Chapter of Solid state stability

Physical stability

Whether an amorphous drug dispersed in a polymer stays amorphous on storage, and why.

What this chapter covers

how a few percent of polymer slows nucleation and crystal growth of the amorphous drug, and why the two steps can respond differently to the same polymer; which drug–polymer contacts make a polymer protective (hydrogen bonds between complementary groups, acid–base pairs) and how an intramolecular bond in the drug limits them; how a chiral polymer can discriminate between enantiomers, how a low-Tg polymer can speed growth, and how polymers act differently on polymorphs and on either side of the temperature of fastest growth; how the polymorph, the free surface and the particle size change crystallization; how surfactants change growth and water-induced separation; how far dispersion Tg, Tg-scaled temperature and bulk mobility measures explain the rankings; how much water dispersions take up and how it plasticizes them; how sorbed water speeds nucleation and growth and splits initially mixed dispersions into drug-rich and polymer-rich amorphous phases, depending on the drug's donor group, its hydrophobicity, the polymer's hygroscopicity and the way water reaches the film; whether a drug-rich phase present from preparation predicts crystallization; which stress conditions can rank polymers; how the manufacturing route can make a marketed product unstable; and what crystallinity gained in storage does to dissolution. The papers of 2006–2014 use felodipine as the main drug, with nifedipine, pimozide, droperidol, indomethacin and ketoprofen as early comparisons, and PVP K29/32, HPMCAS and HPMC as the main polymers konno2006 M1, M2, M3, M4; rumondor2009c M1, M2, M3, M4, M5; the papers of 2010–2014 add quinidine, indoprofen, clofoctol, probucol, nilutamide, loratadine, flutamide, acetaminophen, resveratrol, celecoxib and curcumin, and PVPVA, E100, CMCAB, PAA, simple vinyl polymers and surfactants rumondor2010c M2, M6; rumondor2011 M1, M2, M3, M4, M5; trasi2012b M1; trasi2012a M1; wegiel2013b M1; mosqueragiraldo2014 M1; wegiel2014 M1. The papers of 2015–2022 add the enantiomers of a chiral model compound, PHB with six compounds, indomethacin polymorphs and miscibility limits, celecoxib binaries and ternaries, miconazole and ritonavir films during water uptake, marketed tacrolimus capsules and lumefantrine with acidic enteric polymers sato2015 M1, M2; sato2016 M7; tian2016 M1; tian2017 M1; xie2016b A1; saboo2017 M1; yang2022b M1; trasi2017 M5; trasi2020 A1; bhujbal2021 A1.

29 papers2006–202235 findings

01Findings map

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

Topic 1 · F1–F5, F17–F22, F27–F30

Crystallization of the amorphous drug in dry dispersions

F1A few percent of PVP, HPMC or HPMCAS lowers dry nucleation of amorphous felodipine about a hundredfold, all three alike.moderateF2Nifedipine nucleates faster than felodipine at equal Tg, with or without PVP and water, in line with its larger driving force.moderateF33 wt% PVP slows felodipine crystal growth from the melt 11–21-fold at 70 °C but only 3–6-fold at 110 °C.moderateF4A few percent of polymer barely lowers the driving force for crystallization; the proposed kinetic routes were not measured.weakF5Dispersion Tg, Tg-scaled temperature and bulk mobility measures do not rank polymers or drugs by crystallization rate.strongF17A polymer can slow nucleation and crystal growth of one amorphous drug by very different amounts, even in opposite directions.moderateF18Polymers slow crystal growth roughly in the order of their hydrogen bonding to a free group of the drug.moderateF193% PVP slows two felodipine polymorphs by a similar factor, so the faster-growing form I stays faster.moderateF20A polymer or surfactant can change which polymorph crystallizes from the amorphous drug and can hold a metastable form.moderateF21Free surfaces crystallize faster than the bulk, so small amorphous particles crystallize sooner, and PVP protects the bulk more.strongF22Surfactants that mix with amorphous celecoxib speed its crystal growth, most at low temperature; with PVP the effects do not add.moderateF27HPMCAS slowed one enantiomer of a chiral compound about twice as much as the other; achiral PVP slowed both alike.moderateF285% of the low-Tg polymer PHB sped crystal growth of three high-Tg compounds up to about tenfold, mostly by lowering Tg.moderateF29Each of three polymers slowed indomethacin α far more than γ at high temperature, unlike two felodipine polymorphs.moderateF30Indomethacin dispersions crystallized within days above the drug loading at which a drug-rich phase appeared, and not below it.moderate

02Which paper supports which finding

Show the table of papers and findings
Crystallization of the amorphous drug in dry dispersionsWater uptake by dispersionsEffect of sorbed water on crystallizationIts morphology and what it means for stability testingStress conditions and dissolution performance
paperF1F2F3F4F5F17F18F19F20F21F22F27F28F29F30F6F7F8F9F10F11F12F13F14F15F16F23F31F32F24F25F26F33F34F35
2006konno2006polymers and dry nucleation of felodipine
2006marsac2006anifedipine against felodipine
2008konno2008polymers and felodipine nucleation with moisture
2008marsac2008anifedipine and felodipine in PVP with sorbed water
2009rumondor2009bpolymer type and RH on bulk crystallization
2009rumondor2009cmoisture-induced immiscibility of drug–PVP dispersions
2010kestur2010bPVP molecular weight, concentration and temperature on melt growth
2010marsac2010temperature and moisture on felodipine–PVP miscibility
2010rumondor2010moisture and felodipine crystal growth
2010rumondor2010amoisture sorption of amorphous drug–polymer blends
2010rumondor2010cpolymer hygroscopicity and moisture-induced separation
2011rumondor2011which dispersions separate: 20 systems and a discriminant model
2012trasi2012apolymers, nucleation and growth of amorphous acetaminophen
2012trasi2012badditives, growth and nucleation of amorphous flutamide
2013kestur2013afelodipine polymorphs with and without PVP
2013kestur2013bparticle size, surfaces and dissolution of felodipine powders
2013wegiel2013bresveratrol dispersions with six polymers
2014mosqueragiraldo2014surfactants and celecoxib growth
2014wegiel2014curcumin dispersions and intramolecular bonding
2015sato2015a chiral polymer and the growth of two enantiomers
2016sato2016PHB and crystal growth of six compounds
2016tian2016indomethacin fluorescence, miscibility limits and dry stability
2016xie2016bcelecoxib binaries and ternaries under heat and humidity
2017saboo2017water-induced separation of miconazole–PVPVA imaged by confocal fluorescence
2017tian2017polymers and the melt growth of three indomethacin polymorphs
2017trasi2017marketed amorphous tacrolimus capsules under stress
2020trasi2020lumefantrine with acidic polymers: stability, protonation and granule release
2021bhujbal2021lumefantrine dispersions by spray anti-solvent precipitation
2022yang2022bsurfactants and water-induced separation of ritonavir–PVPVA
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

Solid state stability / Crystallization tendency

The neat-drug ranking that the dispersions inherit: quenched nifedipine glass stored at 30 °C and 0% RH looked fully crystalline after 3 months, felodipine under the same conditions crystallized only at the edges baird2010 R24, R25, the same order as the nucleation rates of F2; and the growth maximum of pure felodipine near 105 °C with the fall on cooling kestur2010b R7 is the pattern of Crystallization tendency F2 that frames F3. See Crystallization tendency F17, Crystallization tendency F2 and F2, F3.

Gives to

Solid state stability / Crystallization tendency

The felodipine melt growth rates with and without PVP kestur2010b R7, R13 are polymer data of the kind behind the finding that a polymer cuts melt growth by a broadly similar factor; the proposal that uncovered films grow faster than bulk mobility predicts because growth runs at the free surface rumondor2010 C28 bears on surface crystallization. See Crystallization tendency F19, Crystallization tendency F21.

Takes from

Solid state stability / Miscibility and drug-polymer interactions

Drug–PVP χ from melting point depression, the estimated solubility of the drugs in PVP and the reading that the dispersions are supersaturated (builds_on marsac2006b, marsac2009) marsac2006a R18; marsac2008a C47; rumondor2009c R26. The two cited χ values for nifedipine–PVP differ, −3.8 marsac2006a R18 against 0.0 rumondor2009c R26, the reading dependence of Miscibility F7. See Miscibility and drug-polymer interactions F7, Miscibility and drug-polymer interactions F9 and F4.

Shares with Solid state stability / Miscibility and drug-polymer interactions. Two results of F4 and F5 recur in the polymer-chemistry growth studies there: felodipine hydrogen bonds most strongly with PVP among the polymers tested kestur2010a C26, and at 5 wt% polymer neither the dispersion Tg nor the polymer Tg tracked growth inhibition for bifonazole and nimesulide kestur2011 C12. The humid-storage result of F11, PVP losing its advantage, meets the polyphenol case in which PVP dispersions stayed amorphous in humid storage, read there as evidence of strong hydrogen bonding wegiel2013a C40. See Miscibility and drug-polymer interactions F11, Miscibility and drug-polymer interactions F12, Miscibility and drug-polymer interactions F23 and F5, F11, F13.

Shares with Solid state stability / PEG dispersions. The same reasoning on activity coefficients appears in the PVP and the PEO moisture papers of 2008: γ above 1 read as endothermic mixing, with the drugs mixing exothermically with an analogue solvent (NMP, PEG 400) and endothermically with water marsac2008a C34, C37; marsac2008b C14. See PEG dispersions F11 and F2, F13.

Takes from

and gives to Characterization methods / Solid-state methods

The crystallinity values of rumondor2009b come from PLS regression of whole PXRD patterns rumondor2009b P5, the method whose calibration is examined in Solid-state methods F3. The moisture-induced separation of PVP dispersions (F12) was later followed with a pyrene probe: probucol–PVP and ritonavir–PVP separated at high RH, ritonavir–HPMCAS did not purohit2015b C25, C16. See Solid-state methods F3, Solid-state methods F17 and F12, F23.

Gives to

ASD process

The felodipine–PVP separation by humidity and by water in the casting solvent marsac2010 C14, C16 precedes the film and spray-drying studies in which humid storage or trace water during preparation demixed itraconazole–HPMC and evacetrapib dispersions mugheirbi2017 C26, C36; li2017 C33, C44. See ASD process F1, ASD process F6 and F12, F14.

Gives to

Dissolution

The dry and humidified Tg of felodipine from marsac2008a was used to explain faster crystallization of felodipine in solution at 37 than at 25 °C alonzo2010 C34; the ritonavir study that followed hydration into dissolution first showed that ritonavir–PVP and –PVPVA separate on high-RH storage while ritonavir–HPMCAS stays mixed, the pattern seen before for hydrophobic drugs with hygroscopic polymers purohit2017b C1, C45; and the additive-sorption test of F7 was applied to lopinavir dispersions, with sub-additive uptake read as drug–polymer interaction li2018 C33, C34. The papers of 2006–2010 here did not measure dissolution; separation in the hydrating matrix during dissolution is only postulated rumondor2009c C53.

Shares with Solid state stability / Crystallization tendency (2012–2014 papers). PVP slowed five donor drugs by a similar 5–10-fold factor whatever their own rate, and the felodipine polymorph comparison reached the same multiplicative picture between forms, with the same conclusion that fast growers need more polymer trasi2014a C10, C11; kestur2013a C26. Free surfaces grew faster than sandwiched bulk across 14 compounds, the general form of the felodipine surface and particle-size results trasi2014a C8; kestur2013a C2; kestur2013b C24. Acetaminophen's glass formation through separated nucleation and growth zones and resveratrol's rapid-crystallizer class are neat-drug properties that frame the dispersion results trasi2012a C39; wegiel2013b C6. See Crystallization tendency F3, Crystallization tendency F7, Crystallization tendency F14, Crystallization tendency F19, Crystallization tendency F21 and F17, F19, F20, F21, F24.

Takes from

and gives to Solid state stability / Miscibility and drug-polymer interactions (2012–2014 papers)

The hydrogen-bond order of felodipine–polymer bonding and the nimesulide intramolecular bond kestur2010a C26; kestur2011 C27 are the premises that the flutamide, acetaminophen and curcumin papers test with polymers chosen by donor and acceptor group, adding the failure of donor polymers on an intramolecularly held acceptor and the acid–base pair with E100 trasi2012b C51; wegiel2014 C35, C37. The acidic polymer PAA failed for the weakly acidic resveratrol, as the spin-coating screens predict wegiel2013b C44. See Miscibility and drug-polymer interactions F12, F14, F17, F21, F24 and F18, F24.

Shares with Dissolution / D. Crystallization from solution. The decoupling of nucleation and growth by polymers seen in supercooled acetaminophen and felodipine powders recurs in solution, where HPMC cut felodipine nucleation more than a thousandfold but growth only about twofold, and PAA, the best growth inhibitor in the supercooled liquid, did little trasi2012a C53; kestur2013b C36; alonzo2012 C46; trasi2015 C28. Surfactants sped growth in the supercooled liquid as they did in solution mosqueragiraldo2014 C40. See D. Crystallization from solution F6, F18, F27 and F17, F22.

Gives to

Bioperformance and ASD process

Crystallinity gained in storage cut the supersaturation of felodipine powders on dissolution kestur2013b C44, C45, the first in the library of a line that later measured the cost of residual crystals in absorptive dissolution and in dogs and the role of seed origin hate2019 C52; que2018 C54, and the surface crystallization of particles is the target of later atomic layer coatings duong2022c C35. See Bioperformance F28, ASD process F26, ASD process F43 and F21, F26.

Takes from

and gives to Solid state stability / Crystallization tendency (2015–2022 papers)

The temperatures of fastest growth of the PHB and indomethacin papers (0.94 and 0.95 Tm) follow the neat-drug rule, and the indomethacin paper adds that a polymer lowers that temperature sato2016 E2; tian2017 E3, R15; PHB speeding growth extends the list of additives that accelerate growth; tacrolimus, a good glass former, crystallized in a product whose drug was not mixed with the polymer, so the neat-drug class remained only a first flag trasi2016 C13; trasi2017 C28. See Crystallization tendency F2, Crystallization tendency F7, Crystallization tendency F17, Crystallization tendency F19 and F28, F29, F33.

Takes from

and gives to Solid state stability / Miscibility and drug-polymer interactions (2015–2022 papers)

The enantiomer test gives the cleanest support in the library for the hydrogen-bond reading of growth inhibition sato2015 C27; the indomethacin miscibility limits link the dry phase state to storage tian2016 C53; and the lumefantrine papers add protonation by acidic enteric polymers, read there as acid–base contacts, and its failure to rank stability when the dispersion is made in water trasi2020 C36; bhujbal2021 C50; hiew2022a R20. See Miscibility and drug-polymer interactions F12, Miscibility and drug-polymer interactions F17, Miscibility and drug-polymer interactions F18, Miscibility and drug-polymer interactions F21, Miscibility and drug-polymer interactions F26 and F27, F30, F34.

Takes from

and gives to Characterization methods / Solid-state methods and ASD process

The intrinsic-fluorescence and two-dye confocal methods of 2016–2017 and the label-free O-PTIR maps of 2022 extend the probe and AFM-IR methods to the phase state of stored and humidified films tian2016 C55; saboo2017 C49; yang2022b C45; the humid-casting and buffer results for miconazole–PVPVA connect to the film and spray-drying studies of water during preparation saboo2017 C10; li2017 C44. See Solid-state methods F16, Solid-state methods F18, Solid-state methods F19, ASD process F1, ASD process F4, ASD process F6 and F14, F30, F31.

Gives to

Bioperformance

The tacrolimus generic that crystallized in open storage was the material of later studies of compendial and small-volume dissolution, simulated bioequivalence, absorptive dissolution and exposure in dogs purohit2018 R17, C18; hate2019 R12; purohit2019 R9. See Bioperformance F16, Bioperformance F17, Bioperformance F28, Bioperformance F30 and F33, F26.

Shares with Dissolution. The surfactant partitioning of the ritonavir films was measured in buffer with nanodroplets, the method of the amorphous-solubility chapter, and the morphologies of water-induced separation are those that the release papers tie to congruent or blocked release yang2022b C44; yang2022a C13, C14; yang2023 C40; saboo2021 C30; lumefantrine granules released drug-rich nanodroplets above the amorphous solubility trasi2020 C21. See C. Amorphous solubility and LLPS F11, C. Amorphous solubility and LLPS F15 and F31, F32, F34.

Left to other subcategories: the crystallization tendency of the neat drug and its classes (Crystallization tendency); drug–polymer hydrogen bonding, interaction parameters and miscibility of dry dispersions, and the effect of polymer chemistry on growth across drugs (Miscibility and drug-polymer interactions); semicrystalline PEG and PEO carriers (PEG dispersions); the methods that image phase separation and quantify crystallinity (Solid-state methods); water in the solvent during film formation and spray drying, granulation and coatings against surface crystallization (ASD process); the effect of residual crystallinity on absorption and exposure (Bioperformance); and dissolution and supersaturation from dispersions (Dissolution), measured here for felodipine powders before and after storage, for marketed tacrolimus capsules and for lumefantrine granules and powders kestur2013b R19, R20, R21; trasi2017 R3; trasi2020 R14; bhujbal2021 R15.

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

Evidence length

Topic 1 of 5 · 15 findings · F1–F5, F17–F22, F27–F30

Crystallization of the amorphous drug in dry dispersions

F1

Topic 1Crystallization of the amorphous drug in dry dispersions1 of 15

A few percent of PVP, HPMC or HPMCAS lowers dry nucleation of amorphous felodipine about a hundredfold, all three alike.

Felodipine with 0–25% w/w polymer was spin-coated as thin films, stored dry (0% RH) at 22 °C, and nucleation sites (birefringent crystal nuclei seen under polarized light) were counted over time konno2006 P1, P2, E1. The nucleation rate fell from about 1.3 × 10⁵ m⁻³ s⁻¹ for the drug alone to about 2–3 × 10³ with 3% polymer, and 25% PVP gave only about one decade more konno2006 R4, C13. At every content the three polymers gave the same rate "within experimental error" konno2006 C14.

moderateModerate: the drop is large against triplicate error bars, but the equality of the polymers rests mostly on 3–15% polymer with wide scatter on a log axis, and absolute rates of the same system differ about fourfold between papers konno2006 K1, K2, X9; marsac2006a X1.

Felodipine, dry films at 22 °C: nucleation rate, m⁻³ s⁻¹drug alone≈1.3 × 10⁵3% polymerPVP, HPMCAS or HPMC≈2.3–3.0 × 10³7% polymer≈1.1–1.8 × 10³15% polymer≈0.75–1.1 × 10³25% PVP≈3 × 10²

The first 3% removes a 40–60-fold factor and the next 22% about one decade more; from 3 to 15% the three polymers lie within about 1.5-fold of each other. konno2006 R4, R4.a, R4.b, R4.g, X9

drug alone7 wt% PVP25 wt% PVPnifedipine4.3 × 10²1.4 × 10³1.2 × 10⁵felodipine7 × 10¹2.7 × 10²3 × 10⁴101001000100001000001e+06nucleation rate in dry PVP films, m⁻³ s⁻¹ (log scale)

Both drugs drop about two orders of magnitude at 7 wt% PVP and only 3–4-fold further up to 25 wt%. marsac2006a R16, C18, C19

For your drug

  1. Count nucleation sites in dry spin-coated films of the neat amorphous drug and with 3, 7 and 15% of each candidate polymer at one storage temperature below Tg.
  2. A drop of one to two decades at 3–7% followed by a flat curve, with the polymers within about twofold of each other, matches the felodipine pattern; repeat at the storage humidity before choosing a polymer.

konno2006 P2, R4; konno2008 R3.b, C10

How it works and key numbers
  1. A lower driving force through mixing "probably cannot account" for the drop: Flory–Huggins theory with data for comparable systems predicts little change in drug activity below a polymer volume fraction of about 0.5 konno2006 C34, C35, R20.
  2. A pure dilution effect would scale with the polymer fraction; a 3% addition giving a 1.5-order drop rules it out ("clearly not the case") konno2006 C37.
  3. "It seems reasonable to speculate" that the polymers raise the kinetic barrier to moving molecules onto the nucleus, possibly through polymer rejected by the growing nucleus and piling up at its surface konno2006 C39, C40, C41.
  4. With 3% PVP the nucleation activation energy of felodipine below Tg rose from 145 to 201 kJ/mol, which the authors read as a higher barrier ("it appears"); neither the barriers nor the polymer at the nucleus surface were measured (see F4) marsac2006a R3, C20, C48; konno2006 X14.
To feel the numbers. A film volume of 1 mm³ is 10⁻⁹ m³. Without polymer it forms about 1.3 × 10⁵ × 10⁻⁹ × 86,400 s ≈ 11 nuclei per day; with 3% polymer about 3.0 × 10³ × 10⁻⁹ × 86,400 ≈ 0.26 per day, one nucleus in about four days.
1.3 × 10⁵ → 2–3 × 10³ m⁻³ s⁻¹felodipine alone against 3% polymer, dry, 22 °Ckonno2006 R4, C13
3–4-foldfurther drop from 7 to 25 wt% PVP, for both drugsmarsac2006a R16, C18
30–70-folddifference between polymers at 75% RH, hidden when drykonno2008 R3.b

Connections to other chapters

2 more connections
Evidence: data, conditions and papers

Finding F1. A few percent of PVP, HPMC or HPMCAS lowers the dry nucleation rate of amorphous felodipine and nifedipine by about two orders of magnitude, more polymer adds little, and the three polymers do not differ when dry

In short. In dry spin-coated films at 22 °C, amorphous felodipine nucleated at about 1.3 × 10⁵ m⁻³ s⁻¹ alone and at about 2–3 × 10³ m⁻³ s⁻¹ with 3% w/w PVP, HPMCAS or HPMC, "around 1.5 orders of magnitude" lower, while 25% PVP gave only about one decade more (about 3 × 10²) konno2006 R4, C13. At every content the three polymers gave the same rate "within experimental error" konno2006 C14. PVP lowered the nucleation of both felodipine and nifedipine by about two orders of magnitude at 7 wt% and only 3–4-fold further up to 25 wt% marsac2006a R16, C18, C19, and the dry pattern was found again as the baseline of the two moisture studies konno2008 R1, C9; marsac2008a R1, C8.

Type. observation in 2 drugs and 3 polymers Strength. the drop is large against triplicate error bars (konno2006 K1: strong), but "equally effective" rests mostly on 3–15% polymer with wide scatter on a log axis (konno2006 K2: moderate; X9), and the absolute rates of the same system differ about fourfold between papers (marsac2006a X1).

How it was shown

Konno and Taylor (2006) spin-coated felodipine with 0–25% w/w PVP K29/32, HPMCAS or HPMC, stored the films at 0% RH and 22 °C, and took the nucleation rate as the slope of birefringent site density against time, each composition in triplicate konno2006 P1, P2, E1, A2, R18. Marsac, Konno and Taylor (2006) used the same method for nifedipine and felodipine with 0–25 wt% PVP K29/32 marsac2006a P1, P4, A2.

What the data show

The first 3% of polymer removed roughly a 40–60-fold factor (synthesis: 1.3 × 10⁵/3.0 × 10³ = 43 for PVP), and the next 22% about one decade more konno2006 R4.a, R4.b, R4.g. From 3 to 15% the three polymers lay within a factor of about 1.5 of each other konno2006 R4, X9.

papersystem and conditionsresultids
konno2006felodipine with PVP, HPMCAS or HPMC, films, 0% RH, 22 °C, n = 3≈1.3 × 10⁵ alone; ≈2.3–3.0 × 10³ at 3%; ≈3 × 10² m⁻³ s⁻¹ at 25% PVP; polymers equal within errorkonno2006 R4, C13, C14
marsac2006anifedipine and felodipine with PVP K29/32, 0% RH≈1.2 × 10⁵ → 1.4 × 10³ (nifedipine) and ≈3 × 10⁴ → 2.7 × 10² m⁻³ s⁻¹ (felodipine) at 7 wt%; 3–4-fold more to 25 wt%marsac2006a R16, C18
marsac2008asame pair, dry baselinefelodipine 1.4 × 10⁵ → 1.1 × 10³ (7% PVP) → 3 × 10² (25% PVP); nifedipine 4.7 × 10⁵ → 5.6 × 10³ → 1.7 × 10³ m⁻³ s⁻¹marsac2008a R1.a, R1.b, R1.f, R1.g, R1.h, R1.l
trasi2012aacetaminophen melt with 10% w/w of seven polymers, one cooling–reheating cyclenuclei: 10.8 alone; 2.5 (HPMCAS), 5.2 (PVP), 26 (PAA)trasi2012a R12, C46
Fig. 4 of konno2006: nucleation rate of felodipine against polymer content for PVP, HPMCAS and HPMC
Fig. 4 · konno2006nucleation rate of felodipine against polymer content for PVP, HPMCAS and HPMC

On the log axis the drug-alone point sits about 50-fold above every 3% point, and the three symbols overlap at most levels konno2006 R4, X9.

Why

A lower driving force through mixing "probably cannot account" for the drop, and a pure diluent effect, which would scale with polymer fraction, is ruled out by a 1.5-order drop at 3% konno2006 C34, C35, C37. "It seems reasonable to speculate" that the polymers increase the barrier to moving molecules onto the nucleus, possibly through rejected polymer piling up at its surface konno2006 C39, C40. This barrier was not measured konno2006 X14.

Limits and transfer

Dry thin films at 22 °C and two dihydropyridine drugs konno2006 P1, P2; marsac2006a P1, P4. Equality holds for nucleation and only when dry: at 33–75% RH the three polymers separated, PVP being weakest at low content (F11) konno2008 C10. Count nucleation sites in dry films of the neat drug and with 3, 7 and 15% of each candidate polymer, then repeat at the storage humidity before choosing a polymer.

How it was shown

Konno and Taylor (2006) asked whether a polymer's ability to slow nucleation of a molecularly dispersed amorphous drug follows the Tg it gives the dispersion or its hydrogen bonding with the drug konno2006 C6. Felodipine and PVP K29/32, HPMCAS (AQOAT AS-MF) or HPMC (Pharmacoat 606) were dissolved in dichloromethane:ethanol 1:1, spin-coated at about 2500 rpm in a nitrogen glove box below 10% RH, heated briefly to 90 °C and stored over phosphorus pentoxide (0% RH) at 22 °C konno2006 P1, P2, M2, M3, M4. Birefringent nucleation sites were counted under polarized light in 12 areas per film with a 10× objective, converted to a volume density with the depth of field of the objective (0.0144 mm), and the nucleation rate was taken as the slope of site density against time; sites at the film edge were excluded and each composition was run in triplicate at 0, 3, 7, 10, 15, 20 and 25% w/w polymer konno2006 P2, E1, A2, R18. Marsac, Konno and Taylor (2006) used the same film and counting method for nifedipine and felodipine with 0–25 wt% PVP K29/32 marsac2006a P1, P4, A2. Konno and Taylor (2008) reproduced the 2006 dry rates as the 0% RH panel of their moisture study, and Marsac and co-workers (2008) measured both drugs again at 0% RH with 7–25 wt% PVP konno2008 R1, X10; marsac2008a R1, P1, P3.

What the data show

Felodipine alone nucleated at about 1.2–1.35 × 10⁵ m⁻³ s⁻¹; 3% polymer gave about 2.3–3.0 × 10³, 7% about 1.1–1.8 × 10³, 15% about 0.75–1.1 × 10³, 20% about 1.8–5.7 × 10² and 25% PVP about 3 × 10² konno2006 R4. The first 3% therefore removed roughly a 40–60-fold factor (synthesis: 1.3 × 10⁵/3.0 × 10³ = 43 for PVP and 1.2 × 10⁵/2.3 × 10³ = 52 for HPMCAS), and the next 22% about one decade more konno2006 R4.a, R4.b, R4.g. From 3 to 15% the three polymers lay within a factor of about 1.5 of each other; at 20% HPMCAS sat about threefold lower inside error bars spanning about 70 to 1.05 × 10³, and at 25% only the PVP point was plotted konno2006 R4, X9. In the PVP study nifedipine fell from about 1.2 × 10⁵ to 1.4 × 10³ m⁻³ s⁻¹ at 7 wt% PVP and to 4.3 × 10² at 25 wt%, felodipine from about 3 × 10⁴ to 2.7 × 10² and 7 × 10¹ marsac2006a R16. The 2008 dry baseline gave felodipine 1.4 × 10⁵ → 1.1 × 10³ (7% PVP) → 3 × 10² (25% PVP) and nifedipine 4.7 × 10⁵ → 5.6 × 10³ → 1.7 × 10³ m⁻³ s⁻¹ marsac2008a R1.a, R1.b, R1.f, R1.g, R1.h, R1.l.

papersystemmethod and conditionsresultids
konno2006felodipine with PVP, HPMCAS or HPMC, 0–25% w/wspin-coated films, 0% RH, 22 °C, site counts, n = 3≈1.3 × 10⁵ alone; ≈2.3–3.0 × 10³ at 3%; ≈3 × 10² at 25% PVP (m⁻³ s⁻¹); polymers equal within errorR4, C13, C14
marsac2006anifedipine and felodipine with PVP K29/32, 0–25 wt%same method, 0% RH≈1.2 × 10⁵ → 1.4 × 10³ (nifedipine) and ≈3 × 10⁴ → 2.7 × 10² (felodipine) at 7 wt%; 3–4-fold more to 25 wt%R16, C18
konno2008felodipine with the three polymers, dry2006 data reproduced≈0.8–2.9 × 10³ at 3–15% for every polymer; "very little difference"R1, C9, X10
marsac2008anifedipine and felodipine with PVP, dryspin-coated films, 0% RH7% PVP cut the rate about two orders of magnitude; further PVP lowered it gentlyR1, C8
kestur2013bfelodipine powders with 3 wt% PVP K-29/32, 30 °C, dryearly slope of PXRD crystallinity against time60–77-fold slower than the neat glass; a cited 150-fold drop of nucleation at 30 °CR15, R22
trasi2012aacetaminophen melt with 10% w/w of seven polymersnuclei after one cooling–reheating cycle, hot stage, n = 510.8 alone; 2.5 (HPMCAS), 5.2 (PVP), 26 (PAA), 9.2–13.1 for the othersR12, C46
trasi2012bflutamide melt with 10 mol% of five polymersgrowth rate at the DSC exotherm maximum, n = 2lower nucleation with PVAc and PIPA only; no significant effect of PDMA, PVPH, PVPR11, C18
kestur2010a (outside)felodipine melt growth with 3% w/w PVP, PVP/VA, HPMCAS, PVAchot-stage growth at 70–110 °Cgrowth, unlike nucleation, ranked the polymers: about 10-, 7- and 4-fold slower and no effect at 70 °CR6, R7, X2

Figure

Fig. 4 of konno2006: nucleation rate of felodipine against polymer content for PVP, HPMCAS and HPMC
Fig. 4 · konno2006nucleation rate of felodipine against polymer content for PVP, HPMCAS and HPMC

On the log axis the drug-alone point sits about 50-fold above every 3% point, and the three symbols (filled circle PVP, triangle HPMCAS, open diamond HPMC) overlap at most levels; at 25% only PVP is visible konno2006 R4, X9.

Fig. 9 of marsac2006a: nucleation rate of nifedipine and felodipine against PVP content
Fig. 9 · marsac2006anucleation rate of nifedipine and felodipine against PVP content

Both drugs drop about two orders of magnitude at 7 wt% PVP, and nifedipine (circles) stays above felodipine (triangles) at every level marsac2006a R16.

Why

The authors' account, with their hedges: three candidate effects of the polymer were weighed. A lower driving force through mixing "probably cannot account" for the drop, because Flory–Huggins theory with data for comparable systems predicts little change in drug activity below a polymer volume fraction of about 0.5 konno2006 C34, C35, R20. A pure diluent effect would scale with polymer fraction, and a 3% addition giving a 1.5-order drop rules it out ("clearly not the case") konno2006 C37. What remains is a raised kinetic barrier: "it seems reasonable to speculate" that the polymers increase the barrier to moving molecules onto the nucleus, possibly through polymer rejected by the growing nucleus and piling up at its surface, and after the first large drop the effect "appears" set by the amount of polymer rather than its type konno2006 C39, C40, C41. In the PVP study the nucleation activation energy below Tg rose with 3% PVP, significantly for felodipine (145 to 201 kJ/mol), which the authors read as a higher barrier ("it appears") marsac2006a R3, C20, C48. None of these barriers, nor the polymer at the nucleus surface, was measured (see F4) konno2006 X14. (synthesis: the flat part above about 7% is what a barrier saturating with polymer at the interface would give, but the papers do not test this.)

Conditions and limits

Dry storage (0% RH) at 22 °C, thin spin-coated films heated to 90 °C, 3–25% polymer, two dihydropyridine drugs konno2006 P1, P2; marsac2006a P1, P4. Rates are counts per depth-of-field volume and comparable only within a counting method; the 2006 conversion is described as multiplication where division is meant, and absolute rates differ about fourfold between Table II and the figures of the PVP study konno2006 X6; marsac2006a X1, X10. Between papers the felodipine-alone rate is about 3 × 10⁴ in Fig. 9 of marsac2006a but 1.3–1.4 × 10⁵ in the other three papers (synthesis: about fourfold) marsac2006a R16.a; konno2006 R4.a; marsac2008a R1.g. Growth was not measured in these studies konno2006 X14.

Counterexamples and conflicts

Equality holds for nucleation and only when dry: at 33–75% RH the three polymers separated, PVP being weakest at low content (F11) konno2008 C10. For melt crystal growth of felodipine at 3% polymer the polymers differed several-fold (PVP > PVP/VA > HPMCAS > PVAc), so "polymer type does not matter" does not carry over from nucleation to growth kestur2010a R6, R7; konno2006 C14. Across drugs no polymer was best for all (see Miscibility and drug-polymer interactions F15). Nor does the equality carry over to other drugs: in supercooled acetaminophen with 10% w/w polymer the number of nuclei per cooling–reheating cycle ranged tenfold, from 2.5 with HPMCAS to 26 with PAA against 10.8 for the drug alone, and in flutamide two of five polymers lowered nucleation while the others had no significant effect (see F17) trasi2012a R12, C46; trasi2012b R11, C18. (synthesis: the felodipine result of 2006 is therefore a result for one drug in thin films at 22 °C, not a rule for polymers.) A later paper cites the 2006 study for a 150-fold drop of felodipine nucleation with 3% PVP at 30 °C kestur2013b R22, larger than the 40–60-fold drop read from the 2006 rates at 22 °C (synthesis: 1.3 × 10⁵/3.0 × 10³ = 43 konno2006 R4); the 2006 card holds no rates at 30 °C, so the cited value cannot be checked here.

Transfer check

Count nucleation sites in dry spin-coated films of the neat amorphous drug and with 3, 7 and 15% of each candidate polymer at one storage temperature below Tg. A drop of one to two decades at 3–7% followed by a flat curve, with the polymers within about twofold of each other, puts the drug in the felodipine pattern. Repeat at the storage humidity before choosing a polymer, since equal dry behaviour hid a 30–70-fold difference at 75% RH (synthesis: 8.6 × 10⁵/1.3 × 10⁴ = 66 and 8.6 × 10⁵/2.0 × 10⁴ = 43 at 3% konno2008 R3.b).

History

Matsumoto and Zografi (1999, outside the library) had seen PVP inhibit indomethacin crystallization at levels too low to raise Tg, which framed the 2006 question konno2006 C3, R21. Konno and Taylor (2006) first measured the polymer effect on nucleation in the library and found the three polymers equal when dry konno2006 C14; Marsac and co-workers (2006) confirmed the same two-decade drop for nifedipine and felodipine with PVP marsac2006a C18. In 2008 both groups used the dry state as the reference for adding water and found the equality lost in humid air konno2008 C9, C10; marsac2008a C8, C9. Later in the library a polymer was found to cut melt growth rates by a broadly similar factor for fast and slow growers (see Crystallization tendency F19). In 2012 Trasi and Taylor counted nuclei in supercooled acetaminophen and flutamide with several polymers and found the polymers far from equal, and in opposite order to their effect on growth for acetaminophen trasi2012a C46, C53; trasi2012b C45; in 2013 Kestur and co-workers read the 60–77-fold slower crystallization of felodipine powders with 3% PVP as mainly a nucleation effect kestur2013b C36 (see F17).

F2

Topic 1Crystallization of the amorphous drug in dry dispersions2 of 15

Nifedipine nucleates faster than felodipine at equal Tg, with or without PVP and water, in line with its larger driving force.

Amorphous nifedipine and felodipine have nearly the same Tg (onset 42.3 and 43.1 °C) and similar relaxation times at 23.5 °C (6.3 and 4.2 h), yet nifedipine nucleated faster as a pure glass and about 3.5–6 times faster at every PVP level up to 25 wt% marsac2006a R4.c, R4.m, R4.n, R16, C19. With sorbed water the ranking held in all 30 combinations of PVP content and RH, and at equal Tg − T the nifedipine dispersions still nucleated about 5–20 times faster marsac2008a R1, C7, C23.

moderateModerate: the ranking holds in every condition of both papers, but the explanations correlate two properties with the ranking of a single drug pair marsac2006a K1, X7; marsac2008a K1, K5.

nifedipinefelodipinedry, 0% RH3 × 10²1.7 × 10³75% RH2.3 × 10³4.3 × 10⁵same Tg − T, about 15 °C14.5 °C and 15.1 °C1.5 × 10³2.0 × 10⁴1001000100001000001e+06nucleation rate with 25% PVP, m⁻³ s⁻¹ (log scale)

Nifedipine lies above felodipine in every case, also at the same distance below Tg. marsac2008a R1.f, R1.l, R8.e, R8.f, C23

Nearly equal in the two glasses
Tg onset 42.3 vs 43.1 °Crelaxation time 6.3 vs 4.2 hH-bonding to PVP per donorFH activity in PVP 0.84 vs 0.83
Different, each favouring nifedipine crystallization
driving force 9.6 vs 6.2 kJ/molEa below Tg 122 vs 145 kJ/molcrystal solubility in NMP 0.05 vs 0.10

marsac2006a R4.c, R4.m, R4.k, R3, R15, R19; marsac2008a R10

For your drug

  1. For two candidates of similar Tg, compute the Hoffman free energy of crystallization at the storage temperature from Tm and heat of fusion; the larger value points to the faster nucleator.
  2. Confirm by counting nucleation in the neat glass and at the planned PVP level, dry and at 75% RH; the evidence covers dihydropyridines in PVP only.

marsac2006a R4.l; marsac2008a R10, R2

How it works and key numbers
  1. Tg and the DSC relaxation time are the same for both glasses, so either other factors dictate nucleation or this measure of mobility misses the motion involved ("suggests either") marsac2006a C37.
  2. Nifedipine has the larger driving force for crystallization (9.6 against 6.2 kJ/mol at 25 °C), and the difference is enthalpic (enthalpy of crystallization 22.1 against 16.1 kJ/mol) marsac2006a R4.i, R4.j, R4.k, C15.
  3. Felodipine has the higher nucleation activation energy below Tg (145 against 122 kJ/mol); it loses hydrogen-bond strength on crystallizing, so "it would be reasonable to speculate" that it must first weaken its amorphous hydrogen bonds marsac2006a R3, C38, C39.
  4. With water, the authors treat polymer plus water as a co-solvent; crystalline nifedipine is half as soluble in NMP, the liquid analogue of PVP (mole fraction 0.05 against 0.10), and its dispersions sorb more water, so "it is reasoned" that nifedipine is more supersaturated; no supersaturation was computed marsac2008a R10, C42, C49, X4.
To feel the numbers. With 25% PVP at 75% RH, 4.3 × 10⁵ ÷ 2.3 × 10³ ≈ 190, so nifedipine nucleated about 190 times faster; dry, 1.7 × 10³ ÷ 3 × 10² ≈ 6.
9.6 vs 6.2 kJ/molfree energy of crystallization at 25 °C, nifedipine vs felodipinemarsac2006a R4.k
42.3 vs 43.1 °CTg onsets of the two glasses, too close to explain the rankingmarsac2006a R4.c
5–20-foldnifedipine faster at equal Tg − T in humid PVP dispersionsmarsac2008a R8, C23

Connections to other chapters

1 more connection
Evidence: data, conditions and papers

Finding F2. Between two close analogues with the same Tg, the faster-nucleating drug stays faster in PVP dispersions, dry and humid, and the difference follows the crystal-related driving force and nucleation barrier rather than any glass property

In short. Amorphous nifedipine and felodipine have nearly the same Tg (onset 42.3 and 43.1 °C) and similar relaxation times at 23.5 °C (τ 6.3 and 4.2 h), yet nifedipine nucleated faster as a pure glass at 22 °C and from about 25 to 75 °C, and about 3.5–6 times faster at every PVP level up to 25 wt% marsac2006a R4.c, R4.m, R4.n, R2, R16, C13, C19. With sorbed water the gap widened (25% PVP at 75% RH: about 4.3 × 10⁵ against 2.3 × 10³ m⁻³ s⁻¹), and at equal Tg − T the nifedipine dispersions still nucleated about 5–20 times faster marsac2008a R1.f, R1.l, R8, C23. The authors tie the ranking to nifedipine's larger, enthalpic driving force (9.6 against 6.2 kJ/mol at 25 °C), its lower activation energy for nucleation below Tg (122 against 145 kJ/mol) and, with water, a higher supersaturation that they reason from crystal solubility in a liquid analogue of PVP but do not compute marsac2006a R4.k, R3, C49; marsac2008a C49, X4.

Type. observation in 2 drugs, with an author interpretation Strength. the ranking holds in every condition of both papers (marsac2006a K1: strong; marsac2008a K1: strong), but the explanations correlate two properties with one ranking of one drug pair (marsac2006a X7; marsac2008a K5: weak to moderate).

How it was shown

Marsac, Konno and Taylor (2006) compared nifedipine and felodipine alone and in PVP K29/32 dispersions under dry conditions: nucleation in spin-coated films at 22 °C, Arrhenius activation energies, and the free energy of crystallization from DSC, checked against the Hoffman equation marsac2006a P4, P5, A3, P7, P8. Marsac and co-workers (2008) stored the same pairs at 0–75% RH and measured crystal solubility in NMP as a stand-in for PVP marsac2008a P1, P2, P3, P9.

What the data show

Every source ranks nifedipine first marsac2006a R4.a, R1, R16.a, X1. With water the ranking held in all 30 combinations of PVP content and RH, and at equal Tg − T nifedipine still nucleated faster marsac2008a R1, C7, C23.

propertynifedipinefelodipineids
Tg onset; KWW τ at 23.5 °C42.3 °C; 6.3 h43.1 °C; 4.2 hmarsac2006a R4.c, R4.m, R4.n
nucleation of the glasses, films, 22 °C0.39 × 10¹⁰ m⁻³ day⁻¹0.17 × 10¹⁰ m⁻³ day⁻¹marsac2006a R4.a
free energy of crystallization at 25 °C (Hoffman)9.6 (8.8) kJ/mol6.2 (6.2) kJ/molmarsac2006a R4.i, R4.k, R4.l
activation energy below Tg, alone → 3 wt% PVP122 → 127 kJ/mol145 → 201 kJ/molmarsac2006a R3
25% PVP, 0 → 75% RH≈1.7 × 10³ → 4.3 × 10⁵ m⁻³ s⁻¹≈3 × 10² → 2.3 × 10³ m⁻³ s⁻¹marsac2008a R1.f, R1.l
crystal solubility in NMP, mole fraction0.050.10marsac2008a R10
Fig. 7 of marsac2008a: nucleation rate against Tg − T for pure drugs, 10% and 25% PVP
Fig. 7 · marsac2008anucleation rate against Tg − T for pure drugs, 10% and 25% PVP

At the same distance below Tg the open nifedipine curves lie above the filled felodipine curves, most clearly with 25% PVP (panel c) marsac2008a R8.

Why

Tg and DSC relaxation time are the same for both glasses, so either other factors dictate nucleation or this measure of mobility misses the motion involved ("suggests either") marsac2006a C37. Nifedipine has the larger driving force and the difference is enthalpic, while felodipine's higher barrier below Tg is "evidence that kinetic factors are also important" marsac2006a C15, C35, C38. With water, polymer plus water is treated as a co-solvent in which nifedipine's crystal is less soluble, so "it is reasoned" that nifedipine is more supersaturated in every system marsac2008a C42, C43, C49.

Limits and transfer

One drug pair and one polymer; no supersaturation was computed for any dispersion, and the pure drugs converged at Tg − T below 15 °C marsac2008a X4, X7. For two candidates of similar Tg, compute the Hoffman free energy of crystallization at the storage temperature from Tm and heat of fusion, and confirm by counting nucleation in the neat glass and at the planned PVP level, dry and at 75% RH.

How it was shown

Marsac, Konno and Taylor (2006) compared the two dihydropyridine calcium channel blockers alone and in PVP K29/32 dispersions under dry conditions: nucleation rates in spin-coated films at 22 °C and, for the Arrhenius activation energy, at several temperatures between about 25 and 75 °C, alone and with 3 wt% PVP marsac2006a P4, P5, A3. They measured Tm, heat of fusion and heat capacities by DSC and modulated DSC to integrate the configurational enthalpy, entropy and free energy of crystallization, checked them against the Hoffman equation, aged glasses at 23.5 °C for enthalpy recovery (KWW τ and β), read hydrogen bonding from the NH stretch, and computed drug activity in PVP with Flory–Huggins theory and cited interaction parameters marsac2006a P7, P8, P9, P6, P11. Marsac and co-workers (2008) stored the same pairs with 0–25 wt% PVP at 0, 11, 33, 58 and 75% RH, measured nucleation in films, water sorption and Tg of bulk powders at 25 °C, re-plotted nucleation against water content and Tg − T, and measured crystal solubility in 1-methyl-2-pyrrolidone (NMP), water and NMP–water as stand-ins for PVP and the PVP–water mixture marsac2008a P1, P2, P3, P6, P7, P8, P9.

What the data show

Dry: Table II gives 0.39 against 0.17 × 10¹⁰ m⁻³ day⁻¹ for nifedipine and felodipine glasses; the Fig. 2 slopes and Fig. 9 give larger absolute values, but every source ranks nifedipine first by a factor of about 2–4 marsac2006a R4.a, R1, R16.a, X1. Only nifedipine crystallized on heating a melt-quenched glass at 2 °C/min (metastable form at 87 °C) marsac2006a R5, C11. The free energy of crystallization at 25 °C was 9.6 against 6.2 kJ/mol (Hoffman 8.8 and 6.2), from enthalpies of 22.1 and 16.1 kJ/mol against entropy penalties TΔS of 12.5 and 10.0 kJ/mol marsac2006a R4.i, R4.j, R4.k, R4.l. The activation energy below Tg was 122 (11) against 145 (3) kJ/mol, above Tg 78 (8) against 95 (12) kJ/mol, not significantly different marsac2006a R3, C9. In PVP, nifedipine stayed above felodipine at 7–25 wt% (for example 4.3 × 10² against 7 × 10¹ m⁻³ s⁻¹ at 25 wt%), while Tg against composition, enthalpy recovery and drug–PVP hydrogen bonding per donor were alike and Flory–Huggins activity at a PVP volume fraction of 0.2 was 0.84 against 0.83 marsac2006a R16, R17, R7, R15, R19, C43.

With water the ranking held in all 30 combinations of PVP content and RH marsac2008a R1, C7. Nifedipine dispersions were the more RH-sensitive: with 7% PVP the rate rose about 400-fold from 0 to 75% RH for nifedipine and about 100-fold for felodipine marsac2008a C10. Nifedipine systems sorbed more water (75% RH: 1.8 against 1.1 g/100 g pure; 5.5 against 4.6 with 25% PVP), yet at a given water content the two drugs' Tgs were reported statistically equivalent marsac2008a R2, C12, C20, X9. At equal Tg − T nifedipine still nucleated faster, for example 2.0 × 10⁴ at 14.5 °C against 1.5 × 10³ m⁻³ s⁻¹ at 15.1 °C with 25% PVP; only the pure drugs converged when Tg − T was below 15 °C marsac2008a R8.e, R8.f, C23, X7. Crystalline nifedipine was half as soluble in NMP (mole fraction 0.05 against 0.10, γ 0.09 and 0.30), so the difference lies in its lattice term; in water felodipine was 20 times less soluble (γ 2.43 × 10⁵ against 1.89 × 10³) marsac2008a R10, R11, C35, C38. Counting only polymer plus water as the drug's co-solvent, water made up 23 wt% of it in the nifedipine 10% PVP dispersion at 75% RH against about 16 wt% for felodipine marsac2008a R13, E6, C45.

papersystemmethod and conditionsresultids
marsac2006anifedipine vs felodipine glassesfilms, 22 °C, 0% RH0.39 vs 0.17 × 10¹⁰ m⁻³ day⁻¹; nifedipine faster at ≈25–75 °CR4.a, R2, C7, C8
marsac2006asameMDSC; HoffmanΔG at 25 °C 9.6 vs 6.2 kJ/mol (Hoffman 8.8 vs 6.2); ΔH 22.1 vs 16.1R4.i, R4.k, R4.l
marsac2006asame, alone and with 3 wt% PVPArrhenius below and above Tgbelow Tg 122 vs 145; with PVP 127 vs 201 kJ/molR3
marsac2006asameTg, KWW at 23.5 °CTg onset 42.3 vs 43.1 °C; τ 6.3 vs 4.2 h; β 0.36 vs 0.37R4.c, R4.m, R4.n
marsac2006a7–25 wt% PVPfilms, drynifedipine 3.5–6 times faster at every levelR16, C19
marsac2008a25% PVP, 0 → 75% RHfilms, 25 °C stated in Fig. 1nifedipine ≈1.7 × 10³ → 4.3 × 10⁵; felodipine ≈3 × 10² → 2.3 × 10³R1.f, R1.l
marsac2008a10 and 25% PVPnucleation against Tg − Tnifedipine faster at equal Tg − T (5–20-fold)R8, C23
marsac2008acrystals in NMP and watershake flask, UV, 25 °Cx 0.05 vs 0.10 in NMP; 2.6 × 10⁻⁶ vs 1.3 × 10⁻⁷ in waterR10
rumondor2009cnifedipine and felodipineHoffman ΔGc at 25 °C from DSC data8.2 vs 6.1 kJ/molM1, M6
baird2010 (outside)quenched glasses, 0% RHstorage 14–20 °C below Tgnifedipine (class II) appeared fully crystalline after 3 months; felodipine (class III) crystallized only at the edgesR24, R25

Figure

Fig. 7 of marsac2006a: free energy of the crystal relative to the glass against temperature
Fig. 7 · marsac2006afree energy of the crystal relative to the glass against temperature

The zero line is the glass; nifedipine (circles) lies below felodipine (triangles) at every temperature under its melting point, and the solid Hoffman lines run close to the points marsac2006a R11, C14.

Fig. 7 of marsac2008a: nucleation rate against Tg − T for pure drugs, 10% and 25% PVP
Fig. 7 · marsac2008anucleation rate against Tg − T for pure drugs, 10% and 25% PVP

At the same distance below Tg the open nifedipine curves lie above the filled felodipine curves, most clearly with 25% PVP (panel c) marsac2008a R8.

Why

The authors' account, with their hedges: Tg and DSC relaxation time are the same for both glasses, so either other factors dictate nucleation or this measure of mobility misses the motion involved ("suggests either") marsac2006a C37. Thermodynamically, nifedipine has the larger driving force and the difference is enthalpic; an entropy-dominated view (glasses with larger entropies of crystallization crystallize less readily, Zhou and co-workers) would have ranked felodipine first, and Turnbull's rule linking interfacial energy to heat of fusion would also favour felodipine marsac2006a C15, C35, C36, R21, R22. Kinetically, felodipine's higher barrier below Tg is "evidence that kinetic factors are also important"; because nifedipine gains hydrogen-bond strength on crystallizing (crystal NH band about 3318 cm⁻¹, below the glass) while felodipine loses it (about 3363 cm⁻¹, above), "it would be reasonable to speculate" that felodipine must first weaken its amorphous hydrogen bonds marsac2006a C38, C39, R12, C17. Which factor dominates is left open marsac2006a C41. With water, the 2008 authors treat polymer plus water as a co-solvent: nifedipine's crystal is less soluble below about 25 wt% water in that co-solvent, and its dispersions sorb more water, so "it is reasoned" that nifedipine is more supersaturated in every system marsac2008a C42, C43, C48, C49. No supersaturation was computed for any dispersion, NMP stands in for PVP, and the printed cosolvency fits do not reproduce their own points and cross at 16.5 rather than about 25 wt% water marsac2008a X4, C33, X2, X3. (synthesis: both papers point to the crystal side of the free-energy balance; the Hoffman estimate from one DSC melting run already ranked the pair correctly.)

Conditions and limits

One drug pair, one polymer, films at 22–25 °C (the 2008 paper states 25 °C in Fig. 1 and 22 °C in Fig. 7) marsac2008a X1. Nucleation was measured on spin-coated films, Tg, heat capacity and sorption on differently prepared bulk samples marsac2006a X11; marsac2008a X12. The below-Tg restriction of the activation-energy difference is dropped in the abstract marsac2006a X6. Growth rates were not measured.

Counterexamples and conflicts

The pure drugs converged at Tg − T below 15 °C, and two pure felodipine points sit at or above the nifedipine curve, so "always" holds for the dispersions only marsac2008a X7. In the library the driving force pointed the right way for this pair but not for indomethacin against felodipine: indomethacin has the larger driving force yet crystallized less readily under the conditions compared alonzo2010 C42 (see Crystallization tendency F6). In supersaturated aqueous solution the same order appeared: felodipine, a slow crystallizer, exceeded its amorphous solubility, whereas nifedipine crystallized just below it raina2014a C31 (see Crystallization tendency F18).

Transfer check

For two candidates of similar Tg, compute the Hoffman free energy of crystallization at the storage temperature from Tm and heat of fusion; a 1.5-fold or larger difference, as here (synthesis: 8.8/6.2 = 1.4 by Hoffman marsac2006a R4.l), predicts the faster nucleator. Confirm by counting nucleation in neat glass and at the planned PVP level, dry and at 75% RH. Measure the crystal solubility in a liquid analogue of the polymer (NMP for PVP) and in water: the drug with the lower analogue solubility and the higher water uptake falls on the nifedipine side here marsac2008a R10, R2. The evidence covers dihydropyridines in PVP only.

History

Tang, Pikal and Taylor (2002) had shown that hydrogen-bond strength differs among the crystals of these dihydropyridines but not among their glasses marsac2006a R20. Marsac and co-workers (2006) first compared the two drugs dry, alone and in PVP, and concluded that the crystallization tendency of drugs from dispersions "may be dependent" on that of the pure drugs marsac2006a C52. Marsac and co-workers (2008) extended the comparison to sorbed water and replaced the dry driving-force argument with a co-solvent supersaturation argument marsac2008a C49, C51. The 2009 moisture study recomputed the Hoffman driving forces of both drugs (8.2 and 6.1 kJ/mol) and found that this property did not decide moisture-induced phase separation (F13) rumondor2009c M1, M6, C32. The neat-drug classification later placed nifedipine in class II and felodipine in class III baird2010 R24, R25 (see Crystallization tendency F17).

F3

Topic 1Crystallization of the amorphous drug in dry dispersions3 of 15

3 wt% PVP slows felodipine crystal growth from the melt 11–21-fold at 70 °C but only 3–6-fold at 110 °C.

Felodipine form II crystals were grown from the supercooled melt (the liquid below its melting point) with 0.5–4.5 wt% PVP on a hot stage at 70–110 °C, and the growth rate was the slope of crystal diameter against time kestur2010b P1, P2, P3, R2. At 3 wt% PVP growth was 3–6-fold slower at 110 °C but 11–21-fold slower at 70 °C, most with K-90 kestur2010b R8, R2. The logarithm of the growth rate fell linearly with PVP concentration, more steeply at lower temperature kestur2010b R14, R15.

moderateModerate: the growth rates agree across figures and with the text, but replicates are not stated, the fit covers 70–105 °C only, and the chain-length plateau rests on two ratios at one temperature kestur2010b K1, K2, X13, X14, X17.

at 70 °Cat 110 °CPVP K-123×11×PVP K-29/323×15×PVP K-906×21×0510152025growth rate without PVP ÷ with 3 wt% PVP

Inhibition is strongest at large supercooling; each longer chain adds less. kestur2010b R8

felodipine3 wt% PVP K-29/3215×3×acetaminophen10% w/w PVP4.7×9.2×flutamide10 mol% PVP K1211×14×celecoxib10% PVP20×35×29×30405060708090100110120130growth temperature, °C (labels: slowing factor by PVP)

The fall of the PVP factor on heating is a felodipine result: acetaminophen rises, flutamide and celecoxib show no trend (ratios of plot readings). kestur2010b R8; trasi2012a R6.a, R6.e; trasi2012b R3.a, R3.h; mosqueragiraldo2014 R1.a, R1.b

For your drug

  1. Measure melt growth of the polymorph of interest at three temperatures between about Tg + 30 °C and the growth maximum, with 0, 1.5 and 3 wt% of the candidate polymer, and fit ln growth rate against concentration.
  2. A slope that steepens on cooling means the polymer protects most where the melt is most viscous; do not extrapolate the fit to storage temperatures near Tg, and try the middle molecular weight first, since K-90 raised melt viscosity 10–20-fold.

kestur2010b R15, C21, C15, C29

How it works and key numbers
  1. Over 70–110 °C growth slowed with cooling although the driving force rises, so molecular transport dominates and growth is diffusion-limited ("indicating") kestur2010b C22, C23.
  2. PVP left Tg (43.4–44.1 against 43.3 °C) and, with 3% K-12, the melting point (140.7 against 141.5 °C) unchanged, so a thermodynamic cause is "unlikely" and the effect is "most likely kinetic in origin" kestur2010b R1, C26, C28, C34.
  3. "We speculate" that drug–PVP hydrogen bonds lower felodipine mobility, possibly by coupling drug and polymer motions kestur2010b C35.
  4. These bonds weaken on heating, which "would also provide a potential explanation" for the weaker inhibition at high temperature; mobility at the growth temperatures was not measured kestur2010b C37, X12.
To feel the numbers. With the printed constants each added wt% multiplies the growth rate by about 0.44 at 70 °C. Three wt% then give 0.44 × 0.44 × 0.44 ≈ 0.085, about 12-fold slower; at 105 °C the factor 0.61 gives 0.61³ ≈ 0.23, about 4-fold slower.
11–21× vs 3–6×slowing by 3 wt% PVP at 70 °C vs 110 °Ckestur2010b R8
−0.82 → −0.49 per wt%slope of ln growth rate against PVP content, 70 → 105 °Ckestur2010b R15, E1
1.55× then 1.4×gain from K-12 to K-29/32, then to K-90 (about 25 times the molecular weight), 70 °Ckestur2010b R8, M3, M4, C32

Connections to other chapters

2 more connections
Evidence: data, conditions and papers

Finding F3. PVP slows the growth of felodipine crystals from the supercooled melt most at large supercooling, log-linearly with its concentration and with diminishing returns from longer chains

In short. At 3 wt%, PVP cut the growth rate of felodipine form II 3–6-fold at 110 °C but 11–21-fold at 70 °C, K-90 most kestur2010b R8, R2. With PVP K-29/32 the logarithm of the growth rate fell linearly with concentration from 0 to 4.5 wt% between 70 and 105 °C, with slopes from about −0.82 per wt% at 70 °C to about −0.49 at 105 °C that rose linearly with temperature (a = 0.0096, b = -1.494) kestur2010b R14, R15, E1. Longer chains inhibited more but with shrinking gains: at 70 °C K-29/32 was about 1.55 times as effective as K-12, and K-90 only 1.4 times as effective as K-29/32 although its molecular weight is some 25 times higher kestur2010b R8, M3, M4, C32.

Type. single-system observation (felodipine–PVP, three grades, 0.5–4.5 wt%) Strength. the growth rates agree across figures and with the text (kestur2010b K1: strong; K2: moderate to strong), but replicates are not stated, Eq. 1 is fitted to 70–105 °C only, and the molecular-weight plateau rests on two ratios at one temperature (X13, X14, X17).

How it was shown

Kestur and co-workers (2010) cryomilled a 10% PVP dispersion with crystalline felodipine to 0.5–4.5 wt% PVP, melted it between two cover glasses, stored it dry at 40 °C until nuclei formed and grew the nuclei on a hot stage at 70–110 °C; the growth rate was the slope of crystal diameter against time kestur2010b P1, P2, P3. All bulk crystals were the metastable form II by Raman kestur2010b R2, C7.

What the data show

Each temperature gave a straight line of log growth rate against concentration, steeper at lower temperature; each added wt% multiplies the growth rate by about 0.44 at 70 °C and 0.61 at 105 °C (synthesis: e^{-0.822} and e^{-0.486}) kestur2010b R14, C19, E1.

systemconditionsresultids
felodipine form II, no polymermelt films, hot stage 70–110 °C3.5 × 10⁻⁹ (70 °C) to 1.7 × 10⁻⁷ m/s (105 °C, maximum)kestur2010b R7, C9
3 wt% PVP K-12, K-29/32, K-90same11-, 15-, 21-fold slower at 70 °C; 3-, 3-, 6-fold at 110 °Ckestur2010b R8
0.5–4.5 wt% K-29/3270–105 °Cln GR linear in concentration; slope −0.82 (70 °C) to −0.49 per wt% (105 °C)kestur2010b R14, R15, E1
felodipine forms I and II with 3% PVP K-29/32ratio without/with PVP, 60–100 °Cform I ≈15.8 → ≈3.5; form II ≈18.7 → ≈6.5kestur2013a R15
acetaminophen with 10% w/w PVP K12radial growth, 70–110 °C≈4.7-fold (70 °C) to ≈9-fold (100 °C) slower (synthesis)trasi2012a R6
Fig. 4 of kestur2010b: growth rate against temperature, pure felodipine and 3 wt% PVP of three molecular weights
Fig. 4 · kestur2010bgrowth rate against temperature, pure felodipine and 3 wt% PVP of three molecular weights

The top curve (circles, pure felodipine) peaks near 105 °C; the gap to the three PVP curves is the inhibition, widest at 70 °C kestur2010b R7.

Why

Growth slowed with cooling although the driving force rises, so molecular transport dominates, and with Tg and the one melting point unchanged the effect is "most likely kinetic in origin" kestur2010b C22, C23, R1, C34. "We speculate" that drug–PVP hydrogen bonds lower felodipine mobility; the weakening of these bonds on heating "would also provide a potential explanation" for the weaker inhibition at high temperature kestur2010b C35, C37. The hydrogen-bond signal was the same for all three grades, so it cannot explain the molecular-weight effect kestur2010b R9, C30.

Limits and transfer

One drug, form II only, and Eq. 1 is restricted to temperatures well above Tg and below the growth maximum kestur2010b A1, C21. For acetaminophen the PVP factor fell on cooling, and for flutamide and celecoxib it showed no trend (synthesis) trasi2012a R6; trasi2012b R3; mosqueragiraldo2014 R1. Measure growth of the polymorph of interest with 0, 1.5 and 3 wt% polymer at three temperatures, fit ln growth rate against concentration, and try K-29/32 before K-90, which raised melt viscosity 10–20-fold kestur2010b C15, C29.

How it was shown

Kestur and co-workers (2010) asked how PVP chain length, PVP amount and temperature set the growth rate of felodipine crystals from the melt, and whether the slowing is thermodynamic or kinetic kestur2010b A1, A2, A3. A 10% PVP dispersion made by rotary evaporation was cryomilled with crystalline felodipine to 0.5–4.5 wt% PVP, melted between two cover glasses, quenched to −5 °C and stored dry at 40 °C until nuclei formed; the nuclei were grown on a hot stage at 70, 80, 90, 95, 100, 105 and 110 °C and the growth rate was the slope of crystal diameter against time kestur2010b P1, P2, P3. Raman showed that all bulk crystals were the metastable form II; form I crystals at the cover-glass edges of pure felodipine were excluded kestur2010b R2, C7. Tg (onset), one Tm (3% K-12), the NH stretch of 20 wt% PVP films at 25 °C and melt viscosity at 90–110 °C were measured alongside kestur2010b P5, P6, P7, P4. Later melt-growth series used the same hot-stage method: ATP enantiomers with 5% w/w PVP K-12 at 40–90 °C, indomethacin polymorphs with 10% w/w PVP K30 from 80 °C to near their melting points, and celecoxib with 10% PVP K29/32 at 80–100 °C sato2015 P4; tian2017 P4; xie2016b P9.

What the data show

Pure felodipine grew at about 3.5 × 10⁻⁹ m/s at 70 °C, 6.6 × 10⁻⁸ at 90 °C and 1.7 × 10⁻⁷ m/s at 105 °C, the maximum, and 1.5 × 10⁻⁷ m/s at 110 °C kestur2010b R7, C9. With 3 wt% PVP the rate at 70 °C was about 3.4 × 10⁻¹⁰ (K-12), 2.3 × 10⁻¹⁰ (K-29/32) and 1.6 × 10⁻¹⁰ m/s (K-90), and at 110 °C about 5.3 × 10⁻⁸, 5.3 × 10⁻⁸ and 2.7 × 10⁻⁸ m/s kestur2010b R7.a, R7.g. In the K-29/32 series the reductions were 2- and 6-fold at 110 °C for 1.5 and 4.5 wt% but 3- and 35-fold at 70 °C kestur2010b R13, C18. Plotted on a log axis against concentration each temperature gave a straight line, steeper at lower temperature kestur2010b R14, C19; with the printed constants each added wt% multiplies the growth rate by about 0.44 at 70 °C and 0.61 at 105 °C (synthesis: e^{-0.822} and e^{-0.486} kestur2010b E1). The crystal shape stayed spherulitic and the growth stayed linear in time over up to 60 h kestur2010b R5, R12, R19.

Three years later the same PVP grade at 3% was tested on both felodipine polymorphs from 60 to 100 °C. The ratio of the growth rate without polymer to that with polymer fell with temperature for both: about 15.8, 17.5, 13.2, 6.8, 3.9 and 3.5 for form I and 18.7, 15.4, 12.5, 8.2, 7.2 and 6.5 for form II at 60, 70, 80, 90, 95 and 100 °C kestur2013a R15. The trend of the 2010 study therefore holds down to 60 °C and for the stable form I as well (see F19). For three other drugs measured in the same years, the PVP factor did not follow the felodipine trend (synthesis: ratios of plot readings): with 10 mol% PVP K12 flutamide grew about 11-, 10-, 8- and 14-fold slower at 40, 50, 60 and 70 °C (1.4/0.13, 5.7/0.59, 20/2.6, 77/5.6) trasi2012b R3.a, R3.h; with 10% w/w PVP acetaminophen grew about 4.7-fold slower at 70 °C and 9.2-fold slower at 100 °C (0.93/0.20, 45/4.9) trasi2012a R6.a, R6.e; and with 10% PVP celecoxib grew about 20-fold slower at 70 °C, 35-fold at 100 °C and 29-fold at 120 °C (0.0020/0.00010, 0.73/0.021, 12/0.42) mosqueragiraldo2014 R1.a, R1.b.

The papers of 2015–2017 measured the PVP factor for three more compounds. With 5% w/w PVP K-12 both enantiomers of the model compound ATP grew about 10 times slower at 50 °C, 5–6 times at 60 °C, 3–4 times at 70 °C and 2–5 times at 80–90 °C, the felodipine trend sato2015 R5.e, R5.f. With 10% w/w PVP K30, indomethacin δ grew about 25 times and α about 16 times slower than without polymer at 80 °C; with rising temperature the δ ratio fell to about 5.7 at 120 °C, while the α ratio rose to about 34 at 120 °C and 558 at 135 °C, above the temperature of fastest growth with PVP (see F29) tian2017 R12, R15. With 10% PVP K29/32, celecoxib grew about 330, 280 and 160 times slower at 80, 90 and 100 °C (synthesis: 0.010/0.00003, 0.14/0.0005 and 0.97/0.006 µm/s xie2016b R21).

papersystemmethod and conditionsresultids
kestur2010bfelodipine form II, no polymermelt films, hot stage 70–110 °C3.5 × 10⁻⁹ (70 °C) to 1.7 × 10⁻⁷ m/s (105 °C, maximum)R7, C9
kestur2013afelodipine forms I and II with 3% PVP K-29/32ratio of growth rates without and with PVP, 60–100 °Cform I ≈15.8 → ≈3.5; form II ≈18.7 → ≈6.5R15
trasi2012bflutamide with 10 mol% PVP K12diameter growth, 40–70 °C, triplicateabout one order of magnitude slower at every temperatureR3, C7
trasi2012aacetaminophen with 10% w/w PVP K12radial growth, 70–110 °C≈4.7-fold (70 °C) to ≈9-fold (100 °C) slower (synthesis)R6
mosqueragiraldo2014celecoxib with 10% PVP K-12seeded bulk growth, 70–120 °C19–38-fold slower, no trend with temperatureR1, C8
kestur2010b3 wt% PVP K-12, K-29/32, K-90same11-, 15-, 21-fold slower at 70 °C; 3-, 3-, 6-fold at 110 °CR8
kestur2010b0.5–4.5 wt% K-29/32sameln GR linear in concentration; slope −0.82 (70 °C) to −0.49 per wt% (105 °C)R14, R15, E1
sato2015ATP(R) and ATP(S) with 5% w/w PVP K-12melt growth, 50–90 °C≈10-fold (50 °C) to 2–5-fold slower (80–90 °C), both enantiomers alikeR5.e, R5.f
tian2017indomethacin δ and α with 10% w/w PVP K30melt growth, 80–135 °Cδ ≈25 → ≈5.7 (80 → 120 °C); α ≈16 → ≈34 (120 °C) → ≈558 (135 °C)R12
xie2016bcelecoxib with 10% PVP K29/32melt growth, 80–100 °C≈330-, 280-, 160-fold slower (synthesis)R21
kestur2010a (outside)felodipine with 3% PVP K-12, PVP/VA, HPMCAS, PVAchot-stage growthat 70 °C about 10-, 7-, 4-fold and none; at 110 °C about 1.1-fold except PVP (2.9)R6, R7, X2
kestur2011 (outside)bifonazole and nimesulide with 5 wt% polymerhot-stage growth, 18–100 °CPAA slowed bifonazole 5-fold at 100 °C and 15-fold at 18 °CR7, R9
trasi2014a (outside)five hydrogen-bond-donor drugs with 10 mol% PVPmelt growth, 40–120 °Croughly 3- to 14-fold slower at most temperaturesR6, C10

Figure

Fig. 4 of kestur2010b: growth rate against temperature, pure felodipine and 3 wt% PVP of three molecular weights
Fig. 4 · kestur2010bgrowth rate against temperature, pure felodipine and 3 wt% PVP of three molecular weights

The top curve (circles, pure felodipine) peaks near 105 °C; the gap to the three PVP curves (triangles K-12, diamonds K-29/32, squares K-90) is the inhibition, widest at 70 °C kestur2010b R7.

Fig. 8 of kestur2010b: log growth rate against PVP K-29/32 concentration at six temperatures
Fig. 8 · kestur2010blog growth rate against PVP K-29/32 concentration at six temperatures

One straight line per temperature, 105 °C at the top and 70 °C at the bottom; the lower lines are steeper kestur2010b R14.

Why

The authors' account, with their hedges: over 70–110 °C growth slowed with cooling although the driving force rises, so molecular transport dominates and growth is diffusion-limited ("indicating") kestur2010b C22, C23. Tg (43.4–44.1 °C against 43.3 °C) and the one melting point (140.7 against 141.5 °C with 3% K-12) did not change, which rules out antiplasticization and makes a thermodynamic cause "unlikely"; the effect is "most likely kinetic in origin" kestur2010b R1, C26, C28, C34. "We speculate" that drug–PVP hydrogen bonds lower felodipine mobility, possibly by coupling drug and polymer motions, and the weakening of these bonds on heating "would also provide a potential explanation" for the weaker inhibition at high temperature kestur2010b C35, C37. The hydrogen-bond signal (NH 3341 → 3337 cm⁻¹) was the same for all three grades and was recorded at 25 °C and 20 wt% PVP, so it cannot explain the molecular-weight effect, and mobility at the growth temperatures was not measured kestur2010b R9, C30, X12. A companion study of polymer chemistry offered a related picture in which growth needs drug–polymer demixing at the front, harder when the bonds are strong and easier at high temperature where they weaken kestur2010a C42, C43. (synthesis: both readings predict the observed loss of inhibition on heating; neither was tested against a measured interfacial composition.)

Conditions and limits

One drug and one polymer chemistry, form II only, bulk growth in films sandwiched between cover glasses at 27–67 °C above Tg (synthesis: 70 − 43 and 110 − 43), polymer 0.5–4.5 wt% kestur2010b A1, A2, A3, M1. The authors themselves restrict Eq. 1 to temperatures well above Tg and below the growth maximum; the 110 °C series is not in the fit, and the printed constants give 40-fold where 35-fold was measured at 70 °C and 4.5 wt% kestur2010b C21, X14. The supercooling is computed from the form I melting point although form II grew kestur2010b X15.

Counterexamples and conflicts

The fall of pure felodipine growth from 105 to 70 °C is about 49-fold in this paper (synthesis: 1.7 × 10⁻⁷/3.5 × 10⁻⁹ kestur2010b R7.a, R7.f; text "approximately 2 orders of magnitude" from 110 to 70 °C kestur2010b C9, X9) but "3 orders of magnitude" in the polymer-chemistry study of the same year kestur2010a C10. At 110 °C K-12 and K-29/32 gave the same 3-fold reduction and the larger step lay between the two highest grades, the opposite of the 70 °C trend kestur2010b R8, X13. Some additives accelerate growth instead (see Crystallization tendency F19 and F22). The rise of the PVP factor on cooling is a felodipine result: for acetaminophen the factor fell on cooling, from about 9 at 100 °C to about 5 at 70 °C, and for flutamide and celecoxib it showed no trend over 40–70 and 70–120 °C (synthesis from the ratios above) trasi2012a R6; trasi2012b R3; mosqueragiraldo2014 R1. The temperature windows differ relative to each drug's Tg and growth maximum, so the comparison is not at matched conditions (synthesis: felodipine 70–110 °C against Tg 43 °C; acetaminophen 70–110 °C against Tg 21.2 °C; celecoxib 70–120 °C against Tg 55.3 °C) kestur2010b R1; trasi2012a R9.a; mosqueragiraldo2014 R5.a. The trend also failed above the temperature of fastest growth: for indomethacin α the PVP factor rose with temperature from 105 °C upward, after the polymer had lowered that temperature from 135 to 125 °C (see F29) tian2017 R12, R15. For celecoxib two papers disagree on the size of the PVP factor at 10% polymer, about 20–35-fold at 70–100 °C in 2014 and about 160–330-fold at 80–100 °C in 2016 (synthesis from the ratios above), with different preparation and growth set-ups mosqueragiraldo2014 P1, P3; xie2016b P9.

Transfer check

Measure melt growth of the drug's polymorph of interest at three temperatures between about Tg + 30 °C and the growth maximum, with 0, 1.5 and 3 wt% of the candidate polymer, and fit ln growth rate against concentration. A slope that steepens on cooling, as here (−0.49 to −0.82 per wt% kestur2010b R15), means the polymer protects most where the melt is most viscous; do not extrapolate the fit to storage temperatures near Tg kestur2010b C21. Choose the middle molecular weight first: K-29/32 gave most of the chain-length benefit while K-90 raised melt viscosity 10–20-fold kestur2010b C15, C29.

History

Konno and Taylor (2006) had seen irregular spherulites with dark droplets at 3% polymer and speculated that rejected polymer slows growth, without measuring growth konno2006 R2, C11, X14. In 2010 two papers from the group measured felodipine growth directly: the polymer-chemistry study ranked four polymers at 3% (see Miscibility and drug-polymer interactions F10) kestur2010a R6, and this study varied PVP amount, chain length and temperature kestur2010b A1, A2, A3. In 2012 the growth method was carried to flutamide and acetaminophen and in 2014 to celecoxib, where PVP slowed growth about tenfold or more but without the felodipine temperature trend trasi2012b C7; trasi2012a C15; mosqueragiraldo2014 C8; in 2013 Kestur and Taylor confirmed the felodipine trend from 60 to 100 °C for form I and form II kestur2013a R15. Later work extended the comparison of polymer effects across many drugs (see Crystallization tendency F19) trasi2014a R6, C11. Sato and Taylor (2015) and Tian and co-workers (2017) added enantiomer and polymorph comparisons with PVP, and Xie and Taylor (2016) a celecoxib series sato2015 C10; tian2017 C28; xie2016b C36; the title of this finding is unchanged.

F4

Topic 1Crystallization of the amorphous drug in dry dispersions4 of 15

A few percent of polymer barely lowers the driving force for crystallization; the proposed kinetic routes were not measured.

Flory–Huggins estimates put the activity (effective concentration) of nifedipine and felodipine in PVP at about 0.96 at a polymer volume fraction of 0.1 and 0.84 at 0.2 marsac2006a R19, C47. With 3 wt% PVP K-12 the felodipine melting point moved by only 0.8 °C kestur2010b R1.e, C26. The papers therefore attribute the inhibition to kinetics, in three different ways, none of them measured konno2006 C39, C40; marsac2006a R3, C48; kestur2010b C35, C42.

weakWeak to moderate: the small change in driving force is a robust estimate, but each kinetic mechanism rests on argument or on a model with inconsistent inputs marsac2006a K5; konno2006 K6; kestur2010b K6, K7, X4, X5.

Melting point depression by the additive, °Cfelodipine + 3 wt% PVP K-120.8 °Csix compounds + 1–10% PHB0–2 °Ccelecoxib + 10% PVP or surfactant1.7–4.5 °Ccelecoxib + 10% TPGS + 10% PVP12.0 °C

At a few percent of one additive the melting point, and with it the driving force, hardly moves; only the polymer–surfactant mixture shifts it markedly. kestur2010b R1.e, C26; sato2016 R7; mosqueragiraldo2014 R5

Flory–Huggins activity of the drug in PVP (nifedipine and felodipine nearly equal)PVP volume fraction 0.10.96PVP volume fraction 0.20.84PVP volume fraction 0.30.67

marsac2006a R19, C47

For your drug

  1. Measure the melting point depression of the drug with 3–5% of the polymer at 1 °C/min; a shift within about 1 °C means the polymer cannot act through the driving force at that level.
  2. Estimate the drug activity with Flory–Huggins and a measured χ; to tell the kinetic routes apart, image the crystal–amorphous interface (for example by nanoscale IR) for polymer enrichment, which none of these papers did.

kestur2010b R1.e; marsac2006a R19

How it works and key numbers
  1. Classical nucleation theory writes the rate as I = A\exp\left(-\left(\Delta G^{*} + \Delta G_{a}\right)/kT\right): a thermodynamic barrier set by interfacial energy against driving force, plus a kinetic barrier for molecules crossing onto the nucleus konno2006 E8, E9, C33.
  2. Route 1: a miscible polymer cannot enter the drug crystal, so a polymer-rich layer builds at the nucleus that "would impede" drug transport konno2006 C39.
  3. Route 2: PVP raises the activation energy for nucleation, more for felodipine (145 → 201 kJ/mol below Tg), whose amorphous hydrogen bonds are stronger than its crystal's marsac2006a R3, C48, C39.
  4. Route 3: drug–PVP hydrogen bonds couple drug and polymer motion and lower drug mobility ("We speculate"); because the growth rate stays constant, "it seems reasonable to conclude" that the chains are encaged in the crystal rather than expelled kestur2010b C35, C38, C42.
  5. Routes 1 and 3 disagree on where the polymer goes; they come from nucleation in films about 20 °C below Tg and growth in melts 57 °C above it, and no paper measured the polymer at an interface (synthesis) konno2006 P2; kestur2010b R23.
Model: PVP weight fraction at the growth front, 3% K-29/32 at 100 °Call PVP expelled (ε = 1)reached within about 52 s0.510% expelled (ε = 0.1)at 500 s0.461% expelled (ε = 0.01)at 500 s, still rising0.07

An expelled polymer should pile up at the front, yet the measured growth stayed constant over up to 60 h. kestur2010b R21, R19, C41

0.96 / 0.84drug activity in PVP at volume fraction 0.1 / 0.2marsac2006a R19, C47
0.8 °Cmelting point shift of felodipine with 3 wt% PVP K-12kestur2010b R1.e, C26
145 → 201 kJ/molfelodipine nucleation activation energy below Tg, without and with 3% PVPmarsac2006a R3, C20

Connections to other chapters

Evidence: data, conditions and papers

Finding F4. At a few percent polymer the driving force for crystallization is barely lowered, so the inhibition is read as kinetic, but the proposed kinetic routes were not measured and partly conflict

In short. Flory–Huggins estimates put the activity of nifedipine and felodipine in PVP at about 0.96 at a polymer volume fraction of 0.1 and 0.84 at 0.2 marsac2006a R19, C47, literature data for comparable systems predict little lowering below a fraction of about 0.5 konno2006 C35, R20, and 3 wt% PVP K-12 moved the felodipine melting point by only 0.8 °C kestur2010b R1.e, C26. All three papers therefore attribute the inhibition to kinetics: a raised barrier at the nucleus, perhaps from a polymer-rich layer konno2006 C39, C40, a higher nucleation activation energy (felodipine below Tg 145 → 201 kJ/mol with 3% PVP) marsac2006a R3, C48, or hydrogen bonds that lower drug mobility while the polymer is encaged in the growing crystal kestur2010b C35, C42. None of these was measured, and a polymer-rich layer at a steadily growing front is what the diffusion model of kestur2010b argues against (synthesis). Later papers found the same small melting-point shifts with 10 mol% or 10% w/w polymer for flutamide (Tm 108–110 against 110 °C) and acetaminophen (166.7–168.6 against 169 °C) and added a further kinetic reading: 3% PVP cut the growth of two felodipine polymorphs by similar factors, which the authors place in the liquid phase rather than at the crystal faces trasi2012b R7, C33; trasi2012a R9, C19; kestur2013a C6, C14.

Type. model result with observations in 2 drugs Strength. to moderate — the small driving-force change is a robust estimate (marsac2006a K5: moderate), but each kinetic mechanism rests on argument or a model with inconsistent inputs (konno2006 K6: weak; kestur2010b K6: weak, K7: weak to moderate; X4, X5).

How it was shown

Marsac and co-workers (2006) computed drug activity in PVP from the Flory–Huggins equation with χ from melting point depression, and measured nucleation activation energies with and without 3% PVP marsac2006a E10, R18, R3. Kestur and co-workers (2010) measured the felodipine melting point with 3 wt% PVP and modelled PVP diffusion around a growing crystal that expels a fraction ε of the polymer kestur2010b P6, P10, E9, E11.

What the data show

The predicted activity reductions were small and nearly the same for both drugs, and the melting point moved within its standard deviation marsac2006a R19, C47; kestur2010b R1.e, X11. In the model expelled PVP piled up just ahead of the front, while the measured growth stayed constant over up to 60 h kestur2010b R21, R19, C41.

testsystemresultids
Flory–Huggins activity, χ −3.8 and −4.2nifedipine and felodipine in PVP≈0.96 (Φ 0.1), ≈0.84 (0.2), ≈0.67 (0.3), nearly equal for bothmarsac2006a R19, R18, C47
DSC melting offset, 1 °C/minfelodipine with 3 wt% PVP K-12140.7 vs 141.5 °C, within the ±1 °C SDkestur2010b R1.e, M1, X11
DSC Tm at 10 °C/minflutamide with 10 mol% of six polymers; acetaminophen with 10% w/w of seven108–110.1 vs 110 °C; 166.7–168.6 vs 169 °Ctrasi2012b R7; trasi2012a R9
Arrhenius slopes below Tg, alone → 3 wt% PVPfelodipine; nifedipine145 → 201; 122 → 127 kJ/molmarsac2006a R3, C20
diffusion model of expelled PVP, 3% K-29/32, 100 °Cfelodipine growth frontsurface PVP 0.5 at ≈52 s (ε = 1); 0.07 at 500 s (ε = 0.01)kestur2010b R21, R19
Fig. 12 of kestur2010b: predicted PVP weight fraction at the crystal surface against time for three expelled fractions
Fig. 12 · kestur2010bpredicted PVP weight fraction at the crystal surface against time for three expelled fractions

If the crystal pushes all polymer out (dotted), the front becomes polymer-rich within a minute; even 1% expulsion (solid) keeps the front composition rising kestur2010b R21.

Why

Three kinetic routes were proposed: a polymer-rich layer at the nucleus that "would impede" drug transport konno2006 C39; a higher activation energy for nucleation, more for felodipine marsac2006a C48; and drug–PVP hydrogen bonds that lower drug mobility, the chains being encaged in the crystal rather than expelled ("it seems reasonable to conclude") kestur2010b C35, C42. (synthesis: the first and third routes disagree on where the polymer goes and come from different regimes, nucleation in films at 22 °C and growth in melts at 100 °C; no paper measured the polymer at an interface) konno2006 P2; kestur2010b R23.

Limits and transfer

Activities are Flory–Huggins estimates for non-equilibrium glasses, and the model's tracer diffusivity cannot be reproduced from the stated solvent viscosity marsac2006a C46; kestur2010b X4. Measure the melting point depression with 3–5% of the polymer at 1 °C/min: a shift within about 1 °C means the polymer cannot act through the driving force at that level.

How it was shown

Konno and Taylor (2006) wrote the nucleation rate with classical nucleation theory as I = A\exp\left(-\left(\Delta G^{*} + \Delta G_{a}\right)/kT\right), a thermodynamic barrier set by interfacial energy against driving force plus a kinetic barrier for molecules crossing onto the nucleus, and estimated the change in drug activity from the Flory–Huggins equation with literature parameters for PVP–sucrose and PVP–water konno2006 E8, E9, C33, C35. Marsac and co-workers (2006) used the same activity equation with χ from melting point depression (−3.8 nifedipine, −4.2 felodipine) and measured activation energies from Arrhenius plots of nucleation with and without 3% PVP marsac2006a E10, R18, E2, R3. Kestur and co-workers (2010) tested the driving force through melting point depression and modelled PVP diffusion around a disk-shaped crystal growing at the measured rate (2.37 × 10⁻⁸ m/s, 3% K-29/32, 100 °C) with a Stokes–Einstein tracer diffusivity (4.98 × 10⁻¹⁶ m²/s) and a fraction ε of polymer expelled by the crystal kestur2010b P6, P10, R23, E9, E11. Sato and Taylor (2016) measured melting points of physical mixtures with 1–20% PHB and IR of melt films sato2016 P4, P5; Tian and co-workers (2017) wrote the Flory–Huggins free energy of mixing without inputs tian2017 E2.

What the data show

The predicted activity reductions were small and nearly the same for both drugs (0.96, 0.84 and 0.67 at PVP volume fractions of 0.1, 0.2 and 0.3), so on the driving-force term alone nifedipine "would be expected" to keep nucleating faster at any PVP level marsac2006a R19, C47. With 3% PVP the activation energy rose for both drugs (nifedipine 122 → 127 below Tg and 78 → 103 kJ/mol above; felodipine 145 → 201 and 95 → 111), significantly for felodipine below Tg and nifedipine above Tg marsac2006a R3, C20. The nucleation rate fell 40–60-fold with 3% of any of three polymers that differ in Tg and hydrogen bonding, whereas dilution alone would scale with the polymer fraction konno2006 R4, C37 (see F1). In the growth model, expelled PVP piled up just ahead of the front: with ε = 1 the surface weight fraction reached 0.5 within about 52 s, with ε = 0.1 about 0.46 at 500 s and even with ε = 0.01 about 0.07 and still rising, while the measured growth stayed constant over up to 60 h kestur2010b R21, R19, C41.

The papers of 2012–2014 measured the melting point with each additive. With 10 mol% of six polymers flutamide melted at 108–110.1 °C against 110 °C, so the authors judge the degree of supercooling hardly changed trasi2012b R7, C33; with 10% w/w of seven polymers acetaminophen melted at 166.7–168.6 °C against 169 °C ("similar for all systems") trasi2012a R9, C19. Celecoxib with 10% of PVP or one surfactant melted 1.7–4.5 °C below the pure drug (163.46 °C), and with 10% TPGS plus 10% PVP 12.0 °C below (151.49 °C) mosqueragiraldo2014 R5. For felodipine, 3% PVP slowed form I and form II by similar factors at 60–80 °C (ratios 15.8–13.2 and 18.7–12.5) kestur2013a R15, and in powders it slowed the early crystallization 60–77-fold but growth only about 2-fold (surface) and 7-fold (bulk) kestur2013b R15, R12.

The papers of 2016–2017 again found small melting-point changes and added a driving-force argument. With 1–10% PHB the melting points of six compounds moved by 0–2 °C, and by up to 4 °C at 20%, and IR showed no band shifts, so the authors infer an unchanged driving force and an effect on mobility (see F28) sato2016 R7, R9, C18, X11. For indomethacin with 10% HPMC, HPMCAS or PVP, Tian and co-workers wrote the Flory–Huggins free energy of mixing and argued that stronger drug–polymer interaction "would" lower the driving force, so that PVP acts "most likely" through both lower mobility and lower driving force; above the temperature of fastest growth they name melting point depression and a smaller driving force as "possible reasons" for the steep rise in inhibition tian2017 E2, C30, C31, C36. Neither the interaction parameter nor the driving force was measured tian2017 X13.

papersystemmethod and conditionsresultids
marsac2006anifedipine and felodipine in PVPFlory–Huggins activity, χ −3.8 and −4.2activity ≈0.96 (Φ 0.1), ≈0.84 (0.2), ≈0.67 (0.3), nearly equal for bothR19, R18, C47
trasi2012bflutamide with 10 mol% of six polymersDSC Tm at 10 °C/min108–110.1 °C against 110 °CR7
trasi2012aacetaminophen with 10% w/w of seven polymers (physical mixtures)DSC onset Tm at 10 °C/min166.7–168.6 °C against 169 °CR9
mosqueragiraldo2014celecoxib with 10% additive; 10% TPGS + 10% PVPDSC Tm1.7–4.5 °C lower; 12.0 °C lower for TPGS + PVPR5
kestur2013afelodipine forms I and II, 3% PVPgrowth-rate ratio, 60–100 °Csimilar factors for both forms within error at 60–80 °CR15, C14
konno2006felodipine with 3–25% polymerargument from PVP–sucrose and PVP–water datasignificant activity lowering only above Φ ≈ 0.5C35, R20
kestur2010bfelodipine with 3 wt% PVP K-12DSC melting offset, 1 °C/min140.7 vs 141.5 °C, within the ±1 °C SDR1.e, M1, X11
marsac2006aalone and with 3 wt% PVPArrhenius slopesfelodipine below Tg 145 → 201 kJ/mol; nifedipine 122 → 127R3, C20
kestur2010b3% K-29/32, 100 °Cdiffusion model of expelled PVPsurface PVP 0.5 at ≈52 s (ε = 1); 0.07 at 500 s (ε = 0.01); growth measured constantR21, R19
sato2016six compounds with 1–20% PHBDSC Tm of physical mixtures; IRTm 0–2 °C lower at 1–10%, up to 4 °C at 20%; no band shiftsR7, R9, X11
tian2017indomethacin with 10% HPMC, HPMCAS, PVPFlory–Huggins argument, not measuredPVP read as lowering both mobility and driving forceE2, C31, X13
marsac2006b (outside)nifedipine with 30 and 40% PVPHoffman with mixing termΔG of crystallization −9.0 → −8.4 and −7.95 kJ/mol at 20 °CR12, C41

Figure

Fig. 13 of marsac2006a: Flory–Huggins drug activity against PVP volume fraction
Fig. 13 · marsac2006aFlory–Huggins drug activity against PVP volume fraction

The nifedipine (solid) and felodipine (dashed) curves nearly coincide and stay above about 0.8 up to a volume fraction of 0.2 marsac2006a R19.

Fig. 12 of kestur2010b: predicted PVP weight fraction at the crystal surface against time for three expelled fractions
Fig. 12 · kestur2010bpredicted PVP weight fraction at the crystal surface against time for three expelled fractions

If the crystal pushes all polymer out (dotted), the front becomes polymer-rich within a minute; even 1% expulsion (solid) keeps the front composition rising kestur2010b R21.

Why

The three kinetic proposals, with the authors' hedges: (1) a miscible polymer cannot enter the drug crystal, is rejected and diffuses away slowly below Tg, so a polymer-rich layer builds at the nucleus that "would impede" drug transport and "may also" raise the surface cost konno2006 C39; the dark droplets on crystallites grown with 3% polymer are "thought" to be such a phase konno2006 R2, C11, C42. (2) PVP raises the activation energy for nucleation, more for felodipine, whose amorphous hydrogen bonds are stronger than its crystal's marsac2006a C48, C39. (3) drug–PVP hydrogen bonds couple drug and polymer motion and lower drug mobility ("We speculate"), and because a constant growth rate requires a constant front composition, "it seems reasonable to conclude" that the chains are encaged in the crystal rather than expelled kestur2010b C35, C38, C42. (synthesis: proposals 1 and 3 disagree on where the polymer goes; they come from different regimes, nucleation in films at 22 °C, about 20 °C below Tg, and growth in melts at 100 °C, 57 °C above it konno2006 P2; kestur2010b R23, so both may hold in their own regime, but no paper measured the polymer at an interface.) The driving-force argument is robust within its own assumptions; the same conclusion was reached for higher PVP contents by the miscibility papers, which found most dispersions supersaturated and their stability "predominantly" kinetic (see Miscibility and drug-polymer interactions F9) marsac2006b C41. (4) Two polymorphs of felodipine have different crystal surfaces but grow from the same liquid, so a polymer acting at the faces should slow them by different factors; the similar ratios "most likely" mean that PVP acts through the amorphous phase kestur2013a C1, C6. (5) For felodipine powders, the authors argue that growth inhibition alone cannot explain a 60–77-fold slower crystallization, so PVP "must" also slow nucleation (see F17) kestur2013b C34, C35. (synthesis: reading 4 is compatible with the coupling of drug and polymer motion proposed in 2010 (proposal 3) and less so with a polymer layer at the face (proposal 1), but neither it nor reading 5 involved a measurement at an interface.)

Conditions and limits

Activities are Flory–Huggins estimates for non-equilibrium glasses with cited χ values and an unprinted volume ratio marsac2006a C46, E10. The felodipine–polymer χ was not known for HPMCAS or HPMC konno2006 C35. Only one Tm (3% K-12) was measured, and the crystal–melt interfacial energy, the other thermodynamic lever, was not measured kestur2010b X11, C27. The model's tracer diffusivity cannot be reproduced from the stated solvent viscosity, the radial front speed is taken as the diameter slope, and predicted weight fractions exceed 1 kestur2010b X4, X5, X16.

Counterexamples and conflicts

For felodipine nucleation, hydrogen-bond strength (PVP > HPMC > HPMCAS) did not correlate with inhibition konno2006 C31, whereas for felodipine melt growth the hydrogen-bond order of four polymers matched the growth-inhibition order kestur2010a C26 (see Miscibility and drug-polymer interactions F12). (synthesis: hydrogen bonding may matter for growth and not for nucleation, or the 70%-polymer IR used by konno2006 misrepresents 3–25% films konno2006 X11.) Konno's droplets suggest polymer outside the crystal, while the 2010 PXRD and model place PVP inside it without changing the lattice; the PXRD shows only three reflections of one family kestur2010b C43, X10. Where melting-point depression is large, the driving force may matter after all: with 10% TPGS plus 10% PVP celecoxib melted 12 °C lower and grew 0.03 times as fast as with PVP alone at 120 °C, which the authors say "could contribute" through a smaller driving force near Tm; but SLS plus PVP, with a 7.3 °C depression, grew faster than PVP alone, so the depression does not order the mixtures (see F22) mosqueragiraldo2014 R5, R2.b, C33, X13. At 90–100 °C the felodipine polymorph ratios differed 1.2–1.9-fold with non-overlapping error bars, and the form I ratios at 70–80 °C do not follow from the plotted rates, which weakens the equal-factor reading kestur2013a X6, X7. Tian and co-workers set their result against the liquid-phase reading of the felodipine polymorph test: each polymer slowed three indomethacin polymorphs by different factors, which they read as action at each crystal–melt interface (see F29) tian2017 C38, C39.

Transfer check

Measure the melting point depression of the drug with 3–5% of the polymer at 1 °C/min: a shift within about 1 °C, as here, means the polymer cannot act through the driving force at that level kestur2010b R1.e. Estimate the drug activity with Flory–Huggins and a measured χ; above about 0.8 at the planned polymer fraction the polymer must act kinetically marsac2006a R19. To tell the kinetic routes apart, image the crystal–amorphous interface (for example by nanoscale IR) for polymer enrichment, which none of these papers did.

History

Crowley and Zografi (2003, outside the library) had proposed polymer accumulation at the crystal front for indomethacin with low PVP konno2006 C39. Konno and Taylor (2006) and Marsac and co-workers (2006) first argued in the library that a few percent of polymer acts on kinetics, not on the driving force konno2006 C40; marsac2006a C47, C48. Kestur and co-workers (2010) tested the front-accumulation idea quantitatively and replaced it by encaging kestur2010b C42. In the same year the polymer-chemistry study linked growth inhibition to drug–polymer demixing at the front (see Miscibility and drug-polymer interactions F12) kestur2010a C42. In 2012 the unchanged melting points with 10 mol% or 10% w/w polymer were found again for flutamide and acetaminophen trasi2012b C33; trasi2012a C19; in 2013 Kestur and co-workers added the polymorph test, placing the PVP effect in the liquid, and the powder argument that PVP acts mainly on nucleation kestur2013a C6; kestur2013b C36; in 2014 a polymer–surfactant mixture gave the first large melting-point depression in the chapter, offered as a partial cause of slower growth mosqueragiraldo2014 C33. The short part of this finding gained one sentence for these papers; its title is unchanged. In 2016 a low-Tg polymer without interactions sped growth with an unchanged melting point (see F28), and in 2017 the indomethacin polymorph study moved the kinetic reading from the liquid to the crystal–melt interface sato2016 C18; tian2017 C39.

F5

Topic 1Crystallization of the amorphous drug in dry dispersions5 of 15

Dispersion Tg, Tg-scaled temperature and bulk mobility measures do not rank polymers or drugs by crystallization rate.

HPMCAS and HPMC left the Tg of felodipine at about 42–45 °C up to 25% polymer while PVP raised it to about 55 °C, yet all three slowed dry nucleation equally konno2006 R6, R4, C26. Adding 0.5–4.5 wt% PVP left Tg unchanged while slowing melt growth up to 35-fold kestur2010b R1, R13. The same held for humid films, for growth of flutamide and acetaminophen, and for storage of resveratrol, curcumin and celecoxib dispersions konno2008 R13, C26; trasi2012b C33; trasi2012a C18; wegiel2013b C33; wegiel2014 C22; xie2016b C46.

strongStrong: sixteen papers each give a clean contrast in which Tg or a mobility measure moves against or out of proportion to crystallization, though Tg was always measured on bulk samples and crystallization on films konno2006 K3, X12; marsac2008a K3, X12.

Felodipine with 25% polymer: dry Tg, °Cfelodipine alone≈44PVP≈55HPMCAS≈44HPMC≈43

Only PVP raises Tg, yet the three polymers slowed dry nucleation equally. konno2006 R6, R4, C26

Resveratrol dispersions: Tg of the polymer, °CPVP K29/32among the most stable159HPMC145CMCAB137PAA128HPMCAS111PVP K-12behaved like K29/3291E100second only to PVP41

The polymer Tg order did not follow storage stability. wegiel2013b M2, M3, M4, M5, M6, M7, M8, R12, R18, C33

For your drug

  1. Do not screen polymers or drug candidates by dispersion Tg or T/Tg at polymer levels below about 25%.
  2. Use Tg only to compare the same formulation across storage conditions, and measure nucleation or growth directly at each condition; a coupling exponent well below 1 warns that Tg-based shelf-life estimates will be optimistic.

rumondor2010 C27; marsac2008a C21

How it works and key numbers
  1. A higher Tg "would certainly contribute" to inhibition but "is not the only factor" konno2006 C27.
  2. Either factors other than Tg decide nucleation, or DSC relaxation does not describe the motion involved; modes of mobility not reflected by Tg "must also be considered" marsac2006a C37; marsac2008a C30.
  3. Bulk melt viscosity "cannot be used as a precise measure" of felodipine mobility in PVP melts: K-90 raised it 10–20-fold without matching inhibition kestur2010b C24, C29.
  4. Below Tg, felodipine crystal growth outpaced the Adam–Gibbs–Vogel mobility and matched it only with a coupling exponent of 0.5, possibly through decoupling of diffusion and viscosity or faster growth at the free surface of the films rumondor2010 R7, C26, C27, C28, C29.
  5. Within one composition Tg still matters: nucleation fell as Tg − T rose, and a miscible surfactant that lowered the Tg of celecoxib by about 10 °C did speed its growth marsac2008a C21; mosqueragiraldo2014 R5, R12.
≈55 vs ≈44 °Cdry Tg with 25% PVP vs 25% HPMCAS, at equal nucleationkonno2006 R6, R4
up to 35-foldslower melt growth with PVP at unchanged Tgkestur2010b R1, R13
0.4 °CTg gap between the most and the least stable curcumin dispersionwegiel2014 R13, C22

Connections to other chapters

2 more connections
Evidence: data, conditions and papers

Finding F5. Dispersion Tg, Tg-scaled temperature and bulk mobility measures do not rank polymers or drugs by crystallization rate

In short. HPMCAS and HPMC left the Tg of felodipine at about 42–45 °C up to 25% while PVP raised it to about 55 °C, yet all three slowed dry nucleation equally konno2006 R6, R4, C26; 0.5–4.5 wt% PVP left Tg at 43.4–44.1 °C against 43.3 °C while slowing melt growth up to 35-fold kestur2010b R1, R13. Nifedipine and felodipine with the same Tg nucleated 2–20 times apart, dry and at equal Tg − T with water marsac2006a C13; marsac2008a C23, and humid felodipine films at the same T/Tg spanned about 30-fold in rate konno2008 R13, C26. Enthalpy relaxation ran against the ranking (the faster-nucleating nifedipine dispersion relaxed more slowly), melt viscosity rose 10–20-fold with K-90 without matching inhibition, and felodipine crystal growth below Tg outpaced the Adam–Gibbs–Vogel mobility, matching it only with a coupling exponent of 0.5 marsac2006a R7; kestur2010b C29; rumondor2010 R7, C26, C27. In 2012–2014 the same held for growth of flutamide and acetaminophen, where 10 mol% or 10% w/w polymer raised Tg by only 1.7–4.2 °C whatever the growth effect, and for storage of resveratrol and curcumin dispersions, where E100 (polymer Tg 41 °C) protected best and dispersion Tg values of 62–68 °C did not follow the polymer ranking trasi2012b R7, C33; trasi2012a R9, C18; wegiel2013b R18, C33; wegiel2014 R13, C22. A miscible surfactant that lowered the Tg of celecoxib by about 10 °C did speed its growth, but even at equal T − Tg the growth rates still differed up to about 12-fold (see F22) mosqueragiraldo2014 R5, R12, X4.

Type. observation in 12 drugs or model compounds, about 20 polymers and additives and 4 mobility measures Strength. sixteen papers, each with a clean contrast in which Tg or a mobility measure moves against or out of proportion to crystallization (konno2006 K3: moderate to strong; marsac2006a K2: moderate to strong; marsac2008a K3: moderate to strong; trasi2012b K3: moderate; wegiel2013b K5 and wegiel2014 K7: moderate to strong), though Tg was always measured on bulk samples and crystallization on films (konno2006 X12; marsac2008a X12).

How it was shown

Konno and Taylor (2006) compared onset Tg and enthalpy relaxation of felodipine dispersions with nucleation rates of spin-coated films konno2006 P3, P6, R6, R9. The 2008 moisture studies plotted nucleation of humid films against T/Tg and Tg − T, and Rumondor and co-workers (2010) compared growth with an Adam–Gibbs–Vogel relaxation time konno2008 P9, R13; marsac2008a P9, R8; rumondor2010 P8, E1, R7. Later papers set Tg against growth or storage outcomes trasi2012a P4, R9; wegiel2014 P7, R13; xie2016b P7.

What the data show

With 25% polymer the dry Tg was about 55 °C with PVP and 42–45 °C with HPMCAS and HPMC, yet the nucleation rates of the three systems were equal konno2006 R6, R4.

systemTg or mobility measurecrystallizationids
felodipine, 3–25% polymer, dryTg ≈42–45 °C (HPMCAS, HPMC) vs ≈55 °C (PVP) at 25%nucleation equalkonno2006 R6, R4, C26
felodipine films, 7–25% polymer, humidrate against T/Tgno single trend; ≈30-fold span at T/Tg ≈0.68konno2008 R13, C26, X1
acetaminophen, 10% w/w polymersTg +1.7–4.2 °Cstrong and weak inhibitors at similar Tgtrasi2012a R9, C18
curcumin 75:25 with five polymersTg 61.7–68.3 °C; E100 and PVP 0.4 °C apartbest and worst in storagewegiel2014 R13, C22
celecoxib 6:4 with five polymers, after 94% RHTg 37.4–42.1 °C for fouroutcomes from under a month to 150 daysxie2016b R17, R23, C46
felodipine films, 13–75% RHAGV relaxation timegrowth less steep than mobility; ξ = 0.5 fitsrumondor2010 R7, C27
Fig. 11 of konno2008: nucleation rate against T/Tg for 7, 15 and 25% polymer
Fig. 11 · konno2008nucleation rate against T/Tg for 7, 15 and 25% polymer

At the same abscissa the rates scatter over more than a decade, with no single trend konno2008 R13.

Why

A higher Tg "would certainly contribute" to inhibition but "is not the only factor" konno2006 C27. Either factors other than Tg decide nucleation, or DSC relaxation does not describe the motion involved marsac2006a C37. Growth faster than AGV mobility predicts may reflect decoupling of diffusion and viscosity or growth at the surface of uncovered films ("Possible explanations") rumondor2010 C28, C29. The later authors draw the same conclusion for growth and storage trasi2012a C18; wegiel2014 C22.

Limits and transfer

Tg was always measured on samples prepared differently from the films konno2006 X12; konno2008 X6. A large Tg drop does change growth: TPGS and sucrose palmitate lowered the Tg of celecoxib by about 10 °C and sped its growth up to about 85-fold at 70 °C mosqueragiraldo2014 R1, R5, R12. Do not screen polymers or drug candidates by dispersion Tg or T/Tg at polymer levels below about 25%; use Tg only to compare the same formulation across storage conditions.

How it was shown

Konno and Taylor (2006) measured onset Tg of rotary-evaporated dispersions at 0–100 wt% polymer by DSC and enthalpy relaxation of 9:1 dispersions aged at 2 °C (KWW fit), and compared both with the nucleation rates of spin-coated films konno2006 P3, P4, P6, R6, R9. Marsac and co-workers (2006) compared Tg and enthalpy recovery at 23.5 °C of the two drugs and their 10 wt% PVP dispersions marsac2006a P7, P9. Konno and Taylor (2008) plotted the nucleation rates of humid films against T/Tg, using Tgs of bulk dispersions equilibrated at each RH konno2008 P9, R13; Marsac and co-workers (2008) plotted nucleation against Tg − T marsac2008a P9, R8. Kestur and co-workers (2010) measured Tg and melt viscosity of felodipine with 3 wt% PVP and scaled growth by viscosity kestur2010b P4, P5, R16. Rumondor and co-workers (2010) compared drug-alone growth from 13 to 75% RH with an Adam–Gibbs–Vogel relaxation time computed from cited Tg values at each RH rumondor2010 P8, E1, R7. Trasi and Taylor (2012) measured onset Tg of flutamide melts with 10 mol% of six additives and of acetaminophen dispersions with 10% w/w of seven polymers by DSC at 10 °C/min after cooling at 15 °C/min, and compared them with growth rates of the same compositions trasi2012b P5, R7; trasi2012a P4, R9. Wegiel and co-workers measured polymer and dispersion Tg (second heating, modulated DSC for PVP) and set them against storage outcomes for resveratrol (2013) and curcumin (2014) wegiel2013b P6, P7, R18; wegiel2014 P7, R13. Mosquera-Giraldo and co-workers (2014) replotted celecoxib growth rates with 10% additive against T − Tg mosqueragiraldo2014 P7, R12. Later papers compared Tg of ATP–polymer glasses with enantiomer growth, Tg of celecoxib dispersions after 3 days at 56–94% RH with storage, Tg of humidified tacrolimus and its HPMC dispersion with storage at 40 °C/75% RH, and Tg of precipitated lumefantrine dispersions with storage sato2015 P6; xie2016b P7; trasi2017 P3; bhujbal2021 P7; the PHB paper replotted growth against T − Tg sato2016 P6.

What the data show

At 7, 15 and 25% polymer the dry Tgs were about 44, 48 and 55 °C with PVP, 42, 44 and 44 °C with HPMCAS and 45, 42 and 43 °C with HPMC, against about 44 °C for felodipine, and the PVP increase starts only near 15% konno2006 R6, X15; the nucleation rates of the three systems were equal konno2006 R4. At 2 °C the 9:1 dispersions relaxed with τ of 208 h (PVP), 319 h (HPMC) and 687 h (HPMCAS), an order that differs from the Tg order and was not related to nucleation by the authors konno2006 R9, X13. Nifedipine and felodipine glasses had Tg onsets of 42.3 and 43.1 °C and τ of 6.3 and 4.2 h; with 10 wt% PVP τ became 42.1 h for nifedipine and 16.7 h for felodipine, so the faster-nucleating dispersion was the slower-relaxing one marsac2006a R4.c, R4.n, R7. Felodipine with 10 wt% PVP lost mobility (65% against 84% of the maximum enthalpy recovery at 16 h) although its Tg fell to 40.5 °C marsac2006a R8, C26. After 75% RH all felodipine films with up to 25% polymer had Tgs of about 30–35 °C, below dry felodipine, yet most nucleated more slowly than dry felodipine konno2008 R7, C27. At T/Tg ≈0.68–0.69 the rates ranged from about 2.9 × 10² (25% HPMC) to 9.4 × 10³ m⁻³ s⁻¹ (7% PVP) konno2008 R13. At a given Tg − T more PVP lowered felodipine nucleation further, about 1.7 orders with 10% and 2.2 orders with 25% PVP at about 15 °C (plot readings) marsac2008a R8, X8. With 3 wt% PVP the zero-shear viscosity at 100 °C was about 58 (K-12), 156 (K-29/32) and 690 Pa·s (K-90) against 44 Pa·s, and viscosity-corrected growth with K-12 lay below that of pure felodipine kestur2010b R10, R16, C24. Between T/Tg ≈0.94 and ≈0.97 log(growth rate) + 1 rose from about −0.59 to −0.23, much less steeply than the AGV mobility line rumondor2010 R7, C26.

In flutamide (Tg −3.1 °C) the six polymers gave onset Tg of −1.07 to 0.6 °C with little difference between them, while their growth effects ranged from none (PAA, Tg not obtained because it crystallized on cooling) to tenfold (PVP); nilutamide raised Tg most (to 2.5 °C) but was not the best inhibitor trasi2012b R7, R3, C33. In acetaminophen (Tg 21.2 °C) the seven polymers gave 22.9–25.4 °C: PAA (+4.2) and PVP (+3.9) were strong growth inhibitors, HPMC (+3.4) and E100 (+3.0) weak ones trasi2012a R9, R6, C18. For resveratrol the polymer Tg order PVP K29/32 (159 °C) > HPMC (145) > CMCAB (137) > PAA (128) > HPMCAS (111) > PVP K-12 (91) > E100 (41 °C) did not follow storage stability, in which PVP K-12 behaved like K29/32 and E100 was second only to PVP; dry dispersion Tg values were 63–85 °C wegiel2013b M2, M3, M4, M5, M6, M7, M8, R12, R18, C33. For curcumin at 75% drug, the dispersions had Tg of 61.7–68.3 °C; the most stable (E100, 62.4 °C) and the least stable (PVP, 62.8 °C) differed by 0.4 °C wegiel2014 R13, C22. With 10% surfactant the Tg of celecoxib fell from 55.34 to 44.81 (TPGS) and 44.46 °C (sucrose palmitate) and growth at 70 °C rose about 85- and 7-fold; replotted at equal T − Tg the binary curves came together to within about 12-fold at about 25 °C above Tg, but TPGS stayed about 8 times above the drug and the PVP-containing ternaries stayed far apart mosqueragiraldo2014 R5, R1, R12, X4.

The papers of 2015–2021 add four cases. HPMCAS-HF slowed one enantiomer of ATP about twice as much as the other while every sample kept a Tg of 14.3–18.4 °C sato2015 R1, R5, C6. Celecoxib dispersions held 3 days at 94% RH had Tgs of 37.4–42.1 °C with four polymers, yet the PVP dispersion crystallized within a month and the PVPVA and HPMCAS ones lasted 150 and 115 days; the authors state that Tg "was not predictive" xie2016b R17, R23, C46. Pure amorphous tacrolimus and its 1:1 HPMC dispersion had similar Tgs after 75% RH (51.4 and 49.0 °C), but only the drug alone crystallized within 4 weeks at 40 °C/75% RH trasi2017 R15, R16. In lumefantrine dispersions the 20:80 compositions had the lowest Tg (45 °C with HPMCAS, 88 °C with HPMCP) and stayed amorphous as long as the others bhujbal2021 R10, R4, C46. The 2014 limit also holds for a polymer: 5–10% PHB lowered the Tg of three high-Tg compounds by 5–12 °C and sped their growth up to tenfold, and against T − Tg the rates fell close to those of the pure compounds (see F28) sato2016 R7, R10, C21.

papersystemmethod and conditionsresultids
konno2006felodipine, 3–25% polymerDSC onset Tg vs film nucleationTg ≈42–45 °C (HPMCAS, HPMC) vs ≈55 °C (PVP) at 25%; nucleation equalR6, R4, C26
trasi2012bflutamide, 10 mol% additivesonset Tg vs diameter growth, 40–70 °CTg +2.0–3.7 °C for polymers, +5.6 °C for nilutamide; no rankingR7, C33
trasi2012aacetaminophen, 10% w/w polymersonset Tg vs radial growth, 70–110 °CTg +1.7–4.2 °C; strong and weak inhibitors at similar TgR9, C18
wegiel2013bresveratrol with seven polymers, 60–85% polymerpolymer and dispersion Tg vs storage at five conditionsE100 (Tg 41 °C) and PVP K-12 (91 °C) among the most stableR18, R12, C33
wegiel2014curcumin 75:25 with five polymersdispersion Tg vs days to crystallinity61.7–68.3 °C; E100 and PVP 0.4 °C apart, best and worstR13, C22
mosqueragiraldo2014celecoxib with 10% surfactantgrowth vs T − Tgspread ≈85-fold at 70 °C narrows to ≈12-fold at equal T − TgR12, C30, X4
konno20069:1 dispersionsenthalpy relaxation at 2 °Cτ 208 (PVP), 319 (HPMC), 687 h (HPMCAS)R9, X13
marsac2006anifedipine vs felodipine, 0 and 10% PVPTg; KWW at 23.5 °Csame Tg; τ 42.1 vs 16.7 h with PVP, nifedipine still fasterR4.c, R7, C13
konno20087–25% polymer, humidrate vs T/Tgno single trend; ≈30-fold span at T/Tg ≈0.68R13, C26, X1
marsac2008a0–25% PVP, humidrate vs Tg − Tnifedipine 5–20 times faster at equal Tg − T; more PVP slower at equal Tg − TR8, C22, C23
kestur2010bfelodipine, 0.5–4.5 wt% PVPTg; viscosity at 90–110 °CTg unchanged; K-90 raises viscosity 10–20-fold with modest extra inhibitionR1, R10, C29
rumondor2010felodipine films, 13–75% RHgrowth vs AGV relaxationgrowth less steep than mobility; ξ = 0.5 fitsR7, C27
sato2015ATP enantiomers with 5% polymersDSC Tg vs growthTg 14.3–18.4 °C in all; HPMCAS-HF splits the enantiomers ≈2-foldR1, R5
xie2016bcelecoxib 6:4 with five polymers after 94% RHDSC Tg vs storage37.4–42.1 °C for four; outcomes from under a month to 150 daysR17, R23, C46
trasi2017amorphous tacrolimus vs 1:1 HPMC dispersionTg after 75% RH vs 40/75 storage51.4 and 49.0 °C; drug crystalline, dispersion amorphous at 4 weeksR15, R16
sato2016griseofulvin, DPB, celecoxib with 5–10% PHBgrowth vs T − Tgspeed-up close to the pure-compound lineR10, C21
kestur2011 (outside)bifonazole and nimesulide, 5 wt% polymerDSC Tg vs growthTg barely changed; no correlation with growth inhibitionC12

Figure

Fig. 11 of konno2008: nucleation rate against T/Tg for 7, 15 and 25% polymer
Fig. 11 · konno2008nucleation rate against T/Tg for 7, 15 and 25% polymer

At the same abscissa the rates scatter over more than a decade, with no single trend; the plotted values reproduce 25/Tg in °C rather than a kelvin ratio, which keeps the order but not the meaning of a reduced temperature konno2008 R13, X1.

Fig. 7 of rumondor2010: growth rate of amorphous felodipine and AGV mobility against T/Tg
Fig. 7 · rumondor2010growth rate of amorphous felodipine and AGV mobility against T/Tg

The 13–75% RH growth points follow the dashed line with a coupling exponent of 0.5, not the solid AGV line; the four high-RH points lie far above both rumondor2010 R7, X9.

Why

The authors' account, with their hedges: a higher Tg "would certainly contribute" to inhibition but "is not the only factor" konno2006 C27; either factors other than Tg decide nucleation, or DSC relaxation does not describe the motion involved marsac2006a C37; modes of mobility not reflected by Tg "must also be considered", and binary mixtures can be less mobile than the pure drug at a similar Tg marsac2008a C30; marsac2006a C26. Bulk viscosity "cannot be used as a precise measure" of felodipine mobility in PVP melts kestur2010b C24, C29. Growth faster than AGV mobility predicts may reflect decoupling of diffusion and viscosity or growth at the surface of uncovered films, much faster than in the bulk ("Possible explanations") rumondor2010 C28, C29. (synthesis: Tg-scaling assumes that every system has the same mobility at its Tg and that crystallization follows that mobility one to one; the polymer effects of F1 and F3 act at low polymer fractions that barely move Tg, and between drugs the crystal side of F2 decides, so Tg cannot carry the ranking.) The later authors draw the same conclusion: Tg rises "cannot completely explain" growth trasi2012b C33, "cannot explain" the differences between polymers trasi2012a C18, and "does not appear to be the only factor" in storage wegiel2013b C33; wegiel2014 C22. For miscible, low-Tg surfactants the authors read the faster growth "most likely" as an effect on mobility, since the Tg-corrected curves come closer mosqueragiraldo2014 C30. The Fox-equation deviations printed for the curcumin dispersions, read there as signs of interaction, were computed with temperatures in °C and the wrong composition; with kelvin and 75% curcumin only the E100 deviation remains large (+18.8 °C) wegiel2014 R18, X1.

Conditions and limits

Tg and relaxation came from bulk powders or melt-quenched glasses, crystallization from films; Tg was always measured on samples prepared differently from the films konno2006 X12; marsac2006a X11; konno2008 X6. Within one composition Tg still matters: nucleation fell as Tg − T rose in every series, and water lowering Tg speeds crystallization (F9) marsac2008a C21.

Counterexamples and conflicts

None found in the library that ranks polymers by dispersion Tg at the low polymer levels studied here; the miscibility papers reached the same conclusion for growth (see Miscibility and drug-polymer interactions F11) kestur2011 C12. For coated high-load dispersions, onset of crystallization in storage did follow the sign of Tg − T at the storage condition moseson2022a C24, so Tg − T can sort conditions within one formulation even where it cannot sort polymers (synthesis). A large Tg drop from a miscible additive does change growth: TPGS and sucrose palmitate lowered the Tg of celecoxib by about 10 °C and sped its growth up to about 85-fold at 70 °C, and the T − Tg replot narrows that spread to about 12-fold (synthesis: about half of the spread on a log scale) mosqueragiraldo2014 R1, R5, R12; the Tg rule fails for small Tg changes between polymers, not for large ones caused by a plasticizer. A large Tg drop from a non-interacting polymer acts the same way: PHB (Tg 0 °C) sped growth of the three compounds whose Tg it lowered and not of the three whose Tg it left unchanged (see F28) sato2016 R7, R11.

Transfer check

Do not screen polymers or drug candidates by dispersion Tg or T/Tg at polymer levels below about 25%. Use Tg only to compare the same formulation across storage conditions, and measure nucleation or growth directly at each condition. For the neat drug, check whether growth below Tg follows its relaxation time; a coupling exponent well below 1, as here (0.5 rumondor2010 C27), warns that Tg-based shelf-life estimates will be optimistic.

History

Van den Mooter and co-workers (2001, outside the library) had stressed the Tg increase from high-Tg polymers konno2006 C2. Konno and Taylor (2006) first showed in the library that no Tg increase was required konno2006 C26; Marsac and co-workers (2006) found the same for two drugs and added that DSC relaxation does not rank them marsac2006a C13, C37. In 2008 both moisture studies showed that neither T/Tg nor Tg − T orders humid films konno2008 C26; marsac2008a C23, and in 2010 melt viscosity and AGV mobility were found equally poor guides kestur2010b C29; rumondor2010 C26. The neat-drug classification reached the matching conclusion for reduced Tg (see Crystallization tendency F12). The papers of 2012–2014 extended the result to flutamide and acetaminophen growth and to resveratrol and curcumin storage trasi2012b C33; trasi2012a C18; wegiel2013b C33; wegiel2014 C22, and the 2014 surfactant study supplied the limit that a 10 °C Tg drop does speed growth mosqueragiraldo2014 C30. The short part and the type line of this finding were extended for these papers; the title is unchanged. Papers of 2015–2021 added a chiral test at constant Tg, Tg after humidity for celecoxib dispersions, the tacrolimus drug–dispersion pair and lumefantrine dispersions in which the lowest-Tg composition was among the most stable sato2015 C6; xie2016b C46; trasi2017 R15; bhujbal2021 C46, and the PHB study a second case of a large Tg drop sato2016 C21; the type line was extended for these papers and the title is unchanged.

F17

Topic 1Crystallization of the amorphous drug in dry dispersions6 of 15

A polymer can slow nucleation and crystal growth of one amorphous drug by very different amounts, even in opposite directions.

In amorphous acetaminophen with 10% w/w polymer, PAA cut the growth rate at 80 °C from about 5.3 to 0.43 µm/s, the largest effect of seven polymers, yet left 26 nuclei per cooling–reheating cycle against 10.8 for the drug alone trasi2012a R6, R12, C46. HPMCAS, among the weakest growth inhibitors (about 1.8 µm/s), left only 2.5 nuclei trasi2012a R6, R12, C46. In flutamide, PVP slowed growth about tenfold but did not change the nucleation read-out, whereas PVAc, a weak growth inhibitor, lowered nucleation trasi2012b R3, C7, R11.b, R11.d, R11.e.

moderateModerate: the decoupling appears in three drugs by three read-outs, but nucleation was counted per thermal cycle, inferred from the growth rate at the DSC exotherm maximum, or inferred from rate ratios, never measured as a rate at storage temperature trasi2012a K5, X8; trasi2012b K5, X4, X5; kestur2013b K5, X7.

Acetaminophen with 10% w/w polymer: nuclei after one cooling–reheating cycledrug alone10.8HPMCAS2.5PVP5.2PVPh9.2HPMC9.3PVPVA12.3E10013.1PAA26

trasi2012a R12

Acetaminophen with 10% w/w polymer: crystal growth rate at 80 °C, µm/sdrug alone≈5.3HPMCAS≈1.8PAA≈0.43

PAA is the strongest growth inhibitor and gives the most nuclei; HPMCAS the reverse. trasi2012a R6.a, R6.b, R6.h, C46

For your drug

  1. After a growth screen, test the two or three best polymers and the weakest one for nucleation as well: a nucleation zone by cooling–reheating DSC and a nuclei count after one cycle take little material.
  2. Check whether the intended storage temperature lies inside the drug's nucleation zone; for a drug that grows fast but nucleates poorly, such as celecoxib, rank polymers by their nucleation effect.

trasi2012a P6, P7, C47; mosqueragiraldo2014 R15, C7

How it works and key numbers
  1. Classical nucleation theory captures the thermodynamic and kinetic factors, but the polymer effects are "not particularly straightforward" to explain with it, and it does not encompass molecular recognition trasi2012a C48, C49.
  2. PAA "may" exert a local ordering effect on acetaminophen that enhances nucleation; HPMCAS "may" act like large additives that lengthen induction times in solution ("we can only speculate") trasi2012a C50, C51.
  3. In flutamide, the analogue nilutamide "may" enter prenuclei (pre-critical clusters) by molecular recognition and block their growth ("quite possible") trasi2012b C47, C48.
  4. In felodipine powders 3% PVP slowed early crystallization 60–77-fold but growth only about 2-fold (surface) and 7-fold (bulk), so "it appears that PVP must" also inhibit nucleation strongly kestur2013b R15, R12, C35, C36.
26 vs 10.8 nucleiPAA vs drug alone per cycle, acetaminophentrasi2012a R12, C46
0.43 vs 5.3 µm/sgrowth with PAA vs drug alone at 80 °Ctrasi2012a R6.a, R6.b
60–77-fold vs 2–7-foldfelodipine with 3% PVP: slower early crystallization vs slower growthkestur2013b R15, R12

Connections to other chapters

Evidence: data, conditions and papers

Finding F17. A polymer can slow nucleation and crystal growth of the same amorphous drug by very different amounts, even in opposite directions, so a growth screen does not rank nucleation inhibitors

In short. With 10% w/w polymer in amorphous acetaminophen, PAA cut the growth rate at 80 °C from about 5.3 to 0.43 µm/s, the largest effect of seven polymers, yet left 26 nuclei per cooling–reheating cycle against 10.8 for the drug alone, while HPMCAS, among the weakest growth inhibitors (about 1.8 µm/s), left 2.5 trasi2012a R6.a, R6.b, R6.h, R12.a, R12.c, R12.e, C46. In flutamide, PVP slowed growth about tenfold but did not change the nucleation read-out, whereas PVAc, a weak growth inhibitor, and PIPA lowered nucleation, and the analogue nilutamide left a single nucleus in the imaged film trasi2012b R3, C7, R11.b, R11.d, R11.e, R12, C43. In felodipine powders 3% PVP slowed early crystallization 60–77-fold but surface and bulk growth only about 2- and 7-fold, which the authors read as mainly a nucleation effect kestur2013b R15, R12, C34, C36.

Type. observation in 3 drugs with 11 additives Strength. the decoupling appears in three drugs by three read-outs (trasi2012a K5: moderate; trasi2012b K5: weak to moderate; kestur2013b K5: weak to moderate), but nucleation was counted per thermal cycle, inferred from the growth rate at the DSC exotherm maximum, or inferred from rate ratios, and never measured as a rate at storage temperature (trasi2012a X8; trasi2012b X4, X5; kestur2013b X7).

How it was shown

Trasi and Taylor (2012) melt-quenched acetaminophen with 10% w/w of seven polymers, measured spherulite growth on a hot stage, and counted the nuclei that grew after one hot-stage cycle to −30 °C trasi2012a P1, P2, P6, P7. For flutamide with 10 mol% additives they read nucleation from the growth rate at the temperature of the DSC crystallization maximum trasi2012b P1, P6, P7. Kestur and co-workers (2013) compared the early crystallization slope of felodipine powders with film growth rates at 30 °C kestur2013b R15, R12, E2.

What the data show

For acetaminophen the nuclei counts ran in a different order from growth: HPMCAS 2.5, PVP 5.2, PVPh 9.2, HPMC 9.3, PVPVA 12.3, E100 13.1 and PAA 26, against 10.8 for the drug trasi2012a R12.

systemmethod and conditionsresultids
acetaminophen with 10% w/w PAA, HPMCAS, PVPgrowth at 80 °C; nuclei per cyclePAA ≈0.43 µm/s, 26 nuclei; HPMCAS ≈1.8 µm/s, 2.5 nuclei; drug ≈5.3 µm/s, 10.8 nucleitrasi2012a R6, R12, C46
same, seven polymersDSC nucleation zone50–60 °C for the drug; −10–30 °C with PAA; 10–45 °C with HPMCAStrasi2012a R12, C22
flutamide with 10 mol% PVP, PIPA, PVAcgrowth at 40 °C; growth rate at TmaxPVP ≈0.13 µm/s, no nucleation effect; PVAc ≈1.0 µm/s and PIPA ≈0.28 µm/s, both lower nucleationtrasi2012b R3, R11, C18
felodipine powders with 3% PVP, 30 °Cearly slope against film growth ratesslope 60–77-fold lower; surface growth ≈2-fold, bulk ≈7-fold lowerkestur2013b R15, R12, C34
Table 2 of trasi2012a: nucleation temperature zones at 10% and 15% polymer and average numbers of nuclei per cycle
Table 2 · trasi2012anucleation temperature zones at 10% and 15% polymer and average numbers of nuclei per cycle

Read the last column against the growth ranking: HPMCAS (2.5) and PVP (5.2) below the drug (10.8), PAA (26) far above it trasi2012a R12.

Why

The polymer effects are "not particularly straightforward" to explain with classical nucleation theory, which does not encompass molecular recognition trasi2012a C48, C49. PAA "may" exert a local ordering effect on acetaminophen that enhances nucleation, "we can only speculate" trasi2012a C50, C51. For felodipine, "it appears that PVP must" also inhibit nucleation strongly kestur2013b C35, C36. The authors of both 2012 papers conclude that the effect of a polymer on nucleation is not predictable from simple properties, unlike growth trasi2012a C52; trasi2012b C45.

Limits and transfer

The acetaminophen counts add up nucleation over the time spent in each zone, and the PAA zone is four times wider trasi2012a X8. The felodipine nucleation effect was not measured in the powders; it rests on rate ratios and a cited 150-fold value kestur2013b X7, R22. After a growth screen, test the best polymers and the weakest one for nucleation as well, with a cooling–reheating DSC zone search and a nuclei count after one cycle.

How it was shown

Trasi and Taylor (2012) melt-quenched acetaminophen with 10% w/w of seven polymers, measured spherulite growth on a hot stage, found the nucleation temperature zone by cooling the melt in the DSC to successively lower end temperatures and reheating, and counted the nuclei that grew after one hot-stage cycle to −30 °C trasi2012a P1, P2, P6, P7. In a companion study they used 10 mol% of six simple polymers and nilutamide in flutamide, located the nucleation zone the same way, and read nucleation from the growth rate at the temperature of the DSC crystallization maximum: fewer nuclei push the exotherm to a higher temperature, where growth is faster trasi2012b P1, P2, P6, P7. Kestur and co-workers (2013) compared the early crystallization slope of felodipine powders with and without 3% PVP against surface and bulk growth rates measured in films at the same temperature, 30 °C kestur2013b R15, R12, E2.

What the data show

For acetaminophen the growth order at 10% w/w was PAA > PVP, PVPh, PVPVA > HPMCAS, E100, HPMC, at 100 °C about 1.6–2.8, 5–7 and 11–15 µm/s against about 45 µm/s trasi2012a R6, C15. The nuclei counts ran in a different order: HPMCAS 2.5, PVP 5.2, PVPh 9.2, HPMC 9.3, PVPVA 12.3, E100 13.1 and PAA 26, against 10.8 for the drug trasi2012a R12. PAA also moved the nucleation zone from 50–60 °C down to −10–30 °C, HPMCAS to 10–45 °C trasi2012a R12.a, R12.c, R12.e. In the drug's own zone growth was only about 0.04–0.23 µm/s (50–60 °C), against about 45 µm/s at 100 °C, which the authors give as the reason acetaminophen forms a glass: its nucleation and growth zones "do not substantially overlap" trasi2012a R8.a, C39. For flutamide, at 40 °C the additives gave growth rates of about 0.13 (PVP), 0.28 (PIPA), 0.43 (nilutamide), 1.0 (PVAc) and 1.6 µm/s (PAA) against about 1.4 µm/s trasi2012b R3. At the exotherm maximum, PVAc and PIPA gave growth rates of 7.7 and 7.0 µm/s against 4.4 for flutamide, read as fewer nuclei, while PVP (5.4), PDMA (4.1) and PVPH (5.9) were classed as no effect trasi2012b R11, C18. For felodipine the early slope fell from 2.21 to 0.037 h⁻¹ (size 1) and from 1.41 to 0.018 h⁻¹ (size 2) with 3% PVP, while PVP cut the surface growth rate from 2.7 × 10⁻⁹ to 1.45 × 10⁻⁹ m/s and the bulk rate from 0.47 × 10⁻⁹ to 6.37 × 10⁻¹¹ m/s kestur2013b R15, R12.

papersystemmethod and conditionsresultids
trasi2012aacetaminophen with 10% w/w PAA, HPMCAS, PVPgrowth at 80 °C; nuclei per cyclePAA ≈0.43 µm/s, 26 nuclei; HPMCAS ≈1.8 µm/s, 2.5 nuclei; drug ≈5.3 µm/s, 10.8 nucleiR6, R12, C46
trasi2012asame, seven polymersDSC nucleation zone50–60 °C for the drug; −10–30 °C with PAA; 10–45 °C with HPMCASR12, C22
trasi2012bflutamide with 10 mol% PVP, PIPA, PVAcgrowth at 40 °C; growth rate at TmaxPVP ≈0.13 µm/s, no nucleation effect; PVAc ≈1.0 µm/s and PIPA ≈0.28 µm/s, both lower nucleationR3, R11, C18
trasi2012bflutamide with 10 mol% nilutamidefilm after cooling to −30 °C and reheatingone nucleus in the imaged regionR12, C16
kestur2013bfelodipine powders with 3% PVP, 30 °Cearly slope against film growth ratesslope 60–77-fold lower; surface growth ≈2-fold, bulk ≈7-fold lowerR15, R12, C34
kestur2013bsamecited nucleation rate≈150-fold lowerR22, C35
alonzo2012 (outside)felodipine in water with 1 µg/mL HPMCnucleation and growth from solutionnucleation ratio 7.05 × 10⁻⁴; growth about 2-foldR17, C46
trasi2015 (outside)acetaminophen in supersaturated solutionpolymer effectsPAA, an excellent growth inhibitor in the supercooled liquid, was largely ineffectiveC26, C28

Figure

Table 2 of trasi2012a: nucleation temperature zones at 10% and 15% polymer and average numbers of nuclei per cycle
Table 2 · trasi2012anucleation temperature zones at 10% and 15% polymer and average numbers of nuclei per cycle

Read the last column against the growth ranking: HPMCAS (2.5) and PVP (5.2) below the drug (10.8), PAA (26) far above it trasi2012a R12.

Fig. 4 of trasi2012a: growth rate of acetaminophen against temperature with 10% w/w polymers
Fig. 4 · trasi2012agrowth rate of acetaminophen against temperature with 10% w/w polymers

On the log axis PAA lies lowest and HPMCAS, E100 and HPMC just below the drug, the reverse of the PAA–HPMCAS order in the nuclei counts trasi2012a R6.

Why

The authors' account, with their hedges: classical nucleation theory captures the thermodynamic and kinetic factors, but the polymer effects are "not particularly straightforward" to explain with it, and it does not encompass molecular recognition trasi2012a C48, C49. PAA "may" exert a local ordering effect on acetaminophen that enhances nucleation, by analogy with polymer-directed polymorphs from solution; HPMCAS "may" act like large additives that lengthen induction times in solution, "we can only speculate" trasi2012a C50, C51. For flutamide, nilutamide "may" enter prenuclei by molecular recognition and, being larger, block their growth ("quite possible"), "most likely" because of its small size relative to a polymer trasi2012b C47, C48. For felodipine, since overall crystallization is nucleation followed by growth, "it appears that PVP must" also inhibit nucleation strongly, so its stabilizing effect is attributed "to a large degree" to nucleation kestur2013b C35, C36. The authors of both 2012 papers conclude that the effect of a polymer on nucleation is not predictable from simple properties, unlike growth, which follows hydrogen bonding (see F18) trasi2012a C52; trasi2012b C45. (synthesis: growth inhibition acts where molecules attach to an existing crystal, nucleation where clusters form in the liquid; an additive that binds the drug strongly can slow attachment and still order the liquid locally, which is one way to read the PAA result.)

Conditions and limits

Growth was measured in melt films far above Tg (synthesis: about 30–110 °C above for acetaminophen, Tg 21.2 °C, and 43–73 °C above for flutamide, Tg −3.1 °C), nucleation in the zones found by DSC at 15 or 5 °C/min cooling, whose limits depend on the scan rates trasi2012a R9.a, C13; trasi2012b R7, P6. The acetaminophen counts add up nucleation over the time spent in each zone, and the PAA zone is four times wider; per second in the zone PAA (about 0.065 nuclei/s) would not exceed the drug (about 0.11/s) (card calculation) trasi2012a X8. The flutamide verdicts rest on two Tmax values per sample and an unnamed test, and the PIPA image does not show fewer nuclei trasi2012b X4, X6. The felodipine nucleation effect was not measured in the powders; it rests on rate ratios and a cited 150-fold value kestur2013b X7, R22.

Counterexamples and conflicts

Some polymers act on both: PVP slowed acetaminophen growth about 5–7-fold at 100 °C and halved the nuclei trasi2012a R6, R12.f, and PVP slowed both felodipine nucleation and growth kestur2013b C36. For flutamide the card reads the data as "no consistent relation" between growth and nucleation effects rather than an absence of nucleation effects among good growth inhibitors: PIPA, a strong growth inhibitor, also lowered nucleation trasi2012b X5. The dry felodipine study of 2006 found PVP, HPMC and HPMCAS equally effective on nucleation at equal weight konno2006 C14, while the same three polymers differ in growth inhibition kestur2010a R6; nucleation and growth were not measured in the same samples there.

Transfer check

After a growth screen, test the two or three best polymers and the weakest one for nucleation as well: a nucleation zone by cooling–reheating DSC and a nuclei count after one cycle take little material trasi2012a P6, P7. Store the candidate at its intended temperature and check whether that temperature lies inside the drug's nucleation zone; HPMCAS lowered the zone and the count for acetaminophen, but the authors note it "could potentially" give more nuclei than PVP over time at room temperature trasi2012a C47. For a drug that grows fast but nucleates poorly, such as celecoxib, the nucleation effect is the one to rank mosqueragiraldo2014 R15, C7.

History

Konno and Taylor (2006) measured dry nucleation rates of felodipine and Kestur and Taylor (2010) growth rates, in different samples konno2006 C13; kestur2010a R6. In 2012 Trasi and Taylor measured both in the same drug, for acetaminophen and for flutamide, and found them decoupled, citing the felodipine nucleation work as an earlier sign trasi2012a C53; trasi2012b C45. In 2013 Kestur and co-workers inferred from rate ratios that PVP protects felodipine mainly through nucleation kestur2013b C36. Later papers found the same decoupling in supersaturated solution: HPMC cut felodipine nucleation more than a thousandfold but growth only about twofold, and PAA, the best growth inhibitor for supercooled acetaminophen, did little in solution alonzo2012 C46; trasi2015 C26, C28 (see D. Crystallization from solution F6 and F27); for nifedipine polymorph conversion the polymers acted most likely on nucleation raina2014b C32.

F18

Topic 1Crystallization of the amorphous drug in dry dispersions7 of 15

Polymers slow crystal growth roughly in the order of their hydrogen bonding to a free group of the drug.

For flutamide, whose amide NH is the free donor, 10 mol% of polymers with strong carbonyl acceptors slowed growth most (PVP about tenfold) and lowered the flutamide NH band by 22–28 cm⁻¹, while the donor polymers PVPH and PAA did little or nothing trasi2012b R3, R14, C7, C8, C39. The authors put the failure of the donors "most likely" down to the flutamide carbonyl being held in an intramolecular CH···O contact (a hydrogen bond within the molecule) trasi2012b C51, C35. For acetaminophen, whose amide carbonyl is free, the donor polymer PAA was the best growth inhibitor on a weight basis, and the polymers without IR shifts were weakest trasi2012a R6, R16, R17, R20, C31.

moderateModerate: the acceptor–donor split is clear for flutamide and the IR order matches growth for flutamide and acetaminophen, but the IR was recorded on films at other compositions, and the intramolecular-bond reading rests on a vacuum calculation and a possibly immiscible PAA blend trasi2012b K1, K2, K4, X9, X12; trasi2012a K4, X15.

Flutamide with 10 mol% additive: crystal growth at 40 °C, µm/sflutamide aloneNH 3315 cm⁻¹1.4PVPacceptor · NH 32870.13PDMAacceptor · NH 32890.23PIPAacceptor · NH 32930.28PVPHdonor only0.73PVAcacceptor · NH 33221.0PAAdonor and acceptor · NH 33151.6

The three polymers that lower the flutamide NH band most are the three best growth inhibitors; the donor polymers fail. trasi2012b R3, R14, C7, C39

Celecoxib with 10% polymer: crystal growth at 80 °C, µm/scelecoxib aloneNH 3268 cm⁻¹0.010HPMCASNH 32370.00031PVPVANH about 31980.00007PVP K29/32NH 31960.00003

Growth falls in the order of the NH shift. xie2016b R21, R3, R4, R5

For your drug

  1. List the drug's donors and acceptors, check whether any is held in an intramolecular bond (crystal structure or conformer calculation), and pick a polymer whose strongest group complements a free group of the drug.
  2. Confirm by IR of a dispersion at the intended composition that the drug band shifts, then measure melt growth at 5–10% polymer at three temperatures; do not rely on Tg rises.

trasi2012b C51, X9, P2; trasi2012a C32, C18

How it works and key numbers
  1. Polymer carbonyls act, "it appears", as competitive acceptors for the flutamide NH, giving a drug–polymer bond more favourable than the drug–drug one trasi2012b C25.
  2. The NH shifts and the computed carbonyl oxygen charges (−0.65 for PVP to −0.598 for PVAc) "strongly support" the view that specific interactions are "extremely important" for growth inhibition trasi2012b R25, C40.
  3. Held in the intramolecular CH···O contact, the flutamide carbonyl is "much less favorable" as an acceptor for donor polymers; PAA also self-associates into dimers, "very likely" at the expense of drug–polymer bonds trasi2012b C35, C37.
  4. For acetaminophen the best donor pairs with the best acceptor: the drug phenol with the pyrrolidone carbonyl, the acid OH of PAA with the drug's amide carbonyl; per hydrogen-bonding group PAA, PVP and PVPh inhibited alike trasi2012a C32, C28, C33.
0.13 vs 1.4 µm/sflutamide growth at 40 °C with PVP vs alonetrasi2012b R3
22–28 cm⁻¹drop of the flutamide NH band with the three best acceptor polymerstrasi2012b R14, C39
0.00003 vs 0.010 µm/scelecoxib growth at 80 °C with PVP vs alonexie2016b R21

Connections to other chapters

2 more connections
Evidence: data, conditions and papers

Finding F18. Polymers slow crystal growth from the supercooled liquid roughly in the order of their hydrogen bonding to a free group of the drug, and donor polymers fail when the drug's acceptor is held in an intramolecular bond

In short. For flutamide, whose amide NH is the free donor, 10 mol% of polymers with strong carbonyl acceptors slowed growth most (PVP about tenfold), the same three polymers lowered the flutamide NH band by 22–28 cm⁻¹, and the donor polymers PVPH and PAA did little or nothing trasi2012b R3, R14, C7, C8, C39. The authors put the donor failure "most likely" down to the flutamide carbonyl being held in an intramolecular CH···O contact trasi2012b C51, C35. For acetaminophen, whose amide carbonyl is free, the donor polymer PAA was the best growth inhibitor on a weight basis, PVP and PVPVA came next, and the polymers without IR shifts (HPMC, HPMCAS, E100) were weakest; per hydrogen-bonding group PAA, PVP and PVPh inhibited alike trasi2012a R6, R8, R16, R17, R18, R20, C31, C33. PVP also slowed celecoxib growth 19–38-fold and shifted its NH and carbonyl bands mosqueragiraldo2014 R1.b, R7, C8, C27. The cleanest test came from two enantiomers, identical except in handedness: with HPMCAS the enantiomer whose free NH2 band was lost more was slowed about twice as much (see F27) sato2015 R13, R14, R5. For celecoxib the order of NH shifts (PVP ≈ PVPVA > HPMCAS) matched the order of growth inhibition xie2016b R3, R4, R5, R21.

Type. observation in 5 drugs or model compounds with about 15 polymers, with an author interpretation Strength. the acceptor–donor split is clear for flutamide (trasi2012b K1: strong) and the IR order matches growth for flutamide and acetaminophen (trasi2012b K2: moderate; trasi2012a K4: moderate), but the IR was recorded on spin-coated films at other compositions, PVPh is unexplained, and the intramolecular-bond reading rests on a vacuum calculation and a possibly immiscible PAA blend (trasi2012b K4: weak to moderate; X9, X12; trasi2012a X6, X15).

How it was shown

Trasi and Taylor (2012) paired flutamide, with an amide NH donor and an amide C=O acceptor, at a 9:1 molar ratio with simple polymers carrying only acceptors (PVP, PDMA, PIPA, PVAc), only donors (PVPH) or both (PAA), and measured growth at 40–70 °C and IR of 1:1 molar films trasi2012b P1, M3, M4, M5, M6, M7, P2, P4. The acetaminophen study used seven polymers at 10% w/w, with IR of 30% w/w films trasi2012a P1, P2, P8.

What the data show

The flutamide NH band fell from 3315 to 3287 cm⁻¹ with PVP, 3289 with PDMA and 3293 with PIPA, rose slightly with PVAc (3322) and stayed with PAA (3315) trasi2012b R14, R15. For acetaminophen HPMC, HPMCAS and E100 gave no noticeable shifts trasi2012a R16, R17, R20.

systemmethod and conditionsresultids
flutamide with 10 mol% acceptor, donor and mixed polymersgrowth at 40 °CPVP ≈0.13, PDMA ≈0.23, PIPA ≈0.28, PVPH ≈0.73, PVAc ≈1.0, PAA ≈1.6 µm/s; drug ≈1.4trasi2012b R3, C7
flutamide with 5% w/w pharmaceutical polymersgrowth at 70 °CPVP ≈4.0, PVPVA ≈12, HPMCAS ≈17.5, HPMC ≈31 µm/s; drug ≈78trasi2012b R5, C9
acetaminophen with 10% w/w polymersgrowth; IR of 30% w/w filmsPAA best, PVP/PVPVA/PVPh next, HPMC/HPMCAS/E100 least; shifts only with PAA, PVP, PVPVAtrasi2012a R6, R16, R17, R18, R20, C31
ATP(R), ATP(S) with HPMCP, HPMCASIR; growth at 5%HPMCP bands equal for R and S, growth alike; HPMCAS bonds one enantiomer more, which grows ≈2-fold slowersato2015 R12, R13, R14, R5
celecoxib with 10% PVP K29/32, PVPVA, HPMCASIR NH band; growth at 80 °C3196, ≈3198, 3237 cm⁻¹; ≈0.00003, 0.00007, 0.00031 µm/s (drug 0.010)xie2016b R3, R4, R5, R21
Fig. 2 of trasi2012b: growth rate of flutamide against temperature with 10 mol% additives
Fig. 2 · trasi2012bgrowth rate of flutamide against temperature with 10 mol% additives

Each decade is a tenfold change; PVP (green) lies lowest, PAA (orange) sits on top of pure flutamide trasi2012b R3.

Why

Polymer carbonyls act, "it appears", as competitive acceptors for the flutamide NH, and the NH shifts and carbonyl charges "strongly support" the view that specific interactions are "extremely important" for growth inhibition trasi2012b C25, C40. Flutamide's carbonyl keeps part of its charge in an intramolecular CH···O contact, which makes it "much less favorable" as an acceptor trasi2012b C35, C37. For acetaminophen PAA's acid OH bonds to the drug's amide carbonyl, and equal inhibition per hydrogen-bonding group "further supported" the role of the interaction trasi2012a C28, C33.

Limits and transfer

IR was recorded on spin-coated films at other compositions than the growth samples, and the intramolecular bond was computed for one molecule in vacuum trasi2012b X9, C35, R23; trasi2012a X15. PAA appears immiscible with flutamide at higher PAA content, so its failure may reflect poor mixing trasi2012b X12, R4, C38. Pick a polymer whose strongest group complements a free group of the drug, after checking for intramolecular bonds, and confirm by IR at the intended composition.

How it was shown

Trasi and Taylor (2012) chose flutamide because it has both a donor (amide NH) and an acceptor (amide C=O) and paired it at a 9:1 molar ratio with six simple polymers carrying only acceptors (PVP, PDMA, PIPA, PVAc), only donors (PVPH) or both (PAA), plus 5% w/w PVP, PVPVA, HPMCAS and HPMC trasi2012b P1, M3, M4, M5, M6, M7. They measured growth at 40–70 °C, IR of 1:1 molar films, NBO charges on the polymer carbonyl oxygen and the energy of flutamide as its amide rotates trasi2012b P2, P4, P9. The acetaminophen study used seven polymers at 10% w/w and three at a 10% molar ratio on a monomer basis, with IR of 30% w/w films trasi2012a P1, P2, P8. The celecoxib study included 10% PVP as the reference inhibitor mosqueragiraldo2014 P3, R1.b. Sato and Taylor (2015) took transmission IR of ATP films with 20–30% polymer and Xie and Taylor (2016) of celecoxib films from 9:1 to 1:9 drug:polymer; both measured melt growth sato2015 P5; xie2016b P2, P9.

What the data show

At 40 °C flutamide grew at about 1.4 µm/s alone and at about 0.13 (PVP), 0.23 (PDMA), 0.28 (PIPA), 0.73 (PVPH), 1.0 (PVAc) and 1.6 µm/s (PAA), in the same order at 50–70 °C trasi2012b R3. The flutamide NH band fell from 3315 to 3287 cm⁻¹ with PVP, 3289 with PDMA and 3293 with PIPA, rose slightly with PVAc (3322) and stayed with PAA (3315); the PVP carbonyl moved from 1679 to 1658 cm⁻¹ trasi2012b R14, R15. The computed carbonyl oxygen charges were −0.65 (PVP), −0.647 (PIPA), −0.64 (PDMA), −0.606 (PAA) and −0.598 (PVAc) trasi2012b R25. In the 5% w/w series growth at 70 °C was about 4.0 (PVP), 12 (PVPVA), 17.5 (HPMCAS) and 31 µm/s (HPMC) against about 78 µm/s trasi2012b R5. The lowest-energy flutamide conformer is planar with the carbonyl next to the ring C(5)–H, and turning the amide costs up to about 23 kJ/mol trasi2012b R23, R24. For acetaminophen PAA moved the drug NH/OH band up to 3320 cm⁻¹ and its own acid carbonyl from 1705 to 1714 cm⁻¹, PVP moved the NH/OH band to 3283 cm⁻¹ and its carbonyl from 1679 to 1657 cm⁻¹, and HPMC, HPMCAS and E100 gave no noticeable shifts trasi2012a R16, R17, R20. At 10% molar the three polymers grew acetaminophen 5–17 times slower than the drug and the two PAA grades no longer differed trasi2012a R8, C16. With celecoxib, PVP moved the lower NH band from 3269 to 3192 cm⁻¹ and its carbonyl from 1681 to 1668 cm⁻¹ mosqueragiraldo2014 R6, R7, C21.

Later papers tested the reading in three ways. In the chiral compound ATP, HPMCP gave new NH and carbonyl bands identical for both enantiomers and slowed them alike, while HPMCAS removed the free NH2 band more for one enantiomer, which then grew about twice as slowly (see F27) sato2015 R12, R13, R14, R5. In celecoxib with 10% polymer at 80 °C, growth was about 0.00003 µm/s with PVP K29/32, 0.00007 with PVPVA and 0.00031 with HPMCAS against 0.010 alone, in the order of the NH shifts (3196, about 3198 and 3237 cm⁻¹ from 3268) xie2016b R21, R3, R4, R5. In indomethacin at 80–100 °C, PVP, the polymer with the strongest bond to the drug in the 2016 fluorescence study, slowed growth most and HPMCAS least, which the authors attribute "perhaps" to weaker interaction; the interactions were cited, not measured tian2017 R12, C32, R16, X13. PHB, with no band shifts, slowed no compound by more than about 2.4-fold (synthesis: 1/0.42) and sped up three (see F28) sato2016 R9, R11.

papersystemmethod and conditionsresultids
trasi2012bflutamide with 10 mol% acceptor, donor and mixed polymersgrowth at 40 °CPVP ≈0.13, PDMA ≈0.23, PIPA ≈0.28, PVPH ≈0.73, PVAc ≈1.0, PAA ≈1.6 µm/s; drug ≈1.4R3, C7
trasi2012b1:1 molar filmsflutamide NH band3315 → 3287 (PVP), 3289 (PDMA), 3293 (PIPA); 3322 (PVAc); 3315 (PAA) cm⁻¹R14, C39
trasi2012bpolymer repeat unitsNBO charge on carbonyl O−0.65 (PVP) to −0.598 (PVAc); PAA −0.606R25, X8
trasi2012bflutamide with 5% w/w pharmaceutical polymersgrowth at 70 °CPVP ≈4.0, PVPVA ≈12, HPMCAS ≈17.5, HPMC ≈31 µm/s; drug ≈78R5, C9
trasi2012aacetaminophen with 10% w/w polymersgrowth; IR of 30% w/w filmsPAA best, PVP/PVPVA/PVPh next, HPMC/HPMCAS/E100 least; shifts only with PAA, PVP, PVPVAR6, R16, R17, R18, R20, C31
trasi2012aacetaminophen with 10% molar PAA, PVP, PVPhgrowth, 50–100 °Cone band, 5–17 times below the drugR8, C33
mosqueragiraldo2014celecoxib with 10% PVPgrowth; IR19–38-fold slower; NH 3269 → 3192, C=O 1681 → 1668 cm⁻¹R1.b, R7, C27
sato2015ATP(R), ATP(S) with HPMCP, HPMCAS (20–30% for IR)IR; growth at 5%HPMCP bands equal for R and S, growth alike; HPMCAS bonds one enantiomer more, which grows ≈2-fold slowerR12, R13, R14, R5
xie2016bcelecoxib with 10% PVP K29/32, PVPVA, HPMCASIR NH band; growth at 80 °C3196, ≈3198, 3237 cm⁻¹; ≈0.00003, 0.00007, 0.00031 µm/s (drug 0.010)R3, R4, R5, R21
tian2017indomethacin with 10% PVP, HPMC, HPMCASgrowth, 80–100 °CPVP 5–25-fold > HPMC 2–12-fold > HPMCAS 2–3-foldR12, C28
sato2016six compounds with 5–20% PHBIR; growthno shifts; ratios ≈0.42–10R9, R11
kestur2011 (outside)nimesulide, NH held intramolecularlygrowth with four polymersdifferences between polymers smaller than expectedC27
trasi2015 (outside)acetaminophen in pH 6.8 solutionPAA as inhibitorlargely ineffective, "could be" its ionizationC26, C27

Figure

Fig. 2 of trasi2012b: growth rate of flutamide against temperature with 10 mol% additives
Fig. 2 · trasi2012bgrowth rate of flutamide against temperature with 10 mol% additives

Each decade is a tenfold change; PVP (green) lies lowest, PAA (orange) sits on top of pure flutamide trasi2012b R3.

