Amorphous solid dispersions: the whole picture

01How the parts fit together

Solid state stabilitywhether the drug stays amorphous: neat class, polymer, miscibility, water→is set by the making routeASD processhow the route sets phase state, residual crystals and degradation→is checked byCharacterization methodswhich method sees crystals, domains and drug-rich phases, and what it misses→reads the solution ofDissolutionrelease, the amorphous solubility as ceiling, and loss of supersaturation→sets the free drug and flux inBioperformanceflux at the ceiling, absorptive tests, residual crystals, animals→is the benchmark forMesoporous silicaa second carrier that adsorbs drug and stays below the ceiling→same release questions forPeptide permeabilitya peptide and an enhancer released from copovidone or a minitablet

Characterization methods → Solid state stability one Tg does not exclude drug-rich domains (F7, F9)
Characterization methods → ASD process SHG and TEM find crystals below the XRPD limit (F7)
Mesoporous silica → Dissolution adsorption keeps silica release below the amorphous solubility (F1)
Peptide permeability → Dissolution co-release with copovidone holds only at a few percent loading (F8)
ASD process → Bioperformance residual crystals cost supersaturation and exposure (F6)

The chain runs from the solid to the membrane; the extra links are where the methods, the second carrier and the peptide meet the main chain. shah2024 R12, R14; purohit2019 R9; dening2018 R22, C32, R35; bapat2025b R10, C21

The categories follow one amorphous drug from the solid to the membrane. Solid state stability asks whether the drug stays amorphous and what a polymer, water and the carrier do to that. ASD process asks how the route that makes the dispersion sets its phase state and leaves crystals or degradation behind. Dissolution asks what the dispersion produces in water: how it releases, how far it supersaturates and how it loses the supersaturation. Bioperformance asks what of that reaches a membrane and an animal. Characterization methods is the toolbox the other categories use, and Mesoporous silica and Peptide permeability put the same questions to a second carrier and to a peptide.

The reference that joins the later categories is the amorphous solubility. The free drug from dispersions, marketed products and silica stops at or below it, membrane flux plateaus there, and dispersions that reached it raised exposure in rats (F1); any component that mixes into the drug-rich phase lowers it (F2); and it can only be read by free drug, activity or flux (F3).

Crystals run through every category. The neat-drug class is a first flag but decides no outcome alone (F4); polymers act on nucleation far more than on growth, so crystals already present bypass them (F5); residual crystals left by the process cost supersaturation in vitro and exposure in dogs (F6); and whether a sample counts as amorphous depends on the method that looked (F7).

Drug loading and water set the phase state of the solid while it is made, stored and wetted. Each category has its own loading threshold (F8), water separates dispersions at every stage with opposite effects on release (F9), and a dispersion can crystallize inside its own wetted solid where a dissolved polymer does not act (F10).

The conflicts appear when one excipient or one test is followed through all stages. No polymer was best at every stage (F11), surfactants raised release and also promoted crystallization (F12), the gastrointestinal sequence changed the outcome for every carrier (F13), and the few animal studies agreed with flux or absorptive read-outs more often than with closed-vessel concentration (F14).

02Categories

category	chapters	papers	years	what it covers	its key findings
Solid state stability	4	56	1997–2022	Crystallization tendency of neat drugs, drug–polymer contacts and miscibility, PEG and PEO carriers, physical stability of dispersions on storage, dry and humid	F1 neat class within one test, F4 nucleation and growth separately, F8 drug-rich phase, F9 polymer in humid storage
ASD process	1	21	2001–2025	Water during spin coating and spray drying, carriers and melt routes, phase diagrams for extrusion, residual crystals, thermal degradation, granulation of two drugs, atomic layer coating	F1 water splits films, F9 extrusion below Tc, F27 matrix crystallization, F43 coatings delay crystallization
Characterization methods	2	14	1998–2018	Raman, PXRD, SHG, AFM-IR, probes, confocal imaging and ssNMR for solids; UV, extinction, fluorescence and lifetime for solutions	F4 blind spots, F5 detection limits and onsets, F7 methods for each question
Dissolution	4	91	2008–2025	Amorphous solubility and LLPS, crystallization from solution, supersaturation from dispersions, release mechanism and limit of congruency	F1 the ceiling, F4 polymers and crystals present, F7 loading switch, F11 gastric stage
Bioperformance	1	18	2014–2026	Membrane flux at the amorphous solubility, solubilizers and media, absorptive test designs, residual crystallinity, exposure in rats, dogs and monkeys	F2 flux plateau, F14 closed against absorptive, F23 rats, F30 dogs
Mesoporous silica	1	5	2018–2020	Drug state in SBA-15 pores, adsorption isotherms from water, incomplete release, surfactants, pH shift and absorptive sink	F3 adsorption near the ceiling, F7 incomplete release, F13 re-adsorption after pH shift, F15 against a polymer dispersion
Peptide permeability	1	2	2025	Release of octreotide, cyclosporine and insulin with sodium caprate or SNAC from copovidone dispersions and minitablets in biorelevant media	F1 separate rates, F4 co-release in copovidone, F5 loading boundary, F6 no permeation measured

03Wiki findings

Conclusions that appear only when the categories are read together. Click a card to read it.

Topic 1 · F1–F3

Amorphous solubility as common reference

F1In every category free drug and membrane flux stop at the amorphous solubility, and formulations are judged by reaching it.strong F2A second drug, a polymer or a bile salt that mixes into the drug-rich phase lowers the amorphous solubility.strong F3Near the amorphous solubility and in micellar media, total drug misleads; free drug or flux has to be read.moderate

Topic 2 · F4–F7

Crystals from neat drug to exposure

F4The crystallization class of the neat drug orders drugs within one test, but carriers, routes and polymers override it.moderate F5Polymers slow nucleation far more than growth, so crystals already present bypass them, and rankings do not transfer.strong F6Residual crystals cost supersaturation from the extruder to the animal; a crystallized tacrolimus capsule lost about half its exposure in dogs.moderate F7Whether a sample is amorphous depends on the method; crystals below the X-ray limit changed dissolution.moderate

Topic 3 · F8–F10

Water and the hydrating solid

F8Every category has a drug-loading threshold, but storage, release, absorption, silica and peptide thresholds are different quantities.strong F9Water separates drug and polymer during manufacture, storage and wetting; the separation raised release in one system and lowered it in another.moderate F10A dispersion can crystallize inside its wetted solid before the drug dissolves; a dissolved polymer does not prevent this.moderate

Topic 4 · F11–F12

Polymers and surfactants across stages

F11No polymer was best at every stage: fast release and thermal protection favoured PVP or PVPVA, inhibition and humid storage HPMCAS.strong F12Surfactants raised release in every category, and in every category they also promoted crystallization or gave no final gain.strong

Topic 5 · F13–F14

Gut conditions and exposure

F13The gastric stage, the pH shift, the medium and food changed the outcome for every carrier.moderate F14Flux and absorptive tests tracked animal exposure better than closed vessels, but animal data cover three drugs and no human dispersion.weak

04Which category each finding draws on

Show the table of categories and findings

	Amorphous solubility as common reference			Crystals from neat drug to exposure				Water and the hydrating solid			Polymers and surfactants across stages		Gut conditions and exposure
chapter	F1	F2	F3	F4	F5	F6	F7	F8	F9	F10	F11	F12	F13	F14
Solid state stability
ASD process
Characterization methods
Dissolution
Bioperformance
Mesoporous silica
Peptide permeability

Dot size = number of chapter findings each category finding draws on.

05Open questions

Do drug-rich nanodroplets add exposure beyond the ceiling? The one enzalutamide dispersion that shed amorphous aggregates gave about 30% more exposure in rats, a trend without a statistical test wilson2018 C46, X6 (Bioperformance F23); transfer kept rising above the amorphous solubility in a hollow-fibre module and in PAMPA with a sink receiver hate2018 R9, E3, E4 (Bioperformance F15); hate2022 R19 (Bioperformance F22); yet droplets brought crystallization sooner wilson2021 R3 (Dissolution F5). See F1.
How much residual crystallinity is acceptable for a given drug, dose and volume? The cost of residual crystals depended on the system, from mainly lost potency for indomethacin–PVPVA to most of the supersaturation for bicalutamide–PVPVA moseson2020a R6, C28; moseson2021 R17, C70 (ASD process F29), and the dog loss was smaller than the small-volume tests predicted purohit2019 R9; hate2019 R13 (Bioperformance F31). See F6.
What happens at the dissolving surface that sets the limit of congruency and matrix crystallization? Cooling below the wet Tg of the drug-rich surface lowered the limit saboo2020 R29, R30, C53 (Dissolution F8), but the wet Tg of the dissolving surface and the proposed hydrated drug-rich trigger of matrix crystallization were not measured moseson2021 K1, K7, X8, X11 (ASD process F27). See F8 and F10.
Which polymer property serves both release and inhibition? The authors call the choice between fast release and inhibition a "trade-off" saboo2020a R15, R14, C55 (Dissolution F9), and the HPMCAS grade order of release and of nucleation delay ran in opposite directions shah2025 R3, R4, R5 (Dissolution F10). See F11.
Why does the best polymer in humid storage reverse between drugs? PVP lost to HPMCAS for felodipine but held polyphenols konno2008 R1, R3; wegiel2013a R9 (Solid state stability F9), and the drug–water interaction parameter that grouped the separating drugs differs by only a small margin rumondor2009c R24, C46, C27, C32 (Solid state stability F10). See F9 and F11.
Do interaction parameters or solubility estimates predict whether a dispersion stays amorphous? Estimates from different routes agreed in sign but not in size, and 20/80 benzocaine and ibuprofen dispersions below their estimated solubility crystallized within hours marsac2009 R9; zhu2011 R5; zhu2012 R23.a (Solid state stability F3). See F8.
Does co-release of a peptide and a permeation enhancer improve absorption? Neither peptide paper measured permeability, transport or absorption, so the benefit of co-release remains an expectation bapat2025b C6; fagan2025 C45 (Peptide permeability F6). See F8 and F14.
What do re-adsorption and release below the ceiling cost a silica formulation in vivo? The authors conclude that silica "might not be the most suitable approach" for weak bases with a high pKa hate2020b C20, C52 (Mesoporous silica F13) and that it "would appear" unable to match polymer dispersions hate2020a C51, C52, C54 (Mesoporous silica F15); no exposure was measured. See F1 and F13.
Why do atomic layer coatings protect stored powders when they leave water uptake nearly unchanged? Coatings of 5–25 nm overlapped the uncoated isotherms up to 75% RH moseson2022a R8, R9, C20 (ASD process F45), and the wet Tg ordered the failures of coated powders only in part moseson2022a R12, X15 (ASD process F44). See F9.
Does any in vitro read-out predict exposure of a dispersion in humans? The simulated bioequivalence of the tacrolimus capsule awaited human data purohit2018 K6, C58, C59, X10 (Bioperformance F17), and the enzalutamide mass-flow ranking is called a "preliminary observation" wilson2018 K5, C52 (Bioperformance F25). See F14.

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 · 3 findings · F1–F3

Amorphous solubility as common reference

F1

Topic 1Amorphous solubility as common reference1 of 3

In every category free drug and membrane flux stop at the amorphous solubility, and formulations are judged by reaching it.

Free drug from dissolving dispersions and six marketed tacrolimus capsules levelled off at about the amorphous solubility (tacrolimus ≈46–50 µg/mL), and membrane flux plateaued from about the same concentration trasi2016 R10, R4, R15, R14; raina2014a R11, R12, R14. In rats the enzalutamide dispersions that reached it beat crystalline drug, while the one that crystallized did not wilson2018 R18, R6, C47. Ritonavir from SBA-15 silica stayed below it even at ten times the dose dening2018 R22, C32, R35.

strongStrong for the cap on free drug and on flux, shown with particle-blind read-outs for several drugs in two categories; moderate for the link to exposure (one drug in rats, three to six animals per arm) and for silica (one silica) raina2014a R11, R12, R14; wilson2018 R18, R6, C47; hate2020a K7, X19; dening2018 C43.

Dispersions that reached the amorphous solubility gave several times the exposure of crystals; the one that crystallized gave less. wilson2018 R16, R17

Marketed dispersions sit at the amorphous solubility (Sa); silica approaches it but stays below even at a tenfold dose. trasi2016 R10, R4, R15, R14; dening2018 R23, R22, M1, R8

For your drug

Measure the amorphous solubility of the drug in the intended medium by an onset method and confirm it by flux or ultracentrifuged supernatant.
Ask of each candidate formulation whether it reaches that value; a silica formulation that stays below it or a dispersion that crystallizes before it will not give the flux of the amorphous drug.

raina2015a R11, X9; dening2018 R22, C32, R35; wilson2018 R18, R6, C47

How it works and key numbers

Beyond the amorphous solubility the excess drug forms a submicron, non-crystalline colloid, for ritonavir ≈350 nm droplets at 20 µg/mL and none at 10 µg/mL ilevbare2013d R1, R2.
Once this second phase is present the thermodynamic activity of the drug is constant, so the flux across a membrane plateaus raina2014a R11, R12, R14.
On silica the adsorption of drug rises steeply as the solution approaches the amorphous solubility, so release "approaches but does not exceed" it and no drug-rich phase forms dening2019 R2, R1; dening2018 C32, C33, C64.
(synthesis: one thermodynamic quantity, measured in one category, sets the free drug, the flux and the benchmark of the other carriers.)

0.91–1.15onset of the drug-rich phase over calculated amorphous solubility, 17 of 24 rowsilevbare2013a R8; almeidaesousa2015 R5, R11; mosqueragiraldo2015 R13

63–71 × 10⁻³ µg/minfelodipine flux plateau at 25 °C from 5 up to 100 µg/mLraina2014a R11, R12, R14

about 4.3–5.2 vs 10.2–11.6 µg/mLreceiver atazanavir from SBA-15 against an HPMC dispersionhate2020a R24, R25, C37

Evidence: data, conditions and papers

Finding F1. The amorphous solubility is the reference of every category: free drug from dispersions and marketed products levels off there, membrane flux plateaus there, dispersions that reached it raised exposure in rats, and mesoporous silica stays below it

In short. Whether supersaturation came from a solvent shift, a pH shift or a dissolving dispersion, the free drug levelled off at the amorphous solubility, and flux, NMR and ultracentrifugation put the free drug from six marketed tacrolimus capsules at about the same value (≈46–50 µg/mL) alonzo2011 R14, M1; jackson2015 R9, R2, M1; trasi2015b R13, M1, M2; trasi2016 R10, R4, R15, R14 (Dissolution F1). Across a membrane the flux rose with donor concentration up to about the concentration of the second phase and then stayed at a plateau, for felodipine at 25 °C 63–71 × 10⁻³ µg/min from 5 up to 100 µg/mL raina2014a R11, R12, R14 (Bioperformance F2). In rats the three enzalutamide dispersions that reached the amorphous solubility beat the crystalline control (p < 0.05), and the one that crystallized gave less than the crystals wilson2018 R18, R6, C47 (Bioperformance F23). Ritonavir from SBA-15 silica dosed at up to ten times its amorphous solubility plateaued at about 24 µg/mL, about 85% of it, with no drug-rich phase, and an atazanavir–silica formulation gave about 4.3–5.2 µg/mL in the receiver against about 10.2–11.6 µg/mL for an HPMC dispersion dening2018 R22, C32, R35; hate2020a R24, R25, C37 (Mesoporous silica F15).

Type. cross-category synthesis of 11 source findings (solvent-shift and pH-shift solutions, dispersions, marketed capsules, diffusion, flow-through, hollow-fibre and PAMPA cells, rats, silica formulations; about 25 drugs) Strength. for the cap on free drug and on flux, shown with particle-blind read-outs for several drugs in two categories (Dissolution F1, Bioperformance F2); moderate for the link to exposure, one drug in rats with three to six animals per arm (Bioperformance F23); moderate for silica, one silica and a direct comparison at one loading and one dose hate2020a K7, X19; dening2018 C43 (Mesoporous silica F15).

How it was shown

Dissolution compared the onset of a drug-rich phase with the calculated amorphous solubility and read the free drug of dissolving dispersions and six marketed tacrolimus capsules by flux, NMR and ultracentrifugation ilevbare2013a R8; almeidaesousa2015 R5, R11; mosqueragiraldo2015 R13. Bioperformance measured flux against donor concentration and dosed four enzalutamide dispersions and crystalline drug to rats raina2014a R11, R12, R14; indulkar2016 R9; wilson2018 R16, R17. Mesoporous silica dosed ritonavir–SBA-15 up to ten times the amorphous solubility and set atazanavir–SBA-15 against a 10% HPMC dispersion in a hollow-fibre module dening2018 R23, R22, M1, R8; hate2020a R24, R25, C37.

What the data show

In rats AUC0–48 was about 770 µg·h/mL for the 10% enzalutamide–copovidone dispersion and about 575 for the two 50% dispersions, against about 61 for the 10% HPMCAS dispersion, which crystallized, and about 91 for crystalline drug wilson2018 R16, R17. From SBA-15 the free ritonavir rose only from about 10 to about 24 µg/mL as the dose rose from 50 to 1000% of the amorphous solubility (27.9 µg/mL) dening2018 R23, R22, M1, R8.

system	read-out	result	ids
about 20 drugs, solvent and pH shift	onset against calculated amorphous solubility	0.91–1.15 times for 17 of 24 rows	ilevbare2013a R8; almeidaesousa2015 R5, R11; mosqueragiraldo2015 R13
six marketed tacrolimus capsules	flux, NMR, ultracentrifugation	free drug at about the amorphous solubility (≈46–50 µg/mL)	trasi2016 R10, R4, R15, R14
felodipine, nifedipine; clotrimazole; telaprevir dispersion	side-by-side and flow-through cells	flux plateau from about the onset of the second phase	raina2014a R11, R12, R14; indulkar2016 R9; mosqueragiraldo2018b R1, R2
four enzalutamide dispersions and crystalline drug	rats, 10 mL/kg gavage	dispersions that reached the ceiling beat crystals (p < 0.05); the crystallizing one did not	wilson2018 R18, R6, C47
atazanavir–SBA-15 against 10% HPMC dispersion	hollow fibre, 200 µg/mL dose	receiver about 4.3–5.2 against 10.2–11.6 µg/mL	hate2020a R24, R25, C37

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

The mass flow rises with concentration and then flattens, and the six marketed products fall in the band on the plateau trasi2016 R15, R14.

Why

The Bioperformance authors read the flux plateau as constant thermodynamic activity once a second phase is present raina2014a R11, R12, R14; the excess drug forms a submicron, non-crystalline colloid ilevbare2013d R1, R2. For silica the authors conclude that release "approaches but does not exceed" the amorphous solubility dening2018 C32, C33, C64, because adsorption onto the silica rises steeply as the solution approaches it dening2019 R2, R1. (synthesis: one thermodynamic quantity sets the free drug, the flux and the benchmark of the other carriers.)

Limits and transfer

In a PAMPA cell with a sink receiver the mass flow kept rising from about 5.0 to 8.8 µg/min between 80 and 1000 µg/mL hate2022 R19. Measure the amorphous solubility of the new drug in the intended medium by an onset method and confirm it by flux or ultracentrifuged supernatant raina2015a R11, X9; a silica formulation that stays below it or a dispersion that crystallizes before it will not give the flux of the amorphous drug dening2018 R22, C32, R35; wilson2018 R18, R6, C47.

How it was shown

Dissolution measured the onset of a drug-rich phase in solvent-shift and pH-shift solutions by extinction, fluorescence and NMR and compared it with the amorphous solubility calculated from crystalline solubility, the free-energy difference and water uptake; it then dissolved amorphous films, salts, dispersions and six marketed tacrolimus capsules and read the free drug by flux, NMR and ultracentrifugation ilevbare2013a R8; almeidaesousa2015 R5, R11; mosqueragiraldo2015 R13 (Dissolution F1). Characterization methods compared the extinction, probe and thermodynamic onsets for six dihydropyridines raina2015a R11, X9 (Characterization methods F5). Bioperformance measured flux against donor concentration in a side-by-side diffusion cell, a flow-through cell and a PAMPA cell raina2014a R11, R12, R14; indulkar2016 R9; hate2022 R1 (Bioperformance F2) and dosed four enzalutamide dispersions and crystalline drug to rats by gavage wilson2018 R16, R17 (Bioperformance F23). Mesoporous silica dosed ritonavir–SBA-15 from half to ten times the amorphous solubility, read dissolution and cellulose-membrane mass flow, and set an atazanavir–SBA-15 formulation against a 10% HPMC dispersion in a hollow-fibre module dening2018 R23, R22, M1, R8 (Mesoporous silica F8); hate2020a R24, R25, C37 (Mesoporous silica F15).

What the data show

The onset of the drug-rich phase lay at 0.91–1.15 times the calculated amorphous solubility for 17 of 24 rows ilevbare2013a R8; almeidaesousa2015 R5, R11; mosqueragiraldo2015 R13 (Dissolution F1), and the extinction, probe and thermodynamic onsets of five of six dihydropyridines lay within a factor of 1.0–1.7 raina2015a R11, X9 (Characterization methods F5). Beyond it the dissolved drug and the membrane flux of telaprevir, ritonavir, lopinavir and paclitaxel stopped rising mosqueragiraldo2015 R10, R12; trasi2015a R2, R1 (Dissolution F1). The same plateau appeared for felodipine at 37 °C (136–149 × 10⁻³ µg/min from 25 µg/mL), nifedipine (about 1.7–1.9 µg/min from about 72 µg/mL), clotrimazole in a flow-through cell and telaprevir released from a dispersion raina2014a R11, R12, R14; indulkar2016 R9; mosqueragiraldo2018b R1, R2 (Bioperformance F2). In rats AUC0–48 was about 770 µg·h/mL for the 10% enzalutamide–copovidone dispersion, about 575 for the 50% copovidone and 50% HPMCAS dispersions, about 61 for the 10% HPMCAS dispersion, which crystallized, and about 91 for crystalline drug wilson2018 R16, R17 (Bioperformance F23). From SBA-15 the free ritonavir rose only from about 10 to about 24 µg/mL as the dose rose from 50 to 1000% of the amorphous solubility (27.9 µg/mL), and membrane mass flow reached that of amorphous ritonavir only at the tenfold dose dening2018 R23, R22, M1, R8 (Mesoporous silica F8). At the end of the chain, a posaconazole dispersion at 50% loading fell to about the LLPS concentration within about 30 min after a pH shift shah2024 R18, C32 (ASD process F41).

source finding	system	conditions	result	ids
Dissolution F1	about 20 drugs, solvent and pH shift	onset against calculated amorphous solubility	0.91–1.15 times for 17 of 24 rows	ilevbare2013a R8; almeidaesousa2015 R5, R11; mosqueragiraldo2015 R13
Dissolution F1	six marketed tacrolimus capsules; felodipine, danazol, ritonavir, lopinavir dispersions	flux, NMR, ultracentrifugation	free drug at about the amorphous solubility (tacrolimus ≈46–50 µg/mL)	alonzo2011 R14, M1; jackson2015 R9, R2, M1; trasi2015b R13, M1, M2; trasi2016 R10, R4, R15, R14
Characterization methods F5	six dihydropyridines	extinction, probe, thermodynamic onset	within a factor of 1.0–1.7 for five of six	raina2015a R11, X9
Bioperformance F2	felodipine, nifedipine; clotrimazole; telaprevir dispersion	side-by-side and flow-through cells	flux plateau from about the onset of the second phase	raina2014a R11, R12, R14; indulkar2016 R9; mosqueragiraldo2018b R1, R2
Bioperformance F23	four enzalutamide dispersions and crystalline drug	rats, 10 mL/kg gavage	dispersions that reached the ceiling beat crystals (p < 0.05); the crystallizing one did not	wilson2018 R18, R6, C47
Mesoporous silica F8	ritonavir–SBA-15	50–1000% of the amorphous solubility	free drug about 10 to 24 µg/mL against 27.9; flux of amorphous drug only at tenfold dose	dening2018 R23, R22, M1, R8
Mesoporous silica F15	atazanavir–SBA-15 against 10% HPMC dispersion	hollow fibre, 200 µg/mL dose	donor about 48–57 against 207 µg/mL; receiver about 4.3–5.2 against 10.2–11.6 µg/mL	hate2020a R24, R25, C37
ASD process F41	posaconazole–HPMCAS, 50% loading	gastric-to-intestinal pH shift	peak and fall to about the LLPS concentration within about 30 min	shah2024 R18, C32

Figure

The mass flow of tacrolimus solutions rises with concentration and then flattens; the six marketed products fall in the band on the plateau, at the amorphous solubility of the pure drug trasi2016 R15, R14 (Dissolution F1).

Fig. 12 of hate2020a: 10% atazanavir–SBA-15 against a 10% HPMC dispersion — Fig. 12 · hate2020a10% atazanavir–SBA-15 against a 10% HPMC dispersion

The dispersion rises above the amorphous solubility and turns turbid, the silica formulation stays below it, and the receiver curves differ by about a factor of two hate2020a R24, R25 (Mesoporous silica F15).

Why

The Bioperformance authors read the flux plateau as constant thermodynamic activity once a second phase is present raina2014a R11, R12, R14 (Bioperformance F2). Beyond the amorphous solubility the excess drug forms a submicron, non-crystalline colloid, for ritonavir ≈350 nm droplets at 20 µg/mL and none at 10 µg/mL ilevbare2013d R1, R2 (Dissolution F1). For silica the authors conclude that release "approaches but does not exceed" the amorphous solubility and that no drug-rich phase forms dening2018 C32, C33, C64 (Mesoporous silica F8), because adsorption of drug onto the silica rises steeply as the solution approaches the amorphous solubility dening2019 R2, R1 (Mesoporous silica F3). (synthesis: one thermodynamic quantity, measured in one category, sets the free drug, the flux and the benchmark of the other carriers; a formulation is judged in every category by whether and for how long it reaches that value.)

Conditions and limits

The cap was measured in buffers and simulated media, with membranes of cellulose, lipid-impregnated PVDF or Caco-2 cells, and the animal result is one drug in rats (Bioperformance F2, Bioperformance F23). The calculated value cannot be recomputed for four of the 2013 predictions, and the best-fitting route changes with the compound (Dissolution F1). (synthesis: the silica results hold for one silica, SBA-15 with 7.1 nm pores loaded from solvent, the only one the Mesoporous silica chapter tested.)

Counterexamples and conflicts

The estimate from melting data failed in FaSSIF (214.6 measured against 308.0 estimated) raina2015c R1; raina2014a X3 (Bioperformance F1). In a hollow-fibre module the transfer of atazanavir did not plateau above the amorphous solubility but rose at a lower slope (AUC slope 5.51 below, 1.29 above) hate2018 R9, E3, E4 (Bioperformance F15), and in a PAMPA cell with a sink receiver the mass flow kept rising from about 5.0 to 8.8 µg/min between 80 and 1000 µg/mL hate2022 R19 (Bioperformance F22). (synthesis: the plateau holds where the receiver does not remove drug faster than the droplets resupply the donor; with a strong sink the droplets add transfer.)

Transfer check

Measure the amorphous solubility of the new drug in the intended medium by an onset method and confirm it by a particle-blind read-out such as flux or ultracentrifuged supernatant raina2015a R11, X9 (Characterization methods F5). Then ask of each candidate formulation whether it reaches that value: a silica formulation that stays below it dening2018 R22, C32, R35 (Mesoporous silica F15) or a dispersion that crystallizes before it wilson2018 R18, R6, C47 (Bioperformance F23) will not give the flux of the amorphous drug.

History

2011–2013: dispersions of felodipine were read by flux, and the onset of a drug-rich phase was set against the calculated amorphous solubility alonzo2011 R14, M1; ilevbare2013a R8 (Dissolution F1). 2014: Raina and co-workers showed the flux plateau at that concentration raina2014a R11, R12, R14 (Bioperformance F2). 2015–2016: the plateau was extended to further drugs and the six marketed tacrolimus capsules were placed on it mosqueragiraldo2015 R10, R12; trasi2016 R10, R4, R15, R14 (Dissolution F1). 2018: the first rat study tied reaching the ceiling to exposure wilson2018 R18, R6, C47 (Bioperformance F23), and silica was measured against it dening2018 R22, C32, R35 (Mesoporous silica F15). 2020–2022: silica was set against a polymer dispersion of the same drug, and PAMPA with a sink receiver showed transfer above the ceiling hate2020a R24, R25, C37 (Mesoporous silica F15); hate2022 R19 (Bioperformance F22). 2024: the LLPS concentration served as the working amorphous solubility of a pH-shift test of extrudates shah2024 R18, C32 (ASD process F41).

Conceptsamorphous solubility liquid-liquid phase separation membrane flux drug-rich nanodroplets drug adsorption onto silica

F2

Topic 1Amorphous solubility as common reference2 of 3

A second drug, a polymer or a bile salt that mixes into the drug-rich phase lowers the amorphous solubility.

With 10 µM lopinavir, paclitaxel or felodipine in solution, ritonavir separated at about 14, 10 and 12 instead of about 26 µg/mL trasi2015a R7, R9, R11. The same lowering appeared in two-drug dispersions, in a co-granule, next to a crystalline co-drug, with HPMCAS-HF and with taurocholate alhalaweh2016 R10, X8, R12, R13, E7, R17; trasi2019 R4, M1, M2; alkalla2026 R7, R9, R13, C25, C26, C28, C29; ueda2020a R1; wilson2021 R8; indulkar2018 R6.

strongStrong for the lowering itself, measured by fluorescence, ultracentrifugation, flux or NMR in each category; moderate for the mechanism, because the composition of the drug-rich phase was calculated or inferred, not measured alhalaweh2016 K1, K3, K4, K6, K2; alkalla2026 K1, K2, K3, K6, X6.

Every added component that enters the drug-rich phase moves the ceiling down, whatever its source. trasi2015a R7, R9, R11; trasi2019 R4, M1, M2; alkalla2026 R7, R9, R13, C25, C26, C28, C29; ueda2020a R1; wilson2021 R8; indulkar2018 R6; ueda2020b R1

For your drug

For a fixed-dose combination, measure each drug's amorphous solubility alone and with the partner at its expected concentration; a fall in proportion to mole fraction means the two drugs should not share one amorphous phase, so granulate them separately.
For a co-medication test a crystalline partner too, and for a polymer grade compare the amorphous solubility with the polymer dissolved at the expected level.

trasi2015a R7, R9, R11; trasi2019 R14, R6; alkalla2026 R7, R9, R13, C25, C26, C28, C29; ueda2020a R1

How it works and key numbers

A second unionized drug mixes into the drug-rich phase and lowers each drug's activity there in proportion to its mole fraction, S_1 = S_{A1} X_1 alhalaweh2016 R12, R13, E7, R17.
Dissolving ritonavir–lopinavir films and dispersions gave five of six mixed values within 0.5 µg/mL of C_{max} = S_a\,x_d trasi2015b R5, E1.
HPMCAS-HF goes into the drug-rich phase and lowers the drug's chemical potential there, while AS-LF moved the amorphous solubility by under a tenth ueda2020a R1.
A drug that is ionized stays out of the drug-rich phase: ionized diclofenac did not lower the ritonavir ceiling trasi2015a R7, R9, R11.
(synthesis: the same ideal-mixing reading explains results in three categories; what differs is only whether the second component comes from the formulation, the co-medication or the medium.)

about 4 vs about 30 µg/mLritonavir from a ritonavir–lopinavir co-granule against granules of ritonavir alone, pH 6.8trasi2019 R4, M1, M2

9.5 × 10⁻⁵ to 2.9 × 10⁻⁵ µg·min⁻¹·cm⁻²atazanavir flux plateau across cellulose next to darunavir hydratealkalla2026 R7, R9, R13, C25, C26, C28, C29

about 160–188 vs about 169 µg/mLritonavir from separate granules against the marketed tablettrasi2019 R14, R6

Evidence: data, conditions and papers

Finding F2. A component that mixes into the drug-rich phase lowers the ceiling in every system tested: a second drug in one dispersion, one granule or a co-dose, a crystalline co-drug, a hydrophobic polymer grade, a dissolved polymer and a bile salt

In short. With 10 µM lopinavir, paclitaxel or felodipine in solution ritonavir separated at about 14, 10 and 12 instead of about 26 µg/mL, while ionized diclofenac stayed out of the ritonavir-rich phase trasi2015a R7, R9, R11 (Dissolution F3). In 90% PVP dispersions ritonavir and atazanavir at 1:1 held about half their single-drug level, and across compositions the free concentration of each drug fell linearly with its mole fraction alhalaweh2016 R10, X8, R12, R13, E7, R17 (Bioperformance F6); in a solvent-granulated co-granule ritonavir reached only about 4 µg/mL at pH 6.8 against about 30 µg/mL from granules of ritonavir alone trasi2019 R4, M1, M2 (ASD process F23). A crystalline co-drug acted too: next to darunavir hydrate atazanavir from a 10% PVP dispersion held about 56 instead of 81 µg/mL at 2 h alkalla2026 R7, R9, R13, C25, C26, C28, C29 (Bioperformance F20). Polymers lowered it as well: HPMCAS-HF lowered the amorphous solubility of atazanavir from 81.5 to 35.5 µg/mL ueda2020a R1 (Bioperformance F19), and taurocholate that of atazanavir from 65 to 38 µg/mL wilson2021 R8; indulkar2018 R6 (Dissolution F3).

Type. cross-category synthesis of 7 source findings (two-drug solutions, dispersions, granules and co-doses; a crystalline co-drug; dissolved and undissolved polymers; bile salts; drug-rich nanoparticles; ritonavir, lopinavir, atazanavir, darunavir, ibuprofen, enzalutamide, telaprevir and phenolphthalein analogues) Strength. for the lowering itself, measured by fluorescence, ultracentrifugation, flux or NMR in each category (Dissolution F3, Bioperformance F6, Bioperformance F19); moderate for the mechanism, because the composition of the drug-rich phase was calculated or inferred and not measured alhalaweh2016 K1, K3, K4, K6, K2 (Bioperformance F6); alkalla2026 K1, K2, K3, K6, X6 (Bioperformance F20).

How it was shown

Dissolution added a second drug or a dissolved polymer to supersaturated solutions and read the onset of the drug-rich phase trasi2015a R7, R9, R11; trasi2015b R5, E1; ueda2020b R1. Bioperformance dissolved two-drug PVP dispersions, set two HPMCAS grades against four drugs and dissolved an atazanavir dispersion next to crystalline darunavir hydrate alhalaweh2016 R10, X8, R12, R13, E7, R17; ueda2020a R1; alkalla2026 R7, R9, R13, C25, C26, C28, C29. ASD process granulated ritonavir and lopinavir with PVPVA, together or separately trasi2019 R4, M1, M2.

What the data show

Ritonavir–lopinavir films and dispersions gave five of six mixed values within 0.5 µg/mL of C_{max} = S_a\,x_d trasi2015b R5, E1, and two-drug PVP dispersions followed S_1 = S_{A1} X_1, with Caco-2 flux from 1:1 solutions halved alhalaweh2016 R12, R13, E7, R17. HPMCAS-HF lowered clozapine from 233.0 to 95.0 µg/mL, while AS-LF moved it by under a tenth ueda2020a R1.

added component	system	result	ids
second drug in solution, 10 µM	ritonavir with lopinavir, paclitaxel, felodipine or diclofenac	about 14, 10, 12 against 26 µg/mL; ionized diclofenac no effect	trasi2015a R7, R9, R11
second drug in one granule	ritonavir–lopinavir–PVPVA co-granule, pH 6.8	ritonavir about 4 against about 30 µg/mL alone	trasi2019 R4, M1, M2
crystalline co-drug	atazanavir dispersion with darunavir hydrate	about 56 against 81 µg/mL	alkalla2026 R7, R9, R13, C25, C26, C28, C29
dissolved polymer	ibuprofen with HPMC or PVP-VA	177.1 to 96.9 and 90.7 µg/mL	ueda2020b R1
bile salt	atazanavir with taurocholate	65 to 38 µg/mL	wilson2021 R8; indulkar2018 R6

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

The analogue whose drug-rich nanoparticles hold the most PVPVA has the lowest limit of congruency deac2023b R3, R8.

Why

A second unionized drug lowers each drug's activity in the drug-rich phase in proportion to its mole fraction alhalaweh2016 R12, R13, E7, R17, and the HPMCAS-HF effect is traced to polymer that goes into the drug-rich phase and lowers the drug's chemical potential there ueda2020a R1. For darunavir the authors infer mixing into the atazanavir-rich phase helped by water alkalla2026 K1, K2, K3, K6, X6. (synthesis: the same ideal-mixing reading explains results in three categories; only the source of the second component differs.)

Limits and transfer

The mole-fraction law rests on a calculated drug-rich phase composition alhalaweh2016 K1, K3, K4, K6, K2, and the grade effect on an indirect NMR read-out at one polymer level ueda2020a K1, K3, K4, X4, X5, X10. For a fixed-dose combination measure each drug's amorphous solubility alone and with the partner trasi2015a R7, R9, R11; separate granulation restored ritonavir release to about 160–188 µg/mL against about 169 for the marketed tablet trasi2019 R14, R6.

How it was shown

Dissolution added a second drug or a dissolved polymer to supersaturated solutions and read the onset of the drug-rich phase, and dissolved ritonavir–lopinavir films and dispersions trasi2015a R7, R9, R11; trasi2015b R5, E1; ueda2020b R1 (Dissolution F3). Bioperformance dissolved single- and two-drug PVP dispersions and measured Caco-2 flux alhalaweh2016 R10, X8, R12, R13, E7, R17 (Bioperformance F6), measured a cellulose acetate suberate dispersion of telaprevir against HPMCAS mosqueragiraldo2018b R8, R1 (Bioperformance F7), set two HPMCAS grades against four drugs ueda2020a R1 (Bioperformance F19), and dissolved an atazanavir dispersion next to crystalline darunavir hydrate alkalla2026 R7, R9, R13, C25, C26, C28, C29 (Bioperformance F20). ASD process granulated ritonavir and lopinavir with PVPVA onto lactose and cellulose, together or separately trasi2019 R4, M1, M2 (ASD process F23); trasi2019 R14, R6 (ASD process F24).

What the data show

Dissolving ritonavir–lopinavir films and dispersions gave five of six mixed values within 0.5 µg/mL of C_{max} = S_a\,x_d trasi2015b R5, E1 (Dissolution F3), and the Bioperformance dispersions followed the same ideal-mixing form, S_1 = S_{A1} X_1, with Caco-2 flux from 1:1 solutions halved alhalaweh2016 R12, R13, E7, R17 (Bioperformance F6). In the co-granule (200:50 mg lopinavir:ritonavir) lopinavir reached about 15 µg/mL against 19 µg/mL alone trasi2019 R4, M1, M2 (ASD process F23). Darunavir hydrate cut the atazanavir flux plateau across cellulose from about 9.5 × 10⁻⁵ to 2.9 × 10⁻⁵ µg·min⁻¹·cm⁻² and its Caco-2 flux by about 36%, while darunavir's own flux did not change alkalla2026 R7, R9, R13, C25, C26, C28, C29 (Bioperformance F20). Dissolved HPMC and PVP-VA lowered the amorphous solubility of ibuprofen from 177.1 to 96.9 and 90.7 µg/mL with its crystalline solubility unchanged ueda2020b R1 (Dissolution F3); HPMCAS-HF lowered clozapine from 233.0 to 95.0 and ketoconazole from 75.0 to 56.0 µg/mL, while AS-LF moved them by under a tenth ueda2020a R1 (Bioperformance F19); a cellulose acetate suberate dispersion of telaprevir gave a flux plateau of about 0.73–0.79 against about 1.05–1.18 µg/min for HPMCAS mosqueragiraldo2018b R8, R1 (Bioperformance F7). In the release chapter PVPVA lowered the amorphous solubility of phenolphthalein from 200 to 27.5 µg/mL, and the order of four analogues by polymer in their drug-rich nanoparticles was the reverse of their limits of congruency deac2023b R3, R8, R1 (Dissolution F3).

source finding	system	conditions	result	ids
Dissolution F3	ritonavir with lopinavir, paclitaxel, felodipine or diclofenac	solvent shift, onset	about 14, 10, 12 against 26 µg/mL; ionized diclofenac no effect	trasi2015a R7, R9, R11
Dissolution F3	ritonavir–lopinavir films and dispersions	dissolution	five of six within 0.5 µg/mL of C_{max} = S_a\,x_d	trasi2015b R5, E1
Bioperformance F6	ritonavir–atazanavir–PVP dispersions	dissolution, Caco-2 flux	about half the single-drug level at 1:1; linear in mole fraction	alhalaweh2016 R10, X8, R12, R13, E7, R17
ASD process F23	ritonavir–lopinavir–PVPVA co-granule	pH 6.8	ritonavir about 4 against about 30 µg/mL alone	trasi2019 R4, M1, M2
Bioperformance F20	atazanavir dispersion with crystalline darunavir hydrate	dissolution, cellulose and Caco-2 flux	about 56 against 81 µg/mL; plateau 2.9 against 9.5 × 10⁻⁵ µg·min⁻¹·cm⁻²	alkalla2026 R7, R9, R13, C25, C26, C28, C29
Bioperformance F19	atazanavir, clozapine, ketoconazole, nifedipine with HPMCAS-HF or -LF	buffer, 37 °C	HF lowers by a quarter to well over half, LF by under a tenth	ueda2020a R1
Bioperformance F7	telaprevir with cellulose acetate suberate	dispersion dissolution, diffusion cell	plateau about 0.73–0.79 against 1.05–1.18 µg/min	mosqueragiraldo2018b R8, R1
Dissolution F3	ibuprofen with HPMC or PVP-VA; atazanavir with taurocholate	dissolved additive	177.1 to 96.9 and 90.7 µg/mL; 65 to 38 µg/mL	ueda2020b R1; wilson2021 R8; indulkar2018 R6

Figure

The analogue whose drug-rich nanoparticles hold the most PVPVA has the lowest limit of congruency, and the order runs through all four deac2023b R3, R8 (Dissolution F3).

Why

In every category the authors explain the lowering by mixing in the drug-rich phase: a second unionized drug lowers each drug's activity in that phase in proportion to its mole fraction alhalaweh2016 R12, R13, E7, R17 (Bioperformance F6), and the HPMCAS-HF effect is traced to polymer that goes into the drug-rich phase and lowers the drug's chemical potential there ueda2020a R1 (Bioperformance F19). For darunavir the authors infer mixing into the atazanavir-rich phase helped by water, although the two dry amorphous drugs stayed in separate phases alkalla2026 K1, K2, K3, K6, X6 (Bioperformance F20). For the co-granule the authors attribute the pH 6.8 deficit to mutual lowering of the two amorphous solubilities in one amorphous phase, not measured on the granule trasi2019 C38, C47, X7 (ASD process F23). (synthesis: the same ideal-mixing reading explains results in three categories; what differs is only whether the second component comes from the formulation, the co-medication or the medium.)

Conditions and limits

The mole-fraction law rests on a calculated drug-rich phase composition alhalaweh2016 K1, K3, K4, K6, K2 (Bioperformance F6); the HPMCAS grade effect rests on an indirect NMR read-out at one polymer level ueda2020a K1, K3, K4, X4, X5, X10 (Bioperformance F19); the link to the limit of congruency rests on cited limits and four analogues (Dissolution F3).

Counterexamples and conflicts

Ionized diclofenac did not lower the ritonavir ceiling trasi2015a R7, R9, R11 (Dissolution F3), and in 0.1 N HCl, where ritonavir is ionized, the co-granule deficit was attributed to a lopinavir-rich surface instead trasi2019 C38, C47, X7 (ASD process F23). Below the ceiling the two HPMCAS grades transported atazanavir and clozapine alike ueda2020a R9 (Bioperformance F19).

Transfer check

For a fixed-dose combination, measure each drug's amorphous solubility alone and in the presence of the partner at its expected concentration trasi2015a R7, R9, R11 (Dissolution F3); a fall in proportion to mole fraction means the two drugs should not share one amorphous phase, and separate granulation restored ritonavir release to about 160–188 µg/mL against about 169 for the marketed tablet trasi2019 R14, R6 (ASD process F24). For a co-medication, test a crystalline partner too alkalla2026 R7, R9, R13, C25, C26, C28, C29 (Bioperformance F20). For a polymer grade, compare the amorphous solubility with the polymer dissolved at the expected level ueda2020a R1 (Bioperformance F19).

History

2015: Trasi and Taylor showed the lowering by a second drug in solution and in dissolving dispersions trasi2015a R7, R9, R11; trasi2015b R5, E1 (Dissolution F3). 2016: Alhalaweh and co-workers extended it to two-drug dispersions and Caco-2 flux alhalaweh2016 R12, R13, E7, R17 (Bioperformance F6). 2018: a polymer that entered the drug-rich phase lowered the telaprevir flux plateau mosqueragiraldo2018b R8, R1 (Bioperformance F7). 2019: the effect appeared in a manufactured co-granule trasi2019 R4, M1, M2 (ASD process F23). 2020: dissolved polymers and the HPMCAS-HF grade lowered the amorphous solubility of several drugs ueda2020b R1 (Dissolution F3); ueda2020a R1 (Bioperformance F19). 2023: the polymer content of drug-rich nanoparticles was ordered against the limit of congruency deac2023b R3, R8, R1 (Dissolution F3). 2026: a crystalline co-drug lowered the ceiling alkalla2026 R7, R9, R13, C25, C26, C28, C29 (Bioperformance F20).

Conceptsideal mixing drug-drug miscibility polymer partitioning into the drug-rich phase amorphous solubility drug-rich phase

F3

Topic 1Amorphous solubility as common reference3 of 3

Near the amorphous solubility and in micellar media, total drug misleads; free drug or flux has to be read.

In situ UV read a danazol dispersion at ≈16.2 µg/mL where flux gave 8.2 ± 1.2 µg/mL, and colloids passed 0.45 µm filters jackson2015 R2, R9; trasi2015b R6, R7, C22, C27. In six media up to human intestinal fluid the flux-based supersaturation of atazanavir stayed at about 50–56 while the solubility ratio fell from about 55 to about 14 elkhabaz2019b R8, R9. From silica, dissolution sampling read less free drug than flux at most doses dening2018 R24, C22, C36.

moderateModerate to strong: each overread or understatement is shown against a particle-blind or activity read-out in the same paper, but the flux calibration assumes that micelles do not cross the membrane and the partition coefficients were calculated vaneerdenbrugh2011b R6.a, M1; elkhabaz2019b K1, K2, K3, K5, X2.

The UV probe counts particles as dissolved drug; a particle-blind read-out on the same sample gives half to a tenth or less. jackson2015 R2, R9; vaneerdenbrugh2011b R6.a, M1; tres2018 R16, R17

Solubilizing media raise the crystalline solubility more than the amorphous one, so the solubility ratio falls while the flux-based value stays. elkhabaz2019b R8, R9

For your drug

For a new dispersion read the free drug by an ultracentrifuged supernatant with HPLC or by flux at least at one point, and add a particle control for in situ UV.
In a micellar or biorelevant medium compare formulations by flux-based supersaturation, not by concentration ratio; for silica read release in diffusion cells.

tres2018 P9; elkhabaz2019b R8, R9; dening2018 R24, C22, C36

How it works and key numbers

Particles absorb and scatter light at the UV wavelength, so in situ UV adds colloid to dissolved drug; this explanation was inferred by exclusion vaneerdenbrugh2011b K1, K3, K4, X4.
Colloids of ritonavir and lopinavir dispersions pass 0.45 µm filters, so filtration does not separate them either trasi2015b R6, R7, C22, C27.
Micelles add proportionally less drug at the amorphous than at the crystalline solubility, so the concentration ratio falls while the activity ratio stays elkhabaz2019b R8, R9.
At matched c/c* of about 4.1–4.5 felodipine flux was 0.052 in buffer, 0.085 in FaSSIF and 0.138 µg/min with TPGS, so the same c/c* gave different flux raina2015c R12.
(synthesis: in all three carriers the driving force for transport is the free drug, and every read-out that adds particles, micelles or bound drug to it changes the ranking.)

about 466 vs 36 µM10% lopinavir dispersion by UV against ultracentrifuged supernatanttres2018 R16, R17

about 33–37.5 vs 65–70concentration ratio against activity ratio of atazanavir in SDSindulkar2017a R11, R13

about 85% vs 99.2%ritonavir from SBA-15 by dissolution against flux at the highest dosedening2018 K2, K3, X8, X14

Evidence: data, conditions and papers

Finding F3. Near the ceiling and in solubilizing media the total drug concentration misleads in every category: UV counts particles, filtration passes colloids, concentration ratios understate the supersaturation, and dissolution sampling from silica reads less free drug than flux

In short. In situ UV read ≈27 µg/mL for a 90:10 HPMC–felodipine dispersion and ≈16.2 µg/mL for a danazol dispersion whose flux gave 8.2 ± 1.2 µg/mL alonzo2011 R1, R14, R15; jackson2015 R2, R9; trasi2015b R6, R7, C22, C27 (Dissolution F2), and a 300 nm felodipine suspension read 8.95 µg/mL "dissolved" against a solubility of 0.81 µg/mL vaneerdenbrugh2011b R6.a, M1 (Characterization methods F6). At c/c* of about 4.1–4.5 the flux of felodipine was 0.052 in buffer, 0.085 in FaSSIF and 0.138 µg/min with 0.04% Vit E TPGS raina2015c R12 (Bioperformance F3), and in six media up to pooled human intestinal fluid the flux-based maximum supersaturation of atazanavir stayed at about 50–56 while the ratio of amorphous to crystalline solubility fell from about 55 to about 14 elkhabaz2019b R8, R9 (Bioperformance F18). From SBA-15 silica dissolution sampling gave lower free-drug percentages than flux at most doses dening2018 R24, C22, C36 (Mesoporous silica F8).

Type. cross-category method comparison of 5 source findings (in situ UV, filtration, ultracentrifugation, flux, NMR; buffers, surfactants, simulated and human fluids; dispersions, suspensions, silica) Strength. to strong: each overread or understatement is shown against a particle-blind or activity read-out in the same paper (Dissolution F2, Characterization methods F6, Bioperformance F18), but the flux calibration assumes that micelles do not cross the membrane and most values come from one laboratory (Dissolution F2).

How it was shown

Dissolution compared in situ UV with flux, NMR and ultracentrifugation, and concentration-based with flux-based supersaturation in SDS alonzo2011 R1, R14, R15; jackson2015 R2, R9; indulkar2017a R11, R13. Characterization methods dosed suspensions of known particle size into the UV probe vaneerdenbrugh2011b R6.a, M1; tres2018 R16, R17. Bioperformance measured flux of felodipine in buffer, FaSSIF and TPGS, and of atazanavir and posaconazole in six media raina2015c R12; elkhabaz2019b R8, R9. Mesoporous silica compared dissolution sampling with membrane mass flow dening2018 R24, C22, C36.

What the data show

A 10% lopinavir dissolution read about 466 µM by UV against 36 µM in the ultracentrifuged supernatant tres2018 R16, R17, and colloids of ritonavir and lopinavir dispersions passed 0.45 µm filters trasi2015b R6, R7, C22, C27. Crystalline felodipine suspensions holding about 1 and about 40 µg/mL dissolved drug gave the same low flux raina2015c R4, R7.

read-outs compared	system	result	ids
in situ UV against flux	danazol dispersion	≈16.2 against 8.2 ± 1.2 µg/mL	jackson2015 R2, R9
UV probe against solubility	felodipine suspension	8.95 against 0.81 µg/mL	vaneerdenbrugh2011b R6.a, M1
concentration against activity	atazanavir in SDS	ratio about 33–37.5 against 65–70	indulkar2017a R11, R13
flux at c/c* about 4.1–4.5	felodipine in buffer, FaSSIF, TPGS	0.052, 0.085, 0.138 µg/min	raina2015c R12
flux ratio against solubility ratio	atazanavir, posaconazole, six media	flux-based about 50–56 and 29–37 throughout; solubility ratio 55 and 36 to 14 and 5	elkhabaz2019b R8, R9
dissolution sampling against mass flow	ritonavir–SBA-15	dissolution lower at most doses	dening2018 R24, C22, C36

Fig. 7 of indulkar2017a: concentration-based and activity-based supersaturation of atazanavir in SDS — Fig. 7 · indulkar2017aconcentration-based and activity-based supersaturation of atazanavir in SDS

At each SDS level the concentration-based supersaturation lies near half of the activity-based value, which stays at the buffer level indulkar2017a R11, R13.

Why

Particles absorb and scatter light at the UV wavelength, an explanation inferred by exclusion vaneerdenbrugh2011b K1, K3, K4, X4. Micelles add proportionally less drug at the amorphous than at the crystalline solubility, so the concentration ratio falls while the activity ratio stays elkhabaz2019b R8, R9. (synthesis: the driving force for transport is the free drug, and every read-out that adds particles, micelles or bound drug to it changes the ranking.)

Limits and transfer

The micellar partition coefficients were calculated from solubilities elkhabaz2019b K1, K2, K3, K5, X2, and at the highest silica dose dissolution (about 85%) and flux (99.2%) disagreed in the other direction dening2018 K2, K3, X8, X14. For a new dispersion read the free drug by ultracentrifuged supernatant or flux at least at one point and add a particle control for in situ UV tres2018 P9; in a micellar or biorelevant medium compare formulations by flux-based supersaturation elkhabaz2019b R8, R9.

How it was shown

Dissolution compared in situ UV with flux, NMR and ultracentrifugation for dissolving dispersions, compared concentration-based and flux-based supersaturation in SDS and in bile salts, and assayed the polymer beside the drug from compacts alonzo2011 R1, R14, R15; jackson2015 R2, R9; indulkar2017a R11, R13; indulkar2019a R12, R13 (Dissolution F2). Characterization methods dosed suspensions of known particle size into the UV probe and compared UV with ultracentrifuged supernatants of dissolving dispersions vaneerdenbrugh2011b R6.a, M1; tres2018 R16, R17 (Characterization methods F6). Bioperformance measured flux of felodipine at matched c/c* in buffer, FaSSIF and TPGS raina2015c R12 (Bioperformance F3), and of atazanavir and posaconazole in six media elkhabaz2019b R8, R9 (Bioperformance F18). Mesoporous silica compared dissolution sampling with membrane mass flow dening2018 R24, C22, C36 (Mesoporous silica F8).

What the data show

A 10% lopinavir dissolution read about 466 µM by UV against 36 µM in the ultracentrifuged supernatant tres2018 R16, R17 (Characterization methods F6); colloids of HPMCAS dispersions of ritonavir and lopinavir passed 0.45 µm filters trasi2015b R6, R7, C22, C27 (Dissolution F2). In SDS the ratio of total concentration to crystalline solubility at the amorphous solubility of atazanavir was about 33–37.5 and the ratio of flux-derived activities about 65–70, as in buffer indulkar2017a R11, R13 (Dissolution F2). For posaconazole the crystalline solubility rose 14-fold from buffer to FaSSIF-V1 but the amorphous solubility only 5-fold, and the flux-based value stayed at about 29–37 elkhabaz2019b R8, R9, R1, R2 (Bioperformance F18). Crystalline felodipine suspensions holding about 1 and about 40 µg/mL dissolved drug gave the same low flux raina2015c R4, R7 (Bioperformance F3). For release the drug curve alone did not show the regime: assaying the polymer from a compact of constant area did indulkar2019a R12, R13; indulkar2017b R8, R9, R1 (Dissolution F2).

source finding	system	conditions	result	ids
Dissolution F2	felodipine, danazol, ritonavir, lopinavir dispersions	in situ UV, filtration against flux and ultracentrifugation	UV ≈16.2 against 8.2 ± 1.2 µg/mL (danazol); colloids pass 0.45 µm	alonzo2011 R1, R14, R15; jackson2015 R2, R9; trasi2015b R6, R7, C22, C27
Characterization methods F6	felodipine suspensions; lopinavir dispersion	UV probe against solubility and supernatant	8.95 against 0.81 µg/mL; about 466 against 36 µM	vaneerdenbrugh2011b R6.a, M1; tres2018 R16, R17
Dissolution F2	atazanavir in SDS	concentration against activity	ratio about 33–37.5 against 65–70	indulkar2017a R11, R13
Bioperformance F3	felodipine, buffer, FaSSIF, TPGS	flux at c/c* about 4.1–4.5	0.052, 0.085, 0.138 µg/min	raina2015c R12
Bioperformance F18	atazanavir, posaconazole, six media	flux ratio against solubility ratio	flux-based about 50–56 and 29–37 throughout; solubility ratio 55 and 36 to 14 and 5	elkhabaz2019b R8, R9
Mesoporous silica F8	ritonavir–SBA-15	dissolution sampling against mass flow	dissolution lower at most doses; diffusion cells recommended	dening2018 R24, C22, C36

Figure

At each SDS level the concentration-based supersaturation at the amorphous solubility lies near half of the activity-based value, which stays at the buffer level indulkar2017a R11, R13 (Dissolution F2).

Why

Particles absorb and scatter light at the UV wavelength, an explanation inferred by exclusion vaneerdenbrugh2011b K1, K3, K4, X4 (Characterization methods F6). Micelles add proportionally less drug at the amorphous than at the crystalline solubility, so the concentration ratio falls while the activity ratio stays elkhabaz2019b R8, R9 (Bioperformance F18). (synthesis: in all three carriers the driving force for transport is the free drug, and every read-out that adds particles, micelles or bound drug to it changes the ranking.)

Conditions and limits

The flux calibration assumes that micelles do not cross the membrane (Dissolution F2); the micellar partition coefficients were calculated from solubilities elkhabaz2019b K1, K2, K3, K5, X2 (Bioperformance F18); the UV failures each rest on one or two drugs (Characterization methods F6).

Counterexamples and conflicts

At the highest silica dose dissolution (about 85% of the amorphous solubility) and flux (99.2%) disagreed in the other direction dening2018 K2, K3, X8, X14 (Mesoporous silica F8).

Transfer check

For a new dispersion read the free drug by an ultracentrifuged supernatant with HPLC or by flux at least at one point, and add a particle control for in situ UV tres2018 P9 (Characterization methods F6); in a micellar or biorelevant medium compare formulations by flux-based supersaturation, not by concentration ratio elkhabaz2019b R8, R9 (Bioperformance F18).

History

2011: UV overreading by particles was shown for felodipine suspensions and dispersions vaneerdenbrugh2011b R6.a, M1 (Characterization methods F6); alonzo2011 R1, R14, R15 (Dissolution F2). 2015: solubilizers that raised the crystalline solubility lowered the flux at fixed concentration raina2015c R4, R7 (Bioperformance F3). 2017–2018: the activity scale was set out in SDS, and UV against supernatant was compared for lopinavir dispersions indulkar2017a R11, R13 (Dissolution F2); tres2018 R16, R17 (Characterization methods F6); silica release was read by flux dening2018 R24, C22, C36 (Mesoporous silica F8). 2019: six media including pooled human fluid were compared on both scales elkhabaz2019b R8, R9 (Bioperformance F18).

Conceptsfree drug concentration supersaturation ratio micellar solubilization light scattering by particles membrane flux

Topic 2 of 5 · 4 findings · F4–F7

Crystals from neat drug to exposure

F4

Topic 2Crystals from neat drug to exposure1 of 4

The crystallization class of the neat drug orders drugs within one test, but carriers, routes and polymers override it.

In dry storage a class I glass crystallized fully within a day and class III glasses only at the edges after 3 months baird2010 R23, R25. In PEG, in supersaturated solution and above Tg, drugs that were slow from the melt crystallized within minutes to hours zhu2012 R2, R3, R23.a; raina2015b C13, C28; moseson2020 R7. Class I pretomanid in solution was held by only one polymer nguyen2023a R5.

moderateModerate: the order within one test is direct but rests on one or two compounds per class, the solution comparison rests on few compounds each, and each break rests on one or two systems baird2010 R23, R25; raina2015b C13, C28.

A carrier or a solution changed the time to crystals by orders of magnitude for drugs of known class. zhu2012 R2, R3, R23.a; nguyen2023a R5

No bulk glass property separated the classes; all 28 melts fitted with the VTF equation were fragile. baird2010 R14, C37; baird2012 R12, C39

For your drug

Classify the drug by one heat–cool–heat cycle and treat class I as a flag for more polymer and stricter storage.
Then measure the induction time of its supersaturated solution with and without the candidate polymers, and before a melt process hold the undercooled melt at the intended temperature and reheat to see whether it has nucleated.

baird2010 C46; vaneerdenbrugh2010b C1; nguyen2023a R5; moseson2020 R7

How it works and key numbers

The class comes from one heat–cool–heat DSC cycle of the neat drug, and Baird and co-workers saw it as a qualitative first risk flag baird2010 C46; vaneerdenbrugh2010b C1.
Within one test the order held: class I drugs had the lowest amorphous index across seven polymers vaneerdenbrugh2010b R4.
In water the second phase is seen only if nucleation is slow relative to LLPS, which is why felodipine passed its amorphous solubility while nifedipine crystallized just below it raina2014a C30, C31, R20.
Held between Tg and Tm for 1 h, the class III drugs posaconazole and bicalutamide nucleated, while indomethacin held 4 h did not moseson2020 R7.
(synthesis: the class measures the neat drug under one thermal history; each later category adds a carrier, a route, water or a polymer that acts on nucleation or growth separately, so the class orders drugs only inside a test that holds those constant.)

1 day vs 3 monthsindoprofen (class I) fully crystalline against clotrimazole and felodipine (class III) at the edges onlybaird2010 R23, R25

within a week vs 3 monthslumefantrine (class III) with PVPVA against HPMCP, Eudragit L100 and CAP at 40% drugtrasi2020 R3, C6

1.6–3.1 min vs more than 1000 minpretomanid crystals with most enteric polymers against HPMCAS-HFnguyen2023a R5

Evidence: data, conditions and papers

Finding F4. The crystallization class of the neat drug is used as a first flag in every category, but no category found it sufficient: carriers, routes and polymers overrode it in storage, solution rankings were finer than the classes, and slow-crystallizing class III drugs nucleated within an hour above Tg

In short. In dry storage and in a spin-coated polymer screen the class of the neat drug kept its order: a class I glass crystallized fully within a day and class III glasses only at the edges after 3 months, and class I drugs had the lowest amorphous index across seven polymers baird2010 R23, R25; vaneerdenbrugh2010b R4 (Solid state stability F1). In water some orderings carried over, felodipine, slow from the melt, passing its amorphous solubility while nifedipine crystallized just below it, but several drugs classed as slow crystallizers from the melt crystallized readily from supersaturated solution raina2014a R20, C31; raina2015b C13, C28; ilevbare2013c R8, C24; hsieh2014 R18, C30 (Crystallization tendency F18). Held between Tg and Tm for 1 h, neat posaconazole and bicalutamide nucleated, while indomethacin held 4 h did not moseson2020 R7 (ASD process F31). For pretomanid, a class I drug, only HPMCAS-HF held a supersaturated solution beyond 1000 min; with most enteric polymers it crystallized within about 1.6–3.1 min nguyen2023a R5 (Bioperformance F27).

Type. cross-category synthesis of 8 source findings (neat glasses, spin-coated films, PEG, PVP and HPMC dispersions, a marketed product, supersaturated solutions, undercooled melts held for extrusion tests, a supersaturation screen) Strength. : the order within one test is direct but rests on one or two compounds per class (Solid state stability F1), the solution comparison rests on several independent comparisons with few compounds each raina2015b C13, C28 (Crystallization tendency F18), and each break rests on one or two systems (Solid state stability F1).

How it was shown

Solid state stability classified neat drugs by one heat–cool–heat DSC cycle, stored quenched glasses dry, screened drugs with seven polymers and followed dispersions and marketed tacrolimus capsules on storage baird2010 R23, R25; vaneerdenbrugh2010b R4; zhu2012 R2, R3, R23.a; trasi2017 R16, C28; trasi2020 R3, C6. Other categories set the classes against crystallization from supersaturated solution and from undercooled melts held between Tg and Tm raina2015b C13, C28; moseson2020 R7; nguyen2023a R5.

What the data show

Within one test the class held baird2010 R23, R25; vaneerdenbrugh2010b R4. Across tests it broke: one tacrolimus generic crystallized faster than the pure amorphous drug trasi2017 R16, C28, and lumefantrine, a class III drug, crystallized with PVPVA within a week trasi2020 R3, C6. No bulk glass property separated the classes: mean Tg/Tm was 0.69 ± 0.02 for class I and 0.73 ± 0.04 for class III baird2010 R14, C37; baird2012 R12, C39.

test	drugs	result	ids
quenched glasses, dry storage	indoprofen (I); clotrimazole, felodipine (III)	complete within 1 day against edges only at 3 months	baird2010 R23, R25
20/80 PEG 3350, 25 °C	ibuprofen, fenofibrate	onset about 100 and 120–180 min against 10 and 17 of 50 neat melts after 3 weeks	zhu2012 R2, R3, R23.a
supersaturated aqueous solution	efavirenz, papaverine, warfarin, glyburide	melt-class slow crystallizers crystallize readily	raina2015b C13, C28; ilevbare2013c R8, C24; hsieh2014 R18, C30
1–4 h between Tg and Tm	posaconazole, bicalutamide; indomethacin	first two nucleated within 1 h; indomethacin not in 4 h	moseson2020 R7
80 µg/mL solution with enteric polymers	pretomanid (I)	crystals within about 1.6–3.1 min; HPMCAS-HF more than 1000 min	nguyen2023a R5

Fig. 4 of vaneerdenbrugh2010b: average amorphous index per drug across seven polymers — Fig. 4 · vaneerdenbrugh2010baverage amorphous index per drug across seven polymers

The class I drugs sit lowest and the class II drugs highest, the same order as their neat-drug classes vaneerdenbrugh2010b R4.

Why

Baird and co-workers saw the class as a qualitative first risk flag baird2010 C46; vaneerdenbrugh2010b C1. The Bioperformance authors explain the nifedipine–felodipine contrast in water by the size of the metastable zone: the second phase is seen only if nucleation is slow relative to LLPS raina2014a C30, C31. (synthesis: the class measures the neat drug under one thermal history; each later category adds a carrier, a route, water or a polymer that acts on nucleation or growth separately.)

Limits and transfer

The solution comparisons used few compounds each raina2015b C13, C28, and an HPMCAS dispersion of class I pretomanid stayed amorphous for months nguyen2023a C62. Treat class I as a flag for more polymer and stricter storage baird2010 C46; vaneerdenbrugh2010b C1, measure the induction time of the supersaturated solution with and without the candidate polymers nguyen2023a R5, and before a melt process hold the undercooled melt at the intended temperature and reheat to see whether it has nucleated moseson2020 R7.

How it was shown

Solid state stability classified neat drugs by one heat–cool–heat DSC cycle and by spin coating, stored quenched glasses dry, screened drugs with seven polymers, and followed PEG, PVP and HPMC dispersions and marketed tacrolimus capsules on storage baird2010 R23, R25; vaneerdenbrugh2010b R4; zhu2012 R2, R3, R23.a; trasi2017 R16, C28; trasi2020 R3, C6 (Solid state stability F1). Its chapter Crystallization tendency set the melt classes against crystallization from supersaturated solution for dihydropyridines, weak bases and other drugs raina2015b C13, C28; ilevbare2013c R8, C24; hsieh2014 R18, C30 (Crystallization tendency F18). ASD process held undercooled melts of three drugs between Tg and Tm by DSC before testing degradation moseson2020 R7 (ASD process F31). Bioperformance screened polymers for a supersaturated solution of pretomanid at 80 µg/mL nguyen2023a R5 (Bioperformance F27).

What the data show

Within one test the class held: indoprofen (class I) was fully crystalline after 1 day while clotrimazole and felodipine (class III) crystallized only at the edges after 3 months, and class I drugs had the lowest amorphous index across seven polymers baird2010 R23, R25; vaneerdenbrugh2010b R4 (Solid state stability F1). Across tests it broke: ibuprofen and fenofibrate began to crystallize in 20/80 PEG 3350 after about 100 and 120–180 min although only 10 and 17 of 50 neat melts had started after 3 weeks zhu2012 R2, R3, R23.a (Solid state stability F1); one tacrolimus generic crystallized faster than the pure amorphous drug trasi2017 R16, C28 (Solid state stability F1); lumefantrine, a class III drug, crystallized with PVPVA within a week while HPMCP, Eudragit L100 and CAP held 40% drug amorphous for 3 months trasi2020 R3, C6 (Solid state stability F1). No bulk glass property separated the classes: mean Tg/Tm was 0.69 ± 0.02 for class I and 0.73 ± 0.04 for class III, and all 28 melts fitted with the VTF equation were fragile baird2010 R14, C37; baird2012 R12, C39 (Solid state stability F2). In solution several melt-class slow crystallizers such as efavirenz, papaverine, warfarin and glyburide crystallized readily raina2015b C13, C28; ilevbare2013c R8, C24; hsieh2014 R18, C30 (Crystallization tendency F18). Above Tg the class III drugs posaconazole and bicalutamide nucleated within 1 h moseson2020 R7 (ASD process F31). The class I drug pretomanid nucleated within 2 min near its amorphous solubility nguyen2023a R1, R5 (Bioperformance F10), and solvent granulation was judged best suited to low-dose, slowly crystallizing drugs trasi2019 C50, C33 (ASD process F22).

source finding	system	conditions	result	ids
Solid state stability F1	indoprofen (I), clotrimazole and felodipine (III)	quenched glasses, dry storage	complete within 1 day against edges only at 3 months	baird2010 R23, R25
Solid state stability F1	ibuprofen, fenofibrate in 20/80 PEG 3350	25 °C	onset about 100 and 120–180 min against 10 and 17 of 50 neat melts after 3 weeks	zhu2012 R2, R3, R23.a
Solid state stability F1	lumefantrine (III) with five polymers	40 °C/75% RH	PVPVA within a week; HPMCP, Eudragit L100, CAP amorphous 3 months	trasi2020 R3, C6
Solid state stability F2	51 molecules; 28 melts	Tg/Tm; VTF fits	0.69 ± 0.02 against 0.73 ± 0.04, not different; all fragile	baird2010 R14, C37; baird2012 R12, C39
Crystallization tendency F18	felodipine, nifedipine; efavirenz, papaverine, warfarin, glyburide	supersaturated aqueous solution	felodipine passes LLPS, nifedipine crystallizes; melt-class slow crystallizers crystallize readily	raina2014a R20, C31; raina2015b C13, C28; ilevbare2013c R8, C24; hsieh2014 R18, C30
ASD process F31	posaconazole, bicalutamide, indomethacin	1–4 h between Tg and Tm	first two nucleated within 1 h; indomethacin not in 4 h	moseson2020 R7
Bioperformance F27	pretomanid with enteric polymers	80 µg/mL solution	crystals within about 1.6–3.1 min; HPMCAS-HF more than 1000 min	nguyen2023a R5

Figure

The class I drugs sit lowest and the class II drugs highest, the same order as their neat-drug classes vaneerdenbrugh2010b R4 (Solid state stability F1).

Why

Baird and co-workers saw the class as a qualitative first risk flag baird2010 C46; vaneerdenbrugh2010b C1 (Crystallization tendency F17). The Bioperformance authors explain the nifedipine–felodipine contrast in water by the size of the metastable zone: the second phase is seen only if nucleation is slow relative to LLPS raina2014a C30, C31 (Bioperformance F10). For the tacrolimus generic the authors write that the result "strongly suggests" a processing cause trasi2017 R16, C28 (Solid state stability F1). (synthesis: the class measures the neat drug under one thermal history; each later category adds a carrier, a route, water or a polymer that acts on nucleation or growth separately, so the class orders drugs only inside a test that holds those constant.)

Conditions and limits

The classes come from DSC of melts and spin coating; the storage test used one or two compounds per class (Solid state stability F1); the solution comparisons used few compounds each (Crystallization tendency F18); the 1 h holds are single DSC series (ASD process F31).

Counterexamples and conflicts

An HPMCAS dispersion of class I pretomanid stayed amorphous for months nguyen2023a C62 (Crystallization tendency F17), whereas its supersaturated solution was held by only one polymer nguyen2023a R5 (Bioperformance F27).

Transfer check

Classify the new drug by one heat–cool–heat cycle and treat class I as a flag for more polymer and stricter storage baird2010 C46; vaneerdenbrugh2010b C1 (Crystallization tendency F17); then measure the induction time of its supersaturated solution with and without the candidate polymers nguyen2023a R5 (Bioperformance F27), and, before choosing a melt process, hold the undercooled melt at the intended temperature and reheat to see whether it has nucleated moseson2020 R7 (ASD process F31).

History

2010: the classes were set out and tested in storage and in a polymer screen baird2010 R23, R25; vaneerdenbrugh2010b R4 (Solid state stability F1). 2012: PEG broke the order zhu2012 R2, R3, R23.a (Solid state stability F1). 2014–2015: solution tests found the classes only partly predictive raina2014a R20, C31; raina2015b C13, C28 (Crystallization tendency F18). 2017: a marketed tacrolimus generic crystallized faster than the neat drug trasi2017 R16, C28 (Solid state stability F1). 2019–2020: solvent granulation was tied to slow crystallizers, and class III melts nucleated in 1 h holds trasi2019 C50, C33 (ASD process F22); moseson2020 R7 (ASD process F31). 2023: a class I drug was held in solution by one polymer only nguyen2023a R5 (Bioperformance F27).

Conceptscrystallization tendency classification crystallization tendency reduced glass transition temperature nucleation induction time

F5

Topic 2Crystals from neat drug to exposure2 of 4

Polymers slow nucleation far more than growth, so crystals already present bypass them, and rankings do not transfer.

In solution 1 µg/mL HPMC slowed felodipine growth 1.6-fold but nucleation about 1,400-fold alonzo2012 R5, R16, R17. In a hydrating bicalutamide solid HPMCAS, a strong growth inhibitor in solution, delayed crystallization by only about 10 min moseson2021 R5, R19, R20. The best enzalutamide inhibitor in solution gave a dispersion with the exposure of a crystalline slurry in rats wilson2020 R1, C32, R6.

strongStrong for the contrast between nucleation and growth inhibition in solution, measured with seeded and unseeded runs in several drugs; moderate in the supercooled liquid and for the rat result, three rats per arm and one shared loading alonzo2012 R5, R16, R17; wilson2020 K1, K4, X15, X16.

In both pairs the polymer acts on nucleation one to three orders of magnitude more than on growth. alonzo2012 R5, R16, R17; xie2016a R12, R13, C40

The longest solution inhibitor gave a dispersion no better than crystals; the authors propose the polymer did not dissolve. wilson2020 R1, C32, R6

For your drug

Test a candidate polymer in three set-ups before ranking: unseeded induction time, seeded growth at the intended supersaturation, and dissolution of the dispersion itself.
Check that the polymer dissolves from the dispersion at the drug loading used.

alonzo2012 R5, R16, R17, R18; moseson2021 R5, R19, R20; wilson2020 M2, M3

How it works and key numbers

In solution a polymer acts mainly on nucleation: 5–50 µg/mL dissolved PVPVA prevented indomethacin nucleation for more than 12 h but slowed seeded growth 18- to 56-fold moseson2020a R3, R4, R5, C11, C12.
The growth inhibition of indomethacin is attributed to polymer adsorbed on the crystal; AFM showed polymer globules spaced 160 ± 50 nm at 5 µg/mL and 70 ± 20 nm at 50 µg/mL moseson2020a R12, R13.
When crystals are already present the nucleation step is bypassed: seeded felodipine with HPMC fell from about 5.1 to 2.2 µg/mL within 58 min while the unseeded solution held alonzo2012 R18.
For the rat result the authors propose that the drug suppressed the dissolution of the insoluble polymer, which was not measured; CPHPC-106 dissolves (cited 43.5 mg/mL) and CA Sub does not (3.0 mg/mL) wilson2020 M2, M3, K1, K4, X15, X16.
(synthesis: a polymer in solution acts where nucleation has not yet happened; a crystal already present, a hydrating solid or a polymer that does not dissolve from the dispersion removes the step on which the ranking was made.)

To feel the numbers. For felodipine with HPMC the polymer acted about 1,400 ÷ 1.6 ≈ 875 times more strongly on nucleation than on growth.

1.3 × 10⁵ to 2.3–3.0 × 10³ m⁻³ s⁻¹felodipine nucleation rate in dry films with 3% PVP, HPMC or HPMCAS, polymers alikekonno2006 R4, C13, C14

26 vs 10.8 nuclei per cycleacetaminophen with PAA, the best growth inhibitor, against drug alonetrasi2012a R6, R12

≈99.5% vs ≈74.5%posaconazole with HPMCAS without and with 10 µg/mL form I seedsshah2024 R22

Evidence: data, conditions and papers

Finding F5. Polymers act on nucleation far more than on growth, in the supercooled liquid and in solution, so crystals already present bypass them, and a polymer ranked for one step or one place did not carry to another: the best solution inhibitor of enzalutamide gave a dispersion no better than crystals in rats

In short. In dry felodipine films 3% PVP, HPMC or HPMCAS lowered the nucleation rate from about 1.3 × 10⁵ to 2.3–3.0 × 10³ m⁻³ s⁻¹ and did not differ, whereas melt growth of the same drug was slowed about 10-, 6.5-, 4.4- and 1.2-fold by PVP, PVP/VA, HPMCAS and PVAc konno2006 R4, C13, C14; kestur2010a R6 (Solid state stability F4). In solution 1 µg/mL HPMC slowed felodipine growth 1.6-fold but nucleation about 1,400-fold alonzo2012 R5, R16, R17 (Dissolution F4), and 5–50 µg/mL dissolved PVPVA prevented indomethacin nucleation for more than 12 h but slowed seeded growth 18- to 56-fold moseson2020a R3, R4, R5, C11, C12 (ASD process F25). HPMCAS, a strong inhibitor of bicalutamide growth in solution, delayed the crystallization of the hydrating solid by only about 10 min moseson2021 R5, R19, R20 (ASD process F27). The best enzalutamide inhibitors in solution held it more than 16 h, yet the cellulose acetate suberate dispersion gave an AUC of 45 µg·h/mL in rats, like the crystalline slurry (43.1), while dispersions of CPHPC-106, which held the solution only about 0.7 h, gave 516 and 305 wilson2020 R1, C32, R6 (Bioperformance F24).

Type. cross-category synthesis of 7 source findings (felodipine, acetaminophen, celecoxib, indomethacin, bicalutamide, posaconazole, enzalutamide and nevirapine; supercooled liquids, solutions, hydrating solids, rats) Strength. for the contrast between nucleation and growth inhibition in solution, measured with seeded and unseeded runs in several drugs (Dissolution F4); moderate in the supercooled liquid, where nucleation was counted per thermal cycle or inferred (Solid state stability F4); moderate for the rat result, three rats per arm and one shared loading wilson2020 K1, K4, X15, X16 (Bioperformance F24).

How it was shown

Solid state stability counted nucleation in dry felodipine films and measured melt growth with polymers konno2006 R4, C13, C14; kestur2010a R6. Dissolution and ASD process measured induction times and seeded growth in supersaturated solutions with dissolved polymers and followed a hydrating bicalutamide solid by PLM and Raman alonzo2012 R5, R16, R17; xie2016a R12, R13, C40; moseson2020a R3, R4, R5, C11, C12; moseson2021 R5, R19, R20. Bioperformance screened 24 polymers on enzalutamide in solution and dosed two as dispersions to rats wilson2020 R1, C32, R6.

What the data show

In acetaminophen PAA cut growth at 80 °C from about 5.3 to 0.43 µm/s yet left 26 nuclei per cycle against 10.8 for the drug alone trasi2012a R6, R12. Polymers did not hold a solution that contained crystals: seeded felodipine with HPMC fell from about 5.1 to 2.2 µg/mL within 58 min while the unseeded solution held alonzo2012 R18.

system	conditions	result	ids
felodipine with 3% PVP, HPMC, HPMCAS; four polymers in the melt	dry films; melt growth	nucleation 1.3 × 10⁵ to 2.3–3.0 × 10³ m⁻³ s⁻¹, polymers alike; growth 10-, 6.5-, 4.4-, 1.2-fold	konno2006 R4, C13, C14; kestur2010a R6
felodipine with HPMC; celecoxib with HPMCAS	supersaturated solution	growth 1.6- and 70-fold; nucleation about 1,400- and ~4000-fold	alonzo2012 R5, R16, R17; xie2016a R12, R13, C40
indomethacin, bicalutamide with PVPVA or HPMCAS	pH 4.5 buffer, seeded and unseeded	no nucleation over 12 h; growth 18–56-fold; bicalutamide 8.6- and 158-fold	moseson2020a R3, R4, R5, C11, C12; moseson2021 R5
bicalutamide–PVPVA extrudate, HPMCAS in medium	hydrating solid, PLM and Raman	delay of about 10 min, growth rate unchanged	moseson2021 R5, R19, R20
enzalutamide, 24 polymers; two dispersions	solution; rats, 50 mg/kg	best inhibitors more than 16 h; CA Sub dispersion AUC 45 against slurry 43.1; CPHPC-106 516 and 305	wilson2020 R1, C32, R6

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

The ASD process authors attribute the growth inhibition of indomethacin to polymer adsorbed on the crystal, seen by AFM as globules moseson2020a R12, R13. For the rat result the authors propose that the drug suppressed the dissolution of the insoluble polymer, which was not measured; CPHPC-106 dissolves (cited 43.5 mg/mL) and CA Sub does not (3.0 mg/mL) wilson2020 M2, M3, K1, K4, X15, X16. (synthesis: a polymer in solution acts where nucleation has not yet happened; a crystal already present, a hydrating solid or a polymer that does not dissolve removes the step on which the ranking was made.)

Limits and transfer

The hydrating-solid kinetics came from 10 mg/mL slurries moseson2021 K1, K7, X8, X11. Test a candidate polymer in three set-ups before ranking: unseeded induction time, seeded growth at the intended supersaturation, and dissolution of the dispersion itself alonzo2012 R5, R16, R17, R18; moseson2021 R5, R19, R20. Check that the polymer dissolves from the dispersion at the drug loading used wilson2020 M2, M3.

How it was shown

Solid state stability counted nucleation in dry films and measured melt growth with polymers, and counted nuclei per cooling–reheating cycle in acetaminophen konno2006 R4, C13, C14; kestur2010a R6; trasi2012a R6, R12 (Solid state stability F4). Dissolution measured induction times and seeded growth in supersaturated solutions with dissolved polymers alonzo2012 R5, R16, R17; xie2016a R12, R13, C40 (Dissolution F4). ASD process measured nucleation and seeded growth of indomethacin, bicalutamide and posaconazole with PVPVA or HPMCAS moseson2020a R3, R4, R5, C11, C12; moseson2021 R5; shah2024 R22 (ASD process F25) and followed the hydrating bicalutamide solid by PLM and Raman moseson2021 R5, R19, R20 (ASD process F27). Bioperformance screened 24 polymers on enzalutamide in solution and dosed two of them as dispersions to rats wilson2020 R1, C32, R6 (Bioperformance F24).

What the data show

In acetaminophen PAA cut growth at 80 °C from about 5.3 to 0.43 µm/s yet left 26 nuclei per cycle against 10.8 for the drug alone, while HPMCAS, a weak growth inhibitor, left 2.5 trasi2012a R6, R12 (Solid state stability F4). In solution 5 µg/mL HPMCAS slowed celecoxib growth about 70-fold but nucleation an estimated ~4000-fold xie2016a R12, R13, C40 (Dissolution F4). Polymers did not hold a solution that contained crystals: seeded felodipine with HPMC fell from about 5.1 to 2.2 µg/mL within 58 min while the unseeded solution held alonzo2012 R18 (Dissolution F4); with HPMCAS at nine times the drug, posaconazole in FaSSIF V2 stayed near its start without seeds (≈99.5% at 30 min) but fell to ≈74.5% with 10 µg/mL form I seeds shah2024 R22 (ASD process F25). The growth factor depended on the pair: PVPVA slowed seeded bicalutamide growth only 8.6-fold and HPMCAS 158-fold moseson2021 R5 (ASD process F25). Nevirapine at 500 µg/mL crystallized in about 5 min without polymer, at about 60 min with 0.1% PVPVA and not within 4 h with 0.05% HPMC-AS hate2017 R2 (Bioperformance F10). A solution screen ranked dispersion dissolution only in order jackson2015 R5, X8; xie2015 C48 (Dissolution F9).

source finding	system	conditions	result	ids
Solid state stability F4	felodipine with 3% PVP, HPMC, HPMCAS; four polymers in the melt	dry films; melt growth	nucleation 1.3 × 10⁵ to 2.3–3.0 × 10³ m⁻³ s⁻¹, polymers alike; growth 10-, 6.5-, 4.4-, 1.2-fold	konno2006 R4, C13, C14; kestur2010a R6
Solid state stability F4	acetaminophen with PAA or HPMCAS	cooling–reheating cycles	PAA best growth inhibitor, 26 nuclei per cycle against 10.8 alone; HPMCAS 2.5	trasi2012a R6, R12
Dissolution F4	felodipine with HPMC; celecoxib with HPMCAS	supersaturated solution	growth 1.6- and 70-fold; nucleation about 1,400- and ~4000-fold	alonzo2012 R5, R16, R17; xie2016a R12, R13, C40
Dissolution F4	felodipine with HPMC, seeded	solution	5.1 to 2.2 µg/mL within 58 min	alonzo2012 R18
ASD process F25	indomethacin, bicalutamide with PVPVA or HPMCAS	pH 4.5 buffer, seeded and unseeded	no nucleation over 12 h; growth 18–56-fold; bicalutamide 8.6- and 158-fold	moseson2020a R3, R4, R5, C11, C12; moseson2021 R5
ASD process F27	bicalutamide–PVPVA extrudate, HPMCAS in medium	hydrating solid, PLM and Raman	delay of about 10 min, growth rate unchanged	moseson2021 R5, R19, R20
Bioperformance F24	enzalutamide, 24 polymers; two dispersions	solution; rats, 50 mg/kg	best inhibitors more than 16 h; CA Sub dispersion AUC 45 against slurry 43.1; CPHPC-106 516 and 305	wilson2020 R1, C32, R6

Figure

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 (Solid state stability F4).

Why

The ASD process authors attribute the growth inhibition of indomethacin to polymer adsorbed on the crystal: AFM showed polymer globules spaced 160 ± 50 nm at 5 µg/mL and 70 ± 20 nm at 50 µg/mL moseson2020a R12, R13 (ASD process F25). For the rat result the authors propose that the drug suppressed the dissolution of the insoluble polymer, which was not measured; CPHPC-106 dissolves (cited 43.5 mg/mL) and CA Sub does not (3.0 mg/mL) wilson2020 M2, M3, K1, K4, X15, X16 (Bioperformance F24). (synthesis: a polymer in solution acts where nucleation has not yet happened; a crystal already present, a hydrating solid or a polymer that does not dissolve from the dispersion removes the step on which the ranking was made.)

Conditions and limits

Nucleation in the supercooled liquid was never measured as a rate at storage temperature (Solid state stability F4); the hydrating-solid kinetics came from 10 mg/mL slurries moseson2021 K1, K7, X8, X11 (ASD process F27); the rat study had three animals per arm (Bioperformance F24).

Counterexamples and conflicts

HPMCAS slowed bicalutamide growth 158-fold, a large growth effect, yet did not protect the hydrating solid moseson2021 R5, R19, R20 (ASD process F27).

Transfer check

Test a candidate polymer in three set-ups before ranking: unseeded induction time, seeded growth at the intended supersaturation, and dissolution of the dispersion itself alonzo2012 R5, R16, R17, R18 (Dissolution F4); moseson2021 R5, R19, R20 (ASD process F27). Check that the polymer dissolves from the dispersion at the drug loading used wilson2020 M2, M3 (Bioperformance F24).

History

2006: polymers were shown to lower dry nucleation alike konno2006 R4, C13, C14 (Solid state stability F4). 2010–2012: melt growth and acetaminophen nucleation separated the two steps kestur2010a R6; trasi2012a R6, R12 (Solid state stability F4); in solution HPMC acted on nucleation far more than on growth and failed with seeds alonzo2012 R5, R16, R17, R18 (Dissolution F4). 2016–2017: the contrast was measured for celecoxib, and nevirapine was held only by HPMC-AS xie2016a R12, R13, C40 (Dissolution F4); hate2017 R2 (Bioperformance F10). 2020–2021: polymers that held solutions did not protect the hydrating solid moseson2020a R3, R4, R5, C11, C12 (ASD process F25); moseson2021 R5, R19, R20 (ASD process F27), and the best solution inhibitor failed in rats wilson2020 R1, C32, R6 (Bioperformance F24). 2024: HPMCAS slowed but did not stop seeded posaconazole growth shah2024 R22 (ASD process F25).

Conceptsnucleation inhibition crystal growth inhibition seeded crystal growth nucleation and crystal growth

F6

Topic 2Crystals from neat drug to exposure3 of 4

Residual crystals cost supersaturation from the extruder to the animal; a crystallized tacrolimus capsule lost about half its exposure in dogs.

Extrusion below the critical temperature left crystals: posaconazole–HPMCAS extruded at 125 °C held 0.3, 3.2 and 19.3 wt% crystals at 10, 25 and 50% loading shah2024 R5, R10. After a pH shift the 10% extrudate with 0.3% crystals fell to about 18.5 µg/mL by 150 min, while the crystal-free one held about 125 µg/mL at 300 min shah2024 R12, R14. A generic tacrolimus capsule crystallized to 88% in 3 weeks at 40 °C/75% RH and gave about half the fresh exposure in six beagles trasi2017 R12, R18, R19; purohit2019 R9.

moderateModerate: the cost of residual crystals is direct in each system, but the systems differ in drug, polymer, loading and supersaturation, and the dog comparison joins species, doses and batches moseson2020a X5, X9; moseson2021 X11; shah2024 X14; purohit2019 X12, C40; purohit2018 C59, K6.

Crystals below the X-ray limit, or 0.3% crystals, already cut the concentration the extrudate can hold. moseson2021 R17; shah2024 R12, R14

The crystallized capsule kept about half of the fresh exposure in the same dogs. purohit2019 R9

For your drug

Set the extrusion temperature at or above the critical temperature from a temperature–composition phase diagram, allowing for the input crystal size.
Test residual crystals by a method that sees below 1% and by dissolution at the highest supersaturation the dose can reach; rank crystallinity levels by a small-volume or absorptive test, but expect the in vivo loss to sit with large-volume conditions when the dose gives low supersaturation.

moseson2018 R5, R4; shah2024 R12, R14; purohit2019 R9; hate2019 R13; purohit2018 R14, R16

How it works and key numbers

Extrusion below the critical temperature from the temperature–composition phase diagram leaves crystals: fifteen 50% indomethacin–PVPVA extrudates made below about 132 °C were never crystal-free moseson2018 R10.k–o; shah2024 R5, R10.
A dissolved polymer acts on nucleation, so it does not hold a solution that already contains crystals: seeds left HPMCAS-held paclitaxel at 7.9–25.3 µg/mL que2018 R3, R13, R14.
Residual crystals seeded more strongly than bulk seeds (extrudates with 0–25% crystallinity fell from about 43.1 to 28.8 µg/mL, bulk seeds only from about 43.2 to 39.8), which the authors attribute to small size, embedded position and possible defects, none measured moseson2020a R6, R9, R10; moseson2020a C40, X9.
The dog dose of 1 mg in about 95 mL gives at most about 10 µg/mL, the level of the large-volume tests purohit2019 R12, C40; hate2019 R7.
(synthesis: the cost of a crystal grows with the supersaturation it can relieve; the process sets how many crystals there are, the dose and fluid volume set how much they cost.)

25.3, 9.31 and 3.84 ng/mLCmax in dogs for the fresh, 50% and 100% crystallized capsulepurohit2019 R9

1–5 µm vs 5–25 µmcrystals formed in the generic against reference crystals, same monohydrate formpurohit2019 R6, R8

about 93% to about 58%compendial test I from 10% to 100% crystallinitypurohit2018 R5

Evidence: data, conditions and papers

Finding F6. Residual crystals cost supersaturation at every step from the extruder to the animal: extrusion below the solubility temperature leaves them, polymers do not hold a solution against them, and a tacrolimus capsule that crystallized in storage lost about half its exposure in dogs, less than the small-volume tests predicted

In short. Fifteen 50% indomethacin–PVPVA extrudates made below the critical temperature of about 132 °C were never crystal-free, and posaconazole–HPMCAS extruded at 125 °C held 0.3, 3.2 and 19.3 wt% crystals at 10, 25 and 50% loading moseson2018 R10.k–o; shah2024 R5, R10 (ASD process F9). After a gastric-to-intestinal shift the 10% posaconazole dispersion without crystals still held about 125 µg/mL at 300 min, the one with 0.3% crystals fell to about 18.5 µg/mL by 150 min shah2024 R12, R14 (ASD process F41), and in solution seeds left HPMCAS-held paclitaxel at 7.9–25.3 µg/mL que2018 R3, R13, R14 (Dissolution F4). One generic tacrolimus capsule crystallized to 88% in 3 weeks at 40 °C/75% RH trasi2017 R12, R18, R19 (Solid state stability F11); in six beagles its 50% and 100% crystallized forms gave AUC0–24 of 22.9 and 21.6 against 42.1 ng·h/mL fresh purohit2019 R9 (Bioperformance F30), about 51% of the fresh exposure against about 17–22% in the absorptive test and about 8% in the simulation with 100 mL input purohit2019 R9; hate2019 R13; purohit2018 R14, R16 (Bioperformance F31).

Type. cross-category synthesis of 13 source findings (indomethacin, bicalutamide and posaconazole extrudates; paclitaxel and delamanid dispersions; a marketed tacrolimus capsule in storage, compendial, small-volume and absorptive tests, a simulation and dogs) Strength. : the cost of residual crystals is direct in each system (ASD process F28, ASD process F41, Bioperformance F28), but the systems differ in drug, polymer, loading and supersaturation moseson2020a X5, X9; moseson2021 X11; shah2024 X14 (ASD process F29), and the dog comparison joins species, doses and batches purohit2019 X12, C40; purohit2018 C59, K6 (Bioperformance F31).

How it was shown

ASD process extruded indomethacin–PVPVA, bicalutamide–PVPVA and posaconazole–HPMCAS above and below the critical temperature from the phase diagram and dissolved the extrudates at non-sink doses and after a pH shift moseson2018 R5, R4; moseson2020a R6, R9, R10; moseson2021 R17; shah2024 R12, R14. Solid state stability stored the contents of six marketed tacrolimus capsules open at 40 °C/75% RH trasi2017 R12, R18, R19. Bioperformance tested the capsule that crystallized in compendial, small-volume and absorptive tests, in a GastroPlus simulation and in dogs purohit2018 R5, R7; hate2019 R9, R12; purohit2019 R9.

