "dissolve sufficiently rapidly" from the ternary to act in solution, according to the authors; their release was not measured xie2015 C50.
  4. In the immiscible PAA–HPMCAS ternaries celecoxib "can be envisaged" in PAA-rich and HPMCAS-rich domains, so part of the drug lacks the inhibitor and the matrix is less protected xie2016a C61, C62.
≈6.5 vs ≈16.7–21.9 µg/mLcelecoxib at 16 h from the PVP-K12 binary against the four 5:4:1 ternariesxie2015 R6
≈16.1 vs ≈6.7–12.4 µg/mLthe same at 2 h: the cost in release ratexie2015 R6
more than 100 days vs 5 days60% drug indomethacin ternary against the binaries, amorphous at 40 °C/75% RHxie2017 R26
Evidence: data, conditions and papers

Finding F20. Pairing a fast-releasing polymer with a minor cellulosic crystallization inhibitor kept released celecoxib and indomethacin supersaturated where the fast polymer alone let them crystallize, at some cost in release rate; at 50% drug the gain was partial and larger when the inhibitor mixed with the carrier polymer

In short. At 50% celecoxib, replacing a fifth of the PVP by HPMCAS or HPMC (5:4:1) removed the desupersaturation of the PVP-K12 dispersion over 16 h (≈16.7–21.9 against ≈6.5 µg/mL at 16 h) but slowed release (≈6.7–12.4 against ≈16.1 µg/mL at 2 h); 5 µg/mL of either inhibitor dissolved in the medium gave the same protection with less loss of rate (≈13.5–13.6 µg/mL at 2 h) xie2015 R6. PAA with 10% HPMCAS or HPMC released celecoxib completely within about 2 h and held it for 16 h at 30% drug, whereas at 50% drug the HPMC ternary released about 85% quickly and the HPMCAS ternaries levelled at ≈16 µg/mL or crept to ≈19 µg/mL by 16 h; IR read PAA and HPMCAS as immiscible and PAA and HPMC as partly miscible xie2016a R14, R17, R20, R21. An indomethacin dispersion with EPO and HPMC (3:5:2) released fast at pH 2.2 into nanodroplets without crystallizing in the 1 h acid stage, while the EPO dispersion crystallized within about 20 min and the HPMC dispersion released slowly xie2017 R10, R11, R15. The authors call combining two polymers "a viable formulation strategy, although attention needs to be paid to the miscibility of the ternary systems" xie2016a C69.

Type. observation in 2 drugs (celecoxib with PVP or PAA; indomethacin with EPO; HPMCAS or HPMC as inhibitor) Strength. to strong for the protection, which is large and seen in triplicate time courses xie2015 K4: moderate to strong; xie2016a K4: strong, K5: moderate; xie2017 K3: moderate to strong; weak to moderate for the miscibility explanation, which rests on IR of spin-coated films rather than on the dissolving dispersions xie2016a K6: weak to moderate, X13; release of the inhibitor from the ternaries was not measured xie2015 C50.

How it was shown

Xie and Taylor (2015) dissolved 50% celecoxib dispersions with PVP and ternaries in which a fifth of the PVP was replaced by HPMCAS or HPMC (5:4:1) in pH 6.8 buffer at 37 °C for 16 h, also into buffer holding 5 µg/mL of the inhibitor xie2015 P1, P5, A5. Xie and Taylor (2016) made PAA ternaries at 10–50% drug and recorded IR of polymer blend films, and Xie and co-workers (2017) tested an indomethacin–EPO–HPMC dispersion at pH 2.2 xie2016a P5, P10; xie2017 P7.

What the data show

The minor cellulosic polymer removed the crash of the fast carrier at some cost in early release; at 50% drug with PAA the gain was partial xie2015 R6; xie2016a R17, R14.

systemconditionsresultids
celecoxib PVP-K12 5:5 against four 5:4:1 ternaries22 µg/mL nominal, pH 6.8, 37 °C, 16 h≈6.5 against ≈16.7–21.9 µg/mL at 16 h; ≈16.1 against ≈6.7–12.4 at 2 hxie2015 R6
PVP-K12 5:5, 5 µg/mL HPMCAS or HPMC in the mediumsame≈13.5–13.6 at 2 h; ≈21.0–22.5 µg/mL at 16 hxie2015 R6
celecoxib–PAA with HPMCAS or HPMC, 3:6:1same≈21.0 and ≈20.4 µg/mL at 2 h, held 16 hxie2016a R14, R17
same at 50% drug: 5:4:1 HPMC; 5:4:1, 5:3:2, 5:2:3 HPMCASsame≈19.1 µg/mL maximum; ≈15.9, ≈18.8, ≈19.4 µg/mL at 16 hxie2016a R17, R14
PAA–HPMCAS; PAA–HPMC filmstransmission IR, carbonyl regionadditive bands; new ≈1735 cm−1 shoulderxie2016a R20, R21
indomethacin EPO–HPMC 3:5:2 against EPO 3:7pH 2.2, 1 h, 37 °C≈93.5 apparent with nanodroplets against 8.8 µg/mL (HPLC)xie2017 R10, R15, R11
Fig. 6 of xie2015: release from 5:4:1 ternary celecoxib dispersions against the PVP binaries
Fig. 6 · xie2015release from 5:4:1 ternary celecoxib dispersions against the PVP binaries

The four ternaries rise more slowly than the PVP binaries but do not fall, while the PVP-K12 binary drops to about 6.5 µg/mL xie2015 R6.

Why

The fast polymer releases the drug quickly, PVP being hydrophilic and PAA fully ionized at pH 6.8, while HPMCAS or HPMC at about 5 µg/mL blocks nucleation in solution xie2016a C24; xie2015 C53, C42. Xie and Taylor (2015) conclude that the cellulose polymers "dissolve sufficiently rapidly" from the ternary to act in solution, which was not measured xie2015 C50. In the immiscible PAA–HPMCAS ternaries celecoxib "can be envisaged" in PAA-rich and HPMCAS-rich domains, so that part of the drug lacked the inhibitor xie2016a C61, C62.

Limits and transfer

The celecoxib dose equalled the amorphous solubility, so the tests ask whether a dispersion reaches the ceiling, not whether it stays above it, and polymer–polymer mixing was not characterized in the dispersions themselves xie2016a X11, X13. Choose a fast carrier whose matrix does not crystallize at the target loading, add 10–20% of an inhibitor that works in a 5 µg/mL induction-time test, check that the two polymers mix, and test release at the target loading xie2016a C33, C69, C68; xie2015 C53.

How it was shown

Xie and Taylor (2015) made celecoxib dispersions at 50% drug with PVP-K12, PVP-K29/32, HPMCAS or HPMC (5:5) and ternaries in which a fifth of the PVP was replaced by HPMCAS or HPMC (5:4:1), dissolved 17.6 mg in 400 mL of pH 6.8 buffer at 37 °C (22 µg/mL if all dissolved) for 16 h in triplicate, also into buffer holding 5 µg/mL HPMCAS or HPMC, and ran induction-time tests with PVP plus HPMCAS xie2015 P1, P5, A5, P4. Xie and Taylor (2016) made PAA ternaries with HPMCAS (5:2:3 to 1:8:1) or HPMC (2:1:1, 5:4:1, 3:6:1) at 10–50% drug, dissolved them in the same test, watched wetted particles under polarized light, and recorded the carbonyl region of spin-coated polymer blend films by IR xie2016a P5, P8, P10. Xie and co-workers (2017) dissolved indomethacin dispersions with EPO (3:7), HPMC and EPO plus HPMC (3:5:2) for 1 h at pH 2.2 and then at pH 5, and stored 60% drug dispersions at 40 °C/75% RH with PXRD up to 100 days xie2017 P7, P16.

What the data show

Celecoxib with PVP. At 2 h the PVP-K12 binary held ≈16.1 µg/mL and at 16 h ≈6.5 µg/mL after peaking at ≈21.0 µg/mL; the 5:4:1 ternaries held ≈10.1 (K12/HPMCAS), ≈11.3 (K29/32/HPMCAS), ≈6.7 (K12/HPMC) and ≈12.4 µg/mL (K29/32/HPMC) at 2 h and ≈21.8, ≈21.9, ≈16.7 and ≈20.8 µg/mL at 16 h without any fall xie2015 R6. In buffer with 5 µg/mL HPMCAS or HPMC the PVP-K12 binary held ≈13.6 and ≈13.5 µg/mL at 2 h and ≈22.5 and ≈21.0 µg/mL at 16 h xie2015 R6. In solution PVP did not impair HPMCAS (≈20.2–20.9 µg/mL at 8 h) xie2015 R2. Celecoxib with PAA. The 3:6:1 HPMCAS ternary reached ≈17 µg/mL within ≈5 min and ≈21 µg/mL by 2 h, the 1:8:1 one ≈21 µg/mL by 2 h, both ≈21.2–21.4 µg/mL at 16 h; the 3:6:1 HPMC ternary ≈20.4 µg/mL at 2 h and ≈20.2 at 16 h, against ≈10.0 µg/mL at 2 h for the HPMC binary xie2016a R14, R17. At 50% drug the 5:4:1 HPMC ternary reached ≈15.8 µg/mL at 1 h and ≈19.1 µg/mL near 5 h (about 85%); the 5:4:1 HPMCAS ternary levelled at ≈15.9 µg/mL, and the 5:3:2 and 5:2:3 ones burst only to ≈5.7 and ≈2.5 µg/mL and reached ≈18.8 and ≈19.4 µg/mL at 16 h, still rising xie2016a R17, R14. Wetted 3:6:1 HPMCAS particles collapsed into fine particles, a 2:1:1 HPMCAS ternary shed particles that dissolved slowly, and the 3:6:1 HPMC particles stayed whole and eroded from their edges xie2016a R15, R16, R18. PAA–HPMCAS films showed the two carbonyl bands (≈1710 and ≈1743 cm−1) simply added; in PAA–HPMC films a ≈1735 cm−1 shoulder grew as HPMC increased, and celecoxib changed neither pattern xie2016a R20, R21. Indomethacin with EPO. At pH 2.2 the ternary read ≈80–93.5 µg/mL from 10 to 60 min with ≈75 nm nanodroplets, the EPO binary peaked near ≈77 µg/mL and fell to 8.8 µg/mL (HPLC) by 1 h, and the HPMC 3:7 binary reached ≈24.5 µg/mL xie2017 R10, R15, R11. After the shift to pH 5 the ternary gave 39.1 of 40 µg/mL (F21) xie2017 R20. At 60% drug both binaries showed crystalline peaks within 5 days at 40 °C/75% RH, while the ternary (6:2.9:1.1) stayed amorphous beyond 100 days xie2017 R26.

papersystemmethod and conditionsresultids
xie2015celecoxib PVP-K12 5:5 against four 5:4:1 ternariesdissolution, 22 µg/mL nominal, pH 6.8, 37 °C, 16 h≈6.5 against ≈16.7–21.9 µg/mL at 16 h; ≈16.1 against ≈6.7–12.4 at 2 hR6
xie2015PVP-K12 5:5 with 5 µg/mL HPMCAS or HPMC in the mediumsame≈13.5–13.6 at 2 h; ≈21.0–22.5 µg/mL at 16 hR6
xie2016acelecoxib–PAA with HPMCAS or HPMC, 3:6:1same≈21.0 and ≈20.4 µg/mL at 2 h, held 16 hR14, R17
xie2016asame at 50% drug, 5:4:1 HPMC; 5:4:1, 5:3:2, 5:2:3 HPMCASsame≈19.1 µg/mL max; ≈15.9, ≈18.8, ≈19.4 µg/mL at 16 hR17, R14
xie2016aPAA–HPMCAS; PAA–HPMC filmstransmission IR, carbonyl regionadditive bands; new ≈1735 cm−1 shoulderR20, R21
xie2017indomethacin EPO–HPMC 3:5:2 against EPO 3:7 and HPMC 3:7pH 2.2, 1 h, 37 °C≈93.5 apparent with nanodroplets; 8.8 (HPLC); ≈24.5 µg/mLR10, R15, R11
xie201760% drug ternary against binaries40 °C/75% RH, PXRDamorphous >100 days against crystals within 5 daysR26
xie2016b (Physical stability)celecoxib PVP-major ternaries with HPMCAS or HPMCstorage, PXRDstability similar to the PVP binary; PVP and HPMCAS miscibleC3, C29
hiew2025 (Release mechanism and LoC)HPMC with HPMCASmixing in THF and acidHPMC has some affinity for the precipitated HPMCAS phaseC16

Figure

Fig. 6 of xie2015: release from 5:4:1 ternary celecoxib dispersions against the PVP binaries
Fig. 6 · xie2015release from 5:4:1 ternary celecoxib dispersions against the PVP binaries

The four ternaries rise more slowly than the PVP binaries but do not fall; the PVP-K12 binary drops to about 6.5 µg/mL xie2015 R6.

Fig. 13 of xie2016a: release from HPMC binaries and PAA–HPMC ternaries
Fig. 13 · xie2016arelease from HPMC binaries and PAA–HPMC ternaries

The 3:6:1 ternary is complete by 2 h, the 5:4:1 one rises fast to about 19 µg/mL, the binaries stay slow xie2016a R17.

Why

The fast polymer releases the drug quickly, PVP being hydrophilic, PAA fully ionized at pH 6.8 ("can presumably be attributed") and EPO ionized at pH 2.2, while HPMCAS or HPMC at about 5 µg/mL blocks nucleation in solution xie2016a C24; xie2017 C29; xie2015 C53, C42. Xie and Taylor (2015) conclude that the cellulose polymers "dissolve sufficiently rapidly" from the ternary to act in solution, which was not measured, and find the slower release "somewhat surprisingly" and "clearly may not be desirable"; since the inhibitor worked from the medium, it "could be potentially" added as a separate component, tested only predissolved xie2015 C50, C56, C57, C58, X15. Xie and Taylor (2016) hold that the inhibitor must stay in close contact with the drug during hydration and be released with it; slow erosion of the HPMC ternary "appears to be beneficial", whereas in the immiscible PAA–HPMCAS ternaries celecoxib "can be envisaged" in PAA-rich and HPMCAS-rich domains, which would explain the two-phase release and the poorer matrix protection xie2016a C54, C53, C61, C62. Polymers mix only with specific interactions, and PAA's acid dimers appear not to be broken by HPMCAS but disrupted by HPMC ("may disrupt") xie2016a C58, C63. For indomethacin the ternary benefits from fast release by EPO and lasting concentration by HPMC, with EPO's solubilization raising the LLPS onset ("could be attributed to") xie2017 C34, C56; its better storage stability was "unexpected" and not explored xie2017 C51, C52. (synthesis: the inhibitor in the medium replaced the inhibitor in the particle for PVP-K12, whose matrix did not crystallize in dissolution, but not for PAA, whose matrix did (F16); a separate inhibitor can stand in only where the carrier itself protects the matrix.)

Conditions and limits

Celecoxib at a dose equal to its amorphous solubility, pH 6.8, 37 °C, 16 h, so the tests ask whether the dispersion reaches the ceiling, not whether it stays above it xie2016a X11; indomethacin at pH 2.2 then pH 5 xie2017 P7. Polymer–polymer mixing was not characterized in the dispersions themselves, and the 2:1:1 HPMCAS ternary used for IR and microscopy was not dissolution-tested xie2016a X13; molecular mixing of the 50% celecoxib dispersions was not checked xie2015 X6. The storage ternary (6:2.9:1.1) differs in ratio from the dissolution ternary (3:5:2) xie2017 X5.

Counterexamples and conflicts

The abstract's "improved drug release" of the PVP ternaries holds only against the cellulosic binaries or at late times; against PVP-K12 the ternaries released more slowly xie2015 X5. At 50% drug no PAA–HPMCAS ternary gave both rapid and complete release xie2016a C46. A storage study of the PVP-major celecoxib ternaries found stability similar to the PVP binary, not better xie2016b C3.

Transfer check

Choose a carrier that dissolves fast at the pH of interest and does not let the matrix crystallize at the target loading (slurry test, F16) xie2016a C33; add 10–20% of an inhibitor that holds the drug at its amorphous solubility in a 5 µg/mL induction-time test xie2015 C53; check that the two polymers mix (IR band shifts, one Tg) xie2016a C69; xie2016b C29; test release at the target loading and storage, since the benefit fell between 30% and 50% drug xie2016a C68.

History

Pairwise polymer blends had been proposed for dispersions and polymer pairs for crystal growth (cited; Crystallization from solution F17) xie2015 C29, C30. Xie and Taylor (2015) were the first in the library to combine a release polymer with a minor solution inhibitor in a dispersion xie2015 C6; Xie and Taylor (2016) extended it to PAA and to the miscibility of the pair xie2016a C69; Xie and co-workers (2017) to indomethacin with EPO and to storage xie2017 C34, C51. A Physical stability paper tested the storage of the PVP-major celecoxib ternaries xie2016b C43, and an enzalutamide study cites the 2016 work for the trade-off between soluble and inhibiting polymers wilson2020 C6.

F21

Topic 7Polymer combinations and pH-shift release2 of 2

After a gastric-to-intestinal pH rise, indomethacin droplets redissolved within minutes, while crystals formed in acid recovered only partly.

In a two-stage test (1 h at pH 2.2, then pH 5), the nanodroplets of an EPO–HPMC dispersion dissolved within about 2 min of the shift, and the dispersion reached 39.1 of 40 µg/mL xie2017 R20. Small α crystals that had precipitated from an EPO dispersion in acid redissolved faster than sieved α crystals but stopped at 32.1 µg/mL xie2017 R19, R17. At pH 6.8 all three 30% dispersions reached 40 µg/mL within 10 min xie2017 R22.

moderateModerate: the end points are HPLC values and the polymorph rests on three methods, but acid-stage UV values are apparent and there is no size-matched crystal control xie2017 K4, K5, X7, X10.

Indomethacin after the shift to pH 5, µg/mL of 40EPO–HPMC dispersionnanodroplets in acid39.1EPO dispersionα crystals under 10 µm in acid32.1sieved α with EPO24.6sieved α106–250 µm17sieved γ≈8

Two-stage test at 37 °C, 4 mg drug; dispersions at 3 h, crystals at 8 h, by HPLC. xie2017 R20, R19, R17, R10, R25, M2

For your drug

  1. For an ionizable drug, run the two-stage test with a final pH at which the dispersions are not all fully soluble (pH 5 here) as well as at pH 6.8.
  2. Identify any precipitate from the acid stage (SHG or Raman in suspension, PXRD, SEM size), compare its redissolution with reference crystals of the same form and similar size, and confirm turbid-stage concentrations by HPLC.

xie2017 C67, C70, X10, R11

How it works and key numbers
  1. At pH 2.2 the EPO dispersion fell from ≈77 to 8.8 µg/mL (HPLC) as small α crystals precipitated, while the ternary held nanospecies of ≈75 nm xie2017 R11, R23, R15.
  2. The pH rise raises the amorphous solubility of the ionized drug (cited), so the droplets dissolved, "consistent with" a reservoir that becomes available after dilution to a higher pH xie2017 C40, C42.
  3. Solubilization by EPO raises the dissolution rate of crystals, but "this effect alone cannot explain" the faster dissolution of the precipitate, which the authors attribute "likely" to the very small crystal size xie2017 C47, C48.
  4. At pH 6.8 every dispersion dissolved quickly, so that pH hid the differences that pH 5 showed, and an intermediate pH "may be informative" xie2017 R22, C66, C67.
≈2 minfor the nanodroplets of the ternary to dissolve after the shift to pH 5xie2017 R20
32.1 vs 17 µg/mLin situ α precipitate against sieved α crystals at pH 5 (of 40)xie2017 R19, R17
under 10 µm vs 106–250 µmsize of the precipitated α crystals against the sieved referencexie2017 R25, M2
Evidence: data, conditions and papers

Finding F21. After a gastric-to-intestinal pH rise, what had separated in acid decided the recovery of indomethacin: nanodroplets redissolved within minutes, small α crystals formed in situ redissolved faster than sieved crystals but only to 32.1 of 40 µg/mL, and a shift to pH 6.8 hid differences that a shift to pH 5 showed

In short. In a two-stage test (1 h at pH 2.2, then pH 5, 37 °C, 4 mg drug), the apparent ≈93.5 µg/mL of the EPO–HPMC dispersion fell to ≈43 µg/mL within about 2 min of the shift as its nanodroplets dissolved, and it reached 39.1 of 40 µg/mL by 3 h xie2017 R10, R20. The precipitate of the EPO dispersion, SHG-active α crystals mostly under 10 µm, rose from ≈21 to ≈32 µg/mL within 20–30 min and levelled at 32.1 µg/mL, while sieved α crystals reached 17 µg/mL (24.6 µg/mL with matched EPO) after 8 h and γ crystals ≈8 µg/mL xie2017 R19, R23, R25, R17, R10. With a shift to pH 6.8 all three 30% dispersions reached 40 µg/mL within 10 min xie2017 R22. The authors find it "critical" to characterize whether a precipitate is amorphous or crystalline and its size xie2017 C70.

Type. single-system observation (indomethacin, EPO and HPMC, two final pH values) Strength. : the end points are HPLC values and the polymorph rests on three methods, but acid-stage UV values are apparent, there is no size-matched crystal control, replicate numbers are not stated and the droplet extinction trace was not available xie2017 K4: moderate, K5: moderate, K6: moderate, X7, X10, X6, X9.

How it was shown

Xie and co-workers (2017) added indomethacin dispersions or crystals holding 4 mg drug to pH 2.2 buffer at 37 °C and, at 1 h, raised the pH to 5 (40 µg/mL at full dissolution) or, in a second scenario, to 6.8 xie2017 P7, P8. HPLC of filtered samples checked the UV readings, and the precipitate of the EPO dispersion was identified by SHG, Raman, PXRD and SEM xie2017 P9, P12, P13, P14, P15.

What the data show

At pH 5 the nanodroplets redissolved within minutes, and the in situ α crystals faster than sieved crystals but not completely xie2017 R20, R19, R17.

systemconditionsresultids
EPO–HPMC 3:5:2 dispersionpH 2.2 → 5, 37 °C≈93.5 → ≈43 µg/mL within ≈2 min; 39.1 of 40 µg/mL at 3 hxie2017 R10, R20
precipitate of the EPO 3:7 dispersionsame≈21 → ≈32 µg/mL in 20–30 min; 32.1 µg/mL at 3 hxie2017 R19
sieved α; α with 9.3 mg EPO; γsame, 8 h17; 24.6; ≈8 µg/mLxie2017 R17, R10
precipitateSHG, Raman, PXRD, SEMα form, mostly under 10 µmxie2017 R23, R24, R25
30% dispersionspH 2.2 → 6.8≈40–41.5 µg/mL within 10 min of the shiftxie2017 R22
Fig. 5 of xie2017: two-stage dissolution of eight indomethacin formulations, pH 2.2 then pH 5
Fig. 5 · xie2017two-stage dissolution of eight indomethacin formulations, pH 2.2 then pH 5

The ternary is highest in acid and at ≈40 µg/mL after the shift; the EPO dispersion crashes and then recovers quickly but not fully xie2017 R10, X7.

Why

The droplet phase disappeared on the pH rise, "consistent with" the higher amorphous solubility of the ionized drug (cited), so the droplets "served as a reservoir" available after dilution to a higher pH xie2017 C40, C42. Solubilization by EPO raises the dissolution rate of crystals through their solubility, but "this effect alone cannot explain" the faster dissolution of the precipitate, which the authors attribute "likely" to the very small crystal size xie2017 C47, C48. The shift to pH 6.8 did not separate the 30% dispersions whereas pH 5 did, so an intermediate pH "may be informative" xie2017 C66, C67.

Limits and transfer

One weak acid was tested in buffers without bile salts, and the α reference was about ten to fifty times larger than the precipitate xie2017 M1, P7, X10. For an ionizable drug, run the two-stage test with a final pH at which the dispersions are not all fully soluble as well as at pH 6.8, identify any acid-stage precipitate, and compare its redissolution with reference crystals of the same form and similar size xie2017 C67, C70, X10.

How it was shown

Xie and co-workers (2017) added dispersions or crystals holding 4 mg indomethacin to 50 mL of pH 2.2 McIlvaine buffer at 37 °C and 300 rpm and, at 1 h, 50 mL of 0.2 M disodium phosphate (pH 5, 100 mL, 40 µg/mL at full dissolution); a second scenario started in 25 mL and added 75 mL (pH 6.8) xie2017 P7, P8. Concentrations came from the 319 nm absorbance minus the 450 nm extinction, with HPLC of filtered samples at 1, 3 and 8 h xie2017 E4, P9. The precipitate of the EPO dispersion was imaged in suspension by SHG (α active, γ and amorphous inactive), filtered for Raman and PXRD and sized by SEM xie2017 P12, P13, P14, P15, C18. The α form was crystallized in-house and both crystal forms were sieved to 106–250 µm xie2017 M2, M1; α solubility at pH 5 was measured with and without polymer xie2017 P2.

What the data show

Before the shift. The ternary read ≈80 to ≈93.5 µg/mL with ≈75 nm nanospecies, the EPO dispersion fell from ≈77 to ≈29.5 µg/mL by UV (8.8 µg/mL by HPLC), the HPMC dispersions rose slowly to ≈18.5–39.5 µg/mL, and the crystals stayed at ≈1.5–5 µg/mL xie2017 R10, R11, R15. After the shift to pH 5. The ternary dropped within ≈2 min to ≈43 µg/mL and settled at ≈39–40 µg/mL (39.1 ± 0.4 µg/mL by HPLC at 3 h), slightly supersaturated relative to α with both polymers at pH 5 (26 µg/mL) xie2017 R20, R2, C41. The EPO precipitate rose to ≈32 µg/mL within ≈20–30 min and then levelled (32.1 ± 0.5 µg/mL at 3 h, ≈33.5 at 480 min) xie2017 R19. The HPMC 3:7 dispersion needed about 90 min to release its remaining drug (39.3 µg/mL), the 1:9 one about 10 min xie2017 R21. Sieved α reached 17 ± 1 µg/mL and α with 9.3 mg predissolved EPO 24.6 ± 0.7 µg/mL at 8 h; γ ≈8 µg/mL xie2017 R17, R10. The α solubility at pH 5 was 15 µg/mL alone and 27 with EPO; no LLPS or crystallization occurred up to 80 µg/mL at pH 5 xie2017 R2, R9. The precipitate. Many bright SHG spots in the suspension, a Raman spectrum matching α without the γ band near ≈1698 cm−1, PXRD matching α, and butterfly-shaped crystals with fine needles, mostly under 10 µm (5–10 µm in the discussion) xie2017 R23, R24, R25. After the shift to pH 6.8. The ternary, EPO and HPMC 3:7 dispersions all read ≈40–41.5 µg/mL within 10 min, α reached ≈39 µg/mL by ≈80 min, and γ ≈39.5 µg/mL only by ≈300 min xie2017 R22.

papersystemmethod and conditionsresultids
xie2017EPO–HPMC 3:5:2 dispersionpH 2.2 → 5, 37 °C≈93.5 → ≈43 µg/mL within ≈2 min; 39.1 of 40 µg/mL at 3 hR10, R20
xie2017precipitate of the EPO 3:7 dispersionsame≈21 → ≈32 µg/mL in 20–30 min; 32.1 µg/mL at 3 hR19
xie2017sieved α; α with 9.3 mg EPO; γsame, 8 h17; 24.6; ≈8 µg/mLR17, R10
xie2017precipitateSHG, Raman, PXRD, SEMα form, mostly under 10 µmR23, R24, R25
xie201730% dispersions; α; γpH 2.2 → 6.8≈40–41.5 µg/mL within 10 min of the shift; α complete within about 20 min; γ more than 4 hR22
purohit2018 (Bioperformance)tacrolimus capsules with 10–100% crystallinitycompendial and non-sink teststhe more non-sink tests discriminate crystallinity betterC57

Figure

Fig. 5 of xie2017: two-stage dissolution of eight indomethacin formulations, pH 2.2 then pH 5
Fig. 5 · xie2017two-stage dissolution of eight indomethacin formulations, pH 2.2 then pH 5

The ternary is highest in acid and at ≈40 µg/mL after the shift; the EPO dispersion crashes and then recovers quickly but not fully; values above 40 µg/mL in acid are apparent xie2017 R10, X7.

Fig. 10 of xie2017: SEM of the precipitate from the EPO dispersion
Fig. 10 · xie2017SEM of the precipitate from the EPO dispersion

Butterfly-shaped α crystals mostly under 10 µm, against 106–250 µm for the sieved reference crystals xie2017 R25, M2.

Why

The droplet phase disappeared on the pH rise, "consistent with" the higher amorphous solubility of the ionized drug (cited), so the droplets "served as a reservoir" that becomes available after dilution to a higher pH xie2017 C40, C42; in this paper the reservoir means redissolution, not replenishment during membrane transport xie2017 X9. Solubilization by EPO raises the dissolution rate of crystals through their solubility (Noyes–Whitney), but "this effect alone cannot explain" the precipitate's faster dissolution; the authors attribute it "likely" to the very small crystal size, helped by released EPO and probably by good wetting, since the crystals formed in the solution xie2017 C47, C48. They count the observation as in vitro support for the "widely held supposition" that a drug precipitating as crystals in vivo redissolves readily, and expect redissolution to be faster still with bile salts xie2017 C62, C63. The shift to pH 6.8 did not separate the 30% dispersions, as reported for ibuprofen sodium formulations (cited), whereas pH 5 did, so including an intermediate pH "may be informative" xie2017 C66, C67, R31. (synthesis: the LLPS chapter reaches the parallel result for a weak base shifted from gastric to intestinal pH, where the dose relative to the amorphous solubility at the final pH decides between colloid and crystals (Amorphous solubility and LLPS F23); for the weak acid indomethacin the higher pH raises the amorphous solubility instead, so the droplets dissolve (Amorphous solubility and LLPS F10).)

Conditions and limits

One weak acid (pKa 4.42), McIlvaine buffers without bile salts or phospholipids, 100 mL final volume, 8 h xie2017 M1, P7. The α reference was about ten to fifty times larger than the precipitate, and no size-matched control was tested xie2017 X10. The ternary's extinction trace after the shift (Fig. S6) was not available xie2017 X9.

Counterexamples and conflicts

The precipitate's redissolution was "comparable" to the HPMC 3:7 dispersion only in its initial rate; it stopped at about 80% of complete xie2017 X8. The droplets of the ternary crystallized after 3 h if the pH stayed at 2.2, so the recovery depends on when the pH rises xie2017 R15. None found in the library on the redissolution of in situ precipitates of other drugs; the crystallization-from-solution chapter finds that what precipitates after a pH shift, crystals or an amorphous solid, is drug-specific (Crystallization from solution F1).

Transfer check

For an ionizable drug, run the two-stage test with a final pH at which the dispersions are not all fully soluble (pH 5 here) as well as at pH 6.8 xie2017 C67. Identify any precipitate formed in the acid stage (SHG or Raman in suspension, PXRD, SEM size) and compare its redissolution with reference crystals of the same form and similar size xie2017 C70, X10. Confirm concentrations in turbid stages by HPLC (F8).

History

A burst and crash of indomethacin–EPO dispersions in acid and the lack of discrimination at pH 6.8 for ibuprofen sodium had been reported (cited) xie2017 R28, R31. Xie and co-workers (2017) were the first in the library to follow the redissolution of precipitates formed from dispersions, droplets against crystals, through a pH rise xie2017 C61. Later papers of the chapter followed weakly basic drugs through two-stage tests and found that the gastric stage itself could crystallize the drug held in an undissolved enteric dispersion and lower release after the pH rise (F24, F25) elkhabaz2019a C56; nguyen2023c C3.

Topic 8 of 8 · 5 findings · F24–F28

Gastric stage and biorelevant media

F24

Topic 8Gastric stage and biorelevant media1 of 5

In gastric media, where the enteric polymer stays undissolved, drug crystallized in the wetted dispersion although the solution was not supersaturated.

Posaconazole–HPMCAS dispersions released only 7.5–11.5% of the dose in FaSSGF, below the crystalline solubility, yet second harmonic generation (SHG) imaging, which detects only crystals, found crystals in every dispersion after 30 min elkhabaz2019a R10, R16. Films of delamanid dispersions were covered with crystals after 1 h at pH 3.0, while the drug concentration in the acid hardly fell nguyen2023b R3; nguyen2023c R19, R23.

moderateModerate to strong that crystals form in acid; weak to moderate for the step from these crystals to lower release, which is inferred without a seeding test or identification of the crystals elkhabaz2019a K2, K3; nguyen2023b K2, K6; nguyen2023c K5, X10.

Posaconazole–HPMCAS in FaSSGF after 60 min, µg/mLreleased by the dispersions10, 25 and 50% drugabout 28–46crystalline solubility115.1

7.5, 10 and 11.5% of a 400 µg/mL dose: the solution stayed subsaturated, yet SHG showed crystals in every dispersion after 30 min. elkhabaz2019a R10, R1, R6, R7, R8, R16

Delamanid films crystal-free after 1 h
HPMCP grades at pH 1.6HPMCP-55 at pH 3.0films under Eudragit L 100-55
Crystals on the films after 1 h
other grades at pH 3.0every grade at pH 5.0HPMCAS-HF at pH 1.6

Salt dispersions with five enteric grades; PXRD of the powders detected no crystals. nguyen2023c R19, R20, R15; nguyen2023b R6

For your drug

  1. Suspend the dispersion, and a film of it, in the gastric medium at two or more pH values for the expected residence time, and look for crystals by SHG, PLM or SEM, since PXRD missed crystal levels that still harmed release.
  2. A concentration that holds in acid and a solution inhibitor that changes nothing point to the matrix as the route; where crystals form, limit the contact of the dispersion with acid, for example with an enteric coating (F27).

elkhabaz2019a P10; nguyen2023c R15, C46, R23, R22, C61

How it works and key numbers
  1. In acid the enteric polymer stays undissolved, and absorbed water lowers the Tg of the matrix and raises mobility nguyen2023c C43.
  2. With a crystal-free dispersion and a subsaturated solution, "Solution-phase crystallization cannot occur", so the crystals formed in the matrix, "likely" mainly at the surface elkhabaz2019a C34; nguyen2023c C43.
  3. For delamanid a constant concentration in acid and an ineffective solution inhibitor (1 mg/mL PVPVA) ruled out the solution as the main route nguyen2023c C37, C39, R22.
  4. The crystals were "apparently 'protected'" from dissolution and carried into the intestinal stage, where they "can act as seeds" elkhabaz2019a C35; nguyen2023c C44.
  5. The small crystal mass is still "potentially catastrophic": "there appear to be two competing processes, drug crystallization and drug release" nguyen2023c C46, C49.
7.5–11.5% of 400 µg/mLposaconazole released in FaSSGF, below its 115.1 µg/mL crystalline solubilityelkhabaz2019a R10, R1
≈0.026 / ≈0.050 / ≈68%estimated matrix crystallization at 10, 25 and 50% posaconazole after 30 minelkhabaz2019a R20
≈44 vs ≈41%delamanid–HPMCP-50 release after pH 3.0 with and without predissolved PVPVAnguyen2023c R22
Evidence: data, conditions and papers

Finding F24. In gastric media, where the enteric polymer stays undissolved, drug in the wetted dispersion crystallized while the medium was subsaturated or only modestly supersaturated, at the surface of delamanid dispersions and massively in a 50% posaconazole–HPMCAS dispersion, and these crystals were carried into the intestinal stage

In short. Posaconazole–HPMCAS dispersions released only 7.5–11.5% of the dose during 60 min in FaSSGF, below the crystalline solubility of 115.1 µg/mL, yet SHG found crystals in every system after 30 min, estimated at about 68% of the undissolved drug at 50% drug against 0.026–0.050% at 10–25% elkhabaz2019a R10, R1, R16, R20. Films of delamanid–HPMCP dispersions, free base or salt, were covered with star- and needle-shaped crystals after 1 h at pH 3.0, and none formed under a 2 µm Eudragit L 100-55 layer nguyen2023b R3, R4, R6. Across five enteric polymer grades, crystals formed on delamanid salt dispersions at pH 3.0 and 5.0, more with HPMCAS, while PXRD of the powders detected none nguyen2023c R19, R20, R15. The authors attribute the crystals to the undissolved, water-plasticized matrix, the solution being ruled out ("Solution-phase crystallization cannot occur") elkhabaz2019a C34; nguyen2023c C43, C37, and conclude that these crystals seeded crystallization after the pH shift elkhabaz2019a C56; nguyen2023c C44.

Type. observation in 2 drugs (posaconazole with HPMCAS-MF at three loadings; delamanid free base and salts with HPMCP and HPMCAS grades), with pretomanid as a comparator Strength. to strong that crystals form in acid (SHG, which sees only crystals, and films imaged by PLM and SEM), moderate for the polymer and pH pattern, weak to moderate for the step from these crystals to lower release, which is inferred without a seeding test or identification of the crystals on the dispersions elkhabaz2019a K2: moderate to strong, K3: weak to moderate; nguyen2023b K2: strong, K6: weak to moderate; nguyen2023c K5: weak to moderate, K6: moderate, X10, X11.

How it was shown

Elkhabaz and co-workers (2019) held crystal-free 10, 25 and 50% posaconazole–HPMCAS-MF dispersions in FaSSGF (pH 1.6) for 60 min before a shift to FaSSIF and imaged them by SHG, which sees only crystals, and by two-photon excited UV fluorescence, which sees drug in any state elkhabaz2019a P1, P6, P10, P11. Nguyen and co-workers (2023) laid films of delamanid salt dispersions with five enteric grades on acid media at pH 1.6, 3.0 and 5.0 for 60 min, and repeated a pH 3.0 → 6.5 test with 1 mg/mL PVPVA predissolved nguyen2023c P13, P14, P16.

What the data show

Crystals formed in acid although the solution was subsaturated or hardly fell, and a solution inhibitor changed nothing elkhabaz2019a R10, R16; nguyen2023c R19, R23, R22.

systemconditionsresultids
posaconazole–HPMCAS 10 / 25 / 50%, FaSSGFHPLC of supernatants, 60 min7.5 / 10 / 11.5% of 400 µg/mL, below the 115.1 µg/mL crystalline solubilityelkhabaz2019a R10, R1
sameSHG and TPE-UVF after 30 minestimated matrix crystallization ≈0.026 / ≈0.050 / ≈68%elkhabaz2019a R16, R20
25% delamanid salt dispersions, five enteric grades, 1 hPXRD of powders; PLM and SEM of filmsno PXRD peaks; films clear (HPMCP, pH 1.6), crystals at pH 3.0 except HPMCP-55, on all at pH 5.0; HPMCAS-HF also at pH 1.6nguyen2023c R15, R19, R20
pH 3.0 → 6.5 release with 1 mg/mL PVPVA predissolvedin situ UV≈44 against ≈41, ≈82 against ≈80.5, ≈7 against ≈10%nguyen2023c R22
HPMCP films with and without 2 µm Eudragit L 100-55pH 3.0, 1 h, PLM and SEMstar- and needle-shaped crystals on all uncoated films; none under the layernguyen2023b R3, R4, R6
Fig. 9 of elkhabaz2019a: SHG images of posaconazole dispersions after 30 min in FaSSGF and after transfer to FaSSIF
Fig. 9 · elkhabaz2019aSHG images of posaconazole dispersions after 30 min in FaSSGF and after transfer to FaSSIF

White spots are crystals, already present after 30 min in acid and far more numerous at 50% drug elkhabaz2019a R16.

Why

With crystal-free dispersions and a subsaturated gastric solution, "Solution-phase crystallization cannot occur", so the crystals formed in the undissolved matrix and were "apparently 'protected'" from dissolution elkhabaz2019a C34, C35. The authors state that these seed crystals "were transferred to the intestinal compartment and promoted further crystallization" elkhabaz2019a C56. For delamanid, absorbed water lowers the Tg of the undissolved matrix, crystals form "likely" mainly at the surface, and the small crystal mass is still "potentially catastrophic" because the crystals "can act as seeds" nguyen2023c C43, C46, C44.

Limits and transfer

The SHG and TPE-UVF volume fractions are uncalibrated against each other, and the delamanid crystals were seen on films and powders rather than tablets and were not identified elkhabaz2019a X6; nguyen2023c X10, X11. Suspend the dispersion, and a film of it, in the gastric medium at two or more pH values for the expected residence time and look for crystals by SHG, PLM or SEM, since PXRD missed crystal levels that still harmed release elkhabaz2019a P10; nguyen2023c R15, C46.

How it was shown

Elkhabaz and co-workers (2019) dispersed 10, 25 and 50% posaconazole–HPMCAS-MF dispersions, crystal-free by polarized light and PXRD, and crushed Noxafil tablets in FaSSGF (pH 1.6) for 60 min before a shift to FaSSIF, and imaged aliquots by SHG, which gives signal only from non-centrosymmetric crystals, and by two-photon excited UV fluorescence (TPE-UVF), which shows drug in any state; the ratio of the two volume fractions after 30 min estimated matrix crystallization elkhabaz2019a P1, R5, P6, P10, P11, E1. Nguyen and co-workers (2023), in the gastric-pH paper, suspended neat amorphous delamanid edisylate at pH 1.6, 3.0, 5.0 and 6.5 for up to 120 h with PXRD, filtered dispersion powders (20 mg in 50 mL) after 1 h in acid for PXRD and SEM, laid spin-coated films on acid media under polarized light for 60 min followed by SEM, and imaged undissolved particles after the full pH-shift test nguyen2023c P11, P12, P13, P14, P15. They repeated the pH 3.0 → 6.5 test with 1 mg/mL PVPVA predissolved, a known inhibitor of delamanid crystallization in solution nguyen2023c P16. The coating paper of the same year immersed 8-µm spin-coated films of free-base, chloride and edisylate dispersions in HPMCP, part covered by about 2 µm of Eudragit L 100-55, in phosphate buffer pH 3.0 for 1 h, with PLM and SEM nguyen2023b P4, P5, R5.

What the data show

Posaconazole. After 60 min in FaSSGF the dispersions had released 7.5, 10 and 11.5% of the 400 µg/mL dose (10, 25, 50% drug) and the tablet powder 8.5%, about 28–46 µg/mL against a crystalline solubility of 115.1 µg/mL elkhabaz2019a R10, R1, R6, R7, R8, R9. SHG showed a few crystals at 10 and 25% drug and in the tablet powder after 30 min, and many large crystals at 50% elkhabaz2019a R16. The SHG/TPE-UVF ratio gave about 0.026, 0.050 and 68% at 10, 25 and 50% drug and 0.047% for the tablet elkhabaz2019a R20. After the shift the 50% dispersion fell from about 17 to about 6 µg/mL within 30 min and never reached the amorphous solubility of about 20 µg/mL, and the undissolved drug of the 50% dispersion persisted for an hour while that of the others vanished within 30 min elkhabaz2019a R8, R2, R19. Neat delamanid salt. Free-base PXRD peaks appeared after 5 min at pH 1.6 and were clear by 1 h at pH 3.0, but only after about 14 h at pH 5.0 and 6.5 nguyen2023c R14. Delamanid dispersions. No dispersion powder showed PXRD peaks after 1 h in acid, a method that detects about 1–5% crystallinity nguyen2023c R15, R16. On films, HPMCP grades stayed clear at pH 1.6; at pH 3.0 crystals covered all films except HPMCP-55; at pH 5.0 small crystals covered all films; HPMCAS-HF crystallized even at pH 1.6 nguyen2023c R19, R20. HPMCAS powders became pitted and porous with agglomerates that increased with pH nguyen2023c R18. Undissolved particles were covered with small crystals within 30 min of the shift to pH 6.5 nguyen2023c R21. Free-base films crystallized at all three gastric pH values, the salt film stayed clear at pH 1.6 nguyen2023c R9, R10, R19. In the coating paper, free-base, chloride and edisylate films all carried star- and needle-shaped crystals after 1 h at pH 3.0, and areas under the Eudragit layer stayed featureless, also overnight according to the text nguyen2023b R3, R4, R6, C18. The solution in acid. Delamanid concentrations hardly fell during the acid stage (for example ≈3.5 → ≈2% for HPMCP-50 at pH 3.0), and predissolved PVPVA left pH 3.0 → 6.5 release at ≈44 against ≈41% (HPMCP-50), ≈82 against ≈80.5% (HPMCP-55) and ≈7 against ≈10% (HPMCAS-MF) nguyen2023c R23, R22.

papersystemmethod and conditionsresultids
elkhabaz2019aposaconazole–HPMCAS 10 / 25 / 50% and Noxafil powder, FaSSGF pH 1.6HPLC of supernatants, 60 min7.5 / 10 / 11.5 and 8.5% of 400 µg/mL, below 115.1 µg/mL crystalline solubilityR10, R1
elkhabaz2019asameSHG and TPE-UVF after 30 mincrystals in all; estimated matrix crystallization ≈0.026 / ≈0.050 / ≈68 / ≈0.047%R16, R20
nguyen2023cneat amorphous delamanid edisylatesuspension, PXRD, pH 1.6 / 3.0 / 5.0 and 6.5free-base peaks after 5 min / by 1 h / after about 14 hR14
nguyen2023c25% delamanid salt dispersions, five enteric grades, 1 h in acidPXRD of powders; PLM and SEM of filmsno PXRD peaks; films clear (HPMCP, pH 1.6), crystals at pH 3.0 except HPMCP-55, small crystals on all at pH 5.0; HPMCAS-HF also at pH 1.6R15, R19, R20
nguyen2023cpH 3.0 → 6.5 release with 1 mg/mL PVPVA predissolvedin situ UV≈44 against ≈41, ≈82 against ≈80.5, ≈7 against ≈10%R22
nguyen2023bfree-base, chloride and edisylate HPMCP films, with and without 2 µm Eudragit L 100-55phosphate pH 3.0, 1 h, PLM and SEMstar- and needle-shaped crystals on all uncoated films; none under the layerR3, R4, R6
nguyen2023a (Bioperformance)pretomanid–HPMCAS-HF dispersions, 1 h in HCl pH 1.6PXRD, SEMPXRD peaks of crystalline pretomanid and needle-shaped surface crystals after immersionR22
shah2024 (ASD process)posaconazole–HPMCAS extrudates, crystal-free and with 0.3–19% residual crystals, 60 min FaSSGFSHGcrystallinity rose only where residual crystals were present (0.3 → 0.4, 3 → 4, 19 → 26%)R21, C36
wegiel2015resveratrol–HPMCAS 25%, pH 1.2, polymer undissolvedRaman ratio, polarized light, 24 hcrystals inside intact particlesR17, R18
chen2015acelecoxib–HPMCAS 33.3%, pH 3, no surfactantsuspension, polarized lightno crystals for 48 h; on or in the particles after about 7 days in Triton X100R14, R20

Figure

Fig. 9 of elkhabaz2019a: SHG images of posaconazole dispersions after 30 min in FaSSGF and after transfer to FaSSIF
Fig. 9 · elkhabaz2019aSHG images of posaconazole dispersions after 30 min in FaSSGF and after transfer to FaSSIF

Rows are the 10, 25 and 50% dispersions and the tablet powder; white spots are crystals, already present after 30 min in acid and far more numerous at 50% drug elkhabaz2019a R16.

Fig. 8 of nguyen2023c: films of delamanid salt dispersions with five enteric polymers after 1 h at pH 1.6, 3.0 and 5.0
Fig. 8 · nguyen2023cfilms of delamanid salt dispersions with five enteric polymers after 1 h at pH 1.6, 3.0 and 5.0

HPMCP films are clear at pH 1.6; crystals appear at pH 3.0 on all but HPMCP-55 and cover every film at pH 5.0 nguyen2023c R19.

Why

For posaconazole the authors argue that, the dispersions being crystal-free and the gastric solution subsaturated, "Solution-phase crystallization cannot occur", so the crystals formed in the undissolved matrix, "perhaps somewhat counterintuitively" in a medium where crystals should dissolve, and were "apparently 'protected'" from dissolution and carried into the intestinal stage elkhabaz2019a C34, C35. HPMCAS prevented crystallization during preparation but not in acid, and the large crystal burden at 50% drug "raises questions" about how well polymers with pH-dependent solubility protect against matrix crystallization elkhabaz2019a C37, C36. After the shift the matrix crystals "are expected to grow rapidly", and the authors state without hedge that "These seed crystals were transferred to the intestinal compartment and promoted further crystallization" elkhabaz2019a C43, C56. For delamanid, Nguyen and co-workers rule out the solution as the main route, since concentrations did not fall in acid, PVPVA changed nothing and the gastric supersaturation did not predict release nguyen2023c C37, C39. Absorbed water lowers the Tg of the undissolved matrix and raises mobility, crystals form "likely" mainly at the surface, and matrix crystallization "seems to be an important failure mechanism" nguyen2023c C43, C45. The crystals "can act as seeds", amorphous drug near them crystallizes as the polymer dissolves, so that "there appear to be two competing processes, drug crystallization and drug release", and the small crystal mass is still "potentially catastrophic" nguyen2023c C44, C49, C46. The salt "likely" delays crystallization because it must first convert to the free base, and HPMCP-50, which dissolves at pH 5.0, "presumably mitigates" surface crystallization by releasing the drug first nguyen2023c C52, C54. The coating paper attributes the crystals to the unionized polymer being a poor inhibitor and/or to a higher crystallization tendency of the drug at certain pH, the surface drug being the most mobile ("can be attributed") nguyen2023b C37. The delamanid salt dispersions of 2022 released less after an acid stage than in a single stage, which "may suggest" physical instability of the drug left in the undissolved matrix duong2022a C63. (synthesis: an enteric polymer in acid holds the drug back (F15, F18) but inhibits crystallization poorly there, which fits the crystallization-from-solution findings that carboxylated cellulose esters lose most of their effect at pH 3.8 and that HPMCAS adsorbed at pH 3 slows growth less than at pH 6.8 (Crystallization from solution F11, Crystallization from solution F23); the surface location fits the faster crystallization of free surfaces in Crystallization tendency F21. For posaconazole, the crystallization-from-solution chapter adds that the HPMCAS chemistry that delays nucleation longest also limits release at low pH (Crystallization from solution F44). For these two fast-crystallizing drugs the matrix route of F1 and F16 acts in the stomach, before the polymer can dissolve.)

Conditions and limits

One gastric residence time (60 min) in all three papers elkhabaz2019a P6; nguyen2023c P8; nguyen2023b P5. The SHG and TPE-UVF volume fractions are uncalibrated against each other, and for the 50% dispersion the crystalline fraction exceeds the undissolved fraction after 120 min elkhabaz2019a X6. The delamanid crystals were seen on films and powders tested separately, not on the tablets, and were not identified; their free-base identity is inferred from the neat salt nguyen2023c X10, X11; nguyen2023b X7. HPMCAS-LF and -MF released poorly after pH 1.6 without crystals reported at that pH nguyen2023c X7. Media were simple HCl and phosphate buffers for delamanid and FaSSGF for posaconazole nguyen2023c X8; elkhabaz2019a P6.

Counterexamples and conflicts

Crystal-free posaconazole–HPMCAS extrudates showed no SHG signal after 60 min in FaSSGF, and crystallinity rose only in extrudates that already held residual crystals, which the authors read as matrix crystallization promoted by those crystals shah2024 R21, C36; the solvent-evaporated, cryo-milled dispersions of 2019 crystallized from a crystal-free start, more at higher loading elkhabaz2019a R5, R20. Slower crystallizers did not crystallize in acid within the test: celecoxib–HPMCAS particles stayed crystal-free for 48 h at pH 3 without surfactant, and lopinavir suspensions of enteric dispersions for 3 h (F14, F15) chen2015a R14; li2016b R21. HPMCP films of delamanid stayed clear at pH 1.6 and HPMCP-55 at pH 3.0 nguyen2023c R19. Crystals of pretomanid formed on HPMCAS-HF dispersions in 1 h at pH 1.6, and total release was lower in the two-stage test, "most likely" through crystallization nguyen2023a R22, C44.

Transfer check

For a dispersion of a weak base or a fast crystallizer in an enteric polymer, suspend the dispersion (and a film of it) in the gastric medium at two or more pH values for the expected residence time, and look for crystals by SHG, PLM or SEM, since PXRD missed crystal levels that still harmed release elkhabaz2019a P10; nguyen2023c R15, C46. Rank loadings by the crystal burden after the acid stage, which rose about three orders of magnitude between 25 and 50% posaconazole elkhabaz2019a R20. A concentration that holds in acid and a solution inhibitor that changes nothing point to the matrix, not the solution, as the route nguyen2023c R23, R22. Where crystals form, limit the drug's contact with acid, for example with an enteric coating (F27) nguyen2023c C61.

History

Wegiel and co-workers (2015) showed resveratrol crystallizing inside intact HPMCAS dispersion particles at pH 1.2, and Chen and co-workers (2015) and Li and co-workers (2016) followed acidified suspensions of enteric dispersions for celecoxib and lopinavir (F1, F14, F15) wegiel2015 R18; chen2015a C38; li2016b C5. Elkhabaz and co-workers (2019) were the first in the library to show by SHG that crystals form in a crystal-free enteric dispersion of a weak base during a gastric stage and are carried into the intestinal stage elkhabaz2019a C23, C56. Duong and co-workers (2022) found lower release after an acid stage for delamanid salt dispersions duong2022a C63. Nguyen and co-workers (2023) mapped surface crystallization of delamanid across gastric pH, polymer grade and drug form nguyen2023c C3, C4, and in the coating paper found it independent of the salt form and prevented by an enteric layer nguyen2023b C17, C18. In the Bioperformance chapter, pretomanid dispersions with HPMCAS crystallized at their surfaces in acid as well nguyen2023a R22, C44.

F25

Topic 8Gastric stage and biorelevant media2 of 5

After a gastric stage, release from enteric dispersions depended on gastric pH and polymer grade, which a single pH 6.5 stage missed.

At pH 6.5 alone, 25% delamanid salt dispersions with HPMCP-50, HPMCP-55 and HPMCAS-LF released alike (≈88–96%) nguyen2023c R11. After 60 min at pH 1.6, 3.0 or 5.0 and transfer to pH 6.5, final release across five enteric grades ranged from about 0 to 101%, and HPMCAS dispersions of neutral praziquantel recovered less after pH 3.0 or 5.0 than after pH 1.6 nguyen2023c R11; alvarenga2025 R7, R10.

strongStrong for the dependence of final release on gastric pH, grade and drug form, measured for every combination with error bars; moderate for the polymer ranking, which reverses after pH 5.0; weak to moderate for the explanations nguyen2023c K1, K2, K8.

after pH 1.6after pH 3.0after pH 5.0HPMCP-50pH 6.5 alone 964182101HPMCP-558912.580.594.5HPMCAS-LF8837.547.550HPMCAS-MF57.51012.540HPMCAS-HF0011802040608010025% delamanid salt dispersions: final release, %

60 min in the gastric medium, then pH 6.5; dashed tick: single stage at pH 6.5. All values approximate. nguyen2023c R11

Same gastric supersaturation, different final release, %HPMCP-55 after pH 3.0ratio in acid ≈7.5≈80.5HPMCAS-MF after pH 3.0ratio in acid ≈7.0≈10

The supersaturation ratio in acid rose from ≈0.9–3.8 at pH 1.6 to ≈11–42 at pH 5.0 but did not order the final release. nguyen2023c R13, R11, C39

For your drug

  1. For an enteric-polymer dispersion of a weakly basic or fast-crystallizing drug, run two-stage tests with gastric stages at pH 1.6, 3.0 and 5.0 as well as the single stage at pH 6.5, and measure polymer release alongside drug release.
  2. Measure drug and polymer solubility across the same pH range, since the risk window is where neither dissolves, and do not rank dispersions by the gastric supersaturation ratio.

nguyen2023c R11, C5, R12, C15, C39

How it works and key numbers
  1. For delamanid the drug dissolves at pH 1.6 while the polymers do not; at pH 3.0 and 5.0 both are poorly soluble; at pH 6.5 the polymers dissolve and the drug hardly at all nguyen2023c C14, C15.
  2. The authors attribute the failures to surface crystallization of the undissolved dispersion, not to crystallization from solution (F24) nguyen2023c C39, C3.
  3. HPMCP-50 dissolves at pH 5.0, so most drug leaves in the acid stage, which "presumably mitigates" surface crystallization; HPMCAS-MF and -HF dissolve poorly even at pH 6.5, leaving more time for matrix crystallization nguyen2023c C54, C56.
  4. For HPMCP-55 at pH 1.6 the authors invoke a lower chemical potential of the drug from stronger drug–polymer interactions ("may"), not measured nguyen2023c C41, C42.
  5. For praziquantel the hold-back is put down to the "minimal ionization of succinoyl groups" of HPMCAS-MF below pH about 6 alvarenga2025 C9.
≈88–96%single-stage release of the HPMCP-50, HPMCP-55 and HPMCAS-LF delamanid dispersionsnguyen2023c R11
≈0–101%final release of the five grades after gastric pH 1.6, 3.0 or 5.0nguyen2023c R11
≈92–103% vs ≈62–77%praziquantel–HPMCAS after a pH 1.6 against a pH 3.0 or 5.0 startalvarenga2025 R7, R10
Evidence: data, conditions and papers

Finding F25. After a gastric stage, release from enteric-polymer dispersions depended on the gastric pH, the polymer grade and the drug form: delamanid salt dispersions ended anywhere from about 0 to 101% depending on pH 1.6, 3.0 or 5.0 and five grades, gastric pH 3.0 or 5.0 was often worse than pH 1.6 also for neutral praziquantel, and a single stage at pH 6.5 ranked dispersions alike that later failed

In short. At pH 6.5 alone, 25% delamanid salt dispersions released ≈96% (HPMCP-50), ≈89% (HPMCP-55), ≈88% (HPMCAS-LF), ≈57.5% (-MF) and ≈0% (-HF); after 60 min at pH 1.6, 3.0 or 5.0 and transfer to pH 6.5 they ended at ≈101, ≈41 and ≈82% (HPMCP-50), ≈94.5, ≈80.5 and ≈12.5% (HPMCP-55), ≈47.5, ≈37.5 and ≈50% (LF), ≈40, ≈10 and ≈12.5% (MF) and ≈18, ≈1 and ≈0% (HF) nguyen2023c R11. The free base with HPMCP-50 ended at ≈62, ≈33.5 and ≈6.5 µg/mL of 100 nguyen2023c R7. Praziquantel–HPMCAS dispersions, a drug neutral above about pH 3, reached ≈92–103% after a pH 1.6 start but ≈62–77% after pH 3.0 or 5.0 starts at 0.667 mg/mL, while HPMC dispersions released ≈88–106% in the first stage whatever its pH alvarenga2025 R4, R7, R10, R13. The gastric supersaturation ratio rose from ≈0.9–3.8 at pH 1.6 to ≈11–42 at pH 5.0 for every delamanid dispersion but did not predict final release nguyen2023c R13, C39. The authors conclude that gastric pH variations "should be evaluated" for dispersions of weakly basic drugs with enteric polymers nguyen2023c C5.

Type. observation in 3 drugs (delamanid free base and salts with five enteric grades; praziquantel with HPMCAS-MF and HPMC; posaconazole with HPMCAS-MF), single source for the pH 1.6–3.0–5.0 grid of each drug Strength. for the dependence of final release on gastric pH, grade and drug form, measured for every combination with error bars; moderate for the polymer ranking, which reverses after pH 5.0; weak to moderate for the explanations nguyen2023c K1: strong, K2: moderate, K8: strong, X3, X13; alvarenga2025 K1: strong; polyzois2024 K9: strong.

How it was shown

Nguyen and co-workers (2023) tested tablets of 25% delamanid edisylate dispersions with HPMCP-50, HPMCP-55 and HPMCAS-LF, -MF and -HF, and of a spray-dried free-base HPMCP-50 dispersion, at pH 6.5 alone or after 60 min at pH 1.6, 3.0 or 5.0 nguyen2023c P5, P6, P7, P8. Alvarenga and co-workers (2025) started 30% praziquantel dispersions for 1 h at pH 1.6, 3.0 or 5.0 before the intestinal stage alvarenga2025 P10, P11.

What the data show

The single stage ranked three delamanid dispersions alike, but after a gastric stage final release spread from about 0 to 101% nguyen2023c R11.

systemgastric stage before pH 6.5resultids
delamanid edisylate 25%, HPMCP-50none; pH 1.6 / 3.0 / 5.0≈96%; ≈101 / ≈41 / ≈82%nguyen2023c R11
same, HPMCP-55same≈89%; ≈94.5 / ≈80.5 / ≈12.5%nguyen2023c R11
same, HPMCAS-LF; -MF; -HFsame≈88, ≈57.5, ≈0%; ≈47.5 / ≈37.5 / ≈50, ≈40 / ≈10 / ≈12.5, ≈18 / ≈1 / ≈0%nguyen2023c R11
delamanid free base, HPMCP-50, spray-driedsame≈81–86 µg/mL alone; ≈62.5 / ≈33.5 / ≈6.5 µg/mLnguyen2023c R7
all six delamanid dispersions, acid stagepH 1.6 / 3.0 / 5.0maximum supersaturation ratio ≈0.9–3.8 / ≈3.3–11.4 / ≈11–42nguyen2023c R13
praziquantel 30% HPMCAS-MF; HPMC E5 LV, 0.667 mg/mLpH 1.6; pH 3.0 or 5.0≈92–103%; ≈62–77%; HPMC ≈88–106% already in the first stagealvarenga2025 R7, R10
Fig. 3 of nguyen2023c: drug and polymer release of delamanid salt dispersions with HPMCP-50 and HPMCP-55 at pH 6.5 and after three gastric pH values
Fig. 3 · nguyen2023cdrug and polymer release of delamanid salt dispersions with HPMCP-50 and HPMCP-55 at pH 6.5 and after three gastric pH values

After the dashed line HPMCP-50 recovers after pH 1.6 and 5.0 but not after pH 3.0, and HPMCP-55 after pH 1.6 and 3.0 but not after pH 5.0 nguyen2023c R11, R12.

Why

For delamanid the drug dissolves at pH 1.6 and the polymers do not, both are poorly soluble at pH 3.0 and 5.0, and at pH 6.5 the polymers dissolve and the drug hardly at all nguyen2023c C14, C15. The failures are attributed to surface crystallization of the undissolved dispersion rather than to crystallization from solution (F24) nguyen2023c C39, C3. HPMCP-50 dissolves at pH 5.0, so most drug leaves in the acid stage, which "presumably mitigates" surface crystallization nguyen2023c C54. For praziquantel the hold-back is put down to the "minimal ionization of succinoyl groups" of HPMCAS-MF below pH about 6 alvarenga2025 C9.

Limits and transfer

The delamanid grid used one loading and one 60-min acid stage in simple media, without stated replicate numbers nguyen2023c X8, X13. For an enteric-polymer dispersion of a weakly basic or fast-crystallizing drug, run two-stage tests with gastric stages at pH 1.6, 3.0 and 5.0 beside the single stage, measure drug and polymer solubility across that pH range, and do not rank dispersions by the gastric supersaturation ratio nguyen2023c R11, C5, C15, C39.

How it was shown

Duong and co-workers (2022) compared single-stage release at pH 6.5 with a two-stage test (1 h in HCl pH 1.6, then pH 6.5) for delamanid free-base and edisylate dispersions in HPMCAS and HPMCP at 10–40% drug duong2022a P15, P16, R14, R24. Nguyen and co-workers (2023), in the gastric-pH paper, made 25% delamanid edisylate dispersions with HPMCP-50, HPMCP-55 and HPMCAS-LF, -MF and -HF by rotary evaporation and a spray-dried free-base HPMCP-50 dispersion, tested tablets holding 5 mg drug in 50 mL of pH 6.5 buffer or for 60 min in 0.02 M HCl pH 1.6, phosphate pH 3.0 or pH 5.0 before a shift to pH 6.4–6.6 for 30 min, followed drug by in situ UV and polymer by HPLC-ELSD, and divided the 1-h acid concentration by the crystalline solubility at that pH nguyen2023c P5, P6, P7, P8, P9, P10, E2. Drug and polymer solubility were measured from pH 1.6 to 6.5, with a Henderson–Hasselbalch fit for the drug nguyen2023c P1, P3, E1. The coating paper of the same year ran the same three gastric pH values with uncoated HPMCP-50 tablets of the free base and of chloride and edisylate salts (F27) nguyen2023b P10, R2. Polyzois and co-workers (2024) ran praziquantel dispersions for 1 h in 45 mL HCl pH 1.6 before adding concentrated buffer to pH 6.5 polyzois2024 P10. Alvarenga and co-workers (2025) started 30% praziquantel dispersions of HPMCAS-MF and HPMC E5 LV for 1 h at pH 1.6, 3.0, 5.0, in FaSSGF or in acetate pH 4.5 before the intestinal stage, at 0.667 and 1.5 mg/mL alvarenga2025 P10, P11, P12.