Table 3 of trasi2012b: NH stretch of flutamide alone and with each additive
Table 3 · trasi2012bNH stretch of flutamide alone and with each additive

The three polymers that lower the NH frequency most are the three best growth inhibitors of Fig. 2 trasi2012b R14, C39.

Why

The authors' account, with their hedges: polymer carbonyls act, "it appears", as competitive acceptors for the flutamide NH, giving a drug–polymer bond more favourable than the drug–drug one; the NH shifts and the carbonyl charges "strongly support" the view that specific interactions are "extremely important" for growth inhibition trasi2012b C25, C40. PVAc's carbonyl, bonded to an oxygen, carries less charge "essentially", and PVPVA was "presumably" weaker than PVP because vinyl acetate interacts weakly; the cellulose polymers "presumably" have less basic acceptors trasi2012b C27, C41. Flutamide's carbonyl keeps part of its charge in the intramolecular CH···O contact, "highly likely" also in the amorphous state, which makes it "much less favorable" as an acceptor; PAA self-associates in dimers and "very likely" prefers itself trasi2012b C35, C37. For acetaminophen interactions are expected between the best donor and the best acceptor: the drug phenol to the pyrrolidone carbonyl, PAA's acid OH to the drug's amide carbonyl, and the polymers with weak groups do little trasi2012a C32, C28, C27. Equal inhibition per hydrogen-bonding group "further supported" the role of the interaction trasi2012a C33. The authors rule out Tg as the cause, since the Tg rises were small and similar for strong and weak inhibitors (see F5), and the small melting-point changes left the degree of supercooling nearly the same for all polymers trasi2012a C18, C19; trasi2012b C33.

Conditions and limits

Growth was measured in melt films at 9:1 molar or 10% w/w, IR on spin-coated films at 1:1 molar or 30% w/w, so the IR ranks interaction strength but does not show the state of the growth samples trasi2012b X9; trasi2012a X15. The charge correlation rests on four carbonyl polymers; PIPA and PDMA differ by 0.007 in charge and grow alike trasi2012b X8. The intramolecular bond was computed for one molecule in vacuum and was not observed in the glass trasi2012b C35, R23. Growth was measured far above Tg; storage stability was not tested in these papers trasi2012b A1; trasi2012a A1. In the flutamide series every polymer was used at the same drug:repeat-unit molar ratio, so dilution was the same for all trasi2012b C32; for nilutamide itself the authors write that dilution plus a higher Tg "can be explained" as the cause of its growth effect, on a corrected curve that is not shown trasi2012b C42, X11.

Counterexamples and conflicts

PVPh slowed acetaminophen growth about as much as PVP although its IR spectrum changed little trasi2012a X6. PAA crystallized flutamide partly on cooling and appears immiscible at higher PAA content, so its failure may reflect poor mixing rather than the intramolecular bond trasi2012b X12, R4, C38. For curcumin, whose keto–enol group is held intramolecularly, PVP gave the largest IR shifts of five polymers yet was the poorest inhibitor in storage, so a large IR shift did not predict storage stability there (see F24) wegiel2014 X7. Outside this set, PVP slowed five donor drugs by a similar 5–10-fold factor, so its effect did not follow the drug's own growth rate trasi2014a C10 (see Crystallization tendency F19). In indomethacin above about 100 °C the polymer order changed with polymorph and temperature, HPMC overtaking PVP for α, so one interaction order does not fix the growth order at every temperature (see F29) tian2017 C15, R12.

Transfer check

List the drug's donors and acceptors and check whether any of them is held in an intramolecular bond in the crystal structure or a conformer calculation; pick a polymer whose strongest group complements a free group of the drug (an acceptor polymer for a free NH or OH donor, a donor polymer for a free carbonyl) trasi2012b C51; trasi2012a C32. Confirm by IR of a dispersion at the intended composition that the drug band shifts trasi2012b X9. Then measure melt growth at 5–10% polymer at three temperatures trasi2012b P2. Do not rely on Tg rises, which were similar for the best and worst inhibitors trasi2012a C18.

History

Kestur and Taylor (2010) matched the IR order of felodipine–polymer bonding with the order of growth inhibition, and Kestur and co-workers (2011) found that an intramolecular NH···O bond in nimesulide flattened the differences between polymers (see Miscibility and drug-polymer interactions F12 and F14) kestur2010a C26; kestur2011 C27. In 2012 Trasi and Taylor tested the idea with polymers chosen for donor or acceptor groups only, for flutamide and acetaminophen, and showed that the best polymer changed with the drug's free group trasi2012b C8; trasi2012a C31. In 2014 PVP served as the hydrogen-bonding reference inhibitor for celecoxib mosqueragiraldo2014 C27, and Wegiel and co-workers carried the intramolecular-bond argument to curcumin storage (see F24) wegiel2014 C35. In solution the same donor polymer failed, which the authors relate to its ionization trasi2015 C27. Sato and Taylor (2015) used two enantiomers to hold everything but the interaction constant and found grade-specific inhibition by HPMCAS (see F27) sato2015 C27; Xie and Taylor (2016) and Tian and co-workers (2017) added celecoxib and indomethacin series xie2016b C36; tian2017 C28; the type line was extended and the title is unchanged.

F19

Topic 1Crystallization of the amorphous drug in dry dispersions8 of 15

3% PVP slows two felodipine polymorphs by a similar factor, so the faster-growing form I stays faster.

Without polymer, bulk form I of felodipine grew faster than form II at every temperature from 40 to 100 °C, by about 15–18-fold at 60–70 °C kestur2013a R8, X5. With 3% PVP the ratio of growth rates without and with polymer was about 15.8 (form I) and 18.7 (form II) at 60 °C and about 3.5 and 6.5 at 100 °C kestur2013a R15. The authors read this as the same inhibition of both forms, hence an effect of PVP on the liquid rather than on the crystal faces ("most likely"), and conclude that a faster-growing crystal will need more polymer kestur2013a C14, C6, C26.

moderateModerate for the similar ratios, weaker for the liquid-phase reading and the polymer-amount conclusion: the error bars separate at 90–100 °C, the form I ratios at 70–80 °C do not follow from the plotted rates, and only 3% PVP was tested kestur2013a K5, K6, K7, X6, X7, X9.

form I (the faster grower)form II60 °C15.818.770 °C15.417.580 °C12.513.290 °C6.88.2100 °C3.56.505101520growth rate without PVP ÷ with 3% PVP

Close at 60–80 °C and apart at 90–100 °C; for both forms the factor falls with temperature. kestur2013a R15, X6

Felodipine bulk growth without polymer, m/sform I, 60 °C5.0 × 10⁻⁹form II, 60 °C2.8 × 10⁻¹⁰form I, 40 °C2.6 × 10⁻⁹form II, 40 °C5.5 × 10⁻¹³

Form I grows faster at every temperature, about 4700-fold at 40 °C. kestur2013a R8.g, R8.c, X5

For your drug

  1. Identify which polymorph actually forms in the product (felodipine powders gave form I, the faster grower) and measure the polymer's effect on that form.
  2. Measure growth at two temperatures below about Tg + 15 °C as well as above; if the stable form grows ten times faster than the metastable one, assume it needs proportionally more polymer and test a higher level.

kestur2013b R10; kestur2013a C27, C7, C18, C26

How it works and key numbers
  1. Polymorphs present different crystal faces but grow from the same liquid, so equal inhibition of both points to PVP changing the amorphous phase ("most likely"); in growth from solution, adsorption of polymer to the crystal faces is the accepted mechanism kestur2013a C1, C6, C28.
  2. Because PVP lowers both rates by about the same factor, faster-growing crystals "will require more polymer" to bring growth to negligible values kestur2013a C26.
  3. Form I alone rose in rate on cooling from 50 to 45 °C, near Tg (bulk about 1.7 × 10⁻⁹ to 4.2 × 10⁻⁹ m/s), which the authors "most likely" assign to the glass-crystal (diffusionless) growth mode, too fast for diffusion kestur2013a R8.e, R8.d, R10, C3, C23.
  4. With 3% PVP form I still jumped, now between 45 and 40 °C, so extrapolating high-temperature growth toward Tg, which assumes a smooth decrease, fails for this form kestur2013a R14, C7.
To feel the numbers. At 60 °C form I grows at 5.0 × 10⁻⁹ m/s; 3% PVP divides this by 15.8, to 5.0 × 10⁻⁹ ÷ 15.8 ≈ 3.2 × 10⁻¹⁰ m/s, still above form II without any polymer (2.8 × 10⁻¹⁰ m/s).
15.8 vs 18.7PVP slowing factor at 60 °C, form I vs form IIkestur2013a R15
3.5 vs 6.5the same at 100 °C, where the error bars separatekestur2013a R15, X6
≈15–18-foldform I faster than form II at 60–70 °C without polymerkestur2013a R8, X5

Connections to other chapters

1 more connection
Evidence: data, conditions and papers

Finding F19. 3% PVP slows the growth of two felodipine polymorphs by a similar factor, so the faster-growing form I stays faster, keeps its jump near Tg, and needs more polymer

In short. Without polymer, bulk form I of felodipine grew faster than form II at every temperature from 40 to 100 °C, by about 15–18-fold at 60–70 °C and about 87-fold at 50 °C (card calculation), and form I alone jumped in rate between 50 and 45 °C, near Tg, which the authors "most likely" assign to the glass-crystal growth mode kestur2013a R8, R10, X5, C3. With 3% PVP the ratio of rates without and with polymer was about 15.8 (form I) and 18.7 (form II) at 60 °C and about 3.5 and 6.5 at 100 °C, which the authors read as the same inhibition for both forms, hence an effect of PVP on the liquid rather than on the crystal faces ("most likely") kestur2013a R15, C14, C6. They conclude that a faster-growing crystal will need more polymer kestur2013a C26.

Type. comparison of two polymorphs of one drug with one polymer level Strength. for the similar ratios (kestur2013a K5: moderate), weak to moderate for the liquid-phase reading (K6) and weak for the polymer-amount conclusion (K7) — the error bars of the two forms do not overlap at 90–100 °C, the form I ratios at 70–80 °C do not follow from the plotted rates, only 3% PVP was tested, and form II with PVP was not measured below 60 °C (X6, X7, X9, X11).

How it was shown

Kestur and Taylor (2013) melt-quenched felodipine films 5–10 µm thick and grew form I at a free surface or in the bulk from seeds, and form II in the bulk between two cover glasses kestur2013a P1, P2, P3. The effect of 3% PVP K-29/32 was expressed as the ratio of the bulk rate without polymer to that with polymer kestur2013a P6, P4, E2, R15.

What the data show

Bulk form I grew faster than form II at every temperature; the authors summarize the gap as "1-2 orders of magnitude" kestur2013a R8, C4, X5. Form I alone rose on cooling from 50 to 45 °C, in the bulk from about 1.7 × 10⁻⁹ to 4.2 × 10⁻⁹ m/s, and with PVP still jumped near Tg, now between 45 and 40 °C kestur2013a R8.e, R8.d, R10, R14, X14.

systemmethod and conditionsresultids
bulk form I vs form II, no polymergrowth rate, 40–100 °Cform I faster at every temperature; ≈4700-fold at 40 °C, ≈15–18-fold at 60–70 °C, 7–9-fold at 80–100 °Ckestur2013a R8, C4, X5
form I and form II with 3% PVPrate ratio without/with PVP, 60–100 °Cform I ≈15.8 → ≈3.5; form II ≈18.7 → ≈6.5kestur2013a R15, C14
form I at 45 °Clayers per relaxation time (in words)≈500 printed; ≈290 recomputed; form II below 1kestur2013a R18, X1, X2
felodipine glass at 30 °Cpolymorph formedform II between cover slips, form I at a free surface and in powderskestur2013b R10, C26
Fig. 4 of kestur2013a: ratio of growth rates without and with 3% PVP for form I and form II against temperature
Fig. 4 · kestur2013aratio of growth rates without and with 3% PVP for form I and form II against temperature

Black squares are form I, red circles form II; both fall from about 16–19 at 60 °C to 3.5–6.5 at 100 °C, close at 60–80 °C and apart at 90–100 °C kestur2013a R15, X6.

Why

Polymorphs present different crystal interfaces but grow from the same liquid, so equal inhibition of both points to PVP changing the amorphous phase ("most likely") kestur2013a C1, C6. The form I jump is "most likely" the glass-crystal mode, too fast for diffusion kestur2013a C3, C23. Because PVP lowers both rates by about the same factor, faster-growing crystals "will require more polymer" to bring growth to negligible values kestur2013a C26.

Limits and transfer

One drug and one polymer level, and form II with PVP was not measured below 60 °C kestur2013a X9, X11. At 90–100 °C PVP slowed form II about 1.2–1.9 times more than form I, and the plotted rates do not reproduce the form I ratios at 60–80 °C kestur2013a X6, X7. Measure the polymer's effect on the polymorph that forms in the product, at temperatures below about Tg + 15 °C as well as above.

How it was shown

Kestur and Taylor (2013) melt-quenched felodipine films 5–10 µm thick and grew form I either at a free surface (top cover glass removed) or in the bulk from seeds placed against the supercooled liquid; form II, which nucleates in unseeded films between two cover glasses, was grown in the bulk kestur2013a P1, P2, P3. Growth rates were measured by polarized light microscopy on a hot stage or in ovens, form I from 18 to 100 °C and form II from 40 °C, with form II data at 70 °C and above taken from earlier papers kestur2013a P6, X4. A 3% PVP K-29/32 dispersion was made by rotary evaporation and cryomill dilution, and the polymer effect was expressed as the ratio of the bulk rate without polymer to that with polymer (in words, Eq. E2) kestur2013a P4, E2, R15. Raman spectra and melting points identified the polymorphs kestur2013a P7. Tian and co-workers (2017) compared three indomethacin polymorphs with 10% of three polymers tian2017 A1, A2.

What the data show

Bulk form I grew at about 5.0 × 10⁻⁹ m/s at 60 °C, form II at about 2.8 × 10⁻¹⁰ m/s; at 40 °C the values were about 2.6 × 10⁻⁹ and 5.5 × 10⁻¹³ m/s kestur2013a R8.g, R8.c. The authors summarize the gap as "1-2 orders of magnitude"; the plotted means give about 4700-fold at 40 °C, about 87-fold at 50 °C, about 15–18-fold at 60–70 °C and only 7–9-fold at 80–100 °C kestur2013a C4, X5. Form II fell smoothly by about five orders of magnitude from 105 to 40 °C kestur2013a R11, R8.n, R8.c. Form I instead rose on cooling from 50 to 45 °C, in the bulk from about 1.7 × 10⁻⁹ to 4.2 × 10⁻⁹ m/s kestur2013a R8.e, R8.d, R10. With 3% PVP the ratios at 60, 70, 80, 90, 95 and 100 °C were about 15.8, 17.5, 13.2, 6.8, 3.9 and 3.5 for form I and 18.7, 15.4, 12.5, 8.2, 7.2 and 6.5 for form II kestur2013a R15. With PVP, form I still jumped near Tg, now between 45 and 40 °C (bulk about 6.8 × 10⁻¹¹ to 3.2 × 10⁻¹⁰ m/s), about 5 °C lower and larger than without polymer kestur2013a R14, R13, X14. For the jump the authors estimate about 500 molecular layers added per structural relaxation time at 45 °C (relaxation time taken as 100 s, molecular radius 9 Å), against 0.1–1 for diffusion-controlled growth and 1700–2400 for the glass-crystal mode of ROY; the card recomputes about 290 from the printed inputs, still in the hundreds kestur2013a R18, R16, X1, X2.

papersystemmethod and conditionsresultids
kestur2013afelodipine bulk form I vs form II, no polymergrowth rate, 40–100 °Cform I faster at every temperature; ≈4700-fold at 40 °C, ≈15–18-fold at 60–70 °C, 7–9-fold at 80–100 °CR8, C4, X5
kestur2013aform I, no polymergrowth on cooling 50 → 45 °Cbulk ≈1.7 × 10⁻⁹ → ≈4.2 × 10⁻⁹ m/sR8.d, R8.e, R10, C3
kestur2013aform I and form II with 3% PVPrate ratio without/with PVP, 60–100 °Cform I ≈15.8 → ≈3.5; form II ≈18.7 → ≈6.5R15, C14
kestur2013aform I with 3% PVPgrowth near Tgjump between 45 and 40 °C, ≈5-foldR14, X14
kestur2013aform I at 45 °Clayers per relaxation time (in words)≈500 printed; ≈290 recomputed; form II below 1R18, X1, X2
kestur2013bfelodipine glass at 30 °Cpolymorph formedform II between cover slips, form I at a free surface and in powdersR10, C26
trasi2014a (outside)five drugs with 10 mol% PVPmelt growthslowed by a similar factor of about 5–10 whatever the drug's own rateC10, C11

Figure

Fig. 4 of kestur2013a: ratio of growth rates without and with 3% PVP for form I and form II against temperature
Fig. 4 · kestur2013aratio of growth rates without and with 3% PVP for form I and form II against temperature

Black squares are form I, red circles form II; both fall from about 16–19 at 60 °C to 3.5–6.5 at 100 °C, close at 60–80 °C and apart at 90–100 °C kestur2013a R15, X6.

Fig. 2 of kestur2013a: growth rate against temperature without polymer for form I at the surface and in the bulk and for form II
Fig. 2 · kestur2013agrowth rate against temperature without polymer for form I at the surface and in the bulk and for form II

The form I points rise from 50 to 45 °C next to the Tg arrow while the form II curve (triangles) falls smoothly kestur2013a R8, R10.

Why

The authors' account, with their hedges: polymorphs present different crystal interfaces but grow from the same liquid, so equal inhibition of both points to PVP changing the amorphous phase, the PVP–felodipine environment being similar for both ("suggest"; abstract: "most likely"); in growth from solution, by contrast, adsorption of trace polymer to the crystal faces is the accepted mechanism kestur2013a C1, C6, C28. The form I jump is "most likely" the glass-crystal or diffusionless mode, too fast for diffusion, and about 500 layers per relaxation time is "supporting the supposition"; whether a polymorph shows the mode "is thought to be related" to its density and packing, form I being the denser (1.45 against 1.42) kestur2013a C3, C23, C24, M1, M2. Because PVP lowers both rates by about the same factor, faster-growing crystals "will require more polymer" to bring growth to negligible values ("suggesting") kestur2013a C26. The authors add that extrapolating high-temperature growth to near or below Tg assumes a smooth decrease, which the form I jump breaks kestur2013a C7. (synthesis: this is the polymorph counterpart of the cross-drug result that PVP slows fast and slow growers by a similar factor; in both, the inhibition is multiplicative, so the absolute rate left over follows the uninhibited rate.)

Conditions and limits

One drug, one polymer at about 3% (basis not stated), bulk ratios at 60–100 °C only, rates from plot readings without stated replicates kestur2013a X9, R15, X13. The measured front changes habit with temperature (compact spherulites below 40 °C, fiber layers at 50–70 °C, faceted crystals higher), so rates at different temperatures do not describe the same front kestur2013a X12. The relaxation time for the layer count is assumed, and the quoted 2.6 × 10⁻⁹ m/s matches the 40 °C rather than the 45 °C point kestur2013a X1. Form II with PVP below 60 °C, where the jump question matters, was not measured kestur2013a X11.

Counterexamples and conflicts

At 90–100 °C PVP slowed form II about 1.2–1.9 times more than form I and the error bars separate, so "the same extent" holds within about a factor of two kestur2013a X6. Dividing the plotted rates of Figs. 2 and 3 does not reproduce the form I ratios at 60–80 °C (about 13, 29 and 22 against 15.8, 17.5 and 13.2), so the evidence for equality is weakest exactly where it is claimed best kestur2013a X7. In felodipine powders of the same year PVP slowed surface growth only about twofold but bulk growth sevenfold, so the inhibition factor also depends on where the crystal grows (see F21) kestur2013b R12. For indomethacin each of PVP, HPMC and HPMCAS slowed the δ, α and γ polymorphs by very different factors, up to about 2900 against 2.9 at 120 °C with HPMC, which the authors read against the liquid-phase explanation (see F29) tian2017 R12, C39. At 80 °C, well below the temperatures of fastest growth as in the felodipine comparison, the indomethacin ratios of the three forms were within a factor of about 2.3 of each other (5.9, 3.5 and 4.7 with HPMC; 25, 16 and 11 with PVP) tian2017 R12.a.

Transfer check

Identify which polymorph actually forms in the product (powders of felodipine gave form I, the faster grower) and measure the polymer's effect on that form kestur2013b R10; kestur2013a C27. Measure growth at two temperatures below about Tg + 15 °C as well as above, because a jump near Tg can make high-temperature data underpredict low-temperature growth kestur2013a C7, C18. If the stable form grows ten times faster than the metastable one, assume it needs proportionally more polymer and test a higher polymer level kestur2013a C26.

History

Kestur and Taylor (2010) measured PVP inhibition of form II only (see F3) kestur2010b R2. In 2013 they compared both polymorphs, found the glass-crystal jump for form I, and placed the PVP effect in the liquid kestur2013a C3, C6; the particle-size study of the same year explained why powders crystallize to form I (see F20, F21) kestur2013b C26. A year later the comparison across five drugs gave the same multiplicative picture between drugs (see Crystallization tendency F19) trasi2014a C10, C11. Tian and co-workers (2017) found polymorph-specific factors for indomethacin and argued against the liquid-phase reading (see F29) tian2017 C38; the title is unchanged.

F20

Topic 1Crystallization of the amorphous drug in dry dispersions9 of 15

A polymer or surfactant can change which polymorph crystallizes from the amorphous drug and can hold a metastable form.

Amorphous curcumin crystallized as form I alone or with E100 or PVP, but as the metastable form II from HPMC, HPMCAS and CMCAB dispersions after 1 day at 98% RH and 60 °C, and form II did not convert during the study wegiel2014 R15, R17, C28. In flutamide every additive gave the usual crystal form except 5% HPMC, with which another polymorph grew trasi2012b R6, C10, R9, C14. In celecoxib, SLS gave some form I where the drug alone and the other surfactants grew form III mosqueragiraldo2014 R14, C38.

moderateModerate for curcumin, weak elsewhere: the flutamide and celecoxib forms rest on Raman shifts or one XRD peak with spectra not shown, and the curcumin CMCAB product may hold some form I wegiel2014 K8, X11, X12; trasi2012b P3; mosqueragiraldo2014 X9.

Additive changed the crystal form
curcumin + HPMC, HPMCAS, CMCAB: form IIflutamide + 5% HPMC: another formcelecoxib + SLS: some form I
Crystal form unchanged
curcumin alone, + E100, + PVP: form Iflutamide + the other additivescelecoxib + TPGS or sucrose palmitate

wegiel2014 R15, R17, C28; trasi2012b R6, C14; mosqueragiraldo2014 R14, C38

For your drug

  1. At each stability pull identify the crystal form, not only the crystallinity, and compare it with the form of the neat amorphous drug under the same condition.
  2. If a polymer gives a metastable form, check whether it persists and how it dissolves before treating the result as a failure or a benefit; in additive growth screens confirm the form of the growing crystal.

wegiel2014 R15, R17, C43, R20; mosqueragiraldo2014 C37, X9

How it works and key numbers
  1. The authors give few mechanisms; for curcumin they state only that the cellulosic polymers "were able to influence" the polymorph wegiel2014 C28.
  2. Polymers can also slow the conversion of one form into another: they delayed the form III to form II transition of acetaminophen on reheating trasi2012a R10, C20.
  3. The growth site matters as well: in felodipine, confinement between two cover slips gave form II, a free surface always form I, and powders form I only, which the faster surface growth of form I "most likely" explains kestur2013a R1, R2, R3, C25; kestur2013b R10.
  4. For celecoxib, "one possible explanation" of the surfactant growth effects "could be" that different polymorphs grew, which XRD ruled out for TPGS and sucrose palmitate mosqueragiraldo2014 C37, C38.
1 day at 98% RH and 60 °Cstress that gave curcumin form II with the cellulosic polymerswegiel2014 R17
5% w/w HPMCthe only flutamide additive that grew another polymorphtrasi2012b R6, R9
491 days at 93% RHfelodipine with 10% HPMCAS gave a mixture with form IIrumondor2009b R13

Connections to other chapters

Evidence: data, conditions and papers

Finding F20. A polymer or surfactant can change which polymorph crystallizes from the amorphous drug, and can hold a metastable form, so stability tests must name the form that appears

In short. Amorphous curcumin crystallized as form I alone or with E100 or PVP, but as the metastable form II from HPMC, HPMCAS and CMCAB dispersions after 1 day at 98% RH and 60 °C and from HPMCAS at 0% RH and 90 °C, and form II did not convert during the study wegiel2014 R15, R17, C28. In flutamide every additive gave the usual crystal form except 5% HPMC, with which another polymorph grew and was "highly stabilized" trasi2012b R6, C10, R9, C14; in celecoxib, SLS gave some form I where the drug alone and the other surfactants grew form III mosqueragiraldo2014 R14, C38. Polymers also delayed the form III to form II transition of acetaminophen on reheating trasi2012a R10, C20.

Type. observation in 5 drugs with 15 additives and two growth sites Strength. for curcumin (wegiel2014 K8: moderate), weak elsewhere — the flutamide and celecoxib forms rest on Raman shifts or one XRD peak with spectra not shown, no PVP-containing celecoxib sample was checked, and the curcumin CMCAB product may hold some form I (trasi2012b P3; mosqueragiraldo2014 X9; wegiel2014 X11, X12).

How it was shown

Wegiel and co-workers (2014) stored 75:25 curcumin dispersions with five polymers at six conditions and identified the crystals by PXRD reflections wegiel2014 P5, R15, R17. Trasi and Taylor (2012) identified flutamide crystals by Raman against the known form and acetaminophen events on DSC reheating by their melting points trasi2012b P3; trasi2012a P4, R10. Mosquera-Giraldo and co-workers (2014) took XRD of celecoxib crystals grown from the melt with each surfactant mosqueragiraldo2014 P6, R14.

What the data show

Neat amorphous curcumin crystallized as form I at every condition where it crystallized wegiel2014 R15, C23. The form II of the cellulosic dispersions matched a polymorph reported in 2011 as metastable, with a higher dissolution rate and solubility than form I wegiel2014 R17, R20, C28.

systemmethod and conditionsresultids
curcumin with HPMC, HPMCAS, CMCABPXRD after 1 day at 98% RH, 60 °Cmetastable form II, no conversion during the studywegiel2014 R17, C28
curcumin alone, with E100 or PVPsameform Iwegiel2014 R15, R17
flutamide with 5% w/w HPMCRaman; DSCanother polymorph, melting onset 90 °Ctrasi2012b R6, R9, C14
celecoxib with 10% SLSXRD of grown crystalssome form I besides form IIImosqueragiraldo2014 R14, C38
felodipine filmscovered vs free surfaceform II in the bulk, form I at a free surfacekestur2013a R1, R2, R3
tacrolimus capsule contents40 °C/75% RHmonohydratetrasi2017 R6, C26
Fig. 13 of wegiel2014: PXRD of the dispersions after 1 day at 98% RH and 60 °C
Fig. 13 · wegiel2014PXRD of the dispersions after 1 day at 98% RH and 60 °C

The right-hand box marks the form II peaks of the HPMC, HPMCAS and CMCAB traces, the left-hand box the form I peaks of E100 ("EUD"), PVP and crystalline curcumin wegiel2014 R17.

Why

For curcumin the authors state only that the cellulosic polymers "were able to influence" the polymorph wegiel2014 C28. For celecoxib, "one possible explanation" of the surfactant growth effects "could be" that different polymorphs grew, which XRD ruled out for TPGS and sucrose palmitate mosqueragiraldo2014 C37, C38. For felodipine, form I's faster surface growth, especially below Tg, and its tendency to nucleate at the surface "most likely" explain why powders give only form I kestur2013a C25.

Limits and transfer

The flutamide Raman spectra are not shown, and the celecoxib forms were checked only for the binary surfactant samples trasi2012b P3; mosqueragiraldo2014 X9. Most additive–drug pairs in these papers did not change the form trasi2012b R6; mosqueragiraldo2014 C38; wegiel2014 R17. At each stability pull identify the crystal form, not only the crystallinity, and in growth screens with additives confirm the form of the growing crystal, since a change of form can masquerade as a change of rate.

How it was shown

Wegiel and co-workers (2014) stored 75:25 curcumin dispersions with five polymers at six conditions and identified the crystals by PXRD reflections (form I at 8.9, 17.4, 23.5 and 25.1° 2θ; form II at 13.9, 26.0 and 27.1° 2θ) wegiel2014 P5, R15, R17. Trasi and Taylor (2012) identified flutamide crystals grown between quartz cover slips by Raman against the known form, and acetaminophen events on DSC reheating by their melting points trasi2012b P3; trasi2012a P4, R10. Mosquera-Giraldo and co-workers (2014) took XRD of celecoxib crystals grown from the melt with each surfactant mosqueragiraldo2014 P6, R14. Kestur and co-workers (2013) noted which form grew in covered films, at free surfaces and in powders kestur2013a R1, R2; kestur2013b R10. Tian and co-workers (2017) identified the indomethacin forms by morphology, Raman, hot-stage melting and XRD tian2017 R2, R3, R4, R6.

What the data show

Neat amorphous curcumin crystallized as form I at every condition where it crystallized wegiel2014 R15, C23. After 1 day at 98% RH and 60 °C the cellulosic dispersions showed form II reflections and no 17.4° peak, E100 and PVP gave form I; the form II of the dispersions matched a polymorph reported in 2011 as metastable, with a higher dissolution rate and solubility than form I wegiel2014 R17, R20, C28. For flutamide all samples grew the same form (CSD WEZCOT) except 5% w/w HPMC, which grew another, identified by small Raman shifts, whose melting with onset 90 °C appeared in DSC; with PDMA a second small exotherm near 84 °C marked a delayed transition between polymorphs trasi2012b R6, R9, R8.d, C13. Melted acetaminophen first crystallized as form III, which on reheating turned to form II before melting at 156 °C; with polymers the transition was delayed, with E100 and HPMC an exotherm near 133–139 °C trasi2012a R2, R10, C20. Celecoxib grown with SLS showed a peak near 8° 2θ (form I) absent with TPGS and sucrose palmitate, which grew the starting form III mosqueragiraldo2014 R14, C38. In felodipine, confinement between two cover slips gave form II and a free surface always form I, and powders gave form I only kestur2013a R1, R2, R3; kestur2013b R10. A 10% HPMCAS felodipine dispersion stored 491 days at 93% RH gave a mixture with form II rumondor2009b R13.

In indomethacin the polymorph that formed depended on storage temperature, δ at 60 °C and α at 80 °C, γ only from seeds, and the polymers retarded nucleation so that a higher temperature was needed to start crystals tian2017 R1, R5, C7. The ATP enantiomers changed growing form between 90 and 100 °C, so all polymer comparisons were kept at or below 90 °C sato2015 R6, C9, X12. Amorphous tacrolimus in a marketed capsule crystallized as the monohydrate, which the authors relate to the larger effect of humidity than of temperature (see F33) trasi2017 R6, C26.

papersystemmethod and conditionsresultids
wegiel2014curcumin with HPMC, HPMCAS, CMCABPXRD after 1 day at 98% RH, 60 °Cmetastable form II, no conversion during the studyR17, C28
wegiel2014curcumin alone, with E100 or PVPsameform IR15, R17
trasi2012bflutamide with 5% w/w HPMCRaman; DSCanother polymorph, melting onset 90 °CR6, R9, C14
trasi2012bflutamide with 10 mol% PDMADSC reheatingsecond exotherm ≈84 °C, delayed transitionR8.d, C13
trasi2012aacetaminophen with 10% polymerDSC reheatingform III to form II transition delayedR10, C20
mosqueragiraldo2014celecoxib with 10% SLSXRD of grown crystalssome form I besides form IIIR14, C38
kestur2013afelodipine filmscovered vs free surfaceform II in the bulk, form I at a free surfaceR1, R2, R3
rumondor2009bfelodipine with 10% HPMCAS, 93% RHPXRD after 491 daysmixture including form IIR13
tian2017amorphous indomethacin filmsstorage at 60 and 80 °C; seedingδ at 60 °C, α at 80 °C, γ only from seeds; polymers retard nucleationR1, R5, C7
sato2015ATP enantiomersgrowth 40–120 °Cchange of growing form between 90 and 100 °CR6, C9
trasi2017tacrolimus capsule contents40 °C/75% RHmonohydrateR6, C26

Figure

Fig. 13 of wegiel2014: PXRD of the dispersions after 1 day at 98% RH and 60 °C
Fig. 13 · wegiel2014PXRD of the dispersions after 1 day at 98% RH and 60 °C

The right-hand box marks the form II peaks of the HPMC, HPMCAS and CMCAB traces, the left-hand box the form I peaks of E100 ("EUD"), PVP and crystalline curcumin wegiel2014 R17.

Fig. 9 of mosqueragiraldo2014: XRD of celecoxib crystals grown with each surfactant
Fig. 9 · mosqueragiraldo2014XRD of celecoxib crystals grown with each surfactant

Only the SLS trace (c) has the extra peak near 8° 2θ of form I; sucrose palmitate (b) and TPGS (d) match celecoxib form III (a) mosqueragiraldo2014 R14.

Why

The authors give few mechanisms. For curcumin they state only that the cellulosic polymers "were able to influence" the polymorph wegiel2014 C28. For celecoxib, "one possible explanation" of the surfactant growth effects "could be" that different polymorphs grew, which XRD ruled out for TPGS and sucrose palmitate mosqueragiraldo2014 C37, C38. For felodipine, form I's faster surface growth, especially below Tg, and its tendency to nucleate at the surface "most likely" explain why powders give only form I kestur2013a C25. (synthesis: an additive can change the form either by changing which nucleus appears first or by slowing the growth or conversion of one form more than another; the HPMC–flutamide and cellulosic–curcumin cases do not separate the two.)

Conditions and limits

The curcumin form II reflections are read differently in text and figure, the same CCDC code is printed for both forms, and the CMCAB trace has a small peak near 17.2° 2θ wegiel2014 X3, X11, X12. The flutamide Raman spectra are not shown trasi2012b P3. The celecoxib forms were checked only for the binary surfactant samples, and the SLS sample, which contained some form I, may have given growth rates of two forms mosqueragiraldo2014 X9. All forms come from melt films or stress conditions of hours to days, except the felodipine HPMCAS mixture after 491 days rumondor2009b R13.

Counterexamples and conflicts

Most additive–drug pairs in these papers did not change the form: every flutamide sample but HPMC, the TPGS and sucrose palmitate celecoxib samples, and E100 and PVP with curcumin trasi2012b R6; mosqueragiraldo2014 C38; wegiel2014 R17. The 2014 curcumin authors call a stabilized metastable form a possible benefit for bioavailability but "clearly" not ideal from a regulatory view wegiel2014 C43.

Transfer check

At each stability pull identify the crystal form, not only the crystallinity, and compare it with the form of the neat amorphous drug under the same condition wegiel2014 R15, R17. If a polymer gives a metastable form, check whether it persists and how it dissolves before treating the result as a failure or a benefit wegiel2014 C43, R20. For growth-rate screens with additives, confirm the form of the growing crystal, since a change of form can masquerade as a change of rate mosqueragiraldo2014 C37, X9; kestur2013a C27.

History

The 2009 humidity study noted form II in an old HPMCAS felodipine sample without analysis rumondor2009b R13. In 2012 Trasi and Taylor recorded a polymer-specific polymorph for flutamide and delayed transitions for flutamide and acetaminophen trasi2012b C10, C13; trasi2012a C20. In 2013 the felodipine papers tied the form to the growth site kestur2013a C25; kestur2013b C26. In 2014 surfactants (SLS) and cellulosic polymers changed the form for celecoxib and curcumin mosqueragiraldo2014 C38; wegiel2014 C28. The neat-drug side, a metastable form often growing first from the supercooled liquid, is in Crystallization tendency F7 lu2016 C7. In 2015–2017 the enantiomer and indomethacin growth papers kept their polymer comparisons within one form per temperature range sato2015 X12; tian2017 R1, and the tacrolimus survey identified a hydrate as the form that grew in humid storage trasi2017 C26; the title is unchanged.

F21

Topic 1Crystallization of the amorphous drug in dry dispersions10 of 15

Free surfaces crystallize faster than the bulk, so small amorphous particles crystallize sooner, and PVP protects the bulk more.

Felodipine form I grew about 6 times faster at a free surface than in the bulk at 18 °C, with no difference above 70 °C kestur2013a R8.a, R9, C2. At 30 °C, 3% PVP cut bulk growth about 7-fold but surface growth only about 2-fold, so the surface/bulk ratio rose from 5.7 to 22.8 kestur2013b R12, C32. In powders the smaller sieve fraction (150–250 µm) crystallized ahead of the larger one (500–710 µm): about 46 against 12% at 24 h for the pure drug by Raman kestur2013b R3.e, R5, C12.

strongStrong for the surface and particle-size effects, weak to moderate for the constant-depth explanation: the depth model is a fit to one point, and the bulk growth rate with PVP would cross the estimated depth in a few days kestur2013a K1; kestur2013b K1, K2, K3, K4, X6, X8.

free surfacebulkno polymer0.47 × 10⁻⁹2.7 × 10⁻⁹3% PVP6.37 × 10⁻¹¹1.45 × 10⁻⁹1e−111e−101e−091e−08felodipine form I growth at 30 °C, m/s (log scale)

PVP about halves surface growth but cuts bulk growth about sevenfold. kestur2013b R12, C32

3% PVP powders stored dry at 30 °C: crystallinity plateau, %150–250 µm≈45500–710 µm≈17500–710 µm, constant-depth modeldepth 17.3 µm from the small fraction16.2 predicted (16.5 measured)

kestur2013b R8, R16, E1, C27, C30

For your drug

  1. Measure growth with the top cover glass removed as well as sandwiched, at one temperature below Tg and one above, and store at least two particle-size fractions of the dispersion, since milling and sieving change the free surface.
  2. If the surface rate is much higher than the bulk rate with the polymer, consider protecting the surface: a polymer or gold coating suppressed surface growth in cited work, and atomic layer coatings slowed surface crystallization of ASD particles in later work.

kestur2013a P2, P3; kestur2013b C2, C12, C3; duong2022c C35

How it works and key numbers
  1. Faster surface growth "may be attributed" to mobile molecules at a more liquid-like surface, as surface diffusion in indomethacin glass far exceeds bulk diffusion kestur2013a C16, R17.
  2. Smaller particles carry more surface per volume, so with faster surface growth they crystallize sooner ("can be attributed in large part") kestur2013b C24.
  3. With PVP the plateaus "may" come from a constant depth of crystallization from the surface, about 17.3 µm, with crystalline fraction X = 1 - \left(\frac{r - d}{r}\right)^{3} for particle radius r and depth d; the fast first stage is "probably" surface growth kestur2013b C28, C33, R16, E1.
  4. Where surface growth exceeds bulk growth, predicting low-temperature stability from high-temperature data without it "may" overpredict stability kestur2013a C18.
To feel the numbers. Small fraction, r = 100 µm: (100 − 17.3) ÷ 100 = 0.827, and 0.827³ ≈ 0.566, so X ≈ 1 − 0.566 ≈ 43%. Large fraction, r = 302.5 µm: (302.5 − 17.3) ÷ 302.5 ≈ 0.943, and 0.943³ ≈ 0.838, so X ≈ 16%.
≈6-foldfaster form I growth at a free surface than in the bulk at 18 °Ckestur2013a R8.a, R9, C2
5.7 → 22.8surface/bulk growth ratio at 30 °C without and with 3% PVPkestur2013b R12, C32
≈46 vs ≈12%crystallinity at 24 h of pure powder, 150–250 vs 500–710 µmkestur2013b R3.e, R5

Connections to other chapters

Evidence: data, conditions and papers

Finding F21. Free surfaces crystallize faster than the bulk, so smaller amorphous particles crystallize sooner, and 3% PVP slows bulk growth far more than surface growth

In short. Felodipine form I grew about 6 times faster at a free surface than in the bulk at 18 °C, with no difference above 70 °C kestur2013a R8.a, R9, C2. At 30 °C the surface/bulk ratio was 5.7 without and 22.8 with 3% PVP, because PVP cut bulk growth about 7-fold but surface growth only about 2-fold kestur2013b R12, C32. In powders the smaller sieve fraction (150–250 µm) crystallized ahead of the larger one (500–710 µm): about 46 against 12% at 24 h for the pure drug by Raman, and plateaus of about 45 against 17% with PVP kestur2013b R3.e, R5, R8, C12. The authors explain the plateaus by a constant depth of crystallization from the surface, about 17.3 µm, which predicts 16.2% for the larger particles against 16.5% measured ("It can be speculated") kestur2013b R16, E1, C28, C30.

Type. observation in one drug, two papers, films and powders Strength. for the surface and particle-size effects (kestur2013a K1: strong; kestur2013b K1: strong; K2: moderate to strong), weak to moderate for the constant-depth and surface-origin explanations (kestur2013b K3, K4: weak to moderate) — the depth model is a fit to one point, the bulk growth rate with PVP would cross the estimated depth in a few days, and the fast-stage comparison sets a powder slope ratio against a film rate ratio (X6, X8).

How it was shown

Kestur and Taylor (2013) grew form I in melt-quenched films with and without a top cover glass from 18 to 100 °C kestur2013a P1, P2, P3, P6. Kestur and co-workers (2013) ground amorphous felodipine and a 3% PVP dispersion, sieved two fractions (150–250 and 500–710 µm), stored them dry at 30 °C and followed crystallinity by Raman and PXRD kestur2013b P2, P3, P4, P5, P6, P7. For the plateaus they treated each particle as a sphere crystallizing inward from the surface kestur2013b E1, C29.

What the data show

Without polymer the two form I rates fell by 3–4 orders of magnitude from 100 to 18 °C and coincided above 70 °C kestur2013a R9, R8.a, C2. Pure powders finished crystallizing within 72–120 h, the smaller fraction first, while with PVP both fractions stalled after 50–60 days kestur2013b R5, R3, R8, C27.

systemmethod and conditionsresultids
felodipine form I films, no polymersurface vs bulk growth, 18–100 °C≈6-fold faster at the surface at 18 °C; equal above 70 °Ckestur2013a R8.a, R9, C2
films at 30 °C, 0 and 3% PVPsurface vs bulk growthratio 5.7 → 22.8; PVP slows bulk ≈7-fold, surface ≈2-foldkestur2013b R12, C13, C32
pure amorphous powders, 30 °CRaman crystallinity, two sieve fractions≈46 vs ≈12% at 24 h; both ≈95–96% at the endkestur2013b R3.e, R5
3% PVP powders, 30 °CRaman and PXRDplateaus ≈45% and ≈17% after 50–60 dayskestur2013b R6, R7, R8, C27
samesphere with a crystallized shelldepth ≈17.3 µm; predicted 16.2%, measured 16.5%kestur2013b R16, E1, C30
Table 1 of kestur2013b: growth rates of form I at 30 °C at the free surface and in the bulk, with and without 3% PVP
Table 1 · kestur2013bgrowth rates of form I at 30 °C at the free surface and in the bulk, with and without 3% PVP

Read across the rows: PVP halves the surface rate but cuts the bulk rate about sevenfold, so the surface/bulk ratio rises from 5.7 to 22.8 kestur2013b R12.

Why

Faster surface growth "may be attributed" to mobile molecules at a more liquid-like surface, as surface diffusion in indomethacin glass far exceeds bulk diffusion kestur2013a C16, R17. The particle-size effect of the pure drug "can be attributed in large part" to the surface-to-volume ratio together with the faster surface growth kestur2013b C24, C25. The PVP plateaus "may" come from a constant penetration depth of surface crystallization kestur2013b C28.

Limits and transfer

One drug, form I, dry conditions, and particle surface area was not measured kestur2013a P1; kestur2013b P3, C24. The bulk rate with PVP corresponds to about 300 µm over 56 days, far beyond the estimated 17.3 µm depth, so the plateau is not explained by the film growth rates (card calculation) kestur2013b X8. Measure growth with the top cover glass removed as well as sandwiched, and store at least two particle-size fractions of the dispersion.

How it was shown

Kestur and Taylor (2013) grew form I in melt-quenched films with and without a top cover glass from 18 to 100 °C kestur2013a P1, P2, P3, P6. Kestur and co-workers (2013) ground amorphous felodipine and a 3% PVP dispersion under dry nitrogen, sieved two fractions (150–250 and 500–710 µm), stored them dry at 30 °C, followed crystallinity by Raman and PXRD calibration models, and measured film growth at the free surface and in the bulk at 30 °C kestur2013b P2, P3, P4, P5, P6, P7, P8. For the plateaus they treated each particle as a sphere of the sieve-midpoint radius crystallizing inward from the surface (in words, Eq. E1) kestur2013b E1, C29:

X = 1 - \left(\frac{r - d}{r}\right)^{3}

(synthesis: the shell-volume form of the stated words, with X the crystalline fraction, r the particle radius and d the depth; it reproduces 17.3 µm from 43.5% at r = 100 µm and 16.2% at r = 302.5 µm kestur2013b R16).

What the data show

Without polymer the two form I rates fell by 3–4 orders of magnitude from 100 to 18 °C, to about 5.4 × 10⁻¹⁰ m/s at the surface and 8.7 × 10⁻¹¹ m/s in the bulk; above 70 °C the two coincided kestur2013a R9, R8.a, C2. In the plotted means the surface/bulk factor is about 6 at 18, 30 and 50 °C but about 3.5–3.7 at 40–45 °C and about 1.5 at 70–80 °C kestur2013a X13. With 3% PVP surface crystals grew 1–1.5 orders of magnitude faster than bulk crystals kestur2013a R14. At 30 °C the rates were 2.7 × 10⁻⁹ (surface) and 0.47 × 10⁻⁹ m/s (bulk) without PVP and 1.45 × 10⁻⁹ and 6.37 × 10⁻¹¹ m/s with it kestur2013b R12. Pure amorphous powders began to crystallize within 3–6 h and finished within 72–120 h, the smaller fraction first (Raman about 88 against 53% at 48 h) kestur2013b R5, R3. With PVP both fractions stalled after 50–60 days, at about 45–50% and 15–20% kestur2013b R8, C27. The PVP powder kinetics were biphasic, the early slope 13–14 times the late one, which the authors compare with the surface/bulk ratio of about 23 kestur2013b R14, C33.

papersystemmethod and conditionsresultids
kestur2013afelodipine form I films, no polymersurface vs bulk growth, 18–100 °C≈6-fold faster at the surface at 18 °C; equal above 70 °CR8.a, R9, C2
kestur2013asame with 3% PVPsamesurface 1–1.5 orders faster than bulkR14, X13
kestur2013bfilms at 30 °C, 0 and 3% PVPsurface vs bulk growthratio 5.7 → 22.8; PVP slows bulk ≈7-fold, surface ≈2-foldR12, C13, C32
kestur2013bpure amorphous powders, 30 °CRaman crystallinity, two sieve fractions≈46 vs ≈12% at 24 h; both ≈95–96% at the endR3.e, R5
kestur2013b3% PVP powders, 30 °CRaman and PXRDplateaus ≈45% and ≈17% after 50–60 daysR6, R7, R8, C27
kestur2013bsamesphere with a crystallized shelldepth ≈17.3 µm; predicted 16.2%, measured 16.5%R16, E1, C30
trasi2014a (outside)14 compounds near Tgsurface vs bulk growththe surface order need not match the bulk orderR4, R5, C8
duong2022c (outside)coated ASD particles, 40 °Cstorageslower surface crystallization at lower loading and thicker coatingC33, C35

Figure

Table 1 of kestur2013b: growth rates of form I at 30 °C at the free surface and in the bulk, with and without 3% PVP
Table 1 · kestur2013bgrowth rates of form I at 30 °C at the free surface and in the bulk, with and without 3% PVP

Read across the rows: PVP halves the surface rate but cuts the bulk rate about sevenfold, so the surface/bulk ratio rises from 5.7 to 22.8 kestur2013b R12.

Fig. 5 of kestur2013b: crystallinity of 3% PVP dispersions against time by Raman for two particle sizes
Fig. 5 · kestur2013bcrystallinity of 3% PVP dispersions against time by Raman for two particle sizes

The 200 µm powder (squares) stalls near 42–45%, the 605 µm powder (triangles) near 15–18%, both after about two months kestur2013b R6.

Why

The authors' account, with their hedges: faster surface growth "may be attributed" to mobile molecules at a more liquid-like surface, as surface diffusion in indomethacin glass far exceeds bulk diffusion kestur2013a C16, R17. The particle-size effect of the pure drug "can be attributed in large part" to the surface-to-volume ratio together with the faster surface growth, and it is weaker than for indomethacin (about 100-fold surface enhancement) because felodipine's surface/bulk difference is smaller ("may be due to") kestur2013b C24, C25, R24. The PVP plateaus "may" come from a constant penetration depth of surface crystallization, and the fast first stage is "probably" surface growth kestur2013b C28, C33. Earlier work found that felodipine grows around PVP molecules without enriching PVP at the front, so a polymer-rich layer is not invoked kestur2013b C31, R27. Where surface growth exceeds bulk growth, predicting low-temperature stability from high-temperature data without it "may" overpredict stability kestur2013a C18.

Conditions and limits

One drug, form I, dry conditions, films 5–10 µm thick and two sieve fractions; particle surface area was not measured kestur2013a P1; kestur2013b P3, C24. Raman and PXRD gave different values for the same powders (about 46 against 31% for the small pure fraction at 24 h) and a smaller size gap by PXRD, which the authors put down to Raman's surface sensitivity kestur2013b X13, C10. The bulk rate with PVP corresponds to about 5.5 µm per day, about 300 µm over 56 days, far beyond the estimated 17.3 µm depth, while the crystallinity barely rose between 56 and 161 days, so the plateau is not explained by the film growth rates (card calculation) kestur2013b X8. The early/late slope ratio (powder % per day) and the surface/bulk ratio (film m/s) are different quantities kestur2013b X6.

Counterexamples and conflicts

Pure felodipine powders showed no biphasic kinetics, unlike indomethacin and griseofulvin, although the surface effect was present kestur2013b C21, R26. At 50 °C, above Tg, the PVP powder crystallized to about 85% rather than 45%, which the authors read as a smaller role of the surface there ("likely") (see F25) kestur2013b R9, C39. Across 14 compounds the surface order of growth rates did not always match the bulk order, so a bulk screen does not rank surface risk trasi2014a C8.

Transfer check

Measure growth with the top cover glass removed as well as sandwiched, at one temperature below Tg and one above kestur2013a P2, P3. Store at least two particle-size fractions of the dispersion, since milling and sieving change the free surface kestur2013b C2, C12. If the surface rate is much higher than the bulk rate with the polymer, consider protecting the surface: a polymer or gold coating suppressed surface growth in cited work, and atomic layer coatings slowed surface crystallization of ASD particles in later work kestur2013b C3; duong2022c C35.

History

Surface-enhanced growth was known for indomethacin, nifedipine and griseofulvin kestur2013a R17; kestur2013b C23. Rumondor and co-workers (2010) suggested surface growth of uncovered films as one reason felodipine grew faster than mobility predicts rumondor2010 C28. In 2013 the two felodipine papers measured the surface effect, its persistence with PVP and its consequence for powder particle size kestur2013a C15; kestur2013b C13, C20. Later work compared surface and bulk growth across 14 compounds (see Crystallization tendency F21) and coated ASD particles against surface crystallization (see ASD process F43) trasi2014a R4, R5; duong2022c C33.

F22

Topic 1Crystallization of the amorphous drug in dry dispersions11 of 15

Surfactants that mix with amorphous celecoxib speed its crystal growth, most at low temperature; with PVP the effects do not add.

At 10% in amorphous celecoxib, TPGS raised the growth rate at 70 °C about 85-fold (about 0.17 against 0.002 µm/s), sucrose palmitate about 7-fold and SLS about 1.5-fold, while all three were close to the drug near 120 °C mosqueragiraldo2014 R1, C8, C9, C36. TPGS and sucrose palmitate lowered Tg by about 10 °C; SLS, largely immiscible, did not mosqueragiraldo2014 R5, C16, C24. With 10% PVP present, SLS raised growth at every temperature, but TPGS lowered it, to about 0.03 of PVP alone at 120 °C and 0.6 at 70 °C mosqueragiraldo2014 R2, C11, C13, X5.

moderateModerate: the acceleration and the TPGS–PVP result are clear in one paper, but the mobility reading is the authors', the IR used five times the surfactant level in spin-coated films, and the 3–7% PVP mixtures are not described mosqueragiraldo2014 K1, K3, K5, K6, X6, X8.

Celecoxib with 10% additive: crystal growth at 70 °C, µm/scelecoxib aloneTg 55.34 °C≈0.002+ TPGSTg 44.81 °C≈0.17+ sucrose palmitateTg 44.46 °C≈0.014+ SLSTg 55.53 °C, largely immiscible≈0.0031+ TPGS + PVP≈0.00006

Miscible surfactants that lower Tg speed growth; with PVP present, TPGS gives the slowest growth of all. mosqueragiraldo2014 R1, R1.a, R1.c, R1.d, R1.e, R2, R5, C11

TPGS speeds growthTPGS slows growth3% PVP + 10% TPGScrossing 110faster with TPGSslower5% PVP + 10% TPGScrossing 100faster with TPGSslower7% PVP + 10% TPGScrossing 90fasterslower10% PVP + 10% TPGSslower at every temperature708090100110120growth temperature, °C

Compared with the same PVP level without TPGS; the more PVP, the lower the crossing temperature. mosqueragiraldo2014 R3, R4, C14, C15, R2, C13

For your drug

  1. Treat any miscible low-Tg excipient (surfactant or plasticizer) as a possible growth accelerator: measure the dispersion Tg with and without it and, if Tg falls, measure melt growth 15–25 °C above the new Tg.
  2. Test the full formulation, not the binary pairs, and find the crossing temperature before extrapolating a high-temperature advantage of a surfactant–polymer combination to storage.

mosqueragiraldo2014 C40, R12, C44, C15

How it works and key numbers
  1. The miscible surfactants "appear to behave" like small-molecule additives that depress Tg and so raise mobility, as water does; after correction for Tg their main effect is "most likely" on celecoxib mobility mosqueragiraldo2014 C29, C30.
  2. SLS, immiscible, has "very little impact" alone; adding PVP "appears to increase" its miscibility, after which it speeds growth mosqueragiraldo2014 C31, C32.
  3. Near the melting point growth is under thermodynamic control, so the large melting-point depression with TPGS and PVP (12 °C, a smaller driving force) "could contribute" to its slow growth at high temperature mosqueragiraldo2014 C25, C33, R5.
  4. A surfactant that mixes with the drug and plasticizes it "would be expected" to raise growth, but the outcome with polymer and surfactant together is "currently difficult" to predict mosqueragiraldo2014 C40, C41.
To feel the numbers. At 70 °C a celecoxib crystal front moves 0.002 × 86,400 s ≈ 170 µm per day alone, and 0.17 × 86,400 ≈ 15,000 µm, about 15 mm, per day with 10% TPGS (0.17 ÷ 0.002 = 85).
≈85-foldfaster growth at 70 °C with 10% TPGSmosqueragiraldo2014 R1, C9
≈10 °CTg drop by TPGS and sucrose palmitate (55.34 → 44.81 and 44.46 °C)mosqueragiraldo2014 R5
110, 100, 90 °Ccrossing temperatures with 3, 5 and 7% PVP, below which TPGS speeds growthmosqueragiraldo2014 R3, R4, C14

Connections to other chapters

Evidence: data, conditions and papers

Finding F22. Surfactants that mix with the amorphous drug speed its crystal growth, most at low temperature, and with a polymer present the effects do not add: TPGS with PVP grew slowest of all above a crossing temperature

In short. At 10% in amorphous celecoxib, TPGS raised the growth rate at 70 °C about 85-fold (about 0.17 against 0.002 µm/s), sucrose palmitate about 7-fold and SLS about 1.5-fold, while all three were close to the drug near 120 °C; 10% PVP cut growth 19–38-fold mosqueragiraldo2014 R1, C8, C9, C36. TPGS and sucrose palmitate lowered Tg by about 10 °C and SLS, largely immiscible, did not mosqueragiraldo2014 R5, C16, C24. With 10% PVP present, SLS raised growth at every temperature, but TPGS lowered it, to about 0.03 of PVP alone at 120 °C and 0.6 at 70 °C mosqueragiraldo2014 R2, C11, C13, X5. At 3, 5 and 7% PVP the TPGS curves were flatter and crossed the PVP-only curves at 110, 100 and 90 °C, below which TPGS made growth faster mosqueragiraldo2014 R3, R4, C14, C15.

Type. observation in one drug with 3 surfactants and one polymer Strength. the acceleration and the TPGS–PVP result are clear in one paper (mosqueragiraldo2014 K1: moderate to strong; K5: strong; K6: moderate), but the mobility reading is the authors' (K3: weak to moderate), the IR used five times the surfactant level in spin-coated films, the 3–7% PVP mixtures are not described, and no PVP-containing sample was checked for polymorph (X6, X8, X9).

How it was shown

Mosquera-Giraldo, Trasi and Taylor (2014) cryomilled celecoxib with 10 wt% surfactant, 10 wt% PVP K-12 or both, melted the powder between cover slips, quenched it, seeded the film at the edge and followed the growth front on a hot stage at 70–120 °C mosqueragiraldo2014 P1, P3, X1. A second series used 3, 5 and 7% PVP with and without 10% TPGS, and Tg and the drug melting point were measured by DSC mosqueragiraldo2014 P2, P4.

What the data show

Pure celecoxib grew at about 0.002 µm/s at 70 °C and 12 µm/s at 120 °C mosqueragiraldo2014 R1.a. TPGS and sucrose palmitate lowered Tg from 55.34 to 44.81 and 44.46 °C, while SLS did not (55.53 °C) mosqueragiraldo2014 R5.a, R5.b, R5.c, R5.e. The TPGS–PVP ternary had the lowest drug melting point (151.49 °C, 12 °C below the drug) mosqueragiraldo2014 R5.f, C18.

systemmethod and conditionsresultids
celecoxib with 10% TPGS, sucrose palmitate, SLSseeded melt growth, 70 °C≈85-, ≈7-, ≈1.5-fold faster than the drugmosqueragiraldo2014 R1, C9
same, 120 °Csameall within about 1.6-fold of the drug (synthesis)mosqueragiraldo2014 R1, C36
10% PVP plus 10% surfactantgrowth, 70–120 °CSLS faster than PVP alone; TPGS slower (≈0.6 → ≈0.03 of PVP alone)mosqueragiraldo2014 R2, C11, C13, X5
3, 5, 7% PVP with and without 10% TPGSgrowth, 80–120 °Ccurves cross at 110, 100, 90 °Cmosqueragiraldo2014 R3, R4, C14
griseofulvin, DPB, celecoxib with 5% PHBmelt growth; DSC Tgup to ≈10-fold faster; Tg −5 to −12 °Csato2016 R4, R7, R11
Fig. 2 of mosqueragiraldo2014: growth rate of celecoxib alone and with 10% PVP or 10% surfactant
Fig. 2 · mosqueragiraldo2014growth rate of celecoxib alone and with 10% PVP or 10% surfactant

TPGS (purple crosses) lies far above the drug (blue diamonds) at 70 °C and joins it near 120 °C; PVP (red squares) lies far below at every temperature mosqueragiraldo2014 R1.

Why

The miscible surfactants "appear to behave" like small-molecule additives that depress Tg and so raise mobility, and after correction for Tg their main effect is "most likely" on celecoxib mobility mosqueragiraldo2014 C29, C30. SLS, immiscible, has "very little impact" alone; adding PVP "appears to increase" its miscibility, after which it speeds growth mosqueragiraldo2014 C31, C32. Near the melting point growth is under thermodynamic control, so the large melting-point depression with TPGS and PVP "could contribute" to its slow growth at high temperature mosqueragiraldo2014 C25, C33.

Limits and transfer

One drug and one polymer grade, growth at 70–120 °C above the Tg of every system; storage at room temperature was not tested mosqueragiraldo2014 P3, A1, X8. Treat any miscible low-Tg excipient as a possible growth accelerator, test the full formulation rather than the binary pairs, and find the crossing temperature before extrapolating a high-temperature advantage to storage.

How it was shown

Mosquera-Giraldo, Trasi and Taylor (2014) cryomilled celecoxib with 10 wt% surfactant, 10 wt% PVP K-12 or both, melted the powder between cover slips, quenched it, seeded the film at the edge and followed the growth front on a hot stage at 70–120 °C mosqueragiraldo2014 P1, P3, X1. A second series used 3, 5 and 7% PVP with and without 10% TPGS mosqueragiraldo2014 P2. Tg and the drug melting point were measured by DSC, interactions by FTIR of spin-coated films with 50% surfactant, growth was replotted against T - T_g, and the grown crystals were checked by XRD mosqueragiraldo2014 P4, P5, P7, P6. Sato and Taylor (2016) measured melt growth with PHB, and Yang and co-workers (2022) imaged surfactant-containing films at high humidity sato2016 P3; yang2022b P4.

What the data show

Pure celecoxib grew at about 0.002 µm/s at 70 °C and 12 µm/s at 120 °C mosqueragiraldo2014 R1.a. At 70 °C the binary systems grew at about 0.17 (TPGS), 0.014 (sucrose palmitate) and 0.0031 µm/s (SLS); at 120 °C at about 17, 7.4 and 13 µm/s mosqueragiraldo2014 R1.c, R1.d, R1.e. The ranking TPGS > sucrose palmitate > SLS holds at 70 and 80 °C only; from 100 °C SLS grew faster than sucrose palmitate, which fell to or below the drug at 110–120 °C mosqueragiraldo2014 X2. Tg was 55.34 °C for celecoxib, 44.81 with TPGS, 44.46 with sucrose palmitate, 55.53 with SLS and 62.40 °C with PVP mosqueragiraldo2014 R5.a, R5.b, R5.c, R5.e, R5.g. In the ternaries, SLS plus PVP grew about 2–20 times faster than PVP alone, sucrose palmitate plus PVP faster below 100 °C and slower above, and TPGS plus PVP slower at every temperature, about 0.00006 µm/s at 70 °C and 0.012 µm/s at 120 °C mosqueragiraldo2014 R2, C11. The TPGS–PVP ternary had the lowest Tg (44.17 °C) of the PVP systems and the lowest drug melting point (151.49 °C, 12 °C below the drug), and at 120 °C grew a large faceted plate instead of a fibrous front mosqueragiraldo2014 R5.f, C18, R13, C34. In the 3–7% PVP series TPGS lowered the 120 °C rate (3% PVP: about 1.9 against 3.0 µm/s) but raised the 80 °C rate (about 0.0089 against 0.0010 µm/s) mosqueragiraldo2014 R3, R4.

A low-Tg polymer acts like the miscible surfactants: 5% PHB (Tg 0 °C) lowered the Tg of griseofulvin, DPB and celecoxib by 5–12 °C and sped their growth up to tenfold, and at equal T − Tg most of the speed-up disappeared (see F28) sato2016 R7, R10, R11. In humid ritonavir–PVPVA films the lipophilic Spans entered the drug-rich phase and sped separation and coarsening, while SDS and Tween 80 delayed visible separation (see F32) yang2022b C7, C58.

papersystemmethod and conditionsresultids
mosqueragiraldo2014celecoxib with 10% TPGS, sucrose palmitate, SLSseeded melt growth, 70 °C≈85-, ≈7-, ≈1.5-fold faster than the drugR1, C9
mosqueragiraldo2014same, 120 °Csameall within about 1.6-fold of the drug (synthesis)R1, C36
mosqueragiraldo2014sameDSC Tg; FTIRTPGS and sucrose palmitate −10.5 and −10.9 °C; SLS no change, sum spectrumR5, R9, R11, C24
mosqueragiraldo201410% PVP plus 10% surfactantgrowth, 70–120 °CSLS faster than PVP alone; TPGS slower (≈0.6 → ≈0.03 of PVP alone)R2, C11, C13, X5
mosqueragiraldo20143, 5, 7% PVP with and without 10% TPGSgrowth, 80–120 °Ccurves cross at 110, 100, 90 °CR3, R4, C14
mosqueragiraldo2014all ternariesDSC Tmdepression 7.3–12 °C; does not order the ternariesR5, X13
sato2016griseofulvin, DPB, celecoxib with 5% PHBmelt growth; DSC Tgup to ≈10-fold faster; Tg −5 to −12 °CR4, R7, R11
yang2022britonavir–PVPVA 30:70 with Span 20, Span 85 vs SDS, Tween 80confocal at high RH, 37 °CSpans separated and coarsened by 5 min; SDS and Tween 80 delayedR5, R6, R7, R8, C7
nguyen2023a (outside)pretomanid–HPMCAS with TPGSDSC TgTg falls with TPGS (≈79 → ≈63 °C at 20% drug)R13, C22
correasoto2022b (outside)atazanavir–PVPVA with surfactantsTgplasticization from low-Tg additivesC39

Figure

Fig. 2 of mosqueragiraldo2014: growth rate of celecoxib alone and with 10% PVP or 10% surfactant
Fig. 2 · mosqueragiraldo2014growth rate of celecoxib alone and with 10% PVP or 10% surfactant

TPGS (purple crosses) lies far above the drug (blue diamonds) at 70 °C and joins it near 120 °C; PVP (red squares) lies far below at every temperature mosqueragiraldo2014 R1.

Fig. 4 of mosqueragiraldo2014: growth rate at 3, 5 and 7% PVP with and without 10% TPGS
Fig. 4 · mosqueragiraldo2014growth rate at 3, 5 and 7% PVP with and without 10% TPGS

Each TPGS curve is flatter than the matching PVP-only curve and crosses it on cooling; pairs are told apart by colour mosqueragiraldo2014 R3, R4, X11.

Why

The authors' account, with their hedges: the miscible surfactants "appear to behave" like small-molecule additives that depress Tg and so raise mobility, as water does, and after correction for Tg their main effect is "most likely" on celecoxib mobility (see F5 for how much of the spread T - T_g removes) mosqueragiraldo2014 C29, C30. SLS, immiscible, has "very little impact" alone; adding PVP "appears to increase" its miscibility, after which it speeds growth mosqueragiraldo2014 C31, C32. Near the melting point growth is under thermodynamic control, so the large melting-point depression with TPGS and PVP, meaning a smaller driving force, "could contribute" to its slow growth at high temperature mosqueragiraldo2014 C25, C33. In general a surfactant that mixes with the drug and plasticizes it "would be expected" to raise growth, but the outcome with polymer and surfactant together is "currently difficult" to predict mosqueragiraldo2014 C40, C41. (synthesis: the crossing curves fit two opposing contributions, a lower driving force that matters near Tm and a higher mobility that matters at low temperature; neither was measured.)

Conditions and limits

One drug, one polymer grade, 10% surfactant, growth at 70–120 °C, above the Tg of every system; storage at room temperature was not tested mosqueragiraldo2014 P3, R5.a, A1. The FTIR evidence for miscibility comes from 50% surfactant films made from solvent mosqueragiraldo2014 X8. Tg differences below about 1 °C are unresolved (for example TPGS–PVP 44.17 against TPGS 44.81 °C) mosqueragiraldo2014 X7. The faceted TPGS–PVP crystal may not be the form III whose growth the other systems report mosqueragiraldo2014 X9.

Counterexamples and conflicts

Tm depression does not order the ternaries: SLS–PVP is depressed more than PVP alone yet grows faster at every temperature mosqueragiraldo2014 X13. With 10% PVP no crossing appeared down to 70 °C, so "at least at higher temperatures" understates the TPGS–PVP advantage at that level mosqueragiraldo2014 X5, C13. Sucrose palmitate, though it lowers Tg like TPGS, grew 1.2–3.8 times slower than the drug at equal distance above Tg mosqueragiraldo2014 X4.

Transfer check

Treat any miscible low-Tg excipient (surfactant or plasticizer) as a possible growth accelerator: measure the dispersion Tg with and without it and, if Tg falls, measure melt growth at a temperature 15–25 °C above the new Tg mosqueragiraldo2014 C40, R12. Test the full formulation, not the binary pairs, since a polymer can cancel or reverse the surfactant effect mosqueragiraldo2014 C44. Do not extrapolate a high-temperature advantage of a surfactant–polymer combination to storage temperatures; find the crossing temperature first mosqueragiraldo2014 C15.

History

Before 2014 the effect of surfactants on solid-state crystallization of dispersions had, in the authors' words, "few, if any" studies mosqueragiraldo2014 C5. Later papers of the same group found TPGS and other surfactants plasticizing PVPVA and HPMCAS dispersions nguyen2023a C22; correasoto2022b C39; correasoto2023 C30, surfactants doubling ritonavir growth in solution (see D. Crystallization from solution F18), and a TPGS dispersion losing release after milling (see ASD process F40). In 2016 a low-Tg polymer was found to accelerate growth in the same way (see F28) sato2016 C29, and in 2022 surfactants were found to change water-induced separation according to the phase they enter (see F32) yang2022b C35; the title is unchanged.

F27

Topic 1Crystallization of the amorphous drug in dry dispersions12 of 15

HPMCAS slowed one enantiomer of a chiral compound about twice as much as the other; achiral PVP slowed both alike.

With 5% w/w polymer in the undercooled melt of the chiral model compound ATP, HPMCAS-HF let ATP(S) grow about 1.9–2.5 times faster than its mirror-image form ATP(R) at 50–80 °C, and HPMCAS-LF let ATP(R) grow about 1.5–1.9 times faster than ATP(S) at 60–70 °C sato2015 R5, R7, R8, X2. PVP and HPMCP kept the small S/R ratio of the pure enantiomers (about 1.2–1.6) sato2015 R5, X2, C10. Infrared showed more loss of the free NH2 band for the enantiomer that was slowed more, and the authors attribute the difference "most likely" to hydrogen bonding of the ATP amino group to the polymer carbonyls sato2015 R13, R14, C29.

moderateModerate: the split is direct, triplicate and agrees across growth, DSC and storage, but the pure enantiomers already differ 1.2–1.6-fold, the text of the paper swaps R and S, and the interaction evidence is qualitative IR at 20–30% polymer sato2015 K1, K3, K4, X1, X2, X5.

ATP(S)ATP(R)HF grade, 50 °C0.00550.011HF grade, 60 °C0.0490.094HF grade, 70 °C0.190.47HF grade, 80 °C0.120.24LF grade, 60 °C0.0150.029LF grade, 70 °C0.0580.0890.0010.010.11ATP growth rate with 5% w/w HPMCAS, µm/s (log scale)

With HPMCAS-HF the S enantiomer grows about twice as fast as R; with HPMCAS-LF the order reverses. sato2015 R5, R7, R8

enantiomers + HPMCAS-HF14–105-foldracemate + PVP or HPMCAS-HFmeasured at 70–90 °Cabout 2-fold110100slowing factor with 5% w/w polymer (log scale)

The racemate, which grows 4–11 times more slowly, barely responds to the polymers. sato2015 R9, X4, C12

For your drug

  1. For a single-enantiomer drug, screen polymers on the enantiomer itself, not on the racemate, which responded about twofold where the enantiomers responded 14–105-fold.
  2. Test at least two grades of a cellulose ester such as HPMCAS, compare the growth ratio against the pure enantiomers' own ratio rather than against 1, and check by IR of the free donor band which enantiomer binds more.

sato2015 R9, X4, R5, X2, R13, R14, X5

How it works and key numbers
  1. The ATP amino group donates hydrogen bonds to polymer carbonyls, as the new NH bands show ("strongly suggests") sato2015 C16, C24.
  2. In HPMCAS some ester carbonyls sit close to the chiral cellulose backbone, so R and S bind to different extents, and the differential inhibition is "most likely due to" differences in their ability to form hydrogen bonds with the polymer sato2015 C26, C29.
  3. In HPMCP the binding carbonyls lie next to the achiral phthalate group, which "may minimize" contact with chiral centres; PVP, being achiral, binds both alike ("it is suggested") sato2015 C25, C30.
  4. Tg stayed at 14.3–18.4 °C in every sample, so the authors read the result as "strongly" supporting compound–polymer interactions as determinants of growth inhibition; why LF and HF favour opposite enantiomers is "not readily explainable" sato2015 R1, C6, C27, C28.
1.9–2.5×ATP(S) faster than ATP(R) with HPMCAS-HF, 50–80 °Csato2015 R5, X2
1.2–1.6×S/R ratio of the pure enantiomers, the baselinesato2015 R5.a, R5.b, X2
14–105-fold vs about 2-foldslowing of the enantiomers vs the racematesato2015 R9, X4, C12

Connections to other chapters

Evidence: data, conditions and papers

Finding F27. A chiral cellulose polymer can slow crystal growth of two enantiomers by different amounts, about twofold, with the favoured enantiomer set by the polymer grade, while achiral PVP slows both alike and the racemate responds far less

In short. With 5% w/w polymer in the undercooled melt of the chiral model compound 2-amino-1,1,3-triphenyl-1-propanol (ATP), HPMCAS-HF let ATP(S) grow about 1.9–2.5 times faster than ATP(R) at 50–80 °C, and HPMCAS-LF let ATP(R) grow about 1.5–1.9 times faster than ATP(S) at 60–70 °C; PVP and HPMCP kept the small S/R ratio of the pure enantiomers (about 1.2–1.6), and PHB barely slowed either sato2015 R5, R7, R8, X2, C10. The direction is read from the figures, the recrystallization onsets (HPMCAS-HF: 81.6 °C for ATP(R) against 77.2 °C for ATP(S)) and a 40 °C storage test; the text of the paper names the enantiomers the other way round sato2015 R1.d, R1.e, R15, X1. Infrared at 20–30% polymer showed more loss of the free amorphous NH2 band for the enantiomer that was slowed more, and the authors attribute the difference "most likely" to hydrogen bonding of the ATP amino group to the polymer carbonyls sato2015 R13, R14, C29. The racemate grew 4–11 times more slowly than the enantiomers and was slowed only about twofold by PVP or HPMCAS-HF, against 14–105-fold for the enantiomers sato2015 R9, X4, C12.

Type. single-system observation (one chiral model compound, five polymers at 5% w/w) Strength. the split is direct, triplicate and agrees across growth, DSC and storage (sato2015 K1: moderate to strong; K3: moderate), but the pure enantiomers already differ 1.2–1.6-fold, the text swaps R and S, and the interaction evidence is qualitative IR at 20–30% polymer (X1, X2, X5; K4: weak to moderate).

How it was shown

Sato and Taylor (2015) mixed ATP(R) and ATP(S), a compound with one NH2 and one OH group and a Tg of 16–17 °C, with 5% w/w of achiral PVP K-12 or of the chiral polymers PHB, HPMCP, HPMCAS-LF or HPMCAS-HF, and followed spherulite growth on a hot stage at 40–120 °C in triplicate sato2015 M1–M7, P1, P3, R1.a, R1.b, P2, P4, E1. DSC gave Tg and recrystallization onsets, and IR was taken on films with 20–30% polymer sato2015 P6, P5, C15.

What the data show

The pure enantiomers already differed, ATP(S) growing about 1.2–1.6 times faster than ATP(R) at every temperature sato2015 R5.a, R5.b, X2. Tg stayed at 14.3–18.4 °C in every sample sato2015 R1, C6.

systemmethod and conditionsresultids
5% w/w PVP K-12 (achiral)melt films, hot stage, n = 3both slowed alike, about 10-fold (50 °C) to 3–4-fold (70 °C)sato2015 R5.e, R5.f, C10
5% w/w HPMCP (chiral)same20–100-fold slower, S/R kept at about 1.2–1.4sato2015 R5.g, R5.h, C10
5% w/w HPMCAS-HF and -LFsame; size–time at 60 °CHF: S 1.9–2.5 times faster than R; LF: R 1.5–1.9 times faster than Ssato2015 R5.i–l, R7, R8
5% HPMCAS-HFDSC Tc; storage at 40 °C, IRTc 81.6 (R) against 77.2 °C (S); S crystalline by 15 h, R partly amorphous at 30 hsato2015 R1.d, R1.e, R15
racemate with PVP or HPMCAS-HFgrowth 70–90 °Cabout 2-fold slower; enantiomers 14–105-fold with HPMCAS-HFsato2015 R9, X4, C12
Fig. 6 of sato2015: growth rate of ATP(S) and ATP(R) against temperature, without polymer and with five polymers
Fig. 6 · sato2015growth rate of ATP(S) and ATP(R) against temperature, without polymer and with five polymers

Filled markers are ATP(S), markers with a light centre ATP(R); the PVP and HPMCP pairs overlap, while the yellow (HPMCAS-HF) and dark-green (HPMCAS-LF) pairs split apart, in opposite directions sato2015 R5.

Why

The ATP amino group donates hydrogen bonds to polymer carbonyls, as the new NH bands show sato2015 C16, C24. In HPMCAS some ester carbonyls sit close to the chiral cellulose backbone, and the differential inhibition is "most likely due to" differences in the ability of each enantiomer to form hydrogen bonds with the polymer sato2015 C26, C29. Why LF and HF favour opposite enantiomers is "not readily explainable" sato2015 C28. Because everything except chirality is the same, the authors read the result as "strongly" supporting compound–polymer interactions as determinants of growth inhibition sato2015 C27.

Limits and transfer

One non-drug model compound at 5% w/w polymer, the racemate measured only at 70–90 °C and with two polymers, and the interactions not measured at the 5% level used for growth sato2015 A1, A3, X5. For a single-enantiomer drug, screen polymers on the enantiomer itself, not on the racemate, test at least two grades of HPMCAS, and compare the growth ratio against the pure enantiomers' own ratio, not against 1.

How it was shown

Sato and Taylor (2015) asked whether a chiral polymer inhibits crystallization of two enantiomers to different extents, which would isolate the role of compound–polymer interactions, since enantiomers differ only in handedness sato2015 C5, C27. ATP(R) and ATP(S), a compound with one NH2 and one OH group and a Tg of 16–17 °C, were mixed with 5% w/w of achiral PVP K-12 or of the chiral polymers PHB, HPMCP (HP-55), HPMCAS-LF or HPMCAS-HF by rotary evaporation, melted about 5 °C above the melting point between coverslips and quenched to clear films sato2015 M1–M7, P1, P3, R1.a, R1.b. Spherulite size was followed on a hot stage at 40–120 °C and the growth rate taken as the slope of size against time, in triplicate; the racemate, made by cryomilling equal amounts of both enantiomers, was measured at 70–90 °C alone and with PVP or HPMCAS-HF sato2015 P2, P4, E1, A3. DSC gave Tg, the onset of recrystallization on heating (Tc) and melting; transmission IR was taken on films with 30% HPMCP, 30% HPMCAS-LF and 20% HPMCAS-HF, levels chosen to make the spectral changes readable; and 5% HPMCAS-HF glasses were held at 40 °C and followed by IR for 30 h sato2015 P6, P5, C15, P7.

What the data show

The pure enantiomers grew from about 0.022–0.032 µm/s at 40 °C to 21–34 µm/s at 90 °C, ATP(S) about 1.2–1.6 times faster than ATP(R) at every temperature, although the text calls the rates "almost exactly the same" sato2015 R5.a, R5.b, X2, C8. PHB changed growth little (about 4.8 against 5.4–6.7 µm/s at 70 °C, R and S together) sato2015 R5.c, R5.d. PVP slowed both enantiomers alike, about 10-fold at 50 °C and 3–4-fold at 70 °C, with overlapping R and S markers at 60, 70 and 90 °C sato2015 R5.e, R5.f. HPMCP slowed growth more, about 50 times at 60 °C and 20–25 times at 70 °C, and kept ATP(S) about 1.2–1.4 times faster, the pure-compound ratio sato2015 R5.g, R5.h, X2. HPMCAS-HF gave about 0.011, 0.094, 0.47 and 0.24 µm/s for ATP(S) and 0.0055, 0.049, 0.19 and 0.12 µm/s for ATP(R) at 50, 60, 70 and 80 °C; HPMCAS-LF gave about 0.015 and 0.058 µm/s for ATP(S) and 0.029 and 0.089 µm/s for ATP(R) at 60 and 70 °C sato2015 R5.i–l. At 60 °C the size–time lines show the split directly: with HPMCAS-LF ATP(R) reached about 33 units in 480 s against about 18 for ATP(S), with HPMCAS-HF ATP(S) about 45 against 23 for ATP(R) sato2015 R7, R8. Tg stayed at 14.3–18.4 °C in every sample, while Tc rose from 58–59 °C to 61.5–63.6 °C with PVP and to 77.2 (S) and 81.6 °C (R) with HPMCAS-HF sato2015 R1, C6, C7. At 40 °C the ATP(S)–HPMCAS-HF glass was fully crystalline by 15 h while ATP(R) was still partly amorphous at 30 h sato2015 R15, C20. In the IR, HPMCP gave a new NH band at 3253 cm⁻¹ and a new carbonyl band at 1699 cm⁻¹, identical for R and S; HPMCAS gave a new band at 3290 cm⁻¹, and the free amorphous NH2 band at 3390 cm⁻¹ nearly vanished with ATP(S) in LF but stayed stronger with ATP(S) in HF sato2015 R12, R13, R14. The racemate grew at about 0.64, 1.9 and 4.7 µm/s at 70, 80 and 90 °C, and at 0.28–2.65 µm/s with PVP or HPMCAS-HF sato2015 R9.c, R9.d, R9.e.

papersystemmethod and conditionsresultids
sato2015ATP(S), ATP(R), no polymermelt films, hot stage 40–120 °C, n = 3S 1.2–1.6 times faster than R; 0.022–0.032 µm/s (40 °C) to 21–34 µm/s (90 °C)R5.a, R5.b, X2
sato20155% w/w PVP K-12 (achiral)sameboth slowed alike, about 10-fold (50 °C) to 3–4-fold (70 °C)R5.e, R5.f, C10
sato20155% w/w HPMCP (chiral)same20–100-fold slower, S/R kept at about 1.2–1.4R5.g, R5.h, C10
sato20155% w/w HPMCAS-HF and -LFsame; size–time at 60 °CHF: S 1.9–2.5 times faster than R; LF: R 1.5–1.9 times faster than SR5.i–l, R7, R8
sato20155% HPMCAS-HFDSC Tc; storage at 40 °C, IRTc 81.6 (R) against 77.2 °C (S); S crystalline by 15 h, R partly amorphous at 30 hR1.d, R1.e, R15
sato2015racemate with PVP or HPMCAS-HFgrowth 70–90 °Cabout 2-fold slower; enantiomers 14–105-fold with HPMCAS-HFR9, X4, C12
polyzois2024 (outside)praziquantel racemate against R-enantiomer in supersaturated solutioninduction time with 1 polymerR-PZQ 37 min (HPMCAS-MF) and 15.5 min (HPMC) against at least 83 min for RS-PZQ; 5 and 5.5 min without polymerR4, R3.a, R3.g, R3.h, C9

Figure

Fig. 6 of sato2015: growth rate of ATP(S) and ATP(R) against temperature, without polymer and with five polymers
Fig. 6 · sato2015growth rate of ATP(S) and ATP(R) against temperature, without polymer and with five polymers

Filled markers are ATP(S), markers with a light centre ATP(R); the PVP and HPMCP pairs overlap, while the yellow (HPMCAS-HF) and dark-green (HPMCAS-LF) pairs split apart, in opposite directions sato2015 R5.

Fig. 8 of sato2015: spherulite size against time at 60 °C with HPMCAS-HF
Fig. 8 · sato2015spherulite size against time at 60 °C with HPMCAS-HF

Both lines are straight through the origin; ATP(S) (squares) grows about twice as fast as ATP(R) (triangles), the reverse of the LF grade in Fig. 7 sato2015 R8, R7.

Why

The authors' account, with their hedges: the ATP amino group donates hydrogen bonds to polymer carbonyls, as the new NH bands show ("consistent with"; "strongly suggests") sato2015 C16, C24. In HPMCAS some ester carbonyls sit close to the chiral cellulose backbone, so R and S bind to different extents ("it is clear"), and the differential inhibition is "most likely due to" differences in the ability of each enantiomer to form hydrogen bonds with the polymer sato2015 C26, C29. In HPMCP the binding carbonyls lie next to the achiral phthalate group, which "may minimize" contact with chiral centres; PVP, being achiral, binds both alike ("it is suggested"); PHB "presumably" interacts little with either sato2015 C25, C30, C23. Why LF and HF favour opposite enantiomers is "not readily explainable", "most likely linked" to their acetate and succinoyl substitution, which was not measured sato2015 C28. Because everything except chirality is the same, the authors read the result as "strongly" supporting compound–polymer interactions as determinants of growth inhibition sato2015 C27. Not measured: the interactions at the 5% level used for growth, the IR of PVP and PHB films, and nucleation sato2015 X5, X6, C22. (synthesis: this is the cleanest test in the chapter of the hydrogen-bond reading of F18, since Tg, Tm and dilution are the same for both enantiomers; it supports that reading for HPMCAS, while the identical HPMCP spectra show that a chiral polymer need not discriminate.)

Conditions and limits

One non-drug model compound, 5% w/w polymer, dry melt films at 40–90 °C, all below the polymorph change of the pure enantiomers at 90–100 °C sato2015 A1, A3, R6, X12. The racemate was measured only at 70–90 °C and only with two polymers sato2015 A3. The factor of 50 quoted in the text for ATP(S) with HPMCAS-HF has no stated temperature; Fig. 6 gives 14–87 for ATP(S) and 28–105 for ATP(R) sato2015 X4. The absolute LF rates in Fig. 7 are about 2.5 times those of Fig. 6, although the ratio agrees sato2015 X3. DSC values are single runs without replicates sato2015 X8.

Counterexamples and conflicts

Chirality alone did not decide: HPMCP and PHB are chiral and did not discriminate sato2015 C10. In the library's only other chiral case, a supersaturated aqueous solution, HPMCAS-MF and HPMC delayed crystallization of racemic praziquantel at least 83 min but of R-praziquantel only 15.5–37 min, while without polymer both crystallized in about 5 min; the authors there name stereoselective binding as one possibility ("it is not unreasonable to speculate"), next to differences in crystal form and conformation polyzois2024 R4, R3.a, R3.g, R3.h, C28. The cited nitrendipine precedent found the enantiomer effect in nucleation and not in growth sato2015 C22.

Transfer check

For a single-enantiomer drug, screen polymers on the enantiomer itself, not on the racemate: here the racemate responded about twofold where the enantiomers responded 14–105-fold, so a racemate screen misranks the polymers sato2015 R9, X4. Test at least two grades of a cellulose ester such as HPMCAS (LF and HF reversed the preferred enantiomer here) and compare the growth ratio against the pure enantiomers' own ratio, not against 1 sato2015 R5, X2. Use IR of the drug's free donor band at the intended polymer level as a check on which enantiomer binds more sato2015 R13, R14, X5.

History

Miyazaki and co-workers (2011, outside the library) had reported chiral polymers changing the crystallization of nitrendipine enantiomers through nucleation sato2015 C22. Kestur and Taylor (2010) and Van Eerdenbrugh and Taylor (2011) had tied growth inhibition to compound–polymer interactions sato2015 C27 (see Miscibility and drug-polymer interactions F12 and F17). Sato and Taylor (2015) first showed in the library a grade-dependent, enantiomer-specific growth inhibition by HPMCAS sato2015 C11. Polyzois and co-workers (2024) cited it when praziquantel ASD polymers were found weaker for the single enantiomer than for the racemate polyzois2024 C28.

F28

Topic 1Crystallization of the amorphous drug in dry dispersions13 of 15

5% of the low-Tg polymer PHB sped crystal growth of three high-Tg compounds up to about tenfold, mostly by lowering Tg.

Polyhydroxybutyrate (PHB, Tg 0 °C) at 5% w/w raised the growth rate of griseofulvin about tenfold at 120 °C, of celecoxib about sixfold at 90 °C and of a dinitrobenzamide (DPB) about fivefold at 80 °C, while flutamide, ATP and acetaminophen grew at about 50–95% of their pure rates sato2016 R4, R6, R3, X13. PHB lowered the Tg of the three accelerated compounds by 5–12 °C and of none of the others, and shifted no infrared bands sato2016 R7, R9. Plotted against T − Tg of each mixture, the 5–10% PHB data lay close to the pure compounds sato2016 R10, C21.

moderateModerate: the speed-up is direct, triplicate and far beyond the error bars, but the ratio plot gives no PHB level or temperature per point, the mobility explanation is not measured, and most of the speed-up follows the Tg drop sato2016 K1, K3, K6, X3, X6, X7.

Growth rate with PHB ÷ without, 30–40 °C above each compound's TgflutamideTg −1 °C0.42ATPTg 17 °C0.75acetaminophenTg 21 °C0.96DPBTg 53 °C5.4celecoxibTg 57 °C6.5griseofulvinTg 90 °C10

Below 1 the polymer slows growth, above 1 it speeds it; the switch follows the Tg of the compound. sato2016 R11, X3

pure compoundwith PHBgriseofulvin7890celecoxib5257DPB4653acetaminophen2122ATP1617flutamide−2−1−100102030405060708090100glass transition temperature, °C

PHB (Tg 0 °C) lowers Tg only for the compounds whose Tg lies far above its own; 5% PHB for the first three rows. sato2016 R7

For your drug

  1. Before using a low-Tg polymer, surfactant or plasticizer with a high-Tg drug, measure the mixture Tg; a fall of 5 °C or more with 5% additive warns of faster growth.
  2. Measure melt growth at two temperatures and compare at equal T − Tg: if the curves collapse, the effect is plasticization and will also apply at storage temperature; an additive whose Tg is close to the drug's is not expected to accelerate.

sato2016 R7, R11, R10, C21

How it works and key numbers
  1. All growth temperatures lie below the expected maximum near 0.94 Tm, so growth "is expected to be" limited by transport sato2016 C15, E2.
  2. PHB left the melting points (within 0–4 °C) and the IR unchanged, so "it can be inferred" that the driving force is unchanged and the polymer "most likely" acts through the mobility of the crystallizing compound sato2016 R7, R9, C18, C19.
  3. The authors relate acceleration to the mobility difference between polymer and host, greatest for the high-Tg compounds; when the difference is small, the PHB chains "most likely" impede transport to the crystal and slow growth sato2016 C24, C28, C25.
  4. 20% PHB and 5% PVAc grew more slowly than their Tg predicts, so the chains also slow growth once enough is present, and Tg is "only a crude indicator" of mobility sato2016 R10, C21, C26.
≈0.015 → ≈0.15 µm/sgriseofulvin growth at 120 °C without and with 5% PHBsato2016 R4.a, R4.c
0.42 → 10growth ratio with/without PHB as compound Tg rises from −1 to 90 °Csato2016 R11
5–12 °CTg drop by 5% PHB in the three accelerated compoundssato2016 R7

Connections to other chapters

Evidence: data, conditions and papers

Finding F28. A polymer whose Tg lies far below that of the drug can speed crystal growth: 5% PHB sped three high-Tg compounds up to about tenfold and slowed or left unchanged three low-Tg ones, and the drop in mixture Tg accounts for most of the speed-up

In short. Polyhydroxybutyrate (PHB, Tg 0 °C) at 5% w/w raised the growth rate of griseofulvin about tenfold at 120 °C (about 0.015 to 0.15 µm/s), of celecoxib about sixfold at 90 °C and of a dinitrobenzamide (DPB) about fivefold at 80 °C, while flutamide grew at about 60% of its pure rate, ATP at about 50–75% and acetaminophen at about 75–95% sato2016 R4, R6, R3, X13. The growth-rate ratio, taken 30–40 °C above each compound's Tg, rose from about 0.42 to 10 as the pure compound's Tg rose from −1 to 90 °C sato2016 R11. PHB lowered the Tg of the three accelerated compounds by 5–12 °C and of none of the others, left melting points within 0–4 °C and shifted no infrared bands sato2016 R7, R9. Plotted against T − Tg of each mixture, the 5–10% PHB data lay close to the pure compounds, while 20% PHB and 5% PVAc grew more slowly than their Tg predicts sato2016 R10, C21. The authors call PHB "the first reported example" of a polymer with compound-specific accelerating or inhibiting effects sato2016 C29.

Type. observation in 6 compounds with 2 polymers Strength. the speed-up is direct, triplicate and far beyond the error bars (sato2016 K1: strong), but the ratio plot gives no PHB level or temperature per point, the mobility explanation is not measured, and most of the speed-up follows the Tg drop (K3: moderate; K6: weak; X3, X6, X7).

How it was shown

Sato and Taylor (2016) blended six compounds with pure-compound Tg from −1 to 90 °C with 1–20% PHB (and griseofulvin with 5% PVAc), melted and quenched the blends between coverslips, and followed spherulite diameter on a hot stage, n = 3, below the expected growth maximum of each compound sato2016 M1–M7, P1, P2, P3, M8. DSC gave the mixture Tg, IR checked for drug band shifts, and the rates were replotted against T − Tg sato2016 P5, P4, P6.

What the data show

Mixture Tg fell from 90 to 78 °C for griseofulvin with 5% PHB, from 53 to 46 °C for DPB and from 57 to 52 °C for celecoxib, while acetaminophen, ATP and flutamide did not change sato2016 R7, X4.

systemmethod and conditionsresultids
griseofulvin (Tg 90 °C) with 5% PHBmelt films, diameter growth, n = 3≈0.015 → ≈0.15 µm/s at 120 °C (about tenfold)sato2016 R4.a, R4.c, R6, C17
celecoxib (57 °C), DPB (53 °C) with 5% PHBsame≈0.025 → ≈0.16 µm/s (90 °C); ≈0.135 → ≈0.72 µm/s (80 °C)sato2016 R4.f, R4.g, R4.i, R4.j
flutamide (−1 °C), ATP (17 °C), acetaminophen (21 °C) with 5–10% PHBsameabout 0.4–0.6, 0.5–0.75 and 0.75–0.95 of the pure ratesato2016 R3, X13
six compoundsratio with/without PHB, 30–40 °C above Tg≈0.42, 0.75, 0.96, 5.4, 6.5, 10 with rising compound Tgsato2016 R11, X3
DPB, griseofulvin, celecoxibrate against T − Tg5–10% PHB near the pure compounds; 20% PHB and PVAc belowsato2016 R10, C21
Fig. 12 of sato2016: ratio of growth rate with PHB to growth rate without PHB against the Tg of the pure compound
Fig. 12 · sato2016ratio of growth rate with PHB to growth rate without PHB against the Tg of the pure compound

From left to right the points are flutamide, ATP, acetaminophen, DPB, celecoxib and griseofulvin; the three left points lie below the line at 1, the three right points at 5–10 sato2016 R11.

Why

PHB left melting points and IR unchanged, so "it can be inferred" that the driving force is unchanged, and the polymers "most likely" act through the mobility of the crystallizing compound sato2016 C18, C19. The authors relate acceleration to the mobility difference between polymer and host, greatest for the high-Tg compounds sato2016 C24, C28. (synthesis: the compounds that PHB accelerated are those whose Tg it lowered, and at 5–10% PHB the speed-up largely disappears against T − Tg, so plasticization accounts for most of it) sato2016 X6.

Limits and transfer

Drug-rich dry melt films above Tg; storage below Tg was not studied, and no viscosity, relaxation or diffusion was measured sato2016 A2, A4, X7. PVAc lowered griseofulvin's Tg only 6 °C and did not speed its growth sato2016 R7.d, C26. Before using a low-Tg polymer, surfactant or plasticizer with a high-Tg drug, measure the mixture Tg; a fall of 5 °C or more with 5% additive warns of faster growth.

How it was shown

Sato and Taylor (2016) asked how a small amount of PHB, a biodegradable semicrystalline polyester considered for implants, changes crystal growth from the supercooled liquid of compounds with pure-compound Tg from −1 to 90 °C sato2016 C4, C5, M1–M7. Blends with 1–20% PHB (and 5% PVAc, Tg 40 °C, with griseofulvin) were made by cryomilling or rotary evaporation, melted between coverslips about 5 °C above the compound's melting point and quenched sato2016 P1, P2, P3, M8. Spherulite diameter was followed on a hot stage in 10 °C steps, n = 3, below the expected growth maximum of each compound; the rates are diameter slopes, twice a radial rate sato2016 P3, E2, E3, X8. DSC gave Tg of the mixtures and Tm of physical mixtures, IR checked for drug band shifts, and the rates were replotted against T − Tg and as a ratio with to without polymer sato2016 P5, P4, P6, P7, E4.

What the data show

For the high-Tg compounds: griseofulvin (Tg 90 °C) grew at about 0.015 µm/s alone and 0.15 µm/s with 5% PHB at 120 °C, 0.022 µm/s with 1% PHB, and with 20% PHB about 0.23 µm/s at 110 °C where the 5% blend grew at about 0.024 µm/s sato2016 R4.a, R4.b, R4.c, R4.d. Celecoxib (57 °C) went from about 0.025 to 0.16 (5%) and 0.19 µm/s (20%) at 90 °C, but only from 3.4 to 5.0 and 3.7 µm/s at 120 °C sato2016 R4.f, R4.g, R4.h. DPB (53 °C) went from about 0.135 to 0.72 (5%) and 1.4 µm/s (20%) at 80 °C and from about 27 to 41 µm/s (5%) at 120 °C sato2016 R4.i, R4.j, R4.l. The gain shrank to about 1.5-fold at the highest temperatures sato2016 X5. For the low-Tg compounds: flutamide (−1 °C) grew at about 0.031, 0.019 and 0.013 µm/s at 30 °C with 0, 5 and 10% PHB, ATP (17 °C) at about 0.27 and 0.20 µm/s at 50 °C with 0 and 5% PHB, and acetaminophen (21 °C) at about 0.36–13.8 against 0.34–12.8 µm/s at 70–100 °C sato2016 R3.a, R3.b, R3.c, R3.d, R3.e, R3.f, R3.g. The Fig. 12 ratios were about 0.42, 0.75, 0.96, 5.4, 6.5 and 10 for compounds of Tg −1, 17, 21, 53, 57 and 90 °C sato2016 R11. Mixture Tg fell from 90 to 85, 78 and 58 °C for griseofulvin with 1, 5 and 20% PHB, from 53 to 46, 43 and 35 °C for DPB with 5, 10 and 20%, and from 57 to 52 and 41 °C for celecoxib with 5 and 20%, while acetaminophen (21 → 22 °C), ATP (17 → 16 °C) and flutamide (−1 → −2 and 0 °C) did not change; 5% PVAc lowered griseofulvin only to 84 °C sato2016 R7, M1–M6, X4. Near equal T − Tg the rates converged: DPB about 4.2 µm/s (pure, 47 °C) against 3.8 (5% PHB, 44 °C) and 3.7 (10%, 47 °C), griseofulvin 0.74 (pure, 50 °C) against 0.95 (5%, 52 °C); with 20% PHB DPB grew at about 3.7 µm/s at 55 °C against about 16 µm/s for the pure compound at 57 °C, griseofulvin 0.52 at 62 °C against 3.4 at 60 °C, and griseofulvin with PVAc at 0.49 µm/s at 56 °C sato2016 R10. PVAc, with a Tg gap to griseofulvin (50 °C) close to that between PHB and celecoxib (57 °C), left griseofulvin growth at about the pure rate (0.13 against 0.13 µm/s at 130 °C) sato2016 R4.a, R4.e, M1, M2, M7, M8, C26.

papersystemmethod and conditionsresultids
sato2016griseofulvin (Tg 90 °C) with 5% PHBmelt films, diameter growth, n = 3≈0.015 → ≈0.15 µm/s at 120 °C (about tenfold)R4.a, R4.c, R6, C17
sato2016celecoxib (57 °C), DPB (53 °C) with 5% PHBsame≈0.025 → ≈0.16 µm/s (90 °C); ≈0.135 → ≈0.72 µm/s (80 °C)R4.f, R4.g, R4.i, R4.j
sato2016flutamide (−1 °C), ATP (17 °C), acetaminophen (21 °C) with 5–10% PHBsameabout 0.4–0.6, 0.5–0.75 and 0.75–0.95 of the pure rateR3, X13
sato2016six compoundsratio with/without PHB, 30–40 °C above Tg≈0.42, 0.75, 0.96, 5.4, 6.5, 10 with rising compound TgR11, X3
sato2016mixtures with 1–20% PHBDSC Tg; Tm of physical mixtures; IRTg −5 to −12 °C at 5% only for the three high-Tg compounds; Tm 0–4 °C; no band shiftsR7, R9, X11
sato2016DPB, griseofulvin, celecoxibrate against T − Tg5–10% PHB near the pure compounds; 20% PHB and PVAc belowR10, C21
sato2016griseofulvin with 5% PVAc (Tg 40 °C)growth 120–150 °C≈0.02–3.1 against ≈0.015–3.4 µm/s: no speed-upR4.e, C9
mosqueragiraldo2014celecoxib with 10% TPGSseeded melt growth, 70 °C; DSC≈85-fold faster; Tg 55.34 → 44.81 °CR1, R5

Figure

Fig. 12 of sato2016: ratio of growth rate with PHB to growth rate without PHB against the Tg of the pure compound
Fig. 12 · sato2016ratio of growth rate with PHB to growth rate without PHB against the Tg of the pure compound

From left to right the points are flutamide, ATP, acetaminophen, DPB, celecoxib and griseofulvin (matched by Tg); the three left points lie below the line at 1 (retardation), the three right points at 5–10 (acceleration); the axis is logarithmic sato2016 R11.

Fig. 11 of sato2016: growth rate against T − Tg of each mixture
Fig. 11 · sato2016growth rate against T − Tg of each mixture

The 5–10% PHB series fall onto the pure-compound lines, while the 20% PHB squares and griseofulvin with PVAc lie below them sato2016 R10.

Why

The authors' account, with their hedges: all growth temperatures lie below the expected maximum near 0.94 Tm, so growth "is expected to be" limited by transport (see Crystallization tendency F2) sato2016 C15, E2. PHB left melting points and IR unchanged, so "it can be inferred" that the driving force is unchanged, and the polymers "most likely" act through the mobility of the crystallizing compound sato2016 C18, C19. In "broad agreement" with Yu and co-workers, who found only the lowest-Tg polymer, PEG, to speed nifedipine growth, the authors relate acceleration to the mobility difference between polymer and host, greatest for the high-Tg compounds ("suggesting that the polymer increased the molecular mobility") sato2016 C23, C24, C28. When the difference is small, the PHB chains "most likely" impede transport to the crystal and slow growth sato2016 C25. PVAc shows that Tg is "only a crude indicator" of mobility sato2016 C26. No viscosity, relaxation or diffusion was measured sato2016 X7. (synthesis: the compounds that PHB accelerated are exactly those whose Tg it lowered, and at 5–10% PHB the speed-up largely disappears against T − Tg, so plasticization of the drug-rich melt by a low-Tg, non-interacting polymer accounts for most of it sato2016 X6; this is the same pattern as miscible surfactants and water in F22 and F9, and the limit of F5 that large Tg drops do change growth even though small ones do not rank polymers.)

Conditions and limits

Drug-rich mixtures (1–20% polymer for growth) above Tg, in dry melt films; the polymer-rich compositions of a PHB implant and storage below Tg were not studied sato2016 A2, A4. Most films were melted below the PHB melting point (176 °C), so mixing of PHB in the acetaminophen and ATP films rests on one Tg each sato2016 X9. The ratio plot gives neither PHB level nor temperature per point; the flutamide point matches 10% rather than 5% PHB sato2016 X3. The authors' "unchanged Tg at low amounts" fits only the three low-Tg compounds sato2016 X4.

Counterexamples and conflicts

PVAc lowered griseofulvin's Tg only 6 °C and did not speed its growth, although its Tg gap to the drug is similar to that of PHB to celecoxib sato2016 R7.d, C26. 20% PHB grew more slowly than its Tg predicts, so the polymer chain also slows growth once enough of it is present sato2016 C21. Usually polymers at a few percent slow growth, often without changing Tg (see F3, F5 and F18) sato2016 C16; the polymers that did so in this chapter have Tg above the drug's or bind it, which PHB does not (synthesis: from the Tg data and IR in F5 and F18).

Transfer check

Before using a low-Tg polymer, surfactant or plasticizer with a high-Tg drug, measure the mixture Tg; a fall of 5 °C or more with 5% additive, as for the three accelerated compounds here, warns of faster growth sato2016 R7, R11. Then measure melt growth at two temperatures and compare at equal T − Tg: if the curves collapse, the effect is plasticization and will also apply at storage temperature; if growth stays below the Tg prediction, as with 20% PHB, the chain also impedes transport sato2016 R10, C21. An additive whose Tg is close to the drug's (here acetaminophen, ATP, flutamide) is not expected to accelerate sato2016 R11.

History

Powell and co-workers (2013, outside the library) had found PEG, the lowest-Tg polymer tested, to accelerate nifedipine growth sato2016 C23. In 2014 miscible low-Tg surfactants were found to speed celecoxib growth (see F22) mosqueragiraldo2014 C9, C30. Sato and Taylor (2016) showed the same with a polymer and tied the direction to the compound's Tg sato2016 C27, C29; the neat-drug chapter lists the result among additives that accelerate growth (see Crystallization tendency F19).

F29

Topic 1Crystallization of the amorphous drug in dry dispersions14 of 15

Each of three polymers slowed indomethacin α far more than γ at high temperature, unlike two felodipine polymorphs.

In undercooled indomethacin with 10% w/w polymer, the ratio of growth rate without to with polymer at 120 °C was about 2900 for α against 2.9 for γ with HPMC, 34 against 3.9 with PVP and 17 against 1.6 with HPMCAS tian2017 R12.i, C37. HPMC lowered the temperature of fastest α growth from 135 to 100 °C, and above that temperature the ratios rose steeply tian2017 R15, C34, C35. The authors conclude that "it appears" the polymers act on the crystal–melt interface of each polymorph differently tian2017 C39.

moderateModerate: the indomethacin rates are direct and replicated over whole growth curves, but the largest ratios rest on single, very slow points, the γ-least rule fails at 80 °C, and neither the interface nor the driving-force explanation was measured tian2017 K2, K3, K6, X5, X13, X14, X16.

indomethacin αindomethacin γindomethacin δfelodipine form I and form IIHPMC, 120 °C2.92900PVP, 120 °C3.934HPMCAS, 120 °C1.617HPMC, 80 °C3.54.75.9felodipine + 3% PVP, 60 °Cform I 15.8form II 18.71101001000growth rate without ÷ with polymer (log scale)

At 120 °C each polymer slows α far more than γ; at 80 °C the three indomethacin forms lie close together, like the two felodipine forms. tian2017 R12.i, R12.a, C37; kestur2013a R15

Indomethacin α with 10% w/w polymer: temperature of fastest growth, °Cno polymer135PVP125HPMCAS110HPMC100

tian2017 R15, C34

For your drug

  1. Identify which polymorph appears in the product or process and measure the polymer effect on that form, not on another; do not assume that the most stable form is slowed most (here it was slowed least).
  2. When the product is exposed to high temperature (hot melt extrusion), measure growth on both sides of the temperature of fastest growth and record how the polymer shifts it.

tian2017 C37, C33, R15; kestur2013a C27

How it works and key numbers
  1. Growth needs mobility and a driving force; below the temperature of fastest growth mobility limits it, above it the driving force does tian2017 C22.
  2. The higher melt viscosity of PVP (log viscosity at 80 °C 4.9 against 4.3 and 4.1) "correlates" with its stronger effect where mobility controls growth, but viscosity "Clearly" cannot explain why HPMC beats HPMCAS tian2017 R13.a, C28, C29.
  3. Above the maximum, melting point depression and a smaller driving force "may be possible reasons" for the steep rise in inhibition tian2017 C36.
  4. The steep α ratios arise where the pure α rate is still rising toward its 135 °C maximum while the rate with HPMC has passed its own maximum at 100 °C, so the ratio compares two regimes (synthesis) tian2017 R9, R15.
  5. Because one polymer acts differently on polymorphs growing from the same liquid, a liquid-phase explanation alone is excluded; none of the interactions, driving forces or interfacial properties was measured tian2017 C39, X13, X14.
≈2900 vs ≈2.9slowing of α vs γ by HPMC at 120 °Ctian2017 R12.i, C37
135 → 100 °Ctemperature of fastest α growth without and with HPMCtian2017 R15, C34
5–25 / 2–12 / 2–3-foldslowing at 80–100 °C by PVP / HPMC / HPMCAStian2017 R12, C28

Connections to other chapters

1 more connection
Evidence: data, conditions and papers

Finding F29. A polymer can slow different polymorphs of one drug by very different factors: each of three polymers slowed indomethacin γ least and α most, unlike the similar factors for two felodipine polymorphs, and inhibition rose steeply above the temperature of fastest growth

In short. In undercooled indomethacin with 10% w/w polymer, the ratio of growth rate without to with polymer at 120 °C was about 2900 for α against 2.9 for γ with HPMC, 34 against 3.9 with PVP and 17 against 1.6 with HPMCAS tian2017 R12.i, C37. At 80–100 °C the polymers slowed growth 5–25-fold (PVP), 2–12-fold (HPMC) and 2–3-fold (HPMCAS) tian2017 R12, C28. HPMC lowered the temperature of fastest α growth from 135 to 100 °C, and above that temperature the ratios rose steeply tian2017 R15, C34, C35. Because the polymorphs grow from the same liquid, the authors conclude that "it appears" the polymers act on the crystal–melt interface of each polymorph differently, against the liquid-phase reading of the felodipine study, in which 3% PVP slowed two polymorphs by similar factors (see F19) tian2017 C39, C38; kestur2013a R15, C6.

Type. comparison of 3 polymorphs of one drug with 3 polymers, against a 2-polymorph comparison of another drug Strength. the indomethacin rates are direct, replicated over whole growth curves (tian2017 K2: strong; K3: moderate to strong), but the largest ratios rest on single, very slow points, the γ-least rule fails at 80 °C, and neither the interface nor the driving-force explanation was measured (K6: weak; X5, X13, X14, X16).

How it was shown

Tian and co-workers (2017) melted indomethacin alone or with 10% w/w HPMC, HPMCAS or PVP between coverslips and quenched it; storage at 60 °C gave mainly δ, 80 °C α, and γ was grown from seeds tian2017 P1, P2, P3, R1. The growth front was followed on a hot stage from 80 °C to near each melting point, and melt viscosity was measured at 80–130 °C tian2017 P4, P9.

What the data show

Without polymer α grew fastest, peaking at 4.34 × 10⁻⁶ m/s at 135 °C tian2017 R7, C10. At 80 °C the ratios of growth rate without to with polymer were about 5.9, 3.5 and 4.7 (δ, α, γ) with HPMC and 25, 16 and 11 with PVP tian2017 R12.a.

systemmethod and conditionsresultids
indomethacin δ, α, γ, no polymermelt growth 80 °C to near Tm, n ≥ 3maxima 1.5 × 10⁻⁷ (δ, 110 °C), 4.34 × 10⁻⁶ (α, 135 °C), 4.07 × 10⁻⁷ m/s (γ, 135 °C)tian2017 R7, R8, R9, R10
10% w/w PVP, HPMC, HPMCASratio without/with polymer, 80–100 °C5–25 (PVP), 2–12 (HPMC), 2–3-fold (HPMCAS)tian2017 R12, C28
same, 120 °Cratio by polymorphα ≈2900, γ ≈2.9 (HPMC); α ≈34, γ ≈3.9 (PVP); α ≈17, γ ≈1.6 (HPMCAS)tian2017 R12.i, C37
sametemperature of fastest growthα 135 → 100 (HPMC), 110 (HPMCAS), 125 °C (PVP)tian2017 R15, C34
felodipine forms I and II, 3% PVPratio without/with PVP, 60–100 °C≈15.8 → 3.5 (form I); ≈18.7 → 6.5 (form II)kestur2013a R15, C14
Fig. 7 of tian2017: growth rates with and without polymer for δ, α and γ, and the ratios without/with polymer for HPMC, HPMCAS and PVP
Fig. 7 · tian2017growth rates with and without polymer for δ, α and γ, and the ratios without/with polymer for HPMC, HPMCAS and PVP

In the lower panels (D–F) the y-axes are broken and the dashed line is a ratio of 1; the α series shoot up at high temperature while γ stays low tian2017 R12.

Why

Below the temperature of fastest growth mobility limits growth, and above it the driving force does tian2017 C22. PVP's higher melt viscosity "correlates" with its stronger effect where mobility controls growth, but viscosity "Clearly" cannot explain why HPMC beats HPMCAS tian2017 C28, C29. Because one polymer acts differently on polymorphs growing from the same liquid, "it appears" the polymers act on each polymorph's crystal–melt interface tian2017 C39.

Limits and transfer

One drug and melts at 80 °C and above; the highest ratios rest on single points with growth rates near 10⁻¹⁰ m/s, and none of the interactions, driving forces or interfacial properties was measured tian2017 A2, X16, X13, X14. Measure the polymer effect on the polymorph that appears in the product, on both sides of the temperature of fastest growth when the product meets high temperature, as in hot melt extrusion.

How it was shown

Tian and co-workers (2017) asked whether HPMC (Methocel E5), HPMCAS (MF) and PVP (K30) slow the growth of the δ, α and γ polymorphs of indomethacin to the same extent tian2017 M2, M3, M4, A1, A2. Indomethacin alone or as a 10% w/w polymer dispersion was melted at 170 °C between coverslips and quenched; storage at 60 °C gave mainly δ, 80 °C α, and γ was grown from seeds tian2017 P1, P2, P3, R1. The growth front was followed on a hot stage from 80 °C to near each melting point (δ 127, α 152, γ 160 °C) in 5 or 10 °C steps, three or more independently prepared samples per point; polymorphs were identified by morphology, Raman, hot-stage melting and XRD tian2017 P4, M1, R2, R3, R4, R6. Melt viscosity of the three polymer systems was measured at 80–130 °C and fitted with an Arrhenius relation, \log\eta = \log\eta_0 + E_\eta/(2.303RT) tian2017 P9, E1. The felodipine comparison is Kestur and Taylor (2013): form I and form II with 3% PVP K-29/32 at 60–100 °C (see F19) kestur2013a P4, R15.

What the data show

Without polymer, α grew fastest, peaking at 4.34 × 10⁻⁶ m/s at 135 °C; γ peaked at 4.07 × 10⁻⁷ m/s at the same temperature and δ at about 1.5 × 10⁻⁷ m/s at 110 °C, each maximum near 0.95 of the melting temperature in kelvin (predicted 107, 131 and 138 °C against 110, 135 and 135 °C) tian2017 R7, E3, C10. The differences remained after a driving-force normalization tian2017 R11, C24. All three polymers slowed all three polymorphs at every temperature tian2017 C11. At 80 °C the ratios were about 5.9, 3.5 and 4.7 (δ, α, γ) with HPMC, 2.7, 1.8 and 2.2 with HPMCAS and 25, 16 and 11 with PVP tian2017 R12.a. With rising temperature the α ratios climbed: with HPMC about 11 at 100 °C, 131 at 110 °C and 2900 at 120 °C; with HPMCAS about 283 at 130 °C; with PVP about 558 at 135 °C; γ stayed at about 1.5–4.7 up to 130 °C with HPMC and HPMCAS, and with PVP fell from about 11 at 80 °C to 3.5–4 at 115–130 °C tian2017 R12. The temperature of fastest growth fell for α from 135 °C to 100 °C (HPMC), 110 °C (HPMCAS) and 125 °C (PVP), for γ to 125–130 °C, and for δ moved to 105–115 °C tian2017 R15. At 80 °C the log viscosity was about 4.3 (HPMC), 4.1 (HPMCAS) and 4.9 (PVP), with activation energies for flow of 159.7, 143.5 and 190.5 kJ/mol; the pure melt crystallized before its viscosity could be measured tian2017 R13.a, R14, X12. In the felodipine study, by contrast, the PVP ratio was about 15.8 (form I) and 18.7 (form II) at 60 °C and 3.5 and 6.5 at 100 °C kestur2013a R15.

papersystemmethod and conditionsresultids
tian2017indomethacin δ, α, γ, no polymermelt growth 80 °C to near Tm, n ≥ 3maxima 1.5 × 10⁻⁷ (δ, 110 °C), 4.34 × 10⁻⁶ (α, 135 °C), 4.07 × 10⁻⁷ m/s (γ, 135 °C)R7, R8, R9, R10
tian201710% w/w PVP, HPMC, HPMCASratio without/with polymer, 80–100 °C5–25 (PVP), 2–12 (HPMC), 2–3-fold (HPMCAS)R12, C28
tian2017same, 120 °Cratio by polymorphα ≈2900, γ ≈2.9 (HPMC); α ≈34, γ ≈3.9 (PVP); α ≈17, γ ≈1.6 (HPMCAS)R12.i, C37
tian2017sametemperature of fastest growthα 135 → 100 (HPMC), 110 (HPMCAS), 125 °C (PVP)R15, C34
tian2017samemelt viscosity, Arrhenius fitlog η at 80 °C 4.3, 4.1, 4.9; Eη 159.7, 143.5, 190.5 kJ/molR13, R14
kestur2013afelodipine forms I and II, 3% PVPratio without/with PVP, 60–100 °C≈15.8 → 3.5 (form I); ≈18.7 → 6.5 (form II)R15, C14
trasi2014a (outside)five donor drugs with 10 mol% PVPmelt growthsimilar factor of about 5–10 whatever the drug's own rateC10

Figure

Fig. 7 of tian2017: growth rates with and without polymer for δ, α and γ, and the ratios without/with polymer for HPMC, HPMCAS and PVP
Fig. 7 · tian2017growth rates with and without polymer for δ, α and γ, and the ratios without/with polymer for HPMC, HPMCAS and PVP

In the lower panels (D–F) the y-axes are broken and the dashed line is a ratio of 1; the α series shoot up at high temperature while γ stays low tian2017 R12.

Table 2 of tian2017: maximum growth rate and its temperature for each polymorph and system
Table 2 · tian2017maximum growth rate and its temperature for each polymorph and system

The cells are in 10⁻⁸ m/s and the pure-indomethacin δ and γ cells appear interchanged; read the Tmax column, where HPMC moves α from 135 to 100 °C tian2017 R15, X1, X2.

Why

The authors' account, with their hedges: growth needs mobility and a driving force; below the temperature of fastest growth mobility limits it, above it the driving force does tian2017 C22. PVP's higher melt viscosity "correlates" with its stronger effect where mobility controls growth, but viscosity "Clearly" cannot explain why HPMC beats HPMCAS tian2017 C28, C29. Through the Flory–Huggins free energy of mixing, \Delta G_{mix} = RT[\Phi\ln\Phi + \frac{1-\Phi}{m}\ln(1-\Phi) + \chi\Phi(1-\Phi)], stronger drug–polymer interaction "would" lower the driving force; PVP's effect is "most likely" both lower mobility and lower driving force, HPMCAS's weakness "perhaps" its weaker interaction in a ranking cited from the 2016 fluorescence study tian2017 E2, C30, C31, C32, R16. Above the maximum, melting point depression and a smaller driving force "may be possible reasons" for the steep rise tian2017 C36. Because one polymer acts differently on polymorphs growing from the same liquid, a liquid-phase explanation alone is excluded and "it appears" the polymers act on each polymorph's crystal–melt interface tian2017 C39. None of the interactions, driving forces or interfacial properties was measured tian2017 X13, X14. (synthesis: the steep α ratios above 100 °C with HPMC arise where the pure α rate is still rising toward its 135 °C maximum while the HPMC rate has passed its own maximum at 100 °C, so the ratio compares two different regimes; a polymer that lowers the temperature of fastest growth will show its largest ratios just above it tian2017 R9, R15. In the felodipine comparison the two ratios drifted apart at 90–100 °C, near that drug's growth maximum, so the two studies may disagree less below the maximum than above it (see F19) kestur2013a X6.)

Conditions and limits

One drug, 10% w/w of each polymer, melts at 80 °C and above, at least about 33 °C above indomethacin's Tg (synthesis: 80 °C against Tg ≈320 K, about 47 °C tian2016 M1); polymorph identity is documented only for the HPMCAS system tian2017 A2, A3, X6. The highest ratios rest on single points with growth rates near 10⁻¹⁰ m/s tian2017 X16. The nucleation temperature used with polymers is not printed tian2017 X8.

Counterexamples and conflicts

For felodipine, 3% PVP slowed form I and form II by similar factors at 60–80 °C, read there as action in the liquid (see F19) kestur2013a C6, R15. At 80 °C HPMC and HPMCAS slowed γ slightly more than α, and at 130 °C HPMCAS slowed α more than PVP did, so the general rankings hold only in part of the temperature range tian2017 X5, X4. Across five donor drugs, 10 mol% PVP slowed growth by a similar factor whatever the drug's own rate (see Crystallization tendency F19) trasi2014a C10. For itraconazole, cited by the authors, PVPVA64 and HPMCAS inhibited two polymorphs to different extents tian2017 R18.

Transfer check

Identify which polymorph appears in the product or process, and measure the polymer effect on that form, not on another tian2017 C37; kestur2013a C27. Measure growth on both sides of the temperature of fastest growth when the product is exposed to high temperature (hot melt extrusion), since inhibition there can be orders of magnitude larger, and record the shift of that temperature with the polymer tian2017 C33, R15. Do not assume that the most stable form, the likely residual crystal, is slowed most: here it was slowed least tian2017 C37.

History

Kestur and Taylor (2013) compared two felodipine polymorphs with 3% PVP and placed the effect in the liquid kestur2013a C6. Tian and co-workers (2017) compared three indomethacin polymorphs with three polymers, found polymorph-specific factors and argued against the liquid-phase reading tian2017 C38, C39; they also measured, for the first time in the chapter, polymer effects above the temperature of fastest growth, a region they call "likely of great importance" for hot melt extrusion tian2017 C33. The temperatures of fastest growth of the pure indomethacin polymorphs agree with the 0.94–0.95 Tm rule of the neat-drug chapter, the rule that the PHB paper of 2016 used to keep its measurements below the maximum (see Crystallization tendency F2) tian2017 E3; sato2016 E2.

F30

Topic 1Crystallization of the amorphous drug in dry dispersions15 of 15

Indomethacin dispersions crystallized within days above the drug loading at which a drug-rich phase appeared, and not below it.

The emission maximum of the drug's own fluorescence in drop-cast films fell to the range of drug-rich surroundings (476–488 nm) between 50 and 60% drug with HPMC, between 20 and 30% with HPMCAS and between 70 and 80% with PVP, which the authors take as the miscibility limits tian2016 R2.f, R2.g, R3.c, R3.d, R4.h, R4.i, C17, C18, C19. Over desiccant at 40 °C, powders above the limit crystallized in 2–15 days, and those at or below it stayed X-ray amorphous for 14 months (HPMC) and 13 months (HPMCAS) tian2016 R17. PVP powders at 10–90% drug stayed amorphous for the 3 months tested, and DSC gave one Tg at every loading tian2016 R16, R13.

moderateModerate: the loading at which crystallization starts sits at the spectral limit for HPMC and one step above it for HPMCAS, but miscibility was read on films and stability on powders, the 30% HPMCAS powder was separated and still amorphous, and PVP was not followed long enough tian2016 X5, X6, X7, X8, X9.

X-ray amorphouscrystallizedHPMCdomains in films from 60%amorphous 14 monthscrystals in 6–15 daysHPMCASdomains from 30%amorphous 13 monthscrystals in 2–10 daysPVPdomains from 70%amorphous at 3 months, end of test0102030405060708090100indomethacin loading of powders stored dry at 40 °C, %

Crystallization onsets appear only above the loading at which the films showed drug-rich domains; the 30% HPMCAS powder was separated yet amorphous. tian2016 R17, R16, R7, R8, R9, X5

For your drug

  1. Screen candidate loadings for a drug-rich phase with a method that resolves domains of a few hundred nanometres (probe or intrinsic fluorescence, imaging, IR of the drug's self-association band), not with DSC alone.
  2. Choose a loading at least one step below that limit, and expect the limit to depend on preparation route and solvent.

tian2016 C55, R21, C49, X7

How it works and key numbers
  1. Above the miscibility limit a drug-rich phase forms, and with less polymer in that phase crystallization "would be anticipated" to occur more readily tian2016 C4.
  2. The drug-rich domains "led to" the faster crystallization, and homogeneous dispersions resisted it tian2016 C57.
  3. The high PVP limit "can be attributed to" the strong drug–polymer hydrogen bond seen by IR, with bonded bands at 1724 and 1640 cm⁻¹ up to 80% drug tian2016 C29, R12.
  4. The single Tg of HPMC powders above the limit "might result from" remixing during the DSC scan, so DSC did not see any of the limits tian2016 C31, R13.
50–60 / 20–30 / 70–80%miscibility limits with HPMC / HPMCAS / PVP from the emission maximumtian2016 C17, C18, C19
2–15 dayscrystallization onset of powders above the limit, 40 °C drytian2016 R17
13–14 monthspowders at or below the limit still X-ray amorphoustian2016 R17

Connections to other chapters

Evidence: data, conditions and papers

Finding F30. Dry indomethacin dispersions crystallized within days above the drug loading at which a drug-rich phase appeared and stayed amorphous for more than a year below it with HPMC and HPMCAS, while PVP, which mixed up to 70–80% drug, kept every loading amorphous for 3 months

In short. The emission maximum of indomethacin's own fluorescence in drop-cast films fell from about 511–513 nm to the 476–488 nm range of drug-rich surroundings between 50 and 60% drug with HPMC, between 20 and 30% with HPMCAS and between 70 and 80% with PVP, which the authors take as the miscibility limits tian2016 R2.f, R2.g, R3.c, R3.d, R4.h, R4.i, C17, C18, C19. Fluorescence imaging and IR placed the limits within one loading step of these values, while DSC gave one Tg at every loading tian2016 R21, R13. Over desiccant at 40 °C, rotary-evaporated powders above the limit crystallized in 2–15 days, and those at or below it stayed X-ray amorphous for 14 months (HPMC, up to 50% drug) and 13 months (HPMCAS, up to 30% drug); PVP powders at 10–90% drug stayed amorphous for the 3 months tested tian2016 R17, R16. The authors call this "a good correlation" between miscibility and physical stability tian2016 C53.

Type. observation in 1 drug × 3 polymers at 9–11 loadings, by four miscibility methods Strength. the loading at which crystallization starts sits at the spectral limit for HPMC and one step above it for HPMCAS, but miscibility was read on films and stability on powders, the 30% HPMCAS powder was separated and still amorphous, PVP was not tested for long enough, and onsets are bounded by the sampling interval (tian2016 X5, X6, X7, X8, X9).

How it was shown

Tian, Tang and Taylor (2016) used indomethacin as its own fluorescent probe: amorphous indomethacin emits at about 476 nm, and dispersed in a polymer at 5% drug at 508–520 nm tian2016 M1, R1, C13. Films with 5–95% drug in HPMC, HPMCAS or PVP were drop-cast for emission spectra, images and IR, powders with 10–90% drug were made by rotary evaporation, and both were stored over desiccant at 40 °C tian2016 P1, P3, P4, P5, P2, P7, P8.

What the data show

Images became heterogeneous from 60% (HPMC), 30% (HPMCAS) and 70% drug (PVP), while DSC gave one Tg throughout tian2016 R7, R8, R9, R13. PVP films showed crystals only at 80% drug and above tian2016 R20.

systemmethod and conditionsresultids
indomethacin–HPMC, –HPMCAS, –PVP films, 5–95% drugemission maximum of the drugdrop to 476–488 nm between 50–60%, 20–30% and 70–80% drugtian2016 R2, R3, R4, C17–C19
HPMC powders40 °C, desiccant, XRD60–90% drug crystalline at 6–15 days; up to 50% amorphous at 14 monthstian2016 R17
HPMCAS powderssame40–90% drug crystalline at 2–10 days; up to 30% amorphous at 13 monthstian2016 R17, X5
PVP powders and filmssamepowders 10–90% amorphous at 3 months; films crystals only from 80% drugtian2016 R16, R20, X6
Fig. 17 of tian2016: miscibility range against crystallization onset for HPMC and HPMCAS powders
Fig. 17 · tian2016miscibility range against crystallization onset for HPMC and HPMCAS powders

Red circles are HPMC, blue squares HPMCAS; crystallization onsets appear only at loadings to the right of the miscibility band (50–60% and 20–30% drug), and loadings that stayed amorphous carry no point tian2016 R17, R21.

Why

Above the miscibility limit a drug-rich phase forms, and with less polymer in that phase crystallization "would be anticipated" to occur more readily tian2016 C4. The high PVP limit "can be attributed to" the strong drug–polymer hydrogen bond seen by IR tian2016 C29. The 480 nm band "could be due to" indomethacin dimers or other drug–drug contacts, so for PVP the spectra "might be" following dimers rather than a separate phase tian2016 C46, C50.

Limits and transfer

Dry storage at 40 °C only; miscibility was read on drop-cast films and stability on powders, so the two thresholds do not refer to the same samples, and PVP powders were followed only 3 months tian2016 P8, X7, X8, X6. The 30% HPMCAS powder held a drug-rich phase yet stayed amorphous for 13 months tian2016 X5. Screen candidate loadings for a drug-rich phase with a method that resolves domains of a few hundred nanometres, not DSC alone, and choose a loading at least one step below the limit.

How it was shown

Tian, Tang and Taylor (2016) used indomethacin as its own fluorescent probe: amorphous indomethacin emits at about 476 nm, and dispersed in a polymer at 5% drug at 508–520 nm tian2016 M1, R1, C13. Films with 5–95% drug in HPMC (E5), HPMCAS (MF) or PVP (K30) were drop-cast from methanol–dichloromethane onto quartz for emission spectra and fluorescence images, and onto KRS-5 for IR tian2016 M2, M3, M4, P1, P3, P4, P5. Powders with 10–90% drug were made by rotary evaporation at 60 °C and tested by modulated DSC tian2016 P2, P6. Films and powders were stored over desiccant at 40 °C; films were imaged after 5–30 days and powders followed by XRD from 2 days to 14 months tian2016 P7, P8, A4.

What the data show

With HPMC the emission maximum stayed at about 511–515 nm up to 50% drug and dropped to about 488 nm at 60% (spread 478–499 nm), with HPMCAS from about 513 to 480 nm between 20 and 30%, and with PVP from about 511 to 476 nm between 70 and 80% tian2016 R2.f, R2.g, R3.c, R3.d, R4.h, R4.i, X15. Images became heterogeneous from 60% (HPMC), from 30%, with first marks at 20% (HPMCAS), and from 70% (PVP), at a resolution of about 300–500 nm tian2016 R7, R8, R9, X12, C44. In IR the 1709 cm⁻¹ band of indomethacin acid dimers was absent at 5% drug in HPMC and returned from 60%; PVP showed bonded bands at 1724 and 1640 cm⁻¹ up to 80% drug; HPMCAS bands overlapped the drug bands tian2016 R10, C26, C27, R12, C28, R11. DSC gave one Tg throughout; it levelled at about 320–324 K from 50% drug in HPMC and 317–322 K from 30% in HPMCAS, while with PVP it fell steadily from 412 to 328 K tian2016 R13. In storage the HPMC powders crystallized at 15 days (60% drug) and 6 days (70–90%), the HPMCAS powders at 10 days (40%), 6 (50%), 8 (60%), 4 (70%), 2 (80%) and 4 days (90%), and the PVP powders not at all in 3 months tian2016 R17, R16. PVP films showed crystals only at 80% drug and above, by 5–30 days tian2016 R20.

papersystemmethod and conditionsresultids
tian2016indomethacin–HPMC, –HPMCAS, –PVP films, 5–95% drugemission maximum of the drugdrop to 476–488 nm between 50–60%, 20–30% and 70–80% drugR2, R3, R4, C17–C19
tian2016samefluorescence imaging; IR; DSCimaging and IR within one step of the spectra; one Tg everywhere, plateau from 50% (HPMC) and 30% (HPMCAS)R7–R13, R21
tian2016HPMC powders40 °C, desiccant, XRD60–90% drug crystalline at 6–15 days; up to 50% amorphous at 14 monthsR17
tian2016HPMCAS powderssame40–90% drug crystalline at 2–10 days; up to 30% amorphous at 13 monthsR17, X5
tian2016PVP powders and filmssamepowders 10–90% amorphous at 3 months; films crystals only from 80% drugR16, R20, X6
purohit2015a (outside)itraconazole–HPMCauthors' premise, stated without dataa phase-separated dispersion will be more prone to crystallization in storage and dissolutionC35
li2016c (outside)telaprevir–polymer filmsauthors' generalizationthe lower the polymer content of the drug-rich phase, the greater the risk of crystallizationC41

Figure

Fig. 17 of tian2016: miscibility range against crystallization onset for HPMC and HPMCAS powders
Fig. 17 · tian2016miscibility range against crystallization onset for HPMC and HPMCAS powders

Red circles are HPMC, blue squares HPMCAS; crystallization onsets in days appear only at loadings to the right of the miscibility band (50–60% and 20–30% drug); loadings that stayed amorphous carry no point tian2016 R17, R21.

Fig. 3 of tian2016: emission spectra and emission maximum against drug loading for indomethacin–HPMC films
Fig. 3 · tian2016emission spectra and emission maximum against drug loading for indomethacin–HPMC films

The maximum stays near 511–515 nm to 50% drug, drops to about 488 nm with a wide error bar at 60%, then reaches the amorphous-drug value tian2016 R2.

Why

The authors' account, with their hedges: above the miscibility limit a drug-rich phase forms, and with less polymer in that phase crystallization "would be anticipated" to occur more readily tian2016 C4. The drug-rich domains "led to" the faster crystallization, and homogeneous dispersions resisted it tian2016 C57. The 480 nm band "could be due to" indomethacin dimers or other drug–drug contacts, so for PVP the spectra "might be" following dimers rather than a separate phase tian2016 C46, C50. The high PVP limit "can be attributed to" the strong drug–polymer hydrogen bond seen by IR tian2016 C29. The single Tg of HPMC powders above the limit "might result from" remixing during the DSC scan (see F14) tian2016 C31. (synthesis: the onset times above the limit, 2–15 days, show no trend with loading for HPMCAS between 40 and 90% drug tian2016 R17, which fits crystallization from a drug-rich phase of roughly fixed composition, as in F15.)

Conditions and limits

One drug, dry storage at 40 °C only, no humidity tian2016 P8. Miscibility was read on drop-cast films made at about 20 °C and storage on powders made at 60 °C, so the two thresholds do not refer to the same samples; the 50% HPMC film crystallized by 12 days while the 50% powder lasted 14 months, and the 40% HPMCAS film lasted 26 days while the powder crystallized by 10 days tian2016 X7, X8. Each onset lies between the previous sampling time and the reported one tian2016 X9. PVP powders were followed only 3 months, against 13–14 months for the cellulosic polymers tian2016 X6.

Counterexamples and conflicts

At 30% drug in HPMCAS spectra, images and DSC all show a drug-rich phase, yet the powder stayed amorphous for 13 months, so the correlation holds from the next step, 40% drug tian2016 X5. PVP films at 70–80% drug looked separated but did not crystallize in powders within 3 months tian2016 X6. A cited ssNMR study found indomethacin–PVP mixed at about 5 nm at 10–50% polymer, which agrees with the present PVP data except at high loading tian2016 R23, C48. DSC, the usual screen, did not see any of the limits as two Tgs, the same blind spot as for itraconazole–HPMC (see Solid-state methods F19) tian2016 R13; mugheirbi2017 C31.

Transfer check

Screen candidate loadings for a drug-rich phase with a method that resolves domains of a few hundred nanometres (probe or intrinsic fluorescence, imaging, IR of the drug's self-association band), not with DSC alone tian2016 C55, R21. If the drug fluoresces, compare its emission in a 5% dispersion and in the neat glass; a shift toward the neat value as loading rises marks the limit tian2016 R1, C13. Choose a loading at least one step below that limit, and expect the limit to depend on preparation route and solvent tian2016 C49, X7.

History

The premise that miscible dispersions are more stable was long stated without a loading-by-loading test purohit2015a C35; li2016c C41. Added fluorescent probes had been used in 2015 to read the polarity and phase state of dispersions (see Solid-state methods F16 and F19); Tian and co-workers (2016) used the drug's own emission and paired the limits with storage outcomes tian2016 C53. Mugheirbi and co-workers (2017) used the same idea, assigning an extra emission peak to self-associated itraconazole mugheirbi2017 R22, C31. The drug–polymer thermodynamics behind the limits are in Miscibility and drug-polymer interactions F18 and F19.

Topic 2 of 5 · 3 findings · F6–F8

Water uptake by dispersions

F6

Topic 2Water uptake by dispersions1 of 3

Dispersions take up more water than the amorphous drug, most with PVP, and the water erases PVP's dry Tg gain.

At 75% RH and 25 °C pure PVP K29/32 held about 33 g water per 100 g, HPMC about 10–11, HPMCAS about 6 and amorphous felodipine about 0.7–1.1 konno2008 R8; rumondor2010a R1. Uptake of the dispersions rose with polymer content, most with PVP konno2008 R9.d, C18. The dry Tg advantage of 25% PVP (about 54–55 °C against 43–48 °C) was gone at 75–76% RH, where all systems sat near 28–36 °C konno2008 R5, C15; marsac2008a R6, C17.

strongStrong: five papers with gravimetric isotherms and humidified Tgs agree on the order and size of uptake, although the 7–25% PVP values of one paper differ 1.4–2-fold between its figures and the isotherms carry no replicates konno2008 K3, X2; marsac2008a X9; rumondor2010a X12.

Water taken up near 75% RH and 25 °C, g per 100 gPVP K29/32≈33PVPVAcited isotherm, near 76% RH≈17HPMC10.4–10.9HPMCAS6.2–6.3amorphous indomethacin≈1.55amorphous felodipine0.7–1.1

konno2008 R8; rumondor2010c R19; rumondor2010a R1.h, R1.j

dry, 0% RHafter 75% RHPVP31.154.9HPMCAS35.644.2HPMC34.443.12530354045505560Tg of felodipine with 25% polymer, °C

The PVP dispersion has the highest Tg dry and the lowest after humid storage; the curves cross between about 33 and 75% RH. konno2008 R5, C15, X12

For your drug

  1. Measure the full isotherm of the dispersion at the storage temperature, with steps held to a stable weight (about 1000 min for PVP-rich samples), then the Tg of samples equilibrated at the storage RH.
  2. Estimate the wet Tg from the dry Tg with about 5–10 °C per 1% water, and treat a wet Tg near or below the storage temperature as a warning.

marsac2008a R3; konno2008 R5

How it works and key numbers
  1. The drug is hydrophobic, so the water a dispersion sorbs "is likely" to depend largely on the polymer konno2008 C6.
  2. The number and type of polar groups that hydrogen-bond with water set the uptake; the steeper rise with PVP is "presumably" due to its higher polarity konno2008 C5; rumondor2010a C8.
  3. Per gram of water the drug alone loses Tg fastest: pure nifedipine fell about 12 °C with 1.15 g/100 g, while the 25% PVP dispersion needed about 2 g/100 g to fall 11 °C marsac2008a R7, C19.
  4. Plasticization by water is "directly related to the hygroscopicity of polymer": PVP dispersions take up so much more water at a given RH that their Tg ends lowest konno2008 C20, R5.
To feel the numbers. Pure nifedipine loses 12 ÷ 1.15 ≈ 10 °C of Tg per 1% water; the 25% PVP dispersion loses 11 ÷ 2 ≈ 5.5 °C per 1%, but holds 5.5 g/100 g at 75% RH against 1.8 for the drug alone.
≈33 vs 0.7–1.1 g/100 gwater in pure PVP vs amorphous felodipine at 75% RHkonno2008 R8; rumondor2010a R1
54.9 → 31.1 °CTg of felodipine with 25% PVP, 0 → 75% RHkonno2008 R5
PVP ≫ PVPVA > HPMC > HPMCASorder of water uptake of the four polymersrumondor2010c R19; konno2008 R8

Connections to other chapters

Evidence: data, conditions and papers

Finding F6. Dispersions take up more water than the amorphous drug, in amounts set by polymer type and content (PVP ≫ PVPVA > HPMC > HPMCAS), and the water erases the Tg gain that the polymer gives when dry

In short. At 75% RH and 25 °C pure PVP K29/32 held about 33 g water per 100 g, HPMC about 10–11, HPMCAS about 6 and amorphous felodipine about 0.7–1.1 konno2008 R8; rumondor2010a R1. Uptake of the dispersions rose with polymer content, most with PVP: with 25% polymer about 4.7 (PVP), 2.3 (HPMC) and 1.7 (HPMCAS) g/100 g at 75% RH konno2008 R9.d, C18; rumondor2010a C7, and above about 75% RH uptake turned steeply upward (70 wt% PVP: about 15 at 75% and 55.5 wt% at 95% RH) marsac2010 R9, R10, C11. Nifedipine systems took up more than felodipine systems (5.5 against 4.6 g/100 g with 25% PVP at 75% RH) marsac2008a R2, C12. Sorbed water lowered every Tg; the dry Tg advantage of 25% PVP (about 54–55 °C against 43–48 °C) was gone at 75–76% RH, where all systems sat near 28–36 °C konno2008 R5, C15; marsac2008a R6, C17. PVPVA lies between PVP and the cellulose polymers: at about 85% RH the cited polymer isotherms give roughly 50 (PVP), 24 (PVPVA) and 8 g/100 g (HPMCAS), and 75:25 dispersions of felodipine and quinidine took up 6.4 and 5.3 (PVP), 3.6 and 3.4 (PVPVA) and 2.4 g/100 g (HPMCAS) rumondor2010c R19, R18, C20.

Type. observation in 4 drugs and 4 polymers Strength. five papers with gravimetric isotherms and humidified Tgs agree on the order and size of uptake (konno2008 K3: strong), although the 7–25% PVP values of one paper differ 1.4–2-fold between its figures (konno2008 X2) and isotherms carry no replicates (marsac2008a X9; rumondor2010a X12).

How it was shown

Konno and Taylor (2008), Marsac and co-workers (2008) and Rumondor and co-workers (2010) measured water sorption gravimetrically on bulk dispersions at 25 °C, and Rumondor and Taylor (2010) added PVPVA at 85% RH konno2008 P2, P7; marsac2008a P6; rumondor2010a P2; rumondor2010c P8, R18. Tg after equilibration at each RH was measured by DSC on hermetically sealed samples konno2008 P6; marsac2008a P7.

What the data show

At 75% RH pure PVP held about 33.2–33.5 g water per 100 g, HPMC 10.4–10.9, HPMCAS 6.2–6.3 and felodipine 0.7–1.1 konno2008 R8.a, R8.h, R8.o, R8.v; rumondor2010a R1.h, R1.j. The PVP Tg curve crossed the cellulose curves between about 33 and 75% RH konno2008 R5, C15, X12.

systemmethod and conditionsresultids
75:25 felodipine and quinidine dispersionssingle-RH plateau, 25 °C, 85% RHPVP 6.4 and 5.3; PVPVA 3.6 and 3.4; HPMCAS 2.4 and 2.4 g/100 grumondor2010c R18, C20
nifedipine and felodipine, 0 / 10 / 25% PVPsingle-RH plateau, 25 °C, 75% RH1.8 / 3.0 / 5.5 (nifedipine) and 1.1 / 1.9 / 4.6 (felodipine) g/100 gmarsac2008a R2
felodipine with 25% polymerDSC Tg after 2 days at each RH, 0 → 75% RHPVP 54.9 → 31.1, HPMCAS 44.2 → 35.6, HPMC 43.1 → 34.4 °Ckonno2008 R5
pure drugs and 25% PVPDSC Tg at sorption plateauall systems 26–33 °C at 76% RHmarsac2008a R6, C17
celecoxib 5:5 dispersionsDVS, 25 °C, 95% RHK12 ≈21.8, K29/32 ≈17.2, HPMC ≈8.0, PVPVA ≈7.0, HPMCAS ≈3.6 g/100 gxie2016b R13, C24
Fig. 5 of konno2008: water sorption isotherms of felodipine dispersions with PVP, HPMCAS and HPMC
Fig. 5 · konno2008water sorption isotherms of felodipine dispersions with PVP, HPMCAS and HPMC

Uptake rises with RH and polymer content; note the different y scales, up to about 80% for PVP, 14% for HPMCAS and 25% for HPMC konno2008 R8.

Why

The drug is hydrophobic, so the water a dispersion sorbs "is likely" to depend largely on the polymer and its polar groups konno2008 C6, C5. Plasticization by water is "directly related to the hygroscopicity of polymer", while water is "a more effective plasticizer for the drug alone" per gram of water konno2008 C20; marsac2008a C19. (synthesis: per 1% water the pure drugs drop about 10 °C and the 25% polymer dispersions about 5 °C, but PVP dispersions take up so much more water at a given RH that their Tg ends lowest) marsac2008a R7.a; ilevbare2013a E15; konno2008 R6.

Limits and transfer

Bulk powders at 25 °C without replicates, while crystallization was measured on films konno2008 X6; marsac2008a X9, X12. The celecoxib–PVPVA dispersion took up about as little as the HPMC one, out of the polymer order xie2016b C24. Measure the isotherm at the storage temperature with steps held to a stable weight, then the Tg of samples equilibrated at the storage RH, and treat a wet Tg near or below the storage temperature as a warning.

How it was shown

All four papers used gravimetric vapour sorption (VTI SGA-100) on rotary-evaporated bulk dispersions at 25 °C: Konno and Taylor (2008) ran 5–95% RH isotherms of felodipine with 0–100% PVP, HPMCAS or HPMC, holding PVP samples 1000 min per step konno2008 P2, P7; Marsac and co-workers (2008) held nifedipine and felodipine powders with 0, 10 and 25% PVP at one RH between 5 and 75% until the weight levelled off, about 600 min for the drugs and 1000 min for the dispersions marsac2008a P6, R3; Marsac and co-workers (2010) exposed 30–70 wt% PVP dispersions to 75, 85 and 95% RH for 5 h marsac2010 P10; Rumondor and co-workers (2010) measured plateau uptake at 5–95% RH for felodipine and indomethacin blends with PVP, HPMC and HPMCAS rumondor2010a P2. Rumondor and Taylor (2010) held 75:25 drug:polymer powders of felodipine and quinidine with PVP, PVPVA or HPMCAS at 25 °C and 85% RH until the first plateau, two of the six values being taken from a thesis, and cited isotherms of the three polymers rumondor2010c P8, R18, R19. Tg after equilibration at each RH was measured by DSC on hermetically sealed samples konno2008 P6; marsac2008a P7. Xie and Taylor (2016) ran full isotherms of five polymers, amorphous celecoxib and 5:5 dispersions at 25 °C, and Trasi and co-workers (2017) of tacrolimus capsule fills xie2016b P8; trasi2017 P4.

What the data show

For the pure components at 75% RH: PVP about 33.2–33.5, HPMC 10.4–10.9, HPMCAS 6.2–6.3, amorphous indomethacin about 1.55 and felodipine 0.7–1.1 g/100 g; at 95% RH PVP reached about 75 konno2008 R8.a, R8.h, R8.o, R8.v; rumondor2010a R1.h, R1.j. In felodipine–PVP at 85% RH uptake rose from about 1.1 (no PVP) through 6.8 (25%) and 15.7 (50%) to 50.0 g/100 g (pure PVP), whereas felodipine–HPMCAS reached only about 2.5 at 25% and 8.2 at 100% polymer rumondor2010a R2, R4. Konno's Fig. 6 inset gives 4.7 g/100 g for 25% PVP at 75% RH but the isotherm figure of the same paper about 2.3 konno2008 R9.d, R8.e, X2; two independent papers measured 4.6 g/100 g for felodipine with 25% PVP at 75% RH marsac2008a R2.f; rumondor2010a R2.c, which supports the higher value (synthesis). The 5 h values of marsac2010 (4.8 g/100 g at 50% PVP and 75% RH, below the 5.6 of 30% PVP) are about half the plateau value of the 2010 isotherm study at 50% PVP (about 9.4) marsac2010 R10, X3; rumondor2010a R2.d, consistent with incomplete equilibration in 5 h when dispersions need about 1000 min (synthesis) marsac2008a R3.

Tg fell with RH in every system. With 25% polymer, from about 54.9 to 31.1 °C (PVP), 44.2 to 35.6 °C (HPMCAS) and 43.1 to 34.4 °C (HPMC) between 0 and 75% RH; the PVP curve crossed the cellulose curves between about 33 and 75% RH konno2008 R5, C15, X12. Pure nifedipine went from about 43 to 26 °C at 76% RH and with 25% PVP from about 54 to 29 °C; felodipine from about 46 to 33 °C and with 25% PVP from about 48 to 28 °C marsac2008a R6. With PVP at 75% RH, Tg peaked near 70% polymer (about 51.8 °C) and fell to about 10.3 °C for pure PVP, which had a ΔTg of about 158 °C konno2008 R7.f, R7.h, R9.h, C16. Per gram of water the drug alone lost Tg fastest: pure nifedipine fell about 12 °C with 1.15 g/100 g, while the 25% PVP dispersion needed about 2 g/100 g to fall 11 °C marsac2008a R7, C19. At similar water content the 25% PVP system lost more Tg than the cellulose systems (about 13.3 °C at 1.1% water against 6.2 °C for HPMCAS) konno2008 R6, C14.

The polymer isotherms cited in 2010 put PVPVA at about 17 g/100 g near 76% RH and 24 at 85% RH, against about 33 and 50 for PVP and 6 and 8 for HPMCAS rumondor2010c R19; at 75% RH HPMC holds about 10.4–10.9 konno2008 R8; rumondor2010a R1, so the order of the four polymers is PVP ≫ PVPVA > HPMC > HPMCAS (synthesis: from two papers at nearly the same RH). The 75:25 dispersions followed the same order for both drugs: felodipine 6.4 / 3.6 / 2.4 and quinidine 5.3 / 3.4 / 2.4 g/100 g with PVP / PVPVA / HPMCAS at 85% RH rumondor2010c R18. The felodipine–PVP value agrees with the 6.8 g/100 g measured for 25% PVP at 85% RH in the blend study (synthesis) rumondor2010a R2.