What the data show

Indomethacin–PVPVA extrudates with 0–25% crystallinity gave a 12 h concentration falling from about 43.1 to about 28.8 µg/mL, whereas bulk seeds up to 100% of the amorphous dose lowered it only from about 43.2 to about 39.8 µg/mL moseson2020a R6, R9, R10.

step	system	result	ids
extrusion below and above Tc	indomethacin–PVPVA 50%; posaconazole–HPMCAS	crystal-free only at or above Tc; 0.3, 3.2, 19.3 wt% at 125 °C	moseson2018 R10.k–o; shah2024 R5, R10
dissolution, 150 µg/mL, 4 h	bicalutamide–PVPVA	about 35, 24.5, 10.5 µg/mL for none, TEM-only, 30%	moseson2021 R17
pH shift	posaconazole–HPMCAS 10%	125 µg/mL at 300 min against 18.5 µg/mL by 150 min with 0.3% crystals	shah2024 R12, R14
open storage, 40 °C/75% RH	six marketed tacrolimus capsules	one generic 88% crystalline in 3 weeks	trasi2017 R12, R18, R19
dogs, 1 mg	the crystallized capsule	AUC0–24 42.1, 22.9, 21.6 ng·h/mL	purohit2019 R9
ratio crystalline/fresh	same capsule across tests	dogs about 51%; absorptive about 22, 17, 17.5%; simulation about 8% (100 mL)	purohit2019 R9; hate2019 R13; purohit2018 R14, R16

Fig. 6 of shah2024: 10% loading, concentration (a), SHG and TPE-UVF images (b, d) and FBRM counts (c, e) for the extrudates made at 175 and 125 °C — Fig. 6 · shah202410% loading, concentration (a), SHG and TPE-UVF images (b, d) and FBRM counts (c, e) for the extrudates made at 175 and 125 °C

The extrudate made below the calculated Tc, with 0.3% crystals, reaches the same peak but loses its supersaturation within about 150 min shah2024 R12, R14.

Why

The ASD process authors attribute the extra potency of residual crystals to their small size, embedded position and possible defects, none of which was measured moseson2020a C40, X9; moseson2021 C65, C66, X10. Crystals formed in the generic measured 1–5 µm against 5–25 µm for the reference crystals purohit2019 R6, R8. The dog dose of 1 mg in about 95 mL gives at most about 10 µg/mL, the level of the large-volume tests purohit2019 R12, C40; hate2019 R7. (synthesis: the process sets how many crystals there are, the dose and fluid volume set how much they cost.)

Limits and transfer

The tacrolimus crystallinities were nominal and the "100%" sample was not fully crystalline hate2019 K1, K2, K3, K4, X9, X13. Set the extrusion temperature at or above the critical temperature from a temperature–composition phase diagram moseson2018 R5, R4, and test residual crystals by a method that sees below 1% and by dissolution at the highest supersaturation the dose can reach shah2024 R12, R14. Use a small-volume or absorptive test to rank crystallinity levels, but expect the in vivo loss to sit with large-volume conditions when the dose gives low supersaturation purohit2019 R9; hate2019 R13; purohit2018 R14, R16.

How it was shown

ASD process extruded indomethacin–PVPVA, bicalutamide–PVPVA and posaconazole–HPMCAS above and below the critical temperature from the phase diagram, quantified crystals by PLM, XRPD, DSC, TEM and SHG, and dissolved the extrudates at non-sink doses and after a pH shift moseson2018 R5, R4 (ASD process F8); moseson2018 R10.k–o; shah2024 R5, R10 (ASD process F9); moseson2020a R6, R9, R10 (ASD process F26); moseson2021 R17 (ASD process F28); shah2024 R12, R14 (ASD process F41). Dissolution seeded paclitaxel solutions and dissolved delamanid dispersions with residual crystals que2018 R3, R13, R14; duong2022a R14, R15, C56 (Dissolution F4). Solid state stability stored the contents of six marketed tacrolimus capsules open at 40 °C/75% RH trasi2017 R12, R18, R19 (Solid state stability F11). Bioperformance tested that capsule at nominal crystallinities in compendial, 100 mL and absorptive hollow-fibre tests, in a GastroPlus simulation and in dogs purohit2018 R5, R7 (Bioperformance F16); hate2019 R9, R12 (Bioperformance F28); purohit2018 R13, R14, R15, R16, R17 (Bioperformance F17); purohit2019 R9 (Bioperformance F30).

What the data show

Indomethacin–PVPVA extrudates with 0–25% crystallinity gave a 12 h concentration falling from about 43.1 to about 28.8 µg/mL, whereas bulk seeds up to 100% of the amorphous dose lowered it only from about 43.2 to about 39.8 µg/mL moseson2020a R6, R9, R10 (ASD process F26). In bicalutamide–PVPVA the 4 h concentration at 150 µg/mL was about 35 µg/mL without crystals, about 24.5 with crystals only TEM could find and about 10.5 with 30% moseson2021 R17 (ASD process F28). Residual crystals in delamanid dispersions left release incomplete "once any level of residual crystallinity could be detected" duong2022a R14, R15, C56 (Dissolution F4). For tacrolimus, compendial test I fell only from about 93% at 10% crystallinity to about 58% at 100% purohit2018 R5 (Bioperformance F16); in the absorptive test the receiver AUC0–120 in 100 mL fell from about 682 (fresh) to 583, 272 and 117 µg/mL·min at 20, 50 and 100% hate2019 R9, R12 (Bioperformance F28); the simulation lost bioequivalence from 20% crystallinity with 100 mL input and from 40% with 900 mL input purohit2018 R13, R14, R15, R16, R17 (Bioperformance F17). In dogs Cmax was 25.3, 9.31 and 3.84 ng/mL for the fresh, 50% and 100% crystallized capsules purohit2019 R9 (Bioperformance F30).

source finding	system	conditions	result	ids
ASD process F9	indomethacin–PVPVA 50%; posaconazole–HPMCAS	extrusion below and above Tc	crystal-free only at or above Tc; 0.3, 3.2, 19.3 wt% at 125 °C	moseson2018 R10.k–o; shah2024 R5, R10
ASD process F26	indomethacin–PVPVA extrudates against bulk seeds	50 µg/mL, 12 h	about 43.1 to 28.8 µg/mL against 43.2 to 39.8	moseson2020a R6, R9, R10
ASD process F28	bicalutamide–PVPVA	150 µg/mL, 4 h	about 35, 24.5, 10.5 µg/mL for none, TEM-only, 30%	moseson2021 R17
ASD process F41	posaconazole–HPMCAS 10%	pH shift	125 µg/mL at 300 min against 18.5 µg/mL by 150 min with 0.3% crystals	shah2024 R12, R14
Dissolution F4	paclitaxel with HPMCAS; delamanid dispersions	seeded solution; dissolution	7.9–25.3 µg/mL left with seeds; release incomplete with detectable crystals	que2018 R3, R13, R14; duong2022a R14, R15, C56
Solid state stability F11	six marketed tacrolimus capsules	40 °C/75% RH, open	one generic 88% crystalline in 3 weeks	trasi2017 R12, R18, R19
Bioperformance F28	the crystallized tacrolimus capsule	absorptive test, 100 mL	receiver AUC about 682, 583, 272, 117 µg/mL·min	hate2019 R9, R12
Bioperformance F30	same capsule	six beagles, 1 mg	AUC0–24 42.1, 22.9, 21.6 ng·h/mL	purohit2019 R9
Bioperformance F31	same capsule across tests	ratio crystalline/fresh	dogs about 51%; absorptive about 22, 17, 17.5%; simulation about 8% (100 mL) and 55% (900 mL)	purohit2019 R9; hate2019 R13; purohit2018 R14, R16

Figure

The extrudate made below the calculated Tc, with 0.3% crystals, reaches the same peak but loses its supersaturation within about 150 min shah2024 R12, R14 (ASD process F41).

Fig. 4a of purohit2019: mean blood profiles of fresh and fully crystallized Accord — Fig. 4a · purohit2019mean blood profiles of fresh and fully crystallized Accord

The crystallized capsule gives a lower and flatter profile than the fresh one in the same dogs purohit2019 R9 (Bioperformance F30).

Why

The ASD process authors attribute the extra potency of residual crystals to their small size, embedded position and possible defects, none of which was measured moseson2020a C40, X9; moseson2021 C65, C66, X10 (ASD process F26), and name the polymer's growth inhibition, the seed properties, the crystallization route and the supersaturation as the risk factors moseson2020a R6, C28; moseson2021 R17, C70 (ASD process F29). Crystals formed in the generic measured 1–5 µm against 5–25 µm for the reference crystals, of the same monohydrate form purohit2019 R6, R8 (Bioperformance F30). The dog dose of 1 mg in about 95 mL gives at most about 10 µg/mL, the level of the large-volume tests (synthesis in the source finding) purohit2019 R12, C40; hate2019 R7 (Bioperformance F31). (synthesis: the cost of a crystal grows with the supersaturation it can relieve; the process sets how many crystals there are, the dose and fluid volume set how much they cost.)

Conditions and limits

The tacrolimus crystallinities were nominal and the "100%" sample was not fully crystalline hate2019 K1, K2, K3, K4, X9, X13 (Bioperformance F28); the simulation assumed no precipitation in the gut purohit2018 K6, C58, C59, X10 (Bioperformance F17); the extrusion series were single runs at each condition moseson2018 K2, K3, X13, X14 (ASD process F9).

Counterexamples and conflicts

In indomethacin–PVPVA up to 25% residual crystals mainly lowered the reachable concentration, the low-risk scenario, while below 1% crystals already cut bicalutamide–PVPVA moseson2020a R6, C28; moseson2021 R17, C70 (ASD process F29). The crystallized capsule gave about four times the exposure of a suspension of reference crystals purohit2019 R9 (Bioperformance F30).

Transfer check

Set the extrusion temperature at or above the critical temperature from a temperature–composition phase diagram and allow for the input crystal size moseson2018 R5, R4 (ASD process F8). Test residual crystals by a method that sees below 1% and by dissolution at the highest supersaturation the dose can reach shah2024 R12, R14 (ASD process F41). Use a small-volume or absorptive test to rank crystallinity levels, but expect the in vivo loss to sit with large-volume conditions when the dose gives low supersaturation purohit2019 R9; hate2019 R13; purohit2018 R14, R16 (Bioperformance F31).

History

2017: a marketed tacrolimus generic crystallized in open storage trasi2017 R12, R18, R19 (Solid state stability F11). 2018: the phase diagram set the extrusion floor, and seeds were shown to cost paclitaxel supersaturation moseson2018 R5, R4 (ASD process F8); que2018 R3, R13, R14 (Dissolution F4); compendial and small-volume tests and a simulation were applied to the tacrolimus capsule purohit2018 R5, R7 (Bioperformance F16). 2019: the absorptive test and the dog study measured its cost hate2019 R9, R12 (Bioperformance F28); purohit2019 R9 (Bioperformance F30). 2020–2021: residual crystals were shown to seed more strongly than bulk crystals moseson2020a R6, R9, R10 (ASD process F26); moseson2021 R17 (ASD process F28). 2022: delamanid dispersions failed with any detectable crystals duong2022a R14, R15, C56 (Dissolution F4). 2024: 0.3% crystals ended posaconazole supersaturation after a pH shift shah2024 R12, R14 (ASD process F41).

Conceptsresidual crystallinity crystal seeding formulation critical temperature absorptive dissolution testing

F7

Topic 2Crystals from neat drug to exposure4 of 4

Whether a sample is amorphous depends on the method; crystals below the X-ray limit changed dissolution.

SHG dated the first crystals of spray-dried flutamide at 11 days against 53 days by XRPD kestur2012 R7, R6, R8; correasoto2017 R1, R8; moseson2021 R6. TEM found crystals below 100 nm in an X-ray-amorphous extrudate with one Tg, and SHG measured 0.3% crystals in a posaconazole extrudate where pXRD saw nothing moseson2018a R5, R6, R9, R11, R12, R17; shah2024 R9, R10, P6, X4, X5. Crystals that only TEM could find cut the 4 h bicalutamide concentration from about 35 to about 24.5 µg/mL moseson2021 R17.

moderateModerate to strong: the order of methods is shown within single samples and, for bicalutamide and posaconazole, tied to performance, but no paper put one sample through every method moseson2021 X6, X9; shah2024 X4; kestur2012 K3, X10; correasoto2017 K2, X7.

SHG saw the first crystals weeks before XRPD in the same samples. kestur2012 R7, R6, R8; correasoto2017 R1, R8; moseson2021 R6

saw crystals in X-ray-amorphous samples

SHGTEMPLMSEM

missed them or needed more

XRPDDSC

In extrudates and stored powders the sensitive detectors found crystals that XRPD and DSC did not. moseson2018 R11, R12, R15, C27, C31, C63; moseson2021 R6, R17, R21; shah2024 R9, R10, P6, X4, X5; duong2022c R16, R18, C36

For your drug

Pair a sensitive detector (SHG or TEM) with a quantifying one (XRPD or ssNMR).
Judge whether a crystal content is acceptable by dissolution at the highest expected supersaturation, not by the detection limit alone.

correasoto2017 R1, R9, R12; moseson2021 R17

How it works and key numbers

Quoted detection limits for crystals in amorphous powders run from about 10 ppm for SHG (calculated) to 1% or more for XRPD, Raman and DSC kestur2012 R7, R6, R8; correasoto2017 R1, R8; moseson2021 R6.
A dark SHG image says only that no SHG-active crystal above about 100 nm is present wanapun2010 R13; kestur2012 R17, C34; moseson2018a R9, C10.
XRPD calibrated with bulk crystals may underestimate the crystallinity of extruded dispersions moseson2020a C44, and crystals grown in a dispersion gave an SHG ratio of about 3.1 against a standard, explained by habit and orientation, inferred by exclusion correasoto2017 R9, R12, C20; correasoto2017 K5, K6, X14.
One Tg does not mean one phase: itraconazole–HPMC showed one Tg of 87 °C with drug-rich domains purohit2017a R3, R7, R16, R17.
(synthesis: a detection limit expressed per mass of crystal is not a limit on effect, because a few small crystals provide many growth sites; the method has to be chosen for the smallest crystal content that changes the dissolution result.)

19 days vs 3 monthscrystals in stored uncoated ezetimibe–HPMCAS by SEM against PXRDduong2022c R16, R18, C36; moseson2022a R11, R13, X14

3.5% and 30%the only bicalutamide extrudates in which XRPD saw crystals; DSC saw only the 30% onemoseson2021 R6, R17, R21

0.3%posaconazole crystals at the stated pXRD limit of detection that ended supersaturation earlyshah2024 R12, R14

Evidence: data, conditions and papers

Finding F7. Whether a sample counts as amorphous depends on the method that looked, and crystals below the X-ray limit changed performance: SHG, TEM, PLM and SEM found crystals that XRPD and DSC missed in extrudates, spray-dried and stored powders and dissolution media

In short. Quoted detection limits for crystals in amorphous powders run from about 10 ppm (SHG, calculated) to 1% or more (XRPD, Raman, DSC), and SHG dated the first crystals of spray-dried flutamide at 11 days against 53 days by XRPD kestur2012 R7, R6, R8; correasoto2017 R1, R8; moseson2021 R6 (Characterization methods F5). In extrudates PLM showed crystals that XRPD called amorphous, TEM found crystals below 100 nm in an X-ray-amorphous extrudate with one Tg, and SHG measured 0.3% crystals in a posaconazole extrudate where pXRD saw nothing moseson2018 R11, R12, R15, C27, C31, C63; moseson2018a R5, R6, R9, R11, R12, R17; shah2024 R9, R10, P6, X4, X5 (ASD process F10). Those crystals mattered: crystals only TEM could find cut the 4 h bicalutamide concentration at 150 µg/mL from about 35 to about 24.5 µg/mL moseson2021 R17 (ASD process F28). In dissolution media SHG showed the first crystals as the concentration fell elkhabaz2017 R9, R13, R14, R18, R22 (Bioperformance F12), and one Tg did not mean one phase purohit2017a R3, R7, R16, R17 (Characterization methods F4).

Type. cross-category method comparison of 8 source findings (flutamide, ezetimibe, indomethacin, bicalutamide, posaconazole, lumefantrine, itraconazole; extrudates, spray-dried and stored powders, films, dissolution media) Strength. to strong: the order of methods is shown within single samples and, for bicalutamide and posaconazole, tied to performance moseson2018 K4; moseson2018a X4; moseson2019 X7; moseson2021 X6, X9; shah2024 X4; moseson2022a X21 (ASD process F10), but no paper put one sample through every method kestur2012 K3, X10; correasoto2017 K2, X7 (Characterization methods F4).

How it was shown

Characterization methods compared Raman, PXRD with chemometrics, DSC and SHG on powders and spray-dried dispersions, and DSC, probes and confocal imaging on itraconazole–HPMC kestur2012 R7, R6, R8; correasoto2017 R1, R8; purohit2017a R3, R7, R16, R17. ASD process compared PLM, XRPD, DSC, TEM, SEM and SHG on extrudates and stored coated powders moseson2018 R11, R12, R15, C27, C31, C63; moseson2021 R6, R17, R21; shah2024 R9, R10, P6, X4, X5; duong2022c R16, R18, C36. Bioperformance used SHG in buffer, FeSSIF and a nutrition drink elkhabaz2017 R9, R13, R14, R18, R22.

What the data show

In four bicalutamide extrudates DSC saw crystals only in the one with 30%, XRPD in the two with 3.5% and 30%, and only TEM in the extrudate below the XRPD limit moseson2021 R6, R17, R21. A dark SHG image says only that no SHG-active crystal above about 100 nm is present wanapun2010 R13; kestur2012 R17, C34; moseson2018a R9, C10. After a pH shift, 0.3% posaconazole crystals, at the stated pXRD limit of detection, ended supersaturation early shah2024 R12, R14.

system	methods	result	ids
crystals in amorphous powders; spray-dried flutamide	method comparison; storage	limits about 10 ppm (SHG) to ≥1%; first crystals 11 against 53 days	kestur2012 R7, R6, R8; correasoto2017 R1, R8; moseson2021 R6
itraconazole–HPMC	DSC against probe and confocal	one Tg of 87 °C with drug-rich domains	purohit2017a R3, R7, R16, R17
stored uncoated ezetimibe–HPMCAS	SEM against PXRD	crystals at 19 days against 3 months	duong2022c R16, R18, C36; moseson2022a R11, R13, X14
bicalutamide–PVPVA	dissolution, 150 µg/mL, 4 h	TEM-only crystals: about 24.5 against 35 µg/mL	moseson2021 R17
flutamide grown in dispersion	SHG against standard	ratio about 3.1; XRPD 1–2%	correasoto2017 R9, R12, C20

Fig. 8 of moseson2018: experimental process operating design space, each run placed by temperature and residence time and coloured by the most sensitive method that still called it amorphous — Fig. 8 · moseson2018experimental process operating design space, each run placed by temperature and residence time and coloured by the most sensitive method that still called it amorphous

The same set of runs has a different amorphous region for each method moseson2018 R11, R12, R15.

Why

The ASD process authors add that XRPD calibrated with bulk crystals may underestimate the crystallinity of extruded dispersions moseson2020a C44. The Characterization methods authors explain the failed SHG calibration by habit and orientation of crystals grown in the dispersion, inferred by exclusion correasoto2017 K5, K6, X14. (synthesis: a detection limit expressed per mass of crystal is not a limit on effect, because a few small crystals provide many growth sites.)

Limits and transfer

In stored uncoated lumefantrine–PVPVA powders SEM found crystals at 1 week while XRPD showed none through 48 weeks, a case where the more sensitive method did not tie to a measured performance loss duong2022c R16, R18, C36; moseson2022a R11, R13, X14. Pair a sensitive detector (SHG or TEM) with a quantifying one (XRPD or ssNMR) correasoto2017 R1, R9, R12, and judge acceptability by dissolution at the highest expected supersaturation, not by the detection limit alone moseson2021 R17.

How it was shown

Characterization methods compared Raman, PXRD with chemometrics, DSC and SHG on powders and spray-dried dispersions, and DSC, probes and confocal imaging on itraconazole–HPMC kestur2012 R7, R6, R8; correasoto2017 R1, R8 (Characterization methods F5); purohit2017a R3, R7, R16, R17 (Characterization methods F4). ASD process compared PLM, XRPD, DSC, TEM, SEM and SHG on extrudates and stored coated powders moseson2018 R11, R12, R15, C27, C31, C63; moseson2021 R6, R17, R21; shah2024 R9, R10, P6, X4, X5; duong2022c R16, R18, C36; moseson2022a R11, R13, X14 (ASD process F10). Bioperformance used SHG in buffer, FeSSIF and a nutrition drink elkhabaz2017 R9, R13, R14, R18, R22 (Bioperformance F12).

What the data show

SHG dated the first crystals of ezetimibe at 15 days against none within 60 days by XRPD kestur2012 R7, R6, R8; correasoto2017 R1, R8; moseson2021 R6 (Characterization methods F5). In the 15 indomethacin extrudates DSC detected a dissolution endotherm only in the four 2 min samples at or below 131 °C, so the amorphous zone of the process map had three boundaries moseson2018 R11, R12, R15, C27, C31, C63 (ASD process F10). In four bicalutamide extrudates DSC saw crystals only in the one with 30%, XRPD in the two with 3.5% and 30%, and only TEM in the extrudate below the XRPD limit moseson2021 R6, R17, R21 (ASD process F10). Stored uncoated ezetimibe–HPMCAS showed crystals by SEM at 19 days where PXRD needed 3 months duong2022c R16, R18, C36; moseson2022a R11, R13, X14 (ASD process F10). A dark SHG image says only that no SHG-active crystal above about 100 nm is present wanapun2010 R13; kestur2012 R17, C34; moseson2018a R9, C10 (Characterization methods F4). Flutamide crystals grown in a dispersion gave an SHG ratio of about 3.1 against a standard that a fully crystalline sample should not exceed, while XRPD gave 1–2% correasoto2017 R9, R12, C20 (Characterization methods F6). After a pH shift, 0.3% posaconazole crystals, at the stated pXRD limit of detection, ended supersaturation early shah2024 R12, R14 (ASD process F41).

source finding	system	conditions	result	ids
Characterization methods F5	crystals in amorphous powders; spray-dried flutamide	method comparison; storage	limits about 10 ppm (SHG) to ≥1%; first crystals 11 against 53 days	kestur2012 R7, R6, R8; correasoto2017 R1, R8; moseson2021 R6
Characterization methods F4	itraconazole–HPMC; extrudate	DSC against probe and confocal; TEM against XRPD	one Tg of 87 °C with drug-rich domains; crystals below 100 nm under a halo	purohit2017a R3, R7, R16, R17; wanapun2010 R13; kestur2012 R17, C34; moseson2018a R9, C10
ASD process F10	indomethacin, bicalutamide, posaconazole extrudates; stored powders	PLM, XRPD, DSC, TEM, SHG, SEM	DSC sees fewest, TEM and SHG most; SEM 19 days against PXRD 3 months	moseson2018 R11, R12, R15, C27, C31, C63; moseson2021 R6, R17, R21; shah2024 R9, R10, P6, X4, X5; duong2022c R16, R18, C36
ASD process F28	bicalutamide–PVPVA	150 µg/mL, 4 h	TEM-only crystals: about 24.5 against 35 µg/mL	moseson2021 R17
ASD process F41	posaconazole–HPMCAS 10%	pH shift	0.3% crystals: about 18.5 µg/mL by 150 min against 125 µg/mL at 300 min	shah2024 R12, R14
Bioperformance F12	ezetimibe dispersions	SHG in buffer, FeSSIF, Ensure Plus	first crystals with the fall in concentration	elkhabaz2017 R9, R13, R14, R18, R22
Characterization methods F6	flutamide grown in dispersion	SHG against standard	ratio about 3.1; XRPD 1–2%	correasoto2017 R9, R12, C20

Figure

The same set of runs has a different amorphous region for each method moseson2018 R11, R12, R15 (ASD process F10).

Why

The ASD process authors add that XRPD calibrated with bulk crystals may underestimate the crystallinity of extruded dispersions moseson2020a C44 (ASD process F10). The Characterization methods authors explain the failed SHG calibration by habit and orientation of crystals grown in the dispersion, inferred by exclusion correasoto2017 K5, K6, X14 (Characterization methods F6). (synthesis: a detection limit expressed per mass of crystal is not a limit on effect, because a few small crystals provide many growth sites; the method has to be chosen for the smallest crystal content that changes the dissolution result.)

Conditions and limits

No crystalline fraction was measured for the TEM-detected crystals, and the 0.3% posaconazole value equals the stated pXRD limit of detection (ASD process F10); the SHG rate unit of the dissolution study is implausible at face value elkhabaz2017 K8, K6, X7, X8 (Bioperformance F12).

Counterexamples and conflicts

In stored uncoated lumefantrine–PVPVA powders SEM found crystals at 1 week while XRPD showed none through 48 weeks, a case where the more sensitive method did not tie to a measured performance loss duong2022c R16, R18, C36; moseson2022a R11, R13, X14 (ASD process F10).

Transfer check

Pair a sensitive detector (SHG or TEM) with a quantifying one (XRPD or ssNMR) correasoto2017 R1, R9, R12 (Characterization methods F7), and judge acceptability by dissolution at the highest expected supersaturation, not by the detection limit alone moseson2021 R17 (ASD process F28).

History

2010–2012: SHG and its detection limits were established wanapun2010 R13; kestur2012 R17, C34 (Characterization methods F4). 2017: SHG dated crystallization in spray-dried dispersions weeks before XRPD, and one Tg was shown not to exclude domains correasoto2017 R1, R8 (Characterization methods F5); purohit2017a R3, R7, R16, R17 (Characterization methods F4); SHG followed crystals in biorelevant media elkhabaz2017 R9, R13, R14, R18, R22 (Bioperformance F12). 2018–2021: TEM found crystals in X-ray-amorphous extrudates that changed dissolution moseson2018a R5, R6, R9, R11, R12, R17 (ASD process F10); moseson2021 R17 (ASD process F28). 2022–2024: SEM in stored powders and SHG at 0.3% in a pH-shift test duong2022c R16, R18, C36 (ASD process F10); shah2024 R12, R14 (ASD process F41).

Conceptssecond harmonic generation limit of detection residual crystallinity single-Tg miscibility criterion

Topic 3 of 5 · 3 findings · F8–F10

Water and the hydrating solid

F8

Topic 3Water and the hydrating solid1 of 3

Every category has a drug-loading threshold, but storage, release, absorption, silica and peptide thresholds are different quantities.

Indomethacin dispersions above about 50% drug with HPMC and above 30% with HPMCAS crystallized in 2–15 days, while those below stayed amorphous for 13–14 months tian2016 R17. Ritonavir–PVPVA tablets released ≈97% of their drug in 60 min at 25% loading, ≈29% at 30% and at most ≈2% at 35–50% indulkar2019a R11, C2, C31; saboo2019 R5, R6, X8. In SBA-15 ritonavir loadings above the calculated monolayer of 25.3% w/w lowered the mass flow dening2018 R27, R4.

strongStrong for the existence of each threshold, measured directly in its own category; moderate for the comparison across categories, because the thresholds were measured on different drugs, polymers, sample forms and read-outs tian2016 R17; indulkar2019a R11, C2, C31; moseson2022b R6, R7.

The thresholds fall at different loadings and measure different things: a dry mixture, a wetted gel, a pore surface. tian2016 R17; indulkar2019a R11, C2, C31; moseson2022b C36, C48, X15; hate2018 R11; dening2018 R27, R4; bapat2025b R10, C21, R11.i, C23, C24

One 5% step past the limit of congruency took release from nearly complete to about a third. indulkar2019a R11, C2, C31; saboo2019 R5, R6, X8

For your drug

For a new drug–polymer pair measure, on samples made by the intended route, the miscibility limit and the limit of congruency with both components assayed from constant-area compacts, and choose a loading below the lower of the two.
Check that the low loading does not crystallize in dissolution, and for silica stay below the calculated monolayer.

tian2016 R17; indulkar2019a R11, C2, C31; wilson2018 R6, R17; dening2018 R27, R4

How it works and key numbers

In storage, above the miscibility limit a drug-rich phase forms, and with less polymer in it crystallization "would be anticipated" to occur more readily tian2016 C4.
In release, discrete drug-rich droplets up to about 2 µm left the gel with the polymer at 10–20% ritonavir, while from 30% a continuous drug-rich layer stayed behind yang2022a R6, R10, R11, R12, R13; deac2024b R35, R37.
In silica, above the monolayer filled or blocked pores may obstruct water entry and drug exit ("might") dening2018 C60, C62; hate2020a C44, C45.
For the peptide the remaining compacts were amorphous, so the release plateaus were not crystallization of the peptide bapat2025b R15, C25.
(synthesis: the storage limit is a property of the dry mixture, the release limit a property of the wetted gel, and the silica limit a property of the pore surface; they need not coincide for one drug and polymer.)

To feel the numbers. From 25 to 30% ritonavir the released drug fell 97 ÷ 29 ≈ 3.3-fold, and from 25% to 35–50% about 97 ÷ 2 ≈ 50-fold.

about 60- and 360-foldcut in drug release rate by one 5% step past the limit, nilvadipine and cilnidipinesaboo2019 R5, R6, R8

49 vs 48 µM; 19 µMritonavir in the supernatant from 10% dispersion against its amorphous solubility; 50% dispersiontres2018 R6, R9

about 10 µg/mLthe 10% enzalutamide–HPMCAS dispersion, which crystallized, while the 50% one reached the ceilingwilson2018 R6, R17

Evidence: data, conditions and papers

Finding F8. Drug loading sets a threshold in every category, and the thresholds are not the same quantity: the miscibility limit in storage, the limit of congruency in release, the loading that reaches the ceiling in absorptive tests, the loading that escapes matrix crystallization, the monolayer in silica and a few percent for a peptide

In short. Indomethacin dispersions above about 50% drug with HPMC and above 30% with HPMCAS crystallized in 2–15 days while those below stayed amorphous for 13–14 months tian2016 R17 (Solid state stability F7). Ritonavir–PVPVA tablets released ≈97% of their drug in 60 min at 25% loading, ≈29% at 30% and at most ≈2% at 35–50% indulkar2019a R11, C2, C31; saboo2019 R5, R6, X8 (Dissolution F7); of nine atazanavir dispersions only the three at 10% exceeded the amorphous solubility hate2018 R11 (Bioperformance F8); bicalutamide–PVPVA at 5 and 10% released drug and polymer together and stayed at about 91 and 96% of the dose, while 20–50% released the polymer first and ended at about 88–73% moseson2022b R6, R7 (ASD process F38). In SBA-15 ritonavir loadings above the calculated monolayer of 25.3% w/w lowered the mass flow from 5.1–5.4 to 4.37 and 4.10 ng/min dening2018 R27, R4 (Mesoporous silica F11), and a peptide released with copovidone at 1.6% loading but cyclosporine reached only ≈12% in 60 min from the 5% binary bapat2025b R10, C21, R11.i, C23, C24 (Peptide permeability F5).

Type. cross-category synthesis of 8 source findings (storage of indomethacin and lumefantrine dispersions; release of ritonavir, nilvadipine, cilnidipine, bicalutamide and peptides; absorptive tests of atazanavir, telaprevir and enzalutamide; silica loadings of ritonavir and atazanavir) Strength. for the existence of each threshold, measured directly in its own category (Dissolution F7, ASD process F38, Solid state stability F7); moderate for the comparison across categories, because the thresholds were measured on different drugs, polymers, sample forms and read-outs (synthesis).

How it was shown

Solid state stability read the miscibility limit of indomethacin dispersions by the drug's emission and stored powders over a range of loadings tian2016 R17; hiew2022a R6. Dissolution and ASD process assayed drug and polymer release in steps of loading indulkar2019a R11, C2, C31; saboo2019 R5, R6, X8; moseson2022b R6, R7. Bioperformance dissolved dispersions at several loadings with or without an absorptive sink hate2018 R11; mosqueragiraldo2018b R5, R16; wilson2018 R6, R17. Mesoporous silica varied the loading in SBA-15, and Peptide permeability took cyclosporine–copovidone from 1.6 to 20% loading dening2018 R27, R4; hate2020a R15; bapat2025b R10, C21, R11.i, R12.i, R13.i, C23, C24.

What the data show

One 5% step past the limit of congruency cut the drug release rate about 60-fold for nilvadipine and about 360-fold for cilnidipine saboo2019 R5, R6, R8.

category	system	threshold	ids
storage	indomethacin with HPMC, HPMCAS	about 50% and 30% drug	tian2016 R17
release	ritonavir–PVPVA compacts	between 25 and 30%	indulkar2019a R11, C2, C31; saboo2019 R5, R6, X8
release	bicalutamide–PVPVA powders	congruent at 5–10%, polymer first from 20%	moseson2022b R6, R7
absorptive test	atazanavir with HPMCAS, HPMC, PVPVA	only 10% exceeded the amorphous solubility	hate2018 R11
silica	ritonavir–SBA-15	drop at the calculated monolayer of 25.3% w/w	dening2018 R27, R4
peptide	cyclosporine–copovidone	co-release at 1.6%, ≈12% at 5%	bapat2025b R10, C21, R11.i, C23, C24

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

Drug and polymer release lie together near complete up to 25% loading; at 30% the drug drops to about a third and beyond it to a few percent indulkar2019a R11, R3.

Why

Above the miscibility limit a drug-rich phase forms, and with less polymer in it crystallization "would be anticipated" to occur more readily tian2016 C4. In the gel of a dissolving compact discrete drug-rich droplets up to about 2 µm left with the polymer at 10–20% ritonavir, while a continuous drug-rich layer stayed from 30% yang2022a R6, R10, R11, R12, R13; deac2024b R35, R37. For silica the authors propose that filled or blocked pores obstruct water entry and drug exit dening2018 C60, C62; hate2020a C44, C45. (synthesis: the storage limit is a property of the dry mixture, the release limit of the wetted gel and the silica limit of the pore surface; they need not coincide.)

Limits and transfer

A lower loading is not always better: the 10% enzalutamide–HPMCAS dispersion reached only about 10 µg/mL and crystallized, while the 50% one reached the ceiling in 3–4 h wilson2018 R6, R17. For a new drug–polymer pair measure the miscibility limit and the limit of congruency, and choose a loading below the lower of the two tian2016 R17; indulkar2019a R11, C2, C31; for silica stay below the calculated monolayer dening2018 R27, R4.

How it was shown

Solid state stability read the miscibility limit of indomethacin dispersions by the drug's emission and stored powders over a range of loadings, and stored lumefantrine–PVPVA at 5–50% drug tian2016 R17; hiew2022a R6 (Solid state stability F7). Dissolution assayed drug and polymer from constant-area compacts in steps of loading indulkar2019a R11, C2, C31; saboo2019 R5, R6, X8 (Dissolution F7). Characterization methods compared 10% and 50% ritonavir dispersions by lifetime, extinction and ultracentrifuged supernatant tres2018 R6, R9; purohit2017b C30, C33, C34, C37 (Characterization methods F2). Bioperformance dissolved atazanavir, telaprevir and enzalutamide dispersions at several loadings with or without an absorptive sink hate2018 R11; mosqueragiraldo2018b R5, R16; wilson2018 R6, R17 (Bioperformance F8). ASD process measured drug and polymer release of bicalutamide–PVPVA at 5–50% loading and spray-dried ritonavir–PVPVA at 25–75% moseson2022b R6, R7 (ASD process F38); li2020 R10, C37 (ASD process F21). Mesoporous silica varied the loading of ritonavir and atazanavir in SBA-15 dening2018 R27, R4; hate2020a R15 (Mesoporous silica F11). Peptide permeability took cyclosporine–copovidone dispersions from 1.6 to 20% loading bapat2025b R10, C21, R11.i, R12.i, R13.i, C23, C24 (Peptide permeability F5).

What the data show

Storage: lumefantrine–PVPVA dispersions crystallized after 1, 2, 4 and 8 weeks at 50, 25, 10 and 5% drug hiew2022a R6 (Solid state stability F7). Release: one 5% step past the limit cut the drug rate about 60-fold for nilvadipine and about 360-fold for cilnidipine, and below the limit drug and polymer left at one normalized rate (nilvadipine 2.13–2.53 against 0.002 mg/min/cm² for the neat amorphous drug) saboo2019 R5, R6, R8 (Dissolution F7). In the dissolution medium the 10% ritonavir–Kollidon VA64 dispersion left 49 µM in the supernatant against an amorphous solubility of 48 µM and the 50% dispersion only 19 µM tres2018 R6, R9 (Characterization methods F2). Spray-dried ritonavir–PVPVA at 50 and 75% released at 0.0053–0.0063 and 0.0031–0.0040, close to neat amorphous ritonavir (about 0.0026), whatever the solvent li2020 R10, C37 (ASD process F21). Absorption: under a sink the 10% cellulosic atazanavir dispersions transferred the most drug (AUC about 1220 and 1170 µg·min/mL against 555–760 for the 50% dispersions) hate2018 R15 (Bioperformance F8). Silica: atazanavir at 5, 10, 20, 30 and 50% w/w released about 73, 80.5, 66.5, 52 and 36% in 90 min with an absorptive sink hate2020a R15 (Mesoporous silica F11). Peptide: at 10 and 20% loading the decanoate ternaries released all their polymer while the peptide stalled at ≈54.5% and ≈16% bapat2025b R11.i, R12.i, R13.i, C23, C24 (Peptide permeability F5).

source finding	system	conditions	threshold	ids
Solid state stability F7	indomethacin with HPMC, HPMCAS	storage of powders	about 50% and 30% drug	tian2016 R17
Dissolution F7	ritonavir–PVPVA; nilvadipine, cilnidipine	constant-area compacts	between 25 and 30%; one 5% step cuts rate 60- and 360-fold	indulkar2019a R11, C2, C31; saboo2019 R5, R6, X8
Characterization methods F2	ritonavir–Kollidon VA64	supernatant at 10 and 50%	49 against 48 µM (10%); 19 µM (50%)	tres2018 R6, R9
Bioperformance F8	atazanavir with HPMCAS, HPMC, PVPVA	200 µg/mL dose	only 10% exceeded the amorphous solubility	hate2018 R11
ASD process F38	bicalutamide–PVPVA	powder release, 5–50%	congruent at 5–10%, polymer first from 20%	moseson2022b R6, R7
ASD process F21	spray-dried ritonavir–PVPVA	surface-normalized rate	at 50 and 75% near neat amorphous drug	li2020 R10, C37
Mesoporous silica F11	ritonavir–SBA-15	mass flow	drop at the calculated monolayer of 25.3% w/w	dening2018 R27, R4
Peptide permeability F5	cyclosporine–copovidone	normalized release	co-release at 1.6%, ≈12% at 5%	bapat2025b R10, C21, R11.i, C23, C24

Figure

Drug and polymer release lie together near complete up to 25% loading; at 30% the drug drops to about a third and beyond it to a few percent while the polymer still dissolves in part indulkar2019a R11, R3 (Dissolution F7).

Why

Above the miscibility limit a drug-rich phase forms, and with less polymer in it crystallization "would be anticipated" to occur more readily tian2016 C4 (Solid state stability F7). In the gel of a dissolving compact discrete drug-rich droplets up to about 2 µm left with the polymer at 10–20% ritonavir, while a continuous drug-rich layer stayed from 30%, and measured phase diagrams put the critical point near the limit of congruency yang2022a R6, R10, R11, R12, R13; deac2024b R35, R37 (Dissolution F7). For silica the authors propose that filled or blocked pores obstruct water entry and drug exit ("might") dening2018 C60, C62; hate2020a C44, C45 (Mesoporous silica F11). For the peptide the remaining compacts were amorphous, so the plateaus were not crystallization of the peptide bapat2025b R15, C25 (Peptide permeability F5). (synthesis: the storage limit is a property of the dry mixture, the release limit a property of the wetted gel, and the silica limit a property of the pore surface; they are measured differently and need not coincide for one drug and polymer.)

Conditions and limits

Miscibility was read on films and stability on powders (Solid state stability F7); the link from the release switch to the supersaturation outcome rests on co-occurrence (Dissolution F7); the limit of congruency of bicalutamide–PVPVA was not located, only bracketed between 10 and 20% moseson2022b C36, C48, X15 (ASD process F38); only one peptide was taken through the loading series bapat2025b K4, X2, X7 (Peptide permeability F5).

Counterexamples and conflicts

A lower loading is not always better: the 10% enzalutamide–HPMCAS dispersion reached only about 10 µg/mL and crystallized, while the 50% one reached the ceiling in 3–4 h wilson2018 R6, R17 (Bioperformance F8). For silica a higher loading brings less silica into the vessel at a fixed dose, so adsorption alone would predict the opposite trend (synthesis in the source finding) hate2020a X14 (Mesoporous silica F11).

Transfer check

For a new drug–polymer pair measure, on samples made by the intended route, the miscibility limit tian2016 R17 (Solid state stability F7) and the limit of congruency with both components assayed from constant-area compacts indulkar2019a R11, C2, C31 (Dissolution F7), and choose a loading below the lower of the two. For silica stay below the calculated monolayer dening2018 R27, R4 (Mesoporous silica F11).

History

2016: the miscibility limit of indomethacin dispersions was tied to storage tian2016 R17 (Solid state stability F7). 2018: only low-loading dispersions reached the ceiling in absorptive tests, ritonavir loading changed the drug left in solution, and silica loading lowered flux above the monolayer hate2018 R11 (Bioperformance F8); tres2018 R6, R9 (Characterization methods F2); dening2018 R27, R4 (Mesoporous silica F11). 2019: the limit of congruency was measured for ritonavir, nilvadipine and cilnidipine indulkar2019a R11, C2, C31; saboo2019 R5, R6, X8 (Dissolution F7). 2020: water in the spray solvent mattered only at the congruent loading li2020 R10, C37 (ASD process F21). 2022: lumefantrine storage and bicalutamide release followed loading hiew2022a R6 (Solid state stability F7); moseson2022b R6, R7 (ASD process F38). 2025: the threshold for a peptide lay between 1.6 and 5% bapat2025b R10, C21, R11.i, C23, C24 (Peptide permeability F5).

Conceptsdrug loading limit of congruency drug-polymer miscibility monolayer coverage congruent release

F9

Topic 3Water and the hydrating solid2 of 3

Water separates drug and polymer during manufacture, storage and wetting; the separation raised release in one system and lowered it in another.

Water in the spin-coating air or the spray solvent gave drug-rich domains in evacetrapib and itraconazole films and powders li2017 R3, R5; mugheirbi2017 R1, R3, R10; mugheirbi2017 R26, R27. Sorbed water separated stored pimozide–PVP, which showed one Tg dry and two wet rumondor2009c R17, R7, R9, R12, R14, R16. Separated lopinavir–HPMC films released faster than miscible ones, while water in the spray solvent lowered the release of 25% ritonavir–PVPVA li2019 R2; li2020 R10, R11, X5.

moderateModerate: the separation is seen by several methods in each category, but no paper measured the water content of drying films, and the two release results come from different drugs, polymers and processes li2017 K1, X14; mugheirbi2017 K1, X4.

Here separated films released faster; at 15% loading all three gave about 15–17 µg/mL. li2019 R2

Here water lowered release, in the order of the rising surface drug content. li2020 R10, R11, X5

For your drug

Control water in the solvent and the humidity of drying for any polymer that sorbs water, and image the product at the intended loading by a method that resolves domains, since one Tg does not exclude them.
Measure the drug–water interaction parameter or the separation at high RH before choosing a hygroscopic polymer for a hydrophobic donor drug, and if a separated product is considered, dissolve it against the miscible product at the intended loading.

li2017 R12, R15; rumondor2009c R17; rumondor2009c R24, C46, C27, C32; li2019 R2

How it works and key numbers

During drying water leaves more slowly than the volatile solvents, so it concentrates in the drying film li2017 C17, C18; mugheirbi2018 C34, C36.
In storage the drug's affinity for water, not log P or melting data, set what sorbed water did: the drug–water Flory–Huggins parameter was 2.84–3.58 for four drugs that separated and 2.50–2.71 for two that did not rumondor2009c R24, C46, C27, C32.
The separated state was held after drying and reversed only slowly by heating well above Tg marsac2010 R17.
On wetting, release rose when fast-dissolving polymer-rich phases freed discrete drug-rich domains li2019 C58, and fell when a drug-rich continuous phase or a drug-rich surface held the drug back li2019 R15, R16; li2020 C67, C40.
(synthesis: what decides release is which phase is continuous and what lies at the particle surface, not separation as such.)

22 h–6 days vs 46 and 125 dayscrystallization of separated against mixed PVP dispersions at 94% RHrumondor2009c R17, R7, R9, R12, R14, R16

20 µL vs 10 µL water per mLsplit and did not split a 50% evacetrapib–HPMC film spun at 18% RHli2017 R12, R15

about 1.565 to about 1.29pyrene ratio of the leftover ritonavir–PVP film at 30 min in pH 6.8 buffer; HPMCAS rose to 1.50–1.53purohit2015b R6, R13, R15, R11, R14

Evidence: data, conditions and papers

Finding F9. Water separates drug–polymer dispersions at every stage, while they are made, in storage and when they are wetted, but a separation made before dissolution raised release in one system and lowered it in another

In short. Films spin coated from methanol-containing solvents were featureless at low humidity and carried discrete drug-rich domains at higher humidity, for evacetrapib and itraconazole li2017 R3, R5; mugheirbi2017 R1, R3, R10 (ASD process F1), and 1–12% water in the spray solvent gave domains in spray-dried itraconazole–HPMC mugheirbi2017 R26, R27 (ASD process F3). In storage, sorbed water made the same state in mixed dispersions: pimozide–PVP 50:50 showed one Tg dry and two wet, and separated dispersions crystallized within 22 h to 6 days against 46 and 125 days for mixed ones rumondor2009c R17, R7, R9, R12, R14, R16 (Solid state stability F8). On wetting, ritonavir–PVP films at 97% RH read like the pure drug with pyrene while ritonavir–HPMCAS did not purohit2015b R6, R13, R15, R11, R14 (Characterization methods F2). The effect on release ran both ways: lopinavir–HPMC films separated with water released faster than miscible films at 33–85% loading li2019 R2 (ASD process F14), whereas water in the spray solvent lowered the release rate of 25% ritonavir–PVPVA from about 3.5 to 2.27 and 0.90 li2020 R10, R11, X5 (ASD process F21).

Type. cross-category synthesis of 10 source findings (evacetrapib, itraconazole, lopinavir, ritonavir, felodipine, pimozide and other drugs with HPMC, HPMCAS, PVP and PVPVA; spin-coated films, spray-dried powders, stored powders, wetted films) Strength. : the separation is seen by several methods in each category (ASD process F1, Solid state stability F8, Characterization methods F2), but no paper measured the water content of drying films li2017 K1, X14; mugheirbi2017 K1, X4 (ASD process F1), and the two release results come from different drugs, polymers and processes (synthesis).

How it was shown

ASD process spin coated and spray dried dispersions at set humidities and with water added to the solvent, and stored dry-made films humid li2017 R3, R5, R19, R22, C28; mugheirbi2017 R1, R3, R10, R26, R27. Solid state stability followed dispersions of about 17 drugs with PVP under humidity by IR and DSC rumondor2009c R17, R7, R9, R12, R14, R16. Characterization methods followed probe signals in films at 97% RH and in buffer purohit2015b R6, R13, R15, R11, R14. ASD process then dissolved separated and miscible lopinavir films and spray-dried ritonavir powders li2019 R2; li2020 R10, R11, X5.

What the data show

In PVP the drug–water Flory–Huggins parameter was 2.84–3.58 for four drugs that separated and 2.50–2.71 for two that did not rumondor2009c R24, C46, C27, C32. The surface ritonavir content of 25% spray-dried powders rose from about 21% to about 43% and about 70% with water in the solvent, in the order of the falling release rate li2020 R10, R11, X5.

stage	system	result	ids
spin coating at 7–50% RH	evacetrapib, itraconazole films	featureless at low RH; drug-rich domains at higher RH	li2017 R3, R5; mugheirbi2017 R1, R3, R10
storage at 94% RH	pimozide–PVP; about 17 drugs with PVP	one Tg dry, two wet; separated crystallize in 22 h–6 days, mixed 46 and 125 days	rumondor2009c R17, R7, R9, R12, R14, R16
wetting at 97% RH, pH 6.8 buffer	ritonavir–PVP and –HPMCAS films	PVP film to the drug value; HPMCAS stays mixed	purohit2015b R6, R13, R15, R11, R14
release, 33–85% loading	lopinavir–HPMC films	separated films faster (13.3 and 9.8 against 8.1 µg/mL at 33%)	li2019 R2
release, 25% loading	ritonavir–PVPVA spray dried	rate about 3.5 to 2.27 and 0.90 with water in solvent	li2020 R10, R11, X5

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 in the dry dispersion; two steps in the wet and in the re-dried sample rumondor2009c R17.

Why

The ASD process authors conclude that water is concentrated in the drying film because it leaves more slowly than the volatile solvents li2017 C17, C18; mugheirbi2018 C34, C36. The lopinavir authors attribute the release gain to fast-dissolving polymer-rich phases that free discrete drug-rich domains li2019 C58; the ritonavir authors attribute the loss to surface drug enrichment and fewer low-loading domains, neither measured directly li2020 C67, C40. (synthesis: what decides release is which phase is continuous and what lies at the particle surface, not separation as such.)

Limits and transfer

The ritonavir effect rests on one comparison at 10:90 li2020 K3, K4, C38, X3, X5. Control water in the solvent and the humidity of drying for any polymer that sorbs water, and image the product by a method that resolves domains, since one Tg does not exclude them li2017 R12, R15; rumondor2009c R17. If a separated product is considered, dissolve it against the miscible product at the intended loading li2019 R2.

How it was shown

ASD process spin coated and spray dried dispersions at set humidities and with water added to the solvent, and stored dry-made films humid, imaging them by AFM, TEM, EDX, fluorescence, nanoTA, pyrene and XPS li2017 R3, R5; mugheirbi2017 R1, R3, R10 (ASD process F1); mugheirbi2017 R26, R27; li2020 R6, R7, R4 (ASD process F3); li2017 R19, R22, C28 (ASD process F6). Solid state stability followed dispersions of about 17 drugs with PVP under humidity by IR and DSC rumondor2009c R17, R7, R9, R12, R14, R16 (Solid state stability F8) and compared drug–water interaction parameters rumondor2009c R24, C46, C27, C32 (Solid state stability F10). Characterization methods followed probe signals in films at 97% RH and immersed in buffer purohit2015b R6, R13, R15, R11, R14 (Characterization methods F2). ASD process then dissolved separated and miscible lopinavir films and spray-dried ritonavir powders li2019 R2 (ASD process F14); li2020 R10, R11, X5 (ASD process F21).

What the data show

Adding 20 µL water per mL of stock split a 50% evacetrapib–HPMC film spun at 18% RH, 10 µL did not li2017 R12, R15 (ASD process F1). Initially miscible evacetrapib–PVPVA films stored 7 days at 97% RH formed net-like structures with the drug-rich phase continuous, the opposite of the drug-rich spheres formed by humid preparation li2017 R19, R22, C28 (ASD process F6). The separated state was held after drying and reversed only slowly by heating well above Tg marsac2010 R17 (Solid state stability F8). In PVP the drug–water Flory–Huggins parameter was 2.84–3.58 for four drugs that separated and 2.50–2.71 for two that did not rumondor2009c R24, C46, C27, C32 (Solid state stability F10). In pH 6.8 buffer the leftover ritonavir–PVP film fell from a pyrene ratio of about 1.565 to about 1.29 at 30 min, while the HPMCAS film rose to 1.50–1.53 purohit2015b R6, R13, R15, R11, R14 (Characterization methods F2). At 33% loading lopinavir reached about 8.1 µg/mL after 10 min from a miscible film, 13.3 from a film made with 4% water and 9.8 from a film stored humid; at 15% loading all three gave about 15–17 µg/mL li2019 R2 (ASD process F14). The surface ritonavir content of the 25% spray-dried powders rose from about 21% to about 43% and about 70% with water in the solvent, in the order of the falling release rate li2020 R10, R11, X5 (ASD process F21).

source finding	system	conditions	result	ids
ASD process F1	evacetrapib, itraconazole films	spin coating at 7–50% RH	featureless at low RH; drug-rich domains at higher RH	li2017 R3, R5; mugheirbi2017 R1, R3, R10
ASD process F3	itraconazole–HPMC E3	spray drying with 1–12% water	dark domains, extra emission at 373 nm	mugheirbi2017 R26, R27
ASD process F6	evacetrapib–PVPVA	7 days at 97% RH	drug-rich continuous network with polymer-rich holes	li2017 R19, R22, C28
Solid state stability F8	pimozide–PVP; about 17 drugs with PVP	94% RH	one Tg dry, two wet; separated crystallize in 22 h–6 days, mixed 46 and 125 days	rumondor2009c R17, R7, R9, R12, R14, R16
Solid state stability F10	six drugs in PVP	drug–water χ	2.84–3.58 separated; 2.50–2.71 mixed	rumondor2009c R24, C46, C27, C32
Characterization methods F2	ritonavir–PVP and –HPMCAS films	97% RH; pH 6.8 buffer	PVP film to the drug value; HPMCAS stays mixed	purohit2015b R6, R13, R15, R11, R14
ASD process F14	lopinavir–HPMC films	33–85% loading, pH 6.5	separated films release faster (13.3 and 9.8 against 8.1 µg/mL at 33%)	li2019 R2
ASD process F21	ritonavir–PVPVA spray dried	25% loading	release rate about 3.5 to 2.27 and 0.90 with water in solvent	li2020 R10, R11, X5

Figure

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 (Solid state stability F8).

Why

The ASD process authors conclude that water is concentrated in the drying film because it leaves more slowly than the volatile solvents li2017 C17, C18; mugheirbi2018 C34, C36 (ASD process F2). In storage the drug's affinity for water, not log P or melting data, set what sorbed water did rumondor2009c R24, C46, C27, C32 (Solid state stability F10). For release, the lopinavir authors attribute the gain to fast-dissolving polymer-rich phases that free discrete drug-rich domains li2019 C58 (ASD process F14), and the release falls again when too much water leaves a drug-rich continuous phase li2019 R15, R16 (ASD process F15); the ritonavir authors attribute the loss to surface drug enrichment and to fewer low-loading domains, neither measured directly li2020 C67, C40 (ASD process F21). (synthesis: what decides release is which phase is continuous and what lies at the particle surface, not separation as such; a polymer-rich continuous phase can carry drug-rich domains out, a drug-rich surface or network holds the drug back.)

Conditions and limits

The drying path was never followed in composition, and domain size is a line-profile height or an image impression li2017 K2, C18; mugheirbi2018 K3, X8 (ASD process F2); the lopinavir release result is one slowly crystallizing drug in films only li2019 K1, X11, C55 (ASD process F14); the ritonavir effect rests on one comparison at 10:90 li2020 K3, K4, C38, X3, X5 (ASD process F21).

Counterexamples and conflicts

Higher drug loading resisted storage separation in the evacetrapib powders li2017 R24, R25, C52 (ASD process F6), and ritonavir–HPMCAS stayed mixed when wetted purohit2015b R6, R13, R15, R11, R14 (Characterization methods F2).

Transfer check

Control water in the solvent and the humidity of drying for any polymer that sorbs water, and image the product at the intended loading by a method that resolves domains, since one Tg does not exclude them li2017 R12, R15 (ASD process F1); rumondor2009c R17 (Solid state stability F8). Measure the drug–water interaction parameter or the separation at high RH before choosing a hygroscopic polymer for a hydrophobic donor drug rumondor2009c R24, C46, C27, C32 (Solid state stability F10). If a separated product is considered, dissolve it against the miscible product at the intended loading li2019 R2 (ASD process F14).

History

2009–2010: moisture-induced separation was shown in stored PVP dispersions and tied to the drug–water parameter rumondor2009c R24, C46, C27, C32 (Solid state stability F10); rumondor2009c R17; marsac2010 R17 (Solid state stability F8). 2015: probes followed separation of wetted films purohit2015b R6, R13, R15, R11, R14 (Characterization methods F2). 2017: water during film formation was shown to split miscible films, in spin coating and spray drying li2017 R3, R5; mugheirbi2017 R1, R3, R10 (ASD process F1); mugheirbi2017 R26, R27 (ASD process F3). 2019: separated lopinavir films released faster li2019 R2 (ASD process F14). 2020: water in the spray solvent lowered ritonavir release at 25% loading li2020 R10, R11, X5 (ASD process F21).

Conceptsmoisture-induced phase separation solvent-induced phase separation amorphous-amorphous phase separation surface drug enrichment hygroscopicity

F10

Topic 3Water and the hydrating solid3 of 3

A dispersion can crystallize inside its wetted solid before the drug dissolves; a dissolved polymer does not prevent this.

A crystal-free bicalutamide–PVPVA extrudate never exceeded about 38–40 µg/mL against an amorphous solubility of 150 µg/mL, with crystals at the particle edges from about 10–20 min moseson2021 R12, R13, R14, R17, R18, R19, R25. The same pair at 5 and 10% loading released drug and polymer together and escaped this, while a 30% compact carried a drug-enriched boundary layer with crystals moseson2022b R6, R7, R14, R15. Wetted nifedipine and celecoxib crystallized with or without a polymer in the medium raina2014b C11, R2; xie2015 R9, R10.

moderateModerate: dissolution, PLM, Raman and XRPD agree for bicalutamide, but crystals in the wetted solid are inferred in some systems, the telaprevir case rests on one micrograph, and the proposed trigger was not measured moseson2021 K1, K7, X8, X11; mosqueragiraldo2018b K4, K5, X13.

Bicalutamide stopped far below its amorphous solubility; for delamanid a salt that raised the Tg restored release. moseson2021 R12, R13, R14, R17, R18, R19, R25; duong2022a M1, R3, R8, R20, R26

For your drug

Dissolve the dispersion at a dose above the amorphous solubility and examine the undissolved solid by PLM or SHG within the first 30 min; a plateau far below the amorphous solubility with crystals in the particles points to matrix crystallization.
Check whether drug and polymer release are congruent at the chosen loading, and avoid milling steps for loadings above the limit.

moseson2021 R12, R13, R14, R17, R18, R19, R25; moseson2022b R6, R7; moseson2022b R1, R4, R5, M1

How it works and key numbers

The authors propose a hydrated, drug-rich solid with a Tg below 37 °C as the trigger, which was not measured moseson2021 K1, K7, X8, X11.
PVPVA left the bicalutamide solid faster than the drug, and the amorphous solid turned to the metastable form 2 after 20–30 min moseson2021 R12, R13, R14, R17, R18, R19, R25.
Matrix crystallization is surface-mediated, and congruent release "may be a strategy to avoid" it moseson2022b C36, C48, X15.
The water-plasticized Tg of the drug sits at the centre of two opposite failures, release failing when it is well above the test temperature and crystallization when it is below alonzo2010 R2, C33, C34.
(synthesis: a polymer in the medium meets only the drug that has already dissolved; only a release in which drug and polymer leave together keeps the drug from staying behind in a drug-rich, wetted layer.)

94 ± 8 µmdrug-enriched boundary layer of a 30% bicalutamide compact, with crystals after 1 hmoseson2022b R6, R7, R14, R15

about 50% of the dose4 h level of 30% bicalutamide after 2–5 min cryomilling; a 10% powder survived 10 minmoseson2022b R1, R4, R5, M1

about 68%undissolved posaconazole that crystallized in acid at 50% loadingelkhabaz2019a R10, R1, R16, R20

Evidence: data, conditions and papers

Finding F10. A dispersion can crystallize inside its own wetted solid before the drug reaches the solution, a route that a polymer dissolved in the medium does not stop and that a low, congruently released loading avoided

In short. Wetted amorphous nifedipine and celecoxib crystallized with or without a polymer in the medium raina2014b C11, R2; xie2015 R9, R10 (Dissolution F4), and hydrated felodipine above its Tg at 37 °C crystallized faster than it dissolved alonzo2010 R2, C33, C34 (Dissolution F8). A crystal-free bicalutamide–PVPVA extrudate never exceeded about 38–40 µg/mL against an amorphous solubility of 150 µg/mL, with crystals at the particle edges from about 10–20 min moseson2021 R12, R13, R14, R17, R18, R19, R25 (ASD process F27); the same pair at 5 and 10% loading released drug and polymer together and escaped it, while a 30% compact carried a 94 ± 8 µm drug-enriched boundary layer with crystals after 1 h moseson2022b R6, R7, R14, R15 (ASD process F38). The 50% telaprevir–HPMCAS dispersion showed birefringent domains in its particles at 20 min and passed 90 µg/mL only after about 600 min mosqueragiraldo2018b R16, R18, R19 (Bioperformance F9), and in acid, where an enteric polymer stays undissolved, about 68% of the undissolved posaconazole crystallized at 50% loading elkhabaz2019a R10, R1, R16, R20 (Dissolution F11).

Type. cross-category synthesis of 8 source findings (nifedipine, celecoxib, felodipine, indomethacin methyl ester, bicalutamide, telaprevir, atazanavir, posaconazole, delamanid and pretomanid; slurries, powders, compacts and dissolving dispersions) Strength. : dissolution, PLM, Raman and XRPD agree for bicalutamide moseson2021 K1, K7, X8, X11 (ASD process F27), but crystals in the wetted solid are inferred in some systems (Dissolution F4), the telaprevir case rests on one micrograph mosqueragiraldo2018b K4, K5, X13 (Bioperformance F9), and the proposed trigger, a hydrated drug-rich solid with a low Tg, was not measured in any category.

How it was shown

Dissolution slurried wetted amorphous solids and dispersions, imaged dissolving compacts and ran gastric-to-intestinal tests of enteric dispersions raina2014b C11, R2; xie2015 R9, R10; saboo2020 R8, R9, R22, C36, C37; elkhabaz2019a R10, R1, R16, R20. ASD process dissolved crystal-free bicalutamide–PVPVA extrudates at four doses, followed the solid by PLM and Raman, and imaged exposed compacts moseson2021 R12, R13, R14, R17, R18, R19, R25; moseson2022b R6, R7, R14, R15. Bioperformance dissolved telaprevir and atazanavir dispersions under an absorptive sink and examined the particles mosqueragiraldo2018b R16, R18, R19; hate2018 R14, R15.

What the data show

For bicalutamide the fraction dissolved at 4 h fell from about 0.82 to 0.23 as the dose rose from 3 to 150 µg/mL, and PVPVA left the solid faster than the drug moseson2021 R12, R13, R14, R17, R18, R19, R25. Cryomilling the 30% bicalutamide powder for 2–5 min cut the 4 h level to about 50% of the dose, about the form 2 solubility, while a 10% powder survived 10 min of milling or extrusion moseson2022b R1, R4, R5, M1.

system	conditions	result	ids
bicalutamide–PVPVA, crystal-free	3–150 µg/mL	peak about 38–40 against 150 µg/mL; form 2 after 20–30 min	moseson2021 R12, R13, R14, R17, R18, R19, R25
bicalutamide–PVPVA, 5–50%	powders, compacts	5–10% congruent, no matrix crystals; 30% boundary layer 94 ± 8 µm with crystals	moseson2022b R6, R7, R14, R15
telaprevir–HPMCAS 50%; atazanavir–PVPVA 50%	absorptive tests	birefringent domains at 20 min; donor crystallizes from 80 min	mosqueragiraldo2018b R16, R18, R19; hate2018 R14, R15
posaconazole–HPMCAS	acid stage	about 68% of the undissolved drug crystallized at 50%	elkhabaz2019a R10, R1, R16, R20
pretomanid–HPMCAS-HF	FeSSIF pH 5.0–6.0	at pH 5.5 and below release to about the crystalline solubility	nguyen2023a R19, R1, R20

Fig. 6 of moseson2022b: BCL release (a) and PVPVA release (b) from 5–50% loading dispersions — Fig. 6 · moseson2022bBCL release (a) and PVPVA release (b) from 5–50% loading dispersions

The 5 and 10% curves of drug and polymer rise together, while from 20% the polymer runs ahead of the drug moseson2022b R6, R7.

Why

The ASD process authors propose a hydrated, drug-rich solid with a Tg below 37 °C as the trigger, which was not measured moseson2021 K1, K7, X8, X11, conclude that matrix crystallization is surface-mediated, and that congruent release "may be a strategy to avoid" it moseson2022b C36, C48, X15. The Dissolution chapters place the water-plasticized Tg of the drug at the centre of two opposite failures, release failing when it is well above the test temperature and crystallization when it is below alonzo2010 R2, C33, C34. (synthesis: a polymer in the medium meets only the drug that has already dissolved.)

Limits and transfer

The bicalutamide kinetics come from 10 mg/mL slurries and the boundary layers were measured on compacts, not powders moseson2022b X20, X18. Dissolve the dispersion at a dose above the amorphous solubility and examine the undissolved solid by PLM or SHG within the first 30 min moseson2021 R12, R13, R14, R17, R18, R19, R25. Check whether drug and polymer release are congruent at the chosen loading, and avoid milling steps for loadings above the limit moseson2022b R6, R7, R1, R4, R5, M1.

How it was shown

Dissolution slurried wetted amorphous solids and dispersions, imaged dissolving compacts and ran gastric-to-intestinal tests of enteric dispersions raina2014b C11, R2; xie2015 R9, R10; saboo2020 R8, R9, R22, C36, C37 (Dissolution F4); alonzo2010 R2, C33, C34 (Dissolution F8); elkhabaz2019a R10, R1, R16, R20; nguyen2023c R19, R20 (Dissolution F11). ASD process dissolved crystal-free bicalutamide–PVPVA extrudates at four doses, followed the solid by PLM and Raman, and imaged exposed compacts by SEM, EDX and confocal microscopy moseson2021 R12, R13, R14, R17, R18, R19, R25 (ASD process F27); moseson2022b R6, R7, R14, R15 (ASD process F38). Bioperformance dissolved telaprevir and atazanavir dispersions under an absorptive sink and examined the particles mosqueragiraldo2018b R16, R18, R19; hate2018 R14, R15 (Bioperformance F9).

What the data show

PAA dispersions released only about half their celecoxib while HPMCAS in the medium held the dissolved drug xie2016a R9, R10, C31 (Dissolution F4), and crystals on the dissolving surface of indomethacin methyl ester compacts ended congruent release with 1000 µg/mL HPMC-606 in the medium saboo2020 R8, R9, R22, C36, C37 (Dissolution F4). For bicalutamide the fraction dissolved at 4 h fell from about 0.82 to 0.23 as the dose rose from 3 to 150 µg/mL, the amorphous solid turned to the metastable form 2 after 20–30 min, and PVPVA left the solid faster than the drug moseson2021 R12, R13, R14, R17, R18, R19, R25 (ASD process F27). Cryomilling the 30% bicalutamide powder for 2–5 min cut the 4 h level to about 50% of the dose, about the form 2 solubility, while a 10% powder survived 10 min of milling or extrusion moseson2022b R1, R4, R5, M1 (ASD process F39). The 50:50 atazanavir–PVPVA dispersion crystallized in the donor from about 80 min and transferred least hate2018 R14, R15 (Bioperformance F9). For delamanid, a poor glass former with a Tg of 43.3 °C, sulfonate salts with Tg 83.7–117.8 °C raised release at 25% drug from ≈20 to ≈95–97 µg/mL duong2022a M1, R3, R8, R20, R26 (Dissolution F8). Pretomanid dispersions below FeSSIF pH 5.8 released only to about the crystalline solubility and their particles showed crystalline drug nguyen2023a R19, R1, R20 (Bioperformance F26).

source finding	system	conditions	result	ids
Dissolution F4	nifedipine, celecoxib; celecoxib–PAA; indomethacin methyl ester compacts	slurries; dissolution with polymer in medium	crystallize with or without polymer; about half released; crystals end congruent release	raina2014b C11, R2; xie2015 R9, R10; xie2016a R9, R10, C31; saboo2020 R8, R9, R22, C36, C37
Dissolution F8	felodipine; delamanid salts	37 °C; 25% drug	hydrated drug above Tg crystallizes faster than it dissolves; salts raise release ≈20 to ≈95–97 µg/mL	alonzo2010 R2, C33, C34; duong2022a M1, R3, R8, R20, R26
ASD process F27	bicalutamide–PVPVA, crystal-free	3–150 µg/mL	peak about 38–40 against 150 µg/mL; form 2 after 20–30 min	moseson2021 R12, R13, R14, R17, R18, R19, R25
ASD process F38	bicalutamide–PVPVA, 5–50%	powders, compacts	5–10% congruent, no matrix crystals; 30% boundary layer 94 ± 8 µm with crystals	moseson2022b R6, R7, R14, R15
ASD process F39	bicalutamide–PVPVA 30% and 10%	cryomilling	30% falls to about the form 2 level; 10% survives	moseson2022b R1, R4, R5, M1
Bioperformance F9	telaprevir–HPMCAS 50%; atazanavir–PVPVA 50%	absorptive tests	birefringent domains at 20 min; donor crystallizes from 80 min	mosqueragiraldo2018b R16, R18, R19; hate2018 R14, R15
Dissolution F11	posaconazole–HPMCAS; delamanid	acid stage	about 68% of the undissolved drug crystallized at 50%	elkhabaz2019a R10, R1, R16, R20; nguyen2023c R19, R20
Bioperformance F26	pretomanid–HPMCAS-HF	FeSSIF pH 5.0–6.0	at pH 5.5 and below release to about the crystalline solubility; crystalline drug in particles	nguyen2023a R19, R1, R20

Figure

The 5 and 10% curves of drug and polymer rise together, while from 20% the polymer runs ahead of the drug moseson2022b R6, R7 (ASD process F38).

Why

The ASD process authors propose a hydrated, drug-rich solid with a Tg below 37 °C as the trigger, which was not measured moseson2021 K1, K7, X8, X11 (ASD process F27), conclude that matrix crystallization is surface-mediated, and that congruent release "may be a strategy to avoid" it moseson2022b C36, C48, X15 (ASD process F38). The Dissolution chapters place the water-plasticized Tg of the drug at the centre of two opposite failures, release failing when it is well above the test temperature and crystallization when it is below alonzo2010 R2, C33, C34 (Dissolution F8). For mechanical activation the authors "suggest" high-surface-energy particles, nuclei or phase-separated domains, none measured moseson2022b C54, X9, X19 (ASD process F39). (synthesis: a polymer in the medium meets only the drug that has already dissolved; a drug that crystallizes before it leaves the solid is not acted on by it, and only a release in which drug and polymer leave together keeps the drug from staying behind in a drug-rich, wetted layer.)

Conditions and limits

The bicalutamide kinetics come from 10 mg/mL slurries and the boundary layers were measured on compacts, not powders moseson2022b X20, X18 (ASD process F27); the two sides of the Tg conflict were never tested on one drug (Dissolution F8).

Counterexamples and conflicts

With 5% SDS in the telaprevir dispersion the matrix crystallization was avoided and 90 µg/mL was passed within about 60 min, yet at a higher dose the concentration fell after about 600 min mosqueragiraldo2018b R16, R17 (Bioperformance F9). For fast-crystallizing delamanid a salt that raised the Tg restored release, whereas for lumefantrine salts that raised the Tg lowered the highest loading with good release duong2022a M1, R3, R8, R20, R26; hiew2022b R2, R20 (Dissolution F8).

Transfer check

Dissolve the dispersion at a dose above the amorphous solubility and examine the undissolved solid by PLM or SHG within the first 30 min; a plateau far below the amorphous solubility with crystals in the particles points to matrix crystallization moseson2021 R12, R13, R14, R17, R18, R19, R25 (ASD process F27). Check whether drug and polymer release are congruent at the chosen loading, and avoid milling steps for loadings above the limit moseson2022b R6, R7 (ASD process F38); moseson2022b R1, R4, R5, M1 (ASD process F39).

History

2010: hydrated felodipine above its Tg crystallized faster than it dissolved alonzo2010 R2, C33, C34 (Dissolution F8). 2014–2016: wetted nifedipine and celecoxib crystallized regardless of a dissolved polymer raina2014b C11, R2; xie2015 R9, R10 (Dissolution F4). 2018: matrix crystallization limited high-loading telaprevir and atazanavir dispersions under absorption mosqueragiraldo2018b R16, R18, R19; hate2018 R14, R15 (Bioperformance F9). 2019–2020: posaconazole crystallized in acid inside undissolved enteric dispersions, and crystals on compact surfaces ended congruent release elkhabaz2019a R10, R1, R16, R20 (Dissolution F11); saboo2020 R8, R9, R22, C36, C37 (Dissolution F4). 2021–2022: the route was characterized for bicalutamide and tied to loading and milling moseson2021 R12, R13, R14, R17, R18, R19, R25 (ASD process F27); moseson2022b R6, R7, R14, R15 (ASD process F38). 2023: pretomanid particles crystallized at fed-state pH nguyen2023a R19, R1, R20 (Bioperformance F26).

Conceptsmatrix crystallization plasticization by water drug-rich surface layer congruent release crystallization during dissolution

Topic 4 of 5 · 2 findings · F11–F12

Polymers and surfactants across stages

F11

Topic 4Polymers and surfactants across stages1 of 2

No polymer was best at every stage: fast release and thermal protection favoured PVP or PVPVA, inhibition and humid storage HPMCAS.

At 10% felodipine PVP and PVPVA released ≈3.8 and ≈2.4 mg/min/cm² against ≈0.82 for HPMCAS, but lost congruent release above 10 and 15% while HPMCAS stayed congruent to 50% saboo2020a R15, R14, C55. PVP protected ritonavir in the extruder and held polyphenols in humid storage, but lost to HPMCAS for felodipine in humid storage alvarenga2022 R10, R22, C25; wegiel2013a R9; konno2008 R1, R3. HPMCAS-HF inhibited posaconazole nucleation longest but released least, lowered the amorphous solubility of atazanavir, and lost pretomanid exposure with food shah2025 R3, R4, R5; ueda2020a R1; nguyen2023a R23.

strongStrong for each ranking in its own test, replicated within its category; moderate for the conflict across stages, which no paper measured on one drug with the same polymers in every stage saboo2020a R15, R14, C55; alvarenga2022 R10, R22, C25; konno2008 R1, R3.

PVP or PVPVA best

release at 10% felodipineritonavir after 5 min at 180 °Cpolyphenols in humid storageezetimibe in pH 6.8 bufferdelamanid supersaturation

HPMCAS or cellulosics best

congruent release to 50% drugfelodipine in humid storagedanazol and celecoxib in solutionezetimibe in FeSSIFdelamanid supersaturation

Each stage chose a different polymer; only for delamanid did PVPVA hold supersaturation as long as HPMCAS. saboo2020a R15, R14, C55; alvarenga2022 R10, R22, C25; wegiel2013a R9; konno2008 R1, R3; jackson2015 R5; xie2015 R1; elkhabaz2017 R6, R7; duong2022a R4, R2

In the extruder the order is the reverse of the order for inhibition and humid storage. alvarenga2022 R10, R22, C25

For your drug

Rank candidate polymers for the drug in each stage it will meet: limit of congruency, induction time in the intended medium, humid storage at the target loading and, for a melt process, assay after a hold at the extrusion temperature.
For an enteric grade check release at the lowest expected intestinal pH.

saboo2020a R15, R14, C55; konno2008 R1, R3; alvarenga2022 R10, R22, C25; nguyen2023a R23

How it works and key numbers

The hydrophilic polymers dissolve fast, so drug leaves fast at low loading; the Dissolution authors call the choice between fast release and inhibition a "trade-off" saboo2020a R15, R14, C55.
For HPMCAS grades more acid groups and a more ionized gel dissolve the polymer faster, while more acetyl and less ionization delay nucleation longer: neat LF, MF and HF dissolved at about 1.50, 0.90 and 0.45 mg/min/cm² shah2025 R3, R4, R5; bapat2025a R1, R2, M3, M4, M5.
PVP loses its humid advantage through hygroscopicity, while for the acidic polyphenols the basic E100 and the acceptor PVP offer complementary groups wegiel2013a R9.
HPMCAS-HF enters the drug-rich phase and lowers the amorphous solubility, atazanavir from 81.5 to 35.5 µg/mL ueda2020a R1.
For degradation the authors propose that polymer substituents decide, through water from a dehydration product and acid from protic polymers, which was not measured alvarenga2022 C31, C37, C38, X8, X9.
(synthesis: the polymer property that helps one stage harms another; a polymer choice is a weighting of stages for the given drug.)

51–82% vs 9–28%crystallinity of felodipine with PVP against HPMCAS after about 490 days at 75–93% RHrumondor2009b R9, C13

more than 200 to more than 450 days vs 1–3 daysnaringenin and quercetin with PVP or E100 against HPMCAS before crystalswegiel2013a R9

155% fasted; 72.2% of that fedpretomanid HPMCAS-HF tablet against the crystalline product in monkeysnguyen2023a R23

Evidence: data, conditions and papers

Finding F11. No polymer was best at every stage: PVP and PVPVA released fastest at low loading, protected ritonavir in the extruder and held polyphenols in humid storage, but lost to HPMCAS for felodipine in humid storage and in solution; the most hydrophobic HPMCAS grade inhibited longest but released least, lowered the ceiling and lost exposure with food

In short. At 10% felodipine PVP and PVPVA released ≈3.8 and ≈2.4 mg/min/cm² against ≈0.82 for HPMCAS, but lost congruent release above 10 and 15% while HPMCAS stayed congruent to 50%, and the cellulosic polymers held felodipine, danazol, celecoxib and praziquantel far longer in solution than PVP or PVPVA saboo2020a R15, R14, C55; konno2008a R7; jackson2015 R5; xie2015 R1; polyzois2024 R3 (Dissolution F9). In humid storage 3% PVP gave a felodipine nucleation rate of about 8.6 × 10⁵ against about 1.3 × 10⁴ m⁻³ s⁻¹ for HPMCAS, yet naringenin and quercetin with PVP or E100 showed no crystals for more than 200 to more than 450 days while those with HPMCAS crystallized within 1–3 days konno2008 R1, R3; wegiel2013a R9 (Solid state stability F9). After 5 min at 180 °C ritonavir assayed about 76% with PVP K-30 and 59% with PVPVA 64 but about 3.5% with HPMCAS MF and 0% with HPMCAS LF and HPMC alvarenga2022 R10, R22, C25 (ASD process F34). HPMCAS-HF delayed posaconazole nucleation beyond 240 min but released only about 22–31 µg/mL at pH 6.5 shah2025 R3, R4, R5 (Dissolution F10), lowered the amorphous solubility of atazanavir from 81.5 to 35.5 µg/mL ueda2020a R1 (Bioperformance F19), and its pretomanid tablet fell to 72.2% of its fasted exposure with food nguyen2023a R23 (Bioperformance F26).

Type. cross-category synthesis of 8 source findings (release, supersaturation, humid storage, extrusion degradation, amorphous solubility, monkeys; felodipine, danazol, celecoxib, praziquantel, delamanid, polyphenols, ritonavir, posaconazole, atazanavir, pretomanid) Strength. for each ranking in its own test, replicated within its category (Dissolution F9, ASD process F34, Solid state stability F9); moderate for the conflict across stages, which no paper measured on one drug with the same polymers in every stage (synthesis).

How it was shown

Dissolution measured normalized release from compacts over loadings, ranked polymers by how long dispersions held supersaturation, and compared HPMCAS grades for release and for posaconazole nucleation saboo2020a R15, R14, C55; jackson2015 R5; shah2025 R3, R4, R5; bapat2025a R1, R2, M3, M4, M5. Solid state stability stored felodipine and polyphenol dispersions dry and humid konno2008 R1, R3; rumondor2009b R9, C13; wegiel2013a R9. ASD process assayed ritonavir after heating and extrusion with ten polymers alvarenga2022 R10, R22, C25. Bioperformance set two HPMCAS grades against four drugs and dosed pretomanid tablets to fasted and fed monkeys ueda2020a R1; nguyen2023a R23.

What the data show

HPMCAS at 20–30% felodipine released about 100–225 times faster than PVPVA saboo2020a R15, R14, C55. Neat LF, MF and HF dissolved at about 1.50, 0.90 and 0.45 mg/min/cm² in pH 6.8 phosphate bapat2025a R1, R2, M3, M4, M5. In felodipine powders stored for about 490 days PVP dispersions reached 51–82% crystalline at 75–93% RH against 9–28% for HPMCAS, with no difference at 0–52% RH rumondor2009b R9, C13.

stage	system	best polymer	ids
release, 10% loading	felodipine	PVP, PVPVA fastest; HPMCAS congruent to 50%	saboo2020a R15, R14, C55
dispersion supersaturation	felodipine, danazol, celecoxib, praziquantel; delamanid	cellulosics; PVPVA as good for delamanid	konno2008a R7; jackson2015 R5; xie2015 R1; polyzois2024 R3; duong2022a R4, R2
humid storage	felodipine; naringenin, quercetin	HPMCAS for felodipine; PVP or E100 for polyphenols	konno2008 R1, R3; wegiel2013a R9
5 min at 180 °C; extrusion 130–160 °C	ritonavir with ten polymers	PVP K-30, PVPVA; HPMCAS and HPMC worst	alvarenga2022 R10, R22, C25
nucleation; release	posaconazole, loratadine with HPMCAS grades	HF for nucleation; LF for release	shah2025 R3, R4, R5; bapat2025a R1, R2, M3, M4, M5
monkeys, fasted and fed	pretomanid HPMCAS-HF tablet	155% fasted; 72.2% of fasted with food	nguyen2023a R23

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

PVPVA starts highest and drops by orders of magnitude after 15%, while HPMCAS and EUDS start lower and stay flat to 50% saboo2020a R14.

Why

The Dissolution authors call the choice between fast release and inhibition a "trade-off" saboo2020a R15, R14, C55; for HPMCAS grades more acid groups and a more ionized gel dissolve the polymer faster, while more acetyl and less ionization delay nucleation longer shah2025 R3, R4, R5; bapat2025a R1, R2, M3, M4, M5. PVP loses its humid advantage through hygroscopicity wegiel2013a R9. (synthesis: the polymer property that helps one stage harms another; a polymer choice is a weighting of stages for the given drug.)

Limits and transfer

The degradation ranking is for one drug alvarenga2022 K1, K3, K5, X7, X9, and the best inhibitor ranking reversed between the two enantiomers of praziquantel polyzois2024 R2, R3, R4. Rank candidate polymers for the new drug in each stage it will meet: limit of congruency, induction time in the intended medium, humid storage at the target loading and, for a melt process, assay after a hold at the extrusion temperature saboo2020a R15, R14, C55; konno2008 R1, R3; alvarenga2022 R10, R22, C25. For an enteric grade check release at the lowest expected intestinal pH nguyen2023a R23.

How it was shown

Dissolution measured normalized release from compacts with five polymers over loadings, ranked polymers by how long dispersions held supersaturation and screened growth and nucleation inhibitors in solution, and compared HPMCAS grades for release and for posaconazole nucleation saboo2020a R15, R14, C55; konno2008a R7; jackson2015 R5; xie2015 R1; polyzois2024 R3 (Dissolution F9); shah2025 R3, R4, R5; bapat2025a R1, R2, M3, M4, M5 (Dissolution F10). Solid state stability stored felodipine and polyphenol dispersions dry and humid konno2008 R1, R3; rumondor2009b R9, C13; wegiel2013a R9 (Solid state stability F9). ASD process assayed ritonavir after TGA holds, oven heating and extrusion with ten polymers alvarenga2022 R10, R22, C25 (ASD process F34). Bioperformance set two HPMCAS grades against four drugs, screened polymers in three media, and dosed pretomanid tablets to fasted and fed monkeys ueda2020a R1 (Bioperformance F19); elkhabaz2017 R6, R7 (Bioperformance F11); nguyen2023a R23 (Bioperformance F26).

What the data show

HPMCAS at 20–30% felodipine released about 100–225 times faster than PVPVA saboo2020a R15, R14, C55 (Dissolution F9). Danazol dispersions crystallized after ≈56–70, ≈188–200 and ≈284–319 min with PVP, HPMC and HPMCAS jackson2015 R5 (Dissolution F9), but PVPVA held delamanid as long as HPMCAS and HPMCP duong2022a R4, R2 (Dissolution F9). Neat LF, MF and HF dissolved at about 1.50, 0.90 and 0.45 mg/min/cm² in pH 6.8 phosphate, and 25% loratadine left LF about 25 times faster than HF bapat2025a R1, R2, M3, M4, M5 (Dissolution F10). In felodipine powders stored for about 490 days PVP dispersions reached 51–82% crystalline at 75–93% RH against 9–28% for HPMCAS, with no difference at 0–52% RH rumondor2009b R9, C13 (Solid state stability F9). The ritonavir degradation order PVPVA 64 > HPMCAS MF > HPMC held in extrusion at 130–160 °C, and loading, PVP grade and dispersion Tg (53 to 147 °C) did not explain it alvarenga2022 R10, R22, C25, R14, R17, R4, R18 (ASD process F34). For ezetimibe PVP was best in pH 6.8 buffer and HPMC-AS in FeSSIF elkhabaz2017 R6, R7 (Bioperformance F11). Pretomanid in solution crystallized within minutes with most enteric polymers and not within 1000 min with HPMCAS-HF nguyen2023a R5 (Bioperformance F27), and the HF tablet gave 155% of the crystalline product's exposure when fasted nguyen2023a R23 (Bioperformance F26).

source finding	system	conditions	best polymer	ids
Dissolution F9	felodipine, 10% loading	normalized release	PVP, PVPVA fastest; HPMCAS congruent to 50%	saboo2020a R15, R14, C55
Dissolution F9	felodipine, danazol, celecoxib, praziquantel; delamanid	dispersion supersaturation	cellulosics; PVPVA as good for delamanid	konno2008a R7; jackson2015 R5; xie2015 R1; polyzois2024 R3; duong2022a R4, R2
Solid state stability F9	felodipine; naringenin, quercetin	humid storage	HPMCAS for felodipine; PVP or E100 for polyphenols	konno2008 R1, R3; wegiel2013a R9
ASD process F34	ritonavir with ten polymers	5 min at 180 °C; extrusion 130–160 °C	PVP K-30, PVPVA; HPMCAS and HPMC worst	alvarenga2022 R10, R22, C25
Dissolution F10	posaconazole, loratadine with HPMCAS grades	nucleation; release	HF for nucleation; LF for release	shah2025 R3, R4, R5; bapat2025a R1, R2, M3, M4, M5
Bioperformance F19	atazanavir, clozapine, ketoconazole	amorphous solubility	AS-LF keeps the ceiling; AS-HF lowers it	ueda2020a R1
Bioperformance F11	ezetimibe	buffer against FeSSIF	PVP in buffer, HPMC-AS in FeSSIF	elkhabaz2017 R6, R7
Bioperformance F26	pretomanid HPMCAS-HF tablet	monkeys, fasted and fed	155% fasted; 72.2% of fasted with food	nguyen2023a R23

Figure

PVPVA starts highest and drops by orders of magnitude after 15%, while HPMCAS and EUDS start lower and stay flat to 50% saboo2020a R14 (Dissolution F9).

Why

The Dissolution authors call the choice between fast release and inhibition a "trade-off" saboo2020a R15, R14, C55 (Dissolution F9); for HPMCAS grades more acid groups and a more ionized gel dissolve the polymer faster, while more acetyl and less ionization delay nucleation longer shah2025 R3, R4, R5; bapat2025a R1, R2, M3, M4, M5 (Dissolution F10). PVP loses its humid advantage through hygroscopicity, while for the acidic polyphenols the basic E100 and the acceptor PVP offer complementary groups wegiel2013a R9 (Solid state stability F9). For degradation the authors propose that polymer substituents decide, through water from a dehydration product and acid from protic polymers, which was not measured alvarenga2022 C31, C37, C38, X8, X9 (ASD process F34). The HPMCAS-HF effect on the ceiling is traced to polymer in the drug-rich phase ueda2020a R1 (Bioperformance F19). (synthesis: the polymer property that helps one stage, hydrophilicity for release and thermal stability, hydrophobicity and fewer ionized groups for inhibition and humid storage, harms another; a polymer choice is a weighting of stages for the given drug.)

Conditions and limits

No paper measured release and inhibition of one drug with the same polymers in one design except posaconazole and celecoxib (Dissolution F9); the two humid-storage sets differ in drug, polymer content and protocol (Solid state stability F9); the degradation ranking is for one drug alvarenga2022 K1, K3, K5, X7, X9 (ASD process F34).

Counterexamples and conflicts

A fast polymer with a fifth of a cellulosic inhibitor held released celecoxib for 16 h at some cost in rate xie2015 R6 (Dissolution F9). The best inhibitor ranking reversed between the two enantiomers of praziquantel polyzois2024 R2, R3, R4 (Dissolution F9).

Transfer check

Rank candidate polymers for the new drug in each stage it will meet: limit of congruency, induction time in the intended medium, humid storage at the target loading and, for a melt process, assay after a hold at the extrusion temperature saboo2020a R15, R14, C55 (Dissolution F9); konno2008 R1, R3 (Solid state stability F9); alvarenga2022 R10, R22, C25 (ASD process F34). For an enteric grade check release at the lowest expected intestinal pH nguyen2023a R23 (Bioperformance F26).

History

2008–2009: PVP lost its advantage in humid felodipine storage konno2008 R1, R3; rumondor2009b R9, C13 (Solid state stability F9). 2013: PVP and E100 held polyphenols wegiel2013a R9 (Solid state stability F9). 2015: cellulosics held danazol and celecoxib in dissolution jackson2015 R5; xie2015 R1 (Dissolution F9). 2017: the best polymer for ezetimibe changed with the medium elkhabaz2017 R6, R7 (Bioperformance F11). 2020: PVPVA released fastest but fell off a cliff, and HPMCAS-HF lowered the ceiling saboo2020a R15, R14, C55 (Dissolution F9); ueda2020a R1 (Bioperformance F19). 2022: polymers set ritonavir degradation in the extruder alvarenga2022 R10, R22, C25 (ASD process F34). 2023: the HF grade raised fasted but lost fed exposure in monkeys nguyen2023a R23 (Bioperformance F26). 2025: the HPMCAS grade order of release and of inhibition ran in opposite directions shah2025 R3, R4, R5; bapat2025a R1, R2, M3, M4, M5 (Dissolution F10).

Conceptspolymer hydrophobicity enteric polymer polymer ionization hygroscopicity falling-off-the-cliff effect

F12

Topic 4Polymers and surfactants across stages2 of 2

Surfactants raised release in every category, and in every category they also promoted crystallization or gave no final gain.

Built into a dispersion, 5 parts SDS per 100 raised the ledipasvir–PVPVA limit of congruency from 5 to 30% que2019 R7, R8, R9, C12. The same surfactants sped crystal growth: 10% TPGS about 85-fold in the celecoxib melt, and Tween 80 and TPGS about twice for ritonavir in solution mosqueragiraldo2014 R1, C9; ilevbare2012a R17, R1.g, M17. TPGS raised the in vitro peak of pretomanid dispersions, yet the TPGS tablet gave 141% against 155% for the binary tablet in monkeys nguyen2023a R12, R14, R8, R23.

strongStrong for each effect in its own test; the conflict is seen within one test only for ritonavir with SDS and bicalutamide after milling; weak for every mechanism, which no category measured que2019 R7, R8, R9, C12; yang2023 R21, R13, R2, R16, R17; moseson2022b R10, R12.

Inside the dispersion TPGS, SDS and Span 80 raised the loading at which drug and polymer leave together. que2019 R7, R8, R9, C12; saboo2021 R12; correasoto2022a R17, R18; correasoto2022b R2, R4

TPGS raised release from silica, but both TPGS media crystallized within the hour. dening2019 R17, R18, M3, C34

For your drug

When a surfactant is added to raise release, measure the induction time or seeded growth of the drug at the surfactant level that the dissolving dosage form produces, and examine the dissolving surface for crystals.
Confirm the gain under an absorptive sink or in vivo before relying on a higher peak.

ilevbare2012a R17, R1.g, M17; yang2023 R21, R13, R2, R16, R17; nguyen2023a R12, R14, R8, R23

How it works and key numbers

In the dispersion the surfactant is credited with keeping the gel in one phase, while at the surface it brought crystals: 30% ritonavir–PVPVA with 10 parts SDS stopped near 70% with needle crystals yang2023 R21, R13, R2, R16, R17.
On silica the authors read Vit E TPGS as displacing ritonavir from silanols ("demonstrates") and SDS as "unlikely" to compete because the negatively charged silica repels it dening2019 C55, C56, C34.
0.1% SDS shortened the induction time of seven of nine drugs while 0.1% sodium taurocholate lengthened it for all 11 tested chen2015 R3, C13, C17, C18.
Above their CMC, six solubilizing additives cut the flux of a 50 µg/mL felodipine solution from about 0.14 to 0.010–0.12 µg/min raina2015c R4, R7.
(synthesis: a surfactant raises the rate at which drug reaches the solution and also the mobility or the supersaturation at which crystals grow; whether the net effect is a gain depends on whether the drug is absorbed before crystals form, which only an absorptive test or an animal shows.)

about 60% of the dosecryomilled 3% TPGS bicalutamide–PVPVA dispersion, where release stoppedmoseson2022b R10, R12

about 83 and 37 vs 160–188 µg/mLritonavir from the co-granule with 0.1% Tween 80 or 5% Span 20 against separate granulestrasi2019 R12, R19

about 175–193 vs 155 µg/mLin vitro peak of pretomanid with TPGS against the binary dispersionnguyen2023a R12, R14, R8, R23

Evidence: data, conditions and papers

Finding F12. Surfactants raised release in every category that added them, and in every category they also promoted crystallization or gave no gain in the end: in the supercooled liquid, in solution, in the dissolving dispersion, on silica and in monkeys

In short. In the supercooled liquid 10% TPGS accelerated celecoxib growth about 85-fold mosqueragiraldo2014 R1, C9 (Solid state stability F5), and in solution Tween 80 and TPGS at about a fifth of their CMC made ritonavir crystals grow about twice as fast ilevbare2012a R17, R1.g, M17 (Dissolution F6). Inside a dispersion the same surfactants helped release: 5 parts SDS per 100 raised the ledipasvir–PVPVA limit of congruency from 5 to 30% que2019 R7, R8, R9, C12 (Dissolution F6) and 1.5% SDS made bicalutamide–PVPVA release congruent moseson2022b R9, R11, R13 (ASD process F40); yet 30% ritonavir–PVPVA with 10 parts SDS stopped near 70% with needle crystals on the surface yang2023 R21, R13, R2, R16, R17 (Dissolution F6), and after cryomilling the 3% TPGS bicalutamide dispersion stopped at about 60% of the dose moseson2022b R10, R12 (ASD process F40). Vit E TPGS raised ritonavir release from SBA-15 from 50 to 61 and 69%, but both TPGS media crystallized between 30 and 45 min dening2019 R17, R18, M3, C34 (Mesoporous silica F12). TPGS lifted the in vitro peak of pretomanid dispersions, yet the TPGS tablet gave 141% against 155% for the binary tablet in monkeys nguyen2023a R12, R14, R8, R23 (Bioperformance F27).

Type. cross-category synthesis of 8 source findings (celecoxib, ritonavir, ledipasvir, felodipine, clopidogrel, atazanavir, bicalutamide, telaprevir, pretomanid; supercooled liquids, solutions, compacts, powders, silica, monkeys) Strength. for each effect in its own test (Dissolution F6, Solid state stability F5); the conflict is seen within one test only for ritonavir with SDS and bicalutamide after milling (Dissolution F6, ASD process F40); weak for every mechanism, which no category measured.

How it was shown

Solid state stability measured melt growth of celecoxib with additives mosqueragiraldo2014 R1, C9. Dissolution measured seeded growth and induction times with surfactants below their CMC and the limit of congruency of dispersions with built-in surfactant ilevbare2012a R17, R1.g, M17; chen2015 R3, C13, C17, C18; que2019 R7, R8, R9, C12; saboo2021 R12. ASD process added SDS or TPGS to bicalutamide–PVPVA moseson2022b R9, R11, R13, R10, R12. Bioperformance put TPGS into pretomanid dispersions tested in monkeys nguyen2023a R12, R14, R8, R23, and Mesoporous silica released ritonavir into media with SDS or Vit E TPGS dening2019 R17, R18, M3.