What the data show

Delamanid, drug and polymer. Amorphous solubility fell from 154.5 to 0.76 µg/mL and crystalline from 10.2 to 0.018 µg/mL between pH 1.6 and 6.5; the polymers were insoluble below pH 4.5, at pH 5.0 HPMCP-50 reached 893 and HPMCP-55 189 µg/mL, and HPMCAS-LF and -MF dissolved from pH 5.5 nguyen2023c R1, R2, R4. A Henderson–Hasselbalch fit of the solubilities gave a pKa of 3.94 ± 0.04 against a reported 4.3 nguyen2023c M1, R3. Acid stage. At pH 1.6 the salt dispersions released about 30% (HPMCP-50), under 10% (HPMCP-55) and ≈21–36.5% (HPMCAS grades); at pH 3.0 only about 0.5–3.5%; at pH 5.0 HPMCP-50 released ≈80% within 10 min while the others released almost nothing nguyen2023c R11. Final release. The values of the In short span ≈0–101% nguyen2023c R11. At pH 5.0, HPMCP-55 released ≈65% of its polymer by 60 min but no drug, and HPMCAS-LF dissolved to ≈92% after pH 1.6 while its drug release stayed at ≈47.5% nguyen2023c R12, R11. Supersaturation in acid. The maximum ratio after 1 h was ≈0.9–3.8 at pH 1.6, ≈3.3–11.4 at pH 3.0 and ≈11–42 at pH 5.0; at pH 3.0 HPMCP-55 (≈7.5) ended at ≈80.5% but HPMCAS-MF (≈7.0) at ≈10% nguyen2023c R13, R11. Uncoated HPMCP-50 tablets. After pH 1.6, 3.0 and 5.0 they gave ≈62, ≈33.5 and ≈6.5 µg/mL (free base), ≈86, ≈54 and ≈0.3 (chloride) and ≈93, ≈41 and ≈82 (edisylate), against ≈82–96 in a single stage nguyen2023b R2, R1. The pH 1.6 shift of 2022. It raised the end values of the 20% free-base dispersions (≈35 against ≈6 µg/mL with HPMCAS, ≈87 against ≈53 with HPMCP) but lowered those of 20–30% edisylate HPMCAS dispersions (≈70, ≈47 and ≈30 against ≈87, ≈87 and ≈85) duong2022a R14, R24. Praziquantel. The calculated pKa is 1.14, and amorphous solubility stayed within 1.17–1.43 mg/mL across six buffers alvarenga2025 R4, R1. HPMCAS-MF dispersions of 2024 released ≈17.5 and ≈25% in acid and ≈89.5 and ≈71% after the shift, against ≈100 and ≈94% in a single stage; the HPMC E5 LV dispersion released ≈81% in acid and ≈75% after polyzois2024 R15, R9. In 2025, HPMCAS dispersions released ≈22–28% at pH 1.6 and ≈9–23% at pH 3.0 or 5.0 in the first hour and ended at ≈92–103% and ≈62–77%; at 1.5 mg/mL they ended at ≈69–91% after pH 1.6 and ≈43–58% after pH 3.0 or 5.0; HPMC dispersions released ≈88–106% in every first stage alvarenga2025 R7, R9, R10, R11, R13.

papersystemmethod and conditionsresultids
nguyen2023c25% delamanid edisylate, HPMCP-50 / HPMCP-55 / HPMCAS-LF / -MF / -HFpH 6.5 alone; 60 min at pH 1.6 / 3.0 / 5.0 → pH 6.5, 37 °C≈96 / ≈89 / ≈88 / ≈57.5 / ≈0%; after the three gastric pH: ≈101 / ≈41 / ≈82, ≈94.5 / ≈80.5 / ≈12.5, ≈47.5 / ≈37.5 / ≈50, ≈40 / ≈10 / ≈12.5, ≈18 / ≈1 / ≈0%R11
nguyen2023c25% delamanid free base, HPMCP-50, spray-driedsame≈81–86 µg/mL alone; ≈62.5 / ≈33.5 / ≈6.5 µg/mLR7
nguyen2023call six dispersions, acid stagemaximum concentration over crystalline solubility≈0.9–3.8 / ≈3.3–11.4 / ≈11–42R13
nguyen2023buncoated delamanid–HPMCP-50 tablets, three forms60 min at pH 1.6 / 3.0 / 5.0 → pH 6.5≈0.3–93 µg/mL, against ≈82–96 µg/mL in a single stageR2, R1
duong2022adelamanid free base 20%; edisylate HPMCAS 20–30%pH 6.5 alone against 1 h pH 1.6 → pH 6.5≈6 → ≈35 (HPMCAS), ≈53 → ≈87 µg/mL (HPMCP); ≈85–87 → ≈30–70 µg/mLR14, R24
polyzois2024praziquantel–HPMCAS-MF 20 / 30%; HPMC E5 LVpH 1.6 1 h → pH 6.5, 1.5 mg/mL≈17.5 / ≈25% in acid, ≈89.5 / ≈71% after (single stage ≈100 / ≈94%); ≈81% in acid, ≈75% afterR15, R9
alvarenga2025praziquantel 30% HPMCAS-MF; HPMC E5 LV, 0.667 mg/mL1 h at pH 1.6; pH 3.0 or 5.0 → pH 6.5≈92–103% after pH 1.6; ≈62–77% after pH 3.0 or 5.0; HPMC ≈88–106% already in the first stageR7, R10
alvarenga2025same, 1.5 mg/mLsame≈69–91% after pH 1.6; ≈43–58% after pH 3.0 or 5.0R9, R11
kaur2025 (Release mechanism and LoC)bedaquiline–HPMCAS-LF and -MF 5/9560 min at pH 1.6 / 3.0 / 5.0 → pH 6.5≈19.5–25 µg/mL of 100 at 120 minR12
nguyen2023a (Bioperformance)pretomanid–HPMCAS dispersionssingle against two-stagelower total release after the gastric stage, "most likely" by crystallizationC44

Figure

Fig. 3 of nguyen2023c: drug and polymer release of delamanid salt dispersions with HPMCP-50 and HPMCP-55 at pH 6.5 and after three gastric pH values
Fig. 3 · nguyen2023cdrug and polymer release of delamanid salt dispersions with HPMCP-50 and HPMCP-55 at pH 6.5 and after three gastric pH values

The pH 6.5 control and the three pH-shift tests diverge after the dashed line: HPMCP-50 recovers after pH 1.6 and 5.0 but not after pH 3.0, HPMCP-55 after pH 1.6 and 3.0 but not after pH 5.0 nguyen2023c R11, R12.

Fig. 9 of nguyen2023c: maximum supersaturation ratio after 1 h in acid for six delamanid dispersions
Fig. 9 · nguyen2023cmaximum supersaturation ratio after 1 h in acid for six delamanid dispersions

The ratio rises from pH 1.6 to 5.0 for every dispersion, with three dispersions at 42, the amorphous-to-crystalline ratio, at pH 5.0; it does not order the final release nguyen2023c R13, X9.

Why

For delamanid the authors describe the gastric stage as a window in which the drug dissolves at pH 1.6 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 C14, C15. Release then depends on gastric pH and polymer grade, and none of the HPMCAS dispersions released near completely after the shift nguyen2023c C22, C24. Solution crystallization in acid was ruled out as the main failure route, and the failures are attributed to surface crystallization of the undissolved dispersion (F24) nguyen2023c C39, C3. HPMCP-50 dissolves at pH 5.0, so most drug leaves in the acid stage, which "presumably mitigates" surface crystallization, while HPMCAS-MF and -HF dissolve poorly even at pH 6.5, leaving more time for matrix crystallization ("can be attributed") nguyen2023c C54, C56. For HPMCP-55 at pH 1.6 the authors invoke a lower chemical potential of the drug from stronger drug–polymer interactions ("may"), which were not measured nguyen2023c C41, C42. Polymer solubility and polymer release contribute to drug release, but polymer release did not track it nguyen2023c C60, R12. The salt "matched or outperformed" the free base at every gastric pH but "only partially remediated" the pH dependence nguyen2023c C2, C20. For praziquantel the hold-back is put down to the "minimal ionization of succinoyl groups" of HPMCAS-MF below pH about 6, polymer dissolution not being measured alvarenga2025 C9; why the pH 3.0 and 5.0 starts recovered less than the pH 1.6 start is not discussed alvarenga2025 R7, R10. Polyzois and co-workers offer crystallization of undissolved particles in acid as a possible cause of the post-shift shortfall, which they label speculation polyzois2024 C35. (synthesis: for the weak base delamanid both components change with pH, the drug's solubility by the Henderson–Hasselbalch dependence of Amorphous solubility and LLPS F10 and the polymer's by its own pKa, and the worst case falls where neither dissolves; since praziquantel is neutral above about pH 3 alvarenga2025 R4, its lower recovery after pH 3.0 and 5.0 points to the polymer or the wetted particles rather than to the drug. The dose relative to the amorphous solubility at the final pH, which decided between colloid and crystals in Amorphous solubility and LLPS F23, was the same in all gastric arms here, so it cannot explain the differences between them. The trade-off of grades fits Crystallization from solution F44, where the HPMCAS chemistry that delayed posaconazole nucleation longest also limited release at low pH.)

Conditions and limits

Delamanid at 25% drug only in the gastric-pH grid, one 60-min acid stage, simple HCl and phosphate media without bile salts or food components, replicate numbers not stated, and a salt against free-base comparison confounded with the process (rotary evaporation against spray drying) nguyen2023c X8, X13. The basis of percent release in the acid stage is not stated nguyen2023c X13. Release values far above the amorphous solubility at pH 5.0 and 6.5 were not characterized (F8) nguyen2023c X9. For praziquantel the volume basis of first-stage percent release is not stated, several curves exceed 100%, and the 1.5 mg/mL aqueous curves are given only in the text alvarenga2025 X16, X1. The 2024 two-stage test ran about 50 min after the shift against the 30 min of the methods polyzois2024 X8.

Counterexamples and conflicts

The polymer ranking is not fixed: HPMCP dispersions released better than HPMCAS ones "in general", but after pH 5.0 HPMCP-55 (≈12.5%) ended below HPMCAS-LF (≈50%) nguyen2023c C1, X3. The worst gastric pH differed by form for the uncoated HPMCP-50 tablets: pH 3.0 for the edisylate, pH 5.0 for the free base and the chloride nguyen2023b X5. A gastric stage helped the free-base dispersions of 2022 but hurt the HPMCAS edisylate dispersions duong2022a R14, R24. For praziquantel with HPMC E5 LV the gastric pH hardly mattered, since that polymer dissolves at any pH and released about 70% at 1.5 mg/mL whatever the start alvarenga2025 C27. Bedaquiline–HPMCAS dispersions in the Release mechanism and LoC chapter ended at similar levels (≈19.5–25 µg/mL) after all three gastric pH values kaur2025 R12.

Transfer check

For an enteric-polymer dispersion of a weakly basic or fast-crystallizing drug, run the two-stage test with gastric stages at pH 1.6, 3.0 and 5.0 (fasted to fed) as well as the single stage at pH 6.5, since the single stage ranked HPMCP-50, HPMCP-55 and HPMCAS-LF alike (≈88–96%) nguyen2023c R11, C5. Measure drug and polymer solubility across the same pH range: the risk window is where neither dissolves nguyen2023c C15. Do not use the gastric supersaturation ratio to rank dispersions nguyen2023c C39. Measure polymer release alongside drug release, since dissolved polymer did not guarantee released drug nguyen2023c R12. For a neutral drug, still test more than one gastric pH with an enteric carrier alvarenga2025 R10.

History

Elkhabaz and co-workers (2019) found a two-stage test "essential" to see the effects of an acid stage on a posaconazole dispersion (F24, F26) elkhabaz2019a C54. Duong and co-workers (2022) found that an acid stage could raise or lower delamanid release and called for further studies of gastric pH variation duong2022a C63, C64, C65. Nguyen and co-workers (2023) were the first in the library to vary the gastric pH between 1.6, 3.0 and 5.0 across enteric polymer grades and drug forms, and the coating paper of the same year used the same grid to show that a coat removes the dependence (F27) nguyen2023c C59; nguyen2023b C26. Polyzois and co-workers (2024) found the HPMCAS acid-stage loss for praziquantel and asked for study of its pH sensitivity polyzois2024 C37, and Alvarenga and co-workers (2025) found it larger after pH 3.0 and 5.0 starts alvarenga2025 R10, R11.

F26

Topic 8Gastric stage and biorelevant media3 of 5

With crystals already present, a posaconazole dispersion held its amorphous solubility only while undissolved drug and droplets remained.

After 1 h in FaSSGF and transfer to FaSSIF, a 10% posaconazole–HPMCAS dispersion dosed at ten times the amorphous solubility held ≈22–24 µg/mL to 120 min, whereas a fifth of that dose reached ≈21 µg/mL but fell to ≈8 µg/mL by 120 min elkhabaz2019a R6, R12. SHG imaging had shown crystals in every dispersion before the transfer elkhabaz2019a R16.

weakWeak to moderate for the reservoir explanation, which was not measured; moderate for separating the fall of the concentration from the start of crystallization, since crystals were seen while the concentration held elkhabaz2019a K5, K6, X8.

near amorphous solubility, about 20 µg/mLafter the fallhigh dose200 µg/mL available≈22–24 µg/mL≈6–8one-fifth dose40 µg/mL available≈17–21 µg/mL≈8high dose, no acid stagedissolved directly in FaSSIFabout 2104080120160200time after transfer to FaSSIF, min

10% posaconazole–HPMCAS dispersion; crystals from the acid stage were present at transfer in the two-stage runs. elkhabaz2019a R6, R12, P6, P7, R2

For your drug

  1. Set the in vitro dose relative to the amorphous solubility at the intestinal pH and run at least two doses, since one dose cannot separate a reservoir effect from the crystal burden.
  2. Detect crystals at the start of the intestinal stage (SHG is crystal-specific); if they are present while the concentration holds, read the plateau as growth balanced by redissolution and do not take the time of the fall as an induction time.

elkhabaz2019a P6, C50, R16, C49

How it works and key numbers
  1. Both doses reached the amorphous solubility, so the extent of supersaturation "clearly cannot" explain the difference elkhabaz2019a C47.
  2. With crystals present at transfer, drug removed by crystal growth is replaced from undissolved dispersion and from nanodroplets, a reservoir used up sooner at the lower dose ("most likely") elkhabaz2019a C48.
  3. The concentration therefore falls when crystal growth outpaces the redissolution of amorphous material, not when crystallization starts elkhabaz2019a C49.
  4. Without an acid stage the supersaturation lasted longer, "presumably due to the initial absence of seeds" elkhabaz2019a C51.
Analogy. A buffer holds its pH while its reserve of conjugate base lasts; here undissolved amorphous drug and droplets play the part of the reserve, and the concentration falls only once that reserve is spent.
To feel the numbers. At the high dose about 200 − 20 = 180 µg/mL of drug sits outside the solution as undissolved solid or droplets; at a fifth of the dose only 40 − 20 = 20 µg/mL does, nine times less reserve against the same crystals.
200 vs 40 µg/mLposaconazole available after transfer, high against low dose (amorphous solubility about 20)elkhabaz2019a P6, P7, R2
≈22–24 µg/mL to 120 minhigh dose after the acid stage; the low dose fell to ≈8 µg/mL by 120 minelkhabaz2019a R6, R12
about 21 µg/mL at 180 minthe same dispersion dissolved directly in FaSSIF, without the acid stageelkhabaz2019a R6
Evidence: data, conditions and papers

Finding F26. With crystals already present, a posaconazole dispersion held its amorphous solubility only while undissolved amorphous drug and nanodroplets remained: a fifth of the dose reached the same level but lost it about an hour sooner, so the onset of desupersaturation did not mark the onset of crystallization

In short. After an hour in fasted gastric fluid and a shift to FaSSIF, a 10% posaconazole–HPMCAS dispersion dosed at 200 µg/mL (ten times the amorphous solubility of about 20 µg/mL) held ≈22–24 µg/mL to 120 min and fell to ≈6–8 µg/mL from 180 min, whereas a fifth of the dose reached ≈21 µg/mL but fell to ≈8 µg/mL by 120 min elkhabaz2019a R6, R12, R2. SHG had already shown crystals in every dispersion after 30 min in the acid stage elkhabaz2019a R16. Because both doses reached the amorphous solubility, the authors conclude that the extent of supersaturation "clearly cannot" explain the difference and propose ("most likely") a reservoir of undissolved dispersion and nanodroplets that replaces the drug removed by crystal growth elkhabaz2019a C47, C48. The onset of desupersaturation therefore "does not represent the onset of crystallization", and the dose of an in vitro test "must be chosen" for in vivo relevance and mechanistic insight elkhabaz2019a C49, C50.

Type. single-system observation (posaconazole–HPMCAS at 10% and 25% drug, two doses, two test sequences) Strength. to moderate for the reservoir explanation, which was not measured, and moderate for the separation of desupersaturation from crystallization, which rests on crystals seen by SHG at transfer while the concentration held elkhabaz2019a K5: weak to moderate, K6: moderate, X8.

How it was shown

Elkhabaz and co-workers (2019) held posaconazole–HPMCAS-MF dispersions for 60 min in FaSSGF and then added a FaSSIF concentrate at pH 6.5, so that 200 µg/mL drug was available, ten times the amorphous solubility of about 20 µg/mL; supernatants were analysed by HPLC elkhabaz2019a P6, P4, R2. A fifth of the dose was run the same way, both doses were also dispersed directly in FaSSIF, nanodroplets were sized by nanoparticle tracking, and crystals were imaged by SHG elkhabaz2019a P7, P8, P10.

What the data show

Both doses reached the amorphous solubility after transfer, but the low dose lost it about an hour sooner, although crystals were present from the acid stage elkhabaz2019a R6, R12, R16.

systemconditionsresultids
posaconazole–HPMCAS 10%, 200 µg/mL available after transferFaSSGF 60 min → FaSSIF pH 6.5, HPLC, 37 °C≈22–24 µg/mL to 120 min; ≈6–8 µg/mL from 180 minelkhabaz2019a R6
same, one-fifth of the dose (40 µg/mL after transfer)same≈17–21 µg/mL to 90 min; ≈8 µg/mL at 120 minelkhabaz2019a R12
all dispersions after 30 min in FaSSGFSHG imagingcrystals in every system before transferelkhabaz2019a R16
10% and 25% dispersions, two dosesnanoparticle tracking after transfer≈304–339 and ≈328 nm (high dose); ≈278–320 nm and fewer particles (low dose)elkhabaz2019a R13, R14
10% and 25% dispersions directly in FaSSIFsame analysisabout 21 µg/mL at 180 min; ≈22–23 µg/mL to 60 minelkhabaz2019a R6, R7
Fig. 13 of elkhabaz2019a: the 10% posaconazole–HPMCAS dispersion at the high and the low dose in the two-stage test
Fig. 13 · elkhabaz2019athe 10% posaconazole–HPMCAS dispersion at the high and the low dose in the two-stage test

Both doses reach about 20 µg/mL in FaSSIF; the low dose falls about an hour earlier than the high dose elkhabaz2019a R12, R6.

Why

The extent of supersaturation "clearly cannot" explain the dose effect, since both doses reached the amorphous solubility elkhabaz2019a C47. With crystals present at transfer, the authors propose that drug removed by crystal growth is replaced from undissolved dispersion and nanodroplets, a reservoir used up sooner at the lower dose elkhabaz2019a C48. The onset of desupersaturation then marks the time at which crystal growth outpaces redissolution of amorphous material, not the start of crystallization elkhabaz2019a C49. The longer supersaturation without an acid stage is "presumably due to the initial absence of seeds" elkhabaz2019a C51.

Limits and transfer

No seeding test was run, the reservoir was not measured over time, and micro-centrifuged supernatants may contain nanodroplets elkhabaz2019a X8, X3. Set the in vitro dose relative to the amorphous solubility at the intestinal pH, run at least two doses, and detect crystals at the start of the intestinal stage: if they are present while the concentration still holds, do not take the time of the fall as an induction time elkhabaz2019a P6, C50, R16, C49.

How it was shown

Elkhabaz and co-workers (2019) made posaconazole–HPMCAS-MF dispersions at 10, 25 and 50% drug by rotary evaporation and cryo-milling, crystal-free by polarized light and PXRD, and compared them with crushed Noxafil tablets elkhabaz2019a P1, R5, M2. In the two-stage test, 16 mg of drug was dispersed in 40 mL of FaSSGF (pH 1.6) for 60 min, then 40 mL of a double-strength FaSSIF concentrate was added and the pH set to 6.5, so that 200 µg/mL drug was available, ten times the amorphous solubility; samples were micro-centrifuged (14,800 rpm, 15 min) and the supernatant analysed by HPLC, at 37 °C and 300 rpm, n = 3 elkhabaz2019a P6. A low dose of 3.2 mg (80 µg/mL in the acid stage, 40 µg/mL after transfer) was run the same way, and both doses were also dispersed directly in FaSSIF elkhabaz2019a P6, P7. Supernatants 5 and 30 min after transfer were sized by nanoparticle tracking, and aliquots of a scaled-down two-stage run were imaged by SHG, which sees only crystals, and by two-photon excited UV fluorescence (TPE-UVF), which sees drug in any state elkhabaz2019a P8, P10, P11. The amorphous solubility, about 20 µg/mL, was the LLPS onset in FaSSIF with 20 µg/mL HPMCAS by extinction and fluorescence elkhabaz2019a P4, P5, R2, R3.

What the data show

High dose. After transfer the 10% dispersion gave ≈22–24 µg/mL from 5 to 120 min, ≈19 µg/mL at 150 min and ≈6–8 µg/mL from 180 min; the 25% dispersion ≈21–22 µg/mL to 30 min, ≈18 µg/mL at 60 min and ≈5–8 µg/mL from 90 min elkhabaz2019a R6, R7. Low dose. The 10% dispersion gave ≈21 µg/mL at 5 min, ≈17–20 µg/mL to 90 min and ≈8 µg/mL at 120 min (Fig. 13) elkhabaz2019a R12. The text reports the same earlier fall for the 25% dispersion, no notable change for the 50% dispersion and the tablet powder, and similar FaSSIF-only profiles at both doses; these profiles (Fig. S1) were not supplied elkhabaz2019a R11, C18. Crystals and droplets. SHG showed crystals in all systems after 30 min in FaSSGF and more of them after transfer elkhabaz2019a R16. Nanodroplets measured ≈304 and ≈339 nm (10%, 5 and 30 min) and ≈328 nm (25%) at the high dose and ≈278, ≈293 and ≈320 nm at the low dose, with fewer particles at the low dose and fewer 10% droplets at 30 than at 5 min elkhabaz2019a R13, R14, C19. The TPE-UVF signal of undissolved drug fell to about 0.01–0.03% within 30 min of transfer for the 10% and 25% dispersions elkhabaz2019a R19. Without the acid stage. Dissolved directly in FaSSIF, the 10% dispersion still held about 21 µg/mL at 180 min and the 25% one ≈22–23 µg/mL to 60 min elkhabaz2019a R6, R7.

papersystemmethod and conditionsresultids
elkhabaz2019aposaconazole–HPMCAS 10%, 200 µg/mL available after transferFaSSGF 60 min → FaSSIF pH 6.5, HPLC of supernatants, 37 °C≈22–24 µg/mL to 120 min; ≈6–8 µg/mL from 180 minR6
elkhabaz2019asame, one-fifth of the dose (40 µg/mL after transfer)same≈17–21 µg/mL to 90 min; ≈8 µg/mL at 120 minR12
elkhabaz2019a10% and 25% dispersions, two dosesnanoparticle tracking after transfer≈304–339 and ≈328 nm (high dose); ≈278–320 nm and fewer particles (low dose)R13, R14
elkhabaz2019aall dispersions after 30 min in FaSSGFSHG imagingcrystals in every system before transferR16
elkhabaz2019a10% and 25% dispersions directly in FaSSIFsame analysisabout 21 µg/mL at 180 min; ≈22–23 µg/mL to 60 minR6, R7
hate2019 (Bioperformance)tacrolimus products with crystal seedsabsorptive dissolution at several volumeslarger volumes and membrane loss lowered the maximum supersaturation, so seeds did not always cause crystallizationC46
purohit2018 (Bioperformance)tacrolimus capsules of differing crystallinitycompendial and smaller-volume non-sink teststhe more non-sink tests (100 and 40 mL) discriminated crystallinity betterC57

Figure

Fig. 13 of elkhabaz2019a: the 10% posaconazole–HPMCAS dispersion at the high and the low dose in the two-stage test
Fig. 13 · elkhabaz2019athe 10% posaconazole–HPMCAS dispersion at the high and the low dose in the two-stage test

Both doses reach about 20 µg/mL in FaSSIF; the low dose (orange) falls about an hour earlier than the high dose (blue) elkhabaz2019a R12, R6.

Why

The authors argue that the extent of supersaturation "clearly cannot" explain the dose effect, since both doses reached the amorphous solubility elkhabaz2019a C47. With crystals present at transfer in all dispersions, they propose that the drug removed by crystal growth is replaced from undissolved dispersion and from nanodroplets, a reservoir used up sooner at the lower dose, which "can be most likely be explained by a reservoir effect" elkhabaz2019a C48. From this they argue that the onset of desupersaturation marks the time at which crystal growth outpaces redissolution of amorphous material, not the time at which crystallization starts elkhabaz2019a C49. The longer supersaturation without an acid stage is "presumably due to the initial absence of seeds" elkhabaz2019a C51. No seeding test was run, the reservoir was not measured over time, and crystals were not imaged in the FaSSIF-only runs elkhabaz2019a X8. (synthesis: the account is the dissolving-dispersion form of Amorphous solubility and LLPS F8, where drug added above the amorphous solubility only adds drug-rich phase while the free drug stays at the limit, and of the indomethacin droplets that served as a reservoir after a pH rise (F21); the TPE-UVF signal of undissolved drug was small within 30 min of transfer at 10% drug elkhabaz2019a R19, so on the authors' account most of the reservoir would have been the droplets, which no measurement here quantified.) The paclitaxel–HPMCAS dispersion of F22 points the same way: with 18 wt% seeds it still reached the amorphous solubility, which the authors read as dissolution being much faster than growth que2018 R13, C47.

Conditions and limits

One drug, one polymer grade, one gastric residence time (60 min) and two doses elkhabaz2019a P6, P1. The low-dose and particle-count figures were not supplied, so the 25% result rests on the text elkhabaz2019a R11, R14. Durations are given on the total-time axis in the results and in FaSSIF time in the discussion elkhabaz2019a X1. HPLC supernatants after micro-centrifugation may contain nanodroplets, so values near and above the amorphous solubility may include droplet drug (F8) elkhabaz2019a X3. The FaSSIF-only control is under-specified and its medium differs from the two-stage medium elkhabaz2019a X10.

Counterexamples and conflicts

The 50% dispersion and the tablet powder showed no notable dose effect: the 50% dispersion fell within 30 min of transfer at either dose, which the authors attribute to its large crystal burden from the acid stage (F24) elkhabaz2019a R11, C43. In tacrolimus tests of the Bioperformance chapter the volume worked the other way: larger volumes gave a lower maximum supersaturation, and with membrane loss seeds did not always cause crystallization hate2019 C46. For praziquantel a higher dose gave a lower percentage: 30% HPMCAS-MF dispersions released completely at 667 µg/mL but about 94% at 1.5 mg/mL, a dose at about the amorphous solubility, and the R-praziquantel–HPMC dispersion lost dissolved drug clearly only at the higher dose (F29) polyzois2024 R8, R9; alvarenga2025 R6, R8. No paper in the library measured the size of an amorphous reservoir during desupersaturation.

Transfer check

Set the in vitro dose relative to the amorphous solubility at the intestinal pH (here ten times it) and run at least two doses, since a test at one dose cannot separate a reservoir effect from the crystal burden elkhabaz2019a P6, C50. Image or otherwise detect crystals at the start of the intestinal stage (SHG is crystal-specific): if they are present while the concentration still holds, read the plateau as growth balanced by redissolution, and do not take the time of the fall as an induction time elkhabaz2019a R16, C49. Test crystallinity effects in the more non-sink volumes, which discriminate better purohit2018 C57. Measure dissolved drug by a method that excludes droplets before comparing doses (F8).

History

Xie and co-workers (2017) found indomethacin droplets redissolving as a reservoir after a pH rise (F21) xie2017 C42. Elkhabaz and co-workers (2019) were the first in the library to use a reservoir of undissolved dispersion and nanodroplets to explain the timing of desupersaturation in a test where crystals were already present, and to warn that the onset of desupersaturation is not the onset of crystallization elkhabaz2019a C48, C49. In the Bioperformance chapter, absorptive tests of tacrolimus products with crystals found the outcome set by the supersaturation profile, which depends on the volume available hate2019 C49.

F27

Topic 8Gastric stage and biorelevant media4 of 5

An enteric coat kept gastric medium away from a delamanid–HPMCP tablet, so release after the gastric stage no longer depended on its pH.

Uncoated tablets released ≈82–96 µg/mL of 100 in a single stage, but anywhere from ≈0.3 to ≈93 µg/mL after 60 min at pH 1.6, 3.0 or 5.0 nguyen2023b R1, R2. With a 14–16% Acryl-EZE II coat they released less than 0.5% in every gastric stage and ≈76–86 µg/mL after transfer to pH 6.5 nguyen2023b P3, R10.

moderateModerate to strong for the release of coated tablets across gastric pH; moderate for the coat-integrity window, judged visually on one salt form; weak to moderate for surface crystallization as the cause of the uncoated losses, imaged on films only nguyen2023b K5, K4, K6, X7, X12.

uncoated, after pH 1.6, 3.0 and 5.0coated, after pH 1.6, 3.0 and 5.0free base≈6.5–62≈76–83chloride≈0.3–86≈78–84edisylate≈41–93≈82–86020406080100delamanid released after the gastric stage, µg/mL of 100

25% delamanid in HPMCP-50 tablets; uncoated in a single stage ≈82–96. The two arms used different transfer protocols. nguyen2023b R2, R10, R1, X6

Coat intact
HCl pH 1.6 · 15 hpH 3.0 · more than 17 hFEDGAS pH 4.5 · more than 17 h
Coat failed or dissolved
acetate pH 4.5 · ≈130 minphosphate pH 5.0 · ≈150 minpH 6.0 · 10–30 min

Coated edisylate tablets soaked at 37 °C and photographed; food components in FEDGAS prolonged the coat at pH 4.5. nguyen2023b R7

For your drug

  1. Before coating an enteric-polymer dispersion of a crystallizing weak base, run two-stage tests at gastric pH 1.6, 3.0 and 5.0 and compare them with the single stage: a large spread after the shift is the penalty that a coat can remove.
  2. Test coat integrity across pH 4.5–5.5 for the fed gastric residence of 2–5 h, in buffer and in a fed gastric medium, accept a lag of 10–20 min before release, and confirm that release after the shift reaches the single-stage level.

nguyen2023b R1, R2, C19, R7, C25, X4

How it works and key numbers
  1. At gastric pH HPMCP is unionized and insoluble, yet drug leaves the dispersion; the unionized polymer inhibits crystallization poorly and drug at the surface is the most mobile, so crystals form on the surface ("can be attributed") nguyen2023b C35, C37.
  2. When the pH rises and HPMCP dissolves, these crystals are released and "presumably" seed crystallization of the supersaturated drug, by an amount that depends on the gastric pH nguyen2023b C38.
  3. The coat keeps the medium away from the dispersion during the gastric stage, so no crystals form, and at pH 6.5 coat and HPMCP dissolve after a 10–20 min lag nguyen2023b C43, C46, C25.
  4. Eudragit L 100-55 resists dissolution below pH 5.5, but in buffer at pH 4.5–5.0 the coat failed after about 2–2.5 h, while food components prolonged it ("Interestingly") nguyen2023b C23, C19, R7, C45.
≈0.3–93 µg/mLuncoated release after 60 min at pH 1.6, 3.0 or 5.0, against ≈82–96 in a single stagenguyen2023b R2, R1
≈76–86 µg/mLcoated tablets after every gastric pH, with below 0.5% released in acidnguyen2023b R10
≈130–150 mincoat failure at pH 4.5–5.0 in buffer; more than 17 h in a fed gastric medium at pH 4.5nguyen2023b R7
Evidence: data, conditions and papers

Finding F27. An enteric coat on the tablet kept gastric medium away from a delamanid–HPMCP dispersion and made release after a gastric stage at pH 1.6, 3.0 or 5.0 high and nearly independent of that pH; the coat failed after about 2–2.5 h at pH 4.5–5.0 in buffer, lasted longer with fat, and dissolved within minutes at pH 6.0

In short. Uncoated tablets of 25% delamanid in HPMCP-50 released about 82–96 µg/mL of 100 in a single stage at pH 5.8 or 6.5, but anywhere from ≈0.3 to ≈93 µg/mL after 60 min at pH 1.6, 3.0 or 5.0 and a shift to pH 6.5, depending on gastric pH and drug form nguyen2023b R1, R2. With a 14–16% Acryl-EZE II coat they released less than 0.5% in every gastric stage and ≈76–86 µg/mL after transfer, a spread of about 4–8 µg/mL within a form against ≈52–86 µg/mL uncoated nguyen2023b R10, R2. A 2 µm Eudragit L 100-55 layer prevented the surface crystals that formed on uncoated films at pH 3.0 nguyen2023b R6. The coat stayed intact for 15 to more than 17 h at pH 1.6 and 3.0, failed after about 130–150 min at pH 4.5–5.0 in buffer but lasted more than 17 h in a fed gastric medium at pH 4.5, and dissolved within 10–15 min at pH 6.0 nguyen2023b R7. The authors call release "remarkably improved and less variable" and conclude that the deleterious release "could be remediated" by an enteric coat nguyen2023b C43, C2.

Type. single-system observation (delamanid free base, chloride and edisylate in HPMCP-50, one coat) Strength. to strong for the release of coated tablets across gastric pH, moderate for the coat-integrity window (edisylate tablets only, visual end point), weak to moderate for surface crystallization as the cause of the uncoated losses, which was imaged on films only nguyen2023b K5: moderate to strong, K4: moderate, K6: weak to moderate, X7, X12.

How it was shown

Nguyen and co-workers (2023) spray-dried delamanid with HPMCP P-50 at 25% drug as the free base and as chloride and edisylate salts, pressed tablets and pan-coated them with Acryl-EZE II (Eudragit L 100-55, which dissolves above pH 5.5) to 14–16% weight gain nguyen2023b P1, P2, P3, M11. Uncoated and coated tablets were released at pH 6.5 after 60 min at pH 1.6, 3.0 or 5.0, coated edisylate tablets were soaked in gastric media of pH 1.6–6.0, and films with and without a 2 µm Eudragit layer were examined after 1 h at pH 3.0 nguyen2023b P10, P11, P12, P6, P4, P5.

What the data show

The coat removed most of the dependence of release on gastric pH, within the pH window in which it stayed intact nguyen2023b R2, R10, R7.

systemconditionsresultids
uncoated tablets, free base / chloride / edisylatesingle stage pH 5.8 and 6.5≈82–96 µg/mL of 100nguyen2023b R1
same60 min at pH 1.6 / 3.0 / 5.0, then pH 6.5≈62 / ≈33.5 / ≈6.5; ≈86 / ≈54 / ≈0.3; ≈93 / ≈41 / ≈82 µg/mLnguyen2023b R2
coated tablets, three formsgastric stage at pH 1.6 / 3.0 / 5.0, then fresh pH 6.5below 0.5% in acid; ≈76–86 µg/mL at 120 minnguyen2023b R10
coated edisylate tabletssoak in gastric media, 37 °Cmore than 17 h (pH 3.0); ≈130 min (acetate pH 4.5); ≈150 min (phosphate pH 5.0); more than 17 h (FEDGAS pH 4.5); 10–15 min (pH 6.0)nguyen2023b R7
films with and without 2 µm Eudragit L 100-55pH 3.0, 1 h, PLM, SEMcrystals on all uncoated films; none under the layernguyen2023b R3, R6
Fig. 5 of nguyen2023b: release of coated delamanid tablets in single-stage and two-stage tests for the three drug forms
Fig. 5 · nguyen2023brelease of coated delamanid tablets in single-stage and two-stage tests for the three drug forms

A flat line through every gastric stage, then about 76–86 µg/mL after the transfer at 60 min for all three forms nguyen2023b R10.

Why

At gastric pH HPMCP is unionized and insoluble, yet drug leaves the dispersion, and the unionized polymer inhibits crystallization poorly while drug at the surface is the most mobile, so crystals form on the surface ("can be attributed") nguyen2023b C35, C37. When HPMCP dissolves, these crystals "presumably" seed crystallization of the supersaturated drug nguyen2023b C38. The coat keeps the medium away from the dispersion during the gastric stage, and at pH 6.5 coat and HPMCP dissolve after a 10–20 min lag nguyen2023b C43, C46, C25. Food components prolonged the coat's integrity ("Interestingly") nguyen2023b C45.

Limits and transfer

Integrity was judged from photographs of edisylate tablets only, and coated and uncoated tablets were tested with different two-stage protocols nguyen2023b X12, X6. Before coating, run two-stage tests at gastric pH 1.6, 3.0 and 5.0 against the single stage, and test coat integrity across pH 4.5–5.5 for the fed gastric residence of 2–5 h, in buffer and in a fed gastric medium nguyen2023b R1, R2, C19, R7.

How it was shown

Nguyen and co-workers (2023), in the coating paper, spray-dried delamanid with HPMCP P-50 at 25% drug as the free base and as in situ chloride and edisylate salts, pressed tablets holding 50 mg drug in a 500 mg core, and pan-coated them with an aqueous Acryl-EZE II dispersion (Eudragit L 100-55, which dissolves above pH 5.5) to 14–16% weight gain nguyen2023b P1, P2, P3, M11. Spin-coated dispersion films, part covered by about 2 µm of Eudragit L 100-55, were immersed for 1 h at pH 3.0 and examined by PLM and SEM nguyen2023b P4, P5. Coated edisylate tablets were stirred overnight in 500 mL of HCl pH 1.6, phosphate pH 3.0 and 5.0, acetate pH 3.0, 4.5 and 6.0 and FEDGAS pH 3.0, 4.5 and 6.0 and photographed, and a USP acid-stage tolerance test (pH 4.5–5, 2 h) was run nguyen2023b P6, P7, P15. All release tests used USP apparatus II, 500 mL, 37 °C, 150 rpm and one 50 mg tablet (100 µg/mL = complete): uncoated tablets spent 60 min in gastric buffer before concentrated phosphate raised the pH to 6.5 in the same vessel for 30 min, and coated tablets were moved after 60 min to fresh pH 6.5 buffer for 60 min nguyen2023b P8, P10, P11, P12. The uncoated free-base and edisylate values come from the gastric-pH paper of the same year; the chloride values are new nguyen2023b X10.

What the data show

Uncoated. Single-stage release at pH 5.8 was ≈88, ≈93 and ≈93 µg/mL (free base, chloride, edisylate) and at pH 6.5 ≈82, ≈83 and ≈96 nguyen2023b R1. In the gastric stage the tablets released about 30–41 µg/mL at pH 1.6, about 1–2 µg/mL at pH 3.0, and at pH 5.0 about 7, 0.4 and 83 µg/mL nguyen2023b R2. Thirty minutes after the shift they gave ≈62, ≈86 and ≈93 µg/mL after pH 1.6, ≈33.5, ≈54 and ≈41 after pH 3.0, and ≈6.5, ≈0.3 and ≈82 after pH 5.0 nguyen2023b R2. Films. Star- and needle-shaped crystals covered the uncoated films of all three forms after 1 h at pH 3.0, and areas under the Eudragit layer stayed featureless nguyen2023b R3, R4, R6. Coat integrity. Coated tablets did not disintegrate for more than 17 h in acetate pH 3.0 and FEDGAS pH 3.0, stayed intact for 15 h in HCl pH 1.6 and phosphate pH 3.0, passed the USP acid-stage tolerance test with less than 0.2% release in 2 h, but failed after around 130 min in acetate pH 4.5 and 150 min in phosphate pH 5.0; at pH 6.0 the coat dissolved within 10–15 min in acetate and within about 20–30 min in FEDGAS, and in FEDGAS pH 4.5 it lasted more than 17 h nguyen2023b R7, R8. After the coat failed, drug leached (below 5 µg/mL) and/or crystallized and release after transfer was clearly lower (SI, not supplied) nguyen2023b R9, C22. Coated, release. In single-stage tests release started after about 11–20 min, the time the coat took to dissolve, and reached ≈81.5–92 µg/mL at 60 min nguyen2023b R10, R11, C25. In two-stage tests the gastric stage stayed below 0.5 µg/mL at all three pH values, and at 120 min the free base reached ≈83, ≈84 and ≈76 µg/mL (after pH 1.6, 3.0, 5.0), the chloride ≈84, ≈82 and ≈78, and the edisylate ≈86, ≈82 and ≈85 nguyen2023b R10, C26.

papersystemmethod and conditionsresultids
nguyen2023buncoated delamanid–HPMCP-50 tablets, free base / chloride / edisylatesingle stage pH 5.8 and 6.5≈82–96 µg/mL of 100R1
nguyen2023bsame60 min at pH 1.6 / 3.0 / 5.0, then pH 6.5 in the same vessel≈62 / ≈33.5 / ≈6.5 (free base); ≈86 / ≈54 / ≈0.3 (chloride); ≈93 / ≈41 / ≈82 µg/mL (edisylate)R2
nguyen2023buncoated films with and without 2 µm Eudragit L 100-55pH 3.0, 1 h, PLM, SEMcrystals on all uncoated films; none under the layerR3, R6
nguyen2023bcoated edisylate tabletssoak in gastric media, 37 °Cmore than 17 h (pH 3.0); ≈130 min (acetate pH 4.5); ≈150 min (phosphate pH 5.0); more than 17 h (FEDGAS pH 4.5); 10–15 min (pH 6.0)R7
nguyen2023bcoated tablets, three formsgastric stage at pH 1.6 / 3.0 / 5.0, then fresh pH 6.5below 0.5% in acid; ≈76–86 µg/mL at 120 minR10
nguyen2023cuncoated 25% salt dispersions, five enteric grades60 min at pH 1.6 / 3.0 / 5.0, then pH 6.5final release from ≈0 to ≈101%, by gastric pH and grade (F25)R11
moseson2023 (ASD process)posaconazole–HPMCAS particles at 50% drug, with and without an Al2O3 nanocoatingrelease at pH 6.5, SHG of the residual solidthe coating delayed the onset of matrix crystallization and raised the supersaturation reached in one set of samplesC40, C28
nguyen2023a (Bioperformance)pretomanid–HPMCAS dispersions, fed statepharmacokinetics, in vitro testsmatrix crystallization "likely" exacerbated by delayed release in the fed stateC84

Figure

Fig. 5 of nguyen2023b: release of coated delamanid tablets in single-stage and two-stage tests for the three drug forms
Fig. 5 · nguyen2023brelease of coated delamanid tablets in single-stage and two-stage tests for the three drug forms

A flat line through every gastric stage, then about 76–86 µg/mL after the transfer at 60 min (dashed line) for the free base (A), chloride (B) and edisylate (C) nguyen2023b R10.

Fig. 4 of nguyen2023b: coated tablets in acetate buffer and FEDGAS at pH 3.0, 4.5 and 6.0
Fig. 4 · nguyen2023bcoated tablets in acetate buffer and FEDGAS at pH 3.0, 4.5 and 6.0

Intact for more than 17 h at pH 3.0; failed by 130 min at pH 4.5 in buffer but intact for more than 17 h in FEDGAS; gone by 10 min at pH 6.0 in buffer and by 30 min in FEDGAS nguyen2023b R7.

Why

At gastric pH HPMCP is unionized and insoluble, yet drug leaves the dispersion because it is molecularly dispersed in the polymer, and the unionized polymer inhibits crystallization poorly while drug at the surface is the most mobile, so crystals form on the surface ("can be attributed") nguyen2023b C35, C37. When the pH rises and HPMCP dissolves, these crystals are released and "presumably" seed crystallization of the supersaturated drug, which lowers release by an amount that depends on the gastric pH nguyen2023b C38. The coat keeps the medium away from the dispersion during the gastric stage, so no crystals form, and at pH 6.5 coat and HPMCP dissolve after a 10–20 min lag, giving release close to the single stage nguyen2023b C43, C46, C25. The coat's integrity sets the switch: Eudragit L 100-55 resists dissolution below pH 5.5, survived the 2 h acid stage at pH 4.5–5.0 but not much longer in buffer, and food components prolonged it ("Interestingly"), which the authors relate to fat, carbohydrates and bile salts changing viscosity and water diffusion, not measured here nguyen2023b C23, C45, C24. The gastric pH 30 min after a meal is expected to be 6–6.5, where the coat dissolves, and food prolongs gastric residence to 2–5 h nguyen2023b R22, C19. (synthesis: the dispersion polymer and the coat do different jobs; HPMCP inside the dispersion holds back most of the drug in acid but lets its surface crystallize (F24), in line with the loss of inhibition by carboxylated cellulose esters at low pH (Crystallization from solution F11) and the faster crystallization of free surfaces (Crystallization tendency F21), whereas the coat around the tablet keeps the acid out; the coat therefore removes the gastric penalty rather than adding to the single-stage release, against which coated two-stage values were up to about 15 µg/mL lower nguyen2023b X4.)

Conditions and limits

One drug, one polymer, one drug loading (25%) and one coat level; coat integrity was tested on edisylate tablets only and judged from photographs; replicate numbers are not stated anywhere nguyen2023b P3, X12, X13. Coated and uncoated tablets were tested with different two-stage protocols (in-vessel shift for 30 min against transfer to fresh medium for 60 min), so their values compare only approximately nguyen2023b X6. Crystals were imaged only on films at pH 3.0, not on tablets, at other gastric pH values or after coat failure nguyen2023b X7. Two coated arms stayed just under the stated 80 µg/mL nguyen2023b X3. The data on coat failure, coated Deltyba and acetate pH 6.0 are in the SI, which was not supplied nguyen2023b R9, R12, R11.

Counterexamples and conflicts

The uncoated edisylate tablet showed no gastric penalty at pH 5.0, where it released ≈83 µg/mL in the gastric stage and stayed at ≈82, which the paper does not explain nguyen2023b R2, X11; in the gastric-pH paper the HPMCP-50 salt dispersion behaved the same way at pH 5.0 (F25) nguyen2023c R11. Coating the marketed Deltyba narrowed its pH differences but gave much lower overall release nguyen2023b R12, C27. For pretomanid–HPMCAS dispersions in the Bioperformance chapter, delayed release in the fed state was "likely" to make matrix crystallization worse, so a coat that delays release may shift the risk to a longer residence of the dispersion nguyen2023a C84. In the ASD process chapter an Al2O3 nanocoating of posaconazole–HPMCAS particles delayed matrix crystallization during release at pH 6.5, a coating of the particle rather than the tablet moseson2023 C40.

Transfer check

Before coating an enteric-polymer dispersion of a crystallizing weak base, run two-stage tests at gastric pH 1.6, 3.0 and 5.0 and compare them with the single stage: a large spread after the shift is the penalty the coat can remove nguyen2023b R1, R2. Test coat integrity across pH 4.5–5.5 for the fed gastric residence (2–5 h), in buffer and in a fed gastric medium, since the coat failed after about 2–2.5 h in buffer nguyen2023b C19, R7. Accept a lag of 10–20 min before release and check that release after the shift reaches the single-stage level nguyen2023b C25, X4. Confirm that no crystals form under an intact coat, as on the coated films nguyen2023b R6.

History

An enteric coat had kept a niclosamide–copovidone tablet from crystallizing in acid (cited), but no dispersion made with an enteric polymer had been coated nguyen2023b R21, C10. The gastric-pH paper of 2023 found delamanid surface crystallization in acid and named limiting contact with low pH, for example by an enteric coating, as "may be important" nguyen2023c C61. The coating paper then tested this and was the first in the library to coat a tablet of an enteric-polymer dispersion nguyen2023b C12, C2. In the ASD process chapter, atomic-layer coatings of amorphous powders delayed surface crystallization on storage, and an Al2O3 nanocoating of posaconazole particles delayed matrix crystallization during release moseson2022a R11; moseson2023 C40.

Other chaptersbuilds on D F11
F28

Topic 8Gastric stage and biorelevant media5 of 5

Fed intestinal fluid promoted praziquantel crystallization and lowered release, whereas food components raised delamanid solubility and release.

In FeSSIF-V2, 30% praziquantel dispersions released ≈68–80% at 0.667 mg/mL and about 34–52% at 1.5 mg/mL, against ≈93–102% in fasted fluid, and HPMC residues held crystals alvarenga2025 R16, R18, R12, R22, R27. Delamanid solubility rose from 0.52 µg/mL in FaSSIF V1 to 57.97 µg/mL in a fed gastric medium at pH 3.0, and the marketed tablet released ≈77 against ≈31–37 µg/mL of 100 in fed against fasted intestinal fluid nguyen2023b R13, R14.

moderateModerate: the praziquantel loss is triplicate and shown by PLM and PXRD for HPMC, but by PXRD only for HPMCAS; the delamanid solubility method is not described, and mechanisms were not measured in either paper alvarenga2025 K3, X7; nguyen2023b K7, K8, X8.

30% praziquantel dispersions: released in single-stage tests, %PBS pH 6.5, HPMCAS0.667 mg/mL≈100–104FaSSIF, both polymers0.667 mg/mL≈93–102FeSSIF-V2, both polymers0.667 mg/mL≈68–80FeSSIF-V2, both polymers1.5 mg/mLabout 34–52

HPMCAS-MF and HPMC E5 LV dispersions; bars drawn at the top of each range. alvarenga2025 R6, R12, R16, R18

Crystalline delamanid solubility, µg/mL (log scale)FaSSIF V10.52FeSSIF V22.30FEDGAS pH 4.513.10FEDGAS pH 3.057.97

FEDGAS is a high-fat fed gastric medium; the authors put the gain at about 650- and 100-fold over the corresponding buffers. nguyen2023b R13, C28

For your drug

  1. Measure amorphous and crystalline solubility in fasted and fed media: a large gain predicts better fed release from solubilization, a small one leaves the fed medium to act on crystallization.
  2. Release the dispersion in FeSSIF-V2 at the intended dose and look for crystals by PLM and PXRD, since HPMCAS, the better inhibitor in buffer and fasted fluid, lost much of its effect there.

nguyen2023b R13; alvarenga2025 R1, R18, C29

How it works and key numbers
  1. The higher bile salt and lecithin content of FeSSIF-V2 "promoted crystallization" of praziquantel, which HPMCAS could not inhibit as well as in buffer alvarenga2025 C29.
  2. (synthesis) The praziquantel solubility gain in FeSSIF-V2 is modest (amorphous 1.17 → 1.74 mg/mL for the racemate), so the promotion of crystallization dominated alvarenga2025 R1.
  3. For delamanid the much higher solubility in fed media "likely accounts" for the better release of the marketed tablet and mitigates the effect of any crystallization nguyen2023b C29.
  4. Delamanid dispersions released the same in FaSSIF as in buffer, although the amorphous solubility was about ten times higher there (7.93 against 0.76 µg/mL) duong2022a R13, R1.
  5. Nucleation and growth were not measured in these media for either drug alvarenga2025 X9; nguyen2023b X8.
≈68–80% vs ≈93–102%praziquantel released at 0.667 mg/mL in FeSSIF-V2 against FaSSIFalvarenga2025 R16, R12
0.52 → 57.97 µg/mLdelamanid solubility in FaSSIF V1 against FEDGAS at pH 3.0nguyen2023b R13
≈77 vs ≈31–37 µg/mLmarketed delamanid tablet in FeSSIF V2 against FaSSIF V1 (of 100)nguyen2023b R14
Evidence: data, conditions and papers

Finding F28. Biorelevant media changed release in both directions: fed intestinal fluid promoted praziquantel crystallization with HPMCAS and HPMC and lowered release to about 34–52% at 1.5 mg/mL, whereas food components raised delamanid solubility up to several hundredfold and the release of the marketed tablet; fasted intestinal fluid changed little

In short. In single-stage FeSSIF-V2, 30% praziquantel dispersions released about 68–80% at 0.667 mg/mL and about 34–52% at 1.5 mg/mL with either polymer, against ≈100–104% (HPMCAS) in PBS pH 6.5 and ≈93–102% in FaSSIF at 0.667 mg/mL; HPMC residues gave birefringent crystals from 5 min and clear PZQ PXRD peaks, HPMCAS residues small peaks or none alvarenga2025 R16, R18, R6, R12, R22, R27, R28. The authors conclude that the higher bile salt and lecithin content of FeSSIF-V2 "promoted crystallization" alvarenga2025 C29. For delamanid, solubility rose from 0.52 µg/mL in FaSSIF V1 to 2.30 µg/mL in FeSSIF V2 and to 13.10 and 57.97 µg/mL in a fed gastric medium (FEDGAS) at pH 4.5 and 3.0, and the marketed Deltyba released ≈77 against ≈37 µg/mL of 100 in FeSSIF V2 against FaSSIF V1, which the authors say the higher solubility "likely accounts" for; coated tablets released ≈96 µg/mL in both media nguyen2023b R13, R14, C29, R16. Delamanid dispersions released the same in FaSSIF as in buffer, although the amorphous solubility was ten times higher (7.93 against 0.76 µg/mL) duong2022a R13, R1.

Type. observation in 3 drugs (praziquantel with HPMCAS-MF and HPMC E5 LV; delamanid dispersions, the marketed tablet and coated tablets; posaconazole), against nucleation and solubility studies in biorelevant media Strength. for the fed-medium loss of praziquantel release, which is triplicate and shown by PLM and PXRD for HPMC but by PXRD only for HPMCAS; moderate for the solubility-driven gain of the delamanid tablet, whose solubility method is not described; mechanisms not measured in either paper alvarenga2025 K3: moderate, X7, X10; nguyen2023b K7: moderate, K8: moderate, X8.

How it was shown

Alvarenga and co-workers (2025) measured the amorphous and crystalline solubility of racemic and (R)-praziquantel in nine media, and released 30% dispersions with HPMCAS-MF or HPMC E5 LV in PBS pH 6.5, FaSSIF or FeSSIF-V2 at 0.667 or 1.5 mg/mL, with PLM of aliquots and PXRD of residues alvarenga2025 P7, P8, P9, P6, P5. Nguyen and co-workers (2023) measured delamanid solubility in buffers, FaSSIF V1, FeSSIF V2 and a fed gastric medium (FEDGAS), and released the marketed Deltyba and coated tablets in these media nguyen2023b P13, P15, P12.

What the data show

The fed intestinal medium lowered praziquantel release, while food components raised delamanid solubility and the release of the marketed tablet alvarenga2025 R16, R18; nguyen2023b R13, R14.

systemconditionsresultids
praziquantel 30% HPMCAS-MF and HPMC, 0.667 mg/mLPBS pH 6.5; FaSSIF; FeSSIF-V2≈100–104 (HPMCAS) and ≈82–84% (HPMC); ≈93–102%; ≈68–80%alvarenga2025 R6, R12, R16
same, 1.5 mg/mLFeSSIF-V2≈42–52% (HPMCAS), ≈48% (racemic HPMC), (R)-PZQ–HPMC ≈47 → ≈34%alvarenga2025 R18
residues after fed mediaPLM, PXRDHPMC: crystals from 5 min, clear PZQ peaks; HPMCAS: no birefringence, small peaks or halosalvarenga2025 R22, R27, R28
crystalline delamanidequilibrium solubility0.52 (FaSSIF V1), 2.30 (FeSSIF V2), 13.10 (FEDGAS 4.5), 57.97 µg/mL (FEDGAS 3.0)nguyen2023b R13
Deltyba tablet; coated edisylate tabletsFaSSIF V1 against FeSSIF V2, 120 min≈31–37 against ≈77 µg/mL of 100; ≈96 in bothnguyen2023b R14, R16
delamanid dispersionstablets in biorelevant media against buffersame release; amorphous solubility 7.93 against 0.76 µg/mLduong2022a R13, R1
Fig. 4 of alvarenga2025: praziquantel dispersions in FeSSIF-V2 at 0.667 and 1.5 mg/mL, single stage and after acetate pH 4.5
Fig. 4 · alvarenga2025praziquantel dispersions in FeSSIF-V2 at 0.667 and 1.5 mg/mL, single stage and after acetate pH 4.5

Single-stage FeSSIF-V2 reaches at most about 80% and 55%; after the switch from pH 4.5 the HPMC dispersions fall and the HPMCAS dispersions rise only to about 60% and 30% alvarenga2025 R16, R17, R18, R19.

Why

For praziquantel the higher bile salt and lecithin content of FeSSIF-V2 "promoted crystallization" that HPMCAS could not inhibit as well as in buffer alvarenga2025 C29. Because the solubility gain there is modest, the positive food effect of praziquantel "could depend on factors other than" solubility alvarenga2025 C8. For delamanid the much higher solubility in fed media "likely accounts" for the better release of Deltyba nguyen2023b C29. Nucleation and growth were not measured in any of these media alvarenga2025 X9; nguyen2023b X8.

Limits and transfer

HPMCAS crystals in FeSSIF-V2 rest on PXRD only, the delamanid solubility method is not described, and neither paper measured free drug or flux in the biorelevant media alvarenga2025 X7; nguyen2023b X8. Measure amorphous and crystalline solubility in fasted and fed media: a large gain (delamanid) predicts better fed release, while a small one (praziquantel) leaves the fed medium to act on crystallization, which should be checked by PLM and PXRD after release in FeSSIF-V2 nguyen2023b R13; alvarenga2025 R1, R18, C29.

How it was shown

Alvarenga and co-workers (2025) measured the amorphous solubility of racemic and (R)-praziquantel by light-scattering onset and the crystalline solubility by shake flask in nine media, among them FaSSGF, FaSSIF (3 mM taurocholate, 0.75 mM phospholipid) and FeSSIF-V2 (10 mM taurocholate, 2 mM lecithin, 5 mM glycerol monooleate, 0.8 mM sodium oleate, maleate pH 5.8) alvarenga2025 P7, P8, P2. They released 30% dispersions with HPMCAS-MF or HPMC E5 LV for 2 h in PBS pH 6.5, FaSSIF or FeSSIF-V2 at 0.667 or 1.5 mg/mL, and in two-stage tests from FaSSGF into FaSSIF and from acetate pH 4.5 into FeSSIF-V2, with in situ UV, PLM of aliquots and PXRD of residues alvarenga2025 P9, P11, P12, P6, P5. Nguyen and co-workers (2023), in the coating paper, reported delamanid solubility in buffers, FaSSIF V1, FeSSIF V2 and FEDGAS (a high-fat fed gastric medium) at pH 3.0 and 4.5, and released the marketed Deltyba and coated edisylate tablets in these media, including 17 h in FEDGAS before FeSSIF V2 nguyen2023b P13, P15, P12. Duong and co-workers (2022) measured delamanid solubilities in FaSSGF, FaSSIF V1, FaSSIF V2 and PBS pH 6.5 and compared tablet release in biorelevant media and in buffer duong2022a P1, P2, R13. Elkhabaz and co-workers (2019) located the posaconazole LLPS onset in FaSSIF and in plain buffer elkhabaz2019a P4, P5.

What the data show

Praziquantel solubilities. Amorphous solubility was 1.17 (racemate) and 1.39 mg/mL ((R)-PZQ) in PBS pH 6.5, 1.49 and 1.67 in FaSSIF and 1.74 and 1.70 in FeSSIF-V2; crystalline solubility was highest in FeSSIF-V2 (0.31 and 0.43 mg/mL), a modest gain that the authors read as limited interaction with micelles ("suggests"); the amorphous-to-crystalline ratio was 5.6–7.7 for the racemate and 4.0–5.8 for (R)-PZQ across the nine media alvarenga2025 R1, C6, E1. Fasted fluid. In FaSSIF all dispersions released ≈93–102% within about 30 min at 0.667 mg/mL; at 1.5 mg/mL HPMCAS dispersions released more than 85% within 60 min, whereas HPMC dispersions peaked at 82% and 75% and then dropped by 30%; from FaSSGF into FaSSIF, HPMCAS dispersions reached ≈98–100% alvarenga2025 R12, R14, R13. Fed fluid. In single-stage FeSSIF-V2 release at 120 min was ≈68–80% at 0.667 mg/mL and ≈42–52% (HPMCAS) and ≈48% (racemic HPMC) at 1.5 mg/mL, while (R)-PZQ–HPMC peaked at about 47% and fell to about 34% alvarenga2025 R16, R18. In the fed two-stage test HPMC dispersions released ≈103% or ≈69–74% at pH 4.5 and fell after the switch to ≈79–83% or ≈30–36%, while HPMCAS dispersions rose from ≈12–22% or ≈13–16% to ≈60–63% or ≈26–30% (0.667 and 1.5 mg/mL) alvarenga2025 R17, R19. With HPMC, PLM showed birefringent crystals from 5 min in FeSSIF-V2 and PXRD clear PZQ peaks; with HPMCAS no particle was birefringent, PXRD showed small peaks after the two-stage test and halos after the single stage alvarenga2025 R22, R27, R28. Delamanid. Solubility in buffers followed the Henderson–Hasselbalch curve for a pKa of 4.3, about 10.3 µg/mL in HCl pH 1.6 and below 0.02 µg/mL above pH 5.5 nguyen2023b R13, R18, E1; it was 0.52 ± 0.12 (FaSSIF V1), 2.30 ± 0.31 (FeSSIF V2), 13.10 ± 2.32 (FEDGAS pH 4.5) and 57.97 ± 0.64 µg/mL (FEDGAS pH 3.0), which the authors put at approximately 650- and 100-fold the corresponding buffers for FEDGAS pH 4.5 and the fed intestinal medium nguyen2023b R13, C28. Deltyba released ≈77 µg/mL at 120 min in FeSSIF V2 against a near plateau of ≈31–37 µg/mL in FaSSIF V1, and after a buffer stage at fed gastric pH it crystallized in fed media (SI) nguyen2023b R14, R15, C31. Coated edisylate tablets released ≈96 µg/mL by 60 min in both FaSSIF V1 and FeSSIF V2, and ≈86–87 µg/mL after 17 h in FEDGAS and transfer to FeSSIF V2 nguyen2023b R16, R17. In 2022, amorphous delamanid solubility was 69.9 (FaSSGF), 7.93 (FaSSIF V1), 3.11 (FaSSIF V2) and 0.76 µg/mL (PBS pH 6.5), and tablet release was the same in FaSSIF as in buffer duong2022a R1, R13, C15. Posaconazole. The LLPS onset was about 20 µg/mL in FaSSIF with 20 µg/mL HPMCAS and 8 µg/mL in plain buffer pH 6.5 elkhabaz2019a R2, R4.

papersystemmethod and conditionsresultids
alvarenga2025praziquantel 30% HPMCAS-MF and HPMC, 0.667 mg/mLsingle stage: PBS pH 6.5; FaSSIF; FeSSIF-V2, 37 °C≈100–104 (HPMCAS) and ≈82–84% (HPMC); ≈93–102%; ≈68–80%R6, R12, R16
alvarenga2025same, 1.5 mg/mLFeSSIF-V2, single stage≈42–52% (HPMCAS), ≈48% (racemic HPMC), (R)-PZQ–HPMC ≈47 → ≈34%R18
alvarenga2025sameacetate pH 4.5 → FeSSIF-V2HPMC ≈103 → ≈79–83% and ≈69–74 → ≈30–36%; HPMCAS ≈12–22 → ≈60–63% and ≈13–16 → ≈26–30%R17, R19
alvarenga2025residues after fed mediaPLM, PXRDHPMC: crystals from 5 min, clear PZQ peaks; HPMCAS: no birefringence, small peaks or halosR22, R27, R28
nguyen2023bcrystalline delamanidequilibrium solubility0.52 (FaSSIF V1), 2.30 (FeSSIF V2), 13.10 (FEDGAS 4.5), 57.97 µg/mL (FEDGAS 3.0)R13
nguyen2023bDeltyba tabletFaSSIF V1 against FeSSIF V2, 120 min≈31–37 against ≈77 µg/mL of 100R14
nguyen2023bcoated delamanid edisylate tabletsFaSSIF V1; FeSSIF V2; 17 h FEDGAS → FeSSIF V2≈96; ≈96; ≈86–87 µg/mLR16, R17
duong2022adelamanid dispersionstablets in biorelevant media against buffersame release profiles; amorphous solubility 7.93 against 0.76 µg/mLR13, R1
elkhabaz2019aposaconazole with 20 µg/mL HPMCASLLPS onset, FaSSIF against buffer pH 6.5about 20 against 8 µg/mLR2, R4
elkhabaz2021 (Crystallization from solution)atazanavir and posaconazole without polymerinduction time in buffers, simulated and human fluidearliest in FaSSIF-V1 (0.75 mM lecithin), latest in human fluid; atazanavir ≈49 against ≈72 min in FaSSIF-V1 against V2R6, R7, C24
elkhabaz2019b (Bioperformance)posaconazole, atazanavirsolubilities and flux in micellar mediacrystalline solubility raised proportionally more than amorphous; flux-based maximum supersaturation constant while the concentration ratio fallsR1, R2, C21, C22
nguyen2023a (Bioperformance)pretomanid–HPMCAS-HF dispersion; crystalline referencepharmacokinetics fed against fastednegative food effect of the dispersion; positive for the crystalline reference, in line with its higher FeSSIF solubilityC53, C78

Figure

Fig. 4 of alvarenga2025: praziquantel dispersions in FeSSIF-V2 at 0.667 and 1.5 mg/mL, single stage and after acetate pH 4.5
Fig. 4 · alvarenga2025praziquantel dispersions in FeSSIF-V2 at 0.667 and 1.5 mg/mL, single stage and after acetate pH 4.5

Single-stage FeSSIF-V2 (A, C) reaches at most about 80% and 55%; after the switch from pH 4.5 (B, D) the HPMC dispersions fall and the HPMCAS dispersions rise only to about 60% and 30% alvarenga2025 R16, R17, R18, R19.

Fig. 7 of nguyen2023b: release of the marketed delamanid tablet in fasted and fed media
Fig. 7 · nguyen2023brelease of the marketed delamanid tablet in fasted and fed media

FeSSIF V2 reaches about 77 µg/mL against about 37 in FaSSIF V1; the fed gastric points (FEDGAS) were read by HPLC to 60 min nguyen2023b R14.

Why

For praziquantel, Alvarenga and co-workers state that the higher bile salt and lecithin content of FeSSIF-V2 "promoted crystallization" that HPMCAS could not inhibit as well as in buffer, "in broad agreement" with longer induction times in buffer than in FaSSIF reported for posaconazole and atazanavir; the drop of HPMC release after the switch "may" relate to nearly immediate crystallization alvarenga2025 C29, C18. Because the solubility gain in FeSSIF-V2 is modest, they suggest that the positive food effect of praziquantel "could depend on factors other than" solubility, and they call for studies of supersaturated praziquantel in fed media alvarenga2025 C8, C33. Release at 1.5 mg/mL was higher in FaSSIF than in PBS pH 6.5, "likely" because praziquantel is slightly more soluble there alvarenga2025 C15. For delamanid, Nguyen and co-workers say the much higher solubility in fed media "likely accounts" for the better release of Deltyba and mitigates the effect of any crystallization, and that the release variability of uncoated tablets "can be attributed" to an interplay of pH and food components on solubility and crystallization tendency nguyen2023b C29, C39. They call the impact of fed media on coated tablets "only a minor impact" nguyen2023b C32. Duong and co-workers found release in FaSSIF equal to that in buffer despite the higher solubility, and used buffer throughout duong2022a C15. Nucleation and growth were not measured in any of these media for praziquantel or delamanid alvarenga2025 X9; nguyen2023b X8. (synthesis: the two drugs point to two effects of the same media. Where food components raised the drug's solubility several hundredfold, as for delamanid, the solubilization dominated; where they raised it little, as for praziquantel (amorphous 1.17 → 1.74 mg/mL), the promotion of crystallization by lecithin and lipids dominated. The latter matches the shorter induction times with more lecithin and with digestion products in Crystallization from solution F39 and the medium effects in Crystallization from solution F42; the loss of HPMCAS inhibition in the fed medium fits Crystallization from solution F43, where HPMC-AS gained most in blank buffer and less in FaSSIF. Concentrations measured in micellar media also overstate the free drug, so concentration-based supersaturation in these media is not the driving force (Amorphous solubility and LLPS F16).)

Conditions and limits

Praziquantel at one drug loading (30%), two polymers, two doses; the 1.5 mg/mL aqueous and fasted curves are not printed, HPMCAS crystals in FeSSIF-V2 rest on PXRD only, and the single-stage SE residues show no clear peaks alvarenga2025 A3, X1, X7, X10. The crystal forms in the fed residues were not identified alvarenga2025 X14. The delamanid solubility method is not described, and text and figure values differ for Deltyba (80 and 35 against ≈77 and ≈37 µg/mL) nguyen2023b X8, X2. The Deltyba data in FEDGAS and after a fed gastric stage are in the SI, which was not supplied nguyen2023b R15. Neither paper measured free drug or flux in the biorelevant media.