Celecoxib dispersions of 2016 extend the order with a PVP grade and a fifth polymer. At 95% RH and 25 °C the neat polymers took up about 68 (PVP K29/32), 67 (PVP K12), 48 (PVPVA), 31 (HPMC) and 12 g/100 g (HPMCAS), and amorphous celecoxib about 2.2; the 5:5 dispersions took up about 21.8 (K12), 17.2 (K29/32), 8.0 (HPMC), 7.0 (PVPVA) and 3.6 g/100 g (HPMCAS) xie2016b R12, R13. The PVPVA dispersion was the exception to the polymer order, taking up about as little as the HPMC one ("largely suppressed") xie2016b C24. After 3 days at 94% RH the dry Tgs of 64–103 °C fell to 37.4–42.1 °C for four of the dispersions and to 22 °C for PVP K12 xie2016b R17. In marketed tacrolimus capsules the fill took up 1.6–12.8% water at 95% RH, most in the product with the most croscarmellose (see F33) trasi2017 R4, C16.

papersystemmethod and conditionsresultids
konno2008pure polymers and felodipineDVS isotherm, 25 °C, 75% RHPVP ≈33.5, HPMC ≈10.9, HPMCAS ≈6.2, felodipine ≈0.7 g/100 gR8
rumondor2010cPVP, PVPVA, HPMCAS (cited isotherms)25 °C, read from Fig. 11≈50, ≈24 and ≈8 g/100 g at 85% RHR19
rumondor2010c75:25 felodipine and quinidine dispersionssingle-RH plateau, 25 °C, 85% RHPVP 6.4 and 5.3; PVPVA 3.6 and 3.4; HPMCAS 2.4 and 2.4 g/100 gR18, C20
konno200825% polymer, 75% RHFig. 6PVP ≈4.7, HPMC ≈2.3, HPMCAS ≈1.7 g/100 gR9.d, X2
marsac2008anifedipine and felodipine, 0–25% PVPsingle-RH plateau, 25 °C75% RH: 1.8 / 3.0 / 5.5 (nifedipine) and 1.1 / 1.9 / 4.6 (felodipine) g/100 gR2
rumondor2010afelodipine–PVP 0–100%plateau isotherm, 25 °C85% RH: 1.1 → 6.8 (25%) → 15.7 (50%) → 50.0 (PVP) g/100 gR2
marsac201070 wt% PVPDVS isotherm, 25 °C≈15.0 (75%), ≈22.9 (85%), ≈55.5 wt% (95% RH)R9, C11
konno200825% polymerDSC Tg after 2 days at each RH0 → 75% RH: PVP 54.9 → 31.1, HPMCAS 44.2 → 35.6, HPMC 43.1 → 34.4 °CR5
marsac2008apure drugs and 25% PVPDSC Tg at sorption plateauall systems 26–33 °C at 76% RHR6, C17
xie2016bPVP K29/32, K12, PVPVA, HPMC, HPMCAS; amorphous celecoxibDVS, 25 °C, 95% RH≈68, 67, 48, 31, 12; drug ≈2.2 g/100 gR12
xie2016bcelecoxib 5:5 dispersionssameK12 ≈21.8, K29/32 ≈17.2, HPMC ≈8.0, PVPVA ≈7.0, HPMCAS ≈3.6 g/100 gR13, C24
xie2016bcelecoxib 6:4 dispersionsDSC Tg after 3 days at 94% RH103 → 37.4 (PVP), 81 → 42.1 (PVPVA), 64 → 39 (HPMCAS), 71 → 38 °C (HPMC)R17
trasi2017six tacrolimus capsule fillsDVS, 25 °C, 95% RH1.6–12.8%R4
ilevbare2013a (outside)amorphous solidsrule of thumbTg falls by about 10 °C per 1% sorbed waterE15
duong2022c (outside)coated and uncoated ASD powdersDVS, 37 °Cthick coatings lowered sorption; thin ones barely didC17

Figure

Fig. 5 of konno2008: water sorption isotherms of felodipine dispersions with PVP, HPMCAS and HPMC
Fig. 5 · konno2008water sorption isotherms of felodipine dispersions with PVP, HPMCAS and HPMC

Uptake rises with RH and polymer content in all three panels; note the different y scales, up to about 80% for PVP, 14% for HPMCAS and 25% for HPMC konno2008 R8.

Fig. 6 of marsac2008a: Tg against water content for nifedipine and felodipine with 0, 10 and 25% PVP
Fig. 6 · marsac2008aTg against water content for nifedipine and felodipine with 0, 10 and 25% PVP

The nifedipine and felodipine panels are nearly the same; the pure drugs lose Tg fastest per gram of water marsac2008a R7, C20.

Why

The authors' account, with their hedges: the drug is hydrophobic, so the water a dispersion sorbs "is likely" to depend largely on the polymer, and since the polymers are hydrophilic the dispersion "may actually" hold more water than the drug alone konno2008 C6. The number and type of polar groups that hydrogen-bond with water set the uptake (PVP more than poly(vinylacetate), cited) konno2008 C5; the steeper rise with PVP is "presumably" due to its higher polarity rumondor2010a C8. Plasticization by water is "directly related to the hygroscopicity of polymer" ("it is obvious") konno2008 C20, and water is "a more effective plasticizer for the drug alone" per gram of water ("This result suggests") marsac2008a C19. Nifedipine sorbs more than felodipine because water mixes less badly with it (activity coefficient in water 1.89 × 10³ against 2.43 × 10⁵) marsac2008a R10, C41. (synthesis: the two plasticization statements are compatible. Per gram of sorbed water the pure drugs drop about 10 °C per 1%, as the rule of thumb in the library says, for example nifedipine 43 → 31 °C with 1.15 g/100 g marsac2008a R7.a; ilevbare2013a E15; the 25% polymer dispersions drop only about 5 °C per 1% (25% PVP: 23.7 °C with 4.68%; 25% HPMCAS: 8.6 °C with 1.73% konno2008 R6); but PVP dispersions take up so much more water at a given RH that their Tg ends lowest.)

Conditions and limits

Bulk powders at 25 °C, while crystallization was measured on films at 22–25 °C; the water contents attached to the films are estimates from the powders konno2008 X6; marsac2008a X12. Equilibration differed between polymers (PVP 1000 min per step, cellulose polymers a weight criterion) and between papers (5 h in marsac2010) konno2008 X11; marsac2010 P10. One temperature; isotherms without replicates marsac2008a X9; rumondor2010a X12.

Counterexamples and conflicts

The PVP values of konno2008 disagree internally (X2); the independent 4.6 g/100 g values above favour the higher figure (synthesis). Blends do not take up the weighted sum of their components (F7). None found in the library that reverses the polymer order PVP > HPMC > HPMCAS.

Transfer check

Measure the full isotherm of the dispersion at the storage temperature with steps held to a stable weight (about 1000 min for PVP-rich samples here marsac2008a R3), then the Tg of samples equilibrated at the storage RH. Estimate the wet Tg from the dry Tg with about 5–10 °C per 1% water as a range (synthesis from the values above) and treat a wet Tg near or below the storage temperature as a warning. A PVP dispersion at 25% polymer can lose its whole dry Tg gain at 75% RH, as here konno2008 R5.

History

Hancock and Zografi (outside the library) had related Tg to water content of amorphous solids marsac2008a C1. Konno and Taylor (2008) first measured in the library how polymer type and content set the water uptake of felodipine dispersions konno2008 C17, C18; Marsac and co-workers (2008) added nifedipine and showed both drugs plasticized alike at equal water marsac2008a C20; in 2010 the steep upturn above 75% RH was tied to moisture-induced separation (F12) and the uptake of blends was analysed against additivity (F7) marsac2010 C11; rumondor2010a C10. In the same year Rumondor and Taylor placed PVPVA between PVP and HPMCAS and used the order to explain how readily dispersions separate (see F23) rumondor2010c C20, C31; the title of this finding was widened to include PVPVA. A semicrystalline carrier kept taking up water for months at 94% RH (see PEG dispersions F12). Xie and Taylor (2016) measured five polymers with celecoxib and found the PVPVA dispersion out of the polymer order xie2016b C24; the title is unchanged.

F7

Topic 2Water uptake by dispersions2 of 3

One-phase drug–polymer blends sorb up to about two-thirds less water than their components predict; separated blends sorb about the sum.

Felodipine blends took up to about 64% less water than the weight-averaged sum of drug and polymer uptakes with PVP, up to about 47% less with HPMC and up to about 55% less with HPMCAS rumondor2010a R7, R8, R9, C10, C13. Among five drug–PVP dispersions at 95% RH, the three that separated into two amorphous phases on humid storage took up within 7.4% of the sum, and the two that stayed mixed far less rumondor2009c R22, C24.

moderateModerate: the shortfall is large and seen in all four blend series, and the split by phase behaviour is consistent, but the isotherms appear to be single runs and the explanation is untested rumondor2010a K1, K3, X12, X14; rumondor2009c R22.

separated on humid storagestayed mixednifedipine–PVP 50:5042.5 vs 39.9pimozide–PVP 70:3022.4 vs 24.0droperidol–PVP 70:3024.8 vs 24.9indomethacin–PVP 75:254.9 vs 21.7ketoprofen–PVP 70:3011.4 vs 25.3051015202530354045water uptake at 95% RH, g/100 g: measured and weighted sum

Each bar runs from the measured uptake to the weighted sum of drug and PVP uptakes (first value measured). rumondor2009c R22, C24

10% PVP45–5725% PVP43–6450% PVP32–5975% PVP9–2290% PVP2.4–21010203040506070felodipine–PVP: uptake below the weighted sum, %

Ranges across 15–85% RH; the shortfall is largest at 10–25% PVP. rumondor2010a R7, C10

For your drug

  1. Measure the isotherms of the amorphous drug, the polymer and the dispersion at the storage temperature and compute the weighted sum; a fresh dispersion tens of percent below it is consistent with one phase.
  2. If a sample stored at high RH moves toward additivity, check it by IR against a calculated physical-mixture spectrum and by DSC for a second Tg before trusting its stability data.

rumondor2009c P7, R17; rumondor2010a R7

How it works and key numbers
  1. Additivity requires that the blend behaves like a physical mixture, with every water-binding group as available as in the pure materials rumondor2010a C9.
  2. Drug hydrogen-bond donors bind the single acceptor of the PVP repeat unit, so those sites are lost to water; this predicts the largest shortfall near one donor per repeat unit, 78:22 for felodipine by weight rumondor2010a C11, C12, R10.
  3. HPMC and HPMCAS carry several donors and acceptors per repeat unit and interact more weakly with felodipine, so these blends are less affected ("it is intuitive") rumondor2010a C14.
  4. In a phase-separated blend drug–polymer contacts are fewer, so uptake "would be anticipated" to be closer to additive; no interaction was measured in the blends rumondor2009c C25; rumondor2010a X14.
up to ≈64%shortfall below additivity, felodipine–PVPrumondor2010a R7, C10
3.6 vs 14.0 g/100 gindomethacin with 25% PVP, measured vs predicted, 85% RHrumondor2010a R12.h
within 7.4%separated dispersions against additivity at 95% RHrumondor2009c R22, C24

Connections to other chapters

Evidence: data, conditions and papers

Finding F7. One-phase drug–polymer blends take up less water than the weighted sum of their components, by up to about two-thirds, and near-additive uptake goes with blends that have phase separated

In short. Felodipine blends took up to about 64% less water than the weight-averaged sum of drug and polymer uptakes with PVP, up to about 47% less with HPMC and up to about 55% less with HPMCAS; the shortfall was largest at 10–25% PVP and at 50–70% cellulose polymer rumondor2010a R7, R8, R9, C10, C13. Indomethacin–PVP with 25% PVP took up about 3.6 against 14.0 g/100 g predicted at 85% RH rumondor2010a R12.h. Among five drug–PVP dispersions at 95% RH, the three that separated into two amorphous phases on humid storage took up within 7.4% of additivity, the two that stayed mixed (indomethacin, ketoprofen) far less rumondor2009c R22, C24.

Type. observation in 6 drugs and 3 polymers Strength. the shortfall is large and seen in all four blend series (rumondor2010a K1: strong) and the split by phase behaviour is consistent (rumondor2009c R22), but isotherms appear to be single runs, the explanation is untested (rumondor2010a K3: weak to moderate; X12, X14), and high-RH felodipine–PVP points may already be phase separated (X9).

How it was shown

Rumondor and co-workers (2010) measured plateau uptake at 5–95% RH and 25 °C of felodipine blends with PVP, HPMC and HPMCAS and of indomethacin–PVP blends, and expressed the gap to the weight-averaged sum of the pure isotherms as a percentage of that prediction rumondor2010a P1, P2, E5, E6. Rumondor and co-workers (2009) compared five drug–PVP dispersions at 95% RH with the same weighted sum rumondor2009c P11, P12, E6.

What the data show

Every felodipine–PVP deviation was positive, measured below predicted rumondor2010a R7. In the 2009 set the dispersions that separated sat near additivity and the two that stayed mixed far below it rumondor2009c R22, C24.

systemmethod and conditionsmeasured against weighted sumids
felodipine–PVP 10–90%plateau sorption 15–85% RH, 25 °C43–64% below at 25% PVP; 2.4–21% below at 90% PVPrumondor2010a R7, C10
felodipine–HPMC, felodipine–HPMCASsameup to ≈47% (HPMC) and ≈55% (HPMCAS) below, largest at 50–70% polymerrumondor2010a R8, R9, C13
indomethacin–PVP 25 and 75%85% RH25%: 3.6 measured vs 14.0 predicted; 75%: 36.0 vs 38.0 g/100 grumondor2010a R12.h
nifedipine-, pimozide-, droperidol–PVP (separated)95% RH plateau42.5 vs 39.9, 22.4 vs 24.0, 24.8 vs 24.9 g/100 grumondor2009c R22, C24
indomethacin–PVP, ketoprofen–PVP (stayed mixed)same4.9 vs 21.7 and 11.4 vs 25.3 g/100 grumondor2009c R22
Fig. 6 of rumondor2010a: felodipine–PVP, deviation of measured from additive water uptake against PVP content
Fig. 6 · rumondor2010afelodipine–PVP, deviation of measured from additive water uptake against PVP content

One line per RH from 15 to 85%; positive values mean the blend took up less water than the sum of its parts, highest at 10–25% PVP rumondor2010a R7.

Why

Additivity requires that every water-binding group is as available as in the pure materials rumondor2010a C9. Drug hydrogen-bond donors bind the single acceptor of the PVP repeat unit, so those sites are lost to water, which predicts the largest shortfall near one donor per repeat unit rumondor2010a C11, C12. In a phase-separated system drug–polymer contacts are fewer, so uptake "would be anticipated" to be closer to additive rumondor2009c C25.

Limits and transfer

Single runs, and felodipine–PVP points at 75% RH and above may come from blends that have already separated rumondor2010a X12, X9. Celecoxib–PVP dispersions with two Tg events after 3 days at 94% RH were still 37–51% below additivity (synthesis) xie2016b R13, R18. If a sample stored at high RH moves toward additivity, check it by IR and by DSC for a second Tg, and do not use the additive sum to estimate the water content of a one-phase dispersion.

How it was shown

Rumondor, Konno, Marsac and Taylor (2010) made felodipine–PVP, indomethacin–PVP, felodipine–HPMC and felodipine–HPMCAS blends at 0–100% polymer by solvent evaporation followed by a brief melt, measured plateau uptake at 5–95% RH and 25 °C, and expressed the gap to the weight-averaged sum of the pure isotherms as a percentage of that prediction rumondor2010a P1, P2, P3, E5, E6. Rumondor and co-workers (2009) measured plateau uptake at 25 °C and 95% RH of PVP, five amorphous drugs and one dispersion of each, and compared it with the same weighted sum, expressing the difference relative to the measured value rumondor2009c P11, P12, E6. Xie and Taylor (2016) supplied isotherms of celecoxib dispersions and of their components xie2016b P8.

What the data show

For felodipine–PVP every plotted deviation was positive (measured below predicted): about 45–57% at 10% PVP, 43–64% at 25%, 32–59% at 50%, 9–22% at 75% and 2.4–21% at 90% PVP across 15–85% RH rumondor2010a R7. Felodipine–HPMC reached about 36–47% at 50% and 36.5–44.5% at 70% polymer; felodipine–HPMCAS peaked at about 55% (50% polymer, 15% RH), fell with RH at that composition from about 55 to 25%, and gave the only negative value (about −4.5% at 15% HPMCAS and 85% RH) rumondor2010a R8, R9. The authors place the PVP maximum near one drug hydrogen-bond donor per PVP repeat unit, 78:22 for felodipine and 76:24 for indomethacin by weight, although one RH series of felodipine–PVP peaks at 10% rather than 25% PVP and the indomethacin difference data are not shown rumondor2010a R10, C12, X11. In indomethacin–PVP additivity was far too high at 25% PVP (14.0 against 3.6 g/100 g at 85% RH) and within about 2 g/100 g of the data at 75% PVP (38.0 against 36.0) rumondor2010a R12.h, X8. In the 2009 set, measured and predicted uptakes were 42.5 against 39.9 (nifedipine–PVP 50:50), 22.4 against 24.0 (pimozide–PVP 70:30), 24.8 against 24.9 g/100 g (droperidol–PVP 70:30), but 4.9 against 21.7 (indomethacin–PVP 75:25) and 11.4 against 25.3 (ketoprofen–PVP 70:30) rumondor2009c R22. Expressed against the prediction, as in the 2010 paper, the indomethacin and ketoprofen gaps are about 77% and 55% (synthesis: (21.7 − 4.9)/21.7 and (25.3 − 11.4)/25.3); the printed 341.5% and 121.7% are relative to the measured value rumondor2009c E6.

Celecoxib 5:5 dispersions at 95% RH were also below the weighted sum: about 17.2 against 35.1 g/100 g with PVP K29/32, 21.8 against 34.6 with PVP K12, 7.0 against 25.1 with PVPVA and 3.6 against 7.2 with HPMCAS, shortfalls of about 51, 37, 72 and 50% (synthesis: 0.5 × polymer + 0.5 × drug uptake from xie2016b R12, R13).

papersystemmethod and conditionsresultids
rumondor2010afelodipine–PVP 10–90%plateau sorption 15–85% RH, 25 °C; deviation against prediction43–64% at 25% PVP; 2.4–21% at 90% PVP; all below additivityR7, C10
rumondor2010afelodipine–HPMC, felodipine–HPMCASsameup to ≈47% (HPMC) and ≈55% (HPMCAS), largest at 50–70% polymerR8, R9, C13
rumondor2010aindomethacin–PVP 25 and 75%additivity and ternary FH against data, 85% RH25%: 14.0 predicted vs 3.6 measured; 75%: 38.0 vs 36.0R12.h
rumondor2009cthree separating drug–PVP dispersions95% RH plateau vs weighted sumwithin 0.2–7.4% of additivityR22, C24
rumondor2009cindomethacin–PVP, ketoprofen–PVP (stayed mixed)same4.9 vs 21.7 and 11.4 vs 25.3 g/100 gR22
wegiel2013bresveratrol–PVP K29/32 40:60 dispersion vs physical mixture with crystalline drugDVS, 25 °C, 0–95% RH≈12.8 against ≈36.5% weight gain at 95% RHR19, C37
xie2016bcelecoxib 5:5 with PVP K29/32, K12, PVPVA, HPMCASDVS 95% RH vs weighted sum (synthesis)≈51, 37, 72 and 50% below additivityR12, R13
li2018 (outside)lopinavir, 50% loading, six polymersisotherms at 90% RH vs additiveCA, EUD and CAP close to additive; HPMCAS and HPMCP belowC33
bapat2025b (outside)permeation enhancers with PVPVA, 50:50DVS at 37 °Csorbed more water than the additive predictionC35

Figure

Fig. 6 of rumondor2010a: felodipine–PVP, deviation of measured from additive water uptake against PVP content
Fig. 6 · rumondor2010afelodipine–PVP, deviation of measured from additive water uptake against PVP content

One line per RH from 15 to 85%; positive values mean the blend took up less water than the sum of its parts, highest at 10–25% PVP rumondor2010a R7.

Table 2 of rumondor2009c: water uptake at 95% RH against the additive prediction
Table 2 · rumondor2009cwater uptake at 95% RH against the additive prediction

The three systems that phase separated sit within 7.4% of the prediction; indomethacin and ketoprofen dispersions, which stayed mixed, are far below it rumondor2009c R22.

Why

The authors' account, with their hedges: additivity requires that the blend behaves like a physical mixture, every water-binding group being as available as in the pure materials rumondor2010a C9. Following Crowley and Zografi, drug hydrogen-bond donors bind the single acceptor of the PVP repeat unit, so those sites are lost to water, which predicts the largest shortfall near one donor per repeat unit ("is indeed around") rumondor2010a C11, C12. HPMC and HPMCAS carry several donors and acceptors per repeat unit and interact more weakly with felodipine, so "it is intuitive" that these blends are less affected, and it is "reasonable to speculate" that the size of the shortfall follows the nature of the drug–polymer interactions rumondor2010a C14, C15. In a phase-separated system drug–polymer contacts are fewer, so uptake "would be anticipated" to be closer to additive rumondor2009c C25. No interaction was measured in the blends rumondor2010a X14. (synthesis: the two papers together make additivity a phase-state marker: strongly sub-additive uptake went with one-phase blends, near-additive uptake with blends shown by IR or DSC to have separated.)

Conditions and limits

25 °C; one composition per drug in the 2009 comparison; felodipine–PVP isotherm points at 75% RH and above may come from blends that have already separated (F12) but are still used in the additivity comparison rumondor2010a X9. Single runs; crystallization screening of sorption samples is not described rumondor2010a X12. The two papers normalise the deviation differently (prediction against measured value).

Counterexamples and conflicts

One positive deviation (15% HPMCAS, 85% RH) rumondor2010a R9.a. A resveratrol–PVP dispersion took up about a third of the water of a physical mixture of the same composition (about 12.8 against 36.5% at 95% RH), which the authors take as evidence that resveratrol–PVP hydrogen bonds suppress sorption; the reference held crystalline, not amorphous, resveratrol, and no additive sum of the amorphous components was computed, so this supports the direction of the finding but not its size wegiel2013b R19, C37, X18. Outside the subcategory, two enhancer–PVPVA dispersions sorbed more water than additive bapat2025b C35, and the lopinavir–CA dispersion that matched additivity was the one shown to be largely immiscible by two Tgs li2018 C27, C33, in line with the phase-state reading (synthesis). The celecoxib–PVP dispersions, which showed two Tg events after 3 days at 94% RH, were still 37–51% below additivity in the sorption run (synthesis from the values above), so near-additivity did not mark their separation; the sorption steps were short compared with the 3-day exposure xie2016b R13, R18, P7, P8.

Transfer check

Measure the isotherms of the amorphous drug, the polymer and the dispersion at the storage temperature and compute the weighted sum. A fresh dispersion well below additivity (tens of percent) is consistent with a one-phase blend; if a sample stored at high RH moves toward additivity, check it by IR against a calculated physical-mixture spectrum and by DSC for a second Tg before trusting its stability data (see F12) rumondor2009c P7, R17. Do not use the additive sum to estimate the water content of a one-phase dispersion; it overestimates by up to about two-thirds here rumondor2010a R7.

History

Shamblin and Zografi (1999) and Zhang and Zografi (2001), outside the library, found additivity for sugar–PVP blends unless the sugar crystallized, and Crowley and Zografi (2002) found it for indomethacin–PVP at 60–90% PVP rumondor2010a R18, R19, R16. Rumondor and co-workers (2009) first used near-additivity as evidence of moisture-induced phase separation in the library rumondor2009c C24; Rumondor and co-workers (2010) measured the shortfall across four blend series rumondor2010a C10. Wegiel and co-workers (2013) cited that work when reading the low uptake of a resveratrol–PVP dispersion as hydrogen bonding, using a crystalline physical mixture as the reference wegiel2013b C37, R19. Later work on lopinavir dispersions read the shortfall again as drug–polymer interaction li2018 C34. Xie and Taylor (2016) supplied celecoxib with four polymers xie2016b R13; the title is unchanged.

F8

Topic 2Water uptake by dispersions3 of 3

Water sorption fitted with Flory–Huggins gives robust drug–water and polymer–water parameters, but not the drug–polymer parameter.

The binary Flory–Huggins sorption isotherm fitted each amorphous component with correlation coefficients above 0.985, giving interaction parameters χ with water (higher values mean less favourable mixing) of 3.27 for felodipine, 2.86 for indomethacin, 0.36 for PVP, 1.33 for HPMC and 1.62 for HPMCAS rumondor2010a R11, C18. In the ternary model the drug–polymer term carried only 0.029–0.160% of the interaction adjustment, so the drug–polymer parameter χ23 fitted to blend isotherms ranged from −9.6 to 26.9 for felodipine–PVP rumondor2010a R13, R14. The authors conclude that the method "cannot be used to unambiguously determine" drug–polymer interaction rumondor2010a C30.

moderateModerate: the insensitivity to χ23 follows from the model's own arithmetic and the scatter shows it directly, but the stated water–PVP value cannot be recovered from the plotted isotherm and the mean parameter has no fit statistics rumondor2010a K5, X5, X6, X10.

below the critical 0.5PVP 0.36HPMC 1.33HPMCAS 1.62indomethacin 2.86felodipine 3.2700.8751.752.6253.5Flory–Huggins χ with water, from sorption isotherms at 25 °C

The hydrophobic drugs mix strongly unfavourably with water; HPMC and HPMCAS lie above the critical 0.5, PVP below it. rumondor2010a R11, C18, C19, C20

felodipine–PVP0−9.6 to 26.9indomethacin–PVP0−20.4 to 22.0−25−20−15−10−5051015202530drug–polymer χ23 fitted to blend isotherms

Fitted values scatter over tens of units and change sign, so they carry no information on the drug–polymer interaction. rumondor2010a R14, C30

For your drug

  1. Take the drug–polymer χ from melting point depression or from solubility in a liquid analogue of the polymer, not from water sorption of the blend.
  2. Fit the binary isotherm of the neat amorphous drug to get its water χ; in the 2009 set every drug at 2.84 or above separated in PVP under humidity (F13).

rumondor2009c R24, C46

How it works and key numbers
  1. The ternary equation adds water–drug, water–polymer and drug–polymer terms; for indomethacin–PVP the water–drug share fell from 98.34% at 10% PVP to 42.64% at 90% PVP, while the drug–polymer share stayed between 0.034 and 0.160% rumondor2010a R13, C24.
  2. Because the χ23 term is mathematically small, any change in the other interactions on blending is absorbed by χ23, which "may not be physically meaningful or even show the correct trend" rumondor2010a C29, C31.
  3. The model also assumes that the pair interactions in the blend equal those of the binaries, which the authors consider "unlikely" rumondor2010a C26, C27.
  4. Treating the blend as one solid with a single mean water–blend parameter avoids this assumption; that parameter fell smoothly with polymer content (felodipine–PVP 3.27 → 0.37) rumondor2010a R15, C34, C36.
3.27 / 0.36χ with water of amorphous felodipine / PVPrumondor2010a R11
0.029–0.160%share of the drug–polymer term in the ternary adjustmentrumondor2010a R13
−9.6 to 26.9χ23 fitted for felodipine–PVPrumondor2010a R14

Connections to other chapters

Evidence: data, conditions and papers

Finding F8. Flory–Huggins analysis of water sorption gives robust drug–water and polymer–water interaction parameters, but cannot recover the drug–polymer parameter from blend isotherms

In short. The binary Flory–Huggins sorption isotherm fitted single amorphous components with correlation coefficients above 0.985, giving χ with water of 3.27 for felodipine, 2.86 for indomethacin, 0.36 for PVP, 1.33 for HPMC and 1.62 for HPMCAS rumondor2010a R11, C18; a 2009 study found drug–water χ of 2.50–3.58 for six drugs rumondor2009c R24. In the ternary model the drug–polymer term carried only 0.029–0.160% of the interaction adjustment, so χ23 fitted to blend isotherms ranged from −9.6 to 26.9 for felodipine–PVP and −20.4 to 22.0 for indomethacin–PVP, and the authors conclude the method "cannot be used to unambiguously determine" drug–polymer interaction rumondor2010a R13, R14, C30. A single mean water–blend parameter fell smoothly with polymer content (felodipine–PVP 3.27 → 0.37) rumondor2010a R15, C36.

Type. model result in 6 drugs and 3 polymers Strength. the insensitivity to χ23 follows from the model's own arithmetic and the χ23 scatter shows it directly (rumondor2010a K5: strong), but the stated water–PVP value cannot be recovered from the plotted isotherm, one row of the term table does not reproduce, and the mean parameter has no fit statistics (X5, X6, X10).

How it was shown

Rumondor and co-workers (2010) fitted the binary equation \ln(p/p_0) = \ln\phi_1 + (1 - 1/x_{12})\phi_2 + \chi_{12}\phi_2^{2} to each pure isotherm rumondor2010a E1, P4. They split the interaction terms of the ternary equation into water–drug, water–polymer and drug–polymer shares, fitted χ23 to the felodipine–PVP and indomethacin–PVP isotherms, and fitted one mean water–blend parameter per composition rumondor2010a E2, E3, E4, P5, P6, P7. Rumondor and co-workers (2009) computed drug–water χ from the 95% RH uptake of six amorphous drugs rumondor2009c E5, P13.

What the data show

The binary values put the hydrophobic drugs strongly unfavourable, HPMC and HPMCAS above the critical 0.5 and PVP below it rumondor2010a R11, C19, C20.

systemmethodresultids
felodipine, indomethacin, PVP, HPMC, HPMCASbinary FH fit, 25 °Cχ 3.27, 2.86, 0.36, 1.33, 1.62; r > 0.985rumondor2010a R11, C18
six drugsχ from 95% RH uptake2.84 (nifedipine) to 3.58 (pimozide); 2.50 (indomethacin)rumondor2009c R24
indomethacin–PVP, felodipine–PVPternary FH term sharesdrug–polymer share 0.029–0.160%rumondor2010a R13
sameχ23 fitted to blend isotherms−9.6 to 26.9 (felodipine–PVP); −20.4 to 22.0 (indomethacin–PVP)rumondor2010a R14
four blend seriesmean parameter χ1,233.27 → 0.37 (felodipine–PVP); → 1.32 (HPMC), → 1.61 (HPMCAS)rumondor2010a R15
Table 2 of rumondor2010a: share of the water–drug, water–polymer and drug–polymer terms in the ternary Flory–Huggins adjustment
Table 2 · rumondor2010ashare of the water–drug, water–polymer and drug–polymer terms in the ternary Flory–Huggins adjustment

The last column, the drug–polymer term, never exceeds 0.160% of the adjustment; the water–drug term dominates up to 75% PVP rumondor2010a R13.

Why

The ternary model assumes that the water–drug, water–polymer and drug–polymer interactions in the blend equal those of the binaries, which the authors consider "unlikely" rumondor2010a C26, C27. Since the χ23 term is mathematically small, any such change is absorbed by χ23, which "may not be physically meaningful or even show the correct trend" rumondor2010a C29, C31. The mean parameter "clearly shows" water affinity rising with polymer proportion and hygroscopicity rumondor2010a C39, C40.

Limits and transfer

25 °C, two drugs fitted with the ternary model, and no goodness of fit for the mean parameter; the stated water–PVP χ of 0.36 lies below every point value recomputed from the plotted PVP isotherm rumondor2010a X10, X5. Take drug–polymer χ from melting point depression or from solubility in a liquid analogue of the polymer, not from water sorption of the blend, and fit the binary isotherm of the neat amorphous drug to get its water χ.

How it was shown

Rumondor and co-workers (2010) fitted the binary equation \ln(p/p_0) = \ln\phi_1 + (1 - 1/x_{12})\phi_2 + \chi_{12}\phi_2^{2} to each pure isotherm (p/p0 0.15–0.85 or 0.95) with size ratios of 16.7 (felodipine) and 14.9 (indomethacin) rumondor2010a E1, P4. They used the ternary equation to predict indomethacin–PVP isotherms from the binary parameters and a literature drug–polymer χ, split its interaction terms into water–drug, water–polymer and drug–polymer shares, fitted χ23 to the felodipine–PVP and indomethacin–PVP isotherms, and fitted a pseudobinary equation with one mean parameter per composition, \ln a_1 = \ln\phi_1 + (1 - 1/x_{23})\phi_{23} + \chi_{1,23}\phi_{23}^{2} rumondor2010a E2, E3, E4, P5, P6, P7. Rumondor and co-workers (2009) computed drug–water χ from the 95% RH uptake of six amorphous drugs by the same literature method rumondor2009c E5, P13. Marsac and co-workers (2010) took a water–felodipine χ of about 3.3 from a Flory–Huggins fit of the 2008 sorption data marsac2010 R22, E3.

What the data show

The binary values rank the components as water would expect them: the hydrophobic drugs strongly unfavourable (felodipine 3.27, indomethacin 2.86), HPMC and HPMCAS above the critical 0.5, PVP below it rumondor2010a R11, C19, C20. Felodipine came out at 3.18 in the 2009 set and about 3.3 in the 2010 miscibility paper, within about 0.1 of the 2010 sorption value (synthesis: 3.27 − 3.18 = 0.09) rumondor2009c R24.b; marsac2010 R22. The other 2009 values were 2.84 (nifedipine), 2.85 (droperidol), 3.58 (pimozide), 2.50 (indomethacin) and 2.71 (ketoprofen) rumondor2009c R24. With the binary parameters and a literature χ23, the ternary model matched indomethacin–PVP at 25% PVP (3.8 against 3.6 g/100 g at 85% RH) but fell below it at 75% PVP (26.9 against 36.0) rumondor2010a R12.h, C22. In the term split the water–drug share fell from 98.34% at 10% PVP to 42.64% at 90% for indomethacin–PVP while the drug–polymer share stayed between 0.034 and 0.160%, and felodipine–PVP was almost the same (0.029–0.143%) rumondor2010a R13, C24. The mean parameter fell for felodipine–PVP from 3.27 through 2.41 (25%), 1.58 (50%) and 0.96 (75%) to 0.37, more steeply than for HPMC (to 1.32) or HPMCAS (to 1.61) rumondor2010a R15, C37.

papersystemmethod and conditionsresultids
rumondor2010afelodipine, indomethacin, PVP, HPMC, HPMCASbinary FH fit, 25 °Cχ 3.27, 2.86, 0.36, 1.33, 1.62; r > 0.985R11, C18
rumondor2009csix drugsχ from 95% RH uptake2.84 (nifedipine) to 3.58 (pimozide); 2.50 (indomethacin)R24
marsac2010water–felodipine, water–PVP, felodipine–PVPcited values≈3.3, ≈0.5 and slightly negativeR22
rumondor2010aindomethacin–PVP, felodipine–PVPternary FH term sharesdrug–polymer share 0.029–0.160%R13
rumondor2010asameχ23 fitted to blend isotherms−9.6 to 26.9 (felodipine–PVP); −20.4 to 22.0 (indomethacin–PVP)R14
rumondor2010afour blend seriesmean parameter χ1,233.27 → 0.37 (felodipine–PVP); → 1.32 (HPMC), → 1.61 (HPMCAS)R15
rumondor2010a (citing Crowley and Zografi)indomethacin, ursodeoxycholic acid, indapamide with PVPternary FH fitsdrug–PVP χ 1.27–1.49, suggesting limited miscibility of miscible blendsR16, R20

Figure

Table 2 of rumondor2010a: share of the water–drug, water–polymer and drug–polymer terms in the ternary Flory–Huggins adjustment
Table 2 · rumondor2010ashare of the water–drug, water–polymer and drug–polymer terms in the ternary Flory–Huggins adjustment

The last column, the drug–polymer term, never exceeds 0.160% of the adjustment; the water–drug term dominates up to 75% PVP rumondor2010a R13.

Fig. 10 of rumondor2010a: mean water–blend parameter against polymer content
Fig. 10 · rumondor2010amean water–blend parameter against polymer content

All four series fall smoothly from the drug value; the PVP series fall furthest rumondor2010a R15.

Why

The authors' account, with their hedges: the ternary model assumes that water–drug, water–polymer and drug–polymer interactions in the blend equal those of the binaries, which they consider "unlikely", because drug–polymer interactions "would most likely" change how water interacts with each component and water changes the drug–polymer interactions rumondor2010a C26, C27. Since the χ23 term is mathematically small, any such change is absorbed by χ23, which "may not be physically meaningful or even show the correct trend"; "It is hypothesized" that this explains the scatter rumondor2010a C29, C31. Treating the blend as one solid relaxes the assumption and needs no binary parameters, and the mean parameter "clearly shows" water affinity rising with polymer proportion and hygroscopicity rumondor2010a C34, C39, C40. (synthesis: the same small-term problem does not affect the drug–water parameter, which enters through the dominant term; that is why the drug–water χ could be used to sort drugs by separation risk in F13 while χ23 could not be measured this way.)

Conditions and limits

25 °C, two drugs fitted with the ternary model, one fitted χ1,23 per composition with no goodness of fit and no back-calculated isotherm rumondor2010a X10. The stated water–PVP χ of 0.36 lies below every point value (about 0.47–0.75) recomputed from the plotted PVP isotherm, and the felodipine row of the term table matches a water–felodipine χ of about 2.9 rather than 3.27; the RH and χ23 values behind the table are not stated rumondor2010a X5, X6, X7. The 2009 χ values depend on densities partly approximated as 0.9 of the crystal density rumondor2009c X4.

Counterexamples and conflicts

Crowley and Zografi's ternary fits gave positive drug–PVP χ for blends that IR, a single Tg and PXRD show to be miscible rumondor2010a R16, R20, an example of the problem rather than a counterexample. The water–PVP value differs from the literature value of about 0.5 used elsewhere in the library rumondor2010a R17; marsac2010 R22.

Transfer check

Take drug–polymer χ from melting point depression or from solubility in a liquid analogue of the polymer (see Miscibility and drug-polymer interactions F7 and F8), not from water sorption of the blend. Fit the binary isotherm of the neat amorphous drug to get its water χ; in the 2009 set every drug at 2.84 or above separated in PVP under humidity (F13) rumondor2009c R24, C46.

History

Hancock and Zografi (1993, outside the library) introduced the Flory–Huggins treatment of water sorption by amorphous solids, and Zhang and Zografi (2001) had noted that the ternary equation is insensitive to the third parameter for sugar–PVP rumondor2010a C16, R19. Rumondor and co-workers (2009) first used drug–water χ in the library, as a susceptibility marker rumondor2009c C46; Marsac and co-workers (2010) used water–drug against water–polymer χ for the Δχ argument (F13) marsac2010 C43; Rumondor and co-workers (2010) showed why the drug–polymer χ cannot come from the same data rumondor2010a C30.

Topic 3 of 5 · 3 findings · F9–F11

Effect of sorbed water on crystallization

F9

Topic 3Effect of sorbed water on crystallization1 of 3

Sorbed water speeds nucleation of amorphous felodipine about 20-fold up to 75% RH; crystal growth jumps above 80% RH.

Amorphous felodipine films nucleated about 20 times faster at 75% than at 0% RH (about 1.4 × 10⁵ → 2.9 × 10⁶ m⁻³ s⁻¹), nifedipine about 14 times faster konno2008 R1.a, R3.a, C11; marsac2008a R1.a. Crystal growth of neat felodipine films rose only about twofold from 13 to 80% RH, then reached 2.3–2.8 mm/min at 87–93% RH, with spherulites (radial crystal aggregates) giving way to needles of the same crystal form rumondor2010 R1, R2, R8, C8, C9. Cited sorption and Tg data show no break in that range, and the cause is "currently unknown" rumondor2010 C31, C33.

moderateModerate: the rates are direct and replicated, but the growth jump rests on few crystals with conflicting RH labels and a transition point with both morphologies konno2008 K1; rumondor2010 K1, K2, X1, X2, X13.

Neat felodipine films at 25 °C: crystal growth rate, mm/min13% RH0.03033% RH0.03552% RH0.04475% RH0.06680% RH0.066split conditionlabelled 84, 86 or 87% RHtwo needles 1.3; spherulites 0.04890% RHneedles2.893% RHneedles2.3

About twofold from 13 to 80% RH, then more than an order of magnitude higher, with a change from spherulites to needles. rumondor2010 R1.a, R1.f, R1.g, R1.h, R1.i, R1.j, R1.k, X1

Neat felodipine films at 22 °C: nucleation rate, m⁻³ s⁻¹0% RH1.4 × 10⁵11% RH1.6 × 10⁵33% RH2.7 × 10⁵58% RH9.8 × 10⁵75% RH2.9 × 10⁶

konno2008 R1.a, R4.a, R2.a, R4.h, R3.a

For your drug

  1. Measure nucleation or growth of the neat amorphous drug in films at the storage temperature at 0, 33, 58 and 75% RH, and growth also at 85–93% RH, watching for a change of crystal habit.
  2. A rate that rises tenfold or more between 0 and 75% RH marks a water-sensitive drug; a habit change with a jump in growth marks a regime that accelerated tests at 75% RH would not show.

rumondor2010 R1

How it works and key numbers
  1. Absorbed water plasticizes amorphous materials and raises molecular mobility, so growth "is expected" to rise with water, and this was "indeed observed" up to 80% RH rumondor2010 C23, C24.
  2. For nucleation, water may also raise the chemical potential of the drug, acting as an anti-solvent ("may") marsac2008a C26.
  3. Very small amounts of water had a "dramatic" effect on the drug alone: felodipine nucleation rose about 20-fold over 0–1.1 g/100 g water konno2008 C28; marsac2008a R5.b.
  4. Above 80% RH the abrupt rise and the change to needles "suggest a fundamental change in the mechanism of crystal growth", but neither water uptake nor Tg changes abruptly, and Tg (30 °C at 93% RH) stays above the experiment temperature rumondor2010 C31, C32, C33.
To feel the numbers. From 13 to 80% RH growth rose 0.066 ÷ 0.030 ≈ 2.2-fold, while nucleation rose 2.9 × 10⁶ ÷ 1.4 × 10⁵ ≈ 21-fold from 0 to 75% RH. At 2.8 mm/min a needle crosses a 10 mm film in 10 ÷ 2.8 ≈ 3.6 min.
≈20-foldrise of felodipine nucleation from 0 to 75% RHkonno2008 R1.a, R3.a, C11
0.030 → 0.066 mm/mingrowth of neat felodipine from 13 to 80% RHrumondor2010 R1.a, R1.f
2.3–2.8 mm/mingrowth as needles at 87–93% RHrumondor2010 R1, C9

Connections to other chapters

Evidence: data, conditions and papers

Finding F9. Sorbed water speeds nucleation and crystal growth of the amorphous drug, and growth of neat felodipine jumps 20–40-fold above about 80% RH without a break in water uptake or Tg

In short. Amorphous felodipine films nucleated about 20 times faster at 75% than at 0% RH (about 1.4 × 10⁵ → 2.9 × 10⁶ m⁻³ s⁻¹), nifedipine about 14 times faster (4.7 × 10⁵ → 6.8 × 10⁶) konno2008 R1.a, R3.a, C11; marsac2008a R1.a; per gram of water the drug alone was the most sensitive system (felodipine about 20-fold over 0–1.1 g/100 g) marsac2008a R5.b; konno2008 C28. Crystal growth of neat felodipine films rose only about twofold from 13 to 80% RH (about 0.030 → 0.066 mm/min) and then reached 2.3–2.8 mm/min at 87–93% RH, with spherulites giving way to needles of the same crystal form; cited sorption and Tg data show no break in that range, and the cause is "currently unknown" rumondor2010 R1, R2, R8, C8, C9, C31, C33.

Type. observation in 2 drugs Strength. direct, replicated rates (konno2008 K1: strong; rumondor2010 K1: strong), but the growth jump rests on few crystals with conflicting RH labels and a transition point with both morphologies (rumondor2010 K2: moderate; X1, X2, X13).

How it was shown

Konno and Taylor (2008) and Marsac and co-workers (2008) counted nucleation sites in spin-coated felodipine and nifedipine films at 0, 11, 33, 58 and 75% RH konno2008 P1, P3, P4; marsac2008a P1, P2, P3. Rumondor, Jackson and Taylor (2010) followed the radius of existing felodipine crystals in films on a humidity-controlled stage at 25 °C (about 13–93% RH) and compared crystals of the two shapes by Raman rumondor2010 P1, P3, P5, P6, R8.

What the data show

Up to 80% RH growth was "approximately log−linear" rumondor2010 R1.a, R1.f, C8. At the next condition five of seven crystals grew as tight spherulites at about 0.048 mm/min and two as needles at about 1.3 mm/min, with the same Raman peak positions rumondor2010 R1.g, R1.h, R8, C34.

systemmethod and conditionsresultids
felodipine filmsnucleation, 0 → 75% RH, 22 °C≈1.4 × 10⁵ → 2.9 × 10⁶ m⁻³ s⁻¹ (≈20-fold)konno2008 R1.a, R3.a, C11
nifedipine and felodipine filmsnucleation, 0 → 75% RHnifedipine 4.7 × 10⁵ → 6.8 × 10⁶; felodipine 1.4 × 10⁵ → 3.0 × 10⁶marsac2008a R1.a, R1.g
felodipine filmsrate against water content≈20-fold over 0–1.08 g/100 gmarsac2008a R5.b, C15
felodipine filmsgrowth on a humidity stage, 25 °C≈0.030 → 0.066 mm/min (13–80% RH); 2.3–2.8 mm/min at 87–93% RHrumondor2010 R1, C8, C9
cited felodipine datasorption and Tg against RHsmooth to ≈1.48 g/100 g and ≈29.6 °C at 94% RHrumondor2010 R9, R10, C31
Fig. 1 of rumondor2010: growth rate of amorphous felodipine against storage RH
Fig. 1 · rumondor2010growth rate of amorphous felodipine against storage RH

On the log axis the rate climbs slowly to 80% RH and then jumps more than an order of magnitude rumondor2010 R1.

Why

Absorbed water plasticizes amorphous materials and raises molecular mobility, so growth "is expected" to rise with water rumondor2010 C23, C24. The abrupt rise and the change to needles "suggest a fundamental change in the mechanism of crystal growth", but the reason is "currently unknown", since neither water uptake nor Tg changes abruptly and Tg stays above the experiment temperature rumondor2010 C31, C32, C33.

Limits and transfer

Uncovered thin films, which the authors take to report surface growth, much faster than bulk growth rumondor2010 C28, C29, C30. Bulk powder of pure amorphous felodipine crystallized completely within 12 days at 0% as well as 93% RH rumondor2009b R12, X8. Measure nucleation or growth of the neat amorphous drug at 0–75% RH, and growth also at 85–93% RH, watching for a change of crystal habit that accelerated tests at 75% RH would not show.

How it was shown

Konno and Taylor (2008) stored spin-coated felodipine films over phosphorus pentoxide or saturated salts at 0, 11, 33, 58 and 75% RH and 22 °C and counted nucleation sites as in F1 konno2008 P1, P3, P4. Marsac and co-workers (2008) did the same for nifedipine and felodipine and re-plotted the rates against water contents taken from bulk sorption isotherms marsac2008a P1, P2, P3, P9. Rumondor, Jackson and Taylor (2010) nucleated spherulites in spin-coated films on a 90 °C hot plate and then followed the radius of existing crystals at fixed RH, drug alone on a humidity-controlled stage at 25 °C (about 13–93% RH), from at least four time points per crystal and three or more crystals rumondor2010 P1, P3, P5. Raman microscopy compared crystals of the two shapes rumondor2010 P6, R8.

What the data show

Felodipine alone nucleated at about 1.4 × 10⁵ (0%), 1.6 × 10⁵ (11%), 2.7 × 10⁵ (33%), 9.8 × 10⁵ (58%) and 2.9 × 10⁶ m⁻³ s⁻¹ (75% RH) konno2008 R1.a, R4.a, R2.a, R4.h, R3.a. Marsac's felodipine series was almost the same (1.4 × 10⁵ → 3.0 × 10⁶), and nifedipine rose from 4.7 × 10⁵ to 6.8 × 10⁶ m⁻³ s⁻¹ marsac2008a R1.a, R1.g; the authors note that the pure drugs rose to a similar extent marsac2008a C11. Against water content, felodipine alone went from about 1.4 × 10⁵ to 2.9 × 10⁶ over 0–1.08 g/100 g and nifedipine from 4.9 × 10⁵ to 6.4 × 10⁶ over 0–1.79 g/100 g marsac2008a R5.a, R5.b. Neat felodipine crystals grew at about 0.030 (13% RH), 0.035 (33%), 0.044 (52%), 0.061 (≈67%), 0.066 (75%) and 0.066 mm/min (80%), "approximately log−linear" rumondor2010 R1.a, R1.f, C8. At the next condition five of seven crystals grew as tight spherulites at about 0.048 mm/min and two as needles at about 1.3 mm/min; at about 87, 90 and 93% RH growth was about 2.7, 2.8 and 2.3 mm/min rumondor2010 R1.g, R1.h, R1.i, R1.j, R1.k. Relative to 80% RH that is about 20-fold (needles) to 42-fold (90% RH), while the paper's lower bound of 15-fold is not explained rumondor2010 X2. Spherulite and needle gave the same Raman peak positions, read as the same phase rumondor2010 R8, C34. The cited felodipine data show sorption rising smoothly to about 1.48 g/100 g at 94% RH and Tg falling smoothly from about 45.7 to 29.6 °C, still above the 22–25 °C of the experiments rumondor2010 R9, R10, C31.

papersystemmethod and conditionsresultids
konno2008felodipine filmsnucleation, 0–75% RH, 22 °C≈1.4 × 10⁵ → 2.9 × 10⁶ m⁻³ s⁻¹ (≈20-fold)R1.a, R3.a, C11
marsac2008anifedipine and felodipine filmsnucleation, 0–75% RHnifedipine 4.7 × 10⁵ → 6.8 × 10⁶; felodipine 1.4 × 10⁵ → 3.0 × 10⁶R1.a, R1.g
marsac2008asamerate against water contentfelodipine ≈20-fold over 0–1.08 g/100 gR5.b, C15
rumondor2010felodipine filmsgrowth on a humidity stage, 25 °C≈0.030 → 0.066 mm/min (13–80% RH); 2.3–2.8 mm/min at 87–93% RHR1, C8, C9
rumondor2010cited felodipine datasorption and Tg against RHsmooth to ≈1.48 g/100 g and ≈29.6 °C at 94% RHR9, R10, C31
rumondor2009bpure amorphous felodipine powderstorage at 0% and 93% RHcompletely crystalline in less than 12 days at both (no data shown)R12, X8
correasoto2017 (outside)spray-dried HPMCAS dispersionSHG imaging, 40 °Cfaster crystallization at 82% than at 75% RHC15
moseson2022a (outside)coated and uncoated ASD powdersstorage at 40 °Cshorter onset at higher RH, read as moisture-enhanced mobilityC41

Figure

Fig. 1 of rumondor2010: growth rate of amorphous felodipine against storage RH
Fig. 1 · rumondor2010growth rate of amorphous felodipine against storage RH

On the log axis the rate climbs slowly to 80% RH and then jumps more than an order of magnitude; at about 84% RH five slow spherulites (grey) and two fast needles (black) coexist rumondor2010 R1.

Fig. 2 of konno2008: nucleation rate against storage RH for felodipine with and without polymer
Fig. 2 · konno2008nucleation rate against storage RH for felodipine with and without polymer

The drug-alone symbols (closed circles, top) rise with RH in each panel; every polymer content lies below them konno2008 R4, C11.

Why

The authors' account, with their hedges: absorbed water plasticizes amorphous materials and raises molecular mobility, so growth "is expected" to rise with water and this was "indeed observed" up to 80% RH rumondor2010 C23, C24. The abrupt rise and the change to needles "suggest a fundamental change in the mechanism of crystal growth", but the reason is "currently unknown", since neither water uptake nor Tg changes abruptly and Tg (30 °C at 93% RH) stays above the experiment temperature rumondor2010 C31, C32, C33. For nucleation, water is "anticipated" to raise the rate konno2008 C11; the 2008 PVP paper adds that water may also raise the drug's chemical potential, acting as an anti-solvent ("may") marsac2008a C26. Very small amounts of water had a large effect on the drug alone ("dramatic") konno2008 C28. (synthesis: up to 80% RH the growth rise is far smaller than the nucleation rise over the same span, about twofold against about 20-fold, so water acts more strongly on nucleation than on growth of neat felodipine at these conditions; the high-RH jump is a separate regime.)

Conditions and limits

Uncovered thin films, which the authors take to report surface growth, much faster than bulk growth rumondor2010 C28, C29, C30. Drug-alone growth was measured on a humidity stage at 25 °C, the polymer films over salts at room temperature, partly at different RH levels rumondor2010 X4. The split condition is labelled 84, 86 and 87% RH in different places rumondor2010 X1. Bulk powder of pure amorphous felodipine crystallized completely within 12 days at 0% as well as 93% RH, so at that time resolution humidity made no visible difference rumondor2009b R12, X8.

Counterexamples and conflicts

None found in the library for the direction of the effect. The pure-powder observation above limits it: water accelerates crystallization of the neat drug, but a neat glass that crystallizes within days dry leaves little room to see it rumondor2009b R12. For the PEO carrier, water dissolved crystalline drug rather than crystallizing amorphous drug (see PEG dispersions F11).

Transfer check

Measure nucleation or growth of the neat amorphous drug in films at the storage temperature at 0, 33, 58 and 75% RH, and growth also at 85–93% RH, watching for a change of crystal habit. A rate that rises tenfold or more between 0 and 75% RH, as for felodipine, marks a water-sensitive drug; a habit change with a jump in growth, as above 80% RH here, marks a regime that accelerated tests at 75% RH would not show rumondor2010 R1. Record the wet Tg at each RH (F6).

History

Andronis and co-workers (1997, outside the library) had shown sorbed water speeding crystallization of amorphous indomethacin marsac2008a C2. Konno and Taylor (2008) and Marsac and co-workers (2008) first measured the RH dependence of nucleation in the library konno2008 C11; marsac2008a C11; Rumondor and co-workers (2010) added growth and found the jump above 80% RH, "To our knowledge" not reported before rumondor2010 C10. Later work on coated and spray-dried dispersions saw shorter onsets at higher RH moseson2022a C41; correasoto2017 C15.

F10

Topic 3Effect of sorbed water on crystallization2 of 3

A polymer keeps felodipine nucleation below that of the drug alone at every humidity, although the dispersion holds more water.

At every RH from 0 to 75%, every felodipine film with 3–25% PVP, HPMC or HPMCAS nucleated more slowly than the drug alone, although it held more water konno2008 R3, C13. Against water content, the fitted lines climb about 23-fold over 0.7% water for the drug alone but about 10-fold over 4.7% water with 25% polymer konno2008 R14, C29. Nifedipine with 25% PVP did not flatten: its rate still rose about 250-fold from 0 to 75% RH marsac2008a C10.

moderateModerate: the result is direct and large in both papers, but the water contents of the films are estimated from bulk powders and the fitted lines pool polymers with R² 0.85–0.89 konno2008 K1, K6, X5, X6; marsac2008a K2.

rises steeply with RHrises littlefelodipine alone1.4 × 10⁵ → 2.9 × 10⁶felodipine + 3% PVP≈300×felodipine + 25% PVP3.1 × 10² → 2.4 × 10³felodipine + 25% HPMCAS11 to 75% RHnearly flatnifedipine + 25% PVP≈250×1001000100001000001e+061e+07nucleation rate from dry to 75% RH, m⁻³ s⁻¹ (log scale)

Each bar runs from the dry rate to the rate at 75% RH; every felodipine dispersion stays below the drug alone. konno2008 R3.a, R1.b, R3.b, R4.g, R3.g, C12; marsac2008a R5.b, R5.h, R1.f, C10, C15

For your drug

  1. Compare nucleation (or crystallinity after storage) of the dispersion and of the neat amorphous drug at 0 and 75% RH.
  2. A dispersion that stays at least tenfold below the neat drug at 75% RH and rises less than about tenfold from dry to 75% RH behaves like the 25% cellulose films here; a rise of two decades or more means the polymer level or type does not hold the water effect.

konno2008 R4.g, R3.g, C12; marsac2008a C10

How it works and key numbers
  1. The result is a competition between the polymer, an inhibitor, and water, an enhancer; at these levels the effect of the polymer dominates konno2008 C13; marsac2008a C27.
  2. The polymers "are still able" to inhibit when water has lowered Tg, which rules out Tg as the reason (see F5) konno2008 C27.
  3. For the flatter water dependence at high polymer content, water "may alter the kinetics of crystallization", or more polymer leaves the polymer–water co-solvent less rich in water ("may not remain as rich in water") and so lowers the supersaturation marsac2008a C44, C45, C46.
  4. At 75% RH the water fraction of that co-solvent was lower with 25% than with 10% PVP (nifedipine 18 against 23 wt%) marsac2008a R13, C45.
To feel the numbers. With 3% PVP the rate rose 8.6 × 10⁵ ÷ 2.9 × 10³ ≈ 300-fold from dry to 75% RH, against 2.9 × 10⁶ ÷ 1.4 × 10⁵ ≈ 21-fold for the drug alone: a little hygroscopic polymer made the film more sensitive to humidity, not less.
2.3 × 10³ vs 2.9 × 10⁶ m⁻³ s⁻¹felodipine with 25% PVP vs alone at 75% RHkonno2008 R3, C13
≈23× vs ≈10×rise over 0.7% water (drug alone) vs over 4.7% water (25% polymer)konno2008 R14, C29
≈300-foldrise with RH for felodipine with only 3% PVPkonno2008 C12

Connections to other chapters

Evidence: data, conditions and papers

Finding F10. A polymer keeps nucleation below that of the drug alone at every humidity although it brings more water, and more polymer makes nucleation less sensitive to water for felodipine but not for nifedipine–PVP

In short. At every RH from 0 to 75%, every felodipine film with 3–25% PVP, HPMC or HPMCAS nucleated more slowly than the drug alone, although it held more water; at 75% RH 25% polymer gave about 2.3 × 10³ (PVP), 3.5 × 10² (HPMCAS) and 7.2 × 10² m⁻³ s⁻¹ (HPMC) against 2.9 × 10⁶ for felodipine alone konno2008 R3, C13. Plotted against water content, the fitted lines climb about 23-fold over 0.7% water for the drug alone but about 10-fold over 4.7% water with 25% polymer konno2008 R14, C29, and felodipine with 25% PVP rose about eightfold over 4.6 g/100 g marsac2008a R5.h, C15. For nifedipine with 25% PVP the rate still rose about 250-fold from 0 to 75% RH, and 3% PVP made felodipine more RH-sensitive than the drug alone (about 300-fold) marsac2008a C10; konno2008 C12.

Type. observation in 2 drugs and 3 polymers Strength. the competition result is direct and large in both papers (konno2008 K1: strong; marsac2008a K2: moderate to strong), but the water contents of the films are estimated from bulk powders and the fitted lines pool polymers with R² 0.85–0.89 (konno2008 K6: moderate; X5, X6).

How it was shown

Konno and Taylor (2008) counted nucleation in felodipine films with 0–25% PVP, HPMC or HPMCAS at 0–75% RH and plotted the rates against water contents estimated from isotherms of bulk dispersions konno2008 P3, P4, P8, R14. Marsac and co-workers (2008) did the same with 7–25% PVP for nifedipine and felodipine marsac2008a P2, P3, P9, R5.

What the data show

After 75% RH every film with up to 25% polymer had a Tg below dry felodipine, yet the cellulose films and PVP films above 7% still nucleated more slowly than dry felodipine konno2008 R7, C27, X9.

systemmethod and conditionsresultids
felodipine, 25% polymer, 75% RHnucleation, films, 22 °CPVP ≈2.3 × 10³, HPMCAS ≈3.5 × 10², HPMC ≈7.2 × 10² vs drug ≈2.9 × 10⁶konno2008 R3.g, R3.a
felodipine, 0, 7, 15, 25% polymerrate vs estimated water content≈23-fold over 0.7% water (drug) vs ≈10-fold over 4.7% (25% polymer)konno2008 R14, C29
felodipine, 3% PVPnucleation, dry → 75% RH≈2.9 × 10³ → ≈8.6 × 10⁵, steeper than the drug alonekonno2008 R1.b, R3.b, C12
felodipine, 25% PVPrate vs water≈3.1 × 10² → 2.4 × 10³ over 0–4.61 g/100 gmarsac2008a R5.h, C15
nifedipine, 25% PVPrate vs RH≈1.7 × 10³ → 4.3 × 10⁵ (≈250-fold)marsac2008a R1.f, C10
Fig. 12 of konno2008: nucleation rate against water content, grouped by polymer content
Fig. 12 · konno2008nucleation rate against water content, grouped by polymer content

The drug-alone line (×) rises steeply over less than 1% water; with more polymer the lines flatten although they extend to more water konno2008 R14.

Why

The result is a competition between the polymer, an inhibitor, and water, an enhancer, and at these levels the effect of the polymer dominates konno2008 C13; marsac2008a C27. For the flatter water dependence at high polymer content the 2008 PVP paper gives two explanations: water "may alter the kinetics of crystallization", or more polymer leaves a drier co-solvent ("may not remain as rich in water") and so a lower supersaturation marsac2008a C44, C45, C46.

Limits and transfer

Water contents and Tg come from bulk powders konno2008 X6; marsac2008a X12. At 3% PVP and 75% RH the rate was only about threefold below the drug alone, so a low level of a hygroscopic polymer can make a dispersion more water-sensitive than the neat drug konno2008 R3.b, C12. Compare nucleation of the dispersion and of the neat drug at 0 and 75% RH; a rise of two decades or more, as for 3% PVP or nifedipine–PVP, means the polymer level or type does not hold the water effect.

How it was shown

Konno and Taylor (2008) counted nucleation in films with 0–25% of each polymer at 0, 11, 33, 58 and 75% RH and plotted the rates against water contents estimated from isotherms of bulk dispersions, with one regression line per polymer content konno2008 P3, P4, P8, R14. Marsac and co-workers (2008) did the same with 7–25% PVP for nifedipine and felodipine marsac2008a P2, P3, P9, R5.

What the data show

With 25% HPMCAS the rate stayed at about 2.9–3.5 × 10² m⁻³ s⁻¹ from 11 to 75% RH and with 25% HPMC it rose from about 2.9 × 10² to 7.2 × 10², slopes the authors call close to zero konno2008 R4.g, R3.g, R4.n, C12. Every film with up to 25% polymer had a Tg below dry felodipine after 75% RH, yet the cellulose films and PVP films above 7% still nucleated more slowly than dry felodipine; for 10% PVP the margin was small (about 1.0 × 10⁵ against 1.4 × 10⁵) konno2008 R7, C27, X9. The regression lines of rate against water run from about 1.2 × 10⁵ to 2.7 × 10⁶ (0–0.68% water) for the drug alone, 1.8 × 10³ to 5.9 × 10⁴ (0–1.68%) at 7%, 8.8 × 10² to 1.4 × 10⁴ (0–2.61%) at 15% and 2.4 × 10² to 2.3 × 10³ (0–4.69%) at 25% polymer konno2008 R14. For felodipine–PVP the 2008 PVP study gave 1.4 × 10⁵ → 2.9 × 10⁶ over 0–1.08 g/100 g water (pure), 1.0 × 10³ → 1.4 × 10⁵ over 0–1.64 (7%) and 3.1 × 10² → 2.4 × 10³ over 0–4.61 (25%) marsac2008a R5.b, R5.d, R5.h; nifedipine with 25% PVP went from 1.9 × 10³ to 4.4 × 10⁵ over 0–5.46 g/100 g marsac2008a R5.g. With PVP the polymer benefit outweighed the water it brought, which stayed below about 6% marsac2008a C27. At 75% RH the water fraction of the polymer–water co-solvent was lower with 25% than with 10% PVP (nifedipine 18 against 23 wt%) marsac2008a R13, C45.

papersystemmethod and conditionsresultids
konno2008felodipine, 25% polymer, 75% RHnucleation, films, 22 °CPVP ≈2.3 × 10³, HPMCAS ≈3.5 × 10², HPMC ≈7.2 × 10² vs drug ≈2.9 × 10⁶R3.g, R3.a
konno20080, 7, 15, 25% polymerrate vs estimated water content≈23-fold over 0.7% water (drug) vs ≈10-fold over 4.7% (25% polymer)R14, C29
konno20083% PVP, 11 → 75% RHnucleation≈2.9 × 10³ (dry) → ≈8.6 × 10⁵, steeper than the drug aloneR1.b, R3.b, C12
marsac2008afelodipine, 25% PVPrate vs water≈3.1 × 10² → 2.4 × 10³ over 0–4.61 g/100 gR5.h, C15
marsac2008anifedipine, 25% PVPrate vs RH≈1.7 × 10³ → 4.3 × 10⁵ (≈250-fold)R1.f, C10
marsac2008anifedipine, 10 and 25% PVP, 75% RHco-solvent water fraction23 vs 18 wt% waterR13, E6

Figure

Fig. 12 of konno2008: nucleation rate against water content, grouped by polymer content
Fig. 12 · konno2008nucleation rate against water content, grouped by polymer content

The drug-alone line (×) rises steeply over less than 1% water; with more polymer the lines flatten although they extend to more water, and within each content the three polymers lie near one line konno2008 R14.

Fig. 4 of marsac2008a: nucleation rate against sorbed water for 0, 7, 15 and 25% PVP
Fig. 4 · marsac2008anucleation rate against sorbed water for 0, 7, 15 and 25% PVP

Steep rises for the pure drugs (diamonds), flatter ones with 25% PVP (circles); open symbols nifedipine, filled felodipine marsac2008a R5.

Why

The authors' account, with their hedges: the result is a competition between the polymer, an inhibitor, and water, an enhancer, and at these levels the effect of the polymer dominates konno2008 C13; marsac2008a C27. The polymers "are still able" to inhibit when Tg is reduced, which rules out Tg as the reason konno2008 C27 (see F5). For the flatter water dependence at high polymer content the 2008 PVP paper gives two explanations: water "may alter the kinetics of crystallization", or, thermodynamically, more polymer leaves a drier co-solvent ("may not remain as rich in water") and so a lower supersaturation marsac2008a C44, C45, C46. The kinetic reading of the dry state, a polymer-raised barrier, "presumably" holds with water present as well marsac2008a C29. (synthesis: nifedipine–PVP did not flatten, which fits the co-solvent picture in which nifedipine dispersions, with wetter co-solvents, gain more supersaturation from water marsac2008a C48, but the two explanations were not separated.)

Conditions and limits

Films at 22 °C (the 2008 PVP paper also states 25 °C), polymer up to 25%, RH up to 75%; water contents and Tg come from bulk powders, and the PVP water values of konno2008 differ between figures konno2008 X2, X6; marsac2008a X1, X12. The regression form of the lines is not stated konno2008 X5.

Counterexamples and conflicts

At 3% PVP and 75% RH the rate (about 8.6 × 10⁵) was only about threefold below the drug alone and rose more steeply with RH than the drug alone did konno2008 R3.b, C12, so a low level of a hygroscopic polymer can make a dispersion more water-sensitive than the neat drug. At 86% RH the growth rates of 2.5% and 10% PVP films equalled those of the drug-alone spherulites rumondor2010 C20, X3 (see F11).

Transfer check

Compare nucleation (or crystallinity after storage) of the dispersion and of the neat amorphous drug at 0 and 75% RH. A dispersion that stays at least tenfold below the neat drug at 75% RH and rises less than about tenfold from dry to 75% RH behaves like the 25% cellulose films here konno2008 R4.g, R3.g; a rise of two decades or more, as for 3% PVP or nifedipine–PVP, means the polymer level or type does not hold the water effect konno2008 C12; marsac2008a C10.

History

Konno and Taylor (2008) and Marsac and co-workers (2008) published the competition between polymer and water in the same year, for three polymers and for two drugs konno2008 C13; marsac2008a C27. Rumondor and co-workers (2009, 2010) carried the comparison to bulk crystallization and growth and found that it breaks down at high RH (F11) rumondor2009b C13; rumondor2010 C14.

F11

Topic 3Effect of sorbed water on crystallization3 of 3

PVP equals or beats HPMCAS when dry but becomes the weaker inhibitor in humid storage.

At 75% RH felodipine with 3% PVP nucleated at about 8.6 × 10⁵ m⁻³ s⁻¹ against 1.3 × 10⁴ with HPMCAS, whereas dry the polymers were equal konno2008 R1, R3, C9, C10. Crystal growth followed: PVP was the better growth inhibitor below 52% RH and HPMCAS above about 64% RH rumondor2010 R3, R5, C14. In bulk powders stored about 490 days, PVP dispersions at 75–93% RH reached 51–82% crystallinity against 9–28% for HPMCAS rumondor2009b R9, C12, C13.

strongStrong: nucleation, growth and PXRD crystallinity show the same switch, although the crossover RH depends on polymer content and the statistical statements are not backed by printed tests konno2008 K2; rumondor2009b K1, K2, X3; rumondor2010 K6, X8.

PVP dispersionHPMCAS dispersion0–52% RH25 and 50% polymer1.1–5.08.6–10.775% RH25% polymer13.968.686% RH25% polymer16.477.293% RH25% polymer27.782.1020406080100felodipine crystallized after about 490 days, % (PXRD)

Up to 52% RH the polymers did not differ significantly; from 75% RH the PVP dispersions crystallized several times more. rumondor2009b R9, R19, X4

10% PVP10% HPMCAS13% RH5.8 × 10⁻⁵1.3 × 10⁻³93% RH2.4 × 10⁻³7.3 × 10⁻²1e−050.00010.0010.010.11felodipine crystal growth with 10% polymer, mm/min (log scale)

PVP gives the slower growth at 13% RH and the faster growth at 93% RH; the HPMCAS films show no trend with RH. rumondor2010 R5.a, R3.a, R5.g, R3.g, C13, C19

For your drug

  1. Rank candidate polymers at the intended storage humidity, at least 75% RH for open storage, not dry: dry data could not separate PVP from HPMCAS for felodipine in about 490 days.
  2. Expect PVP or another hygroscopic polymer to lose ground for a drug whose only hydrogen-bond donor is an NH group; for drugs with strong acid or free phenolic donors PVP may hold, but not when the donors are bound inside the molecule, as for curcumin.

rumondor2009b R19; wegiel2014 C33

How it works and key numbers
  1. For nucleation the differences between polymers "appear to be reasonably explained" by the water content of the dispersions, PVP bringing the most, "although it must be conceded that there is considerable scatter" konno2008 C30, C31.
  2. For growth, the dry advantage of PVP "may arise because" it forms stronger specific interactions with felodipine, and absorbed water "may result in disruption" of these interactions rumondor2010 C40, C42.
  3. HPMCAS "may" keep its interaction because its many donors and acceptors can bind water, or "may" adsorb on growth sites ("It is speculated") rumondor2010 C37, C38, C44.
  4. For bulk powders "It is hypothesized" that the more hygroscopic PVP dispersions undergo moisture-induced drug–polymer immiscibility in addition to a lower Tg (F12, F15); none of these was measured on the stored samples rumondor2009b C22, X7; konno2008 X4; rumondor2010 X12.
8.6 × 10⁵ vs 1.3 × 10⁴ m⁻³ s⁻¹felodipine with 3% PVP vs 3% HPMCAS at 75% RHkonno2008 R3.b, C10
51–82% vs 9–28%crystallized after about 490 days at 75–93% RH, PVP vs HPMCASrumondor2009b R9, C13
≈120 vs 6 dayscelecoxib with PVP vs HPMCAS at 80 °C/0% RH; reversed at 94% RHxie2016b R22, R23

Connections to other chapters

Evidence: data, conditions and papers

Finding F11. In humid storage the hygroscopic polymer loses its advantage: PVP equals or beats HPMCAS when dry but is the weaker inhibitor of felodipine from about 64–75% RH and of celecoxib at 94% RH

In short. Dry, PVP, HPMC and HPMCAS were equal nucleation inhibitors for felodipine; at 75% RH 3% PVP gave about 8.6 × 10⁵ m⁻³ s⁻¹ against 1.3 × 10⁴ (HPMCAS) and 2.0 × 10⁴ (HPMC), the gap shrinking to about sevenfold at 25% konno2008 R1, R3, C9, C10. Crystal growth followed: PVP was the better growth inhibitor below 52% RH (10%: about 5.8 × 10⁻⁵ against 1.3 × 10⁻³ mm/min at 13% RH) and HPMCAS above about 64% RH (10%: about 2.4 × 10⁻³ against 7.3 × 10⁻² mm/min at 93% RH) rumondor2010 R3, R5, C14. In bulk powders stored up to about 490 days, 25 and 50% PVP and HPMCAS dispersions crystallized about 11% or less at 0–52% RH, while at 75–93% RH the PVP dispersions reached 51–82% against 9–28% for HPMCAS rumondor2009b R9, C12, C13. For celecoxib the switch appeared only at the highest humidity: PVP dispersions lasted about 120 days at 80 °C/0% RH against 6 days for HPMCAS and under a month against 115 days at room temperature/94% RH, while at 40 °C/75% RH PVP still outlasted HPMCAS (70 against 33 days) xie2016b R22, R23, R24.

Type. observation in 1 drug and 3 polymers by three methods, and in celecoxib and lumefantrine by storage Strength. three independent measurements (nucleation, growth, PXRD crystallinity) show the same switch (konno2008 K2: strong; rumondor2009b K1, K2: strong; rumondor2010 K6: moderate), although the crossover RH depends on polymer content and the statistical statements are not backed by printed tests (rumondor2010 X8; rumondor2009b X3).

How it was shown

Konno and Taylor (2008) counted nucleation in films konno2008 P4. Rumondor and co-workers (2010) measured felodipine growth in films with 2.5, 5 and 10% w/w PVP or HPMCAS at 13–93% RH rumondor2010 P2, P4, P5. Rumondor and co-workers (2009) stored felodipine dispersions with 10–50 wt% PVP or HPMCAS at 0–93% RH for up to 724 days and quantified crystalline felodipine by PXRD rumondor2009b P1, P3, P5. Xie and Taylor (2016) stored celecoxib dispersions at three conditions xie2016b P5, A4.

What the data show

At 75% RH the PVP/HPMCAS nucleation ratio fell from about 66-fold at 3% to 7-fold at 25% polymer konno2008 R3.b, R3.g, C10. PVP growth rates rose with RH at every level, while 10% HPMCAS stayed at about 3.7 × 10⁻⁴ to 2.4 × 10⁻³ mm/min with no trend rumondor2010 R5, R3, C13, C19.

systemmethod and conditionsresultids
felodipine, 3% polymernucleation, dry and 75% RHdry ≈2.5–2.9 × 10³ for all; 75% RH PVP ≈8.6 × 10⁵ vs HPMCAS ≈1.3 × 10⁴, HPMC ≈2.0 × 10⁴konno2008 R1.b, R3.b
felodipine, 10% PVP vs 10% HPMCASgrowth, 13% and 93% RH5.8 × 10⁻⁵ vs 1.3 × 10⁻³ (13%); 7.3 × 10⁻² vs 2.4 × 10⁻³ mm/min (93%)rumondor2010 R5.a, R3.a, R5.g, R3.g
felodipine, 25% and 50% PVP or HPMCASPXRD-PLS crystallinity after ≈490 days0–52% RH ≤11% for all; 75–93% RH PVP 50.8–82.1% vs HPMCAS 9.2–27.7%rumondor2009b R9, C12, C13
celecoxib, 80% drug, PVP vs HPMCAS80 °C/0% RH, PXRD≈120 vs 6 daysxie2016b R22, C38
celecoxib, 60% drugRT/94% RHPVP under a month; HPMCAS 115; PVPVA 150 daysxie2016b R23, C41
celecoxib, 80% drug40 °C/75% RHPVPVA ≈4 months; PVP 70; HPMCAS 33 daysxie2016b R24, C42
Table 1 of rumondor2009b: felodipine crystallized at the last time point for every system and RH
Table 1 · rumondor2009bfelodipine crystallized at the last time point for every system and RH

Read across the 75–93% RH rows: PVP columns 51–82%, HPMCAS columns 9–28%; at 0–52% RH every value is about 11% or less except 10% PVP, read at 724 days rumondor2009b R9, X10, X12.

Why

For nucleation the differences between polymers "appear to be reasonably explained" by the water content of the dispersions konno2008 C30. For growth, absorbed water "may result in disruption" of the specific interactions that PVP forms with felodipine rumondor2010 C40, C42. For bulk crystallization, "It is hypothesized" that the more hygroscopic PVP dispersions undergo moisture-induced drug–polymer immiscibility (F12, F15) rumondor2009b C22. None of these was measured on the stored samples konno2008 X4; rumondor2010 X12; rumondor2009b X7.

Limits and transfer

The ranking depends on the drug: polyphenols with strong OH donors stayed amorphous with PVP for more than 200–450 days under humidity while the HPMCAS dispersions crystallized within days wegiel2013a R9, C22, C40. Rank candidate polymers at the intended storage humidity, at least 75% RH for open storage, not dry, and expect a hygroscopic polymer to lose ground for a drug whose only hydrogen-bond donor is an NH group, as felodipine.

How it was shown

Konno and Taylor (2008) counted nucleation as in F10 konno2008 P4. Rumondor, Jackson and Taylor (2010) measured growth of felodipine crystals in films with 2.5, 5 and 10% w/w PVP or HPMCAS stored over saturated salts at 13, 33, 52, 64, 75, 86 and 93% RH at room temperature rumondor2010 P2, P4, P5. Rumondor, Stanford and Taylor (2009) made felodipine dispersions with 10, 25 and 50 wt% PVP or HPMCAS by rotary evaporation, cryomilled them below 150 µm, stored them at 0–93% RH and 22–25 °C for up to 724 days, and quantified crystalline felodipine by PXRD with one PLS model per composition (RMSEP 3.7–5.3%), testing differences by F-test rumondor2009b P1, P2, P3, P5, P6, R4. Xie and Taylor (2016) stored celecoxib dispersions in open vials at 80 °C/0% RH, room temperature/94% RH and 40 °C/75% RH and read crystallinity by PXRD xie2016b P5, A4; Trasi and co-workers (2020) stored lumefantrine powders open at 40 °C/75% RH trasi2020 P14.

What the data show

Nucleation: at 33% RH, 3% polymer already separated PVP (about 2.0 × 10⁴) from HPMC (8.0 × 10³) and HPMCAS (6.5 × 10³); at 58% RH the PVP/HPMCAS ratio at 3% was about 26-fold; at 75% RH it fell from about 66-fold at 3% to 11-fold at 15% and 7-fold at 25% konno2008 R2.b, R4.i, R3.b, R3.e, R3.g, C10. Growth: at 13% RH 2.5, 5 and 10% PVP gave about 7.0 × 10⁻³, 6.7 × 10⁻⁴ and 5.8 × 10⁻⁵ mm/min, about two orders of magnitude across the PVP range, against 3.4 × 10⁻², 7.3 × 10⁻³ and 1.3 × 10⁻³ with HPMCAS rumondor2010 R5.a, R3.a, C18. PVP rates rose with RH at every level (10% PVP: 5.8 × 10⁻⁵ at 13% to 7.3 × 10⁻² mm/min at 93% RH), while 10% HPMCAS stayed at about 3.7 × 10⁻⁴ to 2.4 × 10⁻³ mm/min with no trend rumondor2010 R5, R3, C13, C19. At 52% RH the order depended on content (2.5%: PVP lower; 10%: HPMCAS lower), and from 75% RH every HPMCAS level lay below the matching PVP level rumondor2010 R3.c, R5.c, X8. Bulk crystallization: at 0, 33 and 52% RH 25 and 50% PVP reached 1.1–5.0% and the HPMCAS dispersions 8.6–10.7% after about 490 days, not significantly different within about two RMSEP; at 75, 86 and 93% RH 25% PVP reached 68.6, 77.2 and 82.1% against 13.9, 16.4 and 27.7% for 25% HPMCAS, and 50% PVP 50.8, 78.4 and 75.1% against 10.6, 9.2 and 16.6% for 50% HPMCAS rumondor2009b R9, R19, X4. 10% PVP, stored up to 724 days, reached 14.2% at 0% RH and 58.0–73.8% at 66–93% RH rumondor2009b R9, X10.

Celecoxib at 60–80% drug gave the same switch at a higher humidity. At 80 °C/0% RH and 80% drug the PVP and PVPVA dispersions showed crystals after about 120 days and the HPMCAS and HPMC ones after 6 days; at room temperature/94% RH and 60% drug PVPVA lasted 150 days, HPMCAS 115 days, and PVP and HPMC under a month; at 40 °C/75% RH and 80% drug PVPVA lasted about 4 months, PVP 70 days and HPMCAS 33 days xie2016b R22, R23, R24, C38, C41, C42. For the weak base lumefantrine the neutral PVPVA dispersion crystallized within 1 week at 40 °C/75% RH while HPMCP, Eudragit L100 and CAP held 40% drug for 3 months (see F34) trasi2020 R3.

papersystemmethod and conditionsresultids
konno2008felodipine, 3% polymernucleation at 0, 33, 75% RHdry ≈2.5–2.9 × 10³ for all; 75% RH PVP ≈8.6 × 10⁵ vs HPMCAS ≈1.3 × 10⁴, HPMC ≈2.0 × 10⁴R1.b, R3.b
konno2008felodipine, 25% polymer, 75% RHsame≈2.3 × 10³ vs 3.5 × 10² and 7.2 × 10²R3.g
rumondor2010felodipine, 10% PVP vs 10% HPMCASgrowth, 13% and 93% RH5.8 × 10⁻⁵ vs 1.3 × 10⁻³ (13%); 7.3 × 10⁻² vs 2.4 × 10⁻³ mm/min (93%)R5.a, R3.a, R5.g, R3.g
rumondor2009b25% and 50% PVP or HPMCASPXRD-PLS crystallinity after ≈490 days0–52% RH ≤11% for all; 75–93% RH PVP 50.8–82.1% vs HPMCAS 9.2–27.7%R9, C12, C13
rumondor2009b50% HPMCASsamenegligible crystals for 35–120 days at 52–93% RH, then a slow riseR17, C11
wegiel2014curcumin 75:25 with PVP, HPMC, HPMCAS, CMCAB, E100PXRD, days to first crystalline peaks84% RH/25 °C: PVP 22, cellulosics 75 (partial), E100 > 350; 50 °C dry: PVP 6, HPMCAS and CMCAB 75, HPMC and E100 > 350R13, C24
wegiel2013bresveratrol with PVP K29/32, PVP K-12, E100 vs HPMC, HPMCAS, CMCAB, PAAPXRD after storage at 84% RH/25 °CPVP and E100 > 100–400 days without crystals; the others crystalline at day 1R12, C35
xie2016bcelecoxib 80% drug, PVP vs HPMCAS80 °C/0% RH, PXRD≈120 vs 6 daysR22, C38
xie2016bcelecoxib 60% drugRT/94% RHPVP under a month; HPMCAS 115; PVPVA 150 daysR23, C41
xie2016bcelecoxib 80% drug40 °C/75% RHPVPVA ≈4 months; PVP 70; HPMCAS 33 daysR24, C42
trasi2020lumefantrine 40:60 with PVPVA vs enteric polymers40 °C/75% RHPVPVA crystals at 1 week; HPMCP, L100, CAP amorphous 3 monthsR3, C6
wegiel2013a (outside)naringenin and quercetin with PVP or E100 vs HPMCAS, HPMC, CMCAB, PAAstorage at 84% RH/25 °C and 75% RH/40 °CPVP and E100 dispersions crystal-free > 200–450 days; the others crystallized in 1–3 daysR9, C22
hiew2022a (outside)lumefantrine with PVPVA vs enteric polymers40 °C/75% RHPVPVA dispersions crystallized after 1–8 weeks; enteric ones only at 50% loadingR6, C10

Figure

Table 1 of rumondor2009b: felodipine crystallized at the last time point for every system and RH
Table 1 · rumondor2009bfelodipine crystallized at the last time point for every system and RH

Read across the 75–93% RH rows: PVP columns 51–82%, HPMCAS columns 9–28%; at 0–52% RH every value is about 11% or less except 10% PVP, which was read at 724 days rumondor2009b R9, X10, X12.

Fig. 5 of rumondor2010: growth rate against RH for 2.5, 5 and 10% PVP films and drug alone
Fig. 5 · rumondor2010growth rate against RH for 2.5, 5 and 10% PVP films and drug alone

At 13% RH the three PVP levels span two decades; they rise with RH and converge from about 64% RH rumondor2010 R5.

Why

The authors' account, with their hedges: for nucleation the differences between polymers "appear to be reasonably explained" by the water content of the dispersions, PVP bringing the most, "although it must be conceded that there is considerable scatter"; "These results suggest" that polymer chemistry matters only through moisture sorption konno2008 C30, C31. For growth, PVP's dry advantage "may arise because" it forms stronger specific interactions with felodipine, and absorbed water "may result in disruption" of these interactions, which PVP binds strongly; HPMCAS "may" keep its interaction because its many donors and acceptors can bind water, or "may" adsorb on growth sites ("It is speculated") rumondor2010 C40, C42, C37, C38, C44. For bulk crystallization, "It is hypothesized" that the more hygroscopic PVP dispersions undergo moisture-induced drug–polymer immiscibility in addition to a lower Tg (F12, F15) rumondor2009b C22. None of these was measured on the stored samples konno2008 X4; rumondor2010 X12; rumondor2009b X7. (synthesis: the three readings are compatible: PVP brings more water, the water weakens or breaks the felodipine–PVP bond, and where the bond breaks the dispersion separates; the separation itself is shown in F12.) For celecoxib the authors read the 40 °C/75% RH order as showing that drug–polymer interactions "became the dominant factor" there, where the difference in water uptake between PVP and HPMCAS dispersions is smaller than at 94% RH xie2016b C53.

Conditions and limits

One drug, felodipine, an NH donor; 2.5–50% polymer; room temperature konno2008 M1; rumondor2009b A2; rumondor2010 A2. At 7% polymer and similar water content PVP still nucleated faster than the cellulose polymers, so water content does not explain everything konno2008 X4. For 25% HPMCAS the extent rose from 8.6% (0% RH) to 27.7% (93% RH) and was still rising after 490 days, so "no RH effect" holds for 50% HPMCAS only rumondor2009b X3, R20.

Counterexamples and conflicts

The ranking depends on the drug: polyphenols with strong OH donors stayed amorphous with PVP for more than 200–450 days under humidity while the HPMCAS dispersions crystallized within days wegiel2013a R9, C22, C40 (see Miscibility and drug-polymer interactions F23). (synthesis: this fits F13, where drugs with stronger acid donors resisted moisture-induced separation in PVP.) Resveratrol, a phenol, behaved the same way: PVP K29/32 and K-12 dispersions showed no crystals at 84% RH for more than 100–400 days while every HPMC, HPMCAS, CMCAB and PAA dispersion held crystals at the first sampling, a contrast the authors call the opposite of the felodipine result and explain either by hydrogen bonds that suppress water sorption or by the lower hydrophobicity of resveratrol (log P 3.1 against 4.5), which may keep it from separating ("Possible explanations") wegiel2013b R12, R20, C35, C36 (see F24). For curcumin, on the other hand, PVP was the poorest inhibitor both humid (22 days at 84% RH against 75 days for the cellulose polymers) and dry at 50 °C (6 against 75 days or more) wegiel2014 R13, C24, so its failure there is not a humidity switch. The weak base lumefantrine, without a specific contact with PVPVA, crystallized from PVPVA within 1–8 weeks hiew2022a R6, C10 (see Miscibility and drug-polymer interactions F26). The humidity at which PVP falls behind depends on the drug: about 64–75% RH for felodipine, above 75% RH for celecoxib xie2016b R24, C53.

Transfer check

Rank candidate polymers at the intended storage humidity, at least 75% RH for open storage, not dry: dry data could not separate PVP from HPMCAS for felodipine in about 490 days rumondor2009b R19. Expect PVP or another hygroscopic polymer to lose ground for a drug whose only hydrogen-bond donor is an NH group, as felodipine; for drugs with strong acid or free phenolic donors PVP may hold (see F13 and F24), but not when the drug's donors are bound inside the molecule, as for curcumin wegiel2014 C33. Measure the dispersion's water uptake at the storage RH and the drug–polymer IR bands after storage.

History

Konno and Taylor (2006) found the three polymers equal when dry konno2006 C14. Konno and Taylor (2008) first showed the split in humid air for nucleation konno2008 C10; Rumondor and co-workers (2009) showed it in bulk crystallization over more than a year and tied it to phase separation rumondor2009b C13, C22; Rumondor and co-workers (2010) showed it for growth and placed the crossover between 52 and 64% RH rumondor2010 C14. Later polymer-selection work found the opposite ranking for polyphenols: resveratrol in 2013 and naringenin and quercetin in the same year wegiel2013b C35; wegiel2013a C40; for curcumin in 2014 PVP was the weakest polymer whether humid or dry wegiel2014 C24. Xie and Taylor (2016) found the switch for celecoxib only at 94% RH xie2016b C41, C42, and Trasi and co-workers (2020) found the neutral polymer weakest for a weak base (see F34) trasi2020 C6; the title of this finding was widened from felodipine to felodipine and celecoxib, and the type line extended.

Topic 4 of 5 · 8 findings · F12–F16, F23, F31, F32

Its morphology and what it means for stability testing

F12

Topic 4Its morphology and what it means for stability testing1 of 8

Sorbed water splits many mixed drug–PVP and drug–PVPVA dispersions into drug-rich and polymer-rich amorphous phases before crystals appear.

After humid storage and drying, the infrared bands of drug–PVP hydrogen bonds fell, and the spectra of nifedipine–, pimozide– and droperidol–PVP came to resemble a calculated physical mixture of the amorphous components within 1 h at 94% RH, without crystal bands rumondor2009c R7, R9, R10, R12, C2, C16. Dried pimozide–PVP 50:50 showed two glass transitions, 61 and 112 °C, the lower at the Tg of amorphous pimozide (60 °C) rumondor2009c R17, C22. For felodipine–PVP, IR, DSC, AFM and TEM agreed, and nine further systems with PVP, PVPVA or HPMCAS behaved in the same way marsac2010 R11, R14, R19, R20, C14, C25; rumondor2010c R3, C10; rumondor2011 R14, C16.

moderateModerate: IR, DSC, AFM, TEM and water uptake agree, but each technique used a different sample form, composition and storage time, most samples were analysed after drying, and two-phase evidence in the wet state exists only for pimozide rumondor2009c K2, X8, X10; marsac2010 K2, X10, X11; rumondor2010c K2, X12; rumondor2011 K1, X7.

one Tg, drytwo Tgs after humid storage and dryingpimozide–PVP 50:506194112quinidine–PVP637081quinidine–PVPVA626976pimozide–PVPVA598397pimozide–HPMCAS6578795060708090100110120glass transition temperature, °C

Powders after 24–72 h at 94% RH and drying; for pimozide–PVP the lower Tg sits at that of amorphous pimozide (60 °C). rumondor2009c R17, C22; rumondor2010c R3, R3.a, R3.b, R3.c, R3.d, R3.e, C10

For your drug

  1. Store a spin-coated film of the dispersion at 75% RH for 1 day and 1 week and at 94% RH for 1 h and 1 day, dry it, and compare its IR spectrum with the crystal and with a physical-mixture spectrum calculated for the composition.
  2. A loss of drug–polymer bands without crystal bands is the signature found here; confirm it by DSC for a second Tg near the drug's own Tg and by near-additive water uptake (F7).

rumondor2009c P7, E7, R17, R22

How it works and key numbers
  1. Sorbed water turns the drug–polymer binary into a ternary system and also raises mobility; separation needs both a driving force and enough mobility rumondor2009c C34.
  2. Water interacts well with PVP and badly with the hydrophobic drug, so the water–PVP "cosolvent" mixes less well with the drug as it takes up water rumondor2009c C37.
  3. A lower free energy is then reached by separating into drug-rich and polymer-rich regions (amorphous–amorphous phase separation); "It is our opinion" that the separation is thermodynamically driven and needs some enhanced mobility rumondor2009c C37, C35.
  4. For felodipine–PVP the large difference between the water–drug (about 3.3) and water–PVP (about 0.5) interaction parameters supports an altered thermodynamics ("it is probable") marsac2010 C42, C43.
  5. More drug–drug and less drug–polymer bonding without crystal bands "strongly suggest[s]" separation rather than crystallization marsac2010 C14; rumondor2009c C15.
1 h at 94% RHtime for the drug–PVP IR bands to fall (nifedipine, pimozide)rumondor2009c R7, R9, R10
61 and 112 °Ctwo Tgs of dried pimozide–PVP 50:50, one Tg (94 °C) beforerumondor2009c R17
0.22 → 17 nmAFM roughness of a felodipine–PVP film after 1 h at 94% RHmarsac2010 R19, C25

Connections to other chapters

Evidence: data, conditions and papers

Finding F12. Sorbed water splits many initially mixed drug–PVP and drug–PVPVA dispersions, and occasionally an HPMCAS one, into a drug-rich and a polymer-rich amorphous phase before any crystals appear

In short. After humid storage and drying, the infrared bands of drug–PVP hydrogen bonds fell and the spectra of nifedipine–, pimozide– and droperidol–PVP came to resemble a calculated physical mixture of the amorphous components within 1 h at 94% RH (pimozide from 54% RH), without crystal bands rumondor2009c R7, R9, R10, R12, C2, C16. Wet pimozide–PVP 50:50 showed two glass transitions (−21 and 44 °C), and after drying 61 and 112 °C, the lower at the Tg of amorphous pimozide (60 °C) rumondor2009c R17, C22. For felodipine–PVP, FTIR (drug–drug band up, drug–PVP band down after 75–94% RH), DSC (an event at 45–50 °C instead of one Tg near 80 °C), AFM (roughness 0.22 → 17 nm and phase contrast within 1 h at 94% RH) and TEM (two regions without diffraction rings) agreed marsac2010 R11, R14, R19, R20, C14, C25; an earlier study had read the same IR change in 25% PVP films as possible partial phase separation ("maybe") konno2008 R10, C34. The next two papers found the same in nine further systems: after storage at 54–94% RH and drying, felodipine–PVPVA, quinidine–PVP, quinidine–PVPVA, pimozide–PVPVA and pimozide–HPMCAS showed two Tgs in place of one (for example 77 → 64 and 77 °C for felodipine–PVPVA), and indoprofen, clofoctol, probucol, nilutamide and loratadine with PVP lost the bonded PVP carbonyl band at 70 and 90% PVP, nilutamide and loratadine at every composition rumondor2010c R3, C10; rumondor2011 R14, C16.

Type. observation in 13 drugs with PVP, PVPVA or HPMCAS Strength. consistent across IR, DSC, AFM, TEM and water uptake (rumondor2009c K2: moderate; marsac2010 K2: moderate; rumondor2010c K2: moderate; rumondor2011 K1: strong), but each technique used a different sample form, composition and storage time, the 2010–2011 samples were all analysed after drying, two-phase evidence in the wet state exists only for pimozide, and several key spectra are not shown (rumondor2009c X8, X10; marsac2010 X10, X11; rumondor2010c X12; rumondor2011 X7).

How it was shown

Rumondor and co-workers (2009) stored drug–PVP films at 54–94% RH, dried them and compared their IR spectra with the crystal and with a spectrum calculated by adding the amorphous drug and PVP spectra, and ran DSC on powders wet and re-dried rumondor2009c P1, P4, P7, E7, P9. Later papers added AFM and TEM of felodipine–PVP, PVPVA and HPMCAS dispersions, and five further drugs in PVP marsac2010 P11, P14, P15; rumondor2010c P1, P7; rumondor2011 P1, P3.

What the data show

In nifedipine–PVP the bonded NH band lost intensity after 1 h at 94% RH and the spectrum came to resemble the physical mixture rumondor2009c R7, C17.

systemmethod and conditionsresultids
pimozide–PVP 50:50 and 70:30DSC dry, wet, re-driedone Tg dry (94, 81 °C); two wet (−21/44, 13/48 °C); two dried (61/112, 59/109 °C)rumondor2009c R17, R18
felodipine–PVP, 46.5 wt% powderDSC after 75–94% RHevent at ≈45–50 °C instead of a single Tg near 80 °Cmarsac2010 R14, C17
felodipine–PVP, 50% filmAFM at 0–16 h of 94% RHRMS 0.22 → 17 nm and > 50° phase contrast at 1 h; birefringence at 4 hmarsac2010 R19, C25
felodipine–PVPVA, quinidine–PVP, quinidine–PVPVA, pimozide–PVPVA, pimozide–HPMCASDSC after 24 h at 94% RH, driedone Tg → two (for example 83 → 59/97 °C for pimozide–PVPVA)rumondor2010c R3, C10
indoprofen, clofoctol, probucol, nilutamide, loratadine with PVP, 10–90%IR after 54–94% RH, driedseparation at 70–90% PVP for all; at every composition for nilutamide and loratadinerumondor2011 R14
celecoxib 6:4 with PVP K12, K29/32DSC after 3 days at 94% RHtwo Tg events; PVPVA, HPMCAS, HPMC onexie2016b R18, C32, C34
Fig. 8 of rumondor2009c: DSC of pimozide–PVP 50:50 dry, after 94% RH and after re-drying
Fig. 8 · rumondor2009cDSC of pimozide–PVP 50:50 dry, after 94% RH and after re-drying

One step at 94 °C in the dry dispersion; two steps in the wet and in the re-dried sample, the lower re-dried one at the Tg of pure amorphous pimozide rumondor2009c R17.

Why

Sorbed water turns the binary into a ternary system and raises mobility; separation needs both a driving force and enough mobility rumondor2009c C34. Water interacts well with PVP and badly with the hydrophobic drug, so a lower free energy is reached by separating into drug-rich and polymer-rich regions rumondor2009c C37. For felodipine–PVP "it is probable" that the immiscibility arises from altered thermodynamics, supported by the large difference between the water–drug (about 3.3) and water–PVP (about 0.5) interaction parameters marsac2010 C42, C43.

Limits and transfer

IR spectra were taken on re-dried films, and different techniques used different compositions and storage times rumondor2009c C11, X10; marsac2010 X10, X11. Indomethacin– and ketoprofen–PVP showed no change for 40 and 68 days at 94% RH (F13) rumondor2009c R14, R16, C20. Store a film at 75% RH for 1 day and 1 week and at 94% RH for 1 h and 1 day, dry it, compare its IR spectrum with a calculated physical-mixture spectrum, and confirm a loss of drug–polymer bands without crystal bands by DSC for a second Tg.

How it was shown

Konno and Taylor (2008) stored felodipine films with 25% PVP, HPMCAS or HPMC at 75% RH for up to 7 weeks, dried them under nitrogen and recorded the NH and carbonyl bands konno2008 P5. Rumondor, Marsac, Stanford and Taylor (2009) spin-coated nifedipine, pimozide, droperidol, indomethacin and ketoprofen with PVP K29/32, stored the films at 54, 75, 84 and 94% RH for 1 h to 125 days, dried them and compared their IR spectra with the crystal and with a spectrum calculated by adding the amorphous drug and PVP spectra (the signature of a separated, non-interacting mixture); DSC of rotary-evaporated powders held at 25 °C and 94% RH for 42–72 h, wet and re-dried, and water uptake at 95% RH tested the IR reading rumondor2009c P1, P4, P7, E7, P9, P11. Marsac, Rumondor and co-workers (2010) followed felodipine–PVP films (30.3 and 46.4 wt% PVP) in a humidity cell and after drying, ran DSC on 46.5 wt% PVP powders after 75–94% RH, imaged 50% PVP films by AFM after 1–16 h at 94% RH and 30% PVP films by TEM with electron diffraction marsac2010 P7, P8, P11, P14, P15. Rumondor and Taylor (2010) spin-coated felodipine, quinidine, pimozide and indomethacin with PVP, PVPVA or HPMCAS at 10–90 wt% polymer, took the same films through 54, 75, 84 and 94% RH with drying before each IR spectrum, and ran DSC on 50:50 rotary-evaporated powders after 24 h at 25 °C and 94% RH and drying to a weight plateau rumondor2010c P1, P4, P7, A5. Rumondor and co-workers (2011) did the same with five drugs chosen for their hydrogen-bond donor (indoprofen, clofoctol, probucol, nilutamide, loratadine) in PVP K29-32 at 10–90% PVP, comparing indoprofen, nilutamide and loratadine with calculated physical-mixture spectra, and checked selected bulk 50:50 powders by PXRD after 18 and 42 h at 84% RH rumondor2011 P1, P3, P5, P6. Xie and Taylor (2016) measured DSC of 6:4 celecoxib dispersions after 3 days at 75 or 94% RH in sealed pans and IR of films at 94% RH xie2016b P7, P4; Saboo and Taylor (2017) imaged miconazole–PVPVA films with two dyes and AFM-IR and measured DSC of humidified powders saboo2017 P9, P7, P12; Yang and co-workers (2022) imaged ritonavir–PVPVA films in a humidity chamber at 37 °C yang2022b P4.

What the data show

In 25% felodipine–PVP films the drug–PVP NH shoulder (3291 cm⁻¹) and the bonded PVP carbonyl shoulder (1655 cm⁻¹) lost intensity over 1–7 weeks at 75% RH, persisting after drying, with no peak at the crystalline 3373 cm⁻¹; 25% HPMCAS and HPMC films did not change konno2008 R10, R11, C21, C22, C24. In nifedipine–PVP the bonded NH band at 3288 cm⁻¹ lost intensity after 1 h at 94% RH while the drug–drug band near 3345 cm⁻¹ grew, and the 24 h and 4 day spectra peaked at about 3343 cm⁻¹ like the physical mixture, with no separate crystal band at 3317 cm⁻¹ rumondor2009c R7, C17, X8. In pimozide–PVP the free drug carbonyl (1709 cm⁻¹) and the bonded PVP carbonyl (1661 cm⁻¹) fell after 1 h at 94% RH; the change grew from 54% RH (3 days) through 75 and 84% (2 days) to 94% RH (1 h), and also occurred, more slowly, at 4 °C rumondor2009c R9, R10, R11, X9. Droperidol behaved the same way rumondor2009c R12, C19. Pimozide–PVP 70:30 gave a dry Tg of 81 °C, wet 13 and 48 °C, re-dried 59 and 109 °C rumondor2009c R18. The three separating dispersions took up within 7.4% of additive water (F7) rumondor2009c R22. In felodipine–PVP the drug–polymer band fell slightly at 33 and 58% RH and distinctly at 75% RH after a week, and after a day at 94% RH the dried spectrum peaked at about 3340 cm⁻¹, close to amorphous felodipine, with no crystal band at 3362 cm⁻¹ marsac2010 R7, R8, R11, C10, C12. Powders stored at 75–94% RH showed a glass-transition-like event at about 45–50 °C, near felodipine's Tg, where one Tg near 80 °C is expected; second scans showed one Tg near 80 °C marsac2010 R14, R21, C17, C20. The AFM film was cloudy after 1 h, with phase regions differing by more than 50°, and birefringent after 4 h; TEM showed darker domains in a lighter matrix with no diffraction rings, the authors estimating islands of about 300–500 nm marsac2010 R19, R20, C23, C27, C41.

In the 2010 polymer study all nine dry dispersions had drug–polymer bands and one Tg between those of drug and polymer (49–83 °C) rumondor2010c R1, R2, R3, C9. After 94% RH and drying the Tg pairs were 64 and 77 °C (felodipine–PVPVA, from 77), 63 and 81 (quinidine–PVP, from 70), 62 and 76 (quinidine–PVPVA, from 69), 59 and 97 (pimozide–PVPVA, from 83) and 65 and 79 °C (pimozide–HPMCAS, from 78); the drug–polymer band fell by 50% (felodipine–PVP, one spectrum) against 17% (felodipine–PVPVA) and by 47% (quinidine–PVP) against 11% (quinidine–PVPVA) at 84% RH rumondor2010c R3.a, R3.b, R3.c, R3.d, R3.e, R4, R5, R6, R7. The same trends were seen at 30 and 70 wt% polymer, no crystals were found, and at 10 and 90 wt% polymer the methods could not decide rumondor2010c R12, C42. In the 2011 study the PVP carbonyl bonded to the drug (1,663 cm⁻¹ for clofoctol, probucol and nilutamide; 1,641 cm⁻¹ for indoprofen) lost intensity against the free band at 1,682 cm⁻¹, and the merged loratadine–PVP band split toward the calculated physical mixture; selected bulk 50:50 powders stayed amorphous by PXRD after 42 h at 84% RH rumondor2011 R2, R4, R5, R9, R10, R12, R13, R8.

Later papers added three drugs. Celecoxib 6:4 dispersions with PVP K12 and K29/32 showed two Tg events on first heating after 3 days at 94% RH (about 28 and 53 °C; about 55 and 84 °C) and one on reheating, while the PVPVA, HPMCAS and HPMC dispersions showed one; after 75% RH the evidence was weaker xie2016b R18, R19, C32, C34, C35. In a celecoxib–PVP 3:7 film at 94% RH the bonded NH band lost intensity and the film had crystallized by 18 days, while HPMCAS and PVPVA films did not change xie2016b R9, C20, R10, C21. Miconazole–PVPVA 50:50 powder had one Tg (26 °C) dry, 10 and 48 °C after 75% RH and −5 and 68 °C after 100% RH, and dry-made films formed drug-rich domains of 1–3 µm within a week at 75% RH without crystals (see F31) saboo2017 R14, R17, R21, R15. Ritonavir–PVPVA films with 30% drug separated within 5 min at high humidity and 37 °C yang2022b R4.

papersystemmethod and conditionsresultids
rumondor2010cfelodipine–PVPVA, quinidine–PVP, quinidine–PVPVA, pimozide–PVPVA, pimozide–HPMCAS (50 wt% polymer)DSC after 24 h at 94% RH, driedone Tg → two (for example 83 → 59/97 °C for pimozide–PVPVA)R3, C10
rumondor2010cfelodipine and quinidine with PVP or PVPVAIR band loss after 84% RH, dried50 / 17% (felodipine), 47 / 11% (quinidine)R4, R5, R6, R7, C33
rumondor2011indoprofen, clofoctol, probucol, nilutamide, loratadine with PVP, 10–90%IR after 54–94% RH at 22 °C, driedseparation at 70–90% PVP for all; at every composition for nilutamide and loratadineR14
konno2008felodipine, 25% PVP vs 25% HPMCAS/HPMCIR after 1–7 weeks at 75% RH, drieddrug–PVP shoulders 3291 and 1655 cm⁻¹ fall; cellulose films unchangedR10, R11, C21
rumondor2009cnifedipine–PVP 50%IR after 94% RH, driedbonded NH band lost within 1 h; spectrum like the physical mixture; no crystal bandR7, C17
rumondor2009cpimozide–PVP 30%IR after 54–94% RHchange from 54% RH (3 days); within 1 h at 94% RHR9, R10, C4
rumondor2009cpimozide–PVP 50:50 and 70:30DSC dry, wet, re-driedone Tg dry (94, 81 °C); two wet (−21/44, 13/48 °C); two dried (61/112, 59/109 °C)R17, R18
marsac2010felodipine–PVP 30.3 and 46.4 wt%IR after 1 week or 1 day, driedsmall change at 33–58% RH; distinct at 75%; amorphous-felodipine-like after 94% RHR7, R8, R11
marsac201046.5 wt% PVP powderDSC after 75–94% RHevent at ≈45–50 °C instead of a single Tg near 80 °CR14, C17
marsac201050% PVP filmAFM at 0–16 h of 94% RHRMS 0.22 → 17 nm and > 50° phase contrast at 1 h; birefringence at 4 hR19, C25
xie2016bcelecoxib 6:4 with PVP K12, K29/32DSC after 3 days at 94% RHtwo Tg events (≈28/53, ≈55/84 °C), one on reheating; PVPVA, HPMCAS, HPMC oneR18, C32, C34
xie2016bcelecoxib–PVP 3:7 filmIR at 94% RH, 1–18 daysbonded NH band falls; crystallized by 18 days; HPMCAS and PVPVA films unchangedR9, R10, C20
saboo2017miconazole–PVPVA 50:50DSC after 75 and 100% RH; confocal26 → 10/48 and −5/68 °C; drug-rich domains 1–3 µm at 7 daysR14, R17, R21, R15
yang2022britonavir–PVPVA 30:70 filmconfocal at high RH, 37 °Cbicontinuous separation within 5 minR4
purohit2015b (outside)probucol–PVP and ritonavir–PVP filmsfluorescence probes, IR, DSC at 97% RH and in bufferprobe signal moved to the pure-drug value; separation also during immersionC25
purohit2017b (outside)ritonavir with PVP, PVPVA, HPMCASpyrene, confocal, AFM, DSC at 97% RHPVP and PVPVA dispersions separated; HPMCAS remained miscibleC1
mugheirbi2017 (outside)itraconazole–HPMC film made miscible at 7% RHstorage at elevated humidity, 24 hitraconazole-rich and HPMC-rich regionsC26

Figure

Fig. 8 of rumondor2009c: DSC of pimozide–PVP 50:50 dry, after 94% RH and after re-drying
Fig. 8 · rumondor2009cDSC of pimozide–PVP 50:50 dry, after 94% RH and after re-drying

One step at 94 °C in the dry dispersion; two steps in the wet and in the re-dried sample, the lower re-dried one at the Tg of pure amorphous pimozide rumondor2009c R17.

Fig. 13 of marsac2010: AFM topography and phase of felodipine–PVP films after 0, 1, 2, 4 and 16 h at 94% RH
Fig. 13 · marsac2010AFM topography and phase of felodipine–PVP films after 0, 1, 2, 4 and 16 h at 94% RH

A flat, uniform film turns rough with strong phase contrast within 1 h; isolated shapes at 4 h and faceted crystal-like structures at 16 h; note the height scale growing from 1.2 to 720 nm down the figure marsac2010 R19.

Why

The authors' account, with their hedges: sorbed water turns the binary into a ternary system and also raises mobility; separation needs both a driving force and enough mobility rumondor2009c C34. Water interacts well with PVP and badly with the hydrophobic drug, so the water–PVP "cosolvent" mixes less well with the drug as it takes up water, and a lower free energy is reached by separating into drug-rich and polymer-rich regions rumondor2009c C37; "It is our opinion" that the separation is thermodynamically driven and needs some enhanced mobility rumondor2009c C35. For felodipine–PVP "it is probable" that the immiscibility arises from altered thermodynamics, supported by the large difference between the water–drug (about 3.3) and water–PVP (about 0.5) interaction parameters, and water "most likely" also raises mobility marsac2010 C42, C43, C44. The rise of drug–drug relative to drug–polymer bonding "strongly suggest[s]" separation rather than crystallization, since crystal bands are absent marsac2010 C14; rumondor2009c C15. Which drugs separate is the subject of F13.

Conditions and limits

PVP K29/32 only, at 25–50% polymer in the IR series, room temperature (4 °C for one pimozide film), 54–94% RH rumondor2009c A1, A2, A4; marsac2010 A2, A3. IR spectra were taken on re-dried films; the check that drying does not create the change was made for nifedipine only and is not shown rumondor2009c R1, C11, X10. Different techniques used different compositions and storage times, and the polymer-rich phase was not characterized marsac2010 X7, X10, X11. The DSC "second Tg" near 124 °C rests on one sample and may instead be depressed melting marsac2010 C18, X7. In the 2010–2011 papers every sample was analysed after drying, the films carried all earlier exposures because one film went through the RH series, the DSC scan behind the Tg pairs is not stated, and separation "as low as 54%" rests on IR alone rumondor2010c X8, X9, X10, C44; storage times are not given in the 2011 study rumondor2011 X7. For celecoxib, the 55 °C event of PVP K29/32 sits on an endotherm shared by other samples, and separation of the ternaries rests on film IR only xie2016b X6, X7.

Counterexamples and conflicts

Indomethacin– and ketoprofen–PVP showed no change for 40 and 68 days at 94% RH rumondor2009c R14, R16, C20 (F13). The 25% HPMCAS and HPMC felodipine films did not change konno2008 R11. Felodipine–, quinidine– and indomethacin–HPMCAS and indomethacin–PVPVA kept one Tg and unchanged bands up to 94% RH, and clofoctol films with 10 and 30% PVP and probucol films with 10% PVP were unchanged rumondor2010c R3.f, R3.g, R3.h, R3.i, R13, R14, R15, R16, C16; rumondor2011 R14.a, R14.b (see F13 and F23). In the AFM film crystals appeared after 4 h at 94% RH, whereas the IR films showed no crystals after 1 day, which the authors attribute "most likely" to stochastic nucleation, preparation and technique sensitivity marsac2010 C26, X10.

Transfer check

Store a spin-coated film of the dispersion at 75% RH for 1 day and 1 week and at 94% RH for 1 h and 1 day, dry it, and compare its IR spectrum with the crystal and with a calculated physical-mixture spectrum weighted by the composition rumondor2009c P7, E7. A loss of drug–polymer bands without crystal bands is the signature found here; confirm it by DSC for a second Tg near the drug's own Tg and by near-additive water uptake (F7) rumondor2009c R17, R22.

History

Vasanthavada and co-workers (2005, outside the library) had reported phase separation of griseofulvin–PVP with moisture rumondor2009c C8. Konno and Taylor (2008) first saw the IR signature in felodipine–PVP and called it "maybe" a partial phase separation konno2008 C34. Rumondor and co-workers (2009) showed it for three of five drugs and measured two Tgs for pimozide rumondor2009c C2, C22; Marsac and co-workers (2010, cited as in press from 2009) confirmed it for felodipine–PVP with four techniques marsac2010 C14, C25. Rumondor and Taylor (2010) extended it to PVPVA and, once, to HPMCAS, and Rumondor and co-workers (2011) to five further drugs in PVP, with the extent depending on drug loading rumondor2010c C36; rumondor2011 C38; the title of this finding was widened from drug–PVP to drug–PVP and drug–PVPVA dispersions and the type line updated. Later papers in the library saw the same with fluorescence probes and for other drugs and polymers (see Solid-state methods F17 and ASD process F6) purohit2015b C25; purohit2017b C1; mugheirbi2017 C26. Xie and Taylor (2016), Saboo and Taylor (2017) and Yang and co-workers (2022) added celecoxib, miconazole and ritonavir, the last two with imaging of the wet films xie2016b C5; saboo2017 C24; yang2022b C1; the type line now counts 13 drugs and the title is unchanged.

F13

Topic 4Its morphology and what it means for stability testing2 of 8

Whether a PVP dispersion separates in humid air followed the drug's hydrogen-bond donor, not log P or melting data.

In PVP the drugs whose donor is an NH group (nifedipine, pimozide, droperidol, and felodipine from earlier work) separated under humidity, while the carboxylic acids indomethacin and ketoprofen stayed one phase at 94% RH for 40–68 days rumondor2009c C55, R14, R16. Log P, Tm, heat of fusion and the Hoffman driving force showed no trend with separation rumondor2009c C27, C29, C32. Two measures did: the drug–water interaction parameter χ and the red shift of the PVP carbonyl band (20–24 cm⁻¹ with the NH drugs against 42–44 cm⁻¹ with the acids) rumondor2009c R24, R29, C46, C48.

moderateModerate: the donor split holds for the PVP rows of a 20-system table with one exception, but donor type, red shift, pKa and drug–water χ divide the drugs into nearly the same groups, and the χ gap between the groups is only 0.13 rumondor2011 K3, X10; rumondor2009c K7, X4, X5.

stayed one phase in humid airseparatedCOOH: indomethacin, ketoprofen42–44COOH: indoprofenpKa 5.841, separated slightlyNH donorsfive drugs18–24OH donorstwo resisted only at high drug loading15–19no donor: loratadine−17−20−1001020304050red shift of the PVP carbonyl band in the dry dispersion, cm⁻¹

PVP rows of the 20-system table: the acids above 40 cm⁻¹ resisted, except indoprofen. rumondor2011 R15, R14.a, R14.b, C31, C32, C36

stayed mixedseparatedindomethacin 2.50ketoprofen 2.71nifedipine 2.84droperidol 2.85felodipine 3.18pimozide 3.582.42.7253.053.3753.7drug–water Flory–Huggins χ from 95% RH sorption

The two groups are separated by only 0.13. rumondor2009c R24, C46, K7

For your drug

  1. Check the drug's hydrogen-bond donor and measure the polymer carbonyl shift in the dry dispersion: 40 cm⁻¹ or more went with resistance, although an acid with a pKa near 5.8 (indoprofen) already gave way.
  2. Fit the water isotherm of the neat amorphous drug for its water χ (2.84 or above fell in the separating group), do not use log P, Tm or heat of fusion, and test at the intended drug loading; confirm by the storage test of F12.

rumondor2009c C55, R24, R29; rumondor2011 R15, C33, R14, C38

How it works and key numbers
  1. Separation needs a positive enthalpy of mixing, since the entropy of mixing favours mixing; it is expected when the three pair interactions of water, PVP and a hydrophobic drug differ strongly rumondor2009c C42, C43.
  2. The acid hydrogen of COOH is the better donor, so COOH–PVP bonds are stronger, as the larger red shift shows, and this "might lead to a greater resistance" to moisture-induced immiscibility rumondor2009c C47, C48, C49.
  3. Mobility alone does not decide: ketoprofen–PVP, whose wet Tg (−23 °C) lay far below room temperature, did not separate, while pimozide–PVP still separated at 4 °C, more slowly rumondor2009c R25, R11, C38, C41.
  4. In a discriminant model of 20 systems the largest weights went to a COOH donor (about +0.53), the carbonyl shift (about +0.40) and pKa (about −0.35), and log P was dropped as insignificant rumondor2011 R16, R17, C32.
42–44 vs 20–24 cm⁻¹PVP carbonyl shift with acid vs NH donorsrumondor2009c R29, C48
2.84–3.58 vs 2.50–2.71drug–water χ of separating vs mixed drugsrumondor2009c R24, C46
1.92–5.34log P range of the six drugs, with no trend to separationrumondor2009c C27

Connections to other chapters

5 more connections
Evidence: data, conditions and papers

Finding F13. Which dispersions separate in humid air is not predicted by drug log P, melting data or mobility; it followed the hydrogen-bond donor of the drug, the PVP carbonyl shift it produces and the drug–water interaction parameter

In short. In PVP the NH-donor drugs (nifedipine, pimozide, droperidol, and felodipine from earlier work) separated under humidity, while the carboxylic acids indomethacin and ketoprofen stayed one phase at 94% RH for 40–68 days, although ketoprofen–PVP sat far above its wet Tg (−23 °C) rumondor2009c C55, R14, R16, R25, C38. Log P (1.92–5.34), Tm, heat of fusion, Hoffman driving force (4.1–11.0 kJ/mol) and activity coefficients showed no trend with separation rumondor2009c C27, C29, C32, M1, M2, M3, M4, M5, M6. Two measures did: the drug–water Flory–Huggins parameter (2.84–3.58 for the four separating drugs against 2.50–2.71) and the red shift of the PVP carbonyl (20–24 cm⁻¹ with the NH drugs against 42–44 cm⁻¹ with the acids) rumondor2009c R24, R29, C46, C48. For felodipine–PVP the authors of a second study point to the gap between water–drug (about 3.3) and water–PVP (about 0.5) parameters, the Δχ effect marsac2010 R22, C43. Two later papers widened the donor split: indomethacin, whose COOH shifted the PVPVA carbonyl by 42–44 cm⁻¹ against 19–22 cm⁻¹ for NH and OH donors, stayed one phase with PVPVA, while the OH donor quinidine separated with PVP and PVPVA rumondor2010c R20, R3.b, R3.c, C28; in a table of 20 systems the carboxylic acids shifted the PVP carbonyl by 41–44 cm⁻¹ and the OH and NH donors by 15–24 cm⁻¹, and a discriminant model gave the largest weights to a COOH donor (about +0.53), the carbonyl shift (about +0.40), pKa (about −0.35) and an NH donor (about −0.28), with log P dropped as insignificant rumondor2011 R15, R16, R17, C31, C32. The acid indoprofen (pKa 5.8, shift 41 cm⁻¹) was the exception and separated slightly rumondor2011 R11, C33, C46.

Type. observation in 12 drugs with PVP, PVPVA or HPMCAS, with an author interpretation and a discriminant model Strength. the donor split holds for the PVP rows of a 20-system table with one exception (rumondor2011 K3: moderate) and for PVPVA in a second paper (rumondor2010c K4: moderate), but donor type, red shift, pKa and drug–water χ divide the drugs into nearly the same groups, the χ gap between groups is only 0.13, the model's training set is not stated, and class labels ignore drug loading (rumondor2009c K7: weak; X4, X5, X13; rumondor2011 X10, X13).

How it was shown

Rumondor and co-workers (2009) tabulated log P, Tm, heat of fusion and the Hoffman driving force of six drugs, computed the drug–water χ from sorption, and read the hydrogen-bond strength from the shift of the PVP carbonyl in the dry dispersions rumondor2009c M1, M6, P10, P13, E5, R29. Rumondor and co-workers (2011) tabulated 20 drug–polymer systems and fitted an OPLS-DA model rumondor2011 A1, P7, P9, R15, R16.

What the data show

Ketoprofen–PVP (wet Tg −23 °C) and indomethacin–PVP K12 (11 °C) did not separate, while pimozide–PVP still separated at 4 °C, more slowly rumondor2009c R25, R21, R11, C38, C41.

testsystemsresultids
calculated log Psix drugs in PVP1.92–5.34; no trend with separationrumondor2009c M1, M2, M3, M4, M5, M6, C27
Hoffman ΔGc at 25 °Csame4.1–11.0 kJ/mol; no trendrumondor2009c M1, M2, M3, M4, M5, M6, C32
drug–water χ from 95% RH sorptionsame2.84–3.58 (separating) vs 2.50–2.71 (mixed)rumondor2009c R24, C46
PVP carbonyl red shift, dryfive dispersions20–24 (NH donors) vs 42–44 cm⁻¹ (COOH donors)rumondor2009c R29, C48
PVP carbonyl shift against class20 drug–polymer systemsacids 41–44, OH and NH donors 15–24 cm⁻¹; acids resist except indoprofenrumondor2011 R15, C31, C32
OPLS-DA loadingssameCOOH ≈+0.53, shift ≈+0.40, pKa ≈−0.35, NH ≈−0.28; log P, Tg, MW excludedrumondor2011 R16, R17
Table 4 of rumondor2009c: activity coefficients and drug–water interaction parameters of six drugs
Table 4 · rumondor2009cactivity coefficients and drug–water interaction parameters of six drugs

Only the last column, χ drug–water, puts the four separating drugs (nifedipine, felodipine, droperidol, pimozide) above the two that stayed mixed rumondor2009c R24.

Why

Separation needs a positive enthalpy of mixing, which is expected when the three pair interactions differ strongly, as for water, PVP and a hydrophobic drug rumondor2009c C42, C43. COOH–PVP bonds are stronger, as the larger red shift shows, and this "might lead to a greater resistance" to moisture-induced immiscibility rumondor2009c C47, C48, C49. "It is our opinion" that the event is thermodynamically driven, mobility setting only its rate rumondor2009c C35, C38, C41. (synthesis: bond strength and drug–water interaction cannot be separated in this set, because the drugs with weaker PVP bonds also have the highest drug–water χ) rumondor2009c R24, R29.

Limits and transfer

Indoprofen, a carboxylic acid with a 41 cm⁻¹ shift, separated slightly before crystallizing, and the pKa values of the model are calculated rumondor2011 R11, C46, P9. For a new drug in PVP or PVPVA, check its hydrogen-bond donor, its water χ and the polymer carbonyl shift in the dry dispersion, and do not use log P, Tm or heat of fusion as a guide.

How it was shown

Rumondor and co-workers (2009) tabulated, for the six drugs, molecular weight, aqueous solubility, calculated log P, Tm and heat of fusion (DSC), the Hoffman driving force at 25 °C and density; they computed the activity coefficient of water in each amorphous drug from its uptake at 95% RH, the activity coefficient of each drug in water from its solubility, and the drug–water χ from the same sorption data, and read the hydrogen-bond strength from the shift of the PVP carbonyl in the dry dispersions rumondor2009c M1, M6, P10, P13, E1, E2, E3, E5, R29. Mobility was tested with two controls: ketoprofen–PVP and a more plasticized indomethacin–PVP K12 dispersion (wet Tg 11 °C), and a pimozide–PVP film stored at 4 °C rumondor2009c R25, R21, R11. Marsac and co-workers (2010) used cited parameters for water–felodipine, water–PVP and felodipine–PVP marsac2010 R22. Rumondor and Taylor (2010) read the PVPVA carbonyl red shift of four drugs from dry films and tested whether the drug with the strongest donor resisted rumondor2010c R20, R1. Rumondor and co-workers (2011) chose five drugs by donor type (COOH, one OH, two OH, NH, none), tabulated 20 drug–polymer systems (5 new, 15 earlier) with molar mass, donor and acceptor numbers and types, pKa (calculated), log P, log S, Tg, ΔCp, Tm, ΔHf, PVP carbonyl shift and a class (1 resists, 0 separates), and fitted an OPLS-DA model with one predictive and two orthogonal components rumondor2011 A1, A5, P7, P9, R15, R16. Xie and Taylor (2016) recorded the celecoxib NH band in films with each polymer xie2016b P2.

What the data show

Log P ranked droperidol (1.92), felodipine (2.24) and nifedipine (2.31), all separating, below ketoprofen (3.31) and indomethacin (3.58), which did not; pimozide (5.34) separated rumondor2009c M1, M2, M3, M4, M5, M6, C27. The Hoffman driving forces were 8.2 (nifedipine), 6.1 (felodipine), 9.2 (droperidol), 11.0 (pimozide), 8.1 (indomethacin) and 4.1 kJ/mol (ketoprofen), with no correlation rumondor2009c M1, M6, M3, M2, M4, M5, C32. The activity coefficients of water in the amorphous drugs (2.54–4.65) and of the drugs in water (9.85 × 10⁴ to 8.88 × 10⁶) were all well above 1 without a trend rumondor2009c R24, C28, C29; the drug-in-water column follows the inverse mole-fraction solubility rather than the printed equation rumondor2009c X1. The drug–water χ split the groups: pimozide 3.58, felodipine 3.18, droperidol 2.85 and nifedipine 2.84 against ketoprofen 2.71 and indomethacin 2.50 rumondor2009c R24, C46. The PVP carbonyl shifted 21 (nifedipine), 20 (pimozide) and 24 (droperidol) cm⁻¹ against 42 (indomethacin) and 44 cm⁻¹ (ketoprofen), and the cited drug–PVP χ was −0.8 for indomethacin against 0.0 for nifedipine rumondor2009c R29, R26, C48, C49. Ketoprofen–PVP had a wet Tg of −23 °C and indomethacin–PVP K12 of 11 °C, both below room temperature, yet neither separated; pimozide–PVP still separated at 4 °C, more slowly rumondor2009c R25, R21, R11, C38, C39, C41.

In the PVPVA dispersions of 2010 the indomethacin shift (42–44 cm⁻¹) was about twice that of felodipine, quinidine and pimozide (19–22 cm⁻¹), and indomethacin–PVPVA kept its 1640 cm⁻¹ band after 7 days at 94% RH and one Tg (63 → 67 °C) rumondor2010c R20, R13, R3.h; from the tabulated positions the quinidine shift is 18 cm⁻¹ rumondor2010c X5. In the 20-system table of 2011 the PVP rows split cleanly by donor type except indoprofen: indomethacin (pKa 4.5, shift 42) and ketoprofen (5.02, 44) resist; indoprofen (5.8, 41) separates slightly; quinidine (OH, 19), droperidol (NH, 24), pimozide (NH, 20), felodipine (NH, 20), nifedipine (NH, 21), clofoctol (OH, 18), probucol (OH, 15), nilutamide (NH, 18) and loratadine (no donor, −17) separate rumondor2011 R15. The model fit was R²Y 0.98 and Q² 0.73 rumondor2011 R16. The two most hydrophobic drugs, clofoctol (log P 8.19) and probucol (10.0), resisted at high drug loading, which the authors put down to too little sorbed water ("it is thought"), although no uptake was measured rumondor2011 R14.a, R14.b, C36, X6.

Two later systems test the reading with PVPVA. Celecoxib, whose sulfonamide NH2 bonds to both PVP and PVPVA (NH band 3268 → 3196 and about 3198 cm⁻¹), separated with PVP at 94% RH but kept one Tg with PVPVA, whose films did not change over 18 days xie2016b R3, R4, R18, R10. Miconazole, described as hydrophobic and weakly basic, separated with PVPVA after a week at 75% RH saboo2017 M1, R15, R17.

papersystemmethod and conditionsresultids
rumondor2010cindomethacin vs felodipine, quinidine, pimozide in PVPVAcarbonyl red shift, dry films; IR and DSC after 94% RH42–44 vs 19–22 cm⁻¹; indomethacin–PVPVA stays one phaseR20, R13, R3.h, C28
rumondor201120 drug–polymer systemsPVP carbonyl shift against classacids 41–44, OH and NH donors 15–24 cm⁻¹; acids resist except indoprofenR15, C31, C32
rumondor2011sameOPLS-DA loadingsCOOH ≈+0.53, shift ≈+0.40, pKa ≈−0.35, NH ≈−0.28; log P, Tg, MW excludedR16, R17
rumondor2009csix drugscalculated log P1.92–5.34; no trend with separationM1, M2, M3, M4, M5, M6, C27
rumondor2009csix drugsHoffman ΔGc at 25 °C4.1–11.0 kJ/mol; no trendM1, M2, M3, M4, M5, M6, C32
rumondor2009csix drugsdrug–water χ from 95% RH sorption2.84–3.58 (separating) vs 2.50–2.71 (mixed)R24, C46
rumondor2009cfive dispersionsPVP carbonyl red shift, dry20–24 (NH donors) vs 42–44 cm⁻¹ (COOH donors)R29, C48
rumondor2009cketoprofen–PVP; indomethacin–PVP K12wet Tg; IR at 94% RH−23 °C and 11 °C; no separationR25, R21, C38, C39
marsac2010felodipine–PVP–watercited χwater–drug ≈3.3, water–PVP ≈0.5, drug–PVP slightly negativeR22, C43
xie2016bcelecoxib (sulfonamide NH2) with PVP vs PVPVAIR; DSC after 94% RHNH 3268 → 3196 and ≈3198 cm⁻¹; two Tg events with PVP, one with PVPVAR3, R4, R18
saboo2017miconazole–PVPVA 50:50DSC after 75% RH; confocaltwo Tgs; drug-rich domainsR17, R15
wegiel2013a (outside)naringenin and quercetin with PVPIR band shifts; humid storagePVP carbonyl shifted 21 and 24 cm⁻¹; dispersions stable at high RH, read as strong hydrogen bondingC40, C42
purohit2017b (outside)ritonavir with PVP, PVPVA, HPMCASstorage at 97% RHPVP and PVPVA separated; HPMCAS, more hydrophobic and less hygroscopic, did notC1, C45
li2017 (outside)evacetrapib with PVPVA and HPMChumid storage after dry preparationthermodynamics decide whether a dispersion separates, mobility limits the rateC44

Figure

Table 4 of rumondor2009c: activity coefficients and drug–water interaction parameters of six drugs
Table 4 · rumondor2009cactivity coefficients and drug–water interaction parameters of six drugs

Only the last column, χ drug–water, puts the four separating drugs (nifedipine, felodipine, droperidol, pimozide) above the two that stayed mixed rumondor2009c R24.

Table II of rumondor2011: properties, PVP carbonyl shift and phase-behaviour class of 20 drug–polymer systems
Table II · rumondor2011properties, PVP carbonyl shift and phase-behaviour class of 20 drug–polymer systems

Read the PVP rows: the carboxylic acids sit above 40 cm⁻¹ and in class 1 (resists) except indoprofen; the OH and NH donors sit at 15–24 cm⁻¹ and in class 0; the PVPVA and HPMAS rows carry no shift except the quinidine rows rumondor2011 R15, X2.

Why

The authors' account, with their hedges: separation needs a positive enthalpy of mixing, since the entropy of mixing favours mixing ("must"); it is expected when the three pair interactions differ strongly, as for water, PVP and a hydrophobic drug rumondor2009c C42, C43. The acid hydrogen of COOH is the better donor, so COOH–PVP bonds are stronger, as the larger red shift shows, and this "might lead to a greater resistance" to moisture-induced immiscibility rumondor2009c C47, C48, C49; "It is speculated" that drug–polymer interaction strength decides susceptibility, with drug–water interaction and total moisture uptake "of likely importance" rumondor2009c C7, C56. The mobility controls argue against a purely kinetic route, in which water would only free a glass already wanting to separate: "It is our opinion" that the event is thermodynamically driven, mobility setting only its rate rumondor2009c C35, C38, C41. For felodipine–PVP, polymer studies of solvent-induced demixing support the thermodynamic origin ("well supported") marsac2010 C36, C43. (synthesis: the two readings, drug–polymer bond strength and drug–water dislike, are two terms of the same ternary balance; the data of this set cannot separate them, because the drugs with weaker PVP bonds are also those that dislike water most.) The 2010 and 2011 authors keep the donor reading: a COOH donor gives the larger red shift and "would result in" a lower drug–polymer χ rumondor2010c C28; a lower pKa is "expected" to make a better donor, and indoprofen's weaker resistance "can most likely be rationalized" by its higher pKa rumondor2011 C30, C33. They add drug loading: the same drug may resist at high loading and separate at low loading, so "the relative proportions" of the components matter rumondor2011 C38.

Conditions and limits

One polymer (PVP K29/32), six drugs, 25 °C sorption and room-temperature storage rumondor2009c A1, A2. Three of the six densities behind χ are approximated as 0.9 of the crystal density, felodipine's sorption input is not reported, and the γ-in-water column is effectively the inverse solubility rumondor2009c X4, X5, X1. Two text rankings of the activity coefficients contradict the table rumondor2009c X2, X3. In the 20-system model the pKa values are calculated, the rows used and the handling of missing values are not stated, and the score plot shows 12 markers for 20 rows; the effects of a lone CO acceptor, ΔCp and fluorine have error bars that span or touch zero rumondor2011 P9, X10, X11. Hygroscopicity is not a variable of the model, so the abstract's statement that the model confirmed it rests on earlier work rumondor2011 C2, X5.

Counterexamples and conflicts

None found in the library among NH-donor drugs in PVP that stayed mixed under humidity. Indoprofen, a carboxylic acid with a 41 cm⁻¹ shift, separated slightly at 50% PVP before crystallizing rumondor2011 R11, C46; quinidine–HPMAS is classed as resisting with a printed PVP shift of 19 cm⁻¹, so the shift rule holds for the PVP rows only rumondor2011 X2. Log P gives conflicting signals: pimozide (log P 5.34) was the only drug to separate with HPMCAS, which the 2010 authors attribute to its hydrophobicity rumondor2010c C35, whereas in 2011 the two most hydrophobic drugs were the only ones that resisted at some compositions and log P was dropped from the model rumondor2011 R14, R16, X14. Outside this set, polyphenols with OH donors stayed amorphous with PVP at high RH, with PVP carbonyl shifts (21–24 cm⁻¹) in the range of the NH drugs here, which the authors read as strong hydrogen bonding wegiel2013a C40, C42; the shift size alone therefore does not decide (synthesis). Total water uptake matters as well: the less hygroscopic HPMCAS resisted separation with ritonavir purohit2017b C1, C45 and with felodipine in this chapter's papers (F11, F12); the polymer order of separation for the same drugs is the subject of F23 konno2008 R11. With PVPVA the NH donor celecoxib kept one Tg after 3 days at 94% RH and showed no film change over 18 days, although its NH shift with PVPVA equals that with PVP; the authors relate this to the lower water uptake of the PVPVA dispersion (see F23) xie2016b R4, R10, R18, C49.

Transfer check

For a new drug in PVP or PVPVA, check its hydrogen-bond donor: in this set every drug whose only donor is an NH group separated, both acids did not rumondor2009c C55. Fit the water isotherm of the neat amorphous drug to obtain its water χ; values at or above 2.84 fell in the separating group here rumondor2009c R24. Measure the polymer carbonyl shift in the dry dispersion; 40 cm⁻¹ or more went with resistance in both the six-drug and the 20-system sets, and a carboxylic acid with a pKa near 5.8 (indoprofen) already gave way rumondor2009c R29; rumondor2011 R15, C33. Do not use log P or the drug's Tm and heat of fusion as a guide rumondor2009c C27, C32; rumondor2011 R16. Test at the intended drug loading, since very hydrophobic drugs resisted only at 70–90% drug rumondor2011 R14, C38. Confirm by the storage test of F12.

History

Rumondor and co-workers (2009) first compared several drugs and proposed donor strength and drug–water χ as the deciding factors rumondor2009c C7, C46. Marsac and co-workers (2010) framed the same balance as the Δχ effect of polymer–solvent theory marsac2010 C43. Rumondor and Taylor (2010) found the acid donor protective with PVPVA as well rumondor2010c C28, and Rumondor and co-workers (2011) tested the donor reading on 20 systems with a discriminant model, adding pKa and drug loading rumondor2011 C40, C38; with this evidence the strength of the finding was raised from weak to moderate to moderate and its title names the carbonyl shift. Later library work tied separation tendency to polymer hygroscopicity and drug hydrophobicity across more systems purohit2017b C45; li2017 C44; the hydrogen-bond contacts themselves are treated in Miscibility and drug-polymer interactions F1 and F2. Xie and Taylor (2016) added an NH donor that separated with PVP but not with PVPVA xie2016b C49; the title is unchanged.

F14

Topic 4Its morphology and what it means for stability testing3 of 8

Heat alone does not separate felodipine–PVP, but water-induced separation persists after drying and reverses only slowly above Tg.

In dry felodipine–PVP films the drug–PVP NH band persisted from 0 °C to as high as 180 °C, and heating and cooling data superimposed, so the authors find the system miscible up to the drug's melt marsac2010 R2, R4, R6, C9, C33. Water-induced changes stayed after a week of drying, and at 125 °C a separated film regained drug–PVP bonds only slowly (band ratio 0.70 at 5 min and 1.41 at 1500 min, against 1.47 for a never-exposed film) marsac2010 R8, C10, R17, C47. Water in the casting solvent, or humid air during spin coating of miconazole–PVPVA, prevented mixing from the start marsac2010 R13, C16; saboo2017 R6, R8, C14.

moderateModerate: the temperature result is direct and reversible and the persistence is seen in two papers, but remixing at 125 °C is still incomplete at 25 h, its 39 h extrapolation has no stated method, and the water-cast comparison is a single unlabelled figure marsac2010 K1, K3, K4, X5, X8.

Separated felodipine–PVP film held at 125 °C: drug–polymer / drug–drug NH band ratio5 min0.7020 min1.0260 min1.17150 min1.26420 min1.341500 min1.41never exposedreference1.47

Remixing is fast at first and then slow, about linear in ln time, and still below the reference after 1500 min. marsac2010 R17, C47

For your drug

  1. After any humidity excursion, re-test the phase state after drying (IR against a never-exposed film, DSC for two Tgs); do not expect a return to the original state at room temperature.
  2. Keep the water content of process solvents and of the casting air controlled and low; remixing a separated batch needs hours to days well above the dispersion Tg, which may not be acceptable chemically.

marsac2010 C53, C48, R17; saboo2017 C14

How it works and key numbers
  1. On heating the drug–PVP band shifts up by a few wavenumbers, a gradual, reversible weakening of hydrogen bonding "readily accounted for" by thermal expansion marsac2010 C6, C9, C34.
  2. After the water leaves, the mixed binary has the lower free energy, but remixing at room temperature "appears" prohibitively slow, "presumably" because both separated phases are glassy (felodipine Tg around 46 °C, PVP about 150 °C) marsac2010 C45, C46.
  3. At 125 °C, well above the Tg of felodipine and of the one-phase dispersion (about 80 °C), mobility returns and the film remixes marsac2010 C47, R21.
  4. During casting the ethanol and dichloromethane were "expected" to evaporate first and concentrate the water, which disrupted the formation of drug–polymer bonds ("suggesting") marsac2010 C15, C16.
To feel the numbers. Between 5 and 1500 min the ratio closed (1.41 − 0.70) ÷ (1.47 − 0.70) = 0.71 ÷ 0.77 ≈ 92% of the gap to the never-exposed film; the authors extrapolate the rest to about 39 h.
0 to 180 °Crange over which dry felodipine–PVP kept its drug–PVP bandmarsac2010 R2, C33
0.70 → 1.41 vs 1.47NH band ratio after 5 and 1500 min at 125 °C vs never exposedmarsac2010 R17
0.1 mL per 1.9 mLwater in the casting solvent that prevented mixingmarsac2010 R13, C16

Connections to other chapters

Evidence: data, conditions and papers

Finding F14. Dry felodipine–PVP and miconazole–PVPVA stay mixed on heating, but water-induced separation is held in place after drying, is reversed only slowly by heating well above Tg, and water in the casting solvent or humid casting air prevents mixing from the start

In short. In dry felodipine–PVP films the drug–PVP NH band persisted from 0 °C to as high as 180 °C, weakening a few wavenumbers on heating, and heating and cooling data superimposed, so the authors find the system miscible up to the drug's melt with no critical solution temperature over the timescales studied marsac2010 R2, R4, R6, C9, C33, C35. Water-induced changes stayed after a week of drying marsac2010 R8, C10 and after drying in 25% PVP films konno2008 R10, C21. Held at 125 °C, a separated film regained drug–PVP bonds slowly: the 3290/3345 cm⁻¹ peak ratio went from about 0.70 at 5 min to 1.41 at 1500 min against 1.47 for a never-exposed film marsac2010 R17, C47. Films cast from solvent containing 0.1 mL water per 1.9 mL lost most of the drug–PVP band and resembled dry-cast films after high RH marsac2010 R13, C16. Miconazole–PVPVA films spin-coated at 45–60% RH instead of 20% RH held drug-rich domains from the start, and the dry powder kept one Tg after 60 min at 100 °C saboo2017 R6, R8, C14, R22.

Type. observation in 2 drug–polymer pairs (felodipine–PVP, miconazole–PVPVA), with a supporting observation Strength. the temperature result is direct and reversible (marsac2010 K1: moderate to strong) and the persistence is seen in two papers, but remixing at 125 °C is still incomplete at 25 h and its 39 h extrapolation has no stated method, and the water-cast comparison is a single unlabelled figure (marsac2010 K3, K4: moderate; X5, X8).

How it was shown

Marsac and co-workers (2010) heated dry felodipine–PVP films with 30–74 wt% PVP in a variable-temperature IR cell from 0 °C to as high as 180 °C, held humidity-exposed films at 125 °C for 1500 min, and followed remixing by the height ratio of the 3290 and 3345 cm⁻¹ bands marsac2010 P5, P6, P13, E2. Saboo and Taylor (2017) spin-coated miconazole–PVPVA films at 20% or 45–60% RH and annealed a dry powder at 100 °C saboo2017 P1, A4, P12.

What the data show

The drug–polymer band was present at every temperature and the heating and cooling points superimposed, while the humidity-induced changes stayed after a week over phosphorus pentoxide at room temperature marsac2010 R2, R6, R8.

systemmethod and conditionsresultids
felodipine–PVP 30–74 wt%, dryvariable-temperature IR, 0–180 °Cdrug–polymer band at every temperature; 3288 → 3296 cm⁻¹ (30%, 5 → 160 °C)marsac2010 R2, R4
50% PVP after 4 h at 94% RHIR at 125 °C, 1500 minratio 0.70 → 1.41; never exposed 1.47marsac2010 R17, C47
30 and 50 wt% PVPcast with 0.1 mL water per 1.9 mL solventmaxima at ≈3340 cm⁻¹; drug–polymer band mostly lostmarsac2010 R13, C16
miconazole–PVPVA 50:50 filmsspin-coated at 20% vs 45–60% RHuniform vs drug-rich domains in a PVPVA-rich matrixsaboo2017 R5, R6, R8, C14
miconazole–PVPVA 50:50 powderDSC after 60 min at 100 °Cone Tg (data not shown)saboo2017 R22, C44
Fig. 12 of marsac2010: drug–polymer to drug–drug NH peak ratio against ln time at 125 °C
Fig. 12 · marsac2010drug–polymer to drug–drug NH peak ratio against ln time at 125 °C

The ratio climbs from about 0.70 toward the never-exposed level (horizontal line, about 1.47) but is still below it after 1500 min marsac2010 R17.

Why

The absence of hysteresis shows that the system is in "equilibrium" with respect to these interactions during the runs marsac2010 C9, C34. After the water leaves, mixing at room temperature "appears" prohibitively slow, "presumably" because both separated phases are glassy marsac2010 C45, C46. During casting the ethanol and dichloromethane were "expected" to evaporate first and concentrate the water, which disrupted the formation of drug–polymer bonds marsac2010 C15, C16. For miconazole the authors take the single Tg after annealing as showing that the pair does "not appear" to be inherently immiscible, water acting as an antisolvent saboo2017 C41, C42, C44.

Limits and transfer

One remixing run at one temperature, and the authors' extrapolation of full recovery to approximately 39 h has no stated method marsac2010 X5, R18, X8. After any humidity excursion, re-test the phase state after drying, and keep the water content of process solvents low, since 5 vol% water in the casting solvent was enough here marsac2010 C53, C48.

How it was shown

Marsac and co-workers (2010) heated dry spin-coated films with 0, 30, 37, 46, 54 and 74 wt% PVP in a variable-temperature IR cell from 0 °C to as high as 180 °C in 5–15 °C steps and read the drug–drug and drug–polymer NH peak positions from second-derivative spectra; a 37 wt% film was heated and then cooled marsac2010 P5, P6, A1. Films exposed to humidity were dried and held at 125 °C for 1500 min, and remixing was followed by the height ratio of the 3290 and 3345 cm⁻¹ bands marsac2010 P13, E2. Films of 30 and 50 wt% PVP were cast from solvent spiked with water marsac2010 P2. DSC heat–cool cycles to rising maximum temperatures followed the separated powder marsac2010 P12. Saboo and Taylor (2017) spin-coated miconazole–PVPVA films at 20% or 45–60% RH and annealed a dry powder at 100 °C for 60 min before DSC saboo2017 P1, A1, A4, P12.

What the data show

The drug–polymer band near 3290–3300 cm⁻¹ was present in every spectrum of the 30–74 wt% films up to the highest temperature marsac2010 R2. At 30 wt% PVP it moved from 3288 cm⁻¹ at 5 °C to 3296 cm⁻¹ at 160 °C, at 54 wt% from about 3290.4 to 3297.2 cm⁻¹ between 0 and 180 °C, with a kink near each Tg (57 and 89 °C), and the heating and cooling points of the 37 wt% film superimposed marsac2010 R4, R5, R6. At room temperature the humidity-induced changes stayed after a week over phosphorus pentoxide, ordered by the previous RH marsac2010 R8. At 125 °C the peak ratio rose steeply at first and then slowly, about linearly in ln time: 0.70 (5 min), 1.02 (20 min), 1.17 (60 min), 1.26 (150 min), 1.34 (420 min), 1.41 (1500 min) marsac2010 R17. The authors extrapolate full recovery to approximately 39 h; a straight extension of the last points reaches the reference only after about 2.5–3 days marsac2010 R18, X8. In DSC cycles the thermal event moved to higher temperature with each cycle, and second scans gave one Tg near 80 °C, read as remixing during heating marsac2010 R15, R14, C20, C21. With water in the casting solvent both films peaked at about 3340 cm⁻¹ instead of about 3300 and 3293 cm⁻¹ marsac2010 R13.

Saboo and Taylor (2017) found the same two halves for miconazole–PVPVA 50:50. Films spin-coated in a glove box at 20% RH were uniform by AFM-IR and confocal imaging, while films cast in laboratory air at 45–60% RH held drug-rich pits of 0.3–0.7 µm and droplets up to about 15 µm in a PVPVA-rich matrix (see F31) saboo2017 R5, R12, R6, R7, R8, R13. The dry rotary-evaporated powder, with one Tg of 26 °C, still showed one Tg after 60 min at 100 °C, about 74 °C above that Tg (synthesis: 100 − 26), so heat alone did not separate it saboo2017 R14, R22, C44.

papersystemmethod and conditionsresultids
marsac2010felodipine–PVP 30–74 wt%, dryvariable-temperature IR, 0–180 °Cdrug–polymer band at every temperature; 3288 → 3296 cm⁻¹ (30%, 5 → 160 °C)R2, R4
marsac201037 wt% PVPheating then coolingpoints superimpose, no hysteresisR6, C9
marsac201030.3 wt% after 1 week at 75% RHIR after 1 week dryingchanges persistR8, C10
konno200825% PVP after 75% RHIR after dryingdrug–PVP shoulders stay reducedR10, C21, C35
marsac201050% PVP after 4 h at 94% RHIR at 125 °C, 1500 minratio 0.70 → 1.41; never exposed 1.47R17, C47
marsac201030 and 50 wt% PVPcast with 0.1 mL water per 1.9 mL solventmaxima at ≈3340 cm⁻¹; drug–polymer band mostly lostR13, C16
saboo2017miconazole–PVPVA 50:50 filmsspin-coated at 20% vs 45–60% RHuniform vs drug-rich domains in a PVPVA-rich matrixR5, R6, R8, C14
saboo201750:50 powderDSC after 60 min at 100 °Cone Tg (data not shown)R22, C44
mugheirbi2017 (outside)spray-dried itraconazole–HPMCwater in the spray solventas little as 1% water induced phase separationC36
purohit2015a (outside)itraconazole–HPMC filmsheating at 165 °Cseparated films mixed on heating; domains glassy at room temperature, so kinetically trappedC46

Figure

Fig. 12 of marsac2010: drug–polymer to drug–drug NH peak ratio against ln time at 125 °C
Fig. 12 · marsac2010drug–polymer to drug–drug NH peak ratio against ln time at 125 °C

The ratio climbs from about 0.70 toward the never-exposed level (horizontal line, about 1.47) but is still below it after 1500 min marsac2010 R17.

Fig. 8 of marsac2010: films cast with and without water in the solvent
Fig. 8 · marsac2010films cast with and without water in the solvent

With water (dashed) both films peak near 3340 cm⁻¹, the drug–drug position, and lose most of the drug–polymer band of the dry-cast films (solid) marsac2010 R13.

Why

The authors' account, with their hedges: the upward shifts on heating reflect a gradual, reversible weakening of hydrogen bonding "readily accounted for" by thermal expansion, and the absence of hysteresis shows that the system is in "equilibrium" with respect to these interactions during the runs marsac2010 C6, C9, C34. After the water leaves, the miscible binary has the lower free energy, but mixing at room temperature "appears" prohibitively slow, "presumably" because both separated phases are glassy (felodipine Tg around 46 °C, PVP about 150 °C) marsac2010 C45, C46; the 2008 study called the dried film "kinetically trapped" konno2008 C35. At 125 °C, well above the Tg of felodipine and of the one-phase dispersion (about 80 °C), mobility returns and remixing "supports the supposition" of miscibility without moisture marsac2010 C47, R21. During casting the ethanol and dichloromethane were "expected" to evaporate first and concentrate the water, which disrupted the formation of drug–polymer bonds ("suggesting") marsac2010 C15, C16. For miconazole the authors take the single Tg after annealing as showing that the pair does "not appear" to be inherently immiscible, water acting as an antisolvent, and conclude that mobility "is not the sole criterion" saboo2017 C41, C42, C44.

Conditions and limits

One drug–polymer pair; temperature scans of minutes per step, so slow demixing on long storage at elevated temperature was not tested marsac2010 C35. One remixing run at one temperature; water-cast films heated more briefly than dry-cast ones, and residual water is not excluded marsac2010 X5. The reversibility statement cites Fig. 8 where Fig. 3 is meant marsac2010 X2.

Counterexamples and conflicts

None found in the library for felodipine–PVP. In itraconazole–HPMC, dispersions that looked mixed by one DSC Tg were separated in films and mixed on heating, the reverse of DSC missing separation (see Miscibility and drug-polymer interactions F18) purohit2015a C46. Lumefantrine dispersions made by spraying a drug–polymer solution into cold dilute acid stayed amorphous for 3 months with HPMCP and HPMCAS, which the authors call surprising since water is the antisolvent; their phase state was not tested bhujbal2021 C42, R4.

Transfer check

After any humidity excursion, re-test the phase state (IR against a never-exposed film, DSC for two Tgs) after drying; a return to the original Tg or spectrum at room temperature should not be expected marsac2010 C53. Keep the water content of process solvents controlled and low; 5 vol% water in the casting solvent was enough here marsac2010 C48. If a separated batch must be remixed, it needs hours to days well above the dispersion Tg (125 °C for a dispersion of Tg about 80 °C), which may not be acceptable chemically marsac2010 R17.

History

Konno and Taylor (2008) first noted that the moisture-induced change did not revert on drying konno2008 C35. Marsac and co-workers (2010) showed that heat alone does not demix felodipine–PVP, that heat remixes a separated film, and that water in the casting solvent prevents mixing marsac2010 C33, C47, C16. Later the library found water during film formation and spray drying to be a general cause of drug-rich domains (see ASD process F1 and ASD process F3) mugheirbi2017 C36. Saboo and Taylor (2017) showed both halves for miconazole–PVPVA, humid casting air separating the film and heat alone not saboo2017 C10, C44; the title of this finding was widened from felodipine–PVP to both pairs and to humid casting air, and the type line changed accordingly.

F15

Topic 4Its morphology and what it means for stability testing4 of 8

Once a dispersion has separated, crystallization stops following the polymer content and runs fast to a plateau.

The three drug–PVP dispersions that separated under humidity showed crystal bands after 22 h (droperidol), 48 h (nifedipine) and 6 days (pimozide) at 94% RH, the two that stayed mixed after 46 (indomethacin) and 125 days (ketoprofen) rumondor2009c R7, R9, R12, R14, R16, C3. In felodipine–PVP powders at 93% RH, 10, 25 and 50% PVP crystallized at about the same initial rate (about 6.4, 5.8 and 5.5 g/day) and stopped within about 20 days at plateaus of about 70, 80 and 75% rumondor2009b R21, R11, C15, C20.

weakWeak to moderate: the timing contrast and the independence from polymer level are consistent across three papers, but the faster crystallization after separation compares different drugs, the rate analysis behind the g/day values is not given, and separation was not measured on the crystallizing powders rumondor2009c K4, X7; rumondor2009b K4, K5, X6, X7.