What the data show

0.1% SDS shortened the induction time of seven of nine drugs while 0.1% sodium taurocholate lengthened it for all 11 tested chen2015 R3, C13, C17, C18. In the ritonavir–lopinavir co-granule 0.1% Tween 80 gave about 83 µg/mL ritonavir and 5% Span 20 only about 37, against about 160–188 for separate granules trasi2019 R12, R19.

place	system	result	ids
supercooled melt	celecoxib, 10% TPGS	growth about 85-fold faster	mosqueragiraldo2014 R1, C9
solution below CMC	ritonavir with Tween 80, TPGS	growth about twice as fast	ilevbare2012a R17, R1.g, M17
compacts with built-in SDS	ledipasvir–PVPVA; ritonavir–PVPVA 30% with 10 parts SDS	limit 5 to 30%; release stops near 70%, needle crystals	que2019 R7, R8, R9, C12; yang2023 R21, R13, R2, R16, R17
powders, milled and unmilled	bicalutamide–PVPVA 30% with SDS or TPGS	congruent with 1.5% SDS; milled TPGS stops at about 60%	moseson2022b R9, R11, R13, R10, R12
silica, closed vessel	ritonavir–SBA-15 with TPGS or SDS	50 to 61 and 69% with TPGS; TPGS media crystallize 30–45 min	dening2019 R17, R18, M3, C34
monkeys	pretomanid–HPMCAS-HF with TPGS	peak about 175–193 against 155 µg/mL; exposure 141 against 155%	nguyen2023a R12, R14, R8, R23

Fig. 8 of ilevbare2012a: growth-inhibition ratio with surfactants, polymers and surfactant–polymer pairs — Fig. 8 · ilevbare2012agrowth-inhibition ratio with surfactants, polymers and surfactant–polymer pairs

The bars for TPGS and Tween 80 lie below 1, faster growth than without additive ilevbare2012a R17.

Why

On silica the authors read Vit E TPGS as displacing ritonavir from silanols ("demonstrates") and SDS as "unlikely" to compete because the negatively charged silica repels it dening2019 C55, C56, C34. In the dispersion the surfactant is credited with keeping the gel in one phase, while at the surface it brought crystals yang2023 R21, R13, R2, R16, R17. (synthesis: a surfactant raises the rate at which drug reaches the solution and also the mobility or the supersaturation at which crystals grow; whether the net effect is a gain depends on whether the drug is absorbed before crystals form.)

Limits and transfer

The bicalutamide surfactant figure labels conflict with the table and text moseson2022b K5, X3, X4, X13, X21, and the monkey arms had four animals nguyen2023a K1, K2, K4, X10. When a surfactant is added to raise release, measure the induction time or seeded growth of the drug at the surfactant level that the dissolving dosage form produces ilevbare2012a R17, R1.g, M17, examine the dissolving surface for crystals yang2023 R21, R13, R2, R16, R17, and confirm the gain under an absorptive sink or in vivo nguyen2023a R12, R14, R8, R23.

How it was shown

Solid state stability measured melt growth of celecoxib with additives mosqueragiraldo2014 R1, C9 (Solid state stability F5). Dissolution measured seeded growth and induction times with surfactants below their CMC and the limit of congruency of dispersions with built-in surfactant ilevbare2012a R17, R1.g, M17; chen2015 R3, C13, C17, C18; que2019 R7, R8, R9, C12; saboo2021 R12; correasoto2022a R17, R18; correasoto2022b R2, R4 (Dissolution F6). ASD process added SDS or TPGS to bicalutamide–PVPVA and surfactants to a two-drug granule moseson2022b R9, R11, R13, R10, R12 (ASD process F40); trasi2019 R12, R19 (ASD process F24). Bioperformance put SDS into a telaprevir dispersion and TPGS into pretomanid dispersions tested in monkeys mosqueragiraldo2018b R16, R17 (Bioperformance F9); nguyen2023a R12, R14, R8, R23 (Bioperformance F27). Mesoporous silica released ritonavir into media with SDS or Vit E TPGS dening2019 R17, R18, M3 (Mesoporous silica F12).

What the data show

0.1% SDS shortened the induction time of seven of nine drugs while 0.1% sodium taurocholate lengthened it for all 11 tested chen2015 R3, C13, C17, C18 (Dissolution F6). TPGS, SDS and Span 80 raised the limits of felodipine (15 → 45%), clopidogrel (40 → 50%) and atazanavir (5 → 15%) saboo2021 R12; correasoto2022a R17, R18; correasoto2022b R2, R4 (Dissolution F6). With 3% SDS one of three bicalutamide replicates lost drug, and after milling the 3% SDS dispersion peaked at about 84% and fell to about 78% moseson2022b R10, R12 (ASD process F40). In the ritonavir–lopinavir co-granule 0.1% Tween 80 gave about 83 µg/mL ritonavir and 5% Span 20 only about 37, against about 160–188 for separate granules trasi2019 R12, R19 (ASD process F24). With 5% SDS the 50% telaprevir dispersion passed 90 µg/mL within about 60 min, but at a higher dose its concentration fell after about 600 min mosqueragiraldo2018b R16, R17 (Bioperformance F9). Six solubilizing additives above their CMC cut the flux of a 50 µg/mL felodipine solution from about 0.14 to 0.010–0.12 µg/min raina2015c R4, R7 (Bioperformance F3). Monomeric SDS left ritonavir release from silica at about 50% dening2019 R17, R18, M3 (Mesoporous silica F12).

source finding	system	conditions	result	ids
Solid state stability F5	celecoxib, 10% TPGS	supercooled melt	growth about 85-fold faster	mosqueragiraldo2014 R1, C9
Dissolution F6	ritonavir with Tween 80, TPGS	5 µg/mL, below CMC	growth about twice as fast	ilevbare2012a R17, R1.g, M17
Dissolution F6	ledipasvir–PVPVA with SDS; felodipine, clopidogrel, atazanavir	built-in surfactant	limit 5 to 30%; 15 to 45, 40 to 50, 5 to 15%	que2019 R7, R8, R9, C12; saboo2021 R12; correasoto2022a R17, R18; correasoto2022b R2, R4
Dissolution F6	ritonavir–PVPVA 30% with 10 parts SDS	compacts	release stops near 70%, needle crystals	yang2023 R21, R13, R2, R16, R17
ASD process F40	bicalutamide–PVPVA 30% with SDS or TPGS	powders, milled and unmilled	congruent with 1.5% SDS; milled TPGS stops at about 60%	moseson2022b R9, R11, R13, R10, R12
Bioperformance F9	telaprevir–HPMCAS 50% with 5% SDS	absorptive test	90 µg/mL within 60 min; fall after 600 min at higher dose	mosqueragiraldo2018b R16, R17
Mesoporous silica F12	ritonavir–SBA-15 with TPGS or SDS	closed vessel	50 to 61 and 69% with TPGS; SDS no change; TPGS media crystallize 30–45 min	dening2019 R17, R18, M3, C34
Bioperformance F27	pretomanid–HPMCAS-HF with TPGS	FaSSIF; monkeys	peak about 175–193 against 155 µg/mL; exposure 141 against 155%	nguyen2023a R12, R14, R8, R23

Figure

The bars for TPGS and Tween 80 lie below 1, faster growth than without additive, and the bars of the esters fall when Tween 80 is added ilevbare2012a R17 (Dissolution F6).

Why

On silica the authors read Vit E TPGS as displacing ritonavir from silanols ("demonstrates") and SDS as "unlikely" to compete because the negatively charged silica repels it dening2019 C55, C56, C34 (Mesoporous silica F12). In the dispersion the surfactant is credited with keeping the gel in one phase, while at the surface it brought crystals yang2023 R21, R13, R2, R16, R17 (Dissolution F6). The mechanisms of the growth acceleration were not measured (Dissolution F6, Solid state stability F5). (synthesis: a surfactant raises the rate at which drug reaches the solution and also the mobility or the supersaturation at which crystals grow; whether the net effect is a gain depends on whether the drug is absorbed before crystals form, which only an absorptive test or an animal shows.)

Conditions and limits

The surfactant levels differ by orders between categories, from below the CMC in solution to percent levels in the solid (Dissolution F6); the bicalutamide surfactant figure labels conflict with the table and text moseson2022b K5, X3, X4, X13, X21 (ASD process F40); the monkey arms had four animals nguyen2023a K1, K2, K4, X10 (Bioperformance F27).

Counterexamples and conflicts

Sodium taurocholate, a bile salt, lengthened induction times instead chen2015 R3, C13, C17, C18 (Dissolution F6). Surfactants did not restore release from the two-drug co-granule trasi2019 R12, R19 (ASD process F24).

Transfer check

When a surfactant is added to raise release, measure the induction time or seeded growth of the drug at the surfactant level that the dissolving dosage form produces ilevbare2012a R17, R1.g, M17 (Dissolution F6), examine the dissolving surface for crystals yang2023 R21, R13, R2, R16, R17 (Dissolution F6), and confirm the gain under an absorptive sink or in vivo before relying on a higher peak nguyen2023a R12, R14, R8, R23 (Bioperformance F27).

History

2012: surfactants below their CMC sped ritonavir growth ilevbare2012a R17, R1.g, M17 (Dissolution F6). 2014–2015: TPGS sped melt growth, and solubilizers lowered flux mosqueragiraldo2014 R1, C9 (Solid state stability F5); raina2015c R4, R7 (Bioperformance F3). 2018: SDS in a telaprevir dispersion prevented matrix crystallization but shortened supersaturation later mosqueragiraldo2018b R16, R17 (Bioperformance F9). 2019: surfactants raised the limit of congruency, raised silica release and did not restore release from a co-granule que2019 R7, R8, R9, C12 (Dissolution F6); dening2019 R17, R18, M3 (Mesoporous silica F12); trasi2019 R12, R19 (ASD process F24). 2022–2023: surfactants raised bicalutamide release but lost their benefit after milling, SDS brought surface crystals in ritonavir compacts, and TPGS gave no more exposure in monkeys moseson2022b R9, R11, R13, R10, R12 (ASD process F40); yang2023 R21, R13, R2, R16, R17 (Dissolution F6); nguyen2023a R12, R14, R8, R23 (Bioperformance F27).

Conceptspolymer–surfactant interaction critical micelle concentration limit of congruency crystal growth

Topic 5 of 5 · 2 findings · F13–F14

Gut conditions and exposure

F13

Topic 5Gut conditions and exposure1 of 2

The gastric stage, the pH shift, the medium and food changed the outcome for every carrier.

Indomethacin droplets formed at pH 2.2 redissolved after a shift to pH 5 and reached 39.1 of 40 µg/mL, whereas small α crystals formed in acid recovered only to 32.1 µg/mL xie2017 R10, R20, R19, R23. From SBA-15, charged ketoconazole and clozapine fell at the shift to pH 6.8 while un-ionized atazanavir did not hate2020b R10, R11, R13, R12. With food the crystalline pretomanid product rose to 163% of its fasted exposure and the HPMCAS-HF dispersion fell to 72.2% nguyen2023a R23.

moderateModerate: release after a gastric stage is measured for every combination and the silica drop is large and triplicated, but the food effect is one drug in four monkeys whose mechanism the authors "hypothesized", and the surface-pH explanation of the peptide tablet was not measured nguyen2023a K5, K6, X15, X16; fagan2025 K4, K5, X4, X5.

Bases released in acid were re-adsorbed onto the silica at the shift; a competing base kept them in solution. hate2020b R10, R11, R13, R12; hate2020b R15, R16

Food raised exposure from the crystalline product and lowered it from the enteric dispersion. nguyen2023a R23

For your drug

Run a gastric stage at the low and high ends of fasted gastric pH before the intestinal stage, and examine the solid after the gastric stage for crystals.
For a weak base on silica check the ionization at intestinal pH, and for an enteric dispersion test release at fed-state pH.

nguyen2023c R11; hate2020b C20, C52; nguyen2023a R19

How it works and key numbers

What forms before the pH rise decides the intestinal stage: amorphous precipitates and droplets redissolve, crystals seed xie2017 R10, R20, R19, R23.
After a pH rise ten weak bases precipitated either as crystals that ended supersaturation within 3.1–14.7 min or as amorphous solids that held 7.2–20.7 times the crystalline solubility hsieh2012 R1, R5, R10.
On silica, drug released in acid is re-adsorbed onto the negatively charged silica at the shift hate2020b C20, C52.
An enteric polymer stays undissolved below its dissolution pH: in FeSSIF at pH 5.5 and below the pretomanid dispersion stayed at the crystalline solubility nguyen2023a R19.
The peptide authors attribute medium-independent release to a raised pH at the tablet surface; saturated with C10, FaSSIF, FeSSIF and FaSSGF reached pH 9.0, 8.8 and 9.2 fagan2025 K4, K5, X4, X5; fagan2025 R5.
(synthesis: in every carrier the outcome depends on a pH-dependent property, the ionization of the drug, of the enteric polymer, of the silica surface or of the enhancer, so a single-stage test at one intestinal pH misses the result.)

about 0 to 101%delamanid salt dispersions after transfer, depending on gastric pH and gradenguyen2023c R11

about 141 vs 49 minatazanavir induction time in pooled human fluid against FaSSIF-V1elkhabaz2021 R6, R7

≈88–92% vs ≈67–83%insulin from minitablets with 72% C10 or SNAC in all media against the enhancer-free tablet in intestinal mediafagan2025 R12, R13, R20, R8, R9

Evidence: data, conditions and papers

Finding F13. The gastrointestinal sequence and the medium changed the outcome for every carrier: crystals formed in acid cut later release, residual crystals ended supersaturation after a pH shift, silica re-adsorbed charged bases, food reversed the effect of an enteric dispersion, and an enhancer-dominated tablet released a peptide independently of the medium

In short. Indomethacin nanodroplets formed at pH 2.2 redissolved within about 2 min after a shift to pH 5 and reached 39.1 of 40 µg/mL, whereas small α crystals formed in acid recovered only to 32.1 µg/mL, and delamanid salt dispersions ended anywhere from about 0 to 101% after transfer depending on gastric pH and grade, which pH 6.5 alone did not show xie2017 R10, R20, R19, R23; nguyen2023c R11 (Dissolution F11). After a gastric stage a 10% posaconazole extrudate with 0.3% crystals lost its supersaturation by 150 min shah2024 R12, R14 (ASD process F41). From SBA-15 ketoconazole and clozapine fell from about 96 to 64% and from 99 to 69% at the shift to pH 6.8, while un-ionized atazanavir did not drop hate2020b R10, R11, R13, R12 (Mesoporous silica F13). With food the crystalline pretomanid product rose to 163% of its fasted exposure and the HPMCAS-HF dispersion fell to 72.2% nguyen2023a R23 (Bioperformance F26). Minitablets with 72% C10 or SNAC released ≈88–92% of their insulin in all six media, whereas the enhancer-free tablet gave ≈67–83% in the four intestinal media fagan2025 R12, R13, R20, R8, R9 (Peptide permeability F3).

Type. cross-category synthesis of 10 source findings (weak bases and acids in pH-shift tests, enteric and coated dispersions, extrudates, silica formulations, monkeys, peptide minitablets; simulated, composite and human intestinal fluids) Strength. : release after a gastric stage is measured for every combination (Dissolution F11), and the silica drop is large and triplicated (Mesoporous silica F13), but the food effect is one drug in four monkeys whose mechanism the authors "hypothesized" nguyen2023a K5, K6, X15, X16 (Bioperformance F26), and the surface-pH explanation of the peptide tablet was not measured fagan2025 K4, K5, X4, X5 (Peptide permeability F3).

How it was shown

Dissolution followed pH-shift precipitation of weak bases, two-stage dissolution of dispersions and coated tablets, and induction times in six media up to pooled human intestinal fluid hsieh2012 R1, R5, R10; xie2017 R10, R20, R19, R23; nguyen2023c R11; nguyen2023b R10, R2; elkhabaz2021 R6, R7. ASD process ran a 60 min gastric stage before pH 6.5 for posaconazole extrudates shah2024 R12, R14. Mesoporous silica released three weak bases at pH 1 and after a shift to pH 6.8 hate2020b R10, R11, R13, R12. Bioperformance dosed pretomanid fasted and fed to monkeys nguyen2023a R23, and Peptide permeability released insulin from minitablets in six simulated fluids fagan2025 R12, R13, R20, R8, R9.

What the data show

After a pH rise ten weak bases precipitated either as crystals that ended supersaturation within 3.1–14.7 min or as amorphous solids that held 7.2–20.7 times the crystalline solubility hsieh2012 R1, R5, R10. Pooled human fluid held atazanavir longest of six media (about 141 min against 49 min in FaSSIF-V1) elkhabaz2021 R6, R7. Triethylamine added at the pH shift kept ketoconazole at about 93–88% released instead of about 64–69% hate2020b R15, R16.

system	sequence or medium	result	ids
indomethacin; delamanid salt dispersions	pH 2.2 to 5; gastric stage then pH 6.5	droplets 39.1, crystals 32.1 of 40 µg/mL; 0–101% by gastric pH and grade	xie2017 R10, R20, R19, R23; nguyen2023c R11
posaconazole–HPMCAS 10%	pH 1.6 then 6.5	0.3% crystals: about 18.5 µg/mL by 150 min	shah2024 R12, R14
ketoconazole, clozapine, atazanavir on SBA-15	pH 1 to 6.8	96 to 64%, 99 to 69%; atazanavir no drop	hate2020b R10, R11, R13, R12
pretomanid HPMCAS-HF against crystalline	monkeys fasted and fed	crystalline 163%, dispersion 72.2% of fasted	nguyen2023a R23
insulin minitablets, 72% C10 or SNAC	six simulated fluids	≈88–92% in all; enhancer-free ≈67–83% in intestinal fluids	fagan2025 R12, R13, R20, R8, R9

Fig. 3 of elkhabaz2021: atazanavir induction times in six media without and with 10 µg/mL HPMC-AS — Fig. 3 · elkhabaz2021atazanavir induction times in six media without and with 10 µg/mL HPMC-AS

Without polymer FaSSIF-V1 crystallizes atazanavir first and human fluid last; with HPMC-AS every medium lasts longer elkhabaz2021 R6.

Why

The Dissolution authors tie the outcome to what forms before the pH rise, amorphous precipitates and droplets redissolving and crystals seeding xie2017 R10, R20, R19, R23. The silica authors read the drop as re-adsorption of drug released in acid onto the negatively charged silica hate2020b C20, C52. The peptide authors attribute medium-independent release to a raised pH at the tablet surface fagan2025 K4, K5, X4, X5. (synthesis: in every carrier the outcome depends on a pH-dependent property, so a single-stage test at one intestinal pH misses the result.)

Limits and transfer

Atazanavir, un-ionized at intestinal pH, kept its gain from silica after the shift hate2020b R10, R11, R13, R12. Run a gastric stage at the low and high ends of fasted gastric pH before the intestinal stage, and examine the solid after the gastric stage for crystals nguyen2023c R11; for a weak base on silica check the ionization at intestinal pH hate2020b C20, C52; for an enteric dispersion test release at fed-state pH nguyen2023a R19.

How it was shown

Dissolution followed pH-shift precipitation of weak bases, two-stage dissolution of dispersions with EPO, HPMC, HPMCAS and HPMCP, coated tablets, and induction times in six media up to pooled human intestinal fluid hsieh2012 R1, R5, R10; xie2017 R10, R20, R19, R23; nguyen2023c R11; nguyen2023b R10, R2 (Dissolution F11); elkhabaz2021 R6, R7 (Dissolution F12). ASD process ran a 60 min gastric stage before pH 6.5 for posaconazole extrudates shah2024 R12, R14 (ASD process F41). Mesoporous silica released three weak bases at pH 1 and after a shift to pH 6.8 hate2020b R10, R11, R13, R12 (Mesoporous silica F13). Bioperformance dosed pretomanid fasted and fed to monkeys and compared media for ezetimibe nguyen2023a R23 (Bioperformance F26); elkhabaz2017 R6, R7 (Bioperformance F11). Peptide permeability released insulin from minitablets in three simulated intestinal and three gastric fluids fagan2025 R8, R9, R1 (Peptide permeability F1); fagan2025 R12, R13, R20, R8, R9 (Peptide permeability F3).

What the data show

After a pH rise ten weak bases precipitated either as crystals that ended supersaturation within 3.1–14.7 min or as amorphous solids that held 7.2–20.7 times the crystalline solubility hsieh2012 R1, R5, R10 (Dissolution F11). An enteric coat kept release after any gastric stage at ≈76–86 µg/mL of 100 nguyen2023b R10, R2 (Dissolution F11). Pooled human fluid held atazanavir longest of six media (about 141 min against 49 min in FaSSIF-V1) elkhabaz2021 R6, R7 (Dissolution F12); FaSSIF raised bedaquiline release from about 17–30% to 87.5–97%, and fed fluid lowered praziquantel release to about 34–52% kaur2025 R13, R15, R5, R6; alvarenga2025 R16, R18, C29 (Dissolution F12). In FeSSIF at pH 5.5 and below the pretomanid dispersion stayed at the crystalline solubility nguyen2023a R19 (Bioperformance F11). Triethylamine added at the pH shift kept ketoconazole at about 93–88% released instead of about 64–69% hate2020b R15, R16 (Mesoporous silica F12). Saturated with C10, FaSSIF, FeSSIF and FaSSGF reached pH 9.0, 8.8 and 9.2 fagan2025 R5 (Peptide permeability F2).

source finding	system	conditions	result	ids
Dissolution F11	indomethacin; delamanid salt dispersions	pH 2.2 to 5; gastric stage then pH 6.5	droplets 39.1, crystals 32.1 of 40 µg/mL; 0–101% by gastric pH and grade	xie2017 R10, R20, R19, R23; nguyen2023c R11
Dissolution F12	atazanavir; bedaquiline; praziquantel	six media; FaSSIF; fed fluid	human fluid longest; release up to 87.5–97%; down to 34–52%	elkhabaz2021 R6, R7; kaur2025 R13, R15, R5, R6; alvarenga2025 R16, R18, C29
ASD process F41	posaconazole–HPMCAS 10%	pH 1.6 then 6.5	0.3% crystals: about 18.5 µg/mL by 150 min	shah2024 R12, R14
Mesoporous silica F13	ketoconazole, clozapine, atazanavir on SBA-15	pH 1 to 6.8	96 to 64%, 99 to 69%; atazanavir no drop	hate2020b R10, R11, R13, R12
Bioperformance F26	pretomanid HPMCAS-HF against crystalline	monkeys fasted and fed	crystalline 163%, dispersion 72.2% of fasted	nguyen2023a R23
Bioperformance F11	ezetimibe with PVP, HPMC-AS	buffer, FeSSIF	best polymer reverses with the medium	elkhabaz2017 R6, R7
Peptide permeability F3	insulin minitablets, 72% C10 or SNAC	six simulated fluids	≈88–92% in all; enhancer-free ≈67–83% in intestinal fluids	fagan2025 R12, R13, R20, R8, R9

Figure

Without polymer FaSSIF-V1 crystallizes atazanavir first and human fluid last; with HPMC-AS every medium lasts longer but FaSSIF-V1 still falls short of the buffers elkhabaz2021 R6 (Dissolution F12).

Why

The Dissolution authors tie the outcome to what forms before the pH rise, amorphous precipitates and droplets redissolving and crystals seeding xie2017 R10, R20, R19, R23 (Dissolution F11). The silica authors read the drop as re-adsorption of drug released in acid onto the negatively charged silica hate2020b C20, C52 (Mesoporous silica F13). The peptide authors attribute medium-independent release to a raised pH at the tablet surface fagan2025 K4, K5, X4, X5 (Peptide permeability F3). (synthesis: in every carrier the outcome depends on a pH-dependent property, the ionization of the drug, of the enteric polymer, of the silica surface or of the enhancer, so a single-stage test at one intestinal pH misses the result.)

Conditions and limits

The step from crystals in acid to lower release is inferred without a seeding test (Dissolution F11); the silica results are one silica (Mesoporous silica F13); intestinal pH, polymer dissolution and crystallization were not measured in the monkeys (Bioperformance F26).

Counterexamples and conflicts

Atazanavir, un-ionized at intestinal pH, kept its gain from silica after the shift and gave a higher receiver peak than a run at pH 6.8 throughout hate2020b R10, R11, R13, R12 (Mesoporous silica F13).

Transfer check

Run a gastric stage at the low and high ends of fasted gastric pH before the intestinal stage, and examine the solid after the gastric stage for crystals nguyen2023c R11 (Dissolution F11); for a weak base on silica check the ionization at intestinal pH hate2020b C20, C52 (Mesoporous silica F13); for an enteric dispersion test release at fed-state pH nguyen2023a R19 (Bioperformance F11).

History

2012: weak bases after a pH rise precipitated as crystals or as amorphous solids hsieh2012 R1, R5, R10 (Dissolution F11). 2017: indomethacin droplets formed in acid redissolved and the best polymer for ezetimibe changed with the medium xie2017 R10, R20, R19, R23 (Dissolution F11); elkhabaz2017 R6, R7 (Bioperformance F11). 2020: silica re-adsorbed charged bases at the shift hate2020b R10, R11, R13, R12 (Mesoporous silica F13). 2021: human intestinal fluid held atazanavir longest elkhabaz2021 R6, R7 (Dissolution F12). 2023: gastric pH decided delamanid release, and food reversed the pretomanid dispersion's advantage nguyen2023c R11 (Dissolution F11); nguyen2023a R23 (Bioperformance F26). 2024–2025: residual crystals ended posaconazole supersaturation after a pH shift, and an enhancer-dominated tablet released insulin in every medium shah2024 R12, R14 (ASD process F41); fagan2025 R12, R13, R20, R8, R9 (Peptide permeability F3).

ConceptspH-shift dissolution biorelevant media food effect gastric pH variability microenvironmental pH

F14

Topic 5Gut conditions and exposure2 of 2

Flux and absorptive tests tracked animal exposure better than closed vessels, but animal data cover three drugs and no human dispersion.

With 0.05% HPMC-AS a nevirapine tablet donor stayed at about 525 µg/mL for 270 min in a closed vessel but fell to about 253 µg/mL with absorption hate2017 R15, R7. In two rat studies of enzalutamide the mass flow across a dialysis membrane ranked the formulations by exposure, apart from one crystallizing dispersion wilson2018 R15, R17, C29; wilson2020 R8, R6. The crystallized tacrolimus capsule kept about 51% of the fresh exposure in dogs, more than the low-volume absorptive and simulated tests predicted purohit2019 R9; hate2019 R13; purohit2018 R14, R16.

weakWeak to moderate: the in vitro differences are large and direct, but the in vitro–in vivo comparisons rest on one drug each and three to six animals per arm, and the authors call the enzalutamide ranking a "preliminary observation" wilson2018 K5, C52; wilson2020 K2, X15.

The dog result lies with the large-volume condition; small volumes exaggerated the loss. purohit2019 R9; hate2019 R13; purohit2018 R14, R16

Mass flow and AUC0–inf (µg·h/mL) as listed in the same order in the source finding; the two orders agree. wilson2020 R8, R6

For your drug

Rank formulations by a flux or absorptive read-out at a dose and volume that give the supersaturation expected in vivo.
Treat a closed-vessel gain in peak concentration as a hypothesis until an animal study confirms it.

wilson2018 R15, R17, C29; purohit2019 R12, C40; hate2019 R7; nguyen2023a R23

How it works and key numbers

In a closed vessel no drug is removed; the Bioperformance authors read the closed-vessel overstatement as removal of drug lowering the driving force for nucleation, which was inferred and not measured hate2017 X17, X14, C57.
With absorption the total nevirapine in donor plus receiver stayed at about 44–49 mg for 120 min, while the dissolved drug in the closed vessel fell to about 26 mg hate2017 R17.
On silica a sink lowers the solution concentration, and the authors read the gain as desorption ("may improve"): atazanavir release at 240 min rose from about 46.5 to 89.5% hate2020a C10; hate2020a R20.
The dog dose gives at most about 10 µg/mL, the level of the large-volume tests purohit2019 R12, C40; hate2019 R7.
(synthesis: a test agrees with exposure when it reproduces the supersaturation the dose reaches in the gut and removes drug as absorption does; closed small-volume tests exaggerate both the supersaturation and its loss, and the source findings contain no human exposure for a dispersion.)

0.632 to 0.063 µg/minmass flow of five enzalutamide formulations after 1 h, in the order of Cmax and AUC0–48 except onewilson2018 R15, R17, C29

about 1.4-foldover-prediction of exposure by the simulation, which assumed no precipitation in the gutpurohit2018 R10, R11, X3, K6, C58, C59, X10

141 and 142% vs 155%pretomanid tablets with TPGS or tris against the binary tablet in fasted monkeysnguyen2023a R23

Evidence: data, conditions and papers

Finding F14. Closed-vessel tests misjudged what reaches an absorbing membrane, and the few animal studies agreed with flux or absorptive read-outs more often than with closed-vessel concentration, but the library holds exposure data for three drugs in animals and none for a dispersion in humans

In short. With 0.05% HPMC-AS a nevirapine tablet donor stayed at about 525 µg/mL for 270 min in a closed vessel but fell to about 253 µg/mL with absorption hate2017 R15, R7 (Bioperformance F14), and an absorptive sink raised atazanavir release from SBA-15 at 240 min from about 46.5 to 89.5% hate2020a R20 (Mesoporous silica F14). In two rat studies of enzalutamide the mass flow of the dissolved formulation across a dialysis membrane ranked the formulations by exposure, apart from one crystallizing dispersion, while closed non-sink dissolution did not wilson2018 R15, R17, C29; wilson2020 R8, R6; wilson2018 R7, C20 (Bioperformance F25). The crystallized tacrolimus capsule kept about 51% of the fresh exposure in dogs, more than in the low-volume absorptive and simulated tests purohit2019 R9; hate2019 R13; purohit2018 R14, R16 (Bioperformance F31). In vitro gains with TPGS and a base did not raise pretomanid exposure in monkeys nguyen2023a R23 (Bioperformance F27), and neither peptide paper measured permeability or absorption bapat2025b C6; fagan2025 C45 (Peptide permeability F6).

Type. cross-category comparison of 8 source findings (closed and absorptive tests of nevirapine, atazanavir, tacrolimus and silica formulations; enzalutamide in rats, tacrolimus in dogs, pretomanid in monkeys; peptide release) Strength. to moderate: the in vitro differences are large and direct (Bioperformance F14, Mesoporous silica F14), but the in vitro–in vivo comparisons rest on one drug each, three to six animals per arm, and the authors call the enzalutamide ranking a "preliminary observation" wilson2018 K5, C52; wilson2020 K2, X15 (Bioperformance F25).

How it was shown

Bioperformance compared closed vessels with a hollow-fibre absorptive module, measured mass flow across a dialysis membrane, and dosed enzalutamide to rats, tacrolimus to dogs and pretomanid to monkeys hate2017 R15, R7, R17; hate2018 R18; wilson2018 R15, R17, C29; wilson2020 R8, R6; purohit2019 R9; nguyen2023a R23. Mesoporous silica ran atazanavir–SBA-15 with and without a hollow-fibre sink hate2020a R20. Peptide permeability measured release only bapat2025b C6; fagan2025 C45.

What the data show

With 0.1% PVPVA at 500 µg/mL the total nevirapine in donor plus receiver stayed at about 44–49 mg for 120 min with absorption, while the dissolved drug in the closed vessel fell to about 26 mg hate2017 R17. For the tacrolimus capsule the crystalline-to-fresh ratio was about 51% in dogs, about 22, 17 and 17.5% in the absorptive test at 240, 100 and 40 mL, and about 55% in the simulation with 900 mL input purohit2019 R9; hate2019 R13; purohit2018 R14, R16.

comparison	system	result	ids
closed against absorptive	nevirapine; atazanavir dispersions	525 against 253 µg/mL donor; release up to 6200–6300 against 4200–4600 µg	hate2017 R15, R7; hate2018 R18
closed against hollow-fibre sink	atazanavir–SBA-15	about 46.5 against 89.5% at 240 min	hate2020a R20
dialysis mass flow against rat exposure	enzalutamide, nine formulation–study pairs	same order except one crystallizing dispersion	wilson2018 R15, R17, C29; wilson2020 R8, R6
dogs, absorptive test, simulation	crystallized tacrolimus capsule	about 51% in dogs; 17–22% absorptive; 8% simulated (100 mL)	purohit2019 R9; hate2019 R13; purohit2018 R14, R16
monkeys, fasted	pretomanid tablets with TPGS or tris	141 and 142% against 155% for the binary tablet	nguyen2023a R23
release only	octreotide, cyclosporine, insulin with enhancers	no permeability or absorption measured	bapat2025b C6; fagan2025 C45

Why

The Bioperformance authors read the closed-vessel overstatement as removal of drug lowering the driving force for nucleation, inferred and not measured hate2017 X17, X14, C57; the silica authors read the sink gain as desorption as the solution concentration falls ("may improve") hate2020a C10. The dog dose gives at most about 10 µg/mL, the level of the large-volume tests purohit2019 R12, C40; hate2019 R7. (synthesis: a test agrees with exposure when it reproduces the supersaturation the dose reaches in the gut and removes drug as absorption does; closed small-volume tests exaggerate both the supersaturation and its loss.)

Limits and transfer

The simulation assumed no precipitation in the gut and over-predicted exposure about 1.4-fold purohit2018 R10, R11, X3, K6, C58, C59, X10. (synthesis: the source findings contain no human exposure for a dispersion; the animal data cover enzalutamide, tacrolimus and pretomanid.) The 10% enzalutamide–HPMCAS dispersion had more than twice the slurry's mass flow but gave less exposure than the crystals wilson2018 R15, R17, C29. Rank formulations by a flux or absorptive read-out at a dose and volume that give the supersaturation expected in vivo wilson2018 R15, R17, C29; purohit2019 R12, C40; hate2019 R7, and treat a closed-vessel gain in peak concentration as a hypothesis until an animal study confirms it nguyen2023a R23.

How it was shown

Bioperformance compared closed vessels with a hollow-fibre absorptive module, measured mass flow across a dialysis membrane after dissolution, and dosed enzalutamide to rats, tacrolimus to dogs and pretomanid to monkeys hate2017 R15, R7, R17; hate2018 R18 (Bioperformance F14); wilson2018 R15, R17, C29; wilson2020 R8, R6 (Bioperformance F25); purohit2019 R9 (Bioperformance F31); nguyen2023a R23 (Bioperformance F27). Mesoporous silica ran atazanavir–SBA-15 with and without a hollow-fibre sink hate2020a R20 (Mesoporous silica F14). Peptide permeability measured release only bapat2025b C6; fagan2025 C45 (Peptide permeability F6).

What the data show

With 0.1% PVPVA at 500 µg/mL the total nevirapine in donor plus receiver stayed at about 44–49 mg for 120 min with absorption, while the dissolved drug in the closed vessel fell to about 26 mg, and the absorptive sink raised the 120 min release of 50% atazanavir dispersions from about 4200, 4600 and 3600 µg to 6200, 6300 and 5000 µg hate2017 R17; hate2018 R18 (Bioperformance F14). For enzalutamide the mass flow after 1 h was 0.632, 0.456, 0.437, 0.147 and 0.063 µg/min, in the order of Cmax and AUC0–48 except the 10% HPMCAS dispersion, and in the later study about 0.53 and 0.49 against 0.068 and 0.063 µg/min, against AUC0–inf of 516, 305, 45 and 43.1 µg·h/mL wilson2018 R15, R17, C29; wilson2020 R8, R6 (Bioperformance F25). For the tacrolimus capsule the crystalline-to-fresh ratio was about 51% in dogs, about 22, 17 and 17.5% in the absorptive test at 240, 100 and 40 mL, about 8% in the simulation with 100 mL input and about 55% with 900 mL input purohit2019 R9; hate2019 R13; purohit2018 R14, R16 (Bioperformance F31). Ketoconazole on silica gained only about ten to fifteen points under a sink after a pH shift hate2020b R17, X10 (Mesoporous silica F14).

source finding	system	conditions	result	ids
Bioperformance F14	nevirapine; atazanavir dispersions	closed against absorptive	525 against 253 µg/mL donor; release up to 6200–6300 against 4200–4600 µg	hate2017 R15, R7; hate2018 R18
Mesoporous silica F14	atazanavir–SBA-15	closed against hollow-fibre sink	about 46.5 against 89.5% at 240 min	hate2020a R20
Bioperformance F25	enzalutamide, nine formulation–study pairs	dialysis mass flow against rat exposure	same order except one crystallizing dispersion	wilson2018 R15, R17, C29; wilson2020 R8, R6
Bioperformance F31	crystallized tacrolimus capsule	dogs, absorptive test, simulation	about 51% in dogs; 17–22% absorptive; 8% simulated (100 mL)	purohit2019 R9; hate2019 R13; purohit2018 R14, R16
Bioperformance F27	pretomanid tablets with TPGS or tris	monkeys, fasted	141 and 142% against 155% for the binary tablet	nguyen2023a R23
Peptide permeability F6	octreotide, cyclosporine, insulin with enhancers	release only	no permeability or absorption measured	bapat2025b C6; fagan2025 C45

Why

The Bioperformance authors read the closed-vessel overstatement as removal of drug lowering the driving force for nucleation, inferred and not measured hate2017 X17, X14, C57 (Bioperformance F14); the silica authors read the sink gain as desorption as the solution concentration falls ("may improve") hate2020a C10 (Mesoporous silica F14). The dog dose gives at most about 10 µg/mL, the level of the large-volume tests purohit2019 R12, C40; hate2019 R7 (Bioperformance F31). (synthesis: a test agrees with exposure when it reproduces the supersaturation the dose reaches in the gut and removes drug as absorption does; closed small-volume tests exaggerate both the supersaturation and its loss.)

Conditions and limits

The simulation assumed no precipitation in the gut and over-predicted exposure about 1.4-fold, with human data pending purohit2018 R10, R11, X3, K6, C58, C59, X10 (Bioperformance F17). (synthesis: the source findings contain no human exposure for a dispersion; the animal data cover enzalutamide, tacrolimus and pretomanid.)

Counterexamples and conflicts

The 10% enzalutamide–HPMCAS dispersion had more than twice the slurry's mass flow but gave less exposure than the crystals wilson2018 R15, R17, C29 (Bioperformance F25). The one dispersion that shed amorphous aggregates gave about 30% more exposure in rats, a trend without a statistical test wilson2018 C46, X6 (Bioperformance F23).

Transfer check

Rank formulations by a flux or absorptive read-out at a dose and volume that give the supersaturation expected in vivo wilson2018 R15, R17, C29 (Bioperformance F25); purohit2019 R12, C40; hate2019 R7 (Bioperformance F31), and treat a closed-vessel gain in peak concentration as a hypothesis until an animal study confirms it nguyen2023a R23 (Bioperformance F27).

History

2017–2018: the hollow-fibre module showed what a closed vessel overstates hate2017 R15, R7; hate2018 R18 (Bioperformance F14). 2018–2020: rat studies of enzalutamide ranked formulations by mass flow wilson2018 R15, R17, C29; wilson2020 R8, R6 (Bioperformance F25), and an absorptive sink was applied to silica hate2020a R20 (Mesoporous silica F14). 2019: the tacrolimus capsule was measured in dogs purohit2019 R9 (Bioperformance F31). 2023: in vitro gains did not raise exposure in monkeys nguyen2023a R23 (Bioperformance F27). 2025: the peptide papers ended at release bapat2025b C6; fagan2025 C45 (Peptide permeability F6).

Conceptsabsorptive dissolution testing absorptive sink in vitro–in vivo correlation non-sink dissolution peptide–enhancer co-release

01Development line across the categories

Every paper of the wiki in year order; the tag names its category and the chips open the chapter findings it supports.