Counterexamples and conflicts

For the racemate at 0.667 mg/mL in FeSSIF-V2 the HPMCAS dispersions ended below the HPMC one (about 70% and 68% against 80%), against the authors' statement that HPMCAS inhibits better alvarenga2025 X18. Delamanid release from dispersions was the same in FaSSIF as in buffer duong2022a R13, whereas the marketed tablet gained about twofold from FaSSIF V1 to FeSSIF V2 nguyen2023b R14. For pretomanid–HPMCAS-HF dispersions the Bioperformance chapter reports a negative food effect in vivo while the crystalline reference gained from food nguyen2023a C53, C78. In human intestinal fluid, posaconazole and atazanavir nucleated later than in buffers and simulated fluids elkhabaz2021 R6, R7, so simulated fed fluid may overstate the promotion found here (synthesis).

Transfer check

Measure amorphous and crystalline solubility of the drug in fasted and fed media: a large gain (delamanid) predicts better fed release from solubilization, a small one (praziquantel) leaves the fed medium to act on crystallization nguyen2023b R13; alvarenga2025 R1. Release the dispersion in FeSSIF-V2 at the intended dose and look for crystals by PLM and PXRD, since HPMCAS, the better inhibitor in buffer and fasted fluid, lost much of its effect there alvarenga2025 R18, C29. Expect concentration ratios in micellar media to understate the activity-based supersaturation and to vary with the medium while flux does not elkhabaz2019b C21, C22. A coated tablet that keeps the dispersion away from the gastric medium removed the fed-medium dependence for delamanid (F27) nguyen2023b C32.

History

Elkhabaz and co-workers (2019) found the posaconazole LLPS onset raised from 8 to about 20 µg/mL in FaSSIF elkhabaz2019a R2, R4, and in the Bioperformance chapter the same group found micelles raising the crystalline solubility more than the amorphous one elkhabaz2019b C35. In the crystallization-from-solution chapter, Elkhabaz and co-workers (2021) found lecithin speeding nucleation of posaconazole and atazanavir and human fluid slowing it elkhabaz2021 C24, C27. Duong and co-workers (2022) found no medium effect on delamanid dispersion release duong2022a C15. Nguyen and co-workers (2023) showed food components raising delamanid solubility and the release of the marketed tablet nguyen2023b C28, C29. Alvarenga and co-workers (2025) were the first in this chapter to find a fed intestinal medium defeating both an enteric and a neutral cellulose polymer alvarenga2025 C23, C29.

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. 2008
    konno2008apolymer type and felodipine dispersion dissolutionfirst proposed

    Effect of polymer type on the dissolution profile of amorphous solid dispersions containing felodipine

    Note
    Known in the library (builds_on: Konno 2006, Konno 2008 on moisture, Marsac 2006): dry felodipine dispersions with PVP, HPMC and HPMCAS nucleated alike, and with moisture HPMCAS and HPMC inhibited crystallization better than PVP at high relative humidity; felodipine thermodynamic data for the Hoffman estimate konno2008a R18, R20.
    Added
    the first dissolution ranking of the three polymers (maxima 14.1, 4.9 and 2.3 µg/mL at 75% polymer), unchanged crystalline solubility with 1 mg/mL polymer, solvent-shift profiles read as growth inhibition, and a solution screen that matched dissolution for PVP and HPMCAS but not HPMC konno2008a R7, R1, C36, C31.
    Relation
    first in the library on the polymer ranking during dispersion dissolution.
    Note
    Findings: F4, F5, F6.
  2. 2010
    alonzo2010two crystallization routes during amorphous dissolutionconfirmsextends

    Understanding the Behavior of Amorphous Pharmaceutical Systems during Dissolution

    Note
    Known in the library (builds_on: Konno 2008 on dissolution, Konno 2006, Marsac 2008): polymer inhibition of felodipine crystallization from solution and the felodipine crystalline solubility alonzo2010 R20, polymers as solid-state inhibitors of felodipine, and the Tg of dry and humid felodipine for the temperature argument.
    Added
    in situ Raman and microscopy that separate crystallization of the wetted solid (felodipine at 37 °C, ≈54% crystalline at 1 min) from crystallization in the liquid (indomethacin at 25 °C), a lag of about 13–20 min that dissolved polymers put before felodipine crystallizes, and the proposal of two polymers for two routes alonzo2010 R2, R19, R6, C46.
    Relation
    extends Konno 2008 to the solid route; confirms its felodipine solution ranking ("in excellent agreement") alonzo2010 C11.
    Note
    Findings: F1, F2, F4, F6.
  3. 2011
    alonzo2011drug loading, nanoparticles and the dissolved-drug ceilingfirst proposed

    Dissolution and Precipitation Behavior of Amorphous Solid Dispersions

    Note
    Known in the library (builds_on: Alonzo 2010, Konno 2008, Van Eerdenbrugh 2011): crystallization limits the observed amorphous supersaturation, PVP is weaker than HPMC against felodipine crystallization from solution, and UV is inflated by felodipine nanosuspensions alonzo2011 C3, R24, R25.
    Added
    the first particle-blind test of dispersions (flux ratios 10.5, 9.5 and 8.5 for 90:10, 50:50 and pure amorphous felodipine, near a predicted 9), NMR, the UV artefact of submicron particles, and fast disintegration of 10% drug dispersions alonzo2011 R14, R15, C27, R4.
    Relation
    first in the library on the dissolved-drug ceiling of dispersions; later papers cite it for that ceiling and for nanodroplets from low-loading dispersions almeidaesousa2016 C9; indulkar2016 R14.
    Note
    Findings: F7, F8, F9, F10, F4, F5.
  4. 2013
    ilevbare2013dritonavir nanodroplets and additivesconfirms

    Influence of Additives on the Properties of Nanodroplets Formed in Highly Supersaturated Aqueous Solutions of Ritonavir

    Note
    Known in the library (builds_on: Ilevbare 2013 on LLPS, Ilevbare 2013 on induction times, Ilevbare 2012, Hsieh 2012, Alonzo 2011): the LLPS concentration of ritonavir and its measurement by solvent shift or pH shift, the induction-time method with a 120 min baseline, cellulose polymers and the Tg of amorphous ritonavir, and the diffusion cap on dissolved dispersions ilevbare2013d R18, R17, R19.
    Added
    the colloid of a dissolving ritonavir dispersion is a non-crystalline drug-rich liquid (Tg about 1 °C) formed at about the LLPS concentration; four classes of 15 additives for droplet size and crystallization; crystallization that appears to start in the droplets ilevbare2013d R1, R2, R14, C39.
    Relation
    confirms and names the ceiling of Alonzo 2011 as the LLPS concentration ilevbare2013d C35; first in the library on additives at drug-rich droplets.
    Note
    Findings: F7, F9, F12, F13, F14.
  5. 2014
    raina2014bnifedipine polymorphs during dissolutionextendscontradicts

    Impact of Polymers on the Crystallization and Phase Transition Kinetics of Amorphous Nifedipine during Dissolution in Aqueous Media

    Note
    Known in the library (builds_on: Alonzo 2010, 2011 and 2012, Marsac 2006 and 2008, Baird 2010, Raina 2014 on LLPS): the two routes and the felodipine polymer effects, nifedipine as a faster crystallizer than felodipine at similar Tg and moisture sorption, and no nifedipine solubility gain with 1 mg/mL polymer raina2014b C1, R17, C26.
    Added
    matrix crystallization of nifedipine glass that dissolved polymer does not change, γ before α on both routes with dissolved polymers lengthening γ (HPMCAS > HPMC > PVP), dispersions that switch the route to solution, and MCR to quantify forms without calibration raina2014b C11, C29, C17, C21, C43.
    Relation
    extends Alonzo 2010 to a fast crystallizer and to polymorph conversion; contradicts the felodipine result that polymer in the medium protects the wetted solid raina2014b C27.
    Note
    Findings: F1, F2, F3, F10.
  6. 2015
    chen2015asurfactants in celecoxib–HPMCAS suspensionsfirst proposed

    Impact of Surfactants on the Crystallization of Aqueous Suspensions of Celecoxib Amorphous Solid Dispersion Spray Dried Particles

    Note
    Known in the library (builds_on: Ilevbare 2013 on induction times): the induction-time method at constant supersaturation chen2015a P9.
    Added
    SDS and polysorbate 80 crystallized acidified suspensions within an hour, STC and Triton X100 slowed nucleation, SDS dissolved far more HPMCAS and drug, and a trace of HPMCAS reversed the Poloxamer 188 result chen2015a R14, R12, R18, R19.
    Relation
    first in the library on surfactants in ASD suspensions; agrees with the surfactant promotion of ritonavir droplet crystallization of 2013 ilevbare2013d R12.
    Note
    Findings: F14, F15, F6, F1.
  7. 2015
    jackson2015danazol dispersions, LLPS, drug loading and polymerconfirmsextends

    Dissolution of Danazol Amorphous Solid Dispersions: Supersaturation and Phase Behavior as a Function of Drug Loading and Polymer Type

    Note
    Known in the library (builds_on: Jackson 2014, Ilevbare 2013 on LLPS, Ilevbare 2013 on nanodroplets, Almeida e Sousa 2015, Raina 2014 on LLPS, Van Eerdenbrugh 2011): danazol crystalline solubility and polymer effects, LLPS onset near the estimated amorphous solubility, the diffusion-cell flux method, the UV overestimate with particles, and ASD dissolution above the amorphous solubility jackson2015 R11, C3, C12, C7.
    Added
    LLPS on dissolution up to 30% drug with three polymers, free drug by flux at 7.1–9.1 µg/mL against 8 µg/mL whatever the polymer, polymer-dependent duration (PVP < HPMC < HPMCAS), and slow release at 50% drug jackson2015 C36, R9, R5, C37.
    Relation
    confirms the ceiling by flux for three polymers ("is confirmed here") jackson2015 C30; extends the 2013 ritonavir colloid to danazol.
    Note
    Findings: F4, F6, F7, F9, F10.
  8. 2015
    trasi2015bbinary amorphous drug combinationsextends

    Dissolution performance of binary amorphous drug combinations—Impact of a second drug on the maximum achievable supersaturation

    Note
    Known in the library (builds_on: Trasi 2015 on a second drug, Ilevbare 2013 on LLPS, Raina 2014 on LLPS): a second drug lowers the amorphous solubility in antisolvent tests, LLPS above the amorphous solubility, and the amorphous solubility caps free drug and membrane transport trasi2015b C7, C4.
    Added
    the drop of each ceiling to about Sa × xd in dissolving films and in PVP and HPMCAS dispersions, the same drop from two dispersions dissolved together, colloids of HPMCAS dispersions that pass 0.45 µm filters, and slower crystallization of the mixed drug-rich phase trasi2015b R5, R13, R11, R7, R15.
    Relation
    extends the antisolvent result of the LLPS chapter to dissolution; first in the library on co-dosed amorphous products trasi2015b C47.
    Note
    Findings: F11, F7, F8, F10, F13.
  9. 2015
    wegiel2015resveratrol dispersions in aqueous mediaextends

    Phase Behavior of Resveratrol Solid Dispersions Upon Addition to Aqueous media

    Note
    Known in the library (builds_on: Alonzo 2010, Van Eerdenbrugh 2010, Alonzo 2011, Wegiel 2013, Raina 2014): the two crystallization routes, resveratrol as a rapid crystallizer, a felodipine dispersion with a flux ten times that of the crystal, and the storage stability of the same resveratrol dispersions (PVP and E100 stable, HPMC, HPMCAS and CMCAB crystallized at high RH); diffusion-cell flux as a measure of free drug wegiel2015 R21, R22, R24.
    Added
    dissolved HPMCAS raised the crystalline solubility of resveratrol from 42 to 414 µg/mL at 10 mg/mL, PVP solutions first dissolved and then precipitated resveratrol with the polymer, only 80% HPMC, 85% HPMCAS or 95% CMCAB stopped matrix crystallization, and more HPMCAS dispersion raised the total concentration while the flux fell wegiel2015 R2, R3, R6, R7, R14, R19, R20.
    Relation
    extends the matrix route of Alonzo 2010 to dispersions of a rapid crystallizer; first in the library to separate a soluble drug–polymer complex from supersaturation by flux during dispersion dissolution wegiel2015 C41.
    Note
    Findings: F16, F17, F1, F7.
  10. 2015
    xie2015celecoxib dispersions with polymer combinationsconfirms

    Dissolution Performance of High Drug Loading Celecoxib Amorphous Solid Dispersions Formulated with Polymer Combinations

    Note
    Known in the library (builds_on: Alonzo 2010, Trasi 2012, Ilevbare 2013 on induction times, Chen 2015, Trasi 2015 on acetaminophen): the matrix and solution routes, PAA as a solid-state growth inhibitor, the induction-time approach and the stronger effect of amphiphilic than hydrophilic polymers on lipophilic drugs, the onset criterion for celecoxib, and a polymer that fails as a solution inhibitor xie2015 C10, C47.
    Added
    HPMCAS and HPMC held 22 µg/mL celecoxib for more than 8 h against about 1–2 h with PVP; neat amorphous celecoxib crystallized on its own particles and gave almost no supersaturation; at 50% drug replacing a fifth of the PVP with HPMCAS or HPMC kept supersaturation for 16 h but slowed release, and 5 µg/mL of either in the medium protected the PVP-K12 dispersion xie2015 R1, R7, R4, R6.
    Relation
    confirms the cellulosic-over-PVP ranking for a third drug; first in the library on two polymers in one dispersion for dissolution, where little earlier work existed xie2015 C30.
    Note
    Findings: F4, F20, F1, F2, F6, F10.
  11. 2016
    li2016blopinavir dispersions leaching in acidextends

    Leaching of Lopinavir Amorphous Solid Dispersions in Acidic Media

    Note
    Known in the library (builds_on: Chen 2015, Raina 2015): the spray-drying procedure, the CMC method and the question of surfactants in ASD suspensions, and the apparent supersaturation C/Ceq in solubilizing media li2016b C3, C7.
    Added
    33% lopinavir dispersions with three HPMCAS grades and HPMCP leached drug to between the crystalline and the amorphous solubility at pH 3 and little polymer; five surfactants raised leaching about as much as the crystalline solubility, so C/Ceq stayed about constant for each polymer; at pH 5 SDS raised drug and polymer leaching sharply; SDS with PVPVA gave the most li2016b R3, R4, R19, R20, R13, R17.
    Relation
    extends Chen 2015 from celecoxib to lopinavir, a slow crystallizer chosen so that leaching could be measured without concurrent crystallization li2016b C5, to more surfactants and to pH 5.
    Note
    Findings: F19, F15, F18.
  12. 2016
    trasi2016commercial tacrolimus capsulesconfirms

    Non-Sink Dissolution Behavior and Solubility Limit of Commercial Tacrolimus Amorphous Formulations

    Note
    Known in the library (builds_on: Alonzo 2011, Raina 2014, Almeida e Sousa 2015, Raina 2015, Trasi 2015 on a second drug, Jackson 2016): a maximum achievable supersaturation set by the amorphous solubility, flux proportional to activity with a plateau there, polymers with minimal impact on the amorphous solubility while small molecules lower and micelles raise it, and high-loading dispersions that may not form nanospecies trasi2016 C25, C32, C34, C41.
    Added
    an amorphous solubility of 49 µg/mL against 1.4 µg/mL for the crystal (ratio about 35); six marketed capsules dissolved to, not past, that limit; their flux reached the pure-drug plateau; 50 µg/mL HPMC delayed crystallization of 50 µg/mL tacrolimus from within 3 h to 6–8 h trasi2016 R4, R16, R13, R14, R15, R9.
    Relation
    confirms the ceiling of the earlier dispersion studies for marketed products; first in the library on the solution-phase behaviour of commercial amorphous formulations trasi2016 C6.
    Note
    Findings: F7, F8, F9, F10, F4.
  13. 2016
    xie2016acelecoxib with PAA and cellulose derivativesextendsrevises

    Improved Release of Celecoxib from High Drug Loading Amorphous Solid Dispersions Formulated with Polyacrylic Acid and Cellulose Derivatives

    Note
    Known in the library (builds_on: Alonzo 2010, Alonzo 2012, Ilevbare 2013 on induction times): the two routes, the seeded-growth method and the nucleation-rate estimate, PAA as a poor nucleation inhibitor and the amphiphilic cellulose derivatives as the best precipitation inhibitors xie2016a C3, C7, C19.
    Added
    5 µg/mL HPMCAS slowed celecoxib nucleation about 4000-fold and seeded growth about 70-fold; PAA dispersions released fast and crystallized, and released only about half even with HPMCAS in the medium, leaving needle crystals in the residue; PAA with 10% HPMCAS or HPMC released completely at 30% drug and partly at 50%; IR read PAA and HPMCAS as immiscible and PAA and HPMC as partly miscible xie2016a R13, R12, R9, R10, R14, R17, R20, R21.
    Relation
    revises, for celecoxib, the growth reading of the 2008 felodipine solutions toward nucleation (F5); extends the polymer combinations of Xie 2015 to PAA.
    Note
    Findings: F4, F5, F10, F16, F2, F20.
  14. 2017
    xie2017indomethacin with EPO and HPMCextends

    Impact of Eudragit EPO and Hydroxypropyl Methylcellulose on Drug Release Rate, Supersaturation, Precipitation Outcome and Redissolution Rate of Indomethacin Amorphous Solid Dispersions

    Note
    Known in the library (builds_on: Alonzo 2010, Raina 2014, Indulkar 2016, Xie 2016): HPMC inhibits indomethacin crystallization and the calculated amorphous solubility at 37 °C, UV extinction for the amorphous solubility, drug-rich nanodroplets as a reservoir, and the ternary of a fast-dissolving polymer with a crystallization inhibitor xie2017 R29, R30, C42.
    Added
    EPO raised both solubilities of indomethacin but did not inhibit crystallization; with HPMC the drug stayed supersaturated up to the amorphous solubility (36 µg/mL), where 70–100 nm droplets formed; the EPO–HPMC ternary released fast into nanodroplets; after a rise to pH 5 these redissolved within about 2 min, while the α precipitate of the EPO dispersion redissolved faster than sieved crystals but only to 32.1 of 40 µg/mL; a shift to pH 6.8 hid the differences; the ternary stayed amorphous in storage xie2017 R1, R3, R4, R6, R15, R20, R19, R22, R26.
    Relation
    extends the ternary idea of Xie 2016 to a polymer that dissolves in acid; first in the library on redissolution of a crystalline precipitate after a pH rise xie2017 C61.
    Note
    Findings: F21, F20, F17, F9, F4, F10, F3.
  15. 2018
    li2018lopinavir with insoluble polymersextends

    Tailoring supersaturation from amorphous solid dispersions

    Note
    Known in the library (builds_on: Ilevbare 2013 on LLPS, Almeida e Sousa 2015, Trasi 2015 on a second drug, Trasi and Taylor 2015, Li 2016): the amorphous solubility as the maximum free drug concentration and its measurement by UV scattering, a second miscible drug that lowers the maximum supersaturation, and lopinavir as a slow crystallizer li2018 C8, C9, C11.
    Added
    insoluble polymers mixed with lopinavir lowered the 48-h concentration below the 17.4 µg/mL amorphous solubility, most at low drug loading, EC and HPMCP at 15% to about the crystalline solubility; the phase-separated CA and EUD dispersions and a physical mixture were hardly suppressed; the most suppressed HPMCP dispersion crystallized slowest in suspension li2018 R3, R8, R14, R6, R7, C61.
    Relation
    extends the second-drug drop of Trasi and Taylor 2015 (F11) from a drug to an undissolved polymer, as its hypothesis li2018 C10; first in the library on solubility suppression by polymers.
    Note
    Findings: F18, F7, F16.
  16. 2018
    que2018paclitaxel seed crystals and HPMCASfirst proposedextends

    Paclitaxel Crystal Seeds with Different Intrinsic Properties and Their Impact on Dissolution of Paclitaxel-HPMCAS Amorphous Solid Dispersions

    Note
    Known in the library (builds_on: Alonzo 2012, Schram 2016, Jackson 2016, Ilevbare 2013 on induction times, Trasi 2017): seeds reduce the amorphous solubility advantage unless growth is inhibited, seeds grown in different environments differ in interface structure and growth rate, polymers inhibit nucleation from solution, and a commercial amorphous tacrolimus product contains crystals que2018 C8, C2, C7.
    Added
    at an equal 18 wt%, seeds of different morphology left ≈7.9–25.3 µg/mL of a 31.6 µg/mL amorphous solubility after 16 h; sonication raised the needle-end area 7–9-fold; HPMCAS held an unseeded solution at S = 88 for more than 16 h but only slowed growth, which the authors trace to a critical two-dimensional nucleus (5.4–7.0 nm) smaller than the spacing of adsorbed polymer (≈10.5–16.8 nm) que2018 R14, R6, R3, R15, R12.
    Relation
    first in the library on seed morphology at equal mass in dispersion dissolution; extends the nucleation-against-growth split of Konno 2008 and Xie 2016 to a seeded dispersion.
    Note
    Findings: F22, F4, F5, F7, F8.
  17. 2019
    elkhabaz2019aposaconazole dispersions through a gastric stage

    Characterization of Phase Transformations for Amorphous Solid Dispersions of a Weakly Basic Drug upon Dissolution in Biorelevant Media

    Note
    Known in the library (builds_on: Alonzo 2010, Li 2018, Raina 2015 on fluorescent probes, Wanapun 2010, Kestur 2012): the two crystallization routes during amorphous dissolution and matrix crystallization as a source of seeds, polymers delaying crystallization by acting on nucleation and growth, enteric polymers suspended at gastric pH, and more release from insoluble-polymer dispersions at higher drug loading elkhabaz2019a C2, C3, C29; fluorescence detection of the LLPS onset and SHG detection of crystals in amorphous powders (builds_on, as listed in the evidence index).
    Added
    crystals form in crystal-free HPMCAS dispersions during an hour in fasted gastric fluid although the medium is subsaturated, about 68% of the undissolved drug at 50% drug against 0.03–0.05% at 10–25%; after the pH shift the low loadings held the amorphous solubility with ≈300 nm droplets while the 50% dispersion never reached it; a fifth of the dose lost supersaturation about an hour sooner elkhabaz2019a R20, R6, R13, R12.
    Relation
    carries the matrix route of Alonzo 2010 into the stomach of a weakly basic drug; first in the library on a gastric stage as the source of the seeds that end intestinal supersaturation.
    Note
    Findings: F24, F26, F1, F4, F9, F10, F16, F18, F19.
  18. 2022
    duong2022adelamanid salts formed inside the dispersionfirst proposed

    Combining enabling formulation strategies to generate supersaturated solutions of delamanid: In situ salt formation during amorphous solid dispersion fabrication for more robust release profiles

    Note
    Known in the library (builds_on: Towler 2008, Ueda 2020, Hate 2020, Moseson 2020): the counterion changes the crystallization tendency of amorphous salts, polymers stabilize drug-rich droplets, and residual crystals in dispersions can seed growth during release duong2022a C5, C11, C55.
    Added
    a fast crystallizer that cannot be vitrified at 50 °C/min left crystals in rotary-evaporated dispersions from 15–20% drug, and release collapsed once crystallinity was detectable; seven of eight sulfonate salts were amorphous with Tg 83.7–117.8 °C, and salts formed in the same step as the dispersion released ≈95–97 µg/mL of 100 at 25% drug against ≈20 for the free base; a polymer screen chose HPMCP and HPMCAS by induction time and droplet size duong2022a R8, R14, R20, R26, R4, R5.
    Relation
    first in the library on in situ salt formation in a polymer dispersion; adds a fast-crystallizing weak base to the residual-crystal problem of Que 2018.
    Note
    Findings: F23, F4, F9, F10, F12, F25, F28.
  19. 2023
    nguyen2023benteric coating on a delamanid dispersion tabletfirst proposed

    Enteric coating of tablets containing an amorphous solid dispersion of an enteric polymer and a weakly basic drug: A strategy to enhance in vitro release

    Note
    Known in the library (builds_on: Nguyen 2023 on gastric pH, Van Duong 2022, Elkhabaz 2019, Schram 2016): delamanid dispersions crystallize at their surfaces at gastric pH and release less afterwards, salt forms did not cure it, posaconazole dispersions crystallized in gastric fluid, and enteric polymers inhibit crystallization where they dissolve nguyen2023b R19, C11, R20, C36.
    Added
    a 14–16% Acryl-EZE II coat cut gastric release below 0.5% and gave ≈76–86 µg/mL after every gastric pH, against ≈0.3–93 µg/mL uncoated; a 2 µm Eudragit L 100-55 layer prevented the surface crystals on dispersion films; the coat failed after about 130–150 min at pH 4.5–5.0 in buffer but lasted more than 17 h in a fed gastric medium; food components raised delamanid solubility up to 57.97 µg/mL and the release of the marketed tablet nguyen2023b R10, R2, R6, R7, R13, R14.
    Relation
    first in the library to coat a tablet of a dispersion made with an enteric polymer; remedies the gastric-pH dependence that the companion paper mapped.
    Note
    Findings: F27, F24, F25, F28, F19.
  20. 2023
    nguyen2023cgastric pH, polymer grade and drug formextends

    Impact of Gastric pH Variations on the Release of Amorphous Solid Dispersion Formulations Containing a Weakly Basic Drug and Enteric Polymers

    Note
    Known in the library (builds_on: Van Duong 2022, Elkhabaz 2019, Li 2016, Li 2018, Almeida e Sousa 2016): the delamanid salt dispersions and their polymer screen, matrix crystallization in a gastric stage, drug leaching from enteric dispersions in acid, suppression of the ceiling by an undissolved polymer, and disproportionation of salts that are not stable in the medium.
    Added
    final release from ≈0 to 101% across three gastric pH values, five enteric grades and two drug forms; polymer release that does not track drug release; a gastric supersaturation ratio rising from ≈0.9–3.8 at pH 1.6 to ≈11–42 at pH 5.0 that does not predict release; conversion of the neat amorphous salt to crystalline free base within 5 min at pH 1.6; surface crystals on films and powders after 1 h in acid, more with HPMCAS nguyen2023c R11, R12, R13, R14, R19.
    Relation
    extends the gastric-stage crystallization of Elkhabaz 2019 across polymer grades and gastric pH, and the salt dispersions of Van Duong 2022 to a pH grid; rules out the solution route in acid.
    Note
    Findings: F25, F24, F1, F2, F8, F10, F16, F18, F19, F23.
  21. 2024
    polyzois2024praziquantel dispersions, racemate and enantiomerfirst proposed

    Amorphous Solid Dispersion Formation for Enhanced Release Performance of Racemic and Enantiopure Praziquantel

    Note
    Known in the library (builds_on: Sato 2015, Indulkar 2019, Saboo 2020, Trasi 2015 on dispersions): cellulose polymers inhibit crystallization of two enantiomers to different extents, release can fall sharply above a threshold drug loading or decline gradually when the polymer controls it polyzois2024 C28, C16, C17.
    Added
    a seven-polymer screen that chose HPMCAS-MF and HPMC E5 LV for the racemate and found both much weaker for the R-enantiomer (37 and 15.5 min against at least 83 min); complete release up to 40–50% drug at 667 µg/mL and a gradual decline at 1.5 mg/mL without a cliff; hot-melt extrusion at least as good as solvent evaporation; commercial tablets at most 16% polyzois2024 R3, R4, R8, R9, R11, R14.
    Relation
    first in the library on a dispersion of a single enantiomer; carries the chiral polymer effect of Sato 2015 from melt growth into solution and release.
    Note
    Findings: F29, F4, F6, F10, F25.
  22. 2025
    alvarenga2025praziquantel dispersions across mediaconfirmsextends

    Release performance and crystallization of racemic and enantiopure praziquantel amorphous solid dispersion in various media

    Note
    Known in the library (builds_on: Polyzois 2024, Elkhabaz 2021, Ilevbare and Taylor on the LLPS onset method): the praziquantel polymer choice and the enantiomer's shorter induction time, longer induction times in buffer than in simulated intestinal fluid for posaconazole and atazanavir, and the light-scattering onset as the amorphous solubility alvarenga2025 C25, C18, P7.
    Added
    amorphous solubility 4.0–7.7 times the crystalline one across nine media and nearly independent of pH for a neutral drug; HPMCAS dispersions that recovered to ≈92–103% after pH 1.6 but only ≈62–77% after pH 3.0 or 5.0; HPMC dispersions that released fast at any pH and crystallized, shown by polarized light and PXRD; a fed intestinal medium that defeated both polymers (≈34–52% at 1.5 mg/mL); an enantiomer advantage limited to simple buffer alvarenga2025 R1, R7, R10, R20, R27, R18, R8.
    Relation
    confirms and extends Polyzois 2024 across media and adds the fed-state failure; relates the medium effect to the nucleation work of the crystallization-from-solution chapter.
    Note
    Findings: F28, F29, F25, F10.
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
konno2008aF1. HPMCAS dispersions reached the highest concentrations, PVP the lowestF4
konno2008aF2. The polymers did not change crystalline solubilityF4, F5
konno2008aF3. HPMC and HPMCAS kept supersaturated felodipine in solution for hours; PVP did notF5
konno2008aF4. The lower the starting supersaturation, the more of it the cellulose polymers keptF5
konno2008aF5. Estimated crystal growth was much slower with HPMC or HPMCAS than with PVP or in bufferF5
konno2008aF6. The solution test predicted the dissolution ranking for PVP and HPMCAS, not for HPMCF6
alonzo2010F1. Amorphous felodipine at 37 °C crystallizes on contact and dissolves like the crystalF1
alonzo2010F2. At 25 °C slower solid crystallization lets felodipine supersaturate brieflyF1
alonzo2010F3. Dissolved polymers delay crystallization of the felodipine solidF2
alonzo2010F4. With the solid protected, felodipine approaches its amorphous solubility, but only the cellulosics hold itF2, F4
alonzo2010F5. Indomethacin stays amorphous longer and supersaturates, then crystallizes from solutionF1
alonzo2010F6. PVP and HPMC raise and hold indomethacin supersaturation, best at 25 °CF4, F6
alonzo2011F1. UV reads 90:10 dispersions far above 50:50 dispersionsF8, F10
alonzo2011F2. Only 90:10 dispersions fall apart in minutes and shed submicron particlesF9, F10
alonzo2011F3. Dispersion-born and methanol-born particles start and grow alike; HPMC slows growthF4, F5, F9
alonzo2011F4. Membrane flux and NMR show the same dissolved level for 90:10, 50:50 and pure amorphous felodipineF7
alonzo2011F5. The 90:10 UV spectrum mixes dissolved and nanocrystalline felodipineF8, F9
ilevbare2013dF1. Droplets appear once dissolved ritonavir passes the LLPS concentration, and redissolve on dilutionF9
ilevbare2013dF2. The droplets are a noncrystalline, ritonavir-rich liquid that later crystallizesF9
ilevbare2013dF3. Polymers barely move the LLPS concentrationF7
ilevbare2013dF4. Inside the ASD, the additive sets droplet size and lifetimeF12
ilevbare2013dF5. Droplets are smaller and grow more slowly in water than in 100 mM bufferF12
ilevbare2013dF6. Additives fall into four classes for droplet size and crystallizationF12, F14
ilevbare2013dF7. Crystallization seems to start in the dropletsF13
raina2014bF1. MCR separates glass, γ and α without calibration samplesF3
raina2014bF2. The neat glass crystallizes in the solid within minutes, polymer or notF1, F2
raina2014bF3. γ forms first and then turns into αF3
raina2014bF4. Dissolved polymers delay the γ-to-α conversion, HPMCAS mostF3
raina2014bF5. In dispersions the drug dissolves and crystallizes from solutionF1, F2, F10
raina2014bF6. Dispersions crystallize and convert faster than the neat glassF3
chen2015aF1. SDS and Polysorbate 80 make the suspension crystallize within an hourF14
chen2015aF2. In solution, three surfactants speed nucleation and two slow itF14, F6
chen2015aF3. SDS drives the most drug into solution, which then crystallizesF15
chen2015aF4. SDS dissolves far more HPMCAS from the particlesF15
chen2015aF5. A trace of HPMCAS slows nucleation with Poloxamer 188 onlyF6
chen2015aF6. Crystals grow in the liquid with SDS and Polysorbate 80, on the particles otherwiseF14, F1
jackson2015F1. Most ASDs dissolve past the amorphous solubility and form a drug-rich phaseF9
jackson2015F2. The drug-rich phase is a submicron droplet population like the antisolvent oneF9
jackson2015F3. The free drug concentration stops at about the amorphous solubilityF7
jackson2015F4. The polymer sets how long supersaturation lasts, as the screening predictedF4, F6
jackson2015F5. At 50% drug loading HPMC and HPMCAS dissolve slowly, and HPMCAS never reaches LLPSF10
trasi2015bF1. In films, a second drug lowers each drug's plateau in step with its shareF11
trasi2015bF2. Ideal mixing predicts the film plateausF11
trasi2015bF3. The same drop appears when dispersions dissolve, in both polymersF11
trasi2015bF4. Dispersion data fall on the ideal-mixing linesF11
trasi2015bF5. The polymer sets the speed and the colloids, not the ceilingF7, F8, F10
trasi2015bF6. Two separate dispersions dissolved together give the same dropF11
trasi2015bF7. Ritonavir keeps lopinavir's drug-rich phase from crystallizing for 5 hF11, F13
wegiel2015F1. Dissolved HPMCAS raises resveratrol's crystal solubility steeply; HPMC barely doesF17
wegiel2015F2. In PVP solution resveratrol first dissolves well, then precipitates with the polymerF17
wegiel2015F3. Staying amorphous in buffer did not raise the concentrationF16, F17
wegiel2015F4. More cellulosic polymer, less crystallization and a larger concentration gainF16
wegiel2015F5. Crystals form in the matrix, not from the solutionF16, F1
wegiel2015F6. More HPMCAS dispersion raised the concentration but lowered the fluxF17, F7
xie2015F1. Cellulosic polymers hold the supersaturated solution; PVP only delays nucleationF4, F6
xie2015F2. Neat amorphous celecoxib crystallises on its own particles and gives almost no supersaturationF1, F2
xie2015F3. In the ASDs, the polymer sets how fast celecoxib is released and how long supersaturation lastsF10, F4
xie2015F4. Replacing a fifth of the PVP with HPMCAS or HPMC keeps supersaturation for 16 h but slows releaseF20
xie2015F5. Trace cellulosic polymer in the medium protects the PVP-K12 ASDF20
li2016bF1. Little polymer leaches, and less from the dispersions than from the pure polymersF19
li2016bF2. LPV leaches to a supersaturated level set by the polymer type, not the HPMCAS gradeF19, F18
li2016bF3. Surfactants raise leaching about as much as they raise crystalline solubilityF19
li2016bF4. The polymers change how the surfactants solubilizeF19
li2016bF5. The apparent supersaturation stays about constant for each polymerF19
li2016bF6. At pH 5 an ionic surfactant raises drug and polymer leaching sharplyF15
li2016bF7. SDS with PVPVA gives the largest leachingF15
trasi2016F1. Amorphous tacrolimus is about 35 times more soluble than the crystalF7
trasi2016F2. All six capsules dissolve to the amorphous solubility and stop thereF7, F10
trasi2016F3. The dissolved products reach the maximum membrane fluxF7
trasi2016F4. No evidence that the products exceeded the amorphous solubilityF8, F9
trasi2016F5. HPMC lengthens the life of the supersaturated solutionF4
xie2016aF1. HPMCAS and HPMC stop celecoxib nucleating; PAA does nothingF4
xie2016aF2. Each polymer alone fails in its own wayF10, F16
xie2016aF3. With HPMCAS in the medium, PAA dispersions stay supersaturated but still release only halfF16, F2
xie2016aF4. HPMCAS also slows growth on seed crystals, but far less than nucleationF5
xie2016aF5. PAA plus HPMCAS: complete release at 30%, a trade-off at 50%F20
xie2016aF6. PAA plus HPMC works better at 50%F20
xie2016aF7. PAA does not mix with HPMCAS but partly mixes with HPMCF20
xie2017F1. With HPMC, indomethacin stays supersaturated up to its amorphous solubility, where droplets formF9, F4
xie2017F2. EPO raises indomethacin solubility but lets it crystallizeF17, F4
xie2017F3. In acid, the EPO dispersion releases fast and crystallizes, HPMC dispersions release slowly, and the ternary releases fast into nanodropletsF10, F20
xie2017F4. At pH 5 the ternary's nanodroplets redissolve at onceF21
xie2017F5. The EPO dispersion's precipitate is small α crystals that redissolve faster than reference crystals, but not completelyF21, F3
xie2017F6. A shift to pH 6.8 hides these differencesF21
xie2017F7. On storage, the ternary stays amorphous while both binaries crystallizeF20
li2018F1. A soluble polymer leaves the amorphous solubility unchangedF7, F18
li2018F2. Insoluble polymers lower the maximum concentration, most at low loadingF18
li2018F3. EC and HPMCP at low loading fall to the crystalline solubilityF18
li2018F4. The polymers that suppress least are the phase-separated onesF18
li2018F5. Mixing, not mere presence, mattersF18
li2018F6. Interaction evidence points to HPMCP and HPMCAS, not CA and EUDF18
li2018F7. Lower supersaturation, slower crystallizationF18, F16
que2018F1. Sonication multiplies the growth area of the needlesF22
que2018F2. Without polymer, seeds with more ends drain supersaturation fastest at firstF22
que2018F3. Without polymer, long S16 needles breed fine crystalsF22
que2018F4. HPMCAS stops nucleation but only slows growth, and splits the needle tipsF22, F5, F4
que2018F5. In ASD dissolution, the seed type decides how much supersaturation is leftF22, F7
que2018F6. At high supersaturation the critical nucleus is smaller than the polymer spacingF22
que2018F7. Seeds made at different supersaturations differ in tip structure and behaviourF22
elkhabaz2019aF1. Amorphous solubility in FaSSIF is about 20 µg/mL; crystalline solubility 1.69 µg/mLF7, F28
elkhabaz2019aF2. Little drug dissolves in the acid stage, and the gastric solution stays subsaturatedF24, F18, F19
elkhabaz2019aF3. Crystals form inside the undissolved ASD during the acid stage, massively at 50% DLF24, F16, F1
elkhabaz2019aF4. After the pH shift, 10% and 25% DL supersaturate; 50% DL does notF24, F26, F10
elkhabaz2019aF5. Nanodroplets of about 300 nm form at 10% and 25% DLF9, F26
elkhabaz2019aF6. Without the acid stage, supersaturation lasts longerF24, F4, F6
elkhabaz2019aF7. A lower dose reaches the same peak but desupersaturates soonerF26
duong2022aF1. Delamanid crystallizes fast and loses most of its solubility at intestinal pHF23, F25
duong2022aF2. HPMCP and HPMCAS hold supersaturation and keep drug-rich droplets smallF4, F12, F9
duong2022aF3. Free-base ASDs contain crystals from 15–20% DL, and release collapsesF23
duong2022aF4. The marketed tablet also releases incompletelyF23
duong2022aF5. Sulfonate salts are amorphous with a much higher Tg, but take up waterF23
duong2022aF6. Salt ASDs have a higher Tg and take up more water than the free-base ASDF23
duong2022aF7. DLM-edisylate ASDs release well up to 25% DL with HPMCPF23, F10, F25
duong2022aF8. All four salt ASDs at 25% DL with HPMCP release almost completelyF23
nguyen2023bF1. Uncoated tablets release well at intestinal pH but poorly and variably after a gastric stageF27, F25
nguyen2023bF2. ASD films crystallize at pH 3.0 whatever the salt form; a thin enteric layer prevents itF24, F27
nguyen2023bF3. The coat holds in acid, fails after about 2–2.5 h at pH 4.5–5.0 in buffer and dissolves at pH 6.0; fat delays failureF27
nguyen2023bF4. Coated tablets hold the drug back in the gastric stage and release well afterwards, nearly independent of gastric pHF27
nguyen2023bF5. Food raises delamanid solubility and commercial-tablet release; coated-tablet release barely changesF28
nguyen2023cF1. The drug dissolves in strong acid, the polymers only near neutral pHF25, F24
nguyen2023cF2. Gastric pH and polymer grade decide how much drug the salt ASDs finally releaseF25
nguyen2023cF3. Polymer release in the acid stage does not track drug releaseF25, F10
nguyen2023cF4. With HPMCP-50, the salt releases more than the free baseF23, F25
nguyen2023cF5. Supersaturation in the acid stage rises with pH but does not predict final releaseF25, F19
nguyen2023cF6. The amorphous salt turns into crystalline free base within minutes at pH 1.6 and 3.0F24
nguyen2023cF7. After 1 h in acid, crystals appear on ASD surfaces, more with HPMCAS and at higher pHF24, F16, F1
polyzois2024F1. HPMCAS-MF and HPMC E5 LV hold off RS-PZQ crystallization longestF4, F6
polyzois2024F2. Both polymers protect R-PZQ much less wellF29
polyzois2024F3. All ASDs were amorphous when made; on storage only the HPMC E5 LV one stayed soF29
polyzois2024F4. At 667 µg/mL release is complete up to high loading, and faster with HPMCAS-MFF10
polyzois2024F5. At 1.5 mg/mL, HPMCAS-MF release falls gradually with loading and HPMC E5 LV lagsF10, F26
polyzois2024F6. R-PZQ releases as well as or better than RS-PZQ from HPMCAS-MF, but not from HPMC E5 LVF29
polyzois2024F7. Hot-melt extruded ASDs release at least as well as solvent-evaporated onesF10
polyzois2024F8. Commercial tablets release at most 16%F29
polyzois2024F9. In a gastric-to-intestinal pH shift, the polymer decides when release happensF25
alvarenga2025F1. Amorphous PZQ is 4 to 8 times more soluble than crystalline PZQ, at any pHF28, F29, F25
alvarenga2025F2. HPMCAS ASDs hold the drug back in acid; HPMC ASDs release fast at any pHF25
alvarenga2025F3. At intestinal pH, HPMCAS keeps PZQ dissolved while HPMC lets it crystallizeF29, F28
alvarenga2025F4. Fed-state fluid defeats both polymersF28
alvarenga2025F5. (R)-PZQ gains over the racemate only in simple buffer, and crystallizes fasterF29
alvarenga2025F6. Extrusion and solvent evaporation give broadly similar releaseF10

01Concepts

non-sink dissolutionthe test condition of every paper: dose above the crystalline, often above the amorphous solubilitymatrix crystallizationcrystallization of the wetted amorphous solid, the first route; the dispersion polymer and its content decide itsolution crystallizationcrystallization from the supersaturated liquid, the second routecrystallization during dissolutionthe competition of both routes with dissolutionsolution-mediated phase transformationdissolution of a metastable solid and growth of a stable one through the solutionsurface crystallizationproposed start of crystallization on wetted particlesplasticization by waterhydrated felodipine above Tg at 37 °C; low Tg of the ritonavir drug-rich phasecrystallization tendencyfast (nifedipine, resveratrol, felodipine in water) against slow (indomethacin, lopinavir) crystallizerscrystallization inhibition by polymersranking of PVP, HPMC, HPMCAS, PAA, EPO and cellulose esters; two routes; a minor inhibitor in a dispersionnucleation inhibitionlonger celecoxib induction times; HPMCAS slowing nucleation far more than growthcrystal growth inhibitiongrowth reading of felodipine plateaus; seeded celecoxib growthcrystal growthparticle growth after release; seeds from the matrixcrystal growth rateslopes of desupersaturation, equal areas assumeddesupersaturationfall of the concentration after the peaknucleationinitial drop, droplet nucleation, α nucleationclassical nucleation theorydependence of nucleation on supersaturation and interfacial tensionheterogeneous nucleationdroplet and crystal interfaces as nucleation sitesinterfacial tensionwhy nuclei may form inside droplets; argued not to explain the celecoxib polymer rankingmetastable zonelabile against metastable zone in the felodipine readingcrystal habitneedle shape and size by route and additivedrug-polymer complexationruled out for felodipine; soluble resveratrol–HPMCAS and resveratrol–PVP complexesamorphous solubility advantagethe estimated or measured ceiling: about 9–10 for felodipine, 35 for tacrolimus, 5.6 for lopinavirHoffman equationsource of the estimatesfree drug concentrationwhat flux and NMR measure, capped at the amorphous solubility, lowered by soluble complexesmembrane fluxparticle-blind read-out of dissolved drug, also for marketed capsulesdrug-rich phasenon-crystalline phase formed by dissolving dispersionsdrug-rich nanodropletsthe submicron colloid and its sizeliquid-liquid phase separationonset during dispersion dissolutionnanodroplet reservoir effectcited reason to formulate for LLPS; indomethacin droplets that redissolve after a pH riseideal mixingceiling of two miscible drugs; proportional-dilution line for lopinavir with polymerschemical potentialwhy the free drug stops and why a second drug or an undissolved polymer lowers itFlory-Huggins interaction parameterargument why a dispersion need not match the pure amorphous drug; strength of lopinavir suppressionpolymer-controlled releasefast release of 10% drug dispersionsdrug-controlled releaseslow release of 50% drug dispersionsNoyes-Whitney equationdissolution arm of the two-route scheme; redissolution of indomethacin precipitatesdrug leachingdrug and polymer passing from suspended particles of celecoxib and lopinavir dispersionspH-dependent polymer solubilityHPMCAS and HPMCP undissolved at pH 2–3; EPO dissolved in acidpolymer ionizationEPO in acid; HPMCAS at pH 5 with SDSpolymer-surfactant complexationproposed reason SDS dissolves HPMCAS; PVPVA–SDSmicellar solubilizationsolubility of celecoxib and lopinavir above each CMCcritical micelle concentrationtest levels just above each CMCmoisture-induced crystallizationthe solid-state comparison of the polymer ranking; storage of resveratrol and indomethacin dispersionsphysical stabilitystorage of ternary indomethacin dispersions; suspension stability of suppressed lopinavir dispersionspH-dependent solubilityindomethacin solubility before and after the pH riseglass-forming abilitytacrolimus judged a good glass former from one DSC runresidual crystallinityseeds added at equal mass and crystals left by preparation; growth area and origin, not masscrystal seedinggastric-stage crystals carried into the intestinal stage; seeds added to a dispersionseeded crystal growththe loss of supersaturation that seeds cause, and how far a polymer slows itenteric polymerHPMCP, HPMCAS grades and Eudragit L in the dispersion and as a tablet coatgastric pH variabilityrelease across gastric stages at pH 1.6, 3.0 and 5.0 and in fed gastric mediapH-dependent solubility of weak basesdelamanid and posaconazole solubility collapsing from gastric to intestinal pHin situ salt formationsulfonate salts of delamanid formed in the same step as the dispersionplasticizationwater in the salts and in the wetted matrix; the drug plasticizing the polymer in extrusionfood effectfed media that raise solubility or promote crystallizationchiralitya single enantiomer against its racemate in solubility, inhibition and release

02Formulas

supersaturation ratioPrinted in words: the supersaturation ratio is the LLPS concentration divided by the equilibrium solubility of the crystalline drug,S = C/Ceq, with Ceq in the same medium; celecoxib and lopinavir in suspension liquidsHoffman equation\Delta G_v = -\frac{\Delta H_{fus}\,(T_{melt,ons} - T)\,T}{T_{melt,ons}^{2}}free-energy estimate behind the amorphous solubilityamorphous solubility advantage from free energy difference\ln x_{SL,L_1} = \ln x_{C,L_1} + \frac{\Delta G_{a\to c}}{RT}ratio of solubilities from ΔG or from the chemical potentials (lopinavir 17.4/3.1)amorphous-to-crystalline solubility ratio\frac{\sigma_a}{\sigma_c} = \frac{\text{LLPS onset concentration}}{\text{crystalline solubility in the same medium}}felodipine and indomethacin estimates; tacrolimus 49/1.4classical nucleation theoryJ \propto \exp\left(-\frac{\Delta G^{*}}{k_B T}\right)dependence of nucleation on supersaturation and interfacial tensioninduction time decompositiont_{ind} = t_n + t_gt_{ind} = t_n + t_g behind the celecoxib induction timesrelative nucleation rate from seeded and unseeded induction times\frac{R}{R_0} = \frac{t_{s,0}}{t_s}HPMCAS effect on celecoxib nucleation, about 4000crystal growth inhibition effectiveness ratioThe polymer effectiveness ratio for crystal growth inhibition is the growth rate without polymer over the rate with polymer:R_0/R_p of seeded celecoxib, 70–158 xie2016a E5membrane flux from concentration differenceJ = \frac{D_{eff}}{l}\left(C_d - C_r\right)dialysis test of dissolved felodipinemembrane flux in terms of solute activityJ = \frac{dM}{dt} = \frac{D\,S\,a}{h\,\gamma_m}danazol flux and free drug; tacrolimus flux plateaumass flow rate from receiver concentration slopeJ = \frac{dC_r}{dt}\times V_r with V_r the receiver volumeresveratrol flux, slope times receiver volume, in words wegiel2015 E1supersaturation from membrane flux ratioIn words: the supersaturation is directly proportional to flux, so S = J/J_{ref} with the flux of a reference solution at the crystalline solubilityresveratrol supersaturation proportional to flux, in words wegiel2015 E3activity-based supersaturation ratioSR = \frac{a}{a^{*}} = \frac{\gamma\,c}{\gamma^{*}\,c^{*}}danazol maximum supersaturation; \ln S = (\mu - \mu^{*})/RT for celecoxibideal-mixing reduction of amorphous solubilityS_a(x_1) = S_a^{\circ}\,x_1C_{max} = S_a x_d for two drugs; proportional dilution by weight for lopinavir with polymersFlory-Huggins activity equationActivity coefficient of the drug in a polymer, with the amorphous drug as the solvent (2006):drug chemical potential in an undissolved polymerNoyes-Whitney equationAs printed for crystals dissolving in a polymer melt (concentration C of dissolved drug in the liquid phase):dissolution arm of the scheme; redissolution of indomethacin precipitatescongruent release relationG_D = \frac{G_C\,A_D}{A_C}carrier-controlled dissolution at 10% drug; Corrigan's coupled dissolution for celecoxibStokes-Einstein equationD_{NMR} = \frac{k_B T}{6\pi\eta r}particle size of tacrolimus colloids, named only trasi2016 E4amorphous solubility advantage with water-sorption correctionC_{\mathrm{amorphous}} = C_{\mathrm{eq}}\,\exp\left(-I(a_2)\right)\,\exp\left(\frac{\Delta G_{a \to c}}{RT}\right)named only, not applied trasi2016 E5; xie2017 E3amorphous solubility advantage from the Hoffman approximation\frac{\sigma_a}{\sigma_c} = e^{\Delta G/RT}, \qquad \Delta G = \frac{\Delta H_f\,\Delta T}{T_m}\cdot\frac{T}{T_m}, \qquad \Delta T = T_m - Tnamed only for indomethacin xie2017 E2amorphous–crystalline free energy difference from heat capacityWith linear reversing heat capacities C_p^{sl} = aT + b and C_p^{c} = cT + dfirst term of the Huang model, not applied li2018 E3additive moisture sorptionPrinted in words in the two moisture papers (weight-averaged sum of the pure-component uptakes)M_{additive} = M_D w_D + M_P w_P; lopinavir dispersions at 90% RH li2018 E1power-law crystal growth rateR_G = k_G\,A\,(C_b - C^{*})^{g}linear growth law of the scheme, R_G \propto (C - C_{eq}) alonzo2010 E5activity from concentrationa_{i1} = x_i\,\gamma_{i1}\ln \gamma c = \ln a, in the argument on solution activity alonzo2011 E6pH-solubility profileC_T = C_B\left(1 + 10^{\,\mathrm{p}K_a - \mathrm{pH}}\right)pKa fit of the delamanid solubility curve and the predicted buffer curveCabrera-Vermilyea step pinning\frac{V_\rho}{V_\infty} = 1 - \frac{\rho_c}{\rho}\upsilon/\upsilon_0 = 1 - \rho_c/l for paclitaxel growth with adsorbed HPMCAS que2018 E3aspect ratio\text{aspect ratio} = \frac{\bar{L}}{\bar{W}}length over width of paclitaxel seeds before and after growth que2018 E5
15 more formulas printed by one paper (table only)
formularole hereexpression
ideal solubility equationtable only: \ln \gamma c = \frac{\Delta H_f\,T_m}{R}\left(\frac{1}{T_m} - \frac{1}{T}\right) as printed, the extra T_m a misprint of the usual form alonzo2011 E5, X14table only
Flory–Huggins enthalpy of mixingtable only: \Delta H_{sol} = RT\chi_{12} n_1 V_2 and \Delta H_{sol} = RT\left(n_1 V_2 \chi_{12} + n_1 V_3 \chi_{13} + n_2 V_3 \chi_{23}\right) alonzo2011 E7, E8table only
CMC from solubilization break pointtable only: CMC where the two straight lines of solubility against surfactant concentration meet (in words) chen2015a E2table only
initial dissolution rate from early concentrationtable only: rate from the concentration at 5 min (in words) konno2008a E6table only
excess concentration above polymer-containing solubilitytable only: apparent supersaturation as the resveratrol concentration above the crystalline solubility in a medium with the same amount of dissolved polymer (in words); one table row does not reproduce wegiel2015 E2table only
induction time inversely proportional to nucleation ratetable only: t_{ind} \propto J^{-1} if steady-state nucleation is reached quickly and t_n \gg t_g xie2015 E2, C41table only
Higuchi–Corrigan critical mixture ratiotable only: N_A/N_B > D_A C_{SA}/(D_B C_{SB}), the condition for component-controlled dissolution (cited) xie2016a E2table only
mass balance of a dissolved capsuletable only: 125 µg/mL total = 50 µg/mL dissolved + 75 µg/mL undissolved (in words), reproduces trasi2016 E3table only
scattering baseline correction of UV absorbancetable only: indomethacin concentration from A_{319} - E_{450} by calibration (in words) xie2017 E4table only
Gibbs–Duhem integration of water sorption for drug activitytable only: the water term of the Huang model, written out on its draft, not applied li2018 E5table only
critical radius of a two-dimensional nucleustable only: \rho_c = \gamma a/(kT\ln S), 5.4–7.0 nm for paclitaxel at S = 88, with the concept page critical radius of a two-dimensional nucleus que2018 E2table only
crystal end area per mass for cuboid crystalstable only: needle-end area per gram from SEM lengths and widths on a cuboid assumption (in words) que2018 E4, C18table only
growth unit areatable only: the area of one paclitaxel growth unit, 2.64 nm², from the crystal structure (in words) que2018 E7table only
estimated matrix crystallization from SHG volume fractionstable only: the SHG volume fraction divided by the TPE-UVF volume fraction of undissolved drug, in words elkhabaz2019a E1table only
HME processing temperature windowtable only: T_{HME} > T_m and 15\ ^{\circ}\mathrm{C} \le T_{HME} - T_{g,poly} \le 60\ ^{\circ}\mathrm{C}, relaxed by plasticization alvarenga2025 E2table only

Sources: B. Supersaturation from ASD dissolution

Every paper cited in the chapter B. Supersaturation from ASD dissolution (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-two rows are the papers of the chapter, 2008–2025, in year order (within 2015, 2016 and 2023 in the order of the subcategory list); the rows after them are papers filed in other subcategories that the findings and drafts use for comparison, also in year order.

keyyeartitleslugcategory / subcategory
konno2008a2008Effect of polymer type on the dissolution profile of amorphous solid dispersions containing felodipine2008-konno-polymer-type-felodipine-asd-dissolutionDissolution / B. Supersaturation from ASD dissolution
alonzo20102010Understanding the Behavior of Amorphous Pharmaceutical Systems during Dissolution2010-alonzo-amorphous-pharmaceutical-dissolution-crystallization-polymersDissolution / B. Supersaturation from ASD dissolution
alonzo20112011Dissolution and Precipitation Behavior of Amorphous Solid Dispersions2011-alonzo-asd-dissolution-precipitation-nanoparticlesDissolution / B. Supersaturation from ASD dissolution
ilevbare2013d2013Influence of Additives on the Properties of Nanodroplets Formed in Highly Supersaturated Aqueous Solutions of Ritonavir2013-ilevbare-ritonavir-nanodroplets-additives-asd-llpsDissolution / B. Supersaturation from ASD dissolution
raina2014b2014Impact of Polymers on the Crystallization and Phase Transition Kinetics of Amorphous Nifedipine during Dissolution in Aqueous Media2014-raina-polymers-nifedipine-crystallization-phase-transition-dissolutionDissolution / B. Supersaturation from ASD dissolution
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
trasi2015b2015Dissolution performance of binary amorphous drug combinations—Impact of a second drug on the maximum achievable supersaturation2015-trasi-taylor-binary-amorphous-drug-combinations-supersaturationDissolution / B. Supersaturation from ASD dissolution
wegiel20152015Phase Behavior of Resveratrol Solid Dispersions Upon Addition to Aqueous media2015-wegiel-resveratrol-solid-dispersions-aqueous-phase-behaviorDissolution / B. Supersaturation from ASD dissolution
xie20152015Dissolution Performance of High Drug Loading Celecoxib Amorphous Solid Dispersions Formulated with Polymer Combinations2015-xie-taylor-celecoxib-high-drug-loading-asd-polymer-combinationsDissolution / B. Supersaturation from ASD dissolution
li2016b2016Leaching of Lopinavir Amorphous Solid Dispersions in Acidic Media2016-li-lopinavir-asd-leaching-acidic-mediaDissolution / B. Supersaturation from ASD dissolution
trasi20162016Non-Sink Dissolution Behavior and Solubility Limit of Commercial Tacrolimus Amorphous Formulations2016-trasi-commercial-tacrolimus-asd-nonsink-amorphous-solubilityDissolution / B. Supersaturation from ASD dissolution
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
xie20172017Impact of Eudragit EPO and Hydroxypropyl Methylcellulose on Drug Release Rate, Supersaturation, Precipitation Outcome and Redissolution Rate of Indomethacin Amorphous Solid Dispersions2017-xie-eudragit-epo-hpmc-indomethacin-asd-supersaturation-redissolutionDissolution / B. Supersaturation from ASD dissolution
li20182018Tailoring supersaturation from amorphous solid dispersions2018-li-tailoring-supersaturation-lopinavir-insoluble-polymer-asdDissolution / B. Supersaturation from ASD dissolution
que20182018Paclitaxel Crystal Seeds with Different Intrinsic Properties and Their Impact on Dissolution of Paclitaxel-HPMCAS Amorphous Solid Dispersions2018-que-paclitaxel-crystal-seeds-hpmcas-asd-dissolutionDissolution / B. Supersaturation from ASD dissolution
elkhabaz2019a2019Characterization of Phase Transformations for Amorphous Solid Dispersions of a Weakly Basic Drug upon Dissolution in Biorelevant Media2019-elkhabaz-posaconazole-asd-phase-transformations-biorelevant-mediaDissolution / B. Supersaturation from ASD dissolution
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
nguyen2023b2023Enteric coating of tablets containing an amorphous solid dispersion of an enteric polymer and a weakly basic drug: A strategy to enhance in vitro release2023-nguyen-enteric-coating-delamanid-hpmcp-asd-releaseDissolution / B. Supersaturation from ASD dissolution
nguyen2023c2023Impact of Gastric pH Variations on the Release of Amorphous Solid Dispersion Formulations Containing a Weakly Basic Drug and Enteric Polymers2023-nguyen-gastric-ph-variations-delamanid-enteric-polymer-asdDissolution / B. Supersaturation from ASD dissolution
polyzois20242024Amorphous Solid Dispersion Formation for Enhanced Release Performance of Racemic and Enantiopure Praziquantel2024-polyzois-praziquantel-racemic-enantiopure-asd-releaseDissolution / B. Supersaturation from ASD dissolution
alvarenga20252025Release performance and crystallization of racemic and enantiopure praziquantel amorphous solid dispersion in various media2025-alvarenga-praziquantel-racemic-enantiopure-asd-release-crystallization-mediaDissolution / B. Supersaturation from ASD dissolution
towler20082008An Investigation into the Influence of Counterion on the Properties of Some Amorphous Organic Salts2008-towler-counterion-amorphous-organic-saltsSolid state stability / Crystallization tendency
rumondor20102010Effects of Moisture on the Growth Rate of Felodipine Crystals in the Presence and Absence of Polymers2010-rumondor-moisture-felodipine-crystal-growth-pvp-hpmcasSolid state stability / Physical stability
vaneerdenbrugh2010b2010Small Scale Screening To Determine the Ability of Different Polymers To Inhibit Drug Crystallization upon Rapid Solvent Evaporation2010-van-eerdenbrugh-polymer-crystallization-inhibition-spin-coating-screenSolid state stability / Miscibility and drug-polymer interactions
alonzo20122012Characterizing the Impact of Hydroxypropylmethyl Cellulose on the Growth and Nucleation Kinetics of Felodipine from Supersaturated Solutions2012-alonzo-hpmc-felodipine-growth-nucleation-supersaturationDissolution / D. Crystallization from solution
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
vaneerdenbrugh2012a2012Molecular Weight Effects on the Miscibility Behavior of Dextran and Maltodextrin with Poly(vinylpyrrolidone)2012-van-eerdenbrugh-dextran-maltodextrin-pvp-molecular-weight-miscibilitySolid state stability / Miscibility and drug-polymer interactions
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
ilevbare2013b2013Impact of Polymers on Crystal Growth Rate of Structurally Diverse Compounds from Aqueous Solution2013-ilevbare-polymers-crystal-growth-structurally-diverse-compoundsDissolution / D. Crystallization from solution
ilevbare2013c2013Maintaining Supersaturation in Aqueous Drug Solutions: Impact of Different Polymers on Induction Times2013-ilevbare-polymers-supersaturation-induction-timesDissolution / D. Crystallization from solution
kestur2013b2013Influence of particle size on the crystallization kinetics of amorphous felodipine powders2013-kestur-particle-size-crystallization-amorphous-felodipine-pvpSolid state stability / Physical stability
wegiel2013b2013Crystallization of Amorphous Solid Dispersions of Resveratrol during Preparation and Storage—Impact of Different Polymers2013-wegiel-resveratrol-asd-polymer-crystallization-stabilitySolid state stability / Physical stability
jackson20142014Impact of Polymers on the Precipitation Behavior of Highly Supersaturated Aqueous Danazol Solutions2014-jackson-polymers-precipitation-supersaturated-danazolDissolution / D. Crystallization from solution
raina2014a2014Enhancements and Limits in Drug Membrane Transport Using Supersaturated Solutions of Poorly Water Soluble Drugs2014-raina-llps-limits-drug-membrane-transport-supersaturated-solutionsBioperformance / Bioperformance
chen20152015Bile Salts as Crystallization Inhibitors of Supersaturated Solutions of Poorly Water-Soluble Compounds2015-chen-bile-salts-crystallization-inhibitors-supersaturated-solutionsDissolution / D. Crystallization from solution
raina2015b2015Trends in the Precipitation and Crystallization Behavior of Supersaturated Aqueous Solutions of Poorly Water-Soluble Drugs Assessed Using Synchrotron Radiation2015-raina-precipitation-crystallization-supersaturated-dihydropyridines-synchrotronDissolution / D. Crystallization from solution
raina2015c2015Impact of Solubilizing Additives on Supersaturation and Membrane Transport of Drugs2015-raina-solubilizing-additives-supersaturation-membrane-transportBioperformance / Bioperformance
trasi2015a2015Thermodynamics of Highly Supersaturated Aqueous Solutions of Poorly Water-Soluble Drugs—Impact of a Second Drug on the Solution Phase Behavior and Implications for Combination Products2015-trasi-second-drug-supersaturated-solutions-drug-rich-phaseDissolution / C. Amorphous solubility and LLPS
sato20152015Chiral discrimination by a cellulose polymer: differential crystallization inhibition of enantiomers in amorphous dispersions2015-sato-cellulose-polymer-chiral-crystallization-inhibition-enantiomersSolid state stability / Physical stability
almeidaesousa20162016Supersaturation Potential of Salt, Co-Crystal, and Amorphous Forms of a Model Weak Base2016-almeida-sousa-supersaturation-salt-cocrystal-amorphous-weak-baseDissolution / C. Amorphous solubility and LLPS
indulkar20162016Exploiting the phenomenon of liquid-liquid phase separation for enhanced and sustained membrane transport of a poorly water soluble drug2016-indulkar-llps-nanodroplet-reservoir-membrane-transportBioperformance / Bioperformance
jackson20162016Characterization of Supersaturated Danazol Solutions – Impact of Polymers on Solution Properties and Phase Transitions2016-jackson-supersaturated-danazol-polymer-phase-transitionsDissolution / D. Crystallization from solution
lu20162016Vemurafenib: A Tetramorphic System Displaying Concomitant Crystallization from the Supercooled Liquid2016-lu-vemurafenib-tetramorphic-cold-crystallization-supercooled-liquidSolid state stability / Crystallization tendency
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
schram20162016Polymer Inhibition of Crystal Growth by Surface Poisoning2016-schram-polymer-inhibition-crystal-growth-surface-poisoningDissolution / D. Crystallization from solution
correasoto20172017Second harmonic generation microscopy as a tool for the early detection of crystallization in spray dried dispersions2017-correa-soto-shg-early-crystallization-spray-dried-asdsCharacterization methods / Solid-state methods
elkhabaz20172017Variation in the Supersaturation and Phase Behavior of Ezetimibe Amorphous Solid Dispersions Upon Dissolution in Different Biorelevant Media2017-elkhabaz-ezetimibe-asd-phase-behavior-biorelevant-mediaBioperformance / Bioperformance
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
lu20172017Maintaining Supersaturation of Active Pharmaceutical Ingredient Solutions with Biologically Relevant Bile Salts2017-lu-bile-salts-telaprevir-supersaturationDissolution / D. Crystallization from solution
trasi20172017Evaluation of the Crystallization Tendency of Commercially Available Amorphous Tacrolimus Formulations Exposed to Different Stress Conditions2017-trasi-commercial-amorphous-tacrolimus-crystallization-stressSolid state stability / Physical stability
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
purohit20182018Investigating the impact of drug crystallinity in amorphous tacrolimus capsules on pharmacokinetics and bioequivalence using discriminatory in vitro dissolution testing and PBPK modeling and simulation2018-purohit-tacrolimus-crystallinity-dissolution-pbpk-bioequivalenceBioperformance / Bioperformance
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
wilson20182018Relationship between Amorphous Solid Dispersion In Vivo Absorption and In Vitro Dissolution: Phase Behavior During Dissolution, Speciation, and Membrane Mass Transport2018-wilson-asd-in-vivo-absorption-dissolution-phase-behavior-mass-transportBioperformance / Bioperformance
hate20192019Absorptive dissolution testing: An improved approach to study the impact of residual crystallinity on the performance of amorphous formulations2019-hate-absorptive-dissolution-residual-crystallinity-amorphous-formulationsBioperformance / Bioperformance
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
li20192019Microstructure Formation for Improved Dissolution Performance of Lopinavir Amorphous Solid Dispersions2019-li-lopinavir-hpmc-asd-microstructure-dissolutionASD process / ASD process
purohit20192019Assessing the impact of endogenously derived crystalline drug on the in vivo performance of amorphous formulations2019-purohit-endogenous-crystallinity-in-vivo-amorphous-tacrolimusBioperformance / Bioperformance
trasi20192019Amorphous solid dispersion formation via solvent granulation – A case study with ritonavir and lopinavir2019-trasi-solvent-granulation-ritonavir-lopinavir-asdASD process / ASD process
elkhabaz2019b2019Interplay of supersaturation and solubilization: Lack of correlation between concentration-based supersaturation measurements and membrane transport rates in simulated and aspirated human fluids2019-elkhabaz-supersaturation-solubilization-activity-flux-biorelevant-mediaBioperformance / Bioperformance
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
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
wilson20202020Amorphous solid dispersions of enzalutamide and novel polysaccharide derivatives: investigation of relationships between polymer structure and performance2020-wilson-enzalutamide-polysaccharide-asd-polymer-performanceBioperformance / Bioperformance
moseson2020a2020Amorphous Solid Dispersions Containing Residual Crystallinity: Influence of Seed Properties and Polymer Adsorption on Dissolution Performance2020-moseson-residual-crystallinity-seed-properties-polymer-adsorptionASD process / ASD process
moseson20212021Amorphous Solid Dispersions Containing Residual Crystallinity: Competition Between Dissolution and Matrix Crystallization2021-moseson-residual-crystallinity-dissolution-matrix-crystallizationASD process / ASD process
ueda20212021Effect of Polymer Species on Maximum Aqueous Phase Supersaturation Revealed by Quantitative Nuclear Magnetic Resonance Spectroscopy2021-ueda-polymer-species-maximum-aqueous-supersaturation-nmrDissolution / C. Amorphous solubility and LLPS
wilson20212021Interaction of Polymers with Enzalutamide Nanodroplets—Impact on Droplet Properties and Induction Times2021-wilson-enzalutamide-nanodroplets-polymer-interactions-induction-timesDissolution / D. Crystallization from solution
elkhabaz20212021Crystallization Kinetics in Fasted-State Simulated and Aspirated Human Intestinal Fluids2021-elkhabaz-crystallization-kinetics-fasted-simulated-aspirated-human-intestinal-fluidsDissolution / D. Crystallization from solution
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
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
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
moseson2022a2022Atomic Layer Coating to Inhibit Surface Crystallization of Amorphous Pharmaceutical Powders2022-moseson-atomic-layer-coating-surface-crystallization-asd-powdersASD process / ASD process
duong2022b2022Phase Behavior and Crystallization Kinetics of a Poorly Water-Soluble Weakly Basic Drug as a Function of Supersaturation and Media Composition2022-duong-posaconazole-phase-behavior-crystallization-kinetics-mediaDissolution / D. Crystallization from solution
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
moseson20232023Impact of Aluminum Oxide Nanocoating on Drug Release from Amorphous Solid Dispersion Particles2023-moseson-aluminum-oxide-nanocoating-drug-release-asd-particlesASD process / ASD process
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
nguyen2023a2023Fed- and Fasted-State Performance of Pretomanid Amorphous Solid Dispersions Formulated with an Enteric Polymer2023-nguyen-pretomanid-hpmcas-asd-fed-fasted-performanceBioperformance / Bioperformance
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
shah20242024Orthogonal Analytical Methods to Elucidate How Low Levels of Residual Crystallinity in Posaconazole Amorphous Solid Dispersions Impact Phase Behavior during Release2024-shah-posaconazole-asd-residual-crystallinity-release-phase-behaviorASD process / ASD process
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
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
For the authors: card issues found while writing

Card issues: B. Supersaturation from ASD dissolution

Material problems found in the cards of the chapter while writing it (slice 1: eight papers of 2008–2015; slice 2: seven papers of 2015–2018; slice 3: seven papers of 2018–2025). Extractor notes (X#) that the cards already contain are not repeated here; for example the misprinted ideal-solubility equation of alonzo2011 is recorded in its X14 and is shown in the Formulas table of the chapter page as printed.