Felodipine–PVP powders at 93% RH: initial crystallization rate, g/day10% PVP≈6.425% PVP≈5.850% PVP≈5.5

Nearly equal whatever the PVP level, inside overlapping error bars; crystallization then stopped at plateaus of about 70, 80 and 75%. rumondor2009b R21, R11, C20

Separated in humid air: first crystals at 94% RH
droperidol–PVP: 22 hnifedipine–PVP: 48 hpimozide–PVP: 6 days
Stayed one phase: first crystals at 94% RH
indomethacin–PVP: 46 daysketoprofen–PVP: 125 days

rumondor2009c R12, R7, R9, R14, R16, C3

For your drug

  1. If a storage sample shows the separation signature of F12, expect its crystallization to stop depending on polymer content; adding more of the same polymer will not then buy stability.
  2. Compare crystallization at two polymer levels at the storage RH: equal rates point to separation, clearly slower rates at higher polymer to a still-mixed dispersion; do not read a plateau below full crystallinity as a stable residual amorphous fraction.

rumondor2009b C20, R10, C32

How it works and key numbers
  1. In the one-phase route the polymer stays with the drug and can inhibit crystallization rumondor2009c C5.
  2. After separation the drug-rich phase holds little polymer, so crystallization "would be anticipated" to be much faster, a "supposition" the crystallization times "support" rumondor2009c C5, C6, C3.
  3. If the phase compositions are set by the extent of immiscibility, the overall rate "would be expected" to become independent of the amount of polymer, "exactly" as seen at 93% RH rumondor2009b C21, C22.
  4. The plateau "possibly represents" drug in a polymer-rich phase that has not crystallized for kinetic reasons ("Further speculation"); pure amorphous felodipine, by contrast, crystallized completely within 12 days at 93% RH rumondor2009b C30, C32, R12.
22 h to 6 days vs 46–125 daysfirst crystal signs at 94% RH, separating vs mixed PVP dispersionsrumondor2009c R12, R9, R14, R16
6.4 / 5.8 / 5.5 g/dayinitial rates with 10, 25 and 50% PVP at 93% RHrumondor2009b R21, C20
≈70–80%plateaus at 86–93% RH; the rest of the drug stayed amorphous for 494–724 daysrumondor2009b R11, C15

Connections to other chapters

Evidence: data, conditions and papers

Finding F15. Once a dispersion has separated, crystallization no longer follows the polymer content: separated systems crystallized within days, the PVP level stopped mattering at high RH, and crystallization stopped at a plateau

In short. The three drug–PVP dispersions that separated under humidity showed crystal bands after 22 h (droperidol), 48 h (nifedipine) and 6 days (pimozide) at 94% RH, the two that stayed mixed after 46 (indomethacin) and 125 days (ketoprofen) rumondor2009c R7, R9, R12, R14, R16, C3. In felodipine–PVP powders at 93% RH, 10, 25 and 50% PVP crystallized at about the same initial rate (about 6.4, 5.8 and 5.5 g/day) and stopped within about 20 days at plateaus of about 70, 80 and 75%, part of the drug staying amorphous for 494–724 days rumondor2009b R21, R11, C15, C20. Growth rates in 2.5–10% PVP films converged from 64% RH rumondor2010 R5, C21, and felodipine–PVP films showed phase contrast after 1 h and crystals by 4 h at 94% RH marsac2010 R19, C25.

Type. observation in 4 drugs with PVP Strength. to moderate — the timing contrast and the polymer-level independence are consistent across three papers, but the faster crystallization after separation compares different drugs, the rate analysis behind the g/day values is not given, and separation was not measured on the crystallizing powders (rumondor2009c K4: weak to moderate; rumondor2009b K4: moderate, K5: weak to moderate; X7 in both, rumondor2009b X6).

How it was shown

The timings come from the IR storage series of F12 rumondor2009c P4. Rumondor and co-workers (2009) followed PXRD crystallinity of felodipine–PVP powders over time and computed for the dispersions at 93% RH the incremental crystallized mass per day rumondor2009b P5, P7. Rumondor and co-workers (2010) measured growth in films with 2.5–10% PVP rumondor2010 P2, P4.

What the data show

At 93% RH most PVP crystallization happened within the first days, at nearly the same initial rate for 10, 25 and 50% PVP, falling to zero from about 34 days rumondor2009b R7.f, R21, C20. At 33% RH, in contrast, 25 and 50% PVP had crystallized significantly less than 10% PVP rumondor2009b R10.

systemmethod and conditionsresultids
droperidol-, nifedipine-, pimozide–PVP (separating)IR at 94% RHcrystal signs after 22 h, 48 h, 6 daysrumondor2009c R12, R7, R9, C3
indomethacin-, ketoprofen–PVP (mixed)samecrystals after 46 and 125 daysrumondor2009c R14, R16
felodipine, 10, 25, 50% PVP, 93% RHdM/dt from PXRD-PLS≈6.4, 5.8, 5.5 g/day; zero from ≈34 daysrumondor2009b R21, C20
same, 86–93% RHplateau extent≈70, 80, 75%; drug still amorphous after 494–724 daysrumondor2009b R11, R9, C15
felodipine, 2.5–10% PVP filmsgrowth vs RHtwo decades apart at 13% RH; converge from 64% RHrumondor2010 R5, C21
Fig. 8 of rumondor2009b: incremental crystallized mass at 93% RH for 10, 25 and 50% PVP
Fig. 8 · rumondor2009bincremental crystallized mass at 93% RH for 10, 25 and 50% PVP

Nearly the same initial rate for the three PVP levels, falling to zero within about a month; the time axis is logarithmic rumondor2009b R21.

Why

After separation the drug-rich phase holds little polymer, so crystallization "would be anticipated" to be much faster, a "supposition" the crystallization times "support" rumondor2009c C5, C6, C3. If the phase compositions are set by the extent of immiscibility, the overall rate "would be expected" to become independent of the amount of polymer, "exactly" as seen at 93% RH rumondor2009b C21, C22. The plateau "seemed to suggest" a solubility limit, but the numbers argue against it, and it "possibly represents" drug in a polymer-rich phase that has not crystallized for kinetic reasons rumondor2009b C30, C32.

Limits and transfer

Separation was not measured on the crystallizing powders, and the timing contrast compares different drugs rumondor2009b X7; rumondor2009c X7. Separation does not always lead to crystals: nilutamide–PVP showed the separation pattern at all five PVP contents without crystalline nilutamide rumondor2011 R12, C24. Compare crystallization at two polymer levels at the storage RH: equal rates, as at 93% RH here, point to separation, and adding more of the same polymer will not then buy stability.

How it was shown

The timings come from the IR storage series of F12 rumondor2009c P4. Rumondor, Stanford and Taylor (2009) followed PXRD crystallinity of felodipine–PVP and –HPMCAS powders over time (F11) and computed for the PVP dispersions at 93% RH the incremental crystallized mass per day rumondor2009b P5, P7. Rumondor, Jackson and Taylor (2010) measured growth in films with 2.5–10% PVP rumondor2010 P2, P4. Marsac and co-workers (2010) imaged a 50% PVP film by AFM after 1–16 h at 94% RH marsac2010 P3, P14. Tian and co-workers (2016) stored indomethacin powders over desiccant at 40 °C and read crystals by XRD tian2016 P8, P7.

What the data show

Droperidol's carbonyl band moved toward the crystal position after 22 h, nifedipine's crystal bands appeared after 48 h and pimozide's after 6 days; indomethacin crystallized as the δ-polymorph after 46 days and ketoprofen showed crystal bands after 125 days rumondor2009c R12, R7, R9, R14, R16, C21. At 93% RH most PVP crystallization happened within the first days (25% PVP about 47% at about 1 day and 81% at about 4 days), with first-interval rates of about 6.4 (10% PVP), 5.8 (25%) and 5.5 g/day (50%) inside overlapping error bars, falling to zero from about 34 days rumondor2009b R7.f, R21, C20. The plateaus at 86–93% RH were about 70, 80 and 75% and did not differ significantly; Table I gives 73.5 and 73.8% (10% PVP), 77.2 and 82.1% (25%), 78.4 and 75.1% (50%) at 86 and 93% RH rumondor2009b R11, R9.f, R9.g. At 33% RH, in contrast, 25 and 50% PVP had crystallized significantly less than 10% PVP rumondor2009b R10. In films at 13% RH the three PVP levels spanned about two decades in growth rate, at 64% RH about 0.015, 0.0040 and 0.0095 mm/min, and at 93% RH about 0.07–0.15 mm/min rumondor2010 R5.a, R5.d, R5.g, C21. The authors' estimate for the plateau: with 20% of the drug left in a 50% PVP dispersion at 93% RH, the residual phase holds about 0.1 g felodipine per 0.86 g PVP–water, while the solubility, taken as at most 0.025 g/g after a tenfold drop from about 0.25 g per g dry PVP, is far lower rumondor2009b E4, R25, R26, C31. Pure amorphous felodipine crystallized completely within 12 days at 93% RH rumondor2009b R12.

Two later papers fit the pattern. Indomethacin powders above the loading at which a drug-rich phase appeared in films crystallized in 2–15 days at 40 °C over desiccant, with no trend in onset between 40 and 90% drug in HPMCAS (see F30) tian2016 R17. Celecoxib–PVP dispersions, the only binaries with two Tg events after 94% RH, crystallized within a month at that humidity, while the PVPVA and HPMCAS dispersions lasted 150 and 115 days xie2016b R18, R23.

papersystemmethod and conditionsresultids
rumondor2009cdroperidol-, nifedipine-, pimozide–PVP (separating)IR at 94% RHcrystal signs after 22 h, 48 h, 6 daysR12, R7, R9, C3
rumondor2009cindomethacin-, ketoprofen–PVP (mixed)samecrystals after 46 and 125 daysR14, R16
rumondor2009b10, 25, 50% PVP, 93% RHdM/dt from PXRD-PLS≈6.4, 5.8, 5.5 g/day; zero from ≈34 daysR21, C20
rumondor2009bsame, 86–93% RHplateau extent≈70, 80, 75%; drug still amorphous after 494–724 daysR11, R9, C15
rumondor2009b50% PVP, 93% RHmass balance in wordsresidual ≈0.1 g per 0.86 g PVP–water vs ≤0.025 g/g solubilityE4, C31, C32
rumondor20102.5–10% PVP filmsgrowth vs RHtwo decades apart at 13% RH; converge from 64% RHR5, C21
marsac201050% PVP filmAFM at 94% RHphase contrast at 1 h; birefringence at 4 h; crystals 220–440 nm high at 16 hR19, C24, C25
tian2016indomethacin above the miscibility limit with HPMC or HPMCAS40 °C, desiccant, XRDcrystalline in 2–15 days; at or below the limit amorphous 13–14 monthsR17, C57
xie2016bcelecoxib–PVP 6:4 (two Tg events after 94% RH)RT/94% RH, PXRDcrystals within a month; PVPVA and HPMCAS binaries 150 and 115 daysR18, R23
li2016c (outside)telaprevir with HPMC, PVPVA, HPMCASAFM-IR of phase-separated filmsthe lower the polymer in the drug-rich phase, the greater the risk of crystallization on storageC41

Figure

Fig. 8 of rumondor2009b: incremental crystallized mass at 93% RH for 10, 25 and 50% PVP
Fig. 8 · rumondor2009bincremental crystallized mass at 93% RH for 10, 25 and 50% PVP

Nearly the same initial rate for the three PVP levels, falling to zero within about a month; the time axis is logarithmic rumondor2009b R21.

Fig. 11 of rumondor2009c: two routes to crystals from a wet dispersion
Fig. 11 · rumondor2009ctwo routes to crystals from a wet dispersion

Route (ii) goes straight from the wet one-phase dispersion to crystals; route (iii) to (iv) passes through drug-rich amorphous regions, which the authors expect to crystallize faster rumondor2009c C5.

Why

The authors' account, with their hedges: in the one-phase route the polymer stays with the drug and can inhibit crystallization; after separation the drug-rich phase holds little polymer, so crystallization "would be anticipated" to be much faster, a "supposition" the crystallization times "support" rumondor2009c C5, C6, C3. If the phase compositions are set by the extent of immiscibility, the overall rate "would be expected" to become independent of the amount of polymer, "exactly" as seen at 93% RH, which supports the reading that the fast crystallization "can be explained in part" by separation, in addition to higher mobility rumondor2009b C21, C22. Growth in films converges for the same reason ("would explain"; abstract: "probably") rumondor2010 C43. The plateau "seemed to suggest" a solubility limit, but the numbers argue against it, and it "possibly represents" drug in a polymer-rich phase that has not crystallized for kinetic reasons ("Further speculation") rumondor2009b C30, C32. In felodipine–PVP films "it appears" that separation comes first and the drug-rich regions then crystallize marsac2010 C25. (synthesis: the plateau says the separated powder is not simply pure felodipine, which crystallized completely within 12 days; drug left in the polymer-rich phase stayed amorphous for more than a year.)

Conditions and limits

Separation was not measured on the crystallizing powders of the 2009 kinetics study, whose mechanism rests on cited work and the polymer-level independence rumondor2009b X7. The dM/dt calculation, its mass basis and time intervals are not given rumondor2009b X6. The pure-drug reference has no data rumondor2009b X8. The plateau estimate assumes 20% uncrystallized, a cited water uptake and a solubility drop transferred from NMP–water rumondor2009b X9.

Counterexamples and conflicts

The timing contrast of the 2009 IR study compares different drugs; none was crystallized both with and without separation, and the mixed indomethacin–PVP system may simply be less mobile (its wet Tg stays above room temperature with high-molecular-weight PVP) while ketoprofen has the smallest driving force (4.1 kJ/mol) rumondor2009c X7, R20, M5. At 75% RH PVP crystallization kept rising for 100–180 days rather than plateauing within days, so the few-day plateau is a 93% RH observation rumondor2009b X5. Separation does not always lead to crystals: nilutamide–PVP showed the separation pattern at all five PVP contents without crystalline nilutamide, loratadine–PVP separated toward the spectrum of a physical mixture, clofoctol–PVP separated at 50–90% PVP without crystal bands, and for probucol–PVP the phase table lists separation at 30–90% PVP and no crystallization, all at storage times that are not printed rumondor2011 R12, C24, R13, C25, R9, R10, R14, X7. Indoprofen, by contrast, first separated (at 54% RH for 30 and 50% PVP) and then crystallized at 75 and 84% RH, while its 70 and 90% PVP films separated without crystallizing; at 10% PVP it crystallized at the lowest RH used, so whether separation came first cannot be told rumondor2011 R11, R14.a, R14.b, R14.c, C22, C23. Pimozide–PVPVA, separated after 94% RH and dried, was still amorphous but crystallized on DSC heating at about 170 °C rumondor2010c R9, C14. (synthesis: separation removes the polymer's protection from the drug-rich phase, but whether crystals follow within the test depends on the drug's own crystallization tendency; nilutamide and loratadine are not known in this set as fast crystallizers, indoprofen is described as one rumondor2011 C45.) A separated dispersion need not crystallize soon: 30% indomethacin in HPMCAS held a drug-rich phase by three methods and stayed amorphous for 13 months, and miconazole–PVPVA films were separated but showed no further change for 4 weeks at 75% RH tian2016 X5; saboo2017 R16.

Transfer check

If a storage sample shows the separation signature of F12, expect its crystallization to stop depending on polymer content; adding more of the same polymer will not then buy stability rumondor2009b C20. Compare crystallization at two polymer levels at the storage RH: equal rates, as at 93% RH here, point to separation; clearly slower rates at higher polymer, as at 33% RH, to a still-mixed dispersion rumondor2009b R10. A plateau below full crystallinity should not be read as a stable residual amorphous fraction rumondor2009b C32.

History

Rumondor and co-workers (2009) first linked moisture-induced separation to faster crystallization, both across five drugs and through the polymer-level independence of felodipine–PVP at 93% RH rumondor2009c C6; rumondor2009b C22. Marsac and co-workers (2010) imaged separation followed by crystallization, and Rumondor and co-workers (2010) read the converging growth rates the same way marsac2010 C25; rumondor2010 C43. Rumondor and co-workers (2011) added drugs that separated and did not crystallize in their tests (nilutamide, loratadine, clofoctol, probucol) and one, indoprofen, that separated and then crystallized rumondor2011 C24, C22; these are recorded above as limits. Later nanoscale work in the library related the polymer content of drug-rich domains to crystallization risk li2016c C41. Tian and co-workers (2016) tied crystallization in dry storage to separation present from preparation (see F30) tian2016 C57; the title is unchanged.

F16

Topic 4Its morphology and what it means for stability testing5 of 8

In storage only 75% RH or above distinguished PVP from HPMCAS, but such humidity can also change the crystallization route.

For felodipine, about 490 days at 0–52% RH could not tell PVP from HPMCAS by PXRD, whereas 75% RH and above did (PVP 51–82% against HPMCAS 9–28% crystallized) rumondor2009b R19, X4, R9, C13. The same humidity drives susceptible PVP dispersions into amorphous–amorphous separation before crystallization, at 75% RH for felodipine and nifedipine and from 54% RH for pimozide rumondor2009c C4; marsac2010 C51. The authors warn that the crystallization route "may be altered at high RH" and need not represent lower-RH behaviour rumondor2009c C52.

moderateModerate: the discriminating power of high RH is shown directly and the change of route is supported by F12 and F15, but the warning about accelerated testing is the authors' generalization, not a comparison of predicted and real shelf life rumondor2009b K1, K3; rumondor2009c C52.

no distinction or no changechange seenregime change in growthPXRD, PVP vs HPMCASfelodipine, about 490 daysno differencePVP crystallizes morenucleation, 3% polymerPVP about threefold fasterseparation, pimozide–PVPfrom 54% RHseparation, felodipine–PVPdistinct from 75% RHgrowth of neat felodipinejump with needles above 80%two Tgs, celecoxib–PVPonly after 94%0102030405060708090100storage relative humidity, %

Rankings and routes change between about 54 and 94% RH, so one high-humidity condition can answer a different question from storage at moderate RH. rumondor2009b R19, R9, C13; konno2008 R2.b; rumondor2009c R10, R9; marsac2010 R7, C10; rumondor2010 R1; xie2016b R18, R19

Fast batch of an unstable tacrolimus generic, 4 weeks at 40 °C: crystalline, %54% RH≈1175% RH≈84.5

trasi2017 R14

For your drug

  1. Run stability at the intended storage RH and at 75% RH, and at each pull check the phase state (IR against a calculated physical mixture, DSC for a second Tg, near-additive water uptake) as well as crystallinity; do not extrapolate rates between a separated and a mixed condition.
  2. Rank polymers at moderate RH with a method sensitive to early nucleation (site counts or SHG), and where a dispersion with a hygroscopic polymer looks mixed after 75% RH, repeat the phase check after 90–95% RH.

rumondor2009c P7; rumondor2010a C10; rumondor2009b R4, R19; xie2016b R18, R19

How it works and key numbers
  1. At 75% RH and above, susceptible PVP dispersions separate into drug-rich and polymer-rich amorphous phases before they crystallize rumondor2009c C4; marsac2010 C51.
  2. In such systems the route of crystallization "may be altered at high RH" and not represent lower RH, which "highlight[s]" a problem with accelerated conditions rumondor2009c C52.
  3. The immiscibility "may compromise the integrity of the dispersion", so the authors "highlight the importance" of considering storage effects on miscibility when interpreting crystallization data marsac2010 C53; rumondor2009b C33.
  4. At low RH, nucleation counts resolved a threefold difference at 33% RH that PXRD crystallinity, with an error of about 4–5%, could not resolve over 490 days (synthesis) konno2008 R2.b; rumondor2009b R4.
0–52% vs 75–93% RHhumidity that did not vs did distinguish PVP from HPMCAS in about 490 daysrumondor2009b R19, C13
54% RHlowest humidity at which a PVP dispersion (pimozide) began to separaterumondor2009c R10, C4
≈11 vs ≈84.5%tacrolimus generic crystallized in 4 weeks at 40 °C/54% vs 40 °C/75% RHtrasi2017 R14

Connections to other chapters

Evidence: data, conditions and papers

Finding F16. Storage at 75% RH or above separates polymers that dry or moderate storage cannot, but it can also switch a susceptible dispersion to another crystallization route, so high-humidity data need a check of the phase state

In short. For felodipine, about 490 days at 0–52% RH could not tell PVP from HPMCAS (all values within about two RMSEP), whereas 75% RH and above did (PVP 51–82% against HPMCAS 9–28% crystallized) rumondor2009b R19, X4, R9, C13. The same humidity drives susceptible PVP dispersions into amorphous–amorphous separation before crystallization, at 75% RH for felodipine and nifedipine and from 54% RH for pimozide, which led the authors to warn that the crystallization route "may be altered at high RH" and need not represent lower-RH behaviour rumondor2009c C4, C52; marsac2010 C51. Nucleation counts separated the polymers already at 33% RH konno2008 R2, C10, and the authors stress that moisture can "virtually" never be excluded from a formulation konno2008 C8.

Type. method comparison (storage humidity and read-out) in 4 drugs with PVP and HPMCAS Strength. the discriminating power of high RH is shown directly (rumondor2009b K1, K3), the route change is supported by F12 and F15, but the warning about accelerated testing is the authors' generalization, not a comparison of predicted and real shelf life (rumondor2009c C52).

How it was shown

The kinetics study stored felodipine powders at six RH levels for up to 724 days and compared them by F-test at the final common time point rumondor2009b P2, P6. The phase-separation papers stored films at 54–94% RH and read their phase state by IR, DSC, AFM and TEM (F12) rumondor2009c P4; marsac2010 P7. Xie and Taylor (2016) compared DSC after 75 and 94% RH, and Trasi and co-workers (2017) stored capsule contents at 40 °C with 54% and 75% RH xie2016b P7; trasi2017 P7.

What the data show

At 0, 33 and 52% RH PVP and HPMCAS were not significantly different, while every PVP dispersion stored at 66% RH or above crystallized significantly more than at lower RH rumondor2009b R19, R9, R10. Separation was seen after 3 days at 54% RH (pimozide–PVP, partial), after 1 week at 75% RH (felodipine–PVP) and within 1 h at 94% RH rumondor2009c R10, X9; marsac2010 R7, C10; rumondor2009c R9.

systemmethod and conditionsresultids
felodipine, 25 and 50% PVP vs HPMCASF-test after ≈490 days, 0–52% RHno significant difference (within ≈2 RMSEP)rumondor2009b R19, X4
same, 75–93% RHsamePVP 50.8–82.1% vs HPMCAS 9.2–27.7%rumondor2009b R9, C13
felodipine, 3% PVP vs HPMCAS, 33% RHnucleation≈2.0 × 10⁴ vs ≈6.5 × 10³ m⁻³ s⁻¹konno2008 R2.b
celecoxib–PVP 6:4DSC after 3 days at 75 vs 94% RHtwo Tg events only after 94% RHxie2016b R18, R19, C35
tacrolimus generic capsule contents, fast batch4 weeks at 40/54 vs 40/75≈11 vs ≈84.5% crystallinetrasi2017 R14
Fig. 3 of rumondor2009b: felodipine crystallized against time for 25% PVP at six RH levels
Fig. 3 · rumondor2009bfelodipine crystallized against time for 25% PVP at six RH levels

Near zero at 0–52% RH for about 493 days; about 81–89% within two weeks at 93% RH and a slower climb at 75% RH rumondor2009b R7.

Why

Separation at RH as low as 75 or 54% "highlight[s]" a problem with accelerated conditions: in susceptible systems the route of crystallization "may be altered at high RH" and not represent lower RH rumondor2009c C52. Felodipine–PVP dispersions "appear" susceptible at 75% RH or above marsac2010 C51.

Limits and transfer

Felodipine-type NH-donor drugs and PVP at room temperature; no study here compared predicted with observed shelf life rumondor2009b A3; rumondor2009c A2. For HPMCAS dispersions of felodipine, high RH changed little and did not separate them rumondor2009b C10; konno2008 R11. Run stability at the intended storage RH and at 75% RH, check the phase state as well as crystallinity at each pull, and do not extrapolate crystallization rates between a condition that separates the dispersion and one that does not.

How it was shown

The kinetics study stored felodipine powders at six RH levels for up to 724 days and compared them by F-test at the final common time point, using the PLS model error when it exceeded the scatter between triplicates rumondor2009b P2, P6. The phase-separation papers stored films at 54–94% RH and read their phase state by IR, DSC, AFM and TEM (F12) rumondor2009c P4; marsac2010 P7. The nucleation study counted sites at five RH levels (F11) konno2008 P3, P4. Xie and Taylor (2016) compared DSC after 75 and 94% RH; Trasi and co-workers (2017) stored capsule contents at 40 °C with 54% and 75% RH xie2016b P7; trasi2017 P7.

What the data show

At 0, 33 and 52% RH the stabilizing ability of PVP and HPMCAS at a given level was not significantly different (PVP 1.1–5.0%, HPMCAS 8.6–10.7% after about 490 days), while every PVP dispersion stored at 66% RH or above crystallized significantly more than at lower RH rumondor2009b R19, R9, R10. In nucleation at 33% RH, 3% PVP already nucleated about threefold faster than 3% HPMCAS (2.0 × 10⁴ against 6.5 × 10³ m⁻³ s⁻¹) konno2008 R2.b (synthesis: nucleation counts resolve differences that PXRD crystallinity, with an error of about 4–5%, could not resolve over 490 days rumondor2009b R4). Separation was seen after 3 days at 54% RH (pimozide–PVP, partial), after 1 week at 75% RH (felodipine–PVP, distinct) and within 1 h at 94% RH rumondor2009c R10, X9; marsac2010 R7, C10; rumondor2009c R9. With PVPVA, one day at 54% RH already weakened the drug–polymer bands of felodipine, quinidine and pimozide, by IR only; at 84% RH the drug–polymer band of quinidine–PVP lost 47% of its relative intensity rumondor2010c R4, R6, R8, X10. HPMCAS dispersions of felodipine and quinidine stayed one phase after 94% RH rumondor2010c R3.f, R3.g, C16. The growth jump of neat felodipine above 80% RH (F9) and the converging PVP growth rates from 64% RH (F15) are further regime changes inside the 64–93% RH range rumondor2010 R1, R5.

For celecoxib the PVP dispersions showed two Tg events only after 94% RH, not after 75% RH, so a phase check after 75% RH would have read them as mixed, and the three storage conditions gave three polymer orders (see F25) xie2016b R18, R19, C35, X15. In the tacrolimus product survey, 40 °C/54% RH crystallized the fast batch of the unstable generic only about 11% in 4 weeks against about 84.5% at 40 °C/75% RH (see F33) trasi2017 R14.

papersystemmethod and conditionsresultids
rumondor2009b25 and 50% PVP vs HPMCASF-test after ≈490 days, 0–52% RHno significant difference (within ≈2 RMSEP)R19, X4
rumondor2009bsame, 75–93% RHsamePVP 50.8–82.1% vs HPMCAS 9.2–27.7%R9, C13
konno20083% PVP vs HPMCAS, 33% RHnucleation≈2.0 × 10⁴ vs ≈6.5 × 10³ m⁻³ s⁻¹R2.b
rumondor2009cpimozide–PVPIR after 3 days at 54% RHpartial separation signatureR10, C4, X9
marsac2010felodipine–PVP 30.3 wt%IR after 1 week at 33, 58, 75% RHsmall, small, distinctR7, R8, C10
rumondor2010cfelodipine–PVPVA, quinidine–PVP, pimozide–PVPVAIR after 1 day at 54 and 84% RH, driedseparation signs from 54% RH; two Tgs measured only after 94% RHR4, R6, R8, X10
rumondor2010felodipine filmsgrowth at 80–93% RH20–40-fold jump with needles above 80% RHR1, X2
xie2016bcelecoxib–PVP 6:4DSC after 3 days at 75 vs 94% RHtwo Tg events only after 94% RHR18, R19, C35
trasi2017tacrolimus generic capsule contents, fast batch4 weeks at 40/54 vs 40/75≈11 vs ≈84.5% crystallineR14
marsac2008b (outside)PEO compactswater uptake over monthspartially crystalline polymers "may" defeat Arrhenius extrapolation in accelerated testsC40
li2019 (outside)lopinavir–HPMC filmsrelease after humid storageseparation from high-RH storage can alter release without crystallizationC57

Figure

Fig. 3 of rumondor2009b: felodipine crystallized against time for 25% PVP at six RH levels
Fig. 3 · rumondor2009bfelodipine crystallized against time for 25% PVP at six RH levels

Near zero at 0–52% RH for about 493 days; about 81–89% within two weeks at 93% RH and a slower climb at 75% RH; the time axis breaks between 180 and 480 days rumondor2009b R7.

Why

The authors' account, with their hedges: separation at RH as low as 75 or 54% "highlight[s]" a problem with accelerated conditions: in susceptible systems the route of crystallization "may be altered at high RH" and not represent lower RH rumondor2009c C52. Felodipine–PVP dispersions "appear" susceptible at 75% RH or above, and the immiscibility "may compromise the integrity of the dispersion" marsac2010 C51, C53. The kinetics authors "highlight the importance" of considering storage effects on miscibility when interpreting crystallization data rumondor2009b C33. Separation during dissolution, when water activity is very high, "can be postulated" but was not tested rumondor2009c C53. (synthesis: a high-RH test therefore answers two different questions at once, whether the polymer protects in a wet one-phase dispersion and whether the dispersion stays one phase; reading it requires knowing which happened.)

Conditions and limits

Felodipine-type NH-donor drugs and PVP, room temperature; no study here compared predicted with observed shelf life or tested temperature as an accelerating factor rumondor2009b A3; rumondor2009c A2. The RH threshold depends on time and composition marsac2010 X9; rumondor2009c X9.

Counterexamples and conflicts

For HPMCAS dispersions of felodipine, high RH changed little and did not separate them rumondor2009b C10; konno2008 R11, so the warning concerns hygroscopic polymers with susceptible drugs. For polyphenols with PVP, high-RH storage did not trigger failure for more than 200 days wegiel2013a R9. The 2011 authors add that a mixing check should follow every environmental stress, not only production, and expect their results to aid the design of accelerated testing regimes rumondor2011 C26, C3. How harsh a stress must be to rank polymers at all is the subject of F25.

Transfer check

Run stability at the intended storage RH and at 75% RH; at each pull check the phase state (IR against a calculated physical mixture, DSC for a second Tg, near-additive water uptake) as well as crystallinity rumondor2009c P7; rumondor2010a C10. If the 75% RH samples separate and the lower-RH samples do not, do not extrapolate crystallization rates between them. Use a method sensitive to early nucleation (site counts or SHG) to rank polymers at moderate RH, since PXRD with a 4–5% error could not do so within 490 days rumondor2009b R4, R19. Where a dispersion with a hygroscopic polymer looks mixed after 75% RH, repeat the phase check after 90–95% RH, as for celecoxib–PVP xie2016b R18, R19.

History

Konno and Taylor (2008) first noted that moisture can practically never be excluded and that ternary drug–polymer–water systems matter in practice konno2008 C8. Rumondor and co-workers (2009) drew the consequence for accelerated testing from the separation data, and Marsac and co-workers (2010) set the felodipine–PVP threshold at about 75% RH rumondor2009c C52; marsac2010 C51. Rumondor and Taylor (2010) saw separation signs with PVPVA from 54% RH and none with HPMCAS for three of four drugs rumondor2010c C36. Later papers in the library found release changes after humid storage even without crystals li2019 C57 (see ASD process F14) and long equilibration of a semicrystalline polymer that undermines short stress tests (see PEG dispersions F12) marsac2008b C40. Xie and Taylor (2016) and Trasi and co-workers (2017) showed outcomes that change between 75 and 94% RH and between 54 and 75% RH xie2016b C35; trasi2017 C26; the title is unchanged.

F23

Topic 4Its morphology and what it means for stability testing6 of 8

The less water the polymer brings in, the less the dispersion separates in humid storage: PVP > PVPVA > HPMCAS.

At 25 °C and 85% RH, 75:25 drug–polymer powders took up 6.4, 3.6 and 2.4 g water per 100 g with felodipine and 5.3, 3.4 and 2.4 g with quinidine for PVP, PVPVA and HPMCAS rumondor2010c R18, C20. After 84% RH the drug–polymer IR band fell by 50% for felodipine–PVP against 17% for felodipine–PVPVA, and with HPMCAS both drugs stayed one phase after 94% RH rumondor2010c R4, R5, R6, R7, C33, R3.f, R3.g, C16. The authors conclude that the extent of separation "appears to be related" to polymer hygroscopicity; pimozide, the most hydrophobic drug (log P 5.34), separated slightly even with HPMCAS rumondor2010c C38, M3, R3.e, C35.

moderateModerate: the polymer order of separation agrees with the water uptake for two drugs and with later ritonavir data, but the uptake was measured on 75:25 powders at 85% RH, not on the 50:50 test samples, and the thermodynamic and mobility readings are not separated rumondor2010c K3, K5, X6, X7, X12.

Drug–polymer IR band lost after 84% RH, % (note: water uptake of the 75:25 dispersion at 85% RH)felodipine–PVP6.4 g/100 g water50%felodipine–PVPVA3.6 g/100 g17%quinidine–PVP5.3 g/100 g47%quinidine–PVPVA3.4 g/100 g11%

With HPMCAS (2.4 g/100 g for both drugs) felodipine and quinidine stayed one phase even after 94% RH. rumondor2010c R4, R5, R6, R7, C33, R18, R3.f, R3.g, C16

Two Tgs after 94% RH: separated
felodipine–PVPVAquinidine–PVPquinidine–PVPVApimozide–PVPVApimozide–HPMCAS
One Tg after 94% RH: stayed mixed
felodipine–HPMCASquinidine–HPMCASindomethacin–PVPVAindomethacin–HPMCAS

rumondor2010c R3, C10, C16

For your drug

  1. For a hydrophobic drug without a carboxylic-acid donor, expect PVP and PVPVA dispersions to be at risk of separating above about 54–75% RH and HPMCAS to be safer.
  2. Measure the water uptake of the dispersion at the intended composition and RH, not only of the polymer; if the drug's calculated log P is about 5 or higher, test even an HPMCAS dispersion for separation.

rumondor2010c C36, C41, X7, C35, M3

How it works and key numbers
  1. The authors read the results with the ternary Flory–Huggins free energy of mixing, applied qualitatively, with W, D and P for water, drug and polymer: \frac{\Delta G_{mix}}{RT} = n_W \ln\phi_W + n_D \ln\phi_D + n_P \ln\phi_P + n_W\phi_D\chi_{WD} + n_W\phi_P\chi_{WP} + n_D\phi_P\chi_{DP} rumondor2010c E1, C26.
  2. The drugs are hydrophobic, so \chi_{WD} is expected to be positive, and the water–drug enthalpy term grows with the water sorbed, which depends on the hygroscopicity of the matrix rumondor2010c C30.
  3. Less water gives a less positive enthalpy of mixing, which "may explain" why felodipine and quinidine separated with PVP and PVPVA but not with HPMCAS: HPMCAS dispersions "simply do not absorb sufficient water" rumondor2010c C31.
  4. Alternatively, "it is possible that" HPMCAS dispersions are less plasticized, so separation is kinetically slower; pimozide's hydrophobicity "would lead to" a larger water–drug parameter and favour separation even at low moisture rumondor2010c C32, C35.
6.4 / 3.6 / 2.4 g/100 gwater uptake of felodipine 75:25 with PVP / PVPVA / HPMCAS at 85% RHrumondor2010c R18
50% vs 17%loss of the felodipine–polymer IR band, PVP vs PVPVA, after 84% RHrumondor2010c R4, R5, C33
150 vs 115 dayscelecoxib with PVPVA vs HPMCAS at 94% RH, against the water orderxie2016b R23, C50

Connections to other chapters

Evidence: data, conditions and papers

Finding F23. For the same drug, the less water the polymer brings in, the less the dispersion separates in humid storage: PVP > PVPVA > HPMCAS, with a very hydrophobic drug as the exception

In short. At 25 °C and 85% RH, 75:25 drug–polymer powders took up 6.4, 3.6 and 2.4 g water per 100 g with felodipine and 5.3, 3.4 and 2.4 g with quinidine for PVP, PVPVA and HPMCAS rumondor2010c R18, C20. After 84% RH the drug–polymer IR band fell by 50% for felodipine–PVP against 17% for felodipine–PVPVA, and by 47% against 11% for the quinidine pair; with HPMCAS both drugs stayed one phase after 94% RH rumondor2010c R4, R5, R6, R7, C33, R3.f, R3.g, C16. Because the red shifts were similar with PVP and PVPVA, the authors explain the difference "most likely" by the water sorbed, and conclude that the extent of separation "appears to be related" to polymer hygroscopicity rumondor2010c C34, C38. Pimozide, the most hydrophobic drug (log P 5.34), separated slightly even with HPMCAS rumondor2010c M3, R3.e, C35.

Type. comparison of 3 polymers with 4 drugs, with a qualitative thermodynamic argument Strength. the polymer order of separation agrees with the water uptake for two drugs (rumondor2010c K3: moderate) and with later ritonavir data, but the uptake was measured on 75:25 powders at 85% RH, not on the 50:50 test samples, the band reductions are given without method, and the thermodynamic and mobility readings are not separated (rumondor2010c K5: weak to moderate; X6, X7, X12).

How it was shown

Rumondor and Taylor (2010) made 50 wt% dispersions of felodipine, quinidine, pimozide and indomethacin with PVP, PVPVA and HPMCAS as spin-coated films and rotary-evaporated powders; films were taken through 54–94% RH and read by IR after drying, and powders were held 24 h at 94% RH and run by DSC rumondor2010c P1, P5, P4, P7. Water uptake was measured at 85% RH on 75:25 powders rumondor2010c P8, R18.

What the data show

The cited isotherms of the polymers alone give roughly 50, 24 and 8 g/100 g at about 85% RH for PVP, PVPVA and HPMCAS rumondor2010c R19. Felodipine–HPMCAS and quinidine–HPMCAS stayed mixed although their drug–polymer bonds are weaker than with PVP or PVPVA rumondor2010c C29.

systemmethod and conditionsresultids
felodipine and quinidine, 75:25 with PVP, PVPVA, HPMCASwater uptake at 25 °C/85% RH6.4/3.6/2.4 and 5.3/3.4/2.4 g/100 grumondor2010c R18, C20
felodipine and quinidine, 50:50 with PVP vs PVPVAIR after 1 day at 84% RHdrug–polymer band −50% vs −17%; −47% vs −11%rumondor2010c R4, R5, R6, R7, C33
nine 50:50 powdersDSC after 94% RHtwo Tgs for five; one Tg for all three HPMCAS pairs but pimoziderumondor2010c R3, C36
celecoxib 5:5 with PVP, PVPVA, HPMCASDVS 95% RH; DSC after 94% RH17.2–21.8, 7.0, 3.6 g/100 g; two Tg events only with PVPxie2016b R13, R18, C49
celecoxib 6:4, PVPVA vs HPMCASRT/94% RH, PXRD150 vs 115 days, against the water orderxie2016b R23, C50
Table 3 of rumondor2010c: Tg before and after humid storage for nine dispersions
Table 3 · rumondor2010cTg before and after humid storage for nine dispersions

Rows a–e show two Tgs after storage, rows f–i one; only one HPMCAS row (pimozide) is among the separated rumondor2010c R3.

Why

The water–drug enthalpy term grows with the water sorbed, which depends on the hygroscopicity of the matrix rumondor2010c C30. Less water gives a less positive enthalpy of mixing, which "may explain" why felodipine and quinidine separated with PVP and PVPVA but not with HPMCAS: HPMCAS dispersions "simply do not absorb sufficient water" rumondor2010c C31. Alternatively, "it is possible that" HPMCAS dispersions are less plasticized, so separation is kinetically slower rumondor2010c C32. Pimozide's hydrophobicity "would lead to" a larger water–drug parameter and favour separation even at low moisture rumondor2010c C35.

Limits and transfer

Uptake was not measured on the 50:50 samples at their storage RH, and the band reductions are given without method or replicate rumondor2010c X7, X6. Resveratrol–PVP, with the most hygroscopic polymer, stayed amorphous for more than 400 days at 84% RH wegiel2013b R12.e, C35. Measure the water uptake of the dispersion at the intended composition and RH, and if the drug's calculated log P is about 5 or higher, test even an HPMCAS dispersion for separation.

How it was shown

Rumondor and Taylor (2010) made 50 wt% dispersions of felodipine, quinidine, pimozide and indomethacin with PVP, PVPVA and HPMCAS as spin-coated films and rotary-evaporated powders rumondor2010c P1, P5. Films were taken through 54, 75, 84 and 94% RH for at least a day each, dried, and read by IR; powders were held 24 h at 94% RH, dried and run by DSC for one or two Tgs rumondor2010c P4, P7. Water uptake was measured gravimetrically at 85% RH on 75:25 powders, two values taken from a thesis, and compared with cited polymer isotherms rumondor2010c P8, R18, R19. The authors read the results with the ternary Flory–Huggins free energy of mixing, applied qualitatively rumondor2010c E1, C26: Xie and Taylor (2016) measured sorption of celecoxib dispersions and DSC after humidity xie2016b P8, P7.

\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}

where the first three terms are the entropy of mixing and the last three the enthalpy, W, D and P standing for water, drug and polymer rumondor2010c E1.

What the data show

The cited isotherms of the polymers alone give roughly 50, 24 and 8 g/100 g at about 85% RH for PVP, PVPVA and HPMCAS rumondor2010c R19. All nine dry dispersions showed drug–polymer IR bands and one Tg rumondor2010c R1, R2, R3, C9. After 94% RH, felodipine–PVPVA, quinidine–PVP, quinidine–PVPVA, pimozide–PVPVA and pimozide–HPMCAS showed two Tgs, while felodipine–HPMCAS, quinidine–HPMCAS, indomethacin–PVPVA and indomethacin–HPMCAS kept one rumondor2010c R3, C10, C16. Felodipine–HPMCAS and quinidine–HPMCAS stayed mixed although their drug–polymer bonds are weaker than with PVP or PVPVA, so interaction strength alone could not explain the HPMCAS result rumondor2010c C29. In the 20-system table of the next year the authors generalize that HPMCAS dispersions are "in general" less susceptible and PVP dispersions "appear to be highly vulnerable", with a susceptibility that depends strongly on the drug rumondor2011 C29.

Celecoxib and two PVPVA systems confirm the order and add a limit. The celecoxib–PVP dispersions, which took up about 17–22 g/100 g at 95% RH, showed two Tg events after 94% RH, and the PVPVA (7.0) and HPMCAS (3.6) dispersions did not xie2016b R13, R18. PVPVA outlasted HPMCAS at 94% RH (150 against 115 days) although its dispersion took up about twice as much water, which the authors attribute "most likely" to the stronger drug–polymer interaction xie2016b R23, R13, C50. For lumefantrine the authors attribute the early failure of PVPVA "most likely" to its hygroscopicity and the drug's high log P, without measuring water uptake trasi2020 C31. Miconazole–PVPVA separated within a week at 75% RH and ritonavir–PVPVA within minutes at high humidity (see F31) saboo2017 R15; yang2022b R4.

papersystemmethod and conditionsresultids
rumondor2010cfelodipine and quinidine, 75:25 with PVP, PVPVA, HPMCASwater uptake at 25 °C/85% RH6.4/3.6/2.4 and 5.3/3.4/2.4 g/100 gR18, C20
rumondor2010cpolymers alonecited isotherms, ≈85% RH≈50, ≈24, ≈8 g/100 gR19
rumondor2010cfelodipine and quinidine, 50:50 with PVP vs PVPVAIR after 1 day at 84% RHdrug–polymer band −50% vs −17%; −47% vs −11%R4, R5, R6, R7, C33
rumondor2010cnine 50:50 powdersDSC after 94% RHtwo Tgs for five; one Tg for all three HPMCAS pairs but pimozideR3, C36
rumondor2010cpimozide–HPMCASIR and DSC after 94% RHslight separation; Tgs 65 and 79 °CR11, R3.e, C15
rumondor201120 drug–polymer systemsphase-behaviour classesHPMCAS less susceptible in general; PVP highly vulnerableR15, C29
xie2016bcelecoxib 5:5 with PVP, PVPVA, HPMCASDVS 95% RH; DSC after 94% RH17.2–21.8, 7.0, 3.6 g/100 g; two Tg events only with PVPR13, R18, C49
xie2016bcelecoxib 6:4, PVPVA vs HPMCASRT/94% RH, PXRD150 vs 115 days, against the water orderR23, C50
saboo2017miconazole–PVPVA 50:50 film75% RH, confocaldrug-rich domains 1–3 µm at 7 daysR15, C24
purohit2017b (outside)ritonavir with PVP, PVPVA, HPMCAShigh-RH storagePVP and PVPVA separate, HPMCAS stays miscibleC1, C45
purohit2015b (outside)ritonavir–HPMCAS 50:50pyrene probe at 97% RH and in bufferno separationC16

Figure

Table 4 of rumondor2010c: water sorbed at 25 °C/85% RH by 75:25 dispersions
Table 4 · rumondor2010cwater sorbed at 25 °C/85% RH by 75:25 dispersions

The same order, PVP > PVPVA > HPMCAS, for both drugs; two of the six values come from a thesis rumondor2010c R18.

Table 3 of rumondor2010c: Tg before and after humid storage for nine dispersions
Table 3 · rumondor2010cTg before and after humid storage for nine dispersions

Rows a–e show two Tgs after storage, rows f–i one; only one HPMCAS row (pimozide) is among the separated rumondor2010c R3.

Why

The authors' account, with their hedges: the drugs are hydrophobic, so the water–drug parameter is expected to be positive, and the water–drug enthalpy term grows with the water sorbed, which depends on the hygroscopicity of the matrix rumondor2010c C30. Less water gives a less positive enthalpy of mixing, which "may explain" why felodipine and quinidine separated with PVP and PVPVA but not with HPMCAS: HPMCAS dispersions "simply do not absorb sufficient water" to make the environment unfavourable for the drug rumondor2010c C31. Alternatively, "it is possible that" HPMCAS dispersions are less plasticized, so separation is kinetically slower rumondor2010c C32. Pimozide's hydrophobicity "would lead to" a larger water–drug parameter and favour separation even at low moisture rumondor2010c C35. Overall, the balance between the enthalpy and entropy of mixing in the ternary is "suggested" to decide susceptibility, and that balance in turn depends on water sorbed and on drug–polymer interaction strength rumondor2010c C39, C40. Later work in the library separates the roles as thermodynamics deciding whether a dispersion separates and mobility setting how fast li2017 C44.

Conditions and limits

Uptake was not measured for the pimozide or indomethacin dispersions or for the 50:50 samples at their storage RH rumondor2010c X7. The band reductions are the authors' estimates without method or replicate, and felodipine–PVP rests on one spectrum without DSC rumondor2010c X6. Separation at 54% RH is IR evidence only; two Tgs were measured only after 94% RH rumondor2010c X10. No χ value was computed: χDP is ranked by red shift, χWD by calculated log P rumondor2010c X13. The pimozide–HPMCAS Tgs are as far apart as those of the PVPVA pairs, so the "minor" separation rests on IR rumondor2010c X11.

Counterexamples and conflicts

Resveratrol–PVP, with the most hygroscopic polymer, stayed amorphous for more than 400 days at 84% RH, which the authors call the opposite of the felodipine results; the PVP dispersion took up about 13% water against 36% for its physical mixture at 95% RH wegiel2013b R12.e, C35, R19. Their two "possible explanations", hydrogen bonds suppressing sorption and a more hydrophilic drug (log P 3.1 against 4.5 for felodipine) not separating, were not tested wegiel2013b C36, R20, X18. Indomethacin, with a strong acid donor, stayed mixed with PVPVA as with HPMCAS, so a strong bond can outweigh the water (see F13) rumondor2010c C28. In the 2011 study the two most hydrophobic drugs resisted at high drug loading, the opposite direction to pimozide rumondor2011 R14, X14. At higher water uptake the polymer that binds the drug more can still give the longer stability: celecoxib–PVPVA outlasted celecoxib–HPMCAS at 94% RH (xie2016b K6: weak to moderate) xie2016b C50.

Transfer check

For a hydrophobic drug without a carboxylic-acid donor, expect PVP and PVPVA dispersions to be at risk of separating above about 54–75% RH and HPMCAS to be safer rumondor2010c C36, C41. Measure the water uptake of the dispersion at the intended composition and RH, not only of the polymer rumondor2010c X7. If the drug's calculated log P is about 5 or higher, test even an HPMCAS dispersion for separation rumondor2010c C35, M3.

History

The 2009 PVP study had tied separation to the drug's donor (see F12, F13) rumondor2009c C47. Rumondor and Taylor (2010) varied the polymer and tied the extent of separation to its hygroscopicity rumondor2010c C38, and Rumondor and co-workers (2011) generalized the polymer effect across 20 systems rumondor2011 C29. Later ritonavir work reached the same polymer order with several methods (see Solid-state methods F17) purohit2017b C1; purohit2015b C25. Xie and Taylor (2016) confirmed the order for celecoxib and found PVPVA ahead of HPMCAS at 94% RH xie2016b C49, C50; Saboo and Taylor (2017) and Yang and co-workers (2022) imaged the PVPVA separation directly (see F31) saboo2017 C24; yang2022b C1; the title is unchanged.

F31

Topic 4Its morphology and what it means for stability testing7 of 8

How water reaches a mixed dispersion sets the pattern of separation; heat without water does not separate it.

Miconazole–PVPVA 50:50 films spin-coated at 20% RH were uniform, while films cast at 45–60% RH held drug-rich pits of 0.3–0.7 µm in a PVPVA-rich matrix saboo2017 R5, R6, R7, R8, C10, C13, C14. Dry-made films stored at 75% RH formed drug-rich domains of 1–3 µm within a week, whereas in pH 6.8 buffer they formed a coarse connected (bicontinuous) structure of 10–25 µm by 30 min saboo2017 R15, R16, C24, R18, R19, C28. Powder annealed at 100 °C for 60 min kept one Tg saboo2017 R22.

moderateModerate: the routes give clearly different patterns and two dye-free methods agree with the dyes, but the buffer and storage samples were dried before imaging, early storage times were not reported, and water contents were not measured saboo2017 K1, K3, X7, X8, X12, X14; yang2022b K1.

drug-rich domains in a polymer-rich matrixpolymer-rich domains or connected networkcast at 45–60% RHpits 0.3–0.7droplets up to 15made dry, 7 days at 75% RH1–3made dry, 5 min in bufferpolymer-rich 4–8made dry, 30 min in bufferbicontinuous 10–250.1110size of separated domains in miconazole–PVPVA films, µm (log scale)

Films cast at 20% RH stayed uniform and dry powder annealed at 100 °C kept one Tg; slow humid routes give drug-rich droplets, liquid water a coarse network within minutes. saboo2017 R5, R6, R8, R13, R15, R18, R19, R22

dry26after 75% RH1048after 100% RH−568−1001020304050607080Tg of miconazole–PVPVA 50:50 powder, °C

One Tg dry, two after humidity, further apart after more water. saboo2017 R14, R17, R21

For your drug

  1. Keep RH low (about 20% in this paper) during film casting or spray drying of a hydrophobic drug with PVPVA.
  2. Test the dry-made material three ways (dry heat, humid storage for at least a week, a few minutes in buffer), image each with a phase-specific probe, and read a continuous drug-rich network after buffer as a warning for release.

saboo2017 R5, C10, R15, R18, R22; yang2022a C13, C14

How it works and key numbers
  1. Water acts as an antisolvent for the hydrophobic drug; because the dry system shows no separation even at 100 °C, the miscibility gap "do[es] not appear" to be inherent, and mobility "is not the sole criterion" saboo2017 C41, C42, C44.
  2. In humid storage separation "may" go by nucleation and growth of drug-rich droplets saboo2017 C40.
  3. In buffer the polymer-rich phase "most likely" dissolves faster, leaving a drug-rich network saboo2017 C29.
  4. For ritonavir–PVPVA the authors place the hydration paths on a schematic ternary diagram: low loading enters the metastable region (nucleation and growth), higher loading the unstable region (spinodal decomposition); 30% drug was bicontinuous by 5 min, 20% drug barely separated at 30 min yang2022b C50, E1, R3, R4.
0.3–0.7 µmdrug-rich pits in films cast at 45–60% RHsaboo2017 R6, R8
1–3 µm in 7 daysdrug-rich domains in dry-made films at 75% RHsaboo2017 R15, C24
10–25 µm in 30 minbicontinuous structure in pH 6.8 buffersaboo2017 R19, C28
Evidence: data, conditions and papers

Finding F31. How water reaches a mixed dispersion sets the pattern of separation: humid air during casting or storage gives drug-rich droplets in a polymer-rich matrix, liquid buffer gives coarse connected domains within minutes, more drug speeds and coarsens the split, and heat without water does not separate

In short. Miconazole–PVPVA 50:50 films spin-coated at 20% RH were uniform, while films cast at 45–60% RH held drug-rich pits of 0.3–0.7 µm in a PVPVA-rich matrix saboo2017 R5, R6, R7, R8, C10, C13, C14. Films made dry and stored at 75% RH formed drug-rich domains of 1–3 µm within a week, with no change to 4 weeks saboo2017 R15, R16, C24. Immersed in pH 6.8 buffer they formed polymer-rich domains of 4–8 µm in a drug-rich matrix within 5 min and a bicontinuous structure of 10–25 µm by 30 min saboo2017 R18, R19, C28. Powder annealed at 100 °C for 60 min kept one Tg saboo2017 R22. In ritonavir–PVPVA films at high humidity and 37 °C, 30% drug had separated into a bicontinuous structure by 5 min and coarsened, while 20% drug was barely separated at 30 min yang2022b R3, R4.

Type. observation in 2 drug–PVPVA systems with 3 routes of water exposure, by confocal fluorescence, AFM-IR and DSC Strength. the routes give clearly different patterns and two dye-free methods agree with the dyes (saboo2017 K1: strong; K3: moderate to strong; yang2022b K1: moderate to strong), but the buffer and storage snapshots were dried before imaging, early storage times were not reported, water contents were not measured, and the ritonavir RH is not printed (saboo2017 X7, X8, X12, X14; yang2022b P4).

How it was shown

Saboo and Taylor (2017) spin-coated 50:50 miconazole–PVPVA films at 20% or at 45–60% RH, and imaged them with prodan (drug-rich phase) and rhodamine 6G (polymer-rich phase) and, dye-free, by AFM-IR saboo2017 M1, M2, P1, A1, P4, P7. Dry-made films were stored at 75% RH for 1–28 days or immersed in pH 6.8 buffer for 5–30 min, and powders were tested by modulated DSC saboo2017 P2, P3, P10, P11, P12. Yang and co-workers (2022) imaged ritonavir–PVPVA films in a humidity chamber at 37 °C yang2022b P2, P4.

What the data show

The dry powder had one Tg of 26 °C; after 75% RH it showed 10 and 48 °C, after 100% RH −5 and 68 °C, and after 60 min at 100 °C still one Tg saboo2017 R14, R17, R21, R22.

systemmethod and conditionsresultids
miconazole–PVPVA 50:50 filmsspin-coated at 20% against 45–60% RH; AFM-IR, confocaluniform against drug-rich pits 0.3–0.7 µm and droplets <1–15 µm in polymer-rich matrixsaboo2017 R5, R6, R8, R13, C14
dry-made films75% RH, 1–28 daysdrug-rich domains 1–3 µm at 7 days, unchanged to 4 weekssaboo2017 R15, R16, C24
dry-made filmspH 6.8 buffer, 5–30 min, driedpolymer-rich 4–8 µm domains (5 min), bicontinuous 10–25 µm (30 min)saboo2017 R18, R19, C28
ritonavir–PVPVA films, 20 and 30% drughigh RH, 37 °C, confocal, 0–30 min20%: barely separated at 30 min; 30%: bicontinuous at 5 min, coarsenedyang2022b R3, R4, C52
Graphical abstract of saboo2017: confocal images of miconazole–PVPVA films made dry, made at high RH, stored at 75% RH and immersed in buffer
Graphical abstract · saboo2017confocal images of miconazole–PVPVA films made dry, made at high RH, stored at 75% RH and immersed in buffer

Green is the drug-rich prodan signal and red the polymer-rich rhodamine signal; the dry film is uniform, humid routes give droplets of drug-rich phase, and buffer gives the coarse connected pattern saboo2017 R5, R13, R15, R18.

Why

Water acts as an antisolvent for the hydrophobic drug, and because the dry system shows no separation even at 100 °C the miscibility gap "do[es] not appear" to be inherent; mobility "is not the sole criterion" saboo2017 C41, C42, C44. Separation in humid storage "may" go by nucleation and growth of drug-rich droplets, while in buffer the polymer-rich phase "most likely" dissolves faster, leaving a drug-rich network saboo2017 C40, C29.

Limits and transfer

Thin films; early storage times were not reported, the water contents were not measured, and buffer-immersed films were dried before imaging saboo2017 X7, X8, X12. Keep RH low during film casting or spray drying of a hydrophobic drug with PVPVA, and test the dry-made material by dry heat, humid storage for at least a week and a few minutes in buffer, imaging each with a phase-specific probe.

How it was shown

Saboo and Taylor (2017) spin-coated 50:50 miconazole (Tg 0 °C) and PVPVA (Tg 107 °C) films about 300 nm thick from methanol–dichloromethane, at 20% RH in a nitrogen glove box or at 45–60% RH in the laboratory saboo2017 M1, M2, P1, A1. Of eight fluorescent dyes, prodan (drug-rich phase) and rhodamine 6G (polymer-rich phase) were chosen because they did not bleach; dye-free films were read by AFM-IR at the drug band (1590 cm⁻¹) and the polymer band (1679 cm⁻¹) and by Lorentz contact resonance saboo2017 P4, R11, C18, C19, P5, P7, P8. Dry-made films were stored at 75% RH for 1–28 days or immersed in pH 6.8 buffer for 5–30 min and dried; 50:50 powders were exposed to 75 or 100% RH or annealed at 100 °C and tested by modulated DSC saboo2017 P2, P3, P10, P11, P12, A4. Yang and co-workers (2022) imaged ritonavir–PVPVA films with Nile red and Alexa Fluor 488 in a humidity chamber at 37 °C, checked against label-free optical photothermal IR (O-PTIR) yang2022b P2, P4, P9, R1, R2, C6.

What the data show

Five AFM-IR spectra of a dry-cast film were identical; a film cast at 60% RH had pits 200–400 nm deep whose spectra were drug-rich, in a polymer-rich matrix, and the confocal images showed prodan droplets from below 1 µm to about 15 µm in a continuous rhodamine phase saboo2017 R5, R12, R6, R7, R8, R13, X5. A film cast at 45% RH showed discrete stiff spots by contact resonance saboo2017 R9, R10, C17. After a week at 75% RH dry-made films held drug-rich domains of 1–3 µm, and no further change by 4 weeks saboo2017 R15, R16. The dry powder had one Tg of 26 °C; after 75% RH it showed 10 and 48 °C, after 100% RH −5 and 68 °C saboo2017 R14, R17, R21, C23, C25. In buffer, polymer-rich domains of 4–8 µm sat in a drug-rich matrix at 5 min and a bicontinuous network of 10–25 µm had formed by 30 min, with the drug-rich regions higher, coarser than after humid storage saboo2017 R18, R19, R20, C28, C46. Annealing at 100 °C for 60 min left one Tg saboo2017 R22. In ritonavir–PVPVA at high humidity, 20% drug showed only a fine bicontinuous texture at 30 min, while 30% drug was bicontinuous at 5 min and had become a coarser drug-rich network at 10–30 min yang2022b R3, R4.

papersystemmethod and conditionsresultids
saboo2017miconazole–PVPVA 50:50 filmsspin-coated at 20% against 45–60% RH; AFM-IR, confocaluniform against drug-rich pits 0.3–0.7 µm and droplets <1–15 µm in polymer-rich matrixR5, R6, R8, R13, C14
saboo2017dry-made films75% RH, 1–28 daysdrug-rich domains 1–3 µm at 7 days, unchanged to 4 weeksR15, R16, C24
saboo2017dry-made filmspH 6.8 buffer, 5–30 min, driedpolymer-rich 4–8 µm domains (5 min), bicontinuous 10–25 µm (30 min)R18, R19, C28
saboo201750:50 powderDSC after 75%, 100% RH; after 100 °C, 60 minTg 26 → 10 and 48 °C; −5 and 68 °C; one Tg after annealingR14, R17, R21, R22
yang2022britonavir–PVPVA films, 20 and 30% drughigh RH, 37 °C, confocal, 0–30 min20%: barely separated at 30 min; 30%: bicontinuous at 5 min, coarsenedR3, R4, C52
purohit2015b (outside)probucol–PVP, ritonavir–PVP filmsimmersion in buffer against high RHseparation faster in bulk water, read as the same processC25
yang2022a (outside)ritonavir–PVPVA compactsrelease with confocal imaging20% drug congruent and complete; 30% polymer faster than drug; 40% and above no drug releaseC12, C13, C14

Figure

Graphical abstract of saboo2017: confocal images of miconazole–PVPVA films made dry, made at high RH, stored at 75% RH and immersed in buffer
Graphical abstract · saboo2017confocal images of miconazole–PVPVA films made dry, made at high RH, stored at 75% RH and immersed in buffer

Green is the drug-rich prodan signal and red the polymer-rich rhodamine signal; the dry film is uniform, humid routes give droplets of drug-rich phase, and buffer gives the coarse connected pattern saboo2017 R5, R13, R15, R18.

Fig. 3 of yang2022b: time-lapse confocal images of ritonavir–PVPVA films at high humidity, binary and with four surfactants
Fig. 3 · yang2022btime-lapse confocal images of ritonavir–PVPVA films at high humidity, binary and with four surfactants

Rows a and b are the binary films with 20 and 30% drug (red: drug-rich, Nile red; green: polymer-rich, Alexa Fluor 488); rows c–f carry surfactants (see F32); rows c and d have 10 µm scale bars, the others 50 µm yang2022b R3, R4, X2.

Why

The authors' account, with their hedges: water acts as an antisolvent for the hydrophobic drug and, because the dry system shows no separation even at 100 °C, the miscibility gap "do[es] not appear" to be inherent; "evidence is provided" for a thermodynamic water-driven (Δχ) effect, and mobility "is not the sole criterion" saboo2017 C41, C42, C43, C44. This agrees with the view that thermodynamics decides whether moisture splits a dispersion and mobility sets how fast li2017 C44. Separation in humid storage "may" go by nucleation and growth of drug-rich droplets saboo2017 C40; in buffer the polymer-rich phase "most likely" dissolves faster, leaving a drug-rich network saboo2017 C29. For ritonavir the authors place the hydration paths on a schematic ternary diagram: low loading enters the metastable region (nucleation and growth), higher loading the unstable region (spinodal decomposition), and the lever rule sets which phase is continuous yang2022b C50, E1. More polymer means a more viscous film and slower demixing yang2022b C52. (synthesis: in both papers the morphology tracks how much water enters and how fast: humid air during casting or storage, a slow supply, gave discrete drug-rich droplets in polymer-rich matrix; bulk water gave a connected drug-rich network within minutes. This is the same pattern as for the films and particles of ASD process F1, F4 and F6.)

Conditions and limits

Thin spin-coated films; the storage study did not report days 1–3, the water contents of the films and powders were not measured, and buffer-immersed films were dried before imaging saboo2017 X7, X8, X12. Confocal images were taken on dyed films and AFM on separate dye-free films saboo2017 X14. The diffraction limit is about 150 nm by the authors' estimate (137 nm recomputed), so finer domains are not resolved saboo2017 E1, X3. The caption of the buffer figure contradicts the text on which phase forms the domains saboo2017 X2. The ritonavir chamber RH is not printed yang2022b P4.

Counterexamples and conflicts

Heating does not separate, but in felodipine–PVP it also did not quickly remix water-induced domains, so a single Tg after annealing does not show that a separated film would remix (see F14) saboo2017 R22; marsac2010 R17, C47. The two papers disagree on what is the matrix in water: in miconazole buffer films the drug-rich phase is continuous saboo2017 R19, while in ritonavir humid films at 30% drug both phases are continuous yang2022b R4.

Transfer check

Keep RH low (about 20% in this paper) during film casting or spray drying of a hydrophobic drug with PVPVA saboo2017 R5, C10. Test the dry-made material three ways: dry heat, humid storage for at least a week, and a few minutes in buffer, and image each with a phase-specific probe saboo2017 R15, R18, R22. Read a continuous drug-rich network after buffer exposure as a warning for release, since in ritonavir–PVPVA a continuous drug-rich layer from 30% drug onward stopped drug release yang2022a C13, C14; yang2021 C33.

History

Separation of PVP and PVPVA dispersions by humidity was shown with IR and DSC in 2009–2011 (see F12), and in buffer by probe fluorescence in 2015 (see Solid-state methods F18) purohit2015b C25. Saboo and Taylor (2017) imaged the patterns of three routes in one system, and Yang and co-workers (2022) added time-lapse at high humidity and tied morphology to loading saboo2017 C49; yang2022b C3. Later work related the morphology to release yang2022a C12, C13, C14.

Formulaslever rule
F32

Topic 4Its morphology and what it means for stability testing8 of 8

In humid ritonavir–PVPVA films, SDS and Tween 80 delayed separation, while Span 20 and Span 85 separated them at once.

With 5 parts surfactant per 100 parts of a 30:70 ritonavir–PVPVA film at high humidity and 37 °C, SDS and Tween 80 films were still homogeneous at 5 min and later held discrete round drug-rich domains yang2022b R5, R6, C7. Span 20 and Span 85 films had separated by 5 min and coarsened into irregular or continuous drug-rich regions, as did the binary film yang2022b R7, R8, R4, C7. Each surfactant sat in the phase its hydrophilicity predicts: SDS in the polymer-rich phase, Tween 80 and Span 85 in the drug-rich phase, Span 20 in the drug-rich phase and at a mixed rim yang2022b R17, R18, R19, R20, R21, R22.

moderateModerate: orthogonal methods agree on where each surfactant goes, but the delay rests on optical images at two magnifications, domains below the resolution were not excluded, and storage and release were not measured yang2022b K4, K5, K6, K7, X2, X3, X10.

Ritonavir in pH 6.8 buffer: concentration at which a drug-rich liquid phase separates, µg/mLritonavir alone≈36+ PVPVA≈36+ SDSHLB 40≈35+ Tween 80HLB 15≈26+ Span 20HLB 8.6≈13+ Span 85HLB 1.8≈15

The more lipophilic surfactants enter the drug-rich phase and lower the concentration at which it forms. yang2022b R10, C18, C19, M3, M4, M5, M6

Delayed separation, round drug-rich domains
SDSTween 80
Located in the drug-rich phase of the film
Tween 80Span 20Span 85

yang2022b R5, R6, R7, R8, R17, R18, R19, R20, R21, R22

For your drug

  1. For a surfactant-containing dispersion of a hydrophobic drug, measure the drug's separation concentration in buffer with and without the surfactant; a fall shows that the surfactant enters the drug-rich phase and will plasticize it.
  2. Expose a film to high humidity and image it at early times: round discrete drug-rich domains are the pattern that later released drug, a continuous drug-rich network the pattern that did not; storage stability with SDS or Tween 80 remains to be tested.

yang2022b R10, C58, C59; yang2023 C40; saboo2021 C30

How it works and key numbers
  1. Each surfactant goes to the phase that its hydrophilicity predicts ("expected"), and the solution data predict the film result yang2022b C35, C44.
  2. Surfactants at the drug–polymer interface, as the zeta potentials suggest for SDS and Tween 80, "would be expected" to slow diffusion and lower the interfacial tension, so domains stay round and ripen slowly, the separation proceeding "likely" by nucleation and growth yang2022b C56, C57.
  3. The Spans sit mainly in the drug-rich phase and "likely" plasticize it, which speeds separation and coalescence into irregular shapes yang2022b C58.
  4. In buffer the Spans lowered the separation concentration of ritonavir from about 36 to 13–15 µg/mL, and NMR showed the more lipophilic surfactants entering the drug-rich nanodroplets yang2022b R10, R13, C18.
36 → 13–15 µg/mLritonavir separation concentration alone vs with Span 20 or Span 85yang2022b R10, C18
5 mintime by which the Span and binary films had separatedyang2022b R4, R7, R8
HLB 40 to 1.8range of the four surfactants, from SDS to Span 85yang2022b M3, M4, M5, M6
Evidence: data, conditions and papers

Finding F32. Surfactants in a ritonavir–PVPVA film change when and how humidity splits it: SDS and Tween 80 delayed visible separation and gave round drug-rich domains, while Span 20 and Span 85 separated it at once into coarse irregular domains, and each surfactant sat in the phase its hydrophilicity predicts

In short. With 5 parts surfactant per 100 parts of a 30:70 ritonavir–PVPVA film at high humidity and 37 °C, SDS and Tween 80 films were still homogeneous at 5 min and later held discrete round drug-rich domains, whereas Span 20 and Span 85 films had separated by 5 min and coarsened into irregular or continuous drug-rich regions, as did the binary film yang2022b R5, R6, R7, R8, R4, C7. O-PTIR placed SDS only in the polymer-rich phase, Tween 80 and Span 85 in the drug-rich phase and Span 20 in the drug-rich phase and at a mixed rim yang2022b R17–R22, C34–C38. In buffer, ritonavir separated as a drug-rich liquid at about 36 µg/mL alone, with PVPVA or with SDS, but at about 26, 13 and 15 µg/mL with Tween 80, Span 20 and Span 85, and NMR showed the more lipophilic surfactants entering the nanodroplets yang2022b R10, R13, C18, C19, C24–C28. The authors expect SDS and Tween 80 dispersions to be more stable in storage ("would be expected"), which was not tested yang2022b C59.

Type. observation in 1 drug–polymer pair with 4 surfactants, by confocal imaging, O-PTIR, NMR, zeta potential and LLPS titration Strength. orthogonal methods agree on where each surfactant goes (yang2022b K4, K5: moderate to strong), but the delay rests on optical images at two magnifications, domains below the resolution were not excluded, the interface location is inferred from zeta potential, and storage and release were not measured (yang2022b X2, X3, X10; K6, K7: weak).

How it was shown

Yang and co-workers (2022) spin-coated ritonavir–PVPVA 30:70 films with 5 parts SDS (HLB 40), Tween 80 (15), Span 20 (8.6) or Span 85 (1.8), labelled the two phases with two dyes, and imaged them at high humidity at 37 °C for 30 min yang2022b M3, M4, M5, M6, P2, P4, A2. Label-free films were mapped by O-PTIR, and in pH 6.8 buffer the separation concentration of the drug and surfactant entry into the drug-rich nanodroplets (¹H NMR) were measured yang2022b P3, P9, P5, P6.

What the data show

Ripening occurred in all films, least visibly with Tween 80 and most with the Spans yang2022b C10.

systemmethod and conditionsresultids
ritonavir–PVPVA 30:70 + 5 parts SDS or Tween 80high RH, 37 °C, confocalhomogeneous at 5 min; discrete round drug-rich domains lateryang2022b R5, R6, C7
+ 5 parts Span 20 or Span 85sameseparated by 5 min; coarse irregular or continuous drug-rich regionsyang2022b R7, R8, C7
ritonavir in pH 6.8 buffer with each additiveLLPS titration, 37 °C≈36 (alone, PVPVA), 35 (SDS), 26 (Tween 80), 13 (Span 20), 15 µg/mL (Span 85)yang2022b R10, C18
nanodroplets with surfactant¹H NMRSDS none; Tween 80 some; Span 20 more; Span 85 most in the drug-rich phaseyang2022b R13, C24–C28
humidified label-free filmsO-PTIR mapsSDS polymer-rich; Tween 80, Span 85 drug-rich; Span 20 drug-rich and rimyang2022b R17–R22, C34–C38
Fig. 10 of yang2022b: O-PTIR ratio maps of humidified ritonavir–PVPVA films with each surfactant
Fig. 10 · yang2022bO-PTIR ratio maps of humidified ritonavir–PVPVA films with each surfactant

Panel a is the binary film, a connected drug-rich network; in the SDS film (c–d) the polymer map and the SDS map coincide, and in the Tween 80 film (e–f) the drug map and the Tween 80 map coincide in round domains of about 6–8 µm yang2022b R23, R24, R25, R26.

Why

Each surfactant goes to the phase that its hydrophilicity predicts ("expected"), and the solution data predict the film result yang2022b C35, C44. Surfactants at the drug–polymer interface, as the zeta potentials suggest for SDS and Tween 80, "would be expected" to slow diffusion and lower the interfacial tension, so domains stay round and ripen slowly yang2022b C56, C57. The Spans sit mainly in the drug-rich phase, plasticize it "likely" and so speed separation and coalescence into irregular shapes yang2022b C58.

Limits and transfer

One drug, polymer, loading and RH, and the SDS and Tween 80 films were imaged at higher magnification, so "retarded" means delayed appearance of optically resolved domains yang2022b A2, P4, X2, X3. Better storage stability with SDS or Tween 80 is a prediction; crystallization was not followed yang2022b C59. Measure the drug's separation concentration in buffer with and without the surfactant, then expose a film to high humidity and image it at early times.

How it was shown

Yang and co-workers (2022) spin-coated ritonavir–PVPVA 30:70 films with 5 parts SDS (HLB 40), Tween 80 (15), Span 20 (8.6) or Span 85 (1.8), labelled the drug-rich phase with Nile red and the polymer-rich phase with Alexa Fluor 488, and imaged them at high humidity at 37 °C for 30 min yang2022b M3, M4, M5, M6, P2, P4, A2. Label-free films were exposed to humidity and mapped by O-PTIR, using bands specific to each component yang2022b P3, P9. In pH 6.8 buffer the authors measured the concentration at which ritonavir separates as a drug-rich liquid (UV extinction during titration), surfactant entry into the drug-rich nanodroplets (¹H NMR at 800 MHz), droplet zeta potential, and PVPVA left in solution after centrifugation yang2022b P5, P6, P7, P8.

What the data show

The binary 30% film was bicontinuous at 5 min and coarsened by 10–30 min yang2022b R4. SDS and Tween 80 films were homogeneous at 0 and 5 min; SDS gave a fine texture at 10 min and discrete round drug-rich domains at 30 min, Tween 80 dense, very small discrete domains at 10 and 30 min yang2022b R5, R6. Span 20 films showed irregular drug-rich domains with bicontinuous regions at 5 min and large polymer-rich areas by 10–30 min; Span 85 films were bicontinuous at 5 min and coarsened to continuous drug-rich regions yang2022b R7, R8. Ripening occurred in all, least visibly with Tween 80 and most with the Spans yang2022b C10. The separation concentration in buffer was about 36 µg/mL alone and with PVPVA, 35 with SDS, 26 with Tween 80, 13 with Span 20 and 15 µg/mL with Span 85 yang2022b R10, C18, C19. NMR found no SDS in the nanodroplets, some Tween 80, more Span 20 and most of the Span 85 yang2022b R13, C24, C25, C26, C27, C28. PVPVA was not depleted from solution (775–860 µg/mL against 800 added) yang2022b R15, C31. Droplets in buffer had a zeta potential of −10.8 mV, about −0.4 to −1.1 mV with PVPVA or Tween 80, −21 to −40 mV with SDS and −9 to −21 mV with the Spans yang2022b R9, C11, C12, C13, C14, C15. In films O-PTIR found SDS only in polymer-rich regions, Tween 80 and Span 85 in drug-rich regions, and Span 20 in drug-rich regions and a mixed rim yang2022b R17, R18, R19, R20, R21, R22.

papersystemmethod and conditionsresultids
yang2022britonavir–PVPVA 30:70, no surfactanthigh RH, 37 °C, confocalbicontinuous at 5 min, coarsened by 10–30 minR4
yang2022b+ 5 parts SDS or Tween 80samehomogeneous at 5 min; discrete round drug-rich domains laterR5, R6, C7
yang2022b+ 5 parts Span 20 or Span 85sameseparated by 5 min; coarse irregular or continuous drug-rich regionsR7, R8, C7
yang2022britonavir in pH 6.8 buffer with each additiveLLPS titration, 37 °C≈36 (alone, PVPVA), 35 (SDS), 26 (Tween 80), 13 (Span 20), 15 µg/mL (Span 85)R10, C18
yang2022bnanodroplets with surfactant¹H NMRSDS none; Tween 80 some; Span 20 more; Span 85 most in the drug-rich phaseR13, C24–C28
yang2022bhumidified label-free filmsO-PTIR mapsSDS polymer-rich; Tween 80, Span 85 drug-rich; Span 20 drug-rich and rimR17–R22, C34–C38
saboo2021 (outside)felodipine–PVPVA with 0–10% TPGSfilms after high RH, AFMirregular semi-continuous domains at 0–2% TPGS, round discrete domains at 5–10%C24, C40, C51
yang2023 (outside)ritonavir–PVPVA with the four surfactantsrelease from compacts with imagingevery releasing system lacked a continuous drug-rich barrierC40, C3

Figure

Fig. 10 of yang2022b: O-PTIR ratio maps of humidified ritonavir–PVPVA films with each surfactant
Fig. 10 · yang2022bO-PTIR ratio maps of humidified ritonavir–PVPVA films with each surfactant

Panel a is the binary film (a connected drug-rich network), b the Span 20 film with an intermediate-ratio rim around drug-rich domains, c–d the SDS film where the polymer map and the SDS map coincide, e–f the Tween 80 film where the drug map and the Tween 80 map coincide in round domains of about 6–8 µm yang2022b R23, R24, R25, R26.

Fig. 3 of the same paper, shown in F31, gives the time-lapse images: compare rows c and d (SDS, Tween 80; 10 µm scale bars) with rows e and f (Spans; 50 µm) yang2022b R5, R6, R7, R8, X2.

Why

The authors' account, with their hedges: each surfactant goes to the phase that its hydrophilicity predicts ("expected"), and the solution data predict the film result yang2022b C35, C44. Surfactants at the drug–polymer interface, as the zeta potentials suggest for SDS and Tween 80, "would be expected" to slow diffusion and to lower the interfacial tension, so domains stay round and ripen slowly, the separation proceeding "likely" by nucleation and growth yang2022b C56, C57. The Spans sit mainly in the drug-rich phase, plasticize it "likely" and so speed separation and coalescence into irregular shapes yang2022b C58. A surfactant "will be likely" to move the spinodal, binodal and vitrification lines of the drug–polymer–water diagram (see F31) yang2022b C54. (synthesis: the Spans lowered the separation concentration of ritonavir 2.4–2.8-fold (36 against 13–15 µg/mL), as a second component that mixes into the drug-rich phase lowers the amorphous solubility (see C. Amorphous solubility and LLPS F11); in the solid they act as plasticizers of that phase, as TPGS and other miscible surfactants speed crystal growth of celecoxib in F22.)

Conditions and limits

One drug, one polymer, one loading (30%), 5 parts surfactant for the time series (10 parts for some maps), one high RH at 37 °C yang2022b A2, P4. SDS and Tween 80 films were imaged at higher magnification, and the authors allow that domains below visible size may already exist at 5 min, so "retarded" means delayed appearance of optically resolved domains yang2022b X2, X3. Interface placement is inferred from zeta potential in solution yang2022b X10. Tgs are only in the supplement yang2022b X13.

Counterexamples and conflicts

Tween 80 partitioned to a different extent in humidified films and in the NMR of nanodroplets, which the authors attribute to different hydration, so the solution measure gives the direction but not the film composition yang2022b C47. For felodipine–PVPVA, TPGS gave discrete round domains only at 5–10%, while 2% TPGS still gave irregular domains, so the effect depends on level saboo2021 C24. Better storage stability with SDS or Tween 80 is a prediction; crystallization was not followed yang2022b C59.

Transfer check

For a surfactant-containing dispersion of a hydrophobic drug, measure the drug's separation concentration in buffer with and without the surfactant; a fall, as with the Spans here, shows the surfactant enters the drug-rich phase and will plasticize it yang2022b R10, C58. Then expose a film to high humidity and image it at early times: round discrete drug-rich domains are the pattern that later released drug, a continuous drug-rich network the pattern that did not yang2023 C40; saboo2021 C30.

History

Mosquera-Giraldo and co-workers (2014) showed that miscible surfactants speed crystal growth (see F22). Saboo and co-workers (2021) found TPGS keeping drug-rich domains discrete in humid films and raising the loading of congruent release saboo2021 C40, C51, C16. Yang and co-workers (2022) compared four surfactants by orthogonal methods and located each in the film yang2022b C46, and Yang and co-workers (2023) related the same surfactants to release yang2023 C3, C40. Release from such dispersions is treated in Bioperformance F9.

Formulaslever rule

Topic 5 of 5 · 6 findings · F24–F26, F33–F35

Stress conditions and dissolution performance

F24

Topic 5Stress conditions and dissolution performance1 of 6

The basic polymer E100 protected both polyphenols; the very strong acceptor PVP protected only the one without an intramolecular bond.

For resveratrol, PVP and E100 were the only polymers whose dispersions stayed amorphous at 84% RH (more than 400 days), while HPMC, HPMCAS, CMCAB and PAA dispersions held crystals at the first sampling wegiel2013b R12, C31. PVP carries the only very strong hydrogen-bond acceptor of the set (pKBHX 2.38 on a hydrogen-bond basicity scale) and E100 a strong basic amine (1.98), whose IR bands vanished as the drug was added wegiel2013b R17.b, R17.d, R7, C38. For curcumin, E100 kept the dispersion amorphous for more than 350 days at 84% RH, but PVP, which gave the largest IR shifts, was the poorest inhibitor (22 days) wegiel2014 R13, R3.f, R4.a, C24.

moderateModerate: the extremes of the storage tables are clear, but the link from interaction type to stability is the authors' reading, IR and storage used different sample forms and loadings, and within each paper the IR ranking does not follow the storage ranking wegiel2013b K4, K6, X10, X11, X12; wegiel2014 K1, K5, K6, X7, X8.

Curcumin 75:25 dispersions at 84% RH and 25 °C: days to first crystalsE100basic polymer> 350HPMC75HPMCAS75CMCAB75PVPlargest IR shifts22curcumin alone14

The polymer with the largest IR shifts gave the shortest time; the basic polymer the longest. wegiel2014 R13, C24, R3, R4

Resveratrol: amorphous for more than 400 days at 84% RH
PVPE100
Curcumin: 75 days or more at 84% RH
E100HPMCHPMCASCMCAB

wegiel2013b R12; wegiel2014 R13

For your drug

  1. For a phenolic drug, try a very strong hydrogen-bond acceptor (PVP class, pKBHX above 2.25) and a basic polymer (E100 class) first.
  2. Check the drug for an intramolecular bond in its crystal structure; if one is present, expect hydrogen-bonding polymers to protect less and look for an ionic partner, read the IR for the type of interaction rather than the size of the shift, and confirm by storage at 84% RH.

wegiel2013b R17, E2, R12; wegiel2014 C35, C44, X7

How it works and key numbers
  1. Polymers that offer resveratrol a better hydrogen-bonding partner than itself "can reasonably be expected" to inhibit crystallization; resveratrol has no strong acceptor, so the strong-donor polymers PAA and CMCAB "may interact poorly" wegiel2013b C29, C31.
  2. With E100 the amine bands at 2820 and 2770 cm⁻¹ were gone by 50% drug, read as an acid–base reaction, and the resistance of E100 to moisture "likely" comes from it wegiel2013b R7, C15, C38.
  3. Amorphous curcumin keeps its keto–enol intramolecular hydrogen bond, so hydrogen bonding with polymers is "impeded"; since resveratrol and curcumin have similar phenols, "it can be supposed" that this bond is "indeed the critical factor" wegiel2014 C11, C33, C35.
  4. An acceptor-only polymer such as PVP can bond only to the drug's donors, whereas donor–acceptor cellulosics "may" disrupt self-association better, which "may well explain" why curcumin–PVP was least stable wegiel2014 C31, C34.
> 400 daysresveratrol with PVP or E100, amorphous at 84% RHwegiel2013b R12, C46
22 vs > 350 dayscurcumin with PVP vs E100 at 84% RHwegiel2014 R13, C24
2.38 / 1.98pKBHX of the PVP acceptor / the E100 aminewegiel2013b R17, E2

Connections to other chapters

4 more connections
Evidence: data, conditions and papers

Finding F24. For two polyphenol drugs, the polymers that accept strong hydrogen bonds or pair with the drug as a base gave the most stable dispersions, but the size of the IR shift did not rank the polymers, and an intramolecular bond in the drug weakened hydrogen-bond protection

In short. For resveratrol, PVP and E100 were the only polymers whose dispersions stayed amorphous at 84% RH (more than 400 days), while HPMC, HPMCAS, CMCAB and PAA dispersions held crystals at the first sampling; PVP carries the only very strong acceptor of the set (pKBHX 2.38) and E100 a strong basic amine (1.98), whose IR bands vanished as the drug was added wegiel2013b R12, R17.b, R17.d, R7, C31, C38. For curcumin, E100 kept the dispersion amorphous for more than 350 days at 84% RH, but PVP, which gave the largest IR shifts with curcumin (OH band at 3187 cm⁻¹, carbonyl shift 27 cm⁻¹), was the poorest inhibitor (22 days) wegiel2014 R13, R3.f, R4.a, C24. The authors attribute the curcumin result to its intramolecular hydrogen bond, which leaves an ionic interaction as the effective one ("appear to be the reason") wegiel2014 C3, C37.

Type. comparison of 7 polymers with 2 polyphenols, with an author interpretation Strength. the extremes of the storage tables are clear (wegiel2013b K4: moderate to strong; wegiel2014 K1: strong), but the link from interaction type to stability is the authors' reading (wegiel2013b K6: weak to moderate; wegiel2014 K5, K6: weak to moderate), IR and storage used different sample forms and loadings, and within each paper the IR ranking does not follow the storage ranking (wegiel2013b X10, X11, X12; wegiel2014 X7, X8, X13).

How it was shown

Wegiel and co-workers (2013) made resveratrol dispersions with seven polymers, read interactions by mid-IR of spin-coated films, classed the polymers' donor and acceptor groups on the pKBHX scale, and stored the dispersions dry at 25, 50, 90 and 120 °C and at 84% RH for up to 400 days wegiel2013b P1, P3, P4, R17, E2. The 2014 curcumin study used five of the polymers at 75:25 and six storage conditions for up to 350 days wegiel2014 P1, P2, P5, R13.

What the data show

With PVP the resveratrol OH band sat at 3193 cm⁻¹, below the crystal, and with E100 the amine bands were gone by 50% drug, read as an acid–base reaction wegiel2013b R5, R6, R7, C14, C15. The authors' IR-based ranking was E100 > PVP > HPMC > HPMCAS > CMCAB > PAA wegiel2013b C21.

systemmethod and conditionsresultids
resveratrol with 6 polymersacceptor class (pKBHX)PVP very strong 2.38; E100 amine strong 1.98; others mediumwegiel2013b R17, E2
resveratrol dispersions at 84% RH, 25 °CXRPD, up to 400 daysPVP and E100 amorphous > 400 days; others crystalline at day 1wegiel2013b R12, C46
curcumin with 5 polymers, 80% drug filmsIRPVP OH 3187 cm⁻¹, C=O −27 cm⁻¹; others ≥ 3386 cm⁻¹, 2–8 cm⁻¹wegiel2014 R3, R4, C14
curcumin 75:25 dispersions, 84% RH, 25 °CPXRD onsetE100 > 350, cellulosics 75, PVP 22, drug 14 dayswegiel2014 R13, C24
curcumin–E100IR; colouramine bands fade; dark red; ionizationwegiel2014 R7, R10, C16, C20
Table 3 of wegiel2014: days before crystallinity of curcumin dispersions at six storage conditions
Table 3 · wegiel2014days before crystallinity of curcumin dispersions at six storage conditions

E100 lasts longest at both humid conditions and PVP shortest, the reverse of PVP's place for resveratrol wegiel2014 R13.

Why

Polymers that offer resveratrol a better hydrogen-bonding partner than itself "can reasonably be expected" to inhibit crystallization, and E100's resistance to moisture "likely" comes from the acid–base interaction wegiel2013b C29, C38. Amorphous curcumin keeps its keto–enol intramolecular bond, so hydrogen bonding with polymers is "impeded", and "it can be supposed" that this bond is "indeed the critical factor" wegiel2014 C11, C33, C35.

Limits and transfer

IR was taken on films at other loadings than the stored powders, and day values are first sampling times at a detection limit of about 5–10% crystallinity wegiel2013b X11, X16; wegiel2014 X8, X10. Within each paper the IR ranking did not follow the storage ranking wegiel2013b X10; wegiel2014 X7. For a phenolic drug, try a very strong hydrogen-bond acceptor and a basic polymer first, check the drug for an intramolecular bond and, if one is present, look for an ionic partner, and read the IR for the type of interaction rather than the size of the shift.

How it was shown

Wegiel and co-workers (2013) made resveratrol dispersions with seven polymers by rotary evaporation in 5% steps of drug loading, read interactions by mid-IR of spin-coated films, classed the polymers' donor and acceptor groups on the pKBHX scale, and stored the dispersions dry at 25, 50, 90 and 120 °C and at 84% RH at room temperature for up to 400 days, reading crystallinity by XRPD wegiel2013b P1, P3, P4, R17, E2. The 2014 curcumin study used five of the polymers at 75:25, IR of films at 80% curcumin and six storage conditions for up to 350 days wegiel2014 P1, P2, P5, R13. The acceptor classes are bounded on the pKBHX scale wegiel2013b E2: Trasi and co-workers (2020) and Bhujbal and co-workers (2021) measured protonation of lumefantrine by XPS of the N 1s signal trasi2020 P15; bhujbal2021 P6.

\text{weak} < 0.75 < \text{medium} < 1.5 < \text{strong} < 2.25 < \text{very strong}

What the data show

The highest X-ray amorphous resveratrol loadings were 60% (E100), 45% (PVP), 40% (HPMC), 35% (HPMCAS, CMCAB) and 15% (PAA) wegiel2013b R2. With PVP the resveratrol OH band sat at 3193 cm⁻¹, below the crystal (3238 cm⁻¹), and a bonded carbonyl shoulder appeared 26 cm⁻¹ below the free band; with E100 the amine bands at 2820 and 2770 cm⁻¹ were gone by 50% drug, read as an acid–base reaction wegiel2013b R5, R6, R7, C14, C15. The authors' IR-based ranking was E100 > PVP > HPMC > HPMCAS > CMCAB > PAA wegiel2013b C21. In storage the PVP dispersions never crystallized, E100 crystallized partly only at 90 and 120 °C, and every cellulosic and PAA dispersion crystallized at 84% RH wegiel2013b R12. For curcumin the OH maxima at 80% drug were 3386–3399 cm⁻¹ with the cellulosics and E100 against 3400 cm⁻¹ alone, and polymer carbonyls moved 2–8 cm⁻¹, PVP's 27 cm⁻¹ wegiel2014 R3, R4. At 84% RH and 25 °C crystals first appeared after more than 350 days (E100), 75 days (HPMC, HPMCAS, CMCAB), 22 days (PVP) and 14 days (curcumin alone) wegiel2014 R13. The E100 dispersion was dark red, which the authors attribute to curcumin's ionization by the basic polymer wegiel2014 R10, C20. In PVP films the bonded carbonyl dominated only at 60% curcumin but already at 50% resveratrol wegiel2014 R8, R9, C32.

papersystemmethod and conditionsresultids
wegiel2013bresveratrol with 6 polymershighest amorphous loading, rotary evaporationE100 60%, PVP 45%, HPMC 40%, HPMCAS and CMCAB 35%, PAA 15%R2, C7
wegiel2013bsameacceptor class (pKBHX)PVP very strong 2.38; E100 amine strong 1.98; others mediumR17, E2
wegiel2013bresveratrol–E100 filmsIRamine bands gone by 50% drug; acid–base reactionR7, C15
wegiel2013bdispersions at 84% RH, 25 °CXRPD, up to 400 daysPVP and E100 amorphous > 400 days; others crystalline at day 1R12, C46
wegiel2014curcumin with 5 polymers, 80% drug filmsIRPVP OH 3187 cm⁻¹, C=O −27 cm⁻¹; others ≥ 3386 cm⁻¹, 2–8 cm⁻¹R3, R4, C14
wegiel201475:25 dispersions, 84% RH, 25 °CPXRD onsetE100 > 350, cellulosics 75, PVP 22, drug 14 daysR13, C24
wegiel2014curcumin–E100IR; colouramine bands fade; dark red; ionizationR7, R10, C16, C20
trasi2020lumefantrine 40:60 with HPMCAS, L100, HPMCP, CAPXPS protonation vs 40 °C/75% RH storage16–61% protonated; 33% and above amorphous 3 months, 16% small peak at 4 weeksR11, R3, C36
bhujbal2021lumefantrine dispersions precipitated into waterXPS vs 40 °C/75% RH storage14–42% protonated; no correlation with stabilityR8, C50

Figure

Table 3 of wegiel2013b: days before crystallization of resveratrol dispersions at five storage conditions
Table 3 · wegiel2013bdays before crystallization of resveratrol dispersions at five storage conditions

The PVP rows never crystallize, E100 only partly at 90 and 120 °C, and every other polymer is crystalline at the first sampling at 84% RH wegiel2013b R12.

Table 3 of wegiel2014: days before crystallinity of curcumin dispersions at six storage conditions
Table 3 · wegiel2014days before crystallinity of curcumin dispersions at six storage conditions

E100 lasts longest at both humid conditions and PVP shortest, the reverse of PVP's place for resveratrol wegiel2014 R13.

Why

The authors' account, with their hedges: polymers that offer resveratrol a better hydrogen-bonding partner than itself "can reasonably be expected" to inhibit crystallization, and with resveratrol having no strong acceptor, the strong-donor polymers PAA and CMCAB "may interact poorly" wegiel2013b C29, C31. The predictions are called in "excellent agreement" with stability, and E100's resistance to moisture "likely" comes from the acid–base interaction wegiel2013b C32, C38. PAA, an acidic polymer, was the worst for the weakly acidic resveratrol, in agreement with earlier screens wegiel2013b C44. For curcumin, amorphous drug keeps the keto–enol intramolecular bond, so hydrogen bonding with polymers is "impeded"; since resveratrol and curcumin have similar phenols, "it can be supposed" that the intramolecular bond is "indeed the critical factor" wegiel2014 C11, C33, C35. An acceptor-only polymer such as PVP can bond only to the drug's donors, whereas donor–acceptor cellulosics "may" disrupt self-association better, which "may well explain" why curcumin–PVP was least stable wegiel2014 C31, C34. For compounds prone to intramolecular bonding the authors recommend polymers that allow other interactions, such as ionic ones wegiel2014 C44. (synthesis: in both drugs the polymer that ionizes the phenol worked under humidity, and the hydrogen-bond acceptor worked only for the drug whose phenols were free.)

Conditions and limits

Resveratrol could not be made amorphous without a polymer and is classed a rapid crystallizer, so every comparison is between dispersions (see Crystallization tendency F14) wegiel2013b R1, C6. IR was taken on spin-coated films at other loadings (resveratrol 30–40%, curcumin 80%) than the stored powders (resveratrol 15–40%, curcumin 75%), and drug content of the stored resveratrol dispersions differed by polymer (40% with PVP, HPMC, E100; 30% with HPMCAS, CMCAB; 15% with PAA) wegiel2013b X11, X12; wegiel2014 X8. Day values are first sampling times at a detection limit of about 5–10% crystallinity wegiel2013b X16; wegiel2014 X10. No proton transfer was measured for E100, and no curcumin analogue without the intramolecular bond was tested wegiel2014 C37, X13. The Fox-equation deviations printed for curcumin come from °C values at the wrong composition; recalculated, only the E100 deviation (about +19 °C) survives, which still fits an ionic interaction wegiel2014 X1, C41.

Counterexamples and conflicts

Within the resveratrol paper, PVP outperformed E100 in storage although the IR ranking put E100 first, HPMC crystallized at 50 °C where HPMCAS and CMCAB did not, and PAA, ranked last, stayed amorphous at 90 °C longer than the cellulosics wegiel2013b X10. Within the curcumin paper the largest IR shifts went with the worst stability wegiel2014 X7. Resveratrol–PVP resisted humidity although PVP is the most hygroscopic polymer (see F23) wegiel2013b C35. For the weak base lumefantrine with acidic enteric polymers, the share of protonated drug ordered stability in powders made without water but not in powders precipitated into water (see F34) trasi2020 C36; bhujbal2021 C50.

Transfer check

For a phenolic drug, try a very strong hydrogen-bond acceptor (PVP class, pKBHX above 2.25) and a basic polymer (E100 class) first wegiel2013b R17, E2. Check the drug for an intramolecular bond in its crystal structure; if one is present, expect hydrogen-bonding polymers to protect less and look for an ionic partner wegiel2014 C35, C44. Read the IR for the type of interaction (new bonded band, loss of amine bands, colour change) rather than ranking polymers by the size of the shift, and confirm with storage at 84% RH wegiel2014 X7; wegiel2013b R12.

History

Van Eerdenbrugh and Taylor's donor–acceptor classification set up the approach, and a mid-IR study of two other polyphenols ran alongside (see Miscibility and drug-polymer interactions F24, F25) wegiel2013b C30. Wegiel and co-workers then followed resveratrol (2013) and curcumin (2014) through preparation and long storage, adding the acid–base pair with E100 and the intramolecular-bond limit wegiel2013b C45; wegiel2014 C3. The growth-rate counterpart of the intramolecular-bond limit, for flutamide and nimesulide, is in F18 trasi2012b C51; kestur2011 C27. In 2020–2021 the acid–base reading was carried to a basic drug with acidic polymers (see F34) trasi2020 C36; bhujbal2021 C50; the title is unchanged.

FormulasFox equation
F25

Topic 5Stress conditions and dissolution performance2 of 6

Stress conditions rank polymers only inside a window, and heat and humidity give different orders.

Curcumin dispersions with five polymers all stayed amorphous for more than 350 days at 25 °C and 0% RH and all crystallized within one day at 90 °C/0% RH and 60 °C/98% RH; only at 50 °C/0% RH, 25 °C/84% RH and 40 °C/75% RH did the polymers differ wegiel2014 R13, C23. For resveratrol, 84% RH crystallized the cellulosic and PAA dispersions completely, whereas 50–90 °C dry gave partial crystallization that stopped at a plateau wegiel2013b R12, R13, R14, C39, X8. A felodipine–PVP powder crystallized about 8 times faster at 50 °C than at 30 °C and to about 85% instead of 45% kestur2013b R9, R17, C38.

moderateModerate: the dependence on condition is plain in two storage tables and one kinetic comparison, but sampling intervals and replicates are not stated, crystallinities of 5–10% sit at the detection limit, and no Tg is printed for the felodipine dispersion wegiel2014 K1, X10; wegiel2013b K7, X15, X16; kestur2013b K6, X9.

PVPE100HPMCASdrug alone, or all samples25 °C / 0% RHall five polymers > 35050 °C / 0% RH3675> 35025 °C / 84% RH142275> 35040 °C / 75% RH11630> 20090 °C / 0% or 60 °C / 98% RHall within 1 day110100curcumin 75:25 dispersions: days to first crystals (log scale)

Only the three middle conditions separate the polymers; the mildest and the harshest separate none. wegiel2014 R13, C23, C21

Felodipine with 3% PVP, 150–250 µm, stored dry: crystallinity, %50 °C, 2 weeks≈7050 °C, 4 weeks≈8430 °C, 14 days≈1530 °C, 56 days≈43

Above Tg the powder crystallizes faster and further; a high-temperature test changes both rate and extent. kestur2013b R9

For your drug

  1. Store at the intended condition and at two stress conditions that differ in kind (one hot and dry, one humid near room temperature), and rank polymers only where the neat amorphous drug crystallizes but not every dispersion does within the test.
  2. Follow crystallinity to a plateau rather than reading only an onset, and check whether the stress temperature crosses the dispersion Tg (dry or wet); if it does, do not extrapolate rates or extents to storage below Tg.

wegiel2014 R13, C23; wegiel2013b R13, R14; kestur2013b C39, C40; moseson2022a C24

How it works and key numbers
  1. For resveratrol, humidity promoted crystallization "to a much greater extent" than heat, and "We do not fully understand" why wegiel2013b C39, C40.
  2. For felodipine at 50 °C, above Tg, surface-enhanced crystallization is "likely" less important for the overall kinetics, while nucleation rises about 7-fold from 30 to 50 °C kestur2013b C39, R23.
  3. Humidity can also change the crystallization route of a susceptible dispersion (see F16), so a ranking made at one condition need not hold at another rumondor2009c C52.
  4. Accelerated studies at high temperature are "often used" to predict lower temperatures, and the different rate and extent at 50 °C "highlights the difficulty" kestur2013b C37, C40.
> 350 days vs 1 dayevery curcumin dispersion at 25 °C/0% RH vs at 90 °C/0% or 60 °C/98% RHwegiel2014 R13, C23
≈8-fold; ≈85 vs ≈45%felodipine–PVP at 50 vs 30 °C: faster start, higher plateaukestur2013b R9, R17, C38
≈36% in 4 weekstacrolimus generic crystallized at 30 °C/75% RH (ICH zone IVb)trasi2017 R14, R26

Connections to other chapters

Evidence: data, conditions and papers

Finding F25. Stress conditions rank polymers only inside a window: the mildest condition separated none, the harshest none, and heat and humidity gave different orders and different final extents

In short. Curcumin dispersions with five polymers all stayed amorphous for more than 350 days at 25 °C and 0% RH and all crystallized within one day at 90 °C/0% RH and 60 °C/98% RH; only at 50 °C/0% RH, 25 °C/84% RH and 40 °C/75% RH did the polymers differ wegiel2014 R13, C23. For resveratrol, 84% RH crystallized the cellulosic and PAA dispersions completely from the first sampling, whereas 50–90 °C dry gave partial crystallization that stopped at a plateau, and PAA, the first to fail in humidity, stayed amorphous more than 175 days at 90 °C wegiel2013b R12, R13, R14, C39, X8. A felodipine–PVP powder crystallized about 8 times faster at 50 °C than at 30 °C and to about 85% instead of 45% kestur2013b R9, R17, C38. The authors of both 2013 papers conclude that these results show how hard it is to choose accelerated conditions wegiel2013b C41; kestur2013b C40.

Type. method comparison (storage temperature and humidity) in 5 drugs with 8 polymers Strength. the condition dependence is plain in two storage tables and one kinetic comparison (wegiel2014 K1: strong; wegiel2013b K7: moderate; kestur2013b K6: moderate), but sampling intervals and replicates are not stated, crystallinities of 5–10% sit at the detection limit, and no Tg is printed for the felodipine dispersion (wegiel2014 X10; wegiel2013b X15, X16; kestur2013b X9).

How it was shown

The resveratrol study stored dispersions at 0% RH and room temperature, at 84% RH and room temperature, and at 0% RH at 50, 90 and 120 °C for up to 400 days wegiel2013b P3, P4. The curcumin study used six conditions, from 25 °C/0% RH to 60 °C/98% RH, for up to 350 days wegiel2014 P5, P6. The felodipine study stored a 3% PVP powder at 30 and 50 °C dry and followed it by Raman kestur2013b P4, R9.

What the data show

For curcumin at 50 °C/0% RH, E100 and HPMC stayed amorphous beyond 350 days, HPMCAS and CMCAB crystallized partly by 75 days, PVP by 6 days and the drug alone by 3 days wegiel2014 R13. Dry at 50, 90 and 120 °C resveratrol–HPMC reached about 5, 20 and 100% crystallinity and then did not change wegiel2013b R14, R13.

systemmethod and conditionsresultids
curcumin with 5 polymers25 °C/0% RHall > 350 days; drug alone > 100 dayswegiel2014 R13, C23
same90 °C/0% RH and 60 °C/98% RHall crystalline within 1 daywegiel2014 R13, C23
resveratrol with 7 polymers84% RH, room temperaturefour polymers crystalline at day 1, then completewegiel2013b R12, R14, R16
felodipine–3% PVP, 150–250 µm50 vs 30 °C, dry≈8-fold faster start; plateau ≈85% vs ≈45%kestur2013b R9, R17, C38
celecoxib with five polymers80 °C/0% RH; RT/94% RH; 40 °C/75% RHthree different polymer ordersxie2016b R22, R23, R24
tacrolimus generic contents, fast batch30/75, 35/75, 40/54, 40/75, 4 weeks≈36, 68, 11, 84.5%trasi2017 R14, C26
Fig. 7 of kestur2013b: crystallinity of the small-particle 3% PVP dispersion at 50 °C and 30 °C
Fig. 7 · kestur2013bcrystallinity of the small-particle 3% PVP dispersion at 50 °C and 30 °C

Open squares (50 °C) lag about 5 days, then climb to about 84% by 4 weeks; filled squares (30 °C) level off near 43% kestur2013b R9.

Why

For resveratrol, humidity promoted crystallization "to a much greater extent" than heat, and "We do not fully understand" why wegiel2013b C39, C40. For felodipine at 50 °C, above Tg, surface-enhanced crystallization is "likely" less important for the overall kinetics, while nucleation rises about 7-fold kestur2013b C39. The different rate and extent at 50 °C "highlights the difficulty" of predicting lower temperatures from accelerated studies kestur2013b C37, C40.

Limits and transfer

Sampling intervals and replicate numbers are not stated, so close values are not resolved, and crystallinities of about 5–10% are at the detection limit wegiel2014 X10; wegiel2013b X16, X15. Store at the intended condition and at two stress conditions that differ in kind, one hot and dry and one humid near room temperature, rank polymers only where the neat drug crystallizes but not every dispersion does, and follow crystallinity to a plateau rather than reading only an onset.

How it was shown

The resveratrol study stored dispersions at 0% RH and room temperature, at 84% RH and room temperature, and at 0% RH at 50, 90 and 120 °C for up to 400 days, reading XRPD at intervals wegiel2013b P3, P4. The curcumin study used six conditions, from 25 °C/0% RH to 60 °C/98% RH, for up to 350 days, with PXRD at periodic sampling wegiel2014 P5, P6. The felodipine study stored the small-particle 3% PVP powder at 30 and 50 °C dry and followed it by Raman kestur2013b P4, R9. Xie and Taylor (2016) stored celecoxib dispersions at several conditions, with results shown for 80 °C/0% RH, room temperature/94% RH and 40 °C/75% RH xie2016b A4; Trasi and co-workers (2017) stored capsule contents at 30, 35 and 40 °C with 75% RH and at 40 °C with 54% RH trasi2017 A3.

What the data show

For curcumin at 50 °C/0% RH, E100 and HPMC stayed amorphous beyond 350 days, HPMCAS and CMCAB crystallized partly by 75 days, PVP by 6 days and the drug alone by 3 days wegiel2014 R13. At 84% RH/25 °C the order was E100 (> 350) > HPMC = HPMCAS = CMCAB (75) > PVP (22) > drug (14), and at 75% RH/40 °C E100 (> 200) > HPMC (100) > HPMCAS = CMCAB (30) > PVP (16) > drug (1) wegiel2014 R13. With the cellulosics, partial crystallization was followed by no further growth over the study wegiel2014 C27, R16. For resveratrol at 84% RH, HPMC was fully crystalline by about 124–126 days and PAA almost entirely by day 275 wegiel2013b R14, R16. Dry at 50, 90 and 120 °C HPMC reached about 5, 20 and 100% crystallinity and then did not change; E100 reached about 10% at 90 °C and stayed there for 200 days, and about 30% at 120 °C wegiel2013b R14, R13. At 120 °C the PAA, HPMCAS, CMCAB and HPMC dispersions crystallized fully, PAA within a day wegiel2013b R12, R16. The PVP dispersions showed no crystallization at any condition wegiel2013b R12.e, R12.f. The felodipine–PVP powder at 50 °C crystallized slowly for 5 days, then reached about 70% by 2 weeks and about 84% by 4 weeks; at 30 °C it was about 15% at 14 days and 43% at 56 days kestur2013b R9. Nucleation of the same dispersion rises about 7-fold from 30 to 50 °C (cited) kestur2013b R23.

The celecoxib study of 2016 gave three orders from three conditions: at 80 °C/0% RH PVP and PVPVA lasted about 120 days and the cellulosic polymers 6; at room temperature/94% RH PVPVA (150 days) and HPMCAS (115) led while PVP and HPMC failed within a month; at 40 °C/75% RH PVPVA (about 4 months) led PVP (70 days) and HPMCAS (33 days) xie2016b R22, R23, R24. For a marketed tacrolimus generic, open storage for 4 weeks at 30, 35 and 40 °C and 75% RH crystallized its fast batch about 36, 68 and 84.5%, and 40 °C/54% RH about 11% trasi2017 R14.

papersystemmethod and conditionsresultids
wegiel2014curcumin with 5 polymers25 °C/0% RHall > 350 days; drug alone > 100 daysR13, C23
wegiel2014same90 °C/0% RH and 60 °C/98% RHall crystalline within 1 dayR13, C23
wegiel2014same50 °C/0%, 25 °C/84%, 40 °C/75% RHpolymers differ; E100 best, PVP worstR13, C21
wegiel2013bresveratrol with 7 polymers84% RH, room temperaturefour polymers crystalline at day 1, then completeR12, R14, R16
wegiel2013bsame0% RH at 50–120 °Cpartial, plateauing crystallization at 50–90 °C; full at 120 °C for fourR12, R13, R14, X8
kestur2013bfelodipine–3% PVP, 150–250 µm50 vs 30 °C, dry≈8-fold faster start; plateau ≈85% vs ≈45%R9, R17, C38
xie2016bcelecoxib with five polymers and two ternaries80 °C/0% RH; RT/94% RH; 40 °C/75% RHthree different polymer ordersR22, R23, R24
trasi2017tacrolimus generic contents, fast batch30/75, 35/75, 40/54, 40/75, 4 weeks≈36, 68, 11, 84.5%R14, C26
marsac2008b (outside)PEO compactslong humid storagepartially crystalline polymers "may" defeat Arrhenius extrapolationC40
moseson2022a (outside)coated ASD powdersstorage at several RHcrystallization most ready when stored above TgC24

Figure

Fig. 7 of kestur2013b: crystallinity of the small-particle 3% PVP dispersion at 50 °C and 30 °C
Fig. 7 · kestur2013bcrystallinity of the small-particle 3% PVP dispersion at 50 °C and 30 °C

Open squares (50 °C) lag about 5 days, then climb to about 84% by 4 weeks; filled squares (30 °C) level off near 43% kestur2013b R9.

Fig. 7 of wegiel2013b: XRPD of the HPMC dispersion after humid and after hot storage
Fig. 7 · wegiel2013bXRPD of the HPMC dispersion after humid and after hot storage

At 84% RH (a) the resveratrol peaks grow from day 1 to near the physical mixture; after hot dry storage (b) they are small at 90 °C and large only at 120 °C wegiel2013b R14.

Why

The authors' account, with their hedges: for resveratrol, humidity promoted crystallization "to a much greater extent" than heat, and "We do not fully understand" why wegiel2013b C39, C40. For curcumin, stability "depended greatly" on both polymer and condition wegiel2014 C21. For felodipine at 50 °C, above Tg, surface-enhanced crystallization is "likely" less important for the overall kinetics, while nucleation rises about 7-fold kestur2013b C39. Accelerated studies at high temperature are "often used" to predict lower temperatures, and the different rate and extent at 50 °C "highlights the difficulty" kestur2013b C37, C40. (synthesis: three things change at once when the stress is raised — mobility, the phase state of a hydrated dispersion (see F16) and, across Tg, the dominant growth site (see F21) — so a polymer ranking made at one condition need not hold at another, and plateaus mean that even the extent of crystallization is condition-dependent.)

Conditions and limits

Day values are first sampling times; the sampling interval and replicate numbers are not stated, so close values (75 against 100 days) are not resolved wegiel2014 X10; wegiel2013b X16. Crystallinities of about 5–10% are at the detection limit wegiel2013b X15. Drug loading differed between resveratrol dispersions wegiel2013b X11. The felodipine comparison is Raman on one particle size, and the statement that 50 °C lies above Tg is not backed by a printed Tg kestur2013b X9, P4. The curcumin authors' claim that E100 lasted "considerably longer" at the two harshest conditions is not supported by the table, which gives one day for every sample wegiel2014 X6.

Counterexamples and conflicts

The resveratrol humidity–heat contrast holds at 50–90 °C but not at 120 °C, where four dispersions crystallized fully wegiel2013b X8. Rankings changed between conditions: HPMC was the best cellulosic for curcumin at 40 °C/75% RH but resveratrol–HPMC was the only dispersion to crystallize at 50 °C dry wegiel2014 R13; wegiel2013b R12.d. For felodipine–PVP, raising RH changed the crystallization route as well as its rate (see F16) rumondor2009c C52.

Transfer check

Store at the intended condition and at two stress conditions that differ in kind (one hot and dry, one humid near room temperature), and rank polymers only where the neat amorphous drug crystallizes but not every dispersion does within the test wegiel2014 R13, C23. Follow crystallinity to a plateau rather than reading only an onset, since heat gave partial crystallization that stopped wegiel2013b R13, R14. Check whether the stress temperature crosses the dispersion Tg (dry or wet); if it does, do not extrapolate rates or extents to storage below Tg kestur2013b C39, C40; moseson2022a C24. For a product, include the intended climatic zone: 30 °C/75% RH, which the authors note corresponds to ICH zone IVb, already crystallized the tacrolimus generic about 36% in 4 weeks trasi2017 R14, R26.

History

The 2009 humidity work had warned that high RH can change the crystallization route of a susceptible dispersion (see F16) rumondor2009c C52. In 2013 the resveratrol and felodipine papers showed that heat and humidity give different rankings and extents, and in 2014 the curcumin paper showed conditions too mild and too harsh to separate any polymer wegiel2013b C41; kestur2013b C40; wegiel2014 C23. Earlier PEO work and later coated-powder work raised the same issue for partially crystalline carriers and for storage above Tg (see PEG dispersions F12) marsac2008b C40; moseson2022a C24. In 2016 the celecoxib study showed dry heat, very high humidity and 40 °C/75% RH giving three polymer orders xie2016b C38, C41, C42, and in 2017 the tacrolimus survey added a temperature–humidity grid for a marketed product (see F33) trasi2017 C26; the type line was extended and the title is unchanged.

F26

Topic 5Stress conditions and dissolution performance3 of 6

Crystallinity gained in storage lowered the supersaturation reached on dissolution and reversed the advantage of small particles.

Fresh 3% PVP felodipine dispersions peaked at 6.97 µg/mL (150–250 µm) and 5.28 µg/mL (500–710 µm) in pH 6.8 buffer at 30 °C, against about 1.3 µg/mL for crystals kestur2013b R20, R18. After 24 weeks of dry storage, when the small particles were about 45% and the large ones about 17% crystalline, the peaks fell to 2.5 and 3.4 µg/mL, so the small fraction went from first to last kestur2013b R21, R8, C18, C19. The authors conclude that crystallinity "dramatically decreases" the supersaturation reached kestur2013b C44, C45.

moderateModerate: the drop in peak concentration after storage is large and consistent with the crystallinity of the stability study, but only two crystallinity levels are compared, crystallinity was not re-measured on the portions dissolved, and size and crystallinity change together kestur2013b K7, K8, X5, X10.

fresh dispersionafter 24 weeks drycrystalline felodipine150–250 µm≈45% crystalline after storage2.56.97500–710 µm≈17% crystalline after storage3.45.28crystals1.0–1.4012345678peak felodipine concentration, µg/mL (pH 6.8, 30 °C)

Storage reverses the order of the two particle sizes. kestur2013b R20, R21, R18, R8

For your drug

  1. Measure dissolution of the dispersion after the stability pull, not only crystallinity, and compare it with the fresh powder at the same dose and medium.
  2. When choosing a particle size, weigh the faster dissolution of a fine powder against its faster crystallization in storage, and judge residual crystallinity against the dissolution volume of the intended use.

kestur2013b R21, C46, C43, C44; hate2019 C52

How it works and key numbers
  1. A transient concentration above crystalline solubility arises when the amorphous solid dissolves faster than it crystallizes or than the solution precipitates kestur2013b C41.
  2. Smaller particles dissolve faster and reach a higher peak before crystallization in solution catches up ("provides an explanation") kestur2013b C42.
  3. Smaller particles also crystallize more readily in storage (see F21), and the lower peak of the stored small fraction "could be attributed" to its higher crystallinity kestur2013b C19, C44.
  4. PVP inside the solid delayed desupersaturation: at the same solution PVP the fresh dispersions held about 3.5–3.75 µg/mL at 2 h against about 2.5 µg/mL for amorphous felodipine kestur2013b R20, R19, C16, X15.
To feel the numbers. Stored peak against fresh peak: 2.5 ÷ 6.97 ≈ 0.36 for the small and 3.4 ÷ 5.28 ≈ 0.64 for the large fraction. Amorphous fraction left: 1 − 0.45 = 0.55 and 1 − 0.17 = 0.83. Both peaks fell further than the amorphous fraction did.
6.97 → 2.5 µg/mLpeak of the 150–250 µm dispersion, fresh vs after 24 weekskestur2013b R20, R21, R8
5.28 → 3.4 µg/mLpeak of the 500–710 µm dispersion, fresh vs after 24 weekskestur2013b R20, R21, R8
≈1.3 µg/mLcrystalline felodipine under the same conditionskestur2013b R18
Evidence: data, conditions and papers

Finding F26. Crystallinity gained in storage cuts the supersaturation an amorphous powder reaches on dissolution, and can reverse the particle-size advantage of the fresh powder

In short. Fresh 3% PVP felodipine dispersions peaked at 6.97 µg/mL (150–250 µm) and 5.28 µg/mL (500–710 µm) in pH 6.8 buffer at 30 °C, against about 1.3 µg/mL for crystals kestur2013b R20, R18. After 24 weeks of dry storage, when the small particles were about 45% and the large ones about 17% crystalline, the peaks fell to 2.5 and 3.4 µg/mL, so the small fraction went from first to last kestur2013b R21, R8, C18, C19. The authors conclude that crystallinity "dramatically decreases" the supersaturation reached and that supersaturation "appears to be correlated" with the extent of crystallization kestur2013b C44, C45. PVP inside the solid, at the same solution PVP, held the fresh dispersions at about 3.5–3.75 µg/mL at 2 h against about 2.5 µg/mL for amorphous felodipine kestur2013b R20, R19, X3, X15.

Type. single-system observation (felodipine with 3% PVP, two particle sizes) Strength. the drop in peak concentration after storage is large and consistent with the crystallinity measured in the stability study (kestur2013b K8: moderate; K7: moderate), but only two crystallinity levels are compared, crystallinity was not re-measured on the portions dissolved, size and crystallinity change together, and no statistical test is given (X5, X10; C45).

How it was shown

Kestur and co-workers (2013) dissolved about 5 mg of amorphous felodipine, fresh 3% PVP dispersions or dispersions stored 24 weeks, each in two sieve fractions, in 18 mL pH 6.8 phosphate buffer at 30 °C with 250 µg/mL PVP pre-dissolved, following concentration by in situ UV kestur2013b P10, P3, C7. The starting crystallinity of the stored powders was taken from the stability study of the same powders kestur2013b R8, X10.

What the data show

Fresh dispersions peaked at 6.97 µg/mL at about 24 min (small) and 5.28 µg/mL at 36–40 min (large) kestur2013b R20, X5. Stored, the small fraction rose fastest but peaked at about 2.5 µg/mL near 18 min, and the large fraction rose more slowly to about 3.4 µg/mL near 48 min kestur2013b R21.

systemmethod and conditionsresultids
crystalline felodipine, two sizesdissolution, pH 6.8, 30 °C≈1.0–1.4 µg/mL plateauskestur2013b R18, X14
amorphous felodipine, two sizessame, PVP 250 µg/mL in mediumpeaks ≈7.0 and ≈5.4 µg/mL; ≈2.5 at 2 hkestur2013b R19, C15
fresh 3% PVP dispersionssamepeaks 6.97 and 5.28 µg/mL; ≈3.5–3.75 at 116 minkestur2013b R20, C16, X3
dispersions after 24 weeks, ≈45% and ≈17% crystallinesamepeaks ≈2.5 (small) and ≈3.4 µg/mL (large)kestur2013b R21, R8, C18, C19
fresh tacrolimus generic vs five other capsulesnon-sink dissolution, 100 mL, pH 4.5peak ≈45.5 µg/mL at 40 min, ≈27 at 2 h vs 43–49 at 2 htrasi2017 R3, C13, C14
Fig. 11 of kestur2013b: dissolution of 3% PVP dispersions after 24 weeks, with crystalline felodipine
Fig. 11 · kestur2013bdissolution of 3% PVP dispersions after 24 weeks, with crystalline felodipine

The 200 µm powder (filled squares), about 45% crystalline, peaks near 2.5 µg/mL, below the 605 µm powder (triangles, about 17% crystalline) near 3.4 kestur2013b R21, R18.

Why

A transient concentration above crystalline solubility arises when the amorphous solid dissolves faster than it crystallizes or than the solution precipitates, so smaller particles, dissolving faster, reach a higher peak ("provides an explanation") kestur2013b C41, C42. The lower peak of the stored small fraction "could be attributed" to its higher crystallinity kestur2013b C19. PVP in the solid delayed desupersaturation, since solution PVP was nearly the same in both tests kestur2013b C16, X15.

Limits and transfer

One drug, one polymer level and one medium, and the crystallinity of the dissolved portions was not measured kestur2013b P10, X10. Later work found that the percentage of crystals alone does not predict the loss, the number and nature of growth sites mattering more que2018 C54, C60. Measure dissolution of the dispersion after the stability pull, not only crystallinity, and weigh the faster dissolution of fine powder against its faster crystallization in storage.

How it was shown

Kestur and co-workers (2013) dissolved about 5 mg of amorphous felodipine, fresh 3% PVP dispersions or dispersions stored 24 weeks, each in two sieve fractions, in 18 mL pH 6.8 phosphate buffer at 30 °C with 250 µg/mL PVP pre-dissolved, following concentration by in situ UV with crystalline felodipine as reference kestur2013b P10, P3, C7. The starting crystallinity of the stored powders was taken from the stability study of the same powders kestur2013b R8, X10. Trasi and co-workers (2017) dissolved the contents of one capsule in 100 mL of pH 4.5 buffer, where the dose equals the amorphous solubility trasi2017 P6, E6.

What the data show

Crystalline felodipine reached about 1.0–1.4 µg/mL within minutes with a small size difference kestur2013b R18, X14. Amorphous felodipine peaked within 30–35 min at about 7.0 (small) and 5.4 µg/mL (large) and fell to about 2.5 and 2.3 µg/mL at 116 min kestur2013b R19. Fresh dispersions peaked at 6.97 µg/mL at about 24 min (small) and 5.28 µg/mL at 36–40 min (large); the two sizes converged from about 48 min kestur2013b R20, X5. Stored dispersions: the small fraction rose fastest but peaked at about 2.5 µg/mL near 18 min, the large fraction rose more slowly to about 3.4 µg/mL near 48 min and held about 3.0 µg/mL at 112 min kestur2013b R21. (synthesis: the stored peaks are about 36% and 64% of the fresh peaks, close to the amorphous fractions left, about 55% and 83%, but not proportional to them.)

In the tacrolimus product survey the generic that later crystallized in storage already dissolved differently when fresh: it reached about 33 µg/mL at 5 min, peaked at about 45.5 µg/mL at 40 min and fell to about 27 µg/mL at 2 h, while the other products reached 43–49 µg/mL at 2 h; the authors read the fall as a sign that seeds "might" be present trasi2017 R3, C13, C14, C31. Later papers measured the cost of the stored generic's crystallinity in dissolution, absorptive tests and dogs (see F33) purohit2018 R17; hate2019 R12; purohit2019 R9.

papersystemmethod and conditionsresultids
kestur2013bcrystalline felodipine, two sizesdissolution, pH 6.8, 30 °C≈1.0–1.4 µg/mL plateausR18, X14
kestur2013bamorphous felodipine, two sizessame, PVP 250 µg/mL in mediumpeaks ≈7.0 and ≈5.4 µg/mL; ≈2.5 at 2 hR19, C15
kestur2013bfresh 3% PVP dispersionssamepeaks 6.97 and 5.28 µg/mL; ≈3.5–3.75 at 116 minR20, C16, X3
kestur2013bdispersions after 24 weeks, ≈45% and ≈17% crystallinesamepeaks ≈2.5 (small) and ≈3.4 µg/mL (large)R21, R8, C18, C19
trasi2017fresh tacrolimus generic vs five other capsulesnon-sink dissolution, 100 mL, pH 4.5peak ≈45.5 µg/mL at 40 min, ≈27 at 2 h vs 43–49 at 2 hR3, C13, C14
alonzo2010 (outside)amorphous felodipine at 37 °Cdissolutioncrystallized on contact faster than it dissolved; no supersaturationC8, C33
hate2019 (outside)amorphous tacrolimus products with residual crystallinityabsorptive dissolutionreceiver AUC fell with % crystallinity at every volumeR12, C52
que2018 (outside)paclitaxel–HPMCAS with seedsresidual concentration after dissolutionpercent crystallinity alone does not predict the loss; growth sites matterR14, C54
purohit2019 (outside)the same generic fresh vs 100% crystallizeddogs, 1 mgAUC 42.1 vs 21.6 ng·h/mLR9

Figure

Fig. 11 of kestur2013b: dissolution of 3% PVP dispersions after 24 weeks, with crystalline felodipine
Fig. 11 · kestur2013bdissolution of 3% PVP dispersions after 24 weeks, with crystalline felodipine

The 200 µm powder (filled squares), about 45% crystalline, peaks near 2.5 µg/mL, below the 605 µm powder (triangles, about 17% crystalline) near 3.4; crystals (open squares) stay near 1.25–1.4 µg/mL kestur2013b R21, R18.

Fig. 10 of kestur2013b: dissolution of fresh 3% PVP dispersions of two particle sizes
Fig. 10 · kestur2013bdissolution of fresh 3% PVP dispersions of two particle sizes

Fresh, the small powder (squares) peaks higher, 6.97 against 5.28 µg/mL, the order that storage reverses kestur2013b R20.

Why

The authors' account, with their hedges: a transient concentration above crystalline solubility arises when the amorphous solid dissolves faster than it crystallizes or than the solution precipitates, so smaller particles, dissolving faster, reach a higher peak before solution crystallization catches up ("provides an explanation") kestur2013b C41, C42. The lower peak of the stored small fraction "could be attributed" to its higher crystallinity kestur2013b C19. The slow fall of amorphous felodipine "can be attributed" to crystal growth slowing as supersaturation drops, and PVP in the solid delayed desupersaturation, since solution PVP was nearly the same in both tests kestur2013b C14, C16, X15. Smaller particles crystallize more readily in storage (see F21), which harms dissolution: the authors stress the need to keep amorphous systems physically stable through manufacture and storage kestur2013b C44, C46. (synthesis: crystals in the powder act twice, removing amorphous drug that would have dissolved and providing seeds that lower the solution peak; these data cannot separate the two.)

Conditions and limits

One drug, one polymer level, one medium with PVP pre-dissolved, 30 °C, about 5 mg in 18 mL kestur2013b P10. The storage period is 24 weeks in the text but the last stability point is at about 161 days, and crystallinity of the dissolved portions was not measured kestur2013b X10. The text values for the fresh dispersions at 2 h (4 µg/mL) are rounded up from the figure kestur2013b X3. Convergence of the two sizes after 40 min holds for the dispersions, not for amorphous felodipine kestur2013b X5.

Counterexamples and conflicts

The fresh-powder result points the other way: a smaller particle size "may be advantageous" for dissolution when precipitation is fast, as with PVP, a poor solution inhibitor for felodipine kestur2013b C43, R29. Whether the gain survives depends on storage, since the same small particles crystallized more kestur2013b C44. Later work found that the percentage of crystals alone does not predict the loss, the number and nature of growth sites mattering more que2018 C54, C60.

Transfer check

Measure dissolution of the dispersion after the stability pull, not only crystallinity, and compare it with the fresh powder at the same dose and medium kestur2013b R21, C46. When choosing a particle size, weigh the faster dissolution of fine powder against its faster crystallization in storage kestur2013b C43, C44. Judge residual crystallinity against the dissolution volume of the intended use, which changes its effect hate2019 C52.

History

Alonzo and co-workers (2010) showed that amorphous felodipine can crystallize on contact with the medium before it dissolves, so no supersaturation forms alonzo2010 C33. In 2013 Kestur and co-workers linked crystallinity gained in storage to lower supersaturation on dissolution and showed that it reverses the size order kestur2013b C44, C45. Later papers quantified the cost of residual crystallinity in absorptive dissolution and in dogs, and the role of seed origin (see Bioperformance F28, F30, ASD process F26 and D. Crystallization from solution F20) hate2019 R12; que2018 C60; purohit2019 C33. The tacrolimus generic that crystallized in storage gave the library its marketed-product case (see F33) trasi2017 C14; the title is unchanged.

F33

Topic 5Stress conditions and dissolution performance4 of 6

Of six marketed amorphous tacrolimus capsules of similar composition, only one generic crystallized, and its manufacturing route was the likely cause.

After 4 weeks in open dishes at 40 °C/75% RH, the capsule contents of the Accord generic showed tacrolimus monohydrate reflections and those of the innovator (Prograf) and four other generics did not; all six held about 1 part HPMC per part drug trasi2017 R6, R7, C18, R1, R2, C11. By synchrotron XRPD the Accord contents reached about 27% crystallinity at 2 days, 59% at 1 week and 88% at 3 weeks, faster than the pure amorphous drug, which crystallized only after 2 weeks trasi2017 R12, R16, C28. Only a model made by ethanolic drug granulation on lactose and croscarmellose dried at 60–70 °C, with HPMC mixed in only afterwards, crystallized within 14 days trasi2017 R18, R19, C35.

moderateModerate: the crystallization and its kinetics are direct, but the reproducing model changed drying temperature and HPMC contact together, the route of the product is inferred, and seeds in the fresh product are suggested, not shown trasi2017 K1, K2, K6, K7, K8, X6, X7, X8.

Accord tacrolimus capsule contents at 40 °C/75% RH: crystallinity by synchrotron XRPD, %1 day7.52 days271 week592 weeks723 weeks88

No lag; Prograf and four other products showed no tacrolimus reflections at 4 weeks. trasi2017 R12, C23, R6, R7

Stayed amorphous at 40 °C/75% RH for 4 weeks
Prograf and four other generics1:1 tacrolimus–HPMC dispersionPrograf + croscarmellose, seeds, millinggranulation with HPMC in liquid or bed
Crystallized
Accord genericpure amorphous drug (after 2 weeks)granulation dried 60–70 °C, HPMC after

trasi2017 R6, R7, R16, R18, R19, C30, C35

For your drug

  1. Stress-test the finished product and each batch, not only the drug–polymer dispersion, at 40 °C/75% RH in open dishes for 4 weeks, and quantify crystallinity with a method that sees a few percent (here synchrotron XRPD, limit of quantification 4%).
  2. If a product crystallizes faster than the pure amorphous drug, look at the process: where the drug was dried, at what temperature, and whether it ever met the polymer in solution.

trasi2017 R11, R13, C28, C35

How it works and key numbers
  1. Croscarmellose, the obvious compositional difference (21.5 mg in Accord against 4.1–8.2 mg), "most likely" explained the extra water sorption, but adding it to Prograf did not destabilize it, and the data "do not support" it as the cause trasi2017 R2, C16, C30.
  2. Seeds added to Prograf did not trigger crystallization, "most likely" because the drug is 2–5% of the fill and seeds rarely touch drug particles trasi2017 C46.
  3. Because Accord crystallized faster than the drug alone, the result "strongly suggests" a processing cause trasi2017 C28.
  4. The authors "believe" Accord holds amorphous drug coated on lactose rather than a drug–HPMC dispersion, and "speculate" that it was made by ethanol granulation dried at elevated temperature with HPMC mixed in afterwards; molecular mixing with the polymer is "considered to be essential" for stabilization trasi2017 C47, C49, C50.
27 → 59 → 88%Accord crystallinity at 2 days, 1 week and 3 weeks at 40/75trasi2017 R12
57–95%four Accord batches at 4 weekstrasi2017 R13, C24
42.1 vs 21.6 ng·h/mLexposure (AUC) in dogs, fresh vs fully crystallized genericpurohit2019 R9

Connections to other chapters

Evidence: data, conditions and papers

Finding F33. Of six marketed amorphous tacrolimus capsules with about the same composition, only one generic crystallized at 40 °C/75% RH, within days and faster than the pure amorphous drug, and only a model made without drug–HPMC contact reproduced it: the manufacturing route, not the formula, set stability

In short. After 4 weeks in open dishes at 40 °C/75% RH, the capsule contents of the Accord generic showed tacrolimus monohydrate reflections and those of the innovator (Prograf) and four other generics did not; Prograf stayed amorphous for up to 2 months trasi2017 R6, R7, C18, R17. All six held about 1 part HPMC per part drug trasi2017 R1, R2, C11. By synchrotron XRPD fresh Accord held under 5% crystals and reached about 27% at 2 days, 59% at 1 week and 88% at 3 weeks; four Accord batches reached 57–95% at 4 weeks trasi2017 R10, R12, R13, C24. A 1:1 tacrolimus–HPMC dispersion stayed amorphous for 4 weeks at 40/75 and the pure amorphous drug crystallized only after 2 weeks trasi2017 R16, C28. Extra croscarmellose, seeds and milling did not destabilize Prograf, while an ethanolic drug granulation on lactose and croscarmellose dried at 60–70 °C, with HPMC mixed in only afterwards, crystallized within 14 days trasi2017 R18, R19, C30, C32, C35.

Type. comparison of 6 marketed products and 4 batches of one, with 9 model formulations Strength. the crystallization and its kinetics are direct (trasi2017 K1, K2: strong), but the reproducing model changed drying temperature and HPMC contact together, the state of HPMC in the stable variants is unclear, the route of the product is inferred, and seeds in the fresh product are suggested, not shown (K6: moderate; K7: weak to moderate; K8: weak; X6, X7, X8).

How it was shown

Trasi, Purohit and Taylor (2017) bought 5 mg capsules of Prograf and five generics, determined their HPMC, croscarmellose and lactose contents, and stored the contents open at 40 °C/75% RH for 4 weeks trasi2017 M5–M10, P7, P11, P12, P13, A1. Crystallinity was quantified by laboratory and synchrotron XRPD trasi2017 P8, P9, P10. Model formulations tested extra croscarmellose, milling, seeds and four ethanol granulations trasi2017 P14–P20, A6.

What the data show

HPMC was 4.8–5.5 mg per 5 mg of drug in every product, croscarmellose 21.5 mg in Accord against 4.1–8.2 mg in the others, and Accord took up 12.8% water at 95% RH against 1.6–5.7% trasi2017 R1, R2, C11, R4. Of the model formulations only the granulation dried at 60–70 °C with HPMC added afterwards crystallized trasi2017 R18, R19.

systemmethod and conditionsresultids
six marketed 5 mg tacrolimus capsules, ≈1:1 drug:HPMCopen dish, 40 °C/75% RH, 4 weeks, XRPDonly Accord crystallized (monohydrate)trasi2017 R6, R7, C18
Accord, synchrotron XRPD40/75, 1 day to 3 weeks7.5% → 27% → 59% → 88%trasi2017 R12, C23
four Accord batches40/75, laboratory XRPD57–95% at 4 weeks; two fast, two slowertrasi2017 R13, C24
pure amorphous drug; 1:1 HPMC dispersion40/75, XRPD; Tg after 75% RHdrug crystalline after 2 weeks; dispersion amorphous 4 weeks; Tg 51.4 and 49.0 °Ctrasi2017 R15, R16, C28
Prograf with extra croscarmellose, seeds, milling40/75, 4 weeksall stabletrasi2017 R18.a, R18.d, R18.e, C30, C32
ethanolic drug granulation on lactose + croscarmellosedried at 60–70 °C, HPMC added aftercrystallized within 14 days; with HPMC in liquid or bed stabletrasi2017 R18.f–i, R19, C35
Fig. 4 of trasi2017: XRPD of six tacrolimus capsule contents after 4 weeks at 40 °C/75% RH
Fig. 4 · trasi2017XRPD of six tacrolimus capsule contents after 4 weeks at 40 °C/75% RH

Only the bottom trace (Accord) carries the arrowed tacrolimus reflections at 8.5, 10.3 and 13.7° 2θ; the extra peaks in the Mylan and Panacea traces are lactose trasi2017 R6, R8.

Why

Croscarmellose "most likely" explained the extra water sorption, but adding it to Prograf did not destabilize it, and the data "do not support" it as the cause trasi2017 C16, C30. Because Accord crystallized faster than the drug alone, the result "strongly suggests" a processing cause trasi2017 C28. The authors "believe" Accord holds amorphous drug coated on lactose rather than a drug–HPMC dispersion, and "speculate" that it was made by ethanol granulation with drying at elevated temperature and HPMC mixed in afterwards trasi2017 C47, C49.

Limits and transfer

One lot per brand and open-dish storage outside the package, and drying temperature and HPMC contact were not separated in the model granulations trasi2017 A1, P7, X6, X7. Stress-test the finished product and each batch, not only the drug–polymer dispersion, and if a product crystallizes faster than the pure amorphous drug, look at where the drug was dried, at what temperature, and whether it ever met the polymer in solution.

How it was shown

Trasi, Purohit and Taylor (2017) bought 5 mg capsules of Prograf and five generics (Mylan, Panacea, Dr. Reddy's, Accord, Sandoz), determined their HPMC, croscarmellose and lactose contents, and stored the contents open at 40 °C/75% RH for 4 weeks trasi2017 M5–M10, P7, P11, P12, P13, A1. Crystallinity was quantified by laboratory and synchrotron XRPD against mixtures of crystalline monohydrate in Prograf contents (laboratory: y = 0.0002x + 0.3923, R^2 = 0.9928; synchrotron limit of quantification 4%) trasi2017 P8, P9, P10, E3, E4, R11. Four Accord batches were compared and two of them stored at 30/75, 35/75, 40/54 and 40/75 trasi2017 A2, A3. Water sorption at 25 °C, Tg before and after 75% RH, non-sink dissolution in 100 mL at pH 4.5, where the dose equals the amorphous solubility (50 µg/mL), and SEM of the insoluble residue were measured trasi2017 P3, P4, P5, P6, E6, M1. Model formulations tested extra croscarmellose, cryomilling, rotary-evaporated drug, ball milling, 4 and 8% seeds and four ethanol granulations trasi2017 P14–P20, A6.

What the data show

HPMC was 4.8–5.5 mg per 5 mg of drug in every product, the drug 2–5% of the fill, and croscarmellose 21.5 mg in Accord against 4.1–8.2 mg in the others trasi2017 R1, R2, C11. Accord took up 12.8% water at 95% RH against 1.6–5.7% for the others trasi2017 R4. Only Accord showed reflections at 8.5, 10.3 and 13.7° 2θ after 4 weeks; the extra peaks of Mylan and Panacea were lactose trasi2017 R6, R7, R8, C19. By synchrotron, Accord went from 7.5% at 1 day to 27% at 2 days, 59% at 1 week, 72% at 2 weeks and 88% at 3 weeks trasi2017 R12. Two batches reached about 66–71% at 1 week, two others about 10–21% at 2 weeks, and the four 95, 85, 76 and 57% at 4 weeks trasi2017 R13. For the fast batch, 4 weeks gave about 36% at 30/75, 68% at 35/75, 11% at 40/54 and 84.5% at 40/75; the slow batch crystallized mainly at 40/75 trasi2017 R14, X5. Tg fell from 63.6 to 51.4 °C for the amorphous drug and from 77.2 to 49.0 °C for the 1:1 HPMC dispersion after 75% RH, so both were glassy at 40 °C trasi2017 R15. In dissolution Accord reached about 33 µg/mL at 5 min (Prograf 13), peaked at about 45.5 µg/mL at 40 min and fell to about 27 µg/mL at 2 h, while the others reached 43–49 µg/mL trasi2017 R3, C13, C14. Of the model formulations only the granulation dried at 60–70 °C with HPMC added afterwards crystallized; drug rotary-evaporated alone and mixed with excipients showed minor crystallization trasi2017 R18, R19, X8. The insoluble residue of Accord looked smooth with holes, like drug coated on lactose, that of Prograf porous, like drug in HPMC trasi2017 R21, C37.

papersystemmethod and conditionsresultids
trasi2017six marketed 5 mg tacrolimus capsules, ≈1:1 drug:HPMCopen dish, 40 °C/75% RH, 4 weeks, XRPDonly Accord crystallized (monohydrate)R6, R7, C18
trasi2017Accord, synchrotron XRPD40/75, 1 day to 3 weeks7.5% → 27% → 59% → 88%R12, C23
trasi2017four Accord batches40/75, laboratory XRPD57–95% at 4 weeks; two fast, two slowerR13, C24
trasi2017Accord fast batch30/75, 35/75, 40/54, 40/75, 4 weeks≈36, 68, 11 and 84.5%R14, C26
trasi2017pure amorphous drug; 1:1 HPMC dispersion40/75, XRPD; Tg after 75% RHdrug crystalline after 2 weeks; dispersion amorphous 4 weeks; Tg 51.4 and 49.0 °CR15, R16, C28
trasi2017Prograf with extra croscarmellose, seeds, milling40/75, 4 weeksall stableR18.a, R18.d, R18.e, C30, C32
trasi2017ethanolic drug granulation on lactose + croscarmellosedried at 60–70 °C, HPMC added aftercrystallized within 14 days; with HPMC in liquid or bed stableR18.f–i, R19, C35
purohit2018 (outside)the same generic, another lot40/75, open dishlag, then fully crystalline at 5 weeksR1
purohit2019 (outside)the same generic, fresh against 100% crystallized1 mg in dogsAUC 42.1 against 21.6 ng·h/mL; Cmax 25.3 against 3.84R9

Figure

Fig. 4 of trasi2017: XRPD of six tacrolimus capsule contents after 4 weeks at 40 °C/75% RH
Fig. 4 · trasi2017XRPD of six tacrolimus capsule contents after 4 weeks at 40 °C/75% RH

Only the bottom trace (Accord) carries the arrowed tacrolimus reflections at 8.5, 10.3 and 13.7° 2θ; the extra peaks in the Mylan and Panacea traces are lactose trasi2017 R6, R8.

Fig. 8 of trasi2017: synchrotron crystallinity of Accord against days at 40 °C/75% RH
Fig. 8 · trasi2017synchrotron crystallinity of Accord against days at 40 °C/75% RH

Crystallinity climbs from below 10% at day 1 to about 88% at 3 weeks without a lag trasi2017 R12.

Why

The authors' account, with their hedges: since tacrolimus crystallizes as a hydrate, humidity is "likely" more important than temperature trasi2017 C26. Croscarmellose, the obvious compositional difference, "most likely" explained the extra water sorption, but adding it to Prograf did not destabilize it, and the data "do not support" it as the cause trasi2017 C16, C30. Seeds added to Prograf did not trigger crystallization, "most likely" because the drug is 2–5% of the fill and seeds rarely touch drug particles trasi2017 C46. Because Accord crystallized faster than the drug alone, the result "strongly suggests" a processing cause trasi2017 C28. "It appears" that intimate drug–HPMC contact and temperature decide; the authors "believe" Accord holds amorphous drug coated on lactose rather than a drug–HPMC dispersion, "speculate" that it was made by ethanol granulation with drying at elevated temperature and HPMC mixed in afterwards, and suggest that hot drying "may" create a low level of crystals trasi2017 C35, C47, C49, C48. Molecular mixing and drug–polymer interactions "are considered to be essential" for stabilization trasi2017 C50. (synthesis: in this chapter's terms, the product holds the drug outside a polymer phase, so it behaves like the unprotected amorphous drug of F1 and F10, in a high-surface coating like the free surfaces of F21, and with extra water from croscarmellose (see F9); tacrolimus itself is a good glass former trasi2016 C13, so a favourable neat-drug class did not protect the product (see Crystallization tendency F17).)

Conditions and limits

One product lot per brand, one batch of Accord for most tests, open-dish storage outside the package trasi2017 A1, P7. The authors note that 30/75 corresponds to ICH zone IVb, and that the packaged product was not tested trasi2017 R26, C41. Drying temperature and HPMC contact were not separated in the model granulations, and whether HPMC was dissolved in the stable variants is unclear trasi2017 X6, X7. The XRPD estimates are called semiquantitative trasi2017 C23. The clinical significance was unknown when the paper appeared trasi2017 C42.

Counterexamples and conflicts

The slow batch crystallized only about 57% in 4 weeks against 95% for the fastest, so batch-to-batch variation within one product is as large as some product differences trasi2017 R13. At 40/54 the fast batch reached only about 11%, so the product passes a moderate-humidity screen trasi2017 R14.

Transfer check

Stress-test the finished product and each batch, not only the drug–polymer dispersion, at 40 °C/75% RH in open dishes for 4 weeks, and quantify crystallinity with a method that sees a few percent (here synchrotron XRPD, limit of quantification 4%) trasi2017 R11, R13. If a product crystallizes faster than the pure amorphous drug, look at the process: where the drug was dried, at what temperature, and whether it ever met the polymer in solution trasi2017 C28, C35. Compendial dissolution tests barely detect such crystallinity (see Bioperformance F16) purohit2018 C18, C19.

History

Trasi and co-workers (2016) had found that all six products were X-ray amorphous when bought and dissolved to the amorphous solubility of about 50 µg/mL, Accord fastest trasi2016 C11, C18, C31. In 2017 the same group found the one product that crystallized trasi2017 C18. Later papers used the crystallized generic to show that 100 mL dissolution and simulated bioequivalence fail at 20% crystallinity with 100 mL input data and 40% with 900 mL input data (see Bioperformance F17) purohit2018 R17, that absorptive dissolution separates the levels (see Bioperformance F28) hate2019 R12, C52, and that exposure in dogs halves (see Bioperformance F30) purohit2019 R9.

F34

Topic 5Stress conditions and dissolution performance5 of 6

Acidic enteric polymers kept 40% lumefantrine amorphous at 40 °C/75% RH for 3 months, where PVPVA crystallized within a week.

Rotary-evaporated 40:60 dispersions of the weak base lumefantrine with HPMCP, Eudragit L100 or CAP showed no crystals after 3 months at 40 °C/75% RH, with HPMCAS a small peak at 4 weeks and with PVPVA crystals at 1 week trasi2020 R3, C6. XPS found 16% (HPMCAS), 33% (L100), 48% (HPMCP) and 61% (CAP) of the drug protonated, against 7% for the neat drug, and the authors find that stability "correlates" with protonation trasi2020 R11, C14, C36. In dispersions made by spraying a drug–polymer solution into cold dilute acid "a correlation is not observed": CAP (32% protonated, 9% water) showed crystals from the first day, and L100, dried for 4 days, was crystalline as made bhujbal2021 R1, R4, R8, R10, R11, C17, C50.

moderateModerate for the polymer split, weaker for protonation or water as the cause: the protonation link is a two-group contrast that the 60% loading does not follow, water uptake of PVPVA was not measured, and the water explanation varies water together with polymer trasi2020 K1, K2, X5, X6; bhujbal2021 K1, K2, X15, C56.

Rotary-evaporated 40:60 lumefantrine dispersions: drug protonated, % (XPS)neat drug7HPMCASsmall peak at 4 weeks16Eudragit L100amorphous at 3 months33HPMCPamorphous at 3 months48CAPamorphous at 3 months61

Storage at 40 °C/75% RH; the neutral PVPVA dispersion crystallized within 1 week. trasi2020 R11, R3, C14, C6

Rotary evaporation, 40% drug: amorphous for 3 months
CAPEudragit L100HPMCP
Precipitated into water, 40% drug: crystalline
CAPEudragit L100

trasi2020 R3; bhujbal2021 R1, R4, R11

For your drug

  1. For a basic drug, screen acidic polymers by XPS or IR for salt formation, check stability at 40/75 for 3 months, and expect neutral PVPVA to fail first.
  2. Measure residual water and drying time of every process that uses water or slow drying and store one portion dry as a control; do not pick the polymer that protonates most without a release test, since CAP released least.

trasi2020 R3, R11, R18, C46, C47; bhujbal2021 R5, R10, R11; hiew2022a C10

How it works and key numbers
  1. Lumefantrine forms a salt with the carboxylic acid groups, and stability "correlates" with the extent of protonation, which "appears to account" for the split between the more and the less protonated systems trasi2020 C36, C37.
  2. Neutral PVPVA "most likely" failed through hygroscopicity and the drug's high log P, leading to amorphous phase separation (see F23) trasi2020 C31.
  3. In powders precipitated into water, the higher water of CAP "could be a reason" for its fast crystallization, and the 4-day drying of L100 prolonged contact with water, which is "known to enhance" crystallization bhujbal2021 C27, C43.
  4. The acid–base contact therefore protects only if the process leaves the powder dry: the precipitated CAP dispersion stored under vacuum stayed amorphous for 3 months (synthesis) bhujbal2021 R5, C17, R10.
3 months vs 1 week40:60 enteric-polymer dispersions vs PVPVA at 40 °C/75% RHtrasi2020 R3, C6
16–61%share of lumefantrine protonated by the acidic polymers (neat drug 7%)trasi2020 R11, C14
9% waterresidual water of the precipitated CAP dispersion, crystalline from day 1bhujbal2021 R10, C17

Connections to other chapters

2 more connections
Evidence: data, conditions and papers

Finding F34. For the weak base lumefantrine, acidic enteric polymers kept 40% drug amorphous at 40 °C/75% RH for 3 months where PVPVA crystallized within a week, and in powders made without water stability followed the share of protonated drug, while in powders precipitated into water the residual water and drying time decided

In short. Rotary-evaporated 40:60 lumefantrine dispersions with HPMCP, Eudragit L100 or CAP showed no crystals after 3 months at 40 °C/75% RH, with HPMCAS a small peak at 4 weeks and with PVPVA crystals at 1 week trasi2020 R3, C6. XPS found 16% (HPMCAS), 33% (L100), 48% (HPMCP) and 61% (CAP) of the drug protonated, against 7% for the neat drug, and the authors find that stability "correlates" with protonation trasi2020 R11, C14, C36. In dispersions made by spraying a dimethylacetamide solution into cold dilute HCl, HPMCP and HPMCAS at 20–40% drug stayed amorphous for 3 months, the CAP dispersion (32% protonated, 9% water) showed crystals from the first day, and the Eudragit L100 dispersions, dried for 4 days instead of about 12 h, were crystalline as made; "a correlation is not observed" with protonation bhujbal2021 R1, R4, R8, R10, R11, C17, C50. The polymer that protonated the drug most, CAP, released the least drug in both papers trasi2020 R14, C17; bhujbal2021 R15, R17.

Type. comparison of 1 drug × 4–5 polymers made by two processes, with an outside third paper Strength. for the polymer split (trasi2020 K1: moderate; bhujbal2021 K1: moderate), weak to moderate for protonation as the cause and for water as the cause of failure (trasi2020 K2; bhujbal2021 K2: weak to moderate) — the protonation link is a two-group contrast that the 60% loading does not follow, water uptake of PVPVA was not measured, and the water explanation varies water with polymer (trasi2020 X5, X6; bhujbal2021 X15, C56).

How it was shown

Trasi and co-workers (2020) made 60:40 and 40:60 lumefantrine dispersions with HPMCP, Eudragit L100, CAP, HPMCAS and PVPVA by rotary evaporation, stored them open at 40 °C/75% RH for up to 3 months, and measured protonation by XPS trasi2020 P1, P5, P6, P14, P15, A1, A2. Bhujbal and co-workers (2021) sprayed a dimethylacetamide solution of drug and enteric polymer into ice-cold 0.02 N HCl, dried the precipitate, and measured stability, water by TGA and protonation bhujbal2021 P1, P4, P6, P8, A1, A2.

What the data show

In the precipitated dispersions protonation was 14–42%, and water was 4–6% in the HPMCP and HPMCAS dispersions and 9% in the CAP one; the vacuum-stored CAP dispersion stayed amorphous for 3 months bhujbal2021 R8, R10, R5, C17.

systemmethod and conditionsresultids
lumefantrine 40:60 with five polymers, rotary evaporation40 °C/75% RH, open dish, XRPDHPMCP, L100, CAP amorphous 3 months; HPMCAS small peak 4 weeks; PVPVA crystals 1 weektrasi2020 R3, C6
same, 60:40sameCAP and L100 2 weeks, HPMCP 6 weeks; HPMCAS and PVPVA crystalline as madetrasi2020 R2, R4, X14
40:60 with acidic polymersXPS N 1sprotonation 16 (HPMCAS), 33 (L100), 48 (HPMCP), 61% (CAP); neat 7%trasi2020 R11, C14
20–40% drug with HPMCP, HPMCAS; 40% with CAPspray anti-solvent precipitation; 40/75, 3 monthsHPMCP, HPMCAS amorphous; CAP peaks from day 1, amorphous under vacuumbhujbal2021 R4, R5, C1, C17
Eudragit L100, all ratiossame process, dried 4 dayscrystalline as madebhujbal2021 R1, R2, R11, C43
Fig. 3 of trasi2020: XRPD of lumefantrine dispersions after storage at 40 °C/75% RH, 40:60 (a) and 60:40 (b)
Fig. 3 · trasi2020XRPD of lumefantrine dispersions after storage at 40 °C/75% RH, 40:60 (a) and 60:40 (b)

In panel a only the PVPVA trace (1 week) carries clear sharp peaks; the CAP, HPMCP and L100 traces at 3 months are halos, and HPMCAS at 4 weeks has one small peak trasi2020 R3.

Why

Lumefantrine forms a salt with the carboxylic acid groups, and stability "correlates" with the extent of protonation trasi2020 C36, C37. PVPVA "most likely" failed through hygroscopicity and the drug's high log P trasi2020 C31. In the precipitated powders the higher water of CAP "could be a reason" for its fast crystallization, the 4-day drying of L100 prolonged contact with water, and the authors conclude that stability was reduced by moisture during manufacture or storage bhujbal2021 C27, C43, C56.

Limits and transfer

One drug; the 60:40 results do not follow the protonation order, and release was measured on granules whose stability was not tested trasi2020 X6, R4, X5. At 40% drug CAP released only about 1.5–2.2 µg/mL from granules and about zero from precipitated powder trasi2020 R14; bhujbal2021 R15, R17. For a basic drug, screen acidic polymers for salt formation, measure the residual water and drying time of any process that uses water, and store one portion dry as a control.

How it was shown

Trasi and co-workers (2020) made 60:40 and 40:60 lumefantrine dispersions with HPMCP-50, Eudragit L100, CAP, HPMCAS-MF and PVPVA by rotary evaporation from organic solvents, stored them open at 40 °C/75% RH for up to 3 months, and measured Tg, ATR-FTIR and XPS protonation of the N 1s signal trasi2020 P1, P5, P6, P14, P15, A1, A2. For release they granulated 40:60 solutions onto microcrystalline cellulose and lactose and dissolved pellets in 100 mL pH 6.8 buffer trasi2020 P2, P7. Bhujbal and co-workers (2021) dissolved drug and HPMCP, HPMCAS, CAP or Eudragit L100 in dimethylacetamide and sprayed it into ice-cold 0.02 N HCl, then dried the precipitate in vacuum, and measured stability at 40/75 (CAP also under vacuum), water by TGA, protonation by XPS, particle size and release in 100 mL pH 6.8 buffer bhujbal2021 P1, P4, P6, P8, P10, P11, A1, A2. Lumefantrine has a Tg of 18 °C and melts at about 129 °C trasi2020 R5, M1.