1997
taylor1997PVP–indomethacin hydrogen bonding in amorphous dispersionsSolid state stabilityfirst proposed
Known before
no earlier library paper is a builds_on base; the card cites earlier dispersion spectra that had been compared with crystalline drug, which changes the spectrum on crystallinity alone [taylor1997 C7].
Added
IR and Raman spectra of γ, α and amorphous indomethacin, of dispersions with 5–70 wt% PVP and of physical mixes of the same compositions, and two liquid models, acetic acid with methyl pyrrolidone and indomethacin in methyl pyrrolidone [taylor1997 R5.a, R10, R11, R12, R15, R16].
Relation
first proposed in this chapter that the indomethacin acid OH bonds the PVP carbonyl at the expense of the acid dimers [taylor1997 C35], with the incomplete binding read from spectral change above the 12% and 24% PVP stoichiometries [taylor1997 C37, R18]; offered as an explanation of how PVP inhibits crystallization at levels where its antiplasticizing effect is minimal [taylor1997 C45].
SupportsF1 F2 F17
1998
taylor1998aFT-Raman crystallinity of indomethacinCharacterization methodsfirst proposed
The Quantitative Analysis of Crystallinity Using FT-Raman Spectroscopy
Known before
the Raman spectra of amorphous and γ indomethacin can be told apart (the group's 1997 study); XRD detects about 10% amorphous content and sorption or microcalorimetry about 1% disorder, and low levels of amorphous material are sought taylor1998a C5, C28, C3.
Added
a two-band ratio calibration of crystallinity over 0–100% with independent validation, an error budget (laser power, instrument, mixing) and detection and quantitation limits, and Raman-equivalent crystallinities of milled samples taylor1998a R6, R8, R9, R10, R11, R12, R14, R16.
Relation
first paper of the chapter; its "about 1%" is the benchmark later SHG papers cite wanapun2010 R1; kestur2012 R17.
SupportsF1 F2 F4 F7
2001
broman2001carrier and process for probucol dispersionsASD processfirst proposed
A comparison of alternative polymer excipients and processing methods for making solid dispersions of a poorly water soluble drug
Known before
PVP inhibits crystallisation of amorphous drug through hydrogen-bonded complexes (1997 PVP–indomethacin study) and a carbonyl shift of PVP is read as hydrogen bonding (builds_on) broman2001 C15, C31.
Added
50 wt% probucol with PVP K30, PAA, PEO and two blends made from solvent, by co-melting and by compression moulding, with Raman and DSC for the solid form and a 29 h release test broman2001 R4, R5, R12.
Relation
first in this chapter: the carrier, not the route, decided whether the drug stayed amorphous, release followed the carrier's behaviour in water, and moulding helped only PEO broman2001 C1, C48, C47.
SupportsF17 F18 F19
2006
konno2006polymers and dry nucleation of felodipineSolid state stabilityfirst 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.
SupportsF1 F4 F5
2006
marsac2006anifedipine against felodipineSolid state stabilityconfirms
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].
SupportsF1 F2 F4 F5
2006
marsac2006bdrug–polymer miscibility and solubility from the interaction parameterSolid state stabilityfirst proposedrevises
Theoretical and Practical Approaches for Prediction of Drug–Polymer Miscibility and Solubility
Known before
the 2006 study of the physical stability of amorphous felodipine and nifedipine, which supplied the miscibility of both drugs with PVP, the nifedipine–PVP hydrogen bonding, the check of the Hoffman equation and the nucleation rates (builds_on).
Added
the entropy of mixing for nifedipine with methyl pyrrolidone and three PVP grades, χ from group-contribution solubility parameters (2.0 and 0.5) and from melting point depression with PVP K12 (−3.8 and −4.2), the change of the Hoffman driving force with PVP, and the predicted solubility of the crystalline drugs in PVP marsac2006b R1, R4, R9, R12, R17.
Relation
first in the chapter to obtain χ for a drug–polymer pair from melting point depression; revises the solubility-parameter route, whose positive χ predicted immiscibility against experiment marsac2006b C23, C24.
SupportsF5 F6 F7 F8 F9
2007
towler2007solution interactions and crystallization outcomeSolid state stabilityfirst proposed
Known before
IR and Raman band assignments of α, γ and amorphous indomethacin, taken from the 1997 PVP–indomethacin study (builds_on).
Added
concentration-dependent IR and Raman spectra of anthranilic acid in five solvents and indomethacin in two, compared with the polymorph that crystallized [towler2007 R6, R13].
Relation
first proposed in this chapter that solution motifs are "not necessarily indicative" of the polymorph crystallized first [towler2007 C33, C35].
SupportsF8
2008
konno2008polymers and felodipine nucleation with moistureSolid state stabilityextends
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.
SupportsF1 F5 F6 F9 F10 F11 F12 F14 F16
2008
konno2008apolymer type and felodipine dispersion dissolutionDissolutionfirst proposed
Effect of polymer type on the dissolution profile of amorphous solid dispersions containing felodipine
Note
Known in the library (builds_on: Konno 2006, Konno 2008 on moisture, Marsac 2006): dry felodipine dispersions with PVP, HPMC and HPMCAS nucleated alike, and with moisture HPMCAS and HPMC inhibited crystallization better than PVP at high relative humidity; felodipine thermodynamic data for the Hoffman estimate konno2008a R18, R20.
Added
the first dissolution ranking of the three polymers (maxima 14.1, 4.9 and 2.3 µg/mL at 75% polymer), unchanged crystalline solubility with 1 mg/mL polymer, solvent-shift profiles read as growth inhibition, and a solution screen that matched dissolution for PVP and HPMCAS but not HPMC konno2008a R7, R1, C36, C31.
Relation
first in the library on the polymer ranking during dispersion dissolution.
Note
Findings: F4, F5, F6.
2008
marsac2008anifedipine and felodipine in PVP with sorbed waterSolid state stabilityconfirmsextends
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].
SupportsF1 F2 F5 F6 F9 F10
2008
marsac2008bcrystalline drugs in PEO under humiditySolid state stabilityfirst proposed
Known before
no kept paper is a builds_on base; the card cites a study outside the library in which ketoprofen in PEO lost crystallinity on heating below the PEO melting point [marsac2008b R19, C4].
Added
six drugs at 10 wt% in PEO compacts at 94% RH graded as complete, moderate or negligible loss, the water uptake of PEO over hours and months, and activity coefficients of the drugs in PEG 400 and water [marsac2008b R2, R4, R7, R10, R11, R14, R16].
Relation
first proposed in this chapter that water together with PEO dissolves crystalline drug and that the extent follows the activity coefficient in water; shows that a PEG 400 stand-in for amorphous PEO did not rank the drugs [marsac2008b C35, C22].
SupportsF11 F12 F3 F4
2008
towler2008counterion and amorphous organic saltsSolid state stabilityextends
Known before
counterion-dependent Tg of amorphous indomethacin salts (2002 Tong) and weight loss during sorption read as crystallization (2007 Gift) (builds_on).
Added
Tg, crystallization on heating and moisture behaviour of propranolol and nicardipine salts with many counterions, and a PLS model of Tg [towler2008 R4, R5, R12, R17].
Relation
extends the salt Tg result to two bases; every salt raised Tg [towler2008 C7], but the counterion effect on crystallization tendency needed "more work" [towler2008 C34].
SupportsF20
2009
marsac2009interaction parameters of five PVP pairs, melting point depression and solubility in a liquid analogueSolid state stabilityextendsrevises
Estimation of Drug–Polymer Miscibility and Solubility in Amorphous Solid Dispersions Using Experimentally Determined Interaction Parameters
Known before
the melting-depression route to χ from marsac2006b, and the miscibility of felodipine and nifedipine with PVP from the 2006 physical stability study (builds_on).
Added
χ for indomethacin, felodipine, nifedipine, ketoconazole and sucrose with PVP K12, for three dextran pairs and itraconazole–Eudragit E100 by melting point depression; χ from solubility in 1-ethyl-2-pyrrolidone; free-energy curves; the PVP carbonyl shift for each drug marsac2009 R6, R7, R9, R10, R12.
Relation
extends the 2006 route to more drugs and polymers and revises its input, using the offset of the melting peak after showing that χ for indomethacin–PVP changes with the point of the peak marsac2009 R6, C16; adds the solubility route as a second estimate, whose χ values differ in size from the melting route marsac2009 R7, R9.
SupportsF2 F5 F7 F8 F9
2009
rumondor2009aDSC, infrared and PXRD tests of drug–polymer miscibilitySolid state stabilityconfirms
Known before
the single Tg and hydrogen bonding in felodipine–PVP (konno2006), the NH hydrogen bond in felodipine–PVP and nifedipine–PVP (marsac2008a) and the calculation of physical-mixture infrared spectra (rumondor2009b) (builds_on).
Added
DSC, infrared spectra read by principal component analysis, and PXRD pair distribution function fits and pure-curve resolution for felodipine–PAA, felodipine–PVP, nifedipine–PVP and ketoconazole–PVP across compositions [rumondor2009a R1, R3, R4, R13, R16, R19, R21].
Relation
confirms the miscibility of felodipine–PVP and nifedipine–PVP that the thermodynamic route of marsac2006b predicted [rumondor2009a C38]; first in the chapter to show that DSC alone leaves a phase state open, in ketoconazole–PVP with one Tg at every ratio [rumondor2009a C42]; finds felodipine–PAA practically immiscible at 30–70% polymer [rumondor2009a C44].
SupportsF3 F4 F17
2009
rumondor2009bpolymer type and RH on bulk crystallizationSolid state stabilityextends
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.
SupportsF11 F15 F16
2009
rumondor2009cmoisture-induced immiscibility of drug–PVP dispersionsSolid state stabilityfirst 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.
SupportsF7 F8 F12 F13 F15 F16
2010
alonzo2010two crystallization routes during amorphous dissolutionDissolutionconfirmsextends
Understanding the Behavior of Amorphous Pharmaceutical Systems during Dissolution
Note
Known in the library (builds_on: Konno 2008 on dissolution, Konno 2006, Marsac 2008): polymer inhibition of felodipine crystallization from solution and the felodipine crystalline solubility alonzo2010 R20, polymers as solid-state inhibitors of felodipine, and the Tg of dry and humid felodipine for the temperature argument.
Added
in situ Raman and microscopy that separate crystallization of the wetted solid (felodipine at 37 °C, ≈54% crystalline at 1 min) from crystallization in the liquid (indomethacin at 25 °C), a lag of about 13–20 min that dissolved polymers put before felodipine crystallizes, and the proposal of two polymers for two routes alonzo2010 R2, R19, R6, C46.
Relation
extends Konno 2008 to the solid route; confirms its felodipine solution ranking ("in excellent agreement") alonzo2010 C11.
Note
Findings: F1, F2, F4, F6.
2010
baird2010DSC classification from undercooled meltsSolid state stabilityfirst proposed
A Classification System to Assess the Crystallization Tendency of Organic Molecules from Undercooled Melts
Known before
no earlier library paper; the methods came from inorganic glass science (Barandiaran–Colmenero and Cabral critical cooling rates, glass-stability parameters, reduced Tg, fragility) (builds_on).
Added
a heat–cool–heat DSC screen of 51 molecules into classes I, II and III, with a liquid-N2 quench splitting class I baird2010 R1, R3, C8, tests of rate robustness baird2010 C13, of critical-rate extrapolation baird2010 C20, of Trg, glass-stability and fragility parameters baird2010 C23, C31, a descriptor PCA baird2010 R20 and storage of glasses baird2010 R23, R24, R25.
Relation
first proposed; offered as a tool for early development baird2010 C64.
SupportsF7 F9 F10 F11 F12 F13 F15 F16 F17
2010
kestur2010apolymer chemistry and the crystal growth rate of felodipineSolid state stabilityfirst proposedextends
Role of polymer chemistry in influencing crystal growth rates from amorphous felodipine
Known before
the PVP–indomethacin hydrogen bond of taylor1997, the felodipine–polymer dispersions of Konno (2006) and the stronger felodipine–PVP interactions in the NH region seen by Marsac (2010) (builds_on).
Added
growth rates of form II felodipine alone and with 3% w/w PVP, PVP/VA, HPMCAS and PVAc from 70 to 110 °C, at 0.5–4.5% polymer at 90 °C, and the infrared NH shift of dispersions of the same polymers kestur2010a R5, R6, R8, R9.
Relation
first in the chapter to rank polymers by growth inhibition at a low content and to match the ranking with the IR hydrogen-bond order kestur2010a C38, C40; extends the hydrogen-bond idea of taylor1997 from one drug and one polymer to a set of polymers; the proposed demixing at the growth front is speculation kestur2010a C42, X6.
SupportsF10 F11 F12 F17
2010
kestur2010bPVP molecular weight, concentration and temperature on melt growthSolid state stabilityfirst proposed
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].
SupportsF3 F4 F5
2010
marsac2010temperature and moisture on felodipine–PVP miscibilitySolid state stabilityconfirms
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.
SupportsF6 F8 F12 F13 F14 F15 F16
2010
rumondor2010moisture and felodipine crystal growthSolid state stabilityconfirmsextends
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].
SupportsF5 F9 F11 F15
2010
rumondor2010amoisture sorption of amorphous drug–polymer blendsSolid state stabilityfirst proposed
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].
SupportsF6 F7 F8
2010
rumondor2010bPLS of PXRD patterns of felodipine–PVP dispersionsCharacterization methodsextends
Known before
the halo of a molecular-level dispersion is not the sum of the pure halos, felodipine crystallizes from dispersions in storage, PXRD detects 5% or less in blends of drug and crystals, and quantification inside a dispersion "has not been widely reported" [rumondor2010b C8, C4, R1, C5].
Added
calibration samples of dispersion plus crystals at three PVP levels, area ratio against whole-pattern PLS (RMSEE 11.2–23.6% against 2.2–4.7%), loading weights and the conversion to per cent of the sample [rumondor2010b R9, R14, R15, R16, R19].
Relation
extends the crystallinity quantification of Taylor and Zografi from pure drug mixtures to dispersions [rumondor2010b C5].
SupportsF3 F4
2010
rumondor2010cpolymer hygroscopicity and moisture-induced separationSolid state stabilityextends
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].
SupportsF6 F12 F13 F15 F16 F23
2010
vaneerdenbrugh2010aclassification after rapid solvent evaporationSolid state stabilityconfirmsextends
Crystallization Tendency of Active Pharmaceutical Ingredients Following Rapid Solvent Evaporation—Classification and Comparison with Crystallization Tendency from Undercooled Melts
Known before
the 51 compounds, their melt classes and DSC descriptors of baird2010 (builds_on).
Added
spin-coated films of 40 drugs from three solvents, sorted into three classes, with slow evaporation as a harsher test vaneerdenbrugh2010a R9, R13.
Relation
confirms the melt classes in 68% of drug–solvent combinations, with 30% one class apart vaneerdenbrugh2010a R16; extends the descriptor analysis to class models for a first-pass prediction vaneerdenbrugh2010a C46.
SupportsF6 F9 F13 F14
2010
vaneerdenbrugh2010bspin-coating screen of polymers against eight drugsSolid state stabilityextends
Small Scale Screening To Determine the Ability of Different Polymers To Inhibit Drug Crystallization upon Rapid Solvent Evaporation
Known before
the crystallization classes of the eight drugs from the spin-coating screen of pure drugs and the DSC classification of Baird (builds_on).
Added
the amorphicity index of 8 drugs × 7 polymers × 7 drug/polymer ratios over 7 days, the solubility of the drugs in ethanol with acid additives, and a comparison with 50/50 rotary-evaporated powders vaneerdenbrugh2010b R2, R3, R4, R5, R7, R8, R9.
Relation
extends the neat-drug class from the Crystallization tendency chapter to dispersions, in that drugs that crystallize readily were harder to protect vaneerdenbrugh2010b C1; first in the chapter to show at screen scale that no polymer is best for all drugs and that the acidic polymers reverse with the acid–base character of the drug vaneerdenbrugh2010b C2, C3.
SupportsF15 F16 F17
2010
wanapun2010SHG imaging of crystallization in amorphous filmsCharacterization methods
Selective Detection and Quantitation of Organic Molecule Crystallization by Second Harmonic Generation Microscopy
Known before
XRPD and spectroscopy reach about 1% crystallinity, optical microscopy needs crystals of several micrometres, and SHG is selective for non-centrosymmetric crystals wanapun2010 R1, C1, C4.
Added
SONICC and optical microscopy on the same field, crystals present at time zero in a film that looked amorphous, the forward/backward ruler and coherence lengths, a size-based detection limit near 10⁻⁹ %, and growth, nucleation and JMA kinetics from one stack with ΔE against a DSC value wanapun2010 R2, R4, R6, R9, R11, R16, R17, R18, R19.
Relation
introduces SHG to the library and takes the Raman 1% as the limit to beat.
SupportsF4 F5 F6 F7 F11
2011
alonzo2011drug loading, nanoparticles and the dissolved-drug ceilingDissolutionfirst proposed
Dissolution and Precipitation Behavior of Amorphous Solid Dispersions
Note
Known in the library (builds_on: Alonzo 2010, Konno 2008, Van Eerdenbrugh 2011): crystallization limits the observed amorphous supersaturation, PVP is weaker than HPMC against felodipine crystallization from solution, and UV is inflated by felodipine nanosuspensions alonzo2011 C3, R24, R25.
Added
the first particle-blind test of dispersions (flux ratios 10.5, 9.5 and 8.5 for 90:10, 50:50 and pure amorphous felodipine, near a predicted 9), NMR, the UV artefact of submicron particles, and fast disintegration of 10% drug dispersions alonzo2011 R14, R15, C27, R4.
Relation
first in the library on the dissolved-drug ceiling of dispersions; later papers cite it for that ceiling and for nanodroplets from low-loading dispersions [almeidaesousa2016 C9; indulkar2016 R14].
Note
Findings: F7, F8, F9, F10, F4, F5.
2011
baird2011eutectic composition and its predictionSolid state stabilityfirst proposed
Known before
the procedure for the calculated additive infrared spectra from a 2009 library paper on moisture-induced immiscibility (builds_on); the Flory–Huggins eutectic model of Lacoulonche is outside the library [baird2011 P4, C5].
Added
measured phase diagrams of four drugs with PEG 3350, the athermal prediction and a model map over drug melting points, back-calculated interaction energies, solubility in PEG 400 and infrared spectra of the melts [baird2011 R1, R2, R5, R6, R7, R8, R9, R10].
Relation
first in the library to tie the eutectic composition to drug lattice energy and to specific drug–PEG interaction; proposes PEG 400 solubility as a screen, the same stand-in that marsac2008b used for another question [baird2011 C25, C36; marsac2008b C18].
SupportsF1 F2 F3
2011
kestur2011polymer chemistry and the crystal growth of bifonazole and nimesulideSolid state stabilityextends
Known before
the growth-rate method and the hydrogen-bond hypothesis of kestur2010a, the felodipine–PVP infrared shifts of Konno (2006), and the finding of vaneerdenbrugh2010b that acidic polymers inhibit crystallization of basic and amide drugs (builds_on).
Added
growth rates of bifonazole with 5 wt% PVP, PVP/VA, HPMCAS and PAA and of nimesulide with PVP K12, PVP/VA and PVAc, the infrared NH region of nimesulide in solution and in dispersions, and a computed geometry with an intramolecular NH···O bond [kestur2011 R7, R8, R9, R10, R11, R13].
Relation
tests the hypothesis of kestur2010a on two chemically different drugs and finds that the best polymer depends on the drug [kestur2011 C4, C9, C10]; extends it by showing that an intramolecular bond of its NH donor narrows the differences between polymers for nimesulide [kestur2011 C11, C20, C27, R10, R11].
SupportsF13 F14 F17
2011
rumondor2011which dispersions separate: 20 systems and a discriminant modelSolid state stabilityconfirms
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].
SupportsF12 F13 F15 F16 F23
2011
vaneerdenbrugh2011adonor and acceptor rules for polymer selectionSolid state stabilityextends
Known before
the spin-coating screen of 8 drugs and 7 polymers, which found that polymer performance depends mainly on drug chemistry, and the crystallization class of the model drugs (builds_on) [vaneerdenbrugh2011a C5, C16].
Added
15 drugs (7 new) with the same 7 polymers in the same film screen, 105 pairs; donor and acceptor classes of every group from Etter's rules, pKBHX and calculated pKa; DFT of flufenamic and anthranilic acid; a crystal-structure survey of amide competition; ATR-FTIR of melts for acid–base reactions, not shown [vaneerdenbrugh2011a R1, R2, R3, R5, R6, R14, R8].
Relation
extends the 2010 screen from 8 to 15 drugs and gives its finding that acidic polymers suit amide and basic drugs a reading through group chemistry [vaneerdenbrugh2011a C5, X9; vaneerdenbrugh2010b C20]; the "ab initio" rank order is never tabulated or scored, and exceptions are explained afterwards [vaneerdenbrugh2011a C55, X5].
SupportsF24 F15 F17 F21 F11 F14
2011
vaneerdenbrugh2011bparticle absorption in fiber-optic UV probesCharacterization methodsfirst proposed
Influence of Particle Size on the Ultraviolet Spectrum of Particulate-Containing Solutions: Implications for In-Situ Concentration Monitoring Using UV/Vis Fiber-Optic Probes
Known before
the spin-coating and film-thickness method of the 2010 crystallization-tendency study and the expectation that amorphous felodipine recrystallizes in water (builds_on); in the dissolution literature particle interference was corrected as scattering only vaneerdenbrugh2011b C2.
Added
a 300 nm felodipine nanosuspension and four coarser suspensions read with a fiber-optic UV probe, NMR solubility, film-derived optical constants and Mie calculations of spheres of 30–4000 nm vaneerdenbrugh2011b R6, R7, R8, R12, R13, P11.
Relation
first showed in the library that submicron particles also absorb and that second-derivative correction leaves this in place vaneerdenbrugh2011b C23, C24.
SupportsF1 F2 F11
2011
zhu2011phase behaviour and microstructure over timeSolid state stabilityextends
Time-Resolved SAXS/WAXS Study of the Phase Behavior and Microstructural Evolution of Drug/PEG Solid Dispersions
Known before
the chlorpropamide and haloperidol phase diagrams and the view that the eutectic composition is set by melting point and interaction, from baird2011, and heats of fusion and drug Tg values from baird2010 (builds_on) zhu2011 C4, R5.
Added
phase diagrams of four more drugs, interaction parameters by melting point depression, solubility in supercooled PEG at 25 °C, infrared spectra of the melts, and time-resolved SAXS/WAXS of six 20/80 blends for 30 min and at 24 h zhu2011 R1, R2, R3, R4, R5, R20, R18.
Relation
extends baird2011 from the melt to the solidified dispersion; first time-resolved view of drug and PEG structure; reports that drugs with a negative interaction parameter enlarge the long period until they crystallize zhu2011 C32, C26.
SupportsF1 F3 F4 F5 F6 F7 F8 F9 F10
2012
alonzo2012HPMC on felodipine growth and nucleationDissolutionfirst proposed
Characterizing the Impact of Hydroxypropylmethyl Cellulose on the Growth and Nucleation Kinetics of Felodipine from Supersaturated Solutions
Known before
the solubility advantage of amorphous felodipine (S about 10), that 1 mg/mL HPMC does not change the felodipine solubility, and the second-derivative UV method with its nanoparticle check (builds_on) alonzo2012 C42, R21, R19, R20.
Added
seeded growth at S 3–12 with 0.2–3.5 µg/mL HPMC, the adsorption isotherm, the Kubota–Mullin factor α (0.7 at S 3 to 0.2 at S 12), the growth order (1.5 to 1.97 ± 0.12), an unseeded induction time of 15.3 against 136.5 min, and a nucleation-rate ratio of 7.05 × 10⁻⁴ alonzo2012 R4, R9, R13, R16, R17.
Relation
first in the library to separate the polymer effect on nucleation from that on growth, and to apply the Kubota–Mullin model to a polymer on a drug crystal alonzo2012 C46, C10.
SupportsF5 F6 F7 F9 F10 F13 F19 F20
2012
baird2012melt viscosity and glass-forming abilitySolid state stabilityconfirmsextends
Role of Viscosity in Influencing the Glass-Forming Ability of Organic Molecules from the Undercooled Melt State
Known before
the classes, Tg values and compound set of baird2010 (builds_on).
Added
melt viscosity from Tm down to crystallization for 34 compounds, its rise on cooling, and VTF fits baird2012 R1, R9, R12.
Relation
extends baird2010 with a kinetic explanation: about 10⁻² Pa·s at Tm appeared as a threshold between glass formers and non-glass formers baird2012 C46, viscosity being "one critical attribute" baird2012 C48; it confirms baird2010 that kinetic fragility does not separate the classes baird2012 C43.
SupportsF5 F12
2012
hsieh2012pH-induced precipitation of ten weak basesDissolutionfirst proposed
pH-Induced Precipitation Behavior of Weakly Basic Compounds: Determination of Extent and Duration of Supersaturation Using Potentiometric Titration and Correlation to Solid State Properties
Known before
crystallization-tendency classes from the undercooled melt and from rapid solvent evaporation (builds_on) hsieh2012 C5, P7.
Added
CheqSol titrations of ten weak bases at 37 °C, two behaviours (type 1 crystalline with supersaturation of 3.1–14.7 min; type 2 amorphous at 7.2–20.7 times the crystalline solubility), the comparison of the type 2 plateau with Hoffman estimates with and without a water-sorption correction, and two absorption models hsieh2012 R1, R5, R10, R14, R15.
Relation
first in the library to tie the form of a precipitate to the solution behaviour, and to propose the plateau as a way of measuring the amorphous solubility hsieh2012 C30, C32, C47.
SupportsF1 F2 F14 F19
2012
ilevbare2012abinary additive combinations on ritonavir growthDissolutionfirst proposed
Effect of Binary Additive Combinations on Solution Crystal Growth of the Poorly Water-Soluble Drug, Ritonavir
Known before
the single polymers ranked in 2012c and 2012b, lower polymer effectiveness at higher supersaturation (alonzo2012), and CAP Adp 0.85 as the best cellulose inhibitor (builds_on) ilevbare2012a C13, C18, C26.
Added
13 polymer pairs (best 12.1 against about 3 for each polymer), an equal-dose control for one pair, buffer strength and supersaturation series, and surfactants below the CMC that doubled growth and cancelled the esters ilevbare2012a R11, R12, R14, R16, R17.
Relation
first to test additive combinations; does not change the single-polymer rankings but shows that they do not predict pair behaviour ilevbare2012a K1, X7.
SupportsF9 F11 F12 F17 F18 F19 F38
2012
ilevbare2012bcellulose polymers: supersaturation, pH and rougheningDissolutionconfirmsextends
Known before
the felodipine–HPMC study, with the adsorption and Kubota–Mullin framework and the nucleation-over-growth argument (builds_on), and the polymer screen of 2012c, with CAP Adp 0.85 as the best cellulose inhibitor [ilevbare2012b R19, R18].
Added
growth inhibition at S 3.8, 7.6 and 15.3; the loss of the adipate esters at pH 3.8 despite higher adsorption; the critical supersaturation of 1.37 (1.74 with polymer); Kubota–Mullin factors of 4.35 and 1.25 [ilevbare2012b R5, R7, R9, R12, R16].
Relation
extends alonzo2012 from felodipine and HPMC to ritonavir and cellulose adipates, confirms that inhibition falls with supersaturation, and first links the loss to kinetic roughening [ilevbare2012b C17, C18, C51].
SupportsF9 F10 F11 F20 F44
2012
ilevbare2012cpolymer properties for ritonavir growth inhibitionDissolutionconfirms
Known before
ritonavir as a slow crystallizer and polymers changing nucleation and growth at low concentration (builds_on) [ilevbare2012c C7, C2].
Added
34 polymers at 5 µg/mL on seeded ritonavir, the solubility window of 14 new cellulose esters, the carboxyl-content trend, a multivariate model, and the effect of Pn-IPAAmd on crystal habit [ilevbare2012c R9, R10, R11, R12, R4].
Relation
confirms for ritonavir that polymers act at low concentration (alonzo2012) and adds the hydrophobicity hypothesis [ilevbare2012c C34, C25].
SupportsF7 F8 F12 F19
2012
kestur2012SONICC in bulk powders and a dispersionCharacterization methodsconfirmsextends
Nonlinear Optical Imaging for Sensitive Detection of Crystals in Bulk Amorphous Powders
Known before
SONICC detected 90 nm crystals in films and gave first evidence of linear scaling, the coherence length is about 100 nm, Raman detects about 1% in pure drug, and dispersion-based standards are needed for PXRD of dispersions kestur2012 R17, C3, C23.
Added
SHG calibration over 0–100% with PXRD and Raman OPLS models on the same blends, a prediction set and a spike test, images of 0.1% crystalline naproxen in 99.9% HPMCAS with a calculated limit of 10 ppm, crystals found in a fresh dispersion that PXRD and Raman called amorphous, and storage kinetics at 60 °C kestur2012 R4, R5, R6, R7, R10, R11, R1, R16.
Relation
extends Wanapun and co-workers from films to powders and dispersions; confirms linear scaling in blends and adopts the dispersion standards of Rumondor and Taylor for the reference methods.
SupportsF3 F4 F7 F8 F9 F10 F11
2012
trasi2012apolymers, nucleation and growth of amorphous acetaminophenSolid state stabilityfirst 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.
SupportsF1 F3 F5 F17 F18 F20
2012
trasi2012badditives, growth and nucleation of amorphous flutamideSolid state stabilityconfirmsextends
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].
SupportsF1 F3 F4 F5 F17 F18 F20
2012
vaneerdenbrugh2012amolecular weight and the miscibility of dextran with PVPSolid state stabilityextends
Known before
the Flory–Huggins entropy argument for a drug with PVP grades (marsac2006b); outside it, dextran–PVP blends of high molecular weight were immiscible and 860 and 1050 Da maltodextrins mixed with PVP K 90 [vaneerdenbrugh2012a R17].
Added
20 polymer pairs at nine compositions by DSC and FTIR; the hydrogen-bonded fraction of PVP carbonyls; the combinatorial entropy per lattice site [vaneerdenbrugh2012a R13, R14, R15].
Relation
extends the entropy argument of 2006 to pairs of two polymers and limits its "any grade" statement to a small drug [vaneerdenbrugh2012a C38, C39; marsac2006b R1].
SupportsF22 F5 F2 F3
2012
vaneerdenbrugh2012bAFM-IR of a felodipine–PAA filmCharacterization methodsfirst proposed
Known before
felodipine–PAA is partially miscible (miscible at 90:10, separating from 30:70), felodipine has a low crystallization tendency, and AFM-IR had not been used on a drug–polymer blend [vaneerdenbrugh2012b R1, C4, C3].
Added
AFM across composition, nanoscale reference spectra, local spectra on domains and matrix of the 50:50 film (1500/1700 band ratio about 1.1 against 0.6), maps and a ratio map [vaneerdenbrugh2012b R2, R3, R4, R6, R9, R10, R11, R13].
Relation
first AFM-IR study of a drug–polymer blend.
SupportsF12 F13 F14 F20
2012
vaneerdenbrugh2012cAFM-IR of dextran/maltodextrin–PVP blendsCharacterization methodsfirst proposedconfirmsextends
Known before
a DSC classification of the nine blends and the felodipine–PAA AFM-IR study with its ratio-map rationale [vaneerdenbrugh2012c R1, C32, C44].
Added
AFM and AFM-IR against the DSC class (eight of nine in agreement), phase identity from the dextran band, a ratio map of DEX40–PVP90, and the rules that dextran-rich phases are thicker and that the lower-MW polymer forms the discrete phase [vaneerdenbrugh2012c R9, R10, R13, R17, R18, C26, C30].
Relation
extends the first AFM-IR paper to polymer pairs with an independent benchmark; confirms the ratio map and adds the caveats of unequal absorptivity and spectral mixing.
SupportsF12 F13 F15
2012
zhu2012crystallization kinetics of drug and carrierSolid state stabilityconfirmsextendscontradicts
Modification of Crystallization Behavior in Drug/Polyethylene Glycol Solid Dispersions
Known before
the phase behaviour, solubility, eutectics and hydrogen bonding of the pairs from zhu2011, the drug–PEG phase diagrams from baird2011 and the crystallization tendency and benzocaine Tg of baird2010 (builds_on) zhu2012 C12, C13, M3.
Added
onset and time course of the drug in four 20/80 comelts by XRD and Raman, 50-sample statistics for neat ibuprofen and fenofibrate, seeding of the supercooled drugs with crystalline PEG, the kinetics of PEG itself at 25 and 40 °C and PEG spherulite growth zhu2012 R2, R3, R9, R14, R15, R19, R4, R22, R23.
Relation
extends zhu2011 from structure to kinetics; contradicts the expectation that the neat-drug tendency carries into the dispersion, since crystalline PEG apparently promotes ibuprofen and fenofibrate; confirms with another method the time scale of ibuprofen crystallization seen by SAXS/WAXS zhu2012 C41, C4, R14; zhu2011 R15.
SupportsF1 F7 F8 F9 F10
2013
baird2013rapid heat–cool calorimetrySolid state stabilityextendsrevises
Known before
the classes, conventional-DSC data and the quenched-in nuclei proposal of baird2010 (builds_on).
Added
cooling and heating at up to about 2000 °C/min, critical cooling rates fitted over a wide rate range and critical heating rates of class II glasses [baird2013 P2, R1, R7, R9].
Relation
revises the baird2010 verdict on critical-rate extrapolation in part, since a wider rate range "seems to improve" the fits [baird2013 C20]; extends the quenched-in nuclei proposal with the cooling–heating asymmetry, reported as a first for organic systems [baird2013 C26, C30].
SupportsF9 F10 F11 F15 F16
2013
harrison2013AFM-IR of griseofulvin nanocrystals in HPMC filmsCharacterization methodsconfirmsextends
Known before
AFM-IR on a drug–polymer blend and on polymer blends from the same group; infrared near-field microscopy reaches about 20 nm at a cost [harrison2013 C7, C6, R15].
Added
identification of agglomerates, a 90 nm particle in an image, spectra of particles of about 100 nm at S/N 5:1, stiffness maps and a size distribution against light scattering [harrison2013 R4, R8, R12, R13, R9, R10].
Relation
extends AFM-IR from blends to embedded drug particles; confirms the thickness dependence of the signal.
SupportsF12 F13 F14
2013
ilevbare2013aLLPS of eight drugs and the ritonavir phase diagramDissolutionfirst proposed
Liquid-Liquid Phase Separation in Highly Supersaturated Aqueous Solutions of Poorly-Water Soluble Drugs – Implications for Solubility Enhancing Formulations
Known before
melting data, Log P, Tg and the slow-crystallizer class of the drugs from the 2010 classification study, and crystal solubilities and the water sorption method from the 2012 pH-induced precipitation study (builds_on).
Added
UV, DLS and pyrene onsets for eight drugs at 37 °C, the isolated ritonavir drug-rich phase (about 95% drug, 4–5% water, Tg 0.4 °C), a ritonavir temperature–concentration diagram, and tests of ionic strength, temperature, Tween 80, PVP and a ritonavir–PVP dispersion ilevbare2013a R8, R5, R6, R11, R13, R14, R16, R17.
Relation
first proposed in the library that the LLPS onset equals the water-corrected amorphous solubility and that this concentration caps free drug ilevbare2013a C3, C5.
SupportsF1 F2 F3 F4 F5 F6 F8 F9 F12 F13
2013
ilevbare2013bpolymers and growth of three structurally diverse drugsDissolutionextends
Known before
felodipine–HPMC (alonzo2012), no secondary nucleation for ritonavir and a pair factor of about 3.3 (2012a), supersaturation and ionization effects with CAP Adp 0.85 (2012b), the hydrophobicity hypothesis (2012c), and the nucleation-inhibitor ranking (2013c) (builds_on) [ilevbare2013b C7, R16, R17, R19, C35].
Added
seeded growth of celecoxib, efavirenz and ritonavir with 16 polymers including three second-generation suberate and sebacate esters, the salt test, N–H band shifts for PVPVA, the pH test for celecoxib, and supersaturation series up to the amorphous level [ilevbare2013b R9, R10, R12, R13, R14, R15].
Relation
extends the hydrophobicity hypothesis to other drugs and shows that the best polymer depends on the drug (HPMC for celecoxib, suberate esters for ritonavir) [ilevbare2013b C21, C43, C44, C60].
SupportsF3 F5 F6 F7 F8 F9 F11 F20
2013
ilevbare2013cpolymers and induction times of three drugsDissolutionconfirmsrevises
Maintaining Supersaturation in Aqueous Drug Solutions: Impact of Different Polymers on Induction Times
Known before
the melt-quench classes of the three drugs, the felodipine–HPMC nucleation result, that polymers inhibit ritonavir growth poorly at high supersaturation, and the same polymer set tested on growth (builds_on) ilevbare2013c C11, R19, M1–M3.
Added
unseeded induction times of ritonavir, efavirenz and celecoxib with 21 polymers at the calculated amorphous solubility, the solubility-parameter rule, the pH 3.8 arm and the 31-fold gain for HPMC at half the supersaturation ilevbare2013c R9, R13, R14, R15.
Relation
confirms alonzo2012 that nucleation can be delayed far more than growth is slowed, and revises the growth rankings: the best nucleation inhibitors differ from the best growth inhibitors ilevbare2013c C40.
SupportsF2 F3 F5 F6 F11 F13 F14 F19 F35
2013
ilevbare2013dritonavir nanodroplets and additivesDissolutionconfirms
Influence of Additives on the Properties of Nanodroplets Formed in Highly Supersaturated Aqueous Solutions of Ritonavir
Note
Known in the library (builds_on: Ilevbare 2013 on LLPS, Ilevbare 2013 on induction times, Ilevbare 2012, Hsieh 2012, Alonzo 2011): the LLPS concentration of ritonavir and its measurement by solvent shift or pH shift, the induction-time method with a 120 min baseline, cellulose polymers and the Tg of amorphous ritonavir, and the diffusion cap on dissolved dispersions ilevbare2013d R18, R17, R19.
Added
the colloid of a dissolving ritonavir dispersion is a non-crystalline drug-rich liquid (Tg about 1 °C) formed at about the LLPS concentration; four classes of 15 additives for droplet size and crystallization; crystallization that appears to start in the droplets ilevbare2013d R1, R2, R14, C39.
Relation
confirms and names the ceiling of Alonzo 2011 as the LLPS concentration ilevbare2013d C35; first in the library on additives at drug-rich droplets.
Note
Findings: F7, F9, F12, F13, F14.
2013
kestur2013afelodipine polymorphs with and without PVPSolid state stabilityfirst 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.
SupportsF3 F4 F19 F20 F21
2013
kestur2013bparticle size, surfaces and dissolution of felodipine powdersSolid state stabilityfirst proposed
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].
SupportsF1 F4 F17 F19 F20 F21 F25 F26
2013
wegiel2013amid-infrared polymer selection for two polyphenolsSolid state stabilityextends
Mid-infrared spectroscopy as a polymer selection tool for formulating amorphous solid dispersions
Known before
the link between drug–polymer interactions and inhibition (kestur2010a, kestur2011), the donor and acceptor classification of vaneerdenbrugh2011a, the reading of IR shifts as hydrogen bonding (taylor1997) and the E100 acid–base contact in resveratrol and curcumin dispersions (builds_on) wegiel2013a C6, C29, R16.
Added
OH and C=O shifts of naringenin and quercetin films with six polymers; the E100 amine bands; the highest X-ray amorphous content; storage at five conditions for up to more than 450 days wegiel2013a R2, R4, R6, R8, R9.
Relation
applies the rule of F17 to two weak-acid polyphenols and finds that the IR ranking holds at the extremes only; extends the E100 contact to two more drugs wegiel2013a X4, C34, C35.
SupportsF25 F21 F23 F2 F13 F14 F11 F12
2013
wegiel2013bresveratrol dispersions with six polymersSolid state stabilitycontradicts
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].
SupportsF5 F7 F11 F23 F24 F25
2014
hsieh2014polymers and pH-induced precipitation by synchrotron WAXSDissolutionextends
Assessing the Impact of Polymers on the pH-Induced Precipitation Behavior of Poorly Water-Soluble Compounds using Synchrotron Wide Angle X-Ray Scattering
Known before
rapid against reluctant crystallizers after a pH shift (hsieh2012), the melt classes, the hydrogen-bond donor and acceptor reasoning for polymers, and polymer hydrophobicity in growth and nucleation inhibition (builds_on) hsieh2014 R22, R18, C35, C39.
Added
four ionizable drugs precipitated alone and with nine polymers at 1 mg/mL, WAXS at 15 min to 6 h, concentration against the polymer-specific crystalline solubility, and a Hoffman check of the warfarin supersaturation hsieh2014 R4, R12, R13, R16.
Relation
extends hsieh2012 to polymers; shows that the same polymers redirect precipitation to an amorphous solid for the two acids and not for the two bases, and that the melt class does not predict the outcome hsieh2014 C4, C9, C30.
SupportsF1 F2 F8 F16 F19
2014
jackson2014polymers and precipitation of supersaturated danazolDissolutionextends
Impact of Polymers on the Precipitation Behavior of Highly Supersaturated Aqueous Danazol Solutions
Known before
SHG detection of crystals, particle-size effects on the UV signal, the UV-extinction method for LLPS with an onset near the amorphous solubility, and the pyrene approach (builds_on) jackson2014 R29, R28, C11–C13.
Added
the danazol onset of 13 µg/mL by two methods, crystallization within 6–10 min, polymers lowering the onset to 8–11 µg/mL and prolonging crystallization to 88–516 min, droplet sizes and zeta potentials jackson2014 R5, R17, R22, R23.
Relation
extends the LLPS onset of ritonavir to a faster crystallizer and, unlike ritonavir, finds polymers lowering the onset jackson2014 C22, C23, R28.
SupportsF2 F4 F14 F15 F19
2014
mosqueragiraldo2014surfactants and celecoxib growthSolid state stabilityfirst 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.
SupportsF3 F4 F5 F20 F22
2014
raina2014aflux ceiling at the amorphous solubilityBioperformancefirst proposed
Enhancements and Limits in Drug Membrane Transport Using Supersaturated Solutions of Poorly Water Soluble Drugs
Known before
LLPS at about the amorphous solubility and the UV-extinction method (Ilevbare 2013), a hint that flux peaks at the amorphous solubility (Alonzo 2010), felodipine a slow and nifedipine a faster crystallizer (Baird 2010) and HPMC as inhibitor (Alonzo 2012) (builds_on) raina2014a R19, R18, R20, C8.
Added
LLPS onsets 20–45 °C for two dihydropyridines, a moisture-corrected prediction of the amorphous solubility, and flux against donor concentration with a plateau at the onset raina2014a R1, R7, R11, R12, R14, R16.
Relation
first in the library to show the flux ceiling for solvent-shift solutions; the reservoir idea is proposed, not tested raina2014a C37, C38.
SupportsF1 F2 F10 F32
2014
raina2014bnifedipine polymorphs during dissolutionDissolutionextendscontradicts
Impact of Polymers on the Crystallization and Phase Transition Kinetics of Amorphous Nifedipine during Dissolution in Aqueous Media
Note
Known in the library (builds_on: Alonzo 2010, 2011 and 2012, Marsac 2006 and 2008, Baird 2010, Raina 2014 on LLPS): the two routes and the felodipine polymer effects, nifedipine as a faster crystallizer than felodipine at similar Tg and moisture sorption, and no nifedipine solubility gain with 1 mg/mL polymer raina2014b C1, R17, C26.
Added
matrix crystallization of nifedipine glass that dissolved polymer does not change, γ before α on both routes with dissolved polymers lengthening γ (HPMCAS > HPMC > PVP), dispersions that switch the route to solution, and MCR to quantify forms without calibration raina2014b C11, C29, C17, C21, C43.
Relation
extends Alonzo 2010 to a fast crystallizer and to polymorph conversion; contradicts the felodipine result that polymer in the medium protects the wetted solid raina2014b C27.
Note
Findings: F1, F2, F3, F10.
2014
trasi2014acrystal growth rates of 31 drug liquidsSolid state stabilityextendscontradicts
Known before
the classes of baird2010, the melt viscosities of baird2012 and the separate polymer effects on nucleation and growth of acetaminophen (trasi2012a) (builds_on).
Added
seeded growth rates of 31 drugs, spanning 4 orders of magnitude in maximum velocity [trasi2014a C23], their relation to viscosity, Tm − Tg and melting entropy [trasi2014a R9, R11], PVP effects [trasi2014a R6] and an extended nucleation-and-growth classification [trasi2014a C17].
Relation
extends the DSC classes with growth; contradicts a reading of class III as slow-growing, since good glass formers include some of the fastest growers [trasi2014a R1, C14].
SupportsF1 F2 F3 F5 F6 F15 F19 F21
2014
trasi2014bnilutamide nucleation far below TgSolid state stabilityconfirmscontradicts
Known before
nilutamide as a class III glass former (baird2010), flutamide and acetaminophen crystallizing on reheating (baird2013), and faster high-temperature growth of stable felodipine forms (kestur2013a) (builds_on).
Added
nucleation mainly far below Tg, a new metastable form I, polymorph growth-rate crossover and polymer effects on growth [trasi2014b R5, R9, R16, R8, R3].
Relation
contradicts the general expectation that low-temperature storage stabilizes amorphous systems [trasi2014b C57] and differs from flutamide and acetaminophen, which nucleate above Tg [trasi2014b C37]; confirms for one drug that good glass formation can come from low nucleation with fast growth [trasi2014b C9].
SupportsF3 F4 F7 F15 F19
2014
wegiel2014curcumin dispersions and intramolecular bondingSolid state stabilityextends
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].
SupportsF5 F11 F18 F20 F24 F25
2015
almeidaesousa2015amorphous solubility of six fast crystallizers; heat-capacity methodDissolutionconfirmsrevises
Assessment of the Amorphous “Solubility” of a Group of Diverse Drugs Using New Experimental and Theoretical Approaches
Known before
the onset method and its link to Eq. 1 from the 2013 paper, and the crystallization free energy of felodipine and nifedipine from the 2006 stability study (builds_on).
Added
six fast-crystallizing drugs at 25 °C, two of them glasses, with extinction and a polarity-probe check; free energies by the Hoffman equation and by a heat-capacity (Cp) method to the supercooled liquid and the glass almeidaesousa2015 R3, R5, R11, C10.
Relation
confirms that the onset matches the calculated amorphous solubility for fast crystallizers and glassy drugs almeidaesousa2015 C42; revises the free-energy route, the Cp method being closer than Hoffman almeidaesousa2015 C43.
SupportsF1 F2 F3 F4 F5 F6 F7
2015
chen2015bile salts as crystallization inhibitors of 11 drugsDissolutionfirst proposedextends
Bile Salts as Crystallization Inhibitors of Supersaturated Solutions of Poorly Water-Soluble Compounds
Known before
STC inhibits celecoxib nucleation and stays below its CMC with the drug, polymers are the benchmark inhibitors, and the induction-time approach (builds_on) chen2015 R9, R11, C3.
Added
induction times of 11 drugs at a matched ratio of concentration to solubility in buffer, with 0.1% STC and with 0.1% SDS (STC 15 to more than 1000 min, SDS shorter for seven of nine drugs), solubility 1.1–3.5-fold higher with STC and up to about 266-fold with SDS, and SGC and SGDC for two drugs chen2015 R1, R3, R4.
Relation
first in the library to test a bile salt across many drugs and to set it against a conventional surfactant; extends the celecoxib result chen2015 C13, C18, C25.
SupportsF3 F18 F19 F28 F31 F38
2015
chen2015asurfactants in celecoxib–HPMCAS suspensionsDissolutionfirst proposed
Note
Known in the library (builds_on: Ilevbare 2013 on induction times): the induction-time method at constant supersaturation [chen2015a P9].
Added
SDS and polysorbate 80 crystallized acidified suspensions within an hour, STC and Triton X100 slowed nucleation, SDS dissolved far more HPMCAS and drug, and a trace of HPMCAS reversed the Poloxamer 188 result [chen2015a R14, R12, R18, R19].
Relation
first in the library on surfactants in ASD suspensions; agrees with the surfactant promotion of ritonavir droplet crystallization of 2013 ilevbare2013d R12.
Note
Findings: F14, F15, F6, F1.
2015
indulkar2015pH dependence for weak basesDissolutionextends
pH-Dependent Liquid−Liquid Phase Separation of Highly Supersaturated Solutions of Weakly Basic Drugs
Known before
the onset as the amorphous solubility, also for a glassy phase (the 2013 and 2015 papers above), and the pH-shift titration method and amorphous precipitation of weak bases from the 2012 pH-induced precipitation study (builds_on).
Added
three weak bases over about ±2 pH units around the pKa, a solvent-free titration, XRPD, microscopy, Nile red, DSC of the precipitates and dissolution of amorphous films indulkar2015 R5, R6, R7, R8, R19, R18.
Relation
extends the framework to ionizable drugs: the onset follows Henderson–Hasselbalch with a constant un-ionized concentration indulkar2015 C3, C46; the calculation fits atazanavir closely and clotrimazole within 1.6-fold indulkar2015 R2, F3.
SupportsF1 F2 F4 F5 F6 F10 F13
2015
jackson2015danazol dispersions, LLPS, drug loading and polymerDissolutionconfirmsextends
Dissolution of Danazol Amorphous Solid Dispersions: Supersaturation and Phase Behavior as a Function of Drug Loading and Polymer Type
Note
Known in the library (builds_on: Jackson 2014, Ilevbare 2013 on LLPS, Ilevbare 2013 on nanodroplets, Almeida e Sousa 2015, Raina 2014 on LLPS, Van Eerdenbrugh 2011): danazol crystalline solubility and polymer effects, LLPS onset near the estimated amorphous solubility, the diffusion-cell flux method, the UV overestimate with particles, and ASD dissolution above the amorphous solubility jackson2015 R11, C3, C12, C7.
Added
LLPS on dissolution up to 30% drug with three polymers, free drug by flux at 7.1–9.1 µg/mL against 8 µg/mL whatever the polymer, polymer-dependent duration (PVP < HPMC < HPMCAS), and slow release at 50% drug jackson2015 C36, R9, R5, C37.
Relation
confirms the ceiling by flux for three polymers ("is confirmed here") jackson2015 C30; extends the 2013 ritonavir colloid to danazol.
Note
Findings: F4, F6, F7, F9, F10.
2015
mosqueragiraldo2015glass–liquid phase separation of telaprevirDissolutionconfirmsextendscontradicts
Glass–Liquid Phase Separation in Highly Supersaturated Aqueous Solutions of Telaprevir
Known before
LLPS at the amorphous solubility for low-Tg drugs (2013 paper), the flux plateau at the LLPS concentration and the reservoir idea from the 2014 membrane-transport study, and the sorption method (builds_on).
Added
a high-Tg, high-melting drug: three onsets (UV, NMR, fluorescence) at 90–92 µg/mL, a pellet Tg of 52 °C, redissolution within about 2 min, NMR and flux plateaus, and three free-energy estimates mosqueragiraldo2015 R13, R2, R8, R10, R12.
Relation
extends the framework to a glassy drug-rich phase; contradicts the Hoffman route for this drug (245 against 90–92 µg/mL) and supports a supercooled-liquid reference state mosqueragiraldo2015 R13, C23, C27; confirms the flux plateau mosqueragiraldo2015 C20.
SupportsF1 F2 F3 F4 F5 F7 F8 F14
2015
purohit2015aitraconazole–HPMC miscibility with fluorescence and AFM-nanoIRSolid state stabilityextends
Miscibility of Itraconazole-Hydroxypropyl Methylcellulose Blends- Insights with High Resolution Analytical Methodologies
Known before
the limits of DSC for miscibility, the use of AFM-nanoIR on dextran–PVP and felodipine–PAA blends, and a debate on the miscibility of itraconazole–HPMC; the single-Tg ambiguity of F3 purohit2015a C3, C4, C6.
Added
pyrene and prodan fluorescence, fluorescence imaging, AFM-nanoIR and nanoTA of films at 10–50% drug, modulated DSC of powders, and heating at 165 °C purohit2015a R1, R3, R6, R7, R10, R11, R12, R13.
Relation
extends F3 to a drug without donors, for which four film methods find domains at every loading where DSC shows one broad Tg, and adds that heating at 165 °C mixes the film purohit2015a C36, C38.
SupportsF18 F3
2015
purohit2015bfluorescent probes in ASD films exposed to waterCharacterization methodsextends
Phase Separation Kinetics in Amorphous Solid Dispersions Upon Exposure to Water
Known before
moisture-induced phase separation of probucol–PVP and of PVP dispersions, resistance of HPMCAS dispersions, and probes used to detect a drug-rich phase in supersaturated solutions purohit2015b R24, R26, R27, C4.
Added
probe calibration in amorphous drug and polymer films, humidity time courses of probucol–PVP, ritonavir–PVP and a ritonavir–HPMCAS control, IR, DSC, XRD and imaging as checks, and immersion in buffer purohit2015b R1, R3, R4, R6, R13, R17, R19, R10, R11.
Relation
carries the solution-state probe approach of the Solution methods chapter to amorphous solids and extends the humidity work of Rumondor and co-workers.
SupportsF16 F17 F18
2015
raina2015aenvironment-sensitive probes for liquid-liquid phase separationCharacterization methodsconfirmsextends
Using Environment-Sensitive Fluorescent Probes to Characterize Liquid-Liquid Phase Separation in Supersaturated Solutions of Poorly Water Soluble Compounds
Known before
LLPS, the amorphous solubility estimate and the membrane-transport role of the drug-rich phase for the same dihydropyridines (raina2014a, raina2015c, raina2015b, ilevbare2013a), the extinction method for a disordered phase (alonzo2010), polymer inhibition of nifedipine crystallization (raina2014b) and the crystallization-tendency classes with the DSC pan method (baird2010) (builds_on); pyrene I1/I3 had been used for danazol solutions jackson2014 R6, R8.
Added
six probes calibrated in solvents, onsets of six dihydropyridines at 25 and 37 °C by probe, extinction and thermodynamic estimate, felodipine as its own indicator, crystallizing nifedipine and nimodipine as negative controls, and the pyrene return on crystallization raina2015a R1, R11, R15, R8, R16.
Relation
extends the pyrene idea to a systematic probe study; confirms the extinction onset with a second read-out and with the estimate raina2015a C16.
SupportsF3 F4 F5 F6 F7 F8 F9
2015
raina2015bsix dihydropyridines by synchrotron WAXSDissolutionextends
Trends in the Precipitation and Crystallization Behavior of Supersaturated Aqueous Solutions of Poorly Water-Soluble Drugs Assessed Using Synchrotron Radiation
Known before
the melt classes of undercooled melts, LLPS above the amorphous solubility, and moderately hydrophobic polymers as inhibitors (builds_on) raina2015b C5, C7, C44.
Added
the first crystalline time of six analogues precipitated from a nominal 10 mg/mL (0.25 to 12 h), eight polymers at 4.5 mg/mL, 3-h concentrations against estimated amorphous solubilities and NMR partitioning of four polymers with felodipine raina2015b R6, R9, R10, R12.
Relation
extends hsieh2014 (WAXS of precipitates with polymers) to a close set of analogues; shows that the melt screen cannot clear slow crystallizers and proposes that an inhibitor needs affinity for both the precipitate and the water raina2015b C29, C48.
SupportsF2 F3 F8 F16 F21 F26 F37
2015
raina2015csolubilizing additivesBioperformanceextendsrevises
Impact of Solubilizing Additives on Supersaturation and Membrane Transport of Drugs
Known before
the method and the plateau of raina2014a, LLPS at the amorphous solubility (Ilevbare 2013), UV-extinction detection (Van Eerdenbrugh 2011) (builds_on) raina2015c C9, C10, R14.
Added
six additives at three levels, FaSSIF, suspensions that fix the activity, the shift of the LLPS onset and the failure of c/c* raina2015c R4, R7, R8, R9, R11, R12.
Relation
extends raina2014a from buffer to solubilizing media; revises the estimate of the amorphous solubility for FaSSIF raina2015c C18.
SupportsF1 F3 F4
2015
sato2015a chiral polymer and the growth of two enantiomersSolid state stabilityfirst proposed
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].
SupportsF27 F18 F3 F5 F20
2015
schram2015HPMCAS conformation and felodipine growthDissolution
Known before
carboxylated cellulose esters were less effective at lower pH although they adsorbed as much, and conformation was proposed as the reason (ilevbare2012b, ilevbare2013b; builds_on) [schram2015 R26, C2].
Added
growth ratios of 2.29 at pH 6.8 and 1.28 at pH 3 on a rotating disc, in-liquid AFM of adsorbed HPMCAS (globules about 44 nm apart at pH 3, a thin layer at pH 6.8), the same area imaged after a pH rise, and AFM-IR [schram2015 R4, R12, R17, R10, R18, R20].
Relation
tests the conformation proposal of the 2012–2013 papers; the link to inhibition is a correlation across two pH values [schram2015 C20, X7].
SupportsF5 F7 F10 F11 F12 F23 F44
2015
trasi2015acetaminophen nucleation and growth with five polymersDissolutionrevises
Known before
the melt ranks of the same five polymers for nucleation and growth (builds_on) [trasi2015 R14].
Added
a Poisson fit of about 80 induction times per sample, crystal counting in a larger vessel, seeded growth and habit at S 1.5 [trasi2015 R1, R3, R10, R11, R12].
Relation
revises the melt ranking for solution (PAA reversed from best growth inhibitor to nucleation promoter), and shows that induction time and count slope rank PVPVA differently [trasi2015 C26, C28, C22].
SupportsF3 F5 F6 F7 F12 F14 F27 F35
2015
trasi2015aa second drug in the drug-rich phaseDissolutionextends
Thermodynamics of Highly Supersaturated Aqueous Solutions of Poorly Water-Soluble Drugs—Impact of a Second Drug on the Solution Phase Behavior and Implications for Combination Products
Known before
the LLPS concentration equals the amorphous solubility and probes mix into the drug-rich phase (2013 paper), flux maximum at LLPS and the ultracentrifuge supernatant as a binodal point (2014 membrane-transport study), and the estimation of the amorphous solubility (builds_on).
Added
ritonavir with lopinavir, paclitaxel, felodipine and diclofenac; onsets by fluorescence, ultracentrifugation and flux; partitioning into a pre-formed ritonavir-rich phase; an ideal-mixing model trasi2015a R7, R13, R9, R16.
Relation
new; extends the ceiling to mixtures, where each drug's amorphous solubility falls with its mole fraction in the shared phase trasi2015a C35, C50.
SupportsF1 F3 F4 F6 F8 F11
2015
trasi2015bbinary amorphous drug combinationsDissolutionextends
Dissolution performance of binary amorphous drug combinations—Impact of a second drug on the maximum achievable supersaturation
Note
Known in the library (builds_on: Trasi 2015 on a second drug, Ilevbare 2013 on LLPS, Raina 2014 on LLPS): a second drug lowers the amorphous solubility in antisolvent tests, LLPS above the amorphous solubility, and the amorphous solubility caps free drug and membrane transport trasi2015b C7, C4.
Added
the drop of each ceiling to about Sa × xd in dissolving films and in PVP and HPMCAS dispersions, the same drop from two dispersions dissolved together, colloids of HPMCAS dispersions that pass 0.45 µm filters, and slower crystallization of the mixed drug-rich phase trasi2015b R5, R13, R11, R7, R15.
Relation
extends the antisolvent result of the LLPS chapter to dissolution; first in the library on co-dosed amorphous products trasi2015b C47.
Note
Findings: F11, F7, F8, F10, F13.
2015
wegiel2015resveratrol dispersions in aqueous mediaDissolutionextends
Note
Known in the library (builds_on: Alonzo 2010, Van Eerdenbrugh 2010, Alonzo 2011, Wegiel 2013, Raina 2014): the two crystallization routes, resveratrol as a rapid crystallizer, a felodipine dispersion with a flux ten times that of the crystal, and the storage stability of the same resveratrol dispersions (PVP and E100 stable, HPMC, HPMCAS and CMCAB crystallized at high RH); diffusion-cell flux as a measure of free drug [wegiel2015 R21, R22, R24].
Added
dissolved HPMCAS raised the crystalline solubility of resveratrol from 42 to 414 µg/mL at 10 mg/mL, PVP solutions first dissolved and then precipitated resveratrol with the polymer, only 80% HPMC, 85% HPMCAS or 95% CMCAB stopped matrix crystallization, and more HPMCAS dispersion raised the total concentration while the flux fell [wegiel2015 R2, R3, R6, R7, R14, R19, R20].
Relation
extends the matrix route of Alonzo 2010 to dispersions of a rapid crystallizer; first in the library to separate a soluble drug–polymer complex from supersaturation by flux during dispersion dissolution [wegiel2015 C41].
Note
Findings: F16, F17, F1, F7.
2015
xie2015celecoxib dispersions with polymer combinationsDissolutionconfirms
Dissolution Performance of High Drug Loading Celecoxib Amorphous Solid Dispersions Formulated with Polymer Combinations
Note
Known in the library (builds_on: Alonzo 2010, Trasi 2012, Ilevbare 2013 on induction times, Chen 2015, Trasi 2015 on acetaminophen): the matrix and solution routes, PAA as a solid-state growth inhibitor, the induction-time approach and the stronger effect of amphiphilic than hydrophilic polymers on lipophilic drugs, the onset criterion for celecoxib, and a polymer that fails as a solution inhibitor xie2015 C10, C47.
Added
HPMCAS and HPMC held 22 µg/mL celecoxib for more than 8 h against about 1–2 h with PVP; neat amorphous celecoxib crystallized on its own particles and gave almost no supersaturation; at 50% drug replacing a fifth of the PVP with HPMCAS or HPMC kept supersaturation for 16 h but slowed release, and 5 µg/mL of either in the medium protected the PVP-K12 dispersion xie2015 R1, R7, R4, R6.
Relation
confirms the cellulosic-over-PVP ranking for a third drug; first in the library on two polymers in one dispersion for dissolution, where little earlier work existed xie2015 C30.
Note
Findings: F4, F20, F1, F2, F6, F10.
2016
alhalaweh2016several drugs in one dispersionBioperformanceextendscontradicts
Compromised in vitro dissolution and membrane transport of multidrug amorphous formulations
Known before
flux linear in free drug with a plateau (Raina 2014, 2015), LLPS onset as the amorphous solubility, and an ideal-mixing model for a second drug in the drug-rich phase (Trasi 2015) (builds_on) alhalaweh2016 R21, R22, C26.
Added
ritonavir, atazanavir and lopinavir in PVP dispersions, in a physical mixture and in antisolvent drug-rich phases; Caco-2 flux; a mole-fraction law for the ceiling alhalaweh2016 R10, R12, R13, R17, R19.
Relation
extends the Trasi model to ASD dissolution and to membrane flux; contradicts the expectation that co-formulation raises dissolution alhalaweh2016 C15.
SupportsF6
2016
almeidaesousa2016salt, co-crystal, glass and ASD of a weak baseDissolutionextendsrevises
Known before
ASD dissolution capped at the amorphous solubility (2011 study), UV probe overreading with submicron particles (2011 methods study), pH-shift supersaturation of weak bases (2012), and Eq. 1 with the onset methods (2013 and 2015 papers) (builds_on).
Added
seven solid forms of CRH1 dissolved at pH 4.6 with and without 20 µg/mL HPMC, pyrene and counterion fluorescence, and centrifugation with HPLC at the UV maximum [almeidaesousa2016 R8, R9, R11, R12].
Relation
extends the ceiling to salts and an ASD, shown for four of seven forms, not for the glass and the co-crystal [almeidaesousa2016 C43, C31]; revises UV readings of a salt with an absorbing counterion [almeidaesousa2016 R12].
SupportsF1 F3 F4 F5 F6 F7 F10 F13 F14
2016
indulkar2016nanodroplet reservoirBioperformancefirst proposed
Exploiting the phenomenon of liquid-liquid phase separation for enhanced and sustained membrane transport of a poorly water soluble drug
Known before
LLPS and nanodroplets (Ilevbare 2013, Indulkar 2015), nanodroplets from fast ASD dissolution (Alonzo 2011, Jackson 2015) and the reservoir idea of raina2014a; earlier transport cells became non-sink (builds_on) indulkar2016 C1, C4, C5, C6.
Added
a flow-through cell with a sink receiver, steady periods that grow with the droplet amount, a coarse-particle control and a compartment model indulkar2016 R6, R7, R11.
Relation
first test of the reservoir proposed in raina2014a; shows the ceiling again in a second device indulkar2016 C19, C25.
SupportsF1 F2 F5 F32
2016
jackson2016supersaturated danazol: polymers and phase transitionsDissolutionconfirmsrevises
Known before
the onset of 13 µg/mL, the estimate of 16 µg/mL and the lower onsets with polymer of the first danazol paper (builds_on) [jackson2016 R12, R4].
Added
an onset of about 8 µg/mL by four methods with and without polymer, a recalculated estimate of 7.8 µg/mL, the flux plateau, the pyrene reading at 15 s, 1 min and 5 min, induction times at 1–1000 µg/mL polymer, zeta potential and droplet size [jackson2016 R3, R8, R10, R13, R17, R18, R19, R21].
Relation
revises jackson2014: the polymers do not lower the onset or the flux, and the 13 µg/mL was a 15 s reading; confirms the induction-time ranking HPMC-AS > HPMC > PVP [jackson2016 C14, C20, C54].
SupportsF2 F4 F5 F15 F19 F22 F37
2016
li2016a13 bile salts comparedDissolutionextends
Known before
STC, SGC and SGDC delay nucleation (chen2015; builds_on) [li2016a R30, C10].
Added
13 bile salts with three drugs at 0.1%, a concentration series with STC, a diffusion-cell check of the driving force, hydrophobicity (LogP'A), simulations of nevirapine with four bile salts and a blend of the six main human bile salts [li2016a R6, R7–R11, R15, R16, R17–R27, R28].
Relation
answers the open question of chen2015 (bile salts are not interchangeable) and extends it to 13 bile salts [li2016a C3, C69].
SupportsF3 F14 F19 F29 F30 F31 F40
2016
li2016blopinavir dispersions leaching in acidDissolutionextends
Note
Known in the library (builds_on: Chen 2015, Raina 2015): the spray-drying procedure, the CMC method and the question of surfactants in ASD suspensions, and the apparent supersaturation C/Ceq in solubilizing media [li2016b C3, C7].
Added
33% lopinavir dispersions with three HPMCAS grades and HPMCP leached drug to between the crystalline and the amorphous solubility at pH 3 and little polymer; five surfactants raised leaching about as much as the crystalline solubility, so C/Ceq stayed about constant for each polymer; at pH 5 SDS raised drug and polymer leaching sharply; SDS with PVPVA gave the most [li2016b R3, R4, R19, R20, R13, R17].
Relation
extends Chen 2015 from celecoxib to lopinavir, a slow crystallizer chosen so that leaching could be measured without concurrent crystallization [li2016b C5], to more surfactants and to pH 5.
Note
Findings: F19, F15, F18.
2016
li2016ctelaprevir with HPMC, HPMCAS and PVPVA at the nanoscaleSolid state stabilityextends
Known before
the limits of DSC, AFM-IR imaging of drug–polymer separation and fluorescence probes that locate the drug-rich phase (builds_on) [li2016c C2, C43].
Added
topography series at 10–80% drug, local AFM-IR spectra, ratio images, nanoTA, Lorentz contact resonance and pyrene fluorescence for three polymers [li2016c R4, R8, R13, R16, R19, R22].
Relation
extends F18 from one polymer to three and shows that the polymer sets the onset loading (HPMC and PVPVA from 10%, HPMCAS from about 30–40%) [li2016c C52].
SupportsF19 F3
2016
lu2016vemurafenib polymorphs from the supercooled liquidSolid state stabilityconfirmsextends
Known before
the preliminary maximum crystal velocity of vemurafenib and the comparison set of trasi2014a (builds_on).
Added
four polymorphs in six morphologies, a temperature map of which forms appear, growth rates per form and their conversions [lu2016 C41, C59, R12].
Relation
confirms the trasi2014a growth maximum near 0.94 Tm within 10 °C [lu2016 C18] and that vemurafenib grows very rapidly [lu2016 C19]; extends the chapter to polymorph selection, where the stable form's larger driving force did not decide the outcome [lu2016 C52].
SupportsF1 F2 F3 F7 F9
2016
mosqueragiraldo2016cellulose polymers and telaprevirDissolutionconfirms
Known before
matching the solubility parameter and ionized carboxylates for polymers of one chemistry (ilevbare2013c), the glass–liquid phase separation of telaprevir and the pH dependence of the HPMCAS conformation (builds_on) [mosqueragiraldo2016 C4, C5, C27, R1, R24].
Added
26 polymers (commercial and 18 new cellulose derivatives) at 80 and 150 µg/mL telaprevir, pH 3.0, polymer levels of 5–50 µg/mL, SEM of the crystals, DFT solvation energies and MD of seven oligomers [mosqueragiraldo2016 R4–R9, R16, R19].
Relation
confines the solubility-parameter rule to uniform chemistry, confirms the need for ionized carboxylates and adds the effect of spacer length [mosqueragiraldo2016 C25, C28, C58].
SupportsF5 F8 F11 F13 F14 F15 F25 F35 F36
2016
sato2016PHB and crystal growth of six compoundsSolid state stabilityfirst proposed
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].
SupportsF28 F4 F5 F18 F22
2016
schram2016surface poisoning and seed originDissolutionfirst proposed
Known before
HPMC and HPMCAS inhibit felodipine growth by adsorption and pinning, and the felodipine solubility (alonzo2012, schram2015; builds_on) [schram2016 C2].
Added
four routes of seed formation, polymer pre-adsorbed on seeds, the pinning spacing and critical radius, and SDS with HPMCAS [schram2016 R2, R3, R12, R14, R16].
Relation
first in the library to show that seed origin changes the inhibition by a polymer and that polymer only pre-adsorbed is overgrown; images the pinning of steps [schram2016 C38, C39].
SupportsF7 F10 F12 F18 F20 F24 F38
2016
tian2016indomethacin fluorescence, miscibility limits and dry stabilitySolid state 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.
SupportsF30 F15 F12
2016
trasi2016commercial tacrolimus capsulesDissolutionconfirms
Non-Sink Dissolution Behavior and Solubility Limit of Commercial Tacrolimus Amorphous Formulations
Note
Known in the library (builds_on: Alonzo 2011, Raina 2014, Almeida e Sousa 2015, Raina 2015, Trasi 2015 on a second drug, Jackson 2016): a maximum achievable supersaturation set by the amorphous solubility, flux proportional to activity with a plateau there, polymers with minimal impact on the amorphous solubility while small molecules lower and micelles raise it, and high-loading dispersions that may not form nanospecies trasi2016 C25, C32, C34, C41.
Added
an amorphous solubility of 49 µg/mL against 1.4 µg/mL for the crystal (ratio about 35); six marketed capsules dissolved to, not past, that limit; their flux reached the pure-drug plateau; 50 µg/mL HPMC delayed crystallization of 50 µg/mL tacrolimus from within 3 h to 6–8 h trasi2016 R4, R16, R13, R14, R15, R9.
Relation
confirms the ceiling of the earlier dispersion studies for marketed products; first in the library on the solution-phase behaviour of commercial amorphous formulations trasi2016 C6.
Note
Findings: F7, F8, F9, F10, F4.
2016
xie2016acelecoxib with PAA and cellulose derivativesDissolutionextendsrevises
Improved Release of Celecoxib from High Drug Loading Amorphous Solid Dispersions Formulated with Polyacrylic Acid and Cellulose Derivatives
Note
Known in the library (builds_on: Alonzo 2010, Alonzo 2012, Ilevbare 2013 on induction times): the two routes, the seeded-growth method and the nucleation-rate estimate, PAA as a poor nucleation inhibitor and the amphiphilic cellulose derivatives as the best precipitation inhibitors xie2016a C3, C7, C19.
Added
5 µg/mL HPMCAS slowed celecoxib nucleation about 4000-fold and seeded growth about 70-fold; PAA dispersions released fast and crystallized, and released only about half even with HPMCAS in the medium, leaving needle crystals in the residue; PAA with 10% HPMCAS or HPMC released completely at 30% drug and partly at 50%; IR read PAA and HPMCAS as immiscible and PAA and HPMC as partly miscible xie2016a R13, R12, R9, R10, R14, R17, R20, R21.
Relation
revises, for celecoxib, the growth reading of the 2008 felodipine solutions toward nucleation (F5); extends the polymer combinations of Xie 2015 to PAA.
Note
Findings: F4, F5, F10, F16, F2, F20.
2016
xie2016bcelecoxib binaries and ternaries under heat and humiditySolid state stabilityconfirms
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].
SupportsF35 F11 F25 F12 F18 F6 F7
2017
correasoto2017SHG in spray-dried dispersions on storageCharacterization methodsextendsrevises
Second harmonic generation microscopy as a tool for the early detection of crystallization in spray dried dispersions
Known before
SONICC limits of 10 ppm and 3.4 × 10⁻⁹ %, SHG-guided detection of trace crystals in other products, and XRPD limits of about 1% in dispersions correasoto2017 R25, C6, C5.
Added
storage tests of flutamide and ezetimibe at 40 °C and two humidities, earlier detection by SHG than by XRPD, computed limits of 0.03–0.047% against 0.4–0.7%, quantitation that agreed for ezetimibe and failed for flutamide, and SEM of the crystals correasoto2017 R1, R8, R9, R21, R15, R16.
Relation
extends Kestur and co-workers to spray-dried powders; revises the assumption that SHG per mass of crystal is constant, which held for naproxen and ezetimibe and not for flutamide.
SupportsF4 F7 F8 F9 F10 F11
2017
elkhabaz2017ezetimibe ASDs in biorelevant mediaBioperformancefirst proposed
Variation in the Supersaturation and Phase Behavior of Ezetimibe Amorphous Solid Dispersions Upon Dissolution in Different Biorelevant Media
Known before
crystallization from the matrix of amorphous drugs (Alonzo 2010), SHG detection of crystals (Wanapun 2010, Kestur 2012), the LLPS method, and bile-salt effects (Lu 2017) (builds_on) elkhabaz2017 C34, C8, C39.
Added
three polymers in buffer, FeSSIF and Ensure Plus, with induction times, concentration profiles, PLM, PXRD and SHG kinetics elkhabaz2017 R6, R7, R10, R14, R21, R23.
Relation
first medium-comparison in the chapter; shows the polymer ranking reversing between buffer and FeSSIF elkhabaz2017 C35.
SupportsF4 F9 F10 F11 F12
2017
hate2017hollow-fibre absorptive dissolutionBioperformance
Absorptive Dissolution Testing of Supersaturating Systems: Impact of Absorptive Sink Conditions on Solution Phase Behavior and Mass Transport
Known before
no discontinuity between sub- and supersaturated transport (Raina 2014) and the slow transfer of small-area cells (Indulkar 2016) (builds_on) hate2017 C18, C2.
Added
a hollow-fibre module with 115 cm², a Cmax calibration, a mass balance, a mass-transfer model and pH-shift runs with three crystallization speeds hate2017 R3, R5, R6, R12, R18.
Relation
changes the test design; shows that a closed vessel overstates supersaturation and crystallization risk hate2017 C53, C55.
SupportsF10 F13 F14 F32
2017
indulkar2017aatazanavir in SDS micellesDissolutionrevises
Impact of Micellar Surfactant on Supersaturation and Insight into Solubilization Mechanisms in Supersaturated Solutions of Atazanavir
Known before
the solvent-shift LLPS onset as the experimental amorphous solubility (2013 paper), the flux maximum at the amorphous solubility and flux as a measure of activity (2014 membrane-transport study), the preparation of atazanavir free base and its glass–liquid phase separation (2015 weak-base paper), flux-based activity with solubilizing additives with about 2:1 activity to concentration ratio for felodipine (2015 additive study) and the nanodroplet reservoir sustaining the maximum flux (2016) (builds_on) indulkar2017a R28, C3.
Added
one drug and one surfactant (0–3.6 mg/mL SDS): crystalline solubility, LLPS onset, flux-derived free drug and activity ratio, the micelle/water partition coefficient with a Langmuir fit, emission, energy transfer to curcumin, molecules per micelle and micelle size by NMR indulkar2017a R7, R8, R11, R13, R14, R16, R22, R24, R25.
Relation
new; shows that the concentration ratio understates supersaturation about twofold while the activity ratio at the amorphous solubility is unchanged by SDS, and revises the crystal-based prediction of the amorphous solubility for micellar media (overshoot twofold) indulkar2017a C21, C16, C43.
SupportsF1 F4 F5 F6 F7 F8 F12 F16 F18
2017
indulkar2017borigin of nanodroplets from dissolving nifedipine dispersions, isotope scramblingDissolutionfirst proposed
Origin of Nanodroplet Formation upon Dissolution of an Amorphous Solid Dispersion: A Mechanistic Isotope Scrambling Study
Note
Known in the library (builds_on: Alonzo 2011, Ilevbare 2013 on LLPS, Jackson 2015, Indulkar 2016): certain dispersions form nanodroplets on dissolution, more often at low loading, depending on polymer type and loading indulkar2017b C6; above the amorphous solubility excess drug separates as water-saturated drug-rich droplets indulkar2017b C3; the droplets sustain the maximum membrane flux as a reservoir indulkar2017b C4; two proposed origins, dissolution followed by LLPS (mechanism I) or release of drug-rich domains formed by AAPS in the hydrated matrix (mechanism II, cited) indulkar2017b C7, C8.
Added
a deuterium label in the medium diluted as full mixing predicts when nifedipine dispersions with HPMC-E5 or PVPVA dissolved at 5 °C, with slow droplet–solution exchange at that temperature, and release that continued into water saturated at the amorphous solubility indulkar2017b R11, R3, R8, R9.
Relation
first in the library to test where the nanodroplets of a dissolving dispersion come from; supports mechanism I for these systems ("strongly suggest") indulkar2017b C26.
Note
Findings: F1, F2, F4, F5.
2017
li2017water in spin-coated evacetrapib dispersionsASD processfirst proposed
Understanding the impact of water on the miscibility and microstructure of amorphous solid dispersions – An AFM/LCR and TEM/EDX study
Known before
moisture-induced phase separation on storage (Rumondor 2009, Marsac 2010), unexplained day-to-day variation of spin-coated films and the LCR method (Li 2016) (builds_on) li2017 C4, C5.
Added
humidity (18, 35, 50% RH) and added water during spin coating, nanoparticle counts of the stock, LCR and TEM-EDX of the phases, and the opposite microstructure after humid storage li2017 R3, R12, R14, R17, R22.
Relation
first in this chapter to show that water carried into the drying solution, not only storage, splits a miscible film, and that the stock stays one phase li2017 C13, C17, C32.
SupportsF1 F2 F4 F6 F7
2017
lu2017maintaining supersaturation with bile saltsDissolutionextends
Known before
the nucleation inhibition by STC and by 13 bile salts (chen2015, li2016a), the activity calibration of telaprevir with each bile salt (chapter C) and the glassy droplets (builds_on) [lu2017 C4, C6, C5].
Added
induction times at equal activity (δ 11.5 and 28.8), 1.86 and 12 mM bile salt, an STC series below its CMC, the zeta potential of droplets, seeded growth with STC and SGC, and HPMCAS-MF as comparator [lu2017 R3, R4, R6, R8, R9, R11].
Relation
extends li2016a to equal activity, adds the monomer–micelle contrast and the effect of a drug-rich phase on the ranking of the bile salts [lu2017 C28, C41, C42].
SupportsF3 F5 F6 F13 F14 F15 F19 F31 F32 F35 F41
2017
lu2017abile salts: growth rate and residual supersaturationDissolution
Known before
the unseeded induction times of lu2017 (taken first because this paper builds on them), chen2015, li2016a with STCDC the strongest, and the effect of seed preparation (schram2016; builds_on) [lu2017a R16, R17, C45].
Added
seeded growth at δ 2.4, 7.9 and 12.5 with six bile salts at 1.86 and 12 mM, 15 h residual free drug, zeta potential of seeds and an estimate of nucleation against growth inhibition [lu2017a R7–R14].
Relation
separates growth from nucleation inhibition for bile salts: STCDC and SGCDC stop growth as monomers, STC, SGC, STDC and SGDC act mainly on nucleation [lu2017a C32, C36, C37].
SupportsF6 F7 F9 F20 F33
2017
lu2017bsix bile salts and telaprevirDissolutionconfirmsextendscontradicts
Impact of Endogenous Bile Salts on the Thermodynamics of Supersaturated Active Pharmaceutical Ingredient Solutions
Known before
telaprevir glass–liquid phase separation at 90–92 µg/mL, the model-drug choice and an earlier onset in 100 mM buffer (2015 paper), flux as a measure of activity and concentration against activity supersaturation with additives (2015 additive study), a miscible second solute lowers the maximum supersaturation (2015 second-drug study) and lower maximum supersaturation and transport with a second solute (2016 multidrug ASD study); STC inhibits crystallization of celecoxib (builds_on) lu2017b R19, R24.
Added
six bile salts at 1.86 and 12 mM in 50 mM pH 6.5 buffer: crystalline solubility, GLPS onset by extinction, ultracentrifugation and flux, flux against concentration, activity against concentration supersaturation and phase boundaries, and an ionic-strength check of the onset lu2017b R1, R2, R6, R9, R12, R13, R17, R18.
Relation
confirms the flux plateau at the GLPS onset for telaprevir and the lowering of the limit by ionic strength; extends the lowering by a miscible second solute to STCDC and SGCDC; shows that concentration-based and activity-based supersaturation drift apart in bile-salt media; contradicts the use of STC alone as a surrogate for the bile salts lu2017b C18, C20, C31, C39, C52.
SupportsF4 F6 F8 F9 F11 F12 F16 F17
2017
mugheirbi2017water in itraconazole–HPMC dispersionsASD processconfirmsextendsrevises
Insights into Water-Induced Phase Separation in Itraconazole–Hydroxypropylmethyl Cellulose Spin Coated and Spray Dried Dispersions
Known before
spin-coated ITZ–HPMC films from DCM:methanol separated for an unexplained reason and spray-dried ITZ–HPMC was separated at all loadings (Purohit 2015, 2017) (builds_on) mugheirbi2017 C2, C37.
Added
films at 7, 20 and 40% RH, four HPMC grades with their water sorption, ITZ's own UV and fluorescence as miscibility markers, an evaporating ITZ solution, and spray drying from dry methanol and from methanol with 1, 5 and 12% water mugheirbi2017 R1, R2, R19, R26, R27.
Relation
confirms li2017 for a second drug; revises the earlier reading of ITZ–HPMC separation as intrinsic immiscibility, attributing it to water; extends the finding to spray drying mugheirbi2017 C1, C38, C39.
SupportsF1 F2 F3 F4 F6 F7
2017
purohit2017aitraconazole–HPMC dispersions by fluorescence and ssNMRCharacterization methodsextends
Insights into Nano- and Micron-Scale Phase Separation in Amorphous Solid Dispersions Using Fluorescence-Based Techniques in Combination with Solid State Nuclear Magnetic Resonance Spectroscopy
Known before
itraconazole–HPMC films are phase separated despite one Tg, a miscible dispersion gives a pyrene ratio between the drug and polymer values, and fluorescence can assess miscibility purohit2017a R25, R24.
Added
pyrene across three routes, two-probe confocal imaging of cast and spin-coated films, ¹H T₁ and T₁ρ of spray-dried and film-cast samples, and domain size against drying rate purohit2017a R7, R16, R17, R21, R22.
Relation
extends the 2015 films to powders; challenged in the same year by work that tied separation in this pair to water in the solvent or air mugheirbi2017 C1, C37.
SupportsF16 F19 F20
2017
purohit2017britonavir dispersions during hydration and dissolutionDissolutionfirst proposed
Phase Behavior of Ritonavir Amorphous Solid Dispersions during Hydration and Dissolution
Note
Known in the library (builds_on: Rumondor 2009, 2010 and 2011, Alonzo 2011, Ilevbare 2013 on LLPS, Purohit 2015 on phase separation kinetics, Raina 2015 on fluorescent probes): water can separate a hydrated dispersion into drug-rich and drug-lean domains (AAPS) purohit2017b C9; hygroscopic polymers favour it purohit2017b C45; 50% ritonavir–PVP and –PVPVA dispersions had separated within 10 s of water contact purohit2017b R20; LLPS above the amorphous solubility, for ritonavir at a similar concentration by several routes purohit2017b C10, C47.
Added
all PVP and PVPVA films separated at 97% RH and HPMCAS films did not purohit2017b C1; only low-loading PVP and PVPVA and all HPMCAS films passed the amorphous solubility and formed nanodroplets, and drug kept pace with the polymer only where they formed purohit2017b R11, R7, C52; humid storage removed LLPS from PVP and PVPVA dispersions purohit2017b C53.
Relation
first in the library to link water-induced phase separation with loss of LLPS on dissolution; argues against matrix domains as the source of the droplets ("we find no evidence") purohit2017b C56.
Note
Findings: F3, F4, F5, F8, F11, F12.
2017
saboo2017water-induced separation of miconazole–PVPVA imaged by confocal fluorescenceSolid state stabilityextends
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].
SupportsF31 F14 F12 F13 F23
2017
tian2017polymers and the melt growth of three indomethacin polymorphsSolid state stabilitycontradicts
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].
SupportsF29 F3 F4 F18 F19 F20
2017
trasi2017marketed amorphous tacrolimus capsules under stressSolid state stabilityfirst 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.
SupportsF33 F5 F6 F16 F20 F25 F26
2017
tres2017fluorescence lifetime and lipid mediaCharacterization methodsconfirmsextends
Known before
the reported onsets of felodipine (19 µM), clotrimazole and efavirenz (22 and 58 µM), the probe approach of raina2015a, the lowering of free concentration by a second aggregating drug (trasi2015b) and the rise of the felodipine onset with micelles (raina2015c) (builds_on).
Added
lifetime and spectra of felodipine itself and of PRODAN with two dark drugs, a 9.04 ns component in a crystallizing felodipine solution, and the onset, lifetimes, spectra and supernatant of felodipine in microsomes and liposomes [tres2017 R1, R10, R11, R5, R6, R7, R8].
Relation
extends raina2015a from spectra to lifetime and confirms the onsets within concentration brackets [tres2017 R14, C18]; first library study of the aggregation onset in vesicle media.
SupportsF5 F6 F9 F12 F13
2017
xie2017indomethacin with EPO and HPMCDissolutionextends
Impact of Eudragit EPO and Hydroxypropyl Methylcellulose on Drug Release Rate, Supersaturation, Precipitation Outcome and Redissolution Rate of Indomethacin Amorphous Solid Dispersions
Note
Known in the library (builds_on: Alonzo 2010, Raina 2014, Indulkar 2016, Xie 2016): HPMC inhibits indomethacin crystallization and the calculated amorphous solubility at 37 °C, UV extinction for the amorphous solubility, drug-rich nanodroplets as a reservoir, and the ternary of a fast-dissolving polymer with a crystallization inhibitor xie2017 R29, R30, C42.
Added
EPO raised both solubilities of indomethacin but did not inhibit crystallization; with HPMC the drug stayed supersaturated up to the amorphous solubility (36 µg/mL), where 70–100 nm droplets formed; the EPO–HPMC ternary released fast into nanodroplets; after a rise to pH 5 these redissolved within about 2 min, while the α precipitate of the EPO dispersion redissolved faster than sieved crystals but only to 32.1 of 40 µg/mL; a shift to pH 6.8 hid the differences; the ternary stayed amorphous in storage xie2017 R1, R3, R4, R6, R15, R20, R19, R22, R26.
Relation
extends the ternary idea of Xie 2016 to a polymer that dissolves in acid; first in the library on redissolution of a crystalline precipitate after a pH rise xie2017 C61.
Note
Findings: F21, F20, F17, F9, F4, F10, F3.
2018
bhardwaj2018surface-area-normalized dissolution of spray-dried and melt-extruded itraconazole–PVPVADissolutionfirst proposed
Note
Known in the library (builds_on: Purohit 2015 on ITZ–HPMC miscibility, Li 2017, Mugheirbi 2017): pyrene fluorescence and TEM contrast to detect drug-rich domains, and water in the solvent as a cause of drug-rich domains [bhardwaj2018 C37].
Added
constant-area compacts with drug and polymer assayed and loading-normalized rates [bhardwaj2018 P6, P7, E4, R11]; amorphous ITZ dissolving about 18 times faster than the crystal [bhardwaj2018 R5]; a switch between 25 and 20% (spray-dried) and 20 and 10% (melt-extruded) [bhardwaj2018 X6]; the spray solvent changing surface drug content and release at 20% [bhardwaj2018 R13, R20].
Relation
first in the library with the surface-normalized two-component method, which the later papers take over saboo2019 P9; saboo2020a P6.
Note
Findings: F1, F2, F3, F6, F14.
2018
dening2018supersaturation and flux from ritonavir–SBA-15Mesoporous silicafirst proposed
Supersaturation Potential of Ordered Mesoporous Silica Delivery Systems. Part 1: Dissolution Performance and Drug Membrane Transport Rates
Known before
flux proportional to activity and constant above the amorphous solubility, the maximum flux at the LLPS concentration and the diffusion cell as a read-out of free drug (builds_on: Raina 2014, Raina 2015, Indulkar 2016, Indulkar 2017), and ritonavir as a slow crystallizer (builds_on: Ilevbare 2013) dening2018 C20, C54, C22, C5.
Added
release of ritonavir and lopinavir from SBA-15 at 50–1000% of the amorphous solubility, membrane flux against amorphous ritonavir, order-of-addition tests with blank and loaded silica, sequential dilution, FaSSIF, a residue redissolution and a loading series with the calculated monolayer dening2018 R6, R8, R13, R14, R17, R18, R19, R21, R23, R27, R4.
Relation
first in the library to show fast but incomplete, dose-dependent release from mesoporous silica without crystallization, and to propose an equilibrium between adsorbed and free drug ("suggest") dening2018 C2, C3, C4.
SupportsF7 F8 F9 F11 F12 F15 F1 F2 F6 F10 F14
2018
hate2018ASDs in the hollow-fibre moduleBioperformanceconfirmsrevises
Insight into Amorphous Solid Dispersion Performance by Coupled Dissolution and Membrane Mass Transfer Measurements
Known before
the apparatus of hate2017, nanodroplets as a reservoir (Indulkar 2016), droplets from ASDs (Alonzo 2011, Jackson 2015), the 369 nm fluorescence band (Indulkar 2017) (builds_on) hate2018 C6, C14, C18.
Added
solutions from 30 to 500 µg/mL, nine ASDs at three loadings and polymers, a dose series, closed against absorptive release hate2018 R9, R11, R13, R15, R17, R18.
Relation
confirms the reservoir for ASD-derived droplets; revises the plateau of the side-by-side cell, since transfer keeps rising above the amorphous solubility in this device hate2018 C25, C46.
SupportsF5 F8 F9 F14 F15 F32
2018
indulkar2018lecithin and a six-bile-salt simulated intestinal fluidDissolutionfirst proposedextends
Crystallization from Supersaturated Solutions: Role of Lecithin and Composite Simulated Intestinal Fluid
Known before
bile salts delay crystallization by different amounts, linked to hydrophobicity (chen2015, li2016a), the flux-based supersaturation of atazanavir in micellar SDS and the solvent-shift onset as the amorphous solubility (chapter C), and supersaturation against solubilization for membrane transport (builds_on) indulkar2018 C4, C1, P7.
Added
atazanavir in 3 mM STC with 0–0.75 mM lecithin (crystalline solubility about 1 µg/mL throughout, amorphous 38 → about 82 µg/mL, flux-based supersaturation about 40 → 63–66, induction time about 595 → 43 min against about 170 in buffer), six single bile salts with lecithin, and FaSSIF-V1 against a Composite-SIF of the six main human bile salts for four drugs at each medium's amorphous solubility indulkar2018 R6, R10, R16, R18, R20.
Relation
first in the library to add lecithin to a bile-salt crystallization test and to compare media at a flux-measured equal supersaturation; extends li2016a (bile salts not interchangeable) to mixed micelles and finds lecithin turning taurocholate from an inhibitor into a medium that crystallizes faster than buffer indulkar2018 C20, C43, C17.
SupportsF3 F19 F29 F31 F35 F39 F40
2018
li2018lopinavir with insoluble polymersDissolutionextends
Note
Known in the library (builds_on: Ilevbare 2013 on LLPS, Almeida e Sousa 2015, Trasi 2015 on a second drug, Trasi and Taylor 2015, Li 2016): the amorphous solubility as the maximum free drug concentration and its measurement by UV scattering, a second miscible drug that lowers the maximum supersaturation, and lopinavir as a slow crystallizer [li2018 C8, C9, C11].
Added
insoluble polymers mixed with lopinavir lowered the 48-h concentration below the 17.4 µg/mL amorphous solubility, most at low drug loading, EC and HPMCP at 15% to about the crystalline solubility; the phase-separated CA and EUD dispersions and a physical mixture were hardly suppressed; the most suppressed HPMCP dispersion crystallized slowest in suspension [li2018 R3, R8, R14, R6, R7, C61].
Relation
extends the second-drug drop of Trasi and Taylor 2015 (F11) from a drug to an undissolved polymer, as its hypothesis [li2018 C10]; first in the library on solubility suppression by polymers.
Note
Findings: F18, F7, F16.
2018
lu2018bile salt mixtures, six-bile-salt lecithin media and HPMCAS-MF with telaprevirDissolutionextends
Known before
the single bile salt induction times and growth ratios of telaprevir at equal activity, the activity calibration in buffer, bile salts not interchangeable with a human blend twice as effective as STC for celecoxib, HPMCAS-MF as one of the strongest telaprevir inhibitors, and the glassy drug-rich phase at δ 28.8 (builds_on) [lu2018 R11, R12, R13, R16, C6].
Added
binary and ternary bile salt mixtures at 1.86 mM (more than 960 min at δ 11.5) and at 3.72–5.58 mM (about 255 min), seeded growth with the binary mixture (ratios about 35.5 and 7.4), buffer about 29 and FaSSIF about 21 min against more than 960 min in two six-bile-salt lecithin media, and 150 µg/mL HPMCAS-MF at δ 28.8 in media with and without lecithin [lu2018 R3, R4, R5, R6, R7, R9].
Relation
extends lu2017 and lu2017a from single bile salts to mixtures (no synergy between bile salts) and to complete media; independently of indulkar2018 (neither cites the other) finds FaSSIF far weaker than a human bile salt mix, and adds that an effective polymer at the amorphous solubility removes the medium effect among lecithin media while lecithin cancels the bile salt contribution [lu2018 C14, C26, C37, C43].
SupportsF3 F12 F17 F32 F33 F35 F39 F40 F43
2018
moseson2018temperature–composition phase diagram for HMEASD processfirst proposed
The application of temperature-composition phase diagrams for hot melt extrusion processing of amorphous solid dispersions to prevent residual crystallinity
Known before
melting point depression and χ from DSC for drug–PVP pairs (Marsac 2006, 2009); the phase diagram had been proposed for HME but tested on systems with little depression (builds_on) moseson2018 C1, C5, C39.
Added
Tc of IDM–PVPVA by DSC offsets extrapolated to zero rate, χ = −1.97, 15 extrusions at 117–161 °C and 2–20 min read by XRPD, PLM and DSC, a hot-stage dissolution test, and a three-regime design space moseson2018 R5, R10, R13, C48.
Relation
first experimental test in the library of the phase diagram against extrusion outcome; shows that the amorphous boundary depends on the detection method moseson2018 C47, C63.
SupportsF8 F9 F10 F11
2018
moseson2018ananometre residual crystals in an HME extrudate; same year, builds on moseson2018ASD processextends
Nanometer-Scale Residual Crystals in a Hot Melt Extruded Amorphous Solid Dispersion: Characterization by Transmission Electron Microscopy
Known before
Tc of 131 °C, the process operating space and the XRPD detection limits of the phase-diagram paper, and TEM signs of crystallinity in ASDs (Li 2017, Mugheirbi 2017) (builds_on) moseson2018a R2, C3, C4.
Added
bright-field TEM with Fourier analysis of a 1:1 IDM–PVPVA extrudate made at Tc, finding two crystal populations, defects and a dissolution front in an extrudate that XRPD and DSC call amorphous moseson2018a R5, R6, R9, R11, R12.
Relation
extends moseson2018: 20 min at Tc did not remove every crystal; first hint of fragmentation, with extruder shear as a competing explanation moseson2018a C14, C31; moseson2019 C5.
SupportsF9 F10 F12 F13
2018
mosqueragiraldo2018afive carboxylated cellulose esters and ethers, nine drugs, simulationsDissolutionextends
Known before
carboxylated polymers beat amide, amine and alcohol analogues and a long-spacer twin failed for telaprevir (mosqueragiraldo2016), polymer structure and acid content govern induction times (ilevbare2013c), and AFM of adsorbed HPMCAS conformation (schram2015) (builds_on) [mosqueragiraldo2018a C26, R13, C37].
Added
induction times of nine drugs with 5 µg/mL of a short- and a long-tether cellulose ester and three ethyl cellulose ethers, AFM of the polymers on amorphous atazanavir, and molecular dynamics of 28-monomer chains alone and next to 25-molecule telaprevir or atazanavir aggregates [mosqueragiraldo2018a R1, R2, R4, R7, R9, R12].
Relation
extends the long-spacer failure of mosqueragiraldo2016 from telaprevir to nine drugs, finds that a second acid per side chain does not help, and puts the drug into the simulations that in 2016 covered oligomers alone; a carboxylated ether outside the solubility-parameter window beat the 2013 polymers for celecoxib [mosqueragiraldo2018a C8, C30, C43, R2].
SupportsF3 F11 F13 F25 F35 F36
2018
mosqueragiraldo2018btelaprevir ASDs: polymer and loadingBioperformanceextends
Influence of Polymer and Drug Loading on the Release Profile and Membrane Transport of Telaprevir
Known before
the glass–liquid onset of telaprevir at about 90–100 µg/mL (Mosquera-Giraldo 2015), a second drug lowering the amorphous solubility (Trasi 2015), complexes lowering flux (Wegiel 2015) and polymer inhibition of crystallization (Mosquera-Giraldo 2016) (builds_on) mosqueragiraldo2018b C8, C33, C5, R24.
Added
five polymer and loading cases reading release and mass flow together, predissolved-polymer tests, pellet composition, a surfactant variant and film dissolution mosqueragiraldo2018b R5, R8, R13, R14, R16, R22.
Relation
extends the second-component logic of alhalaweh2016 to a polymer; adds matrix crystallization as a cause of a missed ceiling mosqueragiraldo2018b C37, C40.
SupportsF2 F7 F8 F9 F10
2018
mugheirbi2018alcohol co-solvents for itraconazole–HPMCASD processextendsrevises
Phase Behavior of Drug-Hydroxypropyl Methylcellulose Amorphous Solid Dispersions Produced from Various Solvent Systems: Mechanistic Understanding of the Role of Polymer using Experimental and Theoretical Methods
Known before
water-induced separation of ITZ–HPMC from DCM:methanol (Purohit 2015; Mugheirbi 2017) (builds_on) mugheirbi2018 C5.
Added
five alcohol co-solvents at several humidities and temperatures, pure-solvent evaporation with and without water, HPMC in drug-free solution by DLS, Hansen distances and molecular dynamics mugheirbi2018 R1, R4, R9, R14, R16, R19.
Relation
extends and partly revises mugheirbi2017: water separates the drug with methanol and ethanol but is needed to keep HPMC dissolved and mixed with n-propanol and n-butanol mugheirbi2018 C12, C29.
SupportsF2 F4 F5 F7
2018
purohit2018residual crystallinity in tacrolimus capsulesBioperformancefirst proposed
Investigating the impact of drug crystallinity in amorphous tacrolimus capsules on pharmacokinetics and bioequivalence using discriminatory in vitro dissolution testing and PBPK modeling and simulation
Known before
polymers inhibit growth better at low supersaturation (Ilevbare 2013), the amorphous solubility of tacrolimus about 50 µg/mL and the stress crystallization of the generic (Trasi 2016, 2017) (builds_on) purohit2018 R21, R4, R20.
Added
capsules with 0–100% crystallinity in five dissolution conditions, sink indices, a PBPK model and virtual bioequivalence trials purohit2018 R4, R5, R7, R8, R13, R17.
Relation
first in the chapter to link dissolution conditions to simulated exposure; shows that compendial tests under-detect crystallinity purohit2018 C62, C63.
SupportsF14 F16 F17 F32
2018
que2018paclitaxel seed crystals and HPMCASDissolutionfirst proposedextends
Paclitaxel Crystal Seeds with Different Intrinsic Properties and Their Impact on Dissolution of Paclitaxel-HPMCAS Amorphous Solid Dispersions
Note
Known in the library (builds_on: Alonzo 2012, Schram 2016, Jackson 2016, Ilevbare 2013 on induction times, Trasi 2017): seeds reduce the amorphous solubility advantage unless growth is inhibited, seeds grown in different environments differ in interface structure and growth rate, polymers inhibit nucleation from solution, and a commercial amorphous tacrolimus product contains crystals que2018 C8, C2, C7.
Added
at an equal 18 wt%, seeds of different morphology left ≈7.9–25.3 µg/mL of a 31.6 µg/mL amorphous solubility after 16 h; sonication raised the needle-end area 7–9-fold; HPMCAS held an unseeded solution at S = 88 for more than 16 h but only slowed growth, which the authors trace to a critical two-dimensional nucleus (5.4–7.0 nm) smaller than the spacing of adsorbed polymer (≈10.5–16.8 nm) que2018 R14, R6, R3, R15, R12.
Relation
first in the library on seed morphology at equal mass in dispersion dissolution; extends the nucleation-against-growth split of Konno 2008 and Xie 2016 to a seeded dispersion.
Note
Findings: F22, F4, F5, F7, F8.
2018
sugihara2018pazopanib after a pH shiftDissolutionconfirmsextends
Evaluation of Pazopanib Phase Behavior Following pH-induced Supersaturation
Known before
pH-induced supersaturation and precipitation of weak bases (2012), the pH-solubility diagram with crystalline and amorphous boundaries and the extinction method (2015 weak-base paper), glass–liquid phase separation with the extinction method and colloid size (2015 telaprevir paper) and the flux maximum at LLPS with colloids replenishing absorbed drug (2016 reservoir paper) (builds_on) sugihara2018 C4, C6.
Added
pazopanib HCl (pKa 6.4): crystalline and amorphous solubility between pH 5 and 8.4, a two-stage pH-shift test at 1, 1/10 and 1/100 of the clinical dose with 0–50 µg/mL HPMC, DLS, NTA, polarized microscopy and DSC of the precipitate sugihara2018 R1, R2, R4, R8, R12, R15, R17, R22, R23.
Relation
extends the diagram of the weak-base paper to a dose-ranging pH-shift test; sets the highest ratio of the chapter (about 600); confirms the cap at the amorphous solubility for a salt; the Tg of the colloids was measured on dried precipitate sugihara2018 C14, C15, C22, C45, X5.
SupportsF1 F2 F3 F4 F5 F6 F7 F8 F10 F13 F14 F23
2018
tres2018ASD dissolution of ritonavir and lopinavirCharacterization methodsconfirmsextends
Mechanistic Understanding of the Phase Behavior of Supersaturated Solutions of Poorly Water-Soluble Drugs
Known before
the PRODAN lifetime method (tres2017), the extinction onsets of ritonavir and lopinavir (trasi2015b), LLPS (ilevbare2013a), the dependence of LLPS on polymer and drug loading for danazol dispersions (jackson2015) and the steady-state PRODAN method (raina2015a) (builds_on); the UV artifact was cited as background tres2018 C37.
Added
lifetime and I1/I2 in solvent-shift tests and during dissolution of 10% and 50% Kollidon VA64 dispersions, ultracentrifuged supernatants, NTA sizes, a filtration control and a polymer-free crystallization test tres2018 R1, R6, R9, R11, R17, R18, R13, R20, R21.
Relation
extends tres2017 to ASD dissolution and crystallization; confirms the UV caveat of vaneerdenbrugh2011b with ritonavir and lopinavir tres2018 R8, R16.
SupportsF3 F5 F9 F10 F11
2018
wilson2018enzalutamide dispersions in ratsBioperformancefirst proposed
Relationship between Amorphous Solid Dispersion In Vivo Absorption and In Vitro Dissolution: Phase Behavior During Dissolution, Speciation, and Membrane Mass Transport
Known before
amorphous solubility as the free-drug ceiling with probe and extinction methods (Ilevbare 2013), aggregates as a depot and the flux ceiling (Raina 2014), diffusion-cell mass flow as a measure of activity (Raina 2015), the reservoir effect shown in vitro (Indulkar 2016) and glass–liquid separation with constant activity afterwards (Mosquera-Giraldo 2015) (builds_on) wilson2018 C7, C8, C12, C25.
Added
dissolution, Nile Red speciation, diffusion-cell mass flow and rat plasma exposure for four dispersions of enzalutamide and a crystalline slurry wilson2018 R6, R10, R13, R15, R16, R17.
Relation
first paper of the chapter with a measurement in animals; tests the reservoir idea in vivo and finds that mass flow, not closed dissolution, follows exposure wilson2018 C8, C51, C57.
SupportsF2 F5 F23 F25 F32
2019
dening2019adsorption isotherm of ritonavir on SBA-15Mesoporous silicaextends
Application of an adsorption isotherm to explain incomplete drug release from ordered mesoporous silica materials under supersaturating conditions
Known before
the incomplete release, the dilution and surfactant-free release data, the calculated monolayer and the loading method from dening2018, and surfactant CMCs and micelles lowering flux from Raina 2015 (builds_on) dening2019 C1, R3, P10, C58.
Added
the first isotherm into the supersaturated range, its Langmuir, Freundlich and BET fits, urea and salt tests, FTIR and XPS of loaded silica, the bound drug during dilution, and release with monomeric and micellar surfactants dening2019 R2, R4, R5, R6, R8, R9, R12, R13, R16, R17, R18, R19.
Relation
tests and extends the equilibrium of dening2018: the release floor matches the BET monolayer, binding is read as hydrogen bonds to silanols, and part of the adsorption as irreversible dening2019 C32, C52, C54.
SupportsF2 F3 F5 F10 F12 F4 F6 F9
2019
elkhabaz2019aposaconazole dispersions through a gastric stageDissolution
Characterization of Phase Transformations for Amorphous Solid Dispersions of a Weakly Basic Drug upon Dissolution in Biorelevant Media
Note
Known in the library (builds_on: Alonzo 2010, Li 2018, Raina 2015 on fluorescent probes, Wanapun 2010, Kestur 2012): the two crystallization routes during amorphous dissolution and matrix crystallization as a source of seeds, polymers delaying crystallization by acting on nucleation and growth, enteric polymers suspended at gastric pH, and more release from insoluble-polymer dispersions at higher drug loading elkhabaz2019a C2, C3, C29; fluorescence detection of the LLPS onset and SHG detection of crystals in amorphous powders (builds_on, as listed in the evidence index).
Added
crystals form in crystal-free HPMCAS dispersions during an hour in fasted gastric fluid although the medium is subsaturated, about 68% of the undissolved drug at 50% drug against 0.03–0.05% at 10–25%; after the pH shift the low loadings held the amorphous solubility with ≈300 nm droplets while the 50% dispersion never reached it; a fifth of the dose lost supersaturation about an hour sooner elkhabaz2019a R20, R6, R13, R12.
Relation
carries the matrix route of Alonzo 2010 into the stomach of a weakly basic drug; first in the library on a gastric stage as the source of the seeds that end intestinal supersaturation.
Note
Findings: F24, F26, F1, F4, F9, F10, F16, F18, F19.
2019
elkhabaz2019bsupersaturation and solubilization in biorelevant mediaBioperformanceextends
Interplay of supersaturation and solubilization: Lack of correlation between concentration-based supersaturation measurements and membrane transport rates in simulated and aspirated human fluids
Known before
flux rises up to the amorphous solubility and the flux ratio measures activity (Raina 2014), solubilization changes the perceived supersaturation (Raina 2015), concentration-dependent micellar partitioning (Indulkar 2017), bile salts that are not interchangeable (Lu 2017) and the composite FaSSIF (Indulkar 2018) (builds_on) elkhabaz2019b C26, C33, C44, R16.
Added
atazanavir and posaconazole in six media including pooled human intestinal fluid: crystalline and amorphous solubility, fluxes from both solid phases, a drug-rich phase in human fluid and partition coefficients elkhabaz2019b R1, R2, R4, R7, R8, R9, R11.
Relation
extends raina2015c from one additive at a time to simulated and human fluids; the flux ratio stays constant while the concentration ratio falls several-fold elkhabaz2019b C21, C25.
SupportsF3 F4 F18
2019
hate2019absorptive test of residual crystallinityBioperformance
Absorptive dissolution testing: An improved approach to study the impact of residual crystallinity on the performance of amorphous formulations
Known before
flux proportional to supersaturation (Raina 2014), the amorphous solubility of tacrolimus and slow crystallization with HPMC (Trasi 2016), crystallization of the generic under stress (Trasi 2017), the hollow-fibre apparatus (Hate 2017), the effect of an absorptive sink on ASD profiles (Hate 2018) and crystallinity lowering supersaturation in a closed vessel (Purohit 2018) (builds_on) hate2019 C16, R5, C27, C9, C35.
Added
capsules at 0–100% crystallinity at 240, 100 and 40 mL, with donor and receiver profiles, total dissolved drug, receiver AUC, virtual bioequivalence, solvent-shift solutions, seeded runs and a rate model hate2019 R8, R10, R11, R12, R13, R14, R17, R18, R19.
Relation
repeats the capsules of purohit2018 in an absorptive test and shows that the verdict depends on the volume; the dog data on the same products are the comparison hate2019 C25, C41, C49.
SupportsF14 F16 F28 F29 F31 F32
2019
indulkar2019aritonavir–copovidone tablets, congruent release and the limit of congruencyDissolutionextends
Insights into the dissolution mechanism of ritonavir-copovidone amorphous solid dispersions: importance of congruent release for enhanced performance
Note
Known in the library (builds_on: Alonzo 2011, Ilevbare 2013 on LLPS, Purohit 2015 on phase separation kinetics, Indulkar 2017, Purohit 2017): the ritonavir amorphous solubility (about 30 µg/mL) and wet Tg (about 0 °C) indulkar2019a M1; impaired release without droplets at high loading for some compounds indulkar2019a C13; water-induced AAPS indulkar2019a C14; the Higuchi two-component model and Corrigan's note that it fails for low-loading dispersions indulkar2019a C23, C24.
Added
the limit of congruency, defined as the highest loading with congruent release (25%), and release "falling off a cliff" above it indulkar2019a C2, C31, R11; release into ritonavir-saturated medium that separates the regimes indulkar2019a R12; a drug-rich tablet surface by IR within minutes at 50% indulkar2019a R16; films that separate on contact with water above the limit and not below indulkar2019a R18.
Relation
names the limit; extends Purohit 2017 from films to tablets and takes the dissolution-then-LLPS route of Indulkar 2017 for the droplets indulkar2019a C49.
Note
Findings: F1, F2, F3, F4, F6, F7, F8.
2019
indulkar2019bmonomeric and micellar SDS, SDS–polymer pairs and atazanavir nucleationDissolutionextends
Known before
a surfactant can bind a polymer in solution and cancel its inhibition (ilevbare2012a), and the CMC of SDS in the buffer with the flux-based supersaturation of atazanavir in SDS (chapter C) (builds_on) [indulkar2019b C11, M2, C12].
Added
atazanavir at each medium's amorphous solubility in 13 SDS levels from 0 to 3.6 mg/mL (about 200 min up to 0.05 mg/mL, about 56 min at 0.3 mg/mL, about 52–68 min above the CMC of 0.5 mg/mL), pyrene in crystal slurries below the CMC, 1 mg/mL PVPVA, HPMC-606 and HPMCAS-MF with 0.1 mg/mL SDS, the aggregation concentration of SDS on each polymer, and a dissolving atazanavir:PVPVA:SDS dispersion [indulkar2019b R3, R6, R4, R8, R5].
Relation
extends the sub-micellar surfactant effects of ilevbare2012a and chen2015 to a threshold well below the CMC and a plateau above it, and shows that the polymer most bound by SDS (PVPVA) is the one that loses its inhibition [indulkar2019b C30, C31, C50].
SupportsF3 F12 F13 F18 F19 F28 F35 F38
2019
li2019lopinavir–HPMC microstructure and dissolutionASD processfirst proposedcontradicts
Microstructure Formation for Improved Dissolution Performance of Lopinavir Amorphous Solid Dispersions
Known before
phase separation by water in the solvent or humid storage (Li 2017), nanoTA (Li 2016), lopinavir as a slow crystalliser with an amorphous solubility of about 17 µg/mL (Li 2016, 2018) and conflicting results on whether phase separation helps or hurts release (builds_on) li2019 C3, C5, C7, C9.
Added
release from miscible, water-prepared and humid-stored films at 15–100% DL and three doses, a water series from 0 to 100%, nanoTA local composition and phase shares, and the particles released by the films li2019 R2, R6, R15, R19, R23.
Relation
first to create phase-separated microstructure on purpose and show a release gain; contradicts, for this pair, the view that humid-storage separation reduces release, which was reported for other systems li2019 C14, C55, C5.
SupportsF3 F6 F7 F14 F15 F16
2019
moseson2019indomethacin crystals dissolving into a copovidone meltASD processconfirms
Dissolution of Indomethacin Crystals into a Polymer Melt: Role of Diffusion and Fragmentation
Known before
dissolution into a melt modelled by Noyes–Whitney, defect-driven dissolution, and the defective nanometre crystals and first hint of fragmentation in an extrudate (Moseson 2018a); the IDM–copovidone solubility temperature of about 78 °C at 1:5 (builds_on) moseson2019 C2, C5, R21.
Added
still, isothermal films at 130 °C followed by XRD, PLM, SEM-EDX and TEM, and a 2D lattice Monte Carlo model with defect maps moseson2019 R4, R5, R9, R10, R20.
Relation
confirms fragmentation without mechanical input and adds a diffusion profile; proposes crystal defects as starting points, which only the model supports moseson2019 C43, C60, X5.
SupportsF10 F11 F12 F13
2019
purohit2019endogenous crystals in dogsBioperformancefirst proposed
Assessing the impact of endogenously derived crystalline drug on the in vivo performance of amorphous formulations
Known before
the amorphous and crystalline solubility of tacrolimus, ratio about 33 (Trasi 2016), crystallization of the generic with residual seeds (Trasi 2017), desupersaturation from small crystalline fractions (Purohit 2018) and seed properties that change growth (Que 2018) (builds_on) purohit2019 C30, C17, C5, C8.
Added
stored capsules at 0, 50 and 100% crystallinity, SEM and XRPD of the crystals, non-sink dissolution and dog pharmacokinetics for generic and innovator capsules and a suspension of reference crystals purohit2019 R1, R4, R6, R8, R9, R11.
Relation
first exposure data for a partly crystalline product of the tacrolimus line; the loss of exposure is smaller than in dissolution and larger than zero, and endogenous crystals give about four times the exposure of reference crystals purohit2019 C46, C56, C40.
SupportsF16 F30 F31 F32
2019
que2019ledipasvir–copovidone, drug loading and drug–polymer interactionsDissolutionextends
Insights into the Dissolution Behavior of Ledipasvir-Copovidone Amorphous Solid Dispersions: Role of Drug Loading and Intermolecular Interactions
Note
Known in the library (builds_on: Rumondor 2009, Purohit 2015 on phase separation kinetics, Indulkar 2016, Purohit 2017, Indulkar 2019, Saboo 2019): the LoC concept and its variability in PVPVA (ritonavir 25%, cited limits for other drugs) que2019 C6, R27; colloids form only under polymer control que2019 C4; colloids as a reservoir que2019 C3; AAPS on contact with water que2019 C34; phase segregation at the dissolution front of polyphase mixtures forming a barrier layer que2019 C5.
Added
a limit of 5–7.5% for a high-Tg drug que2019 C10; surface drug enrichment by XPS within 10 min que2019 R15; drug–drug hydrogen bonds broken by PVPVA up to about 7–10% loading, near the limit que2019 R25, C45; SDS raising the limit to 30% and poloxamer 407 to 7.5%, with smaller colloids que2019 C12, R12.
Relation
extends the limit to a drug with a low value; first in the library to raise it with a surfactant que2019 C56.
Note
Findings: F3, F4, F6, F7, F8, F9, F10, F13.
2019
saboo2019congruent release as a "sweet spot", nilvadipine and cilnidipine in PVPVADissolutionconfirmsrevises
Congruent release of drug and polymer: A “sweet spot” in the dissolution of amorphous solid dispersions
Note
Known in the library (builds_on: Ilevbare 2013 on LLPS, Mosquera-Giraldo 2015, Raina 2015 on dihydropyridines, Saboo 2017, Bhardwaj 2018, Indulkar 2019): polymer-controlled release at low and drug-controlled release at high loading, a picture "likely" oversimplified, with the switch loading poorly understood saboo2019 C4; high RH known to induce phase separation in some dispersions saboo2019 C15; the surface-normalized method and the ritonavir and itraconazole drop-offs (builds_on).
Added
the cliff for two drugs 2.5 log units apart at about the same molar loading, refuting the log P hypothesis saboo2019 R7, C35; nanodroplets only from congruent dispersions ("a clear link") saboo2019 C30; a porous, drug-rich surface above the switch saboo2019 R13, R18; humidity turning a congruent compact incongruent saboo2019 C41; the same cliff in powder dissolution saboo2019 R20, R21.
Relation
confirms the ritonavir cliff for two more drugs; revises the expectation that the more lipophilic drug switches earlier saboo2019 C6, C35.
Note
Findings: F1, F2, F3, F4, F6, F7, F8, F9, F12.
2019
trasi2019solvent granulation of ritonavir and lopinavirASD processfirst proposed
Amorphous solid dispersion formation via solvent granulation – A case study with ritonavir and lopinavir
Known before
a second amorphous drug lowers the first drug's amorphous solubility and maximum supersaturation, and amorphous multidrug formulations dissolve poorly (Trasi 2015a, b; Alhalaweh 2016); ritonavir–PVPVA gives nanodroplets only below 25% DL and releases polymer first above it (Indulkar 2019) (builds_on) trasi2019 C5, C43, C46, R22.
Added
1:1 dichloromethane:methanol granulation of drug and PVPVA onto lactose:MCC, XRPD after one month at 40 °C/75% RH, a 60 g high-shear batch, and release of single-drug, co-granulated and separately granulated drugs at pH 6.8, in 0.1 N HCl and after an acid-to-pH 6.8 shift, against the marketed tablet trasi2019 P1, P2, P3, P9, P11, R1, R2, R4, R6, R14.
Relation
first wet-granulation route in this chapter; applies mutual amorphous solubility reduction to a solid product, adds a barrier hypothesis for acid release (supported only on a polymer-free melt) and separate granulation as a remedy trasi2019 C38, C47, C49, X7.
SupportsF22 F23 F24
2020
enright2020phospholipid digests, cholesterol and volunteer bile acid pools with atazanavirDissolutionconfirmsextendsrevises
Known before
PC shortens the atazanavir induction time and Composite-SIF holds supersaturation longer than FaSSIF (indulkar2018), and bile salts differ as inhibitors with a concentration dependence of taurocholate (li2016a) (builds_on) [enright2020 C5, C4].
Added
atazanavir at each medium's amorphous solubility in buffer (253 ± 65 min), FaSSIF (about 48), Composite-SIF (about 81) and FaSSIF-V3 (23 ± 6 min); PC against lyso-PC and oleate in 2.8 mM glycocholate/taurocholate; cholesterol; one digest lipid fraction with four bile salt fractions; media built from six volunteers' duodenal bile acid pools (23–33 against 112–144 min); and 1 mg/mL HPMC in the two extreme volunteer media (more than 360 min) [enright2020 R2, R10, R14, R18, R28].
Relation
confirms indulkar2018 (FaSSIF shorter than Composite-SIF; phospholipid accelerates) and extends it to the digestion products of PC, which accelerate more; revises indulkar2018 on bile salt alone, since glycocholate/taurocholate without lipid did not lengthen the induction time over buffer (272 against 253 min) whereas 3 mM STC alone had given about 595 against 170 min at a lower supersaturation [enright2020 R6, R2, C24, X10; indulkar2018 X5].
SupportsF3 F19 F28 F35 F39 F40 F41 F43
2020
hate2020aatazanavir: adsorption, loading and an absorptive sinkMesoporous silicaconfirmscontradicts
Interplay of Adsorption, Supersaturation and the Presence of an Absorptive Sink on Drug Release from Mesoporous Silica-Based Formulations
Known before
the incomplete ritonavir release and its lower flux (dening2018), the isotherm explanation (dening2019), and the hollow-fibre apparatus, the atazanavir solubilities and its 10% HPMC dispersion with LLPS (builds_on: Hate 2017, 2018, 2019) hate2020a C12, C1, R29, C16, M1, R28.
Added
atazanavir isotherms at two silica concentrations, the solid state of 5–50% loadings with storage, release against loading with a sink, release into medium with dissolved drug, sink against closed vessel over 240 min, an acid start, and a comparison with an HPMC dispersion hate2020a R2, R4, R8, R9, R15, R17, R20, R22, R24, R25.
Relation
confirms the type II isotherm shape of ritonavir; contradicts the isotherm as the main explanation, since far more drug stays than it predicts; first absorptive test of a silica formulation hate2020a C21, C43, C7.
SupportsF1 F11 F14 F15 F2 F3 F4 F5 F7 F9 F10 F13
2020
hate2020belectrostatic interactions and the pH shiftMesoporous silicafirst proposed
Influence of Drug-Silica Electrostatic Interactions on Drug Release from Mesoporous Silica-Based Oral Delivery Systems
Known before
supersaturation from silica (dening2018), the isotherm and BET approach and urea as a competitor (dening2019), the absorptive apparatus (Hate 2017), the amorphous solubilities of the free bases (Hate 2018, Hsieh 2012) and the atazanavir pKa (Indulkar 2015) (builds_on) hate2020b C12, P2, P5, M3.
Added
the zeta potential of SBA-15 from pH 1 to 10, isotherms of ketoconazole, clozapine and atazanavir at four pH values, single-pH and two-step release, triethylamine and urea as competitors, and an absorptive run for ketoconazole hate2020b R2, R3, R4, R5, R7, R10, R11, R12, R14, R15, R17.
Relation
first to show electrostatic binding of charged bases and their re-adsorption after a gastric-to-intestinal pH shift; shows that the sink effect of hate2020a fails for re-adsorbed ketoconazole hate2020b C20, C28, C24.
SupportsF6 F13 F1 F4 F5 F7 F10 F12 F14
2020
li2020water in the spray solvent of ritonavir–PVPVAASD processconfirmsextends
Water-induced phase separation of spray dried amorphous solid dispersions
Known before
trace water in the solvent splits spin-coated and rotary-evaporated films, feed heterogeneity carries over and local composition governs release (Li 2017, 2019); water-induced separation of spray-dried ITZ–HPMC (Mugheirbi 2017); the 25% DL congruent boundary of ritonavir–PVPVA (Indulkar 2019) (builds_on) li2020 C14, C11, C63.
Added
spray drying from methanol, 10:90 and 60:40 water:methanol at 25, 50 and 75% DL, aged DSC, pyrene fluorescence, XPS, constant-area dissolution and colloid sizing, and a droplet-drying model with a four-component Flory–Huggins phase diagram li2020 P1, P4, P5, P6, P8, P9, P11, P12.
Relation
confirms li2017 and mugheirbi2017 for a second system on a spray dryer and extends the evidence from TEM and the drug's own fluorescence to surface methods; contrasts with li2019, because separation lowered release at 25% DL; the first drying-path calculation in the chapter li2020 C2, C40, C67, C9.
SupportsF2 F3 F6 F7 F16 F20 F21
2020
mccarthy2020indomethacin and its methyl esterMesoporous silicaconfirms
A Comparison of Drug Release and Adsorption Under Supersaturating Conditions for Ordered Mesoporous Silica with Indomethacin or Indomethacin Methyl Ester
Known before
the monolayer equation, ritonavir release under supersaturation and the adsorbed–free equilibrium (dening2018), and the dynamic equilibrium as the explanation of incomplete release (dening2019) (builds_on); the activity scale for adsorption came from Hansen and co-workers outside the library mccarthy2020 E3, C4, R28, R29.
Added
crystalline and amorphous solubilities, FTIR, XPS and pyrene tests, isotherms with three fits, the activity-scale replot, desorption, urea and salt tests, a loading series with PXRD, release at the amorphous solubility, and redissolution of the recovered solid mccarthy2020 R1, R3, R4, R6, R7, R8, R10, R12, R13, R14, R15, R19, R20, R23, R24.
Relation
confirms hydrogen bonding to silanols with a donor-free analogue; first comparison on an activity scale; confirms incomplete release at about half the theoretical supersaturation for two more drugs mccarthy2020 C41, C42, C24, C48.
SupportsF4 F5 F7 F1 F2 F3 F9 F10 F15
2020
moseson2020thermogravimetry and the chemical limit of HMEASD processfirst proposedrevises
Application and Limitations of Thermogravimetric Analysis to Delineate the Hot Melt Extrusion Chemical Stability Processing Window
Known before
HME converts the crystal by dissolution into the polymer and particle size sets the rate (Moseson 2018); slow drug diffusion in a melt, a diffusion layer of about 8 µm (Moseson 2019); class III glass formers (Baird 2010) (builds_on) moseson2020 C15, R21, C5.
Added
nonisothermal and isothermal TGA of three crystalline drugs, six polymers and four dispersions, DSC holds of undercooled melts, and HPLC assay of bicalutamide–PVPVA after TGA holds and after extrusion moseson2020 P7, P8, P9, P12, P13.
Relation
first chemical-stability treatment in the chapter; gives the ceiling for a window whose floor was set by F8–F10; revises the practice of reading TGA onsets from a fast ramp moseson2020 C12, C47, C54.
SupportsF11 F30 F31 F32 F33 F34 F35
2020
moseson2020aresidual crystals, seed properties and polymer adsorptionASD processfirst proposedextends
Amorphous Solid Dispersions Containing Residual Crystallinity: Influence of Seed Properties and Polymer Adsorption on Dissolution Performance
Known before
the eight IDM–PVPVA extrudates with 0–25% crystals and the nanometre, defective residual crystals seen by TEM (Moseson 2018, 2018a); fragmentation during dissolution in a melt (Moseson 2019); surface poisoning by an adsorbed polymer (Schram 2016) and the dependence of seed potency on seed properties (Que 2018) (builds_on) moseson2020a R20, P3, C2, C4.
Added
seeded growth with 0, 5 and 50 µg/mL PVPVA, AFM of adsorbed polymer, non-sink dissolution of the extrudates, SE ASD/physical-mixture blends and bulk-seeded dispersions at constant total and constant amorphous dose, SEM of bulk, cryomilled and residual crystals, and TEM of one extrudate moseson2020a P10, P11, P12, P13, P14, P15, P16, P19.
Relation
first dissolution consequence in the library of the crystals of F9–F10; extends the defect idea of F13 to seed potency; places IDM–PVPVA in the low-risk scenario moseson2020a C28, C39, C40.
SupportsF10 F12 F13 F25 F26 F29
2020
que2020halogen bonding in dispersionsSolid state stability
Known before
drug–PVP hydrogen bonding, whose carbonyl shifts the paper quotes as up to 20–30 cm⁻¹, used as the comparator [que2020 R17.j, R17.q].
Added
XPS of halogen core levels, IR of the VP and VA carbonyls and NMR titration with a monomer analogue for four compounds with Cl, Br or I and no donor [que2020 R7, R9, R11, R12, R13, R16].
Relation
adds a new, weak kind of contact to the hydrogen-bond picture of F1 and F2; the authors call it the first observation in drug–polymer formulations and compare its strength with weak hydrogen bonding [que2020 C3, C25].
SupportsF20 F2 F17
2020
saboo2020indomethacin and its methyl ester in PVPVA: hydrogen bonding, surface crystallization and glass transitionDissolutionfirst proposedrevises
Congruent release of drug and polymer from amorphous solid dispersions: insights into the role of drug-polymer hydrogen bonding, surface crystallization and glass transition
Note
Known in the library (builds_on: Taylor and Zografi 1997 on indomethacin–PVP hydrogen bonding, Rumondor 2009 and 2011, Purohit 2017, Indulkar 2019, Saboo 2019): polymer-controlled, congruent release at low loading with an abrupt decrease at a loading that varies between drug–polymer pairs saboo2020 C2; the same limit for two PVPVA dispersions of very different log P saboo2020 C4; drug–polymer hydrogen bonding considered advantageous to physical stability, with its role in release poorly understood saboo2020 C5.
Added
a limit of 10% for indomethacin against at least 25% for its methyl ester over 5 min, so that the hypothesis that hydrogen bonding raises the limit "appears to be incorrect" saboo2020 C14, C48; the surface of the 25% indomethacin compact followed by EDX, nanoTA and FTIR to about 60–72 wt% drug at 20 min saboo2020 R21, R28, R17, X15; congruent release of the ester stopped after 7.5–20 min by crystals on the surface saboo2020 R8, R22, C17; the indomethacin limit at 10% from 25 to 57 °C, 5% at 17 °C and below 5% at 10 °C, against a wet Tg onset of 18 °C for a 70% dispersion saboo2020 R29, R30.
Relation
first in the library to set a matched analogue without a donor, and the test temperature, against the limit; revises the hypothesis taken from Rumondor 2009 and 2011 that hydrogen bonding favours release saboo2020 C7, C48.
Note
Findings: F1, F2, F3, F4, F6, F7, F8, F10, F15, F17, F18, F19.
2020
saboo2020arelease against drug loading for five polymers, felodipineDissolutionextends
Patterns of drug release as a function of drug loading from amorphous solid dispersions: A comparison of five different polymers.
Note
Known in the library (builds_on: Konno 2006, Purohit 2015 on phase separation kinetics, Purohit 2017, Saboo 2017, Bhardwaj 2018, Indulkar 2019, Que 2019, Saboo 2019): congruent release seen only at low loading, mostly with PVPVA, and a limit thought to depend on drug properties and interactions saboo2020a C4; no correlation between polymer properties and the limit established saboo2020a C5; water-induced AAPS turning congruent into incongruent release saboo2020a C40; no log P effect at low loading saboo2020a C33.
Added
limits of 10, 15 and 10% with PVP, PVPVA and HPMC and none to 50% with HPMCAS and Eudragit S 100 saboo2020a R15; polymer hydrophobicity by water sorption and contact angle saboo2020a R3, R4; the trade-off between fast release at low loading and workable release at higher loading saboo2020a C55; release falling with log P at 40% in HPMCAS saboo2020a R16, C19; no positive correlation between drug–polymer hydrogen bonding and the limit saboo2020a C48; the Higuchi critical ratio far below practical loadings saboo2020a R27.
Relation
extends the limit from a drug property to a polymer property; generalizes Purohit 2017's HPMCAS contrast to five polymers saboo2020a C49.
Note
Findings: F1, F2, F3, F6, F7, F8, F9, F10, F11.
2020
trasi2020lumefantrine with acidic polymers: stability, protonation and granule releaseSolid state stability
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.
SupportsF34 F11 F24
2020
ueda2020aHPMCAS grade and the amorphous solubilityBioperformance
Impact of hypromellose acetate succinate grade on drug amorphous solubility and in vitro membrane transport
Known before
the UV-extinction method (Ilevbare 2013), a second component in the drug-rich phase lowering the chemical potential (Trasi 2015), the drug-rich phase as a reservoir (Indulkar 2016), the flow-through apparatus (Hate 2017) and the hollow-fibre module with a 1:9 atazanavir ASD (Hate 2018) (builds_on) ueda2020a C2, C4, C34, C36.
Added
four drugs with two HPMCAS grades: amorphous solubility, NMR polymer loss from solution, droplet size, receiver profiles and Cmax against donor concentration, and spray-dried 1:9 atazanavir ASDs ueda2020a R1, R2, R5, R7, R8, R9, R10.
Relation
a third case of a component entering the drug-rich phase, after a second drug and cellulose acetate suberate, and the first within one polymer family; the nanodroplet gain above the ceiling is the same for both grades ueda2020a C27, C33, C36.
SupportsF5 F7 F15 F19
2020
ueda2020bthree polymers and ibuprofen, by NMRDissolutionconfirms
Polymer type impacts amorphous solubility and drug-rich phase colloidal stability: A mechanistic study using nuclear magnetic resonance spectroscopy
Known before
the LLPS concept and the extinction method (2013), polymers stabilize the size of drug-rich droplets and adsorb at the amorphous surface (2013 ritonavir nanodroplet study), solubilization raises the amorphous solubility without raising transport (2017 SDS paper) and polymer mixing with the drug-rich phase lowers the amorphous solubility and membrane transport (2018 telaprevir ASD paper) (builds_on) ueda2020b C3, C4, C5.
Added
HPMC, PVP-VA and EUD-E at 300 µg/mL with ibuprofen: crystalline and amorphous solubility, NMR of both phases and of the dissolved polymer, fresh droplet size and zeta potential, and 3 h of stirring ueda2020b R1, R5, R6, R7, R13, R15.
Relation
confirms, with NMR evidence of where each polymer sits, the polymer-mixing mechanism proposed for telaprevir; first paper of the chapter to read polymer partitioning and droplet stability together ueda2020b C32, C33, C52.
SupportsF1 F2 F3 F4 F11 F15 F19 F22
2020
wilson2020enzalutamide and polysaccharide polymersBioperformance
Amorphous solid dispersions of enzalutamide and novel polysaccharide derivatives: investigation of relationships between polymer structure and performance
Known before
induction times and screened polymers (Mosquera-Giraldo 2016), poorly soluble polymers that limit release (Li 2018), the solubility of cellulose acetate suberate (Mosquera-Giraldo 2018), and the diffusion-cell method with the link of flux to exposure (Wilson 2018) (builds_on) wilson2020 R1, C2, C29, M3.
Added
induction times of 24 polymers at 50 µg/mL, three dispersions of two new polymers, rat exposure at 50 mg/kg against a slurry and a lipid formulation, and dialysis-membrane mass flow wilson2020 R1, R6, R8, A3.
Relation
repeats the rat test of wilson2018 with new polymers; the best solution inhibitor made a poor dispersion and a weak but soluble one worked at 50% loading; mass flow again ranked the exposures wilson2020 C22, C27, C44.
SupportsF8 F10 F24 F25 F32
2021
bhujbal2021lumefantrine dispersions by spray anti-solvent precipitationSolid state stabilityrevises
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].
SupportsF34 F14 F24 F5
2021
elkhabaz2021crystallization kinetics in simulated and aspirated human intestinal fluidDissolutionfirst proposedconfirms
Crystallization Kinetics in Fasted-State Simulated and Aspirated Human Intestinal Fluids
Known before
bile salts delay nucleation and differ with structure, slow growth and leave residual supersaturation (chen2015, li2016a, lu2017, lu2017a), lecithin promotes crystallization and atazanavir is a slow nucleator (indulkar2018), two proposed lecithin mechanisms (enright2020), SHG rates of nucleation and growth, and the amorphous solubilities and activity-based supersaturation of the two drugs in the six media (Bioperformance) (builds_on) elkhabaz2021 C4, C24, C25, R4.
Added
induction times of atazanavir and posaconazole at their amorphous solubility in two blank buffers, FaSSIF-V1, FaSSIF-V2, a six-bile-salt composite FaSSIF and pooled aspirated fasted human fluid, without and with HPMC-AS; SHG nucleation and growth rates; desupersaturation rates; needle and plate habit; the atazanavir precipitate form elkhabaz2021 R6, R7, R8, R14, R15, R21, R20.
Relation
first in the library to measure crystallization in aspirated human intestinal fluid; confirms indulkar2018 for atazanavir (composite medium slower than FaSSIF, more lecithin faster) but finds the six-bile-salt medium short of human fluid for posaconazole, and HPMC-AS helping most in blank buffer elkhabaz2021 C24, C27, C28, C32.
SupportsF3 F5 F12 F31 F35 F39 F40 F42 F43
2021
moseson2021residual crystals and matrix crystallization in bicalutamide–PVPVAASD processconfirmsextends
Amorphous Solid Dispersions Containing Residual Crystallinity: Competition Between Dissolution and Matrix Crystallization
Known before
residual crystals more potent than bulk crystals, with low- and high-risk scenarios (Moseson 2020a); phase-diagram-guided extrusion temperature (Moseson 2018) and TEM detection of nanometre crystals (Moseson 2018a); dissolution against matrix crystallization (Alonzo 2010) and incongruent release with a drug-rich layer (Saboo 2019, 2020) (builds_on) moseson2021 C4, C5, C1.
Added
four 30:70 BCL–PVPVA extrudates from 3.5, 38 and 93 µm input crystals at 155 and 180 °C, five solid-state methods, dissolution at 3–150 µg/mL, hot-stage PLM, in-line Raman slurries with and without HPMCAS, PVPVA release by size-exclusion chromatography moseson2021 P1, P2, P13, P15, P16, P14.
Relation
contrasts with moseson2020a (the same kind of crystals are high risk here); confirms the particle-size prediction of F9 on a second pair and extends F10 to a performance consequence; first matrix-crystallization study of an extruded dispersion moseson2021 C70, C5, C38.
SupportsF8 F9 F10 F12 F13 F25 F26 F27 F28 F29 F35
2021
que2021four phenolphthalein analogues in PVPVA: hydrogen bonding, halogen bonding and the limitDissolutionextends
Note
Known in the library (builds_on: Indulkar 2019, Saboo 2019, Que 2019, Que 2020 on halogen bonding, Saboo 2020 on five polymers, Saboo 2020 on indomethacin, Crowley and Zografi 2002): phenolic OH groups can hydrogen-bond to the PVPVA carbonyl and iodine atoms can potentially halogen-bond to the same acceptor [que2021 C2]; halogen bonding to the VP carbonyl and the Me-TIPP data (Que 2020, builds_on); a lower limit for indomethacin than for its ester (Saboo 2020, builds_on).
Added
limits of 5% (PHPH) and 10% (TIPP) for the two phenols against 30% (Me-TIPP) and 40% (Me-PHPH) for their methyl ethers, 0.012–0.115 mol per 100 g [que2021 R19, R20]; VP carbonyl shifts of up to 30 cm⁻¹ for the phenols, 7 cm⁻¹ for Me-TIPP and minimal for Me-PHPH [que2021 R7]; the share of halogen-bonded iodine by XPS falling with loading [que2021 R11, R12]; drug and PVPVA leaving at the neat-polymer rate at every limit [que2021 R21, C39]; no obvious correlation of log P, amorphous solubility, Tg or molecular weight with the limit [que2021 C29].
Relation
extends the indomethacin–ester comparison of Saboo 2020 to two analogue pairs and adds halogen bonding; proposes, without measuring it, that bonds persisting in water slow polymer hydration [que2021 C44].
Note
Findings: F1, F2, F3, F4, F6, F9, F10, F15, F16, F17, F18.
2021
saboo2021TPGS in felodipine–PVPVA dispersions at higher loadingDissolutionextends
Exploring the Role of Surfactants in Enhancing Drug Release from Amorphous Solid Dispersions at Higher Drug Loadings
Note
Known in the library (builds_on: Saboo 2019, Indulkar 2019, Li 2019, Que 2019, Saboo 2020 on five polymers, Saboo 2020 on indomethacin, Han 2019): surfactants raised the limit of ledipasvir–PVPVA but the mechanism "remains elusive" saboo2021 C6; hydrophobic polymers give higher limits but slower release saboo2021 C3; a drug-rich surface layer formed during hydration slows release saboo2021 C28; the transient gel layer model (Saboo 2020 on indomethacin, builds_on).
Added
limits of 25, 35 and 45% with 2, 5 and 10% TPGS against 15% without saboo2021 R12; the gain with TPGS below its CMC, so that micelles play "a negligible role", and no gain with TPGS dissolved in the medium saboo2021 R1, C33, R15; semi-continuous drug-rich domains at 0 and 2% TPGS against discrete domains at 5 and 10% in humidified films, and a porous surface layer only on the 0 and 2% tablets saboo2021 R21, R23, R19; TPGS lowering the dispersion Tg from 89.2 to 71.1 °C saboo2021 R5.
Relation
extends the surfactant result of Que 2019 to a second drug and a graded level; first in the library to tie release to the shape of the drug-rich phase ("appeared to be linked") saboo2021 C53.
Note
Findings: F1, F2, F4, F5, F6, F7, F8, F13, F15, F16, F20, F21.
2021
ueda2021six polymers, quantitative NMRDissolutionextends
Known before
Eq. 1 and its ibuprofen inputs (2015 six-drug paper), a second component lowers the amorphous solubility, eq 2 (2015 second-drug study), the ASD polymer lowers the amorphous solubility (2018), polymer grade lowers the maximum supersaturation (2020 HPMCAS grades) and NMR of dissolved and phase-separated drug with polymer mixing (2020 NMR paper) (builds_on) [ueda2021 C2, C4].
Added
PVP K12, K25, K90, PVP-VA and HPMC 603 and 615 at 25–1000 µg/mL with 50–600 µg/mL ibuprofen: dissolved drug and polymer weight ratio in the drug-rich phase, Flory–Huggins calculation and DVS of ASDs [ueda2021 R5, R8, R10, R11, R12, R13, R17].
Relation
extends the 2020 result to molecular weight, chemistry and amount; shows a ceiling for PVP K25 and PVP-VA and none for HPMC 603; ideal mixing over-predicts the solubility and an interaction term improves it [ueda2021 C13, C24, C33, C39].
SupportsF4 F5 F6 F8 F11 F15 F19 F20
2021
wilson2021polymers and enzalutamide nanodropletsDissolutionextends
Interaction of Polymers with Enzalutamide Nanodroplets—Impact on Droplet Properties and Induction Times
Known before
effective inhibitors distribute between the water and the drug-rich precipitate (raina2015b), the induction-time method and globular polymers as poorer inhibitors (mosqueragiraldo2016), the polymer–drug simulation protocol with extended against globular chains (mosqueragiraldo2018a), NMR depletion of polymer and drug (Bioperformance), and HPMCAS as an inhibitor for enzalutamide (builds_on) wilson2021 C4, C54, P10, P6, C6.
Added
enzalutamide at 30–120 µg/mL across a stated amorphous solubility of 42 µg/mL with HPMCAS, the cellulose ester P177 and Eudragit E PO at 2.5–100 µg/mL, NMR of polymer and drug left in solution, colorimetry of pellets, TEM with EDX, DLS and zeta potential, a dansyl-labelled HPMCAS, and 15 ns simulations of one chain beside a 10-molecule drug cluster wilson2021 R3, R7, R8, R9, R11, R13, R14, R17, R21.
Relation
tests the two-phase criterion of raina2015b: both polymers enter the droplets and lower the dissolved drug alike, but the one with the larger share in the droplets (Eudragit E PO) inhibits worst, so distribution alone does not rank inhibitors; extends the extended-chain reading of mosqueragiraldo2018a to a droplet interface wilson2021 C37, C38, C58.
SupportsF3 F14 F15 F19 F26 F36 F37
2021
yang2021six drugs of different Tg and log P in PVPVA and HPMCASDissolutionextends
Note
Known in the library (builds_on: Indulkar 2019, Saboo 2019, Saboo 2020 on indomethacin, Que 2019, Jackson 2015, Mosquera-Giraldo 2018, Ilevbare 2013 on LLPS, Saboo 2017): high log P drugs were expected to undergo phase separation in the wet matrix more readily and impair release [yang2021 C6], and high-Tg drugs to be detrimental to release and nanodroplet formation [yang2021 C7].
Added
PVPVA powders failing at 25 and 40% for low-Tg loratadine and miconazole and at 5–10% for danazol, elbasvir, paclitaxel and ivacaftor, with no log P trend [yang2021 R7, R8, R9, R10, R11, R12, C19]; a cliff within a 10% loading span in every PVPVA system against a gradual decline with HPMCAS [yang2021 C2]; the loratadine limit falling from 30 to 2% (PVPVA) and 20 to 5% (HPMCAS) on cooling from 37 to 5 °C, below its wet Tg of 13.8 °C [yang2021 R22, M1]; HPMCAS keeping elbasvir and loratadine droplets smaller [yang2021 R3, R6].
Relation
extends the temperature test of Saboo 2020 to a second drug and two polymers; Tg and hydrogen-bond donors went together across the drugs and were not separated [yang2021 C25, C38].
Note
Findings: F1, F2, F3, F4, F6, F8, F9, F11, F15, F16, F17, F18, F19.
2022
alvarenga2022polymer type and thermal degradation of ritonavir dispersionsASD processconfirmsextends
Impact of Polymer Type on Thermal Degradation of Amorphous Solid Dispersions Containing Ritonavir
Known before
the TGA approach to the chemical window and its limits, and the polymer effects on posaconazole and indomethacin (Moseson 2020) (builds_on) alvarenga2022 C5, C1.
Added
ten polymers at 20% DL and loading and grade series, 5 min isothermal TGA with assay, 60 min mass loss, extrusion at 130–160 °C, a convection oven against the TGA, FT-IR, and LC-MS/MS identification of seven degradants alvarenga2022 P1, P2, P8, P9, P10, P12, R27.
Relation
extends moseson2020 from "can TGA set the window" to "why does the polymer change the loss"; confirms that TGA mass loss misleads and that a TGA hold overstates extrusion; the mechanism offered (water from dehydration, acid from protic polymers) is not measured alvarenga2022 C37, C39, X8, X9.
SupportsF30 F32 F33 F34 F35
2022
correasoto2022asurfactants in clopidogrel–copovidone dispersions: drug loading and nanodroplet stabilityDissolutionextends
Impact of Surfactants on the Performance of Clopidogrel-Copovidone Amorphous Solid Dispersions: Increased Drug Loading and Stabilization of Nanodroplets
Note
Known in the library (builds_on: Indulkar 2019, Que 2019, Saboo 2021, Saboo 2019, Saboo 2020 on indomethacin, Yang 2021, Indulkar 2017 on SDS, Indulkar 2016, Ueda 2020): drug-rich nanodroplets benefit bioavailability as a reservoir correasoto2022a C1; a supersaturated solution with a drug-rich phase is metastable and its droplets coarsen correasoto2022a C2; reported limits in PVPVA range from below 5 to about 30% correasoto2022a C45.
Added
a limit of about 40% for a low-Tg drug without hydrogen-bond donors, and 50% with SDS correasoto2022a C46, C47, C55; PVPVA dissolving about twice as fast from the binary dispersions as from the neat compact correasoto2022a R18, C30; SDS, TPGS or Tween 80 keeping the droplets at constant size for 4 h and CTAB agglomerating them correasoto2022a R6, C12; TPGS taken up into the droplets at about 50:17 w/w drug:TPGS correasoto2022a R12; uniform, bicontinuous and drug-continuous films at 40, 50 and 60% correasoto2022a R20.
Relation
raises the limit of a third drug with SDS, as Que 2019 did for ledipasvir, and extends the morphology link of Saboo 2021 to a binary dispersion correasoto2022a C55, C32.
Note
Findings: F1, F2, F3, F4, F6, F8, F13, F15, F16, F17, F18, F19, F20, F21.
2022
correasoto2022bsurfactants and vinylpyrrolidone in atazanavir–PVPVA dispersionsDissolution
Role of surfactants in improving release from higher drug loading amorphous solid dispersions
Note
Known in the library (builds_on: Indulkar 2019, Que 2019, Saboo 2020 on indomethacin, Yang 2021, Saboo 2021, Indulkar 2015, Indulkar 2017 on SDS, Ueda 2021, Devotta 1995, Cooper 1986): the drug Tg plays a role in the limit and high-Tg drugs release poorly unless the loading is very low correasoto2022b C3; surfactants can raise release at higher loading, with selection mostly empirical correasoto2022b C4; the dry and wet Tg of atazanavir, 105 and 55 °C correasoto2022b M1.
Added
a limit of 5% for the binary dispersion, 10% with SDS or CTAB and 15% with Span 80 correasoto2022b R1, C12; every additive raising release at 10% by 4- to 35-fold, vinylpyrrolidone as well as the best surfactants correasoto2022b R20; release of the 10% binary dispersion restored at 55 °C until the drug crystallized correasoto2022b R5; additives lowering the dispersion Tg by 7–16 °C and making wet films separate within 10 min correasoto2022b R20, R10, R11.
Relation
tests plasticization as the cause of the surfactant effect with a plasticizer that is not a surfactant correasoto2022b C9, C40; a high-Tg drug where the clopidogrel paper of the same year studied a low-Tg one (synthesis).
Note
Findings: F1, F2, F3, F4, F6, F8, F13, F15, F18, F19, F20, F21.
2022
duong2022adelamanid salts formed inside the dispersionDissolutionfirst proposed
Combining enabling formulation strategies to generate supersaturated solutions of delamanid: In situ salt formation during amorphous solid dispersion fabrication for more robust release profiles
Note
Known in the library (builds_on: Towler 2008, Ueda 2020, Hate 2020, Moseson 2020): the counterion changes the crystallization tendency of amorphous salts, polymers stabilize drug-rich droplets, and residual crystals in dispersions can seed growth during release duong2022a C5, C11, C55.
Added
a fast crystallizer that cannot be vitrified at 50 °C/min left crystals in rotary-evaporated dispersions from 15–20% drug, and release collapsed once crystallinity was detectable; seven of eight sulfonate salts were amorphous with Tg 83.7–117.8 °C, and salts formed in the same step as the dispersion released ≈95–97 µg/mL of 100 at 25% drug against ≈20 for the free base; a polymer screen chose HPMCP and HPMCAS by induction time and droplet size duong2022a R8, R14, R20, R26, R4, R5.
Relation
first in the library on in situ salt formation in a polymer dispersion; adds a fast-crystallizing weak base to the residual-crystal problem of Que 2018.
Note
Findings: F23, F4, F9, F10, F12, F25, F28.
2022
duong2022bposaconazole phase diagram, supersaturation and mediaDissolutionconfirmscontradicts
Known before
pH-shift supersaturation and precipitation of weak bases (hsieh2012), LLPS above the amorphous solubility and the flux cap there, pH-dependent LLPS of weak bases, the concentration dependence of the micelle–water partition coefficient, unchanged free posaconazole in FaSSIF (chapters C and Bioperformance), nucleation acceleration by oleate and lipid digests (enright2020), and the proposal that surfactants lower the interfacial energy (elkhabaz2021), here tested (builds_on) [duong2022b C2, C3, C8, C9, C33, C51].
Added
crystalline and amorphous solubility of posaconazole at 13 pH values from 1.0 to 7.0 and in five biorelevant media against same-pH buffers, induction times from S 5 to 33.6 in PBS pH 6.5 and in four intestinal media, seeding with nanocrystals from a marketed suspension, and nucleation-theory fits giving the interfacial energy, the pre-exponential factor, the barrier and the critical radius [duong2022b R1, R8, R10, R11, R13, R16, R17].
Relation
confirms for a weak base the constant amorphous-to-crystalline ratio across pH (about 34 from pH 2 to 7) and the lower concentration ratio in micellar media; contradicts the interfacial-energy reading of indulkar2018, indulkar2019b and elkhabaz2021 by placing the medium effect in the pre-exponential factor, an assignment its own data do not make secure [duong2022b C19, C51, C53, X12].
SupportsF2 F3 F14 F19 F20 F34 F35
2022
duong2022csurface nanocoating of high-loading ezetimibe–HPMCAS dispersionsASD processfirst proposed
Surface nanocoating of high drug-loading spray-dried amorphous solid dispersions by atomic layer coating: Excellent physical stability under accelerated storage conditions for two years
Known before
ezetimibe–HPMCAS phase behaviour in biorelevant media (Elkhabaz 2017) and SHG detection of early crystallization in spray-dried dispersions (Correa-Soto 2017) (builds_on); alumina shells had blocked water uptake of amorphous lactose (cited) duong2022c C2, C3, C6.
Added
ezetimibe–HPMCAS at 50 and 70% loading, spray dried, coated with a thin and a thick Al2O3 shell (11.7–39.7 nm by TEM) and stored open at 40 °C/75% RH for 24 months; bulk and tapped density, water sorption, and release fresh and after storage duong2022c P2, P4, P8, P9, P15, P16.
Relation
first coating of an ASD in the library and, by its authors, a proof of concept for higher drug loading; its thickness effect at 70% loading and its drop of water uptake with thick shells are the points that Moseson (2022, 2023) later qualify duong2022c C8, C60, C17, C35.
SupportsF42 F43 F44 F45 F46 F49
2022
hate2022mass transport across PAMPA membranesBioperformanceextends
A Mechanistic Study of Drug Mass Transport from Supersaturated Solutions Across PAMPA Membranes
Known before
amorphous solubility and LLPS (Ilevbare 2013), the plateau above the amorphous solubility (Raina 2014), the nanodroplet reservoir (Indulkar 2016) and the atazanavir amorphous solubility and droplet numbers (Hate 2018) (builds_on) hate2022 C1, C11, C58, M1.
Added
five drugs across lipid-impregnated PVDF filters, SDS or pH 3 in the receiver, atazanavir to 1000 µg/mL and nanodroplets stabilized by polymers and surfactants hate2022 R1, R5, R7, R15, R16, R17, R19.
Relation
extends the plateau of raina2014a to a second device; with a sink receiver transport keeps rising with the number of nanodroplets, as in the hollow-fibre module of hate2018 hate2022 C11, C61, C76.
SupportsF2 F5 F15 F21 F22
2022
hiew2022astability and release of lumefantrine dispersionsSolid state stabilityextends
Balancing Solid-State Stability and Dissolution Performance of Lumefantrine Amorphous Solid Dispersions: The Role of Polymer Choice and Drug−Polymer Interactions
Known before
congruent release and the limit of congruency for PVPVA dispersions, and earlier XPS evidence of lumefantrine protonation by enteric polymers (builds_on) hiew2022a R28, R30, C48.
Added
PVPVA and four enteric polymers at 5–50% drug loading: storage at 40 °C/75% RH, normalized release of drug and polymer, XPS and IR of the interaction, titration of the polymers and a free-carboxylate calculation hiew2022a R6, R13, R19, R20, R22, R25.
Relation
tests the rule of F17 against release and finds that the contact that protects the drug slows the polymer; extends the limit of congruency from PVPVA to enteric polymers hiew2022a C33, C65, C7.
SupportsF26 F21 F23 F14 F17
2022
hiew2022bamorphous salts of lumefantrine in PVPVA: Tg, release and stabilityDissolutionfirst proposed
Combining drug salt formation with amorphous solid dispersions – a double edged sword
Note
Known in the library (builds_on: Hiew 2022 on lumefantrine polymers, Towler 2008, Tong 1999 and 2002, Saboo 2020 on indomethacin, Yang 2021, Que 2019, Indulkar 2019, Narasimhan and Peppas 1996 and 1997): salt formation as a way to raise Tg and reduce recrystallization hiew2022b C6; impaired release from systems with a high Tg against the dissolution temperature hiew2022b C7; congruent release from fast-releasing PVPVA dispersions hiew2022b C25.
Added
salts raising the onset Tg from 19.7 °C to as much as about 101 °C hiew2022b R2; the highest loading with good release falling from 35% (free base) to 2% (sulfate) as the salt Tg rose hiew2022b R20; higher-Tg forms crystallizing later in storage hiew2022b R7, R8; the critical polymer volume fraction of PVPVA, 0.89 at 37 °C hiew2022b R21.
Relation
first in the subcategory to vary the Tg of one drug by salt formation and to show the stability–release trade-off hiew2022b C55, C53.
Note
Findings: F1, F2, F3, F6, F7, F8, F9, F15, F17, F18, F20, F22.
2022
indulkar2022surfactants in ritonavir–copovidone dispersions above the limitDissolutionextends
Role of Surfactants on Release Performance of Amorphous Solid Dispersions of Ritonavir and Copovidone
Note
Known in the library (builds_on: Indulkar 2016, Purohit 2017, Indulkar 2019): the ritonavir–PVPVA limit of about 25%, with polymer-controlled, congruent release below it indulkar2022 R2; water-induced separation impeding release and nanodroplet formation in ritonavir dispersions (Purohit 2017, builds_on); the 30% binary dispersion with a lag, a period of congruent release and then incongruent, incomplete drug release indulkar2022 C30, R1; strategies that raise the limit called "essential" indulkar2022 C5.
Added
five surfactants at 5 parts per 100 parts of 30:70 ritonavir–PVPVA, every one removing the lag and giving congruent release for at least 20 min indulkar2022 C31; near-complete release with Span 85 and TPGS, release stopped near 80% by surface crystals with SDS, and about 41 and 25% with Span 20 and Tween 80 indulkar2022 R8, R9, R5, R15, R7, R6; early PVPVA release about doubled by SDS indulkar2022 C32, R20; a lowered Tg of surface material after dissolution with Tween 80 and Span 20, read as phase separation indulkar2022 R19, C19; released droplets from about 1 µm with the Spans to about 10 µm with Tween 80 indulkar2022 R11, R13.
Relation
extends the surfactant results of Que 2019, Saboo 2021 and the 2022 clopidogrel and atazanavir papers to a drug above its limit (synthesis); first in the subcategory to show a surfactant bringing surface crystallization to a drug that did not crystallize on the binary tablet indulkar2022 C38.
Note
Findings: F1, F8, F13, F15, F16, F19, F20, F21.
2022
moseson2022aatomic layer coating against surface crystallization of ASD powdersASD processextendsrevises
Atomic Layer Coating to Inhibit Surface Crystallization of Amorphous Pharmaceutical Powders
Known before
the ezetimibe–HPMCAS study of Van Duong (2022), the first atomic layer coating of an ASD in the library (entered below, same year); moisture-driven crystallization of felodipine dispersions (Konno 2008; Rumondor 2010) (builds_on) moseson2022a C2, C3.
Added
four drug–polymer systems (erlotinib–HPMCAS, erlotinib–PVPVA, naproxen–HPMCAS, lumefantrine–PVPVA), spray dried or extruded, coated with 5–25 nm Al2O3 or ZnO and stored open at 40 °C and 31–75% RH for up to 48 weeks; wet Tg − T, water sorption, flow moseson2022a P1, P6, P11, P12, P14.
Relation
extends the single system of Van Duong (2022) to four and adds humidity, polymer and the wet Tg; revises the view that a thicker shell protects longer to a finding of no minimum thickness at 5–25 nm, which the ezetimibe study at 70% loading qualifies; finds no change of water uptake where Van Duong (2022) found a drop for thick coatings moseson2022a C37, C20.
SupportsF42 F43 F44 F45 F49
2022
moseson2022bprocessing and formulation strategies against matrix crystallization in BCL–PVPVAASD processconfirmsextends
Formulation and processing strategies which underpin susceptibility to matrix crystallization in amorphous solid dispersions
Known before
matrix crystallization of 30% BCL–PVPVA and the hypothesis that incongruent release leaves a mobile, unprotected drug-rich layer (Moseson 2021); the limit of congruency and drug-rich layers in ritonavir and felodipine dispersions (Indulkar 2019a; Saboo 2019, 2020) (builds_on) moseson2022b C2, C3.
Added
BCL–PVPVA at 5–50% loading by solvent evaporation; mortar, cryomilling for 30 s to 10 min and extrusion; SDS and TPGS; polymer release by size-exclusion chromatography, Raman slurries, ssNMR and, on compacts, SEM-EDX and confocal imaging moseson2022b P1, P2, P3, P5, P10, P11, P12, P14, P15, P16, P17.
Relation
confirms and extends F27 by testing the hypothesis across loadings and showing the drug-rich layer; is the first in the library to link milling and a surfactant to loss of supersaturation, and qualifies the gain from surfactants for milled powders moseson2022b C36, C62, C64, C66.
SupportsF38 F39 F40 F27
2022
moseson2022cinput-crystal attributes and a population balance model of amorphization in HMEASD processconfirmsextends
Known before
Tc from the temperature–composition phase diagram and the size prediction (Moseson 2018), crystals that fragment while they dissolve in a polymer melt (Moseson 2019) and nanometre crystals found by TEM (Moseson 2018a) (builds_on); an earlier HME model had assumed a constant particle count [moseson2022c C7, C45, C9].
Added
five bicalutamide lots from four crystallization routes (D50 3.5–93 µm), extruded 30:70 with PVPVA at Tc = 145 °C in a 5 mL micro-extruder for 2–20 min and read by PXRD; shear-cell flow of the lots; hot-stage PLM of crystals in PVPVA films; a population balance model with dissolution and breakage fitted to the crystallinity [moseson2022c P1, P15, P17, P18, R10, R11, R16].
Relation
confirms the particle-size effect of F9 on a second set and is the first in the library to hold D50 constant and vary the size distribution and agglomeration; extends the fragmentation of F12 from a quiescent film to a model-based claim for the extruder, which was not observed; the defect density behind F13 is again inferred [moseson2022c C46, C59, X6, X9].
SupportsF36 F37 F8 F9 F12 F13
2022
qi2022polymer salts of the enteric polymer HP-50 and their miconazole dispersionsDissolutionfirst proposed
Note
Known in the library (builds_on: Indulkar 2019, Saboo 2020 on five polymers, Yang 2021, Hiew 2022 on lumefantrine polymers): release worsening as the loading of a lipophilic drug rises; drug-dependent changes in enteric polymer dissolution; the miconazole pKa and amorphous solubility (builds_on); a critical ionization of about 83% for HP-50 [qi2022 R19]; the dependence of enteric polymer dissolution on buffer capacity, "well known" from coating work (cited) [qi2022 C20].
Added
HP-50 dissolution set by the buffer species, fastest in BIS-TRIS and slowest in TEA, not by cation size [qi2022 R1, R2, C14]; nine salts dissolving about 3-fold faster than HP-50 whatever the counterion [qi2022 R10, C3]; HP-50-Na keeping its rate at 3 mM/ΔpH where HP-50 slowed 6-fold [qi2022 R12, C4]; dissolution rising with neutralization, the largest step from 80 to 100% [qi2022 R13]; 20% miconazole on HP-50-Na and its triethylamine salt releasing about 84–90% in 60 min against about 9% on HP-50 [qi2022 R14].
Relation
first in the library to pre-ionize an enteric dispersion polymer as a salt [qi2022 C44]; adds an ionizing polymer whose own dissolution, not the drug, limits release to the hydrophobic-polymer contrast of Saboo 2020 (synthesis).
Note
Findings: F3, F15, F23, F24.
2022
ueda2022temperature dependence of polymer partitioningDissolutionextends
Known before
Eq. 1 inputs and the ideal-mixing reduction (2015), NMR detection of the drug-rich phase and the polymer-lowered amorphous solubility (2020), and the same drug, polymers and quantitative NMR with the polymer distribution at 37 °C (2021) (builds_on) [ueda2022 C3, C4].
Added
15–60 °C: polymer weight ratio in the drug-rich phase, amorphous solubility, partition coefficient and ΔG, ΔH, ΔS by a van't Hoff analysis, solid-state NMR of dry ASDs and DSC [ueda2022 R9, R10, R17, R22, R23, R13].
Relation
extends the 2021 result in temperature; shows an endothermic, entropy-driven transfer and a reversal of the polymer ranking; adds the third temperature profile of the chapter [ueda2022 C48, C59, R9].
SupportsF5 F6 F9 F15 F20 F21
2022
yang2022arelease mechanisms of ritonavir–copovidone: phase separation and its morphologyDissolutionfirst proposed
Release mechanisms of amorphous solid dispersions: Role of drug-polymer phase separation and morphology
Note
Known in the library (builds_on: Indulkar 2017, Purohit 2017, Indulkar 2019, Li 2019, Yang 2022 on surfactant-containing dispersions): solution-mediated nanodroplet formation (Indulkar 2017); fluorescent dyes for the phase behaviour of hydrating ritonavir dispersions (Purohit 2017); the limit of 25% yang2022a R15; the falling-off-the-cliff effect of PVPVA dispersions yang2022a C7; conflicting evidence on whether preformed discrete drug-rich domains help release (Li 2019, builds_on).
Added
drug release of about 100, 35 and at most 3% at 20, 30 and 40–50% yang2022a R2; cross-sections with a gel layer at every loading and a drug-rich crust from 30% yang2022a R5, R6, R7; the gel–glass front slowed above the limit yang2022a R8; real-time imaging of droplets of 0.5–2 µm leaving with the polymer at 10–20% and a continuous drug-rich layer at 30–40% yang2022a R10, R11, R12, R13; XPS surface ritonavir rising from 35 to 72% at 40% yang2022a R14.
Relation
first in the library to image the separation in dissolving compacts, in cross-section and in real time yang2022a C5; reconciles the solution route of Indulkar 2017 with water-induced separation at the gel–solution interface yang2022a C50, C51; carries the morphology link of Saboo 2021 and the 2022 clopidogrel paper from humidified films to dissolving compacts (synthesis).
Note
Findings: F1, F3, F5, F6, F7, F8, F18, F20, F25.
2022
yang2022bsurfactants and water-induced separation of ritonavir–PVPVASolid state stabilityextends
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].
SupportsF32 F31 F12 F22 F23
2023
bapat2023media choice for HPMCAS dispersions: buffer capacity, gel pH and releaseDissolutionconfirmsextends
Note
Known in the library (builds_on: Saboo 2020 on indomethacin, Hiew 2022 on lumefantrine polymers, Yang 2022 on release mechanisms, Nguyen 2023 on delamanid): polymer-controlled release in copovidone dispersions (Saboo 2020, Yang 2022); drug release linked to HPMCAS dissolution and the HPMCAS-MF pKa of 4.92 or 5.0 [bapat2023 M3]; HPMCAS solubility rising between pH 5.0 and 6.5 (Nguyen 2023, builds_on).
Added
the neat HPMCAS-MF rate rising about sixfold from 3 to 51 mM/ΔpH in pH 6.8 phosphate [bapat2023 R5]; FaSSIF equal to its blank buffer and no dissolution in FeSSIF V1 at pH 5.0 [bapat2023 R7, R8]; a gel layer only from 13 mM/ΔpH, 3 to 19 µm thick, with an apparent pH of 5.6–6.2 [bapat2023 R14, R15]; drug at the polymer's rate for 10% indomethacin and its methyl ester [bapat2023 R9, R13]; rate linear in the square root of rotation speed without a plateau [bapat2023 R18, R19]; the drugs lowering polymer release and water uptake [bapat2023 R20, C46].
Relation
extends the buffer-capacity result of Qi 2022 from HP-50 to HPMCAS and adds the gel pH [bapat2023 C51]; confirms polymer-controlled release for HPMCAS dispersions of acidic and neutral drugs [bapat2023 C49].
Note
Findings: F1, F2, F11, F15, F23, F24.
2023
correasoto2023plasticizers in PVPVA dispersions of high-Tg drugsDissolutionextends
Note
Known in the library (builds_on: Indulkar 2019, Que 2019, Saboo 2020 on indomethacin, Correa Soto 2022 on atazanavir): binary limits of 25% (ritonavir), 5% (ledipasvir) and 5% (atazanavir), cited [correasoto2023 R14, R11, R1]; the link between drug Tg and the limit (Saboo 2020, builds_on); surfactants raising the limit possibly by plasticization (Correa Soto 2022, builds_on).
Added
the atazanavir limit raised from 5 to 7.5–25% by 5 g per 100 g of nine plasticizers [correasoto2023 R1, C12]; ledipasvir from 5 to 15–20% with 10 g [correasoto2023 R11, C17]; ritonavir from 25 to 30% [correasoto2023 R14]; the Tg of 8:1 drug–plasticizer glasses lowered by 30–53 °C [correasoto2023 R17, R18]; neat PVPVA dissolving faster with GTB or TBC [correasoto2023 R13]; little change in water vapour uptake [correasoto2023 C34].
Relation
extends the vinylpyrrolidone test of Correa Soto 2022 to plasticizers that are not surfactants and to two more drugs [correasoto2023 C28]; the gain was largest for the highest-Tg drugs [correasoto2023 C21].
Note
Findings: F15, F16, F18, F21, F26.
2023
deac2023athe dissolution interface of two phenolphthalein analogues in PVPVADissolutionextends
Note
Known in the library (builds_on: Saboo 2017, Indulkar 2019, Que 2021, Deac 2023 on drug load): the prodan and rhodamine 6G dye pair for confocal imaging (Saboo 2017, builds_on); congruent release, the limit and the surface barrier; limits of 40% for MePHPH and 5% for PHPH [deac2023a R14]; the polymer-rich PHPH drug-rich phase and associative against segregative separation (Deac 2023 on drug load, builds_on).
Added
drug release at 30 min of about 96, 61, 15 and 0% for 20–70% MePHPH and 75 and 0% for 5 and 20% PHPH [deac2023a R1, R2]; drug piling up in the gel at 40 and 50% MePHPH [deac2023a R3]; gel thickness, water content and residence time [deac2023a R4]; in situ imaging of droplets within the gel up to 30% MePHPH, networks at 40% and inversion at 50%, and of PHPH particles beyond the gel at 5% and a network at 10–20% [deac2023a R6, R7, R8]; released drug-rich phases of 98.8 and 26.2 wt% drug [deac2023a R12]; porous drug-rich surfaces above the limit [deac2023a R9, R10].
Relation
extends the real-time imaging of Yang 2022 to two analogues of different limit and adds gel-layer measurements [deac2023a C71]; ties the polymer-rich PHPH phase to the lower loading at which the drug-rich phase connects [deac2023a C65].
Note
Findings: F1, F5, F6, F7, F8, F15, F17, F18, F19, F20, F25, F27.
2023
deac2023bdrug load and molecular interactions: polymer in the drug-rich phaseDissolutionfirst proposed
Dissolution Mechanisms of Amorphous Solid Dispersions: Role of Drug Load and Molecular Interactions
Note
Known in the library (builds_on: Indulkar 2019, Que 2019, Saboo 2020 on indomethacin, Que 2021, Ueda 2022): congruent release and the limit; the drug-rich surface layer of a PVPVA dispersion (Que 2019, builds_on); hydrogen bonding lowering the limit (Saboo 2020, builds_on); limits, interaction types and amorphous solubility with PVPVA of the four analogues deac2023b R8; entropy-driven polymer partitioning into drug-rich phases deac2023b C45.
Added
PVPVA lowering the amorphous solubility of PHPH from 200 to 27.5 µg/mL and raising that of MePHPH from 2.81 to 4.40 deac2023b R1; about 77, 36.5, 9 and 5 wt% PVPVA in the nanoparticles of PHPH, TIPP, MeTIPP and MePHPH, the reverse order of their limits deac2023b R3, R8; PVPVA moving into rather than out of PHPH particles above about 28% deac2023b R4, R5; compact surfaces drifting toward the drug-rich phase above the limit and constant below it deac2023b R6, R7; schematic ternary diagrams with plait points and the lever rule deac2023b C34, C48, C63.
Relation
first in the subcategory to measure where the polymer goes when the analogues separate deac2023b C26; proposes, on schematic diagrams, that associative separation lowers the limit deac2023b C63, X14; the interface paper of the same year builds on it.
Note
Findings: F7, F10, F17, F18, F27.
2023
hiew2023hierarchical co-precipitated particles of grazoprevir–HPMCASDissolutionfirst proposed
Note
Known in the library (builds_on: Bhardwaj 2018, Indulkar 2019, Saboo 2019, Li 2020, Yang 2021, Hiew 2022 on lumefantrine polymers): surface drug enrichment impairing release (Bhardwaj 2018, Li 2020) [hiew2023 C44]; polymer- against drug-controlled release, the limit and the drug-rich surface barrier [hiew2023 C35]; a sloped decline of release with loading in enteric-polymer dispersions (Hiew 2022, builds_on) [hiew2023 C36].
Added
solvent-evaporated dispersions falling from about 102% released at 5% to 27–30% at 50–75% [hiew2023 R8]; binary co-precipitates at 60 and 75% releasing 8–37.5% and wetting poorly [hiew2023 R10, R9]; HPMC or HPC dissolved in the anti-solvent raising release to 56–72% [hiew2023 R10, R12]; surface drug of at most 34% against at least 53% separating good from poor release [hiew2023 R14]; AUC 135 against 73 µM·h in dogs [hiew2023 R15].
Relation
first in the library to lower the surface drug of high-loading particles on purpose and to test the result in dogs [hiew2023 C47, C43]; carries the surface-composition result of Bhardwaj 2018 from spray-dried to co-precipitated particles (synthesis).
Note
Findings: F11, F14, F28.
2023
moseson2023aluminum oxide coating and release of posaconazole–HPMCAS particlesASD processcontradicts
Known before
coatings stabilize high-loading ASDs and lower water uptake with thickness (Van Duong 2022); 5–25 nm coatings inhibit surface crystallization without changing sorption (Moseson 2022); matrix crystallization of bicalutamide (Moseson 2022b) and the phase behaviour of posaconazole (Elkhabaz 2019; Duong 2022) (builds_on) [moseson2023 C3, C4].
Added
hot-melt-extruded posaconazole–HPMCAS at 25 and 50% loading, twelve samples with 11–39 nm Al2O3 grown at a slow, average or fast rate; water-uptake kinetics at 90% RH, release at pH 6.5 and after 30 min to 4 h at pH 1.6 or 4.0, SHG, SEM/EDX of particles incubated in buffer, and cryomilling of a blocked sample [moseson2023 P1, P3, P10, P13, P14, P15].
Relation
contradicts the expectation that a coating slows release (it did not at 25% loading) and proposes water entry and cracking as the reason; reconciles the sorption disagreement of 2022 through kinetics and defects; first blocked sample, linked to a slow deposition rate [moseson2023 C58, C48, C50, C51].
SupportsF42 F45 F46 F47 F27
2023
nguyen2023apretomanid dispersions in fed and fasted monkeysBioperformance
Fed- and Fasted-State Performance of Pretomanid Amorphous Solid Dispersions Formulated with an Enteric Polymer
Known before
the reduced glass transition temperature and class I crystallization tendency (Baird 2010; Van Eerdenbrugh 2010), the extinction and induction-time methods (Ilevbare 2013), HPMCAS dissolving only above a threshold pH (Hiew 2022), polymer salts from added bases (Qi 2022) and pH-shift and gastric-immersion tests for delamanid (Duong 2022; Nguyen 2023) (builds_on) nguyen2023a C26, C59, C63, M3.
Added
crystallization of the neat glass and of solutions, six polymers, blends, surfactants and eight bases, tablets in fasted and fed media and monkey exposure fasted and fed nguyen2023a R1, R5, R12, R14, R19, R22, R23.
Relation
carries the chapter's logic to a drug that crystallizes in minutes; in vitro gains did not carry over, and food reversed the ranking of dispersion and crystalline product nguyen2023a C57, C73, C53.
SupportsF10 F26 F27
2023
nguyen2023benteric coating on a delamanid dispersion tabletDissolutionfirst proposed
Enteric coating of tablets containing an amorphous solid dispersion of an enteric polymer and a weakly basic drug: A strategy to enhance in vitro release
Note
Known in the library (builds_on: Nguyen 2023 on gastric pH, Van Duong 2022, Elkhabaz 2019, Schram 2016): delamanid dispersions crystallize at their surfaces at gastric pH and release less afterwards, salt forms did not cure it, posaconazole dispersions crystallized in gastric fluid, and enteric polymers inhibit crystallization where they dissolve nguyen2023b R19, C11, R20, C36.
Added
a 14–16% Acryl-EZE II coat cut gastric release below 0.5% and gave ≈76–86 µg/mL after every gastric pH, against ≈0.3–93 µg/mL uncoated; a 2 µm Eudragit L 100-55 layer prevented the surface crystals on dispersion films; the coat failed after about 130–150 min at pH 4.5–5.0 in buffer but lasted more than 17 h in a fed gastric medium; food components raised delamanid solubility up to 57.97 µg/mL and the release of the marketed tablet nguyen2023b R10, R2, R6, R7, R13, R14.
Relation
first in the library to coat a tablet of a dispersion made with an enteric polymer; remedies the gastric-pH dependence that the companion paper mapped.
Note
Findings: F27, F24, F25, F28, F19.
2023
nguyen2023cgastric pH, polymer grade and drug formDissolutionextends
Impact of Gastric pH Variations on the Release of Amorphous Solid Dispersion Formulations Containing a Weakly Basic Drug and Enteric Polymers
Note
Known in the library (builds_on: Van Duong 2022, Elkhabaz 2019, Li 2016, Li 2018, Almeida e Sousa 2016): the delamanid salt dispersions and their polymer screen, matrix crystallization in a gastric stage, drug leaching from enteric dispersions in acid, suppression of the ceiling by an undissolved polymer, and disproportionation of salts that are not stable in the medium.
Added
final release from ≈0 to 101% across three gastric pH values, five enteric grades and two drug forms; polymer release that does not track drug release; a gastric supersaturation ratio rising from ≈0.9–3.8 at pH 1.6 to ≈11–42 at pH 5.0 that does not predict release; conversion of the neat amorphous salt to crystalline free base within 5 min at pH 1.6; surface crystals on films and powders after 1 h in acid, more with HPMCAS nguyen2023c R11, R12, R13, R14, R19.
Relation
extends the gastric-stage crystallization of Elkhabaz 2019 across polymer grades and gastric pH, and the salt dispersions of Van Duong 2022 to a pH grid; rules out the solution route in acid.
Note
Findings: F25, F24, F1, F2, F8, F10, F16, F18, F19, F23.
2023
yang2023surfactants in ritonavir–PVPVA dispersions and the drug-rich barrier at the dissolving interfaceDissolutionfirst proposedconfirms
Drug Release from Surfactant-Containing Amorphous Solid Dispersions: Mechanism and Role of Surfactant in Release Enhancement
Note
Known in the library (builds_on: Purohit 2017, Indulkar 2019, Li 2019, Que 2019, Saboo 2021, Correa Soto 2022 on clopidogrel, Yang 2022 on release mechanisms, Yang 2022 on surfactant-containing dispersions): the binary ritonavir–PVPVA limit of 25% and its release yang2023 R1; discrete drug-rich domains released and a continuous layer blocking release at the dissolving interface yang2023 R25, C39; surfactants raising the limit of ledipasvir, felodipine and clopidogrel yang2023 R27; Span partitioning into the drug-rich phase and lowered Tgs of the same four ternary dispersions under water vapour yang2023 R24.
Added
release at 30–50% with 10 parts of SDS, Tween 80, Span 20 or Span 85 (about 50–97% at 30%, 1–57% at 40%) yang2023 R2; confocal images of the interface of ten ternary compacts after partial dissolution and in situ yang2023 R6, R7, R8, R9, R10, R12, R13, R14; the water needed for separation (14.0% without, 24.5% with SDS) yang2023 R21; Tg of ritonavir–Span mixtures yang2023 R22; SDS covering the dissolved surface and needle crystals at 30% yang2023 R17, R16.
Relation
first in the library to image the interface of surfactant-containing dispersions in water yang2023 C1; confirms the barrier picture of the 2022 interface study for ternary dispersions and adds that a layer must persist under flow to block release; confirms the SDS-related surface crystals of the 2022 surfactant study yang2023 C40, R8, C51.
Note
Findings: F3, F6, F8, F15, F16, F19, F20, F21, F25, F26, F30, F31.
2024
bapat2024drug charge and insoluble drug–HPMCAS complexesDissolutionfirst proposed
Interplay of Drug−Polymer Interactions and Release Performance for HPMCAS-Based Amorphous Solid Dispersions
Note
Known in the library (builds_on: Indulkar 2019, Saboo 2020 on five polymers, Hiew 2022 on lumefantrine polymers, Bapat 2023, Deac 2023 on drug load, Nguyen 2023): congruent release and the limit bapat2024 C2; the gradual decline of HPMCAS release with loading bapat2024 C3; ionic drug–polymer interactions proposed to slow enteric polymer dissolution (Hiew 2022, builds_on) bapat2024 C5; the HPMCAS gel pH of 6.0 in 50 mM pH 6.8 phosphate bapat2024 R20; the insoluble PHPH–PVPVA complex bapat2024 C41.
Added
drug and HPMCAS-MF release of eight drugs of different charge at 5–60% bapat2024 R2, R3, R4; the polymer slowed 1.6- to 30-fold by weak bases, most where ionized bapat2024 R5; complexation of HPMCAS at pH 6.0 (5–17% against 60–90%), with drug:COOH ratio, pH and ionic strength bapat2024 R12, R11, R13, R16; a loratadine dispersion releasing faster at pH 7.5 than 6.8, the reverse of the neat drug bapat2024 R4, R7; release on two trendlines against complexation bapat2024 R14.
Relation
first in the library to measure drug–HPMCAS complexes across drug charge and to set them against release bapat2024 C6; limits the gradual HPMCAS pattern of the 2020 five-polymer study to drugs that do not complex the polymer (synthesis).
Note
Findings: F1, F2, F9, F11, F15, F17, F23, F24, F32.
2024
deac2024apolymer molecular weight and a new failure modeDissolutionfirst proposedextends
Note
Known in the library (builds_on: Indulkar 2019, Que 2020, Que 2021, Yang 2022 on release mechanisms, Deac 2023 on the interface, Deac 2024 on ternary phase diagrams): congruent, polymer-controlled release and the limit [deac2024a C5]; drug–polymer interactions and drug Tg lowering the limit [deac2024a C2]; dispersed droplets against a continuous drug-rich phase in the gel layer, here named Failure Mode II [deac2024a C9]; clotrimazole forming no strong interactions with PVP [deac2024a C10].
Added
clotrimazole limits with six PVP grades, below 5% to about 38%, near the computed entanglement weight of 46,620 g/mol [deac2024a R12, E1]; droplet agglomeration in films and at the dissolution front of short-chain compacts [deac2024a R7, R10]; inversion between 30 and 40% and unchanged phase compositions for two grades [deac2024a R8, R11]; no droplet stabilization by PVP in dilute suspension [deac2024a R5].
Relation
first in the library to vary the polymer grade and to describe failure by droplet agglomeration in the gel ("Failure Mode I") [deac2024a C54]; extends the interface picture of 2022–2023 to a failure in which the droplets are discrete when they form (synthesis).
Note
Findings: F1, F2, F3, F4, F6, F8, F15, F16, F20, F25, F29, F30, F31.
2024
deac2024bternary phase diagrams and the limit of congruencyDissolutionfirst proposed
Dissolution Mechanisms of Amorphous Solid Dispersions: Application of Ternary Phase Diagrams To Explain Release Behavior
Note
Known in the library (builds_on: Indulkar 2019, Que 2021, Yang 2022 on release mechanisms, Deac 2023 on the interface, Deac 2023 on drug load): the limit and the cliff deac2024b C1; a continuous drug-rich phase in the gel above the limit deac2024b C2; strong interactions and high drug Tg lowering the limit deac2024b C4; limits and interaction ranks of the four analogues deac2024b R39; polymer partitioning into the drug-rich phases of the analogues deac2024b C5.
Added
measured drug–PVPVA–water diagrams of PHPH and MePHPH at 37 °C, with associative and segregative tie lines deac2024b R15, R17, R22, R23; PC-SAFT diagrams and critical points of all four analogues deac2024b R35, R37; the water that separates MePHPH–PVPVA (under 15 wt%) deac2024b R1, R2; the switch from droplets to a network in films deac2024b R18, R19; Tgs of the hydrated phases deac2024b R29, R30.
Relation
first in the library to measure and compute the phase diagrams of dispersions and to compare the critical-point loading with the limit deac2024b C59; tests the plait-point hypothesis of the 2023 drug-load paper, confirming its order and missing the PHPH film switch deac2024b X5.
Note
Findings: F6, F8, F17, F18, F20, F25, F27, F30.
2024
polyzois2024praziquantel dispersions, racemate and enantiomerDissolutionfirst proposed
Amorphous Solid Dispersion Formation for Enhanced Release Performance of Racemic and Enantiopure Praziquantel
Note
Known in the library (builds_on: Sato 2015, Indulkar 2019, Saboo 2020, Trasi 2015 on dispersions): cellulose polymers inhibit crystallization of two enantiomers to different extents, release can fall sharply above a threshold drug loading or decline gradually when the polymer controls it polyzois2024 C28, C16, C17.
Added
a seven-polymer screen that chose HPMCAS-MF and HPMC E5 LV for the racemate and found both much weaker for the R-enantiomer (37 and 15.5 min against at least 83 min); complete release up to 40–50% drug at 667 µg/mL and a gradual decline at 1.5 mg/mL without a cliff; hot-melt extrusion at least as good as solvent evaporation; commercial tablets at most 16% polyzois2024 R3, R4, R8, R9, R11, R14.
Relation
first in the library on a dispersion of a single enantiomer; carries the chiral polymer effect of Sato 2015 from melt growth into solution and release.
Note
Findings: F29, F4, F6, F10, F25.
2024
shah2024residual crystallinity in posaconazole–HPMCAS dispersions and phase behaviour during releaseASD processconfirmsextends
Orthogonal Analytical Methods to Elucidate How Low Levels of Residual Crystallinity in Posaconazole Amorphous Solid Dispersions Impact Phase Behavior during Release
Known before
the pH-shift design, SHG imaging in media and the loading dependence of posaconazole–HPMCAS crystallization (Elkhabaz 2019); phase-diagram-guided extrusion temperatures (Moseson 2018); seed properties and the low-risk indomethacin case (Moseson 2020a); lower absorption from partly crystalline tacrolimus (Purohit 2018, 2019) (builds_on) shah2024 C2, C21, R24, R26.
Added
PCZ–HPMCAS MF at 10, 25 and 50% loading extruded for 2 min at 125 and 175 °C; pXRD, SHG and two-photon UV fluorescence; a two-stage test at about 10 times the amorphous solubility followed by focused beam reflectance; seeded solutions with and without HPMCAS shah2024 P5, P6, P7, P11, P13, P14, P15, P16.
Relation
confirms the temperature rule of F8–F9 on a third pair (with a positive χ) and extends F10 (SHG finds 0.3% that pXRD misses); places posaconazole in the high-risk class of F29, contrasting with indomethacin–PVPVA (Moseson 2020a), and extends F25 to posaconazole in FaSSIF shah2024 C56, C21, R22, R26.
SupportsF41 F8 F9 F10 F25 F27 F29 F35
2025
alvarenga2025praziquantel dispersions across mediaDissolutionconfirmsextends
Release performance and crystallization of racemic and enantiopure praziquantel amorphous solid dispersion in various media
Note
Known in the library (builds_on: Polyzois 2024, Elkhabaz 2021, Ilevbare and Taylor on the LLPS onset method): the praziquantel polymer choice and the enantiomer's shorter induction time, longer induction times in buffer than in simulated intestinal fluid for posaconazole and atazanavir, and the light-scattering onset as the amorphous solubility alvarenga2025 C25, C18, P7.
Added
amorphous solubility 4.0–7.7 times the crystalline one across nine media and nearly independent of pH for a neutral drug; HPMCAS dispersions that recovered to ≈92–103% after pH 1.6 but only ≈62–77% after pH 3.0 or 5.0; HPMC dispersions that released fast at any pH and crystallized, shown by polarized light and PXRD; a fed intestinal medium that defeated both polymers (≈34–52% at 1.5 mg/mL); an enantiomer advantage limited to simple buffer alvarenga2025 R1, R7, R10, R20, R27, R18, R8.
Relation
confirms and extends Polyzois 2024 across media and adds the fed-state failure; relates the medium effect to the nucleation work of the crystallization-from-solution chapter.
Note
Findings: F28, F29, F25, F10.
2025
bapat2025aHPMCAS grade and the release of weak basesDissolutionfirst proposedextends
Impact of HPMCAS Grade on the Release of Weakly Basic Drugs from Amorphous Solid Dispersions
Note
Known in the library (builds_on: Hiew 2022 on lumefantrine polymers, Bapat 2023, Bapat 2024): the titration method and critical ionization model for enteric polymers, and the MF acid content and pKa bapat2025a C2, M4; MF release and rate data and the surface pH of 6.0 bapat2025a R15, X7; hydrophobic ion pairs of weak bases with HPMCAS-MF and the complexation test bapat2025a C5.
Added
neat rates of HPMCAS LF, MF and HF bapat2025a R1; release of 25% loratadine and cinnarizine from the three grades at pH 6.8 and 7.5 bapat2025a R2, R3; titrated acid contents and pKa bapat2025a M3, M5, R8; complexation by grade, ratio and pH bapat2025a R9, R11, R12.
Relation
first in the library to compare HPMCAS grades for release of weak bases bapat2025a C24; extends the 2024 complexation result from one grade to three.
Note
Findings: F1, F2, F4, F11, F15, F19, F23, F24, F32, F33.
2025
bapat2025bpeptide and enhancer release from copovidone dispersionsPeptide permeabilityfirst proposed
Modification of Peptide and Permeation Enhancer In Vitro Release Rates by Dispersion with a Gel-Forming Polymer
Known before
through this paper's own citations, congruent release of drug and polymer from copovidone dispersions of lipophilic small molecules, the polymer setting the rate, together with the copovidone gel layer of over 200 µm and the rat evidence that synchronized release of a drug with sodium decanoate improves absorption bapat2025b C9, R29, R27.
Added
the measurement that the problem exists — neat octreotide, SNAC and copovidone dissolve at ≈4.5, ≈1.8 and ≈3.2 mg min⁻¹ cm⁻², and neat amorphous cyclosporine not at all — and then that dispersing peptide and enhancer in copovidone at 1.6% peptide loading puts all assayable components on one rate, ≈8.1–8.9 with SNAC and ≈23–25 with sodium decanoate, each above the neat value bapat2025b R2.a–c, R14, R2.f–h, R2.j–k.
Relation
first proposes, for a peptide, that erosion of the polymer gel layer controls all components and that the enhancer and the polymer accelerate each other through the higher water sorption of their blend, neither of which it measures bapat2025b C45, C48, X6, X5. It also sets the boundary: from 5% cyclosporine loading the peptide decouples from the polymer bapat2025b C22.
SupportsF1 F4 F5 F6
2025
benson2025coated ritonavir–PVPVA dispersions: hydration, release and formulationASD processextends
Known before
the coating method, slow coating as a better barrier and the HPMCAS results (Moseson 2023); the stability benefit and the rescue of a conformally coated sample by defects (Moseson 2022); the 25% limit of congruency and phase separation in hydrating ritonavir–PVPVA (Indulkar 2019a; Purohit 2017b; Yang 2022) (builds_on) [benson2025 C3, C12, C17].
Added
ritonavir–PVPVA at 10 and 20% loading by extrusion (and one dye-containing rotary-evaporated powder), nine samples with 9.3–28.3 nm Al2O3; powders and 50 mg tablets at pH 6.8 and in 0.1 N HCl; confocal imaging of particles and tablet edges; disintegrants and formulated tablets [benson2025 P1, P2, P5, P11, P13].
Relation
extends moseson2023 from a non-gelling polymer to a gelling one: defects govern powder release, and in tablets the coating costs release at pH 6.8 unless disintegrants and dilution offset it; first coated-ASD tablets, which describes a lower effective limit of congruency [benson2025 C21, C31, C34, C59].
SupportsF42 F45 F46 F47 F48 F49
2025
fagan2025insulin minitablets with permeation enhancers in biorelevant mediaPeptide permeabilityconfirmsextendscontradicts
Impact of Permeation Enhancers on the Release of Insulin from Tablets in Biorelevant Media
Known before
from its own citations, that SNAC raises the pH of its surroundings at the concentrations found at a tablet surface, that both enhancers are weak-acid salts of pKa about 5, and that peptide solubility is lowest at the isoelectric point, insulin's being about 5.3; how a high enhancer load changes release from a tablet was the stated gap fagan2025 C9, R21.
Added
the pH that an excess of each enhancer produces in each simulated fluid (7.6–9.2, whatever the starting pH), insulin's solubility at exactly those pH values (14.0 and 23.7 mg/mL against 0.1 in blank FaSSIF) and the release from three minitablets in six media fagan2025 R5, R1, R2, R8, R9, R12, R13.
Relation
extends the cited pH effect from SNAC to sodium caprate and from gastric to intestinal fluids, and adds a result the other paper could not see, that peptide and enhancer leave an enhancer-dominated tablet at staggered times, about 30 min against about 10–20 min fagan2025 C9, C11, R20. It neither confirms nor contradicts the gel-layer mechanism, because it contains no gel-forming matrix and holds its peptide at 3% throughout fagan2025 P3.
SupportsF1 F2 F3 F6
2025
hiew2025surface composition and wettability of high-loading particlesDissolutionfirst proposedrevises
Note
Known in the library (builds_on: Indulkar 2019, Deac 2023 on the interface, Deac 2023 on drug load, Hiew 2023): the release decline above a threshold loading in copovidone [hiew2025 C4]; a hydrophobic continuous phase blocking release [hiew2025 C4]; the hierarchical co-precipitation method and 70% grazoprevir particles with HPMC diluting the surface [hiew2025 R22, C7].
Added
release of 75% grazoprevir–HPMCAS particles with seven secondary excipients [hiew2025 R9]; FaSSIF contact angles splitting good from poor materials [hiew2025 R15, R17]; XPS surface drug of 32–50% for good and poor alike [hiew2025 R14]; de-agglomeration by sonication and sieving [hiew2025 R13, R11]; high-shear treatment of a 75% solvent-evaporated dispersion [hiew2025 R10].
Relation
first in the library to screen secondary excipients against wettability [hiew2025 C40]; revises the surface-drug reading of the 2023 study: among diluted surfaces wettability, not surface drug content, separated good from poor release [hiew2025 C35].
Note
Findings: F11, F14, F28, F35.
2025
kaur2025bedaquiline–HPMCAS complexation and biorelevant mediaDissolutionfirst proposedextends
Impact of drug-polymer complexation and media properties on the release performance of amorphous solid dispersions containing a weakly basic drug and hydroxypropyl methylcellulose acetate succinate
Note
Known in the library (builds_on: Duong 2022, Hiew 2022 on lumefantrine polymers, Bapat 2023, Nguyen 2023, Bapat 2024, Bapat 2025): ionic weak base–HPMCAS interactions impeding release kaur2025 C3; the gel pH of HPMCAS-MF and media effects on HPMCAS release kaur2025 R22; insoluble complexes of lipophilic cationic drugs with HPMCAS kaur2025 C3; delamanid dispersions without a biorelevant-media effect, as a contrast kaur2025 C52.
Added
bedaquiline–HPMCAS LF and MF complexation at pH 5.8–10.5 and in FaSSIF-V1 and FeSSIF-V2 kaur2025 R5, R6, R7, R8; drug protonation in the complex and in a dry dispersion by XPS kaur2025 R20; release in buffers after a pH shift and in three biorelevant fluids kaur2025 R12, R13, R15, R16, R17; amorphous residues and induction times with polymer kaur2025 R14, R18.
Relation
first in the library to measure drug–polymer complexation in simulated intestinal fluids kaur2025 C57; extends the complexation results of 2024–2025 to a drug of pKa 8.5 and shows that micelles change release where FaSSIF changed nothing for non-complexing drugs in 2023 (synthesis).
Note
Findings: F1, F16, F19, F23, F24, F32, F33, F34.
2025
shah2025HPMCAS grade and ionization with posaconazoleDissolutionextends
Chemistry and ionization of HPMCAS influences the dissolution and solution-mediated crystallization of posaconazole amorphous solid dispersions
Known before
the ultracentrifugation method for the LLPS concentration, the UV-extinction induction-time method, posaconazole fluorescence and HPMCAS delaying posaconazole crystallization, polymer-controlled dissolution with an HPMCAS pKa of about 4.9, the pH-dependent ionization and solubility of the HPMCAS grades, and posaconazole as a fast crystallizer (builds_on) shah2025 P3, P4, C5, M2, C4.
Added
posaconazole at pH 5.5, 6.5 and 7.5 in FaSSIF-V2 buffer with HPMCAS L, M and H: LLPS concentrations with 900 µg/mL polymer, induction times at 10 µg/mL with 90 µg/mL polymer, fluorescence below and above the LLPS concentration, droplet size, ζ-potential and polymer depletion into the droplets, and release from 10 and 25 wt% dispersions shah2025 R2, R3, R9, R11, R15, R16, R4, R5.
Relation
extends the carboxylate and pH results of 2012–2016 above the polymer pKa, where, unlike at pH 3–3.8, more ionization weakened HPMCAS; against wilson2021, the grade that entered the droplets most (H) inhibited best shah2025 C13, C14, C51.
SupportsF2 F3 F11 F15 F19 F23 F26 F35 F37 F44
2026
alkalla2026a crystalline co-drug lowers the ceiling of an amorphous drugBioperformanceextends
Coadministration of a crystalline drug compromises supersaturation and membrane transport of an amorphous drug
Known before
LLPS by light scattering (Ilevbare 2013), the flux plateau (Raina 2014), the antisolvent method (Sousa 2015), a second drug lowering the ceiling and the side-by-side method (Trasi 2015), mutual loss in amorphous drug pairs (Alhalaweh 2016) and nanoTA for local miscibility (Li 2016) (builds_on) alkalla2026 C7, C11, C12, C16.
Added
atazanavir ASD dissolution with and without darunavir hydrate, flux in diffusion cells and Caco-2 monolayers, darunavir added stepwise to atazanavir solutions, and DSC and nanoTA of the dry mixtures alkalla2026 R7, R9, R11, R13, R15, R17.
Relation
extends the amorphous drug pair of alhalaweh2016 to a crystalline co-drug that dissolves into the drug-rich phase, although the dry drugs stay apart alkalla2026 C4, C31, C37.
SupportsF6 F20