None found. No contradiction between card sections was met while writing the findings of konno2008a, alonzo2010, alonzo2011, ilevbare2013d, raina2014b, chen2015a, jackson2015 and trasi2015b, and a script check showed that every id cited inside these eight cards resolves to a row of the same card (raina2014b gives its three polymers one combined row, M2–M4, for the absence of a nifedipine solubility gain at 1 mg/mL polymer, beside the separate rows M2, M3 and M4).

Slice 2 (wegiel2015, xie2015, li2016b, trasi2016, xie2016a, xie2017, li2018): none found. A script check showed that every id cited inside these seven cards resolves to a row of the same card (the only unmatched token, R0 in xie2016a, is the growth-rate symbol R_0, not an id). The source inconsistencies met while writing (for example the sign of the enthalpy term of li2018 E3 against E6, the HPMCP polysorbate 80 ratio of li2016b, the misreferenced table and equation in xie2015 C43, the HPMCAS row of the wegiel2015 excess-concentration table) are recorded in the cards' own X notes (li2018 X1, li2016b X2, xie2015 X1, wegiel2015 E2 and X3) and are carried into the chapter as such. Two points are not card errors and are noted only to avoid misreading: the SDS CMC with lopinavir in pH 3 citrate buffer (0.050%, li2016b R1) differs from that with celecoxib in pH 3 HCl (0.23%, chen2015a R4) because the media differ; and the wording of F3 of this chapter, which had called α the stable form of indomethacin, was corrected in the chapter from xie2017 M1 (γ stable, α slightly less stable), not in a card.

Slice 3 (que2018, elkhabaz2019a, duong2022a, nguyen2023b, nguyen2023c, polyzois2024, alvarenga2025): none found. A script check showed that every id cited inside these seven cards resolves to a row of the same card (121, 108, 146, 117, 130, 97 and 121 distinct cited ids). Every inconsistency met while writing is already recorded in the cards' own X notes and is carried into the chapter with that note: the paclitaxel UV readings above the HPLC values at 16 h and the reversed order of the two least harmful seeds (que2018 X4), the units of the critical-radius equation and the stand-in interfacial tensions (que2018 X7, C37), the SHG volume fraction of the 50% posaconazole dispersion exceeding its TPE-UVF fraction after 120 min (elkhabaz2019a X6), the two time bases used for the supersaturation durations of the same runs (elkhabaz2019a X1), the delamanid text and table disagreeing on which salts liquefied and degraded (duong2022a X1, X11), the same 25% edisylate formulation ending at ≈100 µg/mL in one figure and ≈89 in another (duong2022a X4), the delamanid polymer solubilities above about 3.3 mg/mL that exceed what 50 mg in 15 mL allows (nguyen2023c X1), the supersaturation ratios printed as 42 at pH 5.0 while the measured concentrations were far above the amorphous solubility (nguyen2023c X9), the mislabelled series in the praziquantel release figure (alvarenga2025 X2), the praziquantel release plateaus above 100% of the dose (polyzois2024 X3) and the stability statement that conflicts with the paper's own diffraction patterns (polyzois2024 X1).

Three points are not card errors and are noted only to avoid misreading. First, the evidence index of this subcategory lists the 2025 praziquantel paper under the first author's name as printed in that index ("2025 Junior"), while the citation key of the library is alvarenga2025; both point to the same card. Second, the delamanid pKa differs between the papers because one fits it to its own solubility data (3.94 ± 0.04, nguyen2023c R3) and one draws a curve for the cited value 4.3 (nguyen2023b E1); neither card is wrong. Third, the two praziquantel papers measure the amorphous solubility of the racemate as 1.1 mg/mL (polyzois2024 R2) and 1.17 mg/mL (alvarenga2025 R1) in PBS pH 6.5 by the same method, a difference the cards report as measured.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 °Chate2019 R12, C24
tacrolimus crystalline suspensionAUC about 87 µg/mL·min at every volumesamehate2019 R12
tacrolimus generic, freshdid not crystallize at 240, 100 or 40 mL, unlike in an earlier closed vesselsamehate2019 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 mLhate2019 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 dose[hate2018 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 B. Supersaturation from ASD dissolution

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% RH[rumondor2009c R10, C4]
felodipine–PVP 30.3 wt%distinct separation after 1 week75% RH[marsac2010 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 storagekestur2013b 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 B. Supersaturation from ASD dissolution

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 compacts[hiew2022a R20]
same, after 2 h in pH 6.8 buffer3, 21, 54, 12%XPS[hiew2022a 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 evaporationwegiel2013b 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, XPS[trasi2020 R11, C14]
lumefantrine with HPMCP, HPMCAS (20–40% drug), CAP, Eudragit L100 (40%)14–42% protonated; amorphous drug 3%powders precipitated into dilute HCl, XPS[bhujbal2021 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 B. Supersaturation from ASD dissolution

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 solutionsbufferraina2015c C32
atazanavir, posaconazoleconcentration-based and activity-based ratios agree in the two buffers and differ in the four micellar mediasix media, 37 °Celkhabaz2019b R8, R9, C42
water in nifedipine, felodipine, droperidol, pimozide, indomethacin, ketoprofen3.19, 4.13, 3.00, 4.65, 2.54, 3.3525 °C, 95% RH[rumondor2009c R24]
same drugs in water4.95 × 10⁵ to 8.88 × 10⁶; ketoprofen 9.85 × 10⁴from solubility[rumondor2009c 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 B. Supersaturation from ASD dissolution

additive cases for amorphous solubility

A classification of drug/additive pairs by where the additive acts on the amorphous solubility S_a (Ueda 2024, review, pp. 28–40). Case I: the additive forms a complex with the drug in the aqueous phase; S_c and S_a rise, the free drug at the limit stays at S_a^0 and the maximum supersaturation ratio stays at S_a^0/S_c^0. Case II: the additive distributes into the drug-rich phase; S_c is about unchanged, and S_a and the maximum supersaturation ratio fall. Case III: both; S_c rises, the free drug at the limit and the maximum supersaturation ratio fall, and S_a/S_c does not give the maximum. The case belongs to the pair, not the additive: ketoprofen is listed with EUD-E (I), PVP (II) and CTAB (III) (pp. 29, 40–41).

Findings

Amorphous solubility: F11, F12, F19. Crystallization from solution: F19. Bioperformance: F4, F7, F18, F19.

Related concepts

acts on amorphous solubility; Case I relates to micellar solubilization; Case II relates to polymer partitioning into the drug-rich phase and drug-rich phase; decides how free drug concentration and the supersaturation ratio move.

Formulas

Case I (Eq. 6) and Case II for a small-molecule additive and a polymer (Eqs. 9 and 10), as printed in the review; the equations page gives the steps between them:

S_a=\frac{S_a^0}{1-f^a_{com}}

S_a=S_a^0\cdot x_{\mathrm{drug}}\cdot e^{\chi(1-x_{\mathrm{drug}})^2}

S_a=S_a^0\cdot\Phi_{\mathrm{drug}}\cdot e^{(1-\frac{1}{r})(1-\Phi_{\mathrm{drug}})+\chi(1-\Phi_{\mathrm{drug}})^2}

How it is measured or obtained

The review assigns the case from reported solubility, flux and phase composition data (Table 1, p. 29). Two measurements separate the cases (synthesis): S_c with the additive, and the maximum flux or free drug with the additive. S_c up and maximum flux unchanged is Case I; S_c unchanged with S_a and flux down is Case II; S_c up with flux down is Case III.

Values in the library
caseS_cS_afree drug at S_amaximum supersaturation ratioS_a/S_c gives the maximum?
no additiveS_c^0S_a^0S_a^0S_a^0/S_c^0yes
Case IrisesrisesS_a^0S_a^0/S_c^0no; generally smaller
Case IIabout S_c^0fallsS_a^0X(S_a^0/S_c^0)Xyes
Case IIIrisesfalls then rises, or risesS_a^0X(S_a^0/S_c^0)Xno

X is the term of the drug-rich phase in Eqs. 9 and 10 below. The table is taken from the review's text and Figs. 6 and 7, with the Case III formulas added (equations page, W7).

case in the review's Table 1system in the libraryvaluesids
Case Ifelodipine, 0.04% vitamin E TPGSonset 10.4 → 177.3 µg/mL; concentration ratio 9.2 → 4.5; maximum flux in the buffer bandraina2015c R9, R11
Case Iatazanavir, 3.6 mg/mL SDScrystalline 1.1 → 45.6 µg/mL; amorphous 70 → about 1450 µg/mL; concentration ratio about 65 → about 33; flux-derived ratio about 65[indulkar2017a R7, R13]
Case Iibuprofen, EUD-Ecrystalline 29.8 → 42.1 µg/mL; amorphous 177.1 → 256.3 µg/mL; ratio 5.94 → 6.09ueda2020b R1
Case IIibuprofen, HPMC; PVP-VAcrystalline 29.8 → 30.0; 30.1 µg/mL; amorphous 177.1 → 96.9; 90.7 µg/mL; ratio 5.94 → 3.23; 3.01ueda2020b R1
Pitfalls and disagreements

The classification comes from a review; the library has not tested it as a whole, and no paper in the library sets out Case III values for one of the pairs listed there. Atazanavir with STC is listed under Case I, yet with 3 mM STC alone the amorphous solubility fell from 65 to 38 µg/mL and the flux-based maximum was about 40 against about 63 in buffer, returning to about 63–66 from 0.075 mM lecithin [indulkar2018 R6, R10], so the assignment holds for STC with lecithin and not for STC alone (synthesis). The same additive can change class with the drug or the medium: EUD-E stays in the water with ibuprofen at pH 2.0 and associates with enzalutamide droplets at pH 6.5 (F19). In Case III S_a depends on the amount of drug-rich phase, so the measured value depends on dose (pp. 39–40). The review gives no partition equation, so x_{\mathrm{drug}} and \Phi_{\mathrm{drug}} must be measured and cannot be predicted from it (equations page).

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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-driedvaneerdenbrugh2012a R13
felodipine–PVP, 30–50% PVPdrug-rich and polymer-rich phases after 94% RHIR, TEM[marsac2010 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 dryer[li2020 R4, R7, R10]
pimozide–PVP 50:50Tgs −21/44 °C wet, 61/112 °C re-dried94% RH, 42 h[rumondor2009c R17]
felodipine–PVP 46.5 wt%event at ≈45–50 °C instead of one Tg near 80 °Cafter 75–94% RH[marsac2010 R14]
felodipine–PVP 50% filmislands of about 300–500 nm (TEM, AFM)94% RH[marsac2010 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, dried[rumondor2010c 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% RH[rumondor2011 R14]
ritonavir with PVP, PVPVA; HPMCASall PVP and PVPVA dispersions separated, from about 1 h; HPMCAS stayed miscible97% RH, films and powders[purohit2017b 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 immersion[purohit2017b 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 days[que2019 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 h[saboo2019 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 dissolution[bhardwaj2018 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% RH[saboo2021 R21]
clopidogrel 40, 50, 60% filmsuniform; bicontinuous; drug-continuous5 min, 100% RH[correasoto2022a R20]
atazanavir 10% filmuniform for 3 h at 37 °C; separated within 10 min at 50 °C100% RH[correasoto2022b 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 6.8[yang2022a 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 dyes[deac2023a 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 B. Supersaturation from ASD dissolution

amorphous-crystalline free energy difference

The Gibbs free energy of converting the crystal to the amorphous drug (supercooled liquid or glass) at the test temperature; it fixes the factor e^{\Delta G/RT} of the amorphous solubility [almeidaesousa2015 E1, E11]. It is estimated from Tm and ΔHf by the Hoffman equation or from temperature-dependent heat capacities by a thermodynamic cycle (the Cp method), to the supercooled liquid or, below Tg, to the glass [almeidaesousa2015 E2, E9, E10, E14].

Findings

F5, F7.

Related concepts

estimated by the Hoffman equation; depends on degree of supercooling; sets the amorphous solubility advantage; reference state discussed under structural relaxation.

Formulas

Hoffman equation, amorphous-crystalline free energy difference from heat capacity, Gibbs free energy relation.

How it is measured or obtained

DSC melting data and modulated-DSC reversing heat capacities fitted linearly in T for crystal, glass and supercooled liquid; the Cp method needs an un-ionized, non-solvated crystal that melts without degradation [almeidaesousa2015 P5, P6, C11; mosqueragiraldo2015 P3].

Values in the library
materialvalue or classconditionspaper ids
ibuprofen, phenylbutazone, tolnaftate3.24/3.56; 4.84/4.59; 5.69/6.13 kJ/mol (Hoffman / Cp, to supercooled liquid)25 °C[almeidaesousa2015 R11]
diclofenac; sorafenib; griseofulvin8.51/9.99; 10.33/10.34; 9.69/9.39 kJ/mol25 °C[almeidaesousa2015 R11]
sorafenib; griseofulvin, to the glass11.37; 10.38 kJ/mol25 °C[almeidaesousa2015 R12]
CRH15.68 (Hoffman); 5.85 (Cp, supercooled liquid); 5.95 kJ/mol (Cp, glass)25 °Calmeidaesousa2016 M1
telaprevir, Hoffman13.31 kJ/mol (extractor recomputation)37 °C[mosqueragiraldo2015 E1]
atazanavir14.55 kJ/mol, Hoffman, recomputed from the printed Table I inputs (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]
Pitfalls and disagreements

The Cp parameters are not printed, so the Cp values cannot be recomputed [almeidaesousa2015 E9, E10]. The claim that the Cp method is more accurate presupposes that the onset equals the supercooled-liquid solubility [almeidaesousa2015 X4]. The glass carries more free energy than the supercooled liquid below Tg [almeidaesousa2015 C29]. For atazanavir (undercooling 171 K, synthesis: 481 − 310 K) the Hoffman inputs printed give the printed ratio of 62 only with 0.22 read as exp[−I(a)], not I(a) as Table I heads the column (synthesis) [indulkar2017a X1; indulkar2015 M2]; for pazopanib the cycle cannot be run because it degrades on melting [sugihara2018 C17].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 baseDSCtowler2008 R4
nicardipine saltsTg 28.5–81.0 °C against 3.2 °C for the baseDSCtowler2008 R5
20 salts of both bases11 amorphous after freeze-dryingDSCtowler2008 R1
propranolol salts0.39–61.90% water uptake at 75% RHvapour sorptiontowler2008 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 B. Supersaturation from ASD dissolution

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 °Calmeidaesousa2016 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–dichloromethanevaneerdenbrugh2010b R2
50/50 drug–PAA, drug–PVP powderscrystalline with PAA for acidic drugs, amorphous with PVProtary evaporation, 7 daysvaneerdenbrugh2010b 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 µm[hiew2022a 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 granulationtrasi2019 R1, R2
ritonavir–PVPVA spray-dried, 25–75% DLX-ray amorphous (methanol powders); one Tg of 91, 75 and 63 °Cspray drying[li2020 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 amorphous[hate2018 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 SHGelkhabaz2017 R8
tacrolimus capsulestacrolimus:HPMC 1:1; drug about 4% of fillgenericpurohit2018 M2, R2
enzalutamide in PVPVA or HPMCAS-MF10 and 50 wt% drug, rotary-evaporated, amorphous by XRPD and FTIRused within 2 weekswilson2018 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 transport[ueda2020a 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-evaporated[rumondor2009c 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 evaporationwegiel2013b 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 dishtrasi2017 R16, R13
ATP enantiomers with 5% w/w polymermelt-quenched films from solvent-evaporated mixturesgrowth at 40–90 °Csato2015 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 B. Supersaturation from ASD dissolution

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 °Craina2015c C29
tacrolimusabout 35 (49/1.4), about 33–36 by method; other drugs 5–65amorphous solubility by ultracentrifugation, pH 4.5, 37 °Ctrasi2016 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 °Cmoseson2020a R1
BCL, pH 6.8 phosphateform 1 4.3, form 2 15, amorphous 150 µg/mL; 35-fold37 °Cmoseson2021 R1, R2
RTV and LPV, pH 6.8crystalline 1.8 and 2.9, amorphous 31 and 19 µg/mL10 mM phosphate, 37 °Ctrasi2019 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 dosemoseson2020a 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 °Cshah2024 R11, C14
ritonavir / atazanavir / lopinavirabout 14 / 83 / 6pH 6.8[alhalaweh2016 R6]
clotrimazole15pH 8indulkar2016 R3
atazanavirobserved ratio in SDS about half that in buffer, with unchanged activity[indulkar2017a 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 mediaelkhabaz2019b 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 4.5purohit2019 C30
enzalutamideabout 14.5 (42/2.9); S "approximately 13" is the theoretical 39/2.9pH 6.5wilson2018 R1, R3, X2
felodipineS of about 10 over the crystal (theoretical and measured)benchmark for the supersaturation range S 3–12alonzo2012 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 °Cilevbare2013c 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 °Cjackson2014 R2, R3, X1
six dihydropyridinesestimated amorphous solubility 0.5, 6.68, 48, 20, 6.3, 19.0 µg/mLbuffer, Hoffman with water correctionraina2015b R10
danazol7.8 µg/mL with heat-capacity data and the water correction; onset 8 µg/mL25 °C, pH 6.8jackson2016 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 °Cduong2022b R1, R6, R7, X5
felodipineabout 10 times the crystal, about 9.5 µg/mL37 °C, pH 6.8 test fluidkonno2008a 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 6.8trasi2015b M1, M2
lopinavirabout 5.6 (17.4/3.1)pH 3, 25 °Cli2018 E2, R1
indomethacin with 100 µg/mL HPMC36 µg/mL against 1.61 (γ) and 2.8 µg/mL (α)pH 2.2, 37 °Cxie2017 R3, R1
paclitaxel31.6 against 0.36 µg/mL, a ratio of about 88pH 6.8, 37 °C, three methodsque2018 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 °Calvarenga2025 R1
posaconazoleabout 20 against 1.69 µg/mL in FaSSIF; 115.1 µg/mL crystalline in FaSSGF37 °Celkhabaz2019a 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 B. Supersaturation from ASD dissolution

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 methodstrasi2015a 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 °Calmeidaesousa2016 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 °C[indulkar2017a 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 °Cueda2021 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 °Craina2014a R16
nifedipine72.09 µg/mL predicted; onset 72.85buffer with 1 mg/mL HPMC, 37 °Craina2014a R16, X3
felodipine, FaSSIFonset 214.6 µg/mL; estimate 308.037 °Craina2015c 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 °Cindulkar2016 R2, R3
atazanavir78 µg/mL (94 with 1.8 mg/mL PVPVA)pH 6.8, 1 mg/mL HPMCAS[hate2018 R2, R3]
ezetimibe21.0 µg/mL buffer; 123 µg/mL FeSSIF37 °Celkhabaz2017 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 Ipurohit2018 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 °Cwilson2018 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 polymer[ueda2020a R1, C13]
nifedipine123 µg/mL with AS-HF against 221 with AS-LFbuffer, 37 °C, 1000 µg/mL polymer[ueda2020a 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 °Celkhabaz2019b 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 conditionshate2019 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 B. Supersaturation from ASD dissolution

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/mLilevbare2013b 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 6.5wilson2021 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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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, DSC[deac2023a 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 °C[deac2024b 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 B. Supersaturation from ASD dissolution

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/g[benson2025 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 °C[benson2025 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 B. Supersaturation from ASD dissolution

BFDH morphology prediction

The Bravais–Friedel–Donnay–Harker prediction of crystal shape from the crystal structure alone (lattice and symmetry, without growth conditions or additives). For ritonavir Form II (orthorhombic, P2₁2₁2₁) it gives a rodlike habit elongated along the a-axis with four fast-growing faces (−1 0 −1), (−1 −1 0), (−1 0 1), (−1 1 0) that expose carbonyl oxygens and thiazole nitrogens [ilevbare2012c R5; ilevbare2012a R5]. For acetaminophen the BFDH shape is a compact polyhedron with the faces {002}, {200}, {102} and {111}, unlike the thin flat elongated crystals grown without polymer [trasi2015 R13, R12].

Findings

F8, F12, F27.

Related concepts

predicts crystal habit; used with polymer adsorption on crystal surfaces.

Formulas

none.

How it is measured or obtained

The BFDH tool in Mercury (version 3.0.1) applied to the Cambridge Structural Database structure (YIGPIO01); the real seeds are compared by SEM and PXRD (the weak (200) reflection near 17.7° 2θ, strong in the predicted pattern) [ilevbare2012c P7, R6; ilevbare2012a P6, R4].

Values in the library
materialvalue or classconditionspaper ids
ritonavir Form IIfastest growth along a; four fast faces; seeds more needle-like than the predicted rodBFDH, Mercury[ilevbare2012c R5; ilevbare2012a R4, R5]
(200) reflectionabout 150 counts in seeds; about 245 after growth with Pn-IPAAmdPXRD[ilevbare2012c R6]
acetaminophencompact polyhedron; real crystals thin platesMercury; microscopy at 40×[trasi2015 R12, R13]
Pitfalls and disagreements

The face-binding argument for Pn-IPAAmd holds only if the BFDH fast faces are the fast faces of the real crystals; the experimental habit is more needle-like than predicted; PXRD intensities differ at other angles too and the sample mass is unknown [ilevbare2012c C45, R5, X14]. The crystal form of acetaminophen used for the prediction is not stated [trasi2015 X12].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 °C[que2020 R12, R13]
loratadine0.65 ± 0.05, 1.11 ± 0.07 M⁻¹ in cyclohexane; 0.35, 0.39 in toluenesame[que2020 R12, R13]
brotrimazole0.56 ± 0.06, 0.81 ± 0.04 M⁻¹ in cyclohexane; 0.30, 0.21 in toluenesame[que2020 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 B. Supersaturation from ASD dissolution

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-SAFT[deac2024b 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 model[li2020 R17, R19, C50, C53]
ritonavir–PVPVA 10%; 20% compactsdroplets near the gel–solution interface; deeper in the gelreal-time confocal, pH 6.8[yang2022a 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 °C[deac2024b 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 B. Supersaturation from ASD dissolution

Burger-Ramberger rules

Thermodynamic rules for polymorph pairs; the heat-of-fusion rule used in the library says that if the higher-melting form also has the larger heat of fusion, the pair is monotropic [lu2016 E3; trasi2014b E2]. Neither paper prints the rule itself; both apply it in words.

Findings

F7.

Related concepts

tests monotropy; part of polymorphism; uses enthalpy of fusion.

Formulas

Burger-Ramberger heat-of-fusion rule.

How it is measured or obtained

From the DSC melting points and enthalpies of fusion of both forms [lu2016 R20; trasi2014b M1, R6].

Values in the library
materialvalue or classconditionspaper ids
vemurafenib α against β271 °C, 53.8 kJ/mol against 248 °C, 33.3 kJ/mol: monotropicDSClu2016 R20, C50
nilutamide stable form against form Iaround 153 °C, ~98 J/g against 141 °C, around 66 J/g: monotropicDSC[trasi2014b M1, R6, C11]
Pitfalls and disagreements

The vemurafenib β enthalpy may be a lower bound because recrystallization overlaps its melting, and the α value differs between parts of the paper lu2016 X12, X1; the conclusion would change only if β's enthalpy reached α's lu2016 X12.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 celltrasi2015a C35, E3
ibuprofenpolymer dilution, extra water and interactions lower itdrug-rich phaseueda2021 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 °C[ueda2020a 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 °Clu2017 R1
enzalutamide above 42 µg/mLequal chemical potential in droplets and water; crystals can start in either phase or at the interfacepH 6.5wilson2021 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 htrasi2015b R16
ritonavir with 180 µg/mL PVP, PAA, HPMC, HPMCASLLPS concentration unchanged, read as no change of the phase's activity37 °Cilevbare2013d R10, C22
tacrolimus solutions, 20–100 µg/mLflux plateau ≈0.0050–0.0055 µg/min from 60 µg/mLpH 4.5, 37 °Ctrasi2016 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 °Cwegiel2015 R19, R20
lopinavir with undissolved HPMCP, 15–85% drug≈0.6–10.5 against 17.4 µg/mLpH 3, 25 °C, 48 hli2018 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 °Cnguyen2023c 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 B. Supersaturation from ASD dissolution

chirality

Evidence table: chirality. Content from the ASD dissolution chapter (praziquantel 2024–2025), the Physical stability chapter and the Solid-state methods chapter.

The handedness of a drug molecule, and with it the difference between a single enantiomer and the racemate as a solid form and as a solute. The two differ in crystalline solubility, in the solid forms they crystallize as, and in how strongly a polymer delays their crystallization: for praziquantel the R-enantiomer is more soluble as a crystal (282.6 against 196.4 µg/mL), crystallizes as hydrates with anti conformation against an anhydrate with syn conformation, and was held for only 37 and 15.5 min by the two polymers that held the racemate beyond an 83-min run polyzois2024 R1, C26, R3, R4. Chirality also makes most crystalline drugs active in second harmonic generation, which is why SHG sees crystals and not amorphous drug correasoto2017 C7.

Findings

F29, F28.

Related concepts

changes crystallization tendency and nucleation inhibition; changes the amorphous solubility advantage; relates to polymorphism and drug-polymer interactions.

Formulas

amorphous-to-crystalline solubility ratio.

How it is measured or obtained

By running the same tests on the enantiomer and the racemate: crystalline solubility by shake flask, amorphous solubility by the onset of light scattering, induction time at each form's own amorphous solubility with the same polymer level, and release from dispersions of equal drug loading polyzois2024 P1, P2, P3, P8; alvarenga2025 P7, P8, P9. Residues are then examined by polarized light and PXRD to see which form crystallized alvarenga2025 P6, P5.

Values in the library
materialvalue or classconditionspaper ids
praziquantel, crystalline: R-enantiomer; racemate282.6 ± 3.3 and 196.4 ± 0.3 µg/mLPBS pH 6.5, 37 °C, 48 hpolyzois2024 R1
the same, amorphous1.4 ± 0.1 and 1.1 ± 0.1 mg/mL at pH 6.5; 1.4 mg/mL for both at pH 1.637 °Cpolyzois2024 R2
the same, amorphous-to-crystalline ratio across nine media4.0–5.8 (R-enantiomer) and 5.6–7.7 (racemate)37 °Calvarenga2025 R1
induction time with HPMCAS-MF; HPMC E5 LV37 and 15.5 min (R-enantiomer) against at least 83 min (racemate)300 µg/mL polymer, PBS pH 6.5, 37 °Cpolyzois2024 R4, R3
release from HPMCAS-MF 30% at 1.5 mg/mLabout 88% (R-enantiomer) against 71% (racemate), maxima ≈1.4 and ≈1.1 mg/mLPBS pH 6.5, 2 halvarenga2025 R8
release from HPMC E5 LV 30% at 1.5 mg/mLR-enantiomer lost dissolved drug in every medium; the racemate only in biorelevant media37 °Calvarenga2025 C36
a chiral amino alcohol with 5% polymer (Physical stability)HPMCAS slowed one enantiomer about twice as much as the other, the favoured one switching between the LF and HF grades; PVP and HPMCP slowed both alikemelt growth at 60 °Csato2015 C10, C11
Pitfalls and disagreements

The praziquantel induction times for the enantiomer rest on two runs with no statistical test, and the two forms were tested at their own amorphous solubilities, so at different concentrations polyzois2024 X12, X14. The racemate and the enantiomer differed in purity (95%+ against 99.9%), so chirality effects are confounded with impurities alvarenga2025 X17. In melt growth the racemate crystallized more slowly than either enantiomer and each polymer inhibited it less sato2015 C12, the opposite order to the solution tests here polyzois2024 R3, R4. Mechanisms offered for the difference, packing, bound water at a carbonyl and stereoselective polymer binding, are all hedged and untested polyzois2024 C26, C27, C28.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

classical nucleation theory

The theory that writes the nucleation rate as a pre-exponential factor times \exp\left[-\frac{W^* + \Delta G_\eta}{kT}\right], with a thermodynamic barrier W^* = \frac{16\pi\sigma^3}{3\,\Delta G_v^2} for a spherical nucleus and an activation energy for viscous flow [baird2012 E1, E2; vaneerdenbrugh2010a E3]. Its main factors are driving force, interfacial energy and mobility, and the library adds molecular recognition [trasi2012a C48; konno2006 C33]. In this chapter it is used qualitatively; solution papers fit it to induction times. New aspect (Crystallization from solution): For nucleation from supersaturated aqueous solution the papers use the form J = A\exp(-\Delta G_{crit}/kT) with a barrier that falls steeply with supersaturation, \Delta G^{*} \propto 1/(\ln S)^{2} (a pre-exponential factor A that depends on molecular mobility); the induction time is then inversely proportional to J if growth is fast [hsieh2012 E7, E8; ilevbare2013c E3, E4]. Two further elements are added: the polymer's effect through the interfacial tension or the cluster reorganization, and the two-step picture in which a disordered solute cluster forms first and then reorganizes, the reorganization being taken as rate-limiting ("we assume") ilevbare2013c C5, C15. The acetaminophen study prints J = A\exp[-16\pi\gamma^3 v^2/(3k^3T^3(\ln S)^2)] to say that temperature, supersaturation and interfacial tension set J, and fits a Poisson model to induction-time distributions for J [trasi2015 E6, C20, E5]. From 2018 the theory is also used to read medium effects: a lower interfacial energy for lecithin, SDS hemimicelles and phospholipid digests, a lower attachment rate in the pre-exponential factor for human fluid, and a fit of \ln(J/S) = \ln A - B/\ln^{2}S to posaconazole induction times in buffer and four media [indulkar2018 C40; indulkar2019b C33; enright2020 C26; elkhabaz2021 C22; duong2022b E7]. New aspect (Physical stability): the physical-stability papers use the theory to sort possible polymer effects into the thermodynamic barrier (driving force, interfacial energy) and the kinetic barrier, and conclude that a few percent of polymer acts on the kinetic barrier [konno2006 C34, C36, C40; marsac2006a C44, C48]. New aspect (Supersaturation from ASD dissolution): used qualitatively for dissolving dispersions: nucleation rises steeply with supersaturation, so amorphous–crystalline systems with a high theoretical solubility ratio are expected to nucleate readily konno2008a C20; at equal supersaturation in two coexisting phases nucleation is favoured in the drug-rich droplets, where the drug concentration is higher and the crystal–liquid interfacial tension lower ilevbare2013d C40, E1. A celecoxib paper of 2015 prints the classical rate with (\ln S)^2 and argues from it that the polymer differences come neither from supersaturation, taken as similar in all polymer solutions, nor from interfacial tension, which adsorbed polymer would lower and so speed nucleation; the theory therefore "does not readily allow for obvious mechanistic insights", and two-step nucleation through dense liquid clusters is offered instead (cited) xie2015 E3, C43, C44, C45. The longer celecoxib induction time at 11 than at 22 µg/mL is read as in agreement with the theory xie2016a C13.

Findings

Crystallization tendency: F3, F6. Crystallization from solution: F1, F5, F13, F14, F27, F34, F39, F42. Physical stability: F2, F4, F17. Supersaturation from ASD dissolution: F4, F5, F9, F13, F22.

Related concepts

models nucleation; depends on thermodynamic driving force for crystallization and melt viscosity; contrasts with heterogeneous nucleation; related to prenucleation clusters; governs nucleation rate and nucleation induction time; depends on interfacial tension; related to crystal-solution interfacial free energy; includes kinetic barrier to nucleation and interfacial free energy; depends on supersaturation.

Formulas

classical nucleation barrier, critical cooling rate to avoid nucleation, classical nucleation theory, induction time decomposition.

How it is measured or obtained

Not fitted for melts in this subcategory: the classes are read through it, a more negative ΔGv giving a lower barrier [baird2010 C61], interfacial energy differences being assumed small [vaneerdenbrugh2010a C39], and a steeper viscosity rise lowering the rate [baird2012 C32]. In solution, the barrier and interfacial energy are fitted from induction times against supersaturation duong2022b E7, E8. Most of the solution-crystallization papers do not fit it; they use it qualitatively to explain why induction times fall with rising supersaturation and why a polymer gains more at a lower one (celecoxib 27.5 min at S 7.3 against 2.4 min at S 14.7) ilevbare2013c R15, R9.a, C45. The posaconazole paper converted induction times into nucleation rates (conversion not stated) and fitted the high-supersaturation points of each medium with ν = 920 ų and T = 310 K duong2022b P15, X10. In the 2006 felodipine and nifedipine film papers it is used as a framework only; no parameter was fitted [konno2006 E8; marsac2006a E9]. In the ASD dissolution papers no rate was computed; the expression is printed in two papers and stated in words in a third konno2008a E3; alonzo2010 E4; ilevbare2013d E1.

Values in the library
materialvalue or classconditionspaper ids
posaconazoleinterfacial energy 3.52 mJ/m²; ΔG* ≈2.73 × 10⁻²¹ JPBS, 310 K, fit to induction timesduong2022b E7, E8
classes I against IIIlower barrier inferred for class I from more negative ΔGvmelt classes, γ assumed similar[baird2010 C61]
felodipine filmsrate described by driving force, kinetic barrier and molecular recognition; nucleation most likely heterogeneous0% RH films[konno2006 C33]
celecoxibinduction time 27.5 ± 0.7 min at S 7.3; about 2.4 min at S 14.737 °Cilevbare2013c R15, R9.a
danazol with HPMC-AS516, 365, 277 min at 10, 15, 20 µg/mL25 °Cjackson2014 R17
type 1 weak basesprecipitate only after a supersaturation of 1.4–26.7 times the titration solubilitypH shift, 37 °C[hsieh2012 R5, C3]
celecoxib dispersions (ASD dissolution chapter)nucleation-rate expression with \ln S and interfacial tension \gamma used to read induction times37 °Cxie2015 E3, C42
acetaminophen, S 1.5, 20 °CJ 1465 (none), 3820 (PAA), 81.86 (HPMCAS), 40.68 (HPMC) # m⁻³ s⁻¹ for V = 1.2 mL10 µg/mL polymer[trasi2015 R3, X1]
posaconazole, PBS, FaSSIF V1, FaSSIF V2, FeSSIF V1γ 3.52, 2.61, 2.73, 3.24 mJ/m²; A 2.44, 5.14, 4.98, 9.87; R² 0.84–0.9737 °C, high-S points (3–9 per medium)duong2022b R15, R16, X11
posaconazole, PBS, S 13 → 33.6ΔG* about 5.11 → 2.72 × 10⁻²¹ J; r* about 5.89 → 4.29 × 10⁻¹⁰ m310 Kduong2022b R17
seven other drugs (cited)γ 0.60–2.80 mJ/m²literatureduong2022b R18
felodipine with 3–25% polymerthermodynamic route "probably cannot account" for the drop; kinetic barrier speculatedargument[konno2006 C35, C40]
nifedipine vs felodipinelarger enthalpic driving force and lower barrier below Tg for the faster nucleatorTable II, Table I[marsac2006a C49]
flutamideprenuclei redissolve unless they exceed a critical radius, the volume free energy against the interfacial termframework[trasi2012b C46]
felodipine (argument)dissolution of the amorphous drug "will be accompanied by rapid crystallization"37 °Ckonno2008a C21
felodipine 90:10 dispersion (argument)almost all drug enters a highly supersaturated state that immediately crystallizes ("We speculate")37 °Calonzo2011 C29
celecoxib, no polymer, 22 against 11 µg/mLonset within 5 min against about 20 minpH 6.8, 37 °Cxie2016a R2
celecoxib 22 µg/mL, 5 µg/mL PVP-K12 / PVP-K29/32 / HPMCAS or HPMConset ≈1 h / ≈2 h / more than 8 hpH 6.8, 37 °Cxie2015 R1
paclitaxel, critical radius of a two-dimensional nucleus5.4–7.0 nm at S = 88 with three stand-in interfacial tensions; ≈6.8–8.8 nm at the residual supersaturation after 16 hpH 6.8, 37 °Cque2018 R15, R17
Pitfalls and disagreements

Pharmaceutical films are not completely described by homogeneous nucleation theory, which ignores stresses and heterogeneous nucleation [marsac2006a C32]. It does not readily explain polymer effects on nucleation or encompass molecular recognition [trasi2012a C49; xie2015 C44]. In the melt papers neither γ nor nucleation rates were measured, so the barrier argument is an inference [vaneerdenbrugh2010a C39; baird2010 C61]. The proportionality of induction time to 1/J assumes nucleation is much slower than growth to detectable size, which was not tested ilevbare2013c X14. The two-step model is assumed, not shown, for these systems ilevbare2013c C5. The critical supersaturation at which precipitation is seen depends on the compound and the conditions and is somewhat variable [hsieh2012 C3]. The printed sample volume (0.0012 m³) and the sign of the exponent in Eq. 5 are misprints [trasi2015 X1, X2]. The human-fluid paper prints the rate equation without the minus sign in the exponent elkhabaz2021 X1. In the posaconazole fits γ and A both differ between media and the critical free energy in the FaSSIF media is less than half the buffer value at equal S, so the assignment of the medium effect to A alone is not secure duong2022b X12. In the felodipine films the homogeneous theory is applied to nucleation that is "most likely heterogeneous" [konno2006 C33; marsac2006a C32]. The reduced-temperature form printed for acetaminophen has typesetting errors (r³ for γ³, a positive kinetic term) [trasi2012a X1]. The 2008 and 2010 dissolution papers print ln S without the square of the classical form konno2008a X8; alonzo2010 X3. The celecoxib supersaturation argument uses crystalline solubilities measured with 22 µg/mL polymer, not the 5 µg/mL of the induction tests, and these differ by 26–43% from the polymer-free value xie2015 X9; the text refers to the wrong equation for interfacial tension xie2015 X1. The paclitaxel values use interfacial tensions of other compounds, and with the printed units the equation gives a dimensionless number que2018 C37, X7.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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/minlu2016 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 saltsDSCtowler2008 R4, C10
rotary-evaporated drug–polymer powdersno exotherm on heatingDSCvaneerdenbrugh2010b 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 B. Supersaturation from ASD dissolution

combinatorial entropy of mixing

The entropy part of the Flory–Huggins activity coefficient and free energy, set by molecular size alone. The activity coefficient of a drug splits into a combinatorial (entropy) part and a residual (enthalpy) part; exothermic mixing lowers and endothermic mixing raises the residual part, and the two are linked because order imposed by exothermic interactions lowers the entropy of mixing [marsac2009 C10]. For the drug in the liquid analogue (1-ethyl-2-pyrrolidone) the combinatorial part is taken as ideal, so only the residual part remains; in PVP it is larger by the factor that the chain length gives, and with equal residual parts the whole difference of ln γ between PVP and the analogue is the combinatorial part [marsac2009 E3, E4, E5, E6, E7, C11]. Per lattice site and for two polymers the term is kT[(\phi_1/N_1)\ln\phi_1 + (\phi_2/N_2)\ln\phi_2], which shrinks as the chains grow vaneerdenbrugh2012a E5, C35.

Findings

F5, F8, F9, F22.

Related concepts

part of entropy of mixing; contrasts with the residual part carried by enthalpy of mixing; used in activity coefficient; part of Flory-Huggins theory.

Formulas

Flory-Huggins activity equation, Flory-Huggins combinatorial entropy of mixing.

How it is measured or obtained

By calculation (Eqs. 3–8 of the 2009 paper): ln γ in PVP = (MV_drug/MV_lattice)[(1/m_drug) ln(Φ_drug/x_drug) + (1/m_drug − 1/m_PVP) Φ_PVP] + ln γ in EP, with the lattice volume equal to that of EP [marsac2009 E8, P7]. As the chain grows, 1/m_polymer vanishes and the term approaches 1/m_drug, which explains the drop of predicted solubility from EP to PVP K12 and its saturation beyond K29/32 [marsac2009 C24]. The inputs (lattice volume, mole-fraction basis in PVP) are not printed [marsac2009 X4, X13].

Values in the library
materialvalue or classconditionspaper ids
five compounds, γ in PVP K123.94, 1.18, 5.04, 1.76, 0.50 (felodipine, nifedipine, ketoconazole, sucrose, indomethacin)scaled from EP with Eq. 8[marsac2009 R9]
same, PVP K29/324.34, 1.30, 5.92, 1.93, 0.54as above[marsac2009 R9]
same, EP at 25 °C0.89, 0.26, 0.68, 0.37, 0.15measured solubility[marsac2009 R9]
dextran–PVP, 20 pairsminimum from about −27 × 10⁻²³ J (DEX1–PVP12) to about 0 (DEX450–PVP90)25 °C, PVP monomer as lattice sitevaneerdenbrugh2012a R15

Evidence table: combinatorial entropy of mixing.

Pitfalls and disagreements

The scaling assumes ideal entropy of mixing with EP, identical drug–EP and drug–PVP contacts, and equal γ at the solubility limit in the polymer; none of these was tested against a measured solubility in a polymer [marsac2009 C11, X17]. The γ of indomethacin in K29/32 is 0.134 in Table III but 0.144 in the text of the paper [marsac2009 X2].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 diskschram2016 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 mediaelkhabaz2021 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 B. Supersaturation from ASD dissolution

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 °Cilevbare2013c 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 shiftraina2015b 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 B. Supersaturation from ASD dissolution

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 drugcited[li2020 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 rpm[li2020 R10]
ritonavir–PVPVA, 50% and 75% DLabout 0.003–0.006 mg·min⁻¹·cm⁻¹, near neat amorphous drug (about 0.0026)same[li2020 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 6.8[benson2025 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 °C[bapat2025b R2.d–e, R3, X18]
octreotide:SNAC:copovidone, 1.6% peptidecongruent in three components; ≈8.1 / ≈8.4 / ≈8.9 mg min⁻¹ cm⁻²same[bapat2025b 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 assayedsame[bapat2025b 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)same[bapat2025b R10, C21]
cyclosporine ternaries, 10–20% peptidenot congruent: polymer complete while peptide reaches ≈54.5% and ≈16% with decanoatesame[bapat2025b 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 6.8[purohit2017b C52, R15, R16, R17]
ritonavir 50:50 HPMCAS filminitially congruent (≈32–34 µg/mL drug within 5 min)same[purohit2017b R17, C38]
ITZ–PVPVA 10% spray-driednormalized drug ≈2000 against polymer ≈2265 µg/min/cm²0.1 N HCl, 37 °C[bhardwaj2018 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 °C[que2019 R3, R4]
ledipasvir–PVPVA with 5 parts SDS, 7.5–30%congruent to 30%; fails at 40%same[que2019 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 °C[saboo2019 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 °C[saboo2020 R3, M5, M6]
indomethacin methyl ester–PVPVA 10–25%congruent at first, drug levels off after 7.5–20 min30 min, 37 °C[saboo2020 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 °C[saboo2021 R12, P6]
loratadine–PVPVA; –HPMCASto 30% and 20% at 37 °C; 2% and 5% at 5 °Ccompacts, t-test[yang2021 R22]
clopidogrel–PVPVAclose to congruent to 40%; 50% with SDScompacts[correasoto2022a C46, C55]
atazanavir–PVPVA5%; 10% with SDS or CTAB; 15% with Span 80compacts[correasoto2022b 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 °C[qi2022 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 °C[yang2022a 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 FaSSIF[bapat2023 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 °C[correasoto2023 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 °C[deac2023a 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 6.8[bapat2025a R2, C13]
clotrimazole–PVP K25 20%, K29/32 30%, K60 35%, K90 38%congruent (>80% of both components)compacts, pH 8.0, 90–120 min[deac2024a 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 B. Supersaturation from ASD dissolution

critical cooling rate

Rcrit (Rcrit,cool) is the slowest cooling of a melt that avoids detectable crystallization; the rate that avoids any nucleation, RNcrit, is faster still, and cooling between the two leaves nuclei in the glass [baird2010 C50; baird2013 C2]. It is the classical measure of glass-forming ability [baird2010 C49].

Findings

F10, F11, F16.

Related concepts

measures glass-forming ability; estimated by Barandiaran-Colmenero method; contrasts with critical heating rate; related to quenched-in nuclei.

Formulas

Barandiaran-Colmenero critical cooling rate, Cabral critical cooling rate, critical cooling rate to avoid nucleation.

How it is measured or obtained

By cooling at progressively slower rates in a rapid heat–cool DSC until crystallization appears [baird2013 P2, R5]; by extrapolation with the Barandiaran–Colmenero or Cabral methods [baird2010 P9; baird2013 P3]; bounded by the fastest rate at which crystallization was still seen [baird2013 R1, X6].

Values in the library
materialvalue or classconditionspaper ids
8 class I-A moleculesabove the fastest rate reached, 800–1100 °C/minrapid heat–cool DSC[baird2013 R1, X6]
antipyrin, chlorpropamide, flufenamic acid, tolbutamide25 °C/minrapid heat–cool DSC[baird2013 R9]
10 class II molecules5 °C/min or lessDSC[baird2013 R9]
7 class I molecules (extrapolated)20 to 3.26 × 10⁴ K/minBC and Cabral, 5–20 °C/min[baird2010 R13]
delamanidabove 50 °C/min (no glass at 50 °C/min)DSCduong2022a R3
Pitfalls and disagreements

Extrapolated values from narrow rate ranges are unreliable [baird2010 C20]. The authors advise that knowing Rcrit,cool exceeds 500 °C/min is "probably sufficient" to flag a difficult drug [baird2013 C21]. A low Rcrit,cool does not imply a stable glass, since reheating rates needed are far higher [baird2013 C24].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 data[hiew2022a 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 phosphate[qi2022 R13]
neat HPMCAS-MF in FeSSIF V1no dissolutionpH 5.0[bapat2023 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, 5.06titration[bapat2025a 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 B. Supersaturation from ASD dissolution

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 °C[indulkar2017a R1, R2, R3]
STC; SGDCCMC about 4 mM; about 2 mMpH 6.5 buffer, 37 °C, with and without 60 µg/mL telaprevirlu2017 R5
Vit E TPGS / Cremophor EL / RH40 / Tween 200.02 / 0.01 / 0.03 / 0.009%levels C1–C3 chosen around itraina2015c 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, buffer[hate2022 R12]
SDS in the PAMPA receiversink effect from 0.15%, no further rise up to 2%atazanavir 150 µg/mL[hate2022 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 °C[saboo2021 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 °Cli2016b R1
SDS with lopinavir and HPMCPbreak near 0.1%pH 3, 25 °Cli2016b 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 6.8[que2019 X19]
SDS, CTAB, TPGS, Tween 80487 ± 34, 50, 40, ≈14 µg/mL50 mM pH 6.8, 37 °C[correasoto2022a R1]
SDS, CTAB, TPGS, Tween 80, Span 20, Span 80, Span 85500, 50, 40, 14, 7.3, 14, 5–50 µg/mLas listed[correasoto2022b 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 B. Supersaturation from ASD dissolution

critical nucleus

The smallest cluster that grows instead of dissolving; the induction time is defined as the time to form a critical nucleus plus the time for it to grow to a detectable size [chen2015 E1, C5; li2016a E4].

Findings

F28, F29, F34.

Related concepts

related to nucleation induction time and classical nucleation theory.

Formulas

induction time decomposition

How it is measured or obtained

Not observed; only the induction time is measured chen2015 C5.

Values in the library
materialvalue or classconditionspaper ids
11 drugs, buffers and 0.1% surfactantinduction time only; nucleation and growth parts not separated25 °Cchen2015 E1, R3
posaconazoler* about 5.89 → 4.29 × 10⁻¹⁰ m (PBS, S 13 → 33.6); 7.21 → 3.93 × 10⁻¹⁰ m (FeSSIF V1, S 6.9 → 34.2)310 K, ν = 920 ųduong2022b R17, E9
Pitfalls and disagreements

Bile salts are proposed to act at the surface of the emerging nucleus, which was not measured [li2016a C58].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

critical radius of a two-dimensional nucleus

The radius \rho_c below which a two-dimensional island on a crystal face cannot grow; it falls as the supersaturation rises, \rho_c = \gamma a/(kT \ln S) (Gibbs–Thomson), and it decides whether adsorbed impurities pin a step: growth is arrested when the spacing of adsorbed molecules equals 2\rho_c alonzo2012 C9, E8; que2018 E2. A step velocity V_\rho/V_\infty = 1 - \rho_c/\rho describes a step of radius \rho alonzo2012 E8.

Findings

F9, F10.

Related concepts

part of two-dimensional nucleation; used by step pinning; depends on interfacial tension.

Formulas

Cabrera-Vermilyea step pinning, Kubota-Mullin impurity effectiveness factor.

How it is measured or obtained

Not measured in the chapter papers; the felodipine paper states the relation without values for γ, a and L alonzo2012 C27. In the ASD dissolution chapter it was calculated for paclitaxel at S 88 from literature surrogates of the crystal–water interfacial tension, giving 5–7 nm que2018 R15, C37.

Values in the library
materialvalue or classconditionspaper ids
paclitaxel\rho_c 5–7 nm, smaller than HPMCAS site spacing of 10–20 nmS 88, 37 °Cque2018 R15, C38
felodipine with HPMCnot given; α falls from 0.7 to 0.2 as S rises from 3 to 12, as eq 7 predicts25 °Calonzo2012 R9, C27
Pitfalls and disagreements

The interfacial tension of the crystal against water could not be determined and enters linearly que2018 C37. Both papers use ln S, not the low-supersaturation approximation S − 1, because the supersaturations are not low alonzo2012 C7.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

crystal defects

Imperfections in a crystal (vacancies, impurities, dislocations, grain boundaries, growth irregularities) that are higher-energy, more mobile sites, may start phase transformations, have been linked to faster dissolution and impose local stress [moseson2019 C3]. In HME residual crystals they appear as edge dislocations, bend contours and lattice planes sheared into several orientations [moseson2018a R12, R13, R15, R16]. In the dissolution papers defects are used to explain why residual crystals seed more strongly than bulk crystals: cryomilled crystals and residual crystals grow needle-like crystallites from all surfaces with PVPVA, "suggesting underlying disorder", but no defect measurement is made moseson2020a C23, C40; moseson2021 C66. Defect density of input crystals was proposed as a critical material attribute for the speed of amorphization but was inferred, not measured, from the order of dissolution of lots with the same median size: the agglomerated lot dissolved faster than a lot with a near-identical size distribution [moseson2022c C44, C46, X6]. Crystals with rough surfaces or grain boundaries are said to dissolve first at high-energy sites and to split [moseson2022c C45, C51].

Findings

F12, F13, F26, F36.

Related concepts

includes bend contours and grain boundary; start fragmentation-based dissolution.

Formulas

none.

How it is measured or obtained

Not measured quantitatively in the library: defects are inferred from Fourier-filtered TEM images (inverse FFT of one spot pair), from TEM contrast of grain boundaries, and from SEM and PLM of growth irregularities [moseson2018a P8; moseson2019 R1, R2, R3].

Values in the library
materialvalue or classconditionspaper ids
IDM crystals, unheatedgrowth irregularities, surface imperfections; grain boundaries dividing one crystal into three regions; surface crystallites and bend contoursSEM, PLM, TEM[moseson2019 R1, R2, R3]
IDM residual crystals in an extrudateedge dislocations, bend contours, one lattice spacing in three orientationsTEM, inverse FFT[moseson2018a R12, R13, R15]
tacrolimus crystals from amorphous powderhigh defect level suspected because the sample stays above the crystalline solubilitydissolutionpurohit2019 C38, C47, C48
cryomilled IDM crystals and HME 117-2 residual crystals grown 24 h with 50 µg/mL PVPVAneedle-like γ crystallites 170 ± 60 and 230 ± 80 nm wide from all surfaces; bulk crystals grow smooth or striated platesSEMmoseson2020a R14, R15, R13
residual crystals in BCL–PVPVA extrudatescalled "highly defective" and "commonly more potent" than bulk seeds, from the literature and growth ratescitedmoseson2021 C66, C74
BCL lots L37 (agglomerated), L38 (rough), L42 (milled), L93 (smooth)defect density not measured; ranking inferred from PXRD at Tc30% BCL–PVPVA, 145 °C[moseson2022c X6, R10]
Pitfalls and disagreements

Defect density was not quantified, and bending or beam damage of thin organic crystals is not excluded as a source of bend contours [moseson2018a X5, X6]. The cited faster dissolution of crystals with higher defect density is not a measurement made in the ASD process papers [moseson2019 R23, X6]. The surface area and defect density of the residual crystals were not measured moseson2020a X9; moseson2021 X10. The inference for the agglomerated lot rests on the 5 min point; at 4 min L37 was still higher than L38 and their coarse tails differ [moseson2022c R10, R1, X5].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 extrudermoseson2021 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 B. Supersaturation from ASD dissolution

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 = 6moseson2020a R5
BCL, PVPVA 70 µg/mL and HPMCAS 1 mg/mLE_G 8.6 and 158150 µg/mL, form 1 seedsmoseson2021 R5
felodipine seeds, HPMCAS 5 µg/mL (outside)E_G about 2 to 12 depending on how the seed crystals were preparedS = 4schram2016 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 polymerkonno2008a 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 solutionshah2024 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; 10.8sameilevbare2013b R9
celecoxib, HPMC; HPMCAS; PVPVA10.2; 8.5; 7.45 µg/mL polymer, S 6.6ilevbare2013b R9
efavirenz, PVPVA; CA 320S Sub 0.90about 4.9S 1.2ilevbare2013b 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 °Calonzo2012 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 °Cque2018 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 °Calvarenga2025 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 B. Supersaturation from ASD dissolution

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 liquidlu2016 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% RHkestur2013b 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 °Crumondor2010 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 °Cilevbare2013b R7
celecoxib; ritonavir at S 6.6; 7.66.23; 6.14 mg min⁻¹ m⁻²sameilevbare2013b 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)sameilevbare2013b 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 °Calonzo2012 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 fieldelkhabaz2021 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 temperaturerumondor2010 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% RHkestur2013b 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 filmssato2015 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 °Ckonno2008a 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 B. Supersaturation from ASD dissolution

crystal growth

The second step of crystallization: existing nuclei or seeds grow by molecules crossing the crystal–liquid interface and attaching to growth sites [trasi2014a C19; tian2017 C22]. The usual growth models (normal, screw dislocation, two-dimensional surface nucleation) differ in the interface structure but all contain a mobility term and a driving-force term [trasi2014a C19]. Because nuclei are detected only after they grow, a measured induction time is the sum of nucleation and growth times chen2015 E1, C5. New aspect (Bioperformance): the growth rate is written as a power law in supersaturation, R_G = k_G A (C_b - C^*)^g, and growth rates of ezetimibe were taken from SHG purohit2018 E3; elkhabaz2017 R23. Growth on tacrolimus seeds was fitted with the same power law, dC/dt = k_g A (C - C^*)^n, with n = 1.677 (R² 0.9896), close to the n of about 2 expected for integration-controlled growth with a polymer adsorbed on the crystal hate2019 E4, E5, R18, C44. New aspect (Supersaturation from ASD dissolution): growth is the second step that empties a supersaturated solution after nucleation; the two-route scheme of dispersion dissolution writes it as proportional to the excess concentration, R_G \propto (C - C_{eq}) (cited) alonzo2010 E5, C43. A celecoxib study states that crystals formed in the wetted matrix act as seeds that grow quickly and limit the supersaturation, and reads the induction time as nucleation plus growth to a detectable size xie2015 C31, E1.

Findings

Crystallization tendency: F1, F19. Bioperformance: F10, F12, F16, F29. Supersaturation from ASD dissolution: F5, F9, F16, F22.

Related concepts

measured by crystal growth rate; contrasts with nucleation; related to crystal growth inhibition by polymers and surface crystallization. Seeded by crystal seeding; inhibited by crystal growth inhibition.

Formulas

Jackson interface-kinetics growth rate. Power-law crystal growth rate, overall mass crystal growth rate.

How it is measured or obtained

As a growth rate (see crystal growth rate); by the morphology of the growing crystals lu2016 R7; in solution by desupersaturation after seeding xie2015 C31. It is inferred from the fall of concentration in non-sink tests purohit2018 C43 and from the SHG mean size over time elkhabaz2017 P11. In dissolving dispersions and in methanol-shift solutions: size of submicron particles against time by light scattering alonzo2011 P5; desupersaturation slopes konno2008a P6.

Values in the library
materialvalue or classconditionspaper ids
bifonazole, nimesulidespherulite size linear in timemelt films[kestur2011 R4]
acetaminophen with polymersspherulites; radius linear in time, R^2 > 0.99melt films[trasi2012a R4]
vemurafenibfour forms in six morphologies (needles, spherulites, feathers, clusters)supercooled liquidlu2016 R7
nilutamide stable formgrowth front smooth at 70 °C, rough at 60 °C, with a 50-fold rate dropseeded films[trasi2014b R4, C7]
flutamide dispersion particlesnumber and size of needle crystals increase with storage40 °C/75% RHcorreasoto2017 R2, C12
ezetimibe ASDsgrowth rate 0.020–1.0 µm/min (as printed)buffer, FeSSIF, Ensure Pluselkhabaz2017 R23
tacrolimusgrowth rate rises steeply with supersaturation; 450 mL gives twice the supersaturation of 900 mLUSP medium Ipurohit2018 C52, C55
FTM ASD (SHG)spots at 8 days, dense field at 60 days75% RHcorreasoto2017 R2, R4
tacrolimus on seedsn 1.677; growth constant 1.17 × 10⁻⁴ (printed unit cm/s, unclear); absorption leads below S about 18.5 and growth above ithollow-fibre module, seeds from the crystallized generichate2019 R18, R19, X3, X16
felodipine particles from a 90:10 HPMC dispersion≈218 nm at 5 min, ≈337 at 90 min, ≈720 nm near 10 h, then settling25 °Calonzo2011 R6
felodipine particles, dispersion against methanol shift with HPMC≈183–203 → ≈280–307 nm in 90 min, alike25 °Calonzo2011 R8
same at 37 °Cdispersion-born ≈259–274 nm against ≈194–219 nm at 5–10 min37 °Calonzo2011 R11
celecoxib seeds, 22 and 11 µg/mL, no polymerno lag; ≈22.5 → ≈4.0 and ≈12.8 → ≈3.7 µg/mL in 30 minpH 6.8, 37 °Cxie2016a R11
paclitaxel with 18 wt% seeds, no polymerfrom 31.6 µg/mL to ≈12–13 µg/mL in 2 min with sonicated seeds against ≈21.6 and ≈26.1 µg/mL with long needlespH 6.8, 37 °Cque2018 R7
Pitfalls and disagreements

Near Tg some crystals switch to diffusionless growth and diffusion decouples from viscosity [trasi2014a C21]. A change in growth morphology can change the rate abruptly [trasi2014b C7]. Once crystallization starts it is expected to continue, so early detection matters correasoto2017 C4. In the SHG study of ezetimibe the nucleation-rate unit is implausible and growth rates are relative elkhabaz2017 X7. In the tacrolimus seed study the unit of the printed growth constant does not fit the equation, the x-axis of the log-log fit is log(C − C*) rather than log(S − 1), and the crossover near S 18.5 assumes a constant crystal area (F29) hate2019 X1, X2, X3, X16. The crystallinity of the early felodipine particles was inferred, not measured by diffraction alonzo2011 X7; the match of dispersion-born and methanol-born particles holds at 25 °C, not at 37 °C alonzo2011 X19. Per unit mass the growth area, not the seed mass, set the loss: sonication raised the needle-end area about 7–9-fold que2018 R6, C5.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

crystal habit

The outer shape of a crystal, here described by length, width and aspect ratio (mean length over mean width) of 50 crystals per sample; additives that adsorb on and slow the fastest-growing faces change it [ilevbare2012c E7, C5]. Ritonavir Form II grows as needles; polymers that inhibit its growth made the crystals wider and the aspect ratio smaller [ilevbare2012c R4; ilevbare2012a R6]. Felodipine seeds crystallized in HPMCAS were small and spiky at an equal imaged area (31.2 against 33.4 µm²), and acetaminophen habit changed with every polymer at 20 µg/mL [schram2016 R8, R9; trasi2015 R12]. New aspect (Supersaturation from ASD dissolution): habit is also recorded as a sign of the crystallization route and of additives: nifedipine crystals from the solution route were below 2 µm against 1–300 µm agglomerates from the matrix route raina2014b R13, R2, and celecoxib grew as thin needles, "consistent with" Form III, in every medium chen2015a R13, C7.

Findings

Crystallization from solution: F12, F8, F24, F27, F42. Supersaturation from ASD dissolution: F3, F12, F14, F22.

Related concepts

predicted by BFDH morphology prediction; changed by polymer adsorption on crystal surfaces; related to crystal growth and surfactant-induced crystallization.

Formulas

aspect ratio.

How it is measured or obtained

SEM of crystals recovered after a growth run, length and width of 50 crystals; the habit expected for the crystal structure from the BFDH tool in Mercury; PXRD relative peak intensities as a proxy for the exposed faces [ilevbare2012c P4, P7, P13; ilevbare2012a P6]. In the ASD dissolution papers: polarized light and SEM images; length over width raina2014b P4; ilevbare2013d P8; chen2015a P10.

Values in the library
materialvalue or classconditionspaper ids
ritonavir seeds; after growth none; Pn-IPAAmdaspect ratio 7.7; 8.8; 4.4 (width 5.8; 5.7; 9.3 µm)S 7.6[ilevbare2012c R4]
ritonavir with CAP Adp 0.85; with the CAP Adp 0.85 + Pn-IPAAmd pair5.2 (rodlike); 4.8S 7.6[ilevbare2012b R6; ilevbare2012a R6]
ritonavir at S 15.4: none; CAP Adp 0.85; Pn-IPAAmd; pair12.1; 7.6; 7.4; 6.5 (all needle-like)20 µg/mLilevbare2012a R6
ritonavir ASD dissolution (ASD dissolution chapter)aspect ratio about 22.4 with Tween 80 against 3.9 with PVP alonecrystals after about 90 minilevbare2013d R8
paclitaxel seeds (ASD dissolution chapter)all needles of high aspect ratio, fast growth at the endsSEMque2018 R4, C14
acetaminophen, 20 µg/mL polymerrods (HPMCAS), prisms (PAA), parallelepipeds (PVPVA), smaller plates (PVP), very small crystals (HPMC)S 1.5, 20 °C[trasi2015 R12]
telaprevir, eight media ± 150 µg/mL HPMCAS-MFsmooth bouquets of prisms (buffer), rough with polymer, smooth plates in FaSSIF with polymerSEM, crystals after induction runs[lu2018 R10]
atazanavir needles, buffer-V1, FaSSIF-V1, composite FaSSIF, aspirated human fluidaspect ratio 12.4 ± 7.4, 54 ± 13, 83 ± 32, 41 ± 14SEM, n = 15 (FaSSIF-V1 n = 10), 37 °Celkhabaz2021 R21
posaconazole platesabout 25–45 nm thick; finger-like ends in human fluidSEMelkhabaz2021 R22, R23
atazanavir in SDS25–100 µm agglomerates below 0.075 mg/mL; about 127–367 nm abovemicroscopy and NTA[indulkar2019b R9, R11]
nifedipine, solution route against matrix routebelow 2 µm against 1–300 µmpH 6.8raina2014b R13, R2
celecoxib crystals from induction runsthin needles in all eight media25 °Cchen2015a R13
celecoxib in SDS and polysorbate 80 suspensionslong free-floating needlespH 3chen2015a R15
paclitaxel seeds before and after growth without polymermean aspect ratio ≈23.6 → ≈17.7 (long needles) against ≈7.3 → ≈14.7 and ≈4.7 → ≈13.7 (sonicated)pH 6.8, 37 °Cque2018 R9
Pitfalls and disagreements

Means of 50 crystals have overlapping spreads; lengths with polymer are not below the seed length, so the ratio falls through width; three of the five S 7.6 rows are cited from earlier papers [ilevbare2012a X9; ilevbare2012b X4]. The printed 5.2 for the CAP Adp 0.85 sample recomputes to 5.14 [ilevbare2012b E15, X5]. A habit change does not by itself show how much growth is slowed: HPMC gave the smallest crystals and PAA the habit nearest the prediction [trasi2015 R12, C19]. The celecoxib needle direction along the c-axis is stated without an indexing basis chen2015a X19; DLS sizes of needle-shaped crystals are spherical equivalents and "likely to be unreliable" ilevbare2013d C19. The fall of the long-needle aspect ratio is read as fine crystals from secondary nucleation que2018 C43.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

crystal-melt interfacial free energy

The free energy per area of the interface between a crystal (or nucleus) and its own supercooled melt or glass; in classical nucleation theory it sets the surface penalty of a nucleus, and in the two-dimensional nucleation model of growth it sets the barrier for a new layer [marsac2006a C31; kestur2010b E3].