What the data show

Right after rotary evaporation every 40:60 dispersion was amorphous and the 60:40 HPMCAS and PVPVA dispersions were crystalline trasi2020 R1, R2, C5. At 60:40 the CAP and L100 dispersions crystallized within 2 weeks and HPMCP within 6 weeks trasi2020 R4, X14. The polymer carbonyl bands moved up with CAP (1677 → 1732 cm⁻¹) and L100 (1701 → 1723 cm⁻¹) and a band near 1560 cm⁻¹ "likely" from carboxylate appeared trasi2020 R9, C11, C12. In the precipitated dispersions protonation was 42, 40 and 37% for HPMCP and 37, 35 and 14% for HPMCAS at 20, 30 and 40% drug, 32% for CAP and 38% for L100 at 40%, and 3% for the amorphous drug bhujbal2021 R8. Water was 4–6% in the HPMCP and HPMCAS dispersions and 9% in the CAP one; the vacuum-stored CAP dispersion stayed amorphous for 3 months bhujbal2021 R10, X20, R5, C17. In the outside comparison of five polymers at 5–50% drug, PVPVA dispersions crystallized at 1–8 weeks at 40/75 depending on loading, HPMCAS at 50% drug in 1 week, L100 at 50% in 8 weeks, HPMCP at 50% in 32 weeks, and CAP showed a drug peak only at 50% after 40 weeks hiew2022a R6. Release from granules after 2 h was about 28 (L100), 27 (HPMCP), 21 (HPMCAS), 1.5–2.2 (CAP) and 1.6 µg/mL (PVPVA), against an amorphous solubility of 2–3 µg/mL; CAP released 2.2, 14.8 and 34 µg/mL at 40, 30 and 20% drug trasi2020 R14, R12, R18, C24. Precipitated dispersions released 23.3 (HPMCP) and 18.4 µg/mL (HPMCAS) at 40% drug, 208.4 and 142.8 µg/mL at 20%, and about zero for CAP bhujbal2021 R15, R16, R17. After 2 h the filtrates of the L100, HPMCAS and HPMCP granules held particles of about 116–179 nm with zeta potentials of −20 to −27 mV, and pyrene reported a hydrophobic environment wherever the concentration exceeded the amorphous solubility, read as drug-rich nanodroplets trasi2020 R15, R16, C21. Drying enlarged the precipitated particles, most with HPMCAS (d50 366–1180 µm against 71.5–160 µm with HPMCP), which the authors offer as a possible reason ("may explain") for the higher HPMCP release, although size and polymer change together bhujbal2021 R13, C39, X19.

papersystemmethod and conditionsresultids
trasi2020lumefantrine 40:60 with five polymers, rotary evaporation40 °C/75% RH, open dish, XRPDHPMCP, L100, CAP amorphous 3 months; HPMCAS small peak 4 weeks; PVPVA crystals 1 weekR3, C6
trasi2020same, 60:40sameCAP and L100 2 weeks, HPMCP 6 weeks; HPMCAS and PVPVA crystalline as madeR2, R4, X14
trasi202040:60 with acidic polymersXPS N 1sprotonation 16 (HPMCAS), 33 (L100), 48 (HPMCP), 61% (CAP); neat 7%R11, C14
bhujbal202120–40% drug with HPMCP, HPMCAS; 40% with CAPspray anti-solvent precipitation; 40/75, 3 monthsHPMCP, HPMCAS amorphous; CAP peaks from day 1, amorphous under vacuumR4, R5, C1, C17
bhujbal2021Eudragit L100, all ratiossame process, dried 4 dayscrystalline as madeR1, R2, R11, C43
bhujbal2021same dispersionsXPS; TGA waterprotonation 14–42%, not ranking stability; water 4–6% against 9% (CAP)R8, R10, C50
trasi2020; bhujbal2021CAP at 40% drugrelease in 100 mL pH 6.8≈1.5–2.2 µg/mL and ≈0 against 18–28 µg/mL for the other enteric polymersR14, C17; R15, R17
hiew2022a (outside)5–50% drug with five polymers40/75, up to 40 weeksPVPVA 1–8 weeks; enteric polymers crystals only at 50% drug, 1–40 weeksR6, C10

Figure

Fig. 3 of trasi2020: XRPD of lumefantrine dispersions after storage at 40 °C/75% RH, 40:60 (a) and 60:40 (b)
Fig. 3 · trasi2020XRPD of lumefantrine dispersions after storage at 40 °C/75% RH, 40:60 (a) and 60:40 (b)

In panel a only the PVPVA trace (1 week) carries clear sharp peaks; the CAP, HPMCP and L100 traces at 3 months are halos, and HPMCAS at 4 weeks has one small peak trasi2020 R3.

Table 1 of bhujbal2021: percent protonation of lumefantrine in the precipitated dispersions
Table 1 · bhujbal2021percent protonation of lumefantrine in the precipitated dispersions

Protonation runs from 14% (40:60 HPMCAS) to 42% (20:80 HPMCP), without the order of storage stability bhujbal2021 R8, C50.

Why

The authors' account, with their hedges: lumefantrine forms a salt with the carboxylic acid groups, and stability "correlates" with the extent of protonation, which "appears to account" for the split between the more and the less protonated systems trasi2020 C36, C37. HPMCAS protonated least, "probably" because of its low acid content, and protonation did not follow the number of acid groups trasi2020 C34, C35. PVPVA "most likely" failed through hygroscopicity and the drug's high log P, leading to amorphous phase separation (see F23) trasi2020 C31. In the precipitated powders the higher water of CAP "could be a reason" for its fast crystallization and the 4-day drying of L100 prolonged contact with water, which is "known to enhance" crystallization; moisture "could have been a cause", and the authors conclude that stability was reduced by moisture during manufacture or storage bhujbal2021 C27, C43, C51, C56. Higher protonation "may confer" stability bhujbal2021 C52. The low release with CAP "could be related" to the strong drug–polymer interaction; the release-limiting "likely" step is drug-controlled, since less than 20% of the CAP dissolved bhujbal2021 C54; trasi2020 C23, C44. (synthesis: the same polymer at the same 40% loading behaved differently with the process: CAP was amorphous for 3 months at 61% protonation after rotary evaporation but crystalline from the first day at 32% protonation and 9% water after precipitation into water, and L100 amorphous for 3 months after rotary evaporation but crystalline as made after 4 days of wet drying trasi2020 R3, R11; bhujbal2021 R1, R4, R8, R10, R11. The acid–base contact protects only if the process leaves it in place and dry, the same water-over-interaction pattern as F11 and F24.)

Conditions and limits

One drug; stability on rotary-evaporated powders, release on granules, so the granules' own stability was not measured trasi2020 X5. The 60:40 results do not follow the protonation order (CAP and L100 failed before HPMCP) trasi2020 X6, R4. Each precipitated trace is a single time point and two features in the 3-month traces are unassigned bhujbal2021 X15, X16. In the precipitated series protonation of HPMCP and L100 is equal within the standard deviation bhujbal2021 X7. Release above the amorphous solubility was measured after 0.22 µm filtration and may include colloids bhujbal2021 X6.

Counterexamples and conflicts

HPMCAS, the least protonating polymer, gave stable precipitated dispersions at every loading for 3 months bhujbal2021 R4, R8.f, while after rotary evaporation it showed crystals at 4 weeks and in the outside study at 1 week (50% drug) trasi2020 R3; hiew2022a R6. CAP's low release is tied to strong interaction, yet the precipitated CAP dispersion was less protonated than HPMCP (32 against 37%), which released 23.3 µg/mL bhujbal2021 X8.

Transfer check

For a basic drug, screen acidic polymers by XPS or IR for salt formation and check stability at 40/75 for 3 months; expect neutral PVPVA to fail first trasi2020 R3, R11; hiew2022a C10. Measure residual water and drying time of every process that uses water or slow drying, and store one portion dry as a control, as the vacuum-stored CAP sample showed bhujbal2021 R5, R10, R11. Do not pick the polymer that protonates most without a release test: lower the loading (CAP gave 34 µg/mL at 20% against 2.2 at 40% drug) or pick a polymer with a balance, here L100 or HPMCP trasi2020 R18, C46, C47.

History

Acid–base contacts between a drug and a polymer had been tied to stability for polyphenols with E100 (see F24). Trasi and co-workers (2020) made lumefantrine dispersions by a simple solvent route and tied stability to protonation trasi2020 C30, C36; Bhujbal and co-workers (2021) made them by precipitation into water and found water to override protonation bhujbal2021 C49, C50. Hiew and co-workers (2022) compared the same polymers over 5–50% drug and placed release against loading (see Miscibility and drug-polymer interactions F21 and F26) hiew2022a R20, C10. Solvent granulation onto excipients for another drug pair is in ASD process F22.

F35

Topic 5Stress conditions and dissolution performance6 of 6

A little HPMCAS or HPMC in place of PVP left a celecoxib dispersion behaving like the PVP binary.

Celecoxib–PVP dispersions with a small part of the PVP replaced by HPMCAS or HPMC (8:1.6:0.4 and 6:3.5:0.5) had one Tg slightly below that of the PVP binary and the same drug–PVP IR bands xie2016b R15, C19. In storage they matched the PVP binary in all three conditions: about 120 days without crystals at 80 °C/0% RH (cellulosic binaries 6 days), crystals within a month at room temperature/94% RH (HPMCAS binary 115 days), and 70 days at 40 °C/75% RH (HPMCAS binary 33 days) xie2016b R22, R23, R24, C38, C41, C42. The authors conclude that the stability of a ternary dispersion "could be largely predicted" from the binary of its main polymer xie2016b C39.

moderateModerate: the ternary and the PVP binary match in all three conditions, but the stated times are not shown, the separation of the ternaries at 94% RH rests on film IR, and at 94% RH the HPMC ternary shows stronger peaks than the binary xie2016b K3, X7, X8, X14.

Celecoxib dispersions: days without crystals80 °C/0% RH: PVP binary≈12080 °C/0% RH: ternaries≈12080 °C/0% RH: HPMCAS binary640 °C/75% RH: PVP binary7040 °C/75% RH: HPMCAS ternary7040 °C/75% RH: HPMCAS binary33

At room temperature and 94% RH the ternaries and the PVP binary crystallized within a month, the HPMCAS binary after 115 days. xie2016b R22, R24, R23, C38, C42

Celecoxib dispersions: water taken up at 95% RH, %PVP K29/32 binary17.2HPMC ternary13.5HPMCAS ternary12.3HPMCAS binary3.6

xie2016b R13, C24

For your drug

  1. When a minor second polymer is added for dissolution, test the ternary itself in at least one dry-heat and one humid condition, and compare it with the binary of the main polymer, not with that of the minor one.
  2. Do not count on a few percent of a non-hygroscopic polymer to protect a hygroscopic main polymer at high RH; a less hygroscopic main polymer (here PVPVA) may serve both storage conditions, at the cost of slower dissolution.

xie2016b C39, R22, R23, C52, R26, C55

How it works and key numbers
  1. "Importantly", the small amount of HPMCAS did not disrupt the drug–PVP interactions "and hence" did not change the crystallization kinetics xie2016b C45.
  2. PVP and HPMCAS formed one phase at every ratio (one Tg and a carbonyl shoulder at 1643 cm⁻¹) xie2016b R7, R16, C16, C29.
  3. In humid storage the hygroscopic PVP dominates, and the strong solution-phase inhibition of the cellulosic polymers "Clearly" does not carry over to the matrix at high RH xie2016b C52, R27.
  4. With 2 parts HPMCAS in 10 the growth rate at 80 °C rose slightly, from about 0.00003 to 0.000053 µm/s, still far below the 0.00031 µm/s with HPMCAS alone xie2016b R21, C36.
To feel the numbers. The ternaries cut water uptake from 17.2 to 12.3–13.5%: (17.2 − 12.3) ÷ 17.2 ≈ 0.28, about a quarter. The HPMCAS binary still took up 12.3 ÷ 3.6 ≈ 3.4 times less than the HPMCAS ternary.
≈120 vs 6 daysternaries and PVP binary vs cellulosic binaries at 80 °C/0% RHxie2016b R22, C38
70 vs 33 daysHPMCAS ternary and PVP binary vs HPMCAS binary at 40 °C/75% RHxie2016b R24, C42
12.3–13.5% vs 17.2%water uptake at 95% RH, ternaries vs PVP binaryxie2016b R13, C24
Evidence: data, conditions and papers

Finding F35. Replacing an eighth to a fifth of the PVP in a celecoxib dispersion with HPMCAS or HPMC left it behaving like the PVP binary in dry heat and in humid storage, so the cellulosic added neither the dry stability of PVP nor the humid stability of HPMCAS

In short. Celecoxib–PVP dispersions with a small part of the PVP replaced by HPMCAS or HPMC (8:1.6:0.4 and 6:3.5:0.5) had one Tg slightly below that of the PVP binary, the same drug–PVP IR bands, and the storage behaviour of the PVP binary: about 120 days without crystals at 80 °C/0% RH (cellulosic binaries 6 days), crystals within a month at room temperature/94% RH (HPMCAS binary 115 days), and 70 days at 40 °C/75% RH (HPMCAS binary 33 days) xie2016b R15, R22, R23, R24, C3, C38, C41, C42. With 2 parts HPMCAS in 10, the growth rate at 80 °C rose from about 0.00003 to 0.000053 µm/s, still far below the 0.00031 µm/s with HPMCAS alone xie2016b R21, C36. The authors conclude that the stability of a ternary dispersion "could be largely predicted" from the binary of its main polymer xie2016b C39.

Type. comparison of 2 ternaries against 5 binaries of one drug at three storage conditions Strength. the ternary and PVP binary match in all three conditions (xie2016b K3: moderate), but the stated times are not shown, the ternary separation at 94% RH rests on film IR, and at 94% RH the HPMC ternary shows stronger peaks than the binary (X7, X8, X14).

How it was shown

Xie and Taylor (2016) prepared celecoxib dispersions with five polymers and PVP-major ternaries with HPMCAS or HPMC by rotary evaporation xie2016b P1, A1, A3. They stored 80% drug samples at 80 °C/0% RH and 40 °C/75% RH and 60% drug samples at room temperature/94% RH, read crystallinity by PXRD, and measured water sorption, Tg and melt growth xie2016b P5, P6, P7, P8, P9, A4.

What the data show

The ternaries had one Tg each, close to but slightly below the PVP binary, and the celecoxib–PVP hydrogen bond persisted xie2016b R15, C19. Film IR of the ternaries at 94% RH changed like that of the PVP binary xie2016b R11.

systemmethod and conditionsresultids
celecoxib:PVP:HPMCAS or HPMC 8:1.6:0.480 °C/0% RH, PXRD≈120 days, like PVP and PVPVA binaries; cellulosic binaries 6 daysxie2016b R22, C38
6:3.5:0.5 ternariesRT/94% RHcrystals within a month, like PVP binary; HPMCAS binary 115 days, PVPVA 150 daysxie2016b R23, C41
HPMCAS ternary 8:1.6:0.440 °C/75% RH70 days, like PVP binary; HPMCAS binary 33 daysxie2016b R24, C42
5:4:1 ternariesDVS, 95% RH13.5 and 12.3% against 17.2% (PVP binary), 3.6% (HPMCAS binary)xie2016b R13, C24
90:8:2 ternariesmelt growth, 80 °C≈0.000053–0.00007 against ≈0.00003–0.000037 (PVP) and ≈0.00031 µm/s (HPMCAS)xie2016b R21, C36
Fig. 9 of xie2016b: PXRD of binary and ternary celecoxib dispersions after storage at 80 °C/0% RH, RT/94% RH and 40 °C/75% RH
Fig. 9 · xie2016bPXRD of binary and ternary celecoxib dispersions after storage at 80 °C/0% RH, RT/94% RH and 40 °C/75% RH

Panel a (6 days, 80 °C): peaks only for the HPMCAS and HPMC binaries; panel b (28 days, 94% RH): peaks for the PVP K29/32 binary and both ternaries; panel c (33 days, 40/75): small features only for the HPMCAS binary xie2016b R22, R23, R24.

Why

"Importantly", the small amount of HPMCAS did not disrupt the drug–PVP interactions "and hence" did not change the crystallization kinetics xie2016b C45. In humid storage the hygroscopic PVP dominates, and the strong solution-phase inhibition of the cellulosic polymers "Clearly" does not carry over to the matrix at high RH xie2016b C52, R27.

Limits and transfer

One drug with PVP as the main polymer; stability times are stated, not plotted, and separation of the ternaries at 94% RH is inferred from film IR only xie2016b A3, X8, X7. In an indomethacin study, a Eudragit E PO–HPMC ternary stayed amorphous at 40 °C/75% RH for more than 100 days while both binaries crystallized within 5 days xie2017 R26, C51. Test the ternary itself in one dry-heat and one humid condition and compare it with the binary of the main polymer, not with the binary of the minor one.

How it was shown

Xie and Taylor (2016) prepared celecoxib dispersions with PVP K29/32, PVP K12, PVPVA, HPMCAS (AS-MF) or HPMC (606) and PVP-major ternaries with HPMCAS or HPMC by rotary evaporation from ethanol–dichloromethane xie2016b P1, A1, A3. They stored 80% drug samples at 80 °C/0% RH and 40 °C/75% RH and 60% drug samples at room temperature/94% RH, read crystallinity by PXRD, measured water sorption, dry Tg, Tg after humidity, film IR at 94% RH and melt growth of 90:10 and 90:8:2 mixtures at 80–100 °C xie2016b P5, P6, P7, P8, P4, P9, A4. Drug-free PVP–HPMCAS blends were tested by IR and DSC xie2016b A7.

What the data show

PVP and HPMCAS formed one phase at every ratio (one Tg; a carbonyl shoulder at 1643 cm⁻¹) xie2016b R7, R16, C16, C29. The ternaries had one Tg each, close to but slightly below the PVP binary, and the celecoxib–PVP hydrogen bond persisted xie2016b R15, C19. Water uptake at 95% RH was 13.5% (HPMC ternary) and 12.3% (HPMCAS ternary) against 17.2% for the PVP K29/32 binary and 3.6% for the HPMCAS binary xie2016b R13, C24. At 80 °C/0% RH the ternaries, like the PVP and PVPVA binaries, crystallized after about 120 days while the HPMCAS and HPMC binaries did so after 6 days xie2016b R22, C38. At room temperature/94% RH the ternaries and the PVP and HPMC binaries crystallized within a month, PVPVA after 150 days and HPMCAS after 115 days; at 40 °C/75% RH the HPMCAS ternary and the PVP binary lasted 70 days, PVPVA about 4 months and HPMCAS 33 days xie2016b R23, R24, C41, C42. Film IR of the ternaries at 94% RH changed like that of the PVP binary xie2016b R11. At 80 °C the 90:8:2 mixtures grew at about 0.000053 (PVP K29/32) and 0.00007 µm/s (PVP K12) against 0.00003 and 0.000037 µm/s for the binaries xie2016b R21.

papersystemmethod and conditionsresultids
xie2016bcelecoxib:PVP:HPMCAS or HPMC 8:1.6:0.480 °C/0% RH, PXRD≈120 days, like PVP and PVPVA binaries; cellulosic binaries 6 daysR22, C38
xie2016b6:3.5:0.5 ternariesRT/94% RHcrystals within a month, like PVP binary; HPMCAS binary 115 days, PVPVA 150 daysR23, C41
xie2016bHPMCAS ternary 8:1.6:0.440 °C/75% RH70 days, like PVP binary; HPMCAS binary 33 daysR24, C42
xie2016b5:4:1 ternariesDVS, 95% RH13.5 and 12.3% against 17.2% (PVP binary), 3.6% (HPMCAS binary)R13, C24
xie2016b90:8:2 ternariesmelt growth, 80 °C≈0.000053–0.00007 against ≈0.00003–0.000037 (PVP) and ≈0.00031 µm/s (HPMCAS)R21, C36
xie2016bternariesDSC; IRone Tg slightly below PVP binary; drug–PVP bond keptR15, C19, C45
xie2017 (outside)indomethacin:Eudragit E PO:HPMC 6:2.9:1.140 °C/75% RH, open vialsamorphous >100 days; both binaries crystallized within 5 daysR26, C51

Figure

Fig. 9 of xie2016b: PXRD of binary and ternary celecoxib dispersions after storage at 80 °C/0% RH, RT/94% RH and 40 °C/75% RH
Fig. 9 · xie2016bPXRD of binary and ternary celecoxib dispersions after storage at 80 °C/0% RH, RT/94% RH and 40 °C/75% RH

Panel a (6 days, 80 °C): peaks only for the HPMCAS and HPMC binaries; panel b (28 days, 94% RH): peaks for the PVP K29/32 binary and both ternaries; panel c (33 days, 40/75): small features only for the HPMCAS binary xie2016b R22, R23, R24.

Why

The authors' account, with their hedges: "Importantly", the small amount of HPMCAS did not disrupt the drug–PVP interactions "and hence" did not change the crystallization kinetics xie2016b C45. In humid storage the hygroscopic PVP dominates, and the strong solution-phase inhibition of the cellulosic polymers "Clearly" does not carry over to the matrix at high RH xie2016b C52, R27. The authors read the unchanged kinetics as proof of concept that miscible polymer pairs could be combined to serve storage and dissolution separately xie2016b C43. (synthesis: since the ternary followed the PVP binary in every condition, the minor cellulosic acted neither as an inhibitor in the solid nor as a water barrier; its sorption cut of about a quarter (17.2 → 12.3–13.5%) did not shift the 94% RH outcome, consistent with F11 and F23, in which the main polymer's water uptake sets the humid ranking.)

Conditions and limits

One drug, ternaries with PVP as the main polymer, the cellulosic at an eighth to a fifth of the polymer xie2016b A3. Stability times are stated, not plotted, and the sampling schedule is not given xie2016b X8. Separation of the ternaries at 94% RH is inferred from film IR only xie2016b X7. Growth rates were measured on 90:10 melts, not on the storage compositions xie2016b X11.

Counterexamples and conflicts

At 94% RH the HPMC ternary showed stronger and more peaks than the PVP binary at 28 days, so "similar" means onset within a month, not equal extent xie2016b X14. In an indomethacin study of the same group, replacing part of Eudragit E PO with HPMC gave a ternary that stayed amorphous at 40 °C/75% RH for more than 100 days while both binaries crystallized within 5 days, contrary to the authors' own expectation ("unexpected") xie2017 R26, C51. So a ternary can follow its main polymer or outperform both binaries depending on the drug and the polymer pair.

Transfer check

When a minor second polymer is added for dissolution, test the ternary itself in the storage conditions that matter, at least one dry-heat and one humid condition, and compare it with the binary of the main polymer, not with the binary of the minor one xie2016b C39, R22, R23. Do not count on a few percent of a non-hygroscopic polymer to protect a hygroscopic main polymer at high RH xie2016b C52. If the main polymer must be PVP for dry stability, a less hygroscopic main polymer (here PVPVA) may serve both storage conditions, at the cost of slower dissolution xie2016b R23, R26, C55.

History

Xie and Taylor (2015) had replaced 20% of the PVP with HPMC or HPMCAS to improve release from high-loading celecoxib dispersions xie2016b R27. Xie and Taylor (2016) tested the storage side and found the ternary tied to the PVP binary xie2016b C3; Xie and Taylor (2017) found an indomethacin ternary better than both binaries xie2017 C51.

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. 2006
    konno2006polymers and dry nucleation of felodipinefirst proposed

    Influence of Different Polymers on the Crystallization Tendency of Molecularly Dispersed Amorphous Felodipine

    Known before
    drug–polymer hydrogen bonding in indomethacin–PVP dispersions (builds_on taylor1997); outside the library, inhibition by PVP without a Tg increase konno2006 C3, C4.
    Added
    nucleation rates of amorphous felodipine films with 0–25% PVP, HPMCAS or HPMC at 0% RH, dispersion Tgs over 0–100% polymer, NH-band hydrogen-bond strengths and enthalpy relaxation at 2 °C konno2006 R4, R6, R16, R9.
    Relation
    first in the library to show that a few percent of any of three polymers lowers nucleation equally, without a Tg rise and without tracking hydrogen-bond strength; proposes a polymer-raised kinetic barrier konno2006 C14, C26, C31, C40.
    SupportsF1F4F5
  2. 2006
    marsac2006anifedipine against felodipineconfirms

    A Comparison of the Physical Stability of Amorphous Felodipine and Nifedipine Systems

    Known before
    drug–PVP interaction parameters from melting point depression (builds_on marsac2006b) marsac2006a R18.
    Added
    nucleation of the two glasses at 22 °C and at several temperatures above and below Tg, alone and with PVP; configurational and Hoffman driving forces; activation energies above and below Tg; Tg, enthalpy recovery, NH bands and Flory–Huggins activity marsac2006a R4, R2, R11, R3, R16, R6, R7, R12, R19.
    Relation
    confirms the large drop of nucleation with a few percent PVP for a second drug and first ties the drug ranking to crystal-related quantities rather than glass properties marsac2006a C18, C49.
    SupportsF1F2F4F5
  3. 2008
    konno2008polymers and felodipine nucleation with moistureextends

    Ability of Different Polymers to Inhibit the Crystallization of Amorphous Felodipine in the Presence of Moisture

    Known before
    the dry nucleation rates and Tgs of the same dispersions (builds_on konno2006) konno2008 C3, X10.
    Added
    nucleation at 0–75% RH with 0–25% of each polymer, water sorption isotherms, Tg after humid storage, rates against T/Tg and water content, IR of humid-stored films konno2008 R1, R2, R3, R4, R8, R7, R13, R14, R10.
    Relation
    extends konno2006 to water; first shows the polymers diverge in humid air (PVP weakest) and first sees the IR signature later identified as moisture-induced phase separation konno2008 C10, C34.
  4. 2008
    marsac2008anifedipine and felodipine in PVP with sorbed waterconfirmsextends

    Recrystallization of Nifedipine and Felodipine from Amorphous Molecular Level Solid Dispersions Containing Poly(vinylpyrrolidone) and Sorbed Water

    Known before
    the dry nucleation data and driving forces of both drugs and the nucleation method (builds_on marsac2006a, konno2006) and the supersaturation framework with estimated solubility in PVP (builds_on marsac2006b) marsac2008a C31, C32.
    Added
    nucleation at 0–75% RH with 0–25% PVP, sorption and Tg of both drug series, rates against water content and Tg − T, crystal solubility in NMP, water and NMP–water, and the water fraction of the polymer–water co-solvent marsac2008a R1, R2, R6, R5, R8, R10, R12, R13.
    Relation
    extends marsac2006a to water; confirms that Tg does not rank the drugs and replaces the dry driving-force argument with a reasoned co-solvent supersaturation marsac2008a C23, C49, X4.
  5. 2009
    rumondor2009bpolymer type and RH on bulk crystallizationextends

    Effects of Polymer Type and Storage Relative Humidity on the Kinetics of Felodipine Crystallization from Amorphous Solid Dispersions

    Known before
    moisture raises felodipine nucleation and PVP and HPMCAS are similar at 0–33% RH (builds_on konno2008); felodipine solubility in PVP (marsac2006b) and its drop with water (marsac2008a); moisture-induced separation of felodipine–PVP (marsac2010, then in press) rumondor2009b R22, R26, R24.
    Added
    PXRD-PLS crystallinity of felodipine dispersions with 10–50% PVP or HPMCAS stored at 0–93% RH for up to 724 days, plateaus, polymer-level independence at 93% RH and an induction period with 50% HPMCAS rumondor2009b R9, R11, R21, R17.
    Relation
    extends konno2008 from nucleation to bulk crystallization over more than a year; first ties fast PVP crystallization at high RH to moisture-induced immiscibility ("It is hypothesized") rumondor2009b C13, C22.
    SupportsF11F15F16
  6. 2009
    rumondor2009cmoisture-induced immiscibility of drug–PVP dispersionsfirst proposed

    Phase Behavior of Poly(vinylpyrrolidone) Containing Amorphous Solid Dispersions in the Presence of Moisture

    Known before
    band assignments of indomethacin–PVP (taylor1997), nifedipine–PVP interactions (marsac2006a), the felodipine–PVP separation hint (konno2008), sorbed water changing thermodynamics (marsac2008a), drug–PVP χ (marsac2009) and the felodipine–PVP precedent (marsac2010, in press) (builds_on) rumondor2009c C8, R26, R27.
    Added
    IR, DSC and sorption evidence that nifedipine, pimozide and droperidol dispersions separate under humidity while indomethacin and ketoprofen do not; drug properties, activity coefficients and drug–water χ tested as predictors rumondor2009c R7, R9, R12, R14, R16, R17, R22, R24.
    Relation
    first multi-drug demonstration of moisture-induced amorphous–amorphous phase separation in the library, with a thermodynamic interpretation ("It is our opinion") rumondor2009c C2, C35.
  7. 2010
    kestur2010bPVP molecular weight, concentration and temperature on melt growthfirst proposed

    Effects of the Molecular Weight and Concentration of Polymer Additives, and Temperature on the Melt Crystallization Kinetics of a Small Drug Molecule

    Known before
    PVP inhibits felodipine at low levels and the interface-accumulation hypothesis (builds_on konno2006); melting point depression as the driving-force test (marsac2009); felodipine–PVP miscibility and weaker hydrogen bonds on heating (marsac2010) kestur2010b C2, C25, C36.
    Added
    felodipine form II growth at 70–110 °C with three PVP grades and 0.5–4.5 wt% K-29/32, the log-linear concentration rule, Tg, Tm, IR, melt viscosity and a diffusion model of polymer at the growth front kestur2010b R7, R8, R13, R15, R1, R9, R10, R21.
    Relation
    first in the library to vary chain length and amount of one polymer for growth; argues the effect is kinetic and that PVP is encaged in the crystal, contrary to accumulation at the front kestur2010b C28, C42.
    SupportsF3F4F5
  8. 2010
    marsac2010temperature and moisture on felodipine–PVP miscibilityconfirms

    Effect of Temperature and Moisture on the Miscibility of Amorphous Dispersions of Felodipine and Poly(vinyl pyrrolidone)

    Known before
    NH band assignment and felodipine–PVP interactions (builds_on konno2006, marsac2006a), predicted miscibility (marsac2006b), sorption data behind the water–felodipine χ (marsac2008a) and a slightly negative felodipine–PVP χ (marsac2009) marsac2010 C5, R22, R23.
    Added
    variable-temperature IR from 0 °C to as high as 180 °C, IR after 33–94% RH and after casting with water, DSC, AFM, TEM, and remixing at 125 °C marsac2010 R2, R6, R7, R11, R13, R14, R19, R20, R17.
    Relation
    confirms the felodipine–PVP separation that konno2008 suspected with four techniques, adds that heat does not demix the dry pair, and introduces the Δχ argument marsac2010 C14, C33, C43; cited as in press by the 2009 papers.
  9. 2010
    rumondor2010moisture and felodipine crystal growthconfirmsextends

    Effects of Moisture on the Growth Rate of Felodipine Crystals in the Presence and Absence of Polymers

    Known before
    the nucleation study it complements and the sorption and Tg data of felodipine (builds_on konno2008, marsac2008a, rumondor2010a); bulk crystallization (rumondor2009b); moisture-induced separation (marsac2010); PVP bonding felodipine more strongly than HPMCAS (konno2006) rumondor2010 C5, R14, R15, R18.
    Added
    growth rates of felodipine crystals in films at 13–93% RH, alone and with 2.5–10% PVP or HPMCAS, the growth jump above 80% RH, and a comparison with AGV mobility rumondor2010 R1, R3, R5, R7.
    Relation
    extends the moisture work from nucleation to growth; confirms PVP losing to HPMCAS at high RH and reads converging PVP rates as phase separation ("probably") rumondor2010 C14, C43.
    SupportsF5F9F11F15
  10. 2010
    rumondor2010amoisture sorption of amorphous drug–polymer blendsfirst proposed

    Analysis of the Moisture Sorption Behavior of Amorphous Drug–Polymer Blends

    Known before
    indomethacin–PVP χ from melting point depression (builds_on marsac2009) and felodipine–PVP immiscibility at high RH (marsac2010); outside the library, additivity for sugar–PVP and ternary fits for drug–PVP rumondor2010a P5, C35, R16, R19.
    Added
    isotherms of felodipine and indomethacin blends with PVP, HPMC and HPMCAS, deviations from additivity, binary χ with water, ternary term shares and fitted χ23, and a mean water–blend parameter rumondor2010a R7, R8, R9, R11, R13, R14, R15.
    Relation
    first in the library to show why χ23 cannot be extracted from blend sorption; generalizes the sub-additive uptake that rumondor2009c used as a phase-state marker rumondor2010a C30, C10.
    SupportsF6F7F8
  11. 2010
    rumondor2010cpolymer hygroscopicity and moisture-induced separationextends

    Effect of Polymer Hygroscopicity on the Phase Behavior of Amorphous Solid Dispersions in the Presence of Moisture

    Known before
    moisture-induced separation of drug–PVP dispersions and the polymer sorption isotherms (builds_on marsac2010, konno2008, rumondor2009c), and weaker felodipine bonding to HPMCAS than to PVP (konno2006) rumondor2010c R22, R19, C29.
    Added
    IR and DSC of nine 50:50 dispersions of felodipine, quinidine, pimozide and indomethacin with PVP, PVPVA and HPMCAS before and after 54–94% RH, water uptake at 85% RH and the PVPVA carbonyl red shifts rumondor2010c R1, R3, R4, R18, R20.
    Relation
    extends rumondor2009c from PVP to two less hygroscopic polymers; first in the library to tie the extent of separation to polymer hygroscopicity ("appears to be related") and to report a separated HPMCAS dispersion rumondor2010c C38, C24.
  12. 2011
    rumondor2011which dispersions separate: 20 systems and a discriminant modelconfirms

    Understanding the Tendency of Amorphous Solid Dispersions to Undergo Amorphous–Amorphous Phase Separation in the Presence of Absorbed Moisture

    Known before
    the PVP, PVPVA and HPMCAS separation studies, sorption of blends and the IR method (builds_on rumondor2009c, rumondor2010c, marsac2010, rumondor2010a, rumondor2009b, rumondor2009a) rumondor2011 R15, C5, C6.
    Added
    five drugs chosen by donor type in PVP films at 10–90% PVP after 54–94% RH, a property table of 20 drug–polymer systems and an OPLS-DA model rumondor2011 A1, R14, R15, R16, R17.
    Relation
    confirms the donor reading of 2009 across 20 systems, adds pKa and drug loading, and finds the most hydrophobic drugs resisting at high loading, against the direction proposed in 2010 rumondor2011 C40, C38, X14.
  13. 2012
    trasi2012apolymers, nucleation and growth of amorphous acetaminophenfirst proposed

    Effect of polymers on nucleation and crystal growth of amorphous acetaminophen

    Known before
    the crystallization classes and the separated-zone hypothesis (builds_on baird2010), hydrogen bonding and growth inhibition for felodipine (kestur2010a), and donor–acceptor matching of drug and polymer (vaneerdenbrugh2011a, vaneerdenbrugh2010b) trasi2012a C7, C32.
    Added
    growth rates with seven polymers at 10% w/w and three at 10% molar, DSC nucleation zones, nuclei counts per cooling–reheating cycle, Tg and Tm, and IR of 30% films trasi2012a R6, R8, R12, R9, R16, R17.
    Relation
    first in the library to measure nucleation and growth of one drug with the same polymers and to find them decoupled, PAA the best growth inhibitor but the strongest nucleation promoter trasi2012a C46, C53.
  14. 2012
    trasi2012badditives, growth and nucleation of amorphous flutamideconfirmsextends

    Effect of Additives on Crystal Growth and Nucleation of Amorphous Flutamide

    Known before
    the felodipine hydrogen-bond–growth correlation it tests (builds_on kestur2010a), the acetaminophen contrast case (trasi2012a) and the lack of an interaction–nucleation link for felodipine (konno2006) trasi2012b R27, C45.
    Added
    growth with six simple polymers chosen as donors or acceptors and with nilutamide at 10 mol%, and with four pharmaceutical polymers at 5% w/w; NH shifts, carbonyl charges, the amide rotation energy, nucleation zones and growth rates at the exotherm maximum trasi2012b R3, R5, R14, R25, R24, R10, R11.
    Relation
    extends the hydrogen-bond reading of growth from bond strength to group type, finds donor polymers failing where the drug's acceptor is held intramolecularly ("most likely"), and confirms that nucleation does not follow hydrogen bonding trasi2012b C8, C51, C45.
  15. 2013
    kestur2013afelodipine polymorphs with and without PVPfirst proposed

    Evaluation of the crystal growth rate of felodipine polymorphs in the presence and absence of additives as a function of temperature

    Known before
    PVP slows felodipine form II growth, with the earlier form II rates reused (builds_on kestur2010b, kestur2010a) kestur2013a C8, X4.
    Added
    growth of form I at the free surface and in the bulk and of form II from 18 to 100 °C, with and without 3% PVP, the near-Tg jump of form I and the rate ratios kestur2013a R8, R13, R10, R15.
    Relation
    first in the library to compare a polymer's effect on two polymorphs; places it in the liquid ("most likely") and reports a glass-crystal mode for form I kestur2013a C6, C3.
  16. 2013
    kestur2013bparticle size, surfaces and dissolution of felodipine powdersfirst proposed

    Influence of particle size on the crystallization kinetics of amorphous felodipine powders

    Known before
    the growth method and form II in sandwiched glass (builds_on kestur2010a, kestur2010b), about 150-fold lower nucleation with 3% PVP (konno2006), the rise of nucleation from 30 to 50 °C (marsac2006a), and the competition of dissolution and crystallization (alonzo2010, konno2008a) kestur2013b R22, R23, C41, R29.
    Added
    crystallinity of two sieve fractions with and without 3% PVP for up to about 161 days, surface and bulk growth at 30 °C, storage at 50 °C and dissolution of fresh and stored powders kestur2013b R3, R6, R12, R9, R19, R20, R21.
    Relation
    first in the library to tie particle size and free surface to the crystallization of a dispersion, and stored crystallinity to lost supersaturation kestur2013b C24, C44.
  17. 2013
    wegiel2013bresveratrol dispersions with six polymerscontradicts

    Crystallization of Amorphous Solid Dispersions of Resveratrol during Preparation and Storage—Impact of Different Polymers

    Known before
    donor–acceptor polymer selection and acceptor classes (builds_on vaneerdenbrugh2011a), the rapid-crystallizer class of resveratrol (vaneerdenbrugh2010a) and the felodipine PVP–HPMCAS humidity comparison (rumondor2009b) wegiel2013b C30, C6, C35.
    Added
    highest amorphous loadings, IR of films with the polymers, storage for up to 400 days at five conditions, Tg and water sorption wegiel2013b R2, R5, R6, R7, R12, R18, R19.
    Relation
    contradicts the felodipine humidity result for a more hydrophilic drug, PVP staying amorphous at 84% RH, and first records an acid–base reaction with E100 as protective ("likely") wegiel2013b C35, C38.
  18. 2014
    mosqueragiraldo2014surfactants and celecoxib growthfirst proposed

    Impact of surfactants on the crystal growth of amorphous celecoxib

    Known before
    hydrogen bonding and polymer growth inhibition (builds_on kestur2010a, kestur2011, taylor1997), the slow-crystallizer class of celecoxib (baird2010) and water as a low-Tg accelerator (rumondor2010) mosqueragiraldo2014 C3, R17, R18, R19.
    Added
    growth of celecoxib with three surfactants, with 10% PVP and with both, Tg, Tm and IR, growth against T − Tg, and XRD of the grown crystals mosqueragiraldo2014 R1, R2, R3, R5, R7, R12, R14.
    Relation
    first in the library on surfactants and solid-state growth ("few, if any" earlier studies); finds the combination with PVP not additive mosqueragiraldo2014 C5, C41, C13.
    SupportsF3F4F5F20F22
  19. 2014
    wegiel2014curcumin dispersions and intramolecular bondingextends

    Curcumin amorphous solid dispersions: the influence of intra and intermolecular bonding on physical stability

    Known before
    the resveratrol methods and the E100 precedent (builds_on wegiel2013b), the nimesulide case of an intramolecular bond (kestur2011) and the interaction premise (kestur2010a, vaneerdenbrugh2011a) wegiel2014 C32, C36, C7.
    Added
    IR of films with five polymers, storage of 75:25 dispersions at six conditions for up to 350 days, Tg with a Fox comparison, and the polymorph that crystallized wegiel2014 R3, R4, R7, R13, R18, R17.
    Relation
    extends wegiel2013b to a drug with an intramolecular bond: PVP, the best polymer for resveratrol, was the poorest, and E100's ionic interaction "appear[s] to be the reason" for the best stability; first in the library to see cellulosic polymers steer a drug to a metastable form wegiel2014 C24, C37, C28.
  20. 2015
    sato2015a chiral polymer and the growth of two enantiomersfirst proposed

    Chiral discrimination by a cellulose polymer: differential crystallization inhibition of enantiomers in amorphous dispersions

    Known before
    compound–polymer interactions as determinants of growth inhibition and interaction-based polymer choice (builds_on kestur2010a, vaneerdenbrugh2011a) sato2015 C27.
    Added
    melt growth of both enantiomers of a chiral model compound and of its racemate with 5% of five polymers, DSC, 40 °C storage and IR of drug–polymer films sato2015 R5, R9, R1, R15, R12, R13, R14.
    Relation
    first in the library to hold everything but handedness constant: HPMCAS slowed the two enantiomers about twofold differently, the grade deciding which, while HPMCP, PVP and PHB did not discriminate; the authors read it as strong support for the interaction view sato2015 C11, C10, C27.
  21. 2016
    sato2016PHB and crystal growth of six compoundsfirst proposed

    Acceleration of the crystal growth rate of low molecular weight organic compounds in supercooled liquids in the presence of polyhydroxybutylate

    Known before
    small polymer amounts delay growth (builds_on vaneerdenbrugh2011a); outside the library, PEG speeding nifedipine growth sato2016 C16, C23.
    Added
    melt growth of six compounds with Tg from −1 to 90 °C with 1–20% PHB and of griseofulvin with PVAc, Tg and Tm of the mixtures, IR, replots against T − Tg and the growth-rate ratio against compound Tg sato2016 R3, R4, R7, R9, R10, R11.
    Relation
    first in the library to show a polymer that speeds growth of some compounds and slows others; the speed-up follows the Tg drop, extending the surfactant result of 2014 to a polymer sato2016 C29, X6.
  22. 2016
    tian2016indomethacin fluorescence, miscibility limits and dry stabilityfirst proposedconfirms

    Investigating the Correlation between Miscibility and Physical Stability of Amorphous Solid Dispersions Using Fluorescence-based Techniques

    Known before
    indomethacin–PVP hydrogen bonding (builds_on taylor1997), probe fluorescence for drug-rich phases (purohit2015b) and the blue shift of an autofluorescent drug (raina2015) tian2016 C13.
    Added
    emission spectra, fluorescence images, IR and DSC of indomethacin with HPMC, HPMCAS and PVP over 5–95% drug, and dry storage of powders at 40 °C for up to 14 months tian2016 R2, R3, R4, R7, R13, R17.
    Relation
    first in the library to pair a loading-by-loading miscibility limit with storage outcomes; confirms the premise that separated dispersions crystallize sooner, with HPMCAS at 30% and PVP as limits tian2016 C53, X5, X6.
    SupportsF30F15F12
  23. 2016
    xie2016bcelecoxib binaries and ternaries under heat and humidityconfirms

    Effect of Temperature and Moisture on the Physical Stability of Binary and Ternary Amorphous Solid Dispersions of Celecoxib

    Known before
    water disrupting drug–PVP bonds and separating dispersions, PVPVA against PVP, the growth method and the ternary rationale from solution (builds_on rumondor2009c, marsac2010, rumondor2010c, kestur2010a, xie2015) xie2016b C48, C49, R27.
    Added
    IR, dry and humid Tg, water sorption, melt growth and storage at three conditions of celecoxib with five polymers and two PVP-major ternaries xie2016b R3, R17, R12, R13, R21, R22, R23, R24.
    Relation
    confirms the PVP-to-HPMCAS switch with humidity for a second drug, but only at 94% RH; finds Tg after humidity not predictive and the ternaries tied to the PVP binary xie2016b C41, C42, C46, C3.
  24. 2017
    saboo2017water-induced separation of miconazole–PVPVA imaged by confocal fluorescenceextends

    Water-induced phase separation of miconazole-poly (vinylpyrrolidone-co-vinyl acetate) amorphous solid dispersions: Insights with confocal fluorescence microscopy

    Known before
    probe fluorescence (purohit2015b, purohit2017), the 2016 indomethacin limits (tian2016), AFM-IR and LCR (li2016c) and water during preparation (li2017) saboo2017 C49.
    Added
    films cast at low and high RH, stored at 75% RH and immersed in buffer, read by two dyes, AFM-IR and LCR; DSC of humidified and annealed powders saboo2017 R5, R6, R15, R18, R17, R22.
    Relation
    extends the felodipine casting-solvent result to humid casting air and adds the morphology of three water routes; heat alone does not separate saboo2017 C10, C46, C44.
  25. 2017
    tian2017polymers and the melt growth of three indomethacin polymorphscontradicts

    Impact of Polymers on the Melt Crystal Growth Rate of Indomethacin Polymorphs

    Known before
    the felodipine polymorph comparison (kestur2013a) and the indomethacin interaction ranking (tian2016) tian2017 C38, R16.
    Added
    growth of δ, α and γ indomethacin from 80 °C to near the melting points, alone and with 10% HPMC, HPMCAS or PVP, temperatures of fastest growth and melt viscosity tian2017 R7, R12, R15, R13.
    Relation
    contradicts the liquid-phase reading of kestur2013a: each polymer slowed γ least and α most; first in the library to measure polymer effects above the temperature of fastest growth tian2017 C37, C39, C33.
  26. 2017
    trasi2017marketed amorphous tacrolimus capsules under stressfirst proposed

    Evaluation of the Crystallization Tendency of Commercially Available Amorphous Tacrolimus Formulations Exposed to Different Stress Conditions

    Known before
    the non-sink dissolution and amorphous solubility of the same products (builds_on trasi2016) trasi2017 E6, C12.
    Added
    composition, water sorption, dissolution and 4-week open storage at 40 °C/75% RH of six products; synchrotron and laboratory XRPD kinetics of four generic batches at four conditions; model formulations trasi2017 R1, R4, R3, R6, R12, R13, R14, R18.
    Relation
    first in the library to find a marketed amorphous product that crystallizes, faster than the pure amorphous drug, and to trace it to the manufacturing route trasi2017 C18, C28, C47.
  27. 2020
    trasi2020lumefantrine with acidic polymers: stability, protonation and granule release

    Physical stability and release properties of lumefantrine amorphous solid dispersion granules prepared by a simple solvent evaporation approach

    Known before
    glass-forming classes (builds_on baird2010), polymer hygroscopicity and separation (rumondor2010c) and loading-dependent release trasi2020 C7, C31.
    Added
    rotary-evaporated 60:40 and 40:60 dispersions with four acidic polymers and PVPVA stored at 40 °C/75% RH for 3 months, XPS protonation, IR, Tg, amorphous solubility and release from granules trasi2020 R3, R4, R11, R9, R8, R12, R14.
    Relation
    carries the acid–base reading to a basic drug: the polymers that protonated lumefantrine more kept 40% drug amorphous, the neutral PVPVA failed within a week trasi2020 C36, C6.
    SupportsF34F11F24
  28. 2021
    bhujbal2021lumefantrine dispersions by spray anti-solvent precipitationrevises

    Physical Stability and Dissolution of Lumefantrine Amorphous Solid Dispersions Produced by Spray Anti-Solvent Precipitation

    Known before
    moisture as a destabilizer (builds_on rumondor2009b, rumondor2011) and the protonation–stability link without water (trasi2020) bhujbal2021 R20, C49.
    Added
    dispersions with HPMCP, HPMCAS, CAP and Eudragit L100 precipitated into dilute HCl, storage at 40 °C/75% RH and under vacuum, residual water, XPS, particle size and release bhujbal2021 R1, R4, R5, R10, R8, R13, R15.
    Relation
    revises trasi2020 for a process with water: protonation no longer ranked stability, and residual water or long drying explained the failures bhujbal2021 C50, C51.
    SupportsF34F14F24F5
  29. 2022
    yang2022bsurfactants and water-induced separation of ritonavir–PVPVAextends

    Phase separation in surfactant-containing amorphous solid dispersions: Orthogonal analytical methods to probe the effects of surfactants on morphology and phase composition

    Known before
    ritonavir separation on hydration (purohit2017b), the confocal dye method (saboo2017), additive partitioning and the LLPS concentration, and surfactant-changed morphology (saboo2021) yang2022b C3.
    Added
    time-lapse confocal images of 20 and 30% drug films with four surfactants at high RH, label-free O-PTIR maps, NMR partitioning, zeta potential and LLPS concentrations in buffer yang2022b R3, R5, R17, R13, R9, R10.
    Relation
    extends saboo2017 to surfactant-containing films: SDS and Tween 80 delayed visible separation, the Spans sped it, and each surfactant sat in the phase its hydrophilicity predicts yang2022b C7, C35.
For the authors: coverage of each paper card's main findings
paperfinding of section 0.3used in
konno2006F1. A few percent of polymer cuts nucleation by more than an order of magnitudeF1
konno2006F2. The three polymers were equally effective at equal weight fractionF1, F11
konno2006F3. Only PVP raised Tg in the range used for nucleationF5
konno2006F4. Felodipine hydrogen-bonds to all three polymers, most strongly to PVPF4, F5
konno2006F5. Neither Tg nor hydrogen-bond strength tracks the nucleation rateF4, F5
marsac2006aF1. Nifedipine nucleates faster than felodipine at every temperature testedF2
marsac2006aF2. Tg and DSC molecular mobility are nearly the same for the two glassesF2, F5
marsac2006aF3. Nifedipine has the larger driving force, and it is enthalpicF2
marsac2006aF4. Below Tg, felodipine has the higher activation energy for nucleationF2, F4
marsac2006aF5. Hydrogen bonding is alike in the glasses but differs relative to the crystalsF2
marsac2006aF6. PVP slows nucleation of both drugs alike, and nifedipine stays fasterF1, F2
marsac2006aF7. In PVP the glass properties of the two drugs stay alikeF2, F4, F5
konno2008F1. Water speeds nucleation; polymer slows it, even though it brings more waterF9, F10
konno2008F2. In humid air PVP is the weakest inhibitor, most at low contentF11, F16
konno2008F3. Polymer raises water uptake, PVP by far the mostF6
konno2008F4. Water lowers Tg, but Tg does not order the nucleation ratesF5, F6
konno2008F5. Against water content, the polymers fall together and polymer blunts the water effectF10, F11
konno2008F6. Humidity breaks felodipine-PVP hydrogen bonds in 25% PVP films, not in cellulose filmsF12, F14
marsac2008aF1. Nifedipine nucleates faster than felodipine under every conditionF2
marsac2008aF2. PVP slows nucleation, but humidity erodes the effect, more so for nifedipineF1, F10
marsac2008aF3. Nifedipine and its dispersions sorb more waterF2, F6
marsac2008aF4. With more PVP, nucleation is less sensitive to sorbed waterF10
marsac2008aF5. Same Tg, different nucleation: Tg does not explain the gapF2, F5
marsac2008aF6. Nifedipine's crystal is less soluble; water lowers felodipine's solubility moreF2
marsac2008aF7. Nifedipine dispersions hold a wetter polymer/water co-solventF2, F10
rumondor2009bF1. Humidity switches PVP dispersions from stable to fast-crystallizingF11, F16
rumondor2009bF2. At high humidity, PVP crystallization stops before it is completeF15
rumondor2009bF3. HPMCAS dispersions crystallize little at any humidityF11
rumondor2009bF4. Similar at low humidity, HPMCAS far better at high humidityF11, F16
rumondor2009bF5. At 93% RH the amount of PVP no longer mattersF15
rumondor2009bF6. With 50% HPMCAS, crystals appear only after a delayF11
rumondor2009cF1. All five dry dispersions start as one phaseF12
rumondor2009cF2. Moisture separated nifedipine, pimozide and droperidol dispersions before they crystallizedF12
rumondor2009cF3. DSC shows two amorphous phases in wet pimozide–PVP, one in indomethacin–PVPF12
rumondor2009cF4. Indomethacin and ketoprofen stayed one phase until they crystallizedF12, F13
rumondor2009cF5. Water uptake is additive only for the separating systemsF7
rumondor2009cF6. The separating systems crystallized soonerF15
rumondor2009cF7. Drug-alone properties do not sort the drugs; drug–water χ and donor type doF13, F8
kestur2010bF1. Pure felodipine grows fastest near 105 °C and about 40 times slower at 70 °CF3
kestur2010bF2. 3 wt% PVP slows growth at every temperature, far more at 70 °C than at 110 °CF3
kestur2010bF3. Longer PVP chains inhibit more, but the gain shrinksF3
kestur2010bF4. Growth falls log-linearly with PVP concentration, more steeply at lower temperatureF3
kestur2010bF5. Tg, Tm, hydrogen bonding and the crystal lattice do not change with PVPF4, F5
kestur2010bF6. Viscosity rises steeply with chain length but does not track inhibitionF5
kestur2010bF7. If the crystal pushed PVP out, PVP would pile up at the front within secondsF4
marsac2010F1. Heat weakens the drug–polymer hydrogen bond but does not break it, and the change reverses on coolingF14
marsac2010F2. Water uptake climbs steeply above about 75% RHF6
marsac2010F3. Humid storage trades drug–polymer for drug–drug hydrogen bonds, and drying does not undo itF12, F14
marsac2010F4. Water in the casting solvent stops the drug–polymer bond from formingF14
marsac2010F5. DSC, AFM and TEM show a drug-rich amorphous phase forming, then crystalsF12, F15
marsac2010F6. Only heat remixes the separated phases, and slowlyF14
rumondor2010F1. Water speeds growth slowly up to 80% RH, then abruptlyF9
rumondor2010F2. Growth is faster than mobility predictsF5
rumondor2010F3. HPMCAS slows growth at every RH, almost independently of RHF11
rumondor2010F4. PVP slows growth strongly when dry, but less as RH risesF11, F15
rumondor2010F5. PVP wins below 52% RH, HPMCAS above 64% RHF11
rumondor2010aF1. PVP sets the water uptake; blends gain water as polymer is addedF6
rumondor2010aF2. Blends sorb far less water than the sum of their partsF7
rumondor2010aF3. The shortfall peaks at different compositions with PVP and with the cellulose polymersF7
rumondor2010aF4. The binary model fits single components and ranks their liking for waterF8
rumondor2010aF5. The drug–polymer term of the ternary model is negligible, so χ23 cannot be pinned downF8
rumondor2010aF6. A mean water–blend parameter falls smoothly with polymer contentF8
rumondor2010cF1. All nine dry dispersions were one phaseF12, F23
rumondor2010cF2. Humid storage split five dispersions into two amorphous phasesF12, F16, F23
rumondor2010cF3. Four dispersions stayed one phase up to 94% RHF13, F23
rumondor2010cF4. Water uptake ranks PVP > PVPVA > HPMCASF6, F23
rumondor2010cF5. PVP dispersions unmixed more than PVPVA dispersionsF23
rumondor2010cF6. Indomethacin's strong hydrogen bond kept PVPVA mixedF13
rumondor2010cF7. Pimozide, the most hydrophobic drug, unmixed even with HPMCASF13, F23
rumondor2011F1. All five drugs mix with PVP when dryF12
rumondor2011F2. Moisture splits the PVP-rich films of all five drugsF12, F15
rumondor2011F3. The two most hydrophobic drugs resist at high drug loadingF13, F23
rumondor2011F4. Indoprofen separates only slightly, then crystallizesF13, F15
rumondor2011F5. Across 20 systems, carboxylic acids with large red shifts stay mixedF13
rumondor2011F6. The model singles out the carboxylic-acid donor, the red shift and pKaF13
trasi2012aF1. Acetaminophen nucleates at 50–60 °C, where its crystals barely growF17
trasi2012aF2. Every polymer slowed growth; PAA most, HPMCAS, HPMC and E100 leastF3, F18
trasi2012aF3. Per hydrogen-bonding group, PAA, PVP and PVPh inhibit growth alikeF18
trasi2012aF4. Tg barely moved, so it cannot explain the growth rankingF5, F18
trasi2012aF5. The best growth inhibitors are the polymers that hydrogen-bond to acetaminophenF18
trasi2012aF6. Nucleation follows a different order: HPMCAS fewest nuclei, PAA mostF1, F17
trasi2012aF7. Polymers move and widen the nucleation zone; PAA shifts it down to −10–30 °CF17
trasi2012bF1. Carbonyl polymers slow growth most; donor polymers barely doF3, F18
trasi2012bF2. Pharmaceutical polymers at 5 wt% follow the same patternF18
trasi2012bF3. Tg barely moves, so mobility does not explain the rankingF4, F5
trasi2012bF4. The NH shift follows growth inhibitionF18
trasi2012bF5. Flutamide's carbonyl is a poor acceptorF18, F24
trasi2012bF6. Nucleation does not follow hydrogen bonding; nilutamide nearly stops itF17
kestur2013aF1. Form I grows faster at the free surface than in the bulk below about 65 °CF21
kestur2013aF2. Near Tg, form I growth jumps instead of slowing downF19
kestur2013aF3. Form II grows more slowly and its rate falls smoothlyF19
kestur2013aF4. 3% PVP slows both polymorphs, and form I keeps its surface and near-Tg behaviourF19, F21
kestur2013aF5. PVP cuts the growth rate of both polymorphs by a similar factor at 60–100 °CF3, F4, F19
kestur2013bF1. Smaller particles of pure amorphous felodipine crystallize fasterF21
kestur2013bF2. 3% PVP slows crystallization and stops it at a plateau set by particle sizeF1, F21
kestur2013bF3. Crystals grow faster at the free surface, and PVP mainly slows bulk growthF17, F21
kestur2013bF4. The PVP kinetics are biphasic and fit a constant depth of surface crystallizationF21
kestur2013bF5. At 50 °C the dispersion crystallizes faster and furtherF25
kestur2013bF6. Smaller amorphous particles reach higher supersaturation, and PVP in the solid slows its lossF26
kestur2013bF7. Crystallinity gained on storage cuts supersaturation and reverses the size orderF26
wegiel2013bF1. Resveratrol cannot be made amorphous on its ownF24
wegiel2013bF2. The polymers differ fourfold in how much drug they keep amorphousF24
wegiel2013bF3. IR: the strongest hydrogen bonds form with PVP, and E100 also reacts as a baseF24
wegiel2013bF4. Only PVP never crystallized; at 84% RH the cellulose and PAA dispersions crystallized from day 1 onF11, F24, F25
wegiel2013bF5. Heat gives partial crystallization that stops at a plateauF25
wegiel2013bF6. Polymer Tg does not explain the rankingF5
wegiel2013bF7. The PVP dispersion takes up far less water than its physical mixtureF7, F23
mosqueragiraldo2014F1. Every surfactant speeds up growth; PVP slows it more than tenfoldF3, F22
mosqueragiraldo2014F2. TPGS and sucrose palmitate lower Tg by about 10 °C; SLS does not mixF5, F22
mosqueragiraldo2014F3. Correcting for Tg narrows the surfactant differences but does not remove themF5, F22
mosqueragiraldo2014F4. With PVP present, TPGS gives the slowest growth of all systemsF22
mosqueragiraldo2014F5. TPGS flattens the temperature dependence, so its advantage reverses on coolingF22
wegiel2014F1. Amorphous curcumin keeps its intramolecular hydrogen bondF24
wegiel2014F2. Curcumin hydrogen-bonds weakly with the polymers, except PVPF18, F24
wegiel2014F3. E100 reacts with curcumin as an acid–base pairF24
wegiel2014F4. The polymer decides how long curcumin stays amorphousF11, F24, F25
wegiel2014F5. Tg does not explain the rankingF5, F24
wegiel2014F6. PVP binds curcumin far less than it binds resveratrolF24
wegiel2014F7. Cellulosic polymers steer crystallization to metastable form IIF20
sato2015F1. Alone, the two enantiomers behave almost alike; the racemate does notF27
sato2015F2. PHB barely slows growth; PVP and HPMCP slow both enantiomers alikeF27, F3
sato2015F3. HPMCAS slows the two enantiomers by different amounts, and the grade decides whichF27
sato2015F4. DSC and a 40 °C storage test agree: HPMCAS-HF holds back ATP(R) moreF27, F5
sato2015F5. IR ties inhibition to hydrogen bonds from the ATP amino group to polymer carbonylsF27, F18
sato2015F6. Polymers slow the racemate far less than the enantiomersF27
sato2016F1. PHB speeds up crystal growth of the three high-Tg compoundsF28
sato2016F2. PHB slightly slows, or leaves unchanged, the three low-Tg compoundsF28, F18
sato2016F3. The size and direction of the effect follow the compound's TgF28
sato2016F4. PHB lowers the Tg of the high-Tg compounds but leaves melting points and IR bands unchangedF28, F4
sato2016F5. After correcting for Tg, the acceleration at 5–10% PHB largely disappears; at 20% PHB growth is slower than Tg predictsF28, F5, F22
sato2016F6. PVAc, with a similar Tg gap, does not accelerate GRIF28
tian2016F1. Indomethacin's emission reports its surroundingsF30
tian2016F2. A drug-rich band appears abruptly at a loading set by the polymerF30
tian2016F3. Imaging, IR and DSC put the limit within about one step of the spectraF30
tian2016F4. HPMC and HPMCAS powders above the limit crystallize within daysF30, F15
tian2016F5. PVP dispersions resisted crystallizationF30
xie2016bF1. PVP and PVP/VA hydrogen-bond with celecoxib; the cellulosics barely doF18, F13
xie2016bF2. In the dry state, the stronger interactors also raise Tg more and slow crystal growth moreF18, F3
xie2016bF3. Dry heat: PVP-based dispersions last about 120 days, cellulosic ones 6 daysF11, F25, F35
xie2016bF4. High humidity reverses part of the rankingF11, F25
xie2016bF5. PVP dispersions take up most water, lose most Tg and show signs of AAPSF6, F7, F12, F23
xie2016bF6. Tg after humidity does not rank stabilityF5
xie2016bF7. At 40 °C/75% RH PVP/VA lasts longest and PVP beats HPMCASF11, F25
xie2016bF8. The ternaries follow the PVP binary in every testF35
saboo2017F1. Water during casting decides whether the film is one phase or twoF31, F14
saboo2017F2. Hydrophobic dyes stain the drug-rich phase, charged dyes the polymer-rich phaseF31
saboo2017F3. With prodan and R6G, confocal images show the same contrast as AFM-IRF31
saboo2017F4. A week at 75% RH separates a miscible film into drug-rich dropletsF31, F12, F23
saboo2017F5. In buffer the film separates within minutes into a coarse, connected structureF31
saboo2017F6. Heat alone does not separate the dry dispersionF14, F31
tian2017F1. The three polymorphs grow at very different rates from the same meltF29
tian2017F2. All three polymers slow growth; at lower temperatures PVP most, HPMCAS leastF29, F3, F18
tian2017F3. Each polymer slows γ least and α mostF29, F19
tian2017F4. Inhibition jumps above the temperature of fastest growth, and HPMC lowers that temperatureF29, F4
tian2017F5. PVP gives the most viscous melt; HPMC and HPMCAS melts are alikeF29
trasi2017F1. Only Accord crystallized during 4 weeks of open storage at 40 °C/75% RHF33
trasi2017F2. Accord crystallizes within days, in every batch testedF33
trasi2017F3. Humidity and temperature both drive the crystallizationF33, F16, F25
trasi2017F4. Accord dissolves fastest, then loses supersaturationF33, F26
trasi2017F5. Accord crystallizes faster than pure amorphous tacrolimus, while a 1:1 HPMC dispersion stays amorphousF33, F5
trasi2017F6. Neither extra CCS, nor seeds, nor milling destabilizes the innovatorF33, F6
trasi2017F7. Only hot-dried ethanol granulation without HPMC contact reproduced the crystallizationF33
trasi2017F8. Drug particles from Accord look like drug dried on lactose; those from Prograf look like drug in HPMCF33
trasi2020F1. At 40% loading every polymer gave an amorphous solid; at 60% HPMCAS and PVPVA did notF34
trasi2020F2. Under 40 °C/75% RH, HPMCP, L100 and CAP kept 40% lumefantrine amorphous for 3 monthsF34, F11
trasi2020F3. Acidic polymers protonate lumefantrine to very different extentsF34, F24
trasi2020F4. The polymers that protonate more keep the drug amorphous longerF34, F24
trasi2020F5. The amorphous solubility of lumefantrine is 2–3 µg/mLF34
trasi2020F6. Granules with L100, HPMCP and HPMCAS supersaturate; CAP and PVPVA granules do notF34
trasi2020F7. Above the amorphous solubility, the granules release drug-rich nanodropletsF34
trasi2020F8. CAP binds the drug most strongly and releases least, but releases well at lower loadingF34
bhujbal2021F1. HPMCP and HPMCAS ASDs stay amorphous; CAP and EL100 do notF34, F14
bhujbal2021F2. The failing ASDs held more water or dried more slowlyF34
bhujbal2021F3. Every polymer protonates lumefantrine, but protonation does not rank stabilityF34, F24
bhujbal2021F4. More polymer gives more release; HPMCP leads at 2 hF34
bhujbal2021F5. Drying enlarges the particles, most for HPMCASF34
yang2022bF1. The two dyes mark the right phasesF31
yang2022bF2. More drug, faster separationF31, F12
yang2022bF3. Surfactants change when and how the drug-rich phase appearsF32, F22
yang2022bF4. Tween 80 and the Spans enter drug-rich nanodroplets; PVPVA and SDS do notF32
yang2022bF5. Zeta potential separates surface adsorbers from the restF32
yang2022bF6. In the films, each surfactant sits in the phase its hydrophilicity predictsF32

01Concepts

nucleation ratesite counts in films, the main read-out of F1, F2, F9–F11nucleationframework of the film studies; delayed nucleation with 50% HPMCASkinetic barrier to nucleationthe polymer effect at low content, Arrhenius activation energiesclassical nucleation theoryframework for sorting driving force and kineticsinterfacial free energysurface penalty of the nucleus; unmeasuredcrystal-melt interfacial free energyused to exclude explanations for nifedipine and for PVPdilution effectrejected explanation of the 3% polymer effectthermodynamic driving force for crystallizationnifedipine against felodipine; barely lowered by a few percent polymercrystallization tendencythe pure-drug ranking carried into dispersionscrystal growth ratemelt growth with PVP and other polymers for five drugs; film growth at fixed RH; surface against bulkspherulitic growthcrystal shape and the needle switch above 80% RHdiffusion-controlled crystal growthtransport-limited melt growth of felodipinesurface-enhanced crystal growthproposed reason why film growth outpaced bulk mobility; measured for felodipine form I, with and without PVP, and behind the particle-size effectpolymer rejection at the crystal growth frontaccumulation idea of 2006, tested by the 2010 modelcrystallization inhibition by polymersthe effect under study, dry and humidamorphous solid dispersionthe dispersions and their preparationglass transition temperatureTg, T/Tg and Tg − T tested as predictorsantiplasticizationTg gain from PVP, absent at low content and lost with waterGordon-Taylor equationideal-mixing Tg linesCouchman-Karasz equationideal-mixing Tg lines with a ΔCp constantmolecular mobilityread from relaxation, viscosity and AGV; does not rank crystallizationenthalpy relaxationKWW relaxation times of glasses and dispersionsKohlrausch-Williams-Watts equationfit of enthalpy recoverystructural relaxation timeAGV relaxation time compared with growthhygroscopicitypolymer-set water uptake of dispersions; PVP > PVPVA > HPMCAS in uptake and in separation; celecoxib dispersions and tacrolimus capsule fillswater sorptionuptake of drugs, polymers and blendswater sorption isothermisotherms and their protocolsplasticization by waterTg loss with sorbed waterplasticizationgeneral Tg lowering by a low-Tg componentmoisture-induced crystallizationfaster nucleation, growth and bulk crystallization with RHFlory-Huggins interaction parameterwater–drug, water–polymer and drug–polymer χFlory-Huggins theoryactivity in PVP; ternary and pseudobinary sorption modelsactivity coefficientof water in the drug and of the drug in water and NMPideal solubilitylattice term of the two dihydropyridinescosolvencyNMP–water and the polymer–water co-solventdrug solubility in polymersolubility in wet PVP behind the plateau estimateenthalpy of mixingpositive mixing enthalpy needed for separationmelting point depressiontest of the driving force with 3% PVPamorphous-amorphous phase separationdrug-rich and polymer-rich amorphous phasesmoisture-induced phase separationthe water-driven form of separationΔχ effectasymmetry of water–drug and water–polymer χremixing of separated amorphous phasesrecovery at 125 °Ckinetic trappingseparated phases glassy after dryingdrug-polymer miscibilitydry miscibility of felodipine–PVP to the melthydrogen bondingNH and carbonyl bands; donor type and susceptibility; drug–polymer bonds and growth inhibitiondrug-polymer interactionsproposed reason for PVP's dry advantage in growthsolid-state crystallization of amorphous drugsbulk crystallization of stored powdersaccelerated stability testinghigh RH as a test and its risksupersaturationco-solvent supersaturation of nifedipine and felodipinepolymorphismform II growth; δ-indomethacin; Form II with 10% HPMCAS; two felodipine forms with PVP; forms changed by polymers and surfactants; three indomethacin forms slowed by different factorslipophilicitylog P as a failed predictornucleation and crystal growththe two steps, decoupled by polymersnucleation temperature zoneDSC zones of acetaminophen and flutamide, shifted by polymersmolecular recognitionproposed for the PAA and nilutamide nucleation effectssupercooled liquidmelt films from which growth is measured; PVP acting in the liquiddegree of supercoolingunchanged by 10% polymer for acetaminophen and flutamidekinetic versus thermodynamic control of crystal growthcrossing growth curves with TPGS and PVPTg-scaled crystal growth ratesurfactant growth against T − Tghydrogen-bond donor and acceptor groupscomplementary groups decide which polymer slows growth or protects in storagehydrogen-bond basicitypKBHX classes of the polymer acceptorsintramolecular hydrogen bondingflutamide and curcumin acceptors held intramolecularlyself-associationPAA dimers; resveratrol and curcumin networksacid-base interactionE100 with resveratrol and curcumin; protonation of lumefantrine by enteric polymerspKaacid donors that resist separation; curcumin against E100hydrophobicitylog P in moisture-induced separationcrystallization tendency classificationresveratrol rapid, curcumin intermediate, celecoxib slow but fast-growingglass-forming abilityacetaminophen glass; resveratrol not made amorphous alonephysical stabilitystorage tables of polyphenol dispersions; dissolution after storage; miscibility limit and dry stability; marketed productsphase separation morphologydroplets, connected and bicontinuous domains after humid air or buffersurfactant partitioning into the drug-rich phasewhere SDS, Tween 80 and the Spans go in separated filmsdrug-rich nanodropletslumefantrine release above the amorphous solubility; surfactant partitioning testsamorphous solubilityceiling of lumefantrine and tacrolimus releasecrystal seedingseeds added to the tacrolimus innovator; seeds suggested in the genericmelt viscosityindomethacin–polymer melts, PVP most viscousdegree of substitutionHPMCAS grades that favour opposite enantiomersspinodal decompositionroute proposed for bicontinuous separationphase-separated domain size0.3–25 µm domains by route of water entryinterfacial tensionsurfactant at the drug–polymer interface slowing coarseningionic interactionslumefantrine–carboxylate salt formation

02Formulas

depth of field of a microscope objectiveAs printed in the four nucleation papers:area-to-volume conversion of nucleation countsclassical nucleation theoryJ \propto \exp\left(-\frac{\Delta G^{*}}{k_B T}\right)framework for driving force and kinetic barrier; reduced-temperature form for acetaminophenArrhenius equationFor the nucleation rate:activation energy of nucleation; viscous flow of indomethacin–polymer meltsHoffman equation\Delta G_v = -\frac{\Delta H_{fus}\,(T_{melt,ons} - T)\,T}{T_{melt,ons}^{2}}driving force of the two dihydropyridines and of six drugsamorphous-crystalline free energy difference from heat capacityWith linear reversing heat capacities C_p^{sl} = aT + b and C_p^{c} = cT + dconfigurational driving forceentropy of fusion\Delta S_{fus} = \frac{\Delta H_{fus}}{T_{melt,ons}}ΔSf of the two dihydropyridinesFlory-Huggins activity equationActivity coefficient of the drug in a polymer, with the amorphous drug as the solvent (2006):drug activity in PVPGordon-Taylor equationAs printed with a density-based constant:ideal-mixing Tg with Simha–Boyer or ΔCp constant; cited in words for acetaminophen Tg rises; named for humidified tacrolimusKohlrausch-Williams-Watts equationAs printed:enthalpy relaxation fitmaximum enthalpy recoveryAs printed:normalization of enthalpy recoveryStokes-Einstein equationD_{NMR} = \frac{k_B T}{6\pi\eta r}PVP tracer diffusivity in the front modeltemperature of maximum crystal growth rateT_{cryst,max} \approx 0.94\,T_mfelodipine growth maximum near 105 °C; 0.94–0.95 Tm for PHB and indomethacin, lowered by polymerssolid-liquid equilibrium solubility equation\ln x_{C,L_1} = -\frac{\Delta G_{a\to c}}{RT} - \ln\gamma_{L_1}lattice and mixing terms of crystal solubilityactivity coefficient from solubility\gamma_d = \frac{1}{x_d}\exp\left(\frac{-\Delta H_{fus,d}\,(T_{melt,d} - T)}{R\,T_{melt,d}^{2}}\right)drug activity coefficients in waterFlory-Huggins water sorption isothermBinary form, water (1) in one amorphous solid (2):χ of water with drugs and polymersmulticomponent Flory-Huggins free energy of mixingWater–drug–polymer system:thermodynamic origin of moisture-induced separation and of the polymer hygroscopicity effectadditive moisture sorptionPrinted in words in the two moisture papers (weight-averaged sum of the pure-component uptakes)weighted sum of component uptakesΔχ effect\left|\Delta\chi\right| = \left|\chi_{12} - \chi_{13}\right|water–drug against water–polymer χlinear crystal growth rate from size-time slopePrinted 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 plotfilm growth rates and powder crystallization slopes; enantiomer and PHB growthcrystal growth inhibition effectiveness ratioThe polymer effectiveness ratio for crystal growth inhibition is the growth rate without polymer over the rate with polymer:PVP factor for two felodipine polymorphs and for surface against bulk growthFox equation\frac{1}{T_g} = \frac{x_1}{T_{g,1}} + \frac{x_2}{T_{g,2}}Tg deviations of curcumin dispersionsFlory-Huggins free energy of mixingIn mole numbers, as printed in the 2006 paper:argument that stronger drug–polymer interaction lowers the driving force for indomethacin growthlever rulePrinted in words: the ratio of the amount of phase A to that of phase B equals the ratio of the length BX to AX, X being the overall composition on the tie line joining A and Bphase amounts and morphology on a schematic ritonavir–PVPVA–water diagram
32 more formulas printed by one paper (table only)
formularole hereexpression
fraction of glass relaxedenthalpy recovery as a fraction\phi(t) = \Delta H_t/\Delta H_{\infty} konno2006 E5
configurational enthalpy and entropy of crystallizationintegrated from the melting point\Delta H_c = \Delta H_f + \int_{T_M}^{T} C_p^{config}\,dT and \Delta S_c = \Delta S_f + \int_{T_M}^{T} (C_p^{config}/T)\,dT marsac2006a E4, E5
degree of supersaturationthermodynamic driving force with water present\sigma = (\mu^{1} - \mu^{0})/RT marsac2008a E1
nucleation rate from site densityslope of volume site density against timeprinted in words marsac2008a E4
log-linear cosolvency modelsolubility in NMP–water\log S = -0.04\,w - 0.89 (nifedipine), \log S = -0.06\,w - 0.56 (felodipine) marsac2008a E5
water weight fraction in the polymer–water co-solventcomposition of the co-solventw_{co} = w_{water}/(w_{water} + w_{PVP}) marsac2008a E6
F-test with RMSEP as error termstatistics of the PXRD crystallinity seriesnamed, not printed rumondor2009b E3
residual amorphous phase composition after crystallizationplateau estimateprinted in words, about 0.1 g drug per 0.86 g PVP–water rumondor2009b E4
water activity with activity coefficient (Raoult's law form)γ of water in amorphous drugsa_{water} = P/P_0 = \gamma_{water}X_{water} rumondor2009c E1
C–C band intensity ratio of a calculated physical mixtureweighting of the physical-mixture IR spectrumprinted in words rumondor2009c E7
growth rate from viscosity and a two-dimensional nucleation barriertest of viscosity as mobilityv = \frac{k}{\eta}\exp\left(\frac{\pi b\gamma^{2}T_m}{k_B T\Delta H_v\Delta T}\right) kestur2010b E5
two-dimensional nucleation barrier and Turnbull approximationparts of the growth equation\Delta G^{*} = -\pi b\gamma^{2}/\Delta G_v and \Delta G_v = -\Delta H_v\Delta T/T_m kestur2010b E3, E4
Fick's second law, Frank similarity solution, mass conservation of expelled polymerPVP profile at the growth frontc(r,t) = -\frac{1}{2}A(t)E_1\left(-\frac{r^{2}}{4D_m t}\right) + c_\infty with \int_{R(t)}^{\infty}2\pi r\left[c(r,t) - c_\infty\right]dr = \varepsilon\pi R(t)^{2}c_\infty kestur2010b E6, E7, E9, E10
Kirkwood–Riseman radius and radius of gyration of an ideal chainPVP coil size for the diffusivityR_h = 0.665R_g, R_g = (C_n n l/6)^{1/2} as printed kestur2010b E12, E13
power-law shear-rate dependence of viscosityshear thinning of the 3% PVP K-90 melt\eta \sim \dot{\gamma}^{\alpha}, α printed 0.28 kestur2010b E14
peak-height ratio of hydrogen-bonded NH bandsremixing at 125 °CI_{rel} = h_{3290}/h_{3345} marsac2010 E2
Adam–Gibbs–Vogel equation and coupling exponentrelaxation time and growth\tau = \tau_0\exp\left[\frac{DT_0}{T - T(T_0/T_f)}\right] and \log(\tau_{T_g}/\tau)^{\xi} rumondor2010 E1, E2
relative deviation from additive moisture sorptionshortfall against additivityprinted in words rumondor2010a E6
Tg/Tm two-thirds ruleestimated Tg of resveratrol, which could not be made amorphousnamed, not printed; the usual form T_g \approx \frac{2}{3}T_m in kelvin gives 83.6 °C against the printed 83.7 °C wegiel2013b E1, M1
pKBHX acceptor strength classesclasses of the polymer acceptor groups\text{weak} < 0.75 < \text{medium} < 1.5 < \text{strong} < 2.25 < \text{very strong} wegiel2013b E2
molecular layers added per structural relaxation timetest of the glass-crystal growth modeprinted in words; ≈500 printed, ≈290 from the printed inputs kestur2013a E1, R18, X2
growth-rate ratio with and without polymeracceleration or retardation by PHBR = u_{polymer}/u_{0}, printed in words sato2016 E4
degree of undercoolingdriving force of indomethacin polymorph growth\Delta T = T_m - T tian2017 E4
driving-force normalization of growth ratescomparison of indomethacin polymorphsnamed, not printed tian2017 E5
Abbe diffraction limitsmallest domain seen by confocal imagingd \approx 0.5\,\lambda/NA saboo2017 E1
XRPD crystallinity indices and linear calibrationstacrolimus crystallinity, laboratory and synchrotronarea ratio A_{10-10.5^{\circ}}/A_{9.5-10.8^{\circ}} with y = 0.0002x + 0.3923; peak-to-baseline ratio I_{8.57^{\circ}}/\bar{I}_{9.1-9.3^{\circ}} with y = 0.0159x + 1.0205 trasi2017 E1, E2, E3, E4
mass balance by differencelactose content of the capsulesm_{lactose} = m_{powder} - (m_{drug} + m_{HPMC} + m_{CCS}) trasi2017 E5
dose-to-volume concentrationnon-sink dissolution of tacrolimusC = \text{dose}/V, 5 mg in 100 mL = 50 µg/mL trasi2017 E6
supersaturation ratiolumefantrine release over crystalline solubilitynamed; the printed "at least 20-fold" recomputes to about 12.5 trasi2020 E1, X4
percentage protonationshare of protonated lumefantrine from the N 1s fitnamed, not printed trasi2020 E2
water content from TGA weight lossresidual water of precipitated dispersionspercent weight loss between 35 and 170 °C bhujbal2021 E1
Carr index, Hausner ratio, spanflow and size of precipitated powdersnamed, not printed bhujbal2021 E2, E3, E4

Sources: Physical stability

Every paper cited in the chapter Physical stability (category Solid state stability) and in the concept and formula drafts written from it. Keys are the global keys of synthesis/citation_keys.csv. The first rows are the twenty-nine papers of the subcategory (2006–2022), in year order; the other cited papers follow in year order. The paper keyed xie2016b carries the year 2016 in its card and in the key list, while its folder name begins with 2017.

keyyeartitleslugcategory / subcategory
konno20062006Influence of Different Polymers on the Crystallization Tendency of Molecularly Dispersed Amorphous Felodipine2006-konno-felodipine-polymer-crystallization-nucleation-solid-dispersionsSolid state stability / Physical stability
marsac2006a2006A Comparison of the Physical Stability of Amorphous Felodipine and Nifedipine Systems2006-marsac-physical-stability-amorphous-felodipine-nifedipineSolid state stability / Physical stability
konno20082008Ability of Different Polymers to Inhibit the Crystallization of Amorphous Felodipine in the Presence of Moisture2008-konno-polymers-inhibit-amorphous-felodipine-moisture-crystallizationSolid state stability / Physical stability
marsac2008a2008Recrystallization of Nifedipine and Felodipine from Amorphous Molecular Level Solid Dispersions Containing Poly(vinylpyrrolidone) and Sorbed Water2008-marsac-nifedipine-felodipine-pvp-sorbed-water-recrystallizationSolid state stability / Physical stability
rumondor2009b2009Effects of Polymer Type and Storage Relative Humidity on the Kinetics of Felodipine Crystallization from Amorphous Solid Dispersions2009-rumondor-polymer-rh-felodipine-crystallization-kineticsSolid state stability / Physical stability
rumondor2009c2009Phase Behavior of Poly(vinylpyrrolidone) Containing Amorphous Solid Dispersions in the Presence of Moisture2009-rumondor-pvp-asd-moisture-induced-immiscibilitySolid state stability / Physical stability
kestur2010b2010Effects of the Molecular Weight and Concentration of Polymer Additives, and Temperature on the Melt Crystallization Kinetics of a Small Drug Molecule2010-kestur-pvp-mw-concentration-temperature-felodipine-melt-crystallizationSolid state stability / Physical stability
marsac20102010Effect of Temperature and Moisture on the Miscibility of Amorphous Dispersions of Felodipine and Poly(vinyl pyrrolidone)2010-marsac-temperature-moisture-miscibility-felodipine-pvp-asdSolid state stability / Physical stability
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
rumondor2010a2010Analysis of the Moisture Sorption Behavior of Amorphous Drug–Polymer Blends2010-rumondor-moisture-sorption-amorphous-drug-polymer-blendsSolid state stability / Physical stability
rumondor2010c2010Effect of Polymer Hygroscopicity on the Phase Behavior of Amorphous Solid Dispersions in the Presence of Moisture2010-rumondor-polymer-hygroscopicity-moisture-phase-separation-asdSolid state stability / Physical stability
rumondor20112011Understanding the Tendency of Amorphous Solid Dispersions to Undergo Amorphous–Amorphous Phase Separation in the Presence of Absorbed Moisture2011-rumondor-asd-moisture-aaps-pvp-oplsSolid state stability / Physical stability
trasi2012a2012Effect of polymers on nucleation and crystal growth of amorphous acetaminophen2012-trasi-taylor-polymers-nucleation-growth-amorphous-acetaminophenSolid state stability / Physical stability
trasi2012b2012Effect of Additives on Crystal Growth and Nucleation of Amorphous Flutamide2012-trasi-flutamide-additives-growth-nucleationSolid state stability / Physical stability
kestur2013a2013Evaluation of the crystal growth rate of felodipine polymorphs in the presence and absence of additives as a function of temperature2013-kestur-felodipine-polymorph-crystal-growth-pvp-additivesSolid state stability / Physical stability
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
mosqueragiraldo20142014Impact of surfactants on the crystal growth of amorphous celecoxib2014-mosquera-giraldo-surfactants-crystal-growth-amorphous-celecoxibSolid state stability / Physical stability
wegiel20142014Curcumin amorphous solid dispersions: the influence of intra and intermolecular bonding on physical stability2014-wegiel-curcumin-asd-intramolecular-bonding-physical-stabilitySolid state stability / Physical stability
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
sato20162016Acceleration of the crystal growth rate of low molecular weight organic compounds in supercooled liquids in the presence of polyhydroxybutylate2016-sato-phb-crystal-growth-supercooled-organic-compoundsSolid state stability / Physical stability
tian20162016Investigating the Correlation between Miscibility and Physical Stability of Amorphous Solid Dispersions Using Fluorescence-based Techniques2016-tian-indomethacin-polymer-miscibility-physical-stability-fluorescenceSolid state stability / Physical stability
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
saboo20172017Water-induced phase separation of miconazole-poly (vinylpyrrolidone-co-vinyl acetate) amorphous solid dispersions: Insights with confocal fluorescence microscopy2017-saboo-water-induced-miconazole-pvpva-asd-phase-separationSolid state stability / Physical stability
tian20172017Impact of Polymers on the Melt Crystal Growth Rate of Indomethacin Polymorphs2017-tian-polymers-melt-crystal-growth-indomethacin-polymorphsSolid state stability / Physical stability
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
trasi20202020Physical stability and release properties of lumefantrine amorphous solid dispersion granules prepared by a simple solvent evaporation approach2020-trasi-lumefantrine-asd-granules-solvent-evaporationSolid state stability / Physical stability
bhujbal20212021Physical Stability and Dissolution of Lumefantrine Amorphous Solid Dispersions Produced by Spray Anti-Solvent Precipitation2021-bhujbal-lumefantrine-asd-spray-antisolvent-precipitationSolid state stability / Physical stability
yang2022b2022Phase separation in surfactant-containing amorphous solid dispersions: Orthogonal analytical methods to probe the effects of surfactants on morphology and phase composition2022-yang-surfactant-containing-rtv-pvpva-asd-phase-separationSolid state stability / Physical stability
taylor19971997Spectroscopic Characterization of Interactions Between PVP and Indomethacin in Amorphous Molecular Dispersions1997-taylor-pvp-indomethacin-amorphous-molecular-dispersionsSolid state stability / Miscibility and drug-polymer interactions
marsac2006b2006Theoretical and Practical Approaches for Prediction of Drug–Polymer Miscibility and Solubility2006-marsac-drug-polymer-miscibility-solubilitySolid state stability / Miscibility and drug-polymer interactions
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
marsac2008b2008Spontaneous Crystallinity Loss of Drugs in the Disordered Regions of Poly(Ethylene Oxide) in the Presence of Water2008-marsac-peo-water-spontaneous-drug-crystallinity-lossSolid state stability / PEG dispersions
rumondor2009a2009Evaluation of Drug-Polymer Miscibility in Amorphous Solid Dispersion Systems2009-rumondor-drug-polymer-miscibility-asd-dsc-ir-pxrdSolid state stability / Miscibility and drug-polymer interactions
marsac20092009Estimation of Drug–Polymer Miscibility and Solubility in Amorphous Solid Dispersions Using Experimentally Determined Interaction Parameters2009-marsac-drug-polymer-miscibility-solubility-asd-interaction-parametersSolid state stability / Miscibility and drug-polymer interactions
alonzo20102010Understanding the Behavior of Amorphous Pharmaceutical Systems during Dissolution2010-alonzo-amorphous-pharmaceutical-dissolution-crystallization-polymersDissolution / B. Supersaturation from ASD dissolution
baird20102010A Classification System to Assess the Crystallization Tendency of Organic Molecules from Undercooled Melts2010-baird-classification-crystallization-tendency-undercooled-meltsSolid state stability / Crystallization tendency
kestur2010a2010Role of polymer chemistry in influencing crystal growth rates from amorphous felodipine2010-kestur-polymer-chemistry-felodipine-crystal-growth-inhibitionSolid state stability / Miscibility and drug-polymer interactions
vaneerdenbrugh2010a2010Crystallization Tendency of Active Pharmaceutical Ingredients Following Rapid Solvent Evaporation—Classification and Comparison with Crystallization Tendency from Undercooled Melts2010-van-eerdenbrugh-api-crystallization-tendency-rapid-solvent-evaporationSolid state stability / Crystallization tendency
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
wanapun20102010Selective Detection and Quantitation of Organic Molecule Crystallization by Second Harmonic Generation Microscopy2010-wanapun-sonicc-amorphous-api-crystallization-detectionCharacterization methods / Solid-state methods
kestur20112011Influence of polymer chemistry on crystal growth inhibition of two chemically diverse organic molecules2011-kestur-polymer-chemistry-crystal-growth-bifonazole-nimesulideSolid state stability / Miscibility and drug-polymer interactions
vaneerdenbrugh2011a2011An ab initio polymer selection methodology to prevent crystallization in amorphous solid dispersions by application of crystal engineering principles2011-van-eerdenbrugh-ab-initio-polymer-selection-asd-crystallizationSolid 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
baird20122012Role of Viscosity in Influencing the Glass-Forming Ability of Organic Molecules from the Undercooled Melt State2012-baird-viscosity-glass-forming-ability-undercooled-meltsSolid state stability / Crystallization tendency
vaneerdenbrugh2012c2012Nanoscale Mid-Infrared Evaluation of the Miscibility Behavior of Blends of Dextran or Maltodextrin with Poly(vinylpyrrolidone)2012-van-eerdenbrugh-nanoscale-mid-ir-dextran-maltodextrin-pvp-miscibilityCharacterization methods / Solid-state methods
ilevbare2013a2013Liquid-Liquid Phase Separation in Highly Supersaturated Aqueous Solutions of Poorly-Water Soluble Drugs – Implications for Solubility Enhancing Formulations2013-ilevbare-llps-supersaturated-poorly-water-soluble-drugsDissolution / C. Amorphous solubility and LLPS
wegiel2013a2013Mid-infrared spectroscopy as a polymer selection tool for formulating amorphous solid dispersions2013-wegiel-mid-ir-polymer-selection-polyphenol-asd-stabilitySolid state stability / Miscibility and drug-polymer interactions
raina2014a2014Enhancements and Limits in Drug Membrane Transport Using Supersaturated Solutions of Poorly Water Soluble Drugs2014-raina-llps-limits-drug-membrane-transport-supersaturated-solutionsBioperformance / Bioperformance
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
trasi2014a2014Factors Influencing Crystal Growth Rates from Undercooled Liquids of Pharmaceutical Compounds2014-trasi-crystal-growth-rates-undercooled-pharmaceutical-liquidsSolid state stability / Crystallization tendency
trasi2014b2014Nucleation and crystal growth of amorphous nilutamide – unusual low temperature behavior2014-trasi-taylor-amorphous-nilutamide-low-temperature-nucleationSolid state stability / Crystallization tendency
purohit2015a2015Miscibility of Itraconazole-Hydroxypropyl Methylcellulose Blends- Insights with High Resolution Analytical Methodologies2015-purohit-itraconazole-hpmc-miscibility-high-resolution-methodsSolid state stability / Miscibility and drug-polymer interactions
purohit2015b2015Phase Separation Kinetics in Amorphous Solid Dispersions Upon Exposure to Water2015-purohit-phase-separation-kinetics-asd-waterCharacterization methods / Solid-state methods
trasi20152015Evaluating the influence of polymers on nucleation and growth in supersaturated solutions of acetaminophen2015-trasi-polymers-nucleation-growth-supersaturated-acetaminophenDissolution / D. Crystallization from solution
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
li2016c2016Nanoscale Infrared, Thermal, and Mechanical Characterization of Telaprevir-Polymer Miscibility in Amorphous Solid Dispersions Prepared by Solvent Evaporation2016-li-telaprevir-polymer-miscibility-nanoscale-afm-irSolid state stability / Miscibility and drug-polymer interactions
lu20162016Vemurafenib: A Tetramorphic System Displaying Concomitant Crystallization from the Supercooled Liquid2016-lu-vemurafenib-tetramorphic-cold-crystallization-supercooled-liquidSolid state stability / Crystallization tendency
schram20162016Polymer Inhibition of Crystal Growth by Surface Poisoning2016-schram-polymer-inhibition-crystal-growth-surface-poisoningDissolution / D. Crystallization from solution
trasi20162016Non-Sink Dissolution Behavior and Solubility Limit of Commercial Tacrolimus Amorphous Formulations2016-trasi-commercial-tacrolimus-asd-nonsink-amorphous-solubilityDissolution / B. Supersaturation from ASD dissolution
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
li20172017Understanding the impact of water on the miscibility and microstructure of amorphous solid dispersions – An AFM/LCR and TEM/EDX study2017-li-water-miscibility-microstructure-asd-afm-tem-edxASD process / ASD process
mugheirbi20172017Insights into Water-Induced Phase Separation in Itraconazole–Hydroxypropylmethyl Cellulose Spin Coated and Spray Dried Dispersions2017-mugheirbi-water-induced-phase-separation-itz-hpmc-asdASD process / ASD process
purohit2017b2017Phase Behavior of Ritonavir Amorphous Solid Dispersions during Hydration and Dissolution2017-purohit-ritonavir-asd-hydration-dissolution-phase-behaviorDissolution / A. Release mechanism and LoC
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
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
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
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
li20202020Water-induced phase separation of spray dried amorphous solid dispersions2020-li-water-induced-phase-separation-spray-dried-asd-ritonavir-pvpvaASD process / ASD process
elkhabaz20212021Crystallization Kinetics in Fasted-State Simulated and Aspirated Human Intestinal Fluids2021-elkhabaz-crystallization-kinetics-fasted-simulated-aspirated-human-intestinal-fluidsDissolution / D. Crystallization from solution
saboo20212021Exploring the Role of Surfactants in Enhancing Drug Release from Amorphous Solid Dispersions at Higher Drug Loadings2021-saboo-tpgs-felodipine-pvpva-asd-release-high-loadingDissolution / A. Release mechanism and LoC
yang20212021Drug Release and Nanodroplet Formation from Amorphous Solid Dispersions: Insight into the Roles of Drug Physicochemical Properties and Polymer Selection2021-yang-asd-nanodroplet-release-drug-properties-polymer-selectionDissolution / A. Release mechanism and LoC
alvarenga20222022Impact of Polymer Type on Thermal Degradation of Amorphous Solid Dispersions Containing Ritonavir2022-alvarenga-polymer-type-thermal-degradation-ritonavir-asdASD process / ASD process
correasoto2022b2022Role of surfactants in improving release from higher drug loading amorphous solid dispersions2022-correa-soto-surfactants-higher-drug-loading-atazanavir-pvpva-asdsDissolution / A. Release mechanism and LoC
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
duong2022c2022Surface nanocoating of high drug-loading spray-dried amorphous solid dispersions by atomic layer coating: Excellent physical stability under accelerated storage conditions for two years2022-van-duong-surface-nanocoating-high-drug-loading-asd-alc-stabilityASD process / ASD process
hiew2022a2022Balancing Solid-State Stability and Dissolution Performance of Lumefantrine Amorphous Solid Dispersions: The Role of Polymer Choice and Drug−Polymer Interactions2022-hiew-lumefantrine-asd-stability-dissolution-polymer-choiceSolid state stability / Miscibility and drug-polymer interactions
moseson2022a2022Atomic Layer Coating to Inhibit Surface Crystallization of Amorphous Pharmaceutical Powders2022-moseson-atomic-layer-coating-surface-crystallization-asd-powdersASD process / ASD process
yang2022a2022Release mechanisms of amorphous solid dispersions: Role of drug-polymer phase separation and morphology2022-yang-release-mechanisms-rtv-pvpva-asd-phase-separation-morphologyDissolution / A. Release mechanism and LoC
correasoto2022a2022Impact of Surfactants on the Performance of Clopidogrel-Copovidone Amorphous Solid Dispersions: Increased Drug Loading and Stabilization of Nanodroplets2022-correa-soto-surfactants-clopidogrel-copovidone-asd-nanodropletsDissolution / A. Release mechanism and LoC
correasoto20232023Release Enhancement by Plasticizer Inclusion for Amorphous Solid Dispersions Containing High Tg Drugs2023-correa-soto-plasticizer-release-enhancement-high-tg-pvpva-asdsDissolution / A. Release mechanism and LoC
nguyen2023a2023Fed- and Fasted-State Performance of Pretomanid Amorphous Solid Dispersions Formulated with an Enteric Polymer2023-nguyen-pretomanid-hpmcas-asd-fed-fasted-performanceBioperformance / Bioperformance
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
deac2023a2023Dissolution Mechanisms of Amorphous Solid Dispersions: A Close Look at the Dissolution Interface2023-deac-asd-dissolution-interfaceDissolution / A. Release mechanism and LoC
deac2023b2023Dissolution Mechanisms of Amorphous Solid Dispersions: Role of Drug Load and Molecular Interactions2023-deac-asd-drug-load-molecular-interactions-locDissolution / A. Release mechanism and LoC
polyzois20242024Amorphous Solid Dispersion Formation for Enhanced Release Performance of Racemic and Enantiopure Praziquantel2024-polyzois-praziquantel-racemic-enantiopure-asd-releaseDissolution / B. Supersaturation from ASD dissolution
deac2024b2024Dissolution Mechanisms of Amorphous Solid Dispersions: Application of Ternary Phase Diagrams To Explain Release Behavior2024-deac-asd-ternary-phase-diagrams-releaseDissolution / A. Release mechanism and LoC
bapat2025b2025Modification of Peptide and Permeation Enhancer In Vitro Release Rates by Dispersion with a Gel-Forming Polymer2025-bapat-peptide-permeation-enhancer-pvpva-synchronous-releasePeptide permeability / Peptide permeability
For the authors: card issues found while writing

Card issues: Physical stability

None found. Differences between papers on the same quantity (water content of PVP at 75% RH, felodipine nucleation rate without polymer, the fall of felodipine growth rate on cooling) come from the sources themselves; they are reported in findings.md and not as card errors.

The cards of 2010–2014 also showed no material card problem: every cited id resolved, and the inconsistencies met (misprinted nucleation equation for acetaminophen, Fox-equation predictions computed in °C, the carbonyl shifts of Table II against the text for the 20-system study, the 500 against about 290 molecular layers for felodipine form I) are source problems that the cards already flag in their extractor notes trasi2012a X1; wegiel2014 X1; rumondor2011 X1; kestur2013a X2. One cited value cannot be checked inside the library: the particle-size paper cites a 150-fold drop of felodipine nucleation with 3% PVP at 30 °C from the 2006 nucleation paper, whose card holds no 30 °C rates kestur2013b R22; this is a citation in the source, not a card error.

The cards of 2015–2022 showed no material card problem either; every cited id resolved. The inconsistencies met are source problems that the cards flag: the text of the enantiomer paper names ATP(R) and ATP(S) the other way round from its figures, DSC and storage data sato2015 X1; the PHB paper names ATP in the text where its figure shows celecoxib sato2016 X2; Table 2 of the indomethacin polymorph paper interchanges the δ and γ maxima of the pure drug tian2017 X1; the buffer figure caption of the miconazole paper contradicts its text, and its diffraction limit recomputes to 137 instead of about 150 nm saboo2017 X2, X3; the stated "at least 20-fold" supersaturation of the lumefantrine granules recomputes to about 12.5, and Table 1 of that paper contradicts the text for one 60:40 dispersion trasi2020 X4, X2; the precipitation paper prints an abstract value that does not match its results, gives "100- and 60-times" where its data give about 116 and 79, and about 10% water where its table gives 9% bhujbal2021 X1, X3, X20; and one slow batch of the tacrolimus generic is "around 40%" crystalline in the text against about 57% in the figures trasi2017 X5. A naming point outside the cards: the paper keyed xie2016b carries the year 2016 in its card and in the key list, while its card folder name begins with 2017; the chapter orders it by the card year.

← Concepts and formulas

concept · as used in Physical stability

accelerated stability testing

Storage at raised humidity and/or temperature to provoke and rank physical instability in less time than at the intended storage condition. In the library the concern is that high RH can change the mechanism, not only the rate, of crystallization of susceptible dispersions rumondor2009c C52.

Findings

F16, F25.

Related concepts

related to moisture-induced phase separation, moisture-induced crystallization and physical stability.

Formulas

Arrhenius equation (temperature extrapolation; used here for nucleation, not for shelf life).

How it is measured or obtained

Storage over saturated salts at fixed RH (here 54–94% RH at room temperature) and read-out by IR, DSC, PXRD or microscopy rumondor2009c P4; rumondor2009b P2, P3; marsac2010 P7.

Values in the library
materialvalue or classconditionspaper ids
pimozide–PVPpartial phase separation after 3 days54% RHrumondor2009c R10, C4
felodipine–PVP 30.3 wt%distinct separation after 1 week75% RHmarsac2010 R7, R8
felodipine with 25–50% PVP vs HPMCASindistinguishable at 0–52% RH in ≈490 days; 51–82% vs 9–28% crystallized at 75–93% RH22–25 °Crumondor2009b R19, R9
PEO compacts (outside)slow water uptake over months; partially crystalline polymers "may" defeat Arrhenius extrapolation94% RHmarsac2008b C40
curcumin dispersions25 °C/0% RH and 90 °C/0% or 60 °C/98% RH separate no polymersix conditionswegiel2014 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 Physical stability

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, filmswegiel2013a R6
resveratrol–E100; curcumin–E100bands absent at 50% resveratrol; eradicated at 60% curcuminIR, filmswegiel2013b R7, C15; wegiel2014 R7, C16
lumefantrine, 25% drug loadingprotonated 19% (HPMCAS), 46% (HPMCP), 55% (CAP), 49% (Eudragit L 100); 0% with PVPVAXPS, dry compactshiew2022a R20
same, after 2 h in pH 6.8 buffer3, 21, 54, 12%XPShiew2022a R20
anthranilic acid, lidocaine, dibucaine with PSSAproton transfer reported; not with PAAATR-FTIR of melts (not shown)vaneerdenbrugh2011a R8, R15, R17
cationic drugs with HPMCAS-MF, 1:1 drug to carboxyl, pH 6.0≥70% of the polymer complexedco-precipitation[bapat2024 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 powderwegiel2014 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 °Cwegiel2014 R13; wegiel2013b R12.g
lumefantrine 40:60 with HPMCAS, Eudragit L100, HPMCP, CAP16, 33, 48, 61% protonated; neat drug 7%rotary-evaporated powders, XPStrasi2020 R11, C14
lumefantrine with HPMCP, HPMCAS (20–40% drug), CAP, Eudragit L100 (40%)14–42% protonated; amorphous drug 3%powders precipitated into dilute HCl, XPSbhujbal2021 R8
fluorescein in miconazole–PVPVA filmslocated in the drug-rich phase, read as a possible acid–base contact with the weakly basic drug ("may arise")confocal dye screensaboo2017 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 Physical stability

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 °Cmarsac2008b 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 solubilitiesmarsac2008b R14
nifedipine; felodipine in water1.89 × 10³; 2.43 × 10⁵25 °Cmarsac2008a R10.c, R10.d
five compounds in an ethyl-pyrrolidone analogue of PVPbelow 1 for all25 °Cmarsac2009 C23, R9
felodipine, nifedipine, ketoconazole, sucrose, indomethacin in EP0.89, 0.26, 0.68, 0.37, 0.1525 °Cmarsac2009 R9
same five in PVP K123.94, 1.18, 5.04, 1.76, 0.50scaled with Eq. 8marsac2009 R9
same five in PVP K29/324.34, 1.30, 5.92, 1.93, 0.54scaled with Eq. 8marsac2009 R9
nifedipine, felodipineχ-based activity from melting depression; no direct γFlory–Hugginsmarsac2006b E6
ritonavir, atazanavirlog γ ordering RTV > ATV (recomputed 4.65 against 3.01)pH 6.8[alhalaweh2016 X1, X2]
felodipine / nifedipine fluxγ/γ* assumed 1 for dilute solutionsbuffer[raina2015c C32]
atazanavir, posaconazoleconcentration-based and activity-based ratios agree in the two buffers and differ in the four micellar mediasix media, 37 °C[elkhabaz2019b R8, R9, C42]
water in nifedipine, felodipine, droperidol, pimozide, indomethacin, ketoprofen3.19, 4.13, 3.00, 4.65, 2.54, 3.3525 °C, 95% RHrumondor2009c R24
same drugs in water4.95 × 10⁵ to 8.88 × 10⁶; ketoprofen 9.85 × 10⁴from solubilityrumondor2009c R24

The amorphous solubility chapter prints no activity coefficient value.

Pitfalls and disagreements

The conversion from mg/mL to mole fraction is not printed in Baird and Taylor; the printed values equal moles of drug per mole of PEG 400 in 1 mL, and a true mole fraction would give 0.766, 0.149, 2.49 and 0.856 instead of 0.614, 0.121, 2.369 and 0.842, leaving the split at 1 unchanged [baird2011 X4]. Loratadine, grouped with haloperidol as close to ideal, dissolves at about 0.42 of its ideal solubility [baird2011 X13]. Several rows of the Marsac and co-workers table are not internally consistent, aqueous solubilities come from three cited sources at unstated temperatures and the ideal solubility temperature is not stated, so the coefficients in water serve only as orders of magnitude marsac2008b X5, X18. Activity coefficients in PEG 400 were measured at 25 °C, far below the 52–61 °C of the molten dispersions, and are not values for molten PEG 3350 [baird2011 X16]. A value below 1 in PEG 400 did not separate the crystalline from the transforming drugs in PEO under humidity: all six were below 1 marsac2008b R14, R16. Ketoconazole has 0.09 in PEG 400 but a positive interaction parameter in PEG 3350 [marsac2008b R14.f; zhu2011 R5.f]. In the amorphous solubility papers the constancy of γ underlies the claim that a solubilizer leaves the maximum supersaturation unchanged, while a later study found the concentration ratio falling [ilevbare2013a C54; raina2015c C29]. There γ is estimated with the ideal dilute solution as standard state, from a buffer calibration [indulkar2017a R11], and is the factor in a = C\gamma; the PEG dispersions chapter defines \gamma_d instead as the ratio of ideal to real solubility in a liquid polymer analogue, so the values tabulated above are not those of the aqueous solutions. The predicted γ in PVP exceeds 1 for four of five compounds (1.18–5.97), so the compounds that dissolve better than ideal in the analogue are predicted to dissolve worse than ideal in the polymer; only indomethacin stays below 1 marsac2009 R9. Lattice volume, heat capacities, ideal solubilities and the mole-fraction basis in PVP are not printed marsac2009 X4, X13. The value of indomethacin in K29/32 differs between table and text marsac2009 X2. In the Bioperformance papers γ/γ* = 1 breaks down with solubilizers [raina2015c C36]; the plotted log γ in the ritonavir–atazanavir figure does not match the recomputation [alhalaweh2016 X1, X2]. The value of \gamma/\gamma_{eq} is not measured; its departure from 1 is read from the gap between the flux ratio and the concentration ratio (F18) [elkhabaz2019b C21, C28]. In the 2009 moisture study the drug-in-water column of the table equals the inverse mole-fraction solubility rather than the printed equation, so it ranks drugs by solubility alone rumondor2009c X1; two text rankings disagree with the table rumondor2009c X2, X3.

← Concepts and formulas

concept · as used in Physical stability

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–dichloromethanepurohit2015a R1, R11, R13, R7
telaprevir–HPMC, –PVPVAdomains from 10% drugspin-coated filmsli2016c R4, R6
telaprevir–HPMCASregular domains only from about 30–40% drugspin-coated films, humidity not controlledli2016c R5, C17, X2, X9
dextran–PVP, 20 pairsphase separated at 0, 0–5, 5–7, 5–9 of nine compositions for DEX1, DEX6, DEX40, DEX450DSC, freeze-dried[vaneerdenbrugh2012a R13]
felodipine–PVP, 30–50% PVPdrug-rich and polymer-rich phases after 94% RHIR, TEMmarsac2010 C14, C27
miconazole–PVPVA 50:50domains after film formation at 60% RH and after 75% RH storageAFM, confocalsaboo2017 R13, R15, C42
telaprevir–PVPVA, 70% PVPVAtwo overlapping Tgs; "may have partially phase separated"mDSC[mosqueragiraldo2018b R23, C53]
ECP–polymerdrug-rich spheres (preparation) or drug-rich network (storage)TEM-EDXli2017 R18, R19, R22
ITZ–HPMCdiscrete drug-rich domains with self-associated ITZ (extra emission near 381 nm)FLOM, AFM, UV, emissionmugheirbi2017 R1, R22
LPV–HPMCdiscrete drug-rich domains 50–500 nm high in a polymer-rich matrix; faster release at 33–85% DLAFM, nanoTA, releaseli2019 R8, R2
ritonavir–PVPVA spray-driedsecond non-reversing DSC event after ageing in 50% DL powders from 10:90 to 40:60; drug-rich surfaces (XPS) from 60:40; SNDR at 25% DL about 3.5 → 2.27 → 0.90 mg·min⁻¹·cm⁻¹BLD-35 dryerli2020 R4, R7, R10
pimozide–PVP 50:50Tgs −21/44 °C wet, 61/112 °C re-dried94% RH, 42 hrumondor2009c R17
felodipine–PVP 46.5 wt%event at ≈45–50 °C instead of one Tg near 80 °Cafter 75–94% RHmarsac2010 R14
felodipine–PVP 50% filmislands of about 300–500 nm (TEM, AFM)94% RHmarsac2010 C41
felodipine–PVP at 93% RHcrystallization independent of PVP level; plateau 70–80%powdersrumondor2009b R21, R11, C20
felodipine, quinidine, pimozide with PVPVA; pimozide with HPMCAStwo Tgs after 94% RH50:50 powders, driedrumondor2010c R3.a, R3.c, R3.d, R3.e
indoprofen, clofoctol, probucol, nilutamide, loratadine with PVPseparation at 70–90% PVP for all; at every composition for nilutamide and loratadineIR, 54–94% RHrumondor2011 R14
ritonavir with PVP, PVPVA; HPMCASall PVP and PVPVA dispersions separated, from about 1 h; HPMCAS stayed miscible97% RH, films and powderspurohit2017b C1, C22
ritonavir 50:50 PVP filmdark domains of about 1–3 µm in a drug-rich continuous phase after 10 s in buffer; 10:90 uniformdried after immersionpurohit2017b R4
ritonavir–PVPVA films 20, 30, 40%uniform; sparse bright domains; dense domains (LoC 25%)seconds in water[indulkar2019a 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 h[saboo2020a 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% RHsaboo2021 R21
clopidogrel 40, 50, 60% filmsuniform; bicontinuous; drug-continuous5 min, 100% RHcorreasoto2022a R20
atazanavir 10% filmuniform for 3 h at 37 °C; separated within 10 min at 50 °C100% RHcorreasoto2022b R9, R12
lumefantrine free base, benzoate; sulfate filmsseparated; homogeneoushigh RH, 37 °C[hiew2022b 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 dissolution[indulkar2022 R19, C19]
ritonavir–PVPVA 10–40% compactsdroplets near the gel–solution boundary (10–20%); continuous drug-rich layer at the interface (30–40%)real-time confocal, pH 6.8yang2022a R10, R11, R12, R13
MePHPH–PVPVA; PHPH–PVPVA compactsseparation in the gel layer of most compacts; segregative (MePHPH) and associative (PHPH)in situ confocal with two dyesdeac2023a R6, R7, C25, C28, C71

Evidence table: amorphous-amorphous phase separation.

Pitfalls and disagreements

A single DSC Tg did not show the separation of itraconazole–HPMC, which the authors attribute to mixing during the scan, a reading supported only by the narrower second-run steps purohit2015a C39, C26, X1. Whether the separation is kinetic (solvent-induced, water-induced) or thermodynamic is not settled, and the phase compositions were not measured: the band-ratio and softening data rank the phases but give no weight fractions purohit2015a C48; li2016c X3, X10. The separation depended on preparation: humidity, solvent water and the alcohol of the solvent changed whether films separated [mugheirbi2017 C39; mugheirbi2018 R1, C50]. For polymer pairs the plot of the miscibility map is not monotonic cell by cell [vaneerdenbrugh2012a X10]. Separation during dissolution or storage was invoked for PVPVA dispersions of lumefantrine but not measured hiew2022a C43, C61, X11. DSC and polarised light microscopy may overestimate miscibility [mugheirbi2018 C4]. Whether separation helps or hurts release depends on the resulting microstructure li2019 C5, C58. The same separation can lower release (ritonavir–PVPVA at 25% DL) or raise it (lopinavir–HPMC at 33–85% DL) li2020 C64; li2019 R2. In the humid felodipine–PVP films the composition of the polymer-rich phase was not determined either; the DSC "second Tg" near 124 °C may be depressed melting marsac2010 X7, C18. Faster crystallization after moisture-induced separation was shown across different drugs, not for one drug with and without separation rumondor2009c X7. In the 2019 ritonavir–PVPVA study AAPS was seen only in films dipped for seconds or in humidified samples, not in a dissolving tablet, and neither its rate nor that of dissolution was measured [indulkar2019a X6]. A drug-rich porous surface also follows from faster polymer dissolution alone [saboo2020a X6]. In the 2022 ritonavir surfactant study separation was inferred from one lowered Tg of material scraped from the wet tablet, without a second Tg or water content, and was not tested for three of the five surfactants [indulkar2022 X10, X4].

← Concepts and formulas

concept · as used in Physical stability

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 °C[almeidaesousa2016 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 Physical stability

amorphous salt

The amorphous form of a drug salt; salt formation adds an ionic interaction between the protonated base and the counterion, taken to dominate over hydrogen bonding in setting Tg [towler2008 C23]. Combining salt formation and amorphization "may be desirable", for example for a lyophilized product [towler2008 C18].

Findings

F20.

Related concepts

depends on glass transition temperature; related to crystallization tendency and physical stability.

Formulas

none in this chapter (counterion descriptors listed in the chapter table).

How it is measured or obtained

Prepared by freeze-drying or melt quenching and checked by DSC [towler2008 P3, P5, R1]; Tg, recrystallization on heating, moisture sorption and storage at high humidity are then measured [towler2008 P6, P8, P9]; later by open-dish storage at 40 °C/75% RH [hiew2022b R7; duong2022a C32].

Values in the library
materialvalue or classconditionspaper ids
propranolol saltsTg 9.0–35.9 °C against −9.3 °C for the baseDSC[towler2008 R4]
nicardipine saltsTg 28.5–81.0 °C against 3.2 °C for the baseDSC[towler2008 R5]
20 salts of both bases11 amorphous after freeze-dryingDSC[towler2008 R1]
propranolol salts0.39–61.90% water uptake at 75% RHvapour sorption[towler2008 R8]
lumefantrine saltsbenzoate, PEG 250 diacid, besylate crystallized within 4 weeks; HCl and sulfate not for at least 16 weeks40 °C/75% RH[hiew2022b R7]
delamanid saltsstable 2 weeks; salt formation raised Tg40 °C/75% RH[duong2022a 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 Physical stability

amorphous solid dispersion

A drug dispersed in a polymer in the amorphous state to raise dissolution rate and supersaturation. In the amorphous solubility and LLPS papers an ASD matters as a route to supersaturation: dissolved beyond the amorphous solubility it gives a drug-rich phase and a cap on the free drug (F8, F13) [ilevbare2013a C52, C5; almeidaesousa2016 C6]. The ASDs tested were ritonavir:PVP 1:9 and CRH1:HPMC 20:80 [ilevbare2013a P13; almeidaesousa2016 M7]. The ueda2020b, ueda2021 and ueda2022 studies add that the polymer of an ASD, once dissolved, enters the drug-rich phase and lowers the amorphous solubility, so a higher polymer:drug ratio in the ASD can "conceivably" reduce the supersaturation advantage further; the studies used dissolved polymers, melt-made ibuprofen ASDs for DVS and solid-state NMR, and no dissolving ASD [ueda2020b C37, C55; ueda2021 P6; ueda2022 P5]. New aspects (Miscibility and drug-polymer interactions): A molecularly mixed, single-phase, homogeneous mixture of drug and polymer, in older wording a "glass solution" in which a solute is dissolved in a glassy solvent kestur2010b C4; taylor1997 C1. Amorphous dispersions are used to raise apparent solubility and dissolution, but the amorphous phase is metastable and may crystallize during storage or dissolution taylor1997 C1, C2; vaneerdenbrugh2010b C6, C7. The miscibility papers hold that the polymer must be in the same amorphous phase as the drug to be effective ("it is generally accepted") and that maximum stabilization "can only be realized" with intimate mixing, so that a physical mix does not inhibit crystallization kestur2010a C2; rumondor2009a C3. Dispersions made by solvent evaporation were not always molecularly mixed: itraconazole–HPMC and telaprevir films carried drug-rich domains purohit2015a C36; li2016c C54, and neat naringenin and quercetin could not be made amorphous by rotary evaporation, so a polymer was needed to make the dispersion at all wegiel2013a R7, C46. Ionizable polymers (E100, HPMCAS, HPMCP, CAP, Eudragit L 100, PAA) add acid–base contacts wegiel2013a M4, M8; hiew2022a M3, M4, M5, M6. New aspects (ASD process): the earliest paper of that chapter asks which carrier and process give a useful solid form of an extremely poorly soluble drug and finds that the carrier set whether probucol stayed amorphous [broman2001 C1, C14]. (synthesis: the paper's "solid dispersions" include samples that are not amorphous, since the probucol–PEO and probucol–PAA dispersions are mainly crystalline Form II [broman2001 R4.c–f].) The ASDs of the process papers were also made by solvent granulation of drug and polymer onto lactose and cellulose [trasi2019 C50], by spray drying from water-containing methanol li2020 P1 and by extrusion of physical mixtures of drug and polymer [moseson2020 P4]. New aspect (Bioperformance): the ASD is a drug dispersed amorphously in a polymer (or, in alhalaweh2016, in a mix with a second drug) that releases drug into supersaturation. Rotary-evaporated dispersions were used in alhalaweh2016, hate2018, mosqueragiraldo2018b and elkhabaz2017, and commercial capsules in purohit2018 [alhalaweh2016 P3; hate2018 P5; mosqueragiraldo2018b P1; elkhabaz2017 P6; purohit2018 M2]. Later papers dose such dispersions to animals: rotary-evaporated enzalutamide dispersions to rats, spray-dried pretomanid tablets to monkeys, and generic and innovator tacrolimus capsules to dogs, the generic being a mainly physical mixture of amorphous drug with HPMC and the innovator an intimate dispersion [wilson2018 P10; wilson2020 P1; nguyen2023a P4, P5; purohit2019 C21]. New aspect (Physical stability): the physical-stability papers call the drug–polymer glass a molecular (one-phase) dispersion when it shows a single Tg and drug–polymer hydrogen bonds by IR konno2006 C8, R5; rumondor2009c C1, and stress that a polymer can inhibit crystallization only while it stays intimately mixed with the drug marsac2010 C31. In the study of marketed tacrolimus capsules the term is used strictly: a product that contains the polymer but holds the drug as an amorphous coating on lactose, not mixed with HPMC, is in the authors' belief not an amorphous solid dispersion, and molecular-level mixing is "considered to be essential" for stabilization trasi2017 C47, C50.

Findings

C. Amorphous solubility and LLPS: F8, F13, F14, F19, F20, F21. Miscibility and drug-polymer interactions: F1, F3, F9, F15, F16, F18, F19, F23, F26. ASD process: F17, F18, F19, F22, F23, F24. Bioperformance: F6, F8, F9, F11, F16, F23, F24. Physical stability: F1, F12, F14, F23, F24, F26, F27, F28, F29, F30, F33, F35.

Related concepts

produces a drug-rich phase above the amorphous solubility; relieved by crystallization unless a polymer is present (F14); requires drug-polymer miscibility; stabilized by drug-polymer interactions and kinetic stabilization; related to crystallization inhibition and supercooled liquid. Processed in the HME operating design space. Sets drug loading effects; related to non-sink dissolution. Can undergo amorphous-amorphous phase separation; stabilized by crystallization inhibition by polymers.

Formulas

Gordon-Taylor equation.

How it is measured or obtained

Rotary evaporation from methanol (ritonavir) or methanol/dichloromethane (CRH1) and incremental or single-dose non-sink dissolution [ilevbare2013a P13, P14; almeidaesousa2016 P2, P11]. The dispersions of the miscibility papers were made by dissolving drug and polymer in a common solvent and removing it: rotary evaporation from methanol, ethanol, chloroform or dichloromethane–ethanol, followed by vacuum drying taylor1997 P3; rumondor2009a P1; vaneerdenbrugh2010b P6; spin coating on coverslips, ZnSe or KRS5 for films vaneerdenbrugh2010b P1; marsac2009 P4; cryomilling of a 10% w/w dispersion with crystalline drug and melt-quenching for the low-polymer growth samples kestur2010a P1, P2. A physical mix of amorphous drug and polymer is the control without molecular mixing taylor1997 C24, C26. Amorphous state is checked by XRPD or polarized light taylor1997 R1; vaneerdenbrugh2010b P2. Further preparations: rotary evaporation at 45–60 °C with 24 h vacuum drying and cryomilling wegiel2013a P1; hiew2022a P5; spin coating on KRS-5, ZnSe or quartz purohit2015a P2, P9; freeze-drying of aqueous polymer blends [vaneerdenbrugh2012a P2]; 50 mg compacts for release hiew2022a P9. In the process papers the solid form was read by Raman and DSC (single Tg between those of the components; polymer-free marker band) [broman2001 P1, P2, R1, R4]. In the Bioperformance papers the dispersions were made by rotary evaporation from methanol and cryomilling, and checked by PXRD, DSC, PLM and SHG [hate2018 P5, P10; elkhabaz2017 R8]. In the physical-stability papers: spin-coated films (dichloromethane:ethanol, ethanol or chloroform, heated to 90 °C) for nucleation, growth and IR; rotary-evaporated and, for low polymer contents, cryomilled powders for DSC, sorption and PXRD konno2006 P1, P3; rumondor2009c P1; rumondor2009b P1; kestur2010b P1. Spin-coated films and rotary-evaporated powders of nine 50:50 drug–polymer pairs rumondor2010c P1, P5; rotary evaporation in 5% steps to find the highest amorphous loading wegiel2013b P1; rotary evaporation followed by cryomilling wegiel2014 P2, P3; a 10% PVP dispersion diluted with crystalline drug by cryomilling, then melted, to reach 3% PVP kestur2013a P4; kestur2013b P2.

Values in the library
materialvalue or classconditionspaper ids
ritonavir:PVP 1:96.4, 11.8, 18.3, 18.0 µg/mL with 6.0, 12.0, 18.0, 24.0 added100 mM pH 6.8, 37 °Cilevbare2013a R17
CRH1:HPMC 20:80about 12.9 µg/mL without polymer in the medium; HPLC maximum about 13.2pH 4.6, 25 °C[almeidaesousa2016 R8, R12]
indomethacin–PVP-K90, 5–70 wt% PVPamorphous by XRPD; interactions in dispersions, none in physical mixesmethanol, rotary evaporationtaylor1997 R1, R10, R11, R12
felodipine–PVP, nifedipine–PVPone amorphous phaseIR, PXRDrumondor2009a 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 filmskestur2010a P1, C5
naringenin, quercetin with six polymershighest X-ray amorphous polyphenol content about 20–85%; E100 highest, PAA lowestrotary evaporation at 60 °C, cryo-milledwegiel2013a R8
lumefantrine with PVPVA and four enteric polymersall X-ray amorphous with one Tg, except 50% HPMCAS (melted at 126.3 °C on heating)rotary evaporation at 45 °C, sieved below 250 µmhiew2022a R4, R6
itraconazole–HPMC, telaprevir–polymersdrug-rich domains in the filmsspin-coated from methanol–dichloromethanepurohit2015a R11; li2016c R4, R5, R6
probucol–PVP K30 50:50amorphous; Tg 95 °C (solvent), 129 °C (moulded)Raman, DSC[broman2001 R4.a, R4.b]
probucol–PAA, –PEOmainly Form IIsame[broman2001 R4.c–f]
probucol–PVP–PAA 50:25:25mainly amorphousboth routes[broman2001 R4.g, R4.h]
ritonavir and lopinavir with PVPVA 1:1 on lactose:MCCX-ray amorphous granules, unchanged for one month at 40 °C/75% RHsolvent granulation[trasi2019 R1, R2]
ritonavir–PVPVA spray-dried, 25–75% DLX-ray amorphous (methanol powders); one Tg of 91, 75 and 63 °Cspray dryingli2020 R1, R2
ritonavir/atazanavir/lopinavir in PVP K29/3290% polymer, Tg 139–160 °C10% drug[alhalaweh2016 R4]
atazanavir in HPMCAS, HPMC, PVPVA10, 30, 50%X-ray 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 SHG[elkhabaz2017 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 weeks[wilson2018 P10, P11]
enzalutamide in CA Sub or CPHPC-106CA Sub 50%; CPHPC-106 10 and 50% drugrotary evaporation[wilson2020 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, DSCkonno2006 R5, C8
five drugs with PVPdry dispersions one phase by IR; single Tg for droperidol and pimozidespin-coated and rotary-evaporatedrumondor2009c R3, R5, C1
felodipine with 0.5–4.5 wt% PVPmade by cryomilling a 10% dispersion with crystalline drug, then meltingto avoid partial crystallization on rotary evaporationkestur2010b 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, cryomillingwegiel2014 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 Tmtian2017 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 Physical stability

amorphous solubility advantage

The factor by which the amorphous drug is more soluble than the crystal, e^{\Delta G/RT} from the crystal–amorphous free-energy difference, reduced by the activity of the water-saturated amorphous drug [ilevbare2013a E1, C60; almeidaesousa2015 E1]. In the amorphous solubility and LLPS papers the measured counterpart is the supersaturation ratio at the LLPS onset (F6). The papers of 2017–2022 add measured values of the ceiling ratio of 63.6 (atazanavir, synthesis: 70 ÷ 1.1), 28.5 (telaprevir, synthesis: 148 ÷ 5.2), about 600 (pazopanib) and 2.5–5.9 (ibuprofen, falling with temperature), and that micelles lower the concentration-based advantage (atazanavir 65 → 33) without lowering the activity-based one [indulkar2017a R4, R6, R13; lu2017b R2, R1; sugihara2018 R4; ueda2022 R16]. New aspect (ASD process): it is the supersaturation an ASD can reach if it stays amorphous and dissolves; crystals in the dispersion "directly" lose their share of it ("potency") and may also consume what is generated [moseson2020a C3]. For bicalutamide the maximum advantage over the stable form is 35-fold [moseson2021 R2]. In the pH-shift test of posaconazole the dose was set at about 10 times the amorphous solubility in the intestinal medium (19.1 µg/mL), that is about 191 µg/mL, and 200 µg/mL at full release [shah2024 P11, X9]. New aspect (Bioperformance): the ratio is computed by the Hoffman estimate with water correction or taken as the LLPS onset over the crystalline solubility [raina2014a R7; raina2015c E8]. New aspect (Crystallization from solution): in the solution-crystallization papers the advantage fixes the highest supersaturation tested: the calculated amorphous solubility over the crystalline solubility gives S 15.3–15.4 for ritonavir and about 14.7 for celecoxib, and the "amorphous benchmark" S of about 10 for felodipine [ilevbare2012b R3; ilevbare2013c E1, R2; alonzo2012 C42]. The measured counterpart is the plateau after a pH shift or the onset of phase separation (F2). For six dihydropyridines the estimated ratios of amorphous to crystalline solubility in buffer were 16.1 (cilnidipine), 9.03, 8.42, 23.0, 11.7 and 22.9, not reproducible from the printed inputs (felodipine 5.93 recomputed against 6.68 µg/mL); for danazol the recalculated estimate of 7.8 µg/mL is a ratio of 8.7 against the earlier 19.6 [raina2015b X2; jackson2016 R3, R4]. New aspect (Supersaturation from ASD dissolution): the calculated advantage is the yardstick for what a dissolving amorphous solid or dispersion should reach, and the question is whether a dispersion can exceed that of the pure amorphous drug: by flux it did not for felodipine, and the authors add that thermodynamics gives "no reason to expect" the two to be equal [alonzo2011 C22, C45]. The advantage is "rarely achieved" because the solid or the solution crystallizes konno2008a C4; alonzo2010 C2. For six marketed tacrolimus capsules the advantage of about 35-fold was "sustained throughout" a 2 h non-sink test trasi2016 C44, C16; mixing the drug with a polymer that does not dissolve lowers the advantage a dispersion can realize li2018 C67.

Findings

Amorphous solubility and LLPS: F5, F6, F7, F12, F14, F16, F21. ASD process: F23, F26, F27, F28, F39, F41. Bioperformance: F1, F4, F18. Crystallization from solution: F2, F9, F14, F19, F21, F22, F34. Supersaturation from ASD dissolution: F1, F5, F7, F18, F22, F23, F28, F29.

Related concepts

same as the ceiling supersaturation ratio; built from amorphous-crystalline free energy difference and water sorption correction of amorphous solubility; gives the amorphous solubility. Realised in non-sink dissolution; lost to residual crystallinity and matrix crystallization; lowered by mutual amorphous solubility reduction. Depends on Hoffman equation; estimated with the Gibbs-Duhem equation water correction; depends on crystalline solubility; related to free drug concentration.

Formulas

amorphous solubility advantage with water-sorption correction, amorphous solubility advantage from free energy difference, supersaturation ratio. Amorphous-to-crystalline solubility ratio, Hoffman equation.

How it is measured or obtained

By calculation (Hoffman or heat-capacity free energy, sorption isotherm) and by the onset [almeidaesousa2015 P9, P10]; also by dissolving an amorphous film ilevbare2013a P4. In the ASD process papers: crystalline solubility by 72 h shake flask; amorphous solubility as the onset of light scattering during solvent-shift addition (liquid–liquid phase separation), in some cases only with a polymer present because the drug crystallised too fast without it [moseson2020a P7, P8; moseson2021 R1, R27]. In the Bioperformance papers it is estimated from melting data or as onset ÷ crystalline solubility [raina2015c P3, P6]. In the crystallization-from-solution papers: calculated with the Hoffman equation and a water-sorption correction; measured by dissolving a spin-coated film (ritonavir), by pH-induced precipitation, and by the onset of phase separation of a solvent-shifted solution [ilevbare2012b P4–P6; hsieh2012 P11; jackson2014 P6, P7]. In the ASD dissolution papers: calculated from melting data with the Hoffman equation and the measured crystalline solubility [konno2008a P7; alonzo2010 P12; alonzo2011 P8]; tested against flux relative to the crystal [alonzo2011 R14].

Values in the library
materialvalue or classconditionspaper ids
ibuprofen to griseofulvinpredicted 3.7/4.2, 7.0/6.4, 9.8/11.7, 28.9/52.5, 48.4/48.6, 34.8/30.9 (Hoffman / Cp method)25 °C[almeidaesousa2015 R13]
clotrimazole; atazanavirpredicted about 9.2 and 62; measured about 13 and about 6337 °C[indulkar2015 R3, R10]
felodipine, buffer; with 0.04% vitamin E TPGS; in FaSSIFabout 9.2; 4.5; 5.0 (concentration-based)37 °C[raina2015c C29]
tacrolimusabout 35 (49/1.4), about 33–36 by method; other drugs 5–65amorphous solubility by ultracentrifugation, pH 4.5, 37 °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 °C[moseson2020a R1]
BCL, pH 6.8 phosphateform 1 4.3, form 2 15, amorphous 150 µg/mL; 35-fold37 °C[moseson2021 R1, R2]
RTV and LPV, pH 6.8crystalline 1.8 and 2.9, amorphous 31 and 19 µg/mL10 mM phosphate, 37 °C[trasi2019 M1, M2]
IDM–PVPVA with 25% residual crystalsC720 about 28.8 against about 43.1 µg/mL: the share of the advantage lost with the crystals50 µg/mL total dose[moseson2020a R6]
posaconazole in FaSSGF and FaSSIF V2LLPS concentration (taken as the amorphous solubility) 2326 and 19.1 µg/mL against crystalline 86.5 and 1.2 µg/mL, ratios about 27 and 16 (arithmetic on the cited values)37 °C[shah2024 R11, C14]
ritonavir / atazanavir / lopinavirabout 14 / 83 / 6pH 6.8[alhalaweh2016 R6]
clotrimazole15pH 8[indulkar2016 R3]
atazanavirobserved ratio in SDS about half that in buffer, with unchanged 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 media[elkhabaz2019b R8, R9]
atazanavir, darunavir58 and 1.37 from the printed solubilities (printed "almost 82-fold" and "1.30")pH 6.8, 37 °C[alkalla2026 R3, R6, X1]
pretomanid8–10 in buffers37 °Cnguyen2023a R1
tacrolimusabout 33pH 4.5purohit2019 C30
enzalutamideabout 14.5 (42/2.9); S "approximately 13" is the theoretical 39/2.9pH 6.5[wilson2018 R1, R3, X2]
felodipineS of about 10 over the crystal (theoretical and measured)benchmark for the supersaturation range S 3–12alonzo2012 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 °C[ilevbare2013c R2]
five weak basesratios 22.2, 11.9, 20.4, 54.6, 7.0 without and 12.3, 9.8, 16.7, 15.3, 4.3 with water correction37 °C[hsieh2012 R10]
glyburide; warfarinabout 60 and 4825 °C[hsieh2014 R16]
danazol19.6 printed (15.4 recomputed); earlier estimates 13.7 and 26.525 °C[jackson2014 R2, R3, X1]
six dihydropyridinesestimated amorphous solubility 0.5, 6.68, 48, 20, 6.3, 19.0 µg/mLbuffer, Hoffman with water correction[raina2015b R10]
danazol7.8 µg/mL with heat-capacity data and the water correction; onset 8 µg/mL25 °C, pH 6.8[jackson2016 R3, R8]
posaconazolemeasured amorphous/crystalline 33.6 at pH 7.0 (32.4–37.3 from pH 2.0 to 7.0); estimate 37.9 printed37 °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 6.8[alonzo2011 M1]
felodipine, flux ratio to the crystal8.5 (pure amorphous), 9.5 (50:50), 10.5 (90:10 HPMC dispersion)dialysis, 37 °C[alonzo2011 R14]
indomethacinabout 21 µg/mL (crystal about 1.2 µg/mL)pH 2.0[alonzo2011 M2]
ritonavir; lopinavir (cited)25 and 17 µg/mL against 1.7 and 2.7 µg/mL crystallinepH 6.8[trasi2015b M1, M2]
lopinavirabout 5.6 (17.4/3.1)pH 3, 25 °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 °C[duong2022a R1, R27]
praziquantel, racemate and R-enantiomerratios 5.6–7.7 and 4.0–5.8 across nine media; amorphous 1.17–1.74 and 1.20–1.70 mg/mL37 °C[alvarenga2025 R1]
posaconazoleabout 20 against 1.69 µg/mL in FaSSIF; 115.1 µg/mL crystalline in FaSSGF37 °C[elkhabaz2019a R2, R1]
Pitfalls and disagreements

The calculated advantage fails for high-melting drugs when the Hoffman free energy is used (F7) [mosqueragiraldo2015 C23, C24]. When additives raise crystalline solubility more than the LLPS concentration, the concentration-based ratio falls (felodipine, about 9.2 in buffer to 4.5 in 0.04% vitamin E TPGS and 5.0 in FaSSIF), while the maximum flux stays in the buffer band, so the advantage in activity is retained [raina2015c R9, R11, C29]. In dispersions, a dose below the amorphous solubility (IDM 50 against about 80 µg/mL) can still lose most of the advantage to crystals; a crystal-free bicalutamide dispersion never reached 40 µg/mL against 150 µg/mL [moseson2020a X17; moseson2021 C41]. The amorphous solubility of ritonavir alone is reduced to about 4 µg/mL in a co-amorphous granule [trasi2019 R4]. In the Bioperformance papers the ratio from concentrations falls with solubilizers although the flux advantage does not [raina2015c C43]; the atazanavir ratio differs between cards because the crystalline solubility differs (F1). In human fluid the flux of a solution at the amorphous solubility was about 30 times that of a crystalline suspension for posaconazole, so the advantage was not lost although the concentration ratio fell to about 5 (F18) [elkhabaz2019b C30, C45]. The printed atazanavir and darunavir ratios do not follow from the printed solubilities [alkalla2026 X1]. With a polymer in the medium the same ratio applied to the polymer-containing solubility overestimates the ceiling (danazol: 43 against an onset of 8–9 µg/mL) [jackson2014 X9]. Celecoxib's measured 2.5 µg/mL is far below the calculated value and is not discussed [ilevbare2013b X9]. The efavirenz run started at S about 2.3, the ratio of calculated amorphous to crystalline solubility being 2.4 [ilevbare2013c X4]. The printed estimates for the dihydropyridines differ between media in ways the equation does not allow [raina2015b X2]. Felodipine dispersion and solution readings of 14.1 and about 11 µg/mL exceed the 9.5 µg/mL estimate of the 2008 paper, measured by UV through a 70-µm filter konno2008a X5. The 25 °C indomethacin range (17–25 µg/mL) does not reproduce from its printed inputs (15.8–23.6) alonzo2010 X2. That a dispersion reached the same activity as the pure amorphous drug "may be purely coincidental" [alonzo2011 C48]. The tacrolimus ratio uses an ultracentrifugation value measured with 10 µg/mL HPMC in the buffer trasi2016 X9. For praziquantel the ratio is lower for the enantiomer because its crystal is more soluble, not because its amorphous solubility is lower [alvarenga2025 R1].

← Concepts and formulas

concept · as used in Physical stability

amorphous solubility

The concentration of dissolved drug at which a supersaturated aqueous solution is in apparent, metastable equilibrium with the amorphous drug, more rigorously with the water-saturated supercooled liquid or glass; it is not a true thermodynamic solubility, which is why the authors keep it in quotation marks [almeidaesousa2015 C3, C39]. In this chapter it is operationally the concentration at which a drug-rich phase first separates (the LLPS or GLPS onset), and the free-drug ceiling above which added drug only makes more drug-rich phase [ilevbare2013a C3, C5; mosqueragiraldo2015 C34]. It exceeds the crystalline solubility by e^{\Delta G/RT} and is lowered by the water the amorphous drug absorbs ilevbare2013a C60. The papers of 2017–2022 add that the dissolved-drug concentration in the presence of a drug-rich phase can be read directly by NMR (ibuprofen 154 µg/mL in buffer against 151 µg/mL calculated) [ueda2021 R5, R6, C10], and that the value changes when a second component enters the drug-rich phase or the water phase: a dissolved polymer that enters the droplets lowers it (ibuprofen 177.1 → 96.9 and 90.7 µg/mL with 300 µg/mL HPMC and PVP-VA) and a polymer that complexes the drug in water raises it (256.3 µg/mL with EUD-E) [ueda2020b R1]; micelles raise the total concentration at the amorphous solubility but not its activity [indulkar2017a R13]; STCDC and SGCDC lower the activity at which it is reached [lu2017b R18]. New aspect (Bioperformance): the highest free-drug concentration that an amorphous (supercooled-liquid or glassy) drug can produce in a medium; above it a second, drug-rich phase separates and the free concentration stays at this value [raina2014a C24, C27; alhalaweh2016 C1; hate2018 C5]. Several papers treat the concentration at which the second phase appears (the LLPS or glass–liquid onset) as the amorphous solubility [indulkar2016 R2; hate2018 R2; alhalaweh2016 R6]. In ASD work it is the ceiling of the free concentration a dispersion can give, and the concentration at which flux stops rising (F2). Enzalutamide, atazanavir, darunavir, clozapine, ketoconazole, nifedipine and pretomanid all take the UV-extinction onset as the amorphous solubility, with the polymer or medium of the test present [wilson2018 R2, C16; ueda2020a R1; alkalla2026 R3; nguyen2023a R1, P2]. In rats the enzalutamide dispersions that reached the ceiling gave several times the exposure of the crystalline drug (F23) [wilson2018 R16, R18].

Findings

Amorphous solubility and LLPS: F3, F4, F5, F6, F7, F8, F9, F10, F11, F12, F13, F14, F15, F16, F17, F18, F19, F20, F21, F23. Bioperformance: F1, F2, F4, F6, F7, F8, F15, F18, F19, F20, F23, F27, F30.

Related concepts

depends on crystalline solubility and water sorption correction of amorphous solubility; measured as the onset of liquid-liquid phase separation; sets the ceiling of supersaturation; lowered by a second component in the drug-rich phase; gives the amorphous solubility advantage. Papers of 2017–2022: lowered by a dissolved polymer that enters the drug-rich phase (polymer partitioning into the drug-rich phase); not raised in activity terms by micelles (activity-based supersaturation); its upper limit on the activity scale is the maximum achievable supersaturation. Depends on Hoffman equation inputs; related to thermodynamic activity.

Formulas

amorphous solubility advantage with water-sorption correction, amorphous solubility advantage from free energy difference, Hoffman equation, amorphous-crystalline free energy difference from heat capacity. Amorphous-to-crystalline solubility ratio, ideal-mixing reduction of amorphous solubility.

How it is measured or obtained

(1) As the onset of scattering during slow addition of a drug stock, confirmed by a polarity probe [ilevbare2013a P5; almeidaesousa2015 P1, P2]. (2) As the drug concentration in the supernatant after ultracentrifugation of a phase-separated solution [trasi2015a P2; almeidaesousa2016 P7]. (3) By dissolving an amorphous film under non-sink conditions [ilevbare2013a P4; indulkar2015 P13]. (4) As the break point of flux against donor concentration [trasi2015a P6]. (5) By calculation from the crystalline solubility, the free-energy difference and the water activity of the amorphous drug ilevbare2013a E1. The papers of 2017–2022 add quantitative ¹H NMR of the dissolved drug beside the drug-rich phase [ueda2021 P3, P4], ultracentrifugation and the flux plateau in bile-salt media [lu2017b P3, P4], and an in-situ UV probe after a pH shift [sugihara2018 P6]. In the Bioperformance papers: (1) solvent-shift UV extinction, a methanol stock pumped into stirred buffer and the onset of scattering read at 350–455 nm [raina2014a P7; alhalaweh2016 P9; indulkar2016 P3; hate2018 P2; elkhabaz2017 P4]; (2) ultracentrifugation or centrifugation of a supersaturated solution and assay of the supernatant [mosqueragiraldo2018b P8; alhalaweh2016 P10]; (3) the flux plateau in a diffusion cell raina2014a R16; (4) estimate from the crystalline solubility with the Hoffman free-energy difference and a water-sorption correction raina2014a E3, E5; (5) the drug's own fluorescence, whose emission intensity rises, and whose peak may shift to shorter wavelengths, when the drug-rich phase forms, at the concentration found by ultracentrifugation in buffers and in pooled human intestinal fluid [elkhabaz2019b R3, C17]; (6) a solvent-shift or antisolvent addition into buffer with the polymer already dissolved, which gives the value in the presence of that polymer [ueda2020a R1; alkalla2026 R3, P7]; (7) for tacrolimus the value of about 50 µg/mL is taken from earlier work and used to define the dose-to-volume conditions of a dissolution test hate2019 R7, C16; purohit2019 C15.

Values in the library
materialvalue or classconditionspaper ids
ritonavir37.2 µg/mL (onset); 39.2 predicted; 34.2 from filmwater, 37 °Cilevbare2013a R8, R13
ritonavir; lopinavir; paclitaxel hydrate26–28; 16–17.3; 27.2–30.1 µg/mL100 mM phosphate pH 6.8, 25 °C, four methods[trasi2015a R1]
telaprevir90–92 µg/mL (UV, NMR, fluorescence)pH 6.8, 37 °C[mosqueragiraldo2015 R13]
clotrimazole; atazanavir7.7; 65.1 µg/mL (un-ionized)37 °C, 0.1 M buffer[indulkar2015 R2]
ibuprofen; sorafenib; griseofulvin125.74; 0.532; 355.96 µg/mLpH 2 or 6.8, 25 °C; griseofulvin with HPMCAS-HF[almeidaesousa2015 R5, R6]
CRH1 free base12.49–13.73 µg/mLpH 4.6 citrate + 20 µg/mL HPMC, 25 °C[almeidaesousa2016 R4]
atazanavir70 µg/mL (onset); 68 predicted; with 3.6 mg/mL SDS about 1450 µg/mL total but 65–70 µg/mL freepH 6.8 buffer, 37 °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 °C[ueda2020b R1]
ibuprofen154 µg/mL (buffer) → 89–131 µg/mL with 1000 µg/mL of six polymersNMR, pH 2.0 (D2O), 37 °C[ueda2021 R5]
ibuprofen in bufferabout 127 µg/mL at 15 °C, about 284 at 60 °CNMR, pH 2.0 (D2O)[ueda2022 R9]
felodipine5.99 / 8.70 µg/mL predicted; onset 6.01 / 8.70pH 6.8 buffer, 25 / 37 °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 °C[raina2015c R1]
ritonavir / atazanavir / lopinavir45.2 / 132.1 / 27.2 µMpH 6.8, 37 °C[alhalaweh2016 R6]
clotrimazole7.5 µg/mL (ratio 15)pH 8, 37 °C[indulkar2016 R2, R3]
atazanavir78 µg/mL (94 with 1.8 mg/mL PVPVA)pH 6.8, 1 mg/mL HPMCAS[hate2018 R2, R3]
ezetimibe21.0 µg/mL buffer; 123 µg/mL FeSSIF37 °C[elkhabaz2017 R3]
telaprevir96–111 µg/mL with 1.05 mg/mL polymerpH 6.8, 37 °C[mosqueragiraldo2018b 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 °C[wilson2018 R1, R2, R3, C16]
atazanavir, clozapine, ketoconazole81.5 / 233.0 / 75.0 µg/mL without polymer; with AS-HF 35.5 / 95.0 / 56.0; with AS-LF 75.8 / 219.0 / 71.2buffer, 37 °C, 1000–2700 µg/mL 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 °C[elkhabaz2019b R1, R2, C15, C16]
pretomanidabout 166 µg/mL in buffer, 226 with SLS, 275 with TPGS, 308 in FaSSIF; crystalline 15–18, ratio 8–10pH 6.5, 37 °Cnguyen2023a R1, R2
tacrolimusabout 50 µg/mL, crystalline 2.5 µg/mL, ratio about 33used to fix the dose-to-volume 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 Physical stability

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 DSCkestur2010a R1
bifonazole with 5% polymersTg 16.4–17.4 °C against 15.2 °Conset DSCkestur2011 R6
nimesulide with 5% polymersTg 19.9–20.8 °C against 19.5 °Conset DSCkestur2011 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 DSCkonno2006 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%; drykestur2010b R1, C34
felodipine–PVP 10 wt%Tg 40.5 °C, below pure felodipine 43.1 °Cdrymarsac2006a R8, C22
felodipine with ≤ 25% polymerTg ≈30–35 °C after 75% RH25 °Ckonno2008 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 Physical stability

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 °Cduong2022c 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 growth[moseson2023 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% RHmoseson2022a 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 Physical stability

Barandiaran-Colmenero method

A DSC method from inorganic glass science to estimate the critical cooling rate: the natural logarithm of the cooling rate is regressed on 1/\Delta T^2, where ΔT is the undercooling at the crystallization peak, and Rcrit is taken as \exp(A), the extrapolated rate at which no crystallization would be seen [baird2010 E1, E2; baird2013 E1, E3]. The Cabral variant subtracts B/T_m^2 from the intercept baird2010 E3.

Findings

F11.

Related concepts

estimates critical cooling rate; uses degree of supercooling; related to glass-forming ability.

Formulas

Barandiaran-Colmenero critical cooling rate, Cabral critical cooling rate.

How it is measured or obtained

Crystallization peak temperatures at several cooling rates, 5–20 °C/min in a conventional DSC baird2010 P2, P9 or 5 to about 800–1100 °C/min with rapid heat–cool DSC [baird2013 P3].

Values in the library
materialvalue or classconditionspaper ids
carbamazepineRcrit 118 K/min, r² 0.995–20 °C/minbaird2010 R13.j
griseofulvin588 K/min, r² 0.975–20 °C/minbaird2010 R13.m
4-biphenylmethanol3.28 × 10⁴ K/min, r² 0.745–20 °C/minbaird2010 R13.b
12 of 19 class I moleculesr^2 < 0.55, no estimate5–20 °C/minbaird2010 R13
phenacetin; benzocaine2.7 × 10³; 6.2 × 10³ K/min5 to ≈1000 °C/min[baird2013 R7.h, R7.d]
benzamide, lidocaine, indoprofenr^2 < 0.555 to ≈1000 °C/min[baird2013 R7]
Pitfalls and disagreements

The method needs undercooling to rise steadily with cooling rate, which often failed because of scattered crystallization temperatures [baird2010 C18; baird2013 C17]. Estimates from 5–20 °C/min contradicted liquid-N2 quench results baird2010 C21; accurate predictions are said to need rates at least two orders of magnitude below Rcrit baird2010 R31.

← Concepts and formulas

concept · as used in Physical stability

bile salt micelles

Aggregates of bile salt above its critical micelle concentration; in the telaprevir studies 1.86 mM is nominally the monomer and 12 mM the micellar level, with micelles of the dihydroxy salts STDC, SGDC and STCDC opposing the monomer effect on nucleation and those of STCDC and SGCDC on growth [lu2017 C14, C41; lu2017a C13, C33].

Findings

F32, F33.

Related concepts

part of critical micelle concentration; related to mixed micelles.

Formulas

none.

How it is measured or obtained

CMC by surface tension (Wilhelmy plate, 37 °C) for STC (about 4 mM) and SGDC (about 2 mM) only; the states of the other salts are cited from companion work [lu2017 R5, X7; lu2017a C13].

Values in the library
materialvalue or classconditionspaper ids
telaprevir δ 11.5, 12 mM STDC, SGDC, STCDCinduction time about 140, 125, 180 min against >960 at 1.86 mMpH 6.5, 37 °C[lu2017 R3]
telaprevir δ 12.5, 12 mM STCDC, SGCDC15 h residual 4.0 of 145.2 and 11.5 of 95.2 µg/mL against 60.5 and 91.7 at 1.86 mMpH 6.5, 37 °C[lu2017a R12]
ternary STC–STDC–STCDC at 5.58 mMabout 254 min against >960 for 12 mM STC; STC protection "reduced by the presence of the other bile salts"δ 11.5, 37 °C[lu2018 R4, C18]
Pitfalls and disagreements

The monomer share was not measured, 1.86 mM is close to the SGDC CMC, and the 18 mM evidence is given in words only [lu2017 X7, X8].

← Concepts and formulas

concept · as used in Physical stability

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% PVPtaylor1997 R18, R11, R12
indomethacin–PVP-K90two bonds per carbonyl: 12 wt% printed, 13.6 wt% recomputedsametaylor1997 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 Physical stability

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 needsschematicli2017 C38
ECP–water–polymer (storage)high-DL films absorb little water and stay in the one-phase region; low-DL films cross the binodalschematicli2017 C42
drug–polymer mixturesbinodal points are the two minima of the free energy of mixing against compositionargumentrumondor2009a E6, C35
MePHPH–PVPVA–waterexperimental binodes and tie lines at 37 °CPC-SAFTdeac2024b R15, R22
ritonavir–PVPVA–methanol–water (25% and 50% DL)the 25% DL path enters the two-phase region from about 12.5:87.5 water:methanol; the 50% DL path from about 11.5:88.5droplet modelli2020 R17, R19, C50, C53
ritonavir–PVPVA 10%; 20% compactsdroplets near the gel–solution interface; deeper in the gelreal-time confocal, pH 6.8yang2022a R10, R11
PHPH–PVPVA; MePHPH–PVPVA hydrophobic binodalabout 72% PVPVA; below 5% PVPVAparticles, 48 h in bufferdeac2023b C52
MePHPH–PVPVA films 10–50%binodal between 75 and 80% RH (≈4.9–9.4 and 9.6–14.6 wt% water)37 °Cdeac2024b R1, R2
Pitfalls and disagreements

The binodal was measured on the low-temperature branch only, four concentrations, and the scan direction on that branch is unresolved ilevbare2013a X6, X7, X17. Raina and co-workers describe the binodal points as the theoretical onset of LLPS in a partially miscible drug–buffer system raina2014a C27. In the film papers the quaternary system with polymer is "much more complex" than the ternary one drawn, and Fig. 12B lacks the letters that the text uses li2017 C36, X9. The computed binodal depends on χ values that are partly assumed and inconsistently described, and keeps the 10:90 path outside the region although the powders separate li2020 X10, X12. The binode drug loads stated in the 2023 text do not exactly match the nanoparticle data deac2023b X18. MePHPH films separated at 80% RH where the computation predicts one phase, and single-phase PHPH mixtures lie inside the computed gap deac2024b C34.

← Concepts and formulas

concept · as used in Physical stability

buffer capacity

Evidence table: buffer capacity. Content from the release-mechanism chapter (2022–2025), with a note from the Peptide permeability chapter.