01Links between findings of different categories

same mechanism · 38conditions differ · 18builds on · 17extends · 9

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Pairs are written once. The direction runs from the finding that needs the other, or whose papers are later, to the finding that supplies its basis, data or caution. The seven parts are Solid state stability, ASD process, Characterization methods, Dissolution, Bioperformance, Mesoporous silica and Peptide permeability. For Solid state stability, Characterization methods and Dissolution the link goes to the category finding, and to a chapter finding only where no category finding covers the point. Relations: builds on, explains, extends, same mechanism, conditions differ, contradicts. Citation keys are in sources.md. Reasoning that goes beyond the cited findings is marked (synthesis).

from	to	relation	why
Bioperformance F1	Dissolution F1	builds on	The onset used as the working ceiling equalled the amorphous solubility predicted from melting enthalpy and water sorption for felodipine (6.01 against 5.99 µg/mL at 25 °C) raina2014a R16, the agreement found for 17 of 24 rows of solvent-shift solutions ilevbare2013a R8; almeidaesousa2015 R5, R11; mosqueragiraldo2015 R13.
Bioperformance F2	Dissolution F1	same mechanism	The flux plateau of felodipine, nifedipine and clotrimazole raina2014a R11, R12, R14; indulkar2016 R9 is the membrane read-out of the level at which the dissolved drug and flux of telaprevir, ritonavir, lopinavir and paclitaxel stopped rising mosqueragiraldo2015 R10, R12; trasi2015a R2, R1.
Bioperformance F3	Dissolution F2	same mechanism	At c/c* of about 4.1–4.5 felodipine flux was 0.052 in buffer, 0.085 in FaSSIF and 0.138 µg/min with TPGS raina2015c R12, as in SDS the concentration ratio of atazanavir understated its activity ratio indulkar2017a R11, R13.
Bioperformance F4	Dissolution F12	same mechanism	Solubilizers moved the felodipine LLPS onset from 10.4 to 177.3 and 214.6 µg/mL at the same maximum flux raina2015c R11, as micellar dihydroxy bile salts doubled both solubilities of telaprevir at unchanged activity boundaries lu2017b R1, R2.
Bioperformance F5	Dissolution F5	conditions differ	Under a sink, droplets held the clotrimazole flux at its peak for up to at least 13 h indulkar2016 R5, R6, R7; in a closed vessel crossing the enzalutamide amorphous solubility cut the induction time with HPMCAS from about 129 to 43 min wilson2021 R3.
Bioperformance F6	Dissolution F3	same mechanism	The free concentration of ritonavir and atazanavir fell linearly with mole fraction in two-drug dispersions alhalaweh2016 R12, R13, E7, R17, as lopinavir, paclitaxel or felodipine lowered the ritonavir onset to about 14, 10 and 12 µg/mL trasi2015a R7, R9, R11.
Bioperformance F7	Dissolution F3	same mechanism	The drug-rich pellet of the cellulose acetate suberate system held a polymer fraction of 0.90 against 0.21–0.27 mosqueragiraldo2018b R13, R14; dissolved HPMC and PVP-VA lowered the amorphous solubility of ibuprofen from 177.1 to 96.9 and 90.7 µg/mL ueda2020b R1.
Bioperformance F19	Dissolution F3	same mechanism	HPMCAS-HF lowered the amorphous solubility of atazanavir from 81.5 to 35.5 µg/mL ueda2020a R1, the grade effect of the polymer-in-the-drug-rich-phase mechanism shown with dissolved HPMC and PVP-VA ueda2020b R1.
Bioperformance F20	Dissolution F3	extends	A crystalline co-drug, darunavir hydrate, lowered the atazanavir ceiling and flux alkalla2026 R9, R11, where the category had shown the effect for amorphous or dissolved second drugs trasi2015a R7, R9, R11.
Bioperformance F8	Dissolution F7	same mechanism	Only the three 10% atazanavir dispersions exceeded the amorphous solubility hate2018 R11; the release chapter places such a switch at the limit of congruency, ritonavir–PVPVA releasing ≈97% at 25% and ≈29% at 30% indulkar2019a R11, C2, C31.
Bioperformance F9	Dissolution F4	same mechanism	The 50% telaprevir–HPMCAS particles showed birefringent domains at 20 min while HPMCAS left ahead of the drug mosqueragiraldo2018b R16, R18, R19; wetted nifedipine and celecoxib crystallized with or without polymer in the medium raina2014b C11, R2; xie2015 R9, R10.
Bioperformance F9	Dissolution F6	same mechanism	5% SDS in the telaprevir dispersion sped release but the concentration fell later at a higher dose mosqueragiraldo2018b R16, R17, as SDS raised the ledipasvir limit of congruency que2019 R7, R8, R9, C12 and brought crystals to ritonavir compacts yang2023 R21, R13, R2, R16, R17.
Bioperformance F10	Crystallization tendency F18	builds on	Nifedipine crystallized below the LLPS onset that felodipine passed raina2014a R1, R5, C30, C31, the solution test of the melt classes, which carried over only partly raina2014a R20, C31; raina2015b C13, C28.
Bioperformance F11	Dissolution F12	conditions differ	For ezetimibe PVP was best in buffer and HPMC-AS in FeSSIF elkhabaz2017 R6, R7; for atazanavir FaSSIF-V1 gave the shortest and human fluid the longest induction time elkhabaz2021 R6, R7.
Bioperformance F12	Characterization methods F5	extends	SHG found the first ezetimibe crystals in turbid buffer, FeSSIF and Ensure Plus as the concentration fell elkhabaz2017 R9, R13, R14, R18, R22, after SHG had dated crystallization of spray-dried powders weeks before XRPD correasoto2017 R1, R8.
Bioperformance F15	Dissolution F1	conditions differ	In the hollow-fibre module atazanavir transfer kept rising above the amorphous solubility at a lower slope (5.51 to 1.29) hate2018 R9, E3, E4, where side-by-side flux stopped rising mosqueragiraldo2015 R10, R12; trasi2015a R2, R1.
Bioperformance F16	Solid state stability F11	builds on	The generic that crystallized to 88% in 3 weeks of open storage trasi2017 R12, R18, R19 was the capsule whose crystallinity compendial tests barely registered and 100 mL tests separated purohit2018 R5, R7.
Bioperformance F18	Dissolution F2	same mechanism	The flux-based maximum supersaturation of atazanavir stayed at about 50–56 in six media while the concentration ratio fell elkhabaz2019b R8, R9, the activity argument of indulkar2017a R11, R13.
Bioperformance F22	Dissolution F5	extends	With a sink receiver PAMPA mass flow kept rising with droplet number from about 5.0 to 8.8 µg/min hate2022 R19; with crystals present a posaconazole dispersion held its amorphous solubility only while droplets remained elkhabaz2019a R6, R12, C47, C48.
Bioperformance F23	Dissolution F1	builds on	The enzalutamide dispersions that reached the amorphous solubility beat crystals in rats (p < 0.05) wilson2018 R18, R6, C47, the ceiling that dispersions and marketed capsules reach but do not exceed trasi2016 R10, R4, R15, R14.
Bioperformance F24	Dissolution F9	extends	The best of 24 enzalutamide solution inhibitors gave a dispersion like crystals in rats wilson2020 R1, C32, R6; a solution screen ranked dispersion dissolution only in order jackson2015 R5, X8; xie2015 C48.
Bioperformance F26	Dissolution F11	extends	Pretomanid particles held crystalline drug below FeSSIF pH 5.8 and the dispersion lost exposure with food nguyen2023a R19, R1, R20; in acid undissolved enteric dispersions of posaconazole and delamanid crystallized elkhabaz2019a R10, R1, R16, R20; nguyen2023c R19, R20.
Bioperformance F26	Dissolution F10	same mechanism	The HPMCAS-HF tablet released only to the crystalline solubility at pH 5.5 and below nguyen2023a R19, R1, R20; HPMCAS-HF released only about 22–31 µg/mL of posaconazole at pH 6.5 shah2025 R3, R4, R5.
Bioperformance F27	Crystallization tendency F17	builds on	Pretomanid and delamanid were placed in class I with reduced Tg 0.67 and 0.64 nguyen2023a C59, the neat-drug class used as a first risk flag baird2010 C46; vaneerdenbrugh2010b C1.
Bioperformance F27	Dissolution F6	conditions differ	TPGS lifted pretomanid release in vitro but not exposure in monkeys nguyen2023a R12, R14, R8, R23; built-in surfactants raised the limits of congruency of felodipine, clopidogrel and atazanavir saboo2021 R12; correasoto2022a R17, R18; correasoto2022b R2, R4.
Bioperformance F28	Dissolution F4	same mechanism	Only at 40 mL did the 20% crystalline tacrolimus capsule lose dissolved drug during the test hate2019 R10, R11, as seeds left HPMCAS-held paclitaxel at 7.9–25.3 µg/mL que2018 R3, R13, R14.
Bioperformance F30	ASD process F26	conditions differ	A capsule that crystallized in storage gave about four times the exposure of reference crystals in dogs purohit2019 R9, while in vitro residual crystals cost more than bulk seeds of larger mass moseson2020a R9, R10; the origin of the crystals changes the result in both (synthesis).
Mesoporous silica F3	Dissolution F1	conditions differ	Adsorption onto SBA-15 rose steeply as ritonavir approached its amorphous solubility, keeping the solution below it dening2019 R2, R1, whereas dissolving amorphous films and dispersions reached it indulkar2015 R18, F6; ilevbare2013a R17, R8, R13.
Mesoporous silica F4	Dissolution F2	same mechanism	On an activity scale the silica isotherms of indomethacin and its methyl ester nearly coincide mccarthy2020 R12, C24, as only the activity scale compares atazanavir supersaturation across SDS levels indulkar2017a R11, R13.
Mesoporous silica F6	Dissolution F10	same mechanism	Weak bases still charged at the test pH bound the negatively charged silica electrostatically hate2020b R3, R4, R5, C28, as lipophilic weak bases ionized at the gel pH took 70–96% of HPMCAS out of solution bapat2024 R12; kaur2025 R5, R13, R14; both are attraction of a cationic drug to an anionic surface or polymer (synthesis).
Mesoporous silica F7	Dissolution F1	conditions differ	Silica stopped at about a third to a half of the dose with the residue amorphous dening2018 R6, R19; mccarthy2020 R20, R21, R23, whereas six marketed tacrolimus capsules reached the amorphous solubility trasi2016 R10, R4, R15, R14.
Mesoporous silica F8	Bioperformance F2	builds on	Mass flow from ritonavir–SBA-15 reached that of amorphous ritonavir only at the tenfold dose dening2018 R8, measured with the diffusion-cell method of the flux plateau raina2014a R11, R12, R14.
Mesoporous silica F8	Dissolution F2	same mechanism	Dissolution sampling from silica gave lower free-drug percentages than flux dening2018 R24, C22, C36, as in situ UV and filtration misread dispersions against flux alonzo2011 R1, R14, R15; jackson2015 R2, R9.
Mesoporous silica F11	Dissolution F7	conditions differ	Silica loading above the calculated monolayer lowered ritonavir mass flow dening2018 R27, R4; in polymer dispersions the threshold is the limit of congruency indulkar2019a R11, C2, C31.
Mesoporous silica F12	Bioperformance F3	conditions differ	Vit E TPGS raised ritonavir release from silica by competing for silanols dening2019 R17, R18, C55, whereas in polymer-free solutions solubilizers above their CMC lowered felodipine flux raina2015c R4, R7.
Mesoporous silica F12	Dissolution F6	same mechanism	Both Vit E TPGS release media crystallized between 30 and 45 min dening2019 C34, as TPGS and Tween 80 below their CMC sped ritonavir growth ilevbare2012a R17, R1.g, M17.
Mesoporous silica F13	Dissolution F11	conditions differ	After a shift to pH 6.8 charged bases re-adsorbed onto silica and lost about 30 points hate2020b R10, R11, R13, while pazopanib from a salt formed non-crystalline colloids that held the intestinal amorphous solubility sugihara2018 R8, R11, R12, R15, R20.
Mesoporous silica F14	Bioperformance F14	same mechanism	An absorptive sink nearly doubled atazanavir release from silica hate2020a R20, as it raised total release of 50% atazanavir dispersions hate2018 R18.
Mesoporous silica F14	Bioperformance F13	builds on	The atazanavir silica runs used the hollow-fibre module hate2020a R20, C49, which moved nevirapine about 28 times faster than a side-by-side cell hate2017 R3.
Mesoporous silica F15	Bioperformance F5	conditions differ	Silica stays below the ceiling and forms no reservoir, giving about half the flux of an HPMC dispersion hate2020a R24, R25, C37; dening2018 C43; droplets of a dispersion held clotrimazole flux at its maximum indulkar2016 R5, R6, R7.
Mesoporous silica F15	Bioperformance F8	builds on	The comparison dispersion was the 10% HPMC dispersion of atazanavir hate2020a R24, R25, the loading at which only the cellulosic dispersions exceeded the amorphous solubility hate2018 R11.
Peptide permeability F2	Bioperformance F3	conditions differ	Excess C10 or SNAC raised the medium to pH 7.6–9.2, where insulin is 140–240 times more soluble fagan2025 R5, R1, R2; for small molecules solubilizers that raise solubility lowered the flux at a fixed concentration raina2015c R4, R7; whether the extra peptide is free was not measured (synthesis).
Peptide permeability F3	Bioperformance F11	conditions differ	A minitablet that is mostly enhancer released insulin alike in six media fagan2025 R12, R13, R20, whereas for ezetimibe the medium decided which polymer held the drug elkhabaz2017 R6, R7.
Peptide permeability F4	Dissolution F7	builds on	Octreotide, SNAC and copovidone released at one normalized rate from the dispersion bapat2025b R2.f–h, R5, the congruent release below the limit at which drug and polymer leave together saboo2019 R5, R6, R8.
Peptide permeability F5	Dissolution F7	extends	Cyclosporine followed copovidone at 1.6% loading but not from 5% bapat2025b R10, C21, R11.i, a far lower boundary than the 25% limit of ritonavir–PVPVA indulkar2019a R11, C2, C31.
ASD process F41	Characterization methods F5	builds on	SHG measured 0.3% crystals in a posaconazole extrudate shah2024 R10, the detector that the methods category ranks most sensitive kestur2012 R7, R6, R8; correasoto2017 R1, R8.
ASD process F41	Dissolution F11	builds on	Posaconazole extrudates were dissolved after a gastric stage at about 10 times the amorphous solubility shah2024 R12, R14, the pH-shift design in which posaconazole–HPMCAS crystallized in acid elkhabaz2019a R10, R1, R16, R20.
ASD process F10	Characterization methods F4	same mechanism	TEM found crystals below 100 nm in an X-ray-amorphous extrudate with one Tg moseson2018a R5, R6, R9, the blind spot of a dark SHG image and of XRPD wanapun2010 R13; kestur2012 R17, C34.
ASD process F10	Characterization methods F5	same mechanism	In four bicalutamide extrudates DSC, XRPD, SEM, PLM and TEM found crystals in different subsets moseson2021 R6, R17, R21, the method ladder whose limits span about three orders kestur2012 R7, R6, R8; correasoto2017 R1, R8.
ASD process F7	Characterization methods F6	same mechanism	EDX, pyrene and XPS ranked phases but gave no compositions, pyrene departing from XPS by up to about 20 points li2017 X6; mugheirbi2017 X7; li2020 R9, X8; signals became amounts only where the standard matched the sample taylor1998a R8, R9; kestur2012 R10.
ASD process F25	Dissolution F4	same mechanism	Dissolved PVPVA prevented indomethacin nucleation for more than 12 h but slowed seeded growth only 18–56-fold moseson2020a R3, R4, R5, as HPMC slowed felodipine nucleation about 1,400-fold and growth 1.6-fold alonzo2012 R5, R16, R17.
ASD process F26	Dissolution F4	same mechanism	Indomethacin extrudates with 0–25% crystals lost concentration from about 43.1 to 28.8 µg/mL moseson2020a R6; residual crystals left delamanid release incomplete once any could be detected duong2022a R14, R15, C56.
ASD process F27	Dissolution F4	same mechanism	HPMCAS in the medium delayed crystallization of the hydrating bicalutamide solid by only about 10 min moseson2021 R5, R19, R20, as wetted nifedipine and celecoxib crystallized with or without a dissolved polymer raina2014b C11, R2; xie2015 R9, R10.
ASD process F27	Dissolution F8	same mechanism	The proposed trigger of bicalutamide matrix crystallization is a hydrated drug-rich solid with a Tg below 37 °C moseson2021 K1, K7, X8, X11; hydrated felodipine above its Tg crystallized faster than it dissolved alonzo2010 R2, C33, C34.
ASD process F38	Dissolution F7	builds on	Bicalutamide–PVPVA released drug and polymer together at 5–10% and the polymer first from 20% moseson2022b R6, R7, the switch measured for ritonavir–PVPVA indulkar2019a R11, C2, C31.
ASD process F21	Dissolution F7	builds on	Water in the spray solvent lowered ritonavir–PVPVA release only at 25% loading, where release is congruent li2020 R10, C37, the limit set in the release chapter indulkar2019a R11, C2, C31.
ASD process F23	Dissolution F3	same mechanism	Ritonavir from the co-granule stayed near 4 µg/mL trasi2019 R4, M1, M2, the mutual lowering that dissolving ritonavir–lopinavir films followed within 0.5 µg/mL trasi2015b R5, E1.
ASD process F23	Bioperformance F6	same mechanism	The co-granule deficit trasi2019 R4, M1, M2 matches the halving of each drug at 1:1 in two-drug PVP dispersions alhalaweh2016 R10, X8.
ASD process F14	Dissolution F7	conditions differ	Lopinavir–HPMC films with discrete drug-rich domains released faster than miscible films at 33–85% loading li2019 R2; in dissolving ritonavir compacts discrete droplets left with the polymer and a continuous drug-rich layer stayed yang2022a R6, R10, R11, R12, R13.
ASD process F16	Dissolution F7	conditions differ	Phase-separated lopinavir films shed particles of several origins, read as a "glue and particle" release li2019 C47, C50, C53; in dissolving ritonavir compacts discrete drug-rich droplets formed in the gel and left with the polymer below the limit yang2022a R6, R10, R11, R12, R13.
ASD process F17	Solid state stability F6	same mechanism	The PVP carbonyl Raman band shifted in the amorphous probucol dispersions broman2001 R5, the acceptor that PVP offers to donor drugs in the complementary-group rule kestur2010a R6.
ASD process F6	Solid state stability F8	same mechanism	Humid storage turned miscible evacetrapib–PVPVA films into a drug-rich network li2017 R19, R22, C28, as sorbed water split pimozide–PVP into two Tg rumondor2009c R17.
ASD process F1	Solid state stability F8	extends	Humid air during film formation split miscible films into drug-rich domains li2017 R3, R5; mugheirbi2017 R1, R3, R10, the domains that film methods found in itraconazole–HPMC under one DSC Tg purohit2015a R1, R7.
ASD process F8	Solid state stability F3	builds on	Melting point depression gave χ = −1.97 for indomethacin–PVPVA and set the extrusion floor moseson2018 R5, R4, using the route whose estimates agree with other routes in sign but not in size marsac2006b R4, R9.
ASD process F9	Solid state stability F11	extends	Extrusion below the critical temperature always left crystals moseson2018 R10.k–o, a further case of the route deciding the result, as slow drying left 22 of 31 class III spin-coat combinations crystalline vaneerdenbrugh2010a R12, R13.
ASD process F22	Solid state stability F1	builds on	Solvent granulation was judged suited to slowly crystallizing drugs trasi2019 C50, C33, the order of the neat-drug classes baird2010 R23, R25.
ASD process F31	Solid state stability F1	conditions differ	Neat class III posaconazole and bicalutamide nucleated within 1 h between Tg and Tm moseson2020 R7, whereas class III glasses below Tg crystallized only at the edges after 3 months baird2010 R23, R25.
ASD process F43	Solid state stability F11	builds on	Atomic layer coatings delayed crystallization of stored powders from 1–3 weeks to 3–24 weeks or longer moseson2022a R11; duong2022c R16, R17, against the free-surface growth that ran about 6 times faster than the bulk kestur2013a R8, R9.
ASD process F44	Solid state stability F12	same mechanism	Coated powders that held at one humidity failed at a higher one moseson2022a R11, X16, as 0–52% RH could not tell PVP from HPMCAS where 75% RH could rumondor2009b R19, R9.
ASD process F29	Bioperformance F28	same mechanism	The authors name seeds, inhibitor and volume as the risk factors of residual crystals and cite the tacrolimus work moseson2020a R6, C28; purohit2019 C54, where the smallest volume showed seed-driven loss hate2019 R10, R11.
ASD process F40	Dissolution F6	same mechanism	SDS and TPGS raised bicalutamide release, ritonavir–PVPVA–SDS compacts crystallized at the surface within 15 min moseson2022b R9, R11, R13; indulkar2022 R15, C38, as 10 parts SDS left ritonavir release near 70% with needle crystals yang2023 R21, R13, R2, R16, R17.
ASD process F34	Solid state stability F9	conditions differ	PVP protected ritonavir against degradation in the extruder alvarenga2022 R10, R22, C25, while in humid felodipine storage PVP lost to HPMCAS konno2008 R1, R3; the polymer ranking depends on the stage (synthesis).
Dissolution F4	Solid state stability F4	same mechanism	In solution HPMC slowed felodipine nucleation far more than growth alonzo2012 R5, R16, R17, as 3% polymer lowered dry nucleation alike while melt growth ranked the polymers konno2006 R4, C13, C14; kestur2010a R6.
Dissolution F6	Solid state stability F5	same mechanism	TPGS and Tween 80 sped ritonavir growth in solution ilevbare2012a R17, R1.g, M17, as 10% TPGS sped celecoxib growth about 85-fold in the supercooled liquid mosqueragiraldo2014 R1, C9.
Dissolution F7	Solid state stability F7	conditions differ	The release limit of ritonavir–PVPVA lies between 25 and 30% indulkar2019a R11, C2, C31; the storage limit of indomethacin dispersions lay at about 50% with HPMC and 30% with HPMCAS tian2016 R17; the two thresholds are measured on different states (synthesis).
Dissolution F9	Solid state stability F9	extends	PVP and PVPVA released felodipine fastest at low loading but inhibited poorly saboo2020a R15, R14, C55; konno2008a R7, and in humid storage PVP lost its advantage for felodipine konno2008 R1, R3.
Characterization methods F2	Dissolution F7	same mechanism	The 10% ritonavir dispersion reached the amorphous solubility and the 50% one did not tres2018 R6, R9; purohit2017b C30, C33, C34, C37, as below the limit ritonavir passed the amorphous solubility within 5–10 min and formed droplets indulkar2019a R9, R20.
Characterization methods F1	Solid state stability F8	builds on	Pyrene in itraconazole–HPMC powders read the value of the drug purohit2015b R6; purohit2017a R7, the drug-rich domains found by film methods under one Tg purohit2015a R1, R7.
Characterization methods F4	Solid state stability F8	same mechanism	Itraconazole–HPMC with one Tg of 87 °C showed drug-rich domains by confocal imaging purohit2017a R3, R7, R16, R17, as indomethacin dispersions gave one Tg at every loading above their miscibility limits tian2016 R13, R2.f, R3.c, R4.h.
Characterization methods F6	Dissolution F2	same mechanism	A UV probe read 300 nm felodipine particles as dissolved drug vaneerdenbrugh2011b R6.a, M1, the overread of in situ UV for dissolving dispersions alonzo2011 R1, R14, R15.
Characterization methods F5	Dissolution F1	same mechanism	Extinction, probe and thermodynamic onsets agreed within 1.0–1.7-fold raina2015a R11, X9, the onset that lay at 0.91–1.15 times the calculated amorphous solubility ilevbare2013a R8; almeidaesousa2015 R5, R11.
Characterization methods F3	Dissolution F5	same mechanism	The probe signal swung back as the drug-rich phase of nifedipine and lopinavir crystallized raina2015a R16; tres2018 R20, R21, as the drug-rich phase gave crystals within minutes for danazol and telaprevir jackson2014 R13, R17.a–c.

For the authors: coverage table

Every category finding of Solid state stability, Characterization methods and Dissolution, and every chapter finding of ASD process, Bioperformance, Mesoporous silica and Peptide permeability, is used in a wiki finding or in links.md, or is listed as standing alone.

part	findings used in a wiki finding or in links.md	findings that stand alone
Solid state stability	F1–F12 (12 of 12)	none
ASD process	F1–F3, F6–F10, F14–F17, F21–F29, F31, F34, F38–F41, F43–F44 (29 of 49)	F4–F5, F11–F13, F18–F20, F30, F32–F33, F35–F37, F42, F45–F49 (20): solvent choice and domain size, crystal dissolution and fragmentation in the melt, the probucol carriers, the droplet-drying model, thermogravimetry and assay, the population balance model, and coating thickness, water uptake, release and powder flow
Characterization methods	F1–F7 (7 of 7)	none
Dissolution	F1–F12 (12 of 12)	none
Bioperformance	F1–F20, F22–F28, F30–F31 (29 of 31)	F21, F29 (2): the unstirred water layer in PAMPA, and the absorption–growth model of tacrolimus
Mesoporous silica	F3–F4, F6–F8, F11–F15 (10 of 15)	F1–F2, F5, F9–F10 (5): drug state in the pores, the two monolayers, hydrogen bonding to silanols, the adsorption–desorption exchange and the residue against the isotherm
Peptide permeability	F1–F6 (6 of 6)	none

Sources: the whole wiki

Every paper cited in the overview pages findings.md, links.md and index.md. Keys are first-author surname plus year; a, b, c, d separate papers of the same author and year, as assigned in synthesis/citation_keys.csv and the source tables of the categories and chapters, from which the rows are copied. Rows are grouped by the category and subcategory of the paper, in the order of the seven parts (Solid state stability, ASD process, Characterization methods, Dissolution, Bioperformance, Mesoporous silica, Peptide permeability), and by year within each subcategory.

key	year	title	slug	category / subcategory
baird2010	2010	A Classification System to Assess the Crystallization Tendency of Organic Molecules from Undercooled Melts	2010-baird-classification-crystallization-tendency-undercooled-melts	Solid state stability / Crystallization tendency
vaneerdenbrugh2010a	2010	Crystallization Tendency of Active Pharmaceutical Ingredients Following Rapid Solvent Evaporation—Classification and Comparison with Crystallization Tendency from Undercooled Melts	2010-van-eerdenbrugh-api-crystallization-tendency-rapid-solvent-evaporation	Solid state stability / Crystallization tendency
baird2012	2012	Role of Viscosity in Influencing the Glass-Forming Ability of Organic Molecules from the Undercooled Melt State	2012-baird-viscosity-glass-forming-ability-undercooled-melts	Solid state stability / Crystallization tendency
marsac2006b	2006	Theoretical and Practical Approaches for Prediction of Drug–Polymer Miscibility and Solubility	2006-marsac-drug-polymer-miscibility-solubility	Solid state stability / Miscibility and drug-polymer interactions
marsac2009	2009	Estimation of Drug–Polymer Miscibility and Solubility in Amorphous Solid Dispersions Using Experimentally Determined Interaction Parameters	2009-marsac-drug-polymer-miscibility-solubility-asd-interaction-parameters	Solid state stability / Miscibility and drug-polymer interactions
kestur2010a	2010	Role of polymer chemistry in influencing crystal growth rates from amorphous felodipine	2010-kestur-polymer-chemistry-felodipine-crystal-growth-inhibition	Solid state stability / Miscibility and drug-polymer interactions
vaneerdenbrugh2010b	2010	Small Scale Screening To Determine the Ability of Different Polymers To Inhibit Drug Crystallization upon Rapid Solvent Evaporation	2010-van-eerdenbrugh-polymer-crystallization-inhibition-spin-coating-screen	Solid state stability / Miscibility and drug-polymer interactions
wegiel2013a	2013	Mid-infrared spectroscopy as a polymer selection tool for formulating amorphous solid dispersions	2013-wegiel-mid-ir-polymer-selection-polyphenol-asd-stability	Solid state stability / Miscibility and drug-polymer interactions
purohit2015a	2015	Miscibility of Itraconazole-Hydroxypropyl Methylcellulose Blends- Insights with High Resolution Analytical Methodologies	2015-purohit-itraconazole-hpmc-miscibility-high-resolution-methods	Solid state stability / Miscibility and drug-polymer interactions
hiew2022a	2022	Balancing Solid-State Stability and Dissolution Performance of Lumefantrine Amorphous Solid Dispersions: The Role of Polymer Choice and Drug−Polymer Interactions	2022-hiew-lumefantrine-asd-stability-dissolution-polymer-choice	Solid state stability / Miscibility and drug-polymer interactions
zhu2011	2011	Time-Resolved SAXS/WAXS Study of the Phase Behavior and Microstructural Evolution of Drug/PEG Solid Dispersions	2011-zhu-time-resolved-saxs-waxs-drug-peg-solid-dispersions	Solid state stability / PEG dispersions
zhu2012	2012	Modification of Crystallization Behavior in Drug/Polyethylene Glycol Solid Dispersions	2012-zhu-api-peg-solid-dispersion-crystallization-behavior	Solid state stability / PEG dispersions
konno2006	2006	Influence of Different Polymers on the Crystallization Tendency of Molecularly Dispersed Amorphous Felodipine	2006-konno-felodipine-polymer-crystallization-nucleation-solid-dispersions	Solid state stability / Physical stability
konno2008	2008	Ability of Different Polymers to Inhibit the Crystallization of Amorphous Felodipine in the Presence of Moisture	2008-konno-polymers-inhibit-amorphous-felodipine-moisture-crystallization	Solid state stability / Physical stability
rumondor2009b	2009	Effects of Polymer Type and Storage Relative Humidity on the Kinetics of Felodipine Crystallization from Amorphous Solid Dispersions	2009-rumondor-polymer-rh-felodipine-crystallization-kinetics	Solid state stability / Physical stability
rumondor2009c	2009	Phase Behavior of Poly(vinylpyrrolidone) Containing Amorphous Solid Dispersions in the Presence of Moisture	2009-rumondor-pvp-asd-moisture-induced-immiscibility	Solid state stability / Physical stability
marsac2010	2010	Effect of Temperature and Moisture on the Miscibility of Amorphous Dispersions of Felodipine and Poly(vinyl pyrrolidone)	2010-marsac-temperature-moisture-miscibility-felodipine-pvp-asd	Solid state stability / Physical stability
trasi2012a	2012	Effect of polymers on nucleation and crystal growth of amorphous acetaminophen	2012-trasi-taylor-polymers-nucleation-growth-amorphous-acetaminophen	Solid state stability / Physical stability
kestur2013a	2013	Evaluation of the crystal growth rate of felodipine polymorphs in the presence and absence of additives as a function of temperature	2013-kestur-felodipine-polymorph-crystal-growth-pvp-additives	Solid state stability / Physical stability
mosqueragiraldo2014	2014	Impact of surfactants on the crystal growth of amorphous celecoxib	2014-mosquera-giraldo-surfactants-crystal-growth-amorphous-celecoxib	Solid state stability / Physical stability
tian2016	2016	Investigating the Correlation between Miscibility and Physical Stability of Amorphous Solid Dispersions Using Fluorescence-based Techniques	2016-tian-indomethacin-polymer-miscibility-physical-stability-fluorescence	Solid state stability / Physical stability
trasi2017	2017	Evaluation of the Crystallization Tendency of Commercially Available Amorphous Tacrolimus Formulations Exposed to Different Stress Conditions	2017-trasi-commercial-amorphous-tacrolimus-crystallization-stress	Solid state stability / Physical stability
trasi2020	2020	Physical stability and release properties of lumefantrine amorphous solid dispersion granules prepared by a simple solvent evaporation approach	2020-trasi-lumefantrine-asd-granules-solvent-evaporation	Solid state stability / Physical stability
broman2001	2001	A comparison of alternative polymer excipients and processing methods for making solid dispersions of a poorly water soluble drug	2001-broman-polymer-excipients-processing-probucol-solid-dispersions	ASD process / ASD process
li2017	2017	Understanding the impact of water on the miscibility and microstructure of amorphous solid dispersions – An AFM/LCR and TEM/EDX study	2017-li-water-miscibility-microstructure-asd-afm-tem-edx	ASD process / ASD process
mugheirbi2017	2017	Insights into Water-Induced Phase Separation in Itraconazole–Hydroxypropylmethyl Cellulose Spin Coated and Spray Dried Dispersions	2017-mugheirbi-water-induced-phase-separation-itz-hpmc-asd	ASD process / ASD process
moseson2018	2018	The application of temperature-composition phase diagrams for hot melt extrusion processing of amorphous solid dispersions to prevent residual crystallinity	2018-moseson-temperature-composition-phase-diagrams-hme-asd-residual-crystallinity	ASD process / ASD process
moseson2018a	2018	Nanometer-Scale Residual Crystals in a Hot Melt Extruded Amorphous Solid Dispersion: Characterization by Transmission Electron Microscopy	2018-moseson-nanometer-residual-crystals-hme-asd-tem	ASD process / ASD process
mugheirbi2018	2018	Phase Behavior of Drug-Hydroxypropyl Methylcellulose Amorphous Solid Dispersions Produced from Various Solvent Systems: Mechanistic Understanding of the Role of Polymer using Experimental and Theoretical Methods	2018-mugheirbi-itz-hpmc-asd-solvent-phase-behavior	ASD process / ASD process
li2019	2019	Microstructure Formation for Improved Dissolution Performance of Lopinavir Amorphous Solid Dispersions	2019-li-lopinavir-hpmc-asd-microstructure-dissolution	ASD process / ASD process
moseson2019	2019	Dissolution of Indomethacin Crystals into a Polymer Melt: Role of Diffusion and Fragmentation	2019-moseson-indomethacin-copovidone-melt-dissolution-fragmentation	ASD process / ASD process
trasi2019	2019	Amorphous solid dispersion formation via solvent granulation – A case study with ritonavir and lopinavir	2019-trasi-solvent-granulation-ritonavir-lopinavir-asd	ASD process / ASD process
li2020	2020	Water-induced phase separation of spray dried amorphous solid dispersions	2020-li-water-induced-phase-separation-spray-dried-asd-ritonavir-pvpva	ASD process / ASD process
moseson2020	2020	Application and Limitations of Thermogravimetric Analysis to Delineate the Hot Melt Extrusion Chemical Stability Processing Window	2020-moseson-tga-hme-chemical-stability-processing-window	ASD process / ASD process
moseson2020a	2020	Amorphous Solid Dispersions Containing Residual Crystallinity: Influence of Seed Properties and Polymer Adsorption on Dissolution Performance	2020-moseson-residual-crystallinity-seed-properties-polymer-adsorption	ASD process / ASD process
moseson2021	2021	Amorphous Solid Dispersions Containing Residual Crystallinity: Competition Between Dissolution and Matrix Crystallization	2021-moseson-residual-crystallinity-dissolution-matrix-crystallization	ASD process / ASD process
alvarenga2022	2022	Impact of Polymer Type on Thermal Degradation of Amorphous Solid Dispersions Containing Ritonavir	2022-alvarenga-polymer-type-thermal-degradation-ritonavir-asd	ASD process / ASD process
duong2022c	2022	Surface nanocoating of high drug-loading spray-dried amorphous solid dispersions by atomic layer coating: Excellent physical stability under accelerated storage conditions for two years	2022-van-duong-surface-nanocoating-high-drug-loading-asd-alc-stability	ASD process / ASD process
moseson2022a	2022	Atomic Layer Coating to Inhibit Surface Crystallization of Amorphous Pharmaceutical Powders	2022-moseson-atomic-layer-coating-surface-crystallization-asd-powders	ASD process / ASD process
moseson2022b	2022	Formulation and processing strategies which underpin susceptibility to matrix crystallization in amorphous solid dispersions	2022-moseson-processing-strategies-matrix-crystallization-bcl-pvpva-asd	ASD process / ASD process
shah2024	2024	Orthogonal Analytical Methods to Elucidate How Low Levels of Residual Crystallinity in Posaconazole Amorphous Solid Dispersions Impact Phase Behavior during Release	2024-shah-posaconazole-asd-residual-crystallinity-release-phase-behavior	ASD process / ASD process
taylor1998a	1998	The Quantitative Analysis of Crystallinity Using FT-Raman Spectroscopy	1998-taylor-ft-raman-crystallinity-indomethacin	Characterization methods / Solid-state methods
wanapun2010	2010	Selective Detection and Quantitation of Organic Molecule Crystallization by Second Harmonic Generation Microscopy	2010-wanapun-sonicc-amorphous-api-crystallization-detection	Characterization methods / Solid-state methods
kestur2012	2012	Nonlinear Optical Imaging for Sensitive Detection of Crystals in Bulk Amorphous Powders	2012-kestur-sonicc-sensitive-crystal-detection-amorphous-powders	Characterization methods / Solid-state methods
purohit2015b	2015	Phase Separation Kinetics in Amorphous Solid Dispersions Upon Exposure to Water	2015-purohit-phase-separation-kinetics-asd-water	Characterization methods / Solid-state methods
correasoto2017	2017	Second harmonic generation microscopy as a tool for the early detection of crystallization in spray dried dispersions	2017-correa-soto-shg-early-crystallization-spray-dried-asds	Characterization methods / Solid-state methods
purohit2017a	2017	Insights into Nano- and Micron-Scale Phase Separation in Amorphous Solid Dispersions Using Fluorescence-Based Techniques in Combination with Solid State Nuclear Magnetic Resonance Spectroscopy	2017-purohit-itraconazole-hpmc-asd-phase-separation-fluorescence-ssnmr	Characterization methods / Solid-state methods
vaneerdenbrugh2011b	2011	Influence of Particle Size on the Ultraviolet Spectrum of Particulate-Containing Solutions: Implications for In-Situ Concentration Monitoring Using UV/Vis Fiber-Optic Probes	2011-van-eerdenbrugh-uv-fiber-optic-particulate-size-concentration-artifact	Characterization methods / Solution methods
raina2015a	2015	Using Environment-Sensitive Fluorescent Probes to Characterize Liquid-Liquid Phase Separation in Supersaturated Solutions of Poorly Water Soluble Compounds	2015-raina-fluorescent-probes-llps-supersaturated-solutions	Characterization methods / Solution methods
tres2018	2018	Mechanistic Understanding of the Phase Behavior of Supersaturated Solutions of Poorly Water-Soluble Drugs	2018-tres-asd-phase-behavior-fluorescence-lifetime-ritonavir-lopinavir	Characterization methods / Solution methods
indulkar2017b	2017	Origin of Nanodroplet Formation upon Dissolution of an Amorphous Solid Dispersion: A Mechanistic Isotope Scrambling Study	2017-indulkar-origin-nanodroplet-formation-asd-isotope-scrambling	Dissolution / A. Release mechanism and LoC
purohit2017b	2017	Phase Behavior of Ritonavir Amorphous Solid Dispersions during Hydration and Dissolution	2017-purohit-ritonavir-asd-hydration-dissolution-phase-behavior	Dissolution / A. Release mechanism and LoC
indulkar2019a	2019	Insights into the dissolution mechanism of ritonavir-copovidone amorphous solid dispersions: importance of congruent release for enhanced performance	2019-indulkar-ritonavir-copovidone-asd-congruent-release-loc	Dissolution / A. Release mechanism and LoC
que2019	2019	Insights into the Dissolution Behavior of Ledipasvir-Copovidone Amorphous Solid Dispersions: Role of Drug Loading and Intermolecular Interactions	2019-que-ledipasvir-copovidone-asd-loc-interactions	Dissolution / A. Release mechanism and LoC
saboo2019	2019	Congruent release of drug and polymer: A “sweet spot” in the dissolution of amorphous solid dispersions	2019-saboo-congruent-drug-polymer-release-asd-sweet-spot	Dissolution / A. Release mechanism and LoC
saboo2020	2020	Congruent release of drug and polymer from amorphous solid dispersions: insights into the role of drug-polymer hydrogen bonding, surface crystallization and glass transition	2020-saboo-congruent-release-hbond-crystallization-tg-pvpva-asd	Dissolution / A. Release mechanism and LoC
saboo2020a	2020	Patterns of drug release as a function of drug loading from amorphous solid dispersions: A comparison of five different polymers.	2020-saboo-asd-drug-loading-polymer-hydrophobicity-release	Dissolution / A. Release mechanism and LoC
saboo2021	2021	Exploring the Role of Surfactants in Enhancing Drug Release from Amorphous Solid Dispersions at Higher Drug Loadings	2021-saboo-tpgs-felodipine-pvpva-asd-release-high-loading	Dissolution / A. Release mechanism and LoC
correasoto2022a	2022	Impact of Surfactants on the Performance of Clopidogrel-Copovidone Amorphous Solid Dispersions: Increased Drug Loading and Stabilization of Nanodroplets	2022-correa-soto-surfactants-clopidogrel-copovidone-asd-nanodroplets	Dissolution / A. Release mechanism and LoC
correasoto2022b	2022	Role of surfactants in improving release from higher drug loading amorphous solid dispersions	2022-correa-soto-surfactants-higher-drug-loading-atazanavir-pvpva-asds	Dissolution / A. Release mechanism and LoC
hiew2022b	2022	Combining drug salt formation with amorphous solid dispersions – a double edged sword	2022-hiew-combining-drug-salt-formation-asd-double-edged-sword	Dissolution / A. Release mechanism and LoC
indulkar2022	2022	Role of Surfactants on Release Performance of Amorphous Solid Dispersions of Ritonavir and Copovidone	2022-indulkar-surfactants-ritonavir-copovidone-asd-release-performance	Dissolution / A. Release mechanism and LoC
yang2022a	2022	Release mechanisms of amorphous solid dispersions: Role of drug-polymer phase separation and morphology	2022-yang-release-mechanisms-rtv-pvpva-asd-phase-separation-morphology	Dissolution / A. Release mechanism and LoC
deac2023b	2023	Dissolution Mechanisms of Amorphous Solid Dispersions: Role of Drug Load and Molecular Interactions	2023-deac-asd-drug-load-molecular-interactions-loc	Dissolution / A. Release mechanism and LoC
yang2023	2023	Drug Release from Surfactant-Containing Amorphous Solid Dispersions: Mechanism and Role of Surfactant in Release Enhancement	2023-yang-surfactant-containing-asd-release-enhancement	Dissolution / A. Release mechanism and LoC
bapat2024	2024	Interplay of Drug−Polymer Interactions and Release Performance for HPMCAS-Based Amorphous Solid Dispersions	2024-bapat-hpmcas-drug-polymer-complexation-release-performance	Dissolution / A. Release mechanism and LoC
deac2024b	2024	Dissolution Mechanisms of Amorphous Solid Dispersions: Application of Ternary Phase Diagrams To Explain Release Behavior	2024-deac-asd-ternary-phase-diagrams-release	Dissolution / A. Release mechanism and LoC
bapat2025a	2025	Impact of HPMCAS Grade on the Release of Weakly Basic Drugs from Amorphous Solid Dispersions	2025-bapat-hpmcas-grade-weak-base-asd-release-complexation	Dissolution / A. Release mechanism and LoC
kaur2025	2025	Impact of drug-polymer complexation and media properties on the release performance of amorphous solid dispersions containing a weakly basic drug and hydroxypropyl methylcellulose acetate succinate	2025-kaur-bdq-hpmcas-complexation-media-asd-release	Dissolution / A. Release mechanism and LoC
konno2008a	2008	Effect of polymer type on the dissolution profile of amorphous solid dispersions containing felodipine	2008-konno-polymer-type-felodipine-asd-dissolution	Dissolution / B. Supersaturation from ASD dissolution
alonzo2010	2010	Understanding the Behavior of Amorphous Pharmaceutical Systems during Dissolution	2010-alonzo-amorphous-pharmaceutical-dissolution-crystallization-polymers	Dissolution / B. Supersaturation from ASD dissolution
alonzo2011	2011	Dissolution and Precipitation Behavior of Amorphous Solid Dispersions	2011-alonzo-asd-dissolution-precipitation-nanoparticles	Dissolution / B. Supersaturation from ASD dissolution
ilevbare2013d	2013	Influence of Additives on the Properties of Nanodroplets Formed in Highly Supersaturated Aqueous Solutions of Ritonavir	2013-ilevbare-ritonavir-nanodroplets-additives-asd-llps	Dissolution / B. Supersaturation from ASD dissolution
raina2014b	2014	Impact of Polymers on the Crystallization and Phase Transition Kinetics of Amorphous Nifedipine during Dissolution in Aqueous Media	2014-raina-polymers-nifedipine-crystallization-phase-transition-dissolution	Dissolution / B. Supersaturation from ASD dissolution
jackson2015	2015	Dissolution of Danazol Amorphous Solid Dispersions: Supersaturation and Phase Behavior as a Function of Drug Loading and Polymer Type	2015-jackson-danazol-asd-dissolution-llps-drug-loading-polymer-type	Dissolution / B. Supersaturation from ASD dissolution
trasi2015b	2015	Dissolution performance of binary amorphous drug combinations—Impact of a second drug on the maximum achievable supersaturation	2015-trasi-taylor-binary-amorphous-drug-combinations-supersaturation	Dissolution / B. Supersaturation from ASD dissolution
xie2015	2015	Dissolution Performance of High Drug Loading Celecoxib Amorphous Solid Dispersions Formulated with Polymer Combinations	2015-xie-taylor-celecoxib-high-drug-loading-asd-polymer-combinations	Dissolution / B. Supersaturation from ASD dissolution
trasi2016	2016	Non-Sink Dissolution Behavior and Solubility Limit of Commercial Tacrolimus Amorphous Formulations	2016-trasi-commercial-tacrolimus-asd-nonsink-amorphous-solubility	Dissolution / B. Supersaturation from ASD dissolution
xie2016a	2016	Improved Release of Celecoxib from High Drug Loading Amorphous Solid Dispersions Formulated with Polyacrylic Acid and Cellulose Derivatives	2016-xie-celecoxib-high-drug-loading-asd-paa-cellulose-derivatives	Dissolution / B. Supersaturation from ASD dissolution
xie2017	2017	Impact of Eudragit EPO and Hydroxypropyl Methylcellulose on Drug Release Rate, Supersaturation, Precipitation Outcome and Redissolution Rate of Indomethacin Amorphous Solid Dispersions	2017-xie-eudragit-epo-hpmc-indomethacin-asd-supersaturation-redissolution	Dissolution / B. Supersaturation from ASD dissolution
que2018	2018	Paclitaxel Crystal Seeds with Different Intrinsic Properties and Their Impact on Dissolution of Paclitaxel-HPMCAS Amorphous Solid Dispersions	2018-que-paclitaxel-crystal-seeds-hpmcas-asd-dissolution	Dissolution / B. Supersaturation from ASD dissolution
elkhabaz2019a	2019	Characterization of Phase Transformations for Amorphous Solid Dispersions of a Weakly Basic Drug upon Dissolution in Biorelevant Media	2019-elkhabaz-posaconazole-asd-phase-transformations-biorelevant-media	Dissolution / B. Supersaturation from ASD dissolution
duong2022a	2022	Combining enabling formulation strategies to generate supersaturated solutions of delamanid: In situ salt formation during amorphous solid dispersion fabrication for more robust release profiles	2022-duong-delamanid-in-situ-salt-asd-release	Dissolution / B. Supersaturation from ASD dissolution
nguyen2023b	2023	Enteric coating of tablets containing an amorphous solid dispersion of an enteric polymer and a weakly basic drug: A strategy to enhance in vitro release	2023-nguyen-enteric-coating-delamanid-hpmcp-asd-release	Dissolution / B. Supersaturation from ASD dissolution
nguyen2023c	2023	Impact of Gastric pH Variations on the Release of Amorphous Solid Dispersion Formulations Containing a Weakly Basic Drug and Enteric Polymers	2023-nguyen-gastric-ph-variations-delamanid-enteric-polymer-asd	Dissolution / B. Supersaturation from ASD dissolution
polyzois2024	2024	Amorphous Solid Dispersion Formation for Enhanced Release Performance of Racemic and Enantiopure Praziquantel	2024-polyzois-praziquantel-racemic-enantiopure-asd-release	Dissolution / B. Supersaturation from ASD dissolution
alvarenga2025	2025	Release performance and crystallization of racemic and enantiopure praziquantel amorphous solid dispersion in various media	2025-alvarenga-praziquantel-racemic-enantiopure-asd-release-crystallization-media	Dissolution / B. Supersaturation from ASD dissolution
ilevbare2013a	2013	Liquid-Liquid Phase Separation in Highly Supersaturated Aqueous Solutions of Poorly-Water Soluble Drugs – Implications for Solubility Enhancing Formulations	2013-ilevbare-llps-supersaturated-poorly-water-soluble-drugs	Dissolution / C. Amorphous solubility and LLPS
almeidaesousa2015	2015	Assessment of the Amorphous “Solubility” of a Group of Diverse Drugs Using New Experimental and Theoretical Approaches	2015-almeida-sousa-amorphous-solubility-diverse-drugs-llps-cp-method	Dissolution / C. Amorphous solubility and LLPS
indulkar2015	2015	pH-Dependent Liquid−Liquid Phase Separation of Highly Supersaturated Solutions of Weakly Basic Drugs	2015-indulkar-ph-dependent-llps-weak-bases-amorphous-solubility	Dissolution / C. Amorphous solubility and LLPS
mosqueragiraldo2015	2015	Glass–Liquid Phase Separation in Highly Supersaturated Aqueous Solutions of Telaprevir	2015-mosquera-giraldo-telaprevir-glass-liquid-phase-separation	Dissolution / C. Amorphous solubility and LLPS
trasi2015a	2015	Thermodynamics of Highly Supersaturated Aqueous Solutions of Poorly Water-Soluble Drugs—Impact of a Second Drug on the Solution Phase Behavior and Implications for Combination Products	2015-trasi-second-drug-supersaturated-solutions-drug-rich-phase	Dissolution / C. Amorphous solubility and LLPS
indulkar2017a	2017	Impact of Micellar Surfactant on Supersaturation and Insight into Solubilization Mechanisms in Supersaturated Solutions of Atazanavir	2017-indulkar-micellar-surfactant-supersaturation-atazanavir-sds	Dissolution / C. Amorphous solubility and LLPS
lu2017b	2017	Impact of Endogenous Bile Salts on the Thermodynamics of Supersaturated Active Pharmaceutical Ingredient Solutions	2017-lu-endogenous-bile-salts-telaprevir-supersaturation-thermodynamics	Dissolution / C. Amorphous solubility and LLPS
sugihara2018	2018	Evaluation of Pazopanib Phase Behavior Following pH-induced Supersaturation	2018-sugihara-pazopanib-ph-induced-supersaturation-phase-behavior	Dissolution / C. Amorphous solubility and LLPS
ueda2020b	2020	Polymer type impacts amorphous solubility and drug-rich phase colloidal stability: A mechanistic study using nuclear magnetic resonance spectroscopy	2020-ueda-polymer-type-amorphous-solubility-drug-rich-phase-colloidal-stability	Dissolution / C. Amorphous solubility and LLPS
alonzo2012	2012	Characterizing the Impact of Hydroxypropylmethyl Cellulose on the Growth and Nucleation Kinetics of Felodipine from Supersaturated Solutions	2012-alonzo-hpmc-felodipine-growth-nucleation-supersaturation	Dissolution / D. Crystallization from solution
hsieh2012	2012	pH-Induced Precipitation Behavior of Weakly Basic Compounds: Determination of Extent and Duration of Supersaturation Using Potentiometric Titration and Correlation to Solid State Properties	2012-hsieh-ph-induced-precipitation-weak-bases-supersaturation-solid-state	Dissolution / D. Crystallization from solution
ilevbare2012a	2012	Effect of Binary Additive Combinations on Solution Crystal Growth of the Poorly Water-Soluble Drug, Ritonavir	2012-ilevbare-ritonavir-binary-additive-crystal-growth	Dissolution / D. Crystallization from solution
ilevbare2013c	2013	Maintaining Supersaturation in Aqueous Drug Solutions: Impact of Different Polymers on Induction Times	2013-ilevbare-polymers-supersaturation-induction-times	Dissolution / D. Crystallization from solution
hsieh2014	2014	Assessing the Impact of Polymers on the pH-Induced Precipitation Behavior of Poorly Water-Soluble Compounds using Synchrotron Wide Angle X-Ray Scattering	2014-hsieh-polymers-ph-induced-precipitation-waxs	Dissolution / D. Crystallization from solution
jackson2014	2014	Impact of Polymers on the Precipitation Behavior of Highly Supersaturated Aqueous Danazol Solutions	2014-jackson-polymers-precipitation-supersaturated-danazol	Dissolution / D. Crystallization from solution
chen2015	2015	Bile Salts as Crystallization Inhibitors of Supersaturated Solutions of Poorly Water-Soluble Compounds	2015-chen-bile-salts-crystallization-inhibitors-supersaturated-solutions	Dissolution / D. Crystallization from solution
raina2015b	2015	Trends in the Precipitation and Crystallization Behavior of Supersaturated Aqueous Solutions of Poorly Water-Soluble Drugs Assessed Using Synchrotron Radiation	2015-raina-precipitation-crystallization-supersaturated-dihydropyridines-synchrotron	Dissolution / D. Crystallization from solution
indulkar2018	2018	Crystallization from Supersaturated Solutions: Role of Lecithin and Composite Simulated Intestinal Fluid	2018-indulkar-lecithin-composite-sif-crystallization-supersaturation	Dissolution / D. Crystallization from solution
elkhabaz2021	2021	Crystallization Kinetics in Fasted-State Simulated and Aspirated Human Intestinal Fluids	2021-elkhabaz-crystallization-kinetics-fasted-simulated-aspirated-human-intestinal-fluids	Dissolution / D. Crystallization from solution
wilson2021	2021	Interaction of Polymers with Enzalutamide Nanodroplets—Impact on Droplet Properties and Induction Times	2021-wilson-enzalutamide-nanodroplets-polymer-interactions-induction-times	Dissolution / D. Crystallization from solution
shah2025	2025	Chemistry and ionization of HPMCAS influences the dissolution and solution-mediated crystallization of posaconazole amorphous solid dispersions	2025-shah-hpmcas-ionization-posaconazole-asd-crystallization	Dissolution / D. Crystallization from solution
raina2014a	2014	Enhancements and Limits in Drug Membrane Transport Using Supersaturated Solutions of Poorly Water Soluble Drugs	2014-raina-llps-limits-drug-membrane-transport-supersaturated-solutions	Bioperformance / Bioperformance
raina2015c	2015	Impact of Solubilizing Additives on Supersaturation and Membrane Transport of Drugs	2015-raina-solubilizing-additives-supersaturation-membrane-transport	Bioperformance / Bioperformance
alhalaweh2016	2016	Compromised in vitro dissolution and membrane transport of multidrug amorphous formulations	2016-alhalaweh-multidrug-asd-dissolution-transport	Bioperformance / Bioperformance
indulkar2016	2016	Exploiting the phenomenon of liquid-liquid phase separation for enhanced and sustained membrane transport of a poorly water soluble drug	2016-indulkar-llps-nanodroplet-reservoir-membrane-transport	Bioperformance / Bioperformance
elkhabaz2017	2017	Variation in the Supersaturation and Phase Behavior of Ezetimibe Amorphous Solid Dispersions Upon Dissolution in Different Biorelevant Media	2017-elkhabaz-ezetimibe-asd-phase-behavior-biorelevant-media	Bioperformance / Bioperformance
hate2017	2017	Absorptive Dissolution Testing of Supersaturating Systems: Impact of Absorptive Sink Conditions on Solution Phase Behavior and Mass Transport	2017-hate-absorptive-dissolution-supersaturating-systems	Bioperformance / Bioperformance
hate2018	2018	Insight into Amorphous Solid Dispersion Performance by Coupled Dissolution and Membrane Mass Transfer Measurements	2018-hate-asd-coupled-dissolution-membrane-mass-transfer	Bioperformance / Bioperformance
mosqueragiraldo2018b	2018	Influence of Polymer and Drug Loading on the Release Profile and Membrane Transport of Telaprevir	2018-mosquera-giraldo-telaprevir-asd-polymer-loading-release-membrane-transport	Bioperformance / Bioperformance
purohit2018	2018	Investigating the impact of drug crystallinity in amorphous tacrolimus capsules on pharmacokinetics and bioequivalence using discriminatory in vitro dissolution testing and PBPK modeling and simulation	2018-purohit-tacrolimus-crystallinity-dissolution-pbpk-bioequivalence	Bioperformance / Bioperformance
wilson2018	2018	Relationship between Amorphous Solid Dispersion In Vivo Absorption and In Vitro Dissolution: Phase Behavior During Dissolution, Speciation, and Membrane Mass Transport	2018-wilson-asd-in-vivo-absorption-dissolution-phase-behavior-mass-transport	Bioperformance / Bioperformance
elkhabaz2019b	2019	Interplay of supersaturation and solubilization: Lack of correlation between concentration-based supersaturation measurements and membrane transport rates in simulated and aspirated human fluids	2019-elkhabaz-supersaturation-solubilization-activity-flux-biorelevant-media	Bioperformance / Bioperformance
hate2019	2019	Absorptive dissolution testing: An improved approach to study the impact of residual crystallinity on the performance of amorphous formulations	2019-hate-absorptive-dissolution-residual-crystallinity-amorphous-formulations	Bioperformance / Bioperformance
purohit2019	2019	Assessing the impact of endogenously derived crystalline drug on the in vivo performance of amorphous formulations	2019-purohit-endogenous-crystallinity-in-vivo-amorphous-tacrolimus	Bioperformance / Bioperformance
ueda2020a	2020	Impact of hypromellose acetate succinate grade on drug amorphous solubility and in vitro membrane transport	2020-ueda-hpmcas-grade-amorphous-solubility-membrane-transport	Bioperformance / Bioperformance
wilson2020	2020	Amorphous solid dispersions of enzalutamide and novel polysaccharide derivatives: investigation of relationships between polymer structure and performance	2020-wilson-enzalutamide-polysaccharide-asd-polymer-performance	Bioperformance / Bioperformance
hate2022	2022	A Mechanistic Study of Drug Mass Transport from Supersaturated Solutions Across PAMPA Membranes	2021-hate-drug-mass-transport-supersaturated-pampa-membranes	Bioperformance / Bioperformance
nguyen2023a	2023	Fed- and Fasted-State Performance of Pretomanid Amorphous Solid Dispersions Formulated with an Enteric Polymer	2023-nguyen-pretomanid-hpmcas-asd-fed-fasted-performance	Bioperformance / Bioperformance
alkalla2026	2026	Coadministration of a crystalline drug compromises supersaturation and membrane transport of an amorphous drug	2026-alkalla-crystalline-darunavir-compromises-amorphous-atazanavir-supersaturation-transport	Bioperformance / Bioperformance
dening2018	2018	Supersaturation Potential of Ordered Mesoporous Silica Delivery Systems. Part 1: Dissolution Performance and Drug Membrane Transport Rates	2018-dening-ordered-mesoporous-silica-supersaturation-dissolution-flux	Mesoporous silica / Mesoporous silica
dening2019	2019	Application of an adsorption isotherm to explain incomplete drug release from ordered mesoporous silica materials under supersaturating conditions	2019-dening-adsorption-isotherm-incomplete-release-sba15	Mesoporous silica / Mesoporous silica
hate2020a	2020	Interplay of Adsorption, Supersaturation and the Presence of an Absorptive Sink on Drug Release from Mesoporous Silica-Based Formulations	2020-hate-atazanavir-mesoporous-silica-adsorption-absorptive-sink-release	Mesoporous silica / Mesoporous silica
hate2020b	2020	Influence of Drug-Silica Electrostatic Interactions on Drug Release from Mesoporous Silica-Based Oral Delivery Systems	2020-hate-drug-silica-electrostatic-interactions-mesoporous-release	Mesoporous silica / Mesoporous silica
mccarthy2020	2020	A Comparison of Drug Release and Adsorption Under Supersaturating Conditions for Ordered Mesoporous Silica with Indomethacin or Indomethacin Methyl Ester	2020-mccarthy-indomethacin-indme-sba15-adsorption-release	Mesoporous silica / Mesoporous silica
bapat2025b	2025	Modification of Peptide and Permeation Enhancer In Vitro Release Rates by Dispersion with a Gel-Forming Polymer	2025-bapat-peptide-permeation-enhancer-pvpva-synchronous-release	Peptide permeability / Peptide permeability
fagan2025	2025	Impact of Permeation Enhancers on the Release of Insulin from Tablets in Biorelevant Media	2025-fagan-permeation-enhancers-insulin-minitablet-biorelevant-media	Peptide permeability / Peptide permeability

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

absorptive dissolution testing

A dissolution test coupled to a membrane that removes dissolved drug into a receiver, as absorption would, so that release, phase behaviour and mass transfer are measured together hate2020a P9; hate2020b P8, C12. With sink maintained the donor concentration over time dictates the transport rate, so the receiver profile reflects dissolution, crystallization and the supersaturation reached hate2017 C36. In the mesoporous-silica papers it tests whether removal of drug frees drug held back by the silica hate2020a C15.