Findings

F2, F4, F29.

Related concepts

special case of interfacial free energy; part of classical nucleation theory; related to enthalpy of fusion.

Formulas

classical nucleation theory; the two-dimensional nucleation barrier \Delta G^{*} = -\pi b\gamma^{2}/\Delta G_v is printed in the melt paper [kestur2010b E3].

How it is measured or obtained

Not measured in the papers of this chapter; it is estimated by analogy (Turnbull's proportionality to the heat of fusion for metals) or argued from adsorption [marsac2006a R22, C36; kestur2010b C27].

Values in the library
materialvalue or classconditionspaper ids
nifedipine vs felodipineif Turnbull's rule held, nifedipine (ΔHfus 39.9 vs 30.8 kJ/mol) would have the larger interfacial energy, the opposite of what its faster nucleation needsargument[marsac2006a C36, R4.g]
felodipine with PVPadsorbed polymer would lower it rather than raise it, so it cannot explain slower growthargument[kestur2010b C27]
indomethacin δ, α, γ with 10% HPMC, HPMCAS, PVPnot measured; invoked to explain polymorph-specific inhibition ("it appears")melt growth, 80 °C to near Tm[tian2017 C39, C26, X14]

Evidence table: crystal-melt interfacial free energy.

Pitfalls and disagreements

It is "hard to measure" for glasses, so both papers use it only to exclude explanations, and the kinetic conclusions rest partly on this unmeasured quantity [marsac2006a C36; kestur2010b X11]. In the indomethacin paper the interface is reached by excluding a liquid-phase explanation; no interfacial property was measured, although the term is an author keyword [tian2017 X14].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

crystal seeding

Crystals already present in a dispersion or added to the medium act as templates for growth and consume supersaturation; the relevant property is the growth area and interface structure of the seeds, not their mass que2018 C5. In the ASD process papers, residual crystals from hot melt extrusion are seeds that are small, embedded in the amorphous solid and possibly defective, and are "routinely" more potent than bulk seeds moseson2020a C55; moseson2021 C65, C66, C74. In the posaconazole–HPMCAS pH-shift tests residual crystals of 0.3–3.2% act as seeds: supersaturation ended earlier, by growth of the crystals present and by secondary nucleation, both inferred from solution concentration and particle counts shah2024 C45, C47, R14. New aspect (Bioperformance): crystals already present in an amorphous product on which dissolved drug can grow without nucleation; their growth removes supersaturation purohit2018 C40, C43. Seeds were taken from the maximally crystallized generic tacrolimus capsule and added to solutions at 20 and 50 µg/mL; crystals that formed inside the product were smaller than purchased reference crystals of the same form hate2019 R17; purohit2019 R6, R8, C56. New aspect (Supersaturation from ASD dissolution): a dispersion can seed itself. Crystals that form in the wetted, undissolved matrix during a gastric stage are released when the polymer dissolves at intestinal pH and then act as seeds for the supersaturated solution; for posaconazole the authors state that "These seed crystals were transferred to the intestinal compartment and promoted further crystallization" elkhabaz2019a C56, and for delamanid that surface crystals "can act as seeds" while release and crystallization compete nguyen2023c C44, C49.

Findings

ASD process: F26, F28, F29, F41. Bioperformance: F16, F28, F29, F30. Supersaturation from ASD dissolution: F22, F24, F25, F26, F27.

Related concepts

produced by residual crystallinity; read through desupersaturation; slowed by crystal growth inhibition; influenced by crystal defects. Related to crystal growth, secondary nucleation and endogenous crystallization; produced by matrix crystallization and surface crystallization; acts through seeded crystal growth; avoided by enteric polymer coating of the tablet.

Formulas

power-law crystal growth rate.

How it is measured or obtained

Seeded desupersaturation: bulk crystals (D50 21.9 µm) added at 10, 25 or 50 µg/mL to 50 µg/mL indomethacin, with the growth rate in µg/s moseson2020a P10, R4; external form 1 seeds equal to 10% of a bicalutamide dose added to a crystal-free dispersion and read by Raman as a relative growth rate moseson2021 P13, P17, R22. Potency of residual seeds is read by comparing extrudates with seeded crystal-free dispersions at the same amorphous dose moseson2020a P13, P14. Seeded desupersaturation of posaconazole in FaSSIF V2: 20 or 100 µg/mL drug, HPMCAS at 0–9 times the drug, seeds of 0–10 µg/mL, percent left at 30 min shah2024 P16, R22. In the tacrolimus capsules crystals were read by XRPD (limit of detection 10%) and inferred from desupersaturation in non-sink dissolution purohit2018 R2, R7. For self-seeding in pH-shift tests: crystals are detected in the acid stage by SHG, which gives signal only from crystals, beside two-photon excited fluorescence of all drug, and their ratio estimates the share of the undissolved drug that is crystalline elkhabaz2019a P10, P11, E1; on dispersion films and powders by polarized light and SEM after 1 h in acid, with PXRD of the powders nguyen2023c P12, P13, P14. The effect is read from the release after the pH shift against a run without an acid stage elkhabaz2019a R6, R7.

Values in the library
materialvalue or classconditionspaper ids
IDM bulk seeds, no polymergrowth rate about 0.33, 0.71, 0.99 µg/s at 10, 25, 50 µg/mL seedsS = 6, pH 4.5moseson2020a R4.a
IDM–PVPVA, 50 µg/mL amorphous dosebulk seeds up to 100% of the dose: C720 about 43.2 → 39.8 µg/mL; extrudates with 3–25% crystals: about 27.0–37.3 µg/mL12 hmoseson2020a R9, R10
BCL–PVPVArelative form 1 growth rate about 0.088 (M/155, 3.5% crystals), about 0.071 (S/155, below 1%), about 0.044 (10% external seeds)Raman slurrymoseson2021 R22
paclitaxel–HPMCAS 49/51 (outside)residual concentration about 25 (bulk API) to about 8–10 µg/mL for other seed types; seed mass not the relevant parameter18 wt% seeds, 16 hque2018 R14, C5
fresh generic tacrolimus capsules (outside)seeds below 5% of the drug cause desupersaturation; growth slow at first because the surface area is smallnon-sink, 100 mLpurohit2018 C45, C46
PCZ 100 µg/mL in FaSSIF V2, seeds 10 µg/mL4.5% left at 30 min without polymer; 10.5% with HPMCAS at 3 times the drug; 43.5% at 9 timesseeded solutionshah2024 R22
PCZ–HPMCAS 10% DL with 0.3% crystalssupersaturation down to about 18.5 µg/mL by 150 min against about 125 µg/mL at 300 min without crystalspH shift at 60 minshah2024 R12, R14
tacrolimus generic capsulesfresh seeds below 5% of the drug (inferred); peak 98% then 39.5% in 100 mLUSP medium Ipurohit2018 C46, R7
felodipine, HPMCnucleation inhibition counts far more than growth inhibitionseeded and unseededalonzo2012 C40
posaconazoleseeded desupersaturation faster with more seeds and more drug, slower with more HPMCASFaSSIF V2shah2024 C37, R22
tacrolimus, seeded solutionsdesupersaturation rate about 0.39 at 50 µg/mL and 0.075 at 20 µg/mLpolymer in solution, hollow fibrehate2019 R17
tacrolimus crystals in the generic capsule1–5 µm against 5–25 µm for reference monohydrate crystals; same formSEM, after 5 weeks at 40 °C/75% RHpurohit2019 R6, R8
posaconazole–HPMCAS 10 / 25 / 50% drugestimated matrix crystallization ≈0.026 / ≈0.050 / ≈68% of the undissolved drug30 min in FaSSGF, 37 °Celkhabaz2019a R20
the same, after transfer10% and 25% held ≈22–24 and ≈21–22 µg/mL for about 150 and 60 min; 50% fell to ≈6 µg/mL within 30 minFaSSIF pH 6.5elkhabaz2019a R6, R7, R8
the same, without an acid stage≈21 µg/mL at 180 min (10%) and ≈22–23 µg/mL to 60 min (25%)FaSSIF onlyelkhabaz2019a R6, R7
delamanid salt dispersions, particles after the pH shiftcovered with small crystals within 30 minpH 6.5nguyen2023c R21
paclitaxel–HPMCAS dispersion with 18 wt% added seedsthe amorphous solubility was still reached, then lost over hourspH 6.8, 37 °Cque2018 R13
Pitfalls and disagreements

Surface area and defects of residual crystals were not measured, so the extra potency is an inference moseson2020a X9; moseson2021 X10. Bulk seeds at a larger mass can grow more slowly than a small mass of embedded residual crystals; micron-sized seeds would "still not approximate" crystals below 100 nm moseson2021 R22; moseson2020a C42. Seed potency also depends on supersaturation and on the polymer moseson2020a C54, C56. 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, and the separate rates of growth and nucleation were not measured shah2024 K3, K4, X14, X13. Added seeds may not mimic crystals formed inside the ASD purohit2018 C7. Growth in the tacrolimus tests was inferred from concentration purohit2018 X9. Seeds did not always cause crystallization: at 240 and 100 mL the lower maximum supersaturation and the membrane loss kept growth small, at 40 mL it was large (F28, F29) hate2019 C46, C49. The rate units printed with the seeded runs are inconsistent with the profiles hate2019 X1. No seeding experiment was run in either pH-shift study, and the crystals on the delamanid dispersions were not identified, so the step from gastric crystals to lower release is inferred elkhabaz2019a X8; nguyen2023c X11. The 50% posaconazole dispersion also lost its supersaturation without an acid stage, so its crystal burden is not the only cause elkhabaz2019a C44.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 °Ctrasi2015a 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 °Calmeidaesousa2016 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 °C[indulkar2017a 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 B. Supersaturation from ASD dissolution

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 °Cilevbare2013c R2
amorphous celecoxib particlebirefringent spot within about 1 min, extensive crystals at 6 minbuffer, 20×ilevbare2013c R4
amorphous efavirenz particlesshrank over 3 h, no birefringencebufferilevbare2013c 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 6.8alonzo2010 R2
danazol (cited)amorphous danazol reached less than a quarter of the expected concentrationrefs in the cardjackson2014 R27
felodipine–HPMCAS melt (10% w/w)small rounded features, steps 0.77 nmpH 3, up to a weekschram2016 R10, R12
indomethacin, neat amorphousconcentration maximum (≈11.2 µg/mL) near the onset of conversion to αpH 2, 37 °Calonzo2010 R13, R7
nifedipine glassglass gone by ≈6 min, γ then α; solution ≈6 µg/mLpH 6.8, 25 and 37 °Craina2014b R6, R14
nifedipine–HPMC 50:50≈100 µg/mL at ≈22 min, ≈41 µg/mL at 150 min5 mg/mL, 37 °Craina2014b R14
resveratrol–HPMCAS 25%, pH 6.8 against pH 1.2Raman ratio ≈0.96 and ≈0.93 after a day37 °Cwegiel2015 R17
neat amorphous celecoxib≈1.70 against ≈1.85 µg/mL for the crystal at 16 hpH 6.8, 37 °Cxie2015 R7
atazanavir–PVPVA 10%64% of the drug and all PVPVA released; drug release ceased at ≈70 min; crystals at 90 min55 °C[correasoto2022b R5]
atazanavir–PVPVA 10% with TPGScrystals after 1 h55 °C[correasoto2022b 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 B. Supersaturation from ASD dissolution

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/minlu2016 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 B. Supersaturation from ASD dissolution

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 dryvaneerdenbrugh2010b R5
amides, bases against acids with PAA and PSSAhighest for amides (64–78) and bases; lowest for acids (8–31)as abovevaneerdenbrugh2010b 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, DSCvaneerdenbrugh2010b 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% RH[hiew2022a R6]
IDM, PVPVA in solutionno nucleation for more than 12 h at 5–50 µg/mL; about 40 min withoutS = 6moseson2020a 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 °Cmoseson2021 R3
BCL–PVPVA dispersion in the slurryHPMCAS in the medium delays crystallisation by about 10 min and leaves form 2 growth unchangedRamanmoseson2021 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 °Calonzo2012 R5, R16, R17
ritonavir, CAB Adp 0.81induction time ≈120 → ≈244 min5 µg/mL, 20 µg/mL drugilevbare2013c R9
celecoxib, HPMC2.4 → 12.6 min (22 µg/mL); 27.5 → 855.5 min (11 µg/mL)5 µg/mL, 37 °Cilevbare2013c R9, R15
danazol, HPMC-AS6–10 → 250–516 min10 µg/mL polymer, 25 °Cjackson2014 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/mLraina2015b 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 6.5wilson2021 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 °Csato2015 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 dishtrasi2017 R16, C40
felodipine dispersions 75% HPMCAS / HPMC / PVPmaxima 14.1 / 4.9 / 2.3 µg/mLpH 6.8, 37 °Ckonno2008a 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 shiftkonno2008a R14
amorphous indomethacin, 250 µg/mL PVP≈23.8 µg/mL held 4 h at 25 °CpH 2alonzo2010 R14
indomethacin solvent shift, 37 °Cnone ≈42 → ≈7.3 µg/mL in 30 min; HPMC ≈39 held about 2.5 hpH 2alonzo2010 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 °Cilevbare2013d R12
nifedipine γ → α, 1 mg/mL polymerγ intact ≈20 (PVP), ≈60 (HPMC), ≈110 min (HPMCAS) against ≈1325 °Craina2014b 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 °Cxie2015 R1; xie2016a R3
tacrolimus 50 µg/mL with 50 µg/mL HPMConset 6–8 h against within 3 hpH 4.5, 37 °Ctrasi2016 R9
indomethacin, 100 µg/mL HPMC against EPOheld ≈1.5 h against crystals during the titrationpH 2.2, 37 °Cxie2017 R5, R8
resveratrol dispersionsno matrix crystallization from 80% HPMC, 85% HPMCAS, 95% CMCABpH 6.8, 37 °Cwegiel2015 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 B. Supersaturation from ASD dissolution

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 DSCraina2015b C12
curcumin; resveratrolintermediate; rapid crystallizersolvent scheme[wegiel2014 R21; wegiel2013b C6]
naringenin; quercetinintermediate; rapidsolvent scheme[wegiel2013a C19]
lumefantrineclass 3melt DSC[trasi2020 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 B. Supersaturation from ASD dissolution

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 saltstowler2008 C32
dihydropyridinescilnidipine slowest, nifedipine fastest in solution; for six drugs the ranking is cilnidipine < felodipine = nisoldipine < nitrendipine = nimodipine < nifedipinesupersaturated buffer; synchrotronraina2015b C13, C28
nifedipine; nimodipinenifedipine a very fast crystallizer; nimodipine faster than the other four dihydropyridinesaqueous media (cited)[raina2015a R17]
felodipinerelatively slow; nifedipine fastercitedraina2014a R20, C31
ritonavir, efavirenz (class III); celecoxib (class II)induction times about 120, 5.1 and 2.4 minsupersaturated buffer, 37 °C, calculated amorphous solubilityilevbare2013c 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 coatingvaneerdenbrugh2010b 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 dryvaneerdenbrugh2010b R4
flurbiprofen (class I/II); chlorpropamide, bifonazole (class II)mean AI 68, 73, 97%as abovevaneerdenbrugh2010b R4
class I films with every polymer at 75/25 drug/polymeralmost all fully crystalline (AI 0)as abovevaneerdenbrugh2010b 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–heat[hiew2022a 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 °Cmoseson2021 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% RHXRPDtrasi2019 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 solutionshah2024 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 polymercited[hate2018 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 shiftraina2015b 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, cryomillingwegiel2013b 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 dishtrasi2017 R12, R16, C28
lumefantrine; artemetherclass 3; class 1DSC heat–cool–heat[trasi2020 R5, R6, C7]
felodipine, neat amorphous≈54% crystalline at 1 minpH 6.8 slurry, 37 °Calonzo2010 R2
indomethacin, neat amorphousamorphous for at least 4 hpH 2 slurry, 25 °Calonzo2010 R11
nifedipine, neat glasscrystalline (γ) by ≈6 min with or without dissolved polymerpH 6.8, 25 °Craina2014b R6, R2
resveratrolrapid crystallizer (cited); Tm 262 °Cstorage and solvent-evaporation classwegiel2015 R22, M1
celecoxib, 22 µg/mL without polymercrystallization within 5 minpH 6.8, 37 °Cxie2016a C13
lopinavirslow crystallization from aqueous solutionpH 3li2016b 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 °Cque2018 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 B. Supersaturation from ASD dissolution

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 dissolutionPXRD[bhardwaj2018 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 B. Supersaturation from ASD dissolution

degree of crystallinity

The share of a sample that is crystalline

The library uses at least five bases for it. Taylor and Zografi write x_c, the mole fraction of the crystalline form in a binary mixture of two pure forms [taylor1998a E3]. Rumondor and Taylor define it per drug, the percent of the felodipine added as crystals, and convert to the sample by multiplying with the drug mass fraction [rumondor2010b E3, X12]. Correa-Soto and co-workers define "% crystallinity" as the weight per cent of crystalline drug in the whole powder and also give the per cent of the drug crystallized correasoto2017 E1, X6. Kestur and co-workers use the field-averaged SHG intensity, background-subtracted and divided by that of a crystalline reference, as "relative crystallinity": for blends the share of crystalline naproxen in the blend, for the dispersion the share of the 25 wt% drug [kestur2012 E8, X11]. Wanapun and co-workers express a limit as a volume fraction [wanapun2010 E3]. The bases are not interchangeable (F4).

Findings

F1, F2, F3, F4, F7, F8, F9, F10.

Related concepts

measured by partial least squares regression and second harmonic generation; limited by limit of detection and limit of quantitation; related to residual crystallinity and polymorphism.

Formulas

drug-basis to powder-basis crystallinity conversion, Kontoyannis two-band intensity ratio calibration, SHG relative crystallinity.

How it is measured or obtained

From the ratio of a crystalline to an amorphous Raman band, corrected for overlap [taylor1998a P7, E5]; from PXRD, as a Bragg-peak area ratio or by whole-pattern PLS or OPLS calibrated on the dispersion plus crystals [rumondor2010b P6, P7; kestur2012 P9]; from Raman spectra by OPLS [kestur2012 P11]; from SHG image intensity normalized to a crystalline standard [kestur2012 P7; correasoto2017 P10]; and from 19F ssNMR spectra deconvoluted into amorphous and crystalline components correasoto2017 P5. Standards are physical mixtures of the two forms or the amorphous dispersion mixed with crystalline drug at fixed total drug content [taylor1998a P4; rumondor2010b P2; correasoto2017 P6]. Their "actual" values are the weighed compositions, which Kestur and co-workers did not verify after milling [kestur2012 X12].

Values in the library
materialvalue or classconditionspaper ids
indomethacin milled 5, 15, 30 min85.0, 77.5, 63.5% (Raman-equivalent, two-state calibration)FT-Raman, Wig-L-Bug with ball[taylor1998a R16, X9]
felodipine–PVP at 25, 50, 75% PVPRMSEE 2.2, 1.9, 4.7% of the drug (PLS); 11.2, 17.0, 23.6% (area ratio)18 calibration samples per level[rumondor2010b R9, P2]
naproxen–HPMCAS 75/25 dispersion, 60 °CSONICC about 24 to 48% of the drug over 0–48 h; PXRD about 27 to 54% and Raman about 26 to 44% from 2 hread from plots[kestur2012 R16]
flutamide–HPMCAS 15%, 40 °CXRPD 1–2% (days 35–53); 19F ssNMR 1, 3.8, 4.6% (days 35, 39, 48)15% = all drug crystallinecorreasoto2017 R12, R14
ezetimibe–HPMCAS 30%, 60 d, 82% RHSHG about 11.5%, XRPD about 12%, ssNMR 17% of the drug; about 3.5% of the powder40 °Ccorreasoto2017 R21, R22, R23
posaconazole HME ASD at 10, 25, 50 wt% DLSHG 0.3, 3.2, 19.3 wt% of the ASD (3.3, 12.7, 38.7 wt% of the drug); pXRD 2.4% at 25 wt% and 23.1% at 50 wt%HME at 125 °Cshah2024 R9, R10
BCL–PVPVA extrudatesbelow 1% (S/155), 3.5% (M/155), 30% (L/155) by XRPDLOD about 1%moseson2021 R6
Pitfalls and disagreements

The basis (mole, mass, volume, per drug, per powder) and the drug loading must be stated; at 15–30% drug a powder-basis figure is 3.3–6.7 times smaller than the per-drug figure (synthesis: 1/0.30 to 1/0.15). A two-state calibration made from physical mixtures gives only an equivalent value for milled material that is partly disordered throughout [taylor1998a C17, X9]. RMSEE is an error on the calibration samples, not a validated prediction error [rumondor2010b X3; kestur2012 X4]. A calibration made from the as-received crystals can fail for crystals grown in the dispersion: flutamide SHG reached about 3 times the fully crystalline standard correasoto2017 R9, C20.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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; 5.7ilevbare2013b 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 NMRwilson2021 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 B. Supersaturation from ASD dissolution

degree of supercooling

\Delta T = T_m - T, how far below its melting point a liquid is held or crystallizes; "undercooling" and "supercooling" are used as synonyms [baird2013 E4; tian2017 E4]. It sets the driving force, which is proportional to ΔT [tian2017 C22]. New aspect (PEG dispersions): in a dispersion the supercooling of each component is set by the melting point of that component in the mixture, which the other component depresses. For benzocaine the authors cite a melting point of around 89 °C for the neat drug and around 48 °C at the eutectic, so the supercooling at 25 °C is much smaller in the PEG dispersion [zhu2012 C32, M3]. PEG's own supercooling falls when a drug lowers its melting point [zhu2011 C21, R1]. New aspect (C. Amorphous solubility and LLPS): in the amorphous solubility papers the undercooling is T_m - T at the temperature of the solution experiment (25 or 37 °C), together with T_g - T_\infty, where T_\infty is the temperature at which crystal and supercooled liquid would have equal enthalpy; both are used to judge whether the Hoffman free-energy estimate is reliable [almeidaesousa2015 C34, C35, R16].

Findings

Crystallization tendency: F2, F7, F10, F11. PEG dispersions: F5, F8, F10. C. Amorphous solubility and LLPS: F7. Physical stability: F18, F28, F29.

Related concepts

related to thermodynamic driving force for crystallization; used by Barandiaran-Colmenero method and critical cooling rate; part of crystallization from the supercooled melt; reduced by melting point depression; governs the accuracy of the Hoffman equation and the amorphous-crystalline free energy difference; related to kinetic versus thermodynamic control of crystal growth.

Formulas

Barandiaran-Colmenero critical cooling rate, Hoffman equation, temperature of maximum crystal growth rate.

How it is measured or obtained

As Tm minus the crystallization peak temperature on cooling at a given rate [baird2010 P2; baird2013 R1]; as the temperature scale for growth data [trasi2014a P5]; in dispersions it shrinks when the polymer depresses the drug's melting point [zhu2011 C20]. In the PEG dispersions it was not measured: the supercooling is inferred from the liquidus of the drug–PEG phase diagram [zhu2012 C32; zhu2011 R1]. The 25 versus 40 °C solidification of pure PEG was used as a control of how much a change of PEG supercooling moves the lamellar long period (about 1 nm) [zhu2011 R8, C21]. In the amorphous solubility papers Tm comes from DSC and T∞ from the enthalpy of conversion with ΔH(c → sl) set to zero in the heat-capacity cycle [almeidaesousa2015 E9, R16]. In the polymer growth papers, from the onset melting temperature of 10% physical mixtures at 10 °C/min [trasi2012a P5, R9].

Values in the library
materialvalue or classconditionspaper ids
caffeine3.0 °CDSC cooling at 20 °C/min[baird2010 R12.j]
tolbutamide80.8 °CDSC cooling at 20 °C/min[baird2010 R12.v]
4-biphenylmethanol; haloperidol15.1; 90.8 °Crapid cooling at 500 °C/min[baird2013 R1.a, R1.f]
class I-A meltscrystallized after about 5–35 °Crheometer[baird2012 R4]
vemurafenibabout 25 °C before crystallizationDSC cooling at 10 °C/minlu2016 R1
benzocaine in PEG 20:80melting point 55 against 92 °C for the pure drugdispersion[zhu2011 C20]
felodipine growth runsΔT 71.4–31.4 °C over 70–110 °Cmelt growth[kestur2010b R17]
benzocaine in PEG 3350supercooling at 25 °C: 89 − 25 = 64 K neat against 48 − 25 = 23 K at the eutectic (synthesis)cited melting points[zhu2012 M3, C32]
PEG 3350 with 20 wt% benzocaine; ibuprofen; fenofibrateliquidus about 54.5, 57, 58.0 °C against about 60.5 °C for PEG, a depression of 6.0, 3.5, 2.5 K (synthesis)read from the phase diagrams[zhu2011 R1.g, R2.g, R1.a; zhu2012 R24.d]
pure PEG 335025 °C: t_{50} about 23 s; 40 °C: about 48–64 ssynchrotron XRD[zhu2012 R4, R16]
ibuprofen, phenylbutazone, tolnaftateTm − T 51, 82, 86 K; Tg − T∞ 81, 42, 143 K25 °C[almeidaesousa2015 R16]
diclofenac, sorafenib, griseofulvinTm − T 147, 180, 192 K; Tg − T∞ 145, 107, 122 K25 °C[almeidaesousa2015 R16]
telaprevirTm 238 °C against 37 °C, a gap of about 200 KHoffman estimate 2.7 times the onset[mosqueragiraldo2015 M1, C23, C24]
CRH1Tm 141.7 °C, so Tm − T = 116.7 K (synthesis: 141.7 − 25)all three free-energy routes agree within 1.3 µg/mLalmeidaesousa2016 M1, R2
acetaminophen with 10% w/w of seven polymersTm 166.7–168.6 against 169 °C; supercooling similar for allDSC[trasi2012a R9, C19]
flutamide with 10 mol% polymersTm 108–110 °C; supercooling hardly changedDSC[trasi2012b R7, C33]
celecoxib with TPGS and PVPTm 151.49 °C, 12 °C below the drugDSC[mosqueragiraldo2014 R5.f, C18]
six compounds with 1–20% PHBTm of physical mixtures 0–4 °C lower, so supercooling taken as unchangedDSC[sato2016 R7, C18]
indomethacin δ, α, γTm 127 (cited), 152 and 160 °CDSC[tian2017 M1]
Pitfalls and disagreements

Undercooling did not always rise with cooling rate and scattered between runs [baird2010 R12, C18]. Hoffman estimates lose accuracy at large undercooling [almeidaesousa2015 C34; mosqueragiraldo2015 C24]. Low polymer levels barely shift Tm, so the supercooling is similar with and without polymer [trasi2012a C19; sato2016 C18]. In the PEG dispersions the supercooling and the mobility of benzocaine were not measured, and the two cited melting points differ between the two PEG papers (89 and 48 °C against 92 and 55 °C for the 20/80 blend) [zhu2012 C32, C33; zhu2011 R1]. The authors do not weigh reduced PEG supercooling as a cause of slower PEG crystallization, only hydrogen bonding [zhu2012 C44]. In the amorphous solubility papers Table 10 does not predict the size of the Hoffman error drug by drug: sorafenib has 180 K undercooling and equal Hoffman and Cp ratios [almeidaesousa2015 X8]. Small melting-point shifts were used to rule the driving force out as the cause of growth differences between polymers [trasi2012a C19; trasi2012b C33].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 values[marsac2010 R22, E1]
six drugs in PVP–waterseparating drugs had water–drug χ 2.84–3.58, non-separating 2.50–2.7125 °C sorption[rumondor2009c R24, C46]
ritonavir with PVP, PVPVA, HPMCAS (outside)larger Δχ, higher tendency to phase separation (argument)stated in words[purohit2017b E4, C43]
loratadine-type ASDs (outside)separation predicted when the difference is large even if drug–polymer χ is negativeargument[yang2021 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 B. Supersaturation from ASD dissolution

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 °Cmoseson2020a R3.a, R3.d
IDM, 50 µg/mL, 5 µg/mL PVPVA, 50 µg/mL seedsabout 50 → 37.1 µg/mL in 720 minsamemoseson2020a 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 dosemoseson2020a R6
BCL–PVPVA S/155 and M/155about 32.4 → 24.5 and about 28.2 → 16.2 µg/mL150 µg/mL dose, 4 hmoseson2021 R12
paclitaxel–HPMCAS with 18 wt% seeds (outside)desupersaturation by crystal growth; HPMCAS cannot block it completely16 hque2018 C30
tacrolimus capsules (outside)steep decline after the maximum shows that seeds grow rapidly in 100 mLpH 4.5purohit2018 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/mLshah2024 R12, R14
PCZ–HPMCAS 25% DL, 3.2% crystals against nonecrystallization after 45 min against about 1.5 hsameshah2024 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 solutionshah2024 R22
ezetimibe PVP ASD, FeSSIF195 µg/mL at 15 min to 41 at 30 min37 °Celkhabaz2017 R14
ezetimibe ASDs, bufferdecline after about 30 minelkhabaz2017 R10, C19
tacrolimus generic, 100 mLabout 98% released at 20–30 min, 39.5% at 120 minmedium Ipurohit2018 R7
felodipine, no polymer, unseededabout 5.35 → 1.54 µg/mL from about 10–15 min to 150 minS 10alonzo2012 R15
paclitaxel–HPMCASnone unseeded; present with 18 wt% seeds16 hque2018 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 6.5wilson2018 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 generichate2019 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 4.5purohit2019 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 °Calonzo2012 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 °Cjackson2014 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 °Cilevbare2013c R16
paclitaxel with 18 wt% seeds (ASD dissolution chapter)desupersaturation immediate without polymer37 °Cque2018 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 breakelkhabaz2021 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 6.5duong2022b 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 °Ckonno2008a R12
indomethacin, solvent shift, no polymer≈27.3 µg/mL held about 25 min, then ≈5.3 at 90 minpH 2, 25 °Calonzo2010 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 °Craina2014b 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 °Cxie2015 R2
celecoxib–PVP-K12 50% dispersion≈21.0 µg/mL near 6 h → ≈6.5 at 16 hpH 6.8, 37 °Cxie2015 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 °Ctrasi2016 R9
indomethacin–EPO 3:7 dispersion≈77 µg/mL (UV) → 8.8 µg/mL (HPLC) at 1 hpH 2.2, 37 °Cxie2017 R11
lopinavir 50%: EUD, CAP / HPMCPloss within ≈10–12 h / none in 48 hpH 3, 25 °Cli2018 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 °Cque2018 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 °Celkhabaz2019a 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 °Calvarenga2025 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 B. Supersaturation from ASD dissolution

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 hcompacts[que2019 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 B. Supersaturation from ASD dissolution

diffusion-controlled crystal growth

Crystal growth whose rate is limited by transport of molecules to the crystal surface rather than by their incorporation into the lattice. From the supercooled melt it shows as growth that slows on cooling although the driving force rises, because transport (viscosity) dominates [kestur2010b C22, C23]. In solution growth an overall growth order of 1 is read as diffusion control and 2 as integration control alonzo2012 C3.

Findings

F3, F19, F28.

Related concepts

part of crystal growth rate; depends on molecular mobility; contrasts with integration-controlled growth; contrasts with glass-crystal growth mode.

Formulas

the two-dimensional nucleation growth rate printed by the melt paper is listed on the chapter page as table only [kestur2010b E5]; Stokes-Einstein equation gives the polymer diffusivity used with it.

How it is measured or obtained

From the temperature dependence of melt growth rates compared with the growth equation v = (k/\eta)\exp\left(-\Delta G^{*}/k_B T\right) [kestur2010b E2, R7]; in solution from the slope of ln growth rate against ln supersaturation alonzo2012 C3.

Values in the library
materialvalue or classconditionspaper ids
felodipine form II with and without PVPgrowth falls on cooling over 70–110 °C (ΔT 71.4–31.4 °C): transport-limitedmelt films[kestur2010b R13, R17, C23]
felodipine in aqueous solution (outside)HPMC shifts growth toward integration controlseeded desupersaturationalonzo2012 C33
diffusion-controlled growth against the glass-crystal mode0.1–1 against 1700–2400 molecular layers per relaxation time (cited); felodipine form II below 1felodipine at 45 °C[kestur2013a R16, R18]
six compounds with and without PHBall growth temperatures below 0.94 Tm, so growth taken as transport-limited ("is expected to be")melt films[sato2016 E2, C15]
low-Tg compounds with PHBretardation attributed to PHB chains impeding transport to the crystal ("most likely")melt films[sato2016 C25]

Evidence table: diffusion-controlled crystal growth.

Pitfalls and disagreements

The supercooling of the felodipine melt study is computed from the form I melting point although form II grew, so the stated ΔT range is too large [kestur2010b X15]. Below the temperature of maximum growth, transport limitation is the expected regime for any melt; it does not by itself identify the polymer mechanism [kestur2010b C23].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 onsetjackson2014 R22
with PVPabout 240–250 nm to 1 h; about 2900 nm at 2 h10 µg/mL polymerjackson2014 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 hsamejackson2014 R22
ritonavir nanodroplets (ASD dissolution chapter)stabilized against coalescence "likely" by charge repulsion between adsorbed polymers37 °Cilevbare2013d C38
danazol droplets, PVP, HPMC, HPMC-ASDLS z-diameter about 350 → 103–136 nm; NTA 181–270 nm1–1000 µg/mL, 25 °Cjackson2016 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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 releaseoutside[bhardwaj2018 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 6.5[li2020 R10, C37]
ritonavir/lopinavir co-granule, 50:50 drug:polymerexpected drug-controlled; polymer leaves first and the surface turns drug-richacidtrasi2019 C46
IDM–PVPVA 1:1dissolution described as drug-controlled; the polymer is expected to dissolve quickly, leaving amorphous drug particlesnon-sink, pH 4.5moseson2020a 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 referencetrasi2016 R19
ritonavir 50:50 films with PVP, PVPVApolymer dissolved; ritonavir ≈18 and ≈9 µg/mL at 240 min, below 27 µg/mL25 °C, pH 6.8[purohit2017b 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 HCl[bhardwaj2018 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 minsame[que2019 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)same[saboo2019 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 °C[saboo2020 R3, M5]
atazanavir–PVPVA 10%≈0.07 against PVPVA ≈0.24 mg/min/cm²pH 6.8, 37 °C[correasoto2022b 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 B. Supersaturation from ASD dissolution

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 mixturetrasi2015a 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 B. Supersaturation from ASD dissolution

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 hli2016b R4
same, polymerbelow 5 µg/mL from the dispersionspH 3li2016b R3
lopinavir–HF with STC; SDS at pH 5; PVPVA + SDS≈25.6; ≈33–39; ≈50 µg/mL25 °Cli2016b 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 °Celkhabaz2019a 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 °Cnguyen2023c 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 °Cnguyen2023b 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 B. Supersaturation from ASD dissolution

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; absorptive[hate2018 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 nanospeciescitedtrasi2016 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 6.5wilson2018 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 → FaSSIF[hiew2023 R8]
binary cPADs at 60; 75%; hierarchical cPAD at ≈73%≈37.5; 17%; ≈71%same[hiew2023 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 B. Supersaturation from ASD dissolution

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 hkonno2008a 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 ethanolvaneerdenbrugh2010b 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 hwegiel2015 R6, R7
resveratrol–HPMCAS 15:85up to ≈1610 µg/mL with flux at most about twice the crystal'spH 6.8, 37 °Cwegiel2015 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)same[bapat2025a 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 B. Supersaturation from ASD dissolution

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 daysvaneerdenbrugh2010b 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 loading[hiew2022a R20]
clotrimazole, loratadine, brotrimazole, Me-DIBF with PVPVAhalogen bond: K_F 0.56–1.11 M⁻¹, carbonyl shift 2–6 cm⁻¹NMR, IR[que2020 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 B. Supersaturation from ASD dissolution

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, FTIRvaneerdenbrugh2012a 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 B. Supersaturation from ASD dissolution

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 powders[purohit2017b 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 B. Supersaturation from ASD dissolution

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, NTAindulkar2016 R4
atazanavir, solvent shift204–226 nm, PDI 0.08–0.15100–500 µg/mL, DLS[hate2018 R6]
atazanavir 90:10 HPMCAS and HPMC ASDs294–326 nmclosed and absorptive[hate2018 R12]
atazanavir with PVPVAabout 245 nm rising to about 700 nm at 75 min and 10 µm at 105 minagglomeration[hate2018 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 dissolutionwilson2018 R10, R11
atazanavir, posaconazole in pooled human fluidspheres of 0.1–0.5 µm, no needlesSEM of pellet, 100 µg/mL HPMC-ASelkhabaz2019b 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 °C[ueda2020a R6]
atazanavir 150 µg/mL with polymer or surfactant additivesdroplets of about 280 and about 1000 nm gave the same mass flowPAMPA, 2% SDS receiver[hate2022 R17]
ritonavir–PVP dispersion at 20 µg/mLabout 350 nm at onset; ≈5590 nm by 120 min100 mM buffer, 37 °Cilevbare2013d R1, R5
ritonavir 20 µg/mL with 5 µg/mL CAAdP 0.33210−214 nm before crystallizationsolvent shiftilevbare2013d R12
danazol 90:10 dispersions246–284 nm25 °Cjackson2015 R6
ritonavir; ritonavir + lopinavir, HPMCAS dispersionsabout 500 nm; about 160 nm in 0.45 µm filtrates1 htrasi2015b 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 films[purohit2017b 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%DLS[que2019 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 h[saboo2019 R11]
indomethacin–PVPVA 5, 10%250–350 nmNTA, 30 min[saboo2020 R7]
felodipine with 5% TPGSZ-average ≈237–279 nmDLS, 60 min[saboo2021 R17]
elbasvir 2.5%; loratadine 10%PVPVA ≈670 → 1190; ≈820 → 2120 nm; HPMCAS ≈280 → 390; ≈420 → 570 nmDLS, 60 min[yang2021 R3, R6]
clopidogrel≈520 nm in buffer; stable with SDS, TPGS or Tween 80; ≈12-fold growth with CTABDLS, 4 h[correasoto2022a R5, R6]
four phenolphthalein analogues179–364 nmDLS, 30 min[que2021 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 minDLS[correasoto2023 R5]
MePHPH–PVPVA 5–30%; PHPH–PVPVA 5%nanoparticles formed within the gel; onset 601 ± 68 µm beyond the 356 ± 18 µm gelin situ confocal[deac2023a 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, DSC[deac2023a 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 B. Supersaturation from ASD dissolution

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, DLS[correasoto2022a 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 hsame[correasoto2022a R6]
clopidogrel–PVPVA 40%; 50%, binary and with Tween 80, TPGS, SDS≈790, ≈510, ≈580, ≈690 nm; ≈1960, ≈780, ≈890, ≈1260 nm90 min of dissolution[correasoto2022a 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 °C[ueda2020a 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 B. Supersaturation from ASD dissolution

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, antisolventtrasi2015a R15
ritonavir–HPMCAS dispersion≈500 nmNTA of 0.45 µm filtrate, 1 htrasi2015b R7
tacrolimus, 60 µg/mL≈220 nm, a second phaseNTA of 0.7 µm filtrate, pH 4.5, 37 °Ctrasi2016 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 °Ctrasi2015a R9, R10
ionized diclofenac with the ritonavir-rich phasefully recovered in bulk25 °Ctrasi2015a 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 °Cueda2021 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 °C[ueda2022 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/mLindulkar2016 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 °Cilevbare2013d 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/I1trasi2015b R15
indomethacin with 100 µg/mL HPMConset 36 µg/mL; droplets 70–100 nmpH 2.2, 37 °Cxie2017 R4, R6
indomethacin EPO–HPMC dispersion≈75 nm species; redissolved within ≈2 min after a rise to pH 537 °Cxie2017 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 B. Supersaturation from ASD dissolution

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 boundariesconfocal[benson2025 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, dried[que2019 R13]
nilvadipine 15:85porous layer within 10 min, growing to 30 minmicro-CT[saboo2019 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, dried[saboo2021 R19]
indomethacin–PVPVA 15, 25%rough, porous surface after 5 min; smooth at 10%SEM[saboo2020 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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 °Cnguyen2023c R4
HPMCAS-LF; -MF1687 ± 47 and 1401 ± 69 µg/mL at pH 5.5the samenguyen2023c R4
HPMCAS-HFdissolves only from about pH 6.0the samenguyen2023c 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 °Cnguyen2023b R7
posaconazole–HPMCAS-MF dispersions in FaSSGF7.5–11.5% of a 400 µg/mL dose released in 60 minpH 1.6, 37 °Celkhabaz2019a R10
praziquantel–HPMCAS-MF dispersions, first stage≈9–29% released against ≈88–106% for HPMC E5 LVpH 1.6–5.0 or FaSSGF, 37 °Calvarenga2025 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 B. Supersaturation from ASD dissolution

enthalpy of fusion

The heat absorbed when a crystal melts (ΔHfus, heat of fusion), measured by DSC; with Tm it gives the entropy of fusion and the Hoffman estimate of the crystallization driving force [vaneerdenbrugh2010a E1, E2], and with the melting points of two polymorphs it decides monotropy by the heat-of-fusion rule lu2016 C50.

Findings

F6, F7, F13.

Related concepts

used by entropy of fusion, Hoffman equation and Burger-Ramberger rules; part of thermodynamic driving force for crystallization.

Formulas

Hoffman equation, entropy of fusion, Burger-Ramberger heat-of-fusion rule.

How it is measured or obtained

By DSC melting endotherms, in kJ/mol or J/g, and per volume with the crystal density [baird2010 P1, P8; lu2016 R20].

Values in the library
materialvalue or classconditionspaper ids
ritonavir; haloperidol65.34; 54.26 kJ/molDSC[baird2010 M51, M17]
caffeine20.81 kJ/molDSC[baird2010 M10]
vemurafenib α; β53.8; 33.3 kJ/molDSClu2016 R20
nilutamide stable form; form I~98; around 66 J/gDSC[trasi2014b M1, R6]
class I against class III≈+0.45 against ≈−0.63 SDper volume[baird2010 R22.b]
nifedipine against felodipinehigher ΔHf and Tm, read as a higher intrinsic crystallization tendencyDSC[marsac2008a C35]
Pitfalls and disagreements

One paper gives three different values for the α-vemurafenib heat of fusion, and its virtual transition temperature depends on the choice lu2016 X1; a melting endotherm overlapped by recrystallization can understate ΔHm lu2016 X12. Fusion properties did not correlate with crystallinity loss of drugs in PEO [marsac2008b C34].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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% RH[rumondor2009c R24, C28]
felodipine and quinidine with HPMCASless sorbed water gives a less positive mixing enthalpy, which "may explain" no separationqualitative[rumondor2010c C31]
indomethacin with PVPVAstronger drug–polymer bonds give a more favourable mixing enthalpyqualitative[rumondor2010c 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 shiftvaneerdenbrugh2012a 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 B. Supersaturation from ASD dissolution

entropy of fusion

The entropy gained on melting, \Delta S_{fus} = \frac{\Delta H_{fus}}{T_m} with Tm in kelvin [baird2010 E26; vaneerdenbrugh2010a E1]. It is read in two ways in the library: as part of the driving force for crystallization [baird2010 C60] and, following Jackson, as a measure of how few melt molecules are correctly oriented to join the crystal [trasi2014a C31]. A related reading takes the entropy of crystallization as the probability that a molecule has the right conformation or orientation for nucleation [marsac2006a C34].

Findings

F6, F13.

Related concepts

depends on enthalpy of fusion; part of thermodynamic driving force for crystallization; related to conformational flexibility.

Formulas

entropy of fusion, linear fit of normalized growth rate on melting entropy.

How it is measured or obtained

From DSC heat of fusion and melting temperature, per mole or, with the crystal density, per volume [baird2010 P8; trasi2014a M1].

Values in the library
materialvalue or classconditionspaper ids
caffeine; haloperidol; ritonavir4.08, 12.8 and 16.4 × 10⁻² kJ mol⁻¹ K⁻¹DSC[baird2010 M10, M17, M51]
felodipine; nifedipine74.4 and 89.6 J mol⁻¹ K⁻¹DSC[marsac2006a E11]
nilutamide; cinnarizineΔSm/R ≈8.7; ≈12.5growth analysis[trasi2014a R11.a, R11.i]
class I against class III≈+0.41 against ≈−0.59 SDper volume[baird2010 R22.c]
spin-coat class I against III≈+0.46 against ≈−0.33 SDper volume[vaneerdenbrugh2010a R20.d]
fast growers (group 1)≈−0.38 SDper mole[trasi2014a R8.f]
Pitfalls and disagreements

Fast melt crystallizers score high on ΔSfus per volume while fast growers score low on ΔSm per mole (synthesis: different bases and read-outs, see F6). For felodipine and nifedipine an entropy-dominated view would predict felodipine to crystallize more easily, which it does not; the enthalpy dominates there [marsac2006a C35]. Fusion properties did not correlate with crystallinity loss of drugs in PEO [marsac2008b C34].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

entropy of mixing

The entropy gained when drug and polymer mix

For a drug with a polymer it is much smaller than with a small solvent, because the configurational entropy of the polymer is reduced by the connectivity of its repeat units, and it is nearly the same for any polymer grade [marsac2006b C10, C11]. For typical drugs (molecular weight 200–600) and polymers (10,000 and above) the contribution is "predicted to be relatively constant" and always favourable, so the enthalpy of mixing decides miscibility [marsac2006b C12, C13; marsac2009 C26]. In the ideal case the entropy of mixing of two components is ΔS = −R(X_u ln X_u + X_v ln X_v), printed without its minus sign in one paper [rumondor2009a E3, X7]. Where an entropy of mixing is not measured, readings of the activity coefficient and of χ as enthalpy rest on the assumption that it is close to ideal [marsac2009 C11]. For two polymers the entropy per lattice site falls with the chain length of both, from about −27 × 10⁻²³ J for a 783 Da maltodextrin with PVP K 12 to about zero for a 450 kDa dextran with PVP K 90, so the grade-independence found for a small drug does not hold between polymers vaneerdenbrugh2012a R15, C34, C35.

Findings

F5, F9, F22.

Related concepts

part of free energy of mixing; includes combinatorial entropy of mixing; contrasts with enthalpy of mixing; related to Flory-Huggins theory.

Formulas

Flory-Huggins free energy of mixing, Gibbs free energy of mixing.

How it is measured or obtained

Not measured: it is computed from the Flory–Huggins expression with χ = 0, for a lattice whose site is one drug molecule [marsac2006b P6, R1]; for a small analogue liquid such as methyl pyrrolidone or 1-ethyl-2-pyrrolidone it is taken as ideal [marsac2006b C46; marsac2009 C11].

Values in the library
materialvalue or classconditionspaper ids
nifedipine with methyl pyrrolidoneminimum near Φ ≈ 0.44χ = 0[marsac2006b R1]
nifedipine with PVP K12, K29/32, K90minimum near Φ ≈ 0.6; K29/32 and K90 virtually identical, K12 slightly lowerχ = 0[marsac2006b R1]
typical molecular weightsAPIs 200–600; polymers 10,000–1,000,000cited[marsac2009 R13]
indomethacin, EP → PVP K12 → K29/32 → K90predicted solubility 0.396 → 0.144 → 0.134 → 0.134entropy term scaled with chain length[marsac2009 R9.e, C24]
maltodextrin (783 Da) with PVP K 12 to K 90minimum about −27 to −21.5 × 10⁻²³ J per site25 °C, no enthalpy termvaneerdenbrugh2012a R15
6 kDa dextran with PVP K 12 to K 90−9.1 to −2.8 × 10⁻²³ Jsamevaneerdenbrugh2012a R15
450 kDa dextran with PVP K 90about 0samevaneerdenbrugh2012a R15, C35

Evidence table: entropy of mixing.

Pitfalls and disagreements

The generalization to all drugs and polymers rests on one simulated drug, with an unscaled axis, and on a PVP grade (K12, 2,500) below the stated polymer range [marsac2006b X7, X8]. The ideal-entropy assumption for the analogue liquid and for equal contacts in analogue and polymer was not tested [marsac2009 C11, X17]. In ternary systems with absorbed water the entropy still favours mixing, and demixing is expected only when the enthalpy of mixing is positive enough [rumondor2010c C27]. Two of the 20 plotted curves (PVP K 12 with 40 kDa and 450 kDa dextran) do not follow from the stated inputs vaneerdenbrugh2012a X1.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

Fick's first law

Steady-state diffusive flux through a membrane written in activity form, J = D S a/(h \gamma_m) raina2014a E6; the concentration form is J = (D_{eff}/l)(C_d - C_r) indulkar2016 E1. The darunavir and posaconazole papers also write it as J = -D\,dC/dx and as the permeability form J = P C [alkalla2026 E1; elkhabaz2019b E5].

Findings

F2, F5, F18, F20.

Related concepts

underlies membrane flux; needs sink conditions.

Formulas

membrane flux in terms of solute activity, membrane flux from concentration difference.

How it is measured or obtained

Used as a model, not fitted: constants D, S, h and γm are assumed constant and not printed [raina2014a E6; hate2017 E1; alhalaweh2016 E1].

Values in the library
materialvalue or classconditionspaper ids
side-by-side cell, activity formJ = DSa/(h\gamma_m), 7.065 cm²felodipine, nifedipineraina2014a E6
flow-through cell, concentration formJ = (D_{eff}/l)(C_d - C_r)clotrimazoleindulkar2016 E1, E4
danazolJ = (dM/dt)(1/S) = D a/(h\gamma_m)ASDjackson2015 E1
atazanavir, posaconazole, six mediapermeability form J = PC: apparent permeability on total concentration fell in micellar media; multiplied by the ratio of total to buffer solubility it was 1.33–1.77 × 10⁻³ (atazanavir) and 2.36–3.03 × 10⁻³ cm/min (posaconazole)side-by-side, 37 °Celkhabaz2019b E5, R12, R13
Pitfalls and disagreements

The text of one paper writes γ for the membrane activity coefficient in Eq. 3 and for the donor in Eq. 4 raina2015c X8. The permeability form with total concentration under-reads permeability where micelles bind drug (F18) elkhabaz2019b R12, R13.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 fits[marsac2010 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 suppliedmoseson2021 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 side[li2020 R15, R16, C72, X10]
water–ritonavir and water–PVPVA (drying model)2.8 and 1.13fitted to dynamic vapour sorption, room temperature[li2020 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 −0.05sameshah2024 R1, R4
water with nifedipine, felodipine, droperidol, pimozide, indomethacin, ketoprofen2.84, 3.18, 2.85, 3.58, 2.50, 2.7125 °C, 95% RH[rumondor2009c 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 susceptibility[rumondor2009c 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 films[rumondor2010c R20, C28]
hydrophobic drugs with water\chi_{WD} expected positive from log Pqualitative[rumondor2010c 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 °Cli2018 C54
lopinavir with CA, EUDtwo Tgs, sorption on the additive line; little suppressionpH 3, 25 °Cli2018 C56
ritonavir with PVP, PVPVA, HPMCASno values; the argument explains AAPS of PVP and PVPVA films at 97% RH25 °C[purohit2017b 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 B. Supersaturation from ASD dissolution

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 termvaneerdenbrugh2012a 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 ASDs[purohit2017b 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 model[li2020 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 lessqualitative[rumondor2010c 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 B. Supersaturation from ASD dissolution

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 °Cnguyen2023b R13
Deltyba tablet≈77 µg/mL in FeSSIF V2 against ≈31–37 µg/mL in FaSSIF V1 at 120 min500 mL, 37 °Cnguyen2023b R14
coated delamanid edisylate tablets≈96 µg/mL in both media; ≈86–87 µg/mL after 17 h in FEDGAS37 °Cnguyen2023b 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 °Calvarenga2025 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 °Calvarenga2025 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 B. Supersaturation from ASD dissolution

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 ASD[que2021 R1, E2]
enzalutamideFox-estimated water-saturated Tg 352 K, so the amorphous drug is glassy at 37 °Cwilson2018 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 B. Supersaturation from ASD dissolution

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 °C[indulkar2017a R11, C19]
ritonavir, lopinavir HPMCAS and PVP dispersionsRTV-PVP maximum about 22 µg/mL even after 2 hultracentrifugedtrasi2015b R12, R13
resveratrol–HPMCASat most about twice saturation; enhancement from a soluble complexwegiel2015 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 bufferwilson2020 R2; wilson2018 R10
posaconazole, atazanavirfree concentration at either solid phase taken as the buffer value in every mediumsix media, 37 °Celkhabaz2019b 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 hultracentrifugedtrasi2015b 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 °Cwegiel2015 R19, R20
six tacrolimus products0.0048–0.0054 µg/min against a pure-drug plateau of ≈0.0050–0.0055pH 4.5, 37 °Ctrasi2016 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 B. Supersaturation from ASD dissolution

free energy of mixing

The free energy change on mixing drug and polymer, ΔGmix = ΔHmix − TΔSmix: a negative ΔGmix with one minimum versus composition means complete miscibility, a positive ΔGmix complete immiscibility, and two minima (the binodal points) with a metastable region between them and an unstable region bounded by the spinodal points partial miscibility; this liquid-mixture theory is extended by the authors to amorphous solids [rumondor2009a C35]. In Flory–Huggins form the first terms are the entropy of mixing, small for a polymer, and the last the interaction term χ [marsac2006b E1, C10]. Large positive χ gives a positive ΔGmix and immiscibility, small χ a negative ΔGmix with one minimum [marsac2006b C17]. In the dextran–PVP paper ΔGmix = ΔHmix − TΔSmix is used to argue that a blend mixes only when the combinatorial entropy outweighs a positive enthalpy vaneerdenbrugh2012a E3, C32; the itraconazole–HPMC paper writes the Flory–Huggins form for the same argument [purohit2015a E1, C41].

Findings

F5, F6, F3, F18, F22.

Related concepts

made of enthalpy of mixing and entropy of mixing; gives drug-polymer miscibility; part of Flory-Huggins theory.

Formulas

Flory-Huggins free energy of mixing, Gibbs free energy of mixing.

How it is measured or obtained

By calculation from χ, volume fractions and molecular volumes (Eq. 1 of the 2006 paper, Eq. 10 of the 2009 paper); no calorimetric ΔGmix is measured in these papers [marsac2006b E1, R2; marsac2009 E10, R10]. The curves in the two papers carry no numbers on the vertical axis, so depths can be compared only within a panel [marsac2006b X7; marsac2009 X12].

Values in the library
materialvalue or classconditionspaper ids
nifedipine–PVP K29/32positive at χ = 2.0 (maximum near Φ ≈ 0.37); shallow at 0.5 and 1.0; single deep minimum near Φ ≈ 0.54 at −3.8, −4.2Flory–Huggins[marsac2006b R2]
indomethacin–PVPminimum ≈2.4 times (melting χ) and ≈5 times (solubility χ) as deep as the athermal minimumΦ_polymer ≈ 0.5–0.6[marsac2009 R10]
felodipine, ketoconazole with PVPthree curves (athermal, melting χ, solubility χ) nearly coincideas above[marsac2009 R10]
sucrose–dextranmelting-route curve above the athermal curve (χ = 0.20)as above[marsac2009 R10]
Pitfalls and disagreements

The condition "the binodal points are the two minima" (first derivative zero) coincides with the common-tangent binodal only for a symmetric curve like the schematic in the paper; the authors apply it to no data [rumondor2009a E6, X15]. Curves for the immiscible pairs are not drawn, because their enthalpy of mixing cannot be accessed [marsac2009 C31]. The temperature and the PVP grade of the 2009 curves are not stated [marsac2009 X12].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 6.5nguyen2023c R11
delamanid free base with HPMCP-50≈62.5 / ≈33.5 / ≈6.5 µg/mL of 100the samenguyen2023c 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 samenguyen2023b 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 mediumnguyen2023b 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 6.5alvarenga2025 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 B. Supersaturation from ASD dissolution

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 °C[benson2025 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 minsame[benson2025 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 min[saboo2021 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 6.8[yang2022a 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 imaging[yang2022a R8]
neat HPMCAS-MF in pH 6.8 phosphate 5; 13; 51 mM/ΔpHno gel; 3 ± 1 µm; 19 ± 5 µmconfocal with prodan, 60 min[bapat2023 R14]
neat HPMCAS-MF gel, pH 6.8 phosphate 13–51 mM/ΔpHapparent pH 5.6–6.2gel scraped after the rotating-disk test[bapat2023 R15]
MePHPH–PVPVA 5–50%; PHPH–PVPVA 5–20%gel layer on every compact; 5% PHPH gel 356 ± 18 µmgravimetric and cross-sectional, steady state[deac2023a 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 °C[deac2024b 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 B. Supersaturation from ASD dissolution

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 °Cjackson2014 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 Q5000raina2015b 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 B. Supersaturation from ASD dissolution

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/minlu2016 R1, C5
tacrolimusgood GFA and stability; melting onset 121 °C, Tg onset 75 °C, no crystallization on reheatingDSC heat–cool–reheattrasi2016 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–heat[trasi2020 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 drugwegiel2013b 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 B. Supersaturation from ASD dissolution

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 °Cwilson2018 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 °Clu2017 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 6.5wilson2021 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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 °CDSCtowler2008 R4
nicardipine base; hydrochloride3.2; 81.0 °CDSCtowler2008 R5
nilutamide32 °C (onset)DSC[trasi2014b M1]
vemurafenib108 °CDSC at 10 °C/minlu2016 M1
felodipine; nifedipine; indomethacin45 °C eachDSC midpoint[baird2010 M37, M32, M40]
lumefantrineabout 18 °C; 19.7 °C (onset)DSC[trasi2020 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 B. Supersaturation from ASD dissolution

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, compacts[que2021 R9]
Me-TIPP–PVPVA 10, 20, 30, 40%60.8, 53.3, 29.9, 22.2% of iodine at the lower binding energyXPS[que2021 R11]
TIPP–PVPVA 10, 20, 30, 40%55.9, 26.5, 15.6, 8.9%XPS[que2021 R11]
TIPP; Me-TIPP in PVPVA, 10–40%≈0.017–0.027; ≈0.029–0.050 mmol lower-binding-energy iodine per 100 mgderived[que2021 R12]
Me-TIPP–PVPVAVP carbonyl shift at most 7 cm⁻¹IR, films[que2021 R7]
clotrimazole, brotrimazole; Me-DIBF in PVPVA (Miscibility chapter)VP carbonyl 1684 → 1682 cm⁻¹ from 10 to 90%; 6 cm⁻¹ downshiftIR, films[que2020 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 B. Supersaturation from ASD dissolution

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 °Cduong2022b 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 polymerwilson2021 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%triplicateilevbare2013c R17
danazol, HPMC-ASinduction time 516 → 277 min as drug concentration rises from 10 to 20 µg/mL25 °Cjackson2014 R17
telaprevir δ 28.8, buffercrystallizes immediately with a drug-rich phase presentpH 6.5, 37 °Clu2017 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 °Cilevbare2013d R16, R12
nifedipine dispersions against glassγ → α complete in ≈5–40 min against ≈40–145 min with dissolved polymer25 °Craina2014b 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 B. Supersaturation from ASD dissolution

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 dissolution[hiew2023 R10, R14]
hierarchical cPADs, HPMC or HPC dissolved in the anti-solvent≈56–72%same[hiew2023 R10, R12]
washed binary cPAD; HPMC suspended in MTBE≈47%; ≈8–15%same[hiew2023 R10, R11]
eight materialssurface drug ≤34% with ≈47–72% release; ≥53% with ≈8–17%XPS[hiew2023 R14]
hierarchical against binary cPAD, ≈73% drugAUC 135 against 73 µM·hdogs, n = 6[hiew2023 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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

HME operating design space

A map of product melt temperature against residence time for hot melt extrusion with regimes: thermal degradation at the top, melting above the drug's melting point, dissolution between Tc and Tm (the drug dissolves into the softened polymer, not melts) and suspension below Tc, plus an inaccessible zone below the polymer's minimum processing temperature [moseson2018a R1; moseson2018 C40, C48]. Higher temperature and longer residence time raise the risk of thermal degradation; lower temperature and shorter residence time the risk of residual crystallinity [moseson2018 C65]. The 2018 map put thermal degradation at the top as a schematic region; the thermogravimetry and assay studies of the ASD process papers give it a measured form, time–temperature contour maps of mass loss and assays of drug after exposure, and show that the lower boundary also moves with the input crystal size [moseson2020 R15, R18; moseson2021 R6]. For 30% bicalutamide–PVPVA, with Tc = 145 °C as the slowest dissolution case, the residence time needed to reach a crystal-free extrudate ranged from 2 min for micronized crystals to more than 20 min for large or broad-distribution crystals [moseson2022c R10].

Findings

F9, F10, F35, F36, F37, F41.

Related concepts

bounded by formulation critical temperature and temperature-composition phase diagram; governs residual crystallinity and crystal dissolution into a polymer melt; the chemical-stability side is the HME processing window.

Formulas

Noyes–Whitney equation.

How it is measured or obtained

By extruding one composition at several melt temperatures and residence times, reading crystallinity with several methods and placing each run on the plane; the zone lines are drawn by the authors between data points and could instead be set by XRPD thresholds (<1%, <2%, <5%) with performance tests [moseson2018 R15, C60].

Values in the library
materialvalue or classconditionspaper ids
50% IDM–PVPVA15 runs; 117–161 °C; 2–20 min; amorphous by all techniques first at 131 °C 20 min, 141 °C 10 min, 161 °C 2 min5 mL recirculating extruder[moseson2018 R10, R15]
1:1 IDM–PVPVAextrudate at 131 °C and 20 min on the lower edge of the dissolution regionschematic from earlier work[moseson2018a R1]
30:70 BCL–PVPVAdissolution regime between Tc = 145 °C and Tm = 195 °C; at 155 °C small input crystals left crystals visible only by TEM, medium and large ones 3.5% and 30%; at 180 °C small crystals left none5 mL extrudermoseson2021 M1, P1, R6
50/50 IDM/PVPVA and 30/70 BCL/PVPVA, chemical sideIDM/PVPVA under 1% mass loss for short times to 200 °C; BCL/PVPVA 1% within 10 min at 180 °C, after 40 min at 165 °C, after more than 100 min at 155 °Cisothermal TGA, 4 h[moseson2020 R15, C44, C45]
20% RTV with PVPVA 64, HPMCAS MF, HPMCextrusion at 130–160 °C, 5 min: assay 95.7–100.5%, polymer-dependent2 mL extruder[alvarenga2022 R22]
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 two5 mL micro-extruder, PXRD[moseson2022c R10]
PCZ–HPMCAS MF, 10 / 25 / 50% DLcrystals 0.3 / 3.2 / 19.3 wt% at 125 °C, none at 175 °C2 min, SHGshah2024 R10
Pitfalls and disagreements

The map assumes controlled particle size, screw configuration and speed; residence time is the time to the first extrudate in a micro-compounder; the X-ray criterion behind the Fig. 8 classes is not stated [moseson2018 C61, X15, X5]. Thermal degradation was not measured and its region is schematic [moseson2018 C65]. The runs of the bicalutamide study are placed by melt temperature only because the residence time and screw speed are in a table that was not supplied moseson2021 P1. The ceiling of the window is treated in HME processing window. Processing at Tc is not practical for most products, and screw speed and shear were not studied [moseson2022c C56, C55].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 formslu2016 R22, E1
felodipineestimated amorphous solubility about 9 µg/mL37 °Calonzo2010 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 °Cilevbare2013c 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 °Calmeidaesousa2016 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/molraina2014a R7
nifedipineprinted ratio 8.78; recomputed 14.45Tm 173 °C, ΔHf 32.5 kJ/molraina2014a R7, X3
atazanavirratio 62, predicted 68 µg/mL310 K[indulkar2017a R5]
indomethacin17–25 µg/mL (25 °C), about 37 µg/mL (37 °C)Hoffman estimatealonzo2010 R8
enzalutamideprinted estimate about 39 µg/mL (13-fold); the printed inputs give 27.737 °C, Tm 470 Kwilson2018 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 °Cjackson2014 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 paperraina2015b 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 26.5duong2022b R7, E3, X2
felodipineratio about 10; about 9.5 µg/mL37 °Ckonno2008a R17
felodipineΔG 5729 J/mol, ratio 9.22 (recomputed) against "around 9"37 °Calonzo2010 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 B. Supersaturation from ASD dissolution

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 valueswegiel2013b 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 B. Supersaturation from ASD dissolution

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 compoundswegiel2013b 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 B. Supersaturation from ASD dissolution

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 filmsvaneerdenbrugh2012a 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 films[hiew2022a 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 B. Supersaturation from ASD dissolution

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 °C[que2019 R6]
poloxamer 407; SDSLoC 7.5%; 30%same[que2019 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 films[yang2022b C61, C35]
SDS, CTAB, TPGS, Tween 80HLB 40, 22, 13.2, 15cited[correasoto2022a R1]
Span 20, Span 80, Span 85HLB 8.6, 15 (as printed), 11cited[correasoto2022b 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 B. Supersaturation from ASD dissolution

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 1.2ilevbare2013b R10
PVPVA on celecoxib; efavirenz7.6 → 7.4; 4.5 → 4.9sameilevbare2013b 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 B. Supersaturation from ASD dissolution

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 dispersions[rumondor2010c M1, M2, M4, M3]
indoprofen, nilutamide, loratadine, clofoctol, probucollog P 2.84, 2.14, 4.13, 8.19, 10.0drugs of PVP films[rumondor2011 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 storagewegiel2013b R20
pimozide with HPMCASthe only HPMCAS dispersion that separated; attributed to hydrophobicity94% RH, dried[rumondor2010c 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 films[rumondor2011 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 B. Supersaturation from ASD dissolution

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 AAPSargument[purohit2017b 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, HPMCAS[rumondor2010c 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% RH[rumondor2010c R18]
PVP, PVPVA, HPMCAS alone≈50, ≈24, ≈8 g per 100 g at ≈85% RHcited isotherms, 25 °C[rumondor2010c R19]
40% resveratrol–PVP dispersion against its physical mixture≈12.8 against ≈36.5% at 95% RH25 °Cwegiel2013b 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 °Ctrasi2017 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 B. Supersaturation from ASD dissolution

ideal mixing

Entropy-driven mixing of two amorphous components in the drug-rich phase with no heat of mixing, so that the chemical potential of each falls by RT\ln x and its amorphous solubility becomes the pure-drug value times its mole fraction in that phase trasi2015a C37, E2, E3, E4. Ritonavir and lopinavir are said to mix "nearly ideally" trasi2015a C40. The papers of 2017–2022 add the polymer case: in the ideal-mixing form S_a = S_a^{0}\,x_{drug} a polymer in the drug-rich phase lowers the amorphous solubility, but the authors note that a polymer's large molar volume and specific interactions make mixing non-ideal, and the volume-fraction Flory–Huggins form over-predicts the measured solubility of ibuprofen with PVP-VA and HPMC 603 ueda2021 E2, C28, C33. New aspect (Supersaturation from ASD dissolution): ideal mixing (cited) is applied to dissolving films and dispersions of two drugs: each drug reaches its amorphous solubility times its mole fraction in the amorphous mixture trasi2015b C38, E1. Li and Taylor draw the amorphous solubility scaled by drug weight fraction as "ideal behavior" for lopinavir mixed with an undissolved polymer; HPMCAS lay slightly above it, CAP near it at 15–50% and EC near it at 50–85% drug, HPMCP below it li2018 E7, C20.