The ability of a medium to take up acid or base with little change of pH, given in mM per pH unit (mM/ΔpH). For an enteric polymer it measures how many buffer species are available to carry away the protons that the polymer releases as it ionizes at the dissolving surface. That the dissolution rate of enteric polymers depends on buffer capacity is described as "well known" (cited) [qi2022 C20]. For HP-50 in four pH 6.8 buffers the rate "appears to trend" with buffer pKa and buffer capacity: slow buffers had higher pKa and lower capacity, fast buffers higher capacity and a pKa near the dissolution pH [qi2022 C14]. HPMCAS-MF dissolution depends strongly on buffer capacity in pH 6.8 phosphate, particularly at low capacity, and "may be approaching" a plateau at higher capacity [bapat2023 C9]. A pre-ionized polymer salt keeps its rate whatever the buffer capacity [qi2022 C4]. In 2024 a stronger buffer (100 against 50 mM pH 6.8 phosphate) sped a 25% loratadine–HPMCAS dispersion about 2.5-fold but neat HPMCAS only about 1.1-fold, and neat HPMCAS dissolved more slowly in 50 mM pH 9.0 glycine (about 0.63 against 0.90 mg/min/cm²), put down to the low buffer capacity of that buffer at the acidic surface [bapat2024 R6, X3, R4, C13].

Findings

Release mechanism and LoC: F23, F24, F32.

Related concepts

sets the microenvironmental pH at the dissolving surface; depends on buffer pKa; acts through the unstirred water layer; its effect is removed by polymer salt formation; related to critical ionization for polymer dissolution and the gel layer of enteric polymers.

Formulas

boundary-layer diffusion flux (film model).

How it is measured or obtained

Phosphate buffers of the same pH at different concentrations: 50 and 5 mM at pH 6.8, given as 29 and 3 mM/ΔpH, the 29 measured by a co-worker with the method not printed [qi2022 R12, M16, M17]; 5, 10, 25, 50 and 100 mM pH 6.8 phosphate given as 3, 5, 13, 26 and 51 mM/ΔpH [bapat2023 A1]. Rates are surface-normalized polymer release rates of compacts on a rotating disk [qi2022 P10; bapat2023 R5].

Values in the library
materialvalue or classconditionspaper ids
HP-50; HP-50-Na compacts≈0.92 → 0.14; ≈2.80 → 2.45 mg/min/cm² from 29 to 3 mM/ΔpHpH 6.8 phosphate, 37 °C[qi2022 R12, C4]
HP-50 in BIS-TRIS, phosphate, Tris, TEA buffers≈44.8 / 28.4 / 6.6 / 1.8% dissolved at 60 min (buffer pKa 6.5 / 7.2 / 8.1 / 10.2)50 mM, pH 6.8[qi2022 R2, C14]
neat HPMCAS-MF≈0.16 / 0.26 / 0.59 / 0.89 / 1.01 mg/min/cm² at 3 / 5 / 13 / 26 / 51 mM/ΔpHpH 6.8 phosphate, 100 rpm[bapat2023 R5]
neat HPMCAS-MFno gel at 5 mM/ΔpH; gel 3 ± 1 µm at 13 and 19 ± 5 µm at 51 mM/ΔpHconfocal, 60 min[bapat2023 R14]
neat HPMCAS-MF; 25% loratadine dispersion≈0.91 → 1.00; ≈0.10 → 0.25 mg/min/cm² (50 → 100 mM)compacts, pH 6.8 phosphate[bapat2024 R6]
Pitfalls and disagreements

The same nominal medium, 50 mM pH 6.8 phosphate, is given 29 mM/ΔpH in the HP-50 paper and 26 mM/ΔpH in the HPMCAS paper (synthesis: from [qi2022 M16] and [bapat2023 A1]), so the two series compare by trend only. The composition and pH of the 5 mM buffer of the HP-50 paper are not printed [qi2022 M17]. In the Peptide permeability chapter a table row labelled "buffer capacity (Osm/L)" carries osmolality values and the buffer capacity is unreported [fagan2025 X1]. In 100 mM phosphate loratadine complexation also fell from about 70 to 48%, a second route for the buffer effect [bapat2024 X11, R16].

← Concepts and formulas

concept · as used in Physical stability

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: monotropicDSCtrasi2014b 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 Physical stability

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)inferred[mosqueragiraldo2018b C37, R14]
ritonavir, atazanavir mixtureeach drug's amorphous solubility times its mole fractionideal mixing[alhalaweh2016 E7]
ritonavir, lopinavir, paclitaxelmax flux drops with a second componentdiffusion cell[trasi2015a C35, E3]
ibuprofenpolymer dilution, extra water and interactions lower itdrug-rich phase[ueda2021 C42]
atazanavir, clozapine, ketoconazole, nifedipine with AS-HFamorphous solubility lowered by a quarter to well over half; AS-LF by under a tenth for threebuffer, 37 °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 °C[lu2017 R1]
enzalutamide above 42 µg/mLequal chemical potential in droplets and water; crystals can start in either phase or at the interfacepH 6.5[wilson2021 C3]
posaconazole droplets with HPMCASpolymer mixed into the droplets "serves to" lower the drug's chemical potential (not measured)pH 6.5[shah2025 C46]
ritonavir + lopinavir mixed drug-rich phasesfree RTV 14.2–15.8 and LPV 7.0–7.5 µg/mL at once and twice the single-drug onsets5 h[trasi2015b R16]
ritonavir with 180 µg/mL PVP, PAA, HPMC, HPMCASLLPS concentration unchanged, read as no change of the phase's activity37 °C[ilevbare2013d R10, C22]
tacrolimus solutions, 20–100 µg/mLflux plateau ≈0.0050–0.0055 µg/min from 60 µg/mLpH 4.5, 37 °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 °C[wegiel2015 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 °C[nguyen2023c R11, R12]
Pitfalls and disagreements

A polymer mixing into the drug-rich phase is later reported to lower the drug's chemical potential and hence the amorphous solubility, as does a second drug in a co-amorphous system [ueda2020a C36; trasi2015b C36; alkalla2026 C12]. Ideal mixing was tested for one pair only [trasi2015a X9]. The chemical potential of the drug in the polymer-containing droplets was not measured in any of the polymer papers [ueda2020b X4; ueda2021 X5, X6]. The activity of telaprevir in the CA Sub-rich phase was not measured, so mixing and complexation are not separated [mosqueragiraldo2018b X12]. For the darunavir case the mixing is inferred; the centrifuged drug-rich phase was not analysed and the light-scattering onset with darunavir present was not measured (F20) [alkalla2026 X6]. A higher concentration is not a higher chemical potential in micellar media [jackson2016 C31]. In the two-drug dispersions the lower chemical potential is inferred, not measured [trasi2015b C36]. CAAdP 0.85 raised the ritonavir LLPS concentration by about 17%, unlike the other polymers [ilevbare2013d X7]. The lower chemical potential in the lopinavir dispersions is inferred from concentrations; χ was not measured and the model is used qualitatively li2018 C46. For delamanid in HPMCP-55 the authors invoke stronger or more extensive drug–polymer interactions lowering the chemical potential of the drug, which were not measured [nguyen2023c C41, C42].

← Concepts and formulas

concept · as used in Physical stability

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 similarbaird2010 C61
felodipine filmsrate described by driving force, kinetic barrier and molecular recognition; nucleation most likely heterogeneous0% RH filmskonno2006 C33
celecoxibinduction time 27.5 ± 0.7 min at S 7.3; about 2.4 min at S 14.737 °C[ilevbare2013c R15, R9.a]
danazol with HPMC-AS516, 365, 277 min at 10, 15, 20 µg/mL25 °C[jackson2014 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 polymertrasi2015 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 speculatedargumentkonno2006 C35, C40
nifedipine vs felodipinelarger enthalpic driving force and lower barrier below Tg for the faster nucleatorTable II, Table Imarsac2006a C49
flutamideprenuclei redissolve unless they exceed a critical radius, the volume free energy against the interfacial termframeworktrasi2012b 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 °C[alonzo2011 C29]
celecoxib, no polymer, 22 against 11 µg/mLonset within 5 min against about 20 minpH 6.8, 37 °C[xie2016a 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 Physical stability

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/minDSCbaird2010 R1
nifedipine glasscrystallized to a metastable form at 87 °C; felodipine did notheating at 2 °C/minmarsac2006a R5
delamanid glassdevitrified just above Tgliquid-N2 quenched[duong2022a R3]
propranolol saltsrecrystallization at 46.5–105.4 °C for four salts; none for nicardipine saltsDSC[towler2008 R4, C10]
rotary-evaporated drug–polymer powdersno exotherm on 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 Physical stability

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. 8marsac2009 R9
same, PVP K29/324.34, 1.30, 5.92, 1.93, 0.54as abovemarsac2009 R9
same, EP at 25 °C0.89, 0.26, 0.68, 0.37, 0.15measured solubilitymarsac2009 R9
dextran–PVP, 20 pairsminimum from about −27 × 10⁻²³ J (DEX1–PVP12) to about 0 (DEX450–PVP90)25 °C, PVP monomer as lattice site[vaneerdenbrugh2012a 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 Physical stability

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 7.6[ilevbare2012a 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 7.6[ilevbare2012a 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 Physical stability

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 moleculesbaird2010 R22.a
solvent classes I against III≈−0.42 against ≈+0.57 SD40 drugsvaneerdenbrugh2010a R20.b
ritonavir18 rotatable bonds, class IIImeltbaird2012 M34
nilutamideone rotatable bond; crystal conformer at 54.4° against a computed minimum near 30°DFT, crystal structuretrasi2014b M1, R19, R24
ritonavir in solution, against celecoxib and efavirenzslow nucleation attributed to higher MW and flexibility; induction time about 120 against 2.4 and 5.1 minaqueous buffer, 37 °C[ilevbare2013c R8, C25]
glyburide, warfarinseveral tautomers may explain slow crystallization; amorphous precipitates for at least 6 h with most polymerspH shift, 1 mg/mL polymer[hsieh2014 R4, R19, C31, C32]
papaverine, dipyridamolereduced conformational freedom proposed; crystalline with every polymer; papaverine adopts its crystal conformation in solutionpH shift[hsieh2014 R4, R19, C33]
six dihydropyridinesno correlation of rotatable bonds with the first crystalline time (0.25–12 h)10 mg/mL solvent shift[raina2015b R6, C31]
Pitfalls and disagreements

Conformer populations were never measured; the argument is inferred from class averages baird2010 C59. Nilutamide, with a single rotatable bond, is nonetheless a good glass former trasi2014b C36. In one solution study the rotatable-bond counts did not follow the conformational-freedom ranking used for dipyridamole and papaverine, and the argument rests on cited data [hsieh2014 X12]. Neither the ritonavir explanation nor the tautomer explanation was tested [ilevbare2013c C25; hsieh2014 C31]. Prediction from structure is called extremely difficult by the authors of the dihydropyridine study [raina2015b C6].

← Concepts and formulas

concept · as used in Physical stability

congruent release

Drug and polymer leave a dispersion at the same normalised rate, so release is governed by the polymer; typical of low drug loading, and the condition for fast, complete release of a copovidone dispersion li2020 C63. Above a drug-specific loading release becomes incongruent and falls to roughly that of the neat amorphous drug (see limit of congruency). In the bicalutamide dispersion, congruent release at 5 and 10% DL went with escape from matrix crystallization; the authors conclude that it "may be a strategy to avoid" it, yet a congruently releasing dispersion with 3% SDS still lost one of three replicates [moseson2022b C36, C48, C51]. In the Peptide permeability papers: The criterion extends from two components to three, and from a small molecule to a peptide with its permeation enhancer: in an octreotide–SNAC–copovidone dispersion all three components released at one normalized rate, which the authors call synchronous release bapat2025b C3, C15. It also survives a component that is not amorphous: both enhancers stayed crystalline in the dispersions and were still carried out with the polymer, which the authors attribute "likely" to the gel-forming properties of copovidone bapat2025b R17, C44. A second usage appears in the same subcategory under the name corelease, judged not by rates but by the times at which each component reaches its maximum release from a tablet, which were about 30 min for insulin and about 10–20 min for the enhancer [fagan2025 R20, C44, C46]; see peptide-enhancer co-release. New aspect (Release mechanism and LoC): in the release-mechanism papers of 2017–2020 congruent release is read from drug and polymer assayed separately from a compact of constant area, as equal rates normalized to each component's weight fraction (no significant difference by t-test) or as overlapping percent-release curves [saboo2019 R8, E4; indulkar2019a R3]. Congruent dispersions keep releasing into a medium presaturated with drug, which the authors take as proof of polymer control [indulkar2019a R12, C43; indulkar2017b C35]. The 2017 ritonavir study ties the colloid to release that is "congruent or close to congruent" purohit2017b C52, and the 2019 dihydropyridine study calls congruent release the "sweet spot" of dispersion dissolution because only it gave drug-rich droplets ("a clear link") [saboo2019 C30]. Congruent release ends at the limit of congruency, which lay between 5 and 30% drug in PVPVA, and with HPMCAS or Eudragit S 100 it lasted to 50% felodipine [que2019 C10; indulkar2019a C2; saboo2020a R15]. The papers of 2020–2022 add that congruent release can end after minutes when crystals form on the dissolving surface (indomethacin methyl ester–PVPVA congruent at 5 min up to 25%, over 30 min only at 5%) [saboo2020 R3, R8, C17], that at the limit the polymer controls release whatever the compound [que2021 C39], and that congruent release at a limit raised by a surfactant is slower than at lower loadings (≈1.8 against ≈2.95–3.2 mg/min/cm² for felodipine with 5% TPGS) saboo2021 X3. For ritonavir at 30%, one loading above its limit, every surfactant built into the dispersion removed the lag phase and gave congruent release for at least 20 min, but only Span 85 and TPGS kept it congruent to about 87–95% at 90 min [indulkar2022 C31, X14]. For two phenolphthalein analogues in PVPVA the morphology of the two phases after separation "appears" to differentiate congruent from incongruent release; during congruent release the drug is carried into the diffusion boundary layer by swelling and release of the polymer chains deac2023a C46, C47. Below the limit the surface drug/polymer ratio of PHPH (5%) and MePHPH (30%) compacts stayed constant during dissolution, as it must if both components release in the dispersion ratio deac2023b C24, C58. The papers of 2023–2025 extend the reading to HPMCAS, where indomethacin, its ester and four weak bases released drug and polymer at matching normalized rates, so that release "appear[s] co-dependent" [bapat2024 C10, C23], and to PVP, where congruency was counted as more than 80% of both components and congruent dispersions released more slowly with higher-molecular-weight grades [deac2024a C36, C19]. In the PVP paper droplets in the gel are held until the polymer is dilute enough to leave and then leave with it, so congruent release is limited by water penetration and the release of chains [deac2024a C34].

Findings

ASD process: F21, F24, F38, F40, F48. Peptide permeability: F4, F5, F6. Release mechanism and LoC: F1, F2, F3, F4, F6, F11, F12, F13, F15, F17, F19, F21, F23, F24, F25, F26, F27, F29, F31, F32, F33.

Related concepts

ends at the limit of congruency; the opposite is incongruent release; belongs to polymer-controlled release; the three-component case for a peptide plus an enhancer is peptide-enhancer co-release; still bounded by the limit of congruency and opposed by incongruent release; the accelerating effect of a co-formulated enhancer connects it to water sorption of the excipient blend. Read by the intrinsic dissolution rate of each component; contradicts the Higuchi two-component dissolution model at low loading; the condition for drug-rich nanodroplets to form; ended early by surface crystallization; coupled to the polymer's own dissolution rate, which a cationic drug can lower through drug-polymer ionic interactions.

Formulas

The same surface-normalized rate is used, printed here as Eq. 1 with the medium volume in the numerator; see surface-normalized release rate bapat2025b E1. Also congruent release relation and saturated-medium condition.

How it is measured or obtained

Constant-area dissolution of compacts with drug and polymer both assayed, expressed as normalised release rates or as fractions released; in the ASD process papers the surface-normalised dissolution rate of ritonavir–PVPVA was used and the congruent boundary of 25% DL was cited from earlier work li2020 P9, E13, R23. In the Peptide permeability papers: As before by constant-area dissolution with every component assayed and converted to a normalized rate, here at 0.5 cm² in 100 mL of 50 mM pH 6.8 phosphate buffer at 37 °C, with reversed-phase HPLC for peptide and SNAC and aqueous size-exclusion chromatography for copovidone bapat2025b P4, P2, E1. The new practical limit is analytical: sodium decanoate could not be quantified at all, so in every decanoate dispersion congruence rests on the peptide and the polymer and the enhancer's co-release is inferred ("presumably") bapat2025b R6, C19, X1. In the release-mechanism papers: Wood's apparatus or a die with one face of about 0.5 cm², drug by HPLC or UV, polymer by size-exclusion chromatography, light-scattering detection or colorimetry, and the rate A = kV/(SN) for each component [indulkar2019a P2, P3, P4; saboo2019 P9, P10; saboo2020a E3, P7; bhardwaj2018 P6, P7, E4]. Later variants: 5-min rates sampled every minute [saboo2020 P5]; the last loading with simultaneous release and at least 80% of the drug in 90 min [que2021 P9]; t-tests of normalized rates yang2021 P17; drug release alone [hiew2022b X6].

Values in the library
materialvalue or classconditionspaper ids
ritonavir–PVPVAcongruent up to 25% DL; at 40–50% DL drug release like neat amorphous drugcitedli2020 R23, C63
ritonavir–PVPVA spray-dried, 25% DLrate about 3.5 mg·min⁻¹·cm⁻¹ from methanol, falling to about 0.90 with 60:40 water:methanolpH 6.5, 100 rpmli2020 R10
ritonavir–PVPVA, 50% and 75% DLabout 0.003–0.006 mg·min⁻¹·cm⁻¹, near neat amorphous drug (about 0.0026)sameli2020 R10
ritonavir–PVPVA (outside)congruent up to 25% DL; polymer leaves first above ittablets[indulkar2019a C2]
felodipine ASDs (outside)PVP and HPMC congruent to 10% DL, PVPVA to 15%; HPMCAS and EUDS congruent to 50% DL37 °C[saboo2020a 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 6.8[moseson2022b R6, R7]
BCL–PVPVA 30% DL with 1.5% SDScongruent; more than 80% in 30 min, about 90–94% at 4 hsame[moseson2022b 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 °Cbapat2025b R2.d–e, R3, X18
octreotide:SNAC:copovidone, 1.6% peptidecongruent in three components; ≈8.1 / ≈8.4 / ≈8.9 mg min⁻¹ cm⁻²samebapat2025b R2.f–h, R5
octreotide:sodium decanoate:copovidone, 1.6% peptide≈23 and ≈25 mg min⁻¹ cm⁻² (peptide, polymer); complete in about 10 min; enhancer not assayedsamebapat2025b R2.j–k, R9, X1
SNAC:copovidone ratio seriescongruent within 30 min from 20:80 upward; 10:90 slower, complete within 40 minsame (SI, text only)bapat2025b R4, C14
sodium decanoate:copovidone ratio seriespolymer complete within about 10 min from 20:80 upward, by 25 min at 10:90same (SI, text only)bapat2025b R8, C18
cyclosporine:copovidone ± enhancer, 1.6% peptidepeptide follows polymer: about 50 min (binary), about 10 min (decanoate), ≈95% at 60 min (SNAC)samebapat2025b R10, C21
cyclosporine ternaries, 10–20% peptidenot congruent: polymer complete while peptide reaches ≈54.5% and ≈16% with decanoatesamebapat2025b R12.i, R13.i, C23
nifedipine 10 and 20% with HPMC-E5 or PVPVAcomplete release in ~20 and < 5 min, also into water saturated with drug5 °C, D2O[indulkar2017b R8, R9, C35]
ritonavir 10:90 films, PVP, PVPVA, HPMCASdrug and polymer dissolved at the same rate; the polymer almost completely in < 10 min25 °C, pH 6.8purohit2017b C52, R15, R16, R17
ritonavir 50:50 HPMCAS filminitially congruent (≈32–34 µg/mL drug within 5 min)samepurohit2017b R17, C38
ITZ–PVPVA 10% spray-driednormalized drug ≈2000 against polymer ≈2265 µg/min/cm²0.1 N HCl, 37 °C[bhardwaj2018 R11]
ritonavir–PVPVA 10, 20, 25% tablets≈97–100% of both by 60 minpH 6.8, 37 °C[indulkar2019a 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 7.4[saboo2020a R14]
nilvadipine, felodipine, cilnidipine 40% in HPMCAS0.42/0.42, 0.34/0.32, 0.26/0.24 mg/min/cm²same[saboo2020a 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 °Csaboo2021 R12, P6
loratadine–PVPVA; –HPMCASto 30% and 20% at 37 °C; 2% and 5% at 5 °Ccompacts, t-testyang2021 R22
clopidogrel–PVPVAclose to congruent to 40%; 50% with SDScompactscorreasoto2022a C46, C55
atazanavir–PVPVA5%; 10% with SDS or CTAB; 15% with Span 80compactscorreasoto2022b C12
ritonavir–PVPVA 30:70 with 5 parts Span 85, TPGS; SDS; Span 20; Tween 80congruent for at least 20 min with every surfactant; ≈87–89% (Span 85, TPGS), ≈78% (SDS), ≈41%, ≈25% of the drug at 90 minpH 6.8, 37 °C[indulkar2022 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 °Cyang2022a R2, C12, C13
indomethacin–HPMCAS-MF 10%; its methyl ester 10%drug and polymer at the same normalized rate within error, ≈0.12 → 0.82 mg/min/cm² over 3–51 mM/ΔpH; rates comparablepH 6.8 phosphate and 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 °Ccorreasoto2023 R6, R7, C13
MePHPH–PVPVA 20, 40, 50, 70%; PHPH–PVPVA 5, 20%drug ≈96 / 61 / 15 / 0%; ≈75 / 0% at 30 mincompacts, pH 6.8, 37 °Cdeac2023a R1, R2
PHPH–PVPVA 5%; MePHPH–PVPVA 30% compactssurface drug content constant over 60 minATR-FTIR of dried surfacesdeac2023b R6, R7
indomethacin, indomethacin methyl ester–HPMCAS-MF 5–60%drug ≈0.85 → 0.50 and 0.66 → 0.39 mg/min/cm² with the polymer alongsidecompacts, pH 6.8 phosphate, 37 °C[bapat2024 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 Physical stability

cosolvency

The change of a solute's solubility in a mixture of two solvents with their ratio; in this chapter water is an anti-solvent for hydrophobic drugs, and polymer plus sorbed water is treated as the drug's co-solvent inside a humid dispersion marsac2008a C39, C26, C33; rumondor2009c C37.

Findings

F2, F10.

Related concepts

related to solid-liquid equilibrium solubility equation via activity coefficient; feeds supersaturation; related to Δχ effect.

Formulas

the log-linear cosolvency model of the 2008 paper is listed on the chapter page as table only.

How it is measured or obtained

Shake-flask solubility of the crystalline drug in a liquid analogue of the polymer (NMP for PVP), in water and in their mixtures at 25 °C, fitted with a log-linear cosolvency line; the water fraction of the polymer–water co-solvent is computed from sorption data marsac2008a P8, E5, E6.

Values in the library
materialvalue or classconditionspaper ids
nifedipine, felodipine in NMP–watermole fraction 0.05 and 0.10 at 0% water; ≈0.015 and ≈0.017 at ≈24 wt% water25 °Cmarsac2008a R12
nifedipine with 10 and 25% PVPco-solvent 23 and 18 wt% water75% RH, 25 °Cmarsac2008a R13
felodipine with 10 and 25% PVP≈16 wt% water75% RHmarsac2008a R13.c, R13.d
drug–PVP–water (argument)water–PVP "cosolvent" mixes less well with the drug as it takes up waterhumid dispersionsrumondor2009c C37, C44
drugs in PEO compacts (outside)water lowers solubility in the water–PEO co-solvent but enlarges the solvent volume94% RHmarsac2008b C33

Evidence table: cosolvency.

Pitfalls and disagreements

The printed cosolvency fits do not reproduce their own points and cross at 16.5 rather than about 25 wt% water; the crossover rests on three water contents marsac2008a X2, X3. NMP stands in for PVP by assumption marsac2008a C33, X4.

← Concepts and formulas

concept · as used in Physical stability

Couchman-Karasz equation

An ideal-mixing prediction of the Tg of a miscible blend in which the constant is the ratio of the heat-capacity steps of the components at their Tg; a measured Tg below the line is read as non-ideal mixing konno2006 E4, R7, C16; rumondor2009a E1, E2.

Findings

F5.

Related concepts

alternative to Gordon-Taylor equation; predicts glass transition temperature of a drug-polymer miscibility blend.

Formulas

the Gordon–Taylor form with a ΔCp-based constant; see Gordon-Taylor equation.

How it is measured or obtained

Calculated from the Tg and ΔCp of the pure components and compared with DSC Tgs of dispersions konno2006 P5; marsac2006a R17.

Values in the library
materialvalue or classconditionspaper ids
felodipine with PVP, HPMCAS, HPMCHPMCAS and HPMC Tgs below the line at mid-range; PVP closeΔCp 0.33, 0.20, 0.31, 0.25 J/g/Kkonno2006 R7, M1, M2, M3, M4
nifedipine–PVP, felodipine–PVP"relatively ideal"DSC, 0–100 wt% PVPmarsac2006a R17, C21
ketoconazole–PVP (outside)single Tg near the line at every ratioDSCrumondor2009a R4

Evidence table: Couchman-Karasz equation.

Pitfalls and disagreements

The 2006 felodipine paper prints the constant as \Delta C_{p1}/\Delta C_{p2}, and neither orientation reproduces its plotted lines; a logarithmic form evaluated with Tg in °C comes close, but the paper does not print it konno2006 X4. Ideality conclusions therefore depend on which form was used.

← Concepts and formulas

concept · as used in Physical stability

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/minbaird2010 R13
delamanidabove 50 °C/min (no glass at 50 °C/min)DSC[duong2022a 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 Physical stability

critical ionization for polymer dissolution

Evidence table: critical ionization for polymer dissolution (names merged there: critical ionization, critical ionization extent, critical ionization fraction, polymer ionization threshold). Content from the release-mechanism chapter (2022–2025), with rows from the Miscibility and drug-polymer interactions chapter.

The minimum fraction of the acid groups of an enteric polymer that must be ionized before its chains dissolve; below it the polymer does not dissolve, or dissolves slowly, whatever the bulk pH. In the Miscibility chapter it was written with the Willson model, dissolution rate ∝ [A⁻]/[HA], and used to explain why CAP and HPMCP dispersions with a basic drug that ties up some acid groups release poorly or slowly hiew2022a E2, C57. For HP-50 the critical ionization of about 83% taken from that work "may explain" the almost 2-fold drop of the dissolution rate of BIS-TRIS salts from 100 to 80% ionization, "perhaps" because hydrophobic ionizable polymers need a minimum ionization to dissolve [qi2022 C36, R19]. For HPMCAS-MF no polymer dissolved in FeSSIF V1 at pH 5.0, "presumably" because the threshold ionization was not reached, and near the threshold pH (FeSSIF-V2, pH 5.8) dissolution was slower than in phosphate of corresponding buffer capacity [bapat2023 C14, C12]. The 2025 papers apply the model to drug–polymer complexes: a drug that binds the carboxylates and blocks their hydration "can impact" dissolution, the more succinoylated HPMCAS-LF is proposed to need less ionization to dissolve by analogy with maleic anhydride copolymers, and about 77% ionization is estimated for HPMCAS from a threshold pH of 5.5 [bapat2025a C2, C3, C25; kaur2025 C28, C46].

Findings

Release mechanism and LoC: F23, F24, F32, F33.

Related concepts

a threshold of polymer ionization and of ionization; reached or not according to the microenvironmental pH and the polymer pKa; bypassed by polymer salt formation; behind the pH-dependent polymer solubility of enteric polymers.

Formulas

The Willson relation is printed only in the Miscibility chapter hiew2022a E2; no shared formula page.

How it is measured or obtained

By extrapolating literature dissolution data of the neat polymer against the ionized fraction or pH hiew2022a R27; indirectly, from dissolution of partially neutralized salts against the amount of base added [qi2022 R13] or from media of different pH [bapat2023 R5, R8].

Values in the library
materialvalue or classconditionspaper ids
CAP; HPMCP (Miscibility chapter)≈0.94; slightly less than 0.83extrapolated from literature datahiew2022a R27
HP-50 (HPMCP)≈83% (cited)[qi2022 R19]
HP-50-BIS-TRIS salts, 20–100 mol% baserate ≈1.22 → 2.93 mg/min/cm², largest step from 80 to 100%50 mM pH 6.8 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 dissolvingestimate[kaur2025 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 Physical stability

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 telaprevir[lu2017 R5]
Vit E TPGS / Cremophor EL / RH40 / Tween 200.02 / 0.01 / 0.03 / 0.009%levels C1–C3 chosen around it[raina2015c A2]
SDS in the telaprevir ASDfinal about 15 µg/mL, far below CMC37 °C[mosqueragiraldo2018b 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 used[ilevbare2012a M16, X16]
TPGS with and without 900 µg/mL PVPVA (ASD dissolution chapter)about 50 µg/mL; about 40 µg/mL with PVPVA (49 ± 4 and 41 ± 3 µg/mL as printed)pH 6.8, 100 mM buffer, 37 °Csaboo2021 R1
SDS in 50 mM phosphate pH 6.8CMC 0.5 mg/mL (cited); induction-time effect from about 0.075 mg/mL, none further above the CMCatazanavir, 37 °C[indulkar2019b M2, R3]
SDS with 1 mg/mL polymercritical aggregation concentration 0.1 (PVPVA), 0.2 mg/mL (HPMC-606, HPMCAS-MF)pyrene I1/I3, no drug[indulkar2019b R8]
lyso-PC against PClower CMC and higher surface activity (cited)reasoning for faster nucleation with digests[enright2020 C22]
SDS with celecoxib at saturation0.23%pH 3, 25 °C[chen2015a R4]
STC0.69% in the text, 0.668% on the figuresame[chen2015a R4, X1]
polysorbate 80; Poloxamer 188; Triton X1000.0058%; 0.16%; 0.022%same[chen2015a R4]
SDS / Poloxamer 188 / polysorbate 80 / STC with lopinavir0.050 / 1.40 / 0.020 / 0.73%pH 3 citrate, 25 °C[li2016b R1]
SDS with lopinavir and HPMCPbreak near 0.1%pH 3, 25 °C[li2016b R11]
ledipasvir–PVPVA with 5 parts surfactant per 100at most ≈0.048 mg/mL surfactant in the medium after complete release (synthesis: 0.048/0.5 ≈ 0.1 of the SDS CMC in buffer [indulkar2017a R1])100 mg compacts, pH 6.8[que2019 X19]
SDS, CTAB, TPGS, Tween 80487 ± 34, 50, 40, ≈14 µg/mL50 mM pH 6.8, 37 °Ccorreasoto2022a R1
SDS, CTAB, TPGS, Tween 80, Span 20, Span 80, Span 85500, 50, 40, 14, 7.3, 14, 5–50 µg/mLas listedcorreasoto2022b M3, M4, M5, M6, M7, M8, M9
Pitfalls and disagreements

The micelle-like origin of the ritonavir profile is "surmised", with no structural data ilevbare2013a C47. The CMC of the other four bile salts in the telaprevir medium was not measured, and the CMC of SDS in buffer is lower than in water [lu2017 C14; indulkar2017a C10]. The CMC basis (w/v or w/w) and source are not printed in Table I of the additive study [raina2015c A2]. In the PAMPA study the receiver sink effect is said to be available at 0.15% SDS, three times the CMC read by pyrene (0.05%); whether 0.15% is a tested level or a misprint is unclear [hate2022 R12, R13, X6]. The two printed TPGS values (212 and about 200 µg/mL) agree only at unit density; both are far above the 5 µg/mL used [ilevbare2012a X16]. Ritonavir solubility in 5 µg/mL Tween 80 was 1.3 ± 0.02 µg/mL, so no solubilization is expected below the CMC [ilevbare2012a R1.g]. Most dihydroxy conjugates and SLC have literature CMCs at or below the 1.86–2.51 mM used, so the monomer assumption is uncertain; CMCs were measured for two bile salts only in the telaprevir study [li2016a X16; lu2017 X7]. The Poloxamer 188 CMC rests on solubility changes of 0.1–0.2 µg/mL and is weakly determined [chen2015a X20]. The test levels lie 6–14% above the printed CMCs, not exactly 11% [chen2015a X2]. SDS and STC acted below their CMC as well [chen2015a C6]. The authors place an aggregation onset with PVPVA below 0.01% SDS, whereas the plotted rise begins between 0.01 and 0.025% [li2016b X9]. Below the CMC in the bulk, the surfactant concentration at the dissolving surface was not known [que2019 C53]. Only about half the TPGS had been released at 60 min, so the bulk stayed below the CMC in every felodipine case saboo2021 X14; one paper prints the TPGS CMC as 40 and as about 50 µg/mL correasoto2022a X1.

← Concepts and formulas

concept · as used in Physical stability

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 °C[chen2015 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 Physical stability

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 Physical stability

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 platesSEM[moseson2020a R14, R15, R13]
residual crystals in BCL–PVPVA extrudatescalled "highly defective" and "commonly more potent" than bulk seeds, from the literature and growth ratescited[moseson2021 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 Physical stability

crystal growth inhibition

Reduction of the crystal growth rate by an additive, here dissolved PVPVA or HPMCAS, expressed as the effectiveness ratio E_G=R_{G,np}/R_{G,p}, the growth rate without polymer over the rate with it [moseson2020a E2; moseson2021 E1]. The mechanism proposed is surface poisoning: polymer globules adsorb on the crystal face and the adsorbed network "appears to limit the sites available for molecular integration" [moseson2020a C48, C50]. HPMCAS at nine times the drug concentration slowed seeded growth of posaconazole in FaSSIF V2 but did not stop it at 100 µg/mL drug: 10 µg/mL seeds left 43.5% at 30 min against 4.5% without polymer [shah2024 R22]. New aspect (Crystallization from solution): The slowing of the growth of drug crystals in a supersaturated aqueous solution by a dissolved additive, usually a polymer, expressed as the ratio of the initial growth rate without additive to that with it, E_g = R_{g0}/R_{gp}; above 1 the additive inhibits growth, below 1 it accelerates it [ilevbare2013b E5; ilevbare2012a E3, E4]. In these papers it is a kinetic effect at constant solubility, shown by solubility controls with the polymer [ilevbare2012c R1, C16]. It is the solution counterpart of the growth inhibition in supercooled liquids described below and is one of two steps of crystallization inhibition, the other being nucleation inhibition. Seeded growth ratios now include HPMCAS on felodipine (2.29 at pH 6.8, 1.28 at pH 3, and 2.7 to 12 depending on how the seeds were made) and bile salts on telaprevir seeds (E_G 1.0–4.6; complete stop with monomeric STCDC) [schram2015 R4; schram2016 R2; lu2017a R7, R10]. New aspect (Supersaturation from ASD dissolution): the 2008 felodipine study reads a flat concentration after an initial drop as growth inhibition: the drop takes the solution from the labile into the metastable zone ("it appears"), where only growth could lower the concentration further, so a plateau "strongly suggests" inhibited growth konno2008a C27, C26. The 2011 study reads slower growth of particles with HPMC than with PVP the same way [alonzo2011 C18]. For celecoxib, seeded desupersaturation with HPMCAS gave growth ratios R_0/R_p of about 70–158, less inhibition at the higher supersaturation, against an estimated nucleation ratio of ~4000, so both steps were slowed but nucleation far more ("it can be surmised") [xie2016a R12, R13, C37, C40]; the slow growth explains why crystals formed in dissolving PAA particles did not empty a medium holding HPMCAS [xie2016a C36]. In the supercooled liquid (formerly the page "crystal growth inhibition by polymers", from Crystallization tendency and Miscibility and drug-polymer interactions): the reduction of the crystal growth rate of a drug by a polymer dissolved in its supercooled liquid; the extent is thought to depend on specific drug–polymer interactions such as hydrogen bonding, and at higher levels on the polymer's effect on mobility trasi2014a C33; trasi2014b C19. The inhibition depends on the chemistry of the polymer at low levels, where it changes neither the Tg nor the melting point of the drug: at 3% w/w felodipine growth was slowed in the order PVP > PVP/VA > HPMCAS > PVAc kestur2010a C17, C32, C36. The factor is not a constant of the polymer: it grows as the temperature falls toward Tg and with polymer content kestur2010a C12, R6, R8, and the best polymer depends on the drug (PAA for bifonazole, PVP and PVP/VA for nimesulide at low temperature) kestur2011 C9, C10, C29. The authors tie the order to the strength or extent of drug–polymer hydrogen bonding and propose, as a "speculation", that crystal growth needs the drug to demix from the polymer at the growth front kestur2010a C40, C42.

Findings

ASD process: F25, F27, F29, F41. Crystallization from solution: F5, F6, F7, F8, F9, F10, F11, F12, F17, F18, F20, F23, F24, F27, F33. Supersaturation from ASD dissolution: F4, F5, F16, F22. Crystallization tendency: F19. Miscibility and drug-polymer interactions: F10, F11, F12, F13, F14, F17.

Related concepts

part of crystallization inhibition by polymers; acts on crystal seeding; slows desupersaturation; related to crystal growth rate; part of crystallization inhibition; contrasts with nucleation inhibition and with polymer effects on nucleation; related to polymer adsorption on crystal surfaces, step pinning and physical stability; contrasts with the polymer's effect on antiplasticization and thermodynamic driving force for crystallization; depends on hydrogen bonding and intramolecular hydrogen bonding.

Formulas

crystal growth inhibition effectiveness ratio, power-law crystal growth rate, initial growth rate from the desupersaturation slope, Kubota-Mullin model, overall mass crystal growth rate, relative nucleation rate from seeded and unseeded induction times, viscosity-limited normal growth law.

How it is measured or obtained

Seeded growth from a supersaturated solution at a stated supersaturation and polymer concentration, with the growth rate from the desupersaturation profile; adsorption by AFM in liquid (globule spacing) and crystal habit by SEM [moseson2020a P10, P15, P16; moseson2021 P12]. In the crystallization-from-solution papers: Seeded desupersaturation: a fixed mass of seed crystals (0.010 g in 50 mL for ritonavir, celecoxib and efavirenz; about 2.5 mg in 18 mL for felodipine) is placed in buffer with predissolved polymer, supersaturation is created by adding drug in methanol, and a fibre-optic UV probe on second-derivative spectra gives the slope of the first 2 min (5 min for felodipine) as the growth rate [ilevbare2013b P10; alonzo2012 P4]. Eg is the ratio of slopes, in triplicate [ilevbare2012c P12]. Rates can be normalized by seed mass and BET area [ilevbare2013b E6]. Unseeded controls and turbidity checks test that the slope is growth [ilevbare2012a R9; ilevbare2013b R5]. Rotating-disc seeds (felodipine) and seeds grown in situ in the vessel (telaprevir); the ratio is R_0/R [schram2015 P2; schram2016 P5; lu2017a P1, P2]. In the ASD dissolution papers: initial slopes of desupersaturation curves with equal crystal surface areas assumed (Eq. 5) konno2008a E5, P6, C28; particle size against time by light scattering [alonzo2011 P5]; seeded desupersaturation with 7 mg seeds in 50 mL, initial slope without polymer against the slope over 16 h with polymer [xie2016a P4, P11]. In the supercooled liquid: by comparing seeded growth rates of the neat drug and of drug with a low polymer level at the same temperatures trasi2014a P3; trasi2014b P2, with FTIR to assess drug–polymer hydrogen bonding trasi2014b P4. For the felodipine, bifonazole and nimesulide dispersions: a 10% w/w polymer dispersion made by rotary evaporation is diluted with crystalline drug in a cryogenic mill to 0.5–4.5% w/w, melted between cover glasses, nucleated over P2O5 at 40 °C (or at ambient temperature) and grown on a hot stage at 70–110 °C (or 18–100 °C), the slope of spherulite diameter against time being the rate kestur2010a P1, P2, P3, P4; kestur2011 P1, P2, P3. Whether the slope is a diameter or radius rate is not always stated, and the felodipine Fig. 3 slopes are about twice the Fig. 4 rates kestur2010a X3; kestur2011 X12. Hydrogen bonding is read separately by IR on films with 20–50 wt% polymer kestur2010a P6, C6.

Values in the library
materialvalue or classconditionspaper ids
IDM, PVPVAE_G 18 (5 µg/mL) and 56 (50 µg/mL polymer)50 µg/mL seeds, S = 6[moseson2020a R5]
BCL, PVPVA 70 µg/mL and HPMCAS 1 mg/mLE_G 8.6 and 158150 µg/mL, form 1 seeds[moseson2021 R5]
felodipine seeds, HPMCAS 5 µg/mL (outside)E_G about 2 to 12 depending on how the seed crystals were preparedS = 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 °C[xie2016a 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 solution[shah2024 R22]
ritonavir, 34 polymersE_g 0.83–3.25; Pn-IPAAmd 3.25, CAP Adp 0.85 2.98, CAB Adp 0.81 2.70, HPMCAS about 2.545 µg/mL polymer, S 7.6, 37 °C[ilevbare2012c R9]
ritonavir, CA 320S Sub 0.90; 0.6312.6; 10.8same[ilevbare2013b R9]
celecoxib, HPMC; HPMCAS; PVPVA10.2; 8.5; 7.45 µg/mL polymer, S 6.6[ilevbare2013b R9]
efavirenz, PVPVA; CA 320S Sub 0.90about 4.9S 1.2[ilevbare2013b R9]
ritonavir, CAP Adp 0.856.40, 2.99, 1.56S 3.8, 7.6, 15.3[ilevbare2012b R5]
ritonavir, CAP Adp 0.85 + Pn-IPAAmdabout 12.1 (S 7.6); 3.3 (S 15.4)5 + 5 µg/mL[ilevbare2012a 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 °Ctrasi2015 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 °C[alonzo2011 R10, R8]
felodipine particles at 37 °C, PVP against HPMC dispersions≈441 nm by 20 min against ≈287–307 nm37 °C[alonzo2011 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 °C[alvarenga2025 R14, C28]
five drugs with 10 mol% PVPgrowth reduced about 3- to 14-fold (authors: "around 5−10"), one point about 50-foldsupercooled liquid, 40–120 °Ctrasi2014a R6, X6, C10
nilutamide≈5 (alone), ≈3.8 (PAA), ≈1.1 µm/s (PVP)supercooled liquid, 80 °Ctrasi2014b 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, meltkestur2010b 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/wmosqueragiraldo2014 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, triplicatekestur2010a 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 contentkestur2010a 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 filmskestur2011 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 filmskestur2011 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 Physical stability

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 melttrasi2014a R1.a
clotrimazoleMCV 0.02 µm/s, the slowestbulk melttrasi2014a 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 filmstrasi2014b R8
felodipinemaximum near 105 °C, 3 orders lower at 70 °Cmelt filmskestur2010a 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 filmskestur2011 R7
flutamidenearly 2 orders lower from 70 to 40 °Cfilmstrasi2012b R3
acetaminophennearly 2 orders lower from 110 to 70 °Cfilmstrasi2012a 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 melttian2017 R7, R8, R9, R10
celecoxib with TPGSabout two orders faster than celecoxib alone at 70 °C10% w/wmosqueragiraldo2014 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 stagekestur2010a 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 IIkestur2010a 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 filmskestur2011 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 filmskestur2011 R9.a, R9.g
ritonavir; celecoxib; efavirenznormalized 0.20; 0.91; 2.97 mg min⁻¹ m⁻² at S 1.2–1.3seeded, 37 °C[ilevbare2013b R7]
celecoxib; ritonavir at S 6.6; 7.66.23; 6.14 mg min⁻¹ m⁻²same[ilevbare2013b R7]
celecoxib; ritonavir at S 14.7; 15.419.08; 14.32 mg min⁻¹ m⁻² (217.5 and 181.5 µg min⁻¹)same[ilevbare2013b R7]
ritonavir without additive, 10 µg/mL1.56 µg mL⁻¹ min⁻¹ (text), about 1.4 (figure)100 mM buffer, S 7.6[ilevbare2012a R10, X5]
ritonavir without additive, S 3.8; 7.6; 15.4about 0.72; 1.4; 3.63 µg mL⁻¹ min⁻¹same[ilevbare2012a 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 filmskestur2010b 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 filmskestur2010b 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 filmskestur2010b 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 ratetrasi2012b R3.a, R3.h
acetaminophen with 10% w/w PAA≈0.43 against ≈5.3 µm/s at 80 °Cmelt films, radial ratetrasi2012a R6.a, R6.h
celecoxib≈0.002 (70 °C) to ≈12 µm/s (120 °C); 19–38-fold slower with 10% PVPseeded melt filmsmosqueragiraldo2014 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 filmskestur2013a 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 filmssato2016 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 Physical stability

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 filmskestur2011 R4
acetaminophen with polymersspherulites; radius linear in time, R^2 > 0.99melt filmstrasi2012a 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 filmstrasi2014b 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 Plus[elkhabaz2017 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 °C[alonzo2011 R6]
felodipine particles, dispersion against methanol shift with HPMC≈183–203 → ≈280–307 nm in 90 min, alike25 °C[alonzo2011 R8]
same at 37 °Cdispersion-born ≈259–274 nm against ≈194–219 nm at 5–10 min37 °C[alonzo2011 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 °C[xie2016a 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 Physical stability

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 needsargumentmarsac2006a C36, R4.g
felodipine with PVPadsorbed polymer would lower it rather than raise it, so it cannot explain slower growthargumentkestur2010b 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 Tmtian2017 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 Physical stability

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 4.5[moseson2020a 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 h[moseson2020a 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 slurry[moseson2021 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 solution[shah2024 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 min[shah2024 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 V2[shah2024 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 °C[elkhabaz2019a 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 6.5[elkhabaz2019a 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 only[elkhabaz2019a R6, R7]
delamanid salt dispersions, particles after the pH shiftcovered with small crystals within 30 minpH 6.5[nguyen2023c 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 Physical stability

crystalline solubility

The equilibrium solubility of the stable crystalline form of the free drug in a given medium, the reference against which supersaturation and the amorphous advantage are defined; Eq. 1 multiplies it by the free-energy and water terms to obtain the amorphous solubility [ilevbare2013a E1; indulkar2015 E2]. For ionizable drugs it is measured at each pH and follows the pH-solubility profile of the free base [indulkar2015 E8, R4]. The papers of 2017–2022 add that it rises steeply with temperature (ibuprofen about 23.5 µg/mL at 25 °C to about 116 µg/mL at 60 °C), that polymers do not change it except one that complexes the drug (EUD-E, 29.8 → 42.1 µg/mL), and that micelles raise it (atazanavir 1.1 → about 45.6 µg/mL at 3.6 mg/mL SDS; telaprevir about twofold with 12 mM dihydroxy bile salts) [ueda2022 R1, R2; ueda2020b R1; indulkar2017a R7; lu2017b R1].

Findings

F5, F6, F9, F10, F12, F4, F15, F17, F18, F23.

Related concepts

reference for amorphous solubility and supersaturation; raised by ionization (pH-dependent solubility) and by micellar solubilization; lowered by salt (F9).

Formulas

solid-liquid equilibrium solubility equation, pH-solubility profile, amorphous solubility advantage with water-sorption correction.

How it is measured or obtained

Shake flask with excess crystals, about 48 h at the test temperature, separation by ultracentrifugation, HPLC or UV assay [ilevbare2013a P1; almeidaesousa2015 P3; indulkar2015 P3; mosqueragiraldo2015 P1; trasi2015a P1; almeidaesousa2016 P5]. A small amount of the stock solvent was added in one study to mimic the onset composition [almeidaesousa2015 P3].

Values in the library
materialvalue or classconditionspaper ids
ritonavir2.4; 1.3; 0.95 µg/mLwater; 100 mM; 200 mM phosphate pH 6.8, 37 °Cilevbare2013a R13
ritonavir; lopinavir; paclitaxel (hydrate); felodipine1.7; 2.7; 0.32; 0.74 µg/mL100 mM pH 6.8, 25 °C[trasi2015a R1]
efavirenz; loratadine; ketoconazole; indomethacin; clotrimazole; clozapine8.2; 1.6; 3.7; 3.0; 0.4; 8.8 µg/mLun-ionizing media, 37 °Cilevbare2013a R8
ibuprofen; tolnaftate; sorafenib29.29; 27.87 × 10⁻³; 9.86 × 10⁻³ µg/mL25 °C[almeidaesousa2015 R5]
telaprevir4.6 ± 0.1 (4.7 with 5 µg/mL HPMCAS) µg/mLpH 6.8, 37 °C[mosqueragiraldo2015 R13]
clotrimazole; atazanavir0.55; 1.04 µg/mL (un-ionized)37 °C[indulkar2015 R2]
CRH1 free base1.20 (pH 6.8); 1.50 µg/mL (pH 4.6 + HPMC)25 °C[almeidaesousa2016 R2]
telaprevir5.2 ± 0.1 µg/mL; 9.6–12.4 with 12 mM STDC, STCDC, SGDC, SGCDC; 6.2–6.9 otherwise50 mM pH 6.5, 37 °C[lu2017b R1]
atazanavir1.1 µg/mL (buffer); about 45.6 µg/mL (3.6 mg/mL SDS)pH 6.8, 37 °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 Physical stability

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/minDSCbaird2010 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 Physical stability

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 stagekestur2010a R6
bifonazole with 5% PAA5-fold at 100 °C, 15-fold at 18 °Chot stagekestur2011 R7
nimesulide with 5% PVP, PVP/VA, PVAcabout 21-, 16-, 3-fold at 18 °Chot stagekestur2011 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 dryvaneerdenbrugh2011a R3, C20, C25
naringenin, quercetinhighest X-ray amorphous content: E100 about 85 and 70%, PAA about 30 and 20%rotary evaporation, PXRDwegiel2013a R8
naringenin, quercetin with E100 and PVPno crystals for >200 to >450 days at five conditionsPXRDwegiel2013a R9
lumefantrine–PVPVA; –enteric polymerscrystals at 1–8 weeks; only at 50% drug loading (1–40 weeks)40 °C/75% RHhiew2022a R6
IDM, PVPVA in solutionno nucleation for more than 12 h at 5–50 µg/mL; about 40 min withoutS = 6[moseson2020a R3, C11]
BCL, PVPVA 70 µg/mL and HPMCAS 1 mg/mL in solutioninduction above 1 h; none in 8 h; without polymer under 30 min37 °C[moseson2021 R3]
BCL–PVPVA dispersion in the slurryHPMCAS in the medium delays crystallisation by about 10 min and leaves form 2 growth unchangedRaman[moseson2021 R19, R20, C51]
neat PCZ and BCL meltsnucleate within 1 h between Tg and Tm; IDM did not in 4 hDSC holds[moseson2020 R7]
twenty commercial polymers on ritonavir growth (outside)five effective: Pn-IPAAmd > HPMCAS > HPMC > CAPh > CMCABseeded growth[ilevbare2012c C22]
bifonazole in melt-quenched films (outside)PAA the most effective polymer; PAA ineffective on acetaminophen in solution5 wt%kestur2011 C9; trasi2015 C26
erlotinib–HPMCAS against erlotinib–PVPVA, coated, 43% RHnone at 48 weeks against about 6 weeks40 °C, SEMmoseson2022a R11, R12
felodipine, 1 µg/mL HPMCgrowth ratio 0.607; induction time 15.3 → 136.5 min; J/J_0 7.05 × 10⁻⁴S 10, 25 °Calonzo2012 R5, R16, R17
ritonavir, CAB Adp 0.81induction time ≈120 → ≈244 min5 µg/mL, 20 µg/mL drug[ilevbare2013c R9]
celecoxib, HPMC2.4 → 12.6 min (22 µg/mL); 27.5 → 855.5 min (11 µg/mL)5 µg/mL, 37 °C[ilevbare2013c R9, R15]
danazol, HPMC-AS6–10 → 250–516 min10 µg/mL polymer, 25 °C[jackson2014 R17]
warfarin, six polymersamorphous precipitate ≥ 6 h; 103–224 µg/mL1 mg/mL, pH shift[hsieh2014 R4]
celecoxib, 5 µg/mL HPMCASsupersaturation held 16 h; J_0/J_p about 4,00022 µg/mL drug[xie2016a R3, R13]
six dihydropyridines, 4.5 mg/mL polymerPVPVA = HPMC = HPMCAS > PVP > CMCAB = CAPAdp > P2VP = PAAnominal 10 mg/mL[raina2015b C16, R9]
telaprevir 150 µg/mL, 5 µg/mL polymerHPMC 243, HPMCAS 175–226, CA-Sub-090 106 min against 14–15 withoutpH 6.8, 37 °C[mosqueragiraldo2016 R4, R5]
acetaminophen S 1.5, 10 µg/mL95% of vials: none 26, PAA 11, HPMCAS 470, HPMC 1043 min20 °Ctrasi2015 R1
atazanavir, volunteer media V5 and V6, 1 mg/mL HPMC134 ± 23 and 45 ± 7 → >360 minpH 6.5, 37 °C[enright2020 R28]
telaprevir δ 28.8, 150 µg/mL HPMCAS-MF, four lecithin mediaabout 357–474 min, no difference37 °C[lu2018 R7]
enzalutamide 120 µg/mL, 50–100 µg/mL HPMCASabout 431–530 min; P177 about 71–125 minpH 6.5[wilson2021 R3]
felodipine with 3% PVP, HPMCAS or HPMCnucleation ≈1.3 × 10⁵ → ≈2–3 × 10³ m⁻³ s⁻¹, equal for all three0% RH, 22 °Ckonno2006 R4, C14
nifedipine and felodipine with 7 wt% PVPabout two orders of magnitude lower; 3–4-fold more to 25 wt%0% RHmarsac2006a R16, C18
felodipine with 3% PVP vs HPMCAS≈8.6 × 10⁵ vs ≈1.3 × 10⁴ m⁻³ s⁻¹75% RHkonno2008 R3.b, C10
felodipine with 3 wt% PVP K-90growth 21-fold slower at 70 °C, 6-fold at 110 °Cmeltkestur2010b R8
felodipine with 25–50% PVP vs HPMCAS51–82% vs 9–28% crystallized after ≈490 days75–93% RHrumondor2009b R9, C13
acetaminophen with PAA or HPMCASPAA the best growth inhibitor but most nuclei; HPMCAS the reverse10% w/wtrasi2012a 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 growthkestur2013a R15
celecoxib with PVP and TPGSslower than PVP alone at 70–120 °C at 10% PVPmelt growthmosqueragiraldo2014 R2.b, C13
resveratrol and curcumin dispersionsPVP and E100 best for resveratrol; E100 best, PVP worst for curcuminstorage at 84% RHwegiel2013b 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 growthsato2016 R11
indomethacin α vs γ with 10% HPMCratio without/with polymer ≈2900 vs ≈2.9 at 120 °Cmelt growthtian2017 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 °C[jackson2015 R5]
ritonavir 20 µg/mL, 5 µg/mL of 15 additivesinduction 23.6 to 242.8 against 119.3 minpH 6.8, 37 °C[ilevbare2013d R12]
nifedipine γ → α, 1 mg/mL polymerγ intact ≈20 (PVP), ≈60 (HPMC), ≈110 min (HPMCAS) against ≈1325 °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 °C[xie2015 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 °C[wegiel2015 R14]

Evidence table: crystallization inhibition.

Pitfalls and disagreements

Inhibition of growth, of nucleation and of overall crystallinity need not coincide: the best growth inhibitor of acetaminophen promoted nucleation trasi2012a C46. Polymers rank differently for different drugs vaneerdenbrugh2010b C20; kestur2011 C29. No polymer property tested at low levels (Tg, melting point, molecular weight) explained the order kestur2010a C32, C34, C35. The hydrogen-bond mechanism is a rank correlation over four polymers, and the demixing step is the authors' "speculation" kestur2010a C38, C42. Film results carried over to bulk powders for six of seven drugs vaneerdenbrugh2010b C42, C43, C44. The IR ranking of the polyphenol polymers separated the best and worst but not the middle ones, and polymer content differed from 30 to 80% in the stability comparison wegiel2013a X4, X3. The same ionic contact that protected lumefantrine dispersions slowed the dissolution of the enteric polymers hiew2022a C53. A polymer that inhibits in solution does not necessarily inhibit in the hydrating solid (HPMCAS and bicalutamide; polymers predissolved with amorphous nifedipine) [moseson2021 C51; raina2014b C11]. The mixing condition fails when the dispersion has phase separated, so water-induced separation can remove the benefit of the polymer rumondor2009c C6. Celecoxib with HPMC or HPMCAS at 22 µg/mL and 5 µg/mL polymer gave induction times of about 10–13 min in one laboratory and more than 8–16 h in another [ilevbare2013c R9; xie2015 R1; xie2016a R3]. Growth and nucleation data for the same polymers are often measured at different supersaturations [ilevbare2013b X15]. A polymer that raises the crystalline solubility or lowers the onset of phase separation changes the supersaturation it is credited with (F19) [jackson2014 X9]. In the solid state, equal effectiveness holds for felodipine nucleation when dry, not for growth (polymers differed several-fold) or in humid air konno2006 C14; kestur2010a R6; konno2008 C10. After moisture-induced phase separation the PVP level stopped mattering for crystallization at 93% RH rumondor2009b C20. The mechanism (barrier at the nucleus, hydrogen-bond coupling, polymer encaged in the crystal) was argued, not measured konno2006 C40; kestur2010b C35, C42. A polymer's effects on nucleation and on growth need not agree trasi2012a C53. Equal inhibition of two polymorphs is read as action in the liquid, unlike adsorption in solution kestur2013a C6, C28. PVP slowed felodipine bulk growth about sevenfold but surface growth only twofold kestur2013b C32. A polymer can also speed growth (PHB with high-Tg compounds) sato2016 C29; the factor depends on the polymorph and on the side of the growth maximum tian2017 C37, C35; and two grades of one polymer can favour opposite enantiomers sato2015 C28. PAA, the most effective polymer for bifonazole in melt-quenched films and the best growth inhibitor for acetaminophen melts, was ineffective on acetaminophen in solution (synthesis: contrast between papers) kestur2011 C9; trasi2012a C46; trasi2015 C26. In the ASD dissolution papers the ranking depends on the drug (PVP worked for indomethacin, not for felodipine, danazol or ritonavir) [alonzo2010 C22; konno2008a R7; jackson2015 R5; ilevbare2013d R12]. Solution screens predict only the rank order, and HPMC was misranked for felodipine [konno2008a C31; jackson2015 X8]. An additive can stabilize droplet size yet promote crystallization [ilevbare2013d R14].

← Concepts and formulas

concept · as used in Physical stability

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 DSCbaird2010 R1
93 drug–solvent combinations39 class I, 23 class II, 31 class IIIspin coatingvaneerdenbrugh2010a R9
felodipineclass III (melt and solvent)both routesbaird2010 M37; vaneerdenbrugh2010a R8.ag
nifedipineclass IImelt DSC[baird2010 M32; raina2015b C12]
celecoxibclass II (melt); class III (solvent)both routesbaird2010 M26; vaneerdenbrugh2010a R8.ae
atenololclass I (melt); class III (solvent)both routesvaneerdenbrugh2010a R17
cilnidipine, nisoldipine, nitrendipineclass IIImelt DSC[raina2015b C12]
curcumin; resveratrolintermediate; rapid crystallizersolvent schemewegiel2014 R21; wegiel2013b C6
naringenin; quercetinintermediate; rapidsolvent schemewegiel2013a C19
lumefantrineclass 3melt DSCtrasi2020 R5
pretomanid, delamanidclass Imelt DSCnguyen2023a C59
nimesulide, nilutamide, celecoxibextended class II (fast growth, low nucleation)extended schemetrasi2014a C17
celecoxibslow crystallizer by the cited scheme, yet growth "quite fast"; "quite hard to nucleate"melt filmsmosqueragiraldo2014 R17, R16, R15, C7
acetaminophenforms a glass because nucleation and growth zones barely overlapDSC and hot stagetrasi2012a 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 Physical stability

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 growthtrasi2014a 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/minmarsac2006a R5, C11
propranolol against nicardipine saltspropranolol salts more prone to crystallizeamorphous salts[towler2008 C32]
dihydropyridinescilnidipine slowest, nifedipine fastest in solution; for six drugs the ranking is cilnidipine < felodipine = nisoldipine < nitrendipine = nimodipine < nifedipinesupersaturated buffer; synchrotron[raina2015b C13, C28]
nifedipine; nimodipinenifedipine a very fast crystallizer; nimodipine faster than the other four dihydropyridinesaqueous media (cited)[raina2015a R17]
felodipinerelatively slow; nifedipine 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 solubility[ilevbare2013c M1–M3, R8]
ritonavirlow tendency; drug-rich phase persists for 213 minno polymer, 24 °C[tres2018 P5, M1, C29, R20]
lopinavirdrug-rich phase lost after an induction period of 94 minno polymer, 24 °C[tres2018 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 coatingwegiel2013a C19, R7
lumefantrineclass III; melting onset 127.9 °C, Tg 19.7 °CDSC heat–cool–heathiew2022a R3
bicalutamide in pH 6.8 buffernucleation in under 30 min without polymer, under 5 min at the highest supersaturation; seeded growth near zero at 30 µg/mL, extremely rapid at 150 µg/mL37 °C[moseson2021 R3, R4]
posaconazole and bicalutamide neat meltsmelting endotherm on reheating after 1 h holds below TmDSC[moseson2020 R7]
indomethacin neat meltonly Tg after 4 h at 130–150 °CDSC[moseson2020 R7]
ritonavir and lopinaviramorphous granules unchanged for one month at 40 °C/75% RHXRPD[trasi2019 R2]
uncoated spray-dried ezetimibe–HPMCAS 50 and 70% DLcrystals by SEM at 19 and 12 daysopen dish, 40 °C/75% RHduong2022c R16, R17
uncoated ASD powders of four drug–polymer systemscrystals within about 1–2 weeks40 °C, 31–75% RHmoseson2022a R11
PCZ 100 µg/mL in FaSSIF V2, seeds 10 µg/mL, HPMCAS 0 / 3 / 9 times the drug% left at 30 min about 4.5 / 10.5 / 43.5seeded solution[shah2024 R22]
nevirapineinduction about 5 min at S 3.9 (fast without polymer)pH 6.5[hate2017 R2]
atazanavirrelatively slow; crystallization inhibited more than 4 h with enough 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 shift[raina2015b R1, R6]
nine drugs (griseofulvin, celecoxib, ezetimibe, danazol fast; telaprevir, nifedipine, nevirapine intermediate; ritonavir, atazanavir slow)induction time without polymer about 1 to 66 min100 mM phosphate pH 6.8, 37 °C; basis of the classes not given[mosqueragiraldo2018a R1, M1–M9, X11]
nifedipine vs felodipine glass0.39 vs 0.17 × 10¹⁰ m⁻³ day⁻¹; only nifedipine crystallized on heating (87 °C)22 °C; 2 °C/minmarsac2006a R4.a, R5
nifedipine vs felodipine with 25% PVP≈4.3 × 10⁵ vs ≈2.3 × 10³ m⁻³ s⁻¹75% RHmarsac2008a 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 evaporationwegiel2014 C9, C1
celecoxibgrows fast but nucleates poorlymelt filmsmosqueragiraldo2014 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–heattrasi2020 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 class[wegiel2015 R22, M1]
celecoxib, 22 µg/mL without polymercrystallization within 5 minpH 6.8, 37 °C[xie2016a C13]
lopinavirslow crystallization from aqueous solutionpH 3[li2016b C5]
delamanidinduction time 2.4 min at pH 1.6 and 10.7 min at pH 6.5 at the amorphous solubility; no glass on cooling the melt at 50 °C/min; Tg 43.3 °C37 °C[duong2022a 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 Physical stability

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 °C[tres2018 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 Physical stability

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 °C[shah2024 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 Physical stability

degree of substitution

The average number of the three hydroxyl groups of an anhydroglucose unit of cellulose that carry a given substituent (maximum 3); DS (CO2H) counts the substituents that end in a free carboxyl (adipate, suberate, sebacate) [ilevbare2012c M23–M36, P8; ilevbare2013b M11–M13]. For the cellulose ω-carboxyalkanoate esters synthesized for ASDs the adipate chain adds hydrophobicity and its terminal carboxyl ionizes at intestinal pH [ilevbare2012c C9, C10]. For telaprevir a high carboxylic acid DS worked (CAP-Adp-085 and CA-Sub-090 about 70 and 106 min at 5 µg/mL; about 472 and 500 min at 50 µg/mL) and a low one failed (CAP-Seb-024, DS 0.24, about 9 min) [mosqueragiraldo2016 R5, M13].

Findings

F8, F11, F25, F36.

Related concepts

related to polymer ionization, polymer hydrophobicity and solubility parameter.

Formulas

none (a ratio of substituents from NMR integrals).

How it is measured or obtained

From ¹H NMR for each substituent; the molecular weight by SEC (polystyrene equivalents) and Tg by DSC complete the polymer description [ilevbare2012c P8, P9, P10]. Total DS runs from 2.16 to 2.98 for the 14 esters of the ritonavir screen and from 2.38 to 2.98 for the five adipates of the pH study [ilevbare2012c M42, X2; ilevbare2012b M2–M7].

Values in the library
materialvalue or classconditionspaper ids
CAP Adp 0.85; CAB Adp 0.81; CA 320S Adp; CAP Seb 0.67; CP Adp; CAP Adp 0.33; CAB Adp 0.25DS (CO2H) 0.85; 0.81; 0.67; 0.67; 0.48; 0.33; 0.25ritonavir growth ratios 2.98; 2.70; 1.83; 0.85; 1.68; 1.64; 0.99[ilevbare2012c R11]
eight esters with DS (CO2H) 0.19–0.26growth ratios 0.83–1.015 µg/mL[ilevbare2012c R11]
CAP Adp 0.85 against 0.33; CAB Adp 0.81 against 0.25same backbone, higher DS (CO2H) gives 2.98 against 1.64 and 2.70 against 0.99ritonavir[ilevbare2012c R11]
CA 320S Sub 0.63; CA 320S Sub 0.90; CA 320S SebDS (CO2H) 0.63; 0.90; 0.57ritonavir growth ratios 10.8; 12.6; 5.7[ilevbare2013b R9, M11–M13]
CAP-Adp-085; CA-Sub-090; CAP-Seb-02470, 106, 9 min (150 µg/mL telaprevir, 5 µg/mL polymer)pH 6.8, 37 °C[mosqueragiraldo2016 R5]
A5a, A5b (carboxylated side chain on cellulose acetate)DS 0.79 and 0.67; acetyl 1.82; modelled at DS 0.50synthesized; MD model[mosqueragiraldo2018a M10, M11, X9]
ECA–ECD (ethyl cellulose ethers)ethyl DS 2.3, side-chain DS 0.69synthesized[mosqueragiraldo2018a M12–M15]
dansyl-labelled HPMCASlabel DS about 0.003 from NMR integrals; hydroxypropyl MS 0.69¹H NMR[wilson2021 R23, E2]
Pitfalls and disagreements

DS (CO2H) and the solubility parameter co-vary within each backbone series, so only two single polymers (CA 398-30 Adp, CAP Seb 0.67) separate their effects [ilevbare2012c X10]. The DS (CO2H) ranks of Table 3 are inconsistent, the Fig. 8 order is not strictly by DS (CO2H), and the outlier is named "CAB Seb 0.67" in places [ilevbare2012c X3, X4]. The total DS of CAB Adp 0.81 is 2.84 or 2.94 [ilevbare2012c X2; ilevbare2012b X6]. The size of the pH 3.8 loss does not follow DS (CO2H) in the middle of the ranking [ilevbare2012b X17]. Polymer compositions are not repeated in the nucleation paper [ilevbare2013c X15]. A5a and A5b differ in side-chain DS (0.79 against 0.58 plus 0.09 unreacted), DS(OH) and Tg as well as spacer length [mosqueragiraldo2016 X25]. The tether pair A5a and A5b also differs in side-chain DS (0.79 against 0.67), so the tether effect is not isolated [mosqueragiraldo2018a X12].

← Concepts and formulas

concept · as used in Physical stability

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/minbaird2010 R12.j
tolbutamide80.8 °CDSC cooling at 20 °C/minbaird2010 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 °Crheometerbaird2012 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 growthkestur2010b 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/mL[almeidaesousa2016 M1, R2]
acetaminophen with 10% w/w of seven polymersTm 166.7–168.6 against 169 °C; supercooling similar for allDSCtrasi2012a R9, C19
flutamide with 10 mol% polymersTm 108–110 °C; supercooling hardly changedDSCtrasi2012b R7, C33
celecoxib with TPGS and PVPTm 151.49 °C, 12 °C below the drugDSCmosqueragiraldo2014 R5.f, C18
six compounds with 1–20% PHBTm of physical mixtures 0–4 °C lower, so supercooling taken as unchangedDSCsato2016 R7, C18
indomethacin δ, α, γTm 127 (cited), 152 and 160 °CDSCtian2017 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 Physical stability

Δχ effect

Demixing of two miscible components caused by a third component, a solvent, that interacts very differently with each of them; the larger the difference between the solvent–component interaction parameters, the stronger the tendency to separate marsac2010 C36, E1; purohit2017b E4. In the library the solvent is water, the components a hydrophobic drug and a hydrophilic polymer marsac2010 C43.

Findings

F12, F13, F14, F31.

Related concepts

mechanism of moisture-induced phase separation; depends on Flory-Huggins interaction parameter; related to cosolvency and enthalpy of mixing.

Formulas

Δχ effect, multicomponent Flory-Huggins free energy of mixing.

How it is measured or obtained

From the absolute difference of the water–drug and water–polymer Flory–Huggins parameters, each obtained from water sorption marsac2010 E1, R22, E3.

Values in the library
materialvalue or classconditionspaper ids
felodipine–PVP–waterχ water–felodipine ≈3.3, water–PVP ≈0.5 (difference 2.8 by subtraction); felodipine–PVP slightly negativecited valuesmarsac2010 R22, E1
six drugs in PVP–waterseparating drugs had water–drug χ 2.84–3.58, non-separating 2.50–2.7125 °C sorptionrumondor2009c R24, C46
ritonavir with PVP, PVPVA, HPMCAS (outside)larger Δχ, higher tendency to phase separation (argument)stated in wordspurohit2017b E4, C43
loratadine-type ASDs (outside)separation predicted when the difference is large even if drug–polymer χ is negativeargumentyang2021 E2
miconazole–PVPVA 50:50no separation dry at 100 °C; separation with water during casting, storage and immersion, read as a water-driven change of the thermodynamics ("evidence is provided")films and powderssaboo2017 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 Physical stability

desupersaturation

The fall of the dissolved concentration after supersaturation was reached, because crystals nucleate or seeds grow; in an ASD it "corresponds to the crystal growth rate exceeding the dissolution rate" [moseson2020a C14]. A plateau is not the same as a fall: a crystal-free bicalutamide dispersion that stayed at about 18 µg/mL (30 µg/mL dose) without desupersaturation was read as crystallisation inside the dissolving solid, which caps the concentration without lowering it afterwards [moseson2021 C17, R14]. In the posaconazole pH-shift test the concentration falls below the LLPS concentration (about 19 µg/mL in the intestinal medium) when crystals present or newly formed consume the supersaturation; this is not a return to the crystalline solubility of 1.2 µg/mL [shah2024 R11, X15]. New aspect (Bioperformance): the loss of supersaturation, mostly by crystallization from solution or in the matrix; its onset is read from a concentration fall [elkhabaz2017 C19, C23]. In dissolution of enzalutamide–PVPVA dispersions and tacrolimus capsules the fall after the maximum was read as crystallization, from seeds in the product or formed in the medium; absorption lowers the donor too [wilson2018 C18; purohit2019 C17, C34; hate2019 C20, C30]. New aspect (Crystallization from solution): with seed crystals present it reflects growth of the seeds; without seeds the crystals must first nucleate, so the profile has a flat start (the induction time) followed by a fall [alonzo2012 P4, P5; ilevbare2013c R7]. New aspect (Supersaturation from ASD dissolution): the fall of the concentration after a dissolving amorphous solid or dispersion has supersaturated the medium, read as crystallization from solution, sometimes together with crystallization of the remaining solid [alonzo2010 C16, C21; jackson2015 C14].

Findings

ASD process: F25, F26, F27, F28, F38, F39, F40, F41, F46. Bioperformance: F9, F10, F11, F12, F14, F16, F23, F28, F29, F30. Crystallization from solution: F4, F5, F14, F20, F23, F24, F27, F33, F42. Supersaturation from ASD dissolution: F4, F5, F6, F15, F16, F20, F22, F26, F28.

Related concepts

read in non-sink dissolution; driven by crystal seeding; slowed by crystal growth inhibition; contrasts with matrix crystallization. Loss of supersaturation; caused by solution crystallization and secondary nucleation; also lowered by an absorptive sink; driven by crystal growth rate and nucleation induction time; summarized by supersaturation factor; related to residual crystallinity.

Formulas

power-law crystal growth rate, initial growth rate from the desupersaturation slope, supersaturation factor, supersaturation ratio, overall mass crystal growth rate.

How it is measured or obtained

From the concentration–time profile after the maximum, or from seeded runs: 50 µg/mL indomethacin made by antisolvent addition and 10–50 µg/mL bulk seeds added, with the growth rate R_G in µg/s taken from the profile (extraction method not printed) [moseson2020a P10, P20, X12]. In the Bioperformance papers: concentration–time profiles, UV at 233 and 350 nm for induction time, with SHG or PLM to confirm crystals [elkhabaz2017 P5, P8, P10]. In the crystallization-from-solution papers: concentration against time by a fibre-optic UV probe on second-derivative spectra (every 2–5 s), in seeded runs (slope of the first 2–5 min as initial growth rate) and unseeded runs (flat start, then fall); light-scattering extinction and pyrene fluorescence give the matching signals for droplets and crystals [alonzo2012 P3; ilevbare2012a P8; jackson2014 R15]. In the ASD dissolution papers: in situ UV during non-sink dissolution or after a solvent shift; a rise of the pyrene ratio confirms loss of the drug-rich phase [konno2008a P5; alonzo2010 P3, P4; jackson2015 P2, P3]; drug in the filtered liquid of suspensions [chen2015a P11].

Values in the library
materialvalue or classconditionspaper ids
IDM, 50 µg/mL, no polymerunseeded about 50 → 25.6 µg/mL at 120 min; with 50 µg/mL seeds about 26.9pH 4.5, 37 °C[moseson2020a R3.a, R3.d]
IDM, 50 µg/mL, 5 µg/mL PVPVA, 50 µg/mL seedsabout 50 → 37.1 µg/mL in 720 minsame[moseson2020a R3.h, X6]
IDM–PVPVA extrudatesslight fall after the peak above 3% crystallinity (131-2 about 40.6 → 39.4; 117-2 about 30.9 → 28.8)50 µg/mL total dose[moseson2020a R6]
BCL–PVPVA S/155 and M/155about 32.4 → 24.5 and about 28.2 → 16.2 µg/mL150 µg/mL dose, 4 h[moseson2021 R12]
paclitaxel–HPMCAS with 18 wt% seeds (outside)desupersaturation by crystal growth; HPMCAS cannot block it completely16 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/mL[shah2024 R12, R14]
PCZ–HPMCAS 25% DL, 3.2% crystals against nonecrystallization after 45 min against about 1.5 hsame[shah2024 R15, C29]
BCL–PVPVA 30% DL, 3% SDS, cryomilled 5 minpeak about 84% at 45–60 min, then about 78% (about 23 µg/mL)dose of at most 30 µg/mL[moseson2022b R10]
PCZ 20 µg/mL in FaSSIF V2, HPMCAS 0 / 9 times the drug; seeds 0 / 5 / 10 µg/mL% left at 30 min about 66 / 46.5 / 25; about 99.5 / 96 / 74.5seeded solution[shah2024 R22]
ezetimibe PVP ASD, FeSSIF195 µg/mL at 15 min to 41 at 30 min37 °C[elkhabaz2017 R14]
ezetimibe ASDs, bufferdecline after about 30 min[elkhabaz2017 R10, C19]
tacrolimus generic, 100 mLabout 98% released at 20–30 min, 39.5% at 120 minmedium 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 6.5[wilson2018 R6, C18]
tacrolimus, seeded solutionsrate about 0.39 at 50 µg/mL against 0.075 at 20 µg/mL; growth order 1.677seeds from the crystallized 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 °C[jackson2014 R15]
celecoxib, HPMC, start S 14.7S 15 for 15 min, 7.8 at 35 min, 4.9 at 100 min, 4.3 at 200–240 min37 °C[ilevbare2013c R16]
paclitaxel with 18 wt% seeds (ASD dissolution chapter)desupersaturation immediate without polymer37 °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 polymertrasi2015 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 °C[alonzo2011 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 °C[jackson2015 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 °C[chen2015a 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 °C[xie2016a 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 °C[elkhabaz2019a R6, R12]
praziquantel–HPMC E5 LV dispersions, 1.5 mg/mLa 30% drop in FaSSIF after about 75–82%; R-enantiomer lost dissolved drug in every medium37 °C[alvarenga2025 R14, C36]
Pitfalls and disagreements

Growth rates are vessel mass rates, not normalised to seed area [moseson2020a X12]. In the bicalutamide tests the desupersaturation at 150 µg/mL is attributed to growth from solution, whereas the overall low plateau is attributed to growth in the solid [moseson2021 C21, C46, X4]. The IDM extrudates may have lost concentration by growth into the surrounding amorphous solid rather than from solution [moseson2020a X15]. In the posaconazole test the focused beam reflectance signature read as secondary nucleation for the crystal-containing 25% dispersion has the same form as the one read as primary nucleation for the crystal-free one [shah2024 K3, K4, X14]. For bicalutamide with cryomilled surfactant powders the loss is attributed to nuclei in the milled matrix and was not measured [moseson2022b C26]. In the Bioperformance papers concentration alone cannot separate LLPS from crystallization in turbid media [elkhabaz2017 C30]. Absorption also lowers the donor (F14). With an absorptive sink the fresh generic tacrolimus did not lose supersaturation at 240, 100 or 40 mL, unlike in a closed vessel; only at 40 mL did total dissolved drug fall for the 20% sample (F14, F28) hate2019 R11, C20, C35. Apparent UV concentration of a colloidal solution is distorted by droplet size changes: at 20 µg/mL danazol the early fall is attributed to droplet coalescence, not crystallization, and orthogonal methods are needed [jackson2014 C29, C54, C55]. The seeded profile includes any secondary nucleation [ilevbare2012b X18]. After crystallization with HPMC the celecoxib solution sat at S 4.3, not 1, at 240 min [ilevbare2013c R16]. In the ASD dissolution papers apparent UV falls above the amorphous solubility can come from particle growth or settling as well as from crystallization [alonzo2011 C14; jackson2015 C12]. With HPMC the felodipine solution kept falling slowly; the PVP and buffer solutions approached but did not reach the crystalline solubility in 4 h konno2008a X10. After crystallization the celecoxib readings settled at ≈2.6–2.9 µg/mL, above the 1.5 µg/mL crystalline solubility measured by HPLC [xie2016a X4]. With crystals present from the start, the onset of desupersaturation marks the time at which growth outpaces redissolution of amorphous material, not the onset of crystallization [elkhabaz2019a C49].

← Concepts and formulas

concept · as used in Physical stability

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 scrambling[indulkar2017b 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 surfaceargument[indulkar2019a 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 Physical stability

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 filmskestur2010b 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 °Ckestur2013a 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 filmssato2016 E2, C15
low-Tg compounds with PHBretardation attributed to PHB chains impeding transport to the crystal ("most likely")melt filmssato2016 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 Physical stability

dilution effect

Slowing of crystallization simply because the polymer dilutes the drug, which would scale directly with the polymer volume fraction konno2006 C36, C37.

Findings

F1, F4, F18.

Related concepts

alternative to kinetic barrier to nucleation; related to crystallization inhibition by polymers.

Formulas

none.

How it is measured or obtained

By comparing the measured reduction in nucleation rate with the reduction expected from the polymer fraction alone konno2006 C37.

Values in the library
materialvalue or classconditionspaper ids
felodipine with 3% w/w polymernucleation ≈1.5 orders of magnitude lower, far more than a 3% dilution: dilution rejecteddry films, 22 °Ckonno2006 R4, C13, C37
flutamide with 10 mol% polymersequal dilution at equal drug:repeat-unit ratiomolar seriestrasi2012b C32
flutamide with nilutamidegrowth effect "can be explained" by dilution plus a higher Tg (curve not shown)melt growthtrasi2012b C42, X11
celecoxib with PVP K29/32 vs PVPVAless drug hydrogen-bonded with PVPVA at equal loading, "presumably" from dilution of the vinylpyrrolidone units; growth faster with PVPVAIR; melt growthxie2016b C13, C37

Evidence table: dilution effect.

Pitfalls and disagreements

The text supporting the rejection cites Fig. 9, which shows infrared spectra; the nucleation rates are in Fig. 4 konno2006 X1.

← Concepts and formulas

concept · as used in Physical stability

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; FTIRmarsac2009 R12.h, R14
nifedipine; felodipine; sucrose9.58; 5.30; 5.40 DDFTmarsac2009 R12.a, R12.b, R12.d
indomethacin; ibuprofen; vinyl pyrrolidone2.68; 1.76; 3.91 DDFTmarsac2009 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 Physical stability

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 rpm[ueda2020b R7]
danazol aloneabout 490 nm at once; about 9800 nm at 1 h25 °C, above the onset[jackson2014 R22]
with PVPabout 240–250 nm to 1 h; about 2900 nm at 2 h10 µg/mL polymer[jackson2014 R22]
with HPMC; HPMC-ASabout 305–345 nm to 2 h and 820 nm at 4 h; about 230–250 nm to 4 h and 1250 nm at 6 hsame[jackson2014 R22]
ritonavir nanodroplets (ASD dissolution chapter)stabilized against coalescence "likely" by charge repulsion between adsorbed polymers37 °C[ilevbare2013d C38]
danazol droplets, PVP, HPMC, HPMC-ASDLS z-diameter about 350 → 103–136 nm; NTA 181–270 nm1–1000 µg/mL, 25 °C[jackson2016 R19, R21]
Pitfalls and disagreements

Coalescence itself was not observed; size growth is read as its sign ilevbare2013a C18. Droplet size also differs with the technique and the drug (about 116–387 nm for the weak bases) [indulkar2015 R14]. For danazol no droplet size was measured in the first minutes for the drug alone: the DLS points are 0 and 1 h, the second after crystallization (induction 6–10 min), so coalescence is inferred from the UV signal [jackson2014 X6]. The danazol concentration for DLS is not printed [jackson2014 X11]. Time after supersaturation and drug level of the 2016 measurement are not stated [jackson2016 X12].

← Concepts and formulas

concept · as used in Physical stability

drug–drug miscibility

Mixing of two drugs in one amorphous phase; it makes a mixed drug-rich phase when both dissolve [alhalaweh2016 C9, C26]. A crystalline drug can also enter an amorphous drug-rich phase from solution: darunavir partitioned into the atazanavir-rich phase in water although the dry amorphous drugs were phase separated [alkalla2026 C4, C5, C30, C31].

Findings

F6, F20.

Related concepts

lowers amorphous solubility through the drug-rich phase; related to Fox equation.

Formulas

ideal-mixing reduction of amorphous solubility.

How it is measured or obtained

Melting-point depression of the crystalline drug by the amorphous second drug and one Tg of the melt-quenched mixture [alhalaweh2016 P7, P8].

Values in the library
materialvalue or classconditionspaper ids
ritonavir with atazanavirmelting onset 394.4 K to about 380.1 K at x_ATV 0.52; one Tg 349–323 KDSC[alhalaweh2016 R8, R9]
ritonavir with lopinavirliquid-state miscibility; one Tg in every mixture[trasi2015a C41; trasi2015b R2, C39]
atazanavir with darunavir, dry amorphous mixturestwo Tgs in every mixture (neat 105 and 62 °C); heterogeneous co-melt-quenched film with nanoTA softening at 118 ± 4 and 92 ± 2 °CDSC, nanoTA[alkalla2026 R15, R16, R17, C30, C31]
atazanavir with darunavir in waterdarunavir enters the atazanavir-rich phase; atazanavir's amorphous solubility falls as the darunavir fraction of the phase risesantisolvent, 150 µg/mL atazanavir, pH 6.8[alkalla2026 R11, C4, C39]
Pitfalls and disagreements

Only miscible, structurally similar drugs were tested; immiscible pairs are outside the evidence [alhalaweh2016 C40]. Miscibility in water and immiscibility in the dry state differ, the mixing in water is inferred from supernatant depletion, and the plotted mole fraction has no printed calculation (F20) [alkalla2026 X5, X6].

← Concepts and formulas

concept · as used in Physical stability

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 6.8[mosqueragiraldo2018b 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 6.5[wilson2018 R6]
enzalutamide in CPHPC-106 10:90 / 50:50AUC0–inf 516 / 305 µg·h/mL; mass flow about 0.53 / 0.49 µg/minrats, 50 mg/kg[wilson2020 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)calculated[hiew2025 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 Physical stability

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 °C[alonzo2011 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 6.0[bapat2024 R11]
crystalline resveratrol in 20 mg/mL PVP709, 1610, 1193, 706, 99 µg/mL at 658–11,037 µg/mL added; amorphous drug–PVP precipitatepH 6.8, 37 °C, 24 h[wegiel2015 R6, R7]
resveratrol–HPMCAS 15:85up to ≈1610 µg/mL with flux at most about twice the crystal'spH 6.8, 37 °C[wegiel2015 R19, R20]
PHPH; MePHPH with 1 mg/mL PVPVAamorphous solubility 200 → 27.5; 2.81 → 4.40 µg/mLUV extinctiondeac2023b R1
PHPH, TIPP, MeTIPP, MePHPH nanoparticles≈77, 36.5, 9, 5 wt% PVPVA60 °C, NMRdeac2023b R3
eight drugs with HPMCAS-MF, 1:1 drug:COOH5 / 7 / 15 / 17 / 60 / 70 / 90% (IND / INDester / RTV / CIL / PHPH / LOR / CNZ)pH 6.0 spike test[bapat2024 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 Physical stability

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 nonetaylor1997 C35, C26, C37
felodipine–PVP, nifedipine–PVPone phase over 10–90% and 25–70% PVP; hydrogen bonding "presumably" behind the second PCIR, PXRDrumondor2009a C38, C20
felodipine–PAAlittle mixing at 30–70% PAA; competition from PAA self-association "speculated"DSC, IR, PXRDrumondor2009a C44, C45
ketoconazole–PVPnear-athermal mixing, no carbonyl shift; dipole–dipole forces "speculated"melting, FTIRmarsac2009 C40, C41, R12.h
felodipine with PVP, PVP/VA, HPMCAS, PVAcstrength PVP > PVP/VA > HPMCAS ≥ PVAcNH shifts at 50 wt% polymerkestur2010a C26, R9
nimesulide with PVP, PVP/VA, PVAcpresent but small; limited by the intramolecular bondIR, 20–50 wt% polymerkestur2011 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 pairsmarsac2009 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, filmswegiel2013a R2, R4, R6
lumefantrine with enteric polymers and PVPVAprotonated 19–55% with HPMCAS, HPMCP, CAP, Eudragit L 100; 0% with PVPVAXPS, 25% drug loadinghiew2022a R20
clotrimazole, loratadine, brotrimazole, Me-DIBF with PVPVAhalogen bond: K_F 0.56–1.11 M⁻¹, carbonyl shift 2–6 cm⁻¹NMR, IR[que2020 R12, R11]
15 drugs, 7 polymerscomplementary donor and acceptor groups give the highest amorphicity indexspin-coated filmsvaneerdenbrugh2011a 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 Physical stability

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 χmarsac2009 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 misciblecitedmarsac2009 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, PXRDrumondor2009a C44, C46
ketoconazole–PVP"suspected" partially miscible, one phase at higher PVP onlyone Tg; IR; PXRDrumondor2009a C40, X1
nifedipine–PVP K29/32predicted miscible at all compositions from χ −3.8Flory–Hugginsmarsac2006b 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; mDSCpurohit2015a C36, R7
telaprevir with HPMC, PVPVA, HPMCASdomains from 10% drug (HPMC, PVPVA); from about 30–40% (HPMCAS)AFM, AFM-IR, nanoTA, LCRli2016c C17, C52
dextran–PVP, 20 pairsmiscible at all compositions for 783 Da maltodextrin; phase separated at all nine for DEX450–PVP90DSC, FTIR[vaneerdenbrugh2012a R13, R14]
probucol–PVP K30 50:50single Tg, "seemed" one-phase; carbonyl shiftsolvent, moulded[broman2001 R4, R5, C14]
ECP–HPMC / PVPVAmiscible over 10–90% DL when dry18% RHli2017 R3.a, C33
ITZ–HPMCthermodynamically miscible when dry, trapped as two phases when wet ("suggest")7% RH vs 20–40% RHmugheirbi2017 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 Physical stability

drug-polymer-water miscibility

Evidence table: drug-polymer-water miscibility. Content from the release-mechanism chapter (2017–2025).

Whether drug and polymer stay mixed once water enters the dispersion. Indulkar and co-workers (2017) state that AAPS depends on drug–polymer miscibility in the presence of water, set by the balance of drug, polymer and water interactions, and varies with drug, polymer type and composition; drug–PVPVA dispersions that dissolve rapidly while staying miscible in water "are expected" to form nanospecies by dissolution followed by LLPS [indulkar2017b C38]. Saboo and co-workers (2020) add that water can impair the miscibility of a dispersion on hydration, which "is expected" to harm dissolution [saboo2020a C39]. In the Flory–Huggins description a hydrophobic drug and a hydrophilic polymer interact very differently with water, which drives separation purohit2017b C43. Measured in 2023 as the water content at which 30% ritonavir–PVPVA films separated within 12 h: 14.0% without surfactant, 24.5% with SDS, 10.5–16.0% with Span 20, Span 85 or Tween 80; the authors read the SDS shift as a larger miscible region ("suggesting"), "likely responsible" for its better release yang2023 R21, C9, C10.

Findings

Release mechanism and LoC: F5, F8, F31.

Related concepts

lost through amorphous-amorphous phase separation; expressed by the Flory-Huggins interaction parameter and the Δχ effect; its loss in time is phase separation kinetics.

Formulas

multicomponent Flory-Huggins free energy of mixing, Δχ effect.

How it is measured or obtained

From films or powders exposed to water or high humidity, imaged by fluorescence or tested by DSC (see amorphous-amorphous phase separation) [purohit2017b R3, R6; saboo2020a R23].

Values in the library
materialvalue or classconditionspaper ids
ritonavir–HPMCASmiscible after 97% RH; PVP and PVPVA dispersions separatedfilms and powderspurohit2017b C1
felodipine 30% with HPMCAS, EUDS; PVP, PVPVA, HPMCuniform; separated97% RH, 24 h[saboo2020a 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 Physical stability

drug-rich barrier layer

Evidence table: drug-rich barrier layer. Content from the release-mechanism chapter (2019–2025).

A drug-rich layer at the dissolution front that blocks release of the drug and of the polymer beneath it. Que and co-workers (2019) take the idea from studies of polyphase mixtures, in which phase segregation at the dissolution front forms a barrier layer (cited), and state for ledipasvir–PVPVA above the limit of congruency that "it appears" the drug-rich layer acts as a physical barrier that stops further release of drug and even of water-soluble PVPVA, leading to swelling [que2019 C5, C32]. Saboo and co-workers (2020) describe surface drug enrichment of hydrophilic-polymer dispersions as "a physical barrier to polymer release from subsurface layers" [saboo2020a C42]. Hiew and Taylor (2022) use it for the release plateau after about 30 min ("could be attributed") and argue that drug and polymer leave together as long as separated drug cannot form a continuous barrier [hiew2022b C16, C46]; for clopidogrel, separation leaving a continuous or semi-continuous drug-rich barrier "is linked to" poor release correasoto2022a C53. In dissolving ritonavir–PVPVA compacts the drug-rich coating impedes polymer dissolution as a barrier to water penetration and "may" also be a physical barrier to polymer release when water penetrates yang2022a C55. The water-poor hydrophobic phase is expected to become more viscous and, once connected and anchored to the gel layer, to persist at the interface as an insoluble barrier, porous in top view deac2023a C56, C57. Above the limit the compact surface evolves toward the hydrophobic binodal composition measured under dilute conditions and is in pseudo-equilibrium with the aqueous phase deac2023b C59, C3. The 2023 surfactant study found every ritonavir–PVPVA–surfactant dispersion with a persistent continuous drug-rich layer releasing minimal drug: Span 20 at 40% carried a layer of about 50–100 µm from 5 min, through whose pores polymer but not drug left, and Span 85 at 40% a thick layer that released neither yang2023 R7, R9, C15, C19, C40. A layer that formed in situ on 30% Span 85 compacts was removed by agitation and did not block release yang2023 R8.

Findings

Release mechanism and LoC: F7, F20, F22, F25, F26, F27, F31.

Related concepts

part of the drug-rich surface layer; formed by surface drug enrichment; found above the limit of congruency; its formation depends on phase separation morphology.

Formulas

none.

How it is measured or obtained

Not measured as a barrier: inferred from surface composition by XPS, from micro-CT of dried tablets and from suppressed polymer release [que2019 R15, R13, R11, X22].

Values in the library
materialvalue or classconditionspaper ids
ledipasvir–PVPVA 20%≈2% of the polymer released in 10 min while surface drug rose to ≈54 wt%pH 6.8, 37 °C[que2019 R11, R15, C36]
felodipine–PVPVA 15 → 20–30%polymer rate ≈1.9 → ≈0.14–0.19 mg/min/cm²same[saboo2020a R14]
felodipine–PVP and –HPMC across the limitPVP about halved; HPMC not reducedsame[saboo2020a X15]
lumefantrine benzoate 20%, tosylate 10%plateau after ≈30 min at ≈58–60% releasedcompacts, 37 °C[hiew2022b R10, C16]
clopidogrel–PVPVA 50, 60%bicontinuous and drug-continuous films; ≈52 and 7% releasedfilms 5 min at 100% RH; compactscorreasoto2022a R20, R17
ritonavir–PVPVA 30%; 40%continuous porous drug-rich layer at the gel–solution interface; rigid layer ≈12 µmreal-time confocal, pH 6.8yang2022a R6, R12, R13
MePHPH–PVPVA 50%; PHPH–PVPVA 20%porous continuous drug-rich phase on the surfacesurfaces after 2–20 mindeac2023a R9, R10, C57
PHPH–PVPVA 15, 50%; MePHPH–PVPVA 50% compactssurface drug content moves toward the hydrophobic binodal compositionATR-FTIR of dried surfaces, 0–60 mindeac2023b R6, R7, C59
ritonavir–PVPVA + Span 20, 40%layer ≈50–100 µm from 5 min; drug ≈8%, polymer ≈78% at 90 minconfocal cross-sections; compactsyang2023 R7, R2, R3
ritonavir–PVPVA + Span 85, 30%layer formed, swept away and re-formed in situ; ≈86% released under rotationin situ confocal; compactsyang2023 R8, R2
Pitfalls and disagreements

The barrier function itself, its composition over time and its permeability were not measured [que2019 X22]. Suppression of polymer release above the limit is polymer-specific [saboo2020a X15]. Whether plasticizers act on barrier formation was not tested; the authors call for a more in-depth evaluation correasoto2023 C32. Persistence depends on the shear: the same Span 85 dispersion formed a layer in a quiet chamber and none under rotation yang2023 C16, R8.

← Concepts and formulas

concept · as used in Physical stability

drug-rich nanodroplets

The dispersed drug-rich phase formed by LLPS, usually of 100–300 nm, which dissolves fast and is expected to replenish absorbed drug [indulkar2016 C4, C25]. Droplets are too large to cross the 3–4 nm (regenerated cellulose, 12–14 kDa) or 15 nm (hollow fibre) pores of the membranes used [indulkar2016 C11; hate2018 C52]. In enzalutamide dispersions the same species is called amorphous aggregates, about 100 nm; in simulated and pooled human intestinal fluids spheres of 0.1–0.5 µm were found [wilson2018 R11, C45; elkhabaz2019b R4, C19, C24]. New aspect (Supersaturation from ASD dissolution): fast-releasing dispersions put drug above the amorphous solubility into a submicron colloid within minutes, and additives decide its size and how soon it crystallizes [ilevbare2013d C59, C60; jackson2015 C29]. New aspect (Release mechanism and LoC): from dissolving dispersions, nanodroplets formed only where release was congruent or close to congruent, so that the drug concentration exceeded the amorphous solubility [purohit2017b C52; indulkar2019a C5; saboo2019 C30]. The 2017 isotope study concludes that they form from drug that has first dissolved, followed by LLPS ("strongly suggest"), not by release of drug-rich domains from the hydrated matrix [indulkar2017b C26]; Purohit and Taylor reach the same reading for ritonavir films ("likely") purohit2017b C57. When drug release is controlled by polymer dissolution, colloid formation is "highly dependent" on drug loading [que2019 C55]. Their size and life after release depend on the drug, the polymer and small amounts of surfactant: HPMCAS kept elbasvir and loratadine droplets small, and SDS, TPGS or Tween 80 at 4–50 µg/mL kept clopidogrel droplets stable for 4 h while CTAB agglomerated them yang2021 C4; correasoto2022a C12, C38. Built into ritonavir–PVPVA at 30%, the Spans kept the released droplets near 1 µm, while TPGS and Tween 80 let them grow to several micrometres, which the authors suggest "could possibly" come from these surfactants partitioning into the droplets and lowering their Tg [indulkar2022 C47, C48]. In dissolving ritonavir–PVPVA compacts at 10 and 20% droplets formed near the gel–solution interface and entered the solution with the dissolving polymer, which the authors explain by a water content needed to cross the binodal yang2022a C34, C35, R10, R11.

Findings

Bioperformance: F5, F8, F15, F19, F22, F23. Supersaturation from ASD dissolution: F8, F9, F12, F13. Release mechanism and LoC: F4, F5, F12, F13, F16, F25, F27.

Related concepts

produced by liquid-liquid phase separation; act as nanodroplet reservoir effect; part of the drug-rich phase; related to droplet coalescence and particle absorption of light; form under congruent release above the amorphous solubility. Coarsen by drug-rich phase coarsening.

Formulas

Stokes-Einstein equation.

How it is measured or obtained

NTA (scattering or fluorescence mode with Nile red), DLS, the 369 nm band of atazanavir [indulkar2016 P4; hate2018 P3, P4, P6]. Nile Red fluorescence of the pellet against aggregate mass, and DLS [wilson2018 R8, R11]; SEM of a centrifuged pellet with the drug's own fluorescence in human fluid [elkhabaz2019b R3, R4]; Z-average by DLS under agitation [ueda2020a R5, R6]; size and zeta potential with polymer or surfactant additives [hate2022 R17]. In the ASD dissolution papers: light scattering in a flow-through cell, nanoparticle tracking of samples or 0.45 µm filtrates, SEM of dried samples [ilevbare2013d P3, P8; jackson2015 P5; trasi2015b P8]. In the release-mechanism papers: NTA, DLS, visible turbidity, environment-sensitive probes in solution and free drug after ultracentrifugation [indulkar2017b R6, R7; purohit2017b R7, R8; indulkar2019a R9; que2019 R5, R12; saboo2019 R11, R12].

Values in the library
materialvalue or classconditionspaper ids
clotrimazole111 / 223 / 246 / 257 nm at 8 / 10 / 15 / 20 µg/mL; 1.2 × 10⁸ to 12.5 × 10⁸ per mLpH 8, NTA[indulkar2016 R4]
atazanavir, solvent shift204–226 nm, PDI 0.08–0.15100–500 µg/mL, 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)NTA[tres2018 R18]
enzalutamide 10:90 and 50:50 copovidone ASDsabout 100 nm; about 50 against about 3 µg/mL of 100 as aggregatespH 6.5, 1 h dissolution[wilson2018 R10, R11]
atazanavir, posaconazole in pooled human fluidspheres of 0.1–0.5 µm, no needlesSEM of pellet, 100 µg/mL HPMC-AS[elkhabaz2019b R4]
atazanavir, clozapine with HPMCAS-LF and -HFAS-LF droplets below 300 nm over 3 h; AS-HF kept the initial size; clozapine about 100 nm (AS-HF) against 250 (AS-LF)300 rpm, 37 °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 °C[ilevbare2013d R1, R5]
ritonavir 20 µg/mL with 5 µg/mL CAAdP 0.33210−214 nm before crystallizationsolvent shift[ilevbare2013d R12]
danazol 90:10 dispersions246–284 nm25 °C[jackson2015 R6]
ritonavir; ritonavir + lopinavir, HPMCAS dispersionsabout 500 nm; about 160 nm in 0.45 µm filtrates1 h[trasi2015b R7]
felodipine 90:10 HPMC dispersion≈185 → ≈300 nm, read as crystalline25 °C[alonzo2011 R8, C33]
nifedipine 10, 20% with HPMC-E5 or PVPVA≈190–222 nmNTA, 5 °C, D2O[indulkar2017b R7]
ritonavir 10:90 films with PVPVA, HPMCAS, PVP200, 250, 315 nmNTA, fresh filmspurohit2017b R8
ritonavir–PVPVA 10% tablet218 ± 15 nm; media of 10–25% turbidDLS at 30 min[indulkar2019a 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 minsaboo2021 R17
elbasvir 2.5%; loratadine 10%PVPVA ≈670 → 1190; ≈820 → 2120 nm; HPMCAS ≈280 → 390; ≈420 → 570 nmDLS, 60 minyang2021 R3, R6
clopidogrel≈520 nm in buffer; stable with SDS, TPGS or Tween 80; ≈12-fold growth with CTABDLS, 4 hcorreasoto2022a R5, R6
four phenolphthalein analogues179–364 nmDLS, 30 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 release[indulkar2022 R11, R13]
plasticized dispersions (systems not specified)500–1500 nm after 90 minDLScorreasoto2023 R5
MePHPH–PVPVA 5–30%; PHPH–PVPVA 5%nanoparticles formed within the gel; onset 601 ± 68 µm beyond the 356 ± 18 µm gelin situ confocaldeac2023a C27, R8, C31
drug-rich phase released from 30% MePHPH; from 5% PHPH98.8 against 26.2 wt% drug; Tg 16.8 against −5.8 °CHPLC, DSCdeac2023a R12
PHPH; MePHPH nanoparticles with PVPVAPVPVA 71.4–78.0; 0.5–7.5 wt%37 °C, two preparation routesdeac2023b R2
Pitfalls and disagreements

The size is quoted as 110, 200, 220 or 250 nm in one paper [indulkar2016 X9]. Size depends on polymer and agglomeration [hate2018 C26, C27]. Counts stop at 150 µg/mL in the atazanavir study [hate2018 X10]. The enzalutamide aggregate amounts come from a Nile Red calibration, and the aggregate-rich ASD also dissolved fastest and left less solid in the dosed suspension (F23) [wilson2018 R8, X13, X14]. Size fell with polymer concentration and was smaller with AS-HF (F19) [ueda2020a C18]; in a PAMPA cell the polymer or surfactant type, not the size, shaped the transport gain (F22) [hate2022 R17]. Droplets pass 0.45 µm filters [trasi2015b C22]. Sizes depend on method (SEM of dried samples against DLS) and medium [ilevbare2013d X12, R9]. Whether the felodipine particles were droplets or crystals was not measured directly [alonzo2011 X7]. Nanodroplets of ritonavir tablets at 20–30% are inferred from turbidity and concentration, not sized [indulkar2019a X5]. The link between congruency and droplets partly follows from the amount of drug released by the sampling time [saboo2019 X14]. The larger cilnidipine droplets at higher loading "could indicate" lower stability or a different formation route [saboo2019 C19]. The slow-exchange premise of the isotope test was shown with solvent-made droplets only [indulkar2017b X5].

← Concepts and formulas

concept · as used in Physical stability

drug-rich phase coarsening

Evidence table: drug-rich phase coarsening. Content from the release-mechanism chapter (2021–2023), with rows from the Bioperformance chapter.

The growth of a separated drug-rich phase into fewer, larger domains or droplets after it has formed, in the hydrated dispersion or in the medium. In solution, clopidogrel nanodroplets grew in buffer, which the authors attribute to the high interfacial energy of the lipophilic drug-rich phase correasoto2022a C37, R6; surfactants "in general" slowed the coarsening of drug-rich nanodroplets formed by LLPS, CTAB excepted, at very low concentrations correasoto2022a C38. In the hydrated dispersion, persistent discrete drug-rich domains with 5 and 10% TPGS "can be rationalized" by TPGS lowering the interfacial energy between the phases and so reducing coarsening, so that the domains can be released intact as the gel layer recedes saboo2021 C40; rapid coarsening without surfactant is "a feasible explanation" for the loss of release saboo2021 C50. In the 40% MePHPH gel heterogeneous domains turned homogeneous between 2 and 20 min, "likely" by movement and coalescence into large domains deac2023a C38, C34.

Findings

Release mechanism and LoC: F16, F20, F25.

Related concepts

acts on drug-rich nanodroplets and on the phase separation morphology of the hydrated dispersion; follows amorphous-amorphous phase separation; slowed by surfactants with surfactant partitioning into the drug-rich phase or at the droplet surface.

Formulas

none.

How it is measured or obtained

Z-average and PDI of droplets by DLS against time, as ratios to the initial value correasoto2022a R6 or at 90 min of dispersion dissolution correasoto2022a R19; in the hydrated dispersion inferred from the morphology of humidified films saboo2021 C51, R21.

Values in the library
materialvalue or classconditionspaper ids
clopidogrel nanodroplets in buffer; with 50 µg/mL CTABZ-average ratio ≈1.5 at 1 h and ≈12 at 2 h; ≈12 at 1 h37 °C, DLScorreasoto2022a R6
clopidogrel nanodroplets with 50 µg/mL SDS, 4 µg/mL TPGS, 5 µg/mL Tween 80Z-average ratio ≈0.92–1.01, ≈0.96–0.99, ≈0.81–0.89 over 4 hsamecorreasoto2022a R6
clopidogrel–PVPVA 40%; 50%, binary and with Tween 80, TPGS, SDS≈790, ≈510, ≈580, ≈690 nm; ≈1960, ≈780, ≈890, ≈1260 nm90 min of dissolutioncorreasoto2022a R19
atazanavir- and clozapine-rich droplets with pre-dissolved HPMCAS-LF; -HF (Bioperformance chapter)grew slightly early and stayed below 300 nm; kept their initial size3 h agitation, 37 °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 Physical stability

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 min[tres2018 R18]
lopinavir, 10% dispersion294.3 ± 67.7 nmsame[tres2018 R18]
ritonavir 30 µg/mL≈360 nmDLS, antisolvent[trasi2015a R15]
ritonavir–HPMCAS dispersion≈500 nmNTA of 0.45 µm filtrate, 1 h[trasi2015b R7]
tacrolimus, 60 µg/mL≈220 nm, a second phaseNTA of 0.7 µm filtrate, pH 4.5, 37 °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 °C[ueda2020b R5]
felodipine aggregatesτ2 ≈1.87–2.04 ns, share a2 14–39%24–38 µM, pH 7.4, HPMC 100 µg/mL[tres2017 R1.d–f]
clotrimazole; efavirenz drug-rich phasesPRODAN second band ≈435 and ≈450 nm; τ2 up to 3.40 and 3.89 nspH 7.4[tres2017 P1, R13, R10, R11]
ritonavir pellet94.85–95.97% drug, 4.03–5.15% water, Tg 0.4 °C10–50 °C, waterilevbare2013a R5, R6
weak-base precipitatesX-ray amorphous halos, no birefringence; Tg about 14 (clotrimazole) and about 51 °C (atazanavir)37 °C[indulkar2015 R19, R20, R21, R22]
lopinavir added to a ritonavir-rich phaseabout a third stays in bulk; about 0.21 at 85 µg/mL ritonavir25 °C[trasi2015a R9, R10]
ionized diclofenac with the ritonavir-rich phasefully recovered in bulk25 °C[trasi2015a R11]
ibuprofen-rich phasepolymer:drug weight ratio 0.40 (PVP K12), 0.52 (K25, K90), 0.87 (PVP-VA), 0.95 (HPMC 603), 1.14 (HPMC 615)1000 µg/mL polymer, 400 µg/mL drug, 37 °C[ueda2021 R5]
ibuprofen-rich phaseratio 0.24 → 0.62 (PVP), 0.46 → 1.32 (PVP-VA), 0.20 → 1.46 (HPMC, to 55 °C)15–60 °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 mL[mosqueragiraldo2018b R14]
telaprevir, 90% HPMCAS / 70% HPMCAS / 90% PVPVApolymer fraction 0.21 / 0.27 / 0.22same[mosqueragiraldo2018b R14]
ritonavir, atazanavirNTA counts: buffer 4.74 × 10⁶; ATV 150 µg/mL 4.15 × 10⁸ per mLantisolvent[alhalaweh2016 R15]
clotrimazole1.2 × 10⁸ to 12.5 × 10⁸ per mL8–20 µg/mL[indulkar2016 R4]
atazanavir with darunavir hydrateatazanavir in the drug-lean phase about 61–63 instead of 91–96 µg/mL at about 196 µg/mL darunavir added150 µg/mL atazanavir, 400 µg/mL HPMCAS, pH 6.8[alkalla2026 R11, C1]
ritonavir phase from a PVP dispersionTg inflection 1.05 °C; pyrene I1/I3 ≈1.43–1.46water, 37 °C[ilevbare2013d R2, R3]
danazol, 90:10 dispersions246–284 nm, 4.1–4.5 × 10⁹ per mL25 °C[jackson2015 R6]
lopinavir alone; with ritonavircrystallized at 1–2 h; no crystallization in 5 hpyrene I3/I1[trasi2015b R15]
indomethacin with 100 µg/mL HPMConset 36 µg/mL; droplets 70–100 nmpH 2.2, 37 °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 Physical stability

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 buffer[moseson2022b 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 h[moseson2022b R15]
same, confocalred layer 55 ± 6 µm at 5 min, 103 ± 9 µm at 30 minNile red[moseson2022b 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, confocal[moseson2022b R15, R17]
10% BCL–PVPVA compactsurface smooth at 30 minSEM[moseson2022b 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 °C[indulkar2019a 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 min[saboo2020a R19]
felodipine 30% with 0, 2% TPGS; 5, 10% TPGSporous surface layer after 10 min; homogeneousmicro-CT, driedsaboo2021 R19
indomethacin–PVPVA 15, 25%rough, porous surface after 5 min; smooth at 10%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 Physical stability

drug-silanol hydrogen bonding

A hydrogen bond between a surface silanol (Si–OH) as donor and an acceptor group of the drug, a carbonyl or a ring nitrogen [dening2019 C28; mccarthy2020 C41; hate2020a C38]. Isolated silanols are taken as the most reactive sites, and siloxane bridges cannot hydrogen-bond [dening2019 C38; mccarthy2020 C8]. The authors read it as the predominant interaction of ritonavir, indomethacin and its methyl ester with SBA-15 ("collectively indicates", "suggest"), the drug's own donor being unnecessary [dening2019 C52; mccarthy2020 C41, C42], and "hypothesize" that strong bonds of this kind make part of the adsorption irreversible [dening2019 C54].

Findings

F5, F10, F12.

Related concepts

part of hydrogen bonding; contrasts with ionic interactions and hydrophobic interactions; probed by competitive adsorption; mechanism of drug adsorption onto silica.

Formulas

none specific; adsorption is quantified with the adsorbed amount by solution depletion.

How it is measured or obtained

ATR-FTIR of loaded silica against a physical mixture: loss of the isolated-silanol band at 3749 cm⁻¹ and shifts of the drug carbonyl bands [dening2019 R11, R12; hate2020a R12; mccarthy2020 R3]. XPS of O 1s and Si 2p [dening2019 R13, R14; mccarthy2020 R4, R5]. Adsorption with 5 M urea as a hydrogen-bond competitor [dening2019 R8; mccarthy2020 R14].

Values in the library
materialvalue or classconditionspaper ids
ritonavir in SBA-15, 38 and 22% w/w3749 cm⁻¹ band absent (present in physical mixture); carbonyl 1715 and 1654 cm⁻¹dry, methanol-loaded[dening2019 R12, R11]
ritonavir in SBA-15, 22% w/wO 1s 532.5 eV between silanol 533.2 and carbonyl 531.3 eV; Si 2p about 0.5 eV lowerXPS[dening2019 R13, R14]
indomethacin; methyl ester in SBA-15carbonyl shifts 1682 → 1669, 1710 → 1688; 1674 → 1663, 1735 → 1725 cm⁻¹ (text); Si 2p 103.8 → 103.4; 103.3 eVdry, ethanol-loaded[mccarthy2020 R3, R4, X1]
atazanavir in SBA-153749 cm⁻¹ band absent from 20% w/w; carbonyl near 1700 at 5%ATR-FTIR[hate2020a R12]
urea effect on adsorptionritonavir 259 → 169; indomethacin 12.4 → 6.1; ester 14.2 → 5.8 mg/g5 M urea[dening2019 R8; mccarthy2020 R14]

Evidence table: drug-silanol hydrogen bonding.

Pitfalls and disagreements

All spectra are of dried, solvent-loaded solids, not of silica that adsorbed drug from water [dening2019 X13]; the loading of the indomethacin spectroscopy samples is not stated [mccarthy2020 X20]. The band shifts in the text exceed those in the figure for some indomethacin bands [mccarthy2020 X1]. The 3300–3600 cm⁻¹ region of hydrogen-bonded silanols in loaded ritonavir is not shown [dening2019 R12]. Urea may lower adsorption through a change of solubility [dening2019 X12]. For ketoconazole, a base partly charged at pH 6.8, hydrogen bonding is a minor part next to electrostatic binding [hate2020b C29, R14].

← Concepts and formulas

concept · as used in Physical stability

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 °Cmarsac2008b 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 usedmarsac2008b R16
nifedipine in PVPmore than 90% polymer needed for no crystallization on a thermodynamic basispredicted with \chi = −3.8marsac2006b R18, R17
most drugs in polymeric matriceslikely low at room temperature unless cohesive interactions are extremely favourablesolubility in an ethyl-pyrrolidone analoguemarsac2009 C46, R9
nifedipine in PVP K29/32; K120.06; 0.07 g/g (0.001 g/g with χ = 0.5)χ −3.8, predictedmarsac2006b R17.a, R17.b
felodipine in PVP K29/32; K120.25; 0.31 g/gχ −4.2, predictedmarsac2006b 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 °Cmarsac2006b 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 EPmarsac2009 R9
same five in EP0.268, 0.215, 0.079, 0.074, 0.396 weight fractionmeasured, 25 °Cmarsac2009 R9
same fivefraction above solubility reaches zero at polymer 0.93, 0.95, 0.99, 0.99, 0.86PVP K29/32marsac2009 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 estimaterumondor2009b R26, C31
felodipine–PVP 50% at 93% RHresidual ≈0.1 g drug per 0.86 g PVP–water, above that boundmass balance in wordsrumondor2009b E4
all dispersions studied (cited)supersaturated with respect to the estimated solubility in PVPnifedipine and felodipinemarsac2008a 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 Physical stability

enteric polymer

Evidence table: enteric polymer. Content from the ASD dissolution chapter (posaconazole 2019, delamanid 2022–2023, praziquantel 2024–2025) and the Bioperformance chapter.

A polymer with acidic groups, such as the succinoyl groups of HPMCAS, the phthalyl groups of HPMCP or the methacrylic acid of the Eudragit L grades, that stays largely undissolved at gastric pH and dissolves above a threshold pH set by its substitution [nguyen2023c R4, C14; nguyen2023b M11]. In a dispersion it holds most of the drug back in the stomach, which an enteric polymer is chosen for, but it is a poor crystallization inhibitor where it is unionized, so the drug in the wetted matrix can crystallize in acid [nguyen2023b C36, C37]. Around a tablet, as a coating, the same chemistry keeps the gastric medium away from the dispersion altogether [nguyen2023b C43]. Weakly acidic polymers with pH-responsive solubility are used more and more in dispersions, while release and crystallization at a pH where the polymer is insoluble are "not well understood" nguyen2023a C1.

Findings

F24, F25, F27, F28.

Related concepts

defined by pH-dependent polymer solubility and polymer ionization; governs drug leaching and polymer-controlled release; risk of surface crystallization in acid; read with gastric pH variability.

Formulas

pH-solubility profile.

How it is measured or obtained

Polymer solubility by hydrolysing the cellulose backbone of the dissolved polymer and assaying it by HPLC-ELSD, checked by phenol–sulfuric acid colorimetry, from pH 1.6 to 6.5 [nguyen2023c P3, P4]; polymer release alongside drug release during a two-stage test by the same assay [nguyen2023c P10]. Coat integrity by stirring coated tablets in gastric media overnight and photographing them, with a USP acid-stage tolerance test [nguyen2023b P6, P7].

Values in the library
materialvalue or classconditionspaper ids
HPMCP-50; HPMCP-55893 ± 95 and 189 ± 18 µg/mL at pH 5.0; insoluble below pH 4.550 mg in 15 mL, 48 h, 37 °C[nguyen2023c R4]
HPMCAS-LF; -MF1687 ± 47 and 1401 ± 69 µg/mL at pH 5.5the same[nguyen2023c R4]
HPMCAS-HFdissolves only from about pH 6.0the same[nguyen2023c R4]
HPMCAS-HF, cited threshold (Bioperformance)the most hydrophobic grade, with the highest acetyl:succinoyl ratio, needs the highest pHcitednguyen2023a C15
Eudragit L 100-55 as an Acryl-EZE II coat, 14–16% weight gainintact 15 to more than 17 h at pH 1.6–3.0; failed after ≈130–150 min at pH 4.5–5.0; dissolved in 10–15 min at pH 6.0500 mL, 37 °C[nguyen2023b R7]
posaconazole–HPMCAS-MF dispersions in FaSSGF7.5–11.5% of a 400 µg/mL dose released in 60 minpH 1.6, 37 °C[elkhabaz2019a R10]
praziquantel–HPMCAS-MF dispersions, first stage≈9–29% released against ≈88–106% for HPMC E5 LVpH 1.6–5.0 or FaSSGF, 37 °C[alvarenga2025 R7, R10, R13]
Pitfalls and disagreements

The polymer that releases best at intestinal pH is not the one that protects best in acid, and the ranking reverses with the gastric pH: delamanid dispersions of HPMCP-55 ended at ≈80.5% after pH 3.0 but ≈12.5% after pH 5.0, below HPMCAS-LF [nguyen2023c R11, X3]. Holding the drug back is incomplete: posaconazole and delamanid dispersions released 7.5–41% of the dose in acid, where the matrix can then crystallize [elkhabaz2019a R10; nguyen2023b R2]. The printed polymer solubilities above about 3.3 mg/mL exceed what the stated amounts allow [nguyen2023c X1].

← Concepts and formulas

concept · as used in Physical stability

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/molDSCbaird2010 M51, M17
caffeine20.81 kJ/molDSCbaird2010 M10
vemurafenib α; β53.8; 33.3 kJ/molDSClu2016 R20
nilutamide stable form; form I~98; around 66 J/gDSCtrasi2014b M1, R6
class I against class III≈+0.45 against ≈−0.63 SDper volumebaird2010 R22.b
nifedipine against felodipinehigher ΔHf and Tm, read as a higher intrinsic crystallization tendencyDSCmarsac2008a 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 Physical stability

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 idealmarsac2008b 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 °Cmarsac2008a R10, C37
six drugs in waterγ water 2.54–4.65; unfavourable drug–water contacts95% RHrumondor2009c R24, C28
felodipine and quinidine with HPMCASless sorbed water gives a less positive mixing enthalpy, which "may explain" no separationqualitativerumondor2010c C31
indomethacin with PVPVAstronger drug–polymer bonds give a more favourable mixing enthalpyqualitativerumondor2010c C28
miscible pairs with PVP\chi near or below zero: athermal or slightly exothermic, miscibility largely driven by entropymelting point depressionmarsac2009 C29
indomethacin–PVPmost exothermic of five PVP pairs (χ −0.82 melting, −1.83 solubility route)melting at 1 °C/min; EP at 25 °Cmarsac2009 R7.e, R9.e, C29
felodipine, ketoconazole, nifedipine, sucrose with PVP K12athermal or slightly exothermic, miscibility "largely driven by entropy"offset meltingmarsac2009 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/minmarsac2006b C35, R9
dextran with ibuprofen or indomethacinadhesive interactions not more favourable than cohesive ones, "speculated"no depressionmarsac2009 C43
dextran–PVPpositive enthalpy inferred where blends separate; dextran–dextran bonds assumed stronger or more numerousphase map; OH band shift[vaneerdenbrugh2012a C36, C37, R13, R16]
itraconazole–HPMCentropy-driven mixing with little favourable enthalpyargument in wordspurohit2015a 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 Physical stability

enthalpy relaxation

The slow loss of excess enthalpy of a glass during ageing below Tg, recovered as an endotherm on reheating; fitted with a stretched exponential, it gives a mean relaxation time τ (longer means less mobile) and a width parameter β konno2006 P6, E7; marsac2006a P9, E7.

Findings

F5.

Related concepts

measures molecular mobility; related to structural relaxation and structural relaxation time; uses Kohlrausch-Williams-Watts equation.

Formulas

Kohlrausch-Williams-Watts equation, maximum enthalpy recovery.

How it is measured or obtained

Glasses or dispersions are aged for set times (here at 2 °C or 23.5 °C), the recovered enthalpy is measured by DSC, divided by the maximum recovery \Delta C_p(T_g - T) and fitted with the Kohlrausch–Williams–Watts function konno2006 P6, E5, E6; marsac2006a E8. A strong recovery peak on the first DSC scan of a humidity-exposed dispersion was also reported marsac2010 R15.

Values in the library
materialvalue or classconditionspaper ids
felodipine with 10% PVP, HPMC, HPMCASτ 208, 319, 687 h; β 0.42, 0.47, 0.45aged at 2 °Ckonno2006 R9
amorphous nifedipine, felodipineτ 6.3 and 4.2 h; β 0.36 and 0.3723.5 °Cmarsac2006a R4.m, R4.n
nifedipine, felodipine with 10 wt% PVPτ 42.1 and 16.7 h23.5 °Cmarsac2006a R7
felodipine, alone and with 10% PVP84% and 65% of the maximum recovery after 16 h23.5 °Cmarsac2006a R8
felodipine–PVP 46.5 wt% after 94% RHstrong recovery peak at ≈55 °C on the first scanDSC cyclingmarsac2010 R15
HPMCAS dispersions and indomethacin–PVPVA after 94% RHendotherm with the single Tg read as enthalpic recoveryDSC after dryingrumondor2010c R17, C17

Evidence table: enthalpy relaxation.

Pitfalls and disagreements

Both papers print the KWW equation with the sign or exponent misplaced; the standard form reproduces the data konno2006 X5; marsac2006a X4. The relaxation times did not rank crystallization: the faster-nucleating nifedipine dispersion was the slower-relaxing one, and the τ order of the three felodipine dispersions differs from their Tg order marsac2006a R7, C37; konno2006 X13.

← Concepts and formulas

concept · as used in Physical stability

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⁻¹DSCbaird2010 M10, M17, M51
felodipine; nifedipine74.4 and 89.6 J mol⁻¹ K⁻¹DSCmarsac2006a E11
nilutamide; cinnarizineΔSm/R ≈8.7; ≈12.5growth analysistrasi2014a R11.a, R11.i
class I against class III≈+0.41 against ≈−0.59 SDper volumebaird2010 R22.c
spin-coat class I against III≈+0.46 against ≈−0.33 SDper volumevaneerdenbrugh2010a R20.d
fast growers (group 1)≈−0.38 SDper moletrasi2014a 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 Physical stability

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 = 0marsac2006b R1
nifedipine with PVP K12, K29/32, K90minimum near Φ ≈ 0.6; K29/32 and K90 virtually identical, K12 slightly lowerχ = 0marsac2006b R1
typical molecular weightsAPIs 200–600; polymers 10,000–1,000,000citedmarsac2009 R13
indomethacin, EP → PVP K12 → K29/32 → K90predicted solubility 0.396 → 0.144 → 0.134 → 0.134entropy term scaled with chain lengthmarsac2009 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 term[vaneerdenbrugh2012a R15]
6 kDa dextran with PVP K 12 to K 90−9.1 to −2.8 × 10⁻²³ Jsame[vaneerdenbrugh2012a R15]
450 kDa dextran with PVP K 90about 0same[vaneerdenbrugh2012a 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 Physical stability

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 classesvaneerdenbrugh2011a R1
PVP, PVPVA pyrrolidonevery strong acceptor (1-methyl-2-pyrrolidone 2.38), no donorTable 2vaneerdenbrugh2011a R2
amide carbonyl of benzamide, phenacetinstrong acceptor (1.81, 1.69); amide N–H medium donorTable 1vaneerdenbrugh2011a R1
benzamide, phenacetin crystalsamide–amide only: 100 and 94% alone; 0% with COOH; 14 and 33% with C(O)NC2CSD surveyvaneerdenbrugh2011a R14
naringenin, quercetinfree phenolic OH donors (two and three) after intramolecular bondsstructurewegiel2013a 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 Physical stability

eutectic

The composition (the eutectic composition) and temperature at which a mixture of two components that mix fully as liquids and not as solids melts at its lowest temperature. In drug–polymer dispersions the eutectic point is the most drug the molten polymer can hold at the eutectic temperature; dispersions with an appreciable drug solubility are eutectic, those in which the drug barely dissolves and hardly lowers the polymer melting point are monotectic [baird2011 C1]. Zhu and co-workers state that eutectic compositions are determined by the pure drug's melting point together with its ability to interact with PEG [zhu2011 C4].

Findings

F1, F2, F8.

Related concepts

part of temperature-composition phase diagram; contrasts with monotectic system; depends on melting point depression, crystal lattice energy and drug-polymer interactions; predicted by semi-empirical eutectic prediction model.

Formulas

Lacoulonche liquidus model.

How it is measured or obtained

From the temperature–composition phase diagram: liquidus by hot-stage microscopy and DSC at 1 °C/min over 0–100 wt% drug; near the eutectic one endotherm appears below both pure melting points, away from it two [baird2011 P2, P3, C13]. The eutectic can also be predicted with a Flory–Huggins model [baird2011 E1, E2, E4].

Values in the library
materialvalue or classconditionspaper ids
chlorpropamide–PEG 335035 wt% drug, 55.0 °Cobserved; predicted 12.8 wt%[baird2011 R1.a; zhu2011 R5.c]
aceclofenac–PEG 335030 wt%observed; predicted 1.5 wt%[baird2011 R1.b]
loratadine–PEG 3350about 5 wt%observed; predicted 6.5 wt%[baird2011 R1.c]
haloperidol–PEG 3350below 1 wt%, monotecticobserved; predicted 0.5 wt%[baird2011 R1.d]
benzocaine; ibuprofen; nilutamide–PEG 335030 wt% at 48.9 °C; 40 wt% at 49.6 °C; 10 wt% at 58.4 °Cobserved[zhu2011 R5.b, R5.d, R5.e]
fenofibrate–PEG 3350minimum about 58 °C at 15–20 wt%CPOM and DSC[zhu2012 R24.c, R24.d, C48]
Pitfalls and disagreements

Observed eutectics were read on a 5–10 wt% grid, and the chlorpropamide value of 35 wt% was not a tested composition [baird2011 X9]. The eutectic temperatures of the chlorpropamide and aceclofenac systems are not established by the drifting low-temperature endotherm [baird2011 X8]. The eutectic composition is a ceiling at the eutectic temperature, not a solubility at storage temperature (see drug solubility in polymer). The 20/80 dispersions of the kinetic study lie at or near the eutectic composition for ibuprofen and fenofibrate and below it for benzocaine [zhu2012 C40, C32].

← Concepts and formulas

concept · as used in Physical stability

extended nucleation and growth classification

A risk classification that combines the DSC nucleation behaviour with the crystal growth rate: class IA (high nucleation and growth, overlapping zones, crystallizes on cooling), IB (high nucleation and growth, little overlap; good glass-forming ability, poor glass stability), II (rapid growth, low nucleation), III (ready nucleation, slow growth) and IV (slow nucleation and growth) trasi2014a C17. Risk for amorphous delivery is ranked I highest, then II, III intermediate, and IV "likely" the most robust trasi2014a C18.

Findings

F3, F15.

Related concepts

extends crystallization tendency classification; built on nucleation and crystal growth rate; related to glass stability.

Formulas

none.

How it is measured or obtained

From the cooling–reheating DSC class and the seeded growth rate of the neat drug trasi2014a C17, R1; nucleation itself is inferred, not measured trasi2014a C15.

Values in the library
materialvalue or classconditionspaper ids
carbamazepine, griseofulvinclass IADSC and growthtrasi2014a C17
acetaminophenclass IBDSC and growthtrasi2014a C17
nimesulide, nilutamide, celecoxibclass IIDSC and growthtrasi2014a C17
cinnarizine, droperidolclass IIIDSC and growthtrasi2014a C17
warfarin, miconazoleclass IVDSC and growthtrasi2014a C17
Pitfalls and disagreements

The labels reuse the numerals of the 2010 classes with different meanings, and some papers mix both schemes trasi2014a X10. The risk ranking assumes that growth-rate rankings above Tg carry over to storage temperatures trasi2014a C16, C35.

← Concepts and formulas

concept · as used in Physical stability

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 plotmarsac2006b R9, R4
indomethacin with PVP K12−6.16 (onset), −1.94 (midpoint), −0.82 (offset)melting point depressionmarsac2009 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 meltingmarsac2009 C17
indomethacin, felodipine, nifedipine, ketoconazole, sucrose with PVP K12offset χ −0.82, −0.08, 0.00, −0.08, 0.021 °C/minmarsac2009 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, EPmarsac2009 R9
sucrose–dextran; ibuprofen–dextran; indomethacin–dextran; itraconazole–Eudragit E1000.20; ≥ 0.38; ≥ 0.72; ≥ 0.11 (lower limits for the last three)offset meltingmarsac2009 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 fitrumondor2010a R14
IDM–PVPVA in four other studies−0.64, −2.06, −2.9, −4.5 (assignment to studies not printed)cited[moseson2018 R7]
water–felodipine, water–PVPabout 3.3 and about 0.5 (Δχ large)sorption isotherms, Flory–Huggins fitsmarsac2010 C43
water with amorphous felodipine, PVP, HPMC and HPMCAS3.27 for felodipine; above 0.5 for HPMC and HPMCAS; the PVP value close to but slightly below other authors' valueswater sorption isotherms, 25 °Crumondor2010a R11, C19, C20
BCL–PVPVA 30% DL−1.57, read as favourable miscibilityphase diagram, SI not supplied[moseson2021 M1, C10]
RTV–PVPVA (drying model)0.5 assumed in the SI; "likely <0.5, and possibly close to zero" in the text; varied −0.5 to 0.5sensitivity moved mainly the drug–polymer sideli2020 R15, R16, C72, X10
water–ritonavir and water–PVPVA (drying model)2.8 and 1.13fitted to dynamic vapour sorption, room temperatureli2020 R15
BCL–PVPVA 30–90% BCL−1.57 (R² 0.994); Tc 145 °C at 30% BCLDSC offsets extrapolated to 0 °C/min[moseson2022c R8, R9]
PCZ–HPMCAS MF, PCZ fractions 0.4–1.0+0.43 (R² 0.991); the fitted line meets B = 0 at A of about −0.05same[shah2024 R1, R4]
water with nifedipine, felodipine, droperidol, pimozide, indomethacin, ketoprofen2.84, 3.18, 2.85, 3.58, 2.50, 2.7125 °C, 95% RHrumondor2009c R24
nifedipine–PVP, felodipine–PVP (cited)−3.8 and −4.2 from melting point depressionused for activitymarsac2006a R18
indomethacin–PVP vs nifedipine–PVP (cited)−0.8 vs 0.0used for susceptibilityrumondor2009c R26
indomethacin against felodipine, quinidine, pimozide with PVPVAlarger carbonyl red shift (42–44 against 19–22 cm⁻¹) "would result" in a lower \chi_{DP}IR of dry filmsrumondor2010c R20, C28
hydrophobic drugs with water\chi_{WD} expected positive from log Pqualitativerumondor2010c C30
indomethacin with HPMC, HPMCAS, PVPχ not measured; stronger interaction "would" lower the driving force for growthargument with the free energy of mixingtian2017 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 °Cpurohit2017b C43, C1
six drugs with PVPVA and HPMCASno χ measured; argument—yang2021 E2, C21
Pitfalls and disagreements

The values of one paper are not comparable with those of another: for the same published diagram of chlorpropamide the two PEG papers give −2.53 and −0.50, and for haloperidol −0.04 and 0.08, so the sign near zero is not robust [baird2011 R9; zhu2011 R5]. The printed expression for the interaction energy in Baird and Taylor does not reproduce, and only signs and ranking are robust [baird2011 X3]. Zhu and co-workers fitted \chi at 50–80% drug, not at the 20/80 composition of the SAXS/WAXS samples, and the normalization cannot be reproduced from printed inputs [zhu2011 X10]. In the PEG study the size of \chi did not rank the size of the long-period increase: chlorpropamide has the most negative \chi and the smallest increase [zhu2011 X5]. The reading as exothermic mixing assumes a near-ideal entropy of mixing [baird2011 C23]. The printed solubility-parameter values (2.0, 0.5) were not reproduced from the inputs (2.36 and 0.70 at 298.15 K) marsac2006b X1. The melting-route χ of one pair spans 7.5-fold with the point of the melting peak read (synthesis: 6.16/0.82) marsac2009 R6. The two experimental routes differ by up to 1.01 and rank the compounds differently marsac2009 X7. The positive values for non-depressing pairs are lower limits marsac2009 C19, X11. The nifedipine volume fractions of the 2006 fit may use felodipine's density marsac2006b X2. A χ determined near the drug melting point is applied at storage temperature without correction marsac2006b C32. The χ of one pair differs between studies (indomethacin–PVPVA −1.97 against −0.64 to −4.5) [moseson2018 R4, R7]. The positive mixing enthalpy of dextran–PVP is inferred from the existence of phase separation, not measured [vaneerdenbrugh2012a C32, X7]. In the extrusion work a single \chi neglects temperature and composition dependence [moseson2018 C18]. Differences between studies "can be attributed" to sample preparation, DSC method or onset versus offset [moseson2018 C21]; the nature of the fit (with or without intercept) also shifts the value [moseson2018 X7]. For ritonavir–PVPVA the main text and the SI disagree on χ, and the basis of the other χ values (vapour sorption or solubility, room temperature or 37 °C) is described differently in the two; the DVS and solubility data are not shown li2020 X10, X11. For posaconazole–HPMCAS χ is a slope with a free intercept, and Tc below 40% PCZ are extrapolations from it [shah2024 R4, X7, X8]. Two values cited in the physical-stability papers for the same pair differ by an order of magnitude: −3.8 and −4.2 (melting onset route, used in 2006) against −0.8 and 0.0 (offset route, used in 2009) for nifedipine–PVP, which reflects the choice of melting-peak point (synthesis; see the onset, midpoint and offset values above) marsac2006a R18; rumondor2009c R26. The drug–water χ split rests on approximated densities and a gap of 0.13 rumondor2009c X4. No χ was computed in the 2010 polymer comparison: \chi_{DP} is ranked by red shift and \chi_{WD} by calculated log P rumondor2010c X13. In the dispersion-dissolution argument, with 90% polymer, fewer drug–drug contacts "would lead to a reduction in the barrier" to dissolution, an argument without χ values [alonzo2011 C43]. The "ideal" line of the lopinavir figure is proportional dilution, not χ = 0 of the equation li2018 X2. No χ values were measured or cited for the ritonavir systems purohit2017b E4.

← Concepts and formulas

concept · as used in Physical stability

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 = 0marsac2006b R1
nifedipine–PVP K29/32miscible over the whole range for χ ≲ 0.6; single deep minimum at χ −3.8, −4.2five χ valuesmarsac2006b R2, R3
five compounds with PVPΔG/RT minima at polymer fractions ≈ 0.5–0.6; indomethacin deepestmelting-route and solubility-route χmarsac2009 R10
nifedipine, felodipine in PVPlittle activity lowering below polymer volume fraction ≈ 0.5χ from melting depressionkonno2006 R20, C35; marsac2006a R19
indomethacin–PVPVAχ −1.97 from the linearized melting relation; one χ describes Tc from 50 to 90% DL (HME phase diagram)offset extrapolated to 0 °C/min[moseson2018 R4, C19]
dextran–PVP, 20 pairscombinatorial entropy per site from about −27 × 10⁻²³ J (783 Da maltodextrin, PVP K 12) to about 0 (450 kDa dextran, PVP K 90)25 °C, no enthalpic term[vaneerdenbrugh2012a R15, E5]
itraconazole–HPMCentropy-driven miscibility, limited at room temperature (UCST-type); no χ measuredargument in wordspurohit2015a C42, C47, E1
ternary water–drug–polymer systemswater lowers the free energy entropically; large positive \chi_{WD} favours drug-rich separationstored ASDspurohit2017b C43
drug in polymer, melting point depression and activityfree energy of mixing and melting point depression from Flory–Hugginsfelodipine, nifedipine with PVPmarsac2006b E1, E3; marsac2006a E10
ritonavir–PVPVA–methanol–waterthe computed solubility boundary is crossed from about 12.5:87.5 initial water:methanol at 25% DLfour-component modelli2020 R17, C50
indomethacin–PVP, felodipine–PVPdrug–polymer term 0.029–0.160% of the ternary adjustment25 °C sorptionrumondor2010a R13
felodipine–PVP, indomethacin–PVPfitted χ23 −9.6 to 26.9 and −20.4 to 22.0samerumondor2010a R14
four blend seriesmean water–blend χ1,23 falls with polymer contentsamerumondor2010a R15
felodipine, quinidine, pimozide, indomethacin with PVP, PVPVA, HPMCASternary free energy of mixing used to explain why less hygroscopic polymers separate lessqualitativerumondor2010c E1, C26, C31, C39
indomethacin–polymer meltsfree energy of mixing used to argue a lower driving force with stronger interactiongrowth, 80–135 °Ctian2017 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 Physical stability

formulation critical temperature

The formulation critical temperature (Tc, also called the solubility temperature) is the lowest temperature at which a homogeneous molecular dispersion of a given drug–polymer composition can in theory form, because all drug crystals can dissolve; for 1:1 IDM–PVPVA it is 131 °C by the Flory–Huggins prediction and 132.3 ± 0.8 °C measured [moseson2018 R5.f, X2; moseson2018a R2, C4]. It is the depressed melting point of the drug at that composition, not an upper or lower critical solution temperature [moseson2018 P2]. For 30:70 BCL–PVPVA Tc is 145 °C and for PCZ–HPMCAS MF 135, 155 and 165 °C at 10, 25 and 50% loading (calculated) [moseson2022c R9; shah2024 R5].

Findings

F8, F9, F36, F41.

Related concepts

obtained from melting point depression; defines the lower edge of the HME operating design space; related to drug solubility in polymer.

Formulas

Flory–Huggins melting point depression.

How it is measured or obtained

DSC melting point offsets of cryomilled physical mixtures at several heating rates extrapolated to 0 °C/min, and a Flory–Huggins fit to extend the line over the composition range [moseson2018 P2, E2].

Values in the library
materialvalue or classconditionspaper ids
IDM–PVPVA 50:50132.3 ± 0.8 °C measured; 131.0 °C predicted; "131 ± 2 °C" usedoffset extrapolation[moseson2018 R5.f, X2]
IDM–PVPVA 1:1 extrudateprocessing at 131 °C melt temperature, 20 min, left nanometre crystalsHME, TEM[moseson2018a R2, R9]
BCL–PVPVA 30:70Tc = 145 °C; extruded at 145 °C the 3.5–38 µm lots were below the PXRD limit within 2–6 min, the 42.2 and 92.7 µm lots held about 2.5 and 15.0% at 20 min5 mL micro-extruder[moseson2022c R9, R10]
PCZ–HPMCAS MF 10 / 25 / 50% DLcalculated 135 / 155 / 165 °C; extruded at 125 °C they held 0.3 / 3.2 / 19.3 wt% crystals2 min, SHG[shah2024 R5, R10]
Pitfalls and disagreements

Processing at Tc gives no margin: 20 min at 131 °C passed XRPD, DSC and (by the phase-diagram paper) PLM, yet TEM found residual crystals [moseson2018 C59; moseson2018a C31]. The measured product temperature can differ from what the melt experiences [moseson2018 C43]. Processing at Tc is not practical for most products and was used as the slowest case [moseson2022c C56]. The low-loading posaconazole values are extrapolations [shah2024 X7].

← Concepts and formulas

concept · as used in Physical stability

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 °C[wilson2018 E8, C14]
Pitfalls and disagreements

The authors call the fit "well described" although the measured values deviate negatively by 3–8 K [alhalaweh2016 C10, X7].

← Concepts and formulas

concept · as used in Physical stability

fragility

How steeply molecular mobility or viscosity changes as a liquid approaches Tg: strong liquids follow Arrhenius behaviour, fragile ones depart from it baird2012 C37. It is expressed by the fragility index m (strong below 40, fragile above 75) or by the VTF strength parameter D (strong above 30, fragile below 10) baird2010 R30. Good glass formers were expected to be strong liquids baird2010 C3.

Findings

F5, F12.

Related concepts

measured by melt viscosity; depends on glass transition temperature; proposed predictor of glass-forming ability; related to reduced glass transition temperature.

Formulas

Vogel-Tammann-Fulcher equation.

How it is measured or obtained

m from the heating- and cooling-rate dependence of Tg (Moynihan) and D from m, or D from the VTF equation with T0 set to the Kauzmann temperature baird2010 P10, E14, E15, E18; D also by fitting the VTF equation to melt viscosity baird2012 P5, E4.

Values in the library
materialvalue or classconditionspaper ids
tolazamidem 18DSC rate dependencebaird2010 R18.k
itraconazolem 731DSC rate dependencebaird2010 R18.r
nifedipinem 33, D 36 from m, D 9 from VTF with TKDSCbaird2010 R18.i
28 compounds of classes I-B to IIID 4.3–8.7VTF fit of melt viscositybaird2012 R12
Pitfalls and disagreements

The category depends on the estimate used: aceclofenac, tolazamide and nifedipine are strong by m but fragile by the VTF-based D baird2010 X14. Fitted T0 values do not satisfy the paper's own T0–D–Tg relation baird2012 X5. Fragility did not separate good from poor glass formers baird2012 C43, and invoking it for outliers in growth data is untested trasi2014a X18.

← Concepts and formulas

concept · as used in Physical stability

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–Hugginsmarsac2006b R2
indomethacin–PVPminimum ≈2.4 times (melting χ) and ≈5 times (solubility χ) as deep as the athermal minimumΦ_polymer ≈ 0.5–0.6marsac2009 R10
felodipine, ketoconazole with PVPthree curves (athermal, melting χ, solubility χ) nearly coincideas abovemarsac2009 R10
sucrose–dextranmelting-route curve above the athermal curve (χ = 0.20)as abovemarsac2009 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 Physical stability

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-EDX[moseson2022b R15]
same, confocalgel layer 440 ± 6 µm; compact swelled from 2092 ± 24 to 2696 ± 50 µm in 60 minNile red, Alexa Fluor 488[moseson2022b R16, R17]
50% BCL–PVPVA compactno gel layer distinguished; swelled from 1988 ± 11 to 2441 ± 12 µmsame[moseson2022b 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 minsaboo2021 R19
PVPVAat least 11% water to start chain disentanglement at 37 °Cestimated[hiew2022b R21]
ritonavir–PVPVA 10–40%gel layer with a sharp boundary to the glassy core at every loading; no grain boundaries in the gelconfocal cross-sections, pH 6.8yang2022a R7, C42
ritonavir–PVPVA 0–20%; 30%, 40%gel–glass front through ≈100% of the compact at 20 min; ≈29 and 17% with a plateaureal-time imagingyang2022a R8
neat HPMCAS-MF in pH 6.8 phosphate 5; 13; 51 mM/ΔpHno gel; 3 ± 1 µm; 19 ± 5 µmconfocal with prodan, 60 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 statedeac2023a R4, C44, C31
ritonavir–PVPVA + Tween 80, 30%≈147.6 → 279.6 (5 → 20 min)confocal cross-sections, unit not printedyang2023 R15, X8
ritonavir–PVPVA + Span 20, 40%≈90.7 → 50.7 (5 → 20 min)sameyang2023 R15
neat PVPVA; 5% PHPH; 5 and 20% MePHPHgel–solution boundary from a linear water gradientternary diagram, 37 °Cdeac2024b R27, E4
Pitfalls and disagreements

Layer thicknesses come from compacts, whereas the authors say polymer loss is much faster from particles than from compacts [moseson2022b C39, X20]. Dye assignments and the polymer-depleted state of the crust are inferred [moseson2022b X16]. The confocal tablet images come from a different compaction and size than the release tablets, and the large red blobs of the uncoated row at 2–3 min are a mounting artefact [benson2025 X5, R15, C29]. That croscarmellose and starch glycolate raise the viscosity of the PVPVA gel is a speculation [benson2025 C50]. Hydrophilic surfactants "would reasonably be expected" to draw more water into the gel–water interface and so speed polymer dissolution, an argument without data correasoto2022b C42. Yang and co-workers read thickness as the balance of water penetration and disentanglement, but water ingress was not measured on the compacts yang2023 C26, C27. The gel-layer region of the 2024 diagrams rests on a fitted water Tg and on gel water contents cited from 2023 deac2024b X11, R40.

← Concepts and formulas

concept · as used in Physical stability

Gibbs-Duhem equation

The relation between the changes of chemical potential of the components of a mixture; integrated with the measured water activity against composition from a sorption isotherm, it gives the activity of the drug in the water-saturated amorphous phase, the term e^{-I(a_2)} of the amorphous solubility estimate (the Murdande method) [almeidaesousa2015 E16, P7; ilevbare2013a P2]. In the solution-crystallization papers the factor lowers the Hoffman estimate of the amorphous solubility, and I(a2) is the sum of a Henry's-law term from zero water to the limit of linearity and a numerical integral \sum \langle (n_1/n_2)(1/a_1)\rangle\,\Delta a_1 over the sorption isotherm up to unit water activity [hsieh2012 E5, E6, P13; ilevbare2013c E6].

Findings

Amorphous solubility and LLPS: F5. Crystallization from solution: F2, F21.

Related concepts

yields the water sorption correction of amorphous solubility; input is water sorption; related to thermodynamic activity; corrects the Hoffman equation; used for the amorphous solubility advantage.

Formulas

Gibbs-Duhem equation, amorphous solubility advantage with water-sorption correction.

How it is measured or obtained

Numerical integration of moles of water per mole of drug against 1/a_1 over the sorption isotherm [hsieh2012 E5]. The papers of this chapter only name the method. The crystallization-from-solution papers measured the isotherm by dynamic vapour sorption of the amorphous solid at the test temperature (37 °C, 5–95% RH in 10% steps, three samples; 25 °C for danazol), with the water content extrapolated to water activity 1 [hsieh2012 P8, P13; jackson2014 P3, P4].

Values in the library

The resulting factors are listed under water sorption correction of amorphous solubility [ilevbare2013a M1; almeidaesousa2015 M6]. Values printed in the crystallization-from-solution papers:

materialvalue or classconditionspaper ids
danazol\exp[-I(a_2)] = 0.935DVS 5–95% RH, 25 °C[jackson2014 E1, R2]
five weak baseswater correction lowers the estimate for every base, for ketoconazole from 202 to 56.6 µg/mLDVS, 37 °C[hsieh2012 R10.d]
ritonavir, efavirenz, celecoxibI(a2) values not printed; theoretical amorphous solubilities 20.6, 19.8, 22.6 µg/mL37 °C[ilevbare2012b E8; ilevbare2013c E6, R2]
six dihydropyridinese^(−I(a2)) 0.74–0.91moisture sorption, TA Q5000[raina2015b M1–M6]
Pitfalls and disagreements

The expression is not printed in the 2015 and 2016 papers (named only) and the integral is not shown in any paper of 2013–2016 [almeidaesousa2015 E16; almeidaesousa2016 E4]. The sorption isotherms, the values of I(a2) and the preparation of the amorphous samples are not printed in the 2012 paper, so the estimates cannot be recomputed [hsieh2012 X14]. The amorphous solids for sorption (melt-quenched) and for dissolution (solvent-evaporated) differ in preparation [ilevbare2013c X17]. The sorption conditions and water contents are not printed [raina2015b P3].

← Concepts and formulas

concept · as used in Physical stability

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/minbaird2010 R1
23 class I molecules8 vitrify on liquid-N2 quench (I-B)melt plunged into liquid N2baird2010 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 datatrasi2012a R1
nilutamidegood glass former; attributed to low nucleationDSC at 15 °C/mintrasi2014b 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–heattrasi2020 R5, R6, C7
acetaminophenglass because nucleation (50–60 °C) and growth barely overlapDSC cool–reheat, hot stagetrasi2012a 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 drugwegiel2014 C9
celecoxibeasily made amorphous by cooling the melthot stagemosqueragiraldo2014 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 quench[duong2022a R3, C44]
bicalutamidehigh GFA but rapid crystallization above Tgcited[moseson2022b 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 Physical stability

glass–liquid phase separation

Phase separation of a supersaturated solution into a water-rich phase and a drug-rich phase that is a glass at the test temperature, because its water-plasticized Tg lies above that temperature; the term was judged "more appropriate" than LLPS for atazanavir (Tg of the precipitate about 51 °C at 37 °C) [indulkar2015 C38]. It is the title phenomenon for telaprevir (pellet Tg 52 °C) [mosqueragiraldo2015 C13, C21]. Griseofulvin and sorafenib were also treated as GLPS drugs [almeidaesousa2015 C40]. The papers of 2017–2022 add pazopanib: the colloids formed after a pH shift were called glass–liquid phase separation from a Tg of about 83 °C measured on the dried precipitate [sugihara2018 R17, C27, C28], and telaprevir with bile salts (GLPS onset 146–149 µg/mL in buffer) [lu2017b R2]. New aspect (Bioperformance): telaprevir with a dry Tg of 103 °C and a wet precipitate Tg of 52 °C [mosqueragiraldo2018b M1, C8]; enzalutamide, whose water-saturated amorphous Tg by Fox estimate lies above 37 °C, forms a glassy precipitate, and its colloidal aggregates are called products of GLPS [wilson2018 R4, C7, C14]. New aspect (Crystallization from solution): telaprevir above its amorphous solubility (about 90–100 µg/mL) separates into glassy drug-rich particles of 200–400 nm, which the authors think may provide interfaces for nucleation; in solutions that contain them the apparent concentration drops twice, the first drop being assigned to the aggregates [mosqueragiraldo2016 R1, R3, C7, C11; lu2017 R12].

Findings

Amorphous solubility and LLPS: F2, F7, F5, F4, F17, F23. Bioperformance: F1, F7, F23. Crystallization from solution: F25, F32, F37, F43.

Related concepts

special case of liquid-liquid phase separation; depends on plasticization by water and structural relaxation; contrasts with supercooled liquid; gives a drug-rich phase; related to heterogeneous nucleation (the glassy particles as possible nucleation interfaces).

Formulas

amorphous-crystalline free energy difference from heat capacity.

How it is measured or obtained

As LLPS (extinction, probe, NMR, flux), with the glassy state read from the Tg of the isolated phase, from storage at high humidity, or from the free-energy match (F2) [mosqueragiraldo2015 P4; indulkar2015 P16; almeidaesousa2015 P8]. The GLPS concentration of telaprevir is about 90–100 µg/mL [mosqueragiraldo2018b M1, R1, R2]. Cryo-SEM of a 150 µg/mL solution and the double fall of the 270 nm signal; zeta potential of droplets formed at 180 µg/mL [mosqueragiraldo2016 R2, R3; lu2017 R8].

Values in the library
materialvalue or classconditionspaper ids
telaprevir phaseTg 52 °C (dry 103 °C); redissolves in about 2 min on dilutionpH 6.8, 37 °C[mosqueragiraldo2015 R2, R8]
atazanavir phaseTg about 51 °C (dry 104 °C)water, 37 °C[indulkar2015 R22]
griseofulvin; sorafenibwet Tg 88 and 49 °C at 97% RH; onset matches the supercooled-liquid estimate25 °C[almeidaesousa2015 R9, R5, R6, R11]
pazopanib precipitateTg about 83 °C (dried); wet Tg not measuredpH 6.5, 37 °C[sugihara2018 R17, X5]
telaprevironset 146–149 (buffer), 311–360 (12 mM STDC, SGDC), 238–290 µg/mL (12 mM STCDC)50 mM pH 6.5, 37 °C[lu2017b R2]
telaprevironset 92 ± 2 µg/mL; precipitate Tg 52 °CpH 6.8, 37 °C[mosqueragiraldo2015 R4, C13]
telaprevir, bile salts149 / 146 µg/mL (pH 6.5, 50 mM); 104 / 102 µg/mL (pH 6.8, 100 mM)ultracentrifugation / UV[lu2017b R9]
enzalutamideonset about 42.5 µg/mL; amorphous precipitate glassy under cross-polarized lightpH 6.5, 37 °C[wilson2018 R2, R4]
telaprevir 150 µg/mL, no polymerconcentration about 162 → 100 µg/mL by about 12 min, then a steep fall at 15–25 minpH 6.8, 37 °C[mosqueragiraldo2016 R3]
telaprevir δ 28.8, 1.86 mM bile saltinduction time SGDC >960, STDC 550, STC 60, SGC 30 minpH 6.5, 37 °C[lu2017 R4]
telaprevir at δ 28.8 with 150 µg/mL HPMCAS-MFturbid in all media (glassy drug-rich phase)five media, 37 °C[lu2018 R8, C35]
enzalutamide above 42 µg/mLglassy droplets of about 100–200 nm; agglomeration without polymer "most likely"pH 6.5[wilson2021 R11, C29]
Pitfalls and disagreements

The glassy phase behaves like a liquid one in onset, probe uptake and redissolution; the phase was never isolated for griseofulvin and sorafenib, and "relaxed" is inferred [almeidaesousa2015 C37, C38; mosqueragiraldo2015 C30]. The state depends on temperature: loratadine droplets are glassy at 5 °C and liquid at 37 °C yang2021 C16. The glassy state of the pazopanib phase rests on a dry Tg; with a water uptake of about 4.6% the rule of about 10 °C per 1% would bring 83 °C close to 37 °C (synthesis) [sugihara2018 X5; ilevbare2013a E15; mosqueragiraldo2015 M1]. The onset of telaprevir depends on buffer strength and pH [lu2017b R9]. Neither HPMCAS dispersion of enzalutamide showed GLPS: the 10% one crystallized and the 50% one did not dissolve above the ceiling (F23) [wilson2018 C23]. For telaprevir the dihydroxy bile salts STCDC and SGCDC cap the activity at δ 21–24, so they could not be tested at δ 28.8 [lu2017 R1].