Findings

F14, F11, F13, F15.

Related concepts

provides an absorptive sink and keeps sink conditions in the receiver; reads membrane flux; contrasts with closed non-sink dissolution; shifts the dynamic adsorption-desorption equilibrium.

Formulas

total release by mass balance, membrane flux in terms of solute activity.

How it is measured or obtained

A flow-through apparatus with a cellulosic hollow-fibre module (100 cm², 15 nm pores), co-current flow of 4 mL/min on both sides at 37 °C, a 50 mL donor with a 10 µm cannula filter, an in-line UV receiver fed with pH 6.8 buffer and HPLC of donor samples; total release is drug in the donor plus drug transferred hate2020a P9, E4; hate2020b P8. The closed-vessel comparison uses the same medium without the module hate2020a P7.

Values in the library

material	value or class	conditions	paper ids
atazanavir–SBA-15, 20% w/w	total release about 89.5% against 46.5% closed at 240 min	pH 6.8, 75 µg/mL, HPMC	hate2020a R20
atazanavir–SBA-15, 5–50% w/w	about 73 / 80.5 / 66.5 / 52 / 36% in 90 min	same	hate2020a R15
atazanavir–SBA-15, pH 1 → 6.8	receiver peak about 6.4 against 3.6 µg/mL (pH 6.8 only)	20% w/w	hate2020a R22
10% atazanavir–SBA-15 against 10% HPMC ASD	receiver about 4.3–5.2 against 10.2–11.6 µg/mL	200 µg/mL	hate2020a R25
ketoconazole–SBA-15, pH 1 → 6.8	about 54–60.5% → 69.5% over 4 h	20% w/w	hate2020b R17
nevirapine with 0.1% PVPVA (not silica)	total drug constant 120 min with absorption; dissolved drug falling after 60 min closed	500 µg/mL, pH 6.5	hate2017 R16, R17

Evidence table: absorptive dissolution testing.

Pitfalls and disagreements

About 5–6% of the drug binds to the membrane, and whether total release counts it is not stated hate2020a R16, X18. Figures share data sets, so the sink, loading and pre-dissolved results are not independent repeats hate2020a X9. The total-release calculation of the ketoconazole run is not described hate2020b X10. Hate and co-workers state that a closed vessel may overestimate the supersaturation at any time and the risk of crystallization of slowly crystallizing solutions, and that an absorptive compartment gives more in vivo relevant insight for silica formulations hate2017 C53, C55; hate2020a C49.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

absorptive sink

A membrane compartment that removes dissolved drug from the dissolution medium while dissolution and phase change go on, as the intestinal wall does in vivo; the test that couples a dissolving donor to such a compartment is called absorptive dissolution testing hate2019 C9, C31, P4. The sink changes concentration–time profiles: it lowers the supersaturation reached in the donor and so the driving force for crystal growth on residual seeds hate2019 C15, C35. In vivo, absorption keeps depleting the lumen after gastric emptying and may lower the driving force for secondary nucleation and growth, and may let a crystalline fraction dissolve once luminal concentrations fall low enough purohit2019 C41. It differs from a sink in the compendial sense, where the medium is large enough to dissolve the dose (sink conditions).

Findings

F14, F28, F29.

Related concepts

contrasts with sink conditions and non-sink dissolution; acts on desupersaturation and crystal seeding; measured with the membrane mass transfer coefficient.

Formulas

hollow-fibre donor depletion, power-law crystal growth rate, mass transferred from receiver AUC.

How it is measured or obtained

A cellulosic hollow-fibre module (100 cm² and 15 nm pores in the tacrolimus study) fed from the dissolution vessel, donor and receiver pumped co-currently at 2 mL/min, receiver read by in-line UV and donor by HPLC; total dissolved drug in donor plus receiver follows crystallization hate2019 P4, P8, C19. Receiver AUC and a test-to-reference ratio with 80–125% limits summarize the result hate2019 P9, E6. The module is described as having 115 cm² of membrane in the nevirapine study hate2017 M10.

Values in the library

material	value or class	conditions	paper ids
tacrolimus generic capsule, fresh	receiver AUC0–120 about 362, 682 and 992 µg/mL·min in 240, 100 and 40 mL	hollow fibre, 37 °C	hate2019 R12, C24
tacrolimus crystalline suspension	AUC about 87 µg/mL·min at every volume	same	hate2019 R12
tacrolimus generic, fresh	did not crystallize at 240, 100 or 40 mL, unlike in an earlier closed vessel	same	hate2019 R11, C35
tacrolimus generic, 20% crystalline	at 40 mL only: total dissolved drug fell from about 2.35 to 1.9 mg after 60 min	5 mg in 40 mL	hate2019 R11, C20
nevirapine tablet donor	about 253 µg/mL after 270 min with absorption against about 525 in a closed vessel	0.05% HPMC-AS	hate2017 R15, R7
atazanavir 50% ASDs	total release at 120 min 6200, 6300, 5000 µg with absorption against 4200, 4600, 3600 closed (HPMCAS, HPMC, PVPVA)	200 µg/mL dose	hate2018 R18

Pitfalls and disagreements

The absorption rate is a property of the apparatus: a closed vessel may overstate crystallization, and an absorptive test may understate it if absorption in vivo is slower hate2019 C12, C35. Two explanations for the missing crystallization of fresh tacrolimus capsules, the polymer and the lower supersaturation from absorption, were not separated, because no run without the sink at the same volume exists hate2019 X15, C22. The area of the same module is 100 cm² in one card and 115 cm² in another hate2019 P4; hate2017 M10. The fitted model constants are not reproducible from the printed values (F29) hate2019 X1, X3, X4.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

additive cases for amorphous solubility

A classification of drug/additive pairs by where the additive acts on the amorphous solubility S_a (Ueda 2024, review, pp. 28–40). Case I: the additive forms a complex with the drug in the aqueous phase; S_c and S_a rise, the free drug at the limit stays at S_a^0 and the maximum supersaturation ratio stays at S_a^0/S_c^0. Case II: the additive distributes into the drug-rich phase; S_c is about unchanged, and S_a and the maximum supersaturation ratio fall. Case III: both; S_c rises, the free drug at the limit and the maximum supersaturation ratio fall, and S_a/S_c does not give the maximum. The case belongs to the pair, not the additive: ketoprofen is listed with EUD-E (I), PVP (II) and CTAB (III) (pp. 29, 40–41).

Findings

Amorphous solubility: F11, F12, F19. Crystallization from solution: F19. Bioperformance: F4, F7, F18, F19.

Related concepts

acts on amorphous solubility; Case I relates to micellar solubilization; Case II relates to polymer partitioning into the drug-rich phase and drug-rich phase; decides how free drug concentration and the supersaturation ratio move.

Formulas

Case I (Eq. 6) and Case II for a small-molecule additive and a polymer (Eqs. 9 and 10), as printed in the review; the equations page gives the steps between them:

S_a=\frac{S_a^0}{1-f^a_{com}}

S_a=S_a^0\cdot x_{\mathrm{drug}}\cdot e^{\chi(1-x_{\mathrm{drug}})^2}

S_a=S_a^0\cdot\Phi_{\mathrm{drug}}\cdot e^{(1-\frac{1}{r})(1-\Phi_{\mathrm{drug}})+\chi(1-\Phi_{\mathrm{drug}})^2}

How it is measured or obtained

The review assigns the case from reported solubility, flux and phase composition data (Table 1, p. 29). Two measurements separate the cases (synthesis): S_c with the additive, and the maximum flux or free drug with the additive. S_c up and maximum flux unchanged is Case I; S_c unchanged with S_a and flux down is Case II; S_c up with flux down is Case III.

Values in the library

case	S_c	S_a	free drug at S_a	maximum supersaturation ratio	S_a/S_c gives the maximum?
no additive	S_c^0	S_a^0	S_a^0	S_a^0/S_c^0	yes
Case I	rises	rises	S_a^0	S_a^0/S_c^0	no; generally smaller
Case II	about S_c^0	falls	S_a^0X	(S_a^0/S_c^0)X	yes
Case III	rises	falls then rises, or rises	S_a^0X	(S_a^0/S_c^0)X	no

X is the term of the drug-rich phase in Eqs. 9 and 10 below. The table is taken from the review's text and Figs. 6 and 7, with the Case III formulas added (equations page, W7).

case in the review's Table 1	system in the library	values	ids
Case I	felodipine, 0.04% vitamin E TPGS	onset 10.4 → 177.3 µg/mL; concentration ratio 9.2 → 4.5; maximum flux in the buffer band	raina2015c R9, R11
Case I	atazanavir, 3.6 mg/mL SDS	crystalline 1.1 → 45.6 µg/mL; amorphous 70 → about 1450 µg/mL; concentration ratio about 65 → about 33; flux-derived ratio about 65	indulkar2017a R7, R13
Case I	ibuprofen, EUD-E	crystalline 29.8 → 42.1 µg/mL; amorphous 177.1 → 256.3 µg/mL; ratio 5.94 → 6.09	ueda2020b R1
Case II	ibuprofen, HPMC; PVP-VA	crystalline 29.8 → 30.0; 30.1 µg/mL; amorphous 177.1 → 96.9; 90.7 µg/mL; ratio 5.94 → 3.23; 3.01	ueda2020b R1

Pitfalls and disagreements

The classification comes from a review; the library has not tested it as a whole, and no paper in the library sets out Case III values for one of the pairs listed there. Atazanavir with STC is listed under Case I, yet with 3 mM STC alone the amorphous solubility fell from 65 to 38 µg/mL and the flux-based maximum was about 40 against about 63 in buffer, returning to about 63–66 from 0.075 mM lecithin indulkar2018 R6, R10, so the assignment holds for STC with lecithin and not for STC alone (synthesis). The same additive can change class with the drug or the medium: EUD-E stays in the water with ibuprofen at pH 2.0 and associates with enzalutamide droplets at pH 6.5 (F19). In Case III S_a depends on the amount of drug-rich phase, so the measured value depends on dose (pp. 39–40). The review gives no partition equation, so x_{\mathrm{drug}} and \Phi_{\mathrm{drug}} must be measured and cannot be predicted from it (equations page).

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

adsorption isotherm

The amount of solute held per gram of adsorbent, Q_a (mg/g), against the solute concentration left in solution at equilibrium, C_e, at constant temperature dening2019 E1, R2. In the mesoporous-silica papers it is measured from subsaturated into supersaturated solution, where the state is a metastable, transient equilibrium held only because no crystallization occurs dening2019 C7; mccarthy2020 C9. The shapes are type II: a rise, a gentler stretch and a second steep rise near the amorphous solubility hate2020a C21; dening2019 R2.

Findings

F3, F4, F6, F2, F10.

Related concepts

measures drug adsorption onto silica; fitted by the BET isotherm, Langmuir adsorption isotherm and Freundlich isotherm; gives monolayer coverage and evidence for multilayer adsorption; plotted on the scale of thermodynamic activity relative to the amorphous solubility.

Formulas

adsorbed amount by solution depletion, liquid-phase BET isotherm, Langmuir isotherm, Freundlich isotherm, solute activity relative to amorphous solubility.

How it is measured or obtained

Batch solution depletion: silica suspended in the medium at 37 °C, drug added from a methanolic stock (methanol below 0.5%), equilibration for 30 min, 2 h or 8 h, centrifugation or 1 µm filtration, HPLC of the supernatant, Q_a = (C_i - C_e)V/m dening2019 P3, E1; hate2020a P13, E3; hate2020b P2, E4; mccarthy2020 P7, E1. Fits with linear Langmuir and Freundlich and nonlinear BET forms dening2019 P12; mccarthy2020 P17; hate2020a P16. Replotting against C_e over the amorphous solubility gives the activity scale mccarthy2020 E2; hate2020b E3.

Values in the library

material	value or class	conditions	paper ids
ritonavir on SBA-15	39 → 424 mg/g over C_i 0.625–30 µg/mL; C_e ≤ about 25 µg/mL	12.5 µg/mL silica, pH 6.8, 30 min	dening2019 R2, X8
indomethacin on SBA-15	up to about 289 mg/g at about 35 µg/mL	125 µg/mL silica, pH 2.2, HPMC, 8 h	mccarthy2020 R7
indomethacin methyl ester on SBA-15	up to about 342 mg/g at about 7.7 µg/mL	same	mccarthy2020 R8
atazanavir on SBA-15	about 20.8 mg/g at about 64.5 µg/mL (300 µg/mL silica); about 193 mg/g at about 63.3 µg/mL (25 µg/mL silica)	HPMC, 2 h	hate2020a R2, R4
ketoconazole; clozapine; atazanavir on SBA-15	top points at pH 6.8 about 66; 53; 21 mg/g	2 h, HPMC	hate2020b R3, R4, R5
HPMC on felodipine seed crystals (not silica)	modified Langmuir K 58.1, n 6.9, adjusted R² 0.79	supersaturated felodipine	alonzo2012 R7
atazanavir into SDS micelles (not silica)	Langmuir, R² 0.998, x_m 0.017	3.6 mg/mL SDS, Region I	indulkar2017a R16

Evidence table: adsorption isotherm.

Pitfalls and disagreements

The silica concentration changed the atazanavir isotherm about sevenfold per gram (about 116 against 16.2 mg/g at C_e about 56–58 µg/mL), which a single isotherm should not do, and the low-silica data rest on small concentration changes hate2020a R2, R4, X15. The indomethacin values exceed the stated mass balance mccarthy2020 X2. Values near the top of the ritonavir isotherm vary by about 90 mg/g between runs dening2019 X4. No isotherm has a point at or above the amorphous solubility dening2019 X8. The pH of the atazanavir isotherm is not stated hate2020a X17. Isotherms from different papers differ in silica concentration, medium and equilibration time and are not directly comparable.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
itraconazole–HPMC 10:90 to 50:50	drug-rich domains at every loading by four film methods; one broad Tg by DSC of powders	solvent-cast from methanol–dichloromethane	purohit2015a R1, R11, R13, R7
telaprevir–HPMC, –PVPVA	domains from 10% drug	spin-coated films	[li2016c R4, R6]
telaprevir–HPMCAS	regular domains only from about 30–40% drug	spin-coated films, humidity not controlled	[li2016c R5, C17, X2, X9]
dextran–PVP, 20 pairs	phase separated at 0, 0–5, 5–7, 5–9 of nine compositions for DEX1, DEX6, DEX40, DEX450	DSC, freeze-dried	[vaneerdenbrugh2012a R13]
felodipine–PVP, 30–50% PVP	drug-rich and polymer-rich phases after 94% RH	IR, TEM	marsac2010 C14, C27
miconazole–PVPVA 50:50	domains after film formation at 60% RH and after 75% RH storage	AFM, confocal	[saboo2017 R13, R15, C42]
telaprevir–PVPVA, 70% PVPVA	two overlapping Tgs; "may have partially phase separated"	mDSC	mosqueragiraldo2018b R23, C53
ECP–polymer	drug-rich spheres (preparation) or drug-rich network (storage)	TEM-EDX	li2017 R18, R19, R22
ITZ–HPMC	discrete drug-rich domains with self-associated ITZ (extra emission near 381 nm)	FLOM, AFM, UV, emission	mugheirbi2017 R1, R22
LPV–HPMC	discrete drug-rich domains 50–500 nm high in a polymer-rich matrix; faster release at 33–85% DL	AFM, nanoTA, release	li2019 R8, R2
ritonavir–PVPVA spray-dried	second 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⁻¹	BLD-35 dryer	li2020 R4, R7, R10
pimozide–PVP 50:50	Tgs −21/44 °C wet, 61/112 °C re-dried	94% RH, 42 h	rumondor2009c R17
felodipine–PVP 46.5 wt%	event at ≈45–50 °C instead of one Tg near 80 °C	after 75–94% RH	marsac2010 R14
felodipine–PVP 50% film	islands of about 300–500 nm (TEM, AFM)	94% RH	marsac2010 C41
felodipine–PVP at 93% RH	crystallization independent of PVP level; plateau 70–80%	powders	rumondor2009b R21, R11, C20
felodipine, quinidine, pimozide with PVPVA; pimozide with HPMCAS	two Tgs after 94% RH	50:50 powders, dried	[rumondor2010c R3.a, R3.c, R3.d, R3.e]
indoprofen, clofoctol, probucol, nilutamide, loratadine with PVP	separation at 70–90% PVP for all; at every composition for nilutamide and loratadine	IR, 54–94% RH	[rumondor2011 R14]
ritonavir with PVP, PVPVA; HPMCAS	all PVP and PVPVA dispersions separated, from about 1 h; HPMCAS stayed miscible	97% RH, films and powders	purohit2017b C1, C22
ritonavir 50:50 PVP film	dark domains of about 1–3 µm in a drug-rich continuous phase after 10 s in buffer; 10:90 uniform	dried after immersion	purohit2017b 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 domains	100% RH, 37 °C, 3 days	que2019 R14, C16
nilvadipine 10:90 film and compact	drug-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, EUDS	discrete domains; uniform	97% RH, 24 h	saboo2020a R23, C23
ITZ–PVPVA 20% spray-dried particles	no separate drug-rich and polymer-rich phases by pyrene or TEM, also with water in the solvent	before dissolution	[bhardwaj2018 C35, C37]
felodipine 30% films with 0–10% TPGS	all separated after 12 h; semi-continuous (0, 2%) against discrete (5, 10%) drug-rich domains	≈100% RH	saboo2021 R21
clopidogrel 40, 50, 60% films	uniform; bicontinuous; drug-continuous	5 min, 100% RH	correasoto2022a R20
atazanavir 10% film	uniform for 3 h at 37 °C; separated within 10 min at 50 °C	100% RH	correasoto2022b R9, R12
lumefantrine free base, benzoate; sulfate films	separated; homogeneous	high RH, 37 °C	hiew2022b R19
ritonavir–PVPVA 30:70:5 with Tween 80; Span 20	Tg onset of surface material 66.01 → 40.25 and 67.85 → 42.18 °C after dissolution, read as a ritonavir-rich phase	DSC, scraped after dissolution	indulkar2022 R19, C19
ritonavir–PVPVA 10–40% compacts	droplets near the gel–solution boundary (10–20%); continuous drug-rich layer at the interface (30–40%)	real-time confocal, pH 6.8	yang2022a R10, R11, R12, R13
MePHPH–PVPVA; PHPH–PVPVA compacts	separation in the gel layer of most compacts; segregative (MePHPH) and associative (PHPH)	in situ confocal with two dyes	[deac2023a R6, R7, C25, C28, C71]

Evidence table: amorphous-amorphous phase separation.

Pitfalls and disagreements

A single DSC Tg did not show the separation of itraconazole–HPMC, which the authors attribute to mixing during the scan, a reading supported only by the narrower second-run steps purohit2015a C39, C26, X1. Whether the separation is kinetic (solvent-induced, water-induced) or thermodynamic is not settled, and the phase compositions were not measured: the band-ratio and softening data rank the phases but give no weight fractions [purohit2015a C48; li2016c X3, X10]. The separation depended on preparation: humidity, solvent water and the alcohol of the solvent changed whether films separated mugheirbi2017 C39; mugheirbi2018 R1, C50. For polymer pairs the plot of the miscibility map is not monotonic cell by cell [vaneerdenbrugh2012a X10]. Separation during dissolution or storage was invoked for PVPVA dispersions of lumefantrine but not measured hiew2022a C43, C61, X11. DSC and polarised light microscopy may overestimate miscibility mugheirbi2018 C4. Whether separation helps or hurts release depends on the resulting microstructure li2019 C5, C58. The same separation can lower release (ritonavir–PVPVA at 25% DL) or raise it (lopinavir–HPMC at 33–85% DL) li2020 C64; li2019 R2. In the humid felodipine–PVP films the composition of the polymer-rich phase was not determined either; the DSC "second Tg" near 124 °C may be depressed melting marsac2010 X7, C18. Faster crystallization after moisture-induced separation was shown across different drugs, not for one drug with and without separation rumondor2009c X7. In the 2019 ritonavir–PVPVA study AAPS was seen only in films dipped for seconds or in humidified samples, not in a dissolving tablet, and neither its rate nor that of dissolution was measured indulkar2019a X6. A drug-rich porous surface also follows from faster polymer dissolution alone saboo2020a X6. In the 2022 ritonavir surfactant study separation was inferred from one lowered Tg of material scraped from the wet tablet, without a second Tg or water content, and was not tested for three of the five surfactants indulkar2022 X10, X4.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir:PVP 1:9	6.4, 11.8, 18.3, 18.0 µg/mL with 6.0, 12.0, 18.0, 24.0 added	100 mM pH 6.8, 37 °C	ilevbare2013a R17
CRH1:HPMC 20:80	about 12.9 µg/mL without polymer in the medium; HPLC maximum about 13.2	pH 4.6, 25 °C	[almeidaesousa2016 R8, R12]
indomethacin–PVP-K90, 5–70 wt% PVP	amorphous by XRPD; interactions in dispersions, none in physical mixes	methanol, rotary evaporation	[taylor1997 R1, R10, R11, R12]
felodipine–PVP, nifedipine–PVP	one amorphous phase	IR, PXRD	[rumondor2009a C38]
8 drugs × 7 polymers	392 spin-coated compositions scored over 7 days	ethanol or ethanol–dichloromethane	vaneerdenbrugh2010b R2
50/50 drug–PAA, drug–PVP powders	crystalline with PAA for acidic drugs, amorphous with PVP	rotary evaporation, 7 days	vaneerdenbrugh2010b R9
felodipine, 0.5–4.5% w/w polymer	made by diluting a 10% dispersion by cryomilling	melt-quenched films	kestur2010a P1, C5
naringenin, quercetin with six polymers	highest X-ray amorphous polyphenol content about 20–85%; E100 highest, PAA lowest	rotary evaporation at 60 °C, cryo-milled	wegiel2013a R8
lumefantrine with PVPVA and four enteric polymers	all X-ray amorphous with one Tg, except 50% HPMCAS (melted at 126.3 °C on heating)	rotary evaporation at 45 °C, sieved below 250 µm	hiew2022a R4, R6
itraconazole–HPMC, telaprevir–polymers	drug-rich domains in the films	spin-coated from methanol–dichloromethane	[purohit2015a R11; li2016c R4, R5, R6]
probucol–PVP K30 50:50	amorphous; Tg 95 °C (solvent), 129 °C (moulded)	Raman, DSC	broman2001 R4.a, R4.b
probucol–PAA, –PEO	mainly Form II	same	broman2001 R4.c–f
probucol–PVP–PAA 50:25:25	mainly amorphous	both routes	broman2001 R4.g, R4.h
ritonavir and lopinavir with PVPVA 1:1 on lactose:MCC	X-ray amorphous granules, unchanged for one month at 40 °C/75% RH	solvent granulation	trasi2019 R1, R2
ritonavir–PVPVA spray-dried, 25–75% DL	X-ray amorphous (methanol powders); one Tg of 91, 75 and 63 °C	spray drying	li2020 R1, R2
ritonavir/atazanavir/lopinavir in PVP K29/32	90% polymer, Tg 139–160 °C	10% drug	alhalaweh2016 R4
atazanavir in HPMCAS, HPMC, PVPVA	10, 30, 50%	X-ray amorphous	hate2018 R10
telaprevir in HPMCAS, HPMC, PVPVA, CA Sub	10, 30, 50%	one Tg for HPMCAS 50%	mosqueragiraldo2018b R15, R23
ezetimibe in PAA, PVP, HPMC-AS	50:50	no crystals by PLM or SHG	elkhabaz2017 R8
tacrolimus capsules	tacrolimus:HPMC 1:1; drug about 4% of fill	generic	purohit2018 M2, R2
enzalutamide in PVPVA or HPMCAS-MF	10 and 50 wt% drug, rotary-evaporated, amorphous by XRPD and FTIR	used within 2 weeks	wilson2018 P10, P11
enzalutamide in CA Sub or CPHPC-106	CA Sub 50%; CPHPC-106 10 and 50% drug	rotary evaporation	wilson2020 P1, A3
atazanavir in AS-LF or AS-HF	1:9, spray-dried	dissolution and transport	ueda2020a P1, M14
pretomanid in HPMCAS-HF, MF, LF blends	20% drug in the monkey tablets, spray-dried; screening powders rotary-evaporated	with TPGS or tris in two tablets	nguyen2023a P4, P5
felodipine with PVP, HPMCAS, HPMC 0–100%	single Tg at every composition	rotary-evaporated, DSC	konno2006 R5, C8
five drugs with PVP	dry dispersions one phase by IR; single Tg for droperidol and pimozide	spin-coated and rotary-evaporated	rumondor2009c R3, R5, C1
felodipine with 0.5–4.5 wt% PVP	made by cryomilling a 10% dispersion with crystalline drug, then melting	to avoid partial crystallization on rotary evaporation	[kestur2010b P1]
resveratrol with E100, PVP, HPMC, HPMCAS, CMCAB, PAA	highest X-ray amorphous loading 60, 45, 40, 35, 35, 15%	rotary evaporation	[wegiel2013b R2]
curcumin with five polymers	75:25 dispersions	rotary evaporation, cryomilling	[wegiel2014 P2, P3]
tacrolimus–HPMC 1:1 (solvent cast) and six marketed capsules	dispersion amorphous 4 weeks at 40 °C/75% RH; one generic 57–95% crystalline at 4 weeks	open dish	trasi2017 R16, R13
ATP enantiomers with 5% w/w polymer	melt-quenched films from solvent-evaporated mixtures	growth at 40–90 °C	[sato2015 P1, P3]
indomethacin with 10% w/w HPMC, HPMCAS or PVP	solvent-evaporated dispersion, then melt-quenched	growth from 80 °C to near Tm	[tian2017 P2]

Pitfalls and disagreements

One composition of one polymer each; the medium of the CRH1 ASD runs in Figs. 7 and 8 is unclear [ilevbare2013a X15; almeidaesousa2016 X5]. The preparation route changes the result: films, rotary-evaporated powders and melt-quenched powders of the same pair can differ (PH–PAA) and the three characterization methods of one study used differently prepared samples [vaneerdenbrugh2010b C44; rumondor2009a X4]. Direct rotary evaporation below 5% w/w polymer would let felodipine crystallize, hence the cryomilled dilution, whose uniformity at the molecular level is assumed, not measured kestur2010a C5. A single Tg does not prove a single phase (see single-Tg miscibility criterion). Thermodynamically stable dispersions are hard to achieve; most are supersaturated and kinetically stabilized marsac2009 C34. The amorphous and single-phase state of the halogen-bond dispersions (up to 50 wt% for XPS, 90 wt% for IR) was not verified [que2020 X10]. Neat naringenin gave an amorphous film only by spin coating, quercetin not at all wegiel2013a R7. Amorphous probucol occurred only with PVP present, so carrier and form are confounded broman2001 X13; amorphous does not mean fastest release broman2001 C35. Two drugs in one dispersion can form a co-amorphous system whose amorphous solubilities are lower than those of the single-drug dispersions trasi2019 C38. In the Bioperformance papers making an ASD does not by itself remove dissolution-rate-limited absorption (high loading) indulkar2016 C41. The lowest loading did not always give the best dispersion (10% enzalutamide in HPMCAS crystallized), and the best solution inhibitor of 24 polymers made a dispersion no better than the crystals (F8, F24) wilson2018 R6, R16; wilson2020 R1, R6. A dispersion that is one phase when dry can separate under humidity and stay separated after drying rumondor2009c C2; marsac2010 C53. Nucleation was measured on films and Tg on powders made differently, so "one phase" is shown on one sample form and assumed for the other konno2006 X12. In the later felodipine growth papers too, below about 5% polymer rotary evaporation was expected to crystallize felodipine partly, hence the two-step dilution [kestur2013b C5]. Interactions were read on spin-coated films at other compositions than the stored powders [wegiel2014 X8; wegiel2013b X12]. Equal composition does not mean equal structure: six tacrolimus products with about one part HPMC per part drug differed in stability because of the manufacturing route trasi2017 R1, R6, C47.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ibuprofen to griseofulvin	predicted 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; atazanavir	predicted about 9.2 and 62; measured about 13 and about 63	37 °C	indulkar2015 R3, R10
felodipine, buffer; with 0.04% vitamin E TPGS; in FaSSIF	about 9.2; 4.5; 5.0 (concentration-based)	37 °C	raina2015c C29
tacrolimus	about 35 (49/1.4), about 33–36 by method; other drugs 5–65	amorphous solubility by ultracentrifugation, pH 4.5, 37 °C	trasi2016 R16, R17, X9
IDM, pH 4.5 acetate	crystalline about 8, amorphous about 80 µg/mL (about 10-fold, synthesis); unchanged by 50 µg/mL PVPVA	37 °C	moseson2020a R1
BCL, pH 6.8 phosphate	form 1 4.3, form 2 15, amorphous 150 µg/mL; 35-fold	37 °C	moseson2021 R1, R2
RTV and LPV, pH 6.8	crystalline 1.8 and 2.9, amorphous 31 and 19 µg/mL	10 mM phosphate, 37 °C	trasi2019 M1, M2
IDM–PVPVA with 25% residual crystals	C720 about 28.8 against about 43.1 µg/mL: the share of the advantage lost with the crystals	50 µg/mL total dose	moseson2020a R6
posaconazole in FaSSGF and FaSSIF V2	LLPS 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 / lopinavir	about 14 / 83 / 6	pH 6.8	alhalaweh2016 R6
clotrimazole	15	pH 8	indulkar2016 R3
atazanavir	observed ratio in SDS about half that in buffer, with unchanged activity		indulkar2017a C64, C45
atazanavir, posaconazole	concentration ratio about 55 and 36 in the buffers, about 14 and 5 in pooled human fluid; flux ratio 50–56 and 29–37	six media	elkhabaz2019b R8, R9
atazanavir, darunavir	58 and 1.37 from the printed solubilities (printed "almost 82-fold" and "1.30")	pH 6.8, 37 °C	alkalla2026 R3, R6, X1
pretomanid	8–10 in buffers	37 °C	nguyen2023a R1
tacrolimus	about 33	pH 4.5	purohit2019 C30
enzalutamide	about 14.5 (42/2.9); S "approximately 13" is the theoretical 39/2.9	pH 6.5	wilson2018 R1, R3, X2
felodipine	S of about 10 over the crystal (theoretical and measured)	benchmark for the supersaturation range S 3–12	alonzo2012 M1, C42
ritonavir	20.6 µg/mL calculated, 19.8 measured; S 15.3–15.4 over 1.3 µg/mL	37 °C	[ilevbare2012b R1, R2, R3]
efavirenz; celecoxib	19.8 and 22.6 µg/mL calculated against 12.3 and 2.5 measured	37 °C	ilevbare2013c R2
five weak bases	ratios 22.2, 11.9, 20.4, 54.6, 7.0 without and 12.3, 9.8, 16.7, 15.3, 4.3 with water correction	37 °C	hsieh2012 R10
glyburide; warfarin	about 60 and 48	25 °C	hsieh2014 R16
danazol	19.6 printed (15.4 recomputed); earlier estimates 13.7 and 26.5	25 °C	jackson2014 R2, R3, X1
six dihydropyridines	estimated amorphous solubility 0.5, 6.68, 48, 20, 6.3, 19.0 µg/mL	buffer, Hoffman with water correction	raina2015b R10
danazol	7.8 µg/mL with heat-capacity data and the water correction; onset 8 µg/mL	25 °C, pH 6.8	[jackson2016 R3, R8]
posaconazole	measured amorphous/crystalline 33.6 at pH 7.0 (32.4–37.3 from pH 2.0 to 7.0); estimate 37.9 printed	37 °C	[duong2022b R1, R6, R7, X5]
felodipine	about 10 times the crystal, about 9.5 µg/mL	37 °C, pH 6.8 test fluid	konno2008a R17
felodipine	about 9.1 µg/mL at 37 °C; 5–6 µg/mL at 25 °C	pH 6.8	alonzo2011 M1
felodipine, flux ratio to the crystal	8.5 (pure amorphous), 9.5 (50:50), 10.5 (90:10 HPMC dispersion)	dialysis, 37 °C	alonzo2011 R14
indomethacin	about 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 crystalline	pH 6.8	trasi2015b M1, M2
lopinavir	about 5.6 (17.4/3.1)	pH 3, 25 °C	[li2018 E2, R1]
indomethacin with 100 µg/mL HPMC	36 µg/mL against 1.61 (γ) and 2.8 µg/mL (α)	pH 2.2, 37 °C	xie2017 R3, R1
paclitaxel	31.6 against 0.36 µg/mL, a ratio of about 88	pH 6.8, 37 °C, three methods	que2018 R1, R2
delamanid	0.76 against 0.018 µg/mL at pH 6.5, a measured ratio of 42.3 against 31.8 from the Hoffman free energy	37 °C	duong2022a R1, R27
praziquantel, racemate and R-enantiomer	ratios 5.6–7.7 and 4.0–5.8 across nine media; amorphous 1.17–1.74 and 1.20–1.70 mg/mL	37 °C	alvarenga2025 R1
posaconazole	about 20 against 1.69 µg/mL in FaSSIF; 115.1 µg/mL crystalline in FaSSGF	37 °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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir	37.2 µg/mL (onset); 39.2 predicted; 34.2 from film	water, 37 °C	ilevbare2013a R8, R13
ritonavir; lopinavir; paclitaxel hydrate	26–28; 16–17.3; 27.2–30.1 µg/mL	100 mM phosphate pH 6.8, 25 °C, four methods	trasi2015a R1
telaprevir	90–92 µg/mL (UV, NMR, fluorescence)	pH 6.8, 37 °C	mosqueragiraldo2015 R13
clotrimazole; atazanavir	7.7; 65.1 µg/mL (un-ionized)	37 °C, 0.1 M buffer	indulkar2015 R2
ibuprofen; sorafenib; griseofulvin	125.74; 0.532; 355.96 µg/mL	pH 2 or 6.8, 25 °C; griseofulvin with HPMCAS-HF	almeidaesousa2015 R5, R6
CRH1 free base	12.49–13.73 µg/mL	pH 4.6 citrate + 20 µg/mL HPMC, 25 °C	[almeidaesousa2016 R4]
atazanavir	70 µg/mL (onset); 68 predicted; with 3.6 mg/mL SDS about 1450 µg/mL total but 65–70 µg/mL free	pH 6.8 buffer, 37 °C	indulkar2017a R5, R6, R11, R13
telaprevir	146–149 µg/mL by three methods; 311–360 with 12 mM STDC or SGDC	50 mM pH 6.5 buffer, 37 °C	lu2017b R2
pazopanib	19.8 µg/mL at pH 6.5; 9.2 at pH 8.4; 60 at pH 5	0.1 M buffers with 5 µg/mL HPMC, 37 °C	sugihara2018 R1
ibuprofen	177.1 (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
ibuprofen	154 µg/mL (buffer) → 89–131 µg/mL with 1000 µg/mL of six polymers	NMR, pH 2.0 (D2O), 37 °C	[ueda2021 R5]
ibuprofen in buffer	about 127 µg/mL at 15 °C, about 284 at 60 °C	NMR, pH 2.0 (D2O)	[ueda2022 R9]
felodipine	5.99 / 8.70 µg/mL predicted; onset 6.01 / 8.70	pH 6.8 buffer, 25 / 37 °C	raina2014a R16
nifedipine	72.09 µg/mL predicted; onset 72.85	buffer with 1 mg/mL HPMC, 37 °C	raina2014a R16, X3
felodipine, FaSSIF	onset 214.6 µg/mL; estimate 308.0	37 °C	raina2015c R1
ritonavir / atazanavir / lopinavir	45.2 / 132.1 / 27.2 µM	pH 6.8, 37 °C	alhalaweh2016 R6
clotrimazole	7.5 µg/mL (ratio 15)	pH 8, 37 °C	indulkar2016 R2, R3
atazanavir	78 µg/mL (94 with 1.8 mg/mL PVPVA)	pH 6.8, 1 mg/mL HPMCAS	hate2018 R2, R3
ezetimibe	21.0 µg/mL buffer; 123 µg/mL FeSSIF	37 °C	elkhabaz2017 R3
telaprevir	96–111 µg/mL with 1.05 mg/mL polymer	pH 6.8, 37 °C	mosqueragiraldo2018b R13
tacrolimus	about 50 µg/mL (cited), ratio about 35	USP medium I	purohit2018 R4; trasi2016 C16
enzalutamide	onset about 42 µg/mL (crystalline 2.9); the printed estimate of about 39 is not reproduced	50 mM phosphate pH 6.5, 37 °C	wilson2018 R1, R2, R3, C16
atazanavir, clozapine, ketoconazole	81.5 / 233.0 / 75.0 µg/mL without polymer; with AS-HF 35.5 / 95.0 / 56.0; with AS-LF 75.8 / 219.0 / 71.2	buffer, 37 °C, 1000–2700 µg/mL polymer	ueda2020a R1, C13
nifedipine	123 µg/mL with AS-HF against 221 with AS-LF	buffer, 37 °C, 1000 µg/mL polymer	ueda2020a R1
atazanavir, darunavir	93.1 ± 1.5 (crystalline 1.6) and 363.8 ± 2.1 µg/mL (hydrate 265.6)	pH 6.8, 37 °C, antisolvent	alkalla2026 R3
atazanavir, posaconazole	79–102 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
pretomanid	about 166 µg/mL in buffer, 226 with SLS, 275 with TPGS, 308 in FaSSIF; crystalline 15–18, ratio 8–10	pH 6.5, 37 °C	nguyen2023a R1, R2
tacrolimus	about 50 µg/mL, crystalline 2.5 µg/mL, ratio about 33	used to fix the dose-to-volume conditions	hate2019 R7; purohit2019 C30

Pitfalls and disagreements

The onset depends on the method by up to about 25% (ritonavir in water at 37 °C, 34–40 µg/mL) and on the medium (water against 100 mM buffer, twofold), so values are comparable only within one medium ilevbare2013a X14, X16, C40. Four of the eight 2013 predictions cannot be recomputed from the printed inputs ilevbare2013a X1. The claim that the onset equals the amorphous solubility is partly circular in the free-energy comparison almeidaesousa2015 X4. For ionizable drugs the value is for the un-ionized form indulkar2015 C47. For ibuprofen the same medium gave 177.1 µg/mL by extinction and 154 µg/mL by NMR, with crystalline solubilities of 29.8 and 43.1 µg/mL, in two papers of one group [ueda2020b R1, X1; ueda2021 R5, R2]. In SDS a prediction from the crystalline solubility overshoots about twofold indulkar2017a C16. For a drug that degrades on melting (pazopanib) the calculation cannot be made sugihara2018 C17. In the Bioperformance papers the onset depends on stirring, addition rate and polymer raina2014a X15. The estimate fails in FaSSIF and for high-melting telaprevir raina2015c C18; mosqueragiraldo2015 C24; the nifedipine prediction cannot be reproduced raina2014a X3. The atazanavir crystalline solubility is 5 µg/mL in one card and about 1.1 µg/mL in two others, so ratios differ hate2018 R1; alhalaweh2016 R6; indulkar2017a E3. A second drug or a polymer in the drug-rich phase lowers it (F6, F7). The value depends on the medium and on the polymer in it: the more hydrophobic HPMCAS grade AS-HF lowered it for four drugs by a quarter to well over half, and a co-dissolved crystalline drug lowered it too (F19, F20) ueda2020a R1, C13; alkalla2026 C1, C39. In simulated and human intestinal fluids the amorphous solubility rose much less than the crystalline solubility, so the ratio of the two fell from about 36 to about 5 for posaconazole (F18) elkhabaz2019b R1, R2. The printed enzalutamide estimate cannot be reproduced from its inputs wilson2018 R3, X1. The amorphous solubility of atazanavir at 37 °C is 75 (cited), 79, 81.5 and 93.1 µg/mL in four later papers, with crystalline values of 1.4, 1.14 and 1.6 µg/mL, so the ratio is 56, 71 or 58 depending on the paper hate2022 M1; elkhabaz2019b R1, R2; ueda2020a R1; alkalla2026 R3 (synthesis: 79/1.4, 81.5/1.14, 93.1/1.6).

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

amphiphilicity

The presence of both hydrophobic and hydrophilic parts in one molecule. For the cellulose ω-carboxyalkanoate esters the hydrophobic ester chains and the ionized terminal carboxyls (pKa about 4.43, nearly fully ionized at pH 6.8) make the polymer amphiphilic, which the authors think "may influence" its adsorbed conformation and so its growth inhibition [ilevbare2012c C40, R15]. CA 320S Sub, a relatively hydrophilic cellulose acetate backbone with an ionizable suberate chain, is said to have a structure that "may promote" interaction with drugs [ilevbare2013b C46]. For telaprevir the ionized carboxylate makes a cellulose polymer amphiphilic, with a free energy of solvation of −86 kcal/mol for ionized adipate against −33 for protonated adipate, but charged long side chains (A5b, A6, A7) fold onto the backbone and are "not truly amphiphilic" [mosqueragiraldo2016 R16, C37, C55].

Findings

F8, F11, F25, F37, F44.

Related concepts

Formulas

none.

How it is measured or obtained

Not measured; it follows from the polymer structure and the degree of ionization at the test pH [ilevbare2012c R15; ilevbare2013b R18].

Values in the library

material	value or class	conditions	paper ids
CA 320S Sub 0.90; 0.63	growth ratio 12.6; 10.8 on ritonavir; 7.2; 6.1 on celecoxib	5 µg/mL	[ilevbare2013b R9]
adipate esters, ionized	ratio 2.98 (CAP Adp 0.85) at pH 6.8, 1.12 at pH 3.8	ritonavir	[ilevbare2012b R7]
hydrophobicity, rigidity and amphiphilicity	"appear to be jointly responsible" for the advantage of the cellulose esters	ritonavir growth	[ilevbare2012c C49, C50]
CA-A5a-079 (short spacer, COOH branch); CA-A5b-067 (long spacer)	induction time about 90 against about 12 min	telaprevir 150 µg/mL, 5 µg/mL polymer	[mosqueragiraldo2016 R6]
HPMCAS L, M, H	amphiphilic; affinity for posaconazole rises with A/S ratio and lower pH, for water the reverse	pH 5.5–7.5	shah2025 C48
HPMCAS against Eudragit E PO	both amphiphilic; HPMCAS "should" be drawn to enzalutamide droplets	pH 6.5	wilson2021 C50, C51, C52

Pitfalls and disagreements

Amphiphilicity, solubility parameter and carboxyl content are interrelated in the new esters and cannot be separated by the data [ilevbare2012c C42, X10]. PAA, with many ionized carboxyls but no hydrophobic part, failed for all three drugs [ilevbare2013b R9.b]. Amphiphilicity was inferred, not measured, and the simulations omit the ester groups of the real polymers [mosqueragiraldo2016 X10, X15].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
felodipine with 3% PVP, PVP/VA, HPMCAS, PVAc	Tg 44.1, 43.7, 42.7, 43.5 °C against 43.3 °C	onset DSC	kestur2010a R1
bifonazole with 5% polymers	Tg 16.4–17.4 °C against 15.2 °C	onset DSC	[kestur2011 R6]
nimesulide with 5% polymers	Tg 19.9–20.8 °C against 19.5 °C	onset DSC	[kestur2011 R6]
felodipine with PVP, HPMC, HPMCAS (other chapter)	PVP raised Tg by 10 °C at 25 wt%; HPMC and HPMCAS no change up to 25 wt%	onset DSC	konno2006 R6, C25
felodipine with PVP (other chapter)	Tg largely unaffected (43.4–44.1 °C against 43.3 °C at 0.5–4.5 wt% PVP); antiplasticization not the cause, yet growth slowed	PVP grades, 3–4.5 wt%; dry	[kestur2010b R1, C34]
felodipine–PVP 10 wt%	Tg 40.5 °C, below pure felodipine 43.1 °C	dry	[marsac2006a R8, C22]
felodipine with ≤ 25% polymer	Tg ≈30–35 °C after 75% RH	25 °C	konno2008 R7, C16
celecoxib with 40% PVP K12 or PVPVA vs HPMCAS or HPMC	dry 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, dry	[xie2016b 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ezetimibe–HPMCAS 50 and 70% DL, spray dried, thin and thick Al2O3	about 12–40 nm by TEM (six places in one cut); oxide residue 1.7–9.2%	rotating-tube reactor, 35 °C	duong2022c R2, R12
erlotinib–HPMCAS, erlotinib–PVPVA, naproxen–HPMCAS, lumefantrine–PVPVA	7.4–24 nm by TGA and BET; 4.4–37.7 nm by TEM; Al2O3 and one ZnO	rotary reactor, 35 °C	moseson2022a R2
posaconazole–HPMCAS 25 and 50% DL, twelve samples	11–39 nm (oxide 0.40–3.68%); one slow-deposited 26 nm	slow, average, fast growth	[moseson2023 R1]
ritonavir–PVPVA 10 and 20% DL, nine coated samples	9.3–28.3 nm; oxide 0.92–5.30%; BET 0.22–0.76 m²/g		[benson2025 R1]
stored powders, uncoated → coated	crystals by SEM within 1–3 weeks → 3–24 weeks, or none within 48 weeks to 2 years	open dishes, 40 °C, 31–75% RH	moseson2022a R11; duong2022c R16, R17
tablets of coated ritonavir–PVPVA particles	about 35–75% of the dose at 60 min against about 95% uncoated	pH 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 Amorphous solid dispersions: the whole picture

BET isotherm

A multilayer adsorption isotherm in which the first layer is held most strongly and further layers more weakly, with no lateral interactions and a homogeneous surface dening2019 C14; hate2020a C23. For adsorption from solution the papers use the liquid-phase form of Ebadi and co-workers, with constants K_S (first layer) and K_L (upper layers) and an infinite number of layers, or a form in the relative concentration X = C_e/C_s with C_s set to the amorphous solubility dening2019 E4; mccarthy2020 E8; hate2020a E1. By analogy with the saturation vapour pressure of gas-phase BET, 1/K_L is proposed to be the saturation concentration of the liquid drug phase, the amorphous solubility ("We propose") dening2019 C48, E7; mccarthy2020 C21.

Findings

F2, F3, F10.

Related concepts

model of multilayer adsorption; gives the BET monolayer coverage; fitted to an adsorption isotherm; contrasts with the Langmuir adsorption isotherm and Freundlich isotherm; 1/K_L related to the amorphous solubility.

Formulas

liquid-phase BET isotherm.

How it is measured or obtained

Nonlinear least-squares fit of the isotherm by solution depletion, in GraphPad Prism or Origin dening2019 P12; mccarthy2020 P17; hate2020a P16. The electrostatics paper names the fit and prints only Q_m hate2020b E2, R21.

Values in the library

material	value or class	conditions	paper ids
ritonavir on SBA-15	R² 0.94; Q_m 103 mg/g; K_S 1.169, K_L 0.031 mL/µg; 1/K_L 32.7 µg/mL	pH 6.8, 37 °C	dening2019 R6, X1
indomethacin on SBA-15	R² 0.94; Q_m 29 mg/g; K_L 0.025; 1/K_L 40 µg/mL	pH 2.2, HPMC	mccarthy2020 R10, R11
indomethacin methyl ester on SBA-15	R² 0.98; Q_m 31 mg/g; K_L 0.118; 1/K_L 8.5 µg/mL	same	mccarthy2020 R10, R11
atazanavir on SBA-15	best of three models; Q_m 4.5 mg/g; K_{BET} not printed	300 µg/mL silica, HPMC	hate2020a R3, E1
three bases on SBA-15	Q_m 0.006–0.275, unit printed "mg/mol"	pH 1–6.8	hate2020b R21, X9

Evidence table: BET isotherm.

Pitfalls and disagreements

The silica surface is heterogeneous, so deviations at low concentration are expected and were seen for atazanavir ("may result") dening2019 C15; hate2020a C24. The ritonavir 1/K_L lies 17% above the measured amorphous solubility, and no isotherm point lies at or above it dening2019 X9, X8. K_S and K_L are printed in "µg/mL⁻¹" where the dimension must be mL/µg dening2019 X1. The BET Q_m from water lies 2.5 to about 60 times below the geometric monolayer (synthesis: 253/103 and 278/4.5) dening2018 R4; dening2019 R6; hate2020a R1, R3. Langmuir and Freundlich fitted worse in all three studies dening2019 R4, R5; mccarthy2020 R10; hate2020a R3.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

bile salt hydroxylation pattern

The number and position of hydroxyl groups on the steroid of a bile salt, which with the glycine or taurine conjugate defines the bile salt: cholates (STC, SGC) carry three hydroxyl groups, deoxycholates (STDC, SGDC) and chenodeoxycholates (STCDC, SGCDC) two, at different positions [indulkar2018 M6–M11; lu2018 M3–M8]. In the crystallization papers the pattern is used to group bile salts by their effect on nucleation; one study states that the effect of a bile salt "largely depends" on the number and position of its hydroxyl groups (from an earlier telaprevir study) [lu2018 C9]. Chenodeoxycholate is made in the liver and deoxycholate from cholate by gut bacteria [enright2020 X16]. The content comes from Dissolution / D. Crystallization from solution (2016–2021).

Findings

F29, F30, F32, F40, F41.

Related concepts

part of biorelevant media; related to bile salt micelles, mixed micelles, nucleation inhibition and lipophilicity.

Formulas

none.

How it is measured or obtained

From the structure; the class is then compared with induction times of single bile salts or of media that differ in their share of trihydroxy and dihydroxy bile salts at the same total bile salt and lecithin [indulkar2018 P3, R18; lu2018 P5; enright2020 P2].

Values in the library

material	value or class	conditions	paper ids
atazanavir, six single bile salts with 0.75 mM lecithin	chenodeoxy (SGCDC 175, STCDC 171 min) > deoxy (STDC 130, SGDC 109) > cholate (STC 50, SGC 38); buffer 170	3 mM, pH 6.5, 37 °C, SRamorph about 65	indulkar2018 R18, R11
Composite-SIF	60% chenodeoxy and deoxy conjugates; FaSSIF none	3 mM bile salt, 0.75 mM lecithin	indulkar2018 P1, C42
telaprevir, MWL-1 (cholate + chenodeoxycholate predominant) and MWL-2 (cholate + deoxycholate)	both >960 min; "minimal impact" of the pattern, censored	δ 11.5, 0.75 mM lecithin	[lu2018 R6, C28, X6]
atazanavir, SIF-2BAMod (TCA + GCDCA) against FaSSIFMod (TCA only)	78 ± 16 against 39 ± 12 min	digest lipid fraction, pH 6.5	[enright2020 R30, R14, X19]
fasted human fluid (cited averages)	trihydroxy share 40% (Composite-SIF), 62% (average volunteer), 47% (discussion)	three sources	[enright2020 X7]
telaprevir, 12 mM micelles	trihydroxy STC and SGC kept >960 min, dihydroxy STDC, SGDC, STCDC lost most of the effect	δ 11.5	[lu2017 R3]

Pitfalls and disagreements

The single-salt ranking with lecithin was measured for atazanavir only and is extended to ritonavir and tacrolimus by argument indulkar2018 X10. In the digest paper hydroxylation and conjugation change together (GCDCA is a glycine conjugate) [enright2020 X19]. Without lecithin, at monomeric levels, all six telaprevir bile salts held more than 960 min, so the pattern shows only at micellar levels or with lecithin [lu2017 R3]. The authors relate the effect to hydrophobicity, which none of these papers measured [indulkar2018 C4; enright2020 C45].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
telaprevir δ 11.5, 12 mM STDC, SGDC, STCDC	induction time about 140, 125, 180 min against >960 at 1.86 mM	pH 6.5, 37 °C	[lu2017 R3]
telaprevir δ 12.5, 12 mM STCDC, SGCDC	15 h residual 4.0 of 145.2 and 11.5 of 95.2 µg/mL against 60.5 and 91.7 at 1.86 mM	pH 6.5, 37 °C	[lu2017a R12]
ternary STC–STDC–STCDC at 5.58 mM	about 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir	TL-L about 11.4, 15.7, 20.0, 24.7 °C at about 58, 50, 46.5, 42.7 µg/mL	buffer or water (medium unresolved), 0.5 °C/min	ilevbare2013a R11, X6
ritonavir	LLPS concentration about 57.9 at 10 °C, 37.1 at 35 °C, 54.8 µg/mL at 65 °C	water	ilevbare2013a R11
ECP–methanol–water	drying path B → D crosses the binodal at C with less water than the spiking path B → E needs	schematic	li2017 C38
ECP–water–polymer (storage)	high-DL films absorb little water and stay in the one-phase region; low-DL films cross the binodal	schematic	li2017 C42
drug–polymer mixtures	binodal points are the two minima of the free energy of mixing against composition	argument	[rumondor2009a E6, C35]
MePHPH–PVPVA–water	experimental binodes and tie lines at 37 °C	PC-SAFT	deac2024b R15, R22
ritonavir–PVPVA–methanol–water (25% and 50% DL)	the 25% DL path enters the two-phase region from about 12.5:87.5 water:methanol; the 50% DL path from about 11.5:88.5	droplet model	li2020 R17, R19, C50, C53
ritonavir–PVPVA 10%; 20% compacts	droplets near the gel–solution interface; deeper in the gel	real-time confocal, pH 6.8	yang2022a R10, R11
PHPH–PVPVA; MePHPH–PVPVA hydrophobic binodal	about 72% PVPVA; below 5% PVPVA	particles, 48 h in buffer	deac2023b C52
MePHPH–PVPVA films 10–50%	binodal between 75 and 80% RH (≈4.9–9.4 and 9.6–14.6 wt% water)	37 °C	deac2024b R1, R2

Pitfalls and disagreements

The binodal was measured on the low-temperature branch only, four concentrations, and the scan direction on that branch is unresolved ilevbare2013a X6, X7, X17. Raina and co-workers describe the binodal points as the theoretical onset of LLPS in a partially miscible drug–buffer system raina2014a C27. In the film papers the quaternary system with polymer is "much more complex" than the ternary one drawn, and Fig. 12B lacks the letters that the text uses li2017 C36, X9. The computed binodal depends on χ values that are partly assumed and inconsistently described, and keeps the 10:90 path outside the region although the powders separate li2020 X10, X12. The binode drug loads stated in the 2023 text do not exactly match the nanoparticle data deac2023b X18. MePHPH films separated at 80% RH where the computation predicts one phase, and single-phase PHPH mixtures lie inside the computed gap deac2024b C34.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

biorelevant media

Dissolution media that simulate gastrointestinal fluids (FaSSIF, FeSSIF, Ensure Plus for the fed stomach) raina2015c M5; elkhabaz2017 C7. Later papers add FaSSIF V1 and V2, a composite FaSSIF with the six main human bile salts, pooled fasted duodenal aspirates (pH 7.3), and FeSSIF V2 at pH 5.0–6.0 for an enteric-polymer ASD elkhabaz2019b M14, P1, X5; nguyen2023a R1, R17, R19. New aspect (Crystallization from solution): in the bile-salt papers the media are characterized mainly through their bile salt; STC is the only bile salt in common recipes (FaSSIF 3 mM, FeSSIF 15 mM), against 1.40–5.90 mM of mixed conjugated bile salts in human duodenum and jejunum [li2016a R29; lu2017 R14]. From 2018 the library compares the media themselves: taurocholate-only FaSSIF against media with the six main human bile salts, lecithin against its digestion products, synthetic media from single volunteers' bile acid pools, and pooled aspirated human fluid [indulkar2018 P1; lu2018 P5; enright2020 P2, P5; elkhabaz2021 P2].

Findings

Bioperformance: F4, F11, F12, F18, F26, F27. Crystallization from solution: F29, F32, F34, F39, F40, F41, F42, F43.

Related concepts

relates to in vitro–in vivo correlation and micellar solubilization, food effect; contains mixed micelles and bile salt micelles; related to bile salt hydroxylation pattern.

Formulas

none.

How it is measured or obtained

Powder-based FeSSIF (version 1) and commercial Ensure Plus; phases of Ensure Plus separated by centrifugation elkhabaz2017 M7, M8, P2. In the bile-salt papers the recipes are compared with the bile salt content of human fluid, and single or blended bile salts replace STC in buffer to test the effect of composition [li2016a R29, P5; lu2017 R14].

Values in the library

material	value or class	conditions	paper ids
ezetimibe	crystalline 0.97 (pH 2 buffer), 18.6 (FeSSIF), 48 and 162 µg/mL (Ensure Plus aqueous, oily)	37 °C	elkhabaz2017 R1
felodipine	FaSSIF solubility about 40-fold buffer	37 °C	raina2015c R1
atazanavir	amorphous 71.4 / 75.9 / 61.1 µg/mL in three media with equal lipid; induction 39 / 74 / 23 min		[enright2020 R13, R14]
celecoxib	induction longer in a six bile-salt blend than in 0.1% taurocholate: 210 ± 21 against 103 ± 35 min	0.1% bile salt, pH 6.5, 37 °C	[li2016a R6, R28, C63, C69]
posaconazole, atazanavir	six media including a pool of aspirates; solubilities in the other rows of this chapter	pH 6.5 (simulated), 7.3 (aspirates)	elkhabaz2019b R1, R2, X5
pretomanid	equilibrium solubility 15–18 µg/mL in buffers, about 3 times that in FaSSIF V1 and about 6 times that in FeSSIF V2; reference tablet reached 110 µg/mL in FeSSIF V2	37 °C	nguyen2023a R1, C33
FaSSIF; FeSSIF; fasted FaSSGF	STC 3 mM (1.613 mg/mL); 15 mM (8.065 mg/mL); 0.08 mM	standard recipes	[li2016a R29]
human jejunum; duodenum	bile salts 1.52–5.30 mM; 1.40–5.90 mM	literature	[li2016a R29]
atazanavir, ritonavir, tacrolimus, cilnidipine	Composite-SIF against FaSSIF-V1: 120 / 43, 740 / 240, 101 / 53, 330 / 330 min	amorphous solubility of each medium, pH 6.5, 37 °C	indulkar2018 R20
telaprevir	buffer about 29, FaSSIF 21, two six-bile-salt lecithin media >960 min	δ 11.5	[lu2018 R6]
atazanavir	buffer 253 ± 65; FaSSIF about 48; Composite-SIF about 81; FaSSIF-V3 23 ± 6 min	pH 6.5, 37 °C	[enright2020 R2]
atazanavir, posaconazole	aspirated fasted human fluid about 141 and 18 min, latest of six media; FaSSIF-V1 earliest	37 °C	elkhabaz2021 R6, R7
posaconazole	FaSSIF V1 2.23 and 46.18; FeSSIF V1 7.80 and 160.89 µg/mL (crystalline, amorphous)	37 °C	[duong2022b R8]

Pitfalls and disagreements

Media differ in pH, salts and lipid at once; single components were not varied elkhabaz2017 X9. The authors state that the pretomanid results show the limits of in vitro assessment in standardized media: additives that helped in FaSSIF did not help in monkeys, and the ASD fell below the crystalline reference in the fed state (F26, F27) nguyen2023a C57, C73. An STC-only medium sat in the middle of the 3 min to more than 16 h range of the six main human bile salts for celecoxib, and ranked bile salts differently with and without a drug-rich phase [li2016a R6; lu2017 R3, R4]. No simulated medium with lecithin was tested in the bile-salt papers of 2016–2017 [li2016a C64]; from 2018 lecithin and its digests were found to shorten induction times (see F39) [indulkar2018 R16; enright2020 R10]. FaSSIF-V1 and V2 differ in buffer as well as lecithin, and aspirated fluid was at pH 7.3 against 6.5 for the simulated media elkhabaz2021 X12, X19. A six-bile-salt medium matched human fluid for atazanavir but not for posaconazole elkhabaz2021 C27.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
HP-50; HP-50-Na compacts	≈0.92 → 0.14; ≈2.80 → 2.45 mg/min/cm² from 29 to 3 mM/ΔpH	pH 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/ΔpH	pH 6.8 phosphate, 100 rpm	[bapat2023 R5]
neat HPMCAS-MF	no gel at 5 mM/ΔpH; gel 3 ± 1 µm at 13 and 19 ± 5 µm at 51 mM/ΔpH	confocal, 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 Amorphous solid dispersions: the whole picture

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.

material	value or class	conditions	paper ids
telaprevir with CA Sub	lowered in the drug-rich phase by polymer (fraction 0.90)	inferred	mosqueragiraldo2018b C37, R14
ritonavir, atazanavir mixture	each drug's amorphous solubility times its mole fraction	ideal mixing	alhalaweh2016 E7
ritonavir, lopinavir, paclitaxel	max flux drops with a second component	diffusion cell	trasi2015a C35, E3
ibuprofen	polymer dilution, extra water and interactions lower it	drug-rich phase	[ueda2021 C42]
atazanavir, clozapine, ketoconazole, nifedipine with AS-HF	amorphous solubility lowered by a quarter to well over half; AS-LF by under a tenth for three	buffer, 37 °C	ueda2020a R1, C36
atazanavir with darunavir	atazanavir ceiling and flux plateau lowered, darunavir partitioning into the atazanavir-rich phase	inferred from supernatant depletion and flux	alkalla2026 R9, R11, C37
telaprevir with six bile salts	δ 11.5 and 28.8 set from the flux ratio	pH 6.5, 37 °C	[lu2017 R1]
enzalutamide above 42 µg/mL	equal chemical potential in droplets and water; crystals can start in either phase or at the interface	pH 6.5	wilson2021 C3
posaconazole droplets with HPMCAS	polymer mixed into the droplets "serves to" lower the drug's chemical potential (not measured)	pH 6.5	shah2025 C46
ritonavir + lopinavir mixed drug-rich phases	free RTV 14.2–15.8 and LPV 7.0–7.5 µg/mL at once and twice the single-drug onsets	5 h	trasi2015b R16
ritonavir with 180 µg/mL PVP, PAA, HPMC, HPMCAS	LLPS concentration unchanged, read as no change of the phase's activity	37 °C	ilevbare2013d R10, C22
tacrolimus solutions, 20–100 µg/mL	flux plateau ≈0.0050–0.0055 µg/min from 60 µg/mL	pH 4.5, 37 °C	trasi2016 R14
resveratrol–HPMCAS solutions	up to ≈1610 µg/mL with flux ≈2.6–4.4 against 2.0 µg/min for the crystal	pH 6.8, 37 °C	[wegiel2015 R19, R20]
lopinavir with undissolved HPMCP, 15–85% drug	≈0.6–10.5 against 17.4 µg/mL	pH 3, 25 °C, 48 h	[li2018 R3]
delamanid edisylate in HPMCP-55 against HPMCP-50, pH 1.6	release ≈9% against ≈30% of the dose, polymer release ≈1–2% in both	25% 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
CAP Adp 0.85 + HPMCAS; + CAPh	pair 2.7; 2.85 against 3.0 for CAP Adp 0.85 alone	ritonavir, S 7.6	ilevbare2012a R11.j, R11.k
Tween 80 + CAP Adp 0.33; + CAP Adp 0.85	0.70; 0.83 against 1.64; 2.97 for the polymers alone and 0.53 for Tween 80 alone	5 µg/mL each, S 7.6	ilevbare2012a R17
HPMCAS 5 µg/mL ± SDS 100 µg/mL on felodipine seeds	growth ratio 2.7 (HPMCAS), 1.07 (both), 0.81 (SDS)	S 4, rotating disk	[schram2016 R16]
telaprevir seeds with STDC and STCDC monomers	both adsorb with different effectiveness ("we can speculate"), giving intermediate growth inhibition	δ 7.9	[lu2018 C20, C21, R5]
HPMC-AS in bile salt media	bile salts and lecithin "may" reduce polymer–drug interaction	six media	elkhabaz2021 C32
ritonavir on SBA-15 + 5 M urea	259 → 169 mg/g	pH 6.8, initial 27.5 µg/mL	dening2019 R8
indomethacin; methyl ester + 5 M urea	12.4 → 6.1; 14.2 → 5.8 mg/g	pH 2.2, activity about 0.2	mccarthy2020 R14
ketoconazole; clozapine + 50 mM triethylamine	about 66 → 8.6; 53 → 25 mg/g	pH 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/g	pH 6.8	dening2019 R17, R18, R19
ritonavir release + SDS 28 µg/mL	about 50%; bound 135 mg/g	pH 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
class I against class III	rotatable bonds ≈−0.54 against ≈+0.66 SD	51 molecules	baird2010 R22.a
solvent classes I against III	≈−0.42 against ≈+0.57 SD	40 drugs	vaneerdenbrugh2010a R20.b
ritonavir	18 rotatable bonds, class III	melt	baird2012 M34
nilutamide	one rotatable bond; crystal conformer at 54.4° against a computed minimum near 30°	DFT, crystal structure	[trasi2014b M1, R19, R24]
ritonavir in solution, against celecoxib and efavirenz	slow nucleation attributed to higher MW and flexibility; induction time about 120 against 2.4 and 5.1 min	aqueous buffer, 37 °C	ilevbare2013c R8, C25
glyburide, warfarin	several tautomers may explain slow crystallization; amorphous precipitates for at least 6 h with most polymers	pH shift, 1 mg/mL polymer	hsieh2014 R4, R19, C31, C32
papaverine, dipyridamole	reduced conformational freedom proposed; crystalline with every polymer; papaverine adopts its crystal conformation in solution	pH shift	hsieh2014 R4, R19, C33
six dihydropyridines	no 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir–PVPVA	congruent up to 25% DL; at 40–50% DL drug release like neat amorphous drug	cited	li2020 R23, C63
ritonavir–PVPVA spray-dried, 25% DL	rate about 3.5 mg·min⁻¹·cm⁻¹ from methanol, falling to about 0.90 with 60:40 water:methanol	pH 6.5, 100 rpm	li2020 R10
ritonavir–PVPVA, 50% and 75% DL	about 0.003–0.006 mg·min⁻¹·cm⁻¹, near neat amorphous drug (about 0.0026)	same	li2020 R10
ritonavir–PVPVA (outside)	congruent up to 25% DL; polymer leaves first above it	tablets	indulkar2019a C2
felodipine ASDs (outside)	PVP and HPMC congruent to 10% DL, PVPVA to 15%; HPMCAS and EUDS congruent to 50% DL	37 °C	saboo2020a C12, C14
BCL–PVPVA 5 and 10% DL, solvent evaporated	drug 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% SDS	congruent; more than 80% in 30 min, about 90–94% at 4 h	same	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 min	pH 6.8	[benson2025 R4]
SNAC:copovidone 50:50	congruent; ≈7.9 and ≈8.7 mg min⁻¹ cm⁻², about 4.4 and 2.7 times the neat rates; complete 25–30 min	pH 6.8, 0.5 cm² compact, 37 °C	bapat2025b R2.d–e, R3, X18
octreotide:SNAC:copovidone, 1.6% peptide	congruent in three components; ≈8.1 / ≈8.4 / ≈8.9 mg min⁻¹ cm⁻²	same	bapat2025b R2.f–h, R5
octreotide:sodium decanoate:copovidone, 1.6% peptide	≈23 and ≈25 mg min⁻¹ cm⁻² (peptide, polymer); complete in about 10 min; enhancer not assayed	same	bapat2025b R2.j–k, R9, X1
SNAC:copovidone ratio series	congruent within 30 min from 20:80 upward; 10:90 slower, complete within 40 min	same (SI, text only)	bapat2025b R4, C14
sodium decanoate:copovidone ratio series	polymer complete within about 10 min from 20:80 upward, by 25 min at 10:90	same (SI, text only)	bapat2025b R8, C18
cyclosporine:copovidone ± enhancer, 1.6% peptide	peptide follows polymer: about 50 min (binary), about 10 min (decanoate), ≈95% at 60 min (SNAC)	same	bapat2025b R10, C21
cyclosporine ternaries, 10–20% peptide	not congruent: polymer complete while peptide reaches ≈54.5% and ≈16% with decanoate	same	bapat2025b R12.i, R13.i, C23
nifedipine 10 and 20% with HPMC-E5 or PVPVA	complete release in ~20 and < 5 min, also into water saturated with drug	5 °C, D2O	indulkar2017b R8, R9, C35
ritonavir 10:90 films, PVP, PVPVA, HPMCAS	drug and polymer dissolved at the same rate; the polymer almost completely in < 10 min	25 °C, pH 6.8	purohit2017b C52, R15, R16, R17
ritonavir 50:50 HPMCAS film	initially congruent (≈32–34 µg/mL drug within 5 min)	same	purohit2017b R17, C38
ITZ–PVPVA 10% spray-dried	normalized drug ≈2000 against polymer ≈2265 µg/min/cm²	0.1 N HCl, 37 °C	[bhardwaj2018 R11]
ritonavir–PVPVA 10, 20, 25% tablets	≈97–100% of both by 60 min	pH 6.8, 37 °C	indulkar2019a R3, R11
ledipasvir–PVPVA 2 and 5%	about 100% of both by 60 min	pH 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 PVPVA	drug 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/cm²	pH 6.8; EUDS pH 7.4	saboo2020a R14
nilvadipine, felodipine, cilnidipine 40% in HPMCAS	0.42/0.42, 0.34/0.32, 0.26/0.24 mg/min/cm²	same	saboo2020a R16
indomethacin; its methyl ester in PVPVA	IND 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 min	30 min, 37 °C	saboo2020 R8
four phenolphthalein analogues at their limits	drug ≈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% TPGS	congruent to 25, 35, 45%	pH 6.8, 37 °C	saboo2021 R12, P6
loratadine–PVPVA; –HPMCAS	to 30% and 20% at 37 °C; 2% and 5% at 5 °C	compacts, t-test	[yang2021 R22]
clopidogrel–PVPVA	close to congruent to 40%; 50% with SDS	compacts	correasoto2022a C46, C55
atazanavir–PVPVA	5%; 10% with SDS or CTAB; 15% with Span 80	compacts	correasoto2022b C12
ritonavir–PVPVA 30:70 with 5 parts Span 85, TPGS; SDS; Span 20; Tween 80	congruent for at least 20 min with every surfactant; ≈87–89% (Span 85, TPGS), ≈78% (SDS), ≈41%, ≈25% of the drug at 90 min	pH 6.8, 37 °C	indulkar2022 C31, R8, R9, R5, R7, R6
miconazole 20% on HP-50; on HP-50-Na; on PTEA	incongruent and slow, drug ≈8.6% at 60 min; drug ≈89.5 and 83.7% at 60 min with the polymer ahead	compacts, 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 min	compacts, pH 6.8, 37 °C	yang2022a R2, C12, C13
indomethacin–HPMCAS-MF 10%; its methyl ester 10%	drug and polymer at the same normalized rate within error, ≈0.12 → 0.82 mg/min/cm² over 3–51 mM/ΔpH; rates comparable	pH 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 ≈2.7	compacts, pH 6.8, 37 °C	[correasoto2023 R6, R7, C13]
MePHPH–PVPVA 20, 40, 50, 70%; PHPH–PVPVA 5, 20%	drug ≈96 / 61 / 15 / 0%; ≈75 / 0% at 30 min	compacts, pH 6.8, 37 °C	[deac2023a R1, R2]
PHPH–PVPVA 5%; MePHPH–PVPVA 30% compacts	surface drug content constant over 60 min	ATR-FTIR of dried surfaces	deac2023b 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 alongside	compacts, pH 6.8 phosphate, 37 °C	bapat2024 R2, R3, C10
loratadine 25% in HPMCAS LF, MF, HF	drug/polymer ≈0.25/0.27, 0.10/0.12, 0.01/0.02	compacts, 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 20	congruent for 20 min (≈48% drug, ≈50% polymer), then ≈92–97% drug	compacts, pH 6.8	yang2023 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
8 class I-A molecules	above the fastest rate reached, 800–1100 °C/min	rapid heat–cool DSC	[baird2013 R1, X6]
antipyrin, chlorpropamide, flufenamic acid, tolbutamide	25 °C/min	rapid heat–cool DSC	[baird2013 R9]
10 class II molecules	5 °C/min or less	DSC	[baird2013 R9]
7 class I molecules (extrapolated)	20 to 3.26 × 10⁴ K/min	BC and Cabral, 5–20 °C/min	baird2010 R13
delamanid	above 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 Amorphous solid dispersions: the whole picture

critical entanglement molecular weight

Evidence table: critical entanglement molecular weight (names merged there: critical entanglement molecular weight, critical molecular weight for entanglement). Content from the release-mechanism chapter (2023–2025).

The molecular weight above which chains of a polymer entangle. Polymers above it are expected to form a gel layer in a good solvent because solvent penetrates faster than the chains disentangle; polymers near or below it may still form a swollen gel through viscosity effects (cited) [bapat2023 C34]. HPMCAS-MF, of about 18,000 Da, is below the critical values estimated for other polysaccharides, which with the rotation data led the authors to judge it "unlikely" to entangle [bapat2023 C45]. The 2024 PVP paper computes M_c \approx 30\,C_\infty M_0 = 46,620 g/mol for PVP (C_\infty = 14, M_0 = 111 g/mol), between K25 and K29/32, and places the rise of the clotrimazole limit from 20 to about 33% close to it [deac2024a E1, C16, C37].

Findings

Release mechanism and LoC: F23, F29.

Related concepts

threshold for polymer chain entanglement; decides whether dissolution goes through polymer chain disentanglement in a gel layer.

Formulas

critical molecular weight for chain entanglement.

How it is measured or obtained

Taken from estimates for other polysaccharides, without a reference [bapat2023 R27].

Values in the library

material	value or class	conditions	paper ids
pullulan; curdlan; xanthan	≈22; 24; 34 kDa (estimates, no reference given)		[bapat2023 R27]
HPMCAS-MF	≈18 kDa		[bapat2023 C45]
PVP	M_c = 46,620 g/mol	Wool estimate	[deac2024a E1]

Pitfalls and disagreements

The polysaccharide values carry no reference, and no value for HPMCAS itself is given [bapat2023 R27]. K25, below M_c, already reached a limit of 20%, so the rise spans K17 to K29/32 [deac2024a X9].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
CAP; HPMCP (Miscibility chapter)	≈0.94; slightly less than 0.83	extrapolated from literature data	hiew2022a R27
HP-50 (HPMCP)	≈83% (cited)		[qi2022 R19]
HP-50-BIS-TRIS salts, 20–100 mol% base	rate ≈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 V1	no dissolution	pH 5.0	[bapat2023 R8]
HPMCAS (pKa ≈5.0), threshold pH 5.5	≈77% ionization to start dissolving	estimate	kaur2025 C28
HPMCAS LF, MF, HF	1.52, 1.19 (cited), 0.76 mmol/g COOH; pKa 4.91, 4.97, 5.06	titration	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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
Tween 80	CMC 23.6 µg/mL (0.018 mM)	used at 500 µg/mL	ilevbare2013a M11, R16
SDS	CMC 0.5 mg/mL (buffer); 2.4 mg/mL (water, cited); Nagg 58–65	50 mM pH 6.8 phosphate, 37 °C	indulkar2017a R1, R2, R3
STC; SGDC	CMC about 4 mM; about 2 mM	pH 6.5 buffer, 37 °C, with and without 60 µg/mL telaprevir	[lu2017 R5]
Vit E TPGS / Cremophor EL / RH40 / Tween 20	0.02 / 0.01 / 0.03 / 0.009%	levels C1–C3 chosen around it	raina2015c A2
SDS in the telaprevir ASD	final about 15 µg/mL, far below CMC	37 °C	mosqueragiraldo2018b R21, C48
taurocholate, glycocholate	0.48% and 0.46% (w/v)	pH 6.5	[li2016a R12]
SDS; CTAB	SDS 0.5 mg/mL (0.05% w/v); CTAB 0.05 mg/mL	pyrene fluorescence, 37 °C, buffer	hate2022 R12
SDS in the PAMPA receiver	sink effect from 0.15%, no further rise up to 2%	atazanavir 150 µg/mL	hate2022 R13, C29
Tween 80	CMC 0.018 mM, about 24 µg/mL	5 µg/mL used (about a fifth)	ilevbare2012a M17, R17
TPGS	CMC 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 °C	saboo2021 R1
SDS in 50 mM phosphate pH 6.8	CMC 0.5 mg/mL (cited); induction-time effect from about 0.075 mg/mL, none further above the CMC	atazanavir, 37 °C	[indulkar2019b M2, R3]
SDS with 1 mg/mL polymer	critical aggregation concentration 0.1 (PVPVA), 0.2 mg/mL (HPMC-606, HPMCAS-MF)	pyrene I1/I3, no drug	[indulkar2019b R8]
lyso-PC against PC	lower CMC and higher surface activity (cited)	reasoning for faster nucleation with digests	[enright2020 C22]
SDS with celecoxib at saturation	0.23%	pH 3, 25 °C	[chen2015a R4]
STC	0.69% in the text, 0.668% on the figure	same	[chen2015a R4, X1]
polysorbate 80; Poloxamer 188; Triton X100	0.0058%; 0.16%; 0.022%	same	[chen2015a R4]
SDS / Poloxamer 188 / polysorbate 80 / STC with lopinavir	0.050 / 1.40 / 0.020 / 0.73%	pH 3 citrate, 25 °C	[li2016b R1]
SDS with lopinavir and HPMCP	break near 0.1%	pH 3, 25 °C	[li2016b R11]
ledipasvir–PVPVA with 5 parts surfactant per 100	at 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 80	487 ± 34, 50, 40, ≈14 µg/mL	50 mM pH 6.8, 37 °C	correasoto2022a R1
SDS, CTAB, TPGS, Tween 80, Span 20, Span 80, Span 85	500, 50, 40, 14, 7.3, 14, 5–50 µg/mL	as listed	correasoto2022b M3, M4, M5, M6, M7, M8, M9

Pitfalls and disagreements

The micelle-like origin of the ritonavir profile is "surmised", with no structural data ilevbare2013a C47. The CMC of the other four bile salts in the telaprevir medium was not measured, and the CMC of SDS in buffer is lower than in water [lu2017 C14; indulkar2017a C10]. The CMC basis (w/v or w/w) and source are not printed in Table I of the additive study raina2015c A2. In the PAMPA study the receiver sink effect is said to be available at 0.15% SDS, three times the CMC read by pyrene (0.05%); whether 0.15% is a tested level or a misprint is unclear hate2022 R12, R13, X6. The two printed TPGS values (212 and about 200 µg/mL) agree only at unit density; both are far above the 5 µg/mL used ilevbare2012a X16. Ritonavir solubility in 5 µg/mL Tween 80 was 1.3 ± 0.02 µg/mL, so no solubilization is expected below the CMC ilevbare2012a R1.g. Most dihydroxy conjugates and SLC have literature CMCs at or below the 1.86–2.51 mM used, so the monomer assumption is uncertain; CMCs were measured for two bile salts only in the telaprevir study [li2016a X16; lu2017 X7]. The Poloxamer 188 CMC rests on solubility changes of 0.1–0.2 µg/mL and is weakly determined [chen2015a X20]. The test levels lie 6–14% above the printed CMCs, not exactly 11% [chen2015a X2]. SDS and STC acted below their CMC as well [chen2015a C6]. The authors place an aggregation onset with PVPVA below 0.01% SDS, whereas the plotted rise begins between 0.01 and 0.025% [li2016b X9]. Below the CMC in the bulk, the surfactant concentration at the dissolving surface was not known que2019 C53. Only about half the TPGS had been released at 60 min, so the bulk stayed below the CMC in every felodipine case saboo2021 X14; one paper prints the TPGS CMC as 40 and as about 50 µg/mL correasoto2022a X1.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

critical point

Evidence table: critical point (names merged there: critical point, plait point). Content from the release-mechanism chapter (2023–2025).

The point on the binodal of a ternary diagram at which the two coexisting phases have the same composition; the 2023 dissolution papers call it the plait point. Because the volume of the hydrophobic phase decides whether it forms a network, a hydration path entering the two-phase region on the high-drug side of the plait point (through the hydrophobic binodal) makes the hydrophobic phase the majority and "should" give a continuous network, one entering on the other side a discrete phase; the plait point position therefore approximates the maximum limit of congruency of a system [deac2023a C68]. Associative systems have the plait point on the low-drug side and can have a low maximum limit, segregative systems on the high-drug side and a higher one, and a smaller miscibility gap also favours a higher maximum limit [deac2023a C69]. Strong drug–polymer interactions are proposed to lower the limit by shifting the plait point to a lower drug/polymer ratio, which raises the polymer content of the hydrophobic binode and the hydrophobic-phase volume at a given load deac2023b C63, C49. In 2024 the critical point was computed for the four analogues, the drug-rich fraction jumping across it, and its loading followed the cited limits in order, so the authors propose it as "a surrogate" for phase inversion and the limit deac2024b R35, R37, C64.

Findings

Release mechanism and LoC: F27, F30.

Related concepts

end point of the binodal and of the tie lines on the ternary phase diagram; sets the step of the lever rule; shifted by associative phase separation; approximates the maximum limit of congruency.

Formulas

none.

How it is measured or obtained

Not measured in these papers; placed on schematic diagrams deac2023b X14. Computed in 2024 with PC-SAFT for four drug–PVPVA–water systems; not measured deac2024b P19, X7.

Values in the library

material	value or class	conditions	paper ids
associative phenolphthalein analogues (PHPH, TIPP)	plait point on the low-drug side, low limit (5, 10%, cited)	schematic	deac2023b C49, R8
segregative analogues (MeTIPP, MePHPH)	plait point on the high-drug side, higher limit (30, 40%, cited)	schematic	deac2023b C48, R8
MePHPH–PVPVA–water	≈29 wt% drug, 59 wt% PVPVA, 12 wt% water (≈33% loading)	PC-SAFT, 37 °C	deac2024b R22, R35
PHPH–PVPVA–water	≈2.6 wt% drug, 59.5 wt% PVPVA, 38 wt% water (≈4.2% loading read from the diagram, synthesis: 2.6/(2.6 + 59.5) ≈ 0.042; 3.7% as the paper states)	same	deac2024b R23, R35
four analogues	≈33.2 / 32.6 / 13.7 / 3.7% loading against cited limits 40 / 30 / 10 / 5%	same	deac2024b R37

Pitfalls and disagreements

The central mechanism of the 2023 paper is drawn on schematic diagrams, one with horizontal tie lines; no diagram, tie line or plait point was measured and the link to the limit rests on the rank order of four analogues deac2023b X14. For PHPH the computed critical point (3.7%) lies below the film switch (10–15%) of the same paper deac2024b X5. Two values stand for the PHPH critical point: the paper states 3.7% loading, while the point read from its PHPH–PVPVA–water diagram (about 2.6 wt% PHPH, 59.5 wt% PVPVA) corresponds to about 4.2% (synthesis: 2.6/(2.6 + 59.5) ≈ 0.042), a difference within the precision of reading the plot deac2024b R23, R35, R37.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
IDM crystals, unheated	growth irregularities, surface imperfections; grain boundaries dividing one crystal into three regions; surface crystallites and bend contours	SEM, PLM, TEM	moseson2019 R1, R2, R3
IDM residual crystals in an extrudate	edge dislocations, bend contours, one lattice spacing in three orientations	TEM, inverse FFT	moseson2018a R12, R13, R15
tacrolimus crystals from amorphous powder	high defect level suspected because the sample stays above the crystalline solubility	dissolution	purohit2019 C38, C47, C48
cryomilled IDM crystals and HME 117-2 residual crystals grown 24 h with 50 µg/mL PVPVA	needle-like γ crystallites 170 ± 60 and 230 ± 80 nm wide from all surfaces; bulk crystals grow smooth or striated plates	SEM	moseson2020a R14, R15, R13
residual crystals in BCL–PVPVA extrudates	called "highly defective" and "commonly more potent" than bulk seeds, from the literature and growth rates	cited	moseson2021 C66, C74
BCL lots L37 (agglomerated), L38 (rough), L42 (milled), L93 (smooth)	defect density not measured; ranking inferred from PXRD at Tc	30% 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 Amorphous solid dispersions: the whole picture

crystal dissolution into a polymer melt

The process by which drug crystals suspended in a softened polymer dissolve into it, below the drug's melting point and above the polymer Tg, forming the homogeneous melt that becomes an ASD on cooling. It is usually described by the Noyes–Whitney equation with a diffusion boundary layer moseson2018 C50, C52; moseson2019 C39, C40. Crystals also break up while dissolving (fragmentation-based dissolution), which the diffusion picture does not contain moseson2019 C43, C44. A crystalline physical mixture lags a dispersion in thermogravimetry when the crystals are large, because the crystals must first dissolve at a rate set by particle size and the drug then diffuse through the viscous melt; in DSC of miscible extrudates this process appears as a dissolution endotherm instead of a melting peak moseson2020 C33, R13; moseson2021 C12. At Tc the melt is most viscous, diffusion slowest and the gradient smallest, so differences between lots of input crystals show most there [moseson2022c C37, C39, C40]. A model with dissolution alone cannot finish within 20 min, whereas one with breakage scaled by the share of agglomerates fits four lots [moseson2022c R12, R16].