Findings

Amorphous solubility and LLPS: F11, F19, F20, F21. Supersaturation from ASD dissolution: F11, F18.

Related concepts

lowers the chemical potential in the drug-rich phase; consequence for the amorphous solubility. Papers of 2017–2022: extended by the interaction term in the Flory-Huggins interaction parameter; requires drug-drug miscibility.

Formulas

ideal-mixing reduction of amorphous solubility.

How it is measured or obtained

The mole fraction in the drug-rich phase follows from mass balance of bulk concentrations after ultracentrifugation; a melting point depression of ritonavir by lopinavir greater than the Schröder–van Laar prediction is offered as confirmation (data not shown) trasi2015a P12, R17. For dissolving two-drug films and dispersions: film plateaus and ultracentrifuged dispersion concentrations against Eq. 1, with amorphous solubilities from the antisolvent study trasi2015b P6, P9, M1, M2.

Values in the library
materialvalue or classconditionspaper ids
ritonavir–lopinavirbulk ritonavir 3.0 → 21.4 µg/mL and lopinavir 15.2 → 4.6 µg/mL for x = 0.06–0.70; ritonavir 2–4 µg/mL above the line25 °Ctrasi2015a R16
ritonavir–lopinavir, 30 + 30 µg/mLpredicted about 10.8 and 10.1 µg/mL against 13.3 and 9.1 measuredextractor checktrasi2015a X9, R13
ibuprofen with PVP-VA, HPMC 603ideal Flory–Huggins: about 129 and 127 µg/mL at polymer ratio 1.0; measured about 89–106 µg/mL37 °Cueda2021 R12, R5
ibuprofen with PVP, PVP-VA, HPMCideal per-chain mole fraction of drug 0.97 or more at the highest ratios, against Sa/Sa0 of 0.52–0.54 (extractor calculation)15–60 °C[ueda2022 X3, R17]
RTV:LPV films 7:3 / 5:5 / 3:7RTV 15.2 / 11.4 / 6.3 against 16.7 / 11.6 / 6.8 µg/mLpH 6.8trasi2015b R5
HPMCAS dispersions, three ratiosRTV on the line; LPV on or up to about 15% below itultracentrifugedtrasi2015b R17, X8
lopinavir, ideal line at 50% drug17.4 × 0.50 = 8.7 µg/mLpH 3, 25 °Cli2018 E7
lopinavir with HPMCAS at 50% drug≈12.3 µg/mLpH 3, 25 °C, 48 hli2018 R3
Pitfalls and disagreements

Tested for one pair; no fit statistic; other pairs "are likely" to be non-ideal trasi2015a X9, C43. Later work draws the same ideal-mixing line for lopinavir–polymer dispersions li2018 E7. Used only qualitatively for polymers; the mole basis of the polymer is not stated [ueda2022 X3]. In the two-drug dissolution study the predictions use cited amorphous solubilities, and the pure films reached about 8% less trasi2015b X14; one nearly ideal pair was tested trasi2015b C39. The diagonal of the lopinavir–polymer study is proportional dilution by weight, not the χ = 0 case of the Flory–Huggins term, which with a large polymer would lie above it li2018 X2.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

impurity effectiveness factor

The factor α of the Kubota–Mullin model that says how strongly a given surface coverage by an adsorbed impurity slows crystal growth; α = 1 means growth stops at full coverage, α above 1 means growth stops before the surface is covered, and α near 0 means no reduction at any concentration [alonzo2012 C25; ilevbare2012b E13]. By the model, α falls as ln S rises and as the spacing L of adsorption sites grows: \alpha = \gamma a/(kT\,(\ln S)\,L) alonzo2012 E7, C8.

Findings

F9, F10.

Related concepts

parameter of Kubota-Mullin model; depends on surface coverage and step pinning.

Formulas

Kubota-Mullin impurity effectiveness factor, Kubota-Mullin model.

How it is measured or obtained

By fitting R/R_0 = 1 - \alpha\theta_{eq} to measured growth-rate ratios with the coverage from an isotherm fit, at each supersaturation separately alonzo2012 P9, R9; the surface energy, molecular area and spacing were not given alonzo2012 C27.

Values in the library
materialvalue or classconditionspaper ids
felodipine with HPMC0.7, 0.5, 0.4, 0.6, 0.2 at S 3, 5, 8, 10, 1225 °Calonzo2012 R9
ritonavir with CAP Adp 0.854.35 (pH 6.8); 1.25 (pH 3.8)σ 0.99, 37 °C[ilevbare2012b R16]
Pitfalls and disagreements

Table 1 of the felodipine study is not monotonic in S, α at S 8 differs between text and caption, and runs at S 3, 8 and 12 were single measurements alonzo2012 X1, X3. The ritonavir α at pH 6.8 is the smallest value consistent with complete inhibition at that coverage [ilevbare2012b X8]. α values depend on the isotherm model and are comparable only within a paper alonzo2012 X12.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 → 6.5nguyen2023b 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 B. Supersaturation from ASD dissolution

incomplete drug release

Release that stops below the dose although the drug has not crystallized; in the library it is the defining problem of drug-loaded mesoporous silica under supersaturating conditions [dening2018 C2, C1; dening2019 C1]. The papers attribute it to adsorption of dissolved drug back onto the silica, in a dynamic and partly irreversible equilibrium [dening2018 C4, C63; dening2019 C32; mccarthy2020 C52; hate2020a C5], with loading, wetting and pore filling as further causes [dening2018 C60; hate2020a C44, C45].

Findings

F7, F8, F9, F10, F11, F12, F13, F14, F15.

Related concepts

caused by drug adsorption onto silica in a dynamic adsorption-desorption equilibrium; contrasts with desupersaturation by crystallization; assessed by absorptive dissolution testing and membrane flux; depends on drug loading.

Formulas

supersaturation ratio, total release by mass balance.

How it is measured or obtained

Closed non-sink dissolution dosed at the amorphous solubility of the medium, with centrifuged or filtered samples over 1–4 h, against the nominal or assayed dose [dening2018 P6; mccarthy2020 P14; hate2020a P7; hate2020b P5]. Free drug by membrane flux against amorphous drug at the same concentration [dening2018 P12]. Recovery, XRPD and assay of the solid after release [dening2018 P9; mccarthy2020 P14]. Release with an absorptive compartment, by mass balance [hate2020a P9, E4].

Values in the library
materialvalue or classconditionspaper ids
ritonavir–SBA-15about 50% (dose at amorphous solubility), 70% (half)pH 6.8, 75 mL, 120 min[dening2018 R6]
ritonavir–SBA-15about 67 → 9% at 50 → 1000% of the amorphous solubilitypH 6.8[dening2018 R23]
ritonavir–SBA-1560–65% after dilution to S about 1; about 71% in FaSSIFpH 6.8; FaSSIF[dening2018 R18, R21]
lopinavir–SBA-1540–50%pH 6.8[dening2018 R19]
indomethacin; methyl ester, 50% monolayerS 7.2 of 15.3; 7.0 of 21.4; 58.8 and 61.8% retainedpH 2.2, HPMC[mccarthy2020 R20, R21, R23]
atazanavir–SBA-15, 20% w/wabout 46.5% closed; about 89.5% with an absorptive sink (240 min)pH 6.8, HPMC[hate2020a R20]
atazanavir–SBA-15, 5–50% w/wabout 73 / 80.5 / 66.5 / 52 / 36% in 90 minabsorptive, pH 6.8[hate2020a R15]
ketoconazole; clozapine; atazanavir, 20% w/wabout 55; 73.5; 40% at pH 6.8; 92; 93; 70% at pH 1 (60 min)HPMC[hate2020b R7, R8, R9]
ketoconazole; clozapine after pH 1 → 6.8about 64–69%; 68–69%HPMC[hate2020b R10, R11]
itraconazole–SBA-15 (outside the library)plateau about 55%simulated gastric fluid[dening2018 R28]

Evidence table: incomplete drug release.

Pitfalls and disagreements

Percent release depends on dose, medium volume and the drug content assumed: the ritonavir percentages rest on a nominal 28 µg/mL, and the dose masses imply about 22% instead of 25% w/w [dening2018 X5]; the indomethacin percentages do not reconcile across text, axes and dose [mccarthy2020 X5]. "Sink" in the dilution test means a total dose equal to the crystalline solubility [dening2018 X7]. "Complete release" with an absorptive sink was about 90% [hate2020a X10]. Release is not incomplete for every drug and medium: charged, soluble bases released 87–97% at pH 1–4.5 [hate2020b R7, R8]. The isotherm accounted for only about a twentieth of the atazanavir held back [hate2020a X14].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 dosemoseson2021 R25
BCL–PVPVA M/155 (3.5% crystals)PVPVA about 54.6 µg/mL at 2.5 min, levelling at about 64samemoseson2021 R25
undissolved solid after 5 minPVPVA:BCL 1:1 (crystal-free), 1:2 (with residual crystals)computedmoseson2021 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 min[saboo2019 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 6.8tablets[benson2025 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, 105same[saboo2019 R5, R6]
nilvadipine 10:90 compact after 12 h at 97% RH≈0.34% drug against ≈2.6% polymer in 15 minsame[saboo2019 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 °C[saboo2020 R3, M5]
clopidogrel–PVPVA 60%drug ≈0.2 against PVPVA ≈4.1 mg/min/cm²compacts[correasoto2022a R18]
atazanavir–PVPVA 10%drug ≈0.07 against PVPVA ≈0.24 mg/min/cm²pH 6.8, 37 °C[correasoto2022b 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 B. Supersaturation from ASD dissolution

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 6.0[bapat2025a 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 betterrelease[trasi2020 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 B. Supersaturation from ASD dissolution

integration-controlled crystal growth

Crystal growth limited by the incorporation of molecules into the lattice at the surface, not by their transport to it; in the empirical law R_G = k_G S^{g} an overall order g of 1 means diffusion control and 2 integration control, with measured orders usually between 1 and 2 alonzo2012 C3, E2. Felodipine grew with g about 1.5 (a mix of the two) and with any HPMC level at g about 2, read as a shift toward integration control ("This suggests") alonzo2012 R13, C32, C33.

Findings

F10.

Related concepts

contrasts with diffusion-controlled growth (named in alonzo2012 C3); related to crystal growth rate and step pinning.

Formulas

power-law crystal growth rate.

How it is measured or obtained

The slope of \ln R_G against \ln S from seeded growth rates over S 3–12, with \ln k_G from the intercept (or from a fixed order) alonzo2012 P8, E3.

Values in the library
materialvalue or classconditionspaper ids
felodipine alone; with 0.2–3.5 µg/mL HPMCg about 1.50 ± 0.04; 1.85–2.17, mean 1.97 ± 0.12S 3–12, 25 °Calonzo2012 R13
felodipine, \ln k_Gabout −4.24 without; −5.42 to −5.86 with HPMC (fits with g fixed at 1.5 and 2)samealonzo2012 R14
absorptive dissolution test with residual crystals (Bioperformance)growth order about 1.7, agrees with the n of about 2 for integration control with an adsorbed polymerseededhate2019 C44
Pitfalls and disagreements

The reading rests on the empirical meaning of g; step pinning and surface kinetics were not observed, the growth rates behind three of the six HPMC levels are not shown, and the k_G values come from fits with different fixed orders alonzo2012 C34, X10, X8.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 °Cschram2016 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 = 4schram2016 C36
felodipine–PVPVA–TPGSTPGS lowering the energy between separated phases slows coarseningASD hydration[saboo2021 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 timesduong2022b R16
posaconazole, FaSSIF V1, FaSSIF V2, FeSSIF V12.61, 2.73, 3.24 mJ/m²; FeSSIF V2 not fittableas aboveduong2022b R16, R15
naproxen, acetaminophen, tolazamide, lovastatin, cefodizime sodium, prasugrel hydrochloride, spironolactone (cited)0.60–2.80 mJ/m²literatureduong2022b 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–Mullinalonzo2012 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 88que2018 R15, C37
supersaturated drugs in surfactant mediasurfactants should lower γ and speed nucleation; human fluid slowed it insteadclassical nucleation theory, 37 °Celkhabaz2021 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 B. Supersaturation from ASD dissolution

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 structuresvaneerdenbrugh2010b 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); IR[hiew2022a 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 B. Supersaturation from ASD dissolution

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 rpm[bhardwaj2018 R4, R5]
PVPVA as received10.4 mg/min/cm² over 4.5 min (8.1 cited)same[bhardwaj2018 R9, R10]
PVPVA; amorphous nilvadipine3.49 ± 0.07; 0.002 mg/min/cm²pH 6.8, 100 rpm, 37 °C[saboo2019 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 cm²[bapat2025b C2, C12]
amorphous ritonavir against 20% ritonavir–PVPVA (ASD process, cited)amorphous drug significantly sloweras cited[benson2025 R24]
neat PVPVA (indomethacin; ester series)≈3.4; ≈3.8 mg/min/cm²5-min rates, 37 °C[saboo2020 R3]
neat PVPVA≈2.6–2.7 mg/min/cm²compacts[correasoto2022a R18]
neat PVPVA at 37 and 55 °C≈2.7; ≈3.7 mg/min/cm²compacts[correasoto2022b R7]
neat PVPVA at 37 and 5 °C≈3.45; ≈1.68 mg/min/cm²compacts[yang2021 X16, R21]
HP-50; nine HP-50 salts≈0.92; ≈2.35–3.09 mg/min/cm²compacts, 50 mM pH 6.8 phosphate, 37 °C[qi2022 R10]
HP-50-BIS-TRIS, 20–100 mol% base≈1.22 → 2.93 mg/min/cm²same[qi2022 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 B. Supersaturation from ASD dissolution

intrinsic solubility

The solubility of the neutral (un-ionized) form of an ionizable drug in equilibrium with its stable crystal; in the pH-titration work it is the neutral-species concentration at the point where the pH gradient crosses zero, so that there is no net dissolution or precipitation [hsieh2012 C6, C11]. The 2014 paper uses the heading "intrinsic solubility" for the crystalline solubility of the neutral form measured with or without polymer [hsieh2014 R4].

Findings

F1, F2, F19.

Related concepts

equals the crystalline solubility of the neutral form; related to ph-dependent solubility and pH-induced precipitation.

Formulas

Bjerrum function.

How it is measured or obtained

From the CheqSol titration at 37 °C and 0.15 M KCl, and by 72 h shake-flask runs at least two pH units above the pKa with HPLC after ultracentrifugation, to compare the two [hsieh2012 P4, P11]. For the polymer series, 72 h shake-flask runs at 25 °C in pH 10 or pH 2 buffer with or without 1 mg/mL polymer [hsieh2014 P5].

Values in the library
materialvalue or classconditionspaper ids
bifonazole; dipyridamole; droperidol; papaverine; pyrimethaminetitration 0.3; 5.7; 3.1; 17.2; 25.4 µg/mL against HPLC <1; 4.0 ± 0.5; 4.1 (30 °C); 20.6 ± 0.5; 25.0 ± 0.437 °C[hsieh2012 R5]
carvedilol; clotrimazole; clozapine; ketoconazole; loratadineHPLC 1.1; 0.4; 8.8; 3.7; 1.6 µg/mL37 °C[hsieh2012 R10]
papaverine, dipyridamole, warfarin12.2, 5.4, 3.7 µg/mL; glyburide 0.2 (titration)25 °C, no polymer[hsieh2014 R4]
papaverine with HPMC; HPMCAS-LF; HPMCAS-HF20.9; 21.9; 19.0 µg/mL1 mg/mL polymer[hsieh2014 R4.d–f]
posaconazoleC_o in the diprotic Henderson–Hasselbalch fit; crystalline 0.27 and amorphous 8.92–9.20 µg/mL where unionized (pH 5.5–7.0)37 °C, 0.14 Mduong2022b E4, R1
Pitfalls and disagreements

Droperidol degraded in the 72 h run at 37 °C, so a literature value at 30 °C is used [hsieh2012 X15]. Titration and HPLC values agree for type 1 bases ("good agreement") [hsieh2012 C11]. The glyburide value of 0.2 µg/mL lies below the HPLC limit of about 1 µg/mL and was assumed for all polymers [hsieh2014 X9, X10].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 4.2trasi2015a M5, R11
CRH1un-ionized and ionized equal at equilibrium at pH 4.6pKa 4.6almeidaesousa2016 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 6.8raina2014a C9
clotrimazoleabout 99% unionizedpH 8indulkar2016 C8
ezetimibebuffer solubility measured at pH 2 because of degradation at neutral pHelkhabaz2017 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 4.48[hate2022 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, 4chen2015 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 1.0–7.0duong2022b R2, R1
HP-50-BIS-TRIS, 20–100 mol% baserate ≈1.22 → 2.93 mg/min/cm²50 mM pH 6.8 phosphate, 37 °C[qi2022 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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

kinetic stabilization

Stabilization of an amorphous drug against crystallization by slowing the process (molecular mobility, nucleation, interfacial factors) while the thermodynamic driving force stays large. Marsac and co-workers conclude from a small predicted reduction of the driving force, a low predicted solubility in PVP and the faster nucleation of the pure drugs that inhibition "can therefore be attributed predominantly to a kinetic stabilization"; molecular-level miscibility is "of critical importance" because it alters "thermodynamics and, more importantly, dynamics" [marsac2006b C41, C42, C55, C56, C59]. The same group states that thermodynamically stable dispersions are hard to achieve and that apparent stability is "most likely achieved through modification of the kinetics" [marsac2009 C34]. For the growth of felodipine with PVP the effect "is believed to be kinetic rather than thermodynamic" [kestur2010b C28].

Findings

F9.

Related concepts

contrasts with thermodynamic driving force for crystallization; depends on drug solubility in polymer; related to crystallization inhibition and amorphous solid dispersion.

Formulas

Hoffman equation.

How it is measured or obtained

Not measured directly in this chapter. It is inferred by elimination: the thermodynamic estimates (Hoffman driving force, predicted solubility) are small or low, while the dispersions stay amorphous [marsac2006b R12, R17, X12; marsac2009 R11, X17]. Kinetic quantities (nucleation rates, mobility) are cited from a companion study or not measured [marsac2006b R16, C59].

Values in the library
materialvalue or classconditionspaper ids
nifedipine with 40% PVPdriving force −7.95 against −9.0 kJ/mol pure at 20 °CHoffman[marsac2006b R12]
nifedipine, felodipine in PVPpredicted solubility 0.06–0.07 and 0.25–0.31 g/gFlory–Huggins[marsac2006b R17]
five compounds in PVP K29/3282–99% of the drug above solubility at 0.50 polymerpredicted[marsac2009 R11]
pure nifedipine and felodipine against their dispersionsnucleation much faster for the pure drugscited[marsac2006b R16]

Evidence table: kinetic stabilization.

Pitfalls and disagreements

The kinetic reading is an inference: no crystallization, nucleation or mobility data are reported in either paper [marsac2006b X12; marsac2009 X17]. Being below the estimated solubility did not make PEG dispersions stable, which points to nucleation by the carrier as another route [zhu2012 X13]. A small dissolved fraction may explain why crystallization of a dispersion is not always complete [marsac2009 C35].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 separateargument[rumondor2009c 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 B. Supersaturation from ASD dissolution

light scattering by particles

Particles suspended in a solution remove light from a beam by scattering and, if they absorb, by absorption; the sum is the extinction. Small particles scatter more at short wavelength (Tyndall effect), larger ones give a flatter, wavelength-independent baseline [vaneerdenbrugh2011b C28, C16, C37]. Extinction measured where the drug does not absorb is used as a read-out for a new phase, which may be crystals or a liquid [raina2015a C9].

Findings

F1, F2, F3, F11.

Related concepts

part of extinction; contrasts with particle absorption of light; related to liquid-liquid phase separation and Mie theory.

Formulas

attenuation coefficient from particle cross-sections, extinction cross-section as sum, Mie theory, scattering baseline correction of UV absorbance.

How it is measured or obtained

Fiber-optic UV/Vis spectra (200–700 nm, 1 cm transflectance dip probes) of suspensions [vaneerdenbrugh2011b P9]; extinction at 450 nm by a dip probe during drug addition or dissolution [raina2015a P6; tres2018 P8]; Mie calculation of the extinction of spheres [vaneerdenbrugh2011b P11].

Values in the library
materialvalue or classconditionspaper ids
felodipine nanosuspensionabsorbance at 425 nm ≈0.10, 0.26, 0.45, 0.5510, 25, 40, 50 µg/mL total, 25 °C[vaneerdenbrugh2011b R3]
felodipine, jetmilledabsorbance at 425 nm ≈0.011 to ≈0.04610 to 50 µg/mL total[vaneerdenbrugh2011b R4]
nonabsorbing spheresextinction at 276 nm ≈0.01 (30 nm) to ≈0.93 (300 nm)Mie, 50 µg/mL, 1 cm[vaneerdenbrugh2011b R13]
ritonavir, 10% and 50% dispersionsextinction at 450 nm ≈0.51 (3 min) against ≈0.01–0.02non-sink dissolutiontres2018 R7
lopinavir, 10% and 50% dispersions≈0.70 (54 min) against ≈0.01sametres2018 R15
Pitfalls and disagreements

Scattering depends on particle size and number, so extinction is not a measure of the amount or composition of the new phase (synthesis: the ritonavir and lopinavir curves differ in time course) tres2018 R7, R15. For spheres of 600–1000 nm nonabsorbing particles lose the Tyndall shape and may upset the usual corrections [vaneerdenbrugh2011b C33, C34].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 407compacts[que2019 C10, R9, C12]
atazanavir–PVPVA5% DL; 10–15% with surfactants (10% with SDS or CTAB, 15% with Span 80)compacts[correasoto2022b C12]
clopidogrel–PVPVAabout 40% DL; 50% with SDScompacts[correasoto2022a C46, C55]
lumefantrine–PVPVA35% DLcompacts[hiew2022a C31]
loratadineHPMCAS 20% at 37 °C, 5% at 5 °C; PVPVA 30% and 2%compacts[yang2021 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, tablets[benson2025 C34]
ITZ–PVPVAswitch between 25 and 20% (spray-dried), 20 and 10% (melt-extruded)0.1 N HCl, compacts[bhardwaj2018 X6, R4]
ritonavir films with PVP; PVPVALLPS up to 20%; only at 10%25 °C, 100 mM pH 6.8[purohit2017b R10, R11]
nilvadipine; cilnidipine in PVPVA10% (6 mol%); 15% (7 mol%); switch at about 6–9 and 7–9 mol%pH 6.8, 37 °C[saboo2019 R5, R6, C14]
indomethacin; its methyl ester in PVPVA10%; at least 25% (5-min rates)37 °C[saboo2020 C14, P5]
indomethacin–PVPVA10% (25–57 °C), 5% (17 °C), below 5% (10 °C)temperature series[saboo2020 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 6.8[saboo2021 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 °C[correasoto2023 R1, C12]
ledipasvir–PVPVA with 10 g TEAC, TBC; GTB5 → 15; 20%same[correasoto2023 R11, C17]
ritonavir–PVPVA with 5 g GTB or TBCcomplete release at 30%, not at 35% (cited limit 25%)same[correasoto2023 R14, R16]
MePHPH–PVPVA 40%; 50%gel drug content 40 → 49%; 50 → 59.5% over 30 minscraped gel, dry basis[deac2023a 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 min[deac2024a 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 °C[deac2024b 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 B. Supersaturation from ASD dissolution

limit of detection

The smallest crystalline (or amorphous) content that can be told from zero by a method. The library has six working definitions: three standard deviations of the crystallinity read on a pure form [taylor1998a E7]; the residual standard deviation of the calibration regression, following ICH Q2(R1) correasoto2017 E5, P9; the single-voxel signal at signal-to-background 3 on a crystal-free sample divided by the signal of 100% crystalline powder [kestur2012 E9]; the smallest crystal size derived from a signal-to-background of 3 and its volume fraction [wanapun2010 E3, P10]; a signal-to-noise ratio of 3:1 on an XRPD peak moseson2021 P2; and visual detection of low-level standards in images correasoto2017 R5, X7. The values are not comparable without the definition and the basis (F4). New aspect (ASD process): the signal-to-noise or 3 SD criterion has the limit of quantification at 10:1 or 10 SD; for XRPD of indomethacin crystals in an amorphous dispersion the limit of detection was about 0.4% and of quantification about 1% [moseson2018 P7]. For crystallinity in an amorphous dispersion (formerly the page "limit of detection for crystallinity", from ASD process): the smallest crystalline fraction a method can distinguish from noise in an amorphous dispersion. For XRPD of IDM–PVPVA extrudates the stated limits are about 0.4% (detection) and 1% (quantification), and routine methods typically have limits on the order of 1% [moseson2018a P3, C36; moseson2018 P7]. A zero reading is a value below the limit of detection, not zero crystals: for bicalutamide in PVPVA by PXRD the limit is about 1% and of quantification about 3% [moseson2022c P16, X8]; for posaconazole in HPMCAS 0.3 and 1.2 wt% shah2024 R9, X4. 0.3% crystals of posaconazole, equal to the pXRD limit, ended supersaturation early after a pH shift shah2024 C56.

Findings

Solid-state methods: F1, F2, F4, F7, F10, F11. ASD process: F10, F28, F36, F41.

Related concepts

pairs with limit of quantitation; depends on signal-to-noise ratio; applied to degree of crystallinity and residual crystallinity (part of residual crystallinity when applied to crystals in an amorphous dispersion).

Formulas

limit of detection and quantification.

How it is measured or obtained

From spiked standards in the matrix of interest (a pure-form SD in the Raman work, regression residuals in the SHG and XRPD work), by calculation on a crystal-free sample, or by size estimation [taylor1998a R14; correasoto2017 R6, R8; kestur2012 P13; wanapun2010 R10]. For XRPD of indomethacin crystals the limit comes from the 3:1 and 10:1 signal-to-noise of a chosen peak (11.7° 2θ) against a fully amorphous reference, the noise being taken from a fully amorphous solvent-evaporated ASD measured in triplicate [moseson2018 P7]. The limit depends on the polymer background, which is small but not zero for SHG [kestur2012 C29].

Values in the library
materialvalue or classconditionspaper ids
indomethacin mixtures, RamanLOD 0.6% (3 × 0.2%); about 1% judged reasonablepure-form SD, 10 measurements[taylor1998a R14, C21]
naproxen–HPMCAS blends, PXRDno peaks below 5 wt%whole-pattern OPLS[kestur2012 R8]
naproxen–HPMCAS, SHG10^{-3} % (10 ppm), calculated; lowest imaged 0.1%single voxel at S/B 3[kestur2012 R7, R6, X10]
griseofulvin and chlorpropamide films, SHG90 and 125 nm; 3.4\times10^{-9} and 9\times10^{-9} % by volumesize back-calculated[wanapun2010 R10, R11]
flutamide and ezetimibe in HPMCAS, SHG0.03 and 0.047%; 0.005% visibleregression residualcorreasoto2017 R8, R5
flutamide and ezetimibe, XRPDabout 0.4 and 0.7%; none seen below 1%peak-window area ratiocorreasoto2017 R8, R7
posaconazole HME ASD (PCZ–HPMCAS), pXRDLOD 0.3 wt%, LOQ 1.2 wt%; pXRD no peaks where SHG found 0.3%, 2.4% against 3.2%, 23.1% against 19.3%18.0° peak, spiked standards; 125 °C extrudatesshah2024 P6, R9, R10, X4
BCL–PVPVA extrudates, XRPDLOD about 1%, LOQ about 3%S/N 3:1 and 10:1moseson2021 P2
tacrolimus capsule contents, XRPDabout 1% (LOQ about 5%); 10% crystallinity (0.38% w/w)spiked standardshate2019 R2; purohit2018 R2
IDM in PVPVA (XRPD), extrudatesLOD about 0.4%, LOQ about 1%3:1 and 10:1 S/N; 5–40° 2θ[moseson2018 P7; moseson2018a P3]
IDM crystals in copovidone at 130 °CXRD may lose the crystals earlier than PLM or TEM show them; loss is also consistent with a small fraction below the limitvariable-temperature XRD[moseson2019 R4, C11, C54, X7]
30% BCL in PVPVA (XRPD), 2022 paperlimit of detection about 1%, of quantification about 3%; calibration 0–65% (R² = 0.9952)17.2° peak, triplicate[moseson2022c P15, P16, X8]
flutamide standards (XRPD)no evidence of crystallinity by XRPD below 1%0.005–0.5% crystalline standardscorreasoto2017 R7
citedlaboratory XRPD 5–7%; synchrotron with processing about 0.2%; ensemble SHG 0.12%literature[correasoto2017 R25; kestur2012 R17]
Pitfalls and disagreements

The 10 ppm of the naproxen work is a calculation and the lowest imaged level was 0.1%; "0.005% readily detected" is visual while the computed limits are 0.03–0.047% [kestur2012 X10; correasoto2017 X7]. A limit from a pure-form SD omits mixing error [taylor1998a R13]. Below the XRPD limit does not mean amorphous: TEM and polarized-light microscopy found crystals in extrudates that XRPD called amorphous [moseson2021 R6; moseson2018a R5, R9]. The posaconazole paper states the pXRD result at 10 wt% loading as below the quantification limit, below the detection limit and "as low as 0.3%" shah2024 X4. Limits quoted for physical mixtures do not carry over to dispersions: SONICC's low limit was shown for blends, and a crystalline level of about 6 wt% in a dispersion lay near the 5 wt% below which PXRD blends showed no peaks [kestur2012 X9, R8]. Crystals below the limit still changed polymorph and supersaturation in the bicalutamide dispersion, so a limit of detection is not a specification moseson2021 R6, R17. Detection is limited by dilution of the drug, crystallite size and crystal quality, so XRPD "may be systematically underestimated" for nanometre, strained crystals [moseson2018a C26, C27; moseson2019 C11]. The x-ray criterion for a "X-ray amorphous" class is not stated [moseson2018 X5].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 °Ctrasi2015a 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, bufferraina2014a R1
nifedipineLLPS only with 1 mg/mL HPMC: 30.86–88.89 µg/mL20–45 °Craina2014a R1, R5
clotrimazoleonset 7.5 µg/mL; droplets 111–257 nmpH 8indulkar2016 R2, R4
atazanavir78 µg/mL; droplets 204–226 nmpH 6.8[hate2018 R2, R6]
ritonavironset about 38 µg/mL in waterUV extinctionilevbare2013a R2
enzalutamideonset about 42 µg/mLpH 6.5, 37 °Cwilson2018 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 °Cilevbare2013d 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 °Cilevbare2013d 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 B. Supersaturation from ASD dissolution

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 6.8moseson2021 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/mLmoseson2021 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 °Craina2014b C10, C11
celecoxib dispersions (outside)polymers dissolved in solution cannot inhibit crystal formation in the matrixhigh drug loadingxie2015 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 waterdissolutionwilson2018 C56
posaconazole ASDs in acid (outside)matrix crystallisation about 68% at 50% DL, about 0.05% at 25% DLSHG over TPE-UVF, 30 minelkhabaz2019a 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, FeSSIFelkhabaz2017 C34, R12, R16
posaconazole ASDs 10 / 25 / 50%SHG crystallinity 0.3–0.4 / 3–4 / 19–26%60 min FaSSGFshah2024 R21
posaconazole ASDs50% DL final crystallinity about 250 times that of 25% DLelkhabaz2019a R18
enzalutamide 10:90 HPMCAS-MF ASDpeak about 10 µg/mL, crystals in the mediumpH 6.5, 100 µg/mL totalwilson2018 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 slurryalonzo2010 R2
felodipine with 500 µg/mL PVP, HPMC, HPMC-AS in the medium50% crystalline at ≈20.5, ≈18.5, ≈13.5 min37 °Calonzo2010 R6
neat amorphous indomethacinα form present at 90 min, like pure α at 120 minpH 2, 37 °Calonzo2010 R12
nifedipine 50:50 dispersions (PVP shown)particles not birefringent; crystals form in the solutionpH 6.8raina2014b R13, X18
nifedipine–HPMCAS 50:50 at pH 2matrix amorphous for 3 hpolymer barely solubleraina2014b 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 °Cwegiel2015 R9
resveratrol, minimum polymer to prevent it80% HPMC, 85% HPMCAS, 95% CMCABpH 6.8, 37 °Cwegiel2015 R14
neat amorphous celecoxibcomplete within an hour; crystals on the particles from 2 minpH 6.8, 37 °Cxie2015 R4, R8
celecoxib–PVP-K12 50%crystalline within 4 h in a slurrypH 6.8, 37 °Cxie2015 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 °Cli2018 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 °Cnguyen2023c R19
same, powderspitted, porous HPMCAS surfaces with agglomerates increasing with pH; HPMCP-50 covered at pH 5.01 h in acidnguyen2023c 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 hnguyen2023b R3, R6
posaconazole–HPMCAS dispersionscrystals by SHG in every system after 30 min in FaSSGF, more numerous after transfer37 °Celkhabaz2019a 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 B. Supersaturation from ASD dissolution

maximum crystal growth velocity

The highest crystal growth rate of a compound over temperature (MCV), reached at Tcryst,max between Tg and Tm; below Tcryst,max growth is limited by mobility, above it by the shrinking driving force [trasi2014a C22]. The MCV is said to occur near 0.94 Tm [trasi2014a C37, E8].

Findings

F1, F2.

Related concepts

part of crystal growth rate; related to degree of supercooling and melt viscosity.

Formulas

temperature of maximum crystal growth rate.

How it is measured or obtained

From growth rates measured at several temperatures; for the 31-drug set the way the maximum was obtained is not stated [trasi2014a X3]; for vemurafenib it is the peak of the measured bell-shaped curve lu2016 R12.

Values in the library
materialvalue or classconditionspaper ids
nimesulide; flutamide; acetaminophen216; 104; 100 µm/sbulk melt[trasi2014a R1.a, R1.b, R1.c]
felodipine; indomethacin0.86; 0.47 µm/sbulk melt[trasi2014a R1.x, R1.z]
clotrimazole0.02 µm/sbulk melt[trasi2014a R1.ae]
vemurafenib α-needles≈106 µm/s at 250 °C; preliminary 106 ± 4 µm/ssupercooled liquidlu2016 R12.o, R25
indomethacin γ; α4.07 × 10⁻⁷; 4.34 × 10⁻⁶ m/spure melt[tian2017 R7]
Pitfalls and disagreements

Several MCVs of the 31-drug set lie far above the highest plotted rate (nimesulide 216 against ≈8.6 µm/s) or below plotted rates (felodipine, indomethacin) [trasi2014a X3]; the printed limit of the fast group is broken by its own members [trasi2014a X2].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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% DLsameshah2024 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 B. Supersaturation from ASD dissolution

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 °Ctrasi2015a R2
ritonavir, lopinavir, paclitaxel in 30 + 30 µg/mL mixturesflux of each drug lower than from the single-drug donor25 °Ctrasi2015a 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 °C[indulkar2017a 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 + HPMCraina2014a R11, R12
nifedipineabout 1.7–1.9 µg/min37 °C, 1 mg/mL HPMCraina2014a R14
clotrimazoleJmax 0.686–0.693 µg/(h·cm²)flow-through, pH 8indulkar2016 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 °Ctrasi2016 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/mLjackson2016 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 HPMCASwilson2018 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 membranewilson2018 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 °Celkhabaz2019b 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 PVDF[hate2022 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/mLjackson2016 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 °Ctrasi2016 R15
resveratrol–HPMCAS solutions; saturated crystal≈4.4 → ≈2.6 µg/min; 2.0 µg/minpH 6.8, 37 °Cwegiel2015 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 B. Supersaturation from ASD dissolution

membrane transport

Passive transfer of dissolved drug across a membrane; in these papers a measure of free drug or activity [alhalaweh2016 C2; hate2017 C36]. Includes diffusion cells, Caco-2 monolayers and a hollow-fibre module.

Findings

F2, F6, F13, F21.

Related concepts

quantified as membrane flux; depends on membrane mass transfer coefficient.

Formulas

membrane flux in terms of solute activity.

How it is measured or obtained

See membrane flux; percentage transferred, receiver Cmax and AUC in the hollow fibre [hate2017 R3, R6].

Values in the library
materialvalue or classconditionspaper ids
nevirapine41.5% in 60 min (hollow fibre) against 1.50% (flat sheet)100 µg/mL[hate2017 R3]
ritonavir, atazanavirCaco-2 flux about halved in a 1:1 solutionHBSS pH 6.5[alhalaweh2016 R17]
telaprevir, bile saltstrihydroxy salts on the buffer curve; dihydroxy at 12 mM about 2-fold lower[lu2017b R10, R12]
Pitfalls and disagreements

Only passive diffusion; active transport and P-gp are not covered raina2014a C42.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 equilibriumraina2015b 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 °Cjackson2014 R15
atazanavir (Bioperformance)metastable equilibrium until crystal nucleation, drug activity equal in both phasesASD-coupled dissolution and membrane transfer[hate2018 C5]
danazol–water, 25 °Cbinodal 4.27 × 10⁻⁷ and 0.92 mole fraction danazolfrom the onset and moisture sorptionjackson2016 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 B. Supersaturation from ASD dissolution

metastable zone

Evidence table: metastable zone. Content from the ASD dissolution chapter (2008, 2010) and the LLPS and Bioperformance chapters.

The range of supersaturation in which a solution is supersaturated with respect to the crystal but does not nucleate spontaneously, so that existing crystals can grow while new ones hardly form; above it lies the labile zone of spontaneous nucleation konno2008a C27. In the scheme of two crystallization routes, nucleation and growth deplete the solution once its concentration exceeds the metastable zone alonzo2010 C43.

Findings

F5.

Related concepts

related to nucleation, classical nucleation theory, supersaturation and binodal.

Formulas

classical nucleation theory.

How it is measured or obtained

Not measured in the ASD dissolution papers; inferred from the shape of concentration–time curves konno2008a C27, X4. On a temperature–concentration diagram of ritonavir the binodal and spinodal of liquid–liquid separation were mapped against the crystal solubility ilevbare2013a R11.

Values in the library
materialvalue or classconditionspaper ids
felodipine with HPMC or HPMCAS after an initial droptaken to sit in the metastable zone ("it appears")pH 6.8, 37 °Ckonno2008a C27, R12
ritonavir (LLPS chapter)crystal-supersaturated region below the binodal; binodal–spinodal gap smallwaterilevbare2013a C32, C34
felodipine, nifedipine (Bioperformance)the amorphous solubility lies within the metastable zone for crystal nucleationbufferraina2014a C30
Pitfalls and disagreements

The metastable-zone limit of felodipine was not measured, so the reading of the plateaus as growth-limited rests on argument konno2008a C27. Seeded and unseeded tests later located the effect of HPMC on felodipine mainly in nucleation alonzo2012 R17.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 °Craina2015c 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 °C[indulkar2017a 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 °Craina2015c R2
nifedipine10.3 to 53.4–90.7 µg/mL37 °Craina2015c 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 6.8[indulkar2017a 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 °Celkhabaz2019b R1, R2
atazanavircrystalline 1.4 to 7.1 µg/mL; amorphous 79 to about 99–102six media, 37 °Celkhabaz2019b 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 °Clu2017 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 1.6–6.5duong2022b R8, R14
atazanavir, posaconazole in aspirated human fluidconcentration ratio about 15 and 5.4 against cited activity ratios 54 and 30pH 7.3, 37 °Celkhabaz2021 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 °Cli2016b R5
lopinavir with HPMCAS-HF, PVPVA and SDS11.4 µg/mLpH 3, 25 °Cli2016b R5
lopinavir with HPMCAS-HF and SDS at pH 56.3 µg/mL25 °Cli2016b 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 °Cnguyen2023b 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 °Calvarenga2025 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 °C[saboo2021 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 °C[correasoto2022a R3]
clopidogrel with 5 µg/mL TPGS, CTAB or 50 µg/mL SDS20 ± 1 µg/mL37 °C[correasoto2022a R3]
neat HPMCAS-MF in FaSSIF; in blank FaSSIF buffer≈0.56; ≈0.57 mg/min/cm²pH 6.5, 12 mM/ΔpH[bapat2023 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 B. Supersaturation from ASD dissolution

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 capacity[qi2022 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 7.5[bapat2023 R15, R16]
HPMCAS-TEA gelapparent pH 6.7, rate ≈1.62 mg/min/cm²50 mM pH 6.8 phosphate[bapat2023 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 media[fagan2025 C36, C8]
HPMCAS LF, MF, HF slurries in waterpH 4.52, 4.61, 4.73overnight stirring[bapat2025a 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 B. Supersaturation from ASD dissolution

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 °Clu2017 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 fluidselkhabaz2019b 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 B. Supersaturation from ASD dissolution

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 hsame[benson2025 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 B. Supersaturation from ASD dissolution

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 °Crumondor2010 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 light[marsac2010 R19, C24]
FTM–HPMCAS spray-dried dispersion (outside)faster crystallization at 82% than at 75% RH40 °C, SHGcorreasoto2017 C15
Accord tacrolimus capsules (outside)rapid crystallization in the powder blend40 °C/75% RHpurohit2019 C33
resveratrol with HPMC, HPMCAS, CMCAB, PAAcrystalline at the first sampling at 84% RH, then fully; PVP and E100 not25 °Cwegiel2013b 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 films[rumondor2011 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 vacuumPXRD[bhujbal2021 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 dishtrasi2017 R14
felodipine dispersions with PVP, HPMC, HPMCAS (cited)no difference dry; HPMCAS ≈ HPMC > PVP at high RHstoragekonno2008a R18
flutamide and ezetimibe HPMCAS dispersions (Solid-state methods)first storage time with detected crystallinity, by methodstoragecorreasoto2017 R1
tacrolimus capsules (Bioperformance)% crystallized against storage timestoragepurohit2019 R1
resveratrol dispersions (storage, cited)PVP, E100 stable; HPMC, HPMCAS, CMCAB crystallized at high RHstoragewegiel2015 R21
indomethacin 60% with HPMC; EPO; EPO–HPMCcrystals within 5 days; within 5 days; amorphous beyond 100 days40 °C/75% RHxie2017 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 B. Supersaturation from ASD dissolution

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% RHTgli2018 R9, C40
nifedipine-, pimozide-, droperidol–PVPseparated within 1 h at 94% RH; pimozide from 54% RHdried films[rumondor2009c R7, R9, R10, R12]
indomethacin-, ketoprofen–PVPone phase for 40 and 68 days at 94% RHsame[rumondor2009c R14, R16]
felodipine–PVPsmall change at 33–58% RH, distinct at 75% RH, amorphous-felodipine-like after 94% RH1 day–1 week[marsac2010 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, DSC[rumondor2010c C38, C33]
20 drug–polymer systemsHPMCAS dispersions less susceptible in general; PVP highly vulnerableclasses[rumondor2011 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 °C[yang2022b 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 B. Supersaturation from ASD dissolution

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% RHrumondor2010 R7, C27
pimozide–PVPmoisture-induced separation much slower at 4 °C than at 22 °C75% RH[rumondor2009c R11, C41]
ketoprofen–PVPwet Tg −23 °C, mobile, yet no separation94% RH[rumondor2009c 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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

monotropy

A polymorph pair in which one form is the more stable at every temperature up to melting, so the other can only convert into it; the free-energy curves would cross only at a virtual transition temperature above both melting points [lu2016 C51; trasi2014b C11].

Findings

F7.

Related concepts

tested by Burger-Ramberger rules; part of polymorphism.

Formulas

Burger-Ramberger heat-of-fusion rule, Hoffman equation.

How it is measured or obtained

By the heat-of-fusion rule from melting data [lu2016 C50; trasi2014b C11]; by Hoffman free-energy curves of both forms lu2016 R22; supported by the direction of observed conversions lu2016 C38.

Values in the library
materialvalue or classconditionspaper ids
vemurafenib α and βmonotropic; virtual transition 319 °Cheat-of-fusion rule and Hoffman curveslu2016 C50, C51, R22
nilutamide stable form and form Imonotropic; form I about 3.4 kJ/mol less stable at 25 °Cmelting data[trasi2014b C11, R7]
Pitfalls and disagreements

The vemurafenib virtual transition temperature depends on which α heat of fusion is used lu2016 X1; the room-temperature conversion that supports α as the stable form is not shown lu2016 X13.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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-throughindulkar2016 R6, X5
clotrimazole + 7.5 mg/mL 150–250 µm particlesno reservoir (0.63 to 0.42 µg/mL)5 hindulkar2016 R7
atazanavir 90:10 ASDsreceiver above AS level 120 min; 4 h: about 200 minhollow fibre[hate2018 R13, R21]
posaconazole ASDs (FaSSGF)longer supersaturation at higher dose, "most likely" reservoirtwo doseselkhabaz2019a 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 °C[ueda2020a 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 PVDF[hate2022 R19, C61]
enzalutamide in ratsaggregate-forming ASD about 30% more AUC than two ASDs that only reached the ceiling (no statistical test)10 mL/kgwilson2018 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 °Cxie2017 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 °Celkhabaz2019a 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 min[que2019 R12]
TIPP, Me-TIPP; PHPH, Me-PHPHcolloids 179–193; 348–364 nmDLS, 30 min[que2021 R22]
clopidogrel dropletsstable with 4–50 µg/mL SDS, TPGS or Tween 80 for 4 hDLS[correasoto2022a 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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 hmoseson2020a 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 °Cmoseson2021 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 filtratetrasi2019 P8, R4
tacrolimus capsules (outside)100 mL gives 50 µg/mL at complete dissolution, equal to the amorphous solubilitypH 4.5, 37 °C, 300 rpmtrasi2017 R3, C12
tacrolimus generic capsules (outside)the more non-sink tests (100 and 40 mL) discriminate crystallinity better than larger volumesUSP and non-pharmacopeial mediapurohit2018 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/mLshah2024 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 Pluselkhabaz2017 P7
ritonavir, atazanavir PVP ASDs150 mg in 15 mL, 120 minpH 6.8[alhalaweh2016 P10]
atazanavir ASDs200 µg/mL in 50 mLclosed vessel[hate2018 P8]
tacrolimus capsules5 mg in 900 / 450 / 100 / 40 mLmedium Ipurohit2018 P7, P8
tacrolimus (Accord)maximum 45 µg/mL within 40 min, about 25 µg/mL at 2 hone capsule in 100 mLtrasi2017 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 testhate2019 R7
tacrolimus capsule contents5 mg in 100 mL, pH 4.5, 50 µg/mL HPC, 300 rpmUSP-type test 1 mediumpurohit2019 P5, E3, C35
enzalutamide ASDs100 µg/mL total in 12.5 mL, pH 6.5, 300 rpmclosed vesselwilson2018 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 rpmkonno2008a 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 °Calonzo2010 P2, R1
neat amorphous indomethacin300 µg/mL; peak ≈14.9 (25 °C) and ≈11.2 µg/mL (37 °C)pH 2alonzo2010 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 °Ctrasi2015b P5
celecoxib dispersions with PVP, HPMCAS, HPMC, PAA, 10–60% drug22 µg/mL nominal (= amorphous solubility) in 400 mLpH 6.8, 37 °C, 16 hxie2015 P5; xie2016a P5
six marketed tacrolimus capsules5 mg in 40 mL (125 µg/mL nominal); plateau ≈46–50 µg/mLpH 4.5, 37 °Ctrasi2016 P11, R10
indomethacin dispersions and crystals4 mg in 50 mL (80 µg/mL), then 100 mL (40 µg/mL)pH 2.2 → 5xie2017 P7
lopinavir films, 15–85% drug2 mg solids in 10 mL, 48 hpH 3, 25 °Cli2018 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 hque2018 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 °Celkhabaz2019a 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 B. Supersaturation from ASD dissolution

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 ASDs[purohit2017b 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. 16alonzo2010 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 °Cxie2017 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 solubilityargument[que2019 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 B. Supersaturation from ASD dissolution

nucleation and crystal growth

The two steps of crystallization, the formation of new crystals and the growth of existing ones; they have different temperature windows and can respond differently to the same additive, and overall crystallization of a powder is nucleation followed by growth [trasi2012a C35, C53; kestur2013b C35, C47]. The term is also used for a route of amorphous–amorphous phase separation, in which discrete domains of the new phase nucleate and grow, as opposed to spinodal decomposition [saboo2017 C40; yang2022b C50, C55].

Findings

F17, F21, F26, F31, F32, F33.

Related concepts

part of solid-state crystallization of amorphous drugs; consists of nucleation and crystal growth rate; located by nucleation temperature zone.

Formulas

classical nucleation theory, linear crystal growth rate from size-time slope.

How it is measured or obtained

Separated by growing seeded or pre-formed crystals on a hot stage and by locating nucleation zones and counting nuclei in cooling–reheating cycles [trasi2012a P2, P6, P7; trasi2012b P2, P6, P7]; or inferred by comparing overall powder crystallization with linear growth rates kestur2013b C47.

Values in the library
materialvalue or classconditionspaper ids
acetaminophennucleation zone 50–60 °C, where growth is ≈0.04–0.23 µm/s against ≈45 µm/s at 100 °CDSC and hot stage[trasi2012a R12.a, R8.a, C39]
acetaminophen with PAA or HPMCASPAA slows growth most but gives most nuclei; HPMCAS the reverse10% w/w[trasi2012a C46]
flutamide with PVP or nilutamidePVP slows growth about tenfold without a nucleation effect; nilutamide nearly stops nucleation10 mol%[trasi2012b C7, R11.e, R12]
felodipine powders with 3% PVPearly crystallization 60–77-fold slower; surface and bulk growth ≈2- and ≈7-fold30 °Ckestur2013b R15, R12, C34
miconazole–PVPVA films after humid casting or storagediscrete drug-rich domains in a polymer-rich matrix, read as separation by nucleation and growth ("may occur")confocal, AFM[saboo2017 C40]
ritonavir–PVPVA films with SDS or Tween 80 vs binary and Spansnucleation and growth vs spinodal decomposition, read from the first morphologyconfocal[yang2022b C55]
tacrolimus genericfall in concentration after 40–50 min read as growth on seeds present before storage ("some evidence")dissolution, 100 mLtrasi2017 C44
Pitfalls and disagreements

Nucleation was counted per thermal cycle or inferred from DSC peak temperatures and rate ratios, never measured as a rate at storage temperature [trasi2012a X8; trasi2012b X4; kestur2013b X7].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 °Cilevbare2013c R8, R9.a
ritonavir, CAB Adp 0.81; efavirenz, CAB Adp 0.81; celecoxib, HPMCabout 244; 28.0; 12.6 min5 µg/mL polymerilevbare2013c R9
celecoxib at 11 µg/mL, none against HPMC27.5 ± 0.7 against 855.5 ± 6.0 minS 7.3ilevbare2013c R15
felodipine, none against 1 µg/mL HPMC15.3 against 136.5 minS 10, 25 °Calonzo2012 R16
danazol, none; PVP; HPMC; HPMC-AS6–10; 88–162; 111–285; 250–516 min10–20 µg/mL, 25 °Cjackson2014 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 °Cque2018 R3
indomethacin S 6 (ASD process chapter)about 40 min; more than 12 h with 5–50 µg/mL PVPVApH 4.5, 37 °Cmoseson2020a 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 °Cchen2015 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 °Clu2017 R3, R4
danazol 15 µg/mL, PVP, HPMC, HPMC-AS 1–1000 µg/mLabout 5 min; 26–412 min25 °Cjackson2016 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 °Celkhabaz2021 R7; duong2022b R10; shah2025 R3
enzalutamide without polymerabout 5–15 min, 30–120 µg/mLpH 6.5wilson2021 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 B. Supersaturation from ASD dissolution

nucleation inhibition

The slowing of crystal nucleation from a supersaturated solution by an additive, measured as a longer nucleation induction time or a lower nucleation rate. Ilevbare and co-workers propose that a polymer inhibits nucleation by joining clusters of solute molecules and hindering their reorganization into an ordered nucleus, which needs a polymer with more affinity for the solute than for water or for itself ("we assume", "would be expected") ilevbare2013c C4, C5, C35. How additives slow nucleation is more speculative than how they slow growth, because the molecular events cannot be observed ilevbare2013c C9. New aspect (Supersaturation from ASD dissolution): for celecoxib released from dispersions, the authors take the polymer effect on nucleation as "of paramount importance" to the desupersaturation profile, because growth needs nuclei xie2015 C40. Extended induction times with polymers indicate a decreased nucleation rate, PVP-K12 being the least effective and HPMCAS or HPMC showing no discernible nucleation or growth for 8 h xie2015 C42, R1; the greater effect of the cellulose derivatives "may relate" to a greater ability to interact with a dense liquid cluster of celecoxib than the more hydrophilic PVP, which also interacts with the solvent xie2015 C46. With 5 µg/mL HPMCAS the relative effect on nucleation (~4000) was far larger than on growth (70) ("it can be surmised") xie2016a C40, R13.

Findings

Crystallization from solution: F6, F13, F14, F15, F20, F27, F28, F31, F32, F33, F36, F40. Supersaturation from ASD dissolution: F4, F5, F20, F29.

Related concepts

contrasts with crystal growth inhibition; part of crystallization inhibition by polymers; measured by nucleation induction time and nucleation rate; related to polymer hydrophobicity; related to interfacial tension.

Formulas

relative nucleation rate from seeded and unseeded induction times, induction time decomposition, classical nucleation theory.

How it is measured or obtained

Unseeded induction times with and without polymer under identical conditions (see nucleation induction time), optionally combined with seeded growth rates into the nucleation-rate ratio J/J_0 alonzo2012 P10, E10. In the celecoxib dispersion papers: solvent shift to 22 µg/mL celecoxib in pH 6.8 phosphate buffer at 37 °C with 5 µg/mL dissolved polymer, the onset read from a rise in 350 nm extinction with a fall in 249 nm absorbance xie2015 P4, R1.

Values in the library
materialvalue or classconditionspaper ids
felodipine, 1 µg/mL HPMCJ/J_0 7.05 × 10⁻⁴ ("more than a thousand fold"); induction 15.3 → 136.5 minS 10, 25 °Calonzo2012 R16, R17, C38
ritonavir; efavirenz; celecoxib, best polymer120 → 244; 5.1 → 28.0; 2.4 → 12.6 min5 µg/mLilevbare2013c R9, R12
celecoxib at S 7.3, HPMC27.5 → 855.5 min (31-fold)5 µg/mLilevbare2013c R15
celecoxib, 5 µg/mL HPMCAS (ASD dissolution chapter)J_0/J_p about 4,00022 µg/mL drugxie2016a R13
paclitaxel, HPMCAS (ASD dissolution chapter)"highly effective" at S 8820 µg/mL polymerque2018 R3, C13
indomethacin, PVPVA 5–50 µg/mL (ASD process chapter)"highly effective" at S 6; stays supersaturated more than 12 hpH 4.5moseson2020a R3, C11
11 drugs, 0.1% STCinduction time lengthened for all, eight by more than 10-fold25 °Cchen2015 R3, X6
telaprevir, 1.86 mM STC, SGCrelative nucleation rate J/J₀ 2.5 × 10⁻³ and 2.9 × 10⁻⁶ (recomputed 2.58 × 10⁻³ and 3.06 × 10⁻⁶)δ 11.5lu2017 R10, X1
acetaminophen, S 1.5J lowered 18-fold (HPMCAS) and 36-fold (HPMC); raised 2.6-fold by PAA10 µg/mL[trasi2015 R3]
telaprevir, 1.86 mM binary and ternary bile salt mixtures>960 min against about 30 in buffer; 3.72–5.58 mM mixtures about 255 minδ 11.5, 37 °C[lu2018 R3, R4]
nine drugs, 5 µg/mL A5aatazanavir 40 → >300, telaprevir 15 → 91 minpH 6.8, 37 °C[mosqueragiraldo2018a R1]
celecoxib 22 µg/mL: no polymer; 5 µg/mL PVP-K12; PVP-K29/32; HPMCAS or HPMCwithin 5 min; ≈1 h; ≈2 h; more than 8 hpH 6.8, 37 °Cxie2015 R1
delamanid at 0.76 µg/mL with 300 µg/mL polymermore than 1000 min with PVPVA, HPMCP and HPMCAS; about 50 min with HPMC; 10.2 min with Eudragit L100 against 10.7 min without polymerPBS pH 6.5, 37 °Cduong2022a R4, R2
racemic praziquantel at 1.1 mg/mL with 300 µg/mL polymer10.9 (PVPVA), 14.3 (HPC), 15.7 (PVA), 24.5 (HPMC 603) and 50.5 min (HPMCAS-LF); HPMCAS-MF and HPMC E5 LV beyond the 83-min runPBS pH 6.5, 37 °Cpolyzois2024 R3
R-praziquantel at 1.4 mg/mL37 min (HPMCAS-MF) and 15.5 min (HPMC E5 LV)PBS pH 6.5, 37 °Cpolyzois2024 R4
Pitfalls and disagreements

The mechanism (cluster association, polymer–solute affinity, self-association, chain rigidity) was not measured; the induction time includes growth to a detectable size ilevbare2013c C5, C39, C43, X14. The nucleation-rate ratio of felodipine rests on one pair of induction times entering to the fourth power alonzo2012 X7. Rankings of polymers differ from rankings of growth inhibition (F6) ilevbare2013c C40. In the celecoxib dispersion papers the induction time includes growth to a detectable size xie2015 E1; the HPMCAS ratio of ~4000 takes the 960-min end of the run as the induction time, so it underestimates the effect xie2016a R13, C40; celecoxib clusters and their interaction with polymers were not measured xie2015 C46. A ranking made with a racemate did not hold for its enantiomer polyzois2024 R4, C8, and the praziquantel run length capped the two best polymers at 83 min so they cannot be ranked against each other polyzois2024 R3.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 °Calonzo2012 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 11.5lu2017 R10
atazanavir, posaconazole, six mediaSHG count rate about 0.1–1.6 and 0.05–48 counts/min37 °C, relative per fieldelkhabaz2021 R14, E5, X13
posaconazole, PBS and three mediaJ from induction times, fitted for A and γ37 °C, S above about 7–13duong2022b 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 B. Supersaturation from ASD dissolution

nucleation temperature zone

The temperature range in which nuclei form at a useful rate; it usually lies below the temperature of fastest growth, and storing outside it helps prevent crystallization [trasi2014b C3]. Each polymorph may have its own zone [trasi2014b C38; lu2016 C42].

Findings

Crystallization tendency: F3, F4. Physical stability: F17.

Related concepts

part of nucleation and of nucleation and crystal growth; includes sub-Tg nucleation; contrasts with the growth window of crystal growth rate; related to glass-forming ability.

Formulas

critical cooling rate to avoid nucleation.

How it is measured or obtained

By cooling the melt to successively lower end points and reheating; the highest end point that gives crystallization on reheating bounds the zone [trasi2014b P1; trasi2012a R12]; by nuclei counts after holds at different temperatures [trasi2014b P7]. The zone limits depend on the cooling and heating rates and serve only to compare samples [trasi2012a C13].

Values in the library
materialvalue or classconditionspaper ids
nilutamidestrong zone near −30 °C; weaker rise from about 50 °C, about 30 °C above TgDSC; surface counts[trasi2014b R5, R9, C41]
acetaminophen50–60 °CDSC[trasi2012a C22]
flutamide10–40 °CDSC[trasi2012b R10]
acetaminophen with 10% w/w HPMC, HPMCAS, E100, PVPh, PVPVA, PVP, PAA10–60, 10–45, 40–60, 40–70, 30–60, 30–50, −10–30 °CDSC cool–reheat[trasi2012a R12]
acetaminophen with 15% w/w PVP, PAA, HPMCASno crystallization in the testsame[trasi2012a R12]
flutamide with 10 mol% PDMA, PVAc, PVPH, PIPA, PVP10–30, 20–40, 30–40, 20–30, 20–40 °Csame[trasi2012b R10]
vemurafenib αapproximately 170–270 °C (inferred)hot stagelu2016 C43
indomethacin γ; α (cited)maxima at about Tg and about 20 °C higherliterature[trasi2014b R32]
Pitfalls and disagreements

The method passes the zone on both cooling and reheating, so the two contributions are not separated [trasi2012a X9]; the polymorph of the counted nuclei was not identified for nilutamide [trasi2014b X6]. Storage inside the zone gives high nucleation; a polymer that lowers the zone (HPMCAS for acetaminophen) "could potentially" still give more nuclei at room temperature than another polymer [trasi2012a C47].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 stagelu2016 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 coatingvaneerdenbrugh2010b R2.an, R2.s, R2.as
celecoxib; efavirenz; ritonavirinduction time about 2.4; 5.1; 120 minat the calculated amorphous solubilityilevbare2013c R8
felodipine, HPMC 1 µg/mLJ/J_0 7.05 × 10⁻⁴S 10alonzo2012 R17
danazol6–10 min without polymer; 88–516 min with 10 µg/mL polymer25 °Cjackson2014 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 °Ckestur2013b R22, C35
ritonavir 17 against 20 µg/mL (below and above LLPS)induction about 284 against 119.3 minpH 6.8, 37 °Cilevbare2013d 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 °Craina2014b 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 B. Supersaturation from ASD dissolution

particle breakage

Mechanical break-up of drug particles under the stresses of mixing, for example in the dispersive or kneading elements of an extruder; the authors expect it to add defects and dissolution surface, and suggest that defect stress fields may be the sites where breakage starts [moseson2019 C45, C56]. Clusters of randomly oriented 5–10 nm domains in an extrudate were first read as a "mechanical origin" [moseson2018a R9, C14]. In the bicalutamide population balance model breakage is a size-dependent selection function (critical size 5 µm, two equal-volume daughters, Gaussian spread 12.5%) scaled by each lot's percentage of agglomerates, and the fit needs it: dissolution alone left 26–73% crystallinity at 20 min [moseson2022c E7, E11, E17, R12, R16]. Mechanical stress at the screw elements is held to break the same weak sites as fragmentation by dissolution [moseson2022c C45, C51].

Findings

F12, F36, F37.

Related concepts

contrasts with fragmentation-based dissolution (a dissolution-driven source of fragments).

Formulas

population balance equation, breakage selection function.

How it is measured or obtained

Not measured directly in the ASD process papers; inferred from TEM clusters of similar fragments and from the absence of mechanical input in still films [moseson2018a R11; moseson2019 R16].