← Concepts and formulas

concept · as used in Physical stability

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 storagebaird2010 C47
class IIIhigh glass-forming ability and high stability on reheatingDSCbaird2010 C34
indoprofen glassfully crystalline after 1 day30 °C, 0% RHbaird2010 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 timesargumenttrasi2012a 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 Physical stability

glass transition temperature

The temperature that separates the glass from the supercooled liquid lu2016 C2; it is a kinetic transition where the system falls out of equilibrium trasi2014b C2. Tg is called "probably" one of the most important properties of an amorphous solid, because storage temperature relative to Tg affects stability [towler2008 C20]. This draft is written from the crystallization-tendency chapter; the evidence table covers far more papers that later chapters will add. New aspect (PEG dispersions): the Tg of the drug relative to the solidification temperature as a possible determinant of whether an amorphous drug is excluded from the crystalline carrier. In polymer blends the additive's mobility, through the blend Tg, is one of three factors that decide exclusion [zhu2011 C2]. In the drug/PEG study a drug Tg above the 25 °C solidification temperature (nilutamide about 33 °C, ketoconazole 44 °C) did not change the pattern [zhu2011 C28, C31]. For water in PEO, Tg describes plasticization (water −136 °C, PEO about −67 °C) marsac2008b M12, M7, C26.

Findings

Crystallization tendency: F4, F12, F20. PEG dispersions: F6, F11.

Related concepts

used in reduced glass transition temperature and Tm − Tg temperature gap; bounds the supercooled liquid; related to fragility, amorphous salt, plasticization and interlamellar incorporation.

Formulas

reduced glass transition temperature, Vogel-Tammann-Fulcher equation.

How it is measured or obtained

By DSC on reheating a melt-quenched or freeze-dried sample, as onset or midpoint [baird2010 P1; trasi2014b M1; towler2008 P6]; for fast crystallizers that give no Tg, estimated from a Tg/Tm ratio or a Trg–molecular-weight fit vaneerdenbrugh2010a E7; baird2010 E27. In the PEG papers the Tg values of the drugs were cited from the crystallization-tendency classification, or measured by DSC (acetaminophen) or estimated with a Tg/Tm ratio (naproxen) [zhu2011 M5, M6; marsac2008b M1, M3, E5].

Values in the library
materialvalue or classconditionspaper ids
propranolol base; hydrochloride−9.3; 35.9 °CDSC[towler2008 R4]
nicardipine base; hydrochloride3.2; 81.0 °CDSC[towler2008 R5]
nilutamide32 °C (onset)DSCtrasi2014b M1
vemurafenib108 °CDSC at 10 °C/minlu2016 M1
felodipine; nifedipine; indomethacin45 °C eachDSC midpointbaird2010 M37, M32, M40
lumefantrineabout 18 °C; 19.7 °C (onset)DSCtrasi2020 R5; hiew2022a R3
five drugs with 10 mol% PVPraised by about 2–3 °CDSCtrasi2014a 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 citedmarsac2008b M1, M2, M3, M4, M5, M6
amorphous PEO; waterabout −67 °C (reported −67 to −55 °C); −136 °Ccitedmarsac2008b 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 Physical stability

Gordon-Taylor equation

The relation T_g=(w_1T_{g1}+Kw_2T_{g2})/(w_1+Kw_2) for the Tg of a miscible binary blend from the weight fractions and Tgs of its components, with K either from true densities and Tgs (Simha–Boyer form, K=\rho_1T_{g1}/\rho_2T_{g2}) or fitted [moseson2018 E3; li2019 E1; konno2006 E3]. In the ASD process chapter it gives the formulation Tg line of the phase diagram and, with K = 0.628 fitted to nanoTA softening temperatures, inverts a local Tg into a local drug content [moseson2018 R5; li2019 R13, R16]. Two later papers print it with the density-based constant: bicalutamide–PVPVA and posaconazole–HPMCAS [moseson2022c E6; shah2024 E2]. New aspects (Physical stability): a measured dispersion Tg below the Gordon–Taylor line was read as non-ideal mixing with weak hetero-interactions (felodipine with HPMCAS and HPMC) konno2006 C16, C32. New aspect (Release mechanism and LoC): Saboo and co-workers (2020) use the equation in reverse to follow the composition of a dissolving surface: the constant k = 0.91 was fitted by partial least squares to nanoTA Tgs of homogeneous indomethacin–PVPVA films (indomethacin 53 °C, PVPVA 130 °C), and the local Tg of a 25% film after immersion and drying was converted into its drug content [saboo2020 R27, R28, E3]. In 2024 dry MePHPH–PVPVA dispersions followed the Gordon–Taylor equation with K = 0.65, while PHPH–PVPVA had Tgs above both components and could not be described by it deac2024b E14, R32, R31.

Findings

ASD process: F7, F8, F15, F41. Physical stability: F5. Release mechanism and LoC: F7, F17, F30.

Related concepts

gives the Tg line of the temperature-composition phase diagram; used to read composition by nanoTA (see glass transition temperature, which it predicts for a blend); alternative to Couchman-Karasz equation. Reads surface drug enrichment from a local glass transition temperature.

Formulas

Gordon–Taylor equation.

How it is measured or obtained

Tg of the blend by modulated DSC against the predicted line [moseson2018 P3]; for nanoTA a calibration of miscible films from 0 to 100% DL fitted with K = 0.628, Tg1 = 367 K, Tg2 = 482 K and inverted to compute local LPV content li2019 P10, R13, E1. In the 2006 physical-stability papers, compared with DSC onset Tgs of rotary-evaporated dispersions at 0–100 wt% polymer konno2006 P4, P5; marsac2006a R17. In the release-mechanism papers: local Tg by AFM-nanoTA on films immersed for 5, 10 and 20 min and dried [saboo2020 R28].

Values in the library
materialvalue or classconditionspaper ids
IDM–PVPVA 50/5072.2 ± 0.5 °C measured, 72.9 °C predicted (K = 0.932 with Tg in K)DSC[moseson2018 R5.f, E3]
LPV–HPMC E5 filmsK = 0.628; local Tg from about 209 °C (HPMC) to about 94 °C (LPV)nanoTAli2019 R13, E1
felodipine and nifedipine with PVPclose to Gordon–Taylor and Couchman–Karasz predictions ("relatively ideal")DSC, 0–100 wt%marsac2006a R17, C21
felodipine with HPMCAS and HPMC at 50 wt%Tg ≈50 and 49 °C against plotted lines ≈63 and 68 °CDSC 20 K/minkonno2006 R6.d, R7
felodipine–PVP 50 wt%≈83 °C above its plotted line (≈70 °C)samekonno2006 R6.d, R7
IND:PVPVA filmsnanoTA Tg and drug content by Gordon–Taylor10–90% DL[saboo2020 R27, E3]
BCL–PVPVA 30%K = 0.987 (Tg in K, densities 1.35 and 1.18 g/mL); Tg 88.5 °C against about 89.6 °C read from the figureDSC[moseson2022c E6, R9]
PCZ–HPMCAS 50/50printed line about 81.5 °C; recomputed 89.1 °C with K = 0.852 (Tg in K) and 81.4 °C with K = 0.504 (Tg in °C)DSC[shah2024 E2, R6]
indomethacin–PVPVA 25% film at 0, 5, 10, 20 minlocal Tg 111, 95, 88, 82 °C; 23, 44, 52, 60 wt% drugnanoTA, immersed and dried[saboo2020 R28]
MePHPH–PVPVA dry dispersionsK = 0.65DSC, midpointdeac2024b R32, E14
Pitfalls and disagreements

The unit of K matters: with Tg in °C the 50/50 IDM–PVPVA prediction would be 62.9 °C instead of 72.9 °C [moseson2018 E3]. A miscible 33% DL lopinavir film reads as about 40% LPV on the fitted curve, so local contents carry about ±10% DL uncertainty li2019 X17. In the posaconazole paper the printed line matches K computed from Tg in °C, whereas in the indomethacin paper it matches K computed from Tg in K; neither paper states the unit [shah2024 E2; moseson2018 E3]. The plotted lines of the 2006 felodipine paper reproduce only with Tg entered in °C in the density-based constant; in kelvin PVP too falls about 14 °C below its line konno2006 X3. HPMC deviates more than HPMCAS although HPMCAS bonds more weakly konno2006 X10. The nanoTA probe is about 50 nm deep and worked on films, while FTIR and EDX of the same chapter worked on tablets, so the surface drug content at 20 min is best quoted as about 60–72 wt% [saboo2020 X15].

← Concepts and formulas

concept · as used in Physical stability

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 Physical stability

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⁻¹baird2012 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 filmskonno2006 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 polymer[wilson2021 C45, C46, R3]
bicalutamidefractures of mechanically activated samples favour heterogeneous nucleationdispersions[moseson2022b C45]
induction-time replicates, 50–80 mL, S 2.4–15.4scatter below 15%triplicate[ilevbare2013c R17]
danazol, HPMC-ASinduction time 516 → 277 min as drug concentration rises from 10 to 20 µg/mL25 °C[jackson2014 R17]
telaprevir δ 28.8, buffercrystallizes immediately with a drug-rich phase presentpH 6.5, 37 °C[lu2017 R4]
atazanavir ASD particlesdissolving ASD did not seed nucleation (about 300 against 350 min)PVPVA + SDS, pH 6.8[indulkar2019b R5, C25]
ritonavir with SDS; Tween 80, below and above LLPSabout 262 against 34.7 min; about 289 against 23.6 min37 °C[ilevbare2013d R16, R12]
nifedipine dispersions against glassγ → α complete in ≈5–40 min against ≈40–145 min with dissolved polymer25 °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 Physical stability

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% testedcalculated[saboo2020a R27, C36]
ritonavir–PVPVAcongruent at 10–25%, contrary to the single-ratio predictiontablets[indulkar2019a C24, C25]
celecoxib (ASD dissolution chapter)Corrigan's condition as the basis of polymer control at low and drug control at high loadingcited[xie2016a 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 Physical stability

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 extruder[moseson2021 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 extruderalvarenga2022 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, SHG[shah2024 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 Physical stability

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 °Cmarsac2006a E3, R4
34 drugsΔGv −8.6 (lidocaine) to −54.7 J/cm³ (acetaminophen)298 Kbaird2012 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 °C[duong2022a R27]
ritonavir, efavirenz, celecoxib≈10.2, ≈2.70, ≈7.74 kJ/mol (extractor calculation)37 °C[ilevbare2013c E7]
six dihydropyridinesused for the yardstick of F5; no ΔG value printed25 and 37 °C[raina2015a E2, R11]
diverse drugsCp method closer to the measured LLPS onsets than the Hoffman equation25 °C[almeidaesousa2015 R11, C43]
ritonavir10.1 kJ/mol (extractor recomputation from Table 2 inputs)37 °Cilevbare2013a E2
ibuprofen to griseofulvin3.24, 4.84, 5.69, 8.51, 10.33, 9.69 kJ/mol25 °C[almeidaesousa2015 R11]
telaprevir13.31 kJ/mol (recomputed); amorphous solubility 245 ± 5 µg/mL, 2.7 times the onset37 °C[mosqueragiraldo2015 E1, R13, R17]
clotrimazole6.26 kJ/mol with a molar mass not printed in the paper (extractor)310 K[indulkar2015 E3]
CRH15.68 kJ/mol; estimate 11.2 µg/mL at pH 4.625 °C[almeidaesousa2016 M1, R2]
atazanavir14.55 kJ/mol (recomputed from Table I); ratio about 62, as printed, with 0.22 read as exp[−I(a)]; about 228 read as I(a)310 K[indulkar2017a E2, X1; indulkar2015 M2]
felodipineHoffman ratio 10.92 (25 °C), 8.64 (37 °C); water factor 0.74, 0.83Tm 147 °C, ΔHf 28.67 kJ/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 K[wilson2018 E1, R3, X1]
ritonavirΔHf 60.4 kJ/mol, Tm 121 °C, 37 °C: ΔG = 10.1 kJ/mol and exp(ΔG/RT) = 50.8 (extractor calculation); calculated amorphous solubility 20.6 µg/mL with the water term37 °C[ilevbare2012b E8, E9, R1]
glyburide; warfarinabout 60-fold and 48-fold (59.9 and 47.7 recomputed) from Tm 175.6 °C, ΔHf 45.5 kJ/mol and Tm 169.2 °C, 43.6 kJ/mol25 °C (assumed)[hsieh2014 R16, E3, M3, M4]
danazolTm 225.4 °C, ΔHf 28.9 kJ/mol: ΔG = 6.95 kJ/mol; ratio with the 0.935 water factor 15.4 recomputed against 19.6 printed25 °C[jackson2014 E1, E2, X1]
five weak basesratios 22.2, 11.9, 20.4, 54.6, 7.0 without water correction (carvedilol, clotrimazole, clozapine, ketoconazole, loratadine)37 °C[hsieh2012 R10]
felodipine (six-dihydropyridine study)e^(ΔG/RT) recomputed 10.84 at 298.15 K from 74.6 J/g and 147 °CDSC data of the paper[raina2015b E1, R1.b]
posaconazoleTm 169.1 °C, ΔHf 76.95 J/g; printed amorphous/crystalline ratio 37.9 with water factor 0.33, estimate 10.22 against 9.08 µg/mL measured310 K; the extractor obtains ΔG = 16.13 J/g and a ratio of about 26.5duong2022b 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 6.8[alonzo2011 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 Physical stability

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 chemistrykestur2010a C24, M3; kestur2011 C26
PVP amide against carboxylic acidthe amide is the more basiccitedtaylor1997 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 classesvaneerdenbrugh2011a R2; wegiel2013a R12
E100 amine; imidazole of bifonazolestrong 1.98 (triethylamine); very strong 2.72 (1-methylimidazole)samevaneerdenbrugh2011a R1, R2
ester, COOH carbonyl, ether, alcoholmedium: 1.07, 1.07, 1.01, 1.02samevaneerdenbrugh2011a R2; wegiel2013a R12
amide carbonyl of benzamide, phenacetinstrong 1.81, 1.69samevaneerdenbrugh2011a R1
PSSA sulfonic acidlow 0.71 (acceptor); very strong donorsamevaneerdenbrugh2011a 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 Physical stability

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 vacuumtrasi2012b R25
flutamideone NH donor; carbonyl and nitro acceptorsstructuretrasi2012b C20
acetaminophenphenol OH the stronger donor; amide carbonyl the much better acceptorstructuretrasi2012a C32
curcumin with PVP against cellulosicsacceptor-only polymer against donor-and-acceptor polymersstorage stabilitywegiel2014 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 Physical stability

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-evaporatedtaylor1997 R5.l, R11, R12
amorphous indomethacinacid dimer at 1710 cm⁻¹ (IR) with no Raman bandquench-cooled melttaylor1997 R5.h, R6
indomethacin, felodipine, sucrose, ketoconazole with PVP K12PVP C=O shift 45, 25, 25 and 0 cm⁻¹one donor per carbonyl, spin-coatedmarsac2009 R12
felodipine with PVP, PVP/VA, HPMCAS, PVAcNH at 3294, 3298, 3348, 3354 cm⁻¹ against 3341 cm⁻¹50 wt% polymer filmskestur2010a R9
nimesulideNH at 3345 cm⁻¹ at every concentrationdichloromethane, 1–100 mg/mlkestur2011 R11
nimesulide with PVPPVP C=O ≈1684 → ≈1680 cm⁻¹, shoulder ≈1657 cm⁻¹20–50 wt% PVPkestur2011 R14
felodipine–PVP, nifedipine–PVPsecond PC with NH and carbonyl loadings10–90% and 25–70% PVPrumondor2009a 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% polyphenolwegiel2013a R2, R4
dextran–PVPPVP C=O 1680 → 1661 cm⁻¹; hydrogen-bonded fraction 1.00 (DEX1–PVP12) to about 0.09 (DEX450–PVP90) at 0.8 dextranspin-coated films[vaneerdenbrugh2012a R2, R14]
benzamide, phenacetin crystalsamide–amide only 100 and 94% alone; 0% with a COOH partner; 14 and 33% with C(O)NC2CSD surveyvaneerdenbrugh2011a R14
lumefantrine–PVPVAcarbonyl bands fixed at 1736 and 1684 cm⁻¹ at 10, 25 and 50% drugdried spin-coated filmshiew2022a R17

Evidence table: hydrogen bonding.

Pitfalls and disagreements

Assignments rest on analogy with liquid models: the same non-bonded acid C=O is assigned at 1735 cm⁻¹ (chain ends) and 1726 cm⁻¹ (PVP-bonded molecule), and how one turns into the other is not shown taylor1997 C32, X4. IR bonds were recorded at 20–50 wt% polymer, whereas the growth effects were measured at 0.5–5 wt% and 70–110 °C kestur2010a X5; kestur2011 X10. The felodipine–PVP carbonyl shift is 25 cm⁻¹ in one paper and about 20 cm⁻¹ in a cited study marsac2009 R12.b; kestur2011 R20. A drug without a donor (ketoconazole) shows no shift yet mixes about athermally marsac2009 R7.c, R12.h. For bifonazole the donor–acceptor picture rests on crystal-structure reasoning and was not measured kestur2011 X9. The bond between indomethacin and PVP is proposed as the reason PVP inhibits crystallization, but no crystallization was measured in that paper taylor1997 X8. The PVP shoulder at 1661 cm⁻¹ with naringenin overlaps the drug's own band, and HPMC and PAA are placed on the IR trend line by projection wegiel2013a X9, X12. The bonded fraction of dextran–PVP rests on references set by one system and on films prepared differently from the DSC samples [vaneerdenbrugh2012a X12, X8]. No hydrogen bond was measured in the 15-drug screen, and its melt spectra are not shown vaneerdenbrugh2011a X13.

← Concepts and formulas

concept · as used in Physical stability

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 filmsyang2022b C61, C35
SDS, CTAB, TPGS, Tween 80HLB 40, 22, 13.2, 15citedcorreasoto2022a R1
Span 20, Span 80, Span 85HLB 8.6, 15 (as printed), 11citedcorreasoto2022b M7, M8, M9
SDS, Tween 80, TPGS, Span 20, Span 85 in ritonavir–PVPVA 30:70HLB 40, 15, 13.2, 8.6, 1.8 (cited); ritonavir ≈78, ≈25, ≈89, ≈41, ≈87% at 90 minpH 6.8, 37 °C[indulkar2022 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 Physical stability

hydrophobicity

The tendency of a drug to avoid water, read in the library from its calculated log P; for the moisture-separation papers a hydrophobic drug is expected to have a positive water–drug interaction parameter, so that sorbed water makes the dispersion less favourable for it rumondor2010c C30, M1, M2, M3, M4. The same papers treat it as one of three factors, with dispersion hygroscopicity and drug–polymer interaction strength, behind moisture-induced amorphous–amorphous phase separation rumondor2011 C1, C28.

Findings

F13, F23.

Related concepts

related to hygroscopicity (the two together set the water–drug term); part of the argument for moisture-induced phase separation; enters Flory-Huggins interaction parameter (\chi_{WD}); related to lipophilicity.

Formulas

multicomponent Flory-Huggins free energy of mixing, through the water–drug parameter \chi_{WD} rumondor2010c E1, C30.

How it is measured or obtained

Calculated log P (ChemBioDraw Ultra) for the drugs rumondor2010c M1; rumondor2011 P9; cited log P for resveratrol and felodipine wegiel2013b R20. The water uptake of the hydrophobic films themselves was not measured rumondor2011 X6.

Values in the library
materialvalue or classconditionspaper ids
felodipine, quinidine, indomethacin, pimozidecalculated log P 2.24, 2.48, 3.58, 5.34drugs of PVP, PVPVA and HPMCAS dispersionsrumondor2010c M1, M2, M4, M3
indoprofen, nilutamide, loratadine, clofoctol, probucollog P 2.84, 2.14, 4.13, 8.19, 10.0drugs of PVP filmsrumondor2011 R15.e, R15.s, R15.t, R15.f, R15.g
resveratrol against felodipinelog P 3.1 against 4.5 (cited)contrast of PVP dispersions in humid storagewegiel2013b R20
pimozide with HPMCASthe only HPMCAS dispersion that separated; attributed to hydrophobicity94% RH, driedrumondor2010c C35, R3.e
clofoctol–PVP (≥ 70% drug), probucol–PVP (90% drug)no separation up to 94% RH; "it is thought" too little water sorbed22 °C filmsrumondor2011 C36, R14
Pitfalls and disagreements

The direction of the effect is disputed within the library: pimozide's high log P is used to explain separation even with HPMCAS rumondor2010c C35, while in the 20-system study the two most hydrophobic drugs were the only ones that resisted at some compositions and log P was dropped from the discriminant model as insignificant rumondor2011 X14, R16. Calculated and cited log P values differ between papers for the same drug: felodipine 2.24 rumondor2010c M1 against 4.5 wegiel2013b R20.

← Concepts and formulas

concept · as used in Physical stability

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% RHmugheirbi2017 R2.a
AFFINISOL2.03, 0.89, 0.19% w/w; about 63% of E3 at 40% RHsamemugheirbi2017 R2.d, C21
PVP, HPMC, HPMCAS (outside)PVP absorbs more water than HPMC, HPMC more than HPMCAS, at the same RH and temperature25 °Crumondor2010a C6, R1
ritonavir ASDs (outside)PVP and PVPVA are more hygroscopic than HPMCAS, so their ASDs are expected to be more prone to moisture-induced AAPSargumentpurohit2017b C45
polymer hygroscopicity and AAPS (outside)the water–drug contribution to the free energy of mixing depends on the water sorbed, which depends on polymer hygroscopicityfelodipine, indomethacin and others in PVP, PVPVA, HPMCASrumondor2010c C30
PVP, HPMC, HPMCAS, felodipine≈33.5, 10.9, 6.2, 0.7 g/100 g75% RH, 25 °Ckonno2008 R8
felodipine with 25% PVP, HPMC, HPMCAS≈4.7, 2.3, 1.7 g/100 g75% RHkonno2008 R9.d
nifedipine vs felodipine with 25% PVP≈5.5 vs 4.6 g/100 g75% RHmarsac2008a R2
felodipine–PVP vs HPMCAS dispersionsPVP dispersions more hygroscopic (cited)93% RHrumondor2009b R25
75:25 felodipine and quinidine with PVP, PVPVA, HPMCAS6.4/3.6/2.4 and 5.3/3.4/2.4 g per 100 g25 °C/85% RHrumondor2010c R18
PVP, PVPVA, HPMCAS alone≈50, ≈24, ≈8 g per 100 g at ≈85% RHcited isotherms, 25 °Crumondor2010c R19
40% resveratrol–PVP dispersion against its physical mixture≈12.8 against ≈36.5% at 95% RH25 °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 °C[saboo2020a R3]
amorphous felodipine≈1.3% at 75% RH37 °C[saboo2020a R3]
40% HPMCAS dispersions of nilvadipine, felodipine, cilnidipine≈5.83, ≈5.67, ≈5.45% at 100% RH (extrapolated)37 °C[saboo2020a 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 Physical stability

ideal solubility

The solubility a crystalline drug would have if it mixed ideally with the solvent; it is set by the melting temperature and the enthalpy of fusion alone marsac2008b E1. The real solubility differs from it by the activity coefficient, \ln[\gamma_d x_d] = -\Delta G_{fus}/(R\,T), with \Delta G_{fus} taken from the Hoffman relation in the PEG study [baird2011 E5, E6, E7]. Marsac and co-workers use it as the reference for the activity coefficients in PEG 400 and in water marsac2008b R14. New aspects (Miscibility and drug-polymer interactions): The mole-fraction solubility a crystal would have if it mixed ideally (γ = 1) is fixed by its heat of fusion, melting point and the heat-capacity difference between liquid and crystal, which enter the equation as integrals from the melting point to the temperature of interest; the real solubility is this value divided by the activity coefficient marsac2006b E5; marsac2009 E1, C4. High melting point and high heat of fusion lower the solubility in any solvent or polymer, so drugs with these properties and no strong polymer interaction "will display very low solubility" and "will most likely be harder to stabilize" marsac2006b C52, C53, C54. New aspects (Physical stability): the lattice term of the solubility equation separated the two dihydropyridines: nifedipine's larger term (higher heat of fusion and melting point) makes its crystal less soluble in NMP although both drugs mix exothermically with it marsac2008a R11, C35.

Findings

PEG dispersions: F3, F11. Miscibility and drug-polymer interactions: F8, F9. Physical stability: F2.

Related concepts

measured by enthalpy of fusion; part of activity coefficient; depends on crystal lattice energy; related to drug solubility in polymer and cosolvency.

Formulas

activity coefficient from solubility; solid-liquid equilibrium solubility equation.

How it is measured or obtained

Calculated from DSC melting data (heating at 10 °C/min in pin-holed pans; or the melting point and heat of fusion of Table 1) [marsac2008b P8, P9; baird2011 E7]. The mole-fraction values of Marsac and co-workers are printed without the relation or the temperature, and the extractor recomputed them at 25 °C from the melting data marsac2008b E1, X5. In the miscibility papers the heat-capacity terms are cited and not printed, and for ketoconazole the heat-capacity difference was approximated by its value at Tg, integrated between Tg and Tm; the ideal solubilities themselves are not printed marsac2009 P7, X4; marsac2006b X11. In the 2008 NMP study the lattice term is obtained from the measured mole-fraction solubility and the activity coefficient, as the first term of \ln x = -\frac{\Delta H_{fus}}{RT}\left(1 - \frac{T}{T_M}\right) - \ln\gamma marsac2008a E3.

Values in the library
materialvalue or classconditionspaper ids
acetaminophen, ketoprofen, naproxen, ibuprofen, felodipine, ketoconazole0.02, 0.10, 0.01, 0.18, 0.03, 2.0 × 10⁻³ mole fraction as printed; extractor's values at 25 °C 0.020, 0.097, 0.0047, 0.18, 0.023, 0.0016from melting datamarsac2008b R14, X5
loratadine in PEG 400about 0.109 ideal against 0.046 measured25 °C, Table 1 inputs[baird2011 X13, R9.c]
nifedipine; felodipineΔHfus 39.89 and 30.83 kJ/mol; Tm 445.25 and 414.75 K (inputs)DSCmarsac2006b M1, M2
indomethacin; ketoconazole; sucroseΔHfus 39.68, 54.10, 44.70 kJ/mol; Tm 432.93, 421.25, 448.84 K (inputs)Table II of the 2009 papermarsac2009 M6, M3, M5
itraconazole; ibuprofenΔHfus 56.70 and 24.11 kJ/mol; Tm 438.35 and 347.88 K (inputs)as abovemarsac2009 M4, M7
nifedipine against felodipinethe lower-melting, lower-ΔHfus felodipine is predicted more soluble in PVP (0.25–0.31 against 0.06–0.07 g/g)with χ −4.2 and −3.8marsac2006b R17, C52
nifedipine; felodipinelattice term ≈−5.3; ≈−3.5 (natural-log units)25 °Cmarsac2008a R11
Pitfalls and disagreements

The temperature of the printed ideal solubilities is not stated, the naproxen row is not consistent with its coefficients (they fit about 0.0045, not 0.01), and the two coefficients printed for felodipine fit different ideal solubilities marsac2008b X5. The naproxen Tg used in the same paper does not follow from the Tg/Tm rule it cites marsac2008b X4. The temperature and the heat-capacity values of the 2006 Table II are not printed, and under recomputation with the heat-capacity terms set to zero one value (felodipine in PVP K29/32) does not match marsac2006b X11. The two-drug comparison of melting properties is confounded by the different χ of the two drugs marsac2006b X13. The melting temperatures of Table II lie 2–3 °C below the plotted pure offsets, so χ cannot be recomputed from the table alone marsac2009 X4. Melting data of the two dihydropyridines are not printed in the 2008 NMP paper; the lattice terms are derived from the solubility data marsac2008a E3.

← Concepts and formulas

concept · as used in Physical stability

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% RH[duong2022a 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% RH[duong2022a 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% RH[duong2022a 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 = complete[duong2022a R26]
delamanid edisylate dispersions with HPMCP, 10–40% drug≈99 / ≈98 / ≈95 / ≈59 / ≈21 µg/mL of 100PBS pH 6.5, 37 °C[duong2022a R24]
chloride and edisylate dispersions with HPMCP-50, uncoated tablets≈86 and ≈93 µg/mL after a pH 1.6 stage against ≈62 µg/mL for the free basepH 1.6 → 6.5[nguyen2023b R2]
Pitfalls and disagreements

No PXRD of any salt dispersion and no storage data for salt dispersions appear in the main text, so the crystal-free state is asserted rather than shown, and the free-base and salt dispersions were cast from different solvents with an unstated drug-loading basis [duong2022a X8, X7, X6]. The salt does not stop crystallization where the polymer stays undissolved: salt dispersion films crystallized at pH 3.0 like the free base, and the salt "only partially remediated" the pH dependence [nguyen2023b C17; nguyen2023c C20]. Three of the four salts chosen for their stability liquefied at 40 °C/75% RH, and release of several salt dispersions was lower after an acid stage than in a single stage [duong2022a X19, C63].

← Concepts and formulas

concept · as used in Physical stability

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 Physical stability

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 penaltyargumentkonno2006 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 hydrationsaboo2021 C40
flutamide prenucleiunfavourable interfacial term outweighs the volume term below a critical radiusframeworktrasi2012b 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 7.6[ilevbare2012a 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 Physical stability

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 cellkestur2011 R11, R17
nimesulideNH ≈3288 (crystal), ≈3276 cm⁻¹ (amorphous)KBr; spin-coated filmkestur2011 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, stabilitytrasi2012b 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; IRwegiel2013a 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 scanvaneerdenbrugh2011a R6, C18
lumefantrineOH···N bond in the crystal; no PVPVA carbonyl shiftcrystal structures (cited); IRhiew2022a R33, R17
flutamideplanar lowest-energy conformer with the carbonyl next to C(5)–H; second minimum ≈2.7 kJ/mol higher; barriers ≈23 kJ/molDFT, vacuumtrasi2012b R23, R24
flutamide crystalamide carbonyl in a bifurcated bond, one contact intramolecularcited structuretrasi2012b R26
amorphous curcuminketo–enol band at 1626 cm⁻¹ as in the crystal; no carbonyl band near 1700 cm⁻¹IRwegiel2014 R2, C11
curcumin against resveratrol with PVPbonded PVP carbonyl dominant only at 60% curcumin, already at 50% resveratrolIR of filmswegiel2014 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 Physical stability

ionic interactions

Attraction or repulsion between charged species

In the mesoporous-silica papers: attraction between a protonated weak base and the deprotonated silanols (SiO⁻) of silica above about pH 2, which the authors take as the primary binding of ketoconazole ("confirmed") and clozapine ("seemed") at intestinal pH [hate2020b C18, C26, C28, C35]; and repulsion, invoked for anionic SDS on negative silica and, "to a small extent", for protonated atazanavir on positive silica at pH 1 [dening2019 C56; hate2020a C50]. Ion exchange was excluded for un-ionized ritonavir because the non-ionizable lopinavir behaved alike [dening2018 C46]. In a crystal-growth study, electrostatic forces were considered unlikely to dominate polymer–polymer complexes because water competes and an ionized adipate group repels [ilevbare2012a C41].

Findings

F6, F12, F13.

Related concepts

depends on the surface charge of silica and the ionization of the drug at its pKa; probed by competitive adsorption; contrasts with drug-silanol hydrogen bonding; causes re-adsorption after pH shift.

Formulas

Henderson-Hasselbalch equation.

How it is measured or obtained

Zeta potential of the silica against pH; ionized fraction of the drug from its pKa; isotherms at several pH values; adsorption with a competing cation (50 mM triethylamine) against a hydrogen-bond competitor (urea); release with the competing cation added at a pH shift [hate2020b P4, P10, P2, P3, P7].

Values in the library
materialvalue or classconditionspaper ids
ketoconazole on SBA-15, pH 6.8about 66 → 8.6 mg/g with 50 mM triethylamine; about 47.7 with 0.5 M urea37 °C, HPMC[hate2020b R14]
clozapine on SBA-15, pH 6.8about 53 → 25 mg/g with triethylamine; about 54 with ureasame[hate2020b R14]
ketoconazole; clozapine, pH 1 → 6.8 with triethylamineabout 93 → 88%; 85 → 80% released, against about 64–69% without50 mL, 37 °C[hate2020b R15, R16]
ritonavir; lopinavir on SBA-15release about 50%; 40–50%, read as no ion exchangepH 6.8[dening2018 R6, R19, C46]

Evidence table: ionic interactions.

Pitfalls and disagreements

The final pH after adding 50 mM triethylamine is not reported [hate2020b X7]. The authors extend electrostatic binding to all three bases, but atazanavir was never tested with competitors and adsorbs least at pH 6.8, where it is almost uncharged [hate2020b C48, X4]. The silica charge was measured in water, not in the test buffers, and is only about +1.7 mV at pH 1, small for the repulsion invoked there [hate2020b R2, X12; hate2020a C50]. The ion-exchange exclusion for ritonavir rests on the similarity of two drugs, with the pore pH unmeasured [dening2018 X11].

← Concepts and formulas

concept · as used in Physical stability

ionization

The fraction of a drug that carries a charge at the pH of the medium, set by the pKa through the Henderson–Hasselbalch equation. In this chapter the un-ionized concentration is what the amorphous solubility limits: "LLPS cannot occur until the concentration of the un-ionized form is exceeded", so more total drug is needed at lower pH for a base [indulkar2015 C47]. An ionized second solute does not mix into a hydrophobic drug-rich phase [trasi2015a C44]. The papers of 2017–2022 add pazopanib (strongest basic group pKa 6.4): fully ionized in gastric fluid and essentially un-ionized at pH 8.4, with a crystalline solubility that falls by more than four orders of magnitude between pH 1.2 and 6.5 [sugihara2018 M1, C9, C19]. New aspect (Bioperformance): only the unionized free drug is thought to cross a membrane passively [raina2015c C49]. In a PAMPA receiver at pH 3 atazanavir (pKa 4.48) ionizes on crossing and keeps the receiver free drug near zero [hate2022 C52]. Most model drugs of the Bioperformance papers were unionized or nearly so at the pH used (synthesis: from the table rows below). New aspect (Crystallization from solution): In the pH-shift studies the ionization of a weak acid or base sets the supersaturation: raising the pH of a base (or lowering that of an acid) beyond the pKa leaves the less soluble neutral form above its crystalline solubility; the final pH was at least two units beyond the pKa [hsieh2012 C1; hsieh2014 P2]. In the growth and nucleation papers the ionization of the polymer matters instead: the carboxylated cellulose esters are nearly fully ionized at pH 6.8 and less than 25% ionized at pH 3.8, whereas the drugs are un-ionized at both (see polymer ionization) [ilevbare2013b R18, C33]. Media were chosen to keep 11 drugs un-ionized (naproxen about 18%, indomethacin about 9% and compound 1 about 20% still ionized by the card's arithmetic); celecoxib is about 7.5% ionized at pH 10 and flibanserin 80% un-ionized at pH 6.5 [chen2015 C6, X3; li2016a R3]. New aspect (Release mechanism and LoC): ionization of the dispersion polymer rather than the drug. For the enteric polymer HP-50, partially neutralized BIS-TRIS salts dissolved more slowly as ionization fell from 100 to 20%, with the largest drop, almost 2-fold, from 100 to 80% [qi2022 C21, R13]; the series "confirms" the importance of the ionized form, and the critical ionization of about 83% estimated for HP-50 "may explain" the drop [qi2022 C36]. Polymer solubilization via ionization, linked to transport of protons across the boundary layer, is called the rate-limiting step of HP-50 dissolution [qi2022 C2]. For weak bases with HPMCAS the 2024–2025 papers compute ionization at the gel pH from pKa: at pH 6.0 HPMCAS about 96% (printed), cinnarizine above 99%, clotrimazole 46% and loratadine 14%; loratadine complexation fell with its calculated ionization from about 20% (pH 5.8) to 0.5% (pH 7.5) [bapat2024 R19, X4; bapat2025a R13, C32]. Bedaquiline was about half protonated (55 ± 4%) in its complex with HPMCAS and in a dry dispersion (52 ± 7%) by XPS [kaur2025 R20].

Findings

Amorphous solubility and LLPS: F10, F11, F13, F14, F23. Bioperformance: F1, F11, F22, F26. Crystallization from solution: F1, F2, F11, F16, F28, F29, F44. Release mechanism and LoC: F24, F32, F33.

Related concepts

quantified by pKa; gives pH-dependent solubility; calculated with the Henderson-Hasselbalch equation; sets the amorphous solubility in total-concentration terms. Related to pH-shift dissolution and polymer dissolution pH threshold. Related to polymer ionization and pH-induced precipitation; of the polymer: critical ionization for polymer dissolution. Of the polymer: critical ionization for polymer dissolution, polymer salt formation, microenvironmental pH.

Formulas

Henderson-Hasselbalch equation, pH-solubility profile. Amorphous solubility advantage with water-sorption correction (ionization term).

How it is measured or obtained

Calculated from the pKa and the pH; the pKa of atazanavir was measured by UV-metric titration in 0.15 M NaCl at 37 °C, the others were taken from the literature or predicted [indulkar2015 P2, E1]. In the Bioperformance papers the ionization is taken from the pKa and not measured: felodipine pKa below 2 and nifedipine below 3.5 at pH 6.8 raina2014a C9, E4; ezetimibe phenol 9.72 [elkhabaz2017 C6]; nevirapine 2.8 [hate2017 C8]; clotrimazole about 6, 99% unionized at pH 8 [indulkar2016 C8]; atazanavir 4.52 or 4.42 [hate2018 C15, X1]. In the pH-shift studies: pKa by UV-metric titration (and cosolvent extrapolation for the poorly soluble bases) at 37 °C and 0.15 M KCl; the neutral-species concentration by mass and charge balance [hsieh2012 P1, P2, P3, P4]. In the release-mechanism papers: degree of ionization set by the amount of base used to make the partial salt, not measured [qi2022 X9]. Henderson–Hasselbalch from pKa [kaur2025 E2; bapat2025a P11]; XPS N 1s with a protonated component near 402 eV [kaur2025 R19; bapat2024 R8].

Values in the library
materialvalue or classconditionspaper ids
clotrimazole98.7% ionized at pH 4; 0.8% at pH 8pKa 5.89[indulkar2015 R18]
atazanavir90.9% ionized at pH 3.5 (91.3% recalculated); 0.0% at pH 9pKa 4.52[indulkar2015 R18, X4]
nicardipine94.1% at pH 6; 0.9% at pH 9 (1.6% recalculated)pKa 7.2[indulkar2015 R18, X4]
ritonavirun-ionized at pH above 7.0pKa 1.8 and 2.6ilevbare2013a C13
diclofenacionized at pH 6.8; did not mix with the ritonavir-rich phasepKa 4.2[trasi2015a M5, R11]
CRH1un-ionized and ionized equal at equilibrium at pH 4.6pKa 4.6[almeidaesousa2016 C13]
pazopanibdissolves in SGF (pH 1.2); essentially un-ionized at pH 8.4pKa 6.4[sugihara2018 C9, C19]
felodipine, nifedipineionization term set to 1pH 6.8raina2014a C9
clotrimazoleabout 99% unionizedpH 8[indulkar2016 C8]
ezetimibebuffer solubility measured at pH 2 because of degradation at neutral pH[elkhabaz2017 C9, X5]
atazanavir, clotrimazoleamorphous solubility rises as pH falls toward the pKa; ratio constant[indulkar2015 C46]
atazanavirpH 3 receiver acts as a sink like 2% SDSPAMPA, pKa 4.48[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, 4[chen2015 X3]
posaconazolepKa 3.6 and 4.6 (cited); unionized at pH 5.5–7.5; crystalline 0.31–0.34 µg/mLFaSSIF-V2 buffer, 37 °C[shah2025 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 1s[bapat2024 R8]
bedaquiline: free base, complex, dry 40% dispersion4, 55, 52% protonatedXPS N 1s[kaur2025 R20]
HPMCAS and bedaquiline at pH 6.0 and 5.891.5 / 88.1% and above 99% ionizedHenderson–Hasselbalch[kaur2025 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 Physical stability

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 °Cmarsac2006a R3
with 3 wt% PVPbelow Tg 127 and 201; above Tg 103 and 111 kJ/molsamemarsac2006a R3.c, R3.d
felodipine with 3–25% PVP, HPMCAS, HPMCspeculated rise of ΔGa, set by amount rather than type of polymer22 °C, drykonno2006 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 Physical stability

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 °CHoffmanmarsac2006b R12
nifedipine, felodipine in PVPpredicted solubility 0.06–0.07 and 0.25–0.31 g/gFlory–Hugginsmarsac2006b R17
five compounds in PVP K29/3282–99% of the drug above solubility at 0.50 polymerpredictedmarsac2009 R11
pure nifedipine and felodipine against their dispersionsnucleation much faster for the pure drugscitedmarsac2006b 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 Physical stability

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, midpointpurohit2015a 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 filmspurohit2015a R1, R12, C38
itraconazole–HPMC, dry against water-containing solventmiscible as a dry binary; trapped separated state with waterfilms, spray-dried particlesmugheirbi2017 C39
evacetrapib–HPMCdrug droplets stay trapped when the water has goneternary diagram argumentli2017 C38
felodipine–PVPdry glass as a trapped one-phase mixture that water plasticises enough to separateargumentrumondor2009c C36
delamanid free-base ASDssolvent evaporation rate decides whether material is trapped before nucleation and growthrotary evaporation[duong2022a 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 Physical stability

kinetic versus thermodynamic control of crystal growth

Growth of a crystal from a supercooled liquid needs both mobility and a driving force: near Tm mobility is high and the driving force low (thermodynamic control), and on cooling the driving force rises while mobility falls (kinetic control) mosqueragiraldo2014 C25. Felodipine growth that slowed on cooling over 70–110 °C was read as transport-limited kestur2010b C22, C23. In the indomethacin polymorph paper mobility limits growth below the temperature of fastest growth and the driving force above it, and the steep rise of polymer inhibition above that temperature is placed in the second region tian2017 C22, C35, C36.

Findings

F3, F22, F29.

Related concepts

depends on thermodynamic driving force for crystallization and molecular mobility; related to melting point depression and degree of supercooling; contrasts with Tg-scaled crystal growth rate.

Formulas

temperature of maximum crystal growth rate.

How it is measured or obtained

From where growth peaks between Tg and Tm and from how an additive's effect changes with temperature trasi2012a C35; mosqueragiraldo2014 C36.

Values in the library
materialvalue or classconditionspaper ids
celecoxib with 10% TPGS and 10% PVPcelecoxib Tm 151.49 °C (12 °C depressed); growth about 0.03 of PVP alone at 120 °C, 0.6 at 70 °Cseeded melt growthmosqueragiraldo2014 R5.f, R2.b, X5
celecoxib with 3, 5, 7% PVP, with and without TPGSpaired curves cross at 110, 100, 90 °Csamemosqueragiraldo2014 R3, R4, C14
felodipine form IIgrowth falls on cooling from 105 to 70 °C although the driving force risesmelt filmskestur2010b C22, C23
acetaminophengrowth maximum closer to Tm, nucleation at larger supercoolingclassical picturetrasi2012a C35
indomethacin α with 10% HPMCfastest growth moved from 135 to 100 °C; ratio without/with polymer ≈11 (100 °C) → ≈2900 (120 °C)melt growthtian2017 R15, R12
Pitfalls and disagreements

The driving force was not calculated for the celecoxib mixtures, and melting-point depression alone does not order them mosqueragiraldo2014 C33, X13. The celecoxib growth temperatures were assumed to lie in the mobility-controlled range mosqueragiraldo2014 C26.

← Concepts and formulas

concept · as used in Physical stability

Kohlrausch-Williams-Watts equation

The stretched-exponential description of relaxation, 1 - \phi(t) = \exp\left(-(t/\tau)^{\beta}\right), used in the library to fit the enthalpy recovered by aged glasses and dispersions; τ is a mean relaxation time and β a width parameter between 0 and 1 konno2006 E7; marsac2006a E7.

Findings

F5.

Related concepts

used for enthalpy relaxation; measure of molecular mobility.

Formulas

Kohlrausch-Williams-Watts equation, maximum enthalpy recovery.

How it is measured or obtained

Fitting the fraction of the maximum enthalpy recovery against ageing time by nonlinear regression konno2006 P6; marsac2006a P9.

Values in the library
materialvalue or classconditionspaper ids
felodipine 9:1 with PVP, HPMCAS, HPMCτ 208, 687, 319 h; β 0.42, 0.45, 0.47; R² > 0.92 °Ckonno2006 R9
nifedipine, felodipine glassesτ 6.3, 4.2 h; β 0.36, 0.3723.5 °Cmarsac2006a R4.m, R4.n
with 10 wt% PVPτ 42.1, 16.7 h; β 0.57, 0.4523.5 °Cmarsac2006a R7

Evidence table: Kohlrausch-Williams-Watts equation.

Pitfalls and disagreements

Both papers print the equation with the minus sign or the exponent misplaced; only the standard form reproduces their τ and β konno2006 X5; marsac2006a X4.

← Concepts and formulas

concept · as used in Physical stability

lever rule

Evidence table: lever rule. Content from the release-mechanism chapter (2023–2025), with rows from the Physical stability chapter.

The rule that gives the relative amounts of two coexisting phases from the position of the overall composition on the tie line joining them: the ratio of the amount of phase A to phase B equals the ratio of the lengths BX to AX yang2022b E1. In the Physical stability chapter it was used on a schematic ritonavir–PVPVA–water diagram to argue that relative phase amounts set bicontinuous or discrete morphology along different hydration paths yang2022b C50. In the 2023 phenolphthalein-analogue paper the majority phase after separation is the binode closer to the initial composition: a polymer/drug ratio above the plait point gives a majority hydrophilic phase with discrete hydrophobic domains, one below it a majority hydrophobic phase, and the hydrophobic-phase volume against drug load is "approximately" a step function with the step at the plait point deac2023b C34, C36. Used quantitatively in 2024: along a hydration path at constant drug-to-polymer ratio the lever rule at the spinodal gives the mass fraction of drug-rich phase, W^{\alpha} = (W_i^T - W_i^{\beta})/(W_i^{\alpha} - W_i^{\beta}), taken as continuous above 0.5 deac2024b E12, P20, C51; in 2023 it was used on a schematic ritonavir diagram with and without SDS yang2023 E2, C41.

Findings

Release mechanism and LoC: F27, F30, F31.

Related concepts

needs a tie line on the ternary phase diagram; its step lies at the critical point; decides phase inversion.

Formulas

lever rule.

How it is measured or obtained

Applied in 2022 and 2023 to schematic ternary diagrams only; no tie line was measured in those papers deac2023b E5, X14; yang2022b E1. In 2024 applied to computed PC-SAFT diagrams deac2024b E12, P20.

Values in the library
materialvalue or classconditionspaper ids
ritonavir–PVPVA–water, schematic (Physical stability chapter)relative phase amounts set bicontinuous against discrete morphologyargument onlyyang2022b C50
phenolphthalein analogue–PVPVA–water, schematichydrophobic-phase volume steps at the plait pointargument onlydeac2023b C36
MePHPH–PVPVAW^{\alpha} ≈0.15 at 27% → ≈0.82 at 39.5%PC-SAFT diagram, spinodal onsetdeac2024b R35
PHPH–PVPVA≈0.16 at 3.0% → ≈0.82 at 4.5%samedeac2024b R35
Pitfalls and disagreements

The 2023 use assumes complete separation to the binodal compositions as soon as the hydration path enters the two-phase region deac2023b E5, and on phases reaching equilibrium as fast as water penetrates, the local equilibrium assumption deac2023b C38. No computed MePHPH point lies between 27 and 39.5% except the critical point, and the fraction comes from the model only deac2024b X8, X16.

← Concepts and formulas

concept · as used in Physical stability

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 °C[indulkar2019a C2, C32]
felodipine, five polymersPVP 10, PVPVA 15, HPMC 10% DL; HPMCAS and EUDS no limit to 50%30% DL test set[saboo2020a 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)compactscorreasoto2022b C12
clopidogrel–PVPVAabout 40% DL; 50% with SDScompactscorreasoto2022a C46, C55
lumefantrine–PVPVA35% DLcompactshiew2022a C31
loratadineHPMCAS 20% at 37 °C, 5% at 5 °C; PVPVA 30% and 2%compactsyang2021 R22
BCL–PVPVAbetween 10 and 20% DL (not located)powders, polymer by size-exclusion chromatography[moseson2022b 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 6.8purohit2017b R10, R11
nilvadipine; cilnidipine in PVPVA10% (6 mol%); 15% (7 mol%); switch at about 6–9 and 7–9 mol%pH 6.8, 37 °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 6.8saboo2021 R12, P6
lumefantrine free base; eight salts in PVPVAat least 35%; 2–25%drug release only[hiew2022b R20, X7]
atazanavir–PVPVA with 5 g plasticizer per 100 g5 → 7.5–25% (citrate esters 20–25%)compacts, pH 6.8, 37 °Ccorreasoto2023 R1, C12
ledipasvir–PVPVA with 10 g TEAC, TBC; GTB5 → 15; 20%samecorreasoto2023 R11, C17
ritonavir–PVPVA with 5 g GTB or TBCcomplete release at 30%, not at 35% (cited limit 25%)samecorreasoto2023 R14, R16
MePHPH–PVPVA 40%; 50%gel drug content 40 → 49%; 50 → 59.5% over 30 minscraped gel, dry basisdeac2023a R3
PHPH, TIPP, MeTIPP, MePHPH–PVPVAlimit 5 / 10 / 30 / 40% (cited) against PVPVA in nanoparticles ≈77 / 36.5 / 9 / 5 wt%nanoparticles at 60 °Cdeac2023b R8, R3
clotrimazole–PVP K12, K17, K25, K29/32, K60, K90<5, <5, 20, ≈33, 35, ≈38%compacts, pH 8.0, >80% drug in 90–120 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 °Cdeac2024b R37
ritonavir–PVPVA + 10 parts Span 20 or Span 85between 30 and 40% (cited 25% without)compacts, pH 6.8yang2023 R2, R1
Pitfalls and disagreements

The limit depends on temperature, drug, polymer and additives, and on how it is defined; the lopinavir–HPMC films of F14 show that phase separation can raise release above a loading at which the miscible film is already drug-controlled li2019 R2. For ritonavir–PVPVA the next loading above 25% was 30% in the later release studies yang2022a C15. For coated ritonavir–PVPVA tablets the shift is inferred because polymer release was not measured [benson2025 X18]. The ritonavir release at the first failing loading (30%) differed about 1.6-fold between two series [indulkar2019a X3]. The molar loadings of the dihydropyridine study cannot be reproduced with one convention [saboo2019 X2]. The coincidence of interaction saturation with the ledipasvir limit "may be coincidental" [que2019 C45]. The link to water-induced phase separation rests on films and humidified compacts, not on dissolving tablets [indulkar2019a X6; saboo2019 X10]. The same pair gave different limits by LLPS in films at 25 °C and by congruency in tablets at 37 °C (ritonavir–PVPVA, 10–20% against 25%) [purohit2017b R11; indulkar2019a C2]. Limits from 5-min rates and from 30-min release differ for a fast crystallizer [saboo2020 X7, R8]; hydrogen bonding and Tg go together across drugs and are hard to separate yang2021 C25; correasoto2022a C49. In the 2022 ritonavir imaging paper release below 30% was measured only at 20%; the 25% limit is cited yang2022a X7. The MePHPH limit is given as 40% from an earlier paper, while the methods of the 2023 interface paper call 30% "at the LoC" deac2023a X1. The plait-point mechanism is drawn on schematic diagrams; no ternary diagram, tie line or plait point was measured deac2023b X14. The phase-diagram paper did not measure release: its limits are cited, and the MePHPH data it shows place the limit only between 30 and 50% deac2024b X9. In the PVP paper the 80% criterion is applied at an unstated time in tests of 90 or 120 min, with some profiles still rising [deac2024a X6]. For ledipasvir with SDS the 2019 study gives 5 → 30% [que2019 C10, C12], while the 2023 surfactant paper cites the gain as 7.5 → 30% yang2023 R27. The PHPH critical-point loading is 3.7% as the paper states; read from its PHPH–PVPVA–water diagram (about 2.6 wt% PHPH, 59.5 wt% PVPVA) it is about 4.2% (synthesis: 2.6/(2.6 + 59.5) ≈ 0.042), see critical point deac2024b R37.

← Concepts and formulas

concept · as used in Physical stability

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-calculatedwanapun2010 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 extrudates[shah2024 P6, R9, R10, X4]
BCL–PVPVA extrudates, XRPDLOD about 1%, LOQ about 3%S/N 3:1 and 10:1[moseson2021 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 Physical stability

lipophilicity

The affinity of a drug for lipid over water, written as log P of the neutral species. In these papers it is a descriptor used to explain solubility, membrane partitioning and transport, and it is quoted or calculated rather than measured [hate2022 C36, C53; alkalla2026 C18, C33]. In a membrane cell a high log P means a large membrane partition coefficient, so that the unstirred water layer rather than the membrane limits transport (F21) [hate2022 C44, C53]. For polymers the corresponding idea is polymer hydrophobicity. In the growth-inhibition papers of 2012–2013 it places three model drugs on a hydrophobicity scale that is then compared with the solubility parameters of the polymers [ilevbare2013b M1–M3; ilevbare2013c M1–M3]. New aspect (Release mechanism and LoC): drug lipophilicity was tested as a predictor of the limit of congruency. Saboo and co-workers (2019) hypothesized that the more hydrophobic drug lowers the hydrophilicity of the drug–polymer blend faster with composition and so releases congruently over a smaller loading range [saboo2019 C6]; for nilvadipine and cilnidipine in PVPVA the hypothesis was "incorrect for the systems evaluated" [saboo2019 C35]. Que and co-workers (2019) found that the limit "does not appear to depend" on hydrophobicity or molecular weight [que2019 C48]. Within congruent release at 40% in HPMCAS, by contrast, drug and polymer release fell with drug log P, which the authors read as support that hydrophobicity influences release "at least" in such systems [saboo2020a C19, C32]. Papers of 2021–2022 found no log P trend across four phenolphthalein analogues and six drugs, and conclude that log P "shows little indication" of dispersion performance [que2021 C29; yang2021 C19, C42]. Lipophilic plasticizers (log P around 2.5) "appear" more effective at higher loading than hydrophilic ones, and TBC or GTB lowered the water sorption of PVPVA more than dilution would correasoto2023 C44, C26. The fall in release rate of MePHPH (log P ~4) dispersions above 20% "may" come from lipophilicity lowering the thermodynamic driving force for water penetration deac2023a C53. In HPMCAS the 2024 paper found drugs of "somewhat comparable" log P (4.1–5.9) losing release with loading very differently, which "strongly" suggests drug–polymer interactions, and attributes the slower release of non-complexing drugs at high loading "likely" to lipophilicity through less hydration [bapat2024 C26, C28, C42]; the 2025 grade paper reads the faster release of loratadine than of cinnarizine from HPMCAS-LF as due to less complexation, not lipophilicity (log P 5.2 against 5.8) [bapat2025a C30].

Findings

Bioperformance: F20, F21, F22, F24. Crystallization from solution: F8, F13, F30, F44. Release mechanism and LoC: F9, F25, F26, F32, F33.

Related concepts

sets the partition into the membrane in membrane asymmetry; limits transport through the unstirred water layer; related to micellar solubilization and crystalline solubility; related to solubility parameter and polymer hydrophobicity. Measured as the octanol-water partition coefficient; tested against the limit of congruency.

Formulas

octanol-water partition coefficient.

How it is measured or obtained

Taken from the literature or calculated: a cited cLogP for enzalutamide in one paper and a MarvinSketch value in the next; log P of atazanavir, posaconazole and darunavir cited from reviews [wilson2018 M1; wilson2020 M1, P4; elkhabaz2019b M1, M2; alkalla2026 M1, M2; hate2022 M1, M6]. Calculated with ChemBioDraw (version 11.0 or 12.0, both named) or taken from the literature [ilevbare2013b X16]. In the release-mechanism papers: calculated (ClogP), cited, or measured by shake flask [saboo2019 A1; que2019 R28; saboo2020a E5].

Values in the library
materialvalue or classconditionspaper ids
enzalutamide2.98 (cLogP, cited from a regulatory report) and 4.75 (MarvinSketch)neutral species[wilson2018 M1; wilson2020 M1, P4]
atazanavirabout 4.5pKa 4.3–4.52[elkhabaz2019b M1; alkalla2026 M1; hate2022 M1]
posaconazole4.6pKa 3.6 and 4.6[elkhabaz2019b M2]
darunavir2.8pKa 2.4[alkalla2026 M2]
acetaminophen0.46 and 0.51 as printedhydrophilic comparator[hate2022 M6, X5]
lumefantrine8.34; good release to 35% in PVPVAbase form, cited[hiew2022b C35, M1, R20]
ritonavir; efavirenz; celecoxibLog P 5.6 (5.98 in the 2012 paper); 4.7; 3.5SP 20.03; 21.89; 23.38 MPa^1/2[ilevbare2013b M1–M3; ilevbare2012c M1]
growth-inhibiting windowcellulose polymers of SP 20.56–23.28 for drugs of Log P 3.5–5.65 µg/mL[ilevbare2013b C43]
13 bile saltsLogP'A of the ionized acid from 2.65 (SDC) to −0.50 (STC); none for STDC, STCDC, SLCliterature[li2016a M4–M16]
posaconazolelog P 4.6 (cited); phase-separates at about 10 µg/mLpH 6.5[shah2025 M1, C48]
nifedipinelog P 3.17 (cited)model drug[indulkar2017b M1]
nilvadipine; cilnidipineClogP 3.04; 5.54; LoC in PVPVA 10 and 15% (about 6–9 and 7–9 mol%)pH 6.8, 37 °C[saboo2019 A1, C35]
ritonavir; ledipasvirlog P 4.3, LoC 25%; LoC 5% for ledipasvircited; PVPVA[que2019 R28, R27, C10]
nilvadipine, felodipine, cilnidipine at 40% in HPMCASlog P 4.06, 4.46, 5.40; rates 0.42, 0.34, 0.26 mg/min/cm²pH 6.8[saboo2020a R16]
TIPP, Me-TIPP, PHPH, Me-PHPHlog P 6.39, 7.60, 2.63, 3.93 (ACD); limits 10, 30, 5, 40%calculated[que2021 M1, M2, M3, M4, R19]
loratadine, miconazole, danazol, elbasvir, paclitaxel, ivacaftorlog P 4.4, 5.69, 3.8, 5.33, 3.96, 5.68; PVPVA drops at 25, 40, 5, 10, 5–10, 5–10%citedyang2021 M1, M2, M3, M4, M5, M6, R7, R8, R9, R10, R11, R12
clopidogrelcLogP 3.8; limit about 40%citedcorreasoto2022a M1, C46
ritonavir (log P 5.7) against loratadine (4.55) in HPMCAS-MF, 25%0.45 against 0.17 mg/min/cm² (table values)compacts, pH 6.8[bapat2024 X18, R2]
Pitfalls and disagreements

The same drug carries two log P values 1.8 units apart in two papers of one group [wilson2018 M1; wilson2020 M1] (synthesis: 4.75 − 2.98). The large crystalline solubility gap between atazanavir (1.6 µg/mL) and darunavir hydrate (265.6 µg/mL) is attributed to crystal packing and the lower log P of darunavir, an attribution that was not tested [alkalla2026 C33, R3]. The higher PAMPA mass flow of atazanavir and nifedipine than of acetaminophen is credited to lipophilicity although the drugs also differ in dose, pKa and concentration (F21) [hate2022 C36, R16]. The Log P source is given as version 12.0 in the text and 11.0 in the table footnote; Log P values are calculated estimates [ilevbare2013b X16]. The papers use Log P only to describe the drugs; the polymer match is made on SP, not on Log P [ilevbare2013c C37]. The two log P sets for nilvadipine and cilnidipine differ (ClogP 3.04 and 5.54 against measured 4.06 and 5.40) [saboo2019 A1; saboo2020a R16]. Two drugs per comparison cannot separate log P from other differences such as the glass transition [que2019 C49]. Miconazole log P is printed as 5.69 and 5.22 yang2021 X1, and two programs give TIPP 6.39 and 8.08 [que2021 M1]. The printed log P values refer to the neutral species; indomethacin is ionized at pH 6.8, so its lipophilicity in the gel is lower than its log P [bapat2024 X18].

← Concepts and formulas

concept · as used in Physical stability

liquid-liquid phase separation

The splitting of a highly supersaturated aqueous drug solution into a water-rich continuous phase and a dispersed, non-crystalline drug-rich phase, before crystals form; the authors call it glass–liquid phase separation when the drug-rich phase is a glass [ilevbare2013a C2; indulkar2015 C38]. The concentration at which it starts is called the LLPS concentration, CL-L or coexistence concentration, and in this chapter equals the amorphous solubility within the accuracy of the methods ilevbare2013a C14, C3. It was earlier discussed as "promiscuous aggregation" in screening assays and as "oiling out" in crystallization ilevbare2013a C7, C9, C35. The papers of 2017–2022 add a weak base shifted from simulated gastric fluid to pH 6.5: pazopanib gave a milky, bluish solution at once, with particles of 495.9 nm (145.4 nm with 50 µg/mL HPMC) and no particles at a dose below its amorphous solubility [sugihara2018 R14, R15, R20], and ibuprofen droplets that measured 3182–5313 nm in buffer and 268–345 nm with HPMC or PVP-VA [ueda2020b R5]. New aspect (Bioperformance): the two phases are in metastable equilibrium with equal activity [raina2014a C3, C4, C33; indulkar2016 C1; hate2018 C5]. For high-Tg drugs such as telaprevir the term glass–liquid phase separation is used [mosqueragiraldo2018b M1]. Drug-rich spheres were also found by SEM in pooled human intestinal fluid, the first such demonstration according to the authors [elkhabaz2019b R4, C24]; a crystalline co-drug lowers the concentration at which atazanavir separates [alkalla2026 C2]. New aspect (Supersaturation from ASD dissolution): dispersion dissolution, unlike dissolution of a neat amorphous drug, can push the concentration past the amorphous solubility, so that LLPS follows dissolution and precedes crystallization [jackson2015 C7, C29]; the colloids of rapidly dissolving ritonavir dispersions "highly likely" originate from LLPS [ilevbare2013d C33].

Findings

Amorphous solubility and LLPS: F1, F2, F3, F4, F5, F8, F9, F11, F13, F15, F16, F22, F23. Bioperformance: F1, F2, F4, F5, F10, F18, F19, F27. Supersaturation from ASD dissolution: F7, F9, F10.

Related concepts

produces the drug-rich phase; special case glass-liquid phase separation; sets the amorphous solubility; described by the binodal and spinodal decomposition; grows by droplet coalescence; precedes crystallization (a precursor, F3). Produces drug-rich nanodroplets; related to metastable equilibrium.

Formulas

binodal condition, amorphous solubility advantage with water-sorption correction, ideal-mixing reduction of amorphous solubility.

How it is measured or obtained

By extinction at a non-absorbing wavelength during slow addition of a drug stock, by a polarity-sensitive probe or the drug's own fluorescence, by DLS or NTA sizing of the droplets, by ultracentrifugation of the phases, by NMR of dissolved drug, by a flux break, and by a solvent-free pH-shift titration for weak bases [ilevbare2013a P5, P10, P11; almeidaesousa2015 P1, P2; mosqueragiraldo2015 P10; trasi2015a P6; indulkar2015 P10] (F4). In the Bioperformance papers: rise of extinction on solvent shift; turbidity without birefringence under polarized light raina2014a R4, C12; droplet size and number by NTA or DLS [indulkar2016 P4; hate2018 R6, R7]; the 369 nm fluorescence band of atazanavir [hate2018 P6, C18]; the flux plateau; antisolvent titration read by 450 nm extinction [alkalla2026 P7, C16]; the drug's own fluorescence intensity and SEM of the centrifuged pellet [elkhabaz2019b R3, R4, C17]. During dispersion dissolution: the pyrene ratio, with the onset read as the UV concentration at the pyrene drop; stepwise dissolution with dilution; turbidity titration with polymer present [jackson2015 P3; ilevbare2013d P4, P2].

Values in the library
materialvalue or classconditionspaper ids
ritonavir dropletsabout 345 nm at 1 min, about 842 nm at 64 minwater, 37 °C, single addition at the onsetilevbare2013a R3
ritonavir drug-rich phase94.85–95.97% drug, 4.03–5.15% water, Tg 0.4 °C10–50 °C, ultracentrifugedilevbare2013a R5, R6
weak-base dropletsZ-average about 116–387 nmclotrimazole, atazanavir, nicardipine, 37 °C[indulkar2015 R14]
telaprevirspecies about 300 nmpH 6.8, 37 °C[mosqueragiraldo2015 R5]
ritonavir dropletsabout 360 nm at 30 µg/mL100 mM pH 6.8, 25 °C[trasi2015a R15]
pazopanib colloids495.9 nm without, 145.4 nm with 50 µg/mL HPMC (DLS); NTA about 50–650 nmpH 6.5 after pH shift, 37 °C[sugihara2018 R15, R16]
ibuprofen droplets3182–5313 nm (buffer); 272–345 (HPMC); 268–320 (PVP-VA); 472–808 nm (EUD-E)pH 2.0 (D2O), 37 °C, fresh[ueda2020b 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 8[indulkar2016 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 °C[wilson2018 R2, C16]
atazanavir, darunavir93.1 and 363.8 µg/mL (antisolvent, 450 nm)pH 6.8, 37 °C[alkalla2026 R3, C16]
pretomanidabout 166 µg/mL in buffer, 308 in FaSSIFpH 6.5, 37 °Cnguyen2023a P2, R2
danazol dispersions (eight)onset about 6.0–10.4 µg/mL against 8 µg/mLpH 6.8, 25 °C[jackson2015 R5, M1]
ritonavir–PVP dispersion, stepwiseonset between 10 and 20 µg/mL37 °C[ilevbare2013d R1, X8]
ritonavir, 180 µg/mL PVP / PAA / HPMC / HPMCAS / CAAdP 0.8518.3 / 18.3 / 18.7 / 18.2 / 21.3 µg/mL (18.2 without)titration, 37 °C[ilevbare2013d R10]
Pitfalls and disagreements

Extinction alone cannot tell droplets from crystals, and a fast crystallizer may crystallize before it phase separates (griseofulvin without polymer) [almeidaesousa2015 C16, C18]. The ritonavir phase diagram rests on four binodal points between about 11 and 29 °C ilevbare2013a X17. Droplet size grows with time by coalescence and varies with drug and technique ilevbare2013a R3, C18. In SDS the 369 nm band that marks the atazanavir drug-rich phase in buffer appears from about 200 µg/mL, far below the amorphous solubility of about 1450 µg/mL, so a spectral marker has to be checked in the micellar medium [indulkar2017a R17, R18, C27]; extinction rose on the first addition to STCDC and SGCDC without visible turbidity [lu2017b R4]. LLPS is seen only if nucleation is slow compared with phase separation; the metastable zone for LLPS is "small" by the authors' reading raina2014a C30, C32. Turbidity does not tell LLPS from crystallization without a crystal-specific method [elkhabaz2017 C30]. Above the onset an inhibitor can still fail: pretomanid with HPMCAS-HF crystallized within minutes in the presence of droplets (F27) nguyen2023a R7, C13. A polymer in the droplets lowers the onset (F19) [ueda2020a R1, C13]. In the danazol dispersion study the overshoot above the amorphous solubility before LLPS was inferred from UV, which is unreliable there [jackson2015 X12]; a slowly releasing dispersion (50:50 HPMCAS danazol) never reached it [jackson2015 C33].

← Concepts and formulas

concept · as used in Physical stability

local equilibrium

Evidence table: local equilibrium. Content from the release-mechanism chapter (2023–2025).

The assumption that phase separation in a hydrating dispersion is at least as fast as water penetration, so that the phases at each depth of the gel layer are in pseudo-equilibrium with the local water content and their compositions can be read from the equilibrium ternary diagram deac2023b C38; deac2023a C70. The gel surface, with water activity near unity, can equilibrate with the solution and resemble the dilute nanoparticle composition, while deeper layers with less water reach other regions of the diagram deac2023b C61. Compacts above the limit formed a surface barrier "in pseudo-equilibrium" with the aqueous phase deac2023b C3. The 2024 phase-diagram paper assumes that the separated phases reach local equilibrium at once along the hydration path, "likely" valid for MePHPH and PHPH because both drug-rich phases are rubbery at 37 °C, and expects high-Tg drugs "may not" conform deac2024b C48, C49, C50, C54.

Findings

Release mechanism and LoC: F25, F27, F30.

Related concepts

lets the ternary phase diagram, its binodal and tie lines describe the gel layer; needs a mobile phase, related to the wet glass transition temperature.

Formulas

none.

How it is measured or obtained

Indirectly: time for nanoparticle composition to settle and for compact surfaces to reach a constant composition deac2023b C38, R2, R6, R7, and comparison of the released hydrophobic phase with equilibrated nanoparticles, with its Tg against the test temperature deac2023a C39, R12.

Values in the library
materialvalue or classconditionspaper ids
PHPH and MePHPH nanoparticles with PVPVAcomposition settled within 5 min37 °Cdeac2023b C38, R2
PHPH and MePHPH compact surfaces above the limitpseudo-equilibrium within 10 minATR-FTIRdeac2023b C38, R6, R7
hydrophobic phase released from 30% MePHPH; 5% PHPHTg 16.8; −5.8 °C, both below 37 °CDSCdeac2023a R12, C39
Pitfalls and disagreements

The assumption "may be valid" when the hydrophobic phase is mobile; dispersions whose hydrophobic phase has a high Tg need further work deac2023a C70.

← Concepts and formulas

concept · as used in Physical stability

matrix crystallization

Crystallisation of the amorphous solid itself while it is in contact with the medium, before the drug has dissolved (also called solid-mediated crystallisation), in competition with dissolution and with crystallisation from solution [moseson2021 C1, C27]. Bicalutamide–PVPVA is the case in point of the ASD process papers: a hydrated, polymer-depleted, drug-rich solid that is "likely" below its Tg at 37 °C becomes mobile enough to crystallise in place, a surface-driven reaction triggered by hydration and polymer loss [moseson2021 C55, C56, C59]. Moseson (2022) tested the route across loadings: bicalutamide–PVPVA at 5 and 10% loading released drug and polymer together and escaped it, whereas 20–50% loading, cryomilling and cryomilled surfactant-containing powders raised the risk. The authors call it surface-mediated: a polymer-depleted, drug-rich boundary layer forms, crystallizes and "could prevent release" [moseson2022b C36, C39, C43, R6, R7]. In posaconazole–HPMCAS at 50% loading a 12 nm coating went with a much lower SHG signal after 3 h and higher release, which the authors suggest is a delay of matrix crystallization [moseson2023 R15, R18, C40]. New aspect (Bioperformance): crystallization inside the undissolved ASD particle during dissolution, as against crystallization from solution [mosqueragiraldo2018b C40; elkhabaz2017 C34]. The poor exposure of the 10% enzalutamide–HPMCAS dispersion was attributed to rapid matrix crystallization on contact with water; the printed evidence is crystals in the medium and a 10 µg/mL maximum [wilson2018 C56, X11]. New aspect (Supersaturation from ASD dissolution): in the first study of the two routes it is called "crystallization from matrix": the amorphous particle converts to crystal on contact with the medium, against nucleation and growth from the supersaturated solution alonzo2010 C43, C47. If it is faster than dissolution, no concentration above that of the crystal can be reached, because the crystal is what dissolves alonzo2010 C33. The papers of 2015–2018 show that the dispersion polymer and its share decide it: resveratrol dispersions needed 80–95% cellulosic polymer to stay amorphous in buffer, PAA failed for celecoxib "irrespective of the drug loading", and an inhibitor dissolved in the medium cannot reach it [wegiel2015 R14; xie2016a C33, C31; xie2015 C35].

Findings

ASD process: F27, F28, F29, F38, F39, F40, F41, F46. Bioperformance: F9, F11, F12, F23, F26, F27, F30. Supersaturation from ASD dissolution: F1, F2, F3, F16, F24, F27.

Related concepts

contrasts with desupersaturation; accelerated by residual crystallinity; not blocked by crystallization inhibition by polymers in solution; accompanies incongruent release and surface drug enrichment; related to surface crystallization; avoided by congruent release; fed by the drug-rich surface layer; delayed by an atomic layer coating in one posaconazole system. Contrasts with solution crystallization; favoured by drug loading; part of crystallization during dissolution; related to plasticization by water.

Formulas

None specific; the competition with dissolution is set out with the Noyes-Whitney equation alonzo2010 E3.

How it is measured or obtained

Time-lapse polarised light microscopy of particles in buffer, in-line Raman of a slurry resolved by MCR-ALS, XRPD and SEM of recovered solids, polymer release by size-exclusion chromatography, and dissolution at several doses read for plateaus below the amorphous solubility and a falling fraction dissolved [moseson2021 P14, P15, P16, R17, R18, R19]. SEM, SEM-EDX (fluorine occurs only in the drug, F/F0) and confocal fluorescence of compacts exposed face down to medium for 5–60 min; Raman slurries resolved by MCR-ALS for the form 2 time course [moseson2022b P12, P14, P15, P16, P17]. SHG of particles after 3 h in buffer [moseson2023 R18]. Polarized light microscopy of particles in buffer [mosqueragiraldo2018b R18]; SHG [elkhabaz2017 P10]; indirectly, a flux ceiling not reached [mosqueragiraldo2018b R16]. In the ASD dissolution papers: in situ Raman of aqueous slurries with a PLS model for crystallinity or marker bands, PXRD of wetted powder after 15 min, and polarized light microscopy of wetted particles alonzo2010 P5, P6, P8; raina2014b P4, P6, P10; the 1630/1605 cm−1 Raman ratio of resveratrol slurries, also in a medium where the enteric polymer does not dissolve (pH 1.2) [wegiel2015 P7, A3]; the amorphous Raman shoulder near 1598 cm−1 of celecoxib slurries xie2015 P3, R3; polarized light of residues retrieved after the release peak [xie2016a P6].

Values in the library
materialvalue or classconditionspaper ids
BCL–PVPVA 30:70, crystal-freeform 2 begins at 20–30 min (half conversion about 36 min); plateau about 37–38 µg/mL against an amorphous solubility of 150 µg/mL60 and 150 µg/mL doses, pH 6.8[moseson2021 R12, R13, R19]
BCL–PVPVA with residual or added form 1 crystalsform 1 first detectable at about 15 min (S/155), 7 min (M/155), from the first spectrum (10% seeds)Raman slurry, 10 mg/mL[moseson2021 R21]
amorphous nifedipine (outside)crystallises mainly by the matrix route within about 10 min; PVP, HPMC or HPMCAS in solution do not change onset or routebuffer, 25 °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 micrographs[mosqueragiraldo2018b C40, C43]
enzalutamide 10:90 HPMCAS (outside)rapid matrix crystallisation on contact with waterdissolution[wilson2018 C56]
posaconazole ASDs in acid (outside)matrix crystallisation about 68% at 50% DL, about 0.05% at 25% DLSHG over TPE-UVF, 30 min[elkhabaz2019a R20, C38]
BCL–PVPVA 5 / 10 / 20 / 30 / 50% DL powdersend level about 91 / 96 / 88 / 86 / 73% of the dose; polymer ahead of drug from 20% DLdose of at most 30 µg/mL, pH 6.8[moseson2022b 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-EDX[moseson2022b R15]
30% DL cryomilled 2 and 5 minabout 50 and 49% of the dose, plateau about 15 µg/mLsame[moseson2022b R4]
10% DL after 10 min of cryomilling or extrusion and 30 s of millingabout 93% of the dosesame[moseson2022b R8]
30% DL with 3% TPGS, cryomilled 5 minstops at about 60% (about 18 µg/mL)same[moseson2022b 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 6.5[moseson2023 R18, R15]
telaprevir 50% HPMCAS ASDbirefringent domains in the particle at 20 min; 0.65 µg/minpH 6.8[mosqueragiraldo2018b R16, R18]
telaprevir 47.5:47.5:5 SDS ASDnone visible; 1.07 µg/minsame[mosqueragiraldo2018b R16, R18]
ezetimibe PAA ASDcrystals within minutes, inferred from the matrixbuffer, FeSSIF[elkhabaz2017 C34, R12, R16]
posaconazole ASDs 10 / 25 / 50%SHG crystallinity 0.3–0.4 / 3–4 / 19–26%60 min FaSSGF[shah2024 R21]
posaconazole ASDs50% DL final crystallinity about 250 times that of 25% DL[elkhabaz2019a R18]
enzalutamide 10:90 HPMCAS-MF ASDpeak about 10 µg/mL, crystals in the mediumpH 6.5, 100 µg/mL total[wilson2018 R6, C56]
pretomanid HPMCAS-HF ASD tabletscrystalline drug in the particles after FeSSIF at pH 5.5 and below, and after a 1 h gastric stagePXRD and SEM, 30 mg in 150 mLnguyen2023a R20, R22
neat amorphous felodipine≈54% crystalline at 1 min (37 °C); 50% after about 8 min (25 °C)pH 6.8 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 °C[chen2015a R20, R14]
resveratrol 35% with HPMC / HPMCAS / CMCABRaman ratio ≈0.87 / ≈0.84 / ≈0.81 (crystal 0.76) within hourspH 6.8, 37 °C[wegiel2015 R9]
resveratrol, minimum polymer to prevent it80% HPMC, 85% HPMCAS, 95% CMCABpH 6.8, 37 °C[wegiel2015 R14]
neat amorphous celecoxibcomplete within an hour; crystals on the particles from 2 minpH 6.8, 37 °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 °C[xie2016a 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 °C[nguyen2023c R19]
same, powderspitted, porous HPMCAS surfaces with agglomerates increasing with pH; HPMCP-50 covered at pH 5.01 h in acid[nguyen2023c R18]
delamanid dispersions in HPMCP, films with and without a 2 µm Eudragit L 100-55 layerstar- and needle-shaped crystals on every uncoated film; none under the layerpH 3.0, 1 h[nguyen2023b R3, R6]
posaconazole–HPMCAS dispersionscrystals by SHG in every system after 30 min in FaSSGF, more numerous after transfer37 °C[elkhabaz2019a R16]
Pitfalls and disagreements

The hydrated-solid mobility mechanism was not measured (the wet Tg of amorphous bicalutamide could not be determined) and the kinetics come from slurries far above the dose concentrations [moseson2021 R27, X8, X11]. Attribution to the matrix route is often inferred: crystals could instead nucleate in the concentrated boundary layer around the dissolving particles, or the evidence is crystals in the medium and a low maximum without a solid-state analysis [xie2016a X6; wilson2018 X11]. Solution-mediated growth is not absent at high dose [moseson2021 X4]. The results and the discussion of the 2022 study disagree on whether 20–30% loading crystallized, the crystals of the compacts were identified by shape and not by diffraction, and the polymer-depleted state of the crust is inferred from a dye [moseson2022b X14, X16, X18]. The Tg and composition of the hydrated layer were not measured [moseson2022b C60]. One micrograph without XRPD supports the telaprevir case [mosqueragiraldo2018b X13]. Matrix and solution crystallization were not separated for enzalutamide: no solid-state analysis of the wetted dispersion is shown (F9) [wilson2018 X11]. In the ASD dissolution papers, slurries held far more solid per unit of polymer than dissolution vessels (about 500–750-fold for felodipine), so their lag times rank systems but do not give the time scale in dissolution alonzo2010 X5. The proposal that crystallization starts at the particle surface and that dissolved polymer delays it there was not tested alonzo2010 C36. For felodipine at 25 °C the fall after the peak may come from the matrix as well as from solution alonzo2010 X6. The PVP-K12 celecoxib dispersion crystallized in a slurry yet released fully in dissolution xie2015 R4, R6. PXRD found no crystals in delamanid dispersion powders after 1 h in acid, a method that detects about 1–5% crystallinity, so the crystal mass that harmed release was small [nguyen2023c R15, R16, C46].

← Concepts and formulas

concept · as used in Physical stability

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 melttrasi2014a R1.a, R1.b, R1.c
felodipine; indomethacin0.86; 0.47 µm/sbulk melttrasi2014a R1.x, R1.z
clotrimazole0.02 µm/sbulk melttrasi2014a 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 melttian2017 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 Physical stability

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 Tmbaird2012 R1.b
ritonavir1.99 Pa·s, the highestat Tmbaird2012 R1.ah
felodipine; nifedipine154.0 and 36.20 × 10⁻³ Pa·sat Tmbaird2012 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 averagesbaird2012 R8
17 drugs\eta(T_m) falls linearly with Tm − Tg, R^2 = 0.7368data of baird2012trasi2014a R9
indomethacin with 10% PVPhigher viscosity than with HPMC or HPMCAS at 80–105 °C; pure indomethacin crystallized during measurementrheometrytian2017 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 Physical stability

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 particlesmarsac2006b R7, R9
indomethacin in PVP K12\chi −6.16 (onset), −1.94 (midpoint), −0.82 (offset)1 °C/minmarsac2009 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/minmarsac2006b R6
felodipine in PVP K12onset ≈141 → ≈122 °C; ≈115.5 °C at Φ ≈ 0.3831 °C/minmarsac2006b R6
indomethacin in PVP K12offset ≈161.5 → ≈155 °C; onset ≈160 → ≈135.5 °CΦ ≈ 0.23marsac2009 R2
ketoconazole in PVP K12offset ≈150.0 → ≈147.5 °CΦ ≈ 0.23marsac2009 R3
itraconazole with Eudragit E100offset ≈168.0 → ≈167.4 °Cpolymer fraction up to ≈0.54marsac2009 R4
felodipine with 3% PVP, PVP/VA, HPMCAS, PVAc140.7, 142.9, 141.4, 142.6 °C against 141.5 °C: noneoffset, 1 °C/minkestur2010a 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–PVPDSCmosqueragiraldo2014 C18
IDM with copovidone (1:5)solubility temperature about 78 °C (cited)phase diagram[moseson2019 R21]
bicalutamide with PVPVA, 30–90% BCLTc 145 °C at 30% BCL to about 192.3 °C at 90%; drug about 193.8 °Coffset extrapolated to 0 °C/min[moseson2022c R8, R9]
posaconazole with HPMCAS MF, PCZ fractions 0.4–1.0Tc about 161.7 °C at 0.4 to about 168.6 °C for neat PCZ; calculated 135 / 155 / 165 °C at 10 / 25 / 50% DLsame[shah2024 R1, R4, R5, X7]
felodipine with 3 wt% PVP K-12140.7 vs 141.5 °C, within the ±1 °C SD1 °C/minkestur2010b R1.e, M1, X11
indomethacin–PVP (cited)χ23 from melting point depression used as input to the ternary sorption modelliteraturerumondor2010a P5
acetaminophen with 10% w/w polymers166.7–168.6 against 169 °Cphysical mixtures, DSCtrasi2012a R9
flutamide with 10 mol% polymers108–110 °CDSCtrasi2012b R7
six compounds with 1–20% PHB0–2 °C (1–10% PHB), up to 4 °C (20%)DSC of physical mixturessato2016 R7, X11
indomethacin with 10% polymernamed as a possible reason for the steep inhibition above the growth maximum; not measuredargumenttian2017 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 Physical stability

membrane flux

The rate at which drug crosses a membrane in a side-by-side diffusion cell, taken as the slope of the receiver concentration against time; with diffusion coefficient, area, thickness and membrane activity coefficient constant, it is proportional to the donor activity [mosqueragiraldo2015 E4, C10; trasi2015a P6]. It rises linearly with concentration up to the amorphous solubility and then plateaus (F8). The papers of 2017–2022 add atazanavir (flux per area, 7.07 cm²) and telaprevir (mass flow rate), both linear up to the amorphous solubility in buffer and flat above it, and flux in micellar media as a free-drug read-out [indulkar2017a E7, R10, R11; lu2017b E1, R6]. New aspect (Bioperformance): the mass of drug crossing a membrane per time (and per area), proportional to the solute activity in the donor when area, diffusion coefficient, membrane thickness and membrane activity coefficient are fixed [raina2014a C11, E6; raina2015c C14]. It is reported as µg/min from receiver slope × volume, as mass flow, or per area (F2). In rats the mass flow of the dissolved formulation across a dialysis membrane ranked formulations by exposure (F25) [wilson2018 R15, R17; wilson2020 R8, C27, C44]. New aspect (Crystallization from solution): it serves as an activity read-out in micellar and polymer media, where a flux plateau marks the maximum free-drug concentration and equal flux means equal activity [jackson2016 E1, E2, C9, C16; li2016a E2, C14]. New aspect (Supersaturation from ASD dissolution): flux used as a particle-blind measure of dissolved drug while dispersions dissolve: across a dialysis membrane, relative to the crystal [alonzo2011 E1, C9], and in a side-by-side cell, converted to free drug with a standard curve [jackson2015 E1, E3, P4].

Findings

Amorphous solubility and LLPS: F4, F8, F11, F16, F17. Bioperformance: F2, F3, F4, F5, F7, F15, F18, F19, F20, F21, F22, F24, F25. Crystallization from solution: F22, F31, F32, F38, F40. Supersaturation from ASD dissolution: F7, F8, F17.

Related concepts

reads thermodynamic activity; plateau marks the amorphous solubility; basis of the claimed nanodroplet reservoir effect. Described by Fick's first law; requires sink conditions; part of membrane transport and membrane asymmetry; measures free drug concentration.

Formulas

membrane flux in terms of solute activity. Flux definition, mass flow rate from receiver concentration slope, membrane flux from permeability and concentration, supersaturation from membrane flux ratio, membrane flux from concentration difference.

How it is measured or obtained

Regenerated cellulose membrane (6–8 kDa cut-off), 30–32 mL per side, 25 or 37 °C, receiver measured by UV probe or HPLC, sink conditions [mosqueragiraldo2015 P11; trasi2015a P6]. In the Bioperformance papers: side-by-side diffusion cell with UV dip probes and a receiver under sink conditions raina2014a P8, P9; flow-through cell with fresh receiver buffer [indulkar2016 P5, P10]; hollow-fibre module [hate2017 P4]; Caco-2 monolayers [alhalaweh2016 P17]; side-by-side cell with a dialysis membrane and a donor taken from a dissolved formulation [wilson2018 P15, P16; wilson2020 R8]; side-by-side cell with a regenerated cellulose membrane in simulated and pooled human intestinal fluids [elkhabaz2019b R7]; lipid-impregnated PVDF (PAMPA) cell with a buffer or surfactant receiver [hate2022 R1, R19]; Caco-2 monolayers with a crystalline co-drug present [alkalla2026 R13]. The flux is normalized by membrane area as J = dm/(dt\,A) [wilson2018 E3; alkalla2026 E2]. In the crystallization-from-solution papers: side-by-side diffusion cell with a regenerated cellulose membrane (6–8 kDa), the same medium on both sides, a donor concentration series and the receiver read by UV dip probe below sink limits [jackson2016 P9; li2016a P8; lu2017 E2]. In the ASD dissolution papers: dialysis bag (6–8 kDa in the text, 10 kDa on the figure) with 500 µg/mL HPMC in the receptor, slope over 10–40 min [alonzo2011 P4, X1]; regenerated cellulose membrane (6–8 kDa), 200 mL per side, 30 mm opening, 25 °C [jackson2015 P4]; PermeGear side-by-side cells, 7.065 cm², regenerated cellulose 6–8 kDa (resveratrol) or 12–14 kDa (tacrolimus), receiver kept below a third of the crystalline solubility [wegiel2015 P10; trasi2016 P9].

Values in the library
materialvalue or classconditionspaper ids
telaprevirabout 0.068 µg/min at 5 µg/mL; about 0.97 at 90; about 1.07 at 130 µg/mL donor37 °C[mosqueragiraldo2015 R12]
ritonavir; lopinavir; paclitaxelplateaus about 0.21–0.22; 0.13–0.14; 0.25–0.27 µg/min25 °C[trasi2015a R2]
ritonavir, lopinavir, paclitaxel in 30 + 30 µg/mL mixturesflux of each drug lower than from the single-drug donor25 °C[trasi2015a R12]
atazanavirabout 0.003 µg/min·cm² at 1 µg/mL, 0.106 at 70, 0.121 at 100, 0.114 at 200 µg/mL; slope 0.0017 mL/min·cm²buffer, 37 °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 8[indulkar2016 R9]
telaprevir1.05–1.18 µg/min above 90 µg/mLASD dose series[mosqueragiraldo2018b 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/mL[jackson2016 R10]
enzalutamideabout 0.18 µg/min at 10 µg/mL, about 0.87 at 50 and 0.81–0.91 up to 100; 10:90 ASD solution and drug with 900 µg/mL polymer both about 0.76side-by-side, 5 µg/mL HPMCAS[wilson2018 R13, R14]
enzalutamide formulations after 1 h of dissolution0.632, 0.456, 0.437, 0.147, 0.063 µg/min (10% and 50% copovidone, 50% HPMCAS, 10% HPMCAS ASDs, slurry)dialysis membrane[wilson2018 R15]
enzalutamide, four formulationsabout 0.53, 0.49, 0.068, 0.063 µg/min (10:90 and 50:50 CPHPC-106 ASDs, CA Sub ASD, slurry)dialysis membrane[wilson2020 R8]
atazanavir, posaconazoleJ_{eq} 2.08–2.48 × 10⁻³ and 5.79–6.97 × 10⁻⁴; J_{amph} 0.105–0.139 and 0.0191–0.0239 µg/(min·cm²)six media, 37 °C[elkhabaz2019b R7]
atazanavir, PAMPAabout 0.33 µg/min at 10 µg/mL, about 1.95 at 70 and 2.0–2.3 above; with 2% SDS receiver about 5.0 at 80 to 8.8 at 1000 µg/mLlipid-impregnated 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/mL[jackson2016 R11]
celecoxib, nevirapine, 0.1% STC or SGC0.44, 0.46, 0.41 and 20.9, 23.4, 21.0 µg/min (no additive, STC, SGC)pH 6.5, 37 °C[li2016a R15]
tacrolimus, cilnidipine at the amorphous solubility0.027–0.031 and 0.0014–0.0018 µg/min·cm² in buffer, FaSSIF-V1, Composite-SIF; flux at the crystalline solubility not measurable37 °C, 7.07 cm², regenerated cellulose 6–8 kD[indulkar2018 R12, R13]
telaprevir, bile salt mixturesmass flow unchanged at 1.86 mM, lower at 3.72 and 5.58 mM50 mM phosphate pH 6.5[lu2018 R2, X2]
felodipine controls 10 and 5 µg/mLratios 10.0 ± 3.4 and 4.8 ± 0.39 to the crystal37 °C[alonzo2011 R14]
felodipine 90:10, 50:50, pure amorphous10.5 ± 1.2, 9.5 ± 1.8, 8.5 ± 1.837 °C[alonzo2011 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 °C[jackson2015 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 °C[wegiel2015 R20]
Pitfalls and disagreements

The plateau still rises by about 10% from 90 to 130 µg/mL [mosqueragiraldo2015 X6]; the low-donor flux traces are curved and the slope window is not stated [mosqueragiraldo2015 X13]. The membrane is described as regenerated cellulose and, once, cellulose acetate [mosqueragiraldo2015 X1]. Whether micelles or drug-loaded aggregates cross the 6–8 kDa membrane is not stated, so lower activity and slower diffusion are not separated; replicates are not stated [lu2017b X8, X4; indulkar2017a X9, X12]. In the Bioperformance papers units are not comparable between papers (µg/min, µg/(h·cm²), mg/min/cm²), and replicates and error definitions are often not stated [raina2015c X12; indulkar2016 X8]. A plateau needs a sink receiver and a stable donor raina2014a C20; the hollow-fibre module shows a continuing rise [hate2018 R9]. The plateau is not universal: with a sink receiver the PAMPA mass flow of atazanavir keeps rising above the amorphous solubility (F22) [hate2022 R19]. The position of the break is known only to within the spacing of the concentrations tested [hate2022 X13]. The area behind a printed µg/min is not always stated [elkhabaz2019b X6; wilson2018 R15]. The flux axes of the danazol paper carry no time unit, replicates are not stated and the crystalline reference flux differs between figures (about 0.0011 and 0.0008) [jackson2016 X9, X10, X11]. In the SDS study the flux values behind the stated supersaturation of about 65 are not printed [indulkar2019b X6]. In the ASD dissolution papers all felodipine ratios share one unreplicated crystalline slope, and no statistical test supports their equality [alonzo2011 X4, X5]. The danazol absolute fluxes do not reproduce from the example profile and the flux window per formulation is not stated [jackson2015 X4, X6]. Below 50 µg/mL the tacrolimus flux rose but did not extrapolate to zero, and the product donors' conditions are unclear trasi2016 X8, X7; flux was measured only for one resveratrol series [wegiel2015 C10]. The upper tacrolimus plateau is read as about 0.0053 µg/min in one chapter and ≈0.0055 µg/min in the ASD dissolution chapter, from the same result trasi2016 R14.

← Concepts and formulas

concept · as used in Physical stability

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 Physical stability

micellar solubilization

Increase of the apparent solubility of a drug by incorporation into surfactant micelles; with Tween 80 above its CMC, ritonavir's crystalline solubility rose 2.7-fold and its LLPS concentration about 2.5-fold (synthesis: 46.1 ÷ 18.8 = 2.45), leaving their ratio about unchanged ilevbare2013a R16, X5. The papers of 2017–2022 add two cases. In 3.6 mg/mL SDS atazanavir's crystalline solubility rose from 1.1 to about 45.6 µg/mL and its amorphous solubility to about 1450 µg/mL, so the concentration ratio fell from about 65 to about 33 while the flux-derived activity ratio stayed at about 65 (molar solubilization ratio κ 0.006, 0.183 and 0.351 for crystal, measured and predicted amorphous) [indulkar2017a R7, R9, R13]. With 12 mM bile salts, STDC, STCDC, SGDC and SGCDC raised telaprevir's crystalline solubility 1.8–2.4 times and its GLPS onset about twofold, while STC and SGC did not [lu2017b R1, R2, X9]. New aspect (Bioperformance): uptake of drug into surfactant or bile-salt micelles raises the equilibrium solubility and the total concentration but not the free drug [raina2015c C30]. In simulated and pooled human intestinal fluids bile salts and lecithin raised the crystalline solubility proportionally more than the amorphous solubility (F18) [elkhabaz2019b C35]; high log P drugs are expected to show a positive food effect for this reason nguyen2023a C77, C78. New aspect (Crystallization from solution): In the bile-salt and surfactant papers the question is whether the surfactant raises the dissolved drug without raising its activity: STC at 0.1% raised the crystalline solubility only 1.1- to 3.5-fold across 11 drugs, whereas SDS at 0.1% raised it up to about 266-fold, and 12 mM dihydroxy bile salts needed about twice the telaprevir for the same activity [chen2015 R1, R2; lu2017 R1]. The 2018–2025 papers carry the question into bile salt–lecithin media and above the CMC of SDS, where micelles raise both the crystalline and the amorphous solubility but not the activity-based supersaturation at the amorphous solubility [indulkar2018 R8, R12; indulkar2019b R1, R2; duong2022b R8]. New aspect (Mesoporous silica): with drug-loaded silica, micelles act in two ways at once, by solubilizing released drug and, for a surfactant that competes for the silica surface, by displacing adsorbed drug; the authors write a three-way metastable equilibrium, drug adsorbed to silica ⇌ drug in solution ⇌ drug solubilized in micelles [dening2019 E11, C57]. They call micellar solubilization "therefore advantageous" for silica systems because it raises release and micellar drug replenishes free drug as it permeates, while cautioning that micelles "may actually reduce" the free fraction and the flux [dening2019 C60, C58, C59]. New aspect (Supersaturation from ASD dissolution): in the celecoxib suspension study each surfactant raised the Form III solubility steeply above its CMC, and supersaturation was referred to the solubility in each medium so that solubilization alone would not raise S [chen2015a R5, C2, C3]. In suspensions of enteric lopinavir dispersions at pH 3, drug leaching followed the solubilization of the crystalline drug by each surfactant, so that the leached concentration rose with the crystalline solubility in the same medium and their ratio stayed nearly constant for a given polymer [li2016b C39, C40]. With a polymer present STC at least doubled the crystalline solubility given by STC alone, and PVPVA with SDS raised it from 3.3 to 11.4 µg/mL [li2016b R5, C43]. A marketed tacrolimus product containing sodium lauryl sulfate reached the same maximal flux as the others, so no solubilization was seen at its level trasi2016 C38. New aspect (Release mechanism and LoC): two surfactant papers of 2021–2022 ask whether micelles explain the higher limit of congruency of surfactant-containing dispersions. Monomeric TPGS did not raise the crystalline solubility of felodipine (about 1.3 µg/mL, as in buffer), so no significant solubilization occurs without micelles saboo2021 C8, R2; since 2% TPGS raised the limit to 25% with TPGS below its CMC, and at 30% both 5% TPGS (below the CMC) and 10% TPGS (above it) released congruently, micellar solubilization plays "a negligible role" in the limit saboo2021 C33. For clopidogrel the effect on the LLPS concentration depended on the surfactant: SDS raised it only above its CMC, while TPGS and Tween 80 raised it at 50 but not at 5 µg/mL correasoto2022a C9, R3; up-field NMR shifts with 50 µg/mL TPGS below and above the LLPS concentration are read as solubilization of clopidogrel in the less polar micelles correasoto2022a C16, R11. The micellar content of FaSSIF did not raise HPMCAS-MF dissolution or release from 10% indomethacin–HPMCAS, consistent with polymer-controlled release [bapat2023 C11, C20]. In the 2025 bedaquiline study simulated intestinal fluids raised the crystalline solubility from undetected (pH 6.5) to 7.8 µg/mL (FaSSIF-V1), from below 0.1 to 258.8 µg/mL (FeSSIF-V2) and to 628 µg/mL (FeSSIF-V1), and cut drug–HPMCAS complexation from up to about 90% to at most about 29%; the authors read the micelle affinity of the drug cation as the reason the complex does not form ("explains") [kaur2025 R2, R6, R8, C36, C39].

Findings

Amorphous solubility and LLPS: F12, F16, F17, F18. Bioperformance: F3, F4, F16, F18. Crystallization from solution: F19, F28, F29, F31, F32, F34, F38. Mesoporous silica: F12. Supersaturation from ASD dissolution: F7, F14, F15, F19, F28. Release mechanism and LoC: F21, F23, F34.

Related concepts

surfactant above the critical micelle concentration; leaves thermodynamic activity unchanged; raises crystalline solubility. Papers of 2017–2022: described by the micelle/water partition coefficient; cost for transport: solubility-permeability interplay; measured on the activity scale by activity-based supersaturation. Contrasts with nanodroplet reservoir effect; lowers free drug concentration; measured by membrane flux; related to mixed micelles. Competes with drug adsorption onto silica together with competitive adsorption of the surfactant; related to supersaturation. Distinct from surfactant partitioning into the drug-rich phase; ruled out as the cause of a higher limit of congruency with TPGS.

Formulas

solid-liquid equilibrium solubility equation. Activity from concentration, micelle-water partition coefficient, membrane flux from permeability and concentration, membrane flux in terms of solute activity, supersaturation from membrane flux ratio, supersaturation ratio.

How it is measured or obtained

Crystalline solubility and LLPS concentration with and without the surfactant, 500 µg/mL Tween 80 in 100 mM phosphate pH 6.8 at 37 °C ilevbare2013a P1, P5, A6. In the Bioperformance papers crystalline solubility is measured against surfactant concentration and free drug by flux or ultracentrifugation [raina2015c P1; indulkar2017a R11]. In the bile-salt and surfactant papers: 48 h shake-flask solubility with and without the surfactant, a membrane mass flow that follows the activity, and an activity-based supersaturation calibrated from the flux [chen2015 P1; li2016a P8, R15; lu2017 E1, E2]. In the Mesoporous silica papers: crystalline and amorphous solubility of ritonavir with SDS (28 µg/mL) and Vit E TPGS (28 and 500 µg/mL; cited CMC 212 µg/mL) in pH 6.8 phosphate at 37 °C, and release from ritonavir–SBA-15 dosed at the amorphous solubility of each medium [dening2019 P1, P2, P9, M3]; release in FaSSIF dosed at its amorphous solubility [dening2018 P6, R21]. In the ASD dissolution papers: excess Form III stirred 48 h at 25 °C in pH 3 HCl with the surfactant, ultracentrifuged and assayed by HPLC [chen2015a P6]; crystalline solubility in every leaching medium, with excess polymer, 48 h at 25 °C, ultracentrifuged [li2016b P5]; break of crystalline solubility against surfactant concentration as the CMC [li2016b P3]. In the release-mechanism papers: crystalline solubility against surfactant concentration with and without 900 µg/mL PVPVA saboo2021 R2; LLPS concentration by UV extinction, centrifugation and diffusion cell with 5 and 50 µg/mL surfactant correasoto2022a R3.

Values in the library
materialvalue or classconditionspaper ids
ritonavir with 500 µg/mL Tween 80crystalline 1.3 → 3.5 µg/mL; LLPS 18.8 → 46.1 µg/mL37 °Cilevbare2013a R16
felodipine with 0.04% vitamin E TPGScrystalline solubility up almost 40-fold; concentration ratio 9.2 → 4.537 °C[raina2015c C29]
atazanavir with SDScrystalline 1.1 → 45.6 µg/mL; κ 0.006 (crystal), 0.183 (amorphous), 0.351 (predicted)0–3.6 mg/mL SDS, pH 6.8, 37 °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 °C[raina2015c R2]
nifedipine10.3 to 53.4–90.7 µg/mL37 °C[raina2015c R3]
atazanavir + SDSconstant about 1 µg/mL to 0.5 mg/mL SDS, then 2.6 / 22.2 / 45.6 µg/mL at 0.6 / 2.0 / 3.6 mg/mLpH 6.8[indulkar2017a R7, R8]
celecoxib Form IIISDS 0.25% 14.5, STC 0.75% 5.8 µg/mL25 °C[chen2015a R5]
posaconazolecrystalline 0.23 (buffer) to 3.2 µg/mL (FaSSIF-V1); amorphous 8.1 to 43.3six media, 37 °C[elkhabaz2019b R1, R2]
atazanavircrystalline 1.4 to 7.1 µg/mL; amorphous 79 to about 99–102six media, 37 °C[elkhabaz2019b R1, R2]
pretomanidequilibrium solubility about 3-fold (FaSSIF V1) and 6-fold (FeSSIF V2) the buffer value37 °Cnguyen2023a R1, C33
11 drugs, 0.1% STC and SDSSTC 1.1–3.5-fold; SDS 1.2–266-fold25 °C (telaprevir 37 °C)[chen2015 R1]
celecoxib, 0.1% STC, SGC, HPMCASsolubility 1.2 → 2.9, 2.4, 2.4 µg/mL; mass flow unchanged (0.44–0.46 µg/min)pH 6.5, 37 °C[li2016a R15]
telaprevir, 12 mM STDC, SGDC, STCDCabout 140 against 60 µg/mL for the same δ 11.5pH 6.5, 37 °C[lu2017 R1]
ritonavir, cilnidipine; buffer, FaSSIF-V1, Composite-SIFamorphous/crystalline ratio 12 → 8.4, 7.8 and 36.5 → 12.9, 13.7; ritonavir SRamorph 9.2–10 throughoutpH 6.5, 37 °C, 3 mM bile salt[indulkar2018 R8, R12]
telaprevir, 3.72 and 5.58 mM bile salt mixturesδ 11.5 at about 72–77 against 60 µg/mL in buffer50 mM phosphate pH 6.5, 37 °C[lu2018 R1.h, R2]
atazanavir, SDS above the CMC (0.5 mg/mL)crystalline about 46 and amorphous about 1480 µg/mL at 3.6 mg/mL; concentration ratio about 35–38 against SRamorph stated about 6550 mM phosphate pH 6.8, 37 °C[indulkar2019b R1, R2, X6]
posaconazole, five biorelevant mediaconcentration ratio 17.9–20.7 against 28.3–33.7 in buffers; Km/w about 635–1820 at the amorphous and about 1440–3240 at the crystalline solubility37 °C, pH 1.6–6.5duong2022b 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 °C[chen2015a R6]
STC 0.10 → 1.50%1.8 → 26.0 µg/mLpH 3[chen2015a R7]
polysorbate 80 0 → 1%1.2 → 198.4 µg/mLpH 3[chen2015a R8]
Triton X100 0 → 0.15%1.2 → 59.6 µg/mLpH 3[chen2015a R9]
Poloxamer 188 0.002 → 3%1.4 → 2.5 µg/mLpH 3[chen2015a R10]
lopinavir with HPMCAS-HF, + SDS / Poloxamer 188 / polysorbate 80 / STC3.3 / 3.0 / 4.5 / 7.2 against 1.9 µg/mLpH 3, 25 °C[li2016b R5]
lopinavir with HPMCAS-HF, PVPVA and SDS11.4 µg/mLpH 3, 25 °C[li2016b R5]
lopinavir with HPMCAS-HF and SDS at pH 56.3 µg/mL25 °C[li2016b R5]
delamanid, crystalline0.52 (FaSSIF V1), 2.30 (FeSSIF V2), 13.10 (FEDGAS pH 4.5) and 57.97 µg/mL (FEDGAS pH 3.0) against below 0.02 µg/mL in buffer above pH 5.537 °C[nguyen2023b R13, R18]
praziquantel, amorphous and crystallineamorphous 1.74 and 1.70, crystalline 0.31 and 0.43 mg/mL in FeSSIF-V2 (racemate, R-enantiomer) against 1.17/1.39 and 0.16/0.23 mg/mL in PBS pH 6.537 °C[alvarenga2025 R1]
delamanid, amorphous69.9 (FaSSGF), 7.93 (FaSSIF V1), 3.11 (FaSSIF V2) and 0.76 µg/mL (PBS pH 6.5)37 °C[duong2022a R1]
felodipine with monomeric TPGScrystalline solubility ≈1.3 µg/mL, as in buffer; slope change near 48 (buffer) and 40 µg/mL TPGS (with PVPVA)37 °Csaboo2021 R2, C8, P1
clopidogrel in buffer; with 50 µg/mL TPGS; with 50 µg/mL Tween 80LLPS concentration 23 ± 3; 29 ± 2; 30 ± 2 µg/mL37 °Ccorreasoto2022a R3
clopidogrel with 5 µg/mL TPGS, CTAB or 50 µg/mL SDS20 ± 1 µg/mL37 °Ccorreasoto2022a R3
neat HPMCAS-MF in FaSSIF; in blank FaSSIF buffer≈0.56; ≈0.57 mg/min/cm²pH 6.5, 12 mM/ΔpH[bapat2023 R7]
bedaquiline in FaSSIF-V1, FeSSIF-V2, FeSSIF-V1crystalline solubility 7.8, 258.8, 628 µg/mL37 °C[kaur2025 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 Physical stability

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 buffers[bapat2024 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 Physical stability

mixed micelles

Aggregates of bile salts with phospholipids and their hydrolysis products, the good drug solubilizers of intestinal fluid; the bile-salt papers worked with single bile salts and name mixed micelles with lecithin as the next, more biorelevant step [chen2015 C4; lu2017 C42]. From 2018 the library measures mixed micelles of bile salt and lecithin directly in crystallization tests: lecithin shortens induction times and raises the amorphous solubility of atazanavir, its digests accelerate more, and the bile salt to phospholipid ratio sets the induction time in volunteer media [indulkar2018 R16, R6; enright2020 R10, R18].

Findings

F28, F32, F39, F40, F41, F43.

Related concepts

related to bile salt micelles and biorelevant media.

Formulas

none.

How it is measured or obtained

Not measured in these papers.

Values in the library
materialvalue or classconditionspaper ids
telaprevir, single bile saltssystems with micelles and a drug-rich phase are called probably the most relevant in vivo and need lecithin mixed micellespH 6.5, 37 °C[lu2017 C42]
FaSSIF-V1, Composite-SIFunimodal 49 ± 4 nm; bimodal 63 ± 4 nm (56%) and 3.9 ± 0.4 nm (44%)DLS, 173°[indulkar2018 R5]
atazanavir, 3 mM STC with 0–0.75 mM lecithininduction time about 595 → 43 min; amorphous solubility 38 → about 82 µg/mLpH 6.5, 37 °C[indulkar2018 R16, R6]
atazanavir, volunteer media with 350 µM phospholipidbile salt:phospholipid 1.6–14.7; 23–33 against 112–144 minpH 6.5, 37 °C[enright2020 R18, E2]
posaconazole, FaSSIF-V1 against FaSSIF-V2more lecithin gives higher amorphous solubility and Km/w for posaconazole, not for atazanavirbiorelevant and human fluids[elkhabaz2019b C38]
Pitfalls and disagreements

Lecithin was absent from all the bile-salt studies of this chapter's papers up to 2017, and may alter solubility and kinetics [li2016a C64]. The two proposed lecithin routes (taurocholate drawn into mixed micelles; lecithin lowering the interfacial energy of the nucleus) were not measured [indulkar2018 C40; elkhabaz2021 C25].

← Concepts and formulas

concept · as used in Physical stability

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% RHduong2022c R9
ezetimibe–HPMCAS 70% DL, uncoated / thin / thickabout 4.88 / 5.21 / 4.35%sameduong2022c R9
posaconazole–HPMCAS 25% DL, 0 / 11 / 23 / 39 nmabout 4.7 / 4.3 / 3.7 / 1.2% at 30 minDVS 37 °C, 90% RH[moseson2023 R7]
posaconazole–HPMCAS 50% DL, slow-deposited 26 nmabout 0.33% at 2 h against about 4.2–4.5%same[moseson2023 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 Physical stability

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 °Ckonno2008 R1.a, R3.a
amorphous nifedipine filmnucleation ≈4.7 × 10⁵ → 6.8 × 10⁶ m⁻³ s⁻¹0 → 75% RHmarsac2008a 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 °Crumondor2009b R9.a, R9.g
felodipine–HPMCAS 50% powder9.2–16.6% at every RH after ≈490 days22–25 °Crumondor2009b R9
felodipine–PVP 50% filmcrystals by 4 h at 94% RH, after phase separationAFM, polarized lightmarsac2010 R19, C24
FTM–HPMCAS spray-dried dispersion (outside)faster crystallization at 82% than at 75% RH40 °C, 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 °Cwegiel2014 R13
indoprofen–PVPseparation at 54% RH, crystals from 75% (30% PVP) or 84% RH (50% PVP)22 °C filmsrumondor2011 R11, R14
lumefantrine–CAP 40:60 precipitated into water (9% water)crystalline from the first day at 40 °C/75% RH; amorphous 3 months under vacuumPXRDbhujbal2021 R4.a, R5, R10, C17
tacrolimus generic capsule contents≈36, 68 and 84.5% at 30, 35 and 40 °C/75% RH, ≈11% at 40 °C/54% RH, 4 weeksopen 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 RHstorage[wegiel2015 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 Physical stability

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 coatedli2017 R3, R5, R12
ECP–PVPVA after 97% RH, 7 daysnet-like structures at 10–80% DL; F/N 0.10 (continuous) against 0.06TEM-EDXli2017 R19, R22
ECP–PVPVA powders after 24 h at 97% RHtwo Tgs at 10–50% DL, one at 60–90%modulated DSCli2017 R24
ITZ–HPMC E3 filmsdomains at 40% and 20% RH, none at 7% RH; network after 24 h at 40 °C/75% RHspin coatedmugheirbi2017 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 phasescitedrumondor2009b R24
telaprevir ASD filmsdry nitrogen (RH below 18%) eliminates water-vapour-induced separationcited[mosqueragiraldo2018b 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 filmsrumondor2009c R7, R9, R10, R12
indomethacin-, ketoprofen–PVPone phase for 40 and 68 days at 94% RHsamerumondor2009c R14, R16
felodipine–PVPsmall change at 33–58% RH, distinct at 75% RH, amorphous-felodipine-like after 94% RH1 day–1 weekmarsac2010 R7, R11
felodipine with 25% HPMCAS or HPMCno change after 7 weeks at 75% RHdried filmskonno2008 R11
same drugs with PVP, PVPVA, HPMCASextent follows polymer hygroscopicity, PVP > PVPVA > HPMCASIR band loss, DSCrumondor2010c C38, C33
20 drug–polymer systemsHPMCAS dispersions less susceptible in general; PVP highly vulnerableclassesrumondor2011 C29
miconazole–PVPVA 50:501–3 µm drug-rich domains after 7 days at 75% RH; 4–25 µm domains within 5–30 min in bufferconfocal, AFM-IRsaboo2017 R15, R18, R19
celecoxib–PVP 6:4two Tg events after 3 days at 94% RH, not after 75% RHDSCxie2016b R18, R19
ritonavir–PVPVA 30:70 with surfactantsSDS and Tween 80 delay visible separation; Spans speed it and coarsen the domainsconfocal at high RH, 37 °Cyang2022b R5, R6, R7, R8, C7
Pitfalls and disagreements

The water content of films and solutions was not measured in the film studies, so "moisture" is inferred from humidity and added water li2017 X14; mugheirbi2017 X4. The water-uptake explanation of the DL effect on storage separation rests on powders after 24 h, not on films li2017 X8. Whether a dry film is miscible or kinetically trapped is open li2017 C43. The effect of water reverses with PrOH and BuOH [mugheirbi2018 C12]. In the drug–PVP storage study, two-phase evidence in the wet state exists only for pimozide; for nifedipine and droperidol it rests on IR of re-dried films and sorption rumondor2009c X10. Donor type, carbonyl red shift and drug–water χ split the drugs the same way rumondor2009c X13. Class labels per system ignore that resistance depended on drug loading rumondor2011 X13, C38. The pattern depends on how water arrives: humid air gives drug-rich droplets in a polymer-rich matrix, bulk water a coarser connected structure saboo2017 C46.

← Concepts and formulas

concept · as used in Physical stability

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 nifedipinedrymarsac2006a 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 °Ckestur2010b 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% RHrumondor2009c R11, C41
ketoprofen–PVPwet Tg −23 °C, mobile, yet no separation94% RHrumondor2009c R25, C38
coated ASD powders (outside)crystallization onset linked to Tg − T at the storage condition40 °Cmoseson2022a C24, C25
ritonavir ASDs (outside)Tg only a crude indicator of mobilitydegradation studyalvarenga2022 C21
celecoxib with miscible surfactantsmain effect "most likely" on mobilityTg-scaled growthmosqueragiraldo2014 C30
felodipine free surfacefaster growth "may be attributed" to mobile surface moleculesfilmskestur2013a 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 Physical stability

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 °Ctrasi2012a 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 reheatedtrasi2012b R12, C47
15 drugs with 7 polymers (other chapter)hydrogen-bond recognition rules applied to choose polymers that prevent crystallizationspin-coated filmsvaneerdenbrugh2011a 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 Physical stability

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 datatrasi2014b 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 Physical stability

nanodroplet reservoir effect

The proposal that the drug-rich phase replenishes drug absorbed from the water phase, keeping the activity and flux at their maximum for as long as it lasts [mosqueragiraldo2015 C39; indulkar2015 C54, C55]. In the Amorphous solubility papers of 2013–2016 it is argued from the flux plateau and from earlier work: none of them depleted the dissolved drug and followed resupply [mosqueragiraldo2015 C39]. The flow-through experiments of 2016 test it, by the length of the steady receiver period against the excess over the onset [indulkar2016 R5, R6]. The papers of 2017–2022 add that Sugihara and Taylor expect the amorphous particles to maintain supersaturation by replenishing absorbed drug ("is expected"), and Indulkar and co-workers that an LLPS system sustains maximum flux while a micellar system at the same total concentration gives lower flux; neither flux with and without particles nor resupply was measured in these papers [sugihara2018 C43; indulkar2017a C61, C62]. New aspect (Bioperformance): replenishment of absorbed free drug by dissolution of drug-rich droplets, which keeps the solution at the amorphous solubility and the flux at its maximum until the droplets are used up [indulkar2016 C25, C31; raina2014a C38]. Micelle-solubilized drug is not an equivalent reservoir [indulkar2016 C26]. A depot role was proposed for amorphous aggregates in vivo, with little in vivo data [wilson2018 C8, C40]; in a PAMPA cell nanodroplets are said to raise the concentration at the donor-side membrane surface and remove the unstirred-layer gradient [hate2022 C58, C61, C76]. New aspect (Mesoporous silica): silica formulations are the library's case where the reservoir is absent. Released drug approached but did not exceed the amorphous solubility, so no drug-rich phase formed to replenish absorbed drug [dening2018 C32, C44], and an acid-first atazanavir–silica run reached the amorphous solubility without LLPS, from which the authors infer that the reservoir "may not occur" with silica [hate2020a R23, C54]. New aspect (Supersaturation from ASD dissolution): in the dispersion-dissolution papers the reservoir idea is cited, not tested: a drug-rich phase in metastable equilibrium with the water "has been suggested" to keep supersaturation constant while drug is absorbed [jackson2015 C8], and a polymer that promotes LLPS "may be preferable" for that reason [trasi2015b C46]. For indomethacin, the droplets that a fast-releasing EPO–HPMC dispersion formed in acid redissolved within minutes when the pH rose to 5, which the authors call a reservoir that becomes available on dilution to higher pH; here the reservoir means redissolution, not replenishment during membrane transport xie2017 C42, X9. New aspect (Release mechanism and LoC): Que and co-workers (2019) take as their starting point "an emerging opinion" that drug-rich colloids act as a reservoir sustaining maximum flux, so that the optimal outcome of ASD dissolution is to exceed the amorphous solubility with colloid formation [que2019 C3]. They add that the smaller colloids formed with surfactants have a larger specific surface area, which "can potentially" improve absorption through faster replenishment, so colloid size should be considered when formulations release alike [que2019 C54]. Papers of 2021–2022 use it as the reason to keep released droplets small: smaller colloids "can potentially" improve absorption by faster replenishment, and surfactants that coarsen droplets "would be a poor choice" [que2021 C37; correasoto2022a C1, C43].

Findings

Amorphous solubility and LLPS: F8, F16, F23. Bioperformance: F5, F8, F19, F22, F23. Mesoporous silica: F8, F15. Supersaturation from ASD dissolution: F7, F9, F21, F26. Release mechanism and LoC: F4, F13, F16.

Related concepts

depends on the drug-rich phase; inferred from membrane flux; related to thermodynamic activity. Needs drug-rich nanodroplets; contrasts with micellar solubilization. Absent where drug adsorption onto silica keeps the solution below the amorphous solubility; related to free drug concentration; the droplets form under congruent release.

Formulas

Receiver concentration-time profile with flow washout, membrane flux in terms of solute activity.

How it is measured or obtained

Not measured in the Amorphous solubility papers of 2013–2016; later papers use donors with and without nanodroplets and a membrane [indulkar2016 R7]. In the Bioperformance papers: a flow-through cell with a sink receiver, taking the length of the steady receiver period against the excess over the onset [indulkar2016 R5, R6] and a comparison with coarse amorphous particles [indulkar2016 R7]; a hollow-fibre receiver above the amorphous-solubility level and a fluorescence ratio falling to the amorphous-solubility level [hate2018 R13, R16]; hollow-fibre receiver Cmax against donor concentration above the amorphous solubility [ueda2020a R10, C26]; and PAMPA mass flow against donor concentration with a sink receiver, with an interface concentration estimated from it [hate2022 R19, C61]. In the Mesoporous silica papers: dissolution of ritonavir–SBA-15 at 200–1000% of the amorphous solubility with 1 µm filtration to count nanodroplets, against membrane flux [dening2018 P10, R8]; side-by-side comparison of atazanavir–SBA-15 with an HPMC dispersion of the same loading at 200 µg/mL in an absorptive apparatus [hate2020a P12]. Not measured in the ASD dissolution papers; the danazol work shows only that the free drug plateau is the same for all dispersions with a drug-rich phase [jackson2015 R9]. In the release-mechanism papers: not measured in these papers; colloid size by DLS [que2019 R12].

Values in the library

None in the Amorphous solubility papers of 2013–2016; the Bioperformance, Mesoporous silica and ASD dissolution papers give the following.

materialvalue or classconditionspaper ids
clotrimazole 10 / 15 / 20 µg/mLsteady period 1 / 5 / at least 13 h16 h flow-through[indulkar2016 R6, X5]
clotrimazole + 7.5 mg/mL 150–250 µm particlesno reservoir (0.63 to 0.42 µg/mL)5 h[indulkar2016 R7]
atazanavir 90:10 ASDsreceiver above AS level 120 min; 4 h: about 200 minhollow fibre[hate2018 R13, R21]
posaconazole ASDs (FaSSGF)longer supersaturation at higher dose, "most likely" reservoirtwo doses[elkhabaz2019a C48]
ritonavir on SBA-15no reservoir at the amorphous solubility without excess drug[dening2018 C44]
ritonavir–SBA-15, 400 and 1000% doseabout 24 µg/mL, about 85% of the amorphous solubility; no drug-rich phase by dissolutionpH 6.8[dening2018 R22, C32]
10% atazanavir–SBA-15 against 10% HPMC ASDdonor about 48–57 against up to about 207 µg/mL with LLPS; receiver about 4.3–5.2 against 10.2–11.6 µg/mL200 µg/mL, absorptive[hate2020a R24, R25]
atazanavir, clozapine, two HPMCAS gradesCmax keeps rising above the amorphous solubility with approximately parallel slopeshollow fibre, 37 °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/kg[wilson2018 R17, C46, X6]
danazol dispersions with LLPSsame maximum flux, read as the maximum transport rate25 °C[jackson2015 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 °C[elkhabaz2019a R12, R6, R14]
delamanid salt dispersions during releasestable drug-rich nanodroplets, smaller with HPMCP than with HPMCASPBS pH 6.5, 37 °C[duong2022a 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 hDLScorreasoto2022a R6
Pitfalls and disagreements

The claim that a colloidal drug-rich phase is favourable for absorption rests on literature and argument ("likely") [indulkar2015 C55, X15]. A plateau of flux shows constant activity but not resupply [trasi2015a C14]. The Amorphous solubility papers of 2013–2016 treat the effect as untested, whereas the flow-through experiments of indulkar2016 follow resupply by the length of the steady receiver period [indulkar2016 R5, R6]; so it is untested only in the former. In the Bioperformance papers depletion times were back-calculated in a way that does not match a mass balance [indulkar2016 X3]; droplet dissolution speed was estimated, not measured [indulkar2016 R18]; with mesoporous silica the effect "may not occur" [hate2020a C54]. The interface concentration of the PAMPA study is derived from mass flow anchored at 75 µg/mL, so the 1000 µg/mL point equals 75 by construction and the plotted values still rise from about 64 at 400 to 75 at 1000; no interface concentration, layer thickness or droplet dissolution rate was measured, so the mechanism is an interpretation (F22) [hate2022 X7, X8]. The rat difference rests on one aggregate-forming ASD that also dissolved fastest (F23) [wilson2018 X14]. Mesoporous silica: at the tenfold ritonavir dose, flux equalled that of amorphous ritonavir while dissolution through a filter that passes the droplets gave about 85% of the amorphous solubility, so whether the LLPS concentration was reached is unresolved [dening2018 X14, C33]. The method used to look for nanodroplets in the acid-first atazanavir run is not described and its data are not shown [hate2020a C54, R23]. In the ASD dissolution papers, for ritonavir the droplets "appear" to promote crystallization, the opposite of a stabilizing role [ilevbare2013d C41]. Danazol transport was measured across a dialysis-type membrane only, without absorption data [jackson2015 X12]. The posaconazole reservoir was inferred from the dose effect; neither the undissolved amorphous drug nor the droplet mass was measured over time [elkhabaz2019a X8]. The three colloid-forming formulations differ in loading and release rate, so the size difference cannot be assigned to the surfactant alone [que2019 X11]. No flux or absorption was measured in these papers [que2019 C54; que2021 C37].

← Concepts and formulas

concept · as used in Physical stability

non-sink dissolution

Dissolution at a dose that would exceed the crystalline solubility if it all dissolved, so that supersaturation can build up and the competing kinetics of dissolution, nucleation and crystal growth can be seen; non-sink testing is called essential for supersaturating systems and more sensitive to crystals than most solid-state methods [moseson2021 C3]. In the ASD process papers it is a statement about the dose against the solubility of each solid form, not one apparatus: ritonavir and lopinavir granules at pH 6.8 were "highly non-sink" against crystalline solubilities of 1.8 and 2.9 µg/mL [trasi2019 C10, M1, M2], and a bicalutamide dose of 3 µg/mL, the lowest that could be weighed and below the form 1 solubility, still "does not meet the traditional definition of sink conditions" [moseson2021 C24]. Further non-sink designs in the later papers: bicalutamide–PVPVA powder at a dose giving at most 30 µg/mL, chosen so that nucleation from solution does not interfere [moseson2022b P10, C7]; posaconazole coated powders at a dose equal to the amorphous solubility (8 µg/mL) [moseson2023 P13]; posaconazole after a gastric-to-intestinal pH shift at about 10 times the amorphous solubility (about 200 µg/mL) [shah2024 P11]; ritonavir powders and tablets at up to 25 µg/mL [benson2025 P11]; and 10 mg ezetimibe in 50 mL duong2022c P15. New aspect (Bioperformance): the dose is larger than the medium can dissolve at the (crystalline or amorphous) solubility, so that supersaturation and its loss can be seen [elkhabaz2017 P7; purohit2018 C30; alhalaweh2016 P10]. Absorptive tests combine non-sink dissolution with a membrane at three volumes, 5 mg of tacrolimus in 240, 100 and 40 mL hate2019 R7, C39. New aspect (Supersaturation from ASD dissolution): in the ASD dissolution papers of 2008–2015 the dose is set against both reference solubilities: non-sink with respect to the crystal so that supersaturation can show, and, in the danazol work, also above the amorphous solubility so that a drug-rich phase can form; danazol films were dosed at 20–30 µg/mL against 8 µg/mL amorphous and about 1 µg/mL crystalline solubility [jackson2015 C10, P1]. Only part of the dose may dissolve: the highest felodipine value, 14.1 µg/mL, was about 28% of a 50 µg/mL nominal dose konno2008a X15. The papers of 2015–2018 add two dose designs: a dose equal to the amorphous solubility (celecoxib, 8.8 mg in 400 mL, 22 µg/mL), at which a dispersion that stays amorphous should release completely while any drug crystallized in the matrix cannot dissolve [xie2015 C17; xie2016a C8], and the whole contents of a marketed capsule in 40 mL, the baseline gastric volume (tacrolimus, 125 µg/mL nominal against an amorphous solubility of about 50 µg/mL) trasi2016 P11, C29.

Findings

ASD process: F14, F21, F23, F26, F27, F28, F29, F38, F39, F40, F41, F46, F47, F48. Bioperformance: F8, F10, F14, F16, F17, F25, F28, F30, F31. Supersaturation from ASD dissolution: F1, F4, F6, F7, F8, F10, F16, F20, F21, F22, F24, F25, F26.

Related concepts

reads desupersaturation; detects residual crystallinity and matrix crystallization; uses the amorphous solubility advantage; also the setting for the release of coated particles (see atomic layer coating) and for the effect of wettability. Contrasts with sink conditions; related to pH-shift dissolution and absorptive sink; measured by free drug concentration; related to supersaturation and amorphous solubility.

Formulas

supersaturation ratio. Sink index, Noyes-Whitney equation.

How it is measured or obtained

IDM: 200 mL of 50 mM pH 4.5 acetate buffer at 37 °C stirred at 300 rpm, a UV dip probe with a scattering-corrected calibration (absorbance at 317 nm minus 450 nm), n = 3, 12 h, maximum 50 µg/mL, S = 6 [moseson2020a P9]. BCL: 3, 30, 60 and 150 µg/mL for 4 h at 37 °C, triplicate [moseson2021 P13]. Ritonavir granules: 250 mL, 150 rpm, 0.45 µm PTFE filtrate assayed by HPLC [trasi2019 P8, P15]. Two-stage pH-shift tests: 60 min in 40 mL fasted-state simulated gastric fluid (pH 1.6), then double-strength intestinal medium added to pH 6.5, samples centrifuged and assayed by HPLC (n = 3), with SHG, two-photon UV fluorescence and focused beam reflectance giving the solid [shah2024 P11, P12, P13, P14, P15]; posaconazole–HPMCAS powders held 30 min to 4 h at pH 1.6 or 4.0 and then moved to pH 6.5 [moseson2023 P13]. In the Bioperformance papers powder or capsule contents are dissolved in a small volume with in situ UV or sampled HPLC [elkhabaz2017 P7; purohit2018 P8; hate2018 P8]. In the ASD dissolution papers: paddle dissolution of powder with UV sampling through a 70-µm filter konno2008a P3; small-volume vessels with fibre-optic UV probes read every minute [alonzo2010 P2; alonzo2011 P2]; film dissolution with pyrene aliquots [jackson2015 P2]; filtered sampling for clear PVP solutions and ultracentrifugation for turbid HPMCAS ones [trasi2015b P5, P9]. Two-stage tests of indomethacin dispersions, 1 h in pH 2.2 buffer and then pH 5 or 6.8 by adding phosphate xie2017 P7, P8; suspensions of enteric dispersions in acid as non-sink leaching tests [li2016b P4]; films cast in vials and stirred 48 h at pH 3 li2018 P4, P5.

Values in the library
materialvalue or classconditionspaper ids
IDM–PVPVA extrudatesC720 about 43.1 → 28.8 µg/mL with 0 → 25% crystalline drug50 µg/mL total dose, pH 4.5, 12 h[moseson2020a P9, R6]
BCL–PVPVA 30:70fraction dissolved at 4 h about 0.82 → 0.23 as the dose rises 3 → 150 µg/mL (crystal-free)pH 6.8, 37 °C[moseson2021 P13, R17]
RTV and LPV granulesRTV about 4 µg/mL in the co-granule against about 30 alone250 mL, pH 6.8, 0.45 µm filtrate[trasi2019 P8, R4]
tacrolimus capsules (outside)100 mL gives 50 µg/mL at complete dissolution, equal to the amorphous solubilitypH 4.5, 37 °C, 300 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 h[moseson2022b R6]
BCL–PVPVA 30% DL, cryomilled 2 and 5 minabout 50 and 49% of the dose (about 15 µg/mL, the form 2 solubility)same[moseson2022b R4, M1]
PCZ–HPMCAS 10% DL, extruded at 175 °C (no crystals) against 125 °C (0.3% crystals)peak about 172.5 against 178 µg/mL; about 125 against 14.5 µg/mL at 300 minpH shift at 60 min, dose about 200 µg/mL[shah2024 R12, R14]
PCZ–HPMCAS 25% DL coated 11–39 nm, pH 6.5about 90% of the dose in 10–20 mindose 8 µg/mL[moseson2023 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 6.5duong2022c R13, R23
ezetimibe ASDs7.5 mg in 15 mL, about 500 µg/mLbuffer, FeSSIF, Ensure Plus[elkhabaz2017 P7]
ritonavir, atazanavir PVP ASDs150 mg in 15 mL, 120 minpH 6.8[alhalaweh2016 P10]
atazanavir ASDs200 µg/mL in 50 mLclosed 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 vessel[wilson2018 R6]
felodipine dispersions, 10–75% PVP, HPMC or HPMCAS30 mg in 600 mL (50 µg/mL nominal); maxima 0.8–14.1 µg/mLpH 6.8, 37 °C, 50 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 °C[alonzo2011 R1]
danazol films, three polymers, three loadings20–30 µg/mL nominal; free drug 5.4–9.1 µg/mLpH 6.8, 25 °C[jackson2015 P1, R9]
ritonavir and lopinavir 20% dispersions20 mg in 40 mLpH 6.8, 25 °C[trasi2015b P5]
celecoxib dispersions with PVP, HPMCAS, HPMC, PAA, 10–60% drug22 µg/mL nominal (= amorphous solubility) in 400 mLpH 6.8, 37 °C, 16 h[xie2015 P5; xie2016a P5]
six marketed tacrolimus capsules5 mg in 40 mL (125 µg/mL nominal); plateau ≈46–50 µg/mLpH 4.5, 37 °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 °C[elkhabaz2019a P6]
delamanid dispersions and tablets100 µg/mL at full release, about 100 times the amorphous solubility at pH 6.5PBS pH 6.5 or pH 1.6 → 6.5, 37 °C[duong2022a 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 Physical stability

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 stagetrasi2012a R12.a, R8.a, C39
acetaminophen with PAA or HPMCASPAA slows growth most but gives most nuclei; HPMCAS the reverse10% w/wtrasi2012a 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, AFMsaboo2017 C40
ritonavir–PVPVA films with SDS or Tween 80 vs binary and Spansnucleation and growth vs spinodal decomposition, read from the first morphologyconfocalyang2022b 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 Physical stability

nucleation induction time

The time from creating a supersaturation until crystals are first detected, t_{ind} = t_n + t_g: the time to form stable nuclei plus the time for them to grow to a detectable size; if growth is quick, t_{ind} \propto J^{-1} and a longer time means a slower nucleation rate [ilevbare2013c E2, E3, C14]. It depends on the detection method, since crystals are seen earlier by SHG than by a probe ratio or light scattering [jackson2014 R25, R17].

Findings

F3, F4, F5, F6, F13, F14, F15, F25, F27, F28, F29, F32, F34, F35, F37, F38, F39, F40, F41, F42, F43, F44.

Related concepts

part of nucleation; gives nucleation rate; modified by nucleation inhibition; measured on supersaturation.

Formulas

induction time decomposition, relative nucleation rate from seeded and unseeded induction times, classical nucleation theory.

How it is measured or obtained

A methanol stock of drug is pumped or injected into stirred buffer with or without predissolved polymer and the signal is followed: extinction at a wavelength where the drug does not absorb (280 or 350 nm) or the fall in UV absorbance, taking the crossing of regression lines through the flat and rising (or falling) parts as the time; pyrene fluorescence and SHG as second read-outs; triplicate [alonzo2012 P5; ilevbare2013c P9, P10; jackson2014 P8]. The stated supersaturation uses a methanol-free solubility; the methanol fraction is about 0.5% v/v [ilevbare2013c X16].

Values in the library
materialvalue or classconditionspaper ids
celecoxib; efavirenz; ritonavir, no polymerabout 2.4; 5.1; 120 minat the calculated amorphous solubility, 37 °C[ilevbare2013c R8, R9.a]
ritonavir, CAB Adp 0.81; efavirenz, CAB Adp 0.81; celecoxib, HPMCabout 244; 28.0; 12.6 min5 µg/mL polymer[ilevbare2013c R9]
celecoxib at 11 µg/mL, none against HPMC27.5 ± 0.7 against 855.5 ± 6.0 minS 7.3[ilevbare2013c R15]
felodipine, none against 1 µg/mL HPMC15.3 against 136.5 minS 10, 25 °Calonzo2012 R16
danazol, none; PVP; HPMC; HPMC-AS6–10; 88–162; 111–285; 250–516 min10–20 µg/mL, 25 °C[jackson2014 R17]
celecoxib 22 µg/mL, 5 µg/mL HPMCAS (ASD dissolution chapter)held for 16 h; J_0/J_p about 4,00037 °C[xie2016a 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 °C[moseson2020a R3]
11 drugs, 0.1% STC and SDS, matched C/Ceqbuffer 7–87 min; STC 15 to >1000; SDS shorter for 7 of 925 °C, telaprevir 37 °C[chen2015 R3]
acetaminophen, S 1.595% of vials 26 min; first crystals 150–785 s20 °Ctrasi2015 R1, R10
celecoxib, nevirapine, flibanserin, 13 bile salts3 min to >16 h (celecoxib); 0–577 (nevirapine); 0–623 min (flibanserin)pH 6.5, 37 °C[li2016a R6]
telaprevir, 80 and 150 µg/mL, 26 polymersHPMC >700 and 243; none 14–15 minpH 6.8, 37 °C[mosqueragiraldo2016 R4]
telaprevir δ 11.5 and 28.8, six bile salts30 min and immediate in buffer; >960 min with 1.86 mMpH 6.5, 37 °C[lu2017 R3, R4]
danazol 15 µg/mL, PVP, HPMC, HPMC-AS 1–1000 µg/mLabout 5 min; 26–412 min25 °C[jackson2016 R17]
atazanavir without additive, five protocolsabout 40, 92–102, 170, 200, 253 ± 65 minnear the amorphous solubility, 37 °C[mosqueragiraldo2018a R1; elkhabaz2021 R6; indulkar2018 R19; indulkar2019b R3; enright2020 R2]
posaconazole without additive, three protocolsabout 5–8, 8.4, 29 ± 5 minpH 6.5, 37 °C[elkhabaz2021 R7; duong2022b R10; shah2025 R3]
enzalutamide without polymerabout 5–15 min, 30–120 µg/mLpH 6.5[wilson2021 R1]
Pitfalls and disagreements

The assumption t_n \gg t_g was not tested; strong inhibitors give gradual onsets whose fitted times depend on where the lines are drawn (rise above baseline at about 25 min against a fitted 31.5 min; about 180 against 260 min) [ilevbare2013c C14, X14]. Methods differ by up to about 40% for single conditions [jackson2014 X5]. The same polymer, drug and concentration gave 10–13 min in one laboratory and more than 8–16 h in another [ilevbare2013c R9; xie2015 R1; xie2016a R3]. The efavirenz run was at S about 2.3, not 15 [ilevbare2013c X4]. Replicate scatter is below 15% [ilevbare2013c R17]. Values above 960 or 720 min are lower bounds set by the run length [lu2017 X16; chen2015 X7]. The control induction time of one drug differs up to about sixfold between protocols, so effects compare only as ratios to a control in the same protocol [mosqueragiraldo2018a R1.b; enright2020 R2]. Several papers do not identify the scattering particles at the induction time [indulkar2018 X14; enright2020 X15].

← Concepts and formulas

concept · as used in Physical stability

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/mL[ilevbare2013c R9, R12]
celecoxib at S 7.3, HPMC27.5 → 855.5 min (31-fold)5 µg/mL[ilevbare2013c R15]
celecoxib, 5 µg/mL HPMCAS (ASD dissolution chapter)J_0/J_p about 4,00022 µg/mL drug[xie2016a 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 4.5[moseson2020a R3, C11]
11 drugs, 0.1% STCinduction time lengthened for all, eight by more than 10-fold25 °C[chen2015 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 11.5[lu2017 R10, X1]
acetaminophen, S 1.5J lowered 18-fold (HPMCAS) and 36-fold (HPMC); raised 2.6-fold by PAA10 µg/mLtrasi2015 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 °C[duong2022a 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 Physical stability

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 °C[xie2016a R13]
acetaminophen, S 1.5J 1465 (none), 3820 (PAA), 81.86 (HPMCAS), 40.68 (HPMC) # m⁻³ s⁻¹1.2 mL vials, 20 °Ctrasi2015 R3
telaprevir with STC, SGCJ/J₀ 2.5 × 10⁻³, 2.9 × 10⁻⁶δ 11.5[lu2017 R10]
atazanavir, posaconazole, six mediaSHG count rate about 0.1–1.6 and 0.05–48 counts/min37 °C, relative per 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 °Ckonno2006 R4
amorphous nifedipine vs felodipine0.39 vs 0.17 × 10¹⁰ m⁻³ day⁻¹0% RH, 22 °Cmarsac2006a R4.a
nifedipine and felodipine with 7% PVP≈1.4 × 10³ and ≈2.7 × 10² m⁻³ s⁻¹0% RHmarsac2006a R16.b
felodipine with 3% PVP vs HPMCAS≈8.6 × 10⁵ vs ≈1.3 × 10⁴ m⁻³ s⁻¹75% RH, 22 °Ckonno2008 R3.b
nifedipine vs felodipine with 25% PVP≈4.3 × 10⁵ vs ≈2.3 × 10³ m⁻³ s⁻¹75% RHmarsac2008a R1.f, R1.l
felodipine (activation energy)145 kJ/mol below Tg; 201 with 3% PVPArrhenius, ≈25–75 °Cmarsac2006a R3
griseofulvin melt (SHG imaging)number density ≈45 → ≈600 mm⁻³ over ≈62–285 min125 °C, SHGwanapun2010 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 Physical stability

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 countstrasi2014b R5, R9, C41
acetaminophen50–60 °CDSCtrasi2012a C22
flutamide10–40 °CDSCtrasi2012b 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–reheattrasi2012a R12
acetaminophen with 15% w/w PVP, PAA, HPMCASno crystallization in the testsametrasi2012a R12
flutamide with 10 mol% PDMA, PVAc, PVPH, PIPA, PVP10–30, 20–40, 30–40, 20–30, 20–40 °Csametrasi2012b R10
vemurafenib αapproximately 170–270 °C (inferred)hot stagelu2016 C43
indomethacin γ; α (cited)maxima at about Tg and about 20 °C higherliteraturetrasi2014b 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 Physical stability

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 °Ctrasi2014b R9
acetaminophennucleation zone 50–60 °CDSC cool–reheattrasi2012a C22
acetaminophen with polymersHPMCAS reduces nuclei to about a third; PAA gives nearly three times more10% w/wtrasi2012a C23
flutamidenucleation zone 10–40 °CDSC cool–reheattrasi2012b R10
nifedipine against felodipinefaster nucleation for nifedipinepure films, 22 °C, 0% RHmarsac2006a R1
felodipine filmsrate rises with storage RH; drug alone fastest22 °C, with polymerskonno2008 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 °Ctian2017 R1, R5, C7
celecoxibsamples "quite hard to nucleate"hot stagemosqueragiraldo2014 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 studymarsac2006b R16
indomethacin–PVPnucleus requires breaking the PVP–drug bond (proposed, untested)no crystallization datataylor1997 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 solubility[ilevbare2013c 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 °C[jackson2014 R17]
nine drugs with carboxylated cellulose derivativescontact with the emerging nucleus "clearly a prerequisite" for disruption5 µg/mL, pH 6.8[mosqueragiraldo2018a C44]
amorphous felodipinerate ≈1.4 × 10⁵ → 2.9 × 10⁶ m⁻³ s⁻¹0 → 75% RH, 22 °Ckonno2008 R1.a, R3.a
nifedipine vs felodipinefaster at every PVP level and RH0–75% RHmarsac2008a R1, C7
felodipine with 50% HPMCASnegligible crystals for 35–120 days at 52–93% RH, read as delayed nucleationPXRD of powdersrumondor2009b 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 curvetrasi2012b R11.b, R11.d, R11.f, C18
flutamide with 10 mol% nilutamideone nucleus in the imaged regioncooled to −30 °C, reheatedtrasi2012b 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 °C[ilevbare2013d R16, R12]
felodipine methanol shift with HPMC, S about 60precipitation not completely suppressed25 °C[alonzo2011 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 Physical stability

octanol-water partition coefficient

Evidence table: octanol-water partition coefficient. Content from the release-mechanism chapter (2019–2022), with rows from the Solid-state methods and Bioperformance chapters.

The ratio of drug concentrations in octanol and in an aqueous buffer at equilibrium, given as log P; it measures drug lipophilicity [saboo2020a E5]. In the release-mechanism papers it was the variable tested against the limit of congruency and against congruent release rates [saboo2019 A1, C6; saboo2020a C32].

Findings

Release mechanism and LoC: F9.

Related concepts

measures lipophilicity; tested against the limit of congruency.

Formulas

octanol-water partition coefficient.

How it is measured or obtained

Shake flask with octanol-saturated pH 6.5 buffer, compounds predominantly un-ionized, concentrations by LC-MS [saboo2020a E5]; calculated (ClogP) [saboo2019 A1]; cited [indulkar2017b M1; que2019 R28]. Shake flask with LC-MS of both phases at pH 2.0 (indomethacin) and pH 6.5 (its methyl ester) [saboo2020 P21, E4]; two calculation programs for the phenolphthalein analogues [que2021 M1].

Values in the library
materialvalue or classconditionspaper ids
nifedipine3.17 (cited)[indulkar2017b M1]
nilvadipine; cilnidipineClogP 3.04; 5.54calculated[saboo2019 A1]
nilvadipine; felodipine; cilnidipine4.06; 4.46; 5.40shake flask (felodipine from the literature)[saboo2020a R16]
ritonavir4.3 (cited)[que2019 R28]
probucol; procaine (Solid-state methods)10; 1.3citedpurohit2015b C5
enzalutamide (Bioperformance)4.75 (calculated)[wilson2020 C18]
indomethacin; its methyl ester4.07; 4.53shake flask[saboo2020 M1, M2]
four phenolphthalein analogues2.63–7.60 (ACD), 4.11–8.14 (MarvinSketch)calculated[que2021 M1, M2, M3, M4]
loratadine, miconazole, danazol, elbasvir, paclitaxel, ivacaftor4.4, 5.69, 3.8, 5.33, 3.96, 5.68citedyang2021 M1, M2, M3, M4, M5, M6
lumefantrine8.34cited[hiew2022b M1]
Pitfalls and disagreements

Calculated and measured values for the same drugs differ by up to about 1 log unit (nilvadipine 3.04 against 4.06) [saboo2019 A1; saboo2020a R16]. A log P difference of about 2.5 units did not change the molar limit of congruency [saboo2019 C35]. Within the analogue series none of the log P values tracked the limit [que2021 C29].

← Concepts and formulas

concept · as used in Physical stability

pH-dependent solubility

The rise of the solubility of an ionizable drug as pH moves toward and past the pKa; for a weak base the total solubility is the free-base solubility times (1 + 10^{\mathrm{p}K_a-\mathrm{pH}}) [indulkar2015 E8]. The amorphous solubility follows the same shape with the amorphous free-base solubility in place of the crystalline one, so the un-ionized concentration at the LLPS onset is constant across pH (F10) [indulkar2015 C46, R9]. The papers of 2017–2022 add pazopanib, for which the crystalline free base follows the curve from pH 5 to 8.4 and the amorphous solubility follows its curve from pH 6 upward but lies below it at pH 5 and 5.5 [sugihara2018 R2, R3, C10, C11]. New aspect (Crystallization from solution): in the pH-shift studies the shift itself generates supersaturation, since weak bases with pKa 5–8 dissolve at gastric pH 1.5–3.5 and can precipitate at duodenal pH 5–7 [hsieh2012 C1]; the Bjerrum plot ties the pH, the total concentration and the solubility of whatever solid is present, and the curve moves by \log_{10}(S_0'/S_0) pH units when the solid's solubility changes (0.85 units for 11.3 against 1.6 µg/mL) [hsieh2012 E2, R9]. New aspect (Supersaturation from ASD dissolution): a weak acid. Indomethacin (pKa 4.42, cited) has an aqueous solubility of 1.5 µg/mL at pH 1.2 and 105 µg/mL at pH 7.4 (cited) xie2017 M1; the measured solubility of the α crystals rose from 2.8 µg/mL at pH 2.2 to 15 µg/mL at pH 5 xie2017 R1, R2. In a two-stage test the rise of pH after the acid stage therefore turns what separated in acid into a solid that can dissolve again: the drug-rich droplets of an EPO–HPMC dispersion disappeared within minutes of a rise to pH 5, "consistent with" an increase in the amorphous solubility on ionization xie2017 C40, R20. Weak bases (formerly the page "pH-dependent solubility of weak bases", from ASD process and Supersaturation from ASD dissolution): the solubility of a weakly basic drug rises when it is ionised at low pH and falls when the pH rises. Ritonavir (pKa 1.8 and 2.6) is "highly, not completely" ionised at pH 1.2, with a crystalline solubility of about 0.4 mg/mL there against 1.8 µg/mL at pH 6.8, so dissolution in 0.1 N HCl is at sink and at pH 6.8 strongly non-sink; lopinavir is not ionised at either pH [trasi2019 M1, M2, C14]. On a pH rise the ionised drug becomes supersaturated and, above its amorphous solubility, forms a drug-rich phase [trasi2019 C40]. For posaconazole the acid stage releases drug that becomes supersaturated at pH 6.5; extruded dispersions release more in acid than amorphous ones because crystalline drug sits apart from HPMCAS, which does not dissolve in acid [shah2024 C41, R12]. Coated posaconazole powders were held 30 min to 4 h at pH 1.6 or 4.0 and then moved to pH 6.5 [moseson2023 R10, R12, R13]; coated and uncoated ritonavir tablets released alike in 0.1 N HCl, where the drug is far more soluble [benson2025 R12]. For a weak base formulated with an enteric polymer, the drug and the polymer change their solubility in opposite directions across the gastric-to-intestinal range, and the window in which neither dissolves well decides the outcome. Delamanid, with a fitted pKa of 3.94 ± 0.04 against a reported 4.3, loses about 500-fold of its crystalline solubility and about 200-fold of its amorphous solubility between pH 1.6 and 6.5, while the enteric polymers dissolve only from about pH 5–6; the authors summarize that at pH 1.6 the drug dissolves and the polymers do not, at pH 3.0 and 5.0 both are poorly soluble, and at pH 6.5 the polymers dissolve and the drug hardly at all [nguyen2023c R1, R2, R3, R4, C14, C15]. Posaconazole shows the same pattern between gastric and intestinal fluid, which the authors attribute to nearly complete ionization in acid [elkhabaz2019a R1, C11].

Findings

Amorphous solubility and LLPS: F10, F23. Crystallization from solution: F1, F2, F34. Supersaturation from ASD dissolution: F21, F24, F25. ASD process: F23, F24, F41, F46, F48.

Related concepts

depends on ionization and pKa; applies to crystalline solubility and amorphous solubility; related to intrinsic solubility and pH-induced precipitation; related to pH-shift dissolution, precipitate redissolution and polymorphism; produces supersaturation read in non-sink dissolution; mixing in the drug-rich phase gives mutual amorphous solubility reduction; sets the window with pH-dependent polymer solubility; drives salt disproportionation; read with gastric pH variability and drug leaching.

Formulas

pH-solubility profile, Henderson-Hasselbalch equation, Bjerrum function, amorphous-to-crystalline solubility ratio.

How it is measured or obtained

Shake-flask crystalline solubility in 0.1 M buffers over about ±2 pH units of the pKa; LLPS onset by antisolvent addition, fluorescence and solvent-free pH-shift titration at each pH [indulkar2015 P3, P8, P9, P10]. In the pH-shift studies the crystalline solubility of the neutral form is measured at a pH at least two units above the pKa for bases (pH 10 buffer) or below it for acids (pH 2 buffer) [hsieh2012 P11; hsieh2014 P5]; potentiometric (CheqSol) titration of the neutral concentration and 72 h shake-flask solubility at fixed pH [hsieh2012 P4, P11]. For indomethacin: shake-flask solubility of the γ and α forms in pH 2.2 McIlvaine buffer (37 °C, 48 h) and of the α form at pH 5, with and without dissolved polymer xie2017 P2, R1, R2. For weak bases in the ASD process papers: dissolution in 0.1 N HCl and pH 6.8 phosphate buffer, and an acid-to-pH 6.8 shift with ultracentrifugation of the supernatant [trasi2019 P8, P9, P11, P12]. In the ASD dissolution papers: crystalline solubility by shake flask in each buffer and amorphous solubility by the onset of light scattering during slow addition of a stock, with a Henderson–Hasselbalch fit over the measured values to give the pKa [nguyen2023c P1, P2, E1]; the same measurements in simulated gastric and intestinal fluids [elkhabaz2019a P2, P4; duong2022a P1, P2].