Findings

F9, F11, F12, F13, F10, F31, F36, F37.

Related concepts

limited by the diffusion boundary layer; includes fragmentation-based dissolution; governed by the HME operating design space; leaves residual crystallinity.

Formulas

Noyes–Whitney equation, Stokes–Einstein equation.

How it is measured or obtained

Isothermal hot-stage microscopy without mixing (time to loss of birefringence), variable-temperature XRD, SEM-EDX chlorine maps of drug in the polymer and TEM of films held at temperature moseson2018 P10, R13; moseson2019 P3, P4, P5, P6, P7. Nonisothermal TGA of a dispersion against crystalline physical mixtures with micronized (3.5 µm) or large (93 µm) crystals moseson2020 P3, R13; the broad endothermic shift of the non-reversing heat flow over 120–170 °C of a 30% crystalline extrudate moseson2021 R7. Residence-time series in a 5 mL recirculating micro-extruder (50 rpm, 145 ± 1 °C, 2–20 min) read by PXRD, with a population balance model fitted to the crystallinity [moseson2022c P15, P16, P18, P19].

Values in the library

material	value or class	conditions	paper ids
IDM in PVPVA (117-2 powder, no mixing)	≈0.01 h at 161 °C; ≈0.32 h at 138 °C; ≈1.86 h at 131 °C; ≈7.8 h at 126 °C; ≈20.2 h at 121 °C	hot stage, n = 3	moseson2018 R13
IDM crystals in copovidone 1:5 at 130 °C	gradient about 7–9 µm after 1 h; plateau about 2.8–3.1 atomic % Cl over about 31–73 µm	SEM-EDX	moseson2019 R9
IDM extrudate at Tc	defective crystals <100 nm, amorphous channels, a dissolution front	TEM	moseson2018a R9, R13, R14
30/70 BCL–PVPVA, mixtures against the dispersion	3.5 µm mixture tracks the dispersion; 93 µm mixture lags by about 10 °C at 1–10 °C/min	nonisothermal TGA	moseson2020 R13
diffusion layer of an IDM crystal in a polymer film (cited)	on the order of 8 µm	high temperature, quiescent	moseson2020 R21
30:70 BCL–PVPVA extrudates at 155 °C from 3.5, 38 and 93 µm crystals	below 1%, 3.5% and 30% crystals left	5 mL extruder	moseson2021 R6, M2, M3
30% BCL–PVPVA at Tc = 145 °C, lots of D50 3.51 / 37.0 / 38.0 / 42.2 / 92.7 µm	below the limit of detection at 2 / 5 / 6 min; about 2.5% and 15.0% at 20 min for the last two	PXRD	[moseson2022c R10, R1]
population balance model, dissolution only	26–73% crystallinity left at 20 min with 0.5 µm/s; 3–61% with 4 µm/s	four lots	[moseson2022c R12]
same with breakage scaled by % agglomerates	dissolution rate constant 0.1002 ± 0.0511 µm/s; breakage rate constant 0.355 ± 0.111	fitted to PXRD	[moseson2022c R16]
BCL crystals in PVPVA film, 170 °C, no mixing	the rough-surfaced crystal splits at 10–15 min; the agglomerate breaks apart; fines of the milled lot vanish while a large crystal barely changes	hot-stage PLM	[moseson2022c R11]

Pitfalls and disagreements

The hot-stage sample was a partly dissolved extrudate, not a physical mixture moseson2018 X8. Between Tc and Tm dissolution was slower than melting because of lower thermal input, higher viscosity and no mixing moseson2018 C33. The nanoscale sequence of fragmentation is assembled from different particles moseson2019 X11. In DSC of miscible extrudates the crystals dissolve during the scan, so DSC under-reads them moseson2021 C12, C36. The fitted dissolution rate constant lies 5–40 times below the assumed values (0.5 and 4 µm/s), which the authors relate to melt viscosity; the printed sign conventions disagree and the size-dependence parameters are undetermined [moseson2022c R16, C30, X11, X21]. The supporting images are quiescent PLM at 170 °C, 25 °C above the melt temperature of the extrusions [moseson2022c X18].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
IDM, PVPVA	E_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/mL	E_G 8.6 and 158	150 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 prepared	S = 4	[schram2016 R2, C13]
celecoxib, HPMCAS (outside)	E_G about 130, 70 and 158 (R_0/R_p at 11/11, 22/5 and 22/22 µg/mL drug/polymer)	11 and 22 µg/mL drug, pH 6.8, 37 °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⁻¹	9.5 µg/mL start, 150 µg/mL polymer	konno2008a R16
PCZ 100 µg/mL in FaSSIF V2, HPMCAS 0 / 3 / 9 times the drug; seeds 0 / 10 µg/mL	% left at 30 min about 13 / 4.5; 66 / 10.5; 95 / 43.5	seeded solution	shah2024 R22
ritonavir, 34 polymers	E_g 0.83–3.25; Pn-IPAAmd 3.25, CAP Adp 0.85 2.98, CAB Adp 0.81 2.70, HPMCAS about 2.54	5 µg/mL polymer, S 7.6, 37 °C	[ilevbare2012c R9]
ritonavir, CA 320S Sub 0.90; 0.63	12.6; 10.8	same	[ilevbare2013b R9]
celecoxib, HPMC; HPMCAS; PVPVA	10.2; 8.5; 7.4	5 µg/mL polymer, S 6.6	[ilevbare2013b R9]
efavirenz, PVPVA; CA 320S Sub 0.90	about 4.9	S 1.2	[ilevbare2013b R9]
ritonavir, CAP Adp 0.85	6.40, 2.99, 1.56	S 3.8, 7.6, 15.3	[ilevbare2012b R5]
ritonavir, CAP Adp 0.85 + Pn-IPAAmd	about 12.1 (S 7.6); 3.3 (S 15.4)	5 + 5 µg/mL	ilevbare2012a R11, R16
felodipine, 1 µg/mL HPMC	growth ratio 0.607	S 10, 25 °C	alonzo2012 R5
felodipine, HPMCAS-LF 5 µg/mL	E_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 polymer	concentration at 24 h 16.1 (HPMC), 15.8 (PVP), 13.4 (PAA), 13.0 (none) mg/mL	S 1.5, 20 °C	[trasi2015 R11]
telaprevir, 1.86 mM bile salts, δ 2.4	E_G 3.2 (STC), 1.5, 1.4, 1.2; STCDC no desupersaturation	pH 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; HPMC	936 nm at 7 min; ≈218 → ≈459 nm (10–90 min); ≈280–307 nm at 90 min	25 °C	alonzo2011 R10, R8
felodipine particles at 37 °C, PVP against HPMC dispersions	≈441 nm by 20 min against ≈287–307 nm	37 °C	alonzo2011 R11
paclitaxel seeds with 20 µg/mL HPMCAS	growth continued at S = 88 and left ≈7.9–25.3 µg/mL after 16 h; seeds grew dendritic fingers ≈10.5–16.8 nm wide	pH 6.8, 37 °C	que2018 R14, R12
praziquantel with HPMCAS-MF against HPMC E5 LV	no concentration drop with HPMCAS outside fed media; HPMC lost dissolved drug at 1.5 mg/mL	37 °C	alvarenga2025 R14, C28
five drugs with 10 mol% PVP	growth reduced about 3- to 14-fold (authors: "around 5−10"), one point about 50-fold	supercooled liquid, 40–120 °C	[trasi2014a R6, X6, C10]
nilutamide	≈5 (alone), ≈3.8 (PAA), ≈1.1 µm/s (PVP)	supercooled liquid, 80 °C	[trasi2014b R3]
felodipine with PVP K-29/32	2- and 6-fold at 110 °C, 3- and 35-fold at 70 °C (1.5 and 4.5 wt%)	supercooled liquid, melt	[kestur2010b R13]
bifonazole with PAA	5-fold at 100 °C, 15-fold at 18 °C	supercooled liquid, 5 wt%	[kestur2011 R7]
flutamide with PVP	about one order of magnitude	supercooled liquid, 10 mol%	[trasi2012b R3]
celecoxib with PVP; with TPGS	more than one order slower; about two orders faster at 70 °C	supercooled liquid, 10% w/w	mosqueragiraldo2014 R1, C9
felodipine with 3% PVP, PVP/VA, HPMCAS, PVAc	rate ratios at 70 °C ≈10.0, 6.5, 4.4, 1.2; at 110 °C ≈2.9, 1.1, 1.1, 1.1	supercooled liquid, form II, hot stage, triplicate	kestur2010a R6
felodipine, 4.5% w/w at 90 °C	≈4.7 × 10⁻⁹ (PVP), 6.4 × 10⁻⁹ (PVP/VA), 1.7 × 10⁻⁸ (HPMCAS), 3.8 × 10⁻⁸ m/s (PVAc) against 6.7 × 10⁻⁸ m/s	supercooled liquid, log-linear in polymer content	kestur2010a R8
bifonazole with 5% PAA; PVP; HPMCAS	ratios ≈15, 5.9, 4.0 at 18 °C; ≈5.1, 2.1, 1.7 at 100 °C	supercooled liquid, melt-quenched films	[kestur2011 R7]
nimesulide with 5% PVP; PVP/VA; PVAc	ratios ≈21, 16, 3.4 at 18 °C; ≈4.7, 3.1, 2.0 at 80 °C	supercooled liquid, melt-quenched films	[kestur2011 R9]

Pitfalls and disagreements

E_G falls as supersaturation rises and depends on seed preparation, polymer concentration and polymer chemistry, so values from different systems are not comparable [ilevbare2012b C56; schram2016 C13; moseson2020a X12]. Adsorption was imaged on bulk crystals only, not on residual crystals moseson2020a X5. The threshold for "effective" is applied loosely: Eg above 1 is the stated rule, but counts of effective polymers match a cut-off near 1.2, and polymers at 1.0–1.4 are called ineffective [ilevbare2013b X3; ilevbare2012c X7]. Eg depends on supersaturation, polymer concentration, pH and buffer strength, so ratios from different papers are comparable only roughly; absolute rates cannot be compared because seed mass, volume and methanol fraction are often not printed [ilevbare2012c X16; ilevbare2012b X12]. Most 2013 ritonavir values were reported before [ilevbare2013b X15]. A polymer that raises the solubility lowers S and so flatters Eg ilevbare2013c X7; ilevbare2012a X6. The ratio depends on the seed route and the dose [schram2016 R2]; rates are not normalised to area in the felodipine and telaprevir papers [schram2016 X12; lu2017a C5]. For a bile salt mixture the "intermediate" ratio rests on an off-scale value for STCDC and a wide spread for the mixture (about 16.7–54.5), and secondary nucleation at δ 7.9 was assumed small [lu2018 X7, C8]. Polymers that form globules on an amorphous drug surface "may" need a higher concentration to block growth, which was not measured [mosqueragiraldo2018a C41]. No precipitate was examined in the 2008 felodipine study and surface areas were assumed equal konno2008a X4, X7. Seeded and unseeded tests of felodipine with HPMC later found growth at 0.607 of the polymer-free rate but an estimated nucleation-rate ratio of 7.05 × 10⁻⁴, placing the main effect on nucleation alonzo2012 R5, R17. For nifedipine polymorph conversion the polymers are read as inhibiting α nucleation, not growth raina2014b C32. The celecoxib slopes are not printed and R_p was taken over 16 h while the plot covers 4 h, so the ratios cannot be reproduced; seeded growth was measured with HPMCAS only, not HPMC xie2016a X8, X5. A polymer that blocks nucleation need not stop growth: HPMCAS held unseeded paclitaxel at S = 88 for more than 16 h but only slowed growth on seeds que2018 R3, C30. In the supercooled liquid: inhibition of growth and of nucleation need not coincide either: for acetaminophen, HPMCAS inhibited nucleation best but growth least trasi2012a C46. Some additives accelerate growth [sato2016 R11]. The molar basis of the PVP level was not defined [trasi2014a X7]. The text of the felodipine paper overstates two points against its own figures: the 105 → 70 °C fall is about 51-fold, not 3 orders of magnitude, and PVP still inhibits about 3-fold at 110 °C where the polymers "appear to have no effect" kestur2010a X1, X2. The nimesulide text gives 2–10-fold, the plot up to about 21-fold [kestur2011 X7]. The hydrogen-bond order was measured at 20–50 wt% polymer and one temperature, and bifonazole–polymer bonding was not measured [kestur2010a X5; kestur2011 X9]. The melting-point argument used form I in physical mixtures while form II grows kestur2010a X7. Only growth was measured, not nucleation kestur2010a X10. The two media are explained differently: in solution the authors propose surface poisoning by adsorbed polymer moseson2020a C48, C50, in the supercooled liquid drug–polymer hydrogen bonding and mobility, with demixing at the growth front as a "speculation" [trasi2014a C33; kestur2010a C40, C42], so ratios from the two media are not interchangeable (synthesis: different media and proposed mechanisms).

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
nimesulide	MCV 216 µm/s, the fastest of 31 drugs	bulk melt	[trasi2014a R1.a]
clotrimazole	MCV 0.02 µm/s, the slowest	bulk melt	[trasi2014a R1.ae]
vemurafenib α-needles; β	≈106 µm/s at 250 °C; ≈110 µm/s at 230 °C	supercooled liquid	[lu2016 R12.o, R12.m]
nilutamide stable form	≈0.00015 µm/s at 30 °C to ≈40 µm/s at 100 °C	seeded films	[trasi2014b R8]
felodipine	maximum near 105 °C, 3 orders lower at 70 °C	melt films	kestur2010a R5, C10
felodipine form I	about 6 times faster at the surface than in the bulk	30 °C, 0% RH	[kestur2013b R12]
felodipine films	about 2-fold rise over 13–80% RH (≈0.030 → 0.066 mm/min), 40-fold at 87% RH (2.3–2.8 mm/min at 87–93% RH)	25 °C	[rumondor2010 R1]
bifonazole	about 5.5 orders lower from 100 to 18 °C	melt-quenched films	[kestur2011 R7]
flutamide	nearly 2 orders lower from 70 to 40 °C	films	[trasi2012b R3]
acetaminophen	nearly 2 orders lower from 110 to 70 °C	films	trasi2012a R6
indomethacin γ; α; δ	MCV 4.07 × 10⁻⁷; 4.34 × 10⁻⁶; ≈1.5 × 10⁻⁷ m/s, at 135, 135 and 110 °C	pure melt	[tian2017 R7, R8, R9, R10]
celecoxib with TPGS	about two orders faster than celecoxib alone at 70 °C	10% w/w	mosqueragiraldo2014 C9
felodipine form II	≈3.5 × 10⁻⁹ (70 °C), ≈6.9 × 10⁻⁸ (90 °C), ≈1.8 × 10⁻⁷ m/s (105 °C)	neat, hot stage	kestur2010a R5.a
felodipine, 3% PVP; PVP/VA; HPMCAS; PVAc	at 70 °C ≈3.5 × 10⁻¹⁰, 5.4 × 10⁻¹⁰, 7.9 × 10⁻¹⁰, 3.0 × 10⁻⁹ m/s	form II	kestur2010a R5.e, R5.d, R5.c, R5.b
bifonazole neat; with 5% PAA	≈1.7 × 10⁻¹² and ≈1.1 × 10⁻¹³ m/s at 18 °C; ≈4.7 × 10⁻⁶ and ≈9.2 × 10⁻⁷ m/s at 100 °C	melt-quenched films	[kestur2011 R7.a, R7.i]
nimesulide neat; with 5% PVP	≈3.7 × 10⁻¹¹ and ≈1.8 × 10⁻¹² m/s at 18 °C; ≈8.5 × 10⁻⁶ and ≈1.8 × 10⁻⁶ m/s at 80 °C	melt-quenched films	[kestur2011 R9.a, R9.g]
ritonavir; celecoxib; efavirenz	normalized 0.20; 0.91; 2.97 mg min⁻¹ m⁻² at S 1.2–1.3	seeded, 37 °C	[ilevbare2013b R7]
celecoxib; ritonavir at S 6.6; 7.6	6.23; 6.14 mg min⁻¹ m⁻²	same	[ilevbare2013b R7]
celecoxib; ritonavir at S 14.7; 15.4	19.08; 14.32 mg min⁻¹ m⁻² (217.5 and 181.5 µg min⁻¹)	same	[ilevbare2013b R7]
ritonavir without additive, 10 µg/mL	1.56 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; 15.4	about 0.72; 1.4; 3.63 µg mL⁻¹ min⁻¹	same	ilevbare2012a R15
felodipine without HPMC, S 3 to 12	about 0.078 to 0.62 µg mL⁻¹ min⁻¹; g about 1.50	25 °C	alonzo2012 R4, R13
telaprevir seeds, no bile salt	5.4, 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 polymer	concentration 4.0 → 1.7 µg/mL in 50 min	S 8, 25 °C, 1000 rpm	[schram2015 R1]
atazanavir, posaconazole, six media	SHG size growth about 2–55 (atazanavir) and 20–156 nm/min (posaconazole); highest in blank buffers	37 °C, relative per field	elkhabaz2021 R15, X13
felodipine form II (PVP grade study)	3.5 × 10⁻⁹ m/s (70 °C) to 1.7 × 10⁻⁷ m/s (105 °C, maximum)	melt films	[kestur2010b R7, C9]
felodipine with 3 wt% PVP K-12, K-29/32, K-90	11-, 15-, 21-fold slower at 70 °C; 3-, 3-, 6-fold at 110 °C	melt films	[kestur2010b R8]
felodipine with 0.5–4.5 wt% PVP K-29/32	ln rate linear in concentration; slope −0.82 (70 °C) to −0.49 per wt% (105 °C)	melt films	[kestur2010b R15, E1]
felodipine with 10% PVP vs 10% HPMCAS	5.8 × 10⁻⁵ vs 1.3 × 10⁻³ mm/min (13% RH); 7.3 × 10⁻² vs 2.4 × 10⁻³ (93% RH)	room temperature	[rumondor2010 R5, R3]
flutamide with 10 mol% PVP	≈0.13 against ≈1.4 µm/s at 40 °C	melt films, diameter rate	[trasi2012b R3.a, R3.h]
acetaminophen with 10% w/w PAA	≈0.43 against ≈5.3 µm/s at 80 °C	melt films, radial rate	trasi2012a R6.a, R6.h
celecoxib	≈0.002 (70 °C) to ≈12 µm/s (120 °C); 19–38-fold slower with 10% PVP	seeded melt films	mosqueragiraldo2014 R1.a, R1.b
felodipine form I against form II, bulk	form I faster at 40–100 °C: ≈4700-fold at 40 °C, 7–9-fold at 80–100 °C	melt films	kestur2013a R8, X5
felodipine form I with 3% PVP	surface 1.45 × 10⁻⁹, bulk 6.37 × 10⁻¹¹ m/s (ratio 22.8)	30 °C, 0% RH	[kestur2013b R12]
ATP(S), ATP(R)	0.022–0.032 µm/s (40 °C) to 21–34 µm/s (90 °C); S 1.2–1.6 times faster	melt films	[sato2015 R5.a, R5.b, X2]
griseofulvin with 5% PHB	≈0.015 → ≈0.15 µm/s at 120 °C (diameter rate)	melt films	[sato2016 R4.a, R4.c]
celecoxib, alone and with 10% PVP K29/32	≈0.010 and ≈0.00003 µm/s at 80 °C	melt films	[xie2016b R21]
felodipine, buffer / PVP / HPMC / HPMCAS	dMc/dt ~0.1399 / ~0.0398 / ~0.0044 / ~0.0021 µg/mL-min	pH 6.8, 37 °C	konno2008a R16

Pitfalls and disagreements

The MCVs of the 31-drug set have no stated derivation and some disagree with the plotted rates; no replicates are given [trasi2014a X3, X17]. Rankings change with the temperature scale (T/Tg against Tm − T) [trasi2014a C7] and between surface and bulk [trasi2014a C8]. Rates above Tg cannot readily be extrapolated to storage temperatures [trasi2014a C35], and surface-enhanced or sudden growth modes near Tg can make high-temperature data overpredict stability kestur2013a C7. Near Tg, diffusion decouples from viscosity [trasi2014a C21]. The text says the felodipine rate falls by 3 orders of magnitude from 105 to 70 °C (the figure in the table above), the plot gives about 51-fold kestur2010a X1. The text says the polymers "appear to have no effect" at 110 °C, but PVP still gives a ratio of about 2.9 kestur2010a X2. All rates of the felodipine, bifonazole and nimesulide studies are plot readings from log axes and the error bars are not defined [kestur2010a X9; kestur2011 X6]. The bifonazole orders of magnitude in the text (5.5, as in the table above) differ from the plot [kestur2011 X6]. In solution, the same no-polymer condition gives 71.0, 69.80 and about 68 µg min⁻¹ for celecoxib in three places of one paper [ilevbare2013b X7]. Seed amount, volume and methanol fraction are often not printed, so absolute solution growth rates cannot be compared across studies [ilevbare2012c X16]. Efavirenz shows secondary nucleation above 10 µg/mL, which confounds its seeded rate [ilevbare2013b R5]. The fall of pure felodipine growth from 105 to 70 °C is about 49-fold in the PVP grade paper (synthesis: 1.7 × 10⁻⁷/3.5 × 10⁻⁹ [kestur2010b R7]) but 3 orders of magnitude in the text of the other 2010 paper kestur2010a C10. The melt growth model takes the diameter slope as the radial front speed [kestur2010b X5]. Replicates and error-bar meaning are not stated for the melt study or for the polymer films at fixed RH [kestur2010b X17; rumondor2010 X7]. Diameter and radial growth rates differ by a factor of two, so flutamide and acetaminophen rates cannot be compared as printed [trasi2012b R3; trasi2012a R6]. The measured felodipine front changes habit with temperature kestur2013a X12. The PHB paper reports diameter rates, twice the radial rate [sato2016 X8]. Table 2 of the indomethacin polymorph paper interchanges the δ and γ maxima of the pure drug [tian2017 X1]. Two celecoxib papers differ about tenfold in the factor by which 10% PVP slows growth [mosqueragiraldo2014 R1; xie2016b R21]. The slopes come from one panel without uncertainty, from curves that start at different 5-min levels, and no surface area was measured konno2008a X7. The buffer slope reproduces from the plotted points (≈0.14 µg/mL-min) konno2008a E5.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
bifonazole, nimesulide	spherulite size linear in time	melt films	[kestur2011 R4]
acetaminophen with polymers	spherulites; radius linear in time, R^2 > 0.99	melt films	trasi2012a R4
vemurafenib	four forms in six morphologies (needles, spherulites, feathers, clusters)	supercooled liquid	[lu2016 R7]
nilutamide stable form	growth front smooth at 70 °C, rough at 60 °C, with a 50-fold rate drop	seeded films	[trasi2014b R4, C7]
flutamide dispersion particles	number and size of needle crystals increase with storage	40 °C/75% RH	correasoto2017 R2, C12
ezetimibe ASDs	growth rate 0.020–1.0 µm/min (as printed)	buffer, FeSSIF, Ensure Plus	elkhabaz2017 R23
tacrolimus	growth rate rises steeply with supersaturation; 450 mL gives twice the supersaturation of 900 mL	USP medium I	purohit2018 C52, C55
FTM ASD (SHG)	spots at 8 days, dense field at 60 days	75% RH	correasoto2017 R2, R4
tacrolimus on seeds	n 1.677; growth constant 1.17 × 10⁻⁴ (printed unit cm/s, unclear); absorption leads below S about 18.5 and growth above it	hollow-fibre module, seeds from the crystallized generic	hate2019 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 settling	25 °C	alonzo2011 R6
felodipine particles, dispersion against methanol shift with HPMC	≈183–203 → ≈280–307 nm in 90 min, alike	25 °C	alonzo2011 R8
same at 37 °C	dispersion-born ≈259–274 nm against ≈194–219 nm at 5–10 min	37 °C	alonzo2011 R11
celecoxib seeds, 22 and 11 µg/mL, no polymer	no lag; ≈22.5 → ≈4.0 and ≈12.8 → ≈3.7 µg/mL in 30 min	pH 6.8, 37 °C	xie2016a R11
paclitaxel with 18 wt% seeds, no polymer	from 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 needles	pH 6.8, 37 °C	que2018 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 Amorphous solid dispersions: the whole picture

crystal habit

The outer shape of a crystal, here described by length, width and aspect ratio (mean length over mean width) of 50 crystals per sample; additives that adsorb on and slow the fastest-growing faces change it [ilevbare2012c E7, C5]. Ritonavir Form II grows as needles; polymers that inhibit its growth made the crystals wider and the aspect ratio smaller [ilevbare2012c R4; ilevbare2012a R6]. Felodipine seeds crystallized in HPMCAS were small and spiky at an equal imaged area (31.2 against 33.4 µm²), and acetaminophen habit changed with every polymer at 20 µg/mL [schram2016 R8, R9; trasi2015 R12]. New aspect (Supersaturation from ASD dissolution): habit is also recorded as a sign of the crystallization route and of additives: nifedipine crystals from the solution route were below 2 µm against 1–300 µm agglomerates from the matrix route raina2014b R13, R2, and celecoxib grew as thin needles, "consistent with" Form III, in every medium [chen2015a R13, C7].

Findings

Crystallization from solution: F12, F8, F24, F27, F42. Supersaturation from ASD dissolution: F3, F12, F14, F22.

Related concepts

predicted by BFDH morphology prediction; changed by polymer adsorption on crystal surfaces; related to crystal growth and surfactant-induced crystallization.

Formulas

aspect ratio.

How it is measured or obtained

SEM of crystals recovered after a growth run, length and width of 50 crystals; the habit expected for the crystal structure from the BFDH tool in Mercury; PXRD relative peak intensities as a proxy for the exposed faces [ilevbare2012c P4, P7, P13; ilevbare2012a P6]. In the ASD dissolution papers: polarized light and SEM images; length over width [raina2014b P4; ilevbare2013d P8; chen2015a P10].

Values in the library

material	value or class	conditions	paper ids
ritonavir seeds; after growth none; Pn-IPAAmd	aspect ratio 7.7; 8.8; 4.4 (width 5.8; 5.7; 9.3 µm)	S 7.6	[ilevbare2012c R4]
ritonavir with CAP Adp 0.85; with the CAP Adp 0.85 + Pn-IPAAmd pair	5.2 (rodlike); 4.8	S 7.6	[ilevbare2012b R6; ilevbare2012a R6]
ritonavir at S 15.4: none; CAP Adp 0.85; Pn-IPAAmd; pair	12.1; 7.6; 7.4; 6.5 (all needle-like)	20 µg/mL	ilevbare2012a R6
ritonavir ASD dissolution (ASD dissolution chapter)	aspect ratio about 22.4 with Tween 80 against 3.9 with PVP alone	crystals after about 90 min	ilevbare2013d R8
paclitaxel seeds (ASD dissolution chapter)	all needles of high aspect ratio, fast growth at the ends	SEM	que2018 R4, C14
acetaminophen, 20 µg/mL polymer	rods (HPMCAS), prisms (PAA), parallelepipeds (PVPVA), smaller plates (PVP), very small crystals (HPMC)	S 1.5, 20 °C	[trasi2015 R12]
telaprevir, eight media ± 150 µg/mL HPMCAS-MF	smooth bouquets of prisms (buffer), rough with polymer, smooth plates in FaSSIF with polymer	SEM, crystals after induction runs	[lu2018 R10]
atazanavir needles, buffer-V1, FaSSIF-V1, composite FaSSIF, aspirated human fluid	aspect ratio 12.4 ± 7.4, 54 ± 13, 83 ± 32, 41 ± 14	SEM, n = 15 (FaSSIF-V1 n = 10), 37 °C	elkhabaz2021 R21
posaconazole plates	about 25–45 nm thick; finger-like ends in human fluid	SEM	elkhabaz2021 R22, R23
atazanavir in SDS	25–100 µm agglomerates below 0.075 mg/mL; about 127–367 nm above	microscopy and NTA	[indulkar2019b R9, R11]
nifedipine, solution route against matrix route	below 2 µm against 1–300 µm	pH 6.8	raina2014b R13, R2
celecoxib crystals from induction runs	thin needles in all eight media	25 °C	[chen2015a R13]
celecoxib in SDS and polysorbate 80 suspensions	long free-floating needles	pH 3	[chen2015a R15]
paclitaxel seeds before and after growth without polymer	mean aspect ratio ≈23.6 → ≈17.7 (long needles) against ≈7.3 → ≈14.7 and ≈4.7 → ≈13.7 (sonicated)	pH 6.8, 37 °C	que2018 R9

Pitfalls and disagreements

Means of 50 crystals have overlapping spreads; lengths with polymer are not below the seed length, so the ratio falls through width; three of the five S 7.6 rows are cited from earlier papers [ilevbare2012a X9; ilevbare2012b X4]. The printed 5.2 for the CAP Adp 0.85 sample recomputes to 5.14 [ilevbare2012b E15, X5]. A habit change does not by itself show how much growth is slowed: HPMC gave the smallest crystals and PAA the habit nearest the prediction [trasi2015 R12, C19]. The celecoxib needle direction along the c-axis is stated without an indexing basis [chen2015a X19]; DLS sizes of needle-shaped crystals are spherical equivalents and "likely to be unreliable" ilevbare2013d C19. The fall of the long-needle aspect ratio is read as fine crystals from secondary nucleation que2018 C43.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
IDM bulk seeds, no polymer	growth rate about 0.33, 0.71, 0.99 µg/s at 10, 25, 50 µg/mL seeds	S = 6, pH 4.5	moseson2020a R4.a
IDM–PVPVA, 50 µg/mL amorphous dose	bulk 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/mL	12 h	moseson2020a R9, R10
BCL–PVPVA	relative 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 parameter	18 wt% seeds, 16 h	que2018 R14, C5
fresh generic tacrolimus capsules (outside)	seeds below 5% of the drug cause desupersaturation; growth slow at first because the surface area is small	non-sink, 100 mL	purohit2018 C45, C46
PCZ 100 µg/mL in FaSSIF V2, seeds 10 µg/mL	4.5% left at 30 min without polymer; 10.5% with HPMCAS at 3 times the drug; 43.5% at 9 times	seeded solution	shah2024 R22
PCZ–HPMCAS 10% DL with 0.3% crystals	supersaturation down to about 18.5 µg/mL by 150 min against about 125 µg/mL at 300 min without crystals	pH shift at 60 min	shah2024 R12, R14
tacrolimus generic capsules	fresh seeds below 5% of the drug (inferred); peak 98% then 39.5% in 100 mL	USP medium I	purohit2018 C46, R7
felodipine, HPMC	nucleation inhibition counts far more than growth inhibition	seeded and unseeded	alonzo2012 C40
posaconazole	seeded desupersaturation faster with more seeds and more drug, slower with more HPMCAS	FaSSIF V2	shah2024 C37, R22
tacrolimus, seeded solutions	desupersaturation rate about 0.39 at 50 µg/mL and 0.075 at 20 µg/mL	polymer in solution, hollow fibre	hate2019 R17
tacrolimus crystals in the generic capsule	1–5 µm against 5–25 µm for reference monohydrate crystals; same form	SEM, after 5 weeks at 40 °C/75% RH	purohit2019 R6, R8
posaconazole–HPMCAS 10 / 25 / 50% drug	estimated matrix crystallization ≈0.026 / ≈0.050 / ≈68% of the undissolved drug	30 min in FaSSGF, 37 °C	elkhabaz2019a R20
the same, after transfer	10% and 25% held ≈22–24 and ≈21–22 µg/mL for about 150 and 60 min; 50% fell to ≈6 µg/mL within 30 min	FaSSIF 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 shift	covered with small crystals within 30 min	pH 6.5	nguyen2023c R21
paclitaxel–HPMCAS dispersion with 18 wt% added seeds	the amorphous solubility was still reached, then lost over hours	pH 6.8, 37 °C	que2018 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir	2.4; 1.3; 0.95 µg/mL	water; 100 mM; 200 mM phosphate pH 6.8, 37 °C	ilevbare2013a R13
ritonavir; lopinavir; paclitaxel (hydrate); felodipine	1.7; 2.7; 0.32; 0.74 µg/mL	100 mM pH 6.8, 25 °C	trasi2015a R1
efavirenz; loratadine; ketoconazole; indomethacin; clotrimazole; clozapine	8.2; 1.6; 3.7; 3.0; 0.4; 8.8 µg/mL	un-ionizing media, 37 °C	ilevbare2013a R8
ibuprofen; tolnaftate; sorafenib	29.29; 27.87 × 10⁻³; 9.86 × 10⁻³ µg/mL	25 °C	almeidaesousa2015 R5
telaprevir	4.6 ± 0.1 (4.7 with 5 µg/mL HPMCAS) µg/mL	pH 6.8, 37 °C	mosqueragiraldo2015 R13
clotrimazole; atazanavir	0.55; 1.04 µg/mL (un-ionized)	37 °C	indulkar2015 R2
CRH1 free base	1.20 (pH 6.8); 1.50 µg/mL (pH 4.6 + HPMC)	25 °C	[almeidaesousa2016 R2]
telaprevir	5.2 ± 0.1 µg/mL; 9.6–12.4 with 12 mM STDC, STCDC, SGDC, SGCDC; 6.2–6.9 otherwise	50 mM pH 6.5, 37 °C	lu2017b R1
atazanavir	1.1 µg/mL (buffer); about 45.6 µg/mL (3.6 mg/mL SDS)	pH 6.8, 37 °C	indulkar2017a R4, R7
pazopanib free base	0.018 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
ibuprofen	29.8 (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 Amorphous solid dispersions: the whole picture

crystallization during dissolution

Crystallization of an amorphous drug while it dissolves, either on the dissolving solid or from the supersaturated solution it creates, so that the solution never reaches the calculated amorphous solubility ilevbare2013c C20, C24. The induction-time runs of the chapter avoid the first route by starting from a solution ilevbare2013c C24. Seeds crystallized from a felodipine–HPMCAS melt in pH 3 buffer for up to a week are the dispersion route of the seed study [schram2016 P3, R10]. New aspect (Supersaturation from ASD dissolution): the frame of two routes (crystallization of the solid matrix and of the solution) and the claim that their kinetics relative to dissolution "in large part shape" the concentration–time profile alonzo2010 C32, C47; for nifedipine both routes pass through a metastable form first raina2014b C29. For resveratrol dispersions crystallization "appeared to occur in or at the surface of the matrix", also where an undissolved polymer blocked release, and the concentration reached depended on the extent of crystallization, the drug–polymer interactions and the amount of dispersion added [wegiel2015 C16, C48]. New aspect (Release mechanism and LoC): in the release papers of 2020–2022 crystallization on the dissolving compact ends release that began well. Heating 10% atazanavir–PVPVA compacts to 55 °C, near the drug's wet Tg, restored release, but drug release ceased at about 70 min at 64% released while PVPVA dissolved completely, and crystals were seen by PLM at 90 min; crystallization "is likely" why release stopped correasoto2022b R5, C14, M1. The TPGS dispersion crystallized after 1 h at 55 °C correasoto2022b R6. For indomethacin methyl ester the route was crystallization at the compact surface saboo2020 C17. The 2025 HPMCAS papers checked and excluded it as the cause of poor weak-base release: no crystals during 1 h or for 12 h after (except loratadine–LF after about 10 h), and amorphous bedaquiline residues bapat2025a R6, C17; kaur2025 R14.

Findings

Crystallization from solution: F2, F3, F24. Supersaturation from ASD dissolution: F1, F2, F3, F16. Release mechanism and LoC: F18, F19, F32.

Related concepts

limits amorphous solubility; related to crystallization tendency and desupersaturation; part: matrix crystallization and solution crystallization; related to solution-mediated phase transformation. At the compact surface it is surface crystallization; ends congruent release; the test temperature is set against the wet glass transition temperature.

Formulas

Noyes-Whitney equation, classical nucleation theory.

How it is measured or obtained

The maximum concentration reached on dissolving a solvent-evaporated or spin-coated amorphous solid by in-situ UV, compared with the calculated value; polarized-light microscopy of melt-quenched particles wetted with buffer [ilevbare2013c P7, P8, R2, R4, R5; ilevbare2012b P5, P6]. In the ASD dissolution papers: concentration–time profiles read side by side with in situ solid-state measurements of slurries (Raman, MCR) and polarized light alonzo2010 P5; raina2014b P6, P10. In the release-mechanism papers: polarized light microscopy of the compact after the run, besides the stop of drug release while the polymer keeps dissolving correasoto2022b R5.

Values in the library

material	value or class	conditions	paper ids
ritonavir; efavirenz; celecoxib	maximum 19.8; 12.3; 2.5 µg/mL against calculated 20.6; 19.8; 22.6	pH 6.8, 37 °C	ilevbare2013c R2
amorphous celecoxib particle	birefringent spot within about 1 min, extensive crystals at 6 min	buffer, 20×	ilevbare2013c R4
amorphous efavirenz particles	shrank over 3 h, no birefringence	buffer	ilevbare2013c R5
felodipine slurry without polymer (ASD dissolution chapter)	more than 50% crystalline at the first acquisition (1 min) at 37 °C; about 8 min to 50% at 25 °C	pH 6.8	alonzo2010 R2
danazol (cited)	amorphous danazol reached less than a quarter of the expected concentration	refs in the card	jackson2014 R27
felodipine–HPMCAS melt (10% w/w)	small rounded features, steps 0.77 nm	pH 3, up to a week	[schram2016 R10, R12]
indomethacin, neat amorphous	concentration maximum (≈11.2 µg/mL) near the onset of conversion to α	pH 2, 37 °C	alonzo2010 R13, R7
nifedipine glass	glass gone by ≈6 min, γ then α; solution ≈6 µg/mL	pH 6.8, 25 and 37 °C	raina2014b R6, R14
nifedipine–HPMC 50:50	≈100 µg/mL at ≈22 min, ≈41 µg/mL at 150 min	5 mg/mL, 37 °C	raina2014b R14
resveratrol–HPMCAS 25%, pH 6.8 against pH 1.2	Raman ratio ≈0.96 and ≈0.93 after a day	37 °C	[wegiel2015 R17]
neat amorphous celecoxib	≈1.70 against ≈1.85 µg/mL for the crystal at 16 h	pH 6.8, 37 °C	xie2015 R7
atazanavir–PVPVA 10%	64% of the drug and all PVPVA released; drug release ceased at ≈70 min; crystals at 90 min	55 °C	correasoto2022b R5
atazanavir–PVPVA 10% with TPGS	crystals after 1 h	55 °C	correasoto2022b R6

Pitfalls and disagreements

For efavirenz the shrinking particles suggest crystallization from the solution after dissolution, not on the solid ("suggesting") ilevbare2013c C23. The theoretical and experimental amorphous solids were made by different routes (melt-quench for the water sorption feeding the calculation, solvent evaporation for the measurement) ilevbare2013c X17. The Tg of the hydrated solid explains the felodipine temperature effect only in part; indomethacin crystallized more slowly despite a similar Tg drop alonzo2010 C34, C42. Supersaturation in the nifedipine slurries was not measured raina2014b X10. (synthesis: the higher temperature that restored release of the 10% dispersion also brought crystallization within the 90-min run) correasoto2022b R5, R6.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
8 drugs, 7 polymers	mean amorphicity index PVP = PVPVA 70 > E100 67 > HPMC 66 > HPMCAS 62 > PAA 49 > PSSA 48	spin-coated films, 7 days dry	vaneerdenbrugh2010b R5
amides, bases against acids with PAA and PSSA	highest for amides (64–78) and bases; lowest for acids (8–31)	as above	vaneerdenbrugh2010b R3, C3
felodipine, 3% PVP, PVP/VA, HPMCAS, PVAc	growth ratio at 70 °C 10.0, 6.5, 4.4, 1.2	hot stage	kestur2010a R6
bifonazole with 5% PAA	5-fold at 100 °C, 15-fold at 18 °C	hot stage	[kestur2011 R7]
nimesulide with 5% PVP, PVP/VA, PVAc	about 21-, 16-, 3-fold at 18 °C	hot stage	[kestur2011 R9, X7]
50/50 powders, acidic drugs with PAA against PVP	about 64–117% against at most about 3% crystalline	rotary evaporation, DSC	vaneerdenbrugh2010b R9
acids, acidic N–H drugs, alcohols (13 drugs)	AI with E100, PVP, PVPVA about 54–100; with PAA, PSSA mostly about 4–31	spin-coated films, 7 days dry	[vaneerdenbrugh2011a R3, C20, C25]
naringenin, quercetin	highest X-ray amorphous content: E100 about 85 and 70%, PAA about 30 and 20%	rotary evaporation, PXRD	wegiel2013a R8
naringenin, quercetin with E100 and PVP	no crystals for >200 to >450 days at five conditions	PXRD	wegiel2013a R9
lumefantrine–PVPVA; –enteric polymers	crystals at 1–8 weeks; only at 50% drug loading (1–40 weeks)	40 °C/75% RH	hiew2022a R6
IDM, PVPVA in solution	no nucleation for more than 12 h at 5–50 µg/mL; about 40 min without	S = 6	moseson2020a R3, C11
BCL, PVPVA 70 µg/mL and HPMCAS 1 mg/mL in solution	induction above 1 h; none in 8 h; without polymer under 30 min	37 °C	moseson2021 R3
BCL–PVPVA dispersion in the slurry	HPMCAS in the medium delays crystallisation by about 10 min and leaves form 2 growth unchanged	Raman	moseson2021 R19, R20, C51
neat PCZ and BCL melts	nucleate within 1 h between Tg and Tm; IDM did not in 4 h	DSC holds	moseson2020 R7
twenty commercial polymers on ritonavir growth (outside)	five effective: Pn-IPAAmd > HPMCAS > HPMC > CAPh > CMCAB	seeded growth	[ilevbare2012c C22]
bifonazole in melt-quenched films (outside)	PAA the most effective polymer; PAA ineffective on acetaminophen in solution	5 wt%	[kestur2011 C9; trasi2015 C26]
erlotinib–HPMCAS against erlotinib–PVPVA, coated, 43% RH	none at 48 weeks against about 6 weeks	40 °C, SEM	moseson2022a R11, R12
felodipine, 1 µg/mL HPMC	growth ratio 0.607; induction time 15.3 → 136.5 min; J/J_0 7.05 × 10⁻⁴	S 10, 25 °C	alonzo2012 R5, R16, R17
ritonavir, CAB Adp 0.81	induction time ≈120 → ≈244 min	5 µg/mL, 20 µg/mL drug	ilevbare2013c R9
celecoxib, HPMC	2.4 → 12.6 min (22 µg/mL); 27.5 → 855.5 min (11 µg/mL)	5 µg/mL, 37 °C	ilevbare2013c R9, R15
danazol, HPMC-AS	6–10 → 250–516 min	10 µg/mL polymer, 25 °C	jackson2014 R17
warfarin, six polymers	amorphous precipitate ≥ 6 h; 103–224 µg/mL	1 mg/mL, pH shift	hsieh2014 R4
celecoxib, 5 µg/mL HPMCAS	supersaturation held 16 h; J_0/J_p about 4,000	22 µg/mL drug	xie2016a R3, R13
six dihydropyridines, 4.5 mg/mL polymer	PVPVA = HPMC = HPMCAS > PVP > CMCAB = CAPAdp > P2VP = PAA	nominal 10 mg/mL	raina2015b C16, R9
telaprevir 150 µg/mL, 5 µg/mL polymer	HPMC 243, HPMCAS 175–226, CA-Sub-090 106 min against 14–15 without	pH 6.8, 37 °C	[mosqueragiraldo2016 R4, R5]
acetaminophen S 1.5, 10 µg/mL	95% of vials: none 26, PAA 11, HPMCAS 470, HPMC 1043 min	20 °C	[trasi2015 R1]
atazanavir, volunteer media V5 and V6, 1 mg/mL HPMC	134 ± 23 and 45 ± 7 → >360 min	pH 6.5, 37 °C	[enright2020 R28]
telaprevir δ 28.8, 150 µg/mL HPMCAS-MF, four lecithin media	about 357–474 min, no difference	37 °C	[lu2018 R7]
enzalutamide 120 µg/mL, 50–100 µg/mL HPMCAS	about 431–530 min; P177 about 71–125 min	pH 6.5	wilson2021 R3
felodipine with 3% PVP, HPMCAS or HPMC	nucleation ≈1.3 × 10⁵ → ≈2–3 × 10³ m⁻³ s⁻¹, equal for all three	0% RH, 22 °C	konno2006 R4, C14
nifedipine and felodipine with 7 wt% PVP	about two orders of magnitude lower; 3–4-fold more to 25 wt%	0% RH	[marsac2006a R16, C18]
felodipine with 3% PVP vs HPMCAS	≈8.6 × 10⁵ vs ≈1.3 × 10⁴ m⁻³ s⁻¹	75% RH	konno2008 R3.b, C10
felodipine with 3 wt% PVP K-90	growth 21-fold slower at 70 °C, 6-fold at 110 °C	melt	[kestur2010b R8]
felodipine with 25–50% PVP vs HPMCAS	51–82% vs 9–28% crystallized after ≈490 days	75–93% RH	rumondor2009b R9, C13
acetaminophen with PAA or HPMCAS	PAA the best growth inhibitor but most nuclei; HPMCAS the reverse	10% w/w	trasi2012a C46, C53
flutamide with acceptor or donor polymers	acceptor polymers (PVP, PDMA, PIPA) slow growth; donor polymers do not	10 mol%	[trasi2012b C8, C50]
felodipine forms I and II with 3% PVP	rate ratios ≈15.8 and ≈18.7 at 60 °C, ≈3.5 and ≈6.5 at 100 °C	melt growth	kestur2013a R15
celecoxib with PVP and TPGS	slower than PVP alone at 70–120 °C at 10% PVP	melt growth	mosqueragiraldo2014 R2.b, C13
resveratrol and curcumin dispersions	PVP and E100 best for resveratrol; E100 best, PVP worst for curcumin	storage at 84% RH	[wegiel2013b R12; wegiel2014 R13]
ATP(S) vs ATP(R) with 5% HPMCAS-HF or -LF	S 1.9–2.5 times faster than R (HF); R 1.5–1.9 times faster than S (LF)	melt growth, 50–80 °C	[sato2015 R5.i–l]
six compounds with 5% PHB	ratio with/without polymer ≈0.42–10, rising with compound Tg	melt growth	[sato2016 R11]
indomethacin α vs γ with 10% HPMC	ratio without/with polymer ≈2900 vs ≈2.9 at 120 °C	melt growth	[tian2017 R12.i]
tacrolimus–HPMC 1:1 vs pure amorphous drug	amorphous at 4 weeks vs crystalline after 2 weeks at 40 °C/75% RH	open dish	trasi2017 R16, C40
felodipine dispersions 75% HPMCAS / HPMC / PVP	maxima 14.1 / 4.9 / 2.3 µg/mL	pH 6.8, 37 °C	konno2008a R7
felodipine 9.5 µg/mL, 150 µg/mL polymer	8.5–9.1 (HPMCAS), 7.8–8.9 (HPMC) µg/mL held; PVP to ≈2.8	solvent shift	konno2008a R14
amorphous indomethacin, 250 µg/mL PVP	≈23.8 µg/mL held 4 h at 25 °C	pH 2	alonzo2010 R14
indomethacin solvent shift, 37 °C	none ≈42 → ≈7.3 µg/mL in 30 min; HPMC ≈39 held about 2.5 h	pH 2	alonzo2010 R17
danazol dispersions PVP / HPMC / HPMCAS	induction ≈56–70 / ≈188–200 / ≈284–319 min	pH 6.8, 25 °C	jackson2015 R5
ritonavir 20 µg/mL, 5 µg/mL of 15 additives	induction 23.6 to 242.8 against 119.3 min	pH 6.8, 37 °C	ilevbare2013d R12
nifedipine γ → α, 1 mg/mL polymer	γ intact ≈20 (PVP), ≈60 (HPMC), ≈110 min (HPMCAS) against ≈13	25 °C	raina2014b R9
celecoxib 22 µg/mL, 5 µg/mL PVP-K12 / PVP-K29/32 / HPMCAS, HPMC / PAA	onset ≈1 h / ≈2 h / more than 8–16 h / as no polymer	pH 6.8, 37 °C	xie2015 R1; xie2016a R3
tacrolimus 50 µg/mL with 50 µg/mL HPMC	onset 6–8 h against within 3 h	pH 4.5, 37 °C	trasi2016 R9
indomethacin, 100 µg/mL HPMC against EPO	held ≈1.5 h against crystals during the titration	pH 2.2, 37 °C	xie2017 R5, R8
resveratrol dispersions	no matrix crystallization from 80% HPMC, 85% HPMCAS, 95% CMCAB	pH 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
51 molecules	23 class I, 11 class II, 17 class III	melt DSC	baird2010 R1
93 drug–solvent combinations	39 class I, 23 class II, 31 class III	spin coating	vaneerdenbrugh2010a R9
felodipine	class III (melt and solvent)	both routes	baird2010 M37; vaneerdenbrugh2010a R8.ag
nifedipine	class II	melt DSC	baird2010 M32; raina2015b C12
celecoxib	class II (melt); class III (solvent)	both routes	baird2010 M26; vaneerdenbrugh2010a R8.ae
atenolol	class I (melt); class III (solvent)	both routes	vaneerdenbrugh2010a R17
cilnidipine, nisoldipine, nitrendipine	class III	melt DSC	raina2015b C12
curcumin; resveratrol	intermediate; rapid crystallizer	solvent scheme	[wegiel2014 R21; wegiel2013b C6]
naringenin; quercetin	intermediate; rapid	solvent scheme	wegiel2013a C19
lumefantrine	class 3	melt DSC	trasi2020 R5
pretomanid, delamanid	class I	melt DSC	nguyen2023a C59
nimesulide, nilutamide, celecoxib	extended class II (fast growth, low nucleation)	extended scheme	[trasi2014a C17]
celecoxib	slow crystallizer by the cited scheme, yet growth "quite fast"; "quite hard to nucleate"	melt films	mosqueragiraldo2014 R17, R16, R15, C7
acetaminophen	forms a glass because nucleation and growth zones barely overlap	DSC and hot stage	trasi2012a C39

Pitfalls and disagreements

The class can be altered by the heating and cooling rates trasi2012a C7, and 7 of 28 class II and III molecules changed behaviour at other rates baird2010 X12. Two schemes are mixed in some papers [trasi2014a X10]. Celecoxib is called a "slow crystallizer" by one later paper although the 2010 screen placed it in class II mosqueragiraldo2014 R17; baird2010 M26. The melt class predicts crystallization from aqueous solution only partly raina2015b C28. A slow class can hide a fast grower: celecoxib is class-slow because it nucleates poorly, not because it grows slowly mosqueragiraldo2014 C7.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
31 drugs	MCV 216 to 0.02 µm/s	melt growth	[trasi2014a R1]
haloperidol, benzocaine	crystallized within seconds after quench cooling	pure melts	zhu2012 R1
ibuprofen; fenofibrate	crystallization probability 0.20 and 0.34 after 3 weeks	pure melts at 25 °C	zhu2012 R2, R3
ketoconazole	amorphous after 24 h at room temperature	pure melt	zhu2011 R6
nifedipine against felodipine	greater tendency for nifedipine	melt-quenched, heated at 2 °C/min	[marsac2006a R5, C11]
propranolol against nicardipine salts	propranolol salts more prone to crystallize	amorphous salts	[towler2008 C32]
dihydropyridines	cilnidipine slowest, nifedipine fastest in solution; for six drugs the ranking is cilnidipine < felodipine = nisoldipine < nitrendipine = nimodipine < nifedipine	supersaturated buffer; synchrotron	raina2015b C13, C28
nifedipine; nimodipine	nifedipine a very fast crystallizer; nimodipine faster than the other four dihydropyridines	aqueous media (cited)	raina2015a R17
felodipine	relatively slow; nifedipine faster	cited	raina2014a R20, C31
ritonavir, efavirenz (class III); celecoxib (class II)	induction times about 120, 5.1 and 2.4 min	supersaturated buffer, 37 °C, calculated amorphous solubility	ilevbare2013c M1–M3, R8
ritonavir	low tendency; drug-rich phase persists for 213 min	no polymer, 24 °C	tres2018 P5, M1, C29, R20
lopinavir	drug-rich phase lost after an induction period of 94 min	no 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 min	pH shift, 25 °C	hsieh2014 R1, R18, C30
pretomanid	neat glass crystallized within minutes	room temperature	nguyen2023a R4, C10
drugs with polymers	pure-drug tendency related to that in dispersions	spin coating	vaneerdenbrugh2010b C1
haloperidol in PEG 3350	onset −100 s, t_{50} 7 s; crystalline from the first SAXS/WAXS frame	20/80, 25 °C	zhu2012 R23.a, R23.b; zhu2011 R9
benzocaine in PEG 3350	onset 120–180 min, t_{50} 110–170 min	20/80, 25 °C	zhu2012 R23.a, R23.b
ibuprofen in PEG 3350	onset about 100 min, t_{50} about 70 min	20/80, 25 °C	zhu2012 R23.a, R23.b
fenofibrate in PEG 3350	onset 120–180 min, t_{50} 140–200 min	20/80, 25 °C	zhu2012 R23.a, R23.b
chlorpropamide; nilutamide in PEG 3350	partially crystalline at 24 h	20/80, 25 °C	zhu2011 R18.c, R18.e
ketoconazole in PEG 3350	amorphous at 24 h	20/80, 25 °C	zhu2011 R18.f
phenacetin, chlorzoxazone, benzamide, lidocaine, flufenamic acid (class I)	mean AI over 7 polymers 47, 47, 48, 55, 59%	spin-coated films, 7 days dry	vaneerdenbrugh2010b R4
flurbiprofen (class I/II); chlorpropamide, bifonazole (class II)	mean AI 68, 73, 97%	as above	vaneerdenbrugh2010b R4
class I films with every polymer at 75/25 drug/polymer	almost all fully crystalline (AI 0)	as above	vaneerdenbrugh2010b R2
naringenin; quercetin	intermediate; rapid crystallizer	neat films, rotary evaporation and spin coating	wegiel2013a C19, R7
lumefantrine	class III; melting onset 127.9 °C, Tg 19.7 °C	DSC heat–cool–heat	hiew2022a R3
bicalutamide in pH 6.8 buffer	nucleation 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/mL	37 °C	moseson2021 R3, R4
posaconazole and bicalutamide neat melts	melting endotherm on reheating after 1 h holds below Tm	DSC	moseson2020 R7
indomethacin neat melt	only Tg after 4 h at 130–150 °C	DSC	moseson2020 R7
ritonavir and lopinavir	amorphous granules unchanged for one month at 40 °C/75% RH	XRPD	trasi2019 R2
uncoated spray-dried ezetimibe–HPMCAS 50 and 70% DL	crystals by SEM at 19 and 12 days	open dish, 40 °C/75% RH	duong2022c R16, R17
uncoated ASD powders of four drug–polymer systems	crystals within about 1–2 weeks	40 °C, 31–75% RH	moseson2022a 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 / 43.5	seeded solution	shah2024 R22
nevirapine	induction about 5 min at S 3.9 (fast without polymer)	pH 6.5	hate2017 R2
atazanavir	relatively slow; crystallization inhibited more than 4 h with enough polymer	cited	hate2018 C13
pretomanid	induction time under 2 min at 160 µg/mL in seven media; melting onset of the crystals 147 °C	DSC, 37 °C	nguyen2023a R1, R3, R4
carvedilol, clotrimazole, clozapine, ketoconazole	class III (melt) and III (solvent evaporation); type 2	pH shift	hsieh2012 M2, M3, M4, M7, R1
loratadine	III and II/III; type 2	same	hsieh2012 M8, R1
bifonazole; dipyridamole; droperidol; papaverine; pyrimethamine	II/II; I/III; II/III; III/II; not classed; all type 1	same	hsieh2012 M1, M5, M6, M9, M10, R1
six dihydropyridines	melt: nifedipine, nimodipine Class II; others Class III; solution: 0.25–12 h	DSC; 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 min	100 mM phosphate pH 6.8, 37 °C; basis of the classes not given	[mosqueragiraldo2018a R1, M1–M9, X11]
nifedipine vs felodipine glass	0.39 vs 0.17 × 10¹⁰ m⁻³ day⁻¹; only nifedipine crystallized on heating (87 °C)	22 °C; 2 °C/min	[marsac2006a R4.a, R5]
nifedipine vs felodipine with 25% PVP	≈4.3 × 10⁵ vs ≈2.3 × 10³ m⁻³ s⁻¹	75% RH	[marsac2008a R1.f, R1.l]
resveratrol	rapid crystallizer; a polymer is needed to make it amorphous	spin coating, rotary evaporation, cryomilling	[wegiel2013b R1, C6, C27]
curcumin	intermediate crystallizer, relatively high tendency	solvent evaporation	[wegiel2014 C9, C1]
celecoxib	grows fast but nucleates poorly	melt films	mosqueragiraldo2014 C7
tacrolimus in a marketed generic capsule	crystallized within days at 40 °C/75% RH, faster than the pure amorphous drug	open dish	trasi2017 R12, R16, C28
lumefantrine; artemether	class 3; class 1	DSC heat–cool–heat	trasi2020 R5, R6, C7
felodipine, neat amorphous	≈54% crystalline at 1 min	pH 6.8 slurry, 37 °C	alonzo2010 R2
indomethacin, neat amorphous	amorphous for at least 4 h	pH 2 slurry, 25 °C	alonzo2010 R11
nifedipine, neat glass	crystalline (γ) by ≈6 min with or without dissolved polymer	pH 6.8, 25 °C	raina2014b R6, R2
resveratrol	rapid crystallizer (cited); Tm 262 °C	storage and solvent-evaporation class	[wegiel2015 R22, M1]
celecoxib, 22 µg/mL without polymer	crystallization within 5 min	pH 6.8, 37 °C	xie2016a C13
lopinavir	slow crystallization from aqueous solution	pH 3	[li2016b C5]
delamanid	induction 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 °C	37 °C	duong2022a R2, R3
praziquantel, racemate and R-enantiomer	about 5.5 and 5 min without polymer at their amorphous solubilities; 83 min and 37 min with HPMCAS-MF	PBS pH 6.5, 37 °C	polyzois2024 R3, R4
paclitaxel	unseeded crystallization within 6 min at S = 88 without polymer	pH 6.8, 37 °C	que2018 R3

Pitfalls and disagreements

The tendency depends on route and medium: rapid and slow drying differ strongly vaneerdenbrugh2010a C26, and the solid-state ranking need not hold in dilute aqueous solution hsieh2014 C30; in the dihydropyridine series, by contrast, the solution ranking and the two drugs that recrystallize from the melt coincide raina2015b C28. No single descriptor captures it vaneerdenbrugh2010a C45. In dispersions, heterogeneous nucleation by the carrier can break the link to the pure drug zhu2012 C41: the link "was found to break down for the slowly crystallizing compounds" ibuprofen and fenofibrate, because crystalline PEG apparently promotes their heterogeneous nucleation zhu2012 C41. The neat ibuprofen and fenofibrate statistics stop at 3 weeks and the dispersion runs have unstated replicates zhu2012 X5, X6. The neat-melt entries of the 2011 PEG paper (chlorpropamide, nilutamide and ibuprofen "within a few hours") come from single melts and sit beside the 50-sample statistics of the 2012 paper for ibuprofen zhu2011 R6; zhu2012 R2. The polymer fraction needed per drug is not tabulated, although the day-by-day scores show the highest drug fraction that stayed amorphous vaneerdenbrugh2010b X13, R2. The class of flurbiprofen depends on the solvent (class I from ethanol–dichloromethane, class II from ethanol), and the HPMC and HPMCAS films used the mixed solvent vaneerdenbrugh2010b X2, X12. Class III drugs were left out on the expectation of stability over a week vaneerdenbrugh2010b C13. Polymer and chemistry change the ranking within a class, so the class is a risk flag, not a prediction (see F15) vaneerdenbrugh2010b C20. The link from the neat drug to the dispersion held in the spin-coating screen vaneerdenbrugh2010b C1 but broke down for ibuprofen and fenofibrate in PEG zhu2012 C41 (synthesis: the two papers differ in carrier and test). Posaconazole, indomethacin and bicalutamide were chosen as class III glass formers, yet neat posaconazole and bicalutamide nucleated within an hour between Tg and Tm; an isothermal hold near Tm tests nucleation differently from the cooling and reheating test that defines the class (synthesis) moseson2020 C5, R7. The granulation conclusion rests on one pair of slow crystallizers trasi2019 C53. In the Bioperformance papers the tendency of the neat melt does not carry into solution with polymer (F10). A rapid crystallizer in the neat state and in solution can still be held by one polymer: HPMCAS-HF kept pretomanid in solution for over 1000 min at S = 5 while most enteric polymers failed within minutes (F27) nguyen2023a R5. In the pH-shift study class III covers all type 2 bases and also three of the four classifiable type 1 bases, so it does not separate the types hsieh2012 X1. Efavirenz is class III yet crystallizes in minutes at S about 2.3 ilevbare2013c R9.a, X4. Failing to crystallize in the DSC screen "does not guarantee" slow crystallization in solution raina2015b C29. The carry-over of the nifedipine–felodipine ranking into PVP dispersions rests on one drug pair and one polymer, and no PVP level giving equal stabilization of the two drugs was found [marsac2006a X7]. A favourable class did not protect a marketed product whose process left the drug outside the polymer: tacrolimus forms a stable glass, yet one generic crystallized faster than the pure amorphous drug trasi2016 C13; trasi2017 C28, C47. In the ASD dissolution papers nifedipine and felodipine have similar Tg and moisture sorption (cited) yet differ in water only when polymers are present raina2014b C27, R17; the felodipine–nifedipine comparison is cross-study raina2014b X16. Delamanid behaved like tacrolimus and bicalutamide, whose residual crystals the polymer does not poison, rather than like indomethacin duong2022a C58.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
nifedipine	crystals in buffer at ≈38 (25 °C) and ≈58 µg/mL (37 °C)	extinction onset with visible crystals	raina2015a R4, R5
nimodipine	crystals at ≈21.5 µg/mL (37 °C)	same	raina2015a R4, R5
nifedipine with HPMC	pyrene I1/I3 back to ≈1.60 at 400 µg/mL after ≈0.76 at 200 µg/mL	25 °C	raina2015a R16
felodipine 108 µM, no HPMC	lifetime component 9.04 ns (17%) after 15 h	pH 7.4	[tres2017 R1.g]
lopinavir, no polymer	lifetime 1.31 ns at 94 min to 1.06 ns at 213 min	pH 7.4, 24 °C	tres2018 P5, R21
itraconazole dispersions	no crystallinity in compacts after dissolution	PXRD	[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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
indomethacin milled 5, 15, 30 min	85.0, 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% PVP	RMSEE 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 °C	SONICC about 24 to 48% of the drug over 0–48 h; PXRD about 27 to 54% and Raman about 26 to 44% from 2 h	read from plots	kestur2012 R16
flutamide–HPMCAS 15%, 40 °C	XRPD 1–2% (days 35–53); 19F ssNMR 1, 3.8, 4.6% (days 35, 39, 48)	15% = all drug crystalline	correasoto2017 R12, R14
ezetimibe–HPMCAS 30%, 60 d, 82% RH	SHG about 11.5%, XRPD about 12%, ssNMR 17% of the drug; about 3.5% of the powder	40 °C	correasoto2017 R21, R22, R23
posaconazole HME ASD at 10, 25, 50 wt% DL	SHG 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 extrudates	below 1% (S/155), 3.5% (M/155), 30% (L/155) by XRPD	LOD 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 Amorphous solid dispersions: the whole picture

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

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

material	value or class	conditions	paper ids
CAP Adp 0.85; CAB Adp 0.81; CA 320S Adp; CAP Seb 0.67; CP Adp; CAP Adp 0.33; CAB Adp 0.25	DS (CO2H) 0.85; 0.81; 0.67; 0.67; 0.48; 0.33; 0.25	ritonavir growth ratios 2.98; 2.70; 1.83; 0.85; 1.68; 1.64; 0.99	[ilevbare2012c R11]
eight esters with DS (CO2H) 0.19–0.26	growth ratios 0.83–1.01	5 µg/mL	[ilevbare2012c R11]
CAP Adp 0.85 against 0.33; CAB Adp 0.81 against 0.25	same backbone, higher DS (CO2H) gives 2.98 against 1.64 and 2.70 against 0.99	ritonavir	[ilevbare2012c R11]
CA 320S Sub 0.63; CA 320S Sub 0.90; CA 320S Seb	DS (CO2H) 0.63; 0.90; 0.57	ritonavir growth ratios 10.8; 12.6; 5.7	[ilevbare2013b R9, M11–M13]
CAP-Adp-085; CA-Sub-090; CAP-Seb-024	70, 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 0.50	synthesized; MD model	[mosqueragiraldo2018a M10, M11, X9]
ECA–ECD (ethyl cellulose ethers)	ethyl DS 2.3, side-chain DS 0.69	synthesized	[mosqueragiraldo2018a M12–M15]
dansyl-labelled HPMCAS	label DS about 0.003 from NMR integrals; hydroxypropyl MS 0.69	¹H 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
felodipine–PVP–water	χ water–felodipine ≈3.3, water–PVP ≈0.5 (difference 2.8 by subtraction); felodipine–PVP slightly negative	cited values	marsac2010 R22, E1
six drugs in PVP–water	separating drugs had water–drug χ 2.84–3.58, non-separating 2.50–2.71	25 °C sorption	rumondor2009c R24, C46
ritonavir with PVP, PVPVA, HPMCAS (outside)	larger Δχ, higher tendency to phase separation (argument)	stated in words	purohit2017b E4, C43
loratadine-type ASDs (outside)	separation predicted when the difference is large even if drug–polymer χ is negative	argument	[yang2021 E2]
miconazole–PVPVA 50:50	no separation dry at 100 °C; separation with water during casting, storage and immersion, read as a water-driven change of the thermodynamics ("evidence is provided")	films and powders	[saboo2017 R22, C41, C43]

Evidence table: Δχ effect.

Pitfalls and disagreements

No ternary phase behaviour was measured; all χ values are cited or derived from sorption marsac2010 C43. Within the six-drug set the gap in water–drug χ between groups is only 0.13 and coincides with a difference in hydrogen-bond donor type, so the two explanations cannot be separated rumondor2009c X4, X13. The miconazole argument rests on one Tg after annealing (data not shown) and on images; no interaction parameters were measured [saboo2017 R22, C43].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
IDM, 50 µg/mL, no polymer	unseeded about 50 → 25.6 µg/mL at 120 min; with 50 µg/mL seeds about 26.9	pH 4.5, 37 °C	moseson2020a R3.a, R3.d
IDM, 50 µg/mL, 5 µg/mL PVPVA, 50 µg/mL seeds	about 50 → 37.1 µg/mL in 720 min	same	moseson2020a R3.h, X6
IDM–PVPVA extrudates	slight 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/155	about 32.4 → 24.5 and about 28.2 → 16.2 µg/mL	150 µg/mL dose, 4 h	moseson2021 R12
paclitaxel–HPMCAS with 18 wt% seeds (outside)	desupersaturation by crystal growth; HPMCAS cannot block it completely	16 h	que2018 C30
tacrolimus capsules (outside)	steep decline after the maximum shows that seeds grow rapidly in 100 mL	pH 4.5	purohit2018 C43
PCZ–HPMCAS 10% DL, 0.3% crystals against none	peak about 178 → 18.5 µg/mL at 150 min against about 172.5 → 125 µg/mL at 300 min	pH shift at 60 min, dose about 200 µg/mL	shah2024 R12, R14
PCZ–HPMCAS 25% DL, 3.2% crystals against none	crystallization after 45 min against about 1.5 h	same	shah2024 R15, C29
BCL–PVPVA 30% DL, 3% SDS, cryomilled 5 min	peak 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 / 74.5	seeded solution	shah2024 R22
ezetimibe PVP ASD, FeSSIF	195 µg/mL at 15 min to 41 at 30 min	37 °C	elkhabaz2017 R14
ezetimibe ASDs, buffer	decline after about 30 min		elkhabaz2017 R10, C19
tacrolimus generic, 100 mL	about 98% released at 20–30 min, 39.5% at 120 min	medium I	purohit2018 R7
felodipine, no polymer, unseeded	about 5.35 → 1.54 µg/mL from about 10–15 min to 150 min	S 10	alonzo2012 R15
paclitaxel–HPMCAS	none unseeded; present with 18 wt% seeds	16 h	que2018 R13
pazopanib	19.8 to about 1 µg/mL at 60 min	pH 6.5	sugihara2018 R8
enzalutamide PVPVA ASDs	maximum close to the amorphous solubility, then fall; 10:90 HPMCAS peak only 10 µg/mL with crystals in the medium	100 µg/mL total, 12.5 mL, pH 6.5	wilson2018 R6, C18
tacrolimus, seeded solutions	rate about 0.39 at 50 µg/mL against 0.075 at 20 µg/mL; growth order 1.677	seeds from the crystallized generic	hate2019 R17, R18, C30
tacrolimus 50% and 100% crystalline capsule contents	15 and 4 µg/mL at 2 h, still above the crystalline solubility	5 mg in 100 mL, pH 4.5	purohit2019 R4
felodipine, 1 µg/mL HPMC, seeded; unseeded	5.1 → 2.17 µg/mL in 58 min; 5.38 → 5.03 over 198 min	S 10, 25 °C	alonzo2012 R18
ritonavir seeded, none; CAP Adp 0.85	10.0 → 6.9; 10.15 → 9.25 µg/mL in 2 min	S 7.6, 37 °C	[ilevbare2012c R7]
danazol 20 µg/mL, no polymer	apparent UV concentration 19.2 → 14.4 → 11.8 → 2.1 → 1.4 µg/mL at 1, 5, 10, 30, 60 min	25 °C	jackson2014 R15
celecoxib, HPMC, start S 14.7	S 15 for 15 min, 7.8 at 35 min, 4.9 at 100 min, 4.3 at 200–240 min	37 °C	ilevbare2013c R16
paclitaxel with 18 wt% seeds (ASD dissolution chapter)	desupersaturation immediate without polymer	37 °C	que2018 R7
telaprevir seeds, 1.86 mM STCDC	flat at about 11.2 and 72 µg/mL for 240 min; buffer 4 and 6	δ 2.4 and 12.5	[lu2017a R11]
telaprevir after 15 h, δ 12.5	residual 60.5 (STCDC), 91.7 (SGCDC), 9.0 (STC) of 65.2–95.2 µg/mL	diffusion cell	[lu2017a R12]
acetaminophen seeded	19.5–19.8 → 13.0 (none) and 16.1 mg/mL (HPMC) at 24 h	S 1.5, 20 µg/mL polymer	[trasi2015 R11]
atazanavir, posaconazole after nucleation, three media	atazanavir 1.0, 4.2, 0.3; posaconazole 0.6, 1.9, 1.7 µg/mL·min (buffer-V1, FaSSIF-V1, composite)	37 °C, slope after the break	elkhabaz2021 R8, E7
posaconazole at S 33.6 with nanocrystal seeds	from about 8.5 to 4.9 µg/mL by 4 min (2 µg/mL seeds), to about 3.4 within about 1 min (20 µg/mL)	PBS pH 6.5	[duong2022b R13]
felodipine 50 µg/mL nominal, 150 µg/mL PVP; none	≈6.3 → ≈1.9 µg/mL in 240 min; ≈2.7 → ≈1.05	solvent shift, 37 °C	konno2008a R12
indomethacin, solvent shift, no polymer	≈27.3 µg/mL held about 25 min, then ≈5.3 at 90 min	pH 2, 25 °C	alonzo2010 R18
felodipine 90:10 HPMC, 90 µg/mL added	apparent ≈75 µg/mL at 5 min, ≈22.6 at 50 min	37 °C	alonzo2011 R2
danazol 90:10 PVP dispersion	≈9.2 µg/mL at 60 min to ≈2.2 at 420 min, pyrene ratio rising	pH 6.8, 25 °C	jackson2015 R12
nifedipine–HPMC 50:50	≈100 µg/mL at ≈22 min to ≈41 at 150 min	37 °C	raina2014b R14
celecoxib–HPMCAS suspension, SDS	S ≈8.6 at about 5 min to ≈3.2 at 1 h	pH 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 h	solvent shift, pH 6.8, 37 °C	xie2015 R2
celecoxib–PVP-K12 50% dispersion	≈21.0 µg/mL near 6 h → ≈6.5 at 16 h	pH 6.8, 37 °C	xie2015 R6
celecoxib 22 µg/mL seeded: none / 5 µg/mL HPMCAS	≈22.5 → ≈4.0 in 30 min / → ≈16.0 µg/mL at 4 h	pH 6.8, 37 °C	xie2016a R11
tacrolimus 50 µg/mL: none / 50 µg/mL HPMC	fall from ≈150 min / from ≈400 min	pH 4.5, 37 °C	trasi2016 R9
indomethacin–EPO 3:7 dispersion	≈77 µg/mL (UV) → 8.8 µg/mL (HPLC) at 1 h	pH 2.2, 37 °C	xie2017 R11
lopinavir 50%: EUD, CAP / HPMCP	loss within ≈10–12 h / none in 48 h	pH 3, 25 °C	[li2018 R6]
paclitaxel–HPMCAS 49/51 with 18 wt% seeds	≈31–33 µg/mL reached, then ≈7.9–25.3 µg/mL left at 16 h depending on the seed type	pH 6.8, 37 °C	que2018 R14
posaconazole–HPMCAS 10% dispersion, high against low dose	≈22–24 µg/mL to 120 min then ≈6–8; ≈17–21 µg/mL to 90 min then ≈8 µg/mL	FaSSGF → FaSSIF, 37 °C	elkhabaz2019a R6, R12
praziquantel–HPMC E5 LV dispersions, 1.5 mg/mL	a 30% drop in FaSSIF after about 75–82%; R-enantiomer lost dissolved drug in every medium	37 °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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir droplets	about 345, 447, 536, 677, 842 nm at about 1, 10, 28, 46, 64 min	water, 37 °C	ilevbare2013a R3
ibuprofen droplets, stirred 3 h	buffer 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 nm	pH 2.0 (D2O), 37 °C, 300 rpm	ueda2020b R7
danazol alone	about 490 nm at once; about 9800 nm at 1 h	25 °C, above the onset	jackson2014 R22
with PVP	about 240–250 nm to 1 h; about 2900 nm at 2 h	10 µg/mL polymer	jackson2014 R22
with HPMC; HPMC-AS	about 305–345 nm to 2 h and 820 nm at 4 h; about 230–250 nm to 4 h and 1250 nm at 6 h	same	jackson2014 R22
ritonavir nanodroplets (ASD dissolution chapter)	stabilized against coalescence "likely" by charge repulsion between adsorbed polymers	37 °C	ilevbare2013d C38
danazol droplets, PVP, HPMC, HPMC-AS	DLS z-diameter about 350 → 103–136 nm; NTA 181–270 nm	1–1000 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 Amorphous solid dispersions: the whole picture

drug adsorption onto silica

Uptake of dissolved drug onto a silica surface

For drug-loaded mesoporous silica the papers hold it responsible for incomplete release: dissolved drug returns to the surface in a dynamic equilibrium dening2018 C23, C4; dening2019 C4. Neutral drugs bind mainly by hydrogen bonds from silanols to their acceptor groups, and weak bases still charged at the test pH mainly electrostatically dening2019 C52; mccarthy2020 C41; hate2020b C28, C35. Adsorption grows with supersaturation, which the authors relate to the higher activity of the dissolved drug ("can be proposed") and which competes with solvation dening2019 C39; hate2020b C9, C31.

Findings

F3, F4, F5, F6, F7, F9.

Related concepts

measured by an adsorption isotherm; occurs through drug-silanol hydrogen bonding or ionic interactions; part of a dynamic adsorption-desorption equilibrium; cause of incomplete drug release; grows with supersaturation.

Formulas

adsorbed amount by solution depletion, competitive solvent-drug adsorption equilibrium.

How it is measured or obtained

Solution depletion with blank silica added to a drug solution, or isotherms over a range of concentrations dening2018 P8; dening2019 P3; hate2020a P13; hate2020b P2; mccarthy2020 P7.

Values in the library

material	value or class	conditions	paper ids
ritonavir, blank SBA-15 about 100 µg/mL	28 → about 22 µg/mL (about 20% adsorbed)	pH 6.8, 2 h	dening2018 R13
ritonavir, loaded SBA-15 in medium at 28 µg/mL	about 600 µg more taken up (27% w/w)	pH 6.8	dening2018 R14, R15
ritonavir on SBA-15	up to 424 mg/g	pH 6.8, isotherm	dening2019 R2
atazanavir on SBA-15	up to about 20.8 mg/g (300 µg/mL silica)	HPMC, 2 h	hate2020a R2
ketoconazole; clozapine; atazanavir on SBA-15	pH 6.8 top points about 66; 53; 21 mg/g	HPMC	hate2020b R3, R4, R5
indomethacin; methyl ester on SBA-15	up to about 289; 342 mg/g	pH 2.2, HPMC	mccarthy2020 R7, R8

Evidence table: drug adsorption onto silica.

Pitfalls and disagreements

The adsorbed amount is always derived from what is missing in solution; no paper measured drug on silica during release dening2019 X18. Per-gram values depend on the silica concentration used hate2020a X15. Blank silica took up only about 20% of ritonavir while loaded silica kept about 50%, so retention "may therefore depend only in part on the adsorption equilibrium" dening2018 C47.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

drug-controlled release

Dissolution paced by the drug itself, slow and typical of high drug loading, in which the driving force vanishes once the amorphous solubility is reached and no droplets form li2019 C48; purohit2017b C50. New aspect (Supersaturation from ASD dissolution): at moderate to high drug loading the polymer leaves the dissolving surface faster than the drug, and a drug-rich interface, "possibly" amorphous, regulates dissolution; if it stays amorphous it "would presumably" cap the concentration at the amorphous level alonzo2011 C37, C46. For marketed tacrolimus capsules the authors "believe" that a 50% drug loading reported for the innovator makes dissolution drug controlled, so that no drug nanospecies form trasi2016 C41; a celecoxib paper recalls the cited analysis in which, at high loading, the polymer dissolves faster and leaves a drug-rich layer xie2016a C4. New aspect (Release mechanism and LoC): above the limit of congruency the polymer leaves first and the drug dissolves from a drug-rich surface, by dx/dt = C(S - x) with S the amorphous solubility, so the concentration cannot pass S and no LLPS occurs purohit2017b E3, C50; indulkar2019a C48. Release stops in a medium presaturated with drug indulkar2019a R12, C42. The authors describe the drug rates as close to the neat amorphous drug saboo2019 C12; saboo2020a C16, but several lie well above it saboo2019 X9. Above the limit indomethacin released at about 5–20 times the rate of amorphous indomethacin alone (synthesis: 0.01/0.002 to 0.04/0.002) saboo2020 R3. The 2022 ritonavir surfactant paper restates the regime with the Nernst–Brunner form and the 50% ritonavir result of 2019 indulkar2022 E2, C21, R3.

Findings

ASD process: F14, F15, F21, F23, F38, F48. Supersaturation from ASD dissolution: F7, F9, F10. Release mechanism and LoC: F1, F3, F6, F7, F14, F17.

Related concepts

contrasts with polymer-controlled release; promoted by surface drug enrichment; related to drug-rich surface layer and drug loading. Follows incongruent release; stops by the Nernst-Brunner equation at the amorphous solubility.

Formulas

Noyes-Whitney equation, saturated-medium condition.

How it is measured or obtained

From release rates close to those of amorphous drug alone, or release into saturated medium li2019 R2; indulkar2019a R13. In the ASD dissolution papers: by slow dissolution of intact particles and slowly rising UV curves alonzo2011 R4, R1; jackson2015 R13. In the release-mechanism papers: from drug rates near a compact of neat amorphous drug in the same die, polymer rates several times higher, and zero release into presaturated medium [bhardwaj2018 R4, R11; saboo2019 R5; indulkar2019a R12].

Values in the library

material	value or class	conditions	paper ids
miscible LPV–HPMC E5	100% DL: about 1.2 µg/mL at 10 min	30 µg/mL dose	li2019 R2.f
ritonavir–copovidone 50% DL	no release into drug-saturated medium	outside	indulkar2019a R13, C42
itraconazole–copovidone	a threshold drug-to-polymer ratio above which amorphous drug controls release	outside	[bhardwaj2018 C66]
ritonavir–PVPVA spray-dried, 50% and 75% DL	about 0.0053–0.0063 and 0.0031–0.0040 mg·min⁻¹·cm⁻¹, near neat amorphous ritonavir (about 0.0026), whatever the solvent	pH 6.5	li2020 R10, C37
ritonavir/lopinavir co-granule, 50:50 drug:polymer	expected drug-controlled; polymer leaves first and the surface turns drug-rich	acid	trasi2019 C46
IDM–PVPVA 1:1	dissolution described as drug-controlled; the polymer is expected to dissolve quickly, leaving amorphous drug particles	non-sink, pH 4.5	moseson2020a C30
BCL–PVPVA 50% DL	polymer about 18% at 10 min and 80% at 2 h; drug plateau about 73% from about 120 min	dose of at most 30 µg/mL	moseson2022b R6, R7
felodipine 50:50 HPMC dispersion	particle intact for at least 30 min; ≈8.9 µg/mL at 60 min	37 °C	alonzo2011 R4, R1
danazol 50:50 HPMC; HPMCAS dispersions	past 8 µg/mL after ≈270 min; ≈6.0 µg/mL plateau	25 °C	jackson2015 R2, R13
celecoxib–HPMCAS 50% and 60% drug	≈21.1 µg/mL only after 16 h; ≈15.8 of 22 µg/mL at 16 h	pH 6.8, 37 °C	xie2016a R4
tacrolimus innovator (cited)	50% drug loading	report, no reference	trasi2016 R19
ritonavir 50:50 films with PVP, PVPVA	polymer dissolved; ritonavir ≈18 and ≈9 µg/mL at 240 min, below 27 µg/mL	25 °C, pH 6.8	purohit2017b R15, R16, R1
ITZ–PVPVA 25, 50%	47–64 µg/min/cm² against 51 for amorphous ITZ; polymer 3.5–4 times faster (normalized)	0.1 N HCl	[bhardwaj2018 R4, R11]
ritonavir–PVPVA 40, 50%	≈3% and ≈0.65% of the drug in 180 min; 0 into saturated medium (50%)	pH 6.8, 37 °C	indulkar2019a R3, R12
ledipasvir–PVPVA 7.5–20%	≤ ≈7% drug and ≈17–23% polymer at 90 min	same	que2019 R3, R4, R11
nilvadipine 15, 20%; cilnidipine 20, 25% in PVPVA	0.035, 0.013; 0.006, 0.002 mg/min/cm² (neat nilvadipine 0.002)	same	saboo2019 R5, R6
felodipine–PVP 15–30%	≈0.005–0.020 mg/min/cm², 5–25 times neat felodipine	same	saboo2020a R14, R13
indomethacin–PVPVA 15–25%	≈0.01–0.04 against 0.002 mg/min/cm² for amorphous drug; PVPVA ≈0.50–0.72	pH 2.1, 37 °C	saboo2020 R3, M5
atazanavir–PVPVA 10%	≈0.07 against PVPVA ≈0.24 mg/min/cm²	pH 6.8, 37 °C	correasoto2022b R3, P5

Pitfalls and disagreements

In the lopinavir films phase separation turns a drug-controlled dissolution at high DL toward polymer-controlled release of the polymer-rich phase, but only partly (33% DL reached about 13 of 30 µg/mL against about 17 for miscible 15% DL) li2019 R2, C58. Drug-controlled release was inferred from the loading and the congruent boundary in the ritonavir studies, not from polymer release measured on the same powders li2020 C66, X13. In the ASD dissolution papers the drug-rich surface layer was not observed alonzo2011 C46. The 50:50 PVP danazol dispersion dissolved as fast as the 90:10 one jackson2015 X9, and the 50:50 danazol films were partly crystalline before dissolution jackson2015 X10. The 50% tacrolimus loading is unreferenced and the generics' loadings are unknown; release rates were not measured trasi2016 X4. The drug-rich layer of ITZ compacts is a "supposition" from the curving polymer profiles [bhardwaj2018 C52]. Nilvadipine above the switch released 17 and 6.5 times faster than the neat amorphous drug, a significant difference saboo2019 X9, R8. The presaturation of the medium is not described indulkar2019a X8.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir with atazanavir	melting onset 394.4 K to about 380.1 K at x_ATV 0.52; one Tg 349–323 K	DSC	alhalaweh2016 R8, R9
ritonavir with lopinavir	liquid-state miscibility; one Tg in every mixture		trasi2015a C41; trasi2015b R2, C39
atazanavir with darunavir, dry amorphous mixtures	two Tgs in every mixture (neat 105 and 62 °C); heterogeneous co-melt-quenched film with nanoTA softening at 118 ± 4 and 92 ± 2 °C	DSC, nanoTA	alkalla2026 R15, R16, R17, C30, C31
atazanavir with darunavir in water	darunavir enters the atazanavir-rich phase; atazanavir's amorphous solubility falls as the darunavir fraction of the phase rises	antisolvent, 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 Amorphous solid dispersions: the whole picture

drug leaching

Evidence table: drug leaching. Content from the ASD dissolution chapter (celecoxib, 2015) and the ASD process chapter.

Passage of drug, and of polymer, out of suspended ASD particles into the surrounding liquid while the particles stay largely undissolved, as in acid for dispersions of enteric polymers. Because the drug is amorphous, leaching can create a supersaturated liquid, whose concentration falls if the drug then crystallizes [chen2015a C13]. For lopinavir dispersions of three HPMCAS grades and HPMCP at pH 3 the leached drug settled between the crystalline and the amorphous solubility, the dispersions leached less polymer than the pure polymers ("consistent with a miscible solid dispersion"), surfactants raised the leached drug in step with its crystalline solubility, and SDS at pH 5 raised drug and polymer leaching together [li2016b R4, R3, C35, C39, C24].

Findings

F15, F18, F19, F24, F25, F27.

Related concepts

depends on pH-dependent polymer solubility and polymer-controlled release; raised by polymer-surfactant complexation; related to solubility suppression by an undissolved, mixed polymer.

Formulas

supersaturation ratio.

How it is measured or obtained

Filtering the suspension liquid (0.45 µm) and assaying drug by HPLC, divided by the crystalline solubility in the same medium, and polymer by colorimetry [chen2015a P11, P12, E1]; drug in acid over time in two-stage tests [moseson2023 R11]. Spray-dried dispersions, 100 mg in 10 mL citrate buffer at 25 °C and 300 rpm, 0.45-µm filtrates to 3 h, lopinavir by HPLC and polymer by phenol–sulfuric acid colorimetry [li2016b P4, P7, P8].

Values in the library

material	value or class	conditions	paper ids
celecoxib–HPMCAS 33.3%, pH 3, no surfactant	S ≈4.3 → ≈6.7 over 48 h, no crystals	10 mg/mL, 25 °C	[chen2015a R17, R14]
same, 0.25% SDS	S ≈8.6 at about 5 min, ≈3.2 at 1 h (crystals)	25 °C	[chen2015a R17]
same, 0.025% Triton X100	S ≈1.6–1.8 for 48 h	25 °C	[chen2015a R17]
posaconazole–HPMCAS dispersions, gastric stage (ASD process)	a low amount of amorphous drug leaches; a coating slows it	pH 1.2 and 4.0 media	[moseson2023 C17, C20]
lopinavir 33% with HPMCAS LF / MF / HF; HPMCP	≈7 µg/mL each; ≈5 µg/mL	pH 3, 25 °C, 3 h	[li2016b R4]
same, polymer	below 5 µg/mL from the dispersions	pH 3	[li2016b R3]
lopinavir–HF with STC; SDS at pH 5; PVPVA + SDS	≈25.6; ≈33–39; ≈50 µg/mL	25 °C	[li2016b R19, R13, R17]
posaconazole–HPMCAS 10 / 25 / 50% drug	7.5 / 10 / 11.5% of a 400 µg/mL dose in 60 min, below the 115.1 µg/mL crystalline solubility	FaSSGF pH 1.6, 37 °C	elkhabaz2019a R10, R1
delamanid salt dispersions, acid stage	≈30% (HPMCP-50), under 10% (HPMCP-55) and ≈21–36.5% (HPMCAS grades) at pH 1.6; about 0.5–3.5% at pH 3.0	25% drug, 37 °C	nguyen2023c R11
uncoated against coated delamanid–HPMCP-50 tablets	≈30–41 µg/mL against below 0.5 µg/mL in the gastric stage	pH 1.6, 37 °C	nguyen2023b R2, R10

Pitfalls and disagreements

The supersaturation in SDS assumes that about 860 µg/mL leached HPMCAS leaves the celecoxib solubility unchanged, which was not tested [chen2015a X10, C11]. The surfactant-free suspension leached to the highest supersaturation without crystallizing [chen2015a X6]. Polymer values from the dispersions lie below detection or near quantitation and differ between figures [li2016b X7, X6]; the amorphous solubility was measured only in plain pH 3 buffer, so leaching with additives cannot be set against it [li2016b X15]. Leaching from an undissolved enteric matrix is attributed to the drug being molecularly dispersed in the polymer, and rose with drug loading for posaconazole nguyen2023b C35; elkhabaz2019a C29.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
atazanavir HPMCAS 10 / 30 / 50%	apparent 248 / 99 / 84 µg/mL at 120 min; AUC 1220 / – / 660	closed; absorptive	hate2018 R11, R15
telaprevir HPMCAS 10 / 30 / 50%	above 90 µg/mL at about 2 / 21 / 600 min	pH 6.8	mosqueragiraldo2018b R5, R16
grazoprevir ASDs	release complete at 5%, about 80% at 10–15%, about 30% at 50–75%		[hiew2023 C18]
tacrolimus commercial ASD	50% loading; higher loading may not generate nanospecies	cited	trasi2016 R19, C41
enzalutamide in HPMCAS-MF 10 / 50%	10%: peak about 10 µg/mL with crystals; 50%: ceiling reached in 3–4 h	100 µg/mL total, pH 6.5	wilson2018 R6
enzalutamide in CPHPC-106 10:90 / 50:50	AUC0–inf 516 / 305 µg·h/mL; mass flow about 0.53 / 0.49 µg/min	rats, 50 mg/kg	wilson2020 R6, R8, C22
grazoprevir–HPMCAS-LF solvent-evaporated, 5–75%	≈102 → 63 → 43 → 27–30% released at 90 min	two-stage SGF → FaSSIF	[hiew2023 R8]
binary cPADs at 60; 75%; hierarchical cPAD at ≈73%	≈37.5; 17%; ≈71%	same	[hiew2023 R17]
grazoprevir–HPMCAS hierarchical particles	73.9% (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 Amorphous solid dispersions: the whole picture

drug-polymer hydrogen bonding

Evidence table: drug-polymer hydrogen bonding. Content from the release-mechanism chapter (2020–2022), with rows from the Physical stability chapter.

A hydrogen bond between a donor group of the drug (NH, OH or COOH) and an acceptor of the polymer, in PVP and PVPVA the carbonyl of the vinylpyrrolidone unit, read from a shift of the polymer carbonyl band to lower wavenumber [saboo2020 R14, C20; que2021 R7]. In the release papers it is tested as a cause of a low limit of congruency: indomethacin, which hydrogen-bonds to PVPVA, had a much lower limit than its methyl ester, which does not, so the hypothesis that hydrogen bonding in the dry dispersion raises the limit "appears incorrect" saboo2020 C48; from the same pair Yang and co-workers (2021) conclude that strong interactions such as hydrogen bonding "are likely to" lower the polymer release rate and hence drug release [yang2021 C29]. In the Physical stability chapter, sorbed water disrupts drug–polymer hydrogen bonds of NH-donor drugs with PVP, producing a drug-rich phase purohit2015b C27, and a larger carbonyl shift with COOH donors than with NH donors is read as a stronger drug–polymer interaction rumondor2009c C48.

Findings

Release mechanism and LoC: F10, F17.

Related concepts

a case of hydrogen bonding and of drug-polymer interactions; the weaker alternative in donor-free analogues is halogen bonding; lowers the limit of congruency in the analogue pairs; may shift the ternary phase diagram.

Formulas

none.

How it is measured or obtained

Infrared spectra of the carbonyl region of dispersions against loading and, for tablets, against dissolution time [saboo2020 R14, R16; que2021 R7]; analogues without donor groups as controls [saboo2020 R18; que2021 R7].