Values in the library
materialvalue or classconditionspaper ids
IDM extrudateclusters of 5.8 ± 1.2 nm domains (n = 20)TEM[moseson2018a R11]
IDM crystals in still filmsfragmentation without mechanical input130 °C[moseson2019 R5, R16, C43]
BCL in PVPVA at Tc, population balance modelbreakage rate constant 0.355 ± 0.111 with breakage scaled by % agglomerates; dissolution only leaves 26–73% crystallinity at 20 minfour lots, 20 min[moseson2022c R16, R12]
Pitfalls and disagreements

The 2018 TEM paper noted that "other explanations are also possible" given the high mechanical input of HME [moseson2019 C5]. Breakage in the extruder was not observed, and the supporting images are quiescent PLM at 170 °C [moseson2022c X9, X18].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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, Ramanraina2014b 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 hli2016b R2
the same from 33% lopinavir dispersionsbelow 5 µg/mLpH 3li2016b R3
HPMCAS-HF from lopinavir dispersions with SDS at pH 5≈74.5–134 µg/mL25 °Cli2016b R13
cellulosic polymers in lopinavir release testsmostly below detection, estimated 3–25 µg/mLpH 3, 25 °Cli2018 R5
HPMCP-50; HPMCP-55893 ± 95 and 189 ± 18 µg/mL at pH 5.0; insoluble below pH 4.548 h, 37 °Cnguyen2023c R4
HPMCAS-LF; -MF; -HF1687 ± 47 and 1401 ± 69 µg/mL at pH 5.5; HF only from about pH 6.048 h, 37 °Cnguyen2023c 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 °Cnguyen2023b 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 °C[bapat2025a R1]
HPMCAS LF, MF slurries in waterpH 4.52, 4.61 (HF 4.73)overnight stirring[bapat2025a 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 B. Supersaturation from ASD dissolution

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 °Calmeidaesousa2016 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 °Cduong2022b R1, R2, E4
indomethacin (cited)1.5 µg/mL at pH 1.2 to 105 µg/mL at pH 7.4; pKa 4.42literaturexie2017 M1
indomethacin γ; α1.61; 2.8 µg/mL at pH 2.2; α 15 µg/mL at pH 537 °C, no polymerxie2017 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 °Cnguyen2023c 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 °Calvarenga2025 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 buffertrasi2019 R8
ritonavir solution without excipientsabout 97 → 16 µg/mL after neutralisation; precipitate not birefringentultracentrifuged supernatanttrasi2019 R9, R10
posaconazole (outside)solubility much higher in the gastric than in the intestinal medium because the drug is nearly completely ionised in acidbiorelevant mediaelkhabaz2019a C11, C40
delamanid (outside)pH-solubility profile of a weak base by the Henderson–Hasselbalch equationbuffers and medianguyen2023b 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 °Cshah2024 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 testshah2024 R12, R15, R18
coated and uncoated 20% DL RTV–PVPVA tablets in 0.1 N HClabout 87–91% at 60 mintablets[benson2025 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 °Celkhabaz2019a R1
posaconazole, amorphousabout 20 µg/mL in FaSSIF with 20 µg/mL HPMCAS; 8 µg/mL in plain buffer pH 6.537 °Celkhabaz2019a 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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 °C[purohit2017b R4, R9]
ritonavir PVP, PVPVA filmsAAPS from about 1 h at 97% RHpyrene I/III[purohit2017b 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% RH[correasoto2022b 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 B. Supersaturation from ASD dissolution

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% RH[saboo2021 R21]
felodipine–PVPVA 30% with 0; 10% TPGScontiguous, elongated drug-rich regions; round, separated drug-rich domains in a continuous drug-lean phaseAFM-nanoIR[saboo2021 R23]
clopidogrel–PVPVA 40, 50, 60%uniform; bicontinuous; continuous drug-rich phase with discrete polymer-rich domains5 min at 100% RH[correasoto2022a R20]
clopidogrel–PVPVA with 5 g SDS per 100 g at 50%homogeneous within the ≈500 nm detection limitsame[correasoto2022a R21]
clopidogrel–PVPVA with TPGS; with Tween 80, at 50 and 60%bicontinuous, then large irregular structures; fine-scale heterogeneous patternsame[correasoto2022a 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-lapse[yang2022b R4, R22, C9]
ritonavir–PVPVA 10–20%; 30%; 40%discrete droplets 0.5–2 µm; porous continuous layer; continuous layerconfocal of dissolving compacts[yang2022a R6, R10, R12, R13]
MePHPH–PVPVA 5–30%; 40%; 50%discrete particles below 1 µm; networks; inverted morphologyin situ confocal of the dissolving edge[deac2023a R6, C26]
PHPH–PVPVA 10–20%networksame[deac2023a 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 B. Supersaturation from ASD dissolution

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, drykestur2013b 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 dish[hiew2022a R6]
lumefantrine at 50% drug loading with HPMCAS, Eudragit L 100, HPMCP, CAPfirst drug crystals after 1, 8, 32 and 40 weekssame[hiew2022a 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 °Cwegiel2013b 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 vialsxie2017 R26
indomethacin 30%, EPO–HPMC against HPMCternary more stable (text only)40 °C/75% RHxie2017 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 inhibitorli2018 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 ≈2.3–3.9sameli2018 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 B. Supersaturation from ASD dissolution

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 printedalmeidaesousa2016 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)computedvaneerdenbrugh2010b M3, M4, M5
chlorzoxazone9.39 (weakly acidic)computedvaneerdenbrugh2010b M6
bifonazole; lidocaine6.69; 7.75 (basic)computedvaneerdenbrugh2010b M7, M8
indoprofen against other carboxylic acids (other chapter)a somewhat weaker acid, with the smallest phase separationPVP dispersions with moisture[rumondor2011 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 = 2[hiew2022a R22]
lumefantrine (tertiary amine)8.73cited[hiew2022a M1]
indomethacin, ketoprofen, indoprofen in PVPpKa 4.5, 5.02, 5.8; resist, resist, separate slightly20-system table[rumondor2011 R15.a, R15.d, R15.e]
20 drug–polymer systemsOPLS-DA loading of pKa ≈ −0.35: lower pKa goes with no separationdiscriminant model[rumondor2011 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 6.8[qi2022 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-neutralization[bapat2025a 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 B. Supersaturation from ASD dissolution

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% RHrumondor2010 R10
pimozide–PVP 50:50wet Tgs −21 and 44 °C94% RH[rumondor2009c R17]
ketoprofen–PVP 70:30wet Tg −23 °C94% RH[rumondor2009c 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% RHDSCtrasi2017 R15
lumefantrine dispersions precipitated into water4–6% water (HPMCP, HPMCAS), 9% (CAP); Tg 45–112 °CTGA; DSC[bhujbal2021 R10]
felodipine (cited)Tg about 45 °C dry, just below 35 °C after 75% RHstorage dataalonzo2010 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/minilevbare2013d R2, M1
indomethacin (cited)Tg falls rapidly with water content, as for felodipineliteraturealonzo2010 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 conditions[que2019 R28]
indomethacin; indomethacin–PVPVA 70%wet Tg 29 °C (estimated); onset 62.64 → 18.48 °C with ≈6% water37 °C, 100% RH[saboo2020 M1, R30]
loratadine, miconazole, danazol, elbasvirwet Tg 13.8 (DSC), −4.7, 73.3, 129.1 °C (rule)37 °C[yang2021 M1, M2, M3, M4]
atazanavirdry 105 °C, wet 55 °Ccited[correasoto2022b 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 B. Supersaturation from ASD dissolution

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% RH[rumondor2009c 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 ASDDSC[correasoto2023 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, confocal[yang2022b 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 °CDSCalvarenga2025 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, dry[saboo2021 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, dry[correasoto2022b R20]
clopidogrel–PVPVA 40–60%PVPVA ≈4.1–6.7 against ≈2.6–2.7 mg/min/cm² for neat PVPVAcompacts, 37 °C[correasoto2022a R18, C48]
loratadine–HPMCAS 5%HPMCAS released faster than from neat HPMCAS, "feasible" plasticization by a low-Tg drugcompacts[yang2021 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 DSC[correasoto2023 R17, R18]
ledipasvir–PVPVA 10% with 5 and 10 g TEACTg 99.1 → 85.8 °C; release 20 → 94% by 90 minDSC; compacts, pH 6.8[correasoto2023 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 B. Supersaturation from ASD dissolution

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 °Cjackson2014 R22
danazol droplets with HPMC; HPMC-ASabout 305–345 nm up to 2 h; about 230–250 nm up to 4 h10 µg/mL polymerjackson2014 R22
zeta potential: alone; PVP; HPMC; HPMC-AS−8.1; −5.3; −2.3; −13.7 mV25 °Cjackson2014 R23
polymer in the dropletsaround 10–20% for HPMC, below about 10% for PVP, none for HPMC-ASpreliminary NMRjackson2014 R26
ritonavir nanodroplets (ASD dissolution chapter)charge repulsion between polymers adsorbed at the ritonavir–water interface "likely" stabilizes against coalescence37 °Cilevbare2013d C38
telaprevir droplets, 1.86 mM six bile saltszeta about −40 (SGC) to −53 mV (STCDC)180 µg/mL, pH 6.5lu2017 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 B. Supersaturation from ASD dissolution

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 halonzo2012 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)AFMmoseson2020a R12
HPMCAS on paclitaxel dendritesadsorption-site spacing about 10–16.8 nmSEM finger widthque2018 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 °Cschram2016 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 °Calonzo2012 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/mLilevbare2013b R12
HPMCAS on paclitaxel seedspolymer slows but does not block growth at S 88seeded ASD dissolutionque2018 C30, C38
HPMCAS, earlier felodipine work"may adsorb at the crystal surface and block growth sites"dilute supersaturated solutionrumondor2010 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 mediaelkhabaz2021 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 B. Supersaturation from ASD dissolution

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 °C[hiew2022a 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 °C[benson2025 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 B. Supersaturation from ASD dissolution

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 timeilevbare2013c 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 B. Supersaturation from ASD dissolution

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 3.8ilevbare2013b C59, R13
PVPVA on indomethacinadsorbed chains described as a flatter train at lower concentration, a thicker layer at higherAFMmoseson2020a 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 nswilson2021 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 B. Supersaturation from ASD dissolution

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 AAPSoutside[purohit2017b C3, C54]
ritonavir ASDsLLPS was seen only for ASDs whose release was polymer-controlled and that stayed miscible during the initial phaseoutside[purohit2017b C6]
ledipasvir–PVPVA at 2 and 5% DLrelease polymer-controlled and congruentoutside[que2019 C9]
indomethacin–PVPVA at 10% DL or lessdrug and polymer release rates resemble the neat polymer rateoutside[saboo2020 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 rpm[li2020 R10]
marketed lopinavir/ritonavir tablet (Aluvia)milky dispersion at pH 6.8, read as nanodroplets; drug loading inferred at 25% or lowernot measuredtrasi2019 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 °Ctrasi2015b 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 °Cxie2015 R6
indomethacin–HPMC 10 / 30 / 50% drug≈39.5 / ≈24.5 / ≈18.5 µg/mL at 60 min (80 nominal)pH 2.2, 37 °Cxie2017 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 °Cnguyen2023c 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 °C[bhardwaj2018 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 °C[saboo2019 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/cm²compacts[que2021 R21]
clopidogrel–PVPVA 40–60%PVPVA ≈4.1–6.7 against neat ≈2.6–2.7 mg/min/cm²compacts[correasoto2022a 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/ΔpH[bapat2023 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 8.0[deac2024a 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 B. Supersaturation from ASD dissolution

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 hydrophilicityelkhabaz2017 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/mLilevbare2013c R13
16 polymers on three drugswindow 20.56–23.28 for drugs of SP 20.03–23.38seeded growthilevbare2013b 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 polymerraina2015b 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 B. Supersaturation from ASD dissolution

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 6.6ilevbare2013b R13
CAP Adp 0.85 on efavirenzinduction time 24.9 → 12.6 min19 µg/mLilevbare2013c 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 °Cli2016b C24
EPO in indomethacin dispersionshighly soluble at pH 2.2 owing to ionization37 °Cxie2017 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 B. Supersaturation from ASD dissolution

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 °Cueda2021 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 polymerueda2021 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 polymer[ueda2022 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 fit[ueda2022 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 °Cwilson2021 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 drugprecipitatesraina2015b C20, R12
ibuprofen, polymerspolymer ratio falls with total drug37 °Cueda2021 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 °C[ueda2020a R8, C20]
felodipine 100 mg, PVPVA 45 mgprecipitate 6.8 mg, supernatant 36.7 mg10% DMSO, pH 6.8raina2015b R12
felodipine, HPMCAS7.1 mg and 34.2 mgsameraina2015b R12
felodipine, PAA; P2VP (18 mg)0.9 and 46.6 mg; 17.7 mg and not detectedsameraina2015b 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 6.5wilson2021 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 B. Supersaturation from ASD dissolution

polymer rejection at the crystal growth front

The idea that a growing drug crystal cannot take a miscible polymer into its lattice and pushes it ahead, so that polymer accumulates at the crystal–amorphous interface and slows drug supply [konno2006 C39]; a related picture holds that growth requires activated drug–polymer demixing at the front [kestur2010a C42].

Findings

F4.

Related concepts

proposed route of crystallization inhibition by polymers; related to kinetic barrier to nucleation and crystal growth rate.

Formulas

the diffusion model of the 2010 melt paper (mass conservation of expelled polymer, Frank similarity solution) is listed on the chapter page as table only; Stokes-Einstein equation gives its diffusivity.

How it is measured or obtained

Inferred from crystal morphology (dark droplets and irregular spherulites with 3% polymer) and tested with a diffusion model of expelled polymer around a growing crystal [konno2006 R2, C42; kestur2010b P10, E9].

Values in the library
materialvalue or classconditionspaper ids
felodipine with 3% polymerdark droplets "thought" to be polymer-rich phase on crystallitesdry films, 22 °C[konno2006 R2, C11, C42]
felodipine with 3% PVP K-29/32model: front PVP 0.5 weight fraction in ≈52 s if all expelled; growth measured constant, so chains judged encaged100 °C[kestur2010b R21, C42]
felodipine with four polymers (outside)stronger drug–polymer bonds make demixing at the front harder; weaker at high temperaturemelt growth[kestur2010a C42, C43]

Evidence table: polymer rejection at the crystal growth front.

Pitfalls and disagreements

The two felodipine papers disagree on where the polymer goes: rejected and accumulating at the nucleus (2006, speculation) or encaged in the crystal (2010, model) [konno2006 C39; kestur2010b C42]. The model's diffusivity and front speed are printed inconsistently, and no paper measured the interface composition [kestur2010b X4, X5; konno2006 X14].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 polymerilevbare2013c 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/mLilevbare2013b 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 B. Supersaturation from ASD dissolution

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 °Cli2016b R8, R13
lopinavir with HF, PVPVA and SDScrystalline solubility 11.4 against 3.3 µg/mL with HF and SDSpH 3li2016b 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 B. Supersaturation from ASD dissolution

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 °C[saboo2021 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 °Cschram2016 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 B. Supersaturation from ASD dissolution

polymorphism

The ability of a molecule to crystallize in more than one crystal structure [towler2007 C2]; the metastable form often crystallizes first, and recrystallization from the undercooled melt "frequently" gives a metastable polymorph [baird2010 C16]. This draft is written from the crystallization-tendency chapter; the evidence table lists further papers that later chapters will add.

Findings

F4, F7, F8.

Related concepts

includes monotropy; tested by Burger-Ramberger rules; related to cold crystallization, conformational flexibility and prenucleation clusters.

Formulas

Burger-Ramberger heat-of-fusion rule, Hoffman equation.

How it is measured or obtained

By Raman (including in liquid N2), XRPD, FTIR, DSC melting and solid-state NMR [baird2010 P5; trasi2014b R15, R20, R25; lu2016 R18, R19]; the polymorph produced is mapped against temperature or supersaturation [lu2016 R10; towler2007 R1].

Values in the library
materialvalue or classconditionspaper ids
indomethacin α and γα above a supersaturation of 4, γ below about 3.5ethanol (cited)[towler2007 R1]
anthranilic acidform II from most solvents below 50 °C; form III from the melt or above 50 °Ccited[towler2007 R2]
vemurafenibat least four forms: α, β, γ, δsupercooled liquidlu2016 C41
nilutamidestable form, forms I and II, a suspected hydratemelt and humidity[trasi2014b R15, C25]
indomethacin δ, α, γdifferent maximum growth rates and nucleation temperaturespure melt[tian2017 R7, R1]
8 of 23 class I moleculesa different polymorph after liquid-N2 quenchRaman[baird2010 R3]
Pitfalls and disagreements

The polymorph obtained from solution is sometimes stated without an identification method [towler2007 X5]. Forms γ and δ of vemurafenib rest on Raman and morphology only lu2016 X6. Solution motifs do not reliably foretell the polymorph [towler2007 C33].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

prenucleation clusters

Aggregates of solute molecules in solution before a stable nucleus forms; clustering is taken as a prime requirement for crystallization, and if their structure could be tied to the final solid the polymorph "might" be controlled [towler2007 C1, C2]. Competing views hold them solvent-rich and disordered, polymorph-like, or a dense liquid that need not resemble the crystal [towler2007 C4].

Findings

F8.

Related concepts

precedes nucleation; related to polymorphism and classical nucleation theory.

Formulas

none.

How it is measured or obtained

Inferred from concentration-dependent IR and Raman bands of the solution [towler2007 P4, P5, R13]; not measured directly.

Values in the library
materialvalue or classconditionspaper ids
indomethacincarboxylic acid dimer bands grow with concentration, even below saturationethanol, nitromethane[towler2007 R13, R15, R17]
indomethacin in ethanol1660 to 1680 cm⁻¹ shift read as solute-rich clusters excluding solventIR[towler2007 C21]
anthranilic acid in tolueneNH2 bands like form III, read as clusters unlike the crystallizing form IIIR[towler2007 C17, R9]
Pitfalls and disagreements

Cluster size and composition were not measured; a constant band position fits single solvated molecules as well as clusters [towler2007 X9]; a bulk spectrum cannot exclude a minority population [towler2007 X10].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

quenched-in nuclei

Nuclei formed while a melt is cooled faster than the rate that avoids detectable crystallization but slower than the rate that avoids nucleation; they cannot grow before vitrification and remain in the glass [baird2010 C50; baird2013 C27].

Findings

F3, F16.

Related concepts

part of nucleation; defined through critical cooling rate; lowers glass stability; detected through critical heating rate.

Formulas

critical cooling rate to avoid nucleation.

How it is measured or obtained

Not observed directly in the library; inferred from crystallization on reheating and from the effect of the prior cooling rate on the critical heating rate [baird2013 C28, C30, X7], or proposed from the class behaviour [baird2010 C55; trasi2012a C40].

Values in the library
materialvalue or classconditionspaper ids
dibucaineRcrit,heat above 1000 °C/min after 20 °C/min cooling, 300 after 800 °C/minrapid heat–cool DSC[baird2013 R9.j, R11]
clofoctolmelting endotherm after 20 °C/min cooling, none after 860 °C/min, at 200 °C/min reheatingrapid heat–cool DSC[baird2013 R12]
class II and quench-glassy class I"most likely" explanation of recrystallization on reheatingDSC classes[baird2010 C55]
acetaminophensuggested; nuclei from cooling not separated from those formed on reheatingDSC and hot stage[trasi2012a C40, X9]
Pitfalls and disagreements

The nuclei were never seen or counted; the clofoctol test assumes equal nucleation during constant cooling [baird2013 X7, C29]. Their role in storage below Tg is proposed, not tested [baird2010 C57; baird2013 X15].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 °C[marsac2010 R17]
felodipine–PVP 46.5 wt% powderthermal event moves up with each DSC cycle; single Tg ≈80 °C on second scansDSC to 60–110 °C[marsac2010 R15, R14]
felodipine–PVP film at room temperatureno remixing after 1 week of drying0% RH[marsac2010 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 B. Supersaturation from ASD dissolution

residual crystallinity

Small amounts of crystalline drug that remain in, or appear soon in, a nominally amorphous sample after preparation. In the solid-state methods papers: submicrometre crystals in a melt-quenched film that looked amorphous by polarized-light microscopy [wanapun2010 R4, C8]; crystals in a freshly rotary-evaporated naproxen–HPMCAS dispersion that PXRD and Raman called amorphous [kestur2012 R1, R2, R3, C7]; and the posaconazole extrudate crystals below the pXRD limit (F10) shah2024 R9, R10. New aspect (ASD process): drug crystals that remain in a nominally amorphous dispersion after processing lose the amorphous solubility advantage, may accelerate crystallization on storage and can consume supersaturation in solution, so a fully amorphous product is desired [moseson2018 C4]. How much, how large and of what kind is acceptable "remains open" [moseson2018a C33]. In the dissolution papers of 2020 and 2021 it is also the share of the drug that cannot dissolve and can seed growth: indomethacin–PVPVA extrudates with 0–25% crystals lost up to about a third of the reachable concentration, and for bicalutamide–PVPVA the authors judge residual crystallinity, "even trace levels", "of high risk" moseson2020a R6; moseson2021 C79. For posaconazole–HPMCAS extruded for 2 min at 125 °C the crystals measured by SHG were 0.3, 3.2 and 19.3 wt% at 10, 25 and 50% loading, and none at 175 °C shah2024 R10. For bicalutamide lots extruded at Tc it is the share left after a given residence time, and it depends on the input crystals' size distribution, agglomeration and defects as well as on the median size [moseson2022c R10, C44, C46]. New aspect (Bioperformance): the question is what crystals in a nominally amorphous product do to dissolved drug and exposure, rather than whether they can be detected. Generic tacrolimus capsules were crystallized in storage to known levels (10 to 100%) and tested for release, supersaturation, absorption and exposure; the amorphous fraction dissolves to a supersaturated solution in which the crystalline fraction cannot dissolve, and the crystals may also grow on that supersaturation hate2019 C36, C37; purohit2019 C32, C54. New aspect (Crystallization from solution): seed crystals that survive or form in an amorphous drug product act as growth sites when the product dissolves into a supersaturated solution; Alonzo and co-workers conclude it "would be extremely important" to minimise residual crystallinity in an amorphous felodipine formulation, because residual seeds "could have a large impact" on the supersaturation maintained even with HPMC alonzo2012 C45. Ilevbare and co-workers add that seeds left from manufacturing "can thus potentially" shorten supersaturation unless a growth inhibitor is present [ilevbare2012b C4]. Seeds that crystallized out of a felodipine–HPMCAS melt grew far more slowly (ratio 12 with HPMCAS in solution) than buffer-grown seeds (2.7), and monomeric STCDC kept telaprevir seeds from growing for 15 h [schram2016 R2; lu2017a R10, R12]. New aspect (Supersaturation from ASD dissolution): crystals present in or added to a dispersion before it dissolves act through the growth area they offer and their origin, not through their mass; at an equal 18 wt% the paclitaxel seed types left between ≈7.9 and ≈25.3 µg/mL of a 31.6 µg/mL amorphous solubility after 16 h, and percent crystallinity "per se is not a predictive indicator" que2018 R14, C5, C54. Crystals can also form during preparation of a fast crystallizer: delamanid dispersions made by rotary evaporation showed drug peaks, and release was incomplete "once any level of residual crystallinity could be detected" duong2022a R8, C56.

Findings

Solid-state methods: F5, F7, F10. ASD process: F9, F10, F12, F26, F27, F28, F29, F36, F37, F41. Bioperformance: F16, F17, F28, F29, F30, F31. Crystallization from solution: F9, F20, F24, F33. Supersaturation from ASD dissolution: F22, F23.

Related concepts

detected by second harmonic generation; limited by limit of detection; part of solid-state crystallization of amorphous drugs; related to degree of crystallinity. Detected within the limit of detection for crystallinity; arises in the HME operating design space; related to crystal dissolution into a polymer melt; the crystals act as crystal seeding and cost the amorphous solubility advantage; in some systems they start matrix crystallization; set by the input-crystal attributes described under particle breakage and crystal defects; its effect in solution is read as desupersaturation. The form formed in the product is endogenous crystallization; tested with an absorptive sink; judged by virtual bioequivalence; related to heterogeneous nucleation, secondary nucleation and crystal growth inhibition; acts through seeded crystal growth; depends on crystal habit and crystallization tendency; countered by in situ salt formation.

Formulas

Sink index, power-law crystal growth rate, supersaturation ratio, Cabrera-Vermilyea step pinning.

How it is measured or obtained

SHG imaging for SHG-active forms; polarized-light microscopy, TEM with electron diffraction, XRPD and DSC for extrudates, with a clear order of sensitivity (F7) [moseson2021 R6; moseson2018 C27, C31]. In the extrusion papers: XRPD (Bragg-Brentano, Cu Kα; limits of detection and quantification about 0.4% and 1% against a calibration of crystalline IDM in a solvent-evaporated ASD), polarised light microscopy of powder in mineral oil, DSC (dissolution endotherm above about 1.5 J/g), bright-field TEM with Fourier analysis and SEM [moseson2018 P7, P8, P9, R12; moseson2018a P3, P7, P9]. The method sets where "amorphous" begins [moseson2018 C63]. For bicalutamide–PVPVA only TEM found the crystals of an extrudate below the XRPD limit of detection (about 1%, quantification about 3%), and DSC saw only the 30% extrudate through a broad dissolution endotherm over 120–170 °C moseson2021 P2, R6, R7. SHG was compared with pXRD for posaconazole–HPMCAS (pXRD limit of detection 0.3 and of quantification 1.2 wt%; SHG calibrated on spiked dispersions, see Solid-state methods F10) shah2024 R9, R10. PXRD of bicalutamide in PVPVA used the 17.2° peak against a 0–65% calibration (R² = 0.9952), limit of detection about 1% and of quantification about 3% [moseson2022c P15, P16]. SEM was the primary detector of surface crystals in stored coated powders, where XRPD missed several arms moseson2022a C22, X14. In the tacrolimus capsules PXRD with a standard curve (R² 0.9808, limit of detection about 1%, limit of quantification about 5%) was used in one study and a limit of detection of 10% in another; tacrolimus is only about 3.7 wt% of the capsule contents, which makes quantification hard hate2019 R2; purohit2018 R2; purohit2019 C12. The level is brought about by storage at 40 °C/75% RH or by blending hate2019 R2; purohit2019 R1, A1. In the crystallization-from-solution papers it is not measured; the seeded experiments model it with a fixed mass of seeds (about 2.5 mg in 18 mL for felodipine; 0.010 g in 50 mL for ritonavir) alonzo2012 P4; ilevbare2013b P10. In the ASD dissolution papers: seeds grown in buffer at a chosen supersaturation for 5.5 h, half of each batch probe-sonicated, sized by SEM over 100 crystals and converted to an end area per gram on a cuboid assumption; as-received drug slurried for the same time as a bulk-API seed que2018 P6, P10, C18. PXRD of dispersions after preparation, with DSC and water sorption duong2022a P9, P10, P12. A spray-dried free-base dispersion was checked against a rotary-evaporated one by PXRD and release nguyen2023c R5, R6.

Values in the library
materialvalue or classconditionspaper ids
griseofulvin film (b)several submicrometre SHG crystals at 0 min; dense field by 12 min120 °C[wanapun2010 R4]
naproxen–HPMCAS 75/25, freshSONICC about 24% of the drug, about 6 wt% of the powder; PXRD halorotary-evaporated, cryomilled[kestur2012 R16, X9]
IDM–PVPVA extrudatediscrete crystals below 100 nm and 5–10 nm domains; XRPD halo; Tg 73.8 ± 2.6 °C, trace birefringence; TEM crystals <100 nm and 5.8 ± 1.2 nm domainsHME at 131 °C, 20 min (1:1, at Tc)[moseson2018a R5, R9, C10, P1, R6, R7, R11]
BCL–PVPVA extrudatesbelow 1%: TEM only; 3.5%: PLM and TEM; 30%: DSC, SEM tooXRPD LOD about 1%moseson2021 R6
posaconazole HME ASD, 125 °C0.3, 3.2, 19.3 wt% of the ASD by SHG at 10, 25, 50 wt% DL; pXRD no peaks / 2.4 / 23.1%; none at 175 °CHME below the dissolution temperature, 2 minshah2024 R10, R9
50% IDM–PVPVA extrudates≈26.1, 16.0, 7.2% (117, 121, 126 °C, 2 min); ≈1.5–1.8% at 10–20 min below Tc; ≈0 at 131 °C 10 minXRPD[moseson2018 R10]
IDM crystals in copovidonelast XRD peak gone by about 135 min; crystals by PLM at 120 min and TEM at 3 h130 °C, still[moseson2019 R4, R5.h, R15]
paclitaxel–HPMCAS with seedsseed mass is not the relevant parameter; growth area and interface structure aredissolutionque2018 C5, C54, C58
tacrolimusPXRD limit of detection about 1%, of quantification about 5%—hate2019 R2
delamanid free-base ASDsresidual crystallinity above 10–15% DL went with incomplete release; drug PXRD peaks from 15% (HPMCAS) and 20% drug (HPMCP)rotary evaporation, after preparationduong2022a R8, C56
50% IDM–PVPVA extrudates, dissolution (0, 1.8, 3, 7, 16, 25% crystallinity)C720 about 43.1, 43.6, 39.4, 34.5, 32.6, 28.8 µg/mL; slight fall after the peak above 3%50 µg/mL total dose, pH 4.5, 12 hmoseson2020a R6
30:70 BCL–PVPVA extrudatesS/180 none by any method; S/155 below the XRPD limit, crystals by TEM only (140 ± 10 nm); M/155 3.5%; L/155 30%5 methodsmoseson2021 R6, R11
same, 4 h concentration at 150 µg/mLabout 35, 24.5, 16.3 and 10.5 µg/mL for none, below 1%, 3.5% and 30% (12.3 with 10% added seeds)pH 6.8, 37 °Cmoseson2021 R17
fresh generic tacrolimus capsulesno detectable crystallinity but seeds below 5% of the drugnon-sink, 100 mLpurohit2018 C44, C46
30% BCL–PVPVA at Tc = 145 °C, lots of D50 3.51 / 37.0 / 38.0 µmbelow the limit of detection at 2 / 5 / 6 minPXRD, triplicate[moseson2022c R10, R1]
same, lots of D50 42.2 µm (D90/D50 4.14) and 92.7 µmabout 2.5% and 15.0% at 20 minPXRD[moseson2022c R10, R1]
PCZ–HPMCAS MF 10 / 25 / 50% DL, after 60 min at pH 1.6SHG 0.3 → 0.4, 3 → 4, 19 → 26%37 °Cshah2024 R21
PCZ–HPMCAS 10% DL, 0.3% crystals against noneabout 14.5 against 125 µg/mL at 300 min after the pH shifttwo-stage testshah2024 R12, R14
tacrolimus generic capsule, 0 / 20 / 50 / 100% crystallinedonor maximum about 40 / 38 / 15 / 5 µg/mL and receiver AUC0–120 about 682 / 583 / 272 / 117 µg/mL·minhollow-fibre absorptive test, 100 mLhate2019 R9, R12
same capsuleAUC0–24 in dogs 42.1 (fresh), 22.9 (50%), 21.6 (100%) ng·h/mL1 mg, n = 6purohit2019 R9
same capsulerelease in 900 mL falls from about 93% (10%) to about 58% (100%); in 100 mL the peak falls from about 76.5% to about 10%compendial and low-volume testspurohit2018 R5, R7
same capsulevirtual bioequivalence lost at 20% with 100 mL input and at 40% with 900 mL inputGastroPlus, 24 subjectspurohit2018 R17
felodipine, seeded against unseeded with 1 µg/mL HPMC5.1 → 2.17 µg/mL in 58 min against 5.4 → 5.03 over 198 minS 10, 25 °Calonzo2012 R18
ritonavir, best single polymergrowth only 1.56-fold slower at S 15.337 °C[ilevbare2012b R5]
paclitaxel–HPMCAS dispersions with 18 wt% seeds (ASD dissolution chapter)desupersaturation by growth to about 8–25 µg/mL depending on the seed type (≈25.3 bulk API, ≈19.2 S 16, ≈10.4 S 80, ≈9.0 and ≈7.9 µg/mL sonicated, against ≈31.6 µg/mL unseeded); HPMCAS does not completely block itpH 6.8, 37 °C, 16 h, HPLCque2018 R14, C30
indomethacin, PVPVA (ASD process chapter)growth ratio 18 and 56 at the highest seed levelS 6, pH 4.5moseson2020a R5
felodipine seeds from the HPMCAS meltgrowth ratio 8.4 (no polymer in solution) and 12.0 (with)S 4, pH 6.8schram2016 R2
paclitaxel seeds: long needles grown at S 16 and S 80end area ≈0.00024 and ≈0.00023 m²/g, mean aspect ratio ≈23.6 and ≈20.1SEM, 100 crystalsque2018 R6, R9
the same, sonicated 10 min≈0.0021 and ≈0.0017 m²/g, aspect ratio ≈7.3 and ≈4.7SEMque2018 R6, R9
the same, release at 10 / 20 / 25% drug≈92 / ≈6 / ≈2 µg/mL (HPMCAS) and ≈98–100 / ≈53 / ≈20 µg/mL (HPMCP) of 100PBS pH 6.5, 37 °Cduong2022a R14
delamanid free base 25% with HPMCP-50, spray-dried against rotary-evaporatedamorphous and more than 80% released against 20%pH 6.5nguyen2023c R5, R6
Pitfalls and disagreements

The mass of crystal is not the only parameter that matters: seeds of different growth area and interface structure changed paclitaxel ASD dissolution at equal weight, so wt% crystallinity limits "often dictated by the detection limit" are arbitrary que2018 C5, C54. Trace crystals detectable only by TEM changed crystallization kinetics, supersaturation and polymorphic form of a BCL–PVPVA extrudate moseson2021 C38, C79, and residual crystals below the pXRD limit reduced the extent or duration of supersaturation of posaconazole ASDs shah2024 C56. In tacrolimus capsules 50% and 100% crystalline contents gave lower exposure than the amorphous product purohit2019 C54; hate2019 C36. A fragmented residual crystal may hinder XRD detection by peak broadening [moseson2019 C54]. In the extrusion papers, "clear" and "X-ray amorphous" extrudates carried crystals; the text and Fig. 8 disagree on the PLM status of two runs; no crystalline fraction was measured for the TEM crystals [moseson2018 R10, X4; moseson2018a X4]. The crystallinities of the IDM extrudates are cited from the 2018 paper and may be underestimated for nanometre defective crystals; "0%" and "<1%" of the bicalutamide extrudates are classifications, not measured values, and the basis of "% crystallinity" is not stated moseson2020a X8, C44; moseson2021 X6, X7. Zeros in the bicalutamide extrusions are below a PXRD limit of detection of about 1%, so crystals of nanometre size were not sought [moseson2022c X8]. In the posaconazole extrudates pXRD saw no peaks at 0.3%, which is its detection limit, while SHG did shah2024 R9, R10, X4. SEM scored crystals in uncoated extruded lumefantrine powders at 1 week where XRPD saw none through 48 weeks moseson2022a R11, R13, X14. In the tacrolimus capsules the level at which exposure is lost depends on the test: 20% crystallinity failed the check at 40 mL in the absorptive test and at 100 mL in simulation, while the dog exposure of the fully crystalline capsule fell by only about half (F31) hate2019 R13; purohit2018 R17; purohit2019 R9. The levels are nominal and the 100% sample dissolved above the crystalline solubility, so it may not be fully crystalline hate2019 X13; purohit2019 X11, C38. Crystals formed inside the product were about four times more bioavailable than purchased reference crystals (F30) purohit2019 C56, C57; (synthesis: a limit set with spiked reference crystals would overstate the loss). What seeds do depends on the volume: at 240 and 100 mL absorption kept growth small, at 40 mL growth was large (F29) hate2019 C46, C49. In the seeded felodipine study the amount of residual crystallinity that would defeat HPMC was not studied, and the µg/mL polymer levels are far below those released from a dispersion alonzo2012 C45; no seeded run without HPMC beyond 5 min is shown alonzo2012 X9. The seeds from the felodipine–HPMCAS dispersion were made by a route that differed in pH, time and solid composition schram2016 X4. The paclitaxel seeds were suspended in the medium, not formed inside the dispersion, at a load (18 wt%) far above any crystallinity limit, and equant crystals were not tested que2018 P9, C56. UV read the seeded runs ≈2–10 µg/mL above HPLC at 16 h and ranked the two least harmful seeds the other way round que2018 X4. For delamanid, crystallinity was not quantified and crystal growth during release was not measured duong2022a X10, C56.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

second harmonic generation

Conversion of laser light into light of twice the frequency (800 → 400 nm; 1064 nm light gives 532 nm shah2024 P7) by material that lacks inversion symmetry. Crystals of many drugs emit it; liquids, glasses and amorphous polymers do not, so the image of a mixed sample shows only the crystals (SONICC, second-order nonlinear optical imaging of chiral crystals) [wanapun2010 C4; kestur2012 C4; correasoto2017 C7]. SHG reports the presence of certain crystal structures, not molecular information [correasoto2017 C7; kestur2012 C37].

Findings

F5, F6, F7, F8, F9, F10, F11.

Related concepts

requires a non-centrosymmetric crystal structure; scales as in coherent and incoherent SHG scaling; limited by SHG coherence length and preferred orientation; detects residual crystallinity.

Formulas

SHG relative crystallinity.

How it is measured or obtained

Beam-scanning microscopes with a femtosecond laser, forward (transmission) and backward (epi) detection by photon counting; powders between cover glasses; images thresholded at signal-to-background 3 or averaged for relative crystallinity (F8).

Values in the library
materialvalue or classconditionspaper ids
griseofulvin and chlorpropamide films800 nm, 100 fs, 80 MHz, 40 mW (about 0.5 nJ per pulse); 10× objective, N.A. 0.3; field 600 × 600 µm; frames 45 s and 25 sforward and backward[wanapun2010 P4, P5]
naproxen–HPMCAS powderssame laser at 20 mW; 4 × 4 × 20 µm³ resolution; frame 25 s; 3D image 3 minepi[kestur2012 P6, P12]
flutamide and ezetimibe spray-dried dispersions1064 nm, 51 MHz, 166 fs; 50 mW (flutamide) and 250 mW (ezetimibe); fields 1925 × 1925 µm; about 1.5 min per sampleepicorreasoto2017 P3
posaconazole HME ASDs1064 nm, 200 mW, 447 ms; standard curve linear, R² 0.999 at 0–25%epishah2024 P7
Pitfalls and disagreements

Only non-centrosymmetric forms are seen; SHG-inactive polymorphs, crystals below about 100 nm and crystals of other orientation distributions give less or no signal (F11, F9). The detector can saturate (flutamide at 82% RH after 58 days) correasoto2017 R11. No chemical or structural information beyond percent crystallinity is given [kestur2012 C37].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

secondary nucleation

The formation of new crystals in the presence of existing ones, from their surface or from fragments of them, with a lower energy barrier than primary nucleation purohit2019 C3; duong2022b C35. In the dissolution papers it enters in two ways: as the reason why seeds in an ASD speed crystallization and desupersaturation beyond their own growth purohit2019 C3, C32, and as a process assumed to be small, so that the fall of the donor concentration reflects growth of the seeds alone hate2019 C42. New aspect (Crystallization from solution): it adds to the loss of dissolved drug in a seeded run and would confound a growth measurement ilevbare2012a C14, C15; ilevbare2013b C12; in seeded runs the authors judged it absent for celecoxib and ritonavir and present for efavirenz above 10 µg/mL ilevbare2013b R5, C13. Turbidity at 370 nm marks it in the telaprevir seeded runs (it rose at δ 7.9 and 12.5, not at 2.4), and STC and STCDC are said to inhibit it because no rise was seen (traces not shown); in acetaminophen PVPVA "does not appear" to stop it [lu2017a R4, R5, C22; trasi2015 C22].

Findings

Bioperformance: F29, F30. Crystallization from solution: F3, F5, F20, F27, F33, F42.

Related concepts

follows from crystal seeding; competes with crystal growth; part of desupersaturation; lowered by an absorptive sink; part of nucleation; a confounder of crystal growth rate; related to heterogeneous nucleation and residual crystallinity.

Formulas

power-law crystal growth rate (the fitted order assumes minimal secondary nucleation).

How it is measured or obtained

Not separated from growth in the Bioperformance papers. Elsewhere: turbidity in seeded runs, the size distribution of the seeds before and after growth, a mass balance of seed volume against solute removed, SEM of small crystals on larger ones, and the rise of a fine-particle count after a pH shift ilevbare2012a R7, R8; ilevbare2013b R5, R6; que2018 R9, R10; shah2024 R14, C28. In the seeded growth papers the turbidity is read at 280 or 350 nm, with an unseeded control at the same supersaturation and a volume balance on the seeds ilevbare2013b P11, R5; ilevbare2012a R7, R8, R9.

Values in the library
materialvalue or classconditionspaper ids
tacrolimus seeded solutionsassumed minimal, so the desupersaturation rate gives the growth order (1.677)hollow-fibre module, S 8–20hate2019 C42, R18
ritonavir, celecoxib; efavirenzno significant secondary nucleation in seeded runs and no turbidity rise between 5 and 22 µg/mL (ritonavir also judged by size distribution and mass balance); efavirenz turbidity rose at every concentration above 10 µg/mL (S 1.2) once macroscopic crystals formedseeded, 37 °C; turbidity, size distributionilevbare2013b R5, R6, C12, C13
telaprevirsecondary nucleation with growth at δ 7.9 and 12.5, none at 2.4; inhibited by 1.86 mM STC or STCDC; extinction without bile salt 0 (δ 2.4), about 0.047 (δ 7.9), about 0.061 (δ 12.5)370 nm extinction, pH 6.5, 37 °C[lu2017a R4, R5, C11, C22]
paclitaxel seedssmall needles on larger crystals in SEM; lower aspect ratio after growthno polymerque2018 R9, R10, C43
posaconazole 10 wt% ASDfine-particle count rose after 15 min following the pH shiftFBRM and SHGshah2024 R14, C28, C47
ritonavir seeds after growthmonomodal size distribution; unseeded 10 µg/mL no loss in 8 hS 7.6ilevbare2012a R7, R9
telaprevir seeds, δ 7.9possible; bulk growth assumed dominant50 mM phosphate pH 6.5, 37 °C[lu2018 C8]
atazanavir needles from buffersecondary growth and small needles on larger ones; none in human fluidSEM, 300 minelkhabaz2021 R17
posaconazole with 0.4–20 µg/mL nanocrystal seedsinduction period removed; immediate desupersaturation at 2 and 20 µg/mLPBS pH 6.5, S 33.6duong2022b R13, C35
Pitfalls and disagreements

Secondary nucleation was assumed small in the tacrolimus growth fit and not tested hate2019 C42. The primary and secondary routes are not separated by induction times or particle counts [trasi2015 X7]. Breakage of seeds gives fine needles that look like secondary nuclei que2018 C45. In vivo, absorption lowers the supersaturation that drives secondary nucleation, and its role in the dog study is only argued purohit2019 C41. At concentrations near the amorphous solubility the 2-min slope of a seeded run may include secondary nucleation or a drug-rich phase, and no measurement separates them [ilevbare2012b X18]. The volume balance on the ritonavir seeds differs by a factor of 2.3 ilevbare2012a X10. For telaprevir secondary nucleation was inferred from turbidity, not measured on its own [lu2017a X10].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

seeded crystal growth

Evidence table: seeded crystal growth. Content from the ASD dissolution chapter (paclitaxel, 2018) and the crystallization-from-solution chapter.

Growth of drug on crystals already present in a supersaturated solution, so that no nucleation step is needed. In a dissolving dispersion it competes with release: the dispersion first raises the concentration and the seeds then lower it, the loss depending on the growth area the seeds offer and on how well the polymer poisons their surfaces que2018 C30, C48. Seeds made in different environments grow at different rates, so seed origin belongs to the description of the system schram2016 C39.

Findings

F22, F23, F24, F26.

Related concepts

needs residual crystallinity or crystal seeding; limited by crystal growth inhibition and step pinning; measured as desupersaturation.

Formulas

Cabrera-Vermilyea step pinning, supersaturation ratio.

How it is measured or obtained

A seeded desupersaturation test: seeds at a fixed weight fraction of the drug added, supersaturation set by a solvent shift, concentration followed in situ and the initial slope taken as the growth rate, with the unseeded run as the reference que2018 P7, P10. In a dispersion, the seed suspension replaces the medium and the residual concentration is read by HPLC after filtration que2018 P8, P9. The ratio of the rates without and with polymer is the effectiveness ratio of the inhibitor schram2016 R2.

Values in the library
materialvalue or classconditionspaper ids
paclitaxel, 18 wt% seeds, no polymer31.6 → ≈12–13 µg/mL in 2 min (sonicated) against ≈21.6 (S 16) and ≈26.1 µg/mL (S 80); ≈3.3 and ≈11.5 µg/mL at 10 minpH 6.8, 37 °Cque2018 R7
paclitaxel–HPMCAS dispersion, 18 wt% seeds≈7.9–25.3 µg/mL left at 16 h against ≈31.6 µg/mL unseededpH 6.8, 37 °Cque2018 R14
paclitaxel seeds grown with HPMCASdendritic fingers ≈10.5–16.8 nm wide at the needle endsTEM, 20 measurements per sampleque2018 R12
felodipine seeds made four ways, 5 µg/mL HPMCAS (Crystallization from solution)growth slowed ≈2.7-fold to ≈12-fold depending on seed origininitial S 4, pH 6.8schram2016 R2
posaconazole with 5 or 10 µg/mL seeds (ASD process)≈46.5 and ≈25% of the starting concentration left at 30 min without polymer; ≈96 and ≈74.5% with 180 µg/mL HPMCASFaSSIF V2, 20 µg/mL drugshah2024 R22
tacrolimus seeds from a crystallized generic (Bioperformance)initial rate ≈0.39 against ≈0.075 on an axis of µg s⁻¹ mL⁻¹ from 50 and 20 µg/mLabsorptive dissolutionhate2019 R17
Pitfalls and disagreements

Seeds added to the medium are not equivalent to crystals formed inside a dispersion: extrudate crystals of indomethacin grew better with polymer than bulk seeds, so bulk seeds are "not an equivalent surrogate" moseson2020a C41, while felodipine seeds crystallized from a dispersion with HPMCAS were slowed more than buffer-grown ones schram2016 R2. Growth on seeds continues where nucleation is fully blocked, so an unseeded induction time overstates how well a polymer protects supersaturation que2018 R3, C30. No seeded-growth curve with polymer alone was shown for paclitaxel, so growth and dissolution are not separated in the polymer case que2018 X15.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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–PVP12vaneerdenbrugh2012a 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 crystal[que2020 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 °Cduong2022b 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, citedwegiel2013b 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 B. Supersaturation from ASD dissolution

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 heatingvaneerdenbrugh2012a 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 B. Supersaturation from ASD dissolution

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 solubilityraina2014a R10, C20
tacrolimus, 900 / 450 / 100 / 40 mLSI amorphous 9 / 4.5 / 1 / 0.4USP medium Ipurohit2018 R4
tacrolimus40 mL non-sink relative to the amorphous solubility; 100 mL needed for exact sink5 mg dosetrasi2016 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 PVDF[hate2022 R15, C30]
tacrolimus 5 mg in 240 / 100 / 40 mLsink index against the amorphous solubility 2.4 / 1 / 0.4dose-to-volumehate2019 R7
danazol diffusion cellreceiver maximum below 0.3 µg/mLregenerated cellulose 6–8 kDa, 25 °Cjackson2016 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 B. Supersaturation from ASD dissolution

solid-state crystallization of amorphous drugs

Crystallization of an amorphous drug or dispersion during storage or isothermal holding, without dissolution, followed as the rise of the crystalline fraction or as the number and growth of crystals. The papers of this chapter add the method side: what is seen first depends on the sensitivity of the method (F10). New aspect (Physical stability): from felodipine dispersions stored for up to about two years, crystallization proceeded quickly to a plateau at 75–93% RH with PVP, slowly and with a lag with HPMCAS, and hardly at all at 0–52% RH [rumondor2009b C7, C10, C11, C15].

Findings

Solid-state methods: F5, F6, F10, F17. Physical stability: F11, F15, F16, F20, F21, F25, F26.

Related concepts

observed through residual crystallinity and degree of crystallinity; limited by limit of detection; related to physical stability and crystallization; includes moisture-induced crystallization; slowed by crystallization inhibition by polymers.

Formulas

Avrami equation. The F-test with RMSEP as error term of the felodipine storage study is listed on the physical stability chapter page as a table entry only.

How it is measured or obtained

SHG imaging with PXRD and Raman in parallel on stored powders [kestur2012 P3, P9, P11; correasoto2017 P2, P3, P4]; SHG, forward/backward ratio and optical microscopy in melt-quenched films above Tg [wanapun2010 P3, P4, P6]; probe fluorescence, polarized-light microscopy, DSC and XRD in humid films [purohit2015b P5, P8, P11, P12]. Kinetics from the SHG stack: crystal counts, growth maps and a JMA fit (F6) [wanapun2010 P7, P8, P9]. PXRD of stored powders quantified with one PLS model per composition, RMSEP 3.7–5.3% [rumondor2009b P5, R4].

Values in the library
materialvalue or classconditionspaper ids
griseofulvin filmfirst crystal 7.5 min by SHG, after 39 min optically120 °C[wanapun2010 R2]
chlorpropamide film125 s by SHG, 500 s optically30 °C[wanapun2010 R5]
griseofulvin filmgrowth 1.16–1.54 µm/min; nucleation 2.85 mm⁻³ min⁻¹; JMA k 3.35 × 10⁻³ min⁻¹; ΔE 140 ± 20 kJ/mol125 °C; five temperatures for ΔE[wanapun2010 R16, R17, R18, R19]
naproxen–HPMCAS 75/25SONICC about 24% of the drug at 0 h; about 48% at 48 h60 °C[kestur2012 R16]
flutamide–HPMCAS 15%SHG at 11 d (75% RH), 8 d (82%); XRPD at 53 d and 29 d40 °Ccorreasoto2017 R1
ezetimibe–HPMCAS 30%SHG at 15 d; XRPD none in 60 d (75% RH), 48 d (82%)40 °Ccorreasoto2017 R1
probucol–PVP 50:50crystals by polarized light at 21 h; XRD peaks at 30 h97% RH[purohit2015b R5, R21]
felodipine–PVP dispersionsfast and extensive at 66–93% RH, extremely low at 0–52% RHroom temperature[rumondor2009b C7]
tacrolimus capsule contentsfully crystallized in 5 weeks after an apparent lag; XRPD LOD 10% crystallinity40 °C, 75% RH, open dishpurohit2018 C14, R2
70% drug-loaded spray-dried ASDscrystallization in the fresh samples induced by DSC heating, consistent with fully amorphous starting materialDSC at 5 °C/min[duong2022c C21]
felodipine with 25% PVP1.2–2.8% (0–52% RH); 68.6–82.1% (75–93% RH) after ≈494 days22–25 °C[rumondor2009b R9]
felodipine with 50% HPMCASlag of 35–120 days at 52–93% RH, then 9.2–16.6%same[rumondor2009b R17, R9]
felodipine with 10% HPMCAStwo crystal forms, one Form II93% RH, 491 days[rumondor2009b R13]
felodipine powders, two sieve fractionscomplete in 72–120 h alone; plateaus ≈45% and ≈17% with 3% PVP30 °C, drykestur2013b R5, R8
felodipine–3% PVP powdersbiphasic, early slope 13–14 times the late onePXRDkestur2013b R14
Pitfalls and disagreements

An onset time is the first positive sampled point of a method with a given limit, so it is an upper bound on the true onset; the abstract and text of one paper give 26 and 29 days, and 48 and 60 days, for two XRPD detections correasoto2017 X1, X2, X8. Crystallization during a DSC scan can be mistaken for crystallization on storage: the 165 °C endotherm of spray-dried itraconazole–HPMC appeared only at 2 °C/min and the powder showed ITZ peaks after that heating [purohit2017a R2, R4, R5, C5]. In the felodipine storage study, values below about 10% lie within two RMSEP of zero [rumondor2009b X4]; the statement that RH did not affect HPMCAS dispersions holds for 50% HPMCAS only [rumondor2009b X3]. The humid range of fast crystallization of the felodipine–PVP dispersions is given as 66–93% RH by the solid-state methods chapter and as 75–93% RH by the physical stability chapter, both from the same paper [rumondor2009b C7, R9].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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)Fedorsilevbare2013c 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; 21.27Fedorsilevbare2013c 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; 23.28Fedorsilevbare2013c R10
Pn-IPAAmd; PAlAmn22.64; 20.70Fedorsilevbare2013c R10
PVPVA; PAA; HPC; PVP; PVPdn-O25.77; 25.92; 25.98; 28.39; 32.24Fedorsilevbare2013c R10
effective polymers, mean SP20.87 (ritonavir); 21.73 (efavirenz); 24.28 (celecoxib)induction timeilevbare2013c 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 B. Supersaturation from ASD dissolution

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 °C[indulkar2017a 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 work[indulkar2017a 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 B. Supersaturation from ASD dissolution

solubilization

Raising the equilibrium (total) solubility by micelles, complexes or proteins, as against raising the activity by supersaturation raina2015c C7, C8. HPMC-AS may slightly solubilize its drugs, which raised the crystalline solubility of ketoconazole 2.4- and 3.8-fold with AS-LF and AS-HF [ueda2020a C15, X2].

Findings

F3, F4.

Related concepts

contrasts with supersaturation; includes micellar solubilization.

Formulas

none.

How it is measured or obtained

Shake-flask solubility with and without additive raina2015c P1.

Values in the library
materialvalue or classconditionspaper ids
felodipine in FaSSIFabout 40-fold (40.8 / 42.8 µg/mL)37 °Craina2015c R1, C16
felodipine, nifedipine + HPMCno solubilization100 µg/mL and 1 mg/mLraina2015c R1, C15
resveratrol + HPMCAScrystalline solubility 42 to 83 µg/mL4.7 mg/mL polymerwegiel2015 R16
danazol + polymersno solubilizationjackson2016 C42, C38
ketoconazole with AS-LF / AS-HFcrystalline solubility 1.38 to 3.26 / 5.30 µg/mL1000 µg/mL polymer, 37 °C[ueda2020a R1, X2]
Pitfalls and disagreements

Solubilization hides a loss of free drug raina2015c C30.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 °Celkhabaz2017 R6
ezetimibe, FeSSIF 123 µg/mLHPMC-AS 50 µg/mL more than 360 min; PVP about 10 min37 °Celkhabaz2017 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 fibre[hate2018 R14]
indomethacin–Eudragit EPO ASDcrystallization after 15–20 min; small α crystals within about 20 minacid stage, pH 2.2, 37 °Cxie2017 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 °Calonzo2010 R19, R11, R7
nifedipine 50:50 dispersionscrystals below 2 µm in solution against 1–300 µm by the matrix routepH 6.8raina2014b 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 °Cxie2015 C20
tacrolimus 50 µg/mLonset within 3 h; 6–8 h with HPMCpH 4.5, 37 °Ctrasi2016 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 °Cnguyen2023c 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 B. Supersaturation from ASD dissolution

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 slurryraina2014b R7, R6, R8
nifedipine γ → α, 1 mg/mL HPMCAS in bufferγ intact to ≈110 min, α complete at 145 min25 °Craina2014b R9, R10
nifedipine 50:50 dispersionsα complete at ≈5 min (PVP), ≈40 min (HPMC, HPMCAS)25 °Craina2014b R12
amorphous indomethacindominant route of supersaturation loss; needles in the liquidpH 2, 25 °Calonzo2010 C44, R19
vemurafenib β → α (Crystallization tendency)solvent-mediated conversion at room temperature, data not shownslurrylu2016 R23
hollow organic crystals (Solid-state methods)reported cases arise from solvent-mediated phase transformationliteraturecorreasoto2017 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 B. Supersaturation from ASD dissolution

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% solids[li2020 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 droplet[li2020 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 B. Supersaturation from ASD dissolution

speciation

The split of total drug into free, micellar, complexed, droplet and crystalline species; only free unionized drug is thought to cross a membrane [hate2018 C48; raina2015c C49]. In enzalutamide dispersions the free drug at the amorphous solubility, amorphous aggregates and filtered-out drug were counted separately after 1 h of dissolution wilson2018 R10, R12.

Findings

F3, F15, F23, F25.

Related concepts

related to free drug concentration.

Formulas

none.

How it is measured or obtained

Mostly inferred from flux, ultracentrifugation and fluorescence [hate2018 P6; raina2015c R13]. In enzalutamide dispersions it was counted: the molecularly dissolved drug in the supernatant, the amorphous aggregates from Nile Red fluorescence calibrated against pellet mass, and the rest removed by filtration wilson2018 R8, R10, R12.

Values in the library
materialvalue or classconditionspaper ids
atazanavirtotal concentration not equal to drug available for permeation[hate2018 C48]
felodipine with BSAflux-based supersaturation 7.3 and 4.2 against 1.3 and 1.1 by totalraina2015c R13
enzalutamide 10:90 with copovidone42 µg/mL molecularly dissolved, 50 µg/mL amorphous aggregates, 8 µg/mL removed by filtration (of 100)pH 6.5, 22 °Cwilson2018 R10
enzalutamide 50:50 with copovidoneabout 3 µg/mL as aggregatespH 6.5, 22 °Cwilson2018 R10
Pitfalls and disagreements

Species were not separated in the hollow-fibre donor [hate2018 X11]. The aggregate count assumes that the free drug sits at the amorphous solubility, and the rat advantage of the aggregate-rich ASD (about 30% more exposure) was not tested statistically (F23) wilson2018 R12, C46, X6.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 positions[vaneerdenbrugh2012c R15, C23]
DEX6–PVP90six spectra alike, pattern of pure PVP90domains 0.3–0.6 µm[vaneerdenbrugh2012c 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 B. Supersaturation from ASD dissolution

spherulitic growth

Growth of a crystal as a round aggregate of radiating fibres (a spherulite) into the supercooled liquid; its diameter grows linearly with time and the slope is the growth rate [kestur2010a C9, R4; kestur2011 R4]. In the felodipine, bifonazole and nimesulide studies all crystals grew as spherulites, with and without polymer [kestur2010a R2; kestur2011 R2]. New aspect (Physical stability): felodipine crystals from amorphous thin films grow as spherulites below about 80% RH and switch to needle-like crystals of the same form at higher RH, with a 20–40-fold faster growth rumondor2010 R2, R8, C9, X2.

Findings

Miscibility and drug-polymer interactions: F10, F13. Physical stability: F3, F9, F19, F22, F27, F28, F29.

Related concepts

part of crystal growth rate and a form of its measurement; observed in supercooled liquid; related to polymorphism and moisture-induced crystallization.

Formulas

none.

How it is measured or obtained

By time-lapse polarized-light microscopy on a hot stage; the polymorph is checked by Raman microscopy and melting point [kestur2010a P4, P5, R3; kestur2011 P4, R3]. In the humid felodipine films, by photomicrographs of crystals at each RH and Raman of the two morphologies rumondor2010 P5, P6.

Values in the library
materialvalue or classconditionspaper ids
felodipine form II, neat and with 3% PVP, HPMCAS, PVP/VA, PVAcsmooth interface to the amorphous matrix in all five systems80 °C[kestur2010a R2]
bifonazolerough fibre-like edges at 18 °C, smoother at higher temperature, sharper edges at 90–100 °Cno polymer; polymers did not change the profile[kestur2011 R2]
nimesulideneedle-like at 18–40 °C, zig-zag edges at 40–60 °C, smooth aboveas above[kestur2011 R2]
felodipine, spin-coated films with polymers (other chapter)irregular boundaries and polymer-rich dark points on the crystallites22 °C, 3% HPMCAS, PVP, HPMC[konno2006 R2, C11]
felodipine with PVP K-12, K-29/32, K-90 (other chapter)no significant change in macroscopic morphology0.5–4.5 wt%[kestur2010b R5, R12, C8]
amorphous felodipine filmround spherulite at 75% RH; needle-like crystal at 93% RH; same Raman peak positions25 °Crumondor2010 R2, R8
felodipine with HPMCASdisrupted spherulites with irregular boundaries, most at 10%32–93% RHrumondor2010 R4
felodipine with PVPseparate spherulitic segments at 64% RH and below; round outline from 75% RH2.5–10%rumondor2010 R6
felodipine form Icompact spherulites below 40 °C, rough edge at 45–65 °C, zigzag above 70 °C (surface)melt films[kestur2013a R5, R6]
acetaminophen with seven polymersspherulitic shape kept10% w/w[trasi2012a R4]
celecoxib with TPGS and PVPa large faceted plate at 120 °C instead of a fibrous frontmelt films[mosqueragiraldo2014 R13, C34]
ATP(R), ATP(S) with 5% polymersspherulites in all; size linear in timemelt filmssato2015 R3, R4
flutamide, DPB with 5% PHBspherulites with a sharp interface, with and without polymermelt films[sato2016 R2]
indomethacin δ and α (spherulites), γ (polycrystalline)morphology identifies the formmelt films[tian2017 R2]

Evidence table: spherulitic growth.

Pitfalls and disagreements

The captions of the bifonazole–nimesulide morphology figure label both drugs' panels a to c, and the row assignment is inferred; the text describes bifonazole at 90 and 100 °C, which are not shown [kestur2011 X3]. The spherulite diameter slope is called a change in radius in one place of the felodipine paper [kestur2010a X3]. The linear size–time relation is assumed to hold for every system, but only single series are plotted for 80 °C [kestur2010a R4]. The Fig. 2 caption of the humid-film growth paper calls both crystals spherulitic although the 93% RH one is needle-like rumondor2010 X6. At about 84–86% RH both morphologies coexisted rumondor2010 X13. Because the felodipine front changes habit with temperature, rates at different temperatures do not refer to the same front [kestur2013a X12].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 outside[yang2022b 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 B. Supersaturation from ASD dissolution

step pinning

The mechanism (Cabrera and Vermilyea, outside the library) by which adsorbed impurity molecules hold back an advancing growth step: the step must bulge between adsorbed molecules, its radius of curvature is limited by their spacing, closer spacing means slower growth, and growth stops when the spacing equals twice the critical radius \rho_c of a two-dimensional nucleus; because \rho_c falls as supersaturation rises, the maximum effect of a fixed impurity spacing falls with S alonzo2012 C9, E8. Ilevbare and co-workers chose it among four mechanisms for adsorbed impurities (surfactant action, incorporation, kink blocking, step pinning) by argument, because large polymers adsorb irreversibly [ilevbare2012b C12]. AFM of felodipine seeds shows steps held at several points by dissolved HPMCAS (spacing 68.5 ± 9.4 nm on buffer-grown seeds, 15.8 ± 7.4 nm on dispersion-grown seeds, step height 0.8 nm) schram2016 R5, R12.

Findings

F9, F10, F23, F24, F12, F42.

Related concepts

part of polymer adsorption on crystal surfaces; depends on critical radius of a two-dimensional nucleus; related to impurity effectiveness factor, Kubota-Mullin model and kinetic roughening.

Formulas

Cabrera-Vermilyea step pinning, Kubota-Mullin model, Kubota-Mullin impurity effectiveness factor.

How it is measured or obtained

Not observed directly in these papers. It is tested through the fall of the growth-rate ratio with coverage, the factor α of the Kubota–Mullin model and the rise of the growth order from about 1.5 to about 2 [alonzo2012 R9, R13; ilevbare2012b R16]. In the ASD dissolution chapter, SEM finger width of paclitaxel dendrites with HPMCAS gives the spacing of adsorption sites (about 10–16.8 nm), and the distance between step pinnings on indomethacin crystals with PVPVA was 270 ± 100 nm que2018 R12; moseson2020a R13.

Values in the library
materialvalue or classconditionspaper ids
felodipine with HPMCα 0.7, 0.5, 0.4, 0.6, 0.2; growth order 1.50 → 1.97 ± 0.12S 3–12, 25 °Calonzo2012 R9, R13
ritonavir with CAP Adp 0.85α 4.35 (pH 6.8), 1.25 (pH 3.8); growth stopped at coverage 0.23σ 0.99[ilevbare2012b R16]
paclitaxel with HPMCAScritical radius 5–7 nm at S 88, smaller than the site spacing of 10–20 nm, so seed growth is not preventedseeded ASD dissolutionque2018 C38
HPMCAS on felodipinel 68.5 and 15.8 nm; ρc 3.98 nmS 4schram2016 R12, R14
posaconazole plates in aspirated human fluidfinger-like ends; step pinning "may be occurring"SEM, 37 °Celkhabaz2021 R23, C39
telaprevir crystals with HPMCAS-MFrough surfaces, related to HPMCAS step pinning on felodipine (cited)SEM[lu2018 R10, C48]
Pitfalls and disagreements

The spacing of adsorbed HPMC on felodipine, the central quantity, was not measured (for HPMCAS on felodipine it was imaged by AFM schram2016 R12); the statement that molecules sit "relatively far apart" is an inference from α alonzo2012 C28. The other mechanisms were excluded by argument [ilevbare2012b C12]. Step pinning applies only below the kinetic roughening transition and was not tested above it [ilevbare2012b X11].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 °C[indulkar2017a 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 nmNTAindulkar2016 R4
ritonavir ASD films200 (PVPVA), 250 (HPMCAS), 315 nm (PVP)NTA[purohit2017b R8, E1]
tacrolimus second phase220 nmNTAtrasi2016 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 °C[saboo2019 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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

sub-Tg nucleation

Nucleation of an amorphous solid in its glassy state, well below Tg, where mobility is low [trasi2014b C10]. It runs against the rule that storage about 50 °C below Tg prevents crystallization [trasi2014b C4].

Findings

F4.

Related concepts

part of nucleation; located by nucleation temperature zone; related to glass transition temperature and polymorphism.

Formulas

none.

How it is measured or obtained

By cooling the melt to low end points and reheating in DSC, by surface nuclei counts after holds below Tg, and by long DSC holds with Raman identification of the product [trasi2014b P1, P7, P8].

Values in the library
materialvalue or classconditionspaper ids
nilutamidecrystallization on reheating only after cooling to −30 °C, about 60 °C below TgDSC[trasi2014b R5]
nilutamide88% form I after 30 min at −30 °Cabout 50 DSC holds[trasi2014b R16]
indomethacin (cited)melting endotherm after storage 55 °C below Tgliterature[trasi2014b R34]
ibuprofen (cited)metastable form nucleates about 60 °C below Tgliterature[trasi2014b R33]
Pitfalls and disagreements

The counts are per sample after 30 min, not rates; longer room-temperature storage nucleated too [trasi2014b X7, X16]. Mechanical stress or beta relaxation have been proposed as causes elsewhere and were not tested [trasi2014b C43, C45].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 glasslu2016 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 filmssato2015 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 conditions[que2019 R28; indulkar2019a M1]
ledipasvirglass under release conditions37 °C[que2019 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 °C[saboo2020 C32, R30]
loratadinesupercooled liquid at 37 °C, glass at 5 °Cwet Tg 13.8 °C[yang2021 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 B. Supersaturation from ASD dissolution

supersaturation ratio

The LLPS (or onset) concentration divided by the equilibrium solubility of the crystalline drug in the same medium [almeidaesousa2015 E15]. For the weak bases it is the amorphous solubility divided by the crystalline solubility, and the authors state that it is "not affected by degree of ionization" [indulkar2015 C46]. It is a concentration-based ratio; it can differ from the activity-based ratio when a second solute is present (F12) raina2015c C29. The papers of 2017–2022 add that the concentration-based ratio can differ from the activity-based ratio in micellar media (F16) and depends on temperature and pH: ibuprofen's fell from about 5.8 to 2.5 between 25 and 60 °C, and pazopanib's from 500–600 at pH 6.4–8.4 to about 103 at pH 5.0 [ueda2022 R16; sugihara2018 R4].

Findings

F6, F10, F12, F16, F17.

Related concepts

same quantity as the amorphous solubility advantage when measured at the ceiling without an additive, or with an additive that only mixes into the drug-rich phase (Case II of Ueda 2024); with an additive that complexes the drug in water (Case I) the maximum supersaturation ratio generally exceeds S_a/S_c, and with both (Case III) S_a/S_c does not give it; part of supersaturation; depends on the additive cases for amorphous solubility; based on crystalline solubility.

Formulas

supersaturation ratio.

How it is measured or obtained

From the printed onsets and crystalline solubilities; the six-drug paper tabulates it by fluorescence and by extinction [almeidaesousa2015 R5].

Values in the library
materialvalue or classconditionspaper ids
ibuprofen; tolnaftate; sorafenib4.3; 20.0; 54.0 (fluorescence)25 °C[almeidaesousa2015 R5]
clotrimazole; atazanavirabout 13; about 6337 °C[indulkar2015 R10]
telaprevirabout 18 stated; 19.6 from 90 ÷ 4.6 (synthesis)37 °C[mosqueragiraldo2015 R14, R13]
CRH1about 10pH 6.8 and pH 4.6almeidaesousa2016 R24
pazopanibabout 603 (pH 6.5); 500–530 (pH 6.4, 7.0, 8.4); about 103 (pH 5.0)37 °C, 0.1 M buffers + 5 µg/mL HPMC[sugihara2018 R4]
atazanavir63.6 (synthesis: 70 ÷ 1.1); predicted 62; flux-derived 65pH 6.8, 37 °C[indulkar2017a R4, R5, R6, R13]
telaprevir28.5 (synthesis: 148 ÷ 5.2)50 mM pH 6.5, 37 °C[lu2017b R2, R1]
ibuprofen5.94 (2020 paper); 3.57 (2021 paper, synthesis: 154 ÷ 43.1); 5.8 → 2.5 (25 → 60 °C)pH 2.0 (D2O)[ueda2020b R1; ueda2021 R5, R2; ueda2022 R16]
Pitfalls and disagreements

The printed diclofenac extinction ratio (51.6) recomputes to 54.3 [almeidaesousa2015 X1]. The clotrimazole ratio is about 8 at pH 4–4.5, not about 13 throughout [indulkar2015 X5]. The range is now about 2 to about 600 [sugihara2018 R4]. Pazopanib's value carries a high experimental uncertainty because its crystalline solubility is so low [sugihara2018 C16].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 4.6almeidaesousa2016 R24
atazanavir in 0–3.6 mg/mL SDSconcentration-based 64.8 → 33.0; activity-based 66.0 → 65.0 at the amorphous solubility37 °C[indulkar2017a 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 solubilitybufferraina2014a R17
felodipine with BSAS 1.3 and 1.1 by concentration ratio; 7.3 and 4.2 from flux50 µg/mLraina2015c 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 cellelkhabaz2019b R8
posaconazole, six mediaactivity-based maximum about 29–37; concentration-based about 35–37 in buffer to 5 in human fluid37 °Celkhabaz2019b R9
tacrolimusS 20 (5 mg in 100 mL) and S 8 (240 mL); maximum ratio about 33solvent-shift solutions, hollow-fibre modulehate2019 R7, R14; purohit2019 C30
tacrolimus, fully crystalline capsule contentsconcentration 2.5 times the crystalline solubility during 2 h5 mg in 100 mL, pH 4.5purohit2019 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 °Calonzo2012 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/mLilevbare2013b 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 °Clu2017 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 °Cduong2022b 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 B. Supersaturation from ASD dissolution

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% RHkestur2013b 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% RHcorreasoto2017 C26
indomethacin methyl ester compactssurface crystals within 10 min of dissolutionPVPVA, 25% DL[saboo2020 R9]
ritonavir–PVPVA–SDS compactsneedle-shaped surface crystals during dissolution30% DLindulkar2022 R15; yang2023 R16
delamanid dispersion filmsrapid surface crystallization at pH 3.01 hnguyen2023b 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 slurryalonzo2010 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 °Cnguyen2023c R19, R18
delamanid dispersions after the pH shiftundissolved particles covered with small crystals within 30 minpH 6.5nguyen2023c R21
indomethacin methyl ester–PVPVA 25%smooth at 5 min; scattered needle-like crystals at 10 min; surface extensively covered at 20 minSEM, pH 6.8[saboo2020 R22, M6]
indomethacin methyl ester–PVPVA 10–25%drug release levelled off after 7.5–20 min30 min runs[saboo2020 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 B. Supersaturation from ASD dissolution

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 spots[li2020 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-FTIRtrasi2019 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, SEMmoseson2021 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 bufferSEM[purohit2017b R9]
ledipasvir–PVPVA 20, 50%17 → 54 and 40 → 61 wt% drug in 10 minXPS[que2019 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, EDX[saboo2019 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 2.1[saboo2020 R21, R28, R17, M5]
ritonavir–PVPVA 40% compactsurface ritonavir ≈35 → 72 wt% after 30 minXPS, pH 6.8[yang2022a 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 min[hiew2023 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 B. Supersaturation from ASD dissolution

surface-enhanced crystal growth

Faster crystal growth at a free surface of an amorphous solid than in its bulk, thought to reflect higher surface mobility near or below Tg [trasi2014a C4]. In this chapter it is offered as one reason why felodipine growth in uncovered thin films outpaced the bulk mobility predicted from Tg rumondor2010 C28, C29.