Values in the library
materialvalue or classconditionspaper ids
clotrimazolecrystalline 0.55 (pH 8) to about 62 µg/mL (pH 4); LLPS 7.7 to 490.2 µg/mL37 °C[indulkar2015 R4, R5, R18]
atazanavircrystalline 1.04 (pH 9) to about 40 µg/mL (pH 3); LLPS about 65 to about 1970 µg/mL37 °C[indulkar2015 R4, R6]
nicardipineLLPS 5.5 (pH 9) to about 355 µg/mL (pH 5.5); no crystalline value37 °C[indulkar2015 R7, R1]
CRH1un-ionized onset about 12 µg/mL at pH 6.8 and pH 4.625 °C[almeidaesousa2016 R24]
pazopanibcrystalline about 0.60 → 0.018 µg/mL; amorphous 60 → 9.2 µg/mL (pH 5 → 8.4); ratio about 103 at pH 5, 500–600 from pH 6.437 °C, 0.1 M buffers + 5 µg/mL HPMC[sugihara2018 R1, R2, R4]
loratadineBjerrum data on the curve for S0 = 11.3 µg/mL, 0.85 pH units from the curve for the crystal (1.6 µg/mL)37 °C[hsieh2012 R9, E2]
dipyridamoledata left the ionization curve at pH about 5.1 and met the crystal curve at pH about 4.037 °C[hsieh2012 R4]
papaverine, dipyridamole, glyburide, warfarincrystalline solubility in pH 10 or pH 2 buffer: 12.2, 5.4, 0.2 (titration), 3.7 µg/mL25 °C, no polymer[hsieh2014 R4]
posaconazolecrystalline 0.27 (pH 5.5–7.0) to 347.03 µg/mL (pH 1.0); amorphous 8.92–9.20 to 7761.96 µg/mL; diprotic HH fitphosphate buffers, 0.14 M, 37 °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 °C[nguyen2023c R1, R2, R3]
praziquantelamorphous 1.17–1.43 mg/mL across six buffers; calculated pKa 1.14, so the drug is neutral above about pH 337 °C[alvarenga2025 R1, R4]
ritonavir from the marketed tabletabout 84 µg/mL in acid falling to about 4.6 after the shift to pH 6.8200 mL acid, 30 min, then NaOH and buffer[trasi2019 R8]
ritonavir solution without excipientsabout 97 → 16 µg/mL after neutralisation; precipitate not birefringentultracentrifuged supernatant[trasi2019 R9, R10]
posaconazole (outside)solubility much higher in the gastric than in the intestinal medium because the drug is nearly completely ionised in acidbiorelevant media[elkhabaz2019a C11, C40]
delamanid (outside)pH-solubility profile of a weak base by the Henderson–Hasselbalch equationbuffers and media[nguyen2023b E1, R13]
posaconazole form Icrystalline solubility 86.5 µg/mL at pH 1.6 (FaSSGF) and 1.2 µg/mL at pH 6.5 (FaSSIF V2); LLPS concentration 2326 and 19.1 µg/mL37 °C[shah2024 R11, C14]
PCZ–HPMCAS extruded at 125 °C against 175 °C, 10 / 25 / 50% DLabout 38 / 43 / 73.5 against 30 / 28.5 / 39.5 µg/mL after 60 min at pH 1.6two-stage test[shah2024 R12, R15, R18]
coated and uncoated 20% DL RTV–PVPVA tablets in 0.1 N HClabout 87–91% at 60 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 °C[duong2022a R1]
posaconazole, crystalline115.1 ± 9.4 µg/mL in FaSSGF against 1.69 ± 0.06 µg/mL in FaSSIF48 h, 37 °C[elkhabaz2019a R1]
posaconazole, amorphousabout 20 µg/mL in FaSSIF with 20 µg/mL HPMCAS; 8 µg/mL in plain buffer pH 6.537 °C[elkhabaz2019a R2, R4]
Pitfalls and disagreements

The predicted amorphous curve is the crystalline curve times one factor, so it is not an independent test of the shape [indulkar2015 X14]. The relation holds where the solution is in equilibrium with the neutral form and not the salt [indulkar2015 E8]. Below pH 6 the amorphous boundary of the pazopanib diagram is a model curve, not a measurement [sugihara2018 X12]. Solubility was measured in other buffers than the precipitation, and buffer compositions are not given [hsieh2014 X8]. The legend of the loratadine Bjerrum figure names the predicted amorphous solubility, the text the supernatant value (11.0 against 11.3 µg/mL) [hsieh2012 X6]. The plotted Henderson–Hasselbalch fit of the posaconazole paper lies far below the data at pH 2.5–3.0 for one assignment of the two pKa values duong2022b X3. The pH profile of indomethacin is cited, not measured, and its amorphous solubility was measured at pH 2.2 only, so the ionization explanation of the droplet disappearance at pH 5 is an inference xie2017 M1, R3, C40. Ionization does not explain the whole pH dependence of release: praziquantel, neutral above about pH 3, still lost release after gastric stages at pH 3.0 and 5.0, so the pH dependence of release need not come from the drug [alvarenga2025 R4, R10]. Acid-stage release does not rule out the problem: the neutral partner drug still lowered ritonavir release in acid, and the fall after the pH shift reflects loss of ionisation, dilution and mixing with the partner (not separated) [trasi2019 C41, C47]. The final pH after the shift was not measured and the acid volume is printed as 250 mL in the caption and 200 mL in the methods [trasi2019 X4, X5]. The fitted curve for delamanid follows the amorphous data but gives about 3.7 instead of the measured 10.2 µg/mL for the crystal at pH 1.6 [nguyen2023c R3]. The gastric supersaturation that the drug's own pH dependence creates did not order the final release of delamanid dispersions [nguyen2023c C39].

← Concepts and formulas

concept · as used in Physical stability

phase inversion

Evidence table: phase inversion. Content from the release-mechanism chapter (2022–2025), with rows from the Solid-state methods chapter.

The change of which of two separated phases is continuous and which forms discrete domains, as their relative amounts change. In dissolving PVPVA dispersions the lower-volume phase forms the discrete phase and the higher-volume phase the continuous one, so inversion from a discrete to a continuous drug-rich phase "is anticipated" as drug loading rises; the low-composition component tends to form the discrete phase, which gives a discrete drug-rich phase and fast congruent release at low loading (cited) yang2022a C46, C59. In MePHPH–PVPVA compacts the morphology inverted at 50% (hydrophobic continuous, hydrophilic discrete), persisted and coarsened deac2023a C26. In the Solid-state methods chapter dry dextran–PVP blends with distinct phases had a dextran-rich continuous phase with PVP-rich domains at high dextran molecular weight and inverted morphology for DEX40-PVP90 and DEX6-PVP90 vaneerdenbrugh2012c C43. The 2024 papers locate it: clotrimazole films with PVP K12 and K29/32 held drug-rich droplets to 30% and a continuous drug-rich phase at 40% after 1 h at 100% RH, named "Failure Mode II" [deac2024a R8, C23, C40]; MePHPH films kept droplets to 30% and were continuous from 50%, PHPH films switched between 10 and 15%, and the lever-rule fraction of drug-rich phase jumps from about 0.15 to 0.82 across the critical point, taken as a surrogate for inversion deac2024b R18, R19, R35, C64.

Findings

Release mechanism and LoC: F20, F25, F27, F29, F30.

Related concepts

part of phase separation morphology; its loading is shifted by associative phase separation and segregative phase separation; relative phase amounts from the lever rule; gives the drug-rich barrier layer when the drug-rich phase becomes continuous.

Formulas

lever rule (relative phase amounts).

How it is measured or obtained

Fluorescence confocal imaging of the edge of a dissolving compact with two dyes that partition into the two phases, and imaging of compact surfaces after partial dissolution deac2023a R6, R9; in dry blends local AFM-IR spectra of the continuous phase and the domains vaneerdenbrugh2012c R15, R17.

Values in the library
materialvalue or classconditionspaper ids
MePHPH–PVPVA 5–30%; 40%; 50%discrete particles below 1 µm; networks; inverted, hydrophobic continuousin situ confocal of the dissolving compact edgedeac2023a R6, C26
MePHPH–PVPVA 30%; 50% compact surfaces50% surface the inverse of the 30% surfaceafter partial dissolutiondeac2023a R9, C35
dextran–PVP blends DEX450-PVP12, DEX40-PVP12; DEX40-PVP90, DEX6-PVP90 (Solid-state methods chapter)dextran-rich continuous phase; phase inversionAFM-IR, dry filmsvaneerdenbrugh2012c C43, R15, R17
clotrimazole–PVP K12, K29/32 filmsdroplets at 20–30%, inverted at 40%100% RH, 1 h, confocal[deac2024a R8]
MePHPH–PVPVA films 10–60%droplets to 30%; co-continuous 1 h, droplets 6 h at 40%; continuous 50–60%100% RH, confocaldeac2024b R18
PHPH–PVPVA films 5–20%droplets 5–10%; continuous 15–20%samedeac2024b R19
Pitfalls and disagreements

For ritonavir the inversion is an expectation argued from phase volumes, not located at a measured loading yang2022a C46. In the dissolving compacts the continuous drug-rich phase appeared at 40% as networks before full inversion at 50%, so the change was gradual over loading deac2023a C26. The loading at which MePHPH becomes continuous is stated as above 40%, 40% or higher, and 35–40% in different parts of the 2024 paper deac2024b X4; for PHPH the computed critical point (3.7% as the paper states; about 4.2% read from its diagram, see critical point) lies below the film switch deac2024b X5. Inversion was imaged for two PVP grades only [deac2024a X8].

← Concepts and formulas

concept · as used in Physical stability

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-coatedpurohit2015a C37, R10, R14, X8
telaprevir–HPMCbelow 50 nm at 10:90; around 100–200 nm in the other filmsAFM heightli2016c R7
telaprevir–HPMCASabout 120 nm wide and 50 nm high at 40% drug; 122 × 13 nm at 50:50, gaps 21 and 25 nmAFM heightli2016c R5, R7
telaprevir–PVPVAabout 280 nm wide and 20 nm high at 10%; about 380 nm and 100 nm at 50%AFM heightli2016c 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 Physical stability

phase separation kinetics

Evidence table: phase separation kinetics. Content from the release-mechanism chapter (2017–2022).

The rate at which a hydrating dispersion undergoes water-induced amorphous–amorphous phase separation, set against the rate at which it dissolves. Saboo and co-workers (2020) state that the thermodynamic favourability of water-induced AAPS depends on drug loading, polymer type, the relative affinity of drug and polymer for water and the water absorbed, and that its kinetics compete with dissolution ("it has been suggested") [saboo2020a C39]. The competition "may be key": if dissolution is faster, drug and polymer release congruently and the surface keeps its composition; if AAPS is faster, the polymer-rich domains dissolve first, the surface turns drug-rich and drug release slows [saboo2020a C41]. The ritonavir and ledipasvir papers explain the steep drop of release over a small loading step the same way, by a faster rate of AAPS relative to dissolution at high loading ("can be attributed"; "may") [indulkar2019a C33; que2019 C35]. Saboo and co-workers (2021) assume separation in the hydrated matrix to be faster than polymer dissolution and propose that TPGS may slow it or slow coarsening saboo2021 C38, C41, C51; Correa Soto and co-workers (2022) find the kinetics and morphology changed by the surfactant, with a significance for release "if any" unknown correasoto2022a C61, and in the atazanavir study separation needs mobility that the surfactants supply correasoto2022b C41.

Findings

Release mechanism and LoC: F8, F20.

Related concepts

the rate of amorphous-amorphous phase separation; proposed cause of the limit of congruency; depends on drug-polymer-water miscibility.

Formulas

none.

How it is measured or obtained

Not measured as a rate in the release papers: inferred from films dipped in water for seconds or held at high humidity, together with the release data [indulkar2019a X6; saboo2020a C41]. The time course was followed only by the pyrene ratio of ritonavir films at 97% RH, where all PVP and PVPVA films began to separate as early as 1 h purohit2017b R2, C22.

Values in the library
materialvalue or classconditionspaper ids
ritonavir 50:50 PVP, PVPVA filmsseparated within 10 s in buffer; 10:90 did not25 °Cpurohit2017b R4, R9
ritonavir PVP, PVPVA filmsAAPS from about 1 h at 97% RHpyrene I/IIIpurohit2017b C22
felodipine dispersions ≤ 10%dissolution thought to outpace AAPS with every polymerargument[saboo2020a C41]
atazanavir–PVPVA 10% filmsbinary uniform for 3 h at 37 °C, separated within 10 min at 50 °C; surfactant films within 10 min100% RHcorreasoto2022b R9, R12, R10, R11
Pitfalls and disagreements

Neither the rate of AAPS nor that of dissolution was measured on the same sample; the competition is the authors' inference from films plus release data [indulkar2019a X6]. At low loading too little drug for a contiguous layer may keep release congruent as well as slower AAPS [saboo2020a C42].

← Concepts and formulas

concept · as used in Physical stability

phase separation morphology

Evidence table: phase separation morphology. Content from the release-mechanism chapter (2021–2023), with rows from the Physical stability chapter.

The shape and connectivity of the drug-rich and polymer-rich phases that form when water separates a drug–polymer dispersion: discrete (circular, separated) drug-rich domains in a continuous polymer-rich phase, bicontinuous structures, or a continuous drug-rich phase with discrete polymer-rich domains saboo2021 R21, R23; correasoto2022a R20. Saboo and co-workers (2021) propose that at high loading whether release is drug- or polymer-controlled "depends largely" on the architecture of the drug-rich phase formed in the hydrated matrix saboo2021 C37; in the abstract discrete spherical drug-rich domains with surfactant "appeared to be linked" to congruent, rapid release and a contiguous drug-rich phase to its loss saboo2021 C53. For clopidogrel the binary films matched the release profiles and "earlier reports" that continuous drug-rich phases go with poor release correasoto2022a C32. Domain size and interconnectivity of the drug-rich domains "appear" critical for release of ritonavir–PVPVA, and a continuous drug-rich phase is called catastrophic for drug release yang2022a C4, C58.

Findings

Release mechanism and LoC: F20, F21, F25.

Related concepts

the outcome of amorphous-amorphous phase separation; kept discrete when drug-rich phase coarsening is slowed; a continuous drug-rich phase acts as a drug-rich barrier layer; set within the gel layer; changed by surfactant partitioning into the drug-rich phase.

Formulas

none.

How it is measured or obtained

AFM topography and deflection and AFM-nanoIR ratio images of 30% felodipine films after 12 h at about 100% RH saboo2021 R21, R23; micro-CT of tablets after 10 min of dissolution saboo2021 R19; fluorescence confocal imaging with Nile red (drug) and Alexa 488 (polymer) of films before and after 5 min at 100% RH, with a detection limit of about 500 nm correasoto2022a R20, R21; time-lapse fluorescence and O-PTIR of ritonavir films (Physical stability chapter) yang2022b R4, R22.

Values in the library
materialvalue or classconditionspaper ids
felodipine–PVPVA 30% with 0, 2% TPGS; 5, 10% TPGSirregular semi-continuous domains; circular, discrete domainsAFM, 12 h at ≈100% RHsaboo2021 R21
felodipine–PVPVA 30% with 0; 10% TPGScontiguous, elongated drug-rich regions; round, separated drug-rich domains in a continuous drug-lean phaseAFM-nanoIRsaboo2021 R23
clopidogrel–PVPVA 40, 50, 60%uniform; bicontinuous; continuous drug-rich phase with discrete polymer-rich domains5 min at 100% RHcorreasoto2022a R20
clopidogrel–PVPVA with 5 g SDS per 100 g at 50%homogeneous within the ≈500 nm detection limitsamecorreasoto2022a R21
clopidogrel–PVPVA with TPGS; with Tween 80, at 50 and 60%bicontinuous, then large irregular structures; fine-scale heterogeneous patternsamecorreasoto2022a R22, R23
ritonavir–PVPVA 30% binary; with SDS or Tween 80; with Span 85 (Physical stability chapter)bicontinuous; discrete circular drug-rich domains; continuous drug-rich phasefilms, time-lapseyang2022b R4, R22, C9
ritonavir–PVPVA 10–20%; 30%; 40%discrete droplets 0.5–2 µm; porous continuous layer; continuous layerconfocal of dissolving compactsyang2022a R6, R10, R12, R13
MePHPH–PVPVA 5–30%; 40%; 50%discrete particles below 1 µm; networks; inverted morphologyin situ confocal of the dissolving edgedeac2023a R6, C26
PHPH–PVPVA 10–20%networksamedeac2023a R7
Pitfalls and disagreements

Morphology was imaged in films or humidified compacts, not in the dissolving gel layer; the contiguous network "likely also forms" there saboo2021 C39. Morphology and release did not track in every system: with TPGS the 50% clopidogrel film was bicontinuous correasoto2022a R22, and Correa Soto and co-workers (2022) find kinetics and morphology changed by the surfactant with a significance for release "if any" unknown correasoto2022a C61.

← Concepts and formulas

concept · as used in Physical stability

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 Tgbaird2010 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, desiccanttian2016 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, desiccanttian2016 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% RH[hiew2022b R7]
delamanid saltsno PXRD peaks after 2 weeks40 °C/75% RH[duong2022a C32]
naringenin, quercetin with E100 and PVPno crystals for >200 to >450 daysfive conditions, 40–50% polymerwegiel2013a R9
naringenin, quercetin with HPMCAS, HPMC, CMCAB, PAAfirst crystals after 1–3 days84% RH/25 °C and 75% RH/40 °C, 30–80% polymerwegiel2013a R9
lumefantrine–PVPVA at 50, 25, 10 and 5% drug loadingfirst crystals after 1, 2, 4 and 8 weeks40 °C/75% RH, open dishhiew2022a R6
lumefantrine at 50% drug loading with HPMCAS, Eudragit L 100, HPMCP, CAPfirst drug crystals after 1, 8, 32 and 40 weekssamehiew2022a R6
resveratrol with PVP K29/32, E100, HPMC, HPMCAS, CMCAB, PAAPVP never crystallized (> 400 days); E100 > 400 days at 84% RH; the others crystalline at day 1 at 84% RH25 °Cwegiel2013b R12
curcumin with E100, cellulosics, PVP; neat> 350, 75, 22 and 14 days at 84% RH25 °Cwegiel2014 R13
curcumin dispersionsall > 350 days at 0% RH/25 °C; all crystalline within 1 day at 90 °C/0% RH and 60 °C/98% RHstoragewegiel2014 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 dish[duong2022a 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 °C[duong2022a 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 Physical stability

pKa

The pH at which half of an ionizable drug is protonated; two pH units above the pKa a weak base is almost fully un-ionized and two units below almost fully ionized, which set the pH range of the weak-base solubility studies [indulkar2015 C16]. New aspects (Miscibility and drug-polymer interactions): The acid dissociation constant is also used to classify the drugs of a polymer screen as acidic, weakly acidic or basic, and as a proxy of donor strength: a lower pKa means a stronger acid and a better hydrogen-bond donor vaneerdenbrugh2010b M3, M4, M5, M6, M7, M8; rumondor2011 C30. The values are computed, not measured. In the later papers the pKa decides whether a proton can move between drug and polymer: PSSA (−1.5) with the basic pKa of anthranilic acid (2.0), lidocaine (amine 7.8) and dibucaine (amine 9.8), and not PAA (4.5) or flufenamic acid (basic −2.1) vaneerdenbrugh2011a R1, R2, R9, C22, C23; lumefantrine (amine 8.73, cited) with enteric polymers of pKa 4.32–6.21 hiew2022a M1, R22. New aspect (Release mechanism and LoC): the pKa of the buffer species, relative to the surface and bulk pH, decides whether a buffer carries protons away from a dissolving enteric polymer. BIS-TRIS (pKa 6.5) and phosphate (7.2) bind protons at the lower surface pH and release them at the bulk pH, BIS-TRIS better because more of it is in the base form at a surface about 0.4 units below bulk; Tris (8.1) and TEA (10.2) are mostly protonated at both and cannot act as proton carriers, which slows HP-50 dissolution [qi2022 C27]. For HPMCAS-MF, pH 7.5 phosphate gave faster dissolution than pH 9.0 phosphate because the latter has a low buffer capacity [bapat2023 C15]. The polymer pKa values used were 4.2 for HP-50 and 4.92 or 5.0 for HPMCAS-MF, both cited [qi2022 C23; bapat2023 M3]. The 2025 grade paper titrated HPMCAS LF and HF, giving pKa 4.91 and 5.06 at the half-neutralization point against a cited 4.97 for MF [bapat2025a R8, C11, M3, M4, M5]; the 2024–2025 papers flag weak bases with pKa above about 5 as at risk of complexing HPMCAS at the gel pH [bapat2024 C45].

Findings

C. Amorphous solubility and LLPS: F10, F23. Miscibility and drug-polymer interactions: F15, F17, F21, F24, F26. Physical stability: F13, F24. Release mechanism and LoC: F23, F32, F33.

Related concepts

sets ionization and pH-dependent solubility; indicates donor strength in hydrogen bonding; related to drug-polymer interactions, hydrogen-bond basicity, acid-base interaction and hydrogen-bond donor and acceptor groups. Of buffer species, sets buffer capacity at a given pH and the microenvironmental pH; of the polymer, sets the critical ionization for polymer dissolution.

Formulas

Henderson-Hasselbalch equation.

How it is measured or obtained

UV-metric titration at 37 °C in 0.15 M NaCl (atazanavir), or taken from the literature or predicted by software (the other drugs) [indulkar2015 P2, M1, M3; almeidaesousa2015 M3]. In the polymer screens, calculated with the ChemAxon plugins of MarvinSketch 5.2.0 from the structures vaneerdenbrugh2010b P9. Functional-group densities of the polymers (mmol/g of COOH, amide, amine) were calculated from the structures in the same way vaneerdenbrugh2010b P10. For the enteric polymers the pKa was measured by potentiometric base-to-acid titration, as the pH at 50% neutralization, with the carboxylic acid content between the two end points (HPMCAS 1.19 mmol/g, pKa 4.97; HPMCP 1.69, 4.32; CAP 2.94, 4.57; Eudragit L 100 4.48, 6.21), giving 99, >99, >99 and 80% ionization at pH 6.8 hiew2022a P17, R22. In the 20-system moisture study, calculated with MarvinSketch unless marked otherwise in the table rumondor2011 P9. In the release-mechanism papers: buffer pKa values calculated or stated (table in the HP-50 paper) [qi2022 C27, X16]; polymer pKa cited [qi2022 C23; bapat2023 M3].

Values in the library
materialvalue or classconditionspaper ids
clotrimazole; atazanavir; nicardipine5.89 (cited); 4.52 (measured); 7.2 (cited)37 °C[indulkar2015 M1, M2, M3]
ritonavir1.8 and 2.6citedilevbare2013a M1
loratadine; efavirenz5.0; 10.2citedilevbare2013a M3, M2
telapreviracid 11.8; base 0.31cited[mosqueragiraldo2015 M1]
CRH14.6 (base)method not printed[almeidaesousa2016 M1]
ibuprofen; phenylbutazone; diclofenac4.35; 4.35; 4.03 (acids)cited[almeidaesousa2015 M1, M2, M4]
pazopanib6.4 (strongest basic group)stated without a source; used for the 37 °C curves[sugihara2018 M1, C9]
flurbiprofen; flufenamic acid; chlorpropamide4.37; 3.88; 4.33 (acidic)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 moisturerumondor2011 C33
PAA; PSSA; E100 amine4.5; −1.5; 8.5computedvaneerdenbrugh2011a R2
anthranilic acid; flufenamic acid (basic pKa)2.0; −2.1computedvaneerdenbrugh2011a R1, R9
HPMCAS, HPMCP, CAP, Eudragit L 1004.97, 4.32, 4.57, 6.21 (acid content 1.19, 1.69, 2.94, 4.48 mmol/g)titration, n = 2hiew2022a R22
lumefantrine (tertiary amine)8.73citedhiew2022a M1
indomethacin, ketoprofen, indoprofen in PVPpKa 4.5, 5.02, 5.8; resist, resist, separate slightly20-system tablerumondor2011 R15.a, R15.d, R15.e
20 drug–polymer systemsOPLS-DA loading of pKa ≈ −0.35: lower pKa goes with no separationdiscriminant modelrumondor2011 R17, C40
curcumin against E100pKa 10.51, 9.88, 8.38 against an average 8.4 for the basic monomeracid–base pairingwegiel2014 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 supplied[kaur2025 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 Physical stability

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% RHkonno2008 R5
felodipine dispersions ≤ 25% polymerTg ≈30–35 °C after 75% RH, below dry felodipine ≈43 °C25 °Ckonno2008 R7, C16
nifedipine pure; 25% PVP≈43 → 26 °C; ≈54 → 29 °C0 → 76% RHmarsac2008a R6
amorphous felodipine (cited)Tg ≈45.7 → 29.6 °C, smooth0 → 94% RHrumondor2010 R10
pimozide–PVP 50:50wet Tgs −21 and 44 °C94% RHrumondor2009c R17
ketoprofen–PVP 70:30wet Tg −23 °C94% RHrumondor2009c R25
celecoxib 6:4 dispersionsTg 64–103 → 22–42.1 °C after 3 days at 94% RHDSCxie2016b R17, R20
tacrolimus; tacrolimus–HPMC 1:163.6 → 51.4 °C; 77.2 → 49.0 °C after 3 days at 75% RHDSCtrasi2017 R15
lumefantrine dispersions precipitated into water4–6% water (HPMCP, HPMCAS), 9% (CAP); Tg 45–112 °CTGA; DSCbhujbal2021 R10
felodipine (cited)Tg about 45 °C dry, just below 35 °C after 75% RHstorage 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/min[ilevbare2013d 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 °Cyang2021 M1, M2, M3, M4
atazanavirdry 105 °C, wet 55 °Ccitedcorreasoto2022b M1
Pitfalls and disagreements

The griseofulvin Tg falls only 2.8 °C with an estimated 2.7% water, against 39 °C for sorafenib with 1.8%, and storage time and water content are not stated [almeidaesousa2015 X11]. The water content of the telaprevir pellet was not measured [mosqueragiraldo2015 X3]. For the coated powders the wet Tg values are not printed, only Tg − T bars, and the definition in words is the reverse of the sign used moseson2022a R12, X24, E2. Uncoated powders failed in about 1–2 weeks across the whole range of Tg − T, so Tg − T orders the coated failures only in part moseson2022a X15. The 0 to +15 °C statement applies to coated powders only moseson2022a C45, R11. The rule of 10 °C per 1% water given in the Definition fits the pure drugs but not the 25% polymer dispersions of the felodipine study, which drop about 5 °C per 1% (synthesis: 23.7 °C with 4.68% water konno2008 R6). Plasticization did not by itself cause phase separation or rank nucleation rumondor2009c C38; konno2008 C26. Plasticization by water did not rank celecoxib dispersions at 94% RH: four Tgs within about 5 °C, very different stability xie2016b C46. The water content of the ritonavir phase was not measured [ilevbare2013d C8]. Plasticization does not rank crystallization: indomethacin, with a similar Tg drop, crystallized much more slowly than felodipine during dissolution alonzo2010 C42. The 17 °C nifedipine value is an estimate from a rule taken from indomethacin; no Tg of water-saturated nifedipine was measured [indulkar2017b X8]. The 70% indomethacin dispersion is a model of the surface layer [saboo2020 X16], and most wet Tgs are rule estimates yang2021 P9.

← Concepts and formulas

concept · as used in Physical stability

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 °Ckonno2008 R5
felodipine–PVP 0–100%ΔTg ≈15 °C (7% PVP) to ≈158 °C (pure PVP)dry minus 75% RHkonno2008 R9
25% polymer dispersionsTg drop ≈13.3 °C at ≈1.1% water (PVP) vs ≈6.2 °C (HPMCAS)25 °Ckonno2008 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 °Cmarsac2008a R7, C19
pimozide–PVP 50:50two Tgs −21 and 44 °C wet against one at 94 °C dry94% RHrumondor2009c R17
PTM–HPMCAS–TPGS (outside)Tg ≈79 → 63 °C with TPGS at 20% loadingDSCnguyen2023a R13, C22
atazanavir and ledipasvir ASDs with plasticizers (outside)lower Tg than the binary ASDDSCcorreasoto2023 C30
celecoxib with 10% TPGS or sucrose palmitateTg 55.34 → 44.81 and 44.46 °C; growth fasterDSCmosqueragiraldo2014 R5, C16
pretomanid–HPMCAS with TPGS (other chapter)Tg falls as TPGS risesDSCnguyen2023a R13, C22
ritonavir–PVPVA with Span 20 or Span 85Spans in the drug-rich phase, read as plasticizing it and speeding separation ("likely")O-PTIR, NMR, confocalyang2022b C58, X13
griseofulvin, DPB, celecoxib with 5% PHBTg −5 to −12 °C; growth up to ≈10-fold fasterDSC; melt growthsato2016 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% RH[duong2022a 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% RH[duong2022a 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% RH[duong2022a 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, sorption[duong2022a R9, R10]
praziquantel, racemate and R-enantiomerTg about 37 and 34 °C, used to place the extrusion temperatures at 150 and 120 °CDSC[alvarenga2025 M2, M1]
felodipine–PVPVA 30% with 0, 2, 5, 10% TPGSTg 89.2, 86.0, 80.8, 71.1 °C (felodipine 44.7, PVPVA 105.4 °C)DSC, drysaboo2021 R5
atazanavir–PVPVA 10% with SDS, CTAB, TPGS, Tween 80, Span 20, Span 80, Span 85, VPTg lowered by 16, 9, 14, 14, 11, 13, 7, 16 °C from the binaryDSC, drycorreasoto2022b R20
clopidogrel–PVPVA 40–60%PVPVA ≈4.1–6.7 against ≈2.6–2.7 mg/min/cm² for neat PVPVAcompacts, 37 °Ccorreasoto2022a R18, C48
loratadine–HPMCAS 5%HPMCAS released faster than from neat HPMCAS, "feasible" plasticization by a low-Tg drugcompactsyang2021 C31, R18
ritonavir–PVPVA 30:70 with 5 parts Tween 80, TPGS, Span 20, Span 85, SDSTg midpoint 70.90, 72.84, 73.24, 77.51, 84.93 °C against 82.24 °CDSC, dry[indulkar2022 R18]
8:1 atazanavir and ledipasvir glasses with nine plasticizersTg lowered by 30.4–43.3 and 47.6–53.1 °Cmodulated DSCcorreasoto2023 R17, R18
ledipasvir–PVPVA 10% with 5 and 10 g TEACTg 99.1 → 85.8 °C; release 20 → 94% by 90 minDSC; compacts, pH 6.8correasoto2023 R9
amorphous ritonavir with Span 20 (80–20, 60–40)onset Tg 14.8, 7.7 °C (46.8 °C neat)DSCyang2023 R22
amorphous ritonavir with Span 85 (80–20, 60–40)27.8, 12.7 °CDSCyang2023 R22

Evidence table: plasticization.

Pitfalls and disagreements

Two framings coexist: water is the more efficient plasticizer of PVP dispersions at equal water content (compared with cellulose dispersions) and the more efficient plasticizer of the drug alone per gram of water (compared with PVP dispersions); both hold, for different comparisons konno2008 C14; marsac2008a C19. A rule of thumb in the library puts the Tg drop at about 10 °C per 1% water yang2021 E3, which fits pure drugs but overestimates the drop of the 25% polymer dispersions, about 5 °C per 1% (synthesis: 23.7 °C with 4.68% water for 25% PVP konno2008 R6). Plasticization alone does not cause moisture-induced phase separation rumondor2009c C38. Lower plasticization by water is offered as an alternative to the thermodynamic reading for HPMCAS dispersions rumondor2010c C32, X12. The Span plasticization rests on Tgs given only in the supplement yang2022b X13. Liquefaction was reported for four salts while the text and the table disagree on which, and the photograph of one looks unliquefied [duong2022a X1, X11]. The water content and Tg of the wetted matrix in acid, on which the mobility argument rests, were not measured [nguyen2023c C43]. For the extrusion window no Tg of a drug–polymer blend was measured [alvarenga2025 C46]. The dispersion Tg of the clopidogrel study is in the SI and not in the main text correasoto2022a R26, and the loratadine–HPMCAS dispersion Tg was not measured yang2021 C31. Among the atazanavir additives the Tg depression and the release enhancement did not rank together (TPGS lowered the Tg by 14 °C and raised release only 4-fold, Span 80 by 13 °C and 35-fold) correasoto2022b R20. The Tg of the drug-rich layer formed in situ was not measured; plasticization is inferred from drug–Span mixtures yang2023 X17.

← Concepts and formulas

concept · as used in Physical stability

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, estimated[hiew2022b R21]
lumefantrine salt–PVPVA dispersions35–55% water at 95% RH, more at lower loading40 °C[hiew2022b R5]
lumefantrine–PVPVA 5–35%; 40–50% (Miscibility chapter)PVPVA ≈4.49–4.91 against 4.58 neat; 0.21–0.004 mg/min/cm²pH 6.8, 37 °Chiew2022a R13, C59
ritonavir–PVPVA tablets (ASD process chapter)discrete drug-rich nanodroplets in the gel layer move into solution as the polymer disentanglesuncoated tablets, 37 °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 Physical stability

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 6.8[mosqueragiraldo2018b M2, M3, M4, M5]
ezetimibe in Ensure Plusopposite polymer ranking in the aqueous and oily phases "raises questions" about hydrophilicity[elkhabaz2017 C52]
ritonavir, cellulose esterssolubility parameter 20.56–23.28 inhibited growth; more hydrophobic ones did not[ilevbare2012c C25, C30]
PVP / HPMCAS filmscontact angle 11.8° / 45°spin-coated[saboo2020a R4]
CPHPC-106 / cellulose acetate suberatedissolves (cited 43.5 mg/mL) / does not (3.0 mg/mL); the better solution inhibitor was the insoluble oneenzalutamide[wilson2020 M2, M3, C35]
14 new cellulose estersSP 19.62–23.28 MPa^1/2; effective (ratio 1.64–2.98) at 20.56–23.28, ineffective (0.83–1.01) at 19.62–20.41ritonavir growth, 5 µg/mL[ilevbare2012c R10]
OPLS-DA of 19 cellulose-based polymersSP loading about 0.70, R²Ycum 0.713, Q²Y 0.512ritonavir growth[ilevbare2012c R12, R14]
effective polymers, ritonavir; efavirenz; celecoxibmean SP 20.87; 21.73; 24.28 against drug SP 20.03; 21.89; 23.38induction time at 5 µg/mL[ilevbare2013c R13]
16 polymers on three drugswindow 20.56–23.28 for drugs of SP 20.03–23.38seeded growth[ilevbare2013b R9, M1–M3]
pH-shift precipitation, nine polymersPAA (very hydrophilic) and CMCAB failed for warfarin; CAP-adipate (most hydrophobic) failed for both acids1 mg/mL[hsieh2014 R4, C39]
celecoxib, HPMCAS; PAAHPMCAS and HPMC effective, very hydrophilic PAA not22 µg/mL drug[xie2016a C18]
PVPVA, HPMC, HPMCAS; PAA, P2VPbeyond 24 h for four drugs; as buffernominal 10 mg/mL, 4.5 mg/mL polymer[raina2015b R9]
six carboxylated cellulose derivatives (neutral structures)Fedors SP 25.5 (A5a), 24.3 (A5b), 19.9–22.2 MPa^1/2 (ethers); ECA (19.9) the most broadly effective5 µg/mL, nine drugs[mosqueragiraldo2018a R6, R2]
HPMCAS L, M, Hmore acetyl, less succinoyl: longer posaconazole induction times, more polymer in dropletspH 5.5–7.5[shah2025 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 Physical stability

polymer ionization

The degree to which the acid or base groups of a polymer are ionized at the test pH. The ω-carboxyalkanoate substituents (adipate, suberate, sebacate) of the new cellulose esters have a pKa of about 4.43, so they are nearly fully ionized at pH 6.8 and less than 25% ionized at pH 3.8; the ritonavir and celecoxib in the growth tests are un-ionized at both pH [ilevbare2012c R15; ilevbare2013b R18, C33]. HPMCAS-LF (pKa 5.5) is taken as nearly fully ionized at pH 6.8 and un-ionized at pH 3; two carboxylated cellulose esters lost their whole effect on telaprevir at pH 3.0; PAA failing for acetaminophen is attributed to its ionization at pH 6.8 [schram2015 C4; mosqueragiraldo2016 R7; trasi2015 C27]. Above the polymer pKa the degree of ionization still matters: for HPMCAS (pKa about 4.9) a rise from pH 5.5 to 7.5 weakened every grade against posaconazole nucleation, and the grade with the least succinoyl was the best inhibitor [shah2025 R3, C14, M2]. New aspect (Supersaturation from ASD dissolution): in the dissolution of dispersions, ionization decides whether the polymer dissolves and so how fast the drug is released: EPO is highly soluble at pH 2.2 "due to ionization", which gave rapid and complete dissolution of the indomethacin–EPO dispersion above the amorphous solubility, followed by crystallization xie2017 C29. In leaching from suspended lopinavir dispersions, a small extent of HPMCAS ionization from pH 3 to pH 5 "significantly enhanced" leaching in media with an ionic surfactant (with SDS drug from about 13 to about 36 µg/mL and polymer from about 21 to about 120 µg/mL), lopinavir itself not ionizing over this range [li2016b C24]. HPMCAS LF, with a lower pKa than HF, is taken as more ionized at pH 5 [li2016b C27]. The authors "can only speculate" that ionized chains become less coiled and expose less polar, uncharged groups to SDS [li2016b C49].

Findings

Crystallization from solution: F11, F13, F16, F23, F25, F27, F36, F44. Supersaturation from ASD dissolution: F10, F15, F20.

Related concepts

related to ionization, degree of substitution, polymer conformation and polymer self-association; related to polymer-surfactant complexation, pH-dependent polymer solubility and drug leaching.

Formulas

none.

How it is measured or obtained

Not measured: the degree of ionization is taken from the pKa of the substituent (literature) and the pH of the medium [ilevbare2012c R15; ilevbare2013c R18]. The effect is read from growth ratios or induction times at two pH, with non-ionizable HPMC as the control [ilevbare2012b R7; ilevbare2013c R14]. In the dispersion-dissolution papers it is likewise not measured but inferred from the medium pH and cited pKa values [li2016b C27, C24].

Values in the library
materialvalue or classconditionspaper ids
adipate, suberate, sebacate substituentspKa about 4.43; about 100% ionized at pH 6.8; less than 25% at pH 3.8literature[ilevbare2012c R15; ilevbare2013c R18]
CAP Adp 0.85; HPMC on ritonavirgrowth ratio 2.98 → 1.12; 2.19 → 2.31 from pH 6.8 to 3.8S 7.6[ilevbare2012b R7]
CA 320S Sub 0.63 on celecoxib6.1 → 1.5 (75% lower)S 6.6[ilevbare2013b R13]
CAP Adp 0.85 on efavirenzinduction time 24.9 → 12.6 min19 µg/mL[ilevbare2013c R14]
HPMCAS, Eudragit E100 in the pH-shift studyHPMCAS unionized at the acidic final pH 1.9–3.3; E100 cationic1 mg/mL[hsieh2014 C36, R4]
PAA in celecoxib dispersions (ASD dissolution chapter)pKa 4.28, completely ionized at pH 6.8pH 6.8[xie2016a 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 °C[shah2025 R3, R15, M2]
carboxylated ethyl cellulose ECD (two acids)modelled fully ionized; partial protonation "possible"MD, 310 K[mosqueragiraldo2018a C32, X9]
HPMCAS-HF lopinavir dispersions with SDS, pH 3 → pH 5drug about 13 → about 36 µg/mL; polymer about 21 → about 120 µg/mL25 °C[li2016b C24]
EPO in indomethacin dispersionshighly soluble at pH 2.2 owing to ionization37 °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 Physical stability

polymer partitioning into the drug-rich phase

The distribution of a dissolved polymer between the aqueous phase and the drug-rich phase that forms above the amorphous solubility, expressed as the polymer:drug weight ratio in the drug-rich phase or as the partition coefficient K = C_p/C_q (polymer in the drug-rich phase over polymer in water) [ueda2021 P4; ueda2022 E3]. For ibuprofen it is seen as the polymer that disappears from the solution NMR spectrum when droplets form, because polymer in the viscous droplets reorients too slowly to give a signal [ueda2020b C22; ueda2021 C7]. Polymer in the drug-rich phase lowers the chemical potential of the drug there and so the amorphous solubility (F19–F21) [ueda2021 C11]. New aspect (Bioperformance): a large share of polymer in the drug-rich phase lowers the chemical potential of the drug there and may lower the flux plateau [mosqueragiraldo2018b C34, C35, C37]. HPMCAS grade AS-HF distributed much more into the drug-rich phase than AS-LF for four drugs, which the authors say accounts for its lower amorphous solubility [ueda2020a C20, C33]; HPMCAS and PVP are not expected to enter the atazanavir–darunavir phase [alkalla2026 C38]. New aspect (Crystallization from solution): the share of a dissolved polymer found in the drug-rich precipitate against the solution, with PVPVA and HPMCAS in both (about 7% of the felodipine precipitate), PAA almost only in the water and P2VP in the precipitate [raina2015b R12, C20]; from 2021 the polymer share in the droplets was set against crystallization inhibition, and it did not rank HPMCAS against Eudragit E PO for enzalutamide but did rank three HPMCAS grades for posaconazole [wilson2021 C38; shah2025 C51].

Findings

Amorphous solubility and LLPS: F15, F19, F20, F21, F22. Bioperformance: F7, F19. Crystallization from solution: F19, F26, F37, F44.

Related concepts

lowers the amorphous solubility through the chemical potential of the drug in the drug-rich phase; driven by the hydrophobic effect and drug–polymer interaction (Flory-Huggins interaction parameter); measured with the help of NMR chemical exchange broadening; affects colloidal stability. Depends on polymer hydrophobicity. Related to amorphous precipitation.

Formulas

van't Hoff equation, Flory-Huggins reduction of amorphous solubility, ideal-mixing reduction of amorphous solubility. Drug-rich phase composition, polymer partitioning into the drug-rich phase by depletion.

How it is measured or obtained

Quantitative ¹H NMR of the dissolved polymer (peak at 2.0 ppm for PVP and PVP-VA, 3.1 ppm for HPMC) against TSP and a calibration line, compared with the polymer concentration before drug is added; the missing part is taken as being in the drug-rich phase and divided by the phase-separated drug [ueda2021 P3, P4]. Variable-temperature NMR gives K and, from a van't Hoff analysis, ΔG, ΔH and ΔS of transfer [ueda2022 P12]. Other methods in the library assay the polymer in the ultracentrifuged pellet or supernatant [mosqueragiraldo2018b R14; shah2025 R16]. Colorimetric assay of polymer in the centrifuged pellet and Nile red fluorescence for drug [mosqueragiraldo2018b P12–P14]. Solution NMR of the polymer with and without droplets (acetyl or hydroxypropyl peak), the lost signal being read as polymer in the droplets [ueda2020a R7, R8]. Ultracentrifugation of the suspension and ¹H NMR of precipitate and supernatant in d6-DMSO, masses scaled to 10 mL [raina2015b P8].

Values in the library
materialvalue or classconditionspaper ids
ibuprofen with six polymerspolymer:drug ratio 0.40 (PVP K12), 0.52 (K25, K90), 0.87 (PVP-VA), 0.95 (HPMC 603), 1.14 (HPMC 615); dissolved drug 131–89 µg/mL1000 µg/mL polymer, 400 µg/mL drug, pH 2.0 (D2O), 37 °C[ueda2021 R5]
ibuprofen with PVP K25, PVP-VA, HPMC 603ratio stops rising above 200 (K25) and 500 µg/mL polymer (PVP-VA); HPMC 603 keeps rising (about 0.08 → 0.95)25–1000 µg/mL polymer[ueda2021 R8]
ibuprofen with HPMC, PVP-VA, EUD-Epolymer still in solution at S_a + 300 µg/mL: about 141, 85, 289 of 300 µg/mL37 °C[ueda2020b 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 °C[mosqueragiraldo2018b 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 °C[shah2025 R16, R17, C30, E3]
enzalutamide dropletsEudragit E PO associates with the droplets more than HPMCASpH 6.5, 37 °C[wilson2021 R7, C19]
telaprevir, CA Sub / HPMCAS / 70% HPMCAS / PVPVApolymer fraction 0.90 / 0.21 / 0.27 / 0.22150 µg/mL[mosqueragiraldo2018b R14]
felodipinePVPVA and HPMCAS distributed; PAA in the supernatant; P2VP with the drugprecipitates[raina2015b C20, R12]
ibuprofen, polymerspolymer ratio falls with total drug37 °C[ueda2021 R10]
atazanavir, nifedipine, clozapine, ketoconazole droplets with 1000 µg/mL AS-LF / AS-HFNMR-detected polymer about 975 / 880, 955 / 480, 920 / 415, 990 / 600 µg/mL37 °C[ueda2020a R8, C20]
felodipine 100 mg, PVPVA 45 mgprecipitate 6.8 mg, supernatant 36.7 mg10% DMSO, pH 6.8[raina2015b R12]
felodipine, HPMCAS7.1 mg and 34.2 mgsame[raina2015b R12]
felodipine, PAA; P2VP (18 mg)0.9 and 46.6 mg; 17.7 mg and not detectedsame[raina2015b R12]
enzalutamide droplets, HPMCAS, Eudragit E PO12.7–24.7 and 40.8–41.0 w/w% (NMR); about 19–23 w/w% both (colorimetry)120 and 70 µg/mL drug, pH 6.5[wilson2021 R7, R9, X4, X5]
Pitfalls and disagreements

The "polymer in the drug-rich phase" is the NMR-invisible polymer and would include polymer adsorbed at droplet surfaces; the droplet composition and the activity of the drug in it were not measured [ueda2021 X4; ueda2020b X4]. The molecular-weight rule fails between PVP K25 and K90, polymer hydrophobicity was not measured, and the ranking of HPMC 603 against PVP-VA reverses with polymer concentration [ueda2021 X7, X8]. Two papers state that polymers used in ASDs have minimal impact on the amorphous solubility or do not take part in the drug-rich phase, which the ibuprofen data contradict for PVP K25 (154 → 121 µg/mL) [trasi2016 C32; alkalla2026 C38; ueda2021 R5]. The transfer enthalpy is per polymer species of different molar masses and has no stated uncertainty [ueda2022 X9, X8]. In the telaprevir study HPMCAS and PVPVA fractions are equal although their solubilities differ twofold [mosqueragiraldo2018b X7]. For atazanavir only about 12% of AS-HF disappeared from the solution signal although the ceiling fell by more than half, and the signal does not separate polymer mixed into the droplet from polymer adsorbed at its surface (F19) [ueda2020a X4, X10]. The felodipine precipitate study used four polymers, one drug and single determinations, and its totals deviate from the stated amounts by up to about 8% [raina2015b X9, X12].

← Concepts and formulas

concept · as used in Physical stability

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 °Ckonno2006 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 °Ckestur2010b R21, C42
felodipine with four polymers (outside)stronger drug–polymer bonds make demixing at the front harder; weaker at high temperaturemelt growthkestur2010a 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 Physical stability

polymer self-association

The association of polymer chains with one another in solution, which frees them less to interact with the drug or to adsorb on the crystal. Ilevbare and co-workers propose it for two cases: a very hydrophobic polymer that "is likely" to interact more favourably with other polymer molecules than with the drug, and un-ionized carboxylic acid polymers at pH 3.8, whose loss of effect "may be attributed to increased self-association" [ilevbare2013b C50; ilevbare2013c C4, C43]. The long-spacer charged cellulose oligomers (A5b, A6) fold onto their backbone in simulation and are said to self-aggregate; A7 was not simulated [mosqueragiraldo2016 R18, C62, X9].

Findings

F11, F13, F25, F36.

Related concepts

related to polymer ionization, polymer hydrophobicity and polymer conformation.

Formulas

none.

How it is measured or obtained

Not measured in either paper; it is inferred from the effect of pH and of polymer hydrophobicity on growth ratios and induction times [ilevbare2013c C5, C43; ilevbare2013b X14].

Values in the library
materialvalue or classconditionspaper ids
efavirenz with CAP Adp 0.85; CAB Adp 0.81induction time 24.9 → 12.6 min; 27.9 → 13.6 min from pH 6.8 to 3.819 µg/mL drug, 5 µg/mL polymer[ilevbare2013c R14]
the most hydrophobic esters (CAB Adp 0.25, CAP Seb, CAB Seb)growth ratios about 0.85–1.3 on celecoxib, efavirenz and ritonavir5 µg/mL[ilevbare2013b R9]
A5b; A6 oligomersRg 0.92 and 1.02 nm; SASA 0.0705 and 0.077 nm² per atomMD 40 ns[mosqueragiraldo2016 R19]
A5b ((CH2)8 tether)most compact chain, shrinking next to the drug; RDF peak only at 6–7 nm; large uneven globules on amorphous atazanavirMD and AFM[mosqueragiraldo2018a R7, R9, R4, C27]
Pitfalls and disagreements

The pH arm changes the buffer species and the polymer-free induction time (5.1 against 6.6 min) as well as the ionization [ilevbare2013c X9]. For growth, the same pH loss is explained by a condensed adsorbed conformation, not by self-association in solution (F11) [ilevbare2012b C46].

← Concepts and formulas

concept · as used in Physical stability

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 7.6[ilevbare2012a R17]
TPGS with and without 900 µg/mL PVPVACMC about 50 µg/mL; about 40 µg/mL with PVPVA, "little-to-no" interactionpH 6.8, 37 °Csaboo2021 R1, C7
surfactants with a crystallization-inhibiting polymerthe polymer can be rendered fully or partly ineffective, particularly when surfactant and polymer interact extensivelyritonavir–PVPVA ASD (argued)[indulkar2022 C42]
felodipine, HPMCAS + SDSgrowth ratio 1.07 against 2.7 (HPMCAS)S 4, 25 °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 6.8[indulkar2022 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 Physical stability

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 humiditytrasi2014b R15, C25
indomethacin δ, α, γdifferent maximum growth rates and nucleation temperaturespure melttian2017 R7, R1
8 of 23 class I moleculesa different polymorph after liquid-N2 quenchRamanbaird2010 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 Physical stability

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 Physical stability

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 classesbaird2010 C55
acetaminophensuggested; nuclei from cooling not separated from those formed on reheatingDSC and hot stagetrasi2012a 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 Physical stability

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 ± 0.02DSCbaird2010 R14
class III (17 molecules)0.73 ± 0.04, not significantly different from class IDSCbaird2010 R14
classes II and III0.65–0.76 and 0.65–0.81DSCbaird2010 F5
ritonavir0.81DSCbaird2010 R18.ab
class II compounds0.65–0.76, not the constant 2/3DSCbaird2012 R14
pretomanid; delamanid0.67; 0.64, both class IDSCnguyen2023a C59
35 compoundsT_{rg} = 0.00021\,\mathrm{MW} + 0.64433,\quad R^2 = 0.44regressionbaird2010 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 Physical stability

remixing of separated amorphous phases

The return of a phase-separated amorphous dispersion to one phase once the cause of separation (here sorbed water) is removed and molecular mobility is high enough; below Tg the separated phases stay apart because both are glassy marsac2010 C45, C46, C47.

Findings

F12, F14, F30.

Related concepts

reverse of amorphous-amorphous phase separation; blocked by kinetic trapping; depends on molecular mobility.

Formulas

the peak-height ratio of hydrogen-bonded NH bands is listed on the chapter page as table only.

How it is measured or obtained

Isothermal IR at 125 °C of a film separated at 94% RH, following the ratio of the drug–polymer (3290 cm⁻¹) to drug–drug (3345 cm⁻¹) NH bands against a never-exposed film; DSC heat–cool cycles to rising temperatures marsac2010 P13, E2, P12.

Values in the library
materialvalue or classconditionspaper ids
felodipine–PVP 50% film after 94% RHband ratio ≈0.70 (5 min) → ≈1.41 (1500 min) vs ≈1.47 never exposed125 °Cmarsac2010 R17
felodipine–PVP 46.5 wt% powderthermal event moves up with each DSC cycle; single Tg ≈80 °C on second scansDSC to 60–110 °Cmarsac2010 R15, R14
felodipine–PVP film at room temperatureno remixing after 1 week of drying0% RHmarsac2010 R8
celecoxib–PVP 6:4 after 94% RHtwo Tg events on first heating, one on reheating; remixing during the scan a "possible explanation"DSCxie2016b R18, C34
indomethacin–HPMC, 50–90% drugsingle Tg above the miscibility limit, which remixing during heating "might" explainDSCtian2016 C31
miconazole–PVPVA 50:50 powderone Tg after 60 min at 100 °CDSCsaboo2017 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 Physical stability

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 °Cwanapun2010 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 min[shah2024 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 preparation[duong2022a 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 h[moseson2020a 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 methods[moseson2021 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 °C[moseson2021 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 °C[shah2024 R21]
PCZ–HPMCAS 10% DL, 0.3% crystals against noneabout 14.5 against 125 µg/mL at 300 min after the pH shifttwo-stage test[shah2024 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 4.5[moseson2020a 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 °C[duong2022a R14]
delamanid free base 25% with HPMCP-50, spray-dried against rotary-evaporatedamorphous and more than 80% released against 20%pH 6.5[nguyen2023c 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 Physical stability

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 distribution[ilevbare2013b 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 SHG[shah2024 R14, C28, C47]
ritonavir seeds after growthmonomodal size distribution; unseeded 10 µg/mL no loss in 8 hS 7.6[ilevbare2012a 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 Physical stability

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 drug[shah2024 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 Physical stability

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 melttaylor1997 R5.g, R5.h, R6, C20
α-indomethacinacid bands in both IR and Raman, read as chainspolymorph referencetaylor1997 R5.e, R5.f, C16, C17
amorphous felodipineNH 3341 cm⁻¹ bonded to a neighbouring carbonyl; carbonyls 1701 and 1682 cm⁻¹spin-coated filmkestur2010a R9.a, R10, R15
bifonazoleweak C–H···N chains along the b axis; no traditional donorcrystal structurekestur2011 R18
PAAdimers and other self-associations, easily disruptedcitedkestur2011 R22
felodipine–PAAPAA self-association "speculated" to limit mixing at 30–70% PAADSC, IR, PXRDrumondor2009a C45, R24
resveratrol, ledipasvir, itraconazole (other chapters)disrupting self-assembly by a polymer thought critical; drug–drug interactions seen by NMR; ITZ aggregates by fluorescencevarious[wegiel2013b C5; que2019 C23; mugheirbi2017 C31]
dextran–PVPdextran–dextran bonds assumed stronger or more numerous than dextran–PVP; OH band 3356–3358 → 3370–3383 cm⁻¹ with more PVPFTIR, DEX1–PVP12[vaneerdenbrugh2012a C36, C37, R16]
carboxylic acid drugs; benzamide, phenacetinacid dimers in crystals; amide–amide only 100 and 94% alone, 0% with COOHcrystal structures, CSDvaneerdenbrugh2011a R7, R14
naringenin, quercetinhydrogen-bonded sheets; two and three free OH after intramolecular bondsstructurewegiel2013a 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 filmstrasi2012b 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 PVPstoragewegiel2014 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; fluorescencetian2016 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 Physical stability

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/minrumondor2009a 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 regimensrumondor2009a R1
felodipine–PVP, nifedipine–PVPone Tg in earlier studiescitedrumondor2009a 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 °Cpurohit2015a R7, C25, C26
dextran–PVP, 20 pairsnone of the maltodextrin pairs phase separated; DEX450–PVP90 phase separated at all nine compositionsDSC 10 °C/min to 200–250 °C, second heating[vaneerdenbrugh2012a R13]
telaprevir 102.7, PVPVA 108, HPMCAS 122, HPMC 140 °CTg of the pure components; no blend run by DSCDSC midpoint, 20 °C/minli2016c 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 Physical stability

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 °Cwanapun2010 R2
chlorpropamide film125 s by SHG, 500 s optically30 °Cwanapun2010 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 ΔEwanapun2010 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% RHpurohit2015b R5, R21
felodipine–PVP dispersionsfast and extensive at 66–93% RH, extremely low at 0–52% RHroom temperaturerumondor2009b 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/minduong2022c C21
felodipine with 25% PVP1.2–2.8% (0–52% RH); 68.6–82.1% (75–93% RH) after ≈494 days22–25 °Crumondor2009b R9
felodipine with 50% HPMCASlag of 35–120 days at 52–93% RH, then 9.2–16.6%samerumondor2009b R17, R9
felodipine with 10% HPMCAStwo crystal forms, one Form II93% RH, 491 daysrumondor2009b 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 Physical stability

solubility parameter

The square root of the cohesive energy density, \delta = \sqrt{\sum_i \Delta e_i / \sum_i \Delta v_i} = \sqrt{\Delta E_v / V} in MPa^1/2, estimated by the Fedors group-contribution method from the structural formula alone; a lower value means a more hydrophobic compound, and water is 49.01 MPa^1/2 [ilevbare2012c E1; ilevbare2013c E5, P1]. In these papers it is the scale on which a polymer's hydrophobicity is compared with the drug's [ilevbare2013c C37, C3]. Fedors SP of the telaprevir polymers: effective acids 22.46–23.18 MPa^1/2, CAP-Seb-024 23.04 (fails), A5a 25.54 (works), A5b 24.29 (fails); no correlation across the chemically diverse set [mosqueragiraldo2016 M12–M14, M24, M25, C25].

Findings

F8, F13, F17, F25, F36.

Related concepts

measures polymer hydrophobicity; related to lipophilicity and degree of substitution.

Formulas

Fedors group-contribution solubility parameter.

How it is measured or obtained

Calculated, not measured: group contributions at 25 °C (Fedors 1974, outside the library) are summed over the repeat unit; for glassy polymers (Tg above 25 °C) an extra molar volume of 4n (n < 3) or 2n (n ≥ 3) is added, n being the number of main-chain atoms in the repeat unit [ilevbare2012c E2, E3, P11]. No uncertainty is stated.

Values in the library
materialvalue or classconditionspaper ids
ritonavir; efavirenz; celecoxib20.03; 21.89; 23.38 MPa^1/2 (Log P 5.6, 4.7, 3.5)Fedors[ilevbare2013c M1–M3; ilevbare2013b M1–M3]
14 new cellulose esters19.62 (CAB Seb) to 23.28 (CP Adp)Fedors with correction[ilevbare2012c R10, M23–M36]
CAB Adp 0.25; CAP Adp 0.33; CAB Adp 0.81; CAP Adp 0.8520.05; 20.56; 20.86; 21.27Fedors[ilevbare2013c R10]
CA 320S Seb; HPMCAS; CAPh; CA 320S Sub; HPMC; CA 320S Adp; CMCAB; CP Adp22.36; 22.44; 22.48; 22.62; 22.68; 22.95; 23.18; 23.28Fedors[ilevbare2013c R10]
Pn-IPAAmd; PAlAmn22.64; 20.70Fedors[ilevbare2013c R10]
PVPVA; PAA; HPC; PVP; PVPdn-O25.77; 25.92; 25.98; 28.39; 32.24Fedors[ilevbare2013c R10]
effective polymers, mean SP20.87 (ritonavir); 21.73 (efavirenz); 24.28 (celecoxib)induction time[ilevbare2013c R13]
CAP-Adp-085, CA-Sub-090, CAP-Seb-02422.46, 23.18, 23.04Fedors, no ionization[mosqueragiraldo2016 M12–M14]
A5a, A5b, ECA, ECB, ECC, ECD25.5, 24.3, 19.9, 22.2, 22.0, 21.4 MPa^1/2 (neutral structures)Fedors method[mosqueragiraldo2018a R6, P12]
Pitfalls and disagreements

The SP values of the commercial and synthetic polymers are not printed in the 2012 paper, so the 20.56–25.98 range and the "similar hydrophobicity" of synthetic polymers cannot be checked there [ilevbare2012c X11]. The mean SP of the effective polymers in Table 6 is over every polymer in each SP window including those coded ineffective [ilevbare2013c X3]. The 2013 growth paper prints the failing range as SP "greater than 20.56", the reverse of its own convention [ilevbare2013b X2]. SP did not predict PVPVA and PVP on ritonavir, PAA, or Pn-IPAAmd [ilevbare2013c X11]. The A5a/A5b difference of 1.25 exceeds the 0.72 spread of the effective acids [mosqueragiraldo2016 X8].

← Concepts and formulas

concept · as used in Physical stability

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 °C[raina2015c R1, C16]
felodipine, nifedipine + HPMCno solubilization100 µg/mL and 1 mg/mL[raina2015c R1, C15]
resveratrol + HPMCAScrystalline solubility 42 to 83 µg/mL4.7 mg/mL polymer[wegiel2015 R16]
danazol + polymersno solubilization[jackson2016 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 Physical stability

solution crystallization

Nucleation and growth of crystals from the supersaturated solution, as against crystallization inside the undissolved ASD (matrix crystallization) [elkhabaz2017 C38; mosqueragiraldo2018b C52]. Crystallization from solution decided the enzalutamide-PVPVA dispersions (fall after the maximum) and the pretomanid case, in which droplets present above the amorphous solubility defeated HPMCAS-HF within minutes [wilson2018 C18, C42; nguyen2023a C13]. New aspect (Supersaturation from ASD dissolution): crystals nucleate and grow in the supersaturated liquid after the amorphous solid has dissolved, the second route by which an amorphous solid loses its advantage alonzo2010 C47. Polymer in a dispersion can move crystallization from the matrix to this route (nifedipine) raina2014b C21. When dispersions release completely, the authors of a celecoxib study take matrix crystallization as suppressed and attribute the differences between polymers to crystallization from solution, which the induction time measures xie2015 C39, C40.

Findings

Bioperformance: F9, F10, F11, F12, F14, F23, F27. Supersaturation from ASD dissolution: F1, F3, F4, F6, F14, F21, F24.

Related concepts

part of desupersaturation; contrasts with matrix crystallization; related to crystal growth and crystallization tendency; part of crystallization during dissolution; measured by nucleation induction time.

Formulas

supersaturation ratio, classical nucleation theory.

How it is measured or obtained

Fall of concentration with SHG, PLM or PXRD for the crystals; induction time by UV extinction [elkhabaz2017 P5, P8, P9, P10; hate2017 P2]. In the ASD dissolution papers: by a fall of the solution concentration together with crystals seen in the liquid rather than in the solid: needles between amorphous particles under polarized light alonzo2010 R19, fine plate-shaped crystals in the solution around dissolving dispersion particles raina2014b R13, free-floating needles in suspensions [chen2015a R15], or a rise of a pyrene ratio as crystals expel the probe [jackson2015 C14].

Values in the library
materialvalue or classconditionspaper ids
ezetimibe, buffer 21 µg/mLinduction about 1 min; PVP 100 µg/mL about 71 min; HPMC-AS about 50 min37 °C[elkhabaz2017 R6]
ezetimibe, FeSSIF 123 µg/mLHPMC-AS 50 µg/mL more than 360 min; PVP about 10 min37 °C[elkhabaz2017 R7]
nevirapine 500 µg/mLabout 5 min; PVPVA about 60 min; HPMC-AS over 4 hpH 6.5[hate2017 R2]
telaprevir 90% PVPVA ASDbelow 90 µg/mL from about 43 min; about 20 µg/mL at 100 min[mosqueragiraldo2018b 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 °C[xie2016a 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 6.5[wilson2020 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 °C[jackson2015 R5]
celecoxib–HPMCAS suspension with SDS; polysorbate 80free needles at 0.5 h; 1 hpH 3, 25 °C[chen2015a 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 °C[nguyen2023c R23, R22]
Pitfalls and disagreements

In the telaprevir and nevirapine solutions crystallization is inferred from concentration, without solid-state analysis [mosqueragiraldo2018b X13; hate2017 C42]. Crystallization of the enzalutamide-PVPVA solutions is inferred from concentration, without a solid-state analysis [wilson2018 X12]. For felodipine with dissolved polymers this route was named dominant without monitoring the solid in the vessel alonzo2010 X7. In the felodipine solvent-shift tests of 2008 no precipitate was examined konno2008a X4. The danazol crystallization is inferred from UV and pyrene, without solid-state identification [jackson2015 C14]. Complete release was taken to exclude matrix crystallization although the HPMC-containing celecoxib dispersions neither released fully nor were checked xie2015 X3. Where the medium is subsaturated, as in the gastric stage of an enteric dispersion, the solution route is excluded and crystals must have formed in the wetted solid [elkhabaz2019a C34; nguyen2023c C39].

← Concepts and formulas

concept · as used in Physical stability

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 solutionmugheirbi2017 R19, R20
ITZ–HPMC spray driedhomogeneous from dry solvents; domains with 1–12% water in methanolBüchi B-290mugheirbi2017 P3, R26, R27
ITZ–HPMC in five alcohol–DCM solventsMeOH, EtOH, IPA separate at 50% RH; PrOH, BuOH mixed at 50% RH and separate at 20% and 7% RHspin coated[mugheirbi2018 R1, R2, R4]
pure DCM:MeOH with 4% waterevaporation about 12 → 40 minTGA[mugheirbi2018 R9]
ritonavir–PVPVA spray-dried from methanol, 10:90, 60:40 water:methanol25% DL surface RTV by XPS 21% / 43% / 70%; aged DSC second phase at 50% DL from 10:90; pyrene ratio lower for 60:40BLD-35 dryer, 4% solidsli2020 R4, R6, R7
same pair, droplet modelthreshold about 12.5:87.5 at 25% DL; peak C/S about 2.4 and about 320 at 12.5:87.5 and 15:8530 µm dropletli2020 R17, R20
Pitfalls and disagreements

The composition path of the drying film was not measured; the azeotrope analysis ignores DCM and the solutes [mugheirbi2018 C35, X8]. Dried solvent at 20% RH reduced but did not remove the ITZ–HPMC domains mugheirbi2017 X21. The model keeps the 10:90 path single-phase although the powders show separation; its threshold "may move higher or lower" li2020 X12, C51.

← Concepts and formulas

concept · as used in Physical stability

spectral mixing

A local AFM-IR spectrum that contains bands of the neighbouring phase or of material below or beside the probed spot, so that both components appear in both phases even if the phases are fully separated: "some prudency is in order" [vaneerdenbrugh2012b C22]. It can occur through the film thickness or laterally below the spatial resolution li2016c C14. New aspects (Miscibility and drug-polymer interactions): In AFM-IR the volume probed is larger than the domain, laterally or through the film thickness, which explains why bands of both drug and polymer appear in both the dispersed and the continuous phase of telaprevir films ("can be caused either" by partial miscibility or by spectral mixing), why the dispersed-phase spectra look richer in drug at higher loading ("a more likely explanation" than a trapped composition), and why the spectra of the two phases of a 50:50 telaprevir–HPMCAS film coincide li2016c C14, C21, C46, R11. The same caveat is stated for earlier AFM-IR work: "some spectral mixing … cannot be excluded, even for a completely phase-separated system" [vaneerdenbrugh2012b C22]. In dextran–PVP blends spectra near a phase boundary were intermediate, and spectral mixing is named among the reasons why the phases of DEX6–PVP90 could not be told apart chemically vaneerdenbrugh2012c C23, C38.

Findings

Solid-state methods: F12, F13, F14, F15. Miscibility and drug-polymer interactions: F19.

Related concepts

degrades spatial resolution; depends on photothermal expansion; related to drug-polymer miscibility; limits the reading of amorphous-amorphous phase separation; depends on phase-separated domain size; contrasts with kinetic trapping as an explanation of changing phase spectra.

Formulas

none.

How it is measured or obtained

Seen as intermediate spectra at phase boundaries, as identical spectra from different positions and as composition trends that depend on domain size vaneerdenbrugh2012c R15, R20; li2016c C21. Not separated experimentally from partial miscibility in any paper of the chapter [vaneerdenbrugh2012b C20, C22]. It is not measured. It is inferred from the size of the domains against the resolution of the method (typical AFM-IR resolution about 100 nm, best about 20 nm, integrating absorption through film thickness) and from spectra that vary with position or loading; ratio images and band ratios reduce the thickness effect li2016c R24, C12, C22, C50.

Values in the library
materialvalue or classconditionspaper ids
DEX450–PVP12boundary spectrum intermediate between domain and matrix spectrasingle positionsvaneerdenbrugh2012c R15, C23
DEX6–PVP90six spectra alike, pattern of pure PVP90domains 0.3–0.6 µmvaneerdenbrugh2012c R20, C38, R19
felodipine–PAA 50:50other component's bands in both phasesfour spectra per phase[vaneerdenbrugh2012b R9, R10, C20]
telaprevir dispersionsapparent drug enrichment of the dispersed phase with loading judged more likely spectral mixingAFM-IRli2016c C21
telaprevir–HPMC 60:40, HPMCAS 80:20, PVPVA 50:50bands of both components in both phaseslocal AFM-IR, 4–5 points per phaseli2016c R8, R9, R10, C14
telaprevir–HPMCAS 50:50spectra of the two phases identical; IR imaging faileddomains 122 × 13 nm, gaps 21–25 nmli2016c 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 → 5:5li2016c 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 Physical stability

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 °Ckestur2010a R2
bifonazolerough fibre-like edges at 18 °C, smoother at higher temperature, sharper edges at 90–100 °Cno polymer; polymers did not change the profilekestur2011 R2
nimesulideneedle-like at 18–40 °C, zig-zag edges at 40–60 °C, smooth aboveas abovekestur2011 R2
felodipine, spin-coated films with polymers (other chapter)irregular boundaries and polymer-rich dark points on the crystallites22 °C, 3% HPMCAS, PVP, HPMCkonno2006 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 filmskestur2013a R5, R6
acetaminophen with seven polymersspherulitic shape kept10% w/wtrasi2012a R4
celecoxib with TPGS and PVPa large faceted plate at 120 °C instead of a fibrous frontmelt filmsmosqueragiraldo2014 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 filmssato2016 R2
indomethacin δ and α (spherulites), γ (polycrystalline)morphology identifies the formmelt filmstian2017 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 Physical stability

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, EDXmugheirbi2017 R7, R8, C48
ITZ–HPMC from IPA–DCM above 30 °Cinhomogeneous fluorescence with spinodal-like microstructureFLOM[mugheirbi2018 R1, C9]
ritonavir–PVPVA filmsbinary and Span films may separate by spinodal decomposition, Tween 80 and SDS films by nucleation and growthcited from outsideyang2022b C55
phenolphthalein analogue–PVPVA–waterseparation assumed spinodal along the hydration pathargument onlydeac2023b C33
Pitfalls and disagreements

Binodal and spinodal exist for four concentrations between about 11 and 29 °C only; the authors read the small gap as a low energy barrier to LLPS ilevbare2013a X17, C31. In the film papers the time-resolved evolution of the structure was not followed ("may have occurred") mugheirbi2017 C48; network-like textures with PrOH and BuOH are read as solvent incompatibility with HPMC instead [mugheirbi2018 C45]. In the 2023 phenolphthalein-analogue paper the mode of separation was not observed; the conclusions are stated not to depend on it deac2023b C33.

← Concepts and formulas

concept · as used in Physical stability

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, ritonavirtrasi2016 E4; purohit2017b E1
IDM in copovidone at 130 °Cslow diffusion in the viscous matrix gives gradients of about 8 µm after 1 hEDX[moseson2019 R9, C41, C51]
clotrimazole droplets111–257 nmNTA[indulkar2016 R4]
ritonavir ASD films200 (PVPVA), 250 (HPMCAS), 315 nm (PVP)NTApurohit2017b R8, E1
tacrolimus second phase220 nmNTAtrasi2016 R11, E4
nifedipine dispersions, HPMC-E5 and PVPVA≈190–222 nmNTA, 5 °C, D2O[indulkar2017b 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 nmcalculated[saboo2020a 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 Physical stability

structural relaxation time

The mean time for molecular rearrangement in a glass or supercooled liquid; in this chapter it is calculated with the Adam–Gibbs–Vogel equation from Tg and fictive temperature and compared with crystal growth rumondor2010 E1, P8.

Findings

F5, F19.

Related concepts

measure of molecular mobility; related to structural relaxation and enthalpy relaxation.

Formulas

the AGV equation and the coupling exponent are listed on the chapter page as table only; Kohlrausch-Williams-Watts equation gives the enthalpy-relaxation time.

How it is measured or obtained

From the AGV equation with cited constants for felodipine (D 9.2, T0 253.4 K, fictive temperature 310 K) and the Tg at each storage RH, assuming that only Tg changes with water rumondor2010 M1, C25; outside the subcategory from viscosity and growth rate trasi2014a E4.

Values in the library
materialvalue or classconditionspaper ids
amorphous felodipinelog(τTg/τ) ≈−1.73 at T/Tg 0.91, ≈−0.92 at 0.95AGV, Tg 317 Krumondor2010 R7.j, E1
amorphous felodipine growthfollows (τTg/τ) to the power 0.5 between T/Tg 0.94 and 0.9713–75% RHrumondor2010 R7, C27
amorphous nifedipine (cited)coupling constant 0.75 between relaxation and crystallizationcitedrumondor2010 R11
nine compounds (outside)normalized growth against melting entropy, R² 0.61viscosity-based τtrasi2014a R11
felodipine at 45 °Ctaken as 100 s to count layers added per relaxation timeassumedkestur2013a R18, X1

Evidence table: structural relaxation time.

Pitfalls and disagreements

The fit with an exponent of 0.5 has no statistic and leaves out the high-RH points; the cited Tg sets differ by about 2 K rumondor2010 X9, X11.

← Concepts and formulas

concept · as used in Physical stability

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 Physical stability

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 TgDSCtrasi2014b R5
nilutamide88% form I after 30 min at −30 °Cabout 50 DSC holdstrasi2014b R16
indomethacin (cited)melting endotherm after storage 55 °C below Tgliteraturetrasi2014b R34
ibuprofen (cited)metastable form nucleates about 60 °C below Tgliteraturetrasi2014b 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 Physical stability

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·srheometrybaird2012 R1
felodipine with 3% polymersgrowth from the supercooled liquid substantially reducedhot stagekestur2010a C28
bifonazole, nimesulidegrowth strongly temperature dependentsupercooled liquidkestur2011 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 stagekestur2010a R5, C10
bifonazolegrowth falls by about 6.4 orders from 100 to 18 °C (plot)melt-quenched filmskestur2011 R7, X6
nimesulidegrowth falls by about 5.4 orders from 80 to 18 °C (plot)melt-quenched filmskestur2011 R9, X6
indomethacin–PVP glassnon-equilibrium supercooled liquid; single Tg citedsolvent-evaporatedtaylor1997 C6, R17
acetaminophenTg 21.2 °C, Tm 169 °CDSC, 10 °C/mintrasi2012a R9.a
flutamideTg −3.1 °C; Tm 108–110 °C with 10 mol% additivesDSCtrasi2012b R7
celecoxibTg 55.34 °C, Tm 163.46 °CDSCmosqueragiraldo2014 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 filmssato2016 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 °Cyang2021 C16, M1
Pitfalls and disagreements

Near Tg diffusion decouples from viscosity, so viscosity-based growth laws fail there trasi2014a C21. Polymer effects on growth from the supercooled liquid act on the liquid phase rather than at the crystal surface for felodipine kestur2013a C6. In the amorphous solubility papers a glass formed in water may behave as a supercooled liquid, which is inferred and not measured [almeidaesousa2015 C37, C38]. The text orders of magnitude (5.5 and 6 for bifonazole) are smaller than the plot readings (6.4 and 6.9) kestur2011 X6. Whether dilute dispersions made by cryomilling are molecularly mixed in the melt is assumed kestur2010a C5. In the acetaminophen and flutamide growth papers, interactions in the liquid were judged from spin-coated films at other compositions, not from the growth samples trasi2012b X9; trasi2012a X15. Two drugs only; the idea was not tested [que2019 C49].

← Concepts and formulas

concept · as used in Physical stability

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 4.6[almeidaesousa2016 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 Physical stability

supersaturation

A solution concentration above the crystalline solubility of the drug [almeidaesousa2016 C2; ilevbare2013a C21]. In this chapter the highest supersaturation a solution can hold without crystals is set by the amorphous solubility: above it the excess forms a drug-rich phase, and the concentration and activity of the continuous phase stay at that ceiling [mosqueragiraldo2015 C34, C35]. Taylor and Zhang 2016 (p. 10) add that the strict upper limit is the spinodal point: a one-phase solution can persist for a time between the binodal and the spinodal, and after phase separation the level is the binodal, which is the amorphous solubility (synthesis). Supersaturation can be generated by solvent shift, pH shift, or dissolution of a high-energy solid form (amorphous drug, dispersion, salt, co-crystal) [almeidaesousa2015 C4, C5; almeidaesousa2016 C2]. The papers of 2017–2022 add that in a micellar medium the supersaturation that matters is the activity ratio a/a^{*} and not the concentration ratio, the two differing about twofold for atazanavir in SDS at the amorphous solubility (65–70 against 33–38) [indulkar2017a R13, C21], and that after a pH shift of a weak-base salt the apparent concentration is held near the amorphous solubility if the dose exceeds it [sugihara2018 R8, R12]. New aspect (Bioperformance): a dissolved drug concentration above the crystalline solubility, with a solute activity above that of a solution saturated with the crystal; the supersaturation ratio is activity over crystal activity, and equals the concentration ratio c/c^* only if the activity coefficients are equal [raina2015c C7, E5, E6, C32]. The highest supersaturation a solution can hold as one phase is set by the amorphous solubility; above it LLPS or crystallization takes over raina2014a C27, C30. Its highest concentration-based value is the ratio of amorphous to crystalline solubility, and that ratio falls when a polymer, a second drug or micelles enter the drug-rich phase or the medium (F18, F19, F20) [ueda2020a E1, C17; alkalla2026 C1, C37; elkhabaz2019b C21, C25]. New aspect (Crystallization from solution): in the crystallization papers supersaturation is the ratio S = C/C_{eq} of the concentration to the crystalline solubility (concentration used in place of activity because the solutions are very dilute), with \sigma = \ln S for growth analyses; the amorphous solubility of ritonavir is S 15.3–15.4 and σ 2.7 [ilevbare2013b E4, C14; ilevbare2012b E1, E2, R3]. The reference solubility is that of the stable crystal, measured without methanol and, to be consistent, with the polymer present (F19) [hsieh2012 P4; ilevbare2013c P9, X16; hsieh2014 C18]. Other scales in these papers: C/Ceq in the medium of interest (1.5–15), S' = C/Cs with the solubility with additive, the activity ratio δ from membrane flux (2.4–28.8), S 1.5 for acetaminophen, and a nominal 10 mg/mL solvent shift [chen2015 E2; li2016a E1; lu2017 E1; trasi2015 P2; raina2015b P1].

Findings

Amorphous solubility and LLPS: F1, F5, F6, F8, F13, F14, F9, F10, F15, F16, F17, F19, F23. Bioperformance: F3, F10, F13, F14, F18, F19, F20, F28, F29. Crystallization from solution: F1, F2, F9, F14, F19, F21, F22, F27, F31, F34.

Related concepts

capped by amorphous solubility; measured against crystalline solubility; expressed as supersaturation ratio or via thermodynamic activity; relieved by crystallization. Papers of 2017–2022: activity-based supersaturation, maximum achievable supersaturation. Lost by desupersaturation; contrasts with solubilization; summarized by supersaturation factor.

Formulas

supersaturation ratio. Activity-based supersaturation ratio, supersaturation from membrane flux ratio, supersaturation factor, power-law crystal growth rate.

How it is measured or obtained

As concentration divided by the crystalline solubility in the same medium (the supersaturation ratio), or in terms of activity from the flux ratio; the concentration-based ratio at the ceiling is the amorphous-to-crystalline ratio (F6) [almeidaesousa2015 E15; mosqueragiraldo2015 R12]. In the Bioperformance papers: concentration ratio by UV or HPLC; activity-based ratio from membrane flux relative to the flux at the crystalline solubility [raina2015c E9, R13]; receiver-derived "effective" supersaturation from a Cmax calibration [hate2017 C49, R18]; generated by solvent shift, pH shift or ASD dissolution [raina2014a P7; hate2017 P7; hate2018 P9]. The activity-based maximum is the ratio of the flux from a solution at the amorphous solubility to the flux from a crystalline suspension in the same medium, J_{amph}/J_{eq} [elkhabaz2019b E2, R8, R9]. A dose is described by its ratio to the crystalline solubility: 5 mg of tacrolimus in 100 mL gives S = 20 and in 240 mL S = 8 hate2019 R7, R14, E2; pretomanid nucleation is compared at S = 5 nguyen2023a E1, R5. In the crystallization-from-solution papers: concentration by fibre-optic UV on second-derivative spectra or by HPLC; S from the crystalline solubility measured in the same buffer (48–72 h at 37 or 25 °C); the supersaturation factor integrates S over time [ilevbare2012a E2; ilevbare2013c E8].

Values in the library
materialvalue or classconditionspaper ids
ibuprofen to sorafenibmaximum ratio 4.3 to 54.025 °C, fluorescence onset[almeidaesousa2015 R5]
telaprevirmaximum ratio about 18 (stated); flux gain about 18pH 6.8, 37 °C[mosqueragiraldo2015 R14, R15]
clotrimazole; atazanavirabout 13; about 6337 °C[indulkar2015 R10]
CRH1about 10pH 6.8 and pH 4.6[almeidaesousa2016 R24]
atazanavir in 0–3.6 mg/mL SDSconcentration-based 64.8 → 33.0; activity-based 66.0 → 65.0 at the amorphous solubility37 °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/mL[raina2015c R13]
nevirapinenominal S 3.9; receiver-derived 2.8 (powder), 4.10 (powder + HPMC-AS)pH shift, 128 µg/mL crystalline[hate2017 R18]
ritonavir (mesoporous-silica study)S 7.8; 3.93.6 µg/mL crystalline[dening2018 E6]
atazanavir, six mediaactivity-based maximum about 50–56; concentration-based 56 in buffer to 14 in pooled human intestinal fluid37 °C, side-by-side cell[elkhabaz2019b R8]
posaconazole, six mediaactivity-based maximum about 29–37; concentration-based about 35–37 in buffer to 5 in human fluid37 °C[elkhabaz2019b R9]
tacrolimusS 20 (5 mg in 100 mL) and S 8 (240 mL); maximum ratio about 33solvent-shift solutions, hollow-fibre 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/mL[ilevbare2013b R7]
type 1 weak basespeak 1.4–26.7 times the titration solubility, lasting 3.1–14.7 minpH shift, 37 °C[hsieh2012 R5]
type 2 weak bases7.2–20.7 times the crystalline solubilitypH shift[hsieh2012 R10]
telaprevir with six bile saltsδ 11.5 and 28.8 need 60 and 150 µg/mL in buffer, 140 and 300–330 with 12 mM STDC/SGDCpH 6.5, 37 °C[lu2017 R1]
atazanavir, ritonavir in buffer, FaSSIF-V1, Composite-SIFflux-based supersaturation at the amorphous solubility 63–65 and 9.2–10pH 6.5, 37 °C[indulkar2018 R12]
posaconazoleamorphous/crystalline about 34 from pH 2 to 7phosphate buffers, 37 °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 Physical stability

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 ≈1.04–1.11trasi2014a R4.g
loratadine≈0.00005 µm/s at the surface, slowest of 14near Tgtrasi2014a R4.n
nilutamidemuch higher nucleation at the surface than in the bulkmelt-cooled filmstrasi2014b R1
ezetimibe spray-dried dispersionscrystals after 19 days (50% DL) and 12 days (70% DL) uncoated40 °C/75% RHduong2022c 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% DL[indulkar2022 R15; yang2023 R16]
delamanid dispersion filmsrapid surface crystallization at pH 3.01 h[nguyen2023b R3, C37]
ezetimibe–HPMCAS 50% DL, uncoatedneedle-like crystals at 19 days; about 26% crystalline at 270 days40 °C/75% RHduong2022c R16, R19
ezetimibe–HPMCAS 70% DL, uncoatedplate-like crystals at 12 days; about 50% crystalline at 270 dayssameduong2022c R16, R19
ezetimibe–HPMCAS coated (50% thin and thick, 70% thick; about 12–40 nm)no crystals by SEM, PXRD or DSC for 24 monthssameduong2022c R16, R17, R18, R20
ezetimibe–HPMCAS 70% thin coating (11.7–15.0 nm)first crystals at 7 months; about 1.5% at 270 dayssameduong2022c 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 °C[moseson2022b 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 °C[chen2015a R20, C37]
same, no surfactantcrystallization only after more than 7 days, apparently from matrix or surfacepH 3[chen2015a C33]
delamanid salt dispersions, five enteric gradescrystals on films and powders after 1 h in acid, more with HPMCAS and at higher pH; HPMCAS-HF also at pH 1.625% drug, 37 °C[nguyen2023c R19, R18]
delamanid dispersions after the pH shiftundissolved particles covered with small crystals within 30 minpH 6.5[nguyen2023c R21]
indomethacin methyl ester–PVPVA 25%smooth at 5 min; scattered needle-like crystals at 10 min; surface extensively covered at 20 minSEM, pH 6.8[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 6.8[indulkar2022 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 Physical stability

surface drug enrichment

A drug-rich layer at the surface of a dispersion or at the dissolving interface. In the lopinavir films, with 50–100% water in the casting solvent the continuous phase softened at 142 ± 11, 116 ± 16 and 124 ± 7 °C (37–92% LPV), which the authors read as drug enrichment at the surface ("suggesting"), lowering release li2019 R15, R16, C30. In spray-dried ritonavir–PVPVA powders XPS gave the outer 0–10 nm composition and the surface drug content rose with the water in the spray solvent; in granules of two drugs a lopinavir-rich surface is proposed to form in acid as ritonavir dissolves first [li2020 R7, R24; trasi2019 C29, C47]. Fluorine EDX (F/F0; fluorine occurs only in the drug) quantified it on bicalutamide–PVPVA compacts: the surface of a 30% compact reached F/F0 = 1.23 ± 0.07 after 30 min in buffer [moseson2022b R14, E1]. New aspect (Release mechanism and LoC): two kinds appear. During dissolution the surface of compacts above the limit of congruency turns drug-rich within minutes, read by IR, XPS and EDX, while congruent compacts keep their composition [indulkar2019a R16, R15; que2019 R15; saboo2019 R18; saboo2020a R22]. Before dissolution the surface of spray-dried particles can already differ from the bulk, set by the spray solvent [bhardwaj2018 R20, C57]. For indomethacin–PVPVA the dissolving surface was followed in time by three methods of different probe depth, whose agreement the authors call "compelling evidence" [saboo2020 C44]. In ritonavir–PVPVA at 40% the surface became enriched in drug during incongruent release by preferential polymer release, in agreement with the drug-rich layer seen in cross-section yang2022a C39, C40. Hiew and co-workers (2023) lowered the surface drug of high-loading co-precipitated particles on purpose, by depositing a water-soluble polymer from the anti-solvent; a surface drug of 50% or more appeared to make release drug-dominated [hiew2023 C45, C53]. In 2023–2025 surface composition was followed during dissolution: SDS kept the ritonavir surface of a 40% compact at its bulk composition (about 41 and 40% before and after 30 min) while covering it itself yang2023 R19, R17, C33, and a 40% bedaquiline–HPMCAS dispersion went from about 32 to 55 wt% surface drug after 1 h at pH 6.5, read as preferential loss of polymer and a second cause of poor release [kaur2025 R20, C26, C43]. For 75% grazoprevir particles, surface drug contents of 32–50% did not separate good from poor secondary excipients [hiew2025 R14, C35].

Findings

ASD process: F15, F3, F21, F23, F27, F38. Release mechanism and LoC: F7, F14, F17, F28, F31, F32, F35.

Related concepts

promotes drug-controlled release; a drug-rich layer follows incongruent release; in dissolution becomes the drug-rich surface layer. Forms the drug-rich barrier layer.

Formulas

molar amount of halogen at the lower XPS binding energy, Gordon-Taylor equation.

How it is measured or obtained

Not measured in depth for the lopinavir films; inferred from nanoTA and a mass balance that is not shown li2019 C30, X18. For other dispersions the drug-rich surface was read from IR, SEM, EDX and XPS of tablet or particle surfaces [indulkar2019a C18, C41; saboo2020a C22; bhardwaj2018 C40]. In the release-mechanism papers: ATR-IR of blotted tablets against reference spectra [indulkar2019a P7]; XPS of the top ~10 nm with pure-component fits [que2019 P7; saboo2019 P17; bhardwaj2018 P11]; EDX of an element carried only by the drug (N/O ratio, chlorine) [saboo2019 P16, E2; saboo2020a P9]. SEM-EDX of the Cl/N ratio (one Cl and one N per indomethacin, one N per PVPVA unit) and AFM-nanoTA local Tg converted to composition by the Gordon–Taylor equation [saboo2020 E2, E3, P14, P18].

Values in the library
materialvalue or classconditionspaper ids
LPV–HPMC E5 33% DL, 50 / 70 / 100% watercontinuous-phase local Tg 142 / 116 / 124 °CnanoTAli2019 R15, R16
ritonavir–PVPVA 50% DL tabletsurface enriched in drug after 5 minIR, SEM (outside)[indulkar2019a C18, C41]
felodipine ASDs 30% DLincongruent PVP, PVPVA and HPMC enrich the interface; congruent HPMCAS and EUDS do not: chlorine ≈3.0 → 6.7, 4.6 → 6.4, 2.6 → 7.3 (PVP, PVPVA, HPMC); ≈2.9 → 3.1 and ≈3.0 → 2.7 (HPMCAS, EUDS; ns)EDX, 10 min (outside)[saboo2020a C22, C28, R22]
spray-dried ITZ–PVPVA, 20%n-hexane batches drug-rich at the surface; water lowered surface drug: 4.2% (water in solvent), 28.1% (DCM–methanol), 31.8–35.7% (n-hexane), bulk 20%XPS N 1s, before dissolution (outside)[bhardwaj2018 C40, C41, R20]
ritonavir–PVPVA spray-dried, 25% DLsurface RTV by XPS (C 1s) about 21% (methanol), 43% (10:90), 70% (60:40); at 50% DL 85–91% from 60:40XPS, at least 4 spotsli2020 R7, R11
polymer-free 200:50 lopinavir:ritonavir melt after 1 h in 0.1 N HCl1630/1718 cm⁻¹ band ratio 7.7 → 11.2, read as ritonavir loss from the surfaceATR-FTIR[trasi2019 R16, C29]
BCL–PVPVA 30:70PVPVA:BCL of the undissolved solid 7:3 → 1:1 within 5 min (computed); surfaces rough and pitted after 20 minSEC, SEM[moseson2021 R24, R26, C32]
30% BCL–PVPVA compact surfaceF/F0 = 1.23 ± 0.07 (about 20% enrichment)30 min in buffer, SEM-EDX[moseson2022b R14]
same, cross-sectionboundary layer F/F0 = 1.41 ± 0.10 over a gel layer of 0.93 ± 0.061 h[moseson2022b R15]
ritonavir 50:50 PVP and PVPVA filmsporous or granular surface after 10 s in bufferSEMpurohit2017b R9
ledipasvir–PVPVA 20, 50%17 → 54 and 40 → 61 wt% drug in 10 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 6.8yang2022a R14
grazoprevir–HPMCAS co-precipitates and one solvent-evaporated dispersion, eight materialssurface drug ≤34% with ≈47–72% release; ≥53% with ≈8–17%XPS; two-stage release at 90 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 buffer[kaur2025 R20]
grazoprevir–HPMCAS 75:25 particles with five excipients≈32–50% before SGF, ≈46–69% afterXPS[hiew2025 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 Physical stability

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 Tgtrasi2014a R4, C4, C8
felodipine form Isurface ≈6 times the bulk at 18 °C; equal above 70 °Cmelt filmskestur2013a 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 Physical stability

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 Physical stability

surfactant partitioning into the drug-rich phase

Evidence table: surfactant partitioning into the drug-rich phase. Content from the release-mechanism chapter (2022–2025), with rows from the Physical stability chapter.

The uptake of a surfactant into the drug-rich phase, nanodroplets in solution or drug-rich domains in a hydrated dispersion, read from its depletion from the aqueous phase or from its spectral bands in the drug-rich phase. TPGS was depleted from the aqueous phase by clopidogrel nanodroplets, and the droplets hold about 50:17 w/w drug:TPGS correasoto2022a C19, R12; non-ionic surfactants partition into the clopidogrel-rich phase while ionic ones act at the nanodroplet–water interface correasoto2022a C60. For atazanavir, PVPVA and VP did not partition into the nanodroplets within detection limits, TPGS solution concentration was only minimally affected, and Span 20, Span 80 and Span 85 "seemed to" partition into them correasoto2022b C26, R17. In ritonavir films (Physical stability chapter) the most hydrophilic surfactant, SDS, resides mainly in the polymer-rich phase and the more hydrophobic ones preferentially in drug-rich domains yang2022b C61. The 2023 surfactant study builds on the vapour-sorption finding that Span 20 and Span 85 partition into the ritonavir-rich phase: a continuous drug-rich layer containing Span 85 "is expected to be more liquid-like" and is removed by shear yang2023 R24, C18, C35.

Findings

Release mechanism and LoC: F16, F21, F31.

Related concepts

distinct from micellar solubilization; may slow drug-rich phase coarsening; changes the phase separation morphology of surfactant-containing dispersions; related to the hydrophilic-lipophilic balance of the surfactant.

Formulas

none.

How it is measured or obtained

Quantitative ¹H NMR of the surfactant left in solution with and without nanodroplets, with HPLC after pelleting the droplets correasoto2022a R12; correasoto2022b R17; NMR peak shifts of drug and surfactant at 50 °C correasoto2022a R13, C18; O-PTIR spectra of the separated phases of films (Physical stability chapter) yang2022b C46.

Values in the library
materialvalue or classconditionspaper ids
70 µg/mL clopidogrel with 50 µg/mL TPGSaqueous TPGS 50 → 33 ± 5.4 µg/mL; droplets ≈50:17 w/w drug:TPGSqNMRcorreasoto2022a R12
200 µg/mL atazanavir with PVPVA, VP, SDS, TPGSadditive in solution reduced by 1, 0, 7, 13%¹H NMR, 37 °Ccorreasoto2022b R17
200 µg/mL atazanavir with 20 µg/mL Span 20, Span 85, Span 80reduced by 65, 25, 68%; droplets ≈29:3, 60:4, 62:5 drug:Span by weightsamecorreasoto2022b R17, R19
ritonavir–PVPVA films with SDS; Tween 80 and Spans (Physical stability chapter)SDS only in the polymer-rich phase; Tween 80 and the Spans in the ritonavir-rich phaseO-PTIRyang2022b C46
Pitfalls and disagreements

Partitioning did not predict release enhancement for atazanavir: SDS shows little affinity for the drug and Span 80 partitions into the droplets, and both enhance release correasoto2022b C45. With the Spans the amorphous solubility of atazanavir fell by about 28% (64 to 46 µg/mL) correasoto2022b R18. The temperature of the TPGS depletion measurement is not stated correasoto2022a R12.

← Concepts and formulas

concept · as used in Physical stability

temperature-composition phase diagram

A plot of the liquidus temperature, the temperature at which the last crystal melts, against the composition of a drug–polymer mixture. For a crystalline polymer such as PEG the diagram has a drug-rich and a PEG-rich branch that meet at the eutectic, or, for a monotectic system, only a steep drug branch [baird2011 R5, R8; zhu2011 R4]. Outside the PEG papers the same construction gives the solubility line of a drug in an amorphous polymer, whose crossing with the formulation Tg and the polymer's minimum melt temperature sets a minimum processing temperature [moseson2018 R8, C22]. New aspect (ASD process): for IDM:PVPVA the diagram plots the experimental and predicted critical (solubility) temperature Tc, falling from 160.6 °C for the pure drug to 131 °C at a drug weight fraction of 0.5, together with the formulation Tg line (Gordon–Taylor), the drug melting point, the polymer Tg and a dotted minimum processing temperature Tmin of 117 °C [moseson2018 R5, R8, R9]. Above the solubility line all crystals can dissolve at equilibrium; below it at 50% DL they cannot [moseson2018 C43]. The diagram guided the choice of the extrusion temperature for posaconazole–HPMCAS: 125 °C, below, and 175 °C, above the calculated solubility temperature at each loading [shah2024 R5, R10, C21].

Findings

PEG dispersions: F1, F2, F4. ASD process: F8, F9, F35, F36, F41.

Related concepts

consists of liquidus temperature; contains eutectic or monotectic system; depends on melting point depression; related to drug solubility in polymer. In extrusion work it consists of formulation critical temperature and is used in the HME operating design space.

Formulas

Lacoulonche liquidus model, Flory-Huggins melting point depression, Gordon–Taylor equation.

How it is measured or obtained

Physical mixtures or fused dispersions are heated at 1 °C/min on a hot stage under polarized light, and the temperature at which the last crystal or particle melts is recorded; DSC offset melting at 1 °C/min is used as a second method [baird2011 P2, P3; zhu2011 P3, P4; zhu2012 P9, P10]. For amorphous polymers the offset temperature is extrapolated to 0 °C/min [moseson2018 R5]. For IDM:PVPVA the model line comes from the Flory–Huggins equation with one \chi, and the Tg line from Gordon–Taylor with a density-based constant [moseson2018 P2, E2, E3]. Extrusion outcome is then placed on a plane of product melt temperature against residence time, coloured by the most sensitive method that still called a run amorphous [moseson2018 R15].

Values in the library
materialvalue or classconditionspaper ids
chlorpropamide, aceclofenac, loratadine, haloperidol with PEG 3350predicted line against DSC and hot-stage points; two systems far below the line at 20–60 wt%0–100 wt%, 1 °C/min[baird2011 R5, R6, R7, R8]
benzocaine, ibuprofen, nilutamide, ketoconazole with PEG 3350eutectic (30, 40, 10 wt%) or monotectichot stage, 1 °C/min[zhu2011 R1, R2, R3, R4, R5]
fenofibrate with PEG 3350eutectic minimum about 58 °C at 15–20 wt%CPOM and DSC[zhu2012 R24]
indomethacin–PVPVATc 131 °C ± 2 °C at 50% drug loadingoffset extrapolated to 0 °C/min[moseson2018 C22, R8]
IDM–PVPVApredicted solubility line crosses Tmin near drug weight fraction 0.39 and the Tg line near 0.23 (about 88 °C); 50% DL point marked 131 ± 2 °CFig. 2, readings[moseson2018 R8, X3]
IDM–PVPVA process mapboundary of "amorphous by all techniques" from about 148 °C at 2 min to about 131 °C at 20 min; "X-ray and DSC amorphous" from about 136 °C at 2 min to about 131 °C at about 6 min15 extrusions[moseson2018 R15]
BCL–PVPVA, 30% DLTc = 145 °C and Tm = 195 °C bound the dissolution regime of the extrusion mapFlory–Huggins model, Fig. S2b not supplied[moseson2021 M1, P1]
BCL–PVPVA 30–90% BCLsolubility line from Tc 145 °C (30%) to about 192.3 °C (90%) with χ = −1.57DSC, Flory–Huggins[moseson2022c R8, R9]
PCZ–HPMCAS MFcalculated Tc 135 / 155 / 165 °C at 10 / 25 / 50% DL; extrusion at 125 °C left 0.3 / 3.2 / 19.3 wt% crystals, at 175 °C none2 min, SHG[shah2024 R5, R10, X7]
Pitfalls and disagreements

DSC and hot-stage liquidus values differ by up to about 16 °C at some compositions [baird2011 X7]. The PEG 3350 liquidus is about 61 °C in the diagrams and 55 °C in the model [baird2011 R5, M5, X10]. The diagram describes melting equilibria, not the state of the stored dispersion: a stored 20/80 dispersion has most of its PEG crystalline within minutes (see semicrystalline solid dispersion) [zhu2012 R4]. For amorphous polymers the experimental points depend on heating rate and the 40% drug-loading point deviated from the model line [moseson2018 R3, C19]. For IDM:PVPVA the 131 °C used is the predicted value, the experimental one is 132.3 ± 0.8 °C, and the origin of the "± 2 °C" is not stated [moseson2018 X2]. The switch from Tc to the polymer's Tmin as the lower bound is placed by the authors at 50% DL although the predicted line crosses Tmin near 39% DL [moseson2018 C22, X3]. The diagram gives thermodynamics only; the process map adds kinetics for one micro-extruder [moseson2018 X15]. The BCL diagram is known only through the two temperatures and χ = −1.57 in the text of the 2021 paper [moseson2021 M1].

← Concepts and formulas

concept · as used in Physical stability

ternary phase diagram

A phase diagram of three components

In the ASD process chapter the authors sketch drug–solvent–water for the preparation route and drug–water–polymer for storage, with the phase boundaries only (kinetics not considered) to show how trace water moves the system across the binodal li2017 C38, C42. New aspect (Release mechanism and LoC): Yang and co-workers (2021) use the drug–polymer–water diagram as "an alternative explanation" for the fall of the loratadine limit of congruency at 5 °C: because the diagram changes with temperature (cited), drug–polymer miscibility in the presence of water may fall at low temperature, giving a drug-rich phase at lower loading yang2021 C36. They expect drug Tg to act on kinetics and hydrogen-bonding ability on thermodynamics and the ternary diagram, and call for work to separate the two yang2021 C38. Deac and co-workers (2023) drew schematic hydration paths in the type I drug–PVPVA–water diagram: straight toward the water vertex for congruent dispersions, deviating within the two-phase region for incongruent ones, and the side of the plait point at which the path enters decides whether the hydrophobic phase is continuous deac2023a C66, C67, C68. Drug–PVPVA–water systems typically form type I diagrams with PVPVA acting as cosolvent, and real systems are likely to have sloped tie lines; associative separation gives positively sloped tie lines with the plait point on the low-drug side, segregative separation negatively sloped ones with the plait point on the high-drug side deac2023b C31, C48. The 2024 phase-diagram paper measured the drug–PVPVA–water diagrams of phenolphthalein (PHPH) and its methyl ether (MePHPH) at 37 °C from dispersion–buffer mixtures equilibrated for up to 147 days and computed all four analogue diagrams with PC-SAFT, each fitted to one dilute tie line; all share fully miscible polymer–water and drug–polymer binaries and a drug–water gap that closes as PVPVA increases deac2024b P4, P19, R22, R23, R24. The 2023 surfactant study argues on a schematic ritonavir–PVPVA–water diagram that SDS enlarges the miscible region yang2023 C42.

Findings

ASD process: F2, F6, F20. Release mechanism and LoC: F18, F27, F30, F31.

Related concepts

shows the binodal; used with moisture-induced phase separation. The thermodynamic alternative to the wet glass transition temperature as the cause of a lower limit of congruency at low temperature; shifted by drug-polymer hydrogen bonding.

Formulas

none.

How it is measured or obtained

Not measured in the ASD process papers; the schematic uses the Raoult's-law uptake of water by methanol and the observed thresholds li2017 C39. In the release-mechanism papers: not measured in the 2021 loratadine study, where it is argued from the temperature dependence of the limit yang2021 C36. In 2024: equilibrated mixtures separated by centrifugation and analysed by quantitative ¹H NMR and HPLC (binodes and tie lines), films at stepped RH for the onset at low water, and PC-SAFT computation of binodal, spinodal and critical point deac2024b P4, P7, P8, P19.

Values in the library
materialvalue or classconditionspaper ids
ECP–methanol–watertrace water moves the system from A to B (still miscible); spin coating carries it along B → D across the binodal at C; water spiking along A → B → E separates at Eschematicli2017 C38
ritonavir–PVPVA–waterhydration paths from different DLs enter the two-phase regionschematic from outsideyang2022b C50
MePHPH–PVPVA–waterPC-SAFT binodal, spinodal and tie lines at 37 °Ccomputed and measureddeac2024b R22
drug–PVPVA–water systemstypically type I diagrams (drug–water immiscible, PVPVA a cosolvent)outsidedeac2023b C31
ritonavir–PVPVA–solvent (pseudo-ternary, solvent = methanol + water)at 11.5:88.5 the 25% DL path bypasses the two-phase region and the 50% DL path runs along its edge; at 15:85 and 30:70 both lie inside for most of their lengthcomputedli2020 R18, C55
loratadine–PVPVA; –HPMCASlimit 30 → 2%; 20 → 5% from 37 to 5 °Ccompactsyang2021 R22, C36
MePHPH–PVPVA–watersegregative; critical point ≈29 wt% drug, 59 wt% PVPVA, 12 wt% watermeasured and PC-SAFT, 37 °Cdeac2024b R22
PHPH–PVPVA–waterassociative; critical point ≈2.6 wt% drug, 59.5 wt% PVPVA, 38 wt% watersamedeac2024b R23
TIPP, MeTIPP–PVPVA–waterplait point ≈10 and ≈23 wt% drugPC-SAFT from one tie-line slopedeac2024b R25
Pitfalls and disagreements

The diagram is much more complex with polymer and with both volatile solvents (quaternary or higher) li2017 C36. The pseudo-ternary treats total solvent as one corner, so the water to methanol ratio is not shown on the axes li2020 P12. The kinetic reading (loratadine glassy below its wet Tg of 13.8 °C) and the thermodynamic reading (lower miscibility at 5 °C) were not separated yang2021 C16, M1, C36, C38. No ternary diagram was measured for the phenolphthalein analogues in 2023; the diagrams are schematic deac2023b X14. For PHPH the measured gap is smaller than computed, and the TIPP slope was measured at pH 2.5 deac2024b C34, X10.

← Concepts and formulas

concept · as used in Physical stability

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 growthmosqueragiraldo2014 R12
same≈12, ≈3.2, ≈13, ≈7.4 µm/s at T - T_g ≈65 °Csamemosqueragiraldo2014 R12
celecoxib with 10% PVP and with PVP plus TPGSTPGS–PVP about two orders of magnitude below PVP at T - T_g ≈26–28 °Csamemosqueragiraldo2014 X4, R12
DPB, griseofulvin, celecoxib with 5–10% PHBrates against T − Tg close to the pure compounds; 20% PHB and 5% PVAc belowmelt filmssato2016 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 Physical stability

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 activity[raina2015c 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 cell[elkhabaz2019b R7, R8, R9]
enzalutamidemass flow rises up to about the amorphous solubility (42 µg/mL), then is roughly constant5 µg/mL HPMCAS, side-by-side cell[wilson2018 R13, C25]
atazanavir, nifedipine and three other drugs, PAMPAbreak from a linear rise at about the amorphous solubilitylipid-impregnated 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 Physical stability

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 Hoffmanmarsac2006a R11
felodipineΔG ≈−18, ≈−13, ≈−7 J/g at 0, 50, 100 °CMDSC and Hoffmanmarsac2006a R11
34 drugsΔGv from −8.6 (lidocaine) to −54.7 J/cm³ (acetaminophen)Hoffman, 298 Kbaird2012 M5, M12
class I against class IIIΔGv ≈−0.40 against ≈+0.57 SD from the meanper volume, 293.15 Kbaird2010 R22.g
spin-coat classes I, II, III≈−0.29, ≈+0.29, ≈+0.13 SDper volumevaneerdenbrugh2010a 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 depressionmarsac2006b C41
drugs in PVPdriving force remains at most practical polymer contentsinteraction parametersmarsac2009 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 readingsmarsac2006b R12
nifedipine, pure; 30% PVP; 40% PVP−5.45, −4.1, −2.7 kJ/mol at 100 °Cas abovemarsac2006b 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/minkestur2010a R1
bifonazole, nimesulide with 5% polymersTg rise 0.4–2.2 °CDSC onsetkestur2011 R6, C12
nifedipine, felodipine, droperidol, pimozide, indomethacin, ketoprofenHoffman ΔGc 8.2, 6.1, 9.2, 11.0, 8.1, 4.1 kJ/mol25 °Crumondor2009c M1, M6, M3, M2, M4, M5
nifedipine vs felodipine crystalsmole-fraction solubility 0.05 vs 0.10 in NMP: larger lattice term for nifedipine25 °Cmarsac2008a R10, C35
nifedipine and felodipine in PVPFlory–Huggins activity ≈0.84 and ≈0.83 at Φ 0.2χ −3.8, −4.2marsac2006a R19
acetaminophen and flutamide with 10% polymerTm barely changed, so the driving force is similar for all polymersDSCtrasi2012a 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 growthmosqueragiraldo2014 R5.f, C33
six compounds with PHBdriving force inferred unchanged from Tm and IR ("can be inferred")DSC; IRsato2016 C18, X11
indomethacin polymorphsdifferences in growth persist after a driving-force normalizationmelt growthtian2017 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 Physical stability

tie line

Evidence table: tie line. Content from the release-mechanism chapter (2023–2025).

The line on a ternary phase diagram joining the compositions of two phases in equilibrium; every overall composition on it separates into the same two phases. Real drug–PVPVA–water systems are "likely" to have sloped tie lines deac2023b C31; associative separation gives positively sloped tie lines and segregative separation negatively sloped ones deac2023b C48. Hydrating a dispersion to the binodal gives a hydrophobic phase that is not in equilibrium with a dilute aqueous phase, and PVPVA diffuses out of it until the polymer/drug ratio reaches that of the dilute-solution binode on the tie line deac2023b C53. Measured in 2024 for MePHPH–PVPVA (sloping down) and PHPH–PVPVA (sloping up) from equilibrated mixtures; each drug's PC-SAFT binary parameter was fitted to its most dilute tie line deac2024b R22, R23, P19.

Findings

Release mechanism and LoC: F27, F30.

Related concepts

joins two points of the binodal and ends at the critical point of the ternary phase diagram; used by the lever rule; its slope distinguishes associative phase separation from segregative phase separation.

Formulas

lever rule.

How it is measured or obtained

Not measured in the 2023 paper, where the slopes are drawn on schematic diagrams deac2023b X14; measured from equilibrated mixtures in 2024 deac2024b R22, R23. The binode compositions in dilute water are estimated from the polymer content of nanoparticles and of particles held in buffer deac2023b C52, R4, R5.

Values in the library
materialvalue or classconditionspaper ids
PHPH–PVPVA; MePHPH–PVPVA particlespolymer diffused out until about 72% and below 5% PVPVA, the hydrophobic binodal compositions48 h in buffer with PVPVAdeac2023b C52, R4, R5
MePHPH–PVPVA–waternegatively slopedmeasured and PC-SAFTdeac2024b R22
PHPH–PVPVA–waterpositively slopedsamedeac2024b R23
Pitfalls and disagreements

One schematic diagram of the 2023 paper uses horizontal tie lines although the text expects sloped ones deac2023b X14, C31. The binode drug loads stated in the text do not exactly match the nanoparticle data (PHPH "roughly 30" against about 22–30%) deac2023b X18. The tie line of the driest MePHPH mixture misses its total composition deac2024b C31, X3.

← Concepts and formulas

concept · as used in Physical stability

Tm − Tg temperature gap

The span between the melting point and the glass transition, the range a melt must cross to become a glass trasi2014a C27. If viscosity at Tg is similar for all compounds, a small Tm − Tg with a high viscosity at Tm means a high viscosity at the temperature of fastest growth and so a low maximum growth rate trasi2014a C27.

Findings

F5, F12.

Related concepts

related to reduced glass transition temperature; related to melt viscosity and crystal growth rate.

Formulas

linear fit of melt viscosity on Tm − Tg.

How it is measured or obtained

From DSC Tm and Tg trasi2014a M1; baird2012 M1.

Values in the library
materialvalue or classconditionspaper ids
ritonavir; tolazamide77; 154 °CDSCbaird2012 M34, M18
chlorpropamide; celecoxib; ketoconazole108; 105; 105 °C, in classes I-B, II, IIIDSCbaird2012 M9, M14, M26
slow and fast growth groups85–117 and 121–146 for drugs with viscosity dataDSCtrasi2014a R9
class means I-A, I-B, II, III123 ± 11, 119 ± 11, 126 ± 20, 108 ± 16 °C, not significantly differentDSCbaird2012 R10
Pitfalls and disagreements

The celecoxib Tm − Tg of 125 in one table conflicts with its own Tm and Tg (108) trasi2014a X1, and the dibucaine row of another table repeats lidocaine baird2012 X1. The gap tracked growth groups but not the DSC classes (synthesis: compare R9 of trasi2014a with R10 of baird2012).

← Concepts and formulas

concept · as used in Physical stability

unstirred water layer

The aqueous boundary layer next to a membrane or solid surface that adds a diffusion resistance; thinner under flow [hate2017 C2, C35, C15]. In a lipid-impregnated PVDF cell the layer, not the membrane, limited the transport of atazanavir and nifedipine; steady diffusion across it is C_b - C_{m1} = J\,\delta_{UWL}/D [hate2022 C32, C44, E6]. New aspect (Release mechanism and LoC): the aqueous boundary layer at a dissolving enteric polymer compact. For HP-50, polymer solubilization via ionization, linked to the transport of protons and other ionic species across the boundary layer, is called the rate-limiting step [qi2022 C2]. A carboxylic acid polymer must ionize before it dissolves: without a gel layer the steps are transport of water and base to the polymer, acid–base reaction, release of polymer from the matrix and transport of polymer and protons through the aqueous boundary layer (cited) [bapat2023 C33]. Faster rotation thins the layer and increases HPMCAS dissolution, and the slope of the stirring dependence differs between media because the interfacial polymer solubility differs [bapat2023 C44]. In the 2025 grade paper polymer solubility at the interface sets how fast the polymer diffuses across the aqueous boundary layer, and the drug follows [bapat2025a C29].

Findings

Bioperformance: F13, F15, F19, F21, F22. Release mechanism and LoC: F23, F33.

Related concepts

part of resistance-in-series permeability model; related to membrane mass transfer coefficient, lipophilicity and membrane asymmetry. Carries the protons that set the microenvironmental pH; its capacity depends on buffer capacity; same layer as the diffusion boundary layer of the dissolving compact.

Formulas

resistances-in-series model, boundary-layer diffusion flux (film model), Levich boundary-layer thickness.

How it is measured or obtained

Not measured directly in the first papers; invoked to explain the higher transfer of a hollow-fibre module (continuous flow thins the layer) and its dependence on flow rate [hate2017 C15, C35]. Drug-rich colloids are suggested to thin it in vivo [hate2018 C7]; Brownian convection of nanoparticles in the boundary layer is one of three untested explanations for the continuing rise above the amorphous solubility [hate2018 C56]. A PAMPA study inferred it from the insensitivity of mass flow to filter, pore size and lipid and from the rise with a solubilizing receiver, and estimated the donor-side interface concentration from mass flow [hate2022 R5, R16, C32, C44]. In the release-mechanism papers: rotation speed of the rotating disk, with the layer thickness from the Levich expression [bapat2023 E3, R18, R19].

Values in the library
materialvalue or classconditionspaper ids
nevirapinetransfer rises with flow rate then falls0.5–9 mL/min, hollow fibre[hate2017 R10, C15]
HPMCAS (polymer dissolution)Levich thickness \delta = 1.612\,D^{1/3}\nu^{1/6}\omega^{-1/2}rotating disc[bapat2023 E3, C44]
atazanavir, nifedipine, acetaminophenatazanavir and nifedipine mass flow changed little with filter or lipid; acetaminophen (log P about 0.5) rose from about 0.19 to 0.50 µg/min with lipidPAMPA, buffer receiver[hate2022 R5, R16]
Caco-2 and donor stirring300 rpm donor and 500 rpm insert shaking to minimise the layerside-by-side and Caco-2[alkalla2026 C15]
neat HPMCAS-MF and HPMCAS-TEArate linear in √rpm, ≈2.9–3.3 times the 100 rpm rate at 700 rpm, no plateaurotating disk, 100–700 rpm[bapat2023 R18, R19, X10]
Pitfalls and disagreements

Boundary-layer effects were not tested by varying stirring in the side-by-side or Caco-2 work [alhalaweh2016 C3]. Smaller nanodroplets "would be expected" to help by diffusing into the layer, but droplets of about 280 and 1000 nm gave the same PAMPA mass flow (F22) [ueda2020a C30, C39; hate2022 R17]. The rate rises above the \omega^{1/2} proportionality at 700 rpm (≈2.88–3.34 against 2.65) [bapat2023 X10].

← Concepts and formulas

concept · as used in Physical stability

van't Hoff equation

The relation d\ln x/dT = \Delta H_f/(R\,T^2) between the temperature dependence of a mole-fraction solubility x and the heat of solution; in the PEG papers it is used to extrapolate the solubility of a drug along its liquidus to 25 °C [zhu2011 E3, P6; zhu2012 E3]. This draft covers the solubility use; the evidence table lists a different use of the relation in another subcategory.

Findings

F4.

Related concepts

measures drug solubility in polymer; uses liquidus temperature; related to ideal solubility.

Formulas

van't Hoff equation.

How it is measured or obtained

\ln x is plotted against 1/T along the drug liquidus of the phase diagram (Figs. 2–5 of zhu2011), a straight line is fitted by linear regression and extended below the PEG melting point to 25 °C, and the result is converted to weight percent [zhu2011 P6, E3]. The same route was used for fenofibrate from the supporting-information diagram [zhu2012 M2, E3].

Values in the library
materialvalue or classconditionspaper ids
benzocaine, chlorpropamide, ibuprofen, nilutamide, haloperidol, ketoconazole in PEG 335028, 26, 25, 11, 0, 0 wt% at 25 °Cextrapolated, supercooled liquid PEG[zhu2011 R5]
fenofibrate in PEG 33506 wt% at 25 °Cas above[zhu2012 M2]
Pitfalls and disagreements

The regression lines, the heats of fusion and the molar masses behind the extrapolation are not printed [zhu2011 E3]. In the second paper the equation is named only [zhu2012 E3]. The nilutamide estimate (11 wt%) is above its eutectic content (10 wt%), although an extrapolation along the liquidus to a lower temperature would normally give a lower value [zhu2011 X4]. (synthesis: the relation assumes a constant heat of solution, while the extrapolation runs from liquidus temperatures well above the PEG melting point down to 25 °C [zhu2011 R1, R2, R3, R4].)

← Concepts and formulas

concept · as used in Physical stability

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 Physical stability

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 °Ckonno2008 R8.a; rumondor2010a R1
HPMC, HPMCAS≈10.4–10.9 and ≈6.2–6.3 g/100 g at 75% RH25 °Ckonno2008 R8; rumondor2010a R1
amorphous felodipine, indomethacin≈1.1 and ≈1.55 g/100 g at 75% RH25 °Crumondor2010a R1.h
felodipine–PVP 70 wt% PVP≈10.3 (65% RH) turning up to ≈55.5 wt% (95% RH)25 °Cmarsac2010 R9
amorphous ritonavir (outside)≈1.55% at 50% RH, rising, extrapolated linearly to 100% RH37 °Cilevbare2013a R7, E14
PVP, PVPVA, HPMCASisotherms at 25 °C, PVP far above the others at high RHcitedrumondor2010c R19
resveratrol–PVP dispersion and physical mixture0–95% RH, mixture above dispersion at every step25 °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 Physical stability

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 °C[ueda2021 R17]
ECP–PVPVA powdersabout 61% (PVPVA), 35% (10% DL), 4–7% (20–50% DL), 0.5–3.6% (60–100% DL)24 h, 97–98% RHli2017 R25, X3
felodipine, indomethacin, PVP, HPMC, HPMCASFlory–Huggins water parameters from isotherms25 °Crumondor2010a R11
clofoctol–PVP with 70% API or more; probucol–PVPresistance to moisture-induced separation attributed to too little moisture sorbed by the hydrophobic systems; no water content or sorption was reported for those filmsoutsiderumondor2011 C36, X6
70 wt% PVP felodipine dispersionwater vapour sorption isotherm at 25 °Coutsidemarsac2010 R9, R10
erlotinib–HPMCAS 60% DL, uncoated against 5–25 nm coatedabout 5.7 against 5.4%DVS 40 °C, 75% RHmoseson2022a R8, R9
ezetimibe–HPMCAS 50% DL, uncoated / thin / thickabout 5.65 / 5.83 / 3.17%DVS 37 °C, 95% RHduong2022c 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% RH[moseson2023 R7]
PCZ–HPMCAS 50% DL, slow-deposited 26 nmabout 0.33% at 2 h against about 4.2–4.5%same[moseson2023 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 °Cmarsac2008a R2
felodipine–PVP 25%43–64% below additivity15–85% RHrumondor2010a R7.b
nifedipine-, pimozide-, droperidol–PVP5.9, 7.4, 0.2% from additivity (phase separated)95% RHrumondor2009c R22
indomethacin–PVP 75:254.9 vs 21.7 g/100 g predicted95% RHrumondor2009c R22.g
40% resveratrol–PVP dispersion≈1.8, ≈5.9, ≈8.7, ≈12.8% at 20, 60, 80, 95% RH, below its physical mixture at every step25 °Cwegiel2013b R19
atazanavir–PVPVA 10%; with SDS or Span 8044%; 49% waterDVS, 37 °C, up to 95% RHcorreasoto2022b R16
amorphous lumefantrine salts≈6.6 (PEG 250 diacid 1:1), 3.3 (sulfate), below 2% (benzoate, besylate, tosylate, camsylate, HCl) at 95% RHDVS[hiew2022b R4]
lumefantrine salt–PVPVA dispersions35–55% water, higher at lower loading95% RH, 40 °C[hiew2022b 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 °Ccorreasoto2023 R22
Pitfalls and disagreements

The relative humidity to which the % moisture of the weak-base table refers is not stated [indulkar2015 M1, M2]. Linear extrapolation to 100% RH is an approximation ilevbare2013a E14. In the film papers, uptake was measured on bulk powders, not on the films imaged by TEM, and the values at 20–50% and 60–80% DL differ by only a few per cent although separation was seen to 80% DL li2017 X8, R19. The same explanation (too little moisture sorbed at high loading) is given for other hydrophobic drug–PVP systems without sorption data rumondor2011 C36, X6. The thin 50% ezetimibe coating protected for two years without lowering uptake duong2022c X7. The slow-sorbing posaconazole samples had not levelled off within 2 h [moseson2023 X17]. The two moisture papers normalise the deviation from additivity differently (against the prediction, against the measured value) rumondor2010a E6; rumondor2009c E6. No sorption was measured on the films in which nucleation and growth were counted marsac2008a X12. The lower uptake of the resveratrol dispersion is read as hydrogen bonds suppressing sorption, but bonding in the wet dispersion was not measured wegiel2013b C37, X18. The dispersion sorption curves of both papers are in SI not supplied [correasoto2022b R16; hiew2022b R5]. The excess-acid PEG 250 diacid (1:1) salt liquified at 95% RH [hiew2022b C10]. Among the HP-50 salts the sodium salt took up the most water without dissolving faster, which weakens hydration as the explanation of the salt effect [qi2022 X17, C35].

← Concepts and formulas

concept · as used in Physical stability

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 buffer[saboo2020a 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 6.5duong2022c 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/mL[moseson2022b R9]
PVPVA; HPMCAS (cited)water contact angle 30.6°; 58.6°literatureyang2021 M7, M8
grazoprevir–HPMCAS 75:25 particles with SDS; with 10 mg/mL HPMC0° from 1 s; ≈30° and 51–52° at 10 sFaSSIF, powder bed[hiew2025 R15]
same with PVP, poloxamer 407; heptane particles; MTBE-treated dispersion≈121°, 131°; 137 ± 5°; ≈119°same[hiew2025 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 Physical stability

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 Physical stability

activity coefficient from solubility

Expression

\gamma_d = \frac{1}{x_d}\exp\left(\frac{-\Delta H_{fus,d}\,(T_{melt,d} - T)}{R\,T_{melt,d}^{2}}\right) [baird2011 E7],

obtained by combining the simplified solubility equation

\ln\left[\gamma_d\,x_d\right] = -\frac{\Delta G_{fus}}{R\,T} [baird2011 E5]

with the Hoffman relation

\Delta G_{fus} = \frac{\Delta H_{fus,d}\,(T_{melt,d} - T)\,T}{T_{melt,d}^{2}} [baird2011 E6].

Marsac and co-workers name the relation without printing it; the card's check finds the printed coefficients equal to the ideal solubility divided by the measured solubility within rounding for four drugs, that is \gamma = S^{ideal}/S marsac2008b E2, X5.

Variables and units

symbolmeaningunits
\gamma_dactivity coefficient of the drug in PEG 400 (or water)dimensionless [baird2011 E7; marsac2008b E2]
x_dmole-fraction solubility of the drugdimensionless; converted from mg/mL by a relation that is not printed [baird2011 X4]
\Delta H_{fus,d}heat of fusion of the drugkJ/mol (24.5 for chlorpropamide) [baird2011 M1, E7]
T_{melt,d}, Tmelting temperature and temperature of the measurementK (399.85 and 298.15 for chlorpropamide at 25 °C) [baird2011 E7]
S^{ideal}, Smole-fraction ideal and measured solubilitydimensionless marsac2008b E1, R14

Assumptions and valid domain

The solubility in liquid PEG 400 is used as a proxy for the polymer, because activity coefficients in viscous, semicrystalline PEG 3350 are hard to determine [baird2011 C21]. A coefficient below 1 is read as favourable drug–PEG interaction only if the entropy of mixing is close to ideal [baird2011 C23; marsac2008b C14]. The temperature of the ideal solubility in Marsac and co-workers is not stated and the aqueous solubilities are cited at unstated temperatures marsac2008b E1, X18. Tested for four drugs in PEG 400 at 25 °C [baird2011 R9] and six drugs in PEG 400 and water marsac2008b R14.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
baird2011\gamma of chlorpropamide, aceclofenac, loratadine, haloperidol in PEG 4000.614, 0.121, 2.369, 0.842printed; reproduces for chlorpropamide (0.614 at T = 298.15 K, T_{melt,d} = 399.85 K, \Delta H_{fus,d} = 24.5 kJ/mol, x_d = 0.250) [baird2011 E7, R9]
marsac2008b\gamma of six drugs in PEG 400 and in water0.02–0.64 in PEG 400; 1.2 × 10¹ to 5.3 × 10⁵ in waternamed only; four rows equal S^{ideal}/S within rounding marsac2008b E2, R14, X5

Where it fails or is disputed

With the mole fraction defined as n_d/(n_d + n_{PEG}) instead of moles of drug per mole of PEG 400 in 1 mL, the four coefficients of Baird and Taylor become 0.766, 0.149, 2.49 and 0.856, with the split at 1 unchanged [baird2011 X4]. Loratadine is called close to ideal although its solubility is about 0.42 of the ideal value [baird2011 X13]. The Table 3 caption cites Equations 5 and 7 for γ and χ, while the text uses 7 and 8 [baird2011 X12]. In the Marsac and co-workers table, naproxen's coefficients fit an ideal solubility of about 0.0045 instead of the printed 0.01, and felodipine's two coefficients fit different ideal solubilities marsac2008b X5. The coefficient was measured at 25 °C, far below the eutectic temperatures of the dispersions [baird2011 X16].

Concepts

activity coefficient, ideal solubility, drug solubility in polymer, enthalpy of mixing. Findings. F3, F11.

← Concepts and formulas

formula · as used in Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

amorphous solubility advantage from free energy difference

Expression

\ln x_{SL,L_1} = \ln x_{C,L_1} + \frac{\Delta G_{a\to c}}{RT} ilevbare2013a E5;

\frac{\mu_1^{\circ} - \mu_{1c}^{\circ}}{RT} = \ln\frac{S_a}{S_c} [trasi2015a E1];

\frac{S_{amorphous}}{S_{crystalline}} \approx \frac{a_{amorphous}}{a_{crystalline}} = \exp\left[\frac{\Delta G_c}{RT}\right] [hsieh2012 E4; hsieh2014 E3].

The ASD dissolution papers print it as

\Delta G_c = RT\ln\frac{a_{\mathrm{amorphous}}}{a_{\mathrm{crystalline}}} \approx RT\ln\frac{S_{\mathrm{amorphous}}}{S_{\mathrm{crystalline}}} konno2008a E1;

\frac{\sigma^{\mathrm{amorph}}}{\sigma^{\mathrm{crystal}}} = e^{\Delta G/RT} [alonzo2011 E2];

\frac{S_A}{S_C} = \exp\left(\frac{\mu_A - \mu_C}{RT}\right) li2018 E2;

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

Variables and units

symbolmeaningunits
x_{SL,L_1}, x_{C,L_1}mole-fraction solubility of the supercooled liquid and of the crystal in waterdimensionless ilevbare2013a E3, E4
\Delta G_{a\to c}free-energy difference amorphous–crystalilevbare2013a E2
\mu_1^{\circ}, \mu_{1c}^{\circ}chemical potential of pure amorphous (supercooled liquid) and crystalline drug[trasi2015a E1]
S_a, S_camorphous and crystalline solubilityµg/mL [trasi2015a E1, R1]
S_{amorphous}, S_{crystalline}solubility of the amorphous and crystalline formsµg/mL [hsieh2012 E4]
a_{amorphous}, a_{crystalline}thermodynamic activity of the solid formdimensionless [hsieh2012 E4]
\Delta G_cfree-energy difference between the forms (Hoffman equation)kJ/mol [hsieh2014 E3]
R, Tgas constant; temperatureJ mol⁻¹ K⁻¹; K
\sigma^{\mathrm{amorph}}, \sigma^{\mathrm{crystal}}solubility of each form (2011 notation)µg/mL [alonzo2011 E2]
S_A, S_Camorphous and crystalline solubility (2018 notation)µg/mL li2018 E2
\mu_A, \mu_Cchemical potential of the drug in the amorphous and the crystalline solidJ/mol li2018 E2
\Delta G; C_a, C_sfree-energy difference; amorphous and crystalline solubility (2022 notation)J/mol; µg/mL [duong2022a E1]

Assumptions and valid domain

The activity coefficient is constant between the crystalline and amorphous concentration; the amorphous phase is a supercooled liquid; the first form omits the water term, which amorphous solubility advantage with water-sorption correction adds [ilevbare2013a C55, C58; trasi2015a C36]. In the activity form the ratio of solubilities equals the ratio of activities; water mixing into the amorphous phase is neglected, which can lower the amorphous solubility by up to 2-fold [hsieh2014 R17]. Used at 25 and 37 °C. In the ASD dissolution papers the activity ratio is approximated by the solubility ratio konno2008a E1; solute–solvent interactions are taken as equal for both solid forms, which the 2011 authors call "unlikely to be true" for a dispersion [alonzo2011 C6, C41]. The drug activity coefficient in solution varies little between the crystalline and the amorphous solubility, and the amorphous form and the solution equilibrate; crystallization, water ingress and glass relaxation hamper that equilibrium li2018 C41.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
ilevbare2013afirst approximation of the amorphous solubility, ritonavirnone printednot applicable (no numerical output) ilevbare2013a E5
trasi2015adefines the amorphous-to-crystalline solubility ratioritonavir 15–16, lopinavir 6.0–6.4, paclitaxel hydrate 85–94, felodipine 7–8 (extractor arithmetic)not applicable; ratios from Table 1 [trasi2015a E1, X12]
hsieh2012uncorrected amorphous solubility of five basesratios 22.2, 11.9, 20.4, 54.6, 7.0ratios reproduce from printed solubilities (24.4/1.1 = 22.2) [hsieh2012 E4, R10]
hsieh2014glyburide and warfarinabout 60 and 48reproduces 59.9 and 47.7 at 25 °C [hsieh2014 E3, R16]
konno2008afelodipine at 37 °Cratio about 10: 10 × 0.94 = 9.4 against printed about 9.5 µg/mLreproduces within rounding konno2008a E1
alonzo2011felodipine at 37 °Cratio about 9 implies ΔG = RT ln 9 ≈ 5.67 kJ/molinputs not printed [alonzo2011 E2]
alonzo2011flux of pure amorphous felodipine against crystalratio 8.5close to the estimate [alonzo2011 R14, C40]
li2018lopinavir, pH 3, 25 °Cmeasured S_A/S_C = 17.4/3.1 = 5.6; \mu_A - \mu_C not printedinputs not printed li2018 E2, R1 (synthesis: RT\ln 5.6 ≈ 4.3 kJ/mol at 298 K)
duong2022aturning a Hoffman free-energy estimate into a delamanid solubility ratiomeasured ratio 42.3 at pH 6.5 against 31.8 estimatedthe two equations are used together; no ΔG value is printed [duong2022a E1, E2, R27]

Where it fails or is disputed

The paclitaxel ratio lies outside the 5–50-fold range quoted in the introduction and rests on a hydrate [trasi2015a X12, R18]. The ketoconazole estimate (54.6-fold) is 2.6 times the measured supernatant, and the water correction brings it to 15.3-fold [hsieh2012 X2, R10.d]. For warfarin with Eudragit E100 the polymer-free supersaturation of 60.5 exceeds the 48-fold ceiling [hsieh2014 X4]. A dispersion and the pure amorphous drug need not give the same solution activity; their measured equality for felodipine "may be purely coincidental" [alonzo2011 C45, C48]. For lopinavir the measured ratio is used; the free-energy difference from thermal data is printed but not applied to data li2018 E3, C43. The delamanid ratio was measured in PBS pH 6.5, where both solubilities are very low (0.76 and 0.018 µg/mL), so small absolute errors move the ratio [duong2022a R1].

Concepts

amorphous solubility advantage, chemical potential, amorphous solubility, Hoffman equation. Findings. Amorphous solubility and LLPS: F6, F11. Crystallization from solution: F2. Supersaturation from ASD dissolution: F7, F18, F23.

← Concepts and formulas

formula · as used in Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

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 ratiodimensionless[moseson2020a E2]
R_{G,np}crystal growth rate without polymerµg/s (vessel mass rate)[moseson2020a E2, X12]
R_{G,p}crystal growth rate with polymerµg/s[moseson2020a E2]
R_{g0}initial growth rate without polymerµg mL⁻¹ min⁻¹ or µg min⁻¹[ilevbare2012a E3]
R_{gp}initial growth rate with polymer or additivesame[ilevbare2012a E3]
E_geffectiveness ratio; 3 means growth three times slowerdimensionless[ilevbare2013b E5]
bulk growth rates (felodipine melt)linear growth rates without and with 3% PVP, read from plotsm/skestur2013a 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 Physical stability

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 Physical stability

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 Physical stability

entropy of fusion

Expression

\Delta S_{fus} = \frac{\Delta H_{fus}}{T_{melt,ons}} baird2010 E26;

\Delta S_{fus} = \frac{\Delta H_{fus}}{T_m} vaneerdenbrugh2010a E1.

Variables and units

symbolmeaningunits
\Delta S_{fus}entropy of fusionkJ mol⁻¹ K⁻¹ baird2010 E26; J cm⁻³ K⁻¹ after volume conversion vaneerdenbrugh2010a E1
\Delta H_{fus}heat of fusion from DSCkJ mol⁻¹ baird2010 E26; J cm⁻³ vaneerdenbrugh2010a E1
T_m, T_{melt,ons}melting point (onset)K baird2010 E26; vaneerdenbrugh2010a E1

Assumptions and valid domain

None stated beyond DSC inputs baird2010 E26; vaneerdenbrugh2010a E1. The 31-drug growth study uses the melting entropy ΔSm per mole in \Delta G \approx \Delta S_m\,\Delta T, an approximation trasi2014a E3.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
baird2010descriptor tables and class PCAhaloperidol 12.8 × 10⁻² kJ mol⁻¹ K⁻¹; class I contribution +0.41reproduces: 54.26/425.15 = 0.1276 baird2010 E26, R22
vaneerdenbrugh2010aclass PCAcontributions +0.46, −0.27, −0.33 for classes I, II, IIIinputs not printed vaneerdenbrugh2010a E1, R20
marsac2006afelodipine and nifedipine74.3 and 89.6 J mol⁻¹ K⁻¹reproduces marsac2006a E11

Where it fails or is disputed

On a volume basis the fast class I has the higher entropy of fusion baird2010 R22; vaneerdenbrugh2010a R20, while on a molar basis the fastest growers had lower melting entropy and the normalized growth rate fell with ΔSm/R trasi2014a R8, R11. (synthesis: the two bases and the two outcomes, class and growth rate, differ, so the signs need not conflict; class I molecules are small, which raises per-volume values.)

Concepts

entropy of fusion, enthalpy of fusion, thermodynamic driving force for crystallization. Findings. F6, F13.

← Concepts and formulas

formula · as used in Physical stability

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 Physical stability

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 temperaturemarsac2006b 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 Physical stability

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 Physical stability

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 Physical stability

Fox equation

Expression

\frac{1}{T_g} = \frac{x_1}{T_{g,1}} + \frac{x_2}{T_{g,2}} [alhalaweh2016 E6].

As printed for curcumin dispersions:

\frac{1}{T_{g,mix}} = \frac{w_1}{T_{g1}} + \frac{w_2}{T_{g2}} wegiel2014 E1

Named without an expression in the 2021 phenolphthalein-analogue study [que2021 E2]. Printed for wet dispersions and separated phases in the 2024 phase-diagram study:

\frac{1}{T_{g,wet}} = \frac{w_{ASD}}{T_{g,ASD}} + \frac{w_{water}}{T_{g,water}} deac2024b E13

Variables and units

symbolmeaningunits
T_gglass transition of the mixtureK
T_{g,1}, T_{g,2}pure-component values (ritonavir 323 K, atazanavir 377 K)K [alhalaweh2016 M1, M2]
x_1, x_2weight fractions–
w_1, w_2; T_{g1}, T_{g2}weight fractions and component Tg in the curcumin formunits not stated; Table 4 lists °C wegiel2014 E1
T_{g,wet}Tg of the wet dispersion or separated phase (2024 form)K deac2024b E13
w_{ASD}, w_{water}weight fractions of dry dispersion and water– deac2024b E13
T_{g,ASD}, T_{g,water}Tg of the dry dispersion; Tg of water, 135 KK deac2024b E13

Assumptions and valid domain

Miscible blend, free-volume additivity; specific interactions violate it wegiel2014 E1. None stated in the 2021 phenolphthalein-analogue study [que2021 E2].

Use in the library

In the phenolphthalein-analogue study the estimate for neat TIPP (84 °C) shows that the Tg measured for TIPP with 10% PVPVA (86.1 °C) is "likely" slightly above that of neat TIPP, so it can stand for the drug in the comparison of the four analogues' Tgs [que2021 C3, R1, M1].

paperused forvalues or fitted parametersstatus / recomputed
alhalaweh2016ritonavir–atazanavir melt-quenched mixturesw_RTV 0.2: 364.8 K against about 365 Kreproduces the line; data 3–8 K below [alhalaweh2016 E6, X7]
que2021neat TIPP Tg357.4 K = 84.2 °Creproduces [que2021 E2]
wilson2018wet Tg of amorphous enzalutamide352 K printed; water Tg and fraction not printednamed only; inputs not printed [wilson2018 E8, C14]
wegiel2014deviation of the dispersion Tg as a marker of drug–polymer interactionprinted predictions 42 (E100), 96 (PVP), 92 (HPMC), 80 (HPMCAS), 89 °C (CMCAB)mismatch: computed in °C at 25% curcumin; with kelvin and the stored 75% curcumin 43.2, 66.6, 64.4, 58.5, 63.1 °C, deviations +18.8, −3.6, +3.6, +6.5, −1.1 °C wegiel2014 E1, R18, X1
deac2024bTg of wet miscible dispersions and of the separated phasesT_{g,water} = 135 Kreproduces ≈51 °C for 5% PHPH at 0.10 water deac2024b E13

Where it fails or is disputed

The measured Tg lie below the line [alhalaweh2016 X7]. In the curcumin paper, after recalculation only the E100 deviation survives, which the authors read as consistent with an ionic interaction; the negative deviations they read as a net loss of interactions disappear wegiel2014 C41, C42, X1.

Concepts

Fox equation, drug–drug miscibility, acid-base interaction, plasticization. Findings. Bioperformance: F6. Physical stability: F5, F24. Release mechanism and LoC: F17, F30.

← Concepts and formulas

formula · as used in Physical stability

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 Physical stability

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 constantrumondor2009a 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 Physical stability

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/Kkonno2006 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 Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

Kohlrausch-Williams-Watts equation

Expression

As printed:

1 - \phi(t) = \exp\left(\left(\frac{-t}{\tau}\right)^{\beta}\right) konno2006 E7

\frac{\Delta H_{t,T}}{\Delta H_{max,T}} = 1 - \exp\left(-\frac{t}{\tau}\right)^{\beta} marsac2006a E7

Both reproduce their data only in the standard stretched-exponential form, 1 - \phi(t) = \exp\left(-(t/\tau)^{\beta}\right) konno2006 X5; marsac2006a X4.

Variables and units

symbolmeaningunits
\phi(t)fraction of the maximum enthalpy recovered after ageing time t– konno2006 E5
\taumean relaxation timeh konno2006 R9
\betastretch exponent– konno2006 R9

Assumptions and valid domain

Fitted to enthalpy recovery of glasses aged below Tg (2 °C, 23.5 °C), nonlinear regression konno2006 P6; marsac2006a P9.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
konno20069:1 felodipine dispersions at 2 °Cτ 208 (PVP), 687 (HPMCAS), 319 h (HPMC); β 0.42–0.47reproduces Fig. 6 with the standard form konno2006 E7, R9
marsac2006aglasses and 10 wt% PVP dispersions at 23.5 °Cτ 6.3, 4.2 h (drugs); 42.1, 16.7 h (with PVP)reproduces Fig. 4 with the standard form marsac2006a E7, R4.n, R7

Where it fails or is disputed

Misprinted in both papers konno2006 X5; marsac2006a X4. The τ values did not rank nucleation marsac2006a C37.

Concepts

enthalpy relaxation, Kohlrausch-Williams-Watts equation, molecular mobility. Findings. F5.

← Concepts and formulas

formula · as used in Physical stability

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 Physical stability

lever rule

Evidence table: lever rule. Content from the release-mechanism chapter (2023–2025), with a row from the Physical stability chapter.

Expression

Printed in words: the ratio of the amount of phase A to that of phase B equals the ratio of the length BX to AX, X being the overall composition on the tie line joining A and B yang2022b E1. Written with these symbols (synthesis: no equation printed):

\frac{m_A}{m_B} = \frac{\overline{BX}}{\overline{AX}}

Named only in the 2023 phenolphthalein-analogue paper deac2023b E5.

Printed in 2024:

W^{\alpha} = \frac{m^{\alpha}}{m^{T}} = \frac{W_i^{T} - W_i^{\beta}}{W_i^{\alpha} - W_i^{\beta}} deac2024b E12

and stated in words for a ritonavir diagram in 2023 yang2023 E2.

Variables and units

symbolmeaningunit
m_A, m_Bamounts of the coexisting phases A and Bany consistent amount
\overline{AX}, \overline{BX}lengths on the tie line from the overall composition X to A and to B–

Assumptions and valid domain

Thermodynamic equilibrium, with the compositions joined by a tie line yang2022b E1; complete separation to the binodal compositions immediately on entering the unstable region deac2023b E5.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
yang2022b (Physical stability)phase amounts along hydration paths of a schematic ritonavir–PVPVA–water diagramnoneinputs not printed yang2022b E1, C50
deac2023bmajority phase and hydrophobic-phase volume against drug load, schematicnonenamed only deac2023b E5, C34, C36
yang2023amount of drug-rich phase on schematic ritonavir–PVPVA–water diagrams with and without SDSnoneschematic yang2023 E2, C41
deac2024bdrug-rich fraction at the spinodal against loading, from PC-SAFT diagramsW^{\alpha} ≈0.15 → 0.82 (MePHPH, 27 → 39.5%)inputs not printed; Table S1 row d fails the mass balance deac2024b E12, R35, X3

Where it fails or is disputed

In the 2023 paper used on schematic diagrams only; no ternary diagram or tie line was measured there deac2023b X14. The 2024 use assumes onset at the spinodal, immediate local equilibrium and inversion at 0.5 deac2024b E12, C51.

Concepts

lever rule, tie line, ternary phase diagram, phase inversion. Findings. Release mechanism and LoC: F27, F30, F31.

← Concepts and formulas

formula · as used in Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

maximum enthalpy recovery

Expression

As printed:

\Delta H_{\infty} = \Delta C_p \times (T_g - T_a) konno2006 E6

\Delta H_{max,T} = \Delta C_P^{T_g}\,(T_g - T) marsac2006a E8

Variables and units

symbolmeaningunits
\Delta H_{\infty}, \Delta H_{max,T}maximum enthalpy recoverable on ageing at T_amJ/mg marsac2006a R8
\Delta C_pheat capacity step at TgJ/g/°C marsac2006a X3
T_g, T_aglass transition and ageing temperatures°C marsac2006a E8

Assumptions and valid domain

Enthalpy of the equilibrium liquid extrapolated below Tg with the heat-capacity step konno2006 E6; marsac2006a E8.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
marsac2006afraction recovered for felodipine, alone and with 10% PVP6.3 and 5.3 mJ/mg maxima; 84% and 65% recovered at 16 hreproduces 0.32 × (43.1 − 23.5) = 6.27 marsac2006a E8, R8
konno2006fractions relaxed of 9:1 dispersions at 2 °Cinputs not printedinputs not printed konno2006 E6

Where it fails or is disputed

The 2006 PVP paper prints ΔCp in J/mol/°C where the values fit J/g/°C, and the onset Tg must be used marsac2006a X3, X12.

Concepts

enthalpy relaxation, glass transition temperature. Findings. F5.

← Concepts and formulas

formula · as used in Physical stability

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 Physical stability

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 Physical stability

octanol-water partition coefficient

Evidence table: octanol-water partition coefficient. Content from the release-mechanism chapter (2020).

Expression

\log P = \log\frac{[\mathrm{drug}]_{\mathrm{octanol}}}{[\mathrm{drug}]_{\mathrm{aqueous}}} [saboo2020a E5]

Variables and units

symbolmeaningunit
[\mathrm{drug}]_{\mathrm{octanol}}, [\mathrm{drug}]_{\mathrm{aqueous}}drug concentration in octanol and in the aqueous buffer, by LC-MSsame unit in both

Assumptions and valid domain

Compounds predominantly un-ionized; pH 6.5 buffer saturated with octanol [saboo2020a E5].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
saboo2020alog P of nilvadipine and cilnidipine (felodipine from the literature)4.06, 5.40 (felodipine 4.46)inputs not printed [saboo2020a E5, R16]
saboo2020log P of indomethacin and its methyl ester4.07, 4.53inputs not printed [saboo2020 E4, M1, M2]

Where it fails or is disputed

The calculated ClogP values of the 2019 paper for the same two drugs (3.04 and 5.54) differ from the measured ones [saboo2019 A1; saboo2020a R16].

Concepts

octanol-water partition coefficient, lipophilicity. Findings. Release mechanism and LoC: F9, F17.

← Concepts and formulas

formula · as used in Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

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 Physical stability

van't Hoff equation

Expression

\frac{d\ln x}{dT} = \frac{\Delta H_f}{R\,T^{2}} [zhu2011 E3].

Zhu and co-workers (2012) name the van't Hoff equation for the same extrapolation without printing it [zhu2012 E3].

The amorphous solubility chapter uses the van't Hoff analysis for the partition coefficient of a polymer between the drug-rich phase (p) and water (q),

K_{p/q} = \frac{C_p}{C_q} [ueda2022 E3],

\Delta G_{q\to p} = -RT\ln K_{p/q} [ueda2022 E4],

\ln K_{p/q} = -\frac{\Delta H_{q\to p}}{RT} + \frac{\Delta S_{q\to p}}{R} [ueda2022 E5],

and, when the straight line fits poorly, with a quadratic term that lets ΔH and ΔS vary with temperature,

\ln K_{p/q} = A + \frac{B}{T} + \frac{C}{T^{2}} [ueda2022 E6],

\Delta H_{q\to p} = -R\left(B + \frac{2C}{T}\right),\qquad \Delta S_{q\to p} = R\left(A - \frac{C}{T^{2}}\right) [ueda2022 E7, E8].

Variables and units

symbolmeaningunits
xmole-fraction solubility of the drug in liquid PEGdimensionless [zhu2011 E3]
\Delta H_fheat of solution (named "heat of solution" in the card)not printed [zhu2011 E3]
R, Tgas constant; temperatureK [zhu2011 E3]
K_{p/q}, C_p, C_qpartition coefficient of the polymer between the drug-rich phase (p) and water (q), and its concentrations in themdimensionless; C_p computed with 0.99 g/cm³ (amorphous ibuprofen) [ueda2022 E3, X2]
\Delta G_{q\to p}, \Delta H_{q\to p}, \Delta S_{q\to p}free energy, enthalpy and entropy of transfer from water into the drug-rich phasekJ/mol for ΔG and ΔH (see the use table); unit of ΔS not stated in the notes [ueda2022 E4, E5]
A, B, Cconstants of the quadratic fit of \ln K_{p/q} against 1/Tnot stated [ueda2022 E6]

Assumptions and valid domain

\ln x against 1/T along the drug liquidus (Figs. 2–5) is fitted by linear regression and extrapolated to 25 °C, below the PEG melting point, so the result refers to supercooled liquid PEG, and is converted to weight percent [zhu2011 E3, C8]. The second paper uses it to extrapolate solubilities from the binary phase diagrams to 25 °C [zhu2012 E3]. Tested on four liquidus series measured here (benzocaine, ibuprofen, nilutamide, ketoconazole) and on the cited chlorpropamide and haloperidol diagrams [zhu2011 R1, R2, R3, R4, R5]. In the amorphous solubility chapter the linear form assumes ΔH and ΔS independent of temperature; the linear fit gave R² of 0.817 (PVP), 0.962 (HPMC) and 0.961 (PVP-VA) and the quadratic fit 0.971 (PVP), 0.996 (HPMC) and 0.994 (PVP-VA) [ueda2022 C47, R20, R21]. The concentration in the drug-rich phase is computed with 0.99 g/cm³ (amorphous ibuprofen), a basis that ignores water in that phase and is not written out [ueda2022 E3, X2]. Valid at 15–60 °C (HPMC 15–55 °C), pH 2.0 in D2O [ueda2022 P12, R3].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
zhu2011solubility of six drugs in PEG 3350 at 25 °C28, 26, 25, 11, 0, 0 wt% (benzocaine, chlorpropamide, ibuprofen, nilutamide, haloperidol, ketoconazole)printed; inputs not printed (liquidus points only plotted; regression lines and molar masses not printed) [zhu2011 E3, R5]
zhu2012solubility of haloperidol, benzocaine, ibuprofen, fenofibrate at 25 °Cbelow 1, 28, 25, 6 wt%named only [zhu2012 E3, M1, M2, M3, M4]
ueda2022ΔG, ΔH, ΔS of transfer of PVP, PVP-VA and HPMC from water into the ibuprofen-rich phaselinear: HPMC ln K = −4.23 × 10³ (1/T) + 19.9; PVP-VA −1.79 × 10³ (1/T) + 12.2; PVP −1.44 × 10³ (1/T) + 10.5; ΔG −12 to −19 kJ/mol; ΔH of HPMC 58 → 12 kJ/molreproduces (HPMC at 288.15 K: ΔH = −8.314 × (38700 − 45740) J/mol = 58.5 kJ/mol; −TΔS = −70.8 kJ/mol; ΔG = −RT ln K = −12.3 kJ/mol) [ueda2022 E4, E5, E7, E8, R20, R21]

Where it fails or is disputed

The nilutamide estimate (11 wt%) is above its eutectic content (10 wt% at 58.4 °C), whereas an extrapolation to a lower temperature would normally give a lower value [zhu2011 X4]. The regression lines and inputs are not printed in either paper, so the estimates cannot be recomputed [zhu2011 E3; zhu2012 E3]. The relation assumes a constant heat of solution over the extrapolated range (synthesis: the extrapolation runs from liquidus temperatures well above the PEG melting point down to 25 °C [zhu2011 R1, R2, R3, R4]). In the amorphous solubility chapter ΔH, ΔS and ΔG are derivatives of three-parameter fits to 9–10 points with no propagated uncertainty, so the temperature slopes of ΔH and ΔS rest on the curvature term; for PVP ΔH is negative at 55 and 60 °C [ueda2022 X8, X1]. The linear fits give temperature-independent ΔH of about 35 (HPMC), 15 (PVP-VA) and 12 kJ/mol (PVP) (extractor calculation), close to the quadratic values at mid-range [ueda2022 X8]. The two chapters apply the relation to different quantities (drug solubility along the liquidus in PEG; polymer partition coefficient between two liquid phases), so their values are not comparable.

Concepts

van't Hoff equation, drug solubility in polymer, liquidus temperature, polymer partitioning into the drug-rich phase, hydrophobic effect. Findings. PEG dispersions: F4. C. Amorphous solubility and LLPS: F21.

← Concepts and formulas

formula · as used in Physical stability

Vogel-Tammann-Fulcher equation

Expression

\tau = \tau_0 \exp\left(\frac{D\,T_0}{T - T_0}\right) baird2010 E12;

\eta = \eta_0 \exp\left(\frac{D\,T_0}{T - T_0}\right) baird2012 E4.

Variables and units

symbolmeaningunits
\tau, \etamean molecular relaxation time, or viscositys; Pa·s baird2010 E12; baird2012 E4
\tau_0, \eta_0value for the unrestricted materialτ0 ≈ 10⁻¹⁴ s baird2010 E12
Dstrength parameterdimensionless baird2012 E4
T_0zero-mobility temperature, for some systems the Kauzmann temperatureK baird2012 E4

Assumptions and valid domain

For the strength parameter D^b: T_0 = T_K, τ(Tg) ≈ 10² s, τ0 ≈ 10⁻¹⁴ s baird2010 E12. Valid from Tm down to about 0.4 Tg on a scale with T_g = 0 and T_m = 1, with D and T0 fitted together baird2012 E4. Strong liquids have D above 30, fragile ones below 10 baird2010 R30.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
baird2010D^b from Tg and Kauzmann temperature for class II and IIIindomethacin D^b 5reproduces: \ln(10^{16}) \times (318.15 - 282.15)/282.15 = 4.70 baird2010 E12, R18
baird2012fits of melt viscosity for 28 compoundsD 4.3–8.7, all below 10inputs not printed (η0 not reported) baird2012 E4, R12

Where it fails or is disputed

The fitted T0 and D do not satisfy the paper's own relation between T0, D and Tg baird2012 X5. The six class I-A compounds were not fitted, though the abstract calls all compounds fragile baird2012 X7. Whether a compound counts as strong or fragile depends on using m or D baird2010 X14. Good and poor glass formers showed the same non-Arrhenius behaviour, so kinetic fragility "may not accurately assess" glass-forming ability baird2012 C43; fragility was also invoked, untested, for two growth-rate outliers trasi2014a C29, X18.

Concepts

fragility, melt viscosity, glass transition temperature, supercooled liquid. Findings. F5, F12.

← Concepts and formulas

formula · as used in Physical stability

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.