Findings

F5, F9, F21, F26.

Related concepts

part of crystal growth rate; related to surface crystallization and molecular mobility.

Formulas

constant-penetration-depth crystallinity estimate.

How it is measured or obtained

Radial growth rates of crystals in films with the top coverslip removed, compared with sandwiched films [trasi2014a R4, R5]; growth in uncovered spin-coated films at fixed RH rumondor2010 P1, P5.

Values in the library
materialvalue or classconditionspaper ids
amorphous felodipine films (uncovered)growth above the AGV mobility line; coupling exponent 0.513–75% RH, 25 °Crumondor2010 R7, C27, C28
14 compounds (outside)surface growth generally faster than bulk; order differs from bulknear Tg[trasi2014a R4, C4, C8]
felodipine form Isurface ≈6 times the bulk at 18 °C; equal above 70 °Cmelt films[kestur2013a R8.a, R9, C2]
felodipine form I with 3% PVPsurface/bulk ratio 22.8 against 5.7 without30 °Ckestur2013b R12, C32
felodipine powders, 150–250 against 500–710 µm≈46 against ≈12% crystalline at 24 h30 °C, Ramankestur2013b R3.e, C24

Evidence table: surface-enhanced crystal growth.

Pitfalls and disagreements

In the felodipine growth study surface growth is one of two "possible explanations", next to diffusion–viscosity decoupling; neither surface nor bulk growth was measured separately there rumondor2010 C28, X12. The authors consider thin uncovered films relevant because crystallization "likely" starts at the surface rumondor2010 C30. The constant-depth picture is not consistent with the bulk growth rate with PVP, which would cross the estimated depth within days kestur2013b X8.

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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:TPGSqNMR[correasoto2022a R12]
200 µg/mL atazanavir with PVPVA, VP, SDS, TPGSadditive in solution reduced by 1, 0, 7, 13%¹H NMR, 37 °C[correasoto2022b 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 weightsame[correasoto2022b 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-PTIR[yang2022b 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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 °Craina2014a E10, R17
felodipine suspensionssame low flux at about 1 and 40 µg/mL dissolvedcrystal fixes activityraina2015c R4, C20
atazanavir + SDSfree drug about 1 to about 65 µg/mL with and without SDS37 °C[indulkar2017a 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 cellelkhabaz2019b 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 cellwilson2018 R13, C25
atazanavir, nifedipine and three other drugs, PAMPAbreak from a linear rise at about the amorphous solubilitylipid-impregnated PVDF[hate2022 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 B. Supersaturation from ASD dissolution

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 liquidlu2016 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 °C[rumondor2009c 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 B. Supersaturation from ASD dissolution

two-dimensional nucleation

The formation of a new molecular layer on a crystal face from a small two-dimensional island (or from a spiral step), the way a face grows at low supersaturation; the growth rate then rises roughly with the square of the supersaturation σ, and above a critical supersaturation the island shrinks to a single growth unit, the layers disappear and growth becomes continuous and linear in σ (kinetic roughening) [ilevbare2012b C9, E3]. The critical radius of the island sets how closely adsorbed impurities must sit to pin a step alonzo2012 C9. On pre-adsorbed felodipine seeds with dissolved HPMCAS the layers started at points and spread outward (birth and spread) instead of crossing the face schram2016 R7, C22.

Findings

F9, F10, F24.

Related concepts

has critical radius critical radius of a two-dimensional nucleus; ends in kinetic roughening; related to step pinning and crystal growth rate.

Formulas

power-law crystal growth rate, critical supersaturation by extrapolation, Cabrera-Vermilyea step pinning.

How it is measured or obtained

Not measured as such; it is inferred from the dependence of the seeded growth rate on supersaturation (power law with order 1–2, a steep linear rise above \sigma_c) and from the shape of the crystal ends [alonzo2012 E3, R13; ilevbare2012b R11, R12, R13].

Values in the library
materialvalue or classconditionspaper ids
ritonavir without polymer; with CAP Adp 0.85growth rises linearly above \sigma_c 1.37 (5.1 µg/mL); 1.74 (7.4 µg/mL)σ 0.14–2.73, 37 °C[ilevbare2012b R11, R12]
ritonavir needle endsflat before growth; slightly rounded at σ 2.0; clearly rounded at σ 2.7SEM[ilevbare2012b R13]
felodipinegrowth order about 1.50 without HPMC; 1.97 ± 0.12 withS 3–12alonzo2012 R13
felodipine seeds pre-soaked in HPMCASlayers spread from points; growth ratio about 5.5S 4schram2016 R7, R2
Pitfalls and disagreements

The face-specific critical supersaturation is taken to be that of the fast-growing faces ("we believe") [ilevbare2012b C35]. The steep high-σ rise could include secondary nucleation or formation of a drug-rich phase [ilevbare2012b X18].

← Concepts and formulas

concept · as used in B. Supersaturation from ASD dissolution

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 mLhate2019 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 B. Supersaturation from ASD dissolution

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 °C[indulkar2017a 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 B. Supersaturation from ASD dissolution

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 °C[marsac2010 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 RHcited[rumondor2010c R19]
resveratrol–PVP dispersion and physical mixture0–95% RH, mixture above dispersion at every step25 °Cwegiel2013b 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 B. Supersaturation from ASD dissolution

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 °C[indulkar2017a 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 °Cueda2021 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 filmsoutside[rumondor2011 C36, X6]
70 wt% PVP felodipine dispersionwater vapour sorption isotherm at 25 °Coutside[marsac2010 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% RH[benson2025 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% RH[rumondor2009c R22]
indomethacin–PVP 75:254.9 vs 21.7 g/100 g predicted95% RH[rumondor2009c 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 °Cwegiel2013b R19
atazanavir–PVPVA 10%; with SDS or Span 8044%; 49% waterDVS, 37 °C, up to 95% RH[correasoto2022b 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 °C[qi2022 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 h[bapat2023 R20, C31]
PVPVA; with 10% TBC; with 10% GTB≈41.8; ≈34.4; ≈32.0% water at 300 min95% RH, 37 °C[correasoto2023 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 B. Supersaturation from ASD dissolution

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 medium[hiew2023 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 itconfocal[benson2025 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°literature[yang2021 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

formula · as used in B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 drugtrasi2015a 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 B. Supersaturation from ASD dissolution

amorphous solubility advantage from the Hoffman approximation

Expression

\frac{\sigma_a}{\sigma_c} = e^{\Delta G/RT}, \qquad \Delta G = \frac{\Delta H_f\,\Delta T}{T_m}\cdot\frac{T}{T_m}, \qquad \Delta T = T_m - T raina2014a E3; raina2015c E1.

Variables and units

symbolmeaningunits
\Delta H_fenthalpy of fusion28.67 kJ/mol (felodipine); 32.5 kJ/mol (nifedipine) raina2014a M1, M2
T_m, Tmelting point and test temperatureK; 147 and 173 °C raina2014a M1, M2

Assumptions and valid domain

A first approximation near T_m that ignores ionization and water sorption raina2014a C10.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
raina2014afelodipine 25 and 37 °Cprinted 10.92 and 8.64; recomputed 10.84 and 8.57reproduces within 1% raina2014a E3
raina2014anifedipine 37 °Cprinted 8.78; recomputed 14.45mismatch raina2014a E3, X3
raina2015csame drugsΔHf and Tm measured, not printedinputs not printed raina2015c E1

Where it fails or is disputed

See the nifedipine mismatch and the telaprevir failure [raina2014a X3; mosqueragiraldo2015 C24].

Concepts

Hoffman equation. Findings. F1, F23.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

Arrhenius equation

Expression

For the nucleation rate:

I = A\exp\left(-\frac{\Delta E}{RT}\right) [marsac2006a E2]

as a slope, for a crystallization rate constant (outside the subcategory):

\frac{d\ln k}{d(1/T)} = -\frac{\Delta E}{R} [wanapun2010 E5]

For melt viscosity:

\log\eta = \log\eta_0 + \frac{E_\eta}{2.303RT} [tian2017 E1]

Variables and units

symbolmeaningunits
Inucleation rateunit not stated on the plot [marsac2006a X2]
Apre-exponential factor– [marsac2006a E2]
\Delta Eactivation energykJ/mol [marsac2006a R3]
R, Tgas constant; absolute temperatureJ mol⁻¹ K⁻¹; K [marsac2006a E2]
\eta, \eta_0melt viscosity; constantunit not printed [tian2017 E1]
E_\etaactivation energy for viscous flowkJ/mol [tian2017 E1]

Assumptions and valid domain

Fitted separately above and below Tg, since the temperature dependence breaks at Tg [marsac2006a P5, C10]. For viscosity the relation "may" hold over small temperature ranges, as a straight line of log η against 1/T [tian2017 E1].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
marsac2006aactivation energy of nucleation, pure and with 3 wt% PVPbelow Tg 122 (nifedipine), 145 (felodipine); with PVP 127, 201 kJ/molreproduces ≈122 kJ/mol from plot readings [marsac2006a E2, R3]
wanapun2010 (outside)activation energy of griseofulvin crystallization by SHG140 ± 20 kJ/molreproduces [wanapun2010 E5]
tian2017melt viscosity of indomethacin with 10% HPMC, HPMCAS, PVP, 80–130 °CEη 159.7, 143.5, 190.5 kJ/molreproduces 159.7 kJ/mol from the printed slope [tian2017 E1, R13, R14]

Where it fails or is disputed

The Arrhenius plot of the 2006 paper has no rate unit and temperatures only on the 1/T axis, so it serves for slopes only [marsac2006a X2]. The activation-energy difference between the two drugs is significant only below Tg [marsac2006a X6]. The viscosity of pure indomethacin could not be measured because it crystallized, so the polymer melts have no reference [tian2017 X12].

Concepts

kinetic barrier to nucleation, nucleation rate, accelerated stability testing. Findings. F2, F4, F29.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

aspect ratio

Expression

\text{aspect ratio} = \frac{\bar{L}}{\bar{W}} [ilevbare2012c E7; ilevbare2012a E5; ilevbare2012b E15]

The aspect ratio is taken from the average length and the average width of 50 crystals, not as the mean of per-crystal ratios.

Variables and units

symbolmeaningunit
L̄mean crystal length (SEM, 50 crystals)µm
W̄mean crystal widthµm

Assumptions and valid domain

Crystals approximated as needles or rods; used for ritonavir Form II before and after seeded growth [ilevbare2012c R4].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
ilevbare2012cseeds; after growth none; Pn-IPAAmd44.4/5.8 = 7.7; 8.8; 4.4reproduces (7.66, 8.84, 4.42) [ilevbare2012c E7]
ilevbare2012bafter growth with CAP Adp 0.8554.0/10.5printed 5.2, recomputed 5.14 [ilevbare2012b E15, X5]
ilevbare2012aS 7.6 and 15.4, with and without polymer4.8–12.1printed 5.2 against 5.1 recomputed for the CAP Adp 0.85 sample; the other eight rows reproduce ilevbare2012a E5, X14
elkhabaz2021atazanavir needles from four medialength / width by SEM12.4 ± 7.4 to 83 ± 32 elkhabaz2021 E4, R21

Where it fails or is disputed

The text of the binary-additive paper gives 7.7 for the seeds grown without polymer at S 7.6, but Table 4 gives 8.8 after growth and 7.7 before ilevbare2012a X2. The means have wide, overlapping spreads, and lengths with polymer after growth are not below the seed length, so the ratio falls through width ilevbare2012a X9.

Concepts

crystal habit. Findings. F12, F42.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

Barandiaran-Colmenero critical cooling rate

Expression

\ln(\text{rate}) = A - \frac{B}{(\Delta T)^2},\quad \Delta T = T_m - T_{crys,max} [baird2010 E1];

R_{crit} = \exp(A) [baird2010 E2; baird2013 E1], with A the intercept of \ln(\text{cooling rate}) regressed on 1/(\Delta T)^2 [baird2013 E3].

Variables and units

symbolmeaningunits
\text{rate}cooling rateK min⁻¹ [baird2010 E1]
\Delta Tundercooling at the crystallization peak on cooling, T_m - T_{crys,max}K [baird2010 E1; baird2013 E4]
A, Bintercept and slope of the regressionB in K² [baird2010 E1]
R_{crit}critical cooling rate, ΔT extrapolated to infinityK min⁻¹ [baird2010 E2; baird2013 E1]

Assumptions and valid domain

Undercooling must rise by an experimentally significant amount with cooling rate [baird2010 E1]; a higher cooling rate must lower the crystallization temperature [baird2013 C17]. Fitted over 5–20 °C/min [baird2010 R13] and over about 5 to above 500 °C/min [baird2013 X16].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
baird2010Rcrit of 19 class I moleculesr² 0.74–0.99 for 7 and below 0.55 for 12; Rcrit from 20 K/min (haloperidol) upwardreproduces (carbamazepine B 701 against 708, A 4.75 against 4.8; haloperidol \exp(3.0) = 20.1) [baird2010 R13, E1, E2]
baird2013Rcrit,cool of class I-A from 5–800 °C/min2.7 × 10³ (phenacetin) to 8.1 × 10³ K/min (4-biphenylmethanol), r² 0.89–0.99reproduces for phenacetin; haloperidol 6.6 × 10³ does not follow from A = 6.5 (6.65 × 10²); felbinac not reproducible [baird2013 R7, X2, X13]

Where it fails or is disputed

Over 5–20 °C/min the estimates contradicted experiment: haloperidol and phenacetin, with the lowest estimates, crystallized on liquid-nitrogen quench, whereas carbamazepine and griseofulvin, with higher estimates, quenched amorphous [baird2010 C21]; the approach "may be of limited utility" for organic molecules [baird2010 C20], and accurate estimates need rates far below Rcrit and spanning several orders [baird2010 R31, C22]. A wider rate range seems to improve fits [baird2013 C20], but the method is clearly inappropriate where undercooling rises and falls with rate (benzamide, lidocaine, indoprofen) [baird2013 C16]. Knowing that Rcrit,cool exceeds 500 °C/min is "probably sufficient" for pharmaceutical use [baird2013 C21].

Concepts

Barandiaran-Colmenero method, critical cooling rate, degree of supercooling, glass-forming ability. Findings. F11.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

Burger-Ramberger heat-of-fusion rule

Expression

Not printed in either paper: applied in words from the relative melting points and enthalpies of fusion [trasi2014b E2]; named as the heat-of-fusion rule lu2016 E3.

Variables and units

symbolmeaningunits
T_m of each formmelting points of the two polymorphs°C [trasi2014b M1, R6; lu2016 R20]
\Delta H_{fus} of each formenthalpies of fusion of the two polymorphsJ/g [trasi2014b R6]; kJ/mol lu2016 R20

Assumptions and valid domain

None stated beyond the citations (refs 19 and 28) [trasi2014b E2; lu2016 E3]. The rule relates the order of melting points and enthalpies of fusion to monotropy or enantiotropy lu2016 E3.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
trasi2014bnilutamide stable form against form Istable Tm about 153 °C, about 98 J/g; form I 141 °C, about 66 J/g; monotropicnamed only [trasi2014b E2, M1, R6, C11]
lu2016vemurafenib α against βα 271 °C, 53.8 kJ/mol; β 248 °C, 33.3 kJ/mol; monotropicnamed only lu2016 E3, R20, C50

Where it fails or is disputed

The vemurafenib α enthalpy differs between places in the paper (51.0, 53.8, 55.9) lu2016 X1, though the order of the two forms does not change. For vemurafenib the Hoffman curves give a virtual transition at 319 °C, above both melting points, which supports monotropy lu2016 C51. The nilutamide free energy difference of about 3.4 kJ/mol rests on a relation that is not printed [trasi2014b X13].

Concepts

Burger-Ramberger rules, monotropy, polymorphism. Findings. F7.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

Cabral critical cooling rate

Expression

R_{crit} = \exp\left(A^* - \frac{B^*}{T_m^2}\right) [baird2010 E3];

R_{crit} = \exp\left[A^* - \frac{B^*}{T_m^2}\right] [baird2013 E2].

Variables and units

symbolmeaningunits
A^*, B^*the intercept and slope of the Barandiaran–Colmenero regressionB* in K² [baird2010 E3; baird2013 E2]
T_mmelting pointK [baird2010 E3; baird2013 E2]
R_{crit}critical cooling rateK min⁻¹ [baird2013 E1]

Assumptions and valid domain

The undercooling is restricted to 0 to Tm − Tg instead of being extrapolated to infinity [baird2010 E3]; otherwise as for the Barandiaran–Colmenero form [baird2013 E2].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
baird2010second Rcrit estimate for class Igriseofulvin 579 K/min; up to 3.26 × 10⁴ K/min (4-biphenylmethanol)reproduces: 588 \times \exp(-3711/491.15^2) = 579 [baird2010 E3, R13]
baird2013Rcrit,cool of class I-Aphenacetin 2.7 × 10³ K/minreproduces (2.68 × 10³); haloperidol printed 6.5 × 10³ against 6.47 × 10² recomputed [baird2013 E2, R7, X2]

Where it fails or is disputed

For griseofulvin B^*/T_m^2 = 3711/241228 = 0.0154, so the Cabral value is about 1.5% below the Barandiaran–Colmenero value (synthesis, from [baird2010 E3]); the two estimates are nearly equal (carbamazepine 118 and 117 K/min [baird2010 R13]) and share the same failures [baird2010 C20, C21; baird2013 C16].

Concepts

critical cooling rate, Barandiaran-Colmenero method. Findings. F11.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

Cabrera-Vermilyea step pinning

Expression

\frac{V_\rho}{V_\infty} = 1 - \frac{\rho_c}{\rho} alonzo2012 E8

Growth is arrested when the spacing of adsorbed impurity molecules equals 2\rho_c alonzo2012 C9.

Variables and units

symbolmeaningunit
V_ρgrowth rate of a two-dimensional nucleus (step) of radius ρm/s
V_∞step growth rate at infinite radiusm/s
ρ_ccritical radius of a two-dimensional nucleusnm
ρradius of curvature of the step between pinning pointsnm

Assumptions and valid domain

The spacing L of adsorbed impurities does not depend on supersaturation; ρc falls as supersaturation rises, so the maximum effect of an additive falls with S alonzo2012 C9. Not tested numerically in the chapter papers (no use of eq 8 in a calculation).

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
alonzo2012argument for the fall of HPMC's effect with Snoneinputs not printed alonzo2012 E8, C9
ilevbare2012bstep pinning chosen among four mechanismsα 4.35, 1.25argument only [ilevbare2012b C12, E7]
que2018critical radius 5–7 nm against site spacing 10–20 nm at S 88 (ASD dissolution chapter)ρc from γ surrogatesderived que2018 R15, C38
schram2015R_P/R_0 = 1 − ρc/l applied qualitatively to the AFM globule spacingl about 44 nm at pH 3; ρc not estimatedinputs not printed [schram2015 E3, X7]
schram2016V_P/V_0 = 1 − ρc/l with measured l and computed ρcl 68.5 and 15.8 nm; ρc 3.98 nm; V_P/V_0 0.94 and 0.75recomputed; predicts rate ratios of 1.06 and 1.34 against 2.7 and about 12 schram2016 E4, R12, R14, X3

Where it fails or is disputed

The spacing of adsorbed HPMC on felodipine, the quantity the equation needs, was not measured alonzo2012 C28. The model's mechanism is chosen by argument against three others [ilevbare2012b C12]. The arrest criterion is l ≤ ρc in one place and l ≤ 2ρc in another schram2016 X1.

Concepts

step pinning, critical radius of a two-dimensional nucleus. Findings. F9, F10, F23, F24.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

critical cooling rate to avoid nucleation

Expression

R_{Ncrit} \sim \frac{1}{\tau_{Nmin}} [baird2010 E21], with the nucleation time \tau_N = \frac{1}{J_N V} [baird2010 E22].

Variables and units

symbolmeaningunits
R_{Ncrit}critical cooling rate to avoid nucleationnot stated [baird2010 E21]
\tau_{Nmin}minimum nucleation time between Tm and Tgnot stated [baird2010 E21]
J_N, Vnucleation rate and sample volumenot stated [baird2010 E22]

Assumptions and valid domain

An approximation [baird2010 E21]. Glass formation requires cooling faster than the maximum crystallization rate; the minimum nucleation time lies between Tm and Tg, where the driving force rising with undercooling meets the viscosity that restricts diffusion near Tg [baird2010 C49].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
baird2010argument for why nucleation and growth windows decide glass formationnoneinputs not printed [baird2010 E21, E22, C49]

Where it fails or is disputed

No nucleation time or rate was measured [baird2010 E21]. Because τN depends on sample volume [baird2010 E22], the critical rate is not a pure material property (synthesis: from the 1/(J_N V) form).

Concepts

critical cooling rate, nucleation, nucleation temperature zone, glass-forming ability. Findings. F3, F16.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

crystal growth inhibition effectiveness ratio

Expression

The polymer effectiveness ratio for crystal growth inhibition is the growth rate without polymer over the rate with polymer:

E_G=\frac{R_{G,np}}{R_{G,p}}

moseson2020a E2; moseson2021 E1. E_G>1 means the polymer slows growth.

The crystallization-from-solution papers print the same ratio as

E_g = \frac{R_{g0}}{R_{gp}}

[ilevbare2012c E5; ilevbare2012a E3; ilevbare2012b E12; ilevbare2013b E5]. The inverse form R/R_0 = R_{gp}/R_{g0} is used in the Kubota–Mullin model [ilevbare2012b E7].

For the melt growth of two felodipine polymorphs it is printed in words: the bulk growth rate without polymer divided by the bulk rate with 3% PVP, per polymorph and temperature [kestur2013a E2].

Variables and units

symbolmeaningunitids
E_Geffectiveness ratiodimensionlessmoseson2020a E2
R_{G,np}crystal growth rate without polymerµg/s (vessel mass rate)moseson2020a E2, X12
R_{G,p}crystal growth rate with polymerµg/smoseson2020a E2
R_{g0}initial growth rate without polymerµg mL⁻¹ min⁻¹ or µg min⁻¹ilevbare2012a E3
R_{gp}initial growth rate with polymer or additivesameilevbare2012a E3
E_geffectiveness ratio; 3 means growth three times slowerdimensionlessilevbare2013b E5
bulk growth rates (felodipine melt)linear growth rates without and with 3% PVP, read from plotsm/s[kestur2013a E2, R8, R13]

Assumptions and valid domain

Evaluated at the highest seed level (50 µg/mL) at S = 6 for indomethacin; for bicalutamide from seeded growth at 150 µg/mL moseson2020a E2, P20; moseson2021 R5. The growth rates are vessel mass rates not normalised to seed surface area and the extraction method is not printed moseson2020a X12. In the seeded-growth papers a ratio above 1 is taken as effective and below 1 as accelerating; the rate is the slope of the dissolved drug over the first 2 min at fixed seed mass and supersaturation ilevbare2013b C17; ilevbare2012a E3, E4. Tested for ritonavir, celecoxib and efavirenz at 37 °C, pH 6.8, 5 µg/mL polymer. In the felodipine polymorph work it is applied to growth from the supercooled melt at 60–100 °C, not from solution [kestur2013a R15, C28].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
moseson2020aindomethacin with 5 and 50 µg/mL PVPVAE_G 18 and 56reproduces from the figure readings: 0.99 / 0.055 = 18 and 0.99 / 0.018 = 55 moseson2020a R5, E2
moseson2021bicalutamide with PVPVA 70 µg/mL and HPMCAS 1 mg/mLE_G 8.6 and 158inputs not printed (growth rates are in a supplement that was not supplied) moseson2021 R5, E1
ilevbare2012c34 polymers on ritonavir0.83–3.25absolute rates not printed [ilevbare2012c E5, R9]
ilevbare2012bpolymers against S and pH6.40, 2.99, 1.56; 2.98 → 1.12not applicable (definition) [ilevbare2012b E12]
ilevbare2012a14 polymers, 13 pairs, surfactantsup to 12.1; 0.49 for TPGSreproduces (3.6/1.1 = 3.27, printed 3.3) ilevbare2012a E3
ilevbare2013b16 polymers on three drugsup to 12.6reproduces (69.80/11.88 = 5.88, text about 6.0) ilevbare2013b E5
schram2015E_g = R_0/R_P of felodipine with HPMCAS-LF2.29 (pH 6.8), 1.28 (pH 3)slopes not tabulated; end-point estimate gives 2.3 and 1.3 [schram2015 E4, R4]
schram2016same, R_0 of buffer-grown seeds without polymer2.7, 5.5, 8.0, 12.0 with HPMCAS in solution; 1.8, 3.0, 8.4 withoutplot readings schram2016 E5, R2
lu2017aE_G at δ 2.4 and E_C at δ 7.9 or 12.5 for telaprevir with bile saltsE_G 1.0–4.6; STCDC no desupersaturationplot readings [lu2017a E2, E3, R7, R8]
lu2018telaprevir seeds with bile salt mixtures, δ 7.9E_G = R_0/R over the first 10 minSTDC 3.8; STCDC >60; binary-L 35.5; binary-H 7.4; inputs not printed [lu2018 E3, R5]
kestur2013awhether PVP acts in the liquid or at the crystal faces of felodipine forms I and IIform I ≈15.8 → ≈3.5, form II ≈18.7 → ≈6.5 (60 → 100 °C)reproduces from Figs. 2 and 3 for form II and for form I at 90–100 °C, not for form I at 60–80 °C [kestur2013a E2, X7]
kestur2013bsurface against bulk growth of felodipine form I with 3% PVP≈2 (surface), ≈7 (bulk)from the printed rates kestur2013b R12

Where it fails or is disputed

The ratio falls as supersaturation rises, depends on how the seeds were prepared and on the polymer concentration, so values from different systems are not comparable [ilevbare2012b C56; schram2016 C13]. A large ratio in solution does not predict protection against crystallisation in the solid moseson2021 C51. The stated rule (E_g above 1 is effective) does not match the counts of effective polymers or the polymers called ineffective at 1.0–1.4 (cut-off near 1.2 in practice) [ilevbare2013b X3; ilevbare2012c X7]. Rates depend on seed mass, volume and methanol fraction, which are not always printed [ilevbare2012c X16]. A polymer that raises the solubility lowers S and flatters the ratio (F19) ilevbare2013c X7. The reference rate R_0 differs: one seed route in the felodipine seed study and the pH-independent single curve in the 2015 paper [schram2016 E5; schram2015 X3]; rates are not normalised to area schram2016 X12. In the felodipine melt work the error bars of the two polymorphs separate at 90–100 °C, so equality of their ratios holds within about a factor of two [kestur2013a X6].

Concepts

crystal growth inhibition, crystallization inhibition by polymers, crystal seeding, crystal growth rate, polymorphism. Findings. ASD process: F25, F27, F29. Crystallization from solution: F7, F8, F9, F17, F18, F23, F24, F33. Physical stability: F3, F19.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

depth of field of a microscope objective

Expression

As printed in the four nucleation papers:

D_{tot} = \frac{\lambda n}{NA^{2}} + \frac{n e}{M \cdot NA} [konno2006 E1; marsac2006a E1; konno2008 E1; marsac2008a E2]

Variables and units

symbolmeaningunits
D_{tot}total depth of field, used as the sampled thicknessmm (0.0144 mm at 10×) [konno2006 E1]
\lambdawavelength of light550 nm [konno2006 E1]
nrefractive index of the medium1.000 (air) [konno2006 E1]
NAnumerical aperturenot printed [konno2006 E1]
esmallest distance resolved by the detector14 µm [konno2006 E1]
Mlateral magnification10× [konno2006 E1]

Assumptions and valid domain

The counted nucleation sites lie within the depth of field, so the site density per volume follows from the density per area and D_{tot} [konno2008 C38]. Used for birefringent sites of about 1 µm or more in spin-coated films [konno2008 C38].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
konno2006volume nucleation rates of felodipine films0.0144 mm at 10×NA not printed; NA = 0.25 reproduces 14.4 µm [konno2006 E1]
marsac2006anifedipine and felodipine nucleation rates0.0144 mm at 10×same check [marsac2006a E1]
konno2008nucleation at 0–75% RH0.0144 mmsame check [konno2008 E1]
marsac2008anucleation with PVP and water0.0144 mm at 10×; other objectives not givensame check [marsac2008a E2, X10]

Where it fails or is disputed

The 2006 and 2008 felodipine papers describe the conversion as multiplication by D_{tot} where a per-volume density needs division [konno2006 X6; konno2008 C38]. Rates are therefore comparable only within this counting method; the film thickness is not printed [marsac2006a X10; konno2008 X7].

Concepts

nucleation rate, nucleation. Findings. F1.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

flux definition

Expression

J = \frac{dm}{A\,dt} indulkar2016 E11.

The same expression is printed for the side-by-side diffusion cell [indulkar2018 E4; indulkar2019b E4].

Variables and units

symbolmeaningunits
mmass transferredµg
Amembrane area1.77 cm² indulkar2016 P5
Jfluxµg/(h·cm²)
Amembrane area of the side-by-side cell7.07 cm² [indulkar2018 P8; indulkar2019b P3]
Jflux, from the slope of receiver concentration against time with receiver volume and areaµg/(min·cm²) [indulkar2018 R12]

Assumptions and valid domain

Receiver concentration of each interval converted to mass; the outflow is non-cumulative indulkar2016 P10, P5. Sink conditions on the receiver side, so that the flux follows the donor activity; donor at the amorphous or the crystalline solubility of each medium, runs of about 40–60 min without crystallization [indulkar2018 C9, P8, R15].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
indulkar2016Jmax of clotrimazole donors0.720 µg/mL × 1.8 mL/h / 1.77 cm² = 0.732 µg/(h·cm²)reproduces indulkar2016 E11
indulkar2017aatazanavir fluxA 7.07 cm²slopes not printed [indulkar2017a E4]
wilson2018enzalutamide mass flowno flux value printed; the 30 mm orifice would give A = 7.07 cm²not applicable wilson2018 E3, R13, R15
indulkar2018flux at the amorphous solubility of tacrolimus and cilnidipine in three media; ratio to the crystalline flux for atazanavir and ritonavir0.027–0.031 and 0.0014–0.0018 µg/(min·cm²); flux at the crystalline solubility not measurable for these two drugsslopes not printed [indulkar2018 E4, R12, R13]
indulkar2019bsupersaturation at the amorphous solubility of atazanavir in SDS mediastated about 65; no flux values printedinputs not printed [indulkar2019b E4, R2, X6]

Where it fails or is disputed

None found in the Bioperformance papers. For tacrolimus and cilnidipine the flux at the crystalline solubility was below what the method could measure, so the supersaturation ratio could not be formed and equality across media was assumed [indulkar2018 R13, X4].

Concepts

membrane flux, sink conditions. Findings. Bioperformance: F2, F25. Crystallization from solution: F31, F38, F40.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 valueraina2014a 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 B. Supersaturation from ASD dissolution

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)°C[saboo2020 E3]
w_1, T_{g1}weight fraction and Tg of indomethacin (53 °C by nanoTA)–, °C[saboo2020 E3]
w_2, T_{g2}weight fraction and Tg of PVPVA (130 °C by nanoTA)–, °C[saboo2020 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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

induction time decomposition

Expression

t_{ind} = t_n + t_g ilevbare2013c E2

t_{ind} \propto J^{-1} ilevbare2013c E3

Both relations are printed in the same form in the celecoxib dispersion papers xie2015 E1, E2; xie2016a E4.

Variables and units

symbolmeaningunit
t_indmeasured induction time, from creating the supersaturation until crystals are detectedmin
t_ntime to form stable nucleimin
t_gtime for nuclei to grow to detectable sizemin
Jnucleation ratem⁻³ s⁻¹

Assumptions and valid domain

The proportionality holds if steady-state nucleation is reached quickly and t_n \gg t_g; nuclei are detectable only after growth ilevbare2013c C14, E2. The relation was not tested for the three drugs or the polymers ilevbare2013c X14. In the celecoxib papers the proportionality is stated as an assumption ("If it is assumed") xie2015 C41; the onset is read from the abrupt rise of extinction at 350 nm together with the fall of absorbance at 249 nm xie2016a C9.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
ilevbare2013creading polymer effects on induction time as nucleation-rate effectsinduction times about 2.4–855.5 mininputs not printed ilevbare2013c E2, E3
xie2015celecoxib dispersions (ASD dissolution chapter); celecoxib 22 µg/mL with 5 µg/mL polymers, pH 6.8, 37 °Cdecomposition printed as E1; proportionality as E2; induction within 5 min without polymer, ≈1 h PVP-K12, ≈2 h PVP-K29/32, more than 8 h HPMCAS, HPMCprinted xie2015 E1, E2; no t_n or t_g printed xie2015 E1, R1
xie2016acelecoxib with PAA and cellulose derivatives; with HPMCASdecomposition printed; 960 min taken as the induction time with HPMCAS, an underestimateprinted xie2016a E4; no component times printed xie2016a E4, C39
chen2015t_ind = t_n + t_g, not separated11 drugsprinted chen2015 E1, C5
li2016asame, with t_n >> t_g assumedthree drugs, 13 bile saltsprinted in words [li2016a E4]
mosqueragiraldo2016T_ind = T_n + T_growthtelaprevir, 26 polymersprinted [mosqueragiraldo2016 E1]
lu2017t_ind = t_n + t_g, read as nucleation when t_n dominatestelaprevir, six bile saltsprinted lu2017 E3, C9
trasi2015t_j = t − t_g with t_g fittedacetaminophen: t_g 7.8–928 sfitted [trasi2015 E4, R3]
indulkar2018lecithin, bile salt and SIF media, four drugsinduction time as first scattering rise; components not separatednot applicable [indulkar2018 E5]
lu2018telaprevir in bile salt mixtures and complete mediat_{ind} = t_n + t_gnot applicable [lu2018 E2]
indulkar2019batazanavir in SDSadditive may act on either partnot applicable [indulkar2019b E5, C29]
enright2020atazanavir in phospholipid-digest and volunteer mediaprinted in wordsnot applicable [enright2020 E1]
elkhabaz2021atazanavir, posaconazole in six mediaT_{ind} = T_{crit} + T_{grow}, read as nucleation onsetnot applicable elkhabaz2021 E1
que2018unseeded paclitaxel at S ≈88 with and without 20 µg/mL HPMCASwithin 6 min against more than 16 hno component times printed; growth on seeds continued in the same system que2018 R3, C30

Where it fails or is disputed

A polymer that slows early growth also lengthens t_{ind}, and for strong inhibitors the extinction rises above the baseline before the fitted onset (about 25 against 31.5 min; about 180 against 260 min), so values depend on where the lines are drawn ilevbare2013c X14, R6. The detection method changes the time (SHG earlier than a probe ratio) jackson2014 R25. The seeded and unseeded comparison shows that for STC and SGC the nucleation part dominates but for STCDC and SGCDC growth does [lu2017 R10; lu2017a R14, C37]; in the acetaminophen study the induction time is the time to massive nucleation [trasi2015 C32]. In the SDS study crystal size and agglomeration change across the same threshold as the induction time, so a change in the growth term cannot be excluded [indulkar2019b X7, X5]. Neither celecoxib paper separates t_n from t_g xie2015 E1; xie2016a E4 (synthesis: growth was slowed about 70-fold with HPMCAS xie2016a R12, so part of the longer induction time may come from t_g). For paclitaxel the polymer that lengthened the unseeded induction time beyond 16 h only slowed growth on seeds, so the induction time of an unseeded test says little about a dispersion that carries crystals que2018 R3, R14.

Concepts

nucleation induction time, nucleation rate, nucleation inhibition. Findings. Crystallization from solution: F3, F5, F13, F14, F27, F28, F29, F31, F32, F33, F35, F38, F39. Supersaturation from ASD dissolution: F4, F6, F20, F22.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

initial growth rate from the desupersaturation slope

Expression

R_g = \text{slope of } C \text{ against } t \text{ over the first 2 min} ilevbare2012a E4

C_t = -R_g\,t + b ilevbare2013b E8

Variables and units

symbolmeaningunit
R_ginitial bulk crystal growth rateµg mL⁻¹ min⁻¹ or µg min⁻¹
C, C_tdissolved drug concentration or amount (in 50 mL) at time tµg/mL or µg
ttime after seedingmin
bintercept (starting amount)µg

Assumptions and valid domain

Desupersaturation reflects growth of the seeds, and the curve is linear over the first 2 min ilevbare2012a C14; ilevbare2013b E8. For felodipine the slope is taken over 5 min alonzo2012 P4. Tested for ritonavir, celecoxib and efavirenz at 37 °C and felodipine at 25 °C.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
ilevbare2012aritonavir growth rates and ratios1.56 µg mL⁻¹ min⁻¹ at 10 µg/mL (text), about 1.4 (figure)concentration–time curves not printed ilevbare2012a E4, X5
ilevbare2013bcelecoxib at 10 µg/mL, no polymer and with CA 320S Sub 0.63−69.80 t + 487.46; −11.88 t + 482.40 µgreproduces (≈488 to ≈348 µg in 2 min gives ≈70 µg min⁻¹) ilevbare2013b E8, R8
schram2015slope of concentration against time over 1 h taken as the growth ratefelodipine S 8[schram2015 C5, E4]
lu2017ainitial slope over 30 min (δ 2.4) or 10 min (higher δ), in µg/min for 50 mL5.4, 58.6, 89.2 µg/min in bufferplot readings; per vessel [lu2017a R2, X12]

Where it fails or is disputed

The same no-polymer condition gives 71.0, 69.80 and about 68 µg min⁻¹ in three places of the celecoxib paper, outside the printed standard deviations ilevbare2013b X7. At near-amorphous-solubility concentrations the slope may include secondary nucleation or a drug-rich phase [ilevbare2012b X18]. Seed mass, volume and methanol fraction are often not printed [ilevbare2012c X16].

Concepts

desupersaturation, crystal growth rate. Findings. F5, F7, F23, F33.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

Kubota-Mullin impurity effectiveness factor

Expression

\alpha = \frac{\gamma\,a}{k\,T\,(\ln S)\,L} alonzo2012 E7

Reading of α: α about 1 means the average spacing l of adsorbed impurities is 2\rho_c at full coverage; α above 1 means l < 2\rho_c [ilevbare2012b E13].

Variables and units

symbolmeaningunit
αimpurity effectiveness factordimensionless
γsurface excess energyJ/m²
asurface area occupied by one crystallizing moleculem²
k, TBoltzmann constant; temperatureJ/K; K
Ssupersaturation ratio (ln S kept in place of S − 1)dimensionless
Lseparation of sites available for impurity adsorptionm

Assumptions and valid domain

ln S is used because the supersaturations are not low enough for S − 1; L does not depend on supersaturation alonzo2012 C7, C9. γ, a and L were not given alonzo2012 C27.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
alonzo2012the a priori prediction that α falls as S risesα 0.7 → 0.2 between S 3 and 12 (eq 7 predicts α proportional to 1/ln S, a 2.3-fold fall; the end values differ 3.5-fold)inputs not printed alonzo2012 E7, R9, X3
ilevbare2012bα interpretation at pH 6.8 and 3.84.35; 1.25not applicable (definition) [ilevbare2012b E13]

Where it fails or is disputed

α is not monotonic in S in the felodipine data (0.4 at S 8, 0.6 at S 10), and runs at S 3, 8 and 12 are single measurements alonzo2012 X3.

Concepts

impurity effectiveness factor, step pinning. Findings. F9, F10.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

Kubota-Mullin model

Expression

\frac{R}{R_0} = 1 - \alpha\,\theta_{eq} [alonzo2012 E5; ilevbare2012b E7]

A model of growth inhibition by an adsorbed impurity based on step pinning: the growth rate with impurity relative to that without falls linearly with the surface coverage, where α is an effectiveness factor that depends on the surface energy, the molecular area, the supersaturation and the spacing of adsorption sites, \alpha = \gamma a/(kT\,(\ln S)\,L) [alonzo2012 E5, E7; ilevbare2012b E7]. It was developed for inorganic systems; Alonzo and co-workers state that, to their knowledge, it had not been used for polymers on organic pharmaceutical crystals alonzo2012 C10. The authors extend its proportionality between step, face and mass growth-rate ratios to bulk de-supersaturation rates alonzo2012 C4, E4. Both felodipine–HPMCAS papers print V_P/V_0 = 1 - \rho_c/l and apply it to AFM spacings: with l 68.5 nm and ρc 3.98 nm it gives 0.94, and with l 15.8 nm it gives 0.75, against measured rate ratios of 2.7 and about 12 [schram2015 E3; schram2016 E4, R12, R14, X3]. (This page also holds the former concept page "Kubota-Mullin model", whose content is about the same equation.)

Variables and units

symbolmeaningunit
R, R_0overall mass growth rate with and without polymerµg mL⁻¹ min⁻¹
αimpurity effectiveness factordimensionless
θ_eqequilibrium surface coverage by adsorbed polymerdimensionless

Assumptions and valid domain

Langmuir-type adsorption (isotherm fit, here shifted by hand for felodipine); the proportionality between step, face and overall mass growth-rate ratios extends to bulk de-supersaturation rates; constant seed surface area and face-area ratios; applies only below the kinetic roughening transition [alonzo2012 C4, C5, C6, C23; ilevbare2012b E7]. How the parameters are obtained: seeded growth rates with and without polymer at several polymer concentrations give R/R_0; the coverage \theta_{eq} comes from an adsorption isotherm fit (modified Langmuir, Langmuir–Freundlich); α is chosen so that the line fits the measured ratios at one supersaturation [alonzo2012 P9; ilevbare2012b P11, E6].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
alonzo2012felodipine with HPMC at S 8α 0.4 (text, table) or 0.45 (Fig. 5 caption)reproduces with 0.45: 1 − 0.45 × 0.631 = 0.716 against 0.71 plotted; mismatch with 0.4 alonzo2012 E5, X1
alonzo2012felodipine with HPMC, α at S 3, 5, 8, 10, 120.7, 0.5, 0.4, 0.6, 0.2 (25 °C)as printed alonzo2012 R9
alonzo2012plateaus of R/R00.65 (S 5) and 0.55 (S 10) quotedmismatch: 1 − α at θ = 1 from Table 1 gives 0.5 and 0.4 alonzo2012 E5, X2
ilevbare2012britonavir with CAP Adp 0.85, σ 0.99, 37 °Cα = (1 − 0.80)/0.16 = 1.25, θ 0.16, R/R0 0.80 (pH 3.8); α = 1/0.23 = 4.35, θ 0.23, R/R0 0 (pH 6.8)reproduces [ilevbare2012b E7, R16]
ilevbare2012b, alonzo2012reading of αα about 1: adsorbed molecules one critical-nucleus diameter apart at full coverage; above 1: closer, so growth can stop below full coverageinterpretation [ilevbare2012b E13; alonzo2012 C25]
schram2015R_P/R_0 = 1 − ρc/l with l the globule spacingpH 3 l 44 nmqualitative [schram2015 E3, C18]
schram2016same with measured spacing and critical radius, HPMCAS on buffer-grown and dispersion-grown felodipine seeds (S 4, 25 °C); see the pinning formulal 68.5 and 15.8 nm; ρc 3.98 nm; predicted rate ratios about 1.06 and 1.34recomputed schram2016 E4, R12, R14, X3

Where it fails or is disputed

α at pH 6.8 was derived from the point it is compared with and is a lower bound; the low-concentration points disagree (0.44–0.09 measured against 1.00–0.96 calculated) [ilevbare2012b X8, R15]. The coverage of the felodipine fit is model-dependent alonzo2012 X12. The model was not tested above σ_c [ilevbare2012b X11]. With the printed l and ρc the model gives much smaller effects than measured schram2016 X3. The felodipine α at S 8 is 0.4 in text and table and 0.45 in the Fig. 5 caption; the plateaus quoted "from the alpha estimates" do not follow from Table 1; the coverage was shifted by hand alonzo2012 X1, X2, X12. The ln S in eq 7 replaces the low-supersaturation approximation S − 1 of the original alonzo2012 C7. The arrest criterion is stated as l ≤ ρc and as l ≤ 2ρc, and ρc was not estimated in the 2015 paper [schram2016 X1; schram2015 X7].

Concepts

impurity effectiveness factor, surface coverage; based on step pinning; related to polymer adsorption. Related formulas. Kubota-Mullin impurity effectiveness factor, Langmuir-Freundlich isotherm, proportionality of step velocity and growth rate ratios. Findings. Crystallization from solution: F9, F10, F11, F23, F24.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

linear crystal growth rate from size-time slope

Expression

Printed in words: the growth rate is the slope of the straight line fitted to the linear region of a crystal size–time plot, and the same rule gives an overall crystallization rate from the linear part of a % crystallinity–time plot kestur2013b E2. Printed in words in a growth-rate survey of the library: the slope of crystal length against time [trasi2014b E1]. In symbols (synthesis):

G = \frac{\Delta L}{\Delta t}

Printed in words in two later papers: growth rate as the slope of spherulite size against time sato2015 E1; slope of crystal diameter against time [sato2016 E3].

Variables and units

symbolmeaningunits
Glinear (radial or diameter) growth ratem/s or µm/s [kestur2013b E2; trasi2014b E1]
Lcrystal size (radius, diameter or length)m or µm [trasi2014b E1]
ttimes [trasi2014b E1]
crystallization slope% crystallinity per unit time, printed as day⁻¹ or h⁻¹kestur2013b E2, X4

Assumptions and valid domain

Size grows linearly with time; for powders, the early and late stages are each linear kestur2013b E2. At low temperature the radius change can be taken from the percentage of area crystallized instead [trasi2014b E1].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
kestur2013bform I growth at the free surface and in the bulk, 30 °C2.7 × 10⁻⁹ and 0.47 × 10⁻⁹ m/s; 1.45 × 10⁻⁹ and 6.37 × 10⁻¹¹ m/s with 3% PVPsingle values, no uncertainty kestur2013b R12, X11
kestur2013bearly and late crystallization slopes of powders0.905 and 0.072 day⁻¹ (size 1); 0.43 and 0.03 day⁻¹ (size 2)reproduces 0.90 day⁻¹ from plot readings; fitted range not printed kestur2013b R14, E2
kestur2013bearly slope, pure drug against 3% PVP2.21 against 0.037 h⁻¹; 1.41 against 0.018 h⁻¹PVP values equal Table 2 divided by 24 kestur2013b R15, X4
trasi2014b (outside)radial growth of nilutamide and other drugsrates per temperatureinputs not printed [trasi2014b E1]
sato2015growth of ATP enantiomers with five polymerssize–time lines through the origin, e.g. at 60 °C with HPMCAS-HFlinear in time sato2015 R4, R7, R8
sato2016growth of six compounds with PHBdiameter rates; griseofulvin with 5% PHB about tenfold faster at 120 °Cdiameter rate = 2 × radial rate [sato2016 R5, R6, X8]

Where it fails or is disputed

The flutamide growth paper reports diameter rates, the acetaminophen paper radial rates, a factor of two apart [trasi2012b R3; trasi2012a R6]. A ratio of powder slopes (% per day) is not the same quantity as a ratio of film growth rates (m/s), although the two were compared kestur2013b X6. The PHB paper takes diameter slopes, twice the radial front speed [sato2016 X8].

Concepts

crystal growth rate, nucleation and crystal growth, surface-enhanced crystal growth. Findings. F3, F17, F18, F21, F27, F28.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

linear fit of melt viscosity on Tm − Tg

Expression

y = -0.0028\,x + 0.3989,\quad R^2 = 0.7368 [trasi2014a E6].

Variables and units

symbolmeaningunits
yviscosity at TmeltPa·s [trasi2014a E6]
xT_m - T_gK [trasi2014a E6]

Assumptions and valid domain

None stated [trasi2014a E6]. Fitted on the 17 compounds with a melt viscosity cited from the 2012 viscosity study, Tm − Tg about 85–146 [trasi2014a R9].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
trasi2014ashowing that slow growers have high melt viscosity and small Tm − Tgslow group at 85–117 with 0.0703–0.191 Pa·s; fast group at 121–146 with 0.0136–0.0513 Pa·sreproduces: slope −0.00277, intercept 0.3991, R² 0.7369 [trasi2014a E6, R9]

Where it fails or is disputed

The authors describe a trend "with considerable scatter" [trasi2014a C26]; three group 2 compounds fall among group 1, explained by fragility and complexity that were not measured [trasi2014a C29, X18]. One Tm − Tg value in the source table does not match its own Tm and Tg [trasi2014a X1]. The fit reaches zero at x = 0.3989/0.0028 = 142.5 K and gives −0.0099 Pa·s at x = 146 (0.3989 - 0.0028 \times 146), so it is not usable at the upper end of its own data (synthesis, from [trasi2014a E6, R9]).

Concepts

melt viscosity, Tm − Tg temperature gap, crystal growth rate. Findings. F5.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

linear fit of normalized growth rate on melting entropy

Expression

y = -0.6\,x - 0.95,\quad R^2 = 0.61 [trasi2014a E7].

Variables and units

symbolmeaningunits
y\log(U_{kin}\,\tau_\alpha/a), growth rate corrected for driving force and normalized by relaxation time and molecular sizedimensionless [trasi2014a E7, E2, E4]
x\Delta S_m/Rdimensionless [trasi2014a E7]

Assumptions and valid domain

None stated [trasi2014a E7]; τ_α is taken from viscosity as \tau_\alpha = \frac{C\eta}{G} [trasi2014a E4], which assumes Stokes–Einstein behaviour away from Tg [trasi2014a C20, C21]. Nine compounds with viscosity–temperature data [trasi2014a R11].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
trasi2014atesting whether melting entropy explains growth differences at equal mobilityslope −0.6, intercept −0.95, R² 0.61reproduces from the nine plotted points: slope ≈ −0.61, intercept ≈ −0.91, R^2 \approx 0.61 [trasi2014a E7, R11]

Where it fails or is disputed

The decrease follows expectation but with "considerable scatter"; entropy "certainly plays a role" while other factors, possibly interactions in the melt and at the interface, are not accounted for [trasi2014a C32].

Concepts

entropy of fusion, crystal growth rate, melt viscosity. Findings. F6.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

mass flow rate from receiver concentration slope

Expression

J = \frac{dC_r}{dt}\times V_r with V_r the receiver volume; printed in words raina2014a E11; mosqueragiraldo2018b E2.

Variables and units

symbolmeaningunits
dC_r/dtslope of the linear region of receiver concentrationµg/mL per min
V_rreceiver volume30 mL raina2014a P9; 32 mL mosqueragiraldo2018b E2
Jmass flowµg/min

Assumptions and valid domain

Sink receiver, linear region, time window chosen after the donor maximum (and before crystallization for PVPVA) mosqueragiraldo2018b P4.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
raina2014afelodipine and nifedipine flux2 µg/mL: about 0.0004 µg/mL/min × 30 mL ≈ 0.012 µg/minreproduces from plot reading raina2014a E11
mosqueragiraldo2018btelaprevir mass flowwindows 10–60 to 800–1000 minslopes not printed mosqueragiraldo2018b E2, X18
hate2022PAMPA mass flow of five drugsslope of receiver concentration against time up to 90 min, normalized by volume, in µg/mininputs not printed [hate2022 E2]

Where it fails or is disputed

One paper cites it as "Eq. (8)", which is the free energy of mixing raina2014a X2. Time windows differ between systems mosqueragiraldo2018b X18.

Concepts

membrane flux. Findings. F2, F7, F9, F21, F22.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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/mLalonzo2010 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/mL[indulkar2019a E1, E2; purohit2017b E3]
C_b, C, C_t, xdrug concentration in the bulk medium at time tµg/mL[indulkar2017b 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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 citednguyen2023c 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 B. Supersaturation from ASD dissolution

power-law crystal growth rate

Expression

R_G = k_G\,A\,(C_b - C^{*})^{g} purohit2018 E3. The log-linearised fit \log(dC/dt) = n\log(S-1) + \text{intercept} is printed for tacrolimus seeds, with n = 1.677 hate2019 E5.

In supersaturation-ratio form, with its linearisation, and against the logarithmic supersaturation:

R_G = k_G\,S^{g} alonzo2012 E2;

\ln R_G = \ln k_G + g\,\ln S alonzo2012 E3;

R_G = k_g\,\sigma^{g} [ilevbare2012b E3].

Variables and units

symbolmeaningunits
R_Gcrystal growth rate–
k_Ggrowth rate coefficientnot determined
Acrystal surface areanot determined
C_b, C^*bulk concentration, crystal solubilityµg/mL
goverall growth order, typically 1 to 2–
R_G (supersaturation form)overall crystal growth rateµg mL⁻¹ min⁻¹ alonzo2012 E2
k_ggrowth rate constant against σas R_G [ilevbare2012b E3]
S, \sigmasupersaturation ratio and its logarithmdimensionless

Assumptions and valid domain

Empirical purohit2018 E3; g = 1 for diffusion control and 2 for integration control in the felodipine–HPMC study alonzo2012 E2, E3. k_G depends on temperature, crystal–solution velocity and impurities but not on supersaturation alonzo2012 C3, C35. Fitted over S 3–12 for felodipine; not fitted for ritonavir [alonzo2012 P8; ilevbare2012b E3].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
purohit2018why 450 mL shows growth and 900 mL notnone fittedinputs not printed purohit2018 E3, C52, C55
alonzo2012growth order of felodipine without and with HPMCg 1.50 ± 0.04; 1.97 ± 0.12; \ln k_G −4.24; −5.42 to −5.86; with HPMC kG about 0.0032, g 2, S 5: RG about 0.080reproduces (1 µg/mL HPMC, S 5: 0.080 against 0.087 µg mL⁻¹ min⁻¹ in Fig. 3) alonzo2012 E2, E3
hate2019tacrolimus on seedsdC/dt = k_g A (C_{in}(0) - C^*)^n with constant area; fit y = 1.677x - 3.136, R² 0.9896E4 reproduces (1.17 × 10⁻⁴ × (25 − 2.5)^1.7 = 0.0233 µg/mL/s); E5 mismatch: printed growth constant 1.17 × 10⁻⁴ "cm/s", 10^(−3.136) = 7.31 × 10⁻⁴ or 1.57 × 10⁻⁴ after dividing by C*^n hate2019 E4, E5, R18, X3
ilevbare2012bgrowth against σ; linear above σ_cno k_g or g reportednot applicable [ilevbare2012b E3]
schram2015R_G = k_G S^g, held at fixed disc speedS 8; no k_G or g reportednot fitted [schram2015 E2, X7]
schram2016R_G = A k_G S^g, area factor in the argument against area as the causeS 4; no k_G or g reportednot fitted schram2016 E2

Where it fails or is disputed

No growth constants were determined for tacrolimus in the dissolution study purohit2018 E3; the absorptive study fitted an order and a constant from seeded runs. The x-axis of the tacrolimus fit is log(C − C*) rather than the log(S − 1) it is labelled with, and the crossover with absorption near S 18.5 rests on a constant crystal area (F29) hate2019 X2, X16. The k_G values come from fits with different fixed orders (1.5 without HPMC, 2 with), so they should be compared at equal S alonzo2012 X8. Above the critical supersaturation the ritonavir rate is linear in σ, not a power law with order 2 [ilevbare2012b R11, R12]. The rotating-disc papers of 2015 and 2016 report neither order nor coefficient [schram2015 X7; schram2016 E2].

Concepts

crystal growth, crystal seeding, crystal growth rate, integration-controlled crystal growth, kinetic roughening. Findings. Bioperformance: F12, F16, F29. Crystallization from solution: F9, F10, F23, F24.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

relative nucleation rate from seeded and unseeded induction times

Expression

\frac{R}{R_0} = \frac{t_{s,0}}{t_s} alonzo2012 E9

\frac{J}{J_0} = \left(\frac{t_s}{t_{s,0}}\right)^{3}\left(\frac{t_{u,0}}{t_u}\right)^{4} alonzo2012 E10

\frac{J}{J_0} = \left(\frac{R_0}{R}\right)^{3}\left(\frac{t_{u,0}}{t_u}\right)^{4}, \qquad E_J = \frac{J_0}{J} [lu2017 E4; lu2017a E4, E5]

With the polymer case in the denominator:

\frac{J_0}{J_p} = \left(\frac{R_p}{R_0}\right)^{3}\left(\frac{t_{u,p}}{t_{u,0}}\right)^{4} xie2016a E6

Variables and units

symbolmeaningunit
J, J_0nucleation rate with and without inhibitorm⁻³ s⁻¹
t_s, t_s,0seeded induction times with and without inhibitormin
t_u, t_u,0unseeded induction times with and without inhibitormin
R/R_0seeded growth-rate ratio, used for t_{s,0}/t_sdimensionless
J_0, J_pnucleation rate without and with polymerm⁻³ s⁻¹
R_0, R_pmass growth rate without and with polymer, from seeded desupersaturation slopesµg/(mL min)
t_{u,0}, t_{u,p}unseeded induction times without and with polymermin

Assumptions and valid domain

Seeded and unseeded runs under identical conditions; the seeded induction-time ratio is replaced by the growth-rate ratio of the de-supersaturation curves (Verdoes 1992, outside the library) alonzo2012 C11, E9. Used for one drug, one polymer level and one supersaturation. For celecoxib R_0 is the slope of the linear region over the first 5 min without polymer; R_p is, for simplicity, the slope over the whole 16 h with HPMCAS xie2016a C38. t_{u,p} = 960 min because no sharp slope change was seen, which underestimates the induction time xie2016a C39.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
alonzo2012felodipine, 1 µg/mL HPMC, S 10t_{u,0} 15.3 min, t_u 136.5 min, R/R_0 0.607; J/J_0 = 7.05 × 10⁻⁴reproduces: 7.06 × 10⁻⁴ with 1.647; 7.00 × 10⁻⁴ with the printed 1.643 alonzo2012 E10, X6
xie2016acelecoxib with HPMCAS (ASD dissolution chapter): 22 µg/mL with 5 µg/mL HPMCAS, pH 6.8, 37 °Ct_{u,p} 960 min, R_0/R_p = 70; J_0/J_p about 4,000derived xie2016a R13; reproduces with t_{u,0} = 5 min from the text: (1/70)^{3}(960/5)^{4} = 3962; the t_{u,0} used by the authors is not printed xie2016a E6, R13
lu2017telaprevir, 1.86 mM STC and SGC, δ 11.5; t_u,0 about 30 min, t_u 960 minJ/J_0 2.5 × 10⁻³ and 2.9 × 10⁻⁶recomputed 2.58 × 10⁻³ and 3.06 × 10⁻⁶ lu2017 E4, R10, X1
lu2017asame with bile salts at 1.86 and 12 mM; rate ratio set to 100 for STCDC and SGCDCE_J about 360 to 3 × 10⁵; about 1 for STCDCreproduced for the 1.86 mM values [lu2017a E4, E5, R14]

Where it fails or is disputed

Rests on one pair of induction times with no stated uncertainty entering to the fourth power; a 10% change in t_u changes J/J_0 about 1.5-fold alonzo2012 X7. The exponents are not derived in the paper. The induction times enter capped at 960 min, so E_J is a bound; the rate ratios used are the δ 12.5 values while the text speaks of growth; the 12 mM inputs are not printed [lu2017 X2; lu2017a X13, X14]. For celecoxib the slopes and t_{u,0} are not printed, and R_p was taken over 16 h while the figure covers 4 h, so the ratio cannot be reproduced from the printed data xie2016a X8. With t_{u,p} capped at 960 min the ratio is a lower bound xie2016a C39, C40. t_{u,0} enters to the fourth power (synthesis: with t_{u,0} of 4 or 6 min the ratio is about 9,700 or 1,900).

Concepts

nucleation rate, nucleation inhibition, crystal growth inhibition. Findings. Crystallization from solution: F5, F6, F20, F32, F33. Supersaturation from ASD dissolution: F5.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 °C[indulkar2017a 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 B. Supersaturation from ASD dissolution

supersaturation factor

Expression

SF = \frac{A + B}{A} [hsieh2012 E10]

SF = \frac{AUC_{sp}}{AUC_{s}} ilevbare2013c E8

A measure of the extent and duration of supersaturation in one number: the area under the concentration–time (or supersaturation–time) profile divided by the area under the equilibrium-solubility line, SF = (A + B)/A in the pH-titration paper and SF = AUC_{sp}/AUC_{s} over 240 min in the induction-time paper [hsieh2012 E10, E9; ilevbare2013c E8]. A value of 1 means a saturated solution. (This page also holds the former concept page "supersaturation factor", whose content is about the same expression.)

Variables and units

symbolmeaningunit
A + Barea under the whole concentration–time profile (Fig. 2b of the titration paper)µg min mL⁻¹
Aarea under the equilibrium-solubility linesame
AUC_sparea under the supersaturation–time curve to 240 minmin
AUC_sthe same area for a saturated solution (S = 1)min

Assumptions and valid domain

Areas by numerical integration; in the induction-time paper to 240 min; the titration version has no stated start and end criterion for the duration [hsieh2012 X5; ilevbare2013c E8]. Numerical integration of the profile: from the titration neutral concentration against time for the weak bases, from the supersaturation–time curve of the celecoxib run for the induction-time study [hsieh2012 R3; ilevbare2013c R16].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
hsieh2012extent and duration of supersaturation of type 1 bases: bifonazole; dipyridamole; droperidol; papaverine; pyrimethamine (CheqSol, 37 °C)3.0; 4.6; 12.9; 4.8; 2.8inputs not printed (profiles only plotted) [hsieh2012 E10, R5]
ilevbare2013ccelecoxib with 5 µg/mL HPMC, start S 7.3 and S 14.7 (240 min, 37 °C)1745/239.0 = 7.3 (S 7.3 start); 1426/239.0 = 5.97 against 5.9 printedreproduces for 7.3; 5.97 rounds to 6.0 ilevbare2013c E8, R16, X12

Where it fails or is disputed

The two papers define the factor differently (whole profile over the equilibrium area, against a fixed 240 min), and Fig. 2b of the titration paper plots the dipyridamole maximum at 12.9 against 12.5 in the text [hsieh2012 X4]. Because the titration version is the whole-profile area with a peak and a decay and the other the area over a fixed 240 min, the values are not comparable; the duration behind the titration value has no stated start and end criterion [hsieh2012 X5; ilevbare2013c E8]. The y-axis of the celecoxib profile is labelled concentration but shows S ilevbare2013c X13.

Concepts

summarizes supersaturation; related to desupersaturation and to the duration of supersaturation, a quantity without a stated criterion [hsieh2012 R2, X5]. Findings. Crystallization from solution: F1, F14.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

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 B. Supersaturation from ASD dissolution

temperature of maximum crystal growth rate

Expression

T_{cryst,max} \approx 0.94\,T_m [trasi2014a E8];

T(\text{max growth}) \approx 0.94\,T_m, printed in words as Naito's rule lu2016 E2.

The physical-stability papers give about 0.94 Tm [sato2016 E2] and about 0.95 Tm:

T_{max} \approx 0.95\,T_m [tian2017 E3].

Variables and units

symbolmeaningunits
T_{cryst,max}temperature of the maximum crystal growth velocityK [trasi2014a E8]
T_mmelting temperature (of the α-form for vemurafenib)K [trasi2014a E8; lu2016 E2]
T_{max}temperature of fastest growthK, for the ratio [tian2017 E3]

Assumptions and valid domain

A cited empirical observation (ref 26) [trasi2014a E8], a typical value (ref 21) lu2016 E2. The ratio holds only in kelvin: in °C the vemurafenib product would be 254.7 °C instead of 238.4 °C lu2016 E2. The rule refers to the pure drug. With 10% polymer the temperature of fastest growth of indomethacin moved, for α from 135 to 100 °C (HPMC), 110 °C (HPMCAS) and 125 °C (PVP), and for δ to 105–115 °C, so the rule does not give the maximum of a drug–polymer melt [tian2017 R15]. In the PHB paper all growth temperatures were placed below 0.94 Tm to read growth as transport-limited [sato2016 E2, C15].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
trasi2014agrouping 31 drugs by maximum growth rateTcryst,max not tabulated; ΔG and ΔSm columns imply 0.90–0.99 Tminputs not printed [trasi2014a E8, X4]
lu2016expected maximum for α-vemurafenib240 °C predicted against 250 °C observedreproduces: 0.94 × 544.15 K = 511.5 K = 238.4 °C lu2016 E2, R24, C18
sato2016position of measured temperatures below the maximum0.94 Tm above all highest growth temperaturesreproduces [sato2016 E2]
tian2017indomethacin polymorphs≈0.95 Tm, within the 5 °C step of the datareproduces [tian2017 E3]
tian2017maxima of indomethacin polymorphs with and without polymerpure drug 110, 135, 135 °C (δ, α, γ); with polymer 100–130 °Cthe rule holds for the pure drug (row above); with polymer the maximum is lower [tian2017 R15, E3]

Where it fails or is disputed

The 0.94 Tm in the conclusions of the 31-drug study is a cited rule, not a result of that paper [trasi2014a X5]. The observed vemurafenib maximum of 250 °C corresponds to 523.15/544.15 = 0.96\,T_m (synthesis, from lu2016 R12.o, E2). Inhibition ratios rise steeply above the polymer-lowered maximum (indomethacin α with HPMC about 11 at 100 °C and 2900 at 120 °C), so a ratio taken between the two maxima compares growth in different regimes [tian2017 R12, C35].

Concepts

maximum crystal growth velocity, crystal growth rate, degree of supercooling, kinetic versus thermodynamic control of crystal growth. Findings. Crystallization tendency: F1, F2. Physical stability: F3, F28, F29.

← Concepts and formulas

formula · as used in B. Supersaturation from ASD dissolution

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.