Values in the library

material	value or class	conditions	paper ids
indomethacin–PVPVA 10–70%	1705 cm⁻¹ dimer band absent; hydrogen-bonded PVP carbonyl band at 1634 cm⁻¹ growing with loading	dry tablets	saboo2020 R14
indomethacin methyl ester–PVPVA 25%	PVP carbonyl region unchanged	dry tablets	saboo2020 R18, C23
TIPP; PHPH in PVPVA	VP carbonyl shifted by up to 30 cm⁻¹; new band at about 1650–1654 cm⁻¹	films 10–90%	[que2021 R7]
Me-TIPP; Me-PHPH in PVPVA	maximum shift 7 cm⁻¹ (halogen bond); minimal shift	same	[que2021 R7]
nifedipine, pimozide, droperidol; indomethacin, ketoprofen with PVP (Physical stability chapter)	PVP carbonyl red shift 20–24; 42–44 cm⁻¹	dry dispersions	rumondor2009c R29
ritonavir–PVP 80:20 (Physical stability chapter)	hydrogen-bond band at 1654 cm⁻¹ lost after 97% RH	films, dried	purohit2015b C17

Pitfalls and disagreements

In the analogue pairs hydrogen bonding goes with a higher Tg and with drug–drug bonding, so the two effects are hard to separate: all high-Tg drugs of the drug-property study can hydrogen-bond with both polymers while the low-Tg drugs lack donors [yang2021 C25], and drugs that hydrogen-bond strongly to PVPVA also had high Tgs correasoto2022a C49. The release papers read the bonds in dry dispersions or after drying; whether they persist in the hydrated matrix was not measured [que2021 C44].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
indomethacin–PVP	acid OH bonded to PVP carbonyl; dimers opened; incomplete binding	IR, 5–70 wt% PVP; physical mixes show none	[taylor1997 C35, C26, C37]
felodipine–PVP, nifedipine–PVP	one phase over 10–90% and 25–70% PVP; hydrogen bonding "presumably" behind the second PC	IR, PXRD	[rumondor2009a C38, C20]
felodipine–PAA	little mixing at 30–70% PAA; competition from PAA self-association "speculated"	DSC, IR, PXRD	[rumondor2009a C44, C45]
ketoconazole–PVP	near-athermal mixing, no carbonyl shift; dipole–dipole forces "speculated"	melting, FTIR	marsac2009 C40, C41, R12.h
felodipine with PVP, PVP/VA, HPMCAS, PVAc	strength PVP > PVP/VA > HPMCAS ≥ PVAc	NH shifts at 50 wt% polymer	kestur2010a C26, R9
nimesulide with PVP, PVP/VA, PVAc	present but small; limited by the intramolecular bond	IR, 20–50 wt% polymer	[kestur2011 C23, C24, C27]
amide and basic drugs with PAA, PSSA	highest crystallization resistance; acidic drugs lowest	spin-coated films, 7 days	vaneerdenbrugh2010b C23, C24, C27
indomethacin–PVP K12	χ −0.82 (melting), −1.83 (EP solubility)	most favourable of five pairs	marsac2009 R7.e, R9.e, C42
naringenin, quercetin with PVP; with E100	hydrogen bonding strongest with PVP; acid–base contact with E100 (amine bands lost at 50% quercetin)	IR, films	wegiel2013a R2, R4, R6
lumefantrine with enteric polymers and PVPVA	protonated 19–55% with HPMCAS, HPMCP, CAP, Eudragit L 100; 0% with PVPVA	XPS, 25% drug loading	hiew2022a R20
clotrimazole, loratadine, brotrimazole, Me-DIBF with PVPVA	halogen bond: K_F 0.56–1.11 M⁻¹, carbonyl shift 2–6 cm⁻¹	NMR, IR	[que2020 R12, R11]
15 drugs, 7 polymers	complementary donor and acceptor groups give the highest amorphicity index	spin-coated films	[vaneerdenbrugh2011a R3, C20, C33]

Evidence table: drug-polymer interactions.

Pitfalls and disagreements

In every inhibition study cited here the interaction is inferred or measured under other conditions than the crystallization test, and its causal role is argued, not demonstrated [kestur2010a X5, X6; kestur2011 X9, X10; vaneerdenbrugh2010b C33]. The two thermodynamic routes agree in sign but not in size marsac2009 X7. A strong donor polymer is not enough when it bonds to itself (PAA with felodipine) or when the drug donor is tied up intramolecularly (nimesulide) [rumondor2009a C45; kestur2011 C27]. Interaction does not always decide the outcome: PAA, a strong donor, left flutamide growth almost unchanged [trasi2012b R3, C7]. The strength of the ionic and halogen contacts was not measured in the dispersions, and their evidence rests on band loss, binding-energy shifts or spectra that are not shown [wegiel2013a X10; que2020 X11, X12; vaneerdenbrugh2011a X13]. The ionic contact that protects against crystallization also slows the dissolution of the enteric polymers hiew2022a C53, C65. A complementary polymer did not always protect: the IR ranking of the polyphenol polymers held at the extremes only wegiel2013a X4.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

drug-polymer ionic interactions

Evidence table: drug-polymer ionic interactions. Content from the release-mechanism chapter (2024–2025), with rows from the Physical stability and ASD process chapters.

Electrostatic attraction between an ionized drug and oppositely charged groups of the dispersion polymer, here a weakly basic drug cation and the carboxylate of an enteric polymer. In the release papers of 2024–2025 such interactions, when both partners are ionized at the pH of the polymer gel, form an insoluble complex that lowers polymer solubility and so polymer and drug release; ionization of loratadine "is necessary" for its complexation with HPMCAS, which it binds "mainly electrostatically" bapat2024 C38, C46; bapat2025a C34. The interaction can exist before water arrives: bedaquiline was about half protonated in a dry HPMCAS dispersion made from organic solvents kaur2025 C25, C35. In the stability papers the same proton transfer from an acidic polymer to a basic drug is read as a source of physical stability (lumefantrine, erlotinib) [bhujbal2021 C21, C52; moseson2022a C33].

Findings

Release mechanism and LoC: F32, F33, F34, F24.

Related concepts

gives an insoluble drug-polymer complex by hydrophobic ion pairing; depends on ionization at the microenvironmental pH; contrasts with drug-polymer hydrogen bonding; lowers polymer hydration.

Formulas

Henderson-Hasselbalch equation (ionization of drug and polymer at the gel pH).

How it is measured or obtained

XPS of the drug nitrogen, with a protonated N 1s component near 402 eV beside the neutral one near 399 eV, calibrated against a salt [kaur2025 R19, R20; bhujbal2021 C21]; indirectly by the polymer lost from solution when drug and polymer meet in buffer at a set pH (insoluble drug-polymer complex) bapat2025a R9, R11.

Values in the library

material	value or class	conditions	paper ids
bedaquiline free base; HPMCAS-MF complex; dry 40% dispersion	4 ± 4; 55 ± 4; 52 ± 7% protonated N	XPS	kaur2025 R20
bedaquiline 40% dispersion after 1 h at pH 6.5	15 ± 3% protonated at the surface	XPS	kaur2025 R20
cinnarizine–HPMCAS-MF 25%	20% protonated dry, 11% after partial dissolution	XPS	bapat2024 R8
loratadine with HPMCAS LF, MF, HF at 1:1, pH 5.8–7.5	complexation falling with calculated drug ionization (≈20 → 0.5%)	spike test	bapat2025a R11, R13
lumefantrine with HPMCP, HPMCAS, CAP, Eudragit L100 (Physical stability chapter)	14–42% protonated against 3% for amorphous lumefantrine	XPS, dry dispersions	[bhujbal2021 R8]
erlotinib with HPMCAS (ASD process chapter)	acid–base interactions the "likely" reason for better stability (cited)	—	moseson2022a C33, R21

Pitfalls and disagreements

The same interaction is sought for stability and harms release: the 2025 grade paper says the stability gain of drug–polymer salt formation should "ideally" be balanced against reduced release under mutual ionization bapat2025a C23. For lumefantrine the extent of protonation did not rank stability [bhujbal2021 C50]. The release papers infer the interaction in the dissolving gel from solution tests and cited gel pH, not from measurements in the gel bapat2024 X10; kaur2025 X14.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
nifedipine, felodipine, ketoconazole, sucrose, indomethacin with PVP	miscible (cited Tg, FTIR)	classification used for χ	marsac2009 R1.a, R1.b, R1.c, R1.d, R1.e
sucrose–dextran	miscible; ibuprofen–dextran, indomethacin–dextran immiscible	cited and this study (Tg data not shown)	marsac2009 R1.f, R1.g, R1.h, X10
itraconazole–Eudragit E100	partially miscible	cited	marsac2009 R1.i
felodipine–PVP, nifedipine–PVP	one amorphous phase over the compositions studied	IR, PXRD, DSC (cited)	[rumondor2009a C38, X5]
felodipine–PAA	"practically immiscible" at 30–70% PAA; some mixing at 10 and 90%	DSC, IR, PXRD	[rumondor2009a C44, C46]
ketoconazole–PVP	"suspected" partially miscible, one phase at higher PVP only	one Tg; IR; PXRD	[rumondor2009a C40, X1]
nifedipine–PVP K29/32	predicted miscible at all compositions from χ −3.8	Flory–Huggins	marsac2006b R2, C33
itraconazole–HPMC 10:90 to 50:50	phase separated at every loading in solvent-cast films; one broad Tg of powders	fluorescence, AFM-nanoIR, nanoTA; mDSC	purohit2015a C36, R7
telaprevir with HPMC, PVPVA, HPMCAS	domains from 10% drug (HPMC, PVPVA); from about 30–40% (HPMCAS)	AFM, AFM-IR, nanoTA, LCR	[li2016c C17, C52]
dextran–PVP, 20 pairs	miscible at all compositions for 783 Da maltodextrin; phase separated at all nine for DEX450–PVP90	DSC, FTIR	[vaneerdenbrugh2012a R13, R14]
probucol–PVP K30 50:50	single Tg, "seemed" one-phase; carbonyl shift	solvent, moulded	broman2001 R4, R5, C14
ECP–HPMC / PVPVA	miscible over 10–90% DL when dry	18% RH	li2017 R3.a, C33
ITZ–HPMC	thermodynamically miscible when dry, trapped as two phases when wet ("suggest")	7% RH vs 20–40% RH	mugheirbi2017 R1, C39
IDM–PVPVA	melting point depression confirms miscibility at elevated temperature	DSC	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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir–HPMCAS	miscible after 97% RH; PVP and PVPVA dispersions separated	films and powders	purohit2017b C1
felodipine 30% with HPMCAS, EUDS; PVP, PVPVA, HPMC	uniform; separated	97% RH, 24 h	saboo2020a C23
ritonavir–PVPVA 30% films ± 10 parts surfactant	14.0 / 16.0 / 10.5 / 12.5 / 24.5% water (none / Span 85 / Span 20 / Tween 80 / SDS)	saturated-salt RH, 12 h, confocal	yang2023 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper 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/cm²	same	saboo2020a R14
felodipine–PVP and –HPMC across the limit	PVP about halved; HPMC not reduced	same	saboo2020a X15
lumefantrine benzoate 20%, tosylate 10%	plateau after ≈30 min at ≈58–60% released	compacts, 37 °C	hiew2022b R10, C16
clopidogrel–PVPVA 50, 60%	bicontinuous and drug-continuous films; ≈52 and 7% released	films 5 min at 100% RH; compacts	correasoto2022a R20, R17
ritonavir–PVPVA 30%; 40%	continuous porous drug-rich layer at the gel–solution interface; rigid layer ≈12 µm	real-time confocal, pH 6.8	yang2022a R6, R12, R13
MePHPH–PVPVA 50%; PHPH–PVPVA 20%	porous continuous drug-rich phase on the surface	surfaces after 2–20 min	[deac2023a R9, R10, C57]
PHPH–PVPVA 15, 50%; MePHPH–PVPVA 50% compacts	surface drug content moves toward the hydrophobic binodal composition	ATR-FTIR of dried surfaces, 0–60 min	deac2023b R6, R7, C59
ritonavir–PVPVA + Span 20, 40%	layer ≈50–100 µm from 5 min; drug ≈8%, polymer ≈78% at 90 min	confocal cross-sections; compacts	yang2023 R7, R2, R3
ritonavir–PVPVA + Span 85, 30%	layer formed, swept away and re-formed in situ; ≈86% released under rotation	in situ confocal; compacts	yang2023 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
clotrimazole	111 / 223 / 246 / 257 nm at 8 / 10 / 15 / 20 µg/mL; 1.2 × 10⁸ to 12.5 × 10⁸ per mL	pH 8, NTA	indulkar2016 R4
atazanavir, solvent shift	204–226 nm, PDI 0.08–0.15	100–500 µg/mL, DLS	hate2018 R6
atazanavir 90:10 HPMCAS and HPMC ASDs	294–326 nm	closed and absorptive	hate2018 R12
atazanavir with PVPVA	about 245 nm rising to about 700 nm at 75 min and 10 µm at 105 min	agglomeration	hate2018 R20
telaprevir 90% HPMCAS ASD	about 300 nm	DLS (data not shown)	mosqueragiraldo2018b R3
ritonavir ASD (Tres 2018)	696 / 294 nm (ritonavir / lopinavir)	NTA	tres2018 R18
enzalutamide 10:90 and 50:50 copovidone ASDs	about 100 nm; about 50 against about 3 µg/mL of 100 as aggregates	pH 6.5, 1 h dissolution	wilson2018 R10, R11
atazanavir, posaconazole in pooled human fluid	spheres of 0.1–0.5 µm, no needles	SEM of pellet, 100 µg/mL HPMC-AS	elkhabaz2019b R4
atazanavir, clozapine with HPMCAS-LF and -HF	AS-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 additives	droplets of about 280 and about 1000 nm gave the same mass flow	PAMPA, 2% SDS receiver	hate2022 R17
ritonavir–PVP dispersion at 20 µg/mL	about 350 nm at onset; ≈5590 nm by 120 min	100 mM buffer, 37 °C	ilevbare2013d R1, R5
ritonavir 20 µg/mL with 5 µg/mL CAAdP 0.33	210−214 nm before crystallization	solvent shift	ilevbare2013d R12
danazol 90:10 dispersions	246–284 nm	25 °C	jackson2015 R6
ritonavir; ritonavir + lopinavir, HPMCAS dispersions	about 500 nm; about 160 nm in 0.45 µm filtrates	1 h	trasi2015b R7
felodipine 90:10 HPMC dispersion	≈185 → ≈300 nm, read as crystalline	25 °C	alonzo2011 R8, C33
nifedipine 10, 20% with HPMC-E5 or PVPVA	≈190–222 nm	NTA, 5 °C, D2O	indulkar2017b R7
ritonavir 10:90 films with PVPVA, HPMCAS, PVP	200, 250, 315 nm	NTA, fresh films	purohit2017b R8
ritonavir–PVPVA 10% tablet	218 ± 15 nm; media of 10–25% turbid	DLS 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 loadings	DLS, about 1 h	saboo2019 R11
indomethacin–PVPVA 5, 10%	250–350 nm	NTA, 30 min	saboo2020 R7
felodipine with 5% TPGS	Z-average ≈237–279 nm	DLS, 60 min	saboo2021 R17
elbasvir 2.5%; loratadine 10%	PVPVA ≈670 → 1190; ≈820 → 2120 nm; HPMCAS ≈280 → 390; ≈420 → 570 nm	DLS, 60 min	[yang2021 R3, R6]
clopidogrel	≈520 nm in buffer; stable with SDS, TPGS or Tween 80; ≈12-fold growth with CTAB	DLS, 4 h	correasoto2022a R5, R6
four phenolphthalein analogues	179–364 nm	DLS, 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 µm	DLS of the medium during release	indulkar2022 R11, R13
plasticized dispersions (systems not specified)	500–1500 nm after 90 min	DLS	[correasoto2023 R5]
MePHPH–PVPVA 5–30%; PHPH–PVPVA 5%	nanoparticles formed within the gel; onset 601 ± 68 µm beyond the 356 ± 18 µm gel	in situ confocal	[deac2023a C27, R8, C31]
drug-rich phase released from 30% MePHPH; from 5% PHPH	98.8 against 26.2 wt% drug; Tg 16.8 against −5.8 °C	HPLC, DSC	[deac2023a R12]
PHPH; MePHPH nanoparticles with PVPVA	PVPVA 71.4–78.0; 0.5–7.5 wt%	37 °C, two preparation routes	deac2023b 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
clopidogrel nanodroplets in buffer; with 50 µg/mL CTAB	Z-average ratio ≈1.5 at 1 h and ≈12 at 2 h; ≈12 at 1 h	37 °C, DLS	correasoto2022a R6
clopidogrel nanodroplets with 50 µg/mL SDS, 4 µg/mL TPGS, 5 µg/mL Tween 80	Z-average ratio ≈0.92–1.01, ≈0.96–0.99, ≈0.81–0.89 over 4 h	same	correasoto2022a R6
clopidogrel–PVPVA 40%; 50%, binary and with Tween 80, TPGS, SDS	≈790, ≈510, ≈580, ≈690 nm; ≈1960, ≈780, ≈890, ≈1260 nm	90 min of dissolution	correasoto2022a R19
atazanavir- and clozapine-rich droplets with pre-dissolved HPMCAS-LF; -HF (Bioperformance chapter)	grew slightly early and stayed below 300 nm; kept their initial size	3 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir, 10% Kollidon VA64 dispersion	mean size 696.4 ± 213.6 nm	NTA, medium filtered at 1 µm, about 60 min	tres2018 R18
lopinavir, 10% dispersion	294.3 ± 67.7 nm	same	tres2018 R18
ritonavir 30 µg/mL	≈360 nm	DLS, antisolvent	trasi2015a R15
ritonavir–HPMCAS dispersion	≈500 nm	NTA of 0.45 µm filtrate, 1 h	trasi2015b R7
tacrolimus, 60 µg/mL	≈220 nm, a second phase	NTA of 0.7 µm filtrate, pH 4.5, 37 °C	trasi2016 R11
telaprevir (glass, Tg 52 °C)	≈300 nm; redissolves within about 2 min on dilution	37 °C	mosqueragiraldo2015 R4, R5, R8, C13
ibuprofen	micron-sized in buffer; ≈300 nm with HPMC or PVP-VA	pH 2.0, 37 °C	ueda2020b R5
felodipine aggregates	τ2 ≈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 phases	PRODAN second band ≈435 and ≈450 nm; τ2 up to 3.40 and 3.89 ns	pH 7.4	[tres2017 P1, R13, R10, R11]
ritonavir pellet	94.85–95.97% drug, 4.03–5.15% water, Tg 0.4 °C	10–50 °C, water	ilevbare2013a R5, R6
weak-base precipitates	X-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 phase	about a third stays in bulk; about 0.21 at 85 µg/mL ritonavir	25 °C	trasi2015a R9, R10
ionized diclofenac with the ritonavir-rich phase	fully recovered in bulk	25 °C	trasi2015a R11
ibuprofen-rich phase	polymer: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 phase	ratio 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 crystals	pH 6.5 after pH shift	sugihara2018 R11, R17
telaprevir, 90% CA Sub ASD	polymer 9407 µg, drug 1080 µg; polymer fraction 0.90	150 µg/mL, 15 mL	mosqueragiraldo2018b R14
telaprevir, 90% HPMCAS / 70% HPMCAS / 90% PVPVA	polymer fraction 0.21 / 0.27 / 0.22	same	mosqueragiraldo2018b R14
ritonavir, atazanavir	NTA counts: buffer 4.74 × 10⁶; ATV 150 µg/mL 4.15 × 10⁸ per mL	antisolvent	alhalaweh2016 R15
clotrimazole	1.2 × 10⁸ to 12.5 × 10⁸ per mL	8–20 µg/mL	indulkar2016 R4
atazanavir with darunavir hydrate	atazanavir in the drug-lean phase about 61–63 instead of 91–96 µg/mL at about 196 µg/mL darunavir added	150 µg/mL atazanavir, 400 µg/mL HPMCAS, pH 6.8	alkalla2026 R11, C1
ritonavir phase from a PVP dispersion	Tg inflection 1.05 °C; pyrene I1/I3 ≈1.43–1.46	water, 37 °C	ilevbare2013d R2, R3
danazol, 90:10 dispersions	246–284 nm, 4.1–4.5 × 10⁹ per mL	25 °C	jackson2015 R6
lopinavir alone; with ritonavir	crystallized at 1–2 h; no crystallization in 5 h	pyrene I3/I1	trasi2015b R15
indomethacin with 100 µg/mL HPMC	onset 36 µg/mL; droplets 70–100 nm	pH 2.2, 37 °C	xie2017 R4, R6
indomethacin EPO–HPMC dispersion	≈75 nm species; redissolved within ≈2 min after a rise to pH 5	37 °C	xie2017 R15, R20

Pitfalls and disagreements

Its amorphous nature was often inferred, not tested: the supernatant matched the amorphous solubility, but no solid-state measurement was made tres2018 X5. Size varies strongly with drug, medium and technique (about 160–700 nm in the rows above), so no size transfers. Filtration may not remove it jackson2015 C12; trasi2016 R8. Droplets coalesce and grow with time, which changes scattering jackson2014 C29; tres2018 C28. A glassy phase behaves much like a liquid one in these tests mosqueragiraldo2015 C30. In the amorphous solubility papers the ritonavir DSC trace shown stops at 20 °C, so the absence of melting is stated, not shown ilevbare2013a X8. The water content of the telaprevir pellet was not measured mosqueragiraldo2015 X3. The polymer in the phase is the NMR-invisible polymer and the droplet composition is not known [ueda2021 X4; ueda2020b X4]. The composition of the mixed ritonavir–atazanavir phase was calculated, not measured alhalaweh2016 C17; absolute pellet amounts of the telaprevir study are not mass balances mosqueragiraldo2018b X8. The NTA count of the ritonavir–atazanavir mixture is below that of buffer alhalaweh2016 X6. The centrifuged drug-rich phase of the darunavir study was not analysed; its composition is inferred from supernatant depletion and flux (F20) alkalla2026 X6. In the ASD dissolution papers the ritonavir phase's water content was not measured, and the probe run is described in two media ilevbare2013d C8, X1. Tracking cannot tell droplets from crystals jackson2015 X13. For ritonavir the phase "appears" to promote crystallization rather than protect against it ilevbare2013d C41. The non-crystalline state of the indomethacin droplets rests on optical methods; they crystallized after 3 h at pH 2.2 xie2017 X18, R15.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
30% BCL–PVPVA compact surface	F/F0 = 1.23 ± 0.07 (about 20% enrichment)	30 min in buffer	moseson2022b R14
same, cross-section	drug-rich boundary layer 94 ± 8 µm with crystals, F/F0 = 1.41 ± 0.10; gel layer below F/F0 = 0.93 ± 0.06	1 h	moseson2022b R15
same, confocal	red layer 55 ± 6 µm at 5 min, 103 ± 9 µm at 30 min	Nile red	moseson2022b R16
50% BCL–PVPVA compact	5–10 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 min	SEM-EDX, confocal	moseson2022b R15, R17
10% BCL–PVPVA compact	surface smooth at 30 min	SEM	moseson2022b R14
coated ritonavir–PVPVA tablet edge	connected drug-rich regions along particle boundaries	confocal	[benson2025 R14]
ritonavir–PVPVA 50%	amorphous-ritonavir IR spectrum from 5 min; flaky at 15 min	pH 6.8, 37 °C	indulkar2019a R16, R17
ledipasvir–PVPVA 10%	distinct top layer at 10 min; bulging, porous top by 30 min	micro-CT, dried	que2019 R13
nilvadipine 15:85	porous layer within 10 min, growing to 30 min	micro-CT	saboo2019 R13
felodipine 30% in PVP, PVPVA, HPMC	porous layer at the dissolving face	micro-CT, 10 min	saboo2020a R19
felodipine 30% with 0, 2% TPGS; 5, 10% TPGS	porous surface layer after 10 min; homogeneous	micro-CT, dried	saboo2021 R19
indomethacin–PVPVA 15, 25%	rough, porous surface after 5 min; smooth at 10%	SEM	saboo2020 R19

Pitfalls and disagreements

The layers were measured on compacts, and the crystals were identified by shape and not by diffraction moseson2022b X20, X18. The polymer-depleted state of the 50% crust is inferred from the dye, and the authors read the crust as formed and dissolved repeatedly, which would make its slow release only "seemingly congruent" moseson2022b X16, C47. A drug-rich surface is not the only consideration: a TPGS dispersion released incongruently yet completely because little solid was left when nucleation began moseson2022b C50. The layer of the ITZ compacts is a "supposition" [bhardwaj2018 C52]; SEM and micro-CT samples were dried indulkar2019a X11; que2019 X22.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir in SBA-15, 38 and 22% w/w	3749 cm⁻¹ band absent (present in physical mixture); carbonyl 1715 and 1654 cm⁻¹	dry, methanol-loaded	dening2019 R12, R11
ritonavir in SBA-15, 22% w/w	O 1s 532.5 eV between silanol 533.2 and carbonyl 531.3 eV; Si 2p about 0.5 eV lower	XPS	dening2019 R13, R14
indomethacin; methyl ester in SBA-15	carbonyl shifts 1682 → 1669, 1710 → 1688; 1674 → 1663, 1735 → 1725 cm⁻¹ (text); Si 2p 103.8 → 103.4; 103.3 eV	dry, ethanol-loaded	mccarthy2020 R3, R4, X1
atazanavir in SBA-15	3749 cm⁻¹ band absent from 20% w/w; carbonyl near 1700 at 5%	ATR-FTIR	hate2020a R12
urea effect on adsorption	ritonavir 259 → 169; indomethacin 12.4 → 6.1; ester 14.2 → 5.8 mg/g	5 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
benzocaine; chlorpropamide; ibuprofen in PEG 3350	28; 26; 25 wt%	extrapolated to 25 °C from the liquidus	zhu2011 R5.b, R5.c, R5.d
nilutamide in PEG 3350	11 wt% (eutectic 10 wt% at 58.4 °C)	as above	zhu2011 R5.e, X4
haloperidol; ketoconazole in PEG 3350	0 wt%	as above; text for haloperidol: under 1% w/w	zhu2011 R5.a, R5.f; zhu2012 X10
fenofibrate in PEG 3350	6 wt%	as above, from the supporting-information diagram	zhu2012 M2
chlorpropamide; aceclofenac; loratadine; haloperidol in PEG 400	194; 233; 49; 14 mg/mL	24 h, 25 °C	[baird2011 R9]
acetaminophen, ketoprofen, naproxen, ibuprofen, felodipine, ketoconazole in PEG 400	0.32, 0.32, 0.22, 0.28, 0.16, 0.02 mole fraction	24 h, 25 °C	[marsac2008b R14]
the same six drugs in amorphous PEO (9% of 450 mg PEO)	14, 24, 13, 17, 15, 2% of the 50 mg of drug dissolvable	PEG 400 value used	[marsac2008b R16]
nifedipine in PVP	more than 90% polymer needed for no crystallization on a thermodynamic basis	predicted with \chi = −3.8	marsac2006b R18, R17
most drugs in polymeric matrices	likely low at room temperature unless cohesive interactions are extremely favourable	solubility in an ethyl-pyrrolidone analogue	marsac2009 C46, R9
nifedipine in PVP K29/32; K12	0.06; 0.07 g/g (0.001 g/g with χ = 0.5)	χ −3.8, predicted	marsac2006b R17.a, R17.b
felodipine in PVP K29/32; K12	0.25; 0.31 g/g	χ −4.2, predicted	marsac2006b R17.a, R17.b
nifedipine; felodipine in methyl pyrrolidone	predicted 0.15 and 0.48; measured 0.21 ± 0.02 and 0.45 ± 0.07 g/g	25 °C	marsac2006b R17.c, R17.d
felodipine, nifedipine, ketoconazole, sucrose, indomethacin in PVP K29/32	0.065, 0.049, 0.010, 0.015, 0.134 weight fraction	scaled from EP	marsac2009 R9
same five in EP	0.268, 0.215, 0.079, 0.074, 0.396 weight fraction	measured, 25 °C	marsac2009 R9
same five	fraction above solubility reaches zero at polymer 0.93, 0.95, 0.99, 0.99, 0.86	PVP K29/32	marsac2009 R11
IDM in PVPVA, 50% DL	132.3 ± 0.8 °C (predicted 131.0 °C)	DSC offset, 0 °C/min	moseson2018 R5
IDM in copovidone, 1:5	about 78 °C	cited	moseson2019 R21
felodipine in dry PVP (cited)	about 0.25 g/g; taken as at most 0.025 g/g in PVP–water	used for the plateau estimate	rumondor2009b R26, C31
felodipine–PVP 50% at 93% RH	residual ≈0.1 g drug per 0.86 g PVP–water, above that bound	mass balance in words	rumondor2009b E4
all dispersions studied (cited)	supersaturated with respect to the estimated solubility in PVP	nifedipine and felodipine	[marsac2008a C47]

Pitfalls and disagreements

The 25 °C values are extrapolations below the PEG melting point and refer to supercooled liquid PEG, not to the largely crystalline polymer of a stored dispersion; one value (nilutamide) lies above its own eutectic content zhu2011 C8, X4. The eutectic composition is a ceiling at the eutectic temperature, about 49–58 °C, and not a solubility at storage temperature [baird2011 C1; zhu2011 R5]. Estimates of different kinds are not on one scale: weight percent of drug in the saturated PEG solution against percent of the drug in a compact that the amorphous polymer fraction could take up (synthesis: 25 wt% for ibuprofen in PEG 3350 against 17% in a PEO compact [zhu2011 R5.d; marsac2008b R16.d]). The PEG 400 estimate did not predict the humid-storage outcome in PEO [marsac2008b C22], and nominal solubilities above the 20% loading did not keep benzocaine and ibuprofen amorphous in PEG zhu2012 X13. PEG 400 may differ from PEG 3350 and PEO through its end groups [baird2011 C22; marsac2008b C19]. All values in PVP are predictions: the temperature and heat-capacity terms are not printed, the only check (methyl pyrrolidone) is about 30% low for nifedipine, and no solubility in a polymer was measured in either paper marsac2006b X10, X11; marsac2009 X17. The 2009 summary extends five compounds to "most drugs" marsac2009 C46, X17. The solubility in PVP K29/32 of indomethacin is 0.134 in the table and 0.144 in part of the text marsac2009 X2. The text and Fig. 6 of the 2009 paper do not agree on the definition of the fraction plotted marsac2009 X13. In the extrusion work, microscopy implied a lower Tc than DSC, which the authors attribute to degradation during long holds or crystals below about 600 nm going undetected ("could be due to"), and the agreement depends on the 2 h window moseson2018 C37, C38, X9. In the moisture papers the tenfold drop with water is transferred from the NMP system to PVP by assumption [rumondor2009b X9; marsac2008a X4].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

dynamic adsorption-desorption equilibrium

A reversible exchange between drug adsorbed on silica and drug in solution, written as adsorbed drug + solvent in solution ⇌ adsorbed solvent + drug in solution: water displaces drug from the surface, and more drug in solution shifts the balance toward the adsorbed side dening2018 E4, C53; dening2019 E9, C2; mccarthy2020 E5, C47. With a supersaturated solution the equilibrium is metastable, since crystallization would reach a lower energy dening2019 C7. The papers find it partly irreversible: part of the drug does not leave on dilution dening2019 C32; mccarthy2020 C27.

Findings

F9, F8, F10, F14.

Related concepts

describes drug adsorption onto silica in contact with solution; quantified by an adsorption isotherm; involves competitive adsorption of water; shifted by absorptive dissolution testing; explains incomplete drug release.

Formulas

competitive solvent-drug adsorption equilibrium, adsorbed amount by solution depletion.

How it is measured or obtained

Not measured directly; inferred from order-of-addition tests (blank silica into drug solution, loaded silica into presaturated medium), release into medium with pre-dissolved drug, redissolution of the recovered solid, dilution and desorption at sink, and release against dose dening2018 P7, P8, P9, A1; hate2020a P8; mccarthy2020 P15, P8.

Values in the library

material	value or class	conditions	paper ids
ritonavir, blank SBA-15 in 28 µg/mL	about 22 µg/mL left	pH 6.8	dening2018 R13
ritonavir residue redissolved	about 12 µg/mL, 43% (n = 1)	pH 6.8	dening2018 R17
ritonavir, dilution to S about 1	release about 40 → 60–66%; bound drug 170 → 100–110 mg/g (calculated)	50 mL, 180 min	dening2018 R18; dening2019 R16
atazanavir, 0 / 20 / 40 µg/mL pre-dissolved	released about 31.2 / 23.9 / 14.8 µg/mL at 90 min	pH 6.8, closed	hate2020a R17
indomethacin; methyl ester, recovered solid	Cmax 16.2; 3.5 µg/mL, as first run (n = 1)	pH 2.2	mccarthy2020 R24
indomethacin; methyl ester, dilution to sink	73%; 57% desorbed in 24 h	pH 2.2	mccarthy2020 R13

Evidence table: dynamic adsorption-desorption equilibrium.

Pitfalls and disagreements

Forward release kept about 50% of ritonavir while blank silica took up only about 20%, so retention "may therefore depend only in part on the adsorption equilibrium" dening2018 C47. Diffusion of drug that is in the pores but not adsorbed would respond to the bulk concentration in the same way, and the tests do not separate it hate2020a X16. The redissolution tests are single runs dening2018 R17; mccarthy2020 X15. An absorptive sink freed little ketoconazole re-adsorbed after a pH shift, read as adsorption "at least partially irreversible" or very slow hate2020b C32.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
HPMCP-50; HPMCP-55	893 ± 95 and 189 ± 18 µg/mL at pH 5.0; insoluble below pH 4.5	50 mg in 15 mL, 48 h, 37 °C	nguyen2023c R4
HPMCAS-LF; -MF	1687 ± 47 and 1401 ± 69 µg/mL at pH 5.5	the same	nguyen2023c R4
HPMCAS-HF	dissolves only from about pH 6.0	the same	nguyen2023c R4
HPMCAS-HF, cited threshold (Bioperformance)	the most hydrophobic grade, with the highest acetyl:succinoyl ratio, needs the highest pH	cited	nguyen2023a C15
Eudragit L 100-55 as an Acryl-EZE II coat, 14–16% weight gain	intact 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 6.0	500 mL, 37 °C	nguyen2023b R7
posaconazole–HPMCAS-MF dispersions in FaSSGF	7.5–11.5% of a 400 µg/mL dose released in 60 min	pH 1.6, 37 °C	elkhabaz2019a R10
praziquantel–HPMCAS-MF dispersions, first stage	≈9–29% released against ≈88–106% for HPMC E5 LV	pH 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
chlorpropamide; aceclofenac with PEG 3350	exothermic mixing implied by \chi_{dp} −2.53 and −6.68 and interaction energies −6.85 and −18.2 kJ/mol	back-calculated	[baird2011 C18, C27, R1.a, R1.b, R9.a, R9.b]
loratadine; haloperidol with PEG 3350	athermal mixing implied by \chi_{dp} 0.13 and −0.04	back-calculated	[baird2011 C27, R9.c, R9.d]
six drugs with PEG 400; with water	exothermic with PEG 400 (\gamma 0.02–0.64); endothermic with water (\gamma 10¹–10⁵)	if mixing entropy is near ideal	[marsac2008b C14]
nifedipine, felodipine with NMP and water	exothermic with NMP (γ 0.09, 0.30), endothermic with water (γ 1.89 × 10³, 2.43 × 10⁵)	assuming near-ideal mixing entropy; 25 °C	[marsac2008a R10, C37]
six drugs in water	γ water 2.54–4.65; unfavourable drug–water contacts	95% RH	rumondor2009c R24, C28
felodipine and quinidine with HPMCAS	less sorbed water gives a less positive mixing enthalpy, which "may explain" no separation	qualitative	[rumondor2010c C31]
indomethacin with PVPVA	stronger drug–polymer bonds give a more favourable mixing enthalpy	qualitative	[rumondor2010c C28]
miscible pairs with PVP	\chi near or below zero: athermal or slightly exothermic, miscibility largely driven by entropy	melting point depression	marsac2009 C29
indomethacin–PVP	most exothermic of five PVP pairs (χ −0.82 melting, −1.83 solubility route)	melting at 1 °C/min; EP at 25 °C	marsac2009 R7.e, R9.e, C29
felodipine, ketoconazole, nifedipine, sucrose with PVP K12	athermal or slightly exothermic, miscibility "largely driven by entropy"	offset melting	marsac2009 R7.a, R7.b, R7.c, R7.d, C29
nifedipine, felodipine with PVP K12	exothermic mixing indicated by χ −3.8 and −4.2	melting at 1 °C/min	marsac2006b C35, R9
dextran with ibuprofen or indomethacin	adhesive interactions not more favourable than cohesive ones, "speculated"	no depression	marsac2009 C43
dextran–PVP	positive enthalpy inferred where blends separate; dextran–dextran bonds assumed stronger or more numerous	phase map; OH band shift	[vaneerdenbrugh2012a C36, C37, R13, R16]
itraconazole–HPMC	entropy-driven mixing with little favourable enthalpy	argument in words	purohit2015a C42

Pitfalls and disagreements

The entropy of mixing was not measured, so an exothermic reading rests on an assumption [baird2011 C23]. The abstract of Baird and Taylor says the interactions were confirmed by infrared spectroscopy, while the spectra show shifts of drug bands against an additive spectrum and no PEG band was analysed [baird2011 X15]. (synthesis: in water the activity coefficient is far above 1 for all six drugs, which is endothermic mixing if the entropy is ideal, yet the drug with the smallest coefficient lost the most crystallinity in PEO [marsac2008b C14, C35].) The two sign conventions of ΔHmix within one paper change the reading of the PAA statement: with the conventional sign, intra-PAA hydrogen bonds make mixing with felodipine less favourable [rumondor2009a X8, C45]. The statement that the solubility of drugs in polymers is low "unless extremely favourable cohesive interactions" form uses "cohesive" where the paper's own definition would give "adhesive" marsac2009 X14. In the miscibility papers the enthalpy was never measured either, so every reading rests on an entropy assumption marsac2009 C11, C29. In the ternary water–drug–polymer case the χ terms also carry non-ideal entropy, so "positive enthalpy" is a statement about positive χ terms rumondor2009c X14. No mixing enthalpy was computed for the HPMCAS and PVPVA dispersions, and a mobility reading is offered alongside [rumondor2010c X13, C32].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
nifedipine with methyl pyrrolidone	minimum near Φ ≈ 0.44	χ = 0	marsac2006b R1
nifedipine with PVP K12, K29/32, K90	minimum near Φ ≈ 0.6; K29/32 and K90 virtually identical, K12 slightly lower	χ = 0	marsac2006b R1
typical molecular weights	APIs 200–600; polymers 10,000–1,000,000	cited	marsac2009 R13
indomethacin, EP → PVP K12 → K29/32 → K90	predicted solubility 0.396 → 0.144 → 0.134 → 0.134	entropy term scaled with chain length	marsac2009 R9.e, C24
maltodextrin (783 Da) with PVP K 12 to K 90	minimum about −27 to −21.5 × 10⁻²³ J per site	25 °C, no enthalpy term	[vaneerdenbrugh2012a R15]
6 kDa dextran with PVP K 12 to K 90	−9.1 to −2.8 × 10⁻²³ J	same	[vaneerdenbrugh2012a R15]
450 kDa dextran with PVP K 90	about 0	same	[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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
carbamazepine, griseofulvin	class IA	DSC and growth	[trasi2014a C17]
acetaminophen	class IB	DSC and growth	[trasi2014a C17]
nimesulide, nilutamide, celecoxib	class II	DSC and growth	[trasi2014a C17]
cinnarizine, droperidol	class III	DSC and growth	[trasi2014a C17]
warfarin, miconazole	class IV	DSC and growth	[trasi2014a 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 Amorphous solid dispersions: the whole picture

falling-off-the-cliff effect

Evidence table: falling-off-the-cliff effect. Content from the release-mechanism chapter (2018–2022), with comparison rows from the ASD dissolution chapter.

The steep fall of drug release over a small increase of drug loading just above the limit of congruency, named "falling off a cliff" for ritonavir–PVPVA, whose drug release at 60 min fell from ≈97% at 25% loading to ≈29% at 30% and below ≈2% at 35–50% indulkar2019a C31, R11. The authors stress that the range of loadings over which release switches from polymer- to drug-controlled is "very narrow" and that the switch changes the drug release rate by "orders of magnitude" indulkar2019a C52. Saboo and co-workers (2020) contrast this "cliff" with the gradual "slope" of HPMCAS dispersions saboo2020a C29. Yang and co-workers (2021) saw the cliff in powders as well as compacts for six drugs in PVPVA and call the HPMCAS decline a negative "slope" instead [yang2021 C2, C41]. Yang and co-workers (2022) hypothesized that the cliff coincides with a continuous drug-rich barrier at the dispersion surface yang2022a C10, C7.

Findings

Release mechanism and LoC: F6, F8, F11, F22.

Related concepts

marks the limit of congruency; separates polymer-controlled release from drug-controlled release.

Formulas

surface-normalized release rate.

How it is measured or obtained

Percent released at a fixed time against loading, or normalized drug rates across the switch, from constant-area compacts indulkar2019a R11; saboo2019 R5, R6; saboo2020a R14.

Values in the library

material	value or class	conditions	paper ids
ritonavir–PVPVA 25 → 30 → 35%	≈97 → ≈29 → ≈1.7% drug at 60 min	pH 6.8, 37 °C	indulkar2019a R11
nilvadipine–PVPVA 10 → 15%	2.13 → 0.035 mg/min/cm² (60-fold)	same	saboo2019 R5, R7
cilnidipine–PVPVA 15 → 20%	2.18 → 0.006 mg/min/cm² (about 360-fold; described as "similar")	same	saboo2019 R6, X8
felodipine–PVP 10 → 15%; –PVPVA 15 → 20%	≈3.8 → ≈0.020; ≈1.9 → ≈0.009 mg/min/cm² (synthesis: 190- and 211-fold)	same	saboo2020a R14
ITZ–PVPVA 20 → 25% (SD); 10 → 20% (HM)	113 → 64; 199 → 48.8 µg/min/cm² (synthesis: 1.8- and 4.1-fold)	0.1 N HCl	[bhardwaj2018 R4]
praziquantel–HPMCAS-MF, HPMC (ASD dissolution chapter)	no cliff; release never declined massively with loading	PBS pH 6.5	polyzois2024 C16, C18
indomethacin–PVPVA 10 → 15%	3.14 → 0.04 mg/min/cm²	5-min rates	saboo2020 R3
loratadine, miconazole, danazol, elbasvir in PVPVA	≈85 → 41 → 8; 93 → 42 → 3; 78 → 9.5; 77 → 13 µg/mL of 100	powders	[yang2021 R7, R8, R9, R10]
atazanavir–PVPVA 5 → 10%	≈100 → below 3% released	compacts, 37 °C	correasoto2022b R1
lumefantrine sulfate–PVPVA 2 → 5%	4.5 → 0.10 mg/min/cm²	compacts	hiew2022b R12
ritonavir–PVPVA 20 → 30 → 40%	drug ≈100 → 35 → 3% at 90 min	compacts, pH 6.8	yang2022a R2

Pitfalls and disagreements

Loadings were tested in 5% steps, so the cliff is located only to the step saboo2020a X11. For HPMC the drop came in two steps (≈0.14 → ≈0.04 → ≈0.005 mg/min/cm²) saboo2020a X11, R14. (synthesis: the height of the cliff is bounded by the ratio of the polymer-controlled to the neat-amorphous rate, so it is small where the amorphous drug alone dissolves fast, as for ITZ in 0.1 N HCl.) Stated cliff loadings mix the last good and the first poor loading [yang2021 X26].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

Fick's first law

Steady-state diffusive flux through a membrane written in activity form, J = D S a/(h \gamma_m) raina2014a E6; the concentration form is J = (D_{eff}/l)(C_d - C_r) indulkar2016 E1. The darunavir and posaconazole papers also write it as J = -D\,dC/dx and as the permeability form J = P C alkalla2026 E1; elkhabaz2019b E5.

Findings

F2, F5, F18, F20.

Related concepts

underlies membrane flux; needs sink conditions.

Formulas

membrane flux in terms of solute activity, membrane flux from concentration difference.

How it is measured or obtained

Used as a model, not fitted: constants D, S, h and γm are assumed constant and not printed raina2014a E6; hate2017 E1; alhalaweh2016 E1.

Values in the library

material	value or class	conditions	paper ids
side-by-side cell, activity form	J = DSa/(h\gamma_m), 7.065 cm²	felodipine, nifedipine	raina2014a E6
flow-through cell, concentration form	J = (D_{eff}/l)(C_d - C_r)	clotrimazole	indulkar2016 E1, E4
danazol	J = (dM/dt)(1/S) = D a/(h\gamma_m)	ASD	jackson2015 E1
atazanavir, posaconazole, six media	permeability form J = PC: apparent permeability on total concentration fell in micellar media; multiplied by the ratio of total to buffer solubility it was 1.33–1.77 × 10⁻³ (atazanavir) and 2.36–3.03 × 10⁻³ cm/min (posaconazole)	side-by-side, 37 °C	elkhabaz2019b E5, R12, R13

Pitfalls and disagreements

The text of one paper writes γ for the membrane activity coefficient in Eq. 3 and for the donor in Eq. 4 raina2015c X8. The permeability form with total concentration under-reads permeability where micelles bind drug (F18) elkhabaz2019b R12, R13.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
chlorpropamide; haloperidol with PEG 3350	−0.50 and 0.08; −2.53 and −0.04	zhu2011 (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, 0.02	melting 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 0.5	slope of the linearized plot	marsac2006b R9, R4
indomethacin with PVP K12	−6.16 (onset), −1.94 (midpoint), −0.82 (offset)	melting point depression	marsac2009 R6
indomethacin with PVPVA	−1.97 (R² = 0.9895); reproduces all predicted Tc of Table III within 0.05 °C	used to predict Tc; slope with free intercept, 50–90% DL	moseson2018 R4, R5, E2
PVP-miscible pairs	negative or near zero; immiscible pairs larger positive values, from −0.82 to 0.72	offset melting	marsac2009 C17
indomethacin, felodipine, nifedipine, ketoconazole, sucrose with PVP K12	offset χ −0.82, −0.08, 0.00, −0.08, 0.02	1 °C/min	marsac2009 R7.a, R7.b, R7.c, R7.d, R7.e
same five compounds	solubility-route χ −1.83, −0.08, −0.81, −0.12, −0.53	25 °C, EP	marsac2009 R9
sucrose–dextran; ibuprofen–dextran; indomethacin–dextran; itraconazole–Eudragit E100	0.20; ≥ 0.38; ≥ 0.72; ≥ 0.11 (lower limits for the last three)	offset melting	marsac2009 R7.f, R7.g, R7.h, R7.i, C19
felodipine–PVP; indomethacin–PVP	−9.6 to 26.9; −20.4 to 22.0 (ranges only)	ternary sorption fit	[rumondor2010a R14]
IDM–PVPVA in four other studies	−0.64, −2.06, −2.9, −4.5 (assignment to studies not printed)	cited	moseson2018 R7
water–felodipine, water–PVP	about 3.3 and about 0.5 (Δχ large)	sorption isotherms, Flory–Huggins fits	marsac2010 C43
water with amorphous felodipine, PVP, HPMC and HPMCAS	3.27 for felodipine; above 0.5 for HPMC and HPMCAS; the PVP value close to but slightly below other authors' values	water sorption isotherms, 25 °C	[rumondor2010a R11, C19, C20]
BCL–PVPVA 30% DL	−1.57, read as favourable miscibility	phase 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 0.5	sensitivity moved mainly the drug–polymer side	li2020 R15, R16, C72, X10
water–ritonavir and water–PVPVA (drying model)	2.8 and 1.13	fitted to dynamic vapour sorption, room temperature	li2020 R15
BCL–PVPVA 30–90% BCL	−1.57 (R² 0.994); Tc 145 °C at 30% BCL	DSC 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 −0.05	same	shah2024 R1, R4
water with nifedipine, felodipine, droperidol, pimozide, indomethacin, ketoprofen	2.84, 3.18, 2.85, 3.58, 2.50, 2.71	25 °C, 95% RH	rumondor2009c R24
nifedipine–PVP, felodipine–PVP (cited)	−3.8 and −4.2 from melting point depression	used for activity	[marsac2006a R18]
indomethacin–PVP vs nifedipine–PVP (cited)	−0.8 vs 0.0	used for susceptibility	rumondor2009c R26
indomethacin against felodipine, quinidine, pimozide with PVPVA	larger carbonyl red shift (42–44 against 19–22 cm⁻¹) "would result" in a lower \chi_{DP}	IR of dry films	[rumondor2010c R20, C28]
hydrophobic drugs with water	\chi_{WD} expected positive from log P	qualitative	[rumondor2010c C30]
indomethacin with HPMC, HPMCAS, PVP	χ not measured; stronger interaction "would" lower the driving force for growth	argument with the free energy of mixing	[tian2017 E2, C30, X13]
lopinavir with HPMCP, EC, HPMCAS	ranked HPMCP > EC > HPMCAS in suppression, read as interaction strength	pH 3, 25 °C	[li2018 C54]
lopinavir with CA, EUD	two Tgs, sorption on the additive line; little suppression	pH 3, 25 °C	[li2018 C56]
ritonavir with PVP, PVPVA, HPMCAS	no values; the argument explains AAPS of PVP and PVPVA films at 97% RH	25 °C	purohit2017b C43, C1
six drugs with PVPVA and HPMCAS	no 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 Amorphous solid dispersions: the whole picture

food effect

Evidence table: food effect. Content from the ASD dissolution chapter (delamanid 2023, praziquantel 2025), the Bioperformance chapter and the Mesoporous silica chapter.

The change of release or exposure when a dose is taken with food rather than fasting. In this chapter it enters through the media: fed gastric and intestinal fluids hold more bile salt, lecithin and lipid than fasted ones, raise the solubility of the drug, and prolong gastric residence at a higher pH nguyen2023b R13, C19. The two effects can pull in opposite directions. Where food raised the solubility of delamanid several hundredfold, the release of the marketed tablet rose with it, which the authors say the higher solubility "likely accounts" for nguyen2023b R14, C29; where it raised praziquantel solubility only modestly, the fed intestinal medium instead "promoted crystallization" that neither polymer could inhibit alvarenga2025 C29. Clinically, a standard meal raised the Cmax and AUC of the delamanid product 3.4- and 2.9-fold nguyen2023b R24.

Findings

F28, F27.

Related concepts

acts through micellar solubilization and gastric pH variability; changes nucleation and crystallization inhibition by polymers; relevant to enteric polymer coats.

Formulas

none.

How it is measured or obtained

By measuring crystalline and amorphous solubility in fasted and fed simulated fluids and running the same release test in each, with a fed gastric stage (FEDGAS or acetate pH 4.5) before a fed intestinal medium nguyen2023b P13, P12; alvarenga2025 P7, P8, P12; crystals in the residues are then sought by polarized light and PXRD alvarenga2025 P6, P5.

Values in the library

material	value or class	conditions	paper ids
delamanid, crystalline	0.52 (FaSSIF V1), 2.30 (FeSSIF V2), 13.10 (FEDGAS pH 4.5), 57.97 µg/mL (FEDGAS pH 3.0)	37 °C	nguyen2023b R13
Deltyba tablet	≈77 µg/mL in FeSSIF V2 against ≈31–37 µg/mL in FaSSIF V1 at 120 min	500 mL, 37 °C	nguyen2023b R14
coated delamanid edisylate tablets	≈96 µg/mL in both media; ≈86–87 µg/mL after 17 h in FEDGAS	37 °C	nguyen2023b R16, R17
praziquantel, amorphous and crystalline	1.74 and 0.31 mg/mL (racemate) in FeSSIF-V2 against 1.17 and 0.16 mg/mL in PBS pH 6.5	37 °C	alvarenga2025 R1
praziquantel dispersions, both polymers	≈68–80% at 0.667 mg/mL and ≈34–52% at 1.5 mg/mL in FeSSIF-V2	2 h, 37 °C	alvarenga2025 R16, R18
pretomanid–HPMCAS-HF dispersion; crystalline reference (Bioperformance)	negative food effect in monkeys for the dispersion; positive for the reference (Cmax +23%, AUC +49%)	single 30 mg dose	nguyen2023a C53, C78

Pitfalls and disagreements

A higher solubility in a fed medium does not predict the direction of the effect for a dispersion: the pretomanid dispersion lost exposure with food while its crystalline reference gained nguyen2023a C53, C78, and praziquantel release fell in fed fluid although its solubility rose alvarenga2025 R18, C8. Delamanid dispersion release was the same in FaSSIF as in buffer although the amorphous solubility was ten times higher duong2022a R13. The delamanid solubility method is not described, and text and figure values differ for the marketed tablet nguyen2023b X8, X2.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
IDM–PVPVA 50:50	132.3 ± 0.8 °C measured; 131.0 °C predicted; "131 ± 2 °C" used	offset extrapolation	moseson2018 R5.f, X2
IDM–PVPVA 1:1 extrudate	processing at 131 °C melt temperature, 20 min, left nanometre crystals	HME, TEM	moseson2018a R2, R9
BCL–PVPVA 30:70	Tc = 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 min	5 mL micro-extruder	[moseson2022c R9, R10]
PCZ–HPMCAS MF 10 / 25 / 50% DL	calculated 135 / 155 / 165 °C; extruded at 125 °C they held 0.3 / 3.2 / 19.3 wt% crystals	2 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir–atazanavir	measured Tg lie 3–8 K below the Fox line; line from about 365 K (w_RTV 0.2) to 323 K	melt-quenched	alhalaweh2016 R9, X7
TIPP with PVPVA	Fox gives 84 °C for neat TIPP	90:10 ASD	[que2021 R1, E2]
enzalutamide	Fox-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 Amorphous solid dispersions: the whole picture

free drug concentration

The concentration of molecularly dissolved drug that can cross a membrane, as against drug in micelles, complexes, droplets or aggregates raina2015c C30, C49; alhalaweh2016 C1. In rat studies of enzalutamide the free drug is inferred from flux: the cellulose acetate suberate dispersion gave free drug like the crystalline form, matching their equal exposure (F24, F25) wilson2020 C10, C40. In micellar media the buffer solubility is taken as the free drug and the excess as micelle-associated elkhabaz2019b C26, C31. New aspect (Supersaturation from ASD dissolution): the free drug concentration, not the total, sets the supersaturation that drives crystallization and membrane transport (cited), and it stops at the amorphous solubility once a drug-rich phase forms jackson2015 C26, C31. Flux separated free from complexed resveratrol: more HPMCAS dispersion gave more total but less free drug, free resveratrol being at most about twice saturation [wegiel2015 C19, C41]; six tacrolimus products reached the free-drug maximum of the pure drug trasi2016 C38.

Findings

Bioperformance: F3, F6, F7, F15, F18, F24, F25. Supersaturation from ASD dissolution: F7, F8, F11, F17.

Related concepts

equals thermodynamic activity in effect; lowered by micellar solubilization; related to additive cases for amorphous solubility, speciation, micelle-water partition coefficient; measured by membrane flux; capped by amorphous solubility.

Formulas

activity from concentration, supersaturation from membrane flux ratio, membrane flux in terms of solute activity, activity-based supersaturation ratio, ideal-mixing reduction of amorphous solubility.

How it is measured or obtained

Supernatant after ultracentrifugation alhalaweh2016 P10; flux against a reference raina2015c E9; fluorescence or filtration are less reliable above the amorphous solubility hate2018 X15. In the ASD dissolution papers: by flux across a membrane against a standard curve jackson2015 P4, by flux relative to the crystal alonzo2011 P4, by solution NMR alonzo2011 P7, and by ultracentrifugation trasi2015b P9.

Values in the library

material	value or class	conditions	paper ids
ritonavir, atazanavir (PVP ASD)	4.3–4.75 × 10⁻⁵ M and 1.38–1.54 × 10⁻⁴ M alone; falls linearly with mole fraction	pH 6.8	alhalaweh2016 R12
atazanavir + SDS	about 65 µg/mL at the amorphous solubility whatever the SDS level	37 °C	indulkar2017a R11, C19
ritonavir, lopinavir HPMCAS and PVP dispersions	RTV-PVP maximum about 22 µg/mL even after 2 h	ultracentrifuged	trasi2015b R12, R13
resveratrol–HPMCAS	at most about twice saturation; enhancement from a soluble complex		[wegiel2015 C41]
telaprevir + CA Sub	not measured; flux 0.91 µg/min with the predissolved polymer		mosqueragiraldo2018b R13
enzalutamide	about 42 µg/mL molecularly dissolved of 70 µg/mL added; the rest colloidal amorphous aggregates	pH 6.5 buffer	wilson2020 R2; wilson2018 R10
posaconazole, atazanavir	free concentration at either solid phase taken as the buffer value in every medium	six media, 37 °C	elkhabaz2019b C26, C27, C31
danazol dispersions with a drug-rich phase	7.1–9.1 µg/mL (amorphous solubility 8)	flux, 25 °C	jackson2015 R9
danazol 50:50 HPMCAS (no drug-rich phase)	5.4 ± 0.8 µg/mL	flux, 25 °C	jackson2015 R9
ritonavir + lopinavir drug-rich phases	RTV 14.2–15.8, LPV 7.0–7.5 µg/mL for 5 h	ultracentrifuged	trasi2015b R16
felodipine 90:10 and 50:50 HPMC dispersions	flux ratios 10.5 and 9.5 to the crystal	37 °C	alonzo2011 R14
resveratrol–HPMCAS 15:85, 6–35 mg/mL	total ≈530 → ≈1610 µg/mL while flux ≈4.4 → ≈2.6 µg/min (crystal 2.0)	pH 6.8, 37 °C	[wegiel2015 R19, R20]
six tacrolimus products	0.0048–0.0054 µg/min against a pure-drug plateau of ≈0.0050–0.0055	pH 4.5, 37 °C	trasi2016 R15, R14

Pitfalls and disagreements

Free drug was not measured in the donor in the hollow-fibre studies, so statements that it equals the amorphous solubility are assumptions hate2018 X11. Equating the buffer solubility with the free drug assumes that bile salts and lecithin do not mix into the drug phases, which the small fall of the posaconazole flux ratio questions (F18) elkhabaz2019b C31, C44. Ueda 2024 (p. 39) gives the general form: the buffer value equals the free drug only in Case I, and in Case III the free drug at the limit falls. In the ASD dissolution papers in situ UV and 0.45 µm filtrates count droplets or particles as dissolved alonzo2011 C27; trasi2015b C22. The danazol standard curve does not pass through zero, so flux cannot be converted to concentration by proportion jackson2015 X5. The inverse link of flux and concentration for resveratrol holds only up to about 18.8 mg/mL loading [wegiel2015 X9].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
nifedipine–PVP K29/32	positive 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, −4.2	Flory–Huggins	marsac2006b R2
indomethacin–PVP	minimum ≈2.4 times (melting χ) and ≈5 times (solubility χ) as deep as the athermal minimum	Φ_polymer ≈ 0.5–0.6	marsac2009 R10
felodipine, ketoconazole with PVP	three curves (athermal, melting χ, solubility χ) nearly coincide	as above	marsac2009 R10
sucrose–dextran	melting-route curve above the athermal curve (χ = 0.20)	as above	marsac2009 R10

Pitfalls and disagreements

The condition "the binodal points are the two minima" (first derivative zero) coincides with the common-tangent binodal only for a symmetric curve like the schematic in the paper; the authors apply it to no data [rumondor2009a E6, X15]. Curves for the immiscible pairs are not drawn, because their enthalpy of mixing cannot be accessed marsac2009 C31. The temperature and the PVP grade of the 2009 curves are not stated marsac2009 X12.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

gastric pH variability

Evidence table: gastric pH variability. Content from the ASD dissolution chapter (delamanid 2023, praziquantel 2024–2025) and the Release mechanism and LoC chapter.

The spread of stomach pH between and within patients, from about 1.6 fasted to 5 or above after a meal, and with age or acid-reducing drugs, which changes how much drug and polymer dissolve during the gastric stage of a dispersion and how long the dispersion sits wetted before the pH rises nguyen2023c C5, C57. In vitro tests are usually standardized at one gastric pH and so do not see it nguyen2023c C5. Food also prolongs gastric residence, cited as 15–60 min fasted and 2–5 h fed, with a gastric pH of 6–6.5 about 30 min after a meal nguyen2023b R22, C19.

Findings

F25, F27, F24.

Related concepts

acts through pH-dependent polymer solubility and pH-dependent solubility of weak bases; risk of surface crystallization; mitigated by an enteric polymer coat; read with food effect.

Formulas

none.

How it is measured or obtained

By repeating a two-stage test with the gastric stage set at several pH values (pH 1.6, 3.0 and 5.0, or FaSSGF and a fed gastric medium) and the same intestinal stage, so that only the gastric pH changes nguyen2023c P8; alvarenga2025 P10, P11, P12; by soaking a coated tablet across the same range to find where the coat fails nguyen2023b P6.

Values in the library

material	value or class	conditions	paper ids
delamanid salt dispersions, five enteric grades	final release ≈101 / ≈41 / ≈82% (HPMCP-50), ≈94.5 / ≈80.5 / ≈12.5% (HPMCP-55), down to ≈18 / ≈1 / ≈0% (HPMCAS-HF)	60 min at pH 1.6 / 3.0 / 5.0 → pH 6.5	nguyen2023c R11
delamanid free base with HPMCP-50	≈62.5 / ≈33.5 / ≈6.5 µg/mL of 100	the same	nguyen2023c R7
uncoated delamanid–HPMCP-50 tablets, three drug forms	≈0.3–93 µg/mL after the shift against ≈82–96 µg/mL in a single stage	the same	nguyen2023b R2, R1
coated delamanid tablets, three drug forms	≈76–86 µg/mL after every gastric pH, a spread of about 4–8 µg/mL within a form	the same, transfer to fresh medium	nguyen2023b R10
praziquantel–HPMCAS dispersions, 0.667 mg/mL	≈92–103% after pH 1.6 or FaSSGF against ≈62–77% after pH 3.0 or 5.0	1 h gastric stage → pH 6.5	alvarenga2025 R7, R10, R13
bedaquiline–HPMCAS 5/95 dispersions (Release mechanism and LoC)	≈19.5–25 µg/mL of 100 at 120 min from all three gastric pH values	60 min at pH 1.6 / 3.0 / 5.0 → pH 6.5	kaur2025 R12

Pitfalls and disagreements

The worst gastric pH is not the lowest and differs by drug form: pH 3.0 for the delamanid edisylate tablet and pH 5.0 for the free base and the chloride nguyen2023b X5. A neutral drug is not exempt: praziquantel, neutral above about pH 3, still recovered less after pH 3.0 and 5.0 starts, which the paper does not explain alvarenga2025 R4, R10. The gastric supersaturation reached does not order the final release nguyen2023c C39. All of these tests used one 60-min gastric stage and simple media without food components nguyen2023c X8.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
30% BCL–PVPVA compact, 1 h	porous gel layer F/F0 0.93 ± 0.06 under a 94 ± 8 µm drug-rich layer	SEM-EDX	moseson2022b R15
same, confocal	gel layer 440 ± 6 µm; compact swelled from 2092 ± 24 to 2696 ± 50 µm in 60 min	Nile red, Alexa Fluor 488	moseson2022b R16, R17
50% BCL–PVPVA compact	no gel layer distinguished; swelled from 1988 ± 11 to 2441 ± 12 µm	same	moseson2022b R17
uncoated ritonavir–PVPVA tablet edge	small discrete red droplets throughout a green gel layer that moves into solution	confocal, 37 °C	[benson2025 R14, R16]
coated ritonavir–PVPVA tablet edge	green and red networks along particle boundaries within 2 min; connected red regions remain outside the receding tablet at 4 min	same	[benson2025 R14, R16]
felodipine–PVPVA 30% with 0, 2% TPGS; 5, 10% TPGS	porous surface layer with voids at the dissolution front; homogeneous section	micro-CT after 10 min	saboo2021 R19
PVPVA	at least 11% water to start chain disentanglement at 37 °C	estimated	hiew2022b R21
ritonavir–PVPVA 10–40%	gel layer with a sharp boundary to the glassy core at every loading; no grain boundaries in the gel	confocal cross-sections, pH 6.8	yang2022a R7, C42
ritonavir–PVPVA 0–20%; 30%, 40%	gel–glass front through ≈100% of the compact at 20 min; ≈29 and 17% with a plateau	real-time imaging	yang2022a R8
neat HPMCAS-MF in pH 6.8 phosphate 5; 13; 51 mM/ΔpH	no gel; 3 ± 1 µm; 19 ± 5 µm	confocal with prodan, 60 min	[bapat2023 R14]
neat HPMCAS-MF gel, pH 6.8 phosphate 13–51 mM/ΔpH	apparent pH 5.6–6.2	gel 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 µm	gravimetric and cross-sectional, steady state	[deac2023a R4, C44, C31]
ritonavir–PVPVA + Tween 80, 30%	≈147.6 → 279.6 (5 → 20 min)	confocal cross-sections, unit not printed	yang2023 R15, X8
ritonavir–PVPVA + Span 20, 40%	≈90.7 → 50.7 (5 → 20 min)	same	yang2023 R15
neat PVPVA; 5% PHPH; 5 and 20% MePHPH	gel–solution boundary from a linear water gradient	ternary diagram, 37 °C	deac2024b R27, E4

Pitfalls and disagreements

Layer thicknesses come from compacts, whereas the authors say polymer loss is much faster from particles than from compacts moseson2022b C39, X20. Dye assignments and the polymer-depleted state of the crust are inferred moseson2022b X16. The confocal tablet images come from a different compaction and size than the release tablets, and the large red blobs of the uncoated row at 2–3 min are a mounting artefact [benson2025 X5, R15, C29]. That croscarmellose and starch glycolate raise the viscosity of the PVPVA gel is a speculation [benson2025 C50]. Hydrophilic surfactants "would reasonably be expected" to draw more water into the gel–water interface and so speed polymer dissolution, an argument without data correasoto2022b C42. Yang and co-workers read thickness as the balance of water penetration and disentanglement, but water ingress was not measured on the compacts yang2023 C26, C27. The gel-layer region of the 2024 diagrams rests on a fitted water Tg and on gel water contents cited from 2023 deac2024b X11, R40.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
51 drug-like molecules	23 crystallize on cooling (low GFA)	DSC, 20 °C/min	baird2010 R1
23 class I molecules	8 vitrify on liquid-N2 quench (I-B)	melt plunged into liquid N2	baird2010 R3
antipyrin, chlorpropamide, flufenamic acid, tolbutamide	glass already at 25 °C/min	rapid heat–cool DSC	[baird2013 R5]
8 class I-A molecules	crystallize even at 800–1100 °C/min	rapid heat–cool DSC	[baird2013 R1, R3]
acetaminophen	forms a glass even at slow cooling	cited DSC data	trasi2012a R1
nilutamide	good glass former; attributed to low nucleation	DSC at 15 °C/min	[trasi2014b R2, C9]
vemurafenib	"relatively poor glass former", about 25 °C supercooling	DSC at 10 °C/min	[lu2016 R1, C5]
tacrolimus	good GFA and stability; melting onset 121 °C, Tg onset 75 °C, no crystallization on reheating	DSC heat–cool–reheat	trasi2016 R3, C13, M1
lumefantrine; artemether	class 3 (Tg ≈18 °C, no crystallization on reheating); class 1 (crystallized on cooling from about 60 °C)	DSC heat–cool–heat	trasi2020 R5, R6, C7
acetaminophen	glass because nucleation (50–60 °C) and growth barely overlap	DSC cool–reheat, hot stage	trasi2012a C39, R12.a, R8.a
resveratrol	not made amorphous by spin coating from four solvents, rotary evaporation or 6 h of cryomilling	neat drug	[wegiel2013b R1, C6]
curcumin	amorphous by spin coating, not in larger amounts by rotary evaporation; cryomilling gave a larger amorphous mass	neat drug	[wegiel2014 C9]
celecoxib	easily made amorphous by cooling the melt	hot stage	mosqueragiraldo2014 R15
delamanid	no glass at up to 50 °C/min; class I; a glass quenched in liquid nitrogen recrystallized just above its Tg of 43.3 °C	DSC; liquid-N2 quench	duong2022a R3, C44
bicalutamide	high GFA but rapid crystallization above Tg	cited	moseson2022b R26
posaconazole, indomethacin, bicalutamide	class III (high glass-forming ability)	cited	moseson2020 C5
posaconazole, bicalutamide neat melts	nucleated within 1 h between Tg and Tm	DSC 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
telaprevir phase	Tg 52 °C (dry 103 °C); redissolves in about 2 min on dilution	pH 6.8, 37 °C	mosqueragiraldo2015 R2, R8
atazanavir phase	Tg about 51 °C (dry 104 °C)	water, 37 °C	indulkar2015 R22
griseofulvin; sorafenib	wet Tg 88 and 49 °C at 97% RH; onset matches the supercooled-liquid estimate	25 °C	almeidaesousa2015 R9, R5, R6, R11
pazopanib precipitate	Tg about 83 °C (dried); wet Tg not measured	pH 6.5, 37 °C	sugihara2018 R17, X5
telaprevir	onset 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
telaprevir	onset 92 ± 2 µg/mL; precipitate Tg 52 °C	pH 6.8, 37 °C	mosqueragiraldo2015 R4, C13
telaprevir, bile salts	149 / 146 µg/mL (pH 6.5, 50 mM); 104 / 102 µg/mL (pH 6.8, 100 mM)	ultracentrifugation / UV	lu2017b R9
enzalutamide	onset about 42.5 µg/mL; amorphous precipitate glassy under cross-polarized light	pH 6.5, 37 °C	wilson2018 R2, R4
telaprevir 150 µg/mL, no polymer	concentration about 162 → 100 µg/mL by about 12 min, then a steep fall at 15–25 min	pH 6.8, 37 °C	[mosqueragiraldo2016 R3]
telaprevir δ 28.8, 1.86 mM bile salt	induction time SGDC >960, STDC 550, STC 60, SGC 30 min	pH 6.5, 37 °C	[lu2017 R4]
telaprevir at δ 28.8 with 150 µg/mL HPMCAS-MF	turbid in all media (glassy drug-rich phase)	five media, 37 °C	[lu2018 R8, C35]
enzalutamide above 42 µg/mL	glassy 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
class II	much lower glass stability than class III	DSC reheating and storage	baird2010 C47
class III	high glass-forming ability and high stability on reheating	DSC	baird2010 C34
indoprofen glass	fully crystalline after 1 day	30 °C, 0% RH	baird2010 R23
class II glasses	Rcrit,heat 12.5 to above 1910 °C/min	rapid heat–cool DSC	[baird2013 R9]
acetaminophen	quenched-in nuclei may matter for stability over longer times	argument	trasi2012a C41

Pitfalls and disagreements

The storage evidence for a link between glass-forming ability and glass stability rests on one or two glasses per class baird2010 X16. Glass-stability parameters ranked class II molecules inconsistently baird2010 X15.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
propranolol base; hydrochloride	−9.3; 35.9 °C	DSC	[towler2008 R4]
nicardipine base; hydrochloride	3.2; 81.0 °C	DSC	[towler2008 R5]
nilutamide	32 °C (onset)	DSC	[trasi2014b M1]
vemurafenib	108 °C	DSC at 10 °C/min	[lu2016 M1]
felodipine; nifedipine; indomethacin	45 °C each	DSC midpoint	baird2010 M37, M32, M40
lumefantrine	about 18 °C; 19.7 °C (onset)	DSC	trasi2020 R5; hiew2022a R3
five drugs with 10 mol% PVP	raised by about 2–3 °C	DSC	[trasi2014a R7]
nilutamide; ketoconazole	about 33 °C; 44 °C	cited	zhu2011 M5, M6
benzocaine	−31 °C	cited	zhu2012 M3
acetaminophen; ketoprofen; naproxen; ibuprofen; felodipine; ketoconazole	22.1; −3.0; 24 (estimated); −43.6; 43.1; 44.4 °C	DSC and cited	[marsac2008b M1, M2, M3, M4, M5, M6]
amorphous PEO; water	about −67 °C (reported −67 to −55 °C); −136 °C	cited	[marsac2008b M7, M12]

Pitfalls and disagreements

Whether a Tg is onset or midpoint is not always stated [towler2008 X7]; Tg of 16 class I molecules is an estimate baird2010 X17. Crystallization tendency cannot be predicted from relaxation times and Tg alone marsac2010 C29, and a high Tg did not prevent a propranolol salt from crystallizing [towler2008 R4.a, R12]. In the solvent screen the Tg contribution separates the classes partly because the storage criterion selects high-Tg compounds vaneerdenbrugh2010a C41. The Tg conclusion in the drug/PEG study rests on two drugs whose Tg lie 8 and 19 °C above 25 °C and that also differ in interaction and crystallization tendency zhu2011 X13. The Tg of haloperidol is given as below 25 °C in the card of Zhu and co-workers and as 33 °C (calculated from the molecular weight) in the classification paper zhu2011 M1; baird2010 M17. The naproxen Tg of 24 °C does not follow from the Tg/Tm rule it cites: the Table 1 melting point gives 26.7 °C [marsac2008b E5, X4]. (synthesis: papers also give different Tg for the same drug, nilutamide 32 °C (onset) against about 33 °C, and felodipine 45 °C (midpoint) against 43.1 °C [trasi2014b M1; zhu2011 M5; baird2010 M37; marsac2008b M5].)

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ibuprofen; fenofibrate	crystals form at a crystalline PEG interface within minutes, none in the bulk	25 °C	zhu2012 R15, R19, C4
neat ibuprofen; fenofibrate	0.20 and 0.34 of 50 samples crystallized after 3 weeks	25 °C, no carrier	zhu2012 R2, R3
ibuprofen; fenofibrate in 20/80 PEG 3350	onset about 100 min; 120–180 min	25 °C	zhu2012 R23.a
class I-A melts	crystallization temperatures higher in the rheometer than in DSC, ascribed to the upper plate	shear 30 s⁻¹	baird2012 R5, C8
class I molecules	scatter of crystallization temperatures ascribed to stochastic and heterogeneous nucleation	DSC pans	[baird2010 C19; baird2013 C18]
felodipine films	nucleation "most likely heterogeneous"	spin-coated films	konno2006 C33
posaconazole	homogeneous at high supersaturation, heterogeneous at low; shallow slope of log t against 1/log²S below S about 12 read as heterogeneous ("has been attributed")	PBS pH 6.5, 37 °C	[duong2022b R10, C28]
enzalutamide with drug-rich droplets	droplets enhance crystallization; droplet/water interface "likely" a favourable site; induction times fall on crossing 42 µg/mL	pH 6.5, 2.5–100 µg/mL polymer	wilson2021 C45, C46, R3
bicalutamide	fractures of mechanically activated samples favour heterogeneous nucleation	dispersions	moseson2022b C45
induction-time replicates, 50–80 mL, S 2.4–15.4	scatter below 15%	triplicate	ilevbare2013c R17
danazol, HPMC-AS	induction time 516 → 277 min as drug concentration rises from 10 to 20 µg/mL	25 °C	jackson2014 R17
telaprevir δ 28.8, buffer	crystallizes immediately with a drug-rich phase present	pH 6.5, 37 °C	[lu2017 R4]
atazanavir ASD particles	dissolving 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 LLPS	about 262 against 34.7 min; about 289 against 23.6 min	37 °C	ilevbare2013d R16, R12
nifedipine dispersions against glass	γ → α complete in ≈5–40 min against ≈40–145 min with dissolved polymer	25 °C	raina2014b R12, R10

Pitfalls and disagreements

Heterogeneous nucleation by a carrier breaks the link between the crystallization of the pure drug and of the drug in the dispersion zhu2012 C41. Homogeneous classical theory is applied to systems that are most likely heterogeneous [konno2006 C33; marsac2006a C32]. The PEG seeding was done in pure supercooled drug, not in the dispersion, and enrichment of the drug in the remaining non-crystalline fraction after PEG crystallizes is an alternative that the experiments cannot separate zhu2012 X13. Whether other slowly crystallizing drugs (nilutamide, ketoconazole) are nucleated by crystalline PEG was not tested; in the same PEG at the same ratio neither was fully crystalline at 24 h zhu2011 R18.e, R18.f. Nucleation by polymers in solution has been reported, outside the library, and most reports of drugs in polymers find retardation of crystallization zhu2012 C35, C36. The attribution to nucleation at the droplet interface is an inference; solutions at 10 µg/mL with HPMC or HPMC-AS are already above their measured onsets jackson2014 X3, X15. Impurity-induced nucleation was expected, not tested ilevbare2013c C16. Neither micelles as nucleation sites nor the nucleation site in the two-phase solutions were observed [lu2017 C34, C40]. Neither the enzalutamide nor the posaconazole paper located the nucleation site; the homogeneous–heterogeneous assignment rests on a slope change [wilson2021 C45; duong2022b X11]. None of the three proposals of the ASD dissolution papers was tested directly raina2014b C36; trasi2015b C31; ilevbare2013d C43.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

hierarchical particle approach

Evidence table: hierarchical particle approach (names merged there: hierarchical particle, hierarchical particle approach). Content from the release-mechanism chapter (2023–2025).

A core amorphous dispersion particle with an additional water-soluble component coating its surface. For co-precipitated amorphous dispersions (cPAD) it was made by pre-dissolving a secondary polymer in the anti-solvent, which deposits on the particle surfaces during isolation and drying [hiew2023 C7]. Diluting the surface drug in this way shifts the release of a high-loading dispersion toward that of a lower loading [hiew2023 C57]. Earlier, incorporating co-precipitated particles into a water-soluble HPMC matrix had managed poor wettability at loadings similar to spray-dried dispersions, leaving open whether it could remedy the slowdown at high loading (cited) [hiew2023 C5]. The 2025 study screened seven secondary excipients in the anti-solvent on 75% grazoprevir–HPMCAS particles and applied HPMC or SDS by high shear to a solvent-evaporated dispersion; only excipients that made the surface wettable helped, and HPMC had to be dissolved, not dispersed, in the anti-solvent [hiew2025 P6, P7, C27, C40]. The authors call the approach "promising" for high loading [hiew2025 C11].

Findings

Release mechanism and LoC: F14, F28, F35.

Related concepts

lowers surface drug enrichment; improves wettability; allows a higher drug loading; acts on particles with a large specific surface area; tested for oral bioavailability.

Formulas

none.

How it is measured or obtained

Co-precipitation of grazoprevir–HPMCAS with HPMC or HPC dissolved or suspended in the anti-solvent, isolation by filtration or rotary evaporation; surface drug by XPS; two-stage dissolution (SGF then FaSSIF); exposure in dogs [hiew2023 R10, R11, R12, R14, P14, R15].

Values in the library

material	value or class	conditions	paper ids
binary grazoprevir–HPMCAS cPADs, 60; 75%	≈37.5; 17% (acidified water), 8% (MTBE) released at 90 min	two-stage dissolution	[hiew2023 R10, R14]
hierarchical cPADs, HPMC or HPC dissolved in the anti-solvent	≈56–72%	same	[hiew2023 R10, R12]
washed binary cPAD; HPMC suspended in MTBE	≈47%; ≈8–15%	same	[hiew2023 R10, R11]
eight materials	surface drug ≤34% with ≈47–72% release; ≥53% with ≈8–17%	XPS	[hiew2023 R14]
hierarchical against binary cPAD, ≈73% drug	AUC 135 against 73 µM·h	dogs, n = 6	[hiew2023 R15]
grazoprevir–HPMCAS 75:25 with 5 mg/mL SDS, TPGS, PEG, HPMC, PVP, gelatin, poloxamer 407	≈37 / 31 / 31 / 23 / 21 / 14 / 13% at 90 min	two-stage SGF → FaSSIF	[hiew2025 R9]
same with 10 mg/mL HPMC	≈47–52%	same	[hiew2025 R9]

Pitfalls and disagreements

The best hierarchical particle is called a 60% material in the discussion but assays 73.4% drug with about 1.6 wt% HPMC retained [hiew2023 X1]. Wetting was judged by eye only [hiew2023 X12]. A recomputation from the plasma profile gives AUCs about 1.3-fold lower than the table, possibly a unit issue; the table values are used [hiew2023 X4].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
felodipine–PVPVA	critical drug:polymer ratio ≈1.7 × 10⁻³, far below the 5–50% tested	calculated	saboo2020a R27, C36
ritonavir–PVPVA	congruent at 10–25%, contrary to the single-ratio prediction	tablets	indulkar2019a C24, C25
celecoxib (ASD dissolution chapter)	Corrigan's condition as the basis of polymer control at low and drug control at high loading	cited	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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
50% IDM–PVPVA	15 runs; 117–161 °C; 2–20 min; amorphous by all techniques first at 131 °C 20 min, 141 °C 10 min, 161 °C 2 min	5 mL recirculating extruder	moseson2018 R10, R15
1:1 IDM–PVPVA	extrudate at 131 °C and 20 min on the lower edge of the dissolution region	schematic from earlier work	moseson2018a R1
30:70 BCL–PVPVA	dissolution 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 none	5 mL extruder	moseson2021 M1, P1, R6
50/50 IDM/PVPVA and 30/70 BCL/PVPVA, chemical side	IDM/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 °C	isothermal TGA, 4 h	moseson2020 R15, C44, C45
20% RTV with PVPVA 64, HPMCAS MF, HPMC	extrusion at 130–160 °C, 5 min: assay 95.7–100.5%, polymer-dependent	2 mL extruder	alvarenga2022 R22
30% BCL–PVPVA at Tc = 145 °C, lots of D50 3.51 / 37.0 / 38.0 / 42.2 / 92.7 µm	below the limit of detection at 2 / 5 / 6 min; about 2.5% and 15.0% at 20 min for the last two	5 mL micro-extruder, PXRD	[moseson2022c R10]
PCZ–HPMCAS MF, 10 / 25 / 50% DL	crystals 0.3 / 3.2 / 19.3 wt% at 125 °C, none at 175 °C	2 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
felodipine; nifedipine	6.2 and 8.8 kJ/mol	25 °C	[marsac2006a E3, R4]
34 drugs	ΔGv −8.6 (lidocaine) to −54.7 J/cm³ (acetaminophen)	298 K	baird2012 M5, M12
vemurafenib α against β	α lower in free energy up to a virtual transition at 319 °C	Tm and ΔHm of both forms	[lu2016 R22, E1]
felodipine	estimated amorphous solubility about 9 µg/mL	37 °C	alonzo2010 R3
delamanid	solubility ratio 31.8 calculated against 42.3 measured	37 °C	duong2022a R27
ritonavir, efavirenz, celecoxib	≈10.2, ≈2.70, ≈7.74 kJ/mol (extractor calculation)	37 °C	ilevbare2013c E7
six dihydropyridines	used for the yardstick of F5; no ΔG value printed	25 and 37 °C	raina2015a E2, R11
diverse drugs	Cp method closer to the measured LLPS onsets than the Hoffman equation	25 °C	almeidaesousa2015 R11, C43
ritonavir	10.1 kJ/mol (extractor recomputation from Table 2 inputs)	37 °C	ilevbare2013a E2
ibuprofen to griseofulvin	3.24, 4.84, 5.69, 8.51, 10.33, 9.69 kJ/mol	25 °C	almeidaesousa2015 R11
telaprevir	13.31 kJ/mol (recomputed); amorphous solubility 245 ± 5 µg/mL, 2.7 times the onset	37 °C	mosqueragiraldo2015 E1, R13, R17
clotrimazole	6.26 kJ/mol with a molar mass not printed in the paper (extractor)	310 K	indulkar2015 E3
CRH1	5.68 kJ/mol; estimate 11.2 µg/mL at pH 4.6	25 °C	[almeidaesousa2016 M1, R2]
atazanavir	14.55 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
felodipine	Hoffman ratio 10.92 (25 °C), 8.64 (37 °C); water factor 0.74, 0.83	Tm 147 °C, ΔHf 28.67 kJ/mol	raina2014a R7
nifedipine	printed ratio 8.78; recomputed 14.45	Tm 173 °C, ΔHf 32.5 kJ/mol	raina2014a R7, X3
atazanavir	ratio 62, predicted 68 µg/mL	310 K	indulkar2017a R5
indomethacin	17–25 µg/mL (25 °C), about 37 µg/mL (37 °C)	Hoffman estimate	alonzo2010 R8
enzalutamide	printed estimate about 39 µg/mL (13-fold); the printed inputs give 27.7	37 °C, Tm 470 K	wilson2018 E1, R3, X1
ritonavir	ΔHf 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 term	37 °C	[ilevbare2012b E8, E9, R1]
glyburide; warfarin	about 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/mol	25 °C (assumed)	hsieh2014 R16, E3, M3, M4
danazol	Tm 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 printed	25 °C	jackson2014 E1, E2, X1
five weak bases	ratios 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 °C	DSC data of the paper	raina2015b E1, R1.b
posaconazole	Tm 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 measured	310 K; the extractor obtains ΔG = 16.13 J/g and a ratio of about 26.5	[duong2022b R7, E3, X2]
felodipine	ratio about 10; about 9.5 µg/mL	37 °C	konno2008a R17
felodipine	ΔG 5729 J/mol, ratio 9.22 (recomputed) against "around 9"	37 °C	alonzo2010 E1
felodipine	about 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
indomethacin–PVP-K90	PVP C=O at 1636 against 1679 cm⁻¹; drug acid C=O at 1726 cm⁻¹	5–70 wt% PVP, solvent-evaporated	[taylor1997 R5.l, R11, R12]
amorphous indomethacin	acid dimer at 1710 cm⁻¹ (IR) with no Raman band	quench-cooled melt	[taylor1997 R5.h, R6]
indomethacin, felodipine, sucrose, ketoconazole with PVP K12	PVP C=O shift 45, 25, 25 and 0 cm⁻¹	one donor per carbonyl, spin-coated	marsac2009 R12
felodipine with PVP, PVP/VA, HPMCAS, PVAc	NH at 3294, 3298, 3348, 3354 cm⁻¹ against 3341 cm⁻¹	50 wt% polymer films	kestur2010a R9
nimesulide	NH at 3345 cm⁻¹ at every concentration	dichloromethane, 1–100 mg/ml	[kestur2011 R11]
nimesulide with PVP	PVP C=O ≈1684 → ≈1680 cm⁻¹, shoulder ≈1657 cm⁻¹	20–50 wt% PVP	[kestur2011 R14]
felodipine–PVP, nifedipine–PVP	second PC with NH and carbonyl loadings	10–90% and 25–70% PVP	[rumondor2009a R7, R9]
naringenin, quercetin with PVP	polyphenol OH band 3138 and 3135 cm⁻¹; PVP C=O shift 21 and 24 cm⁻¹	spin-coated films, 30% polyphenol	wegiel2013a R2, R4
dextran–PVP	PVP C=O 1680 → 1661 cm⁻¹; hydrogen-bonded fraction 1.00 (DEX1–PVP12) to about 0.09 (DEX450–PVP90) at 0.8 dextran	spin-coated films	[vaneerdenbrugh2012a R2, R14]
benzamide, phenacetin crystals	amide–amide only 100 and 94% alone; 0% with a COOH partner; 14 and 33% with C(O)NC2	CSD survey	[vaneerdenbrugh2011a R14]
lumefantrine–PVPVA	carbonyl bands fixed at 1736 and 1684 cm⁻¹ at 10, 25 and 50% drug	dried spin-coated films	hiew2022a R17

Evidence table: hydrogen bonding.

Pitfalls and disagreements

Assignments rest on analogy with liquid models: the same non-bonded acid C=O is assigned at 1735 cm⁻¹ (chain ends) and 1726 cm⁻¹ (PVP-bonded molecule), and how one turns into the other is not shown [taylor1997 C32, X4]. IR bonds were recorded at 20–50 wt% polymer, whereas the growth effects were measured at 0.5–5 wt% and 70–110 °C [kestur2010a X5; kestur2011 X10]. The felodipine–PVP carbonyl shift is 25 cm⁻¹ in one paper and about 20 cm⁻¹ in a cited study [marsac2009 R12.b; kestur2011 R20]. A drug without a donor (ketoconazole) shows no shift yet mixes about athermally marsac2009 R7.c, R12.h. For bifonazole the donor–acceptor picture rests on crystal-structure reasoning and was not measured [kestur2011 X9]. The bond between indomethacin and PVP is proposed as the reason PVP inhibits crystallization, but no crystallization was measured in that paper [taylor1997 X8]. The PVP shoulder at 1661 cm⁻¹ with naringenin overlaps the drug's own band, and HPMC and PAA are placed on the IR trend line by projection wegiel2013a X9, X12. The bonded fraction of dextran–PVP rests on references set by one system and on films prepared differently from the DSC samples [vaneerdenbrugh2012a X12, X8]. No hydrogen bond was measured in the 15-drug screen, and its melt spectra are not shown [vaneerdenbrugh2011a X13].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

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

material	value or class	conditions	paper 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; SDS	LoC 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 domains	humidified films	[yang2022b C61, C35]
SDS, CTAB, TPGS, Tween 80	HLB 40, 22, 13.2, 15	cited	correasoto2022a R1
Span 20, Span 80, Span 85	HLB 8.6, 15 (as printed), 11	cited	correasoto2022b M7, M8, M9
SDS, Tween 80, TPGS, Span 20, Span 85 in ritonavir–PVPVA 30:70	HLB 40, 15, 13.2, 8.6, 1.8 (cited); ritonavir ≈78, ≈25, ≈89, ≈41, ≈87% at 90 min	pH 6.8, 37 °C	indulkar2022 M4, M5, M6, M7, M8, R5, R6, R9, R7, R8
SDS, Tween 80, Span 20, Span 85 in ritonavir–PVPVA	HLB 40, 15.0, 8.6, 1.8 (cited)	10 parts per 100 parts drug and polymer	yang2023 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 Amorphous solid dispersions: the whole picture

hydrophobic effect

The release of the ordered, "iceberg-like" water around apolar groups when a solute leaves the water, which costs enthalpy and gains entropy. Ueda and co-workers invoke it for the transfer of a polymer from water into the ibuprofen-rich phase, which has positive ΔH and ΔS for most of the range, and for the vinyl acetate units of PVP-VA and the methyl groups of HPMC ("should be considered", "are expected") [ueda2022 C49, C50, C54]. The same reasoning is offered for the stronger partitioning of PVP-VA than PVP (entropy cost of hydrating apolar groups) [ueda2021 C30].

Findings

F20, F21.

Related concepts

related to hydrophobic interactions (association of apolar molecules); drives polymer partitioning into the drug-rich phase.

Formulas

van't Hoff equation.

How it is measured or obtained

Not measured; it is inferred from the signs of ΔH and ΔS of transfer and from the negative enthalpies of solution of PVP and HPMC (cited) [ueda2022 R23, R29, C50].

Values in the library

material	value or class	conditions	paper ids
polymer transfer into the ibuprofen-rich phase	ΔH of HPMC 58 → 12, PVP-VA 25 → 5, PVP 30 → 1 kJ/mol; −TΔS −71 → −31 (HPMC)	15–60 °C	[ueda2022 R23]

Pitfalls and disagreements

Water structure around the polymers and the hydration of HPMC with temperature were not measured, and polymer hydrophobicity was not measured [ueda2022 C50, C57; ueda2021 X8]. The explanation of HPMC's temperature dependence by dehydration ("likely reflecting") is untested in these solutions [ueda2022 C57].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

hydrophobic interactions

The association of non-polar drug molecules to minimize contact with water; Ilevbare and Taylor call it "intuitive" that LLPS of drugs with Log P 2.24–5.98 is driven by hydrophobic interactions and attribute the lower LLPS concentration at higher ionic strength to salting-out, which strengthens them ("may be attributed") ilevbare2013a C37, C38, C41. The papers of 2017–2022 add that the lower GLPS onset of telaprevir in 100 mM than in 50 mM phosphate (104/102 against 149/146 µg/mL) is also attributed to hydrophobic aggregation promoted by ionic strength, again untested lu2017b R9, C20; and that the signs of the transfer of polymer into a drug-rich phase (positive ΔH and ΔS) are related to the hydrophobic effect [ueda2022 C50] (see hydrophobic effect). New aspect (Crystallization from solution): in the crystallization-inhibition papers hydrophobic interaction is the proposed driver of polymer adsorption on drug crystals and of polymer–polymer association; salts make water a poorer solvent for hydrophobic groups, so if hydrophobic forces drive the polymer to the crystal, a higher buffer concentration should strengthen the interaction and the inhibition [ilevbare2013b C27, C28]. The cellulose polymers gained from 50 to 100 mM phosphate, which the authors read as hydrophobic interaction "verified"; PVPVA did not and is explained by a hydrogen bond [ilevbare2013b R10, C48, C51]. Polymer pairs were also more effective in 100 mM, taken as support for hydrophobic interpolymer complexes ilevbare2012a C43. New aspect (Mesoporous silica): the possible binding of lipophilic drugs to the hydrophobic siloxane part of a silica surface, expected for drugs of log P above 4 ("considered feasible") but not found: adsorption of ritonavir (log P 5.98), indomethacin (4.27) and its methyl ester (4.6) did not change with ionic strength dening2019 C51, C22, M1; mccarthy2020 C6, C31, M1, M2. A second sense appears for loaded silica: as hydrophobic drug fills the pores the formulation becomes more hydrophobic and water enters more slowly, which "may contribute" to low release at high loading hate2020a C44, C45; hate2020b C43.

Findings

Amorphous solubility and LLPS: F1, F9, F18, F21. Crystallization from solution: F8, F11, F17, F36, F44. Mesoporous silica: F5, F11.

Related concepts

proposed driver of liquid-liquid phase separation; related to the critical micelle concentration analogy for the temperature profile; related to polymer hydrophobicity, interpolymer complex and polymer adsorption; contrasts with drug-silanol hydrogen bonding as a mechanism of drug adsorption onto silica.

Formulas

none.

How it is measured or obtained

Not measured: neither solvent polarity nor drug association was tested ilevbare2013a C41. In the crystallization-inhibition papers it is inferred by comparing effectiveness ratios at two buffer concentrations (50 and 100 mM phosphate, pH 6.8), with buffer molarity standing in for ionic strength [ilevbare2013b P13, X11; ilevbare2012a P12]. In the Mesoporous silica papers the same salting-out logic is applied to adsorption: adsorption in distilled water, 0.1 M and 0.5 M NaCl, where a hydrophobic contribution should raise adsorption at higher ionic strength dening2019 P4, C16; mccarthy2020 P10, C30.

Values in the library

None printed in the amorphous solubility and LLPS papers beyond the telaprevir onsets; the crystallization-from-solution and Mesoporous silica papers give the following.

material	value or class	conditions	paper ids
HPMC on celecoxib; efavirenz	6.45 → 10.15; 1.1 → 2.55 (50 → 100 mM)	S 6.6; S 1.2	[ilevbare2013b R10]
PVPVA on celecoxib; efavirenz	7.6 → 7.4; 4.5 → 4.9	same	[ilevbare2013b R10]
eight polymer pairs on ritonavir	1.1–2.6 → 1.7–4.8	S 4.3 against 7.7	ilevbare2012a R14
telaprevir GLPS onset (amorphous solubility chapter)	lower in 100 than in 50 mM phosphate, attributed to hydrophobic aggregation	37 °C	lu2017b R9, C20
A5a, ECB, ECD with telaprevir and atazanavir	drug–CH3 RDF peaks about 25–36 at 0.4–0.5 nm against carboxylate peaks 10–23 at 1.6–2.6 nm	MD, 10 ns	[mosqueragiraldo2018a R11, C35]
HPMCAS grades with posaconazole	hydrophobic drug–polymer interaction proposed to rise with acetyl content and lower pH	not measured	shah2025 C6, C48
ritonavir on SBA-15	about 91–95, 162–182, 249–294 mg/g at initial 2.5, 7, 14 µg/mL; no significant salt effect	water, 0.1 and 0.5 M NaCl	dening2019 R9
indomethacin; methyl ester on SBA-15	about 0.8–0.9 and 8–9; about 11 and 65–76 mg/g at 2 and 8 µg/mL; no significant salt effect	same	mccarthy2020 R15

Pitfalls and disagreements

The Log P of ritonavir is 5.6 in the table and 5.98 in the text ilevbare2013a X2. Buffer molarity, solubility and supersaturation change together in the pair test, and the growth rate without polymer at 50 mM is not reported [ilevbare2012a X12; ilevbare2013b X11]. The hydrophobic contribution for ritonavir rests on the SP trend alone [ilevbare2013b X14]. Mesoporous silica: the ritonavir salt series was run in unbuffered water, where adsorption was higher than in buffer dening2019 X5; the indomethacin series used equal concentrations, not equal activities, and an unstated pH mccarthy2020 X9. The formulation hydrophobicity invoked for high loadings was not measured hate2020a C44. The same salting-out test reads as a hydrophobic contribution for cellulose polymers on drug crystals [ilevbare2013b R10, C48] but finds none for drug on silica dening2019 R9; mccarthy2020 R15; the chapters agree on the test and differ in its outcome for the two surfaces.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
felodipine, quinidine, indomethacin, pimozide	calculated log P 2.24, 2.48, 3.58, 5.34	drugs of PVP, PVPVA and HPMCAS dispersions	[rumondor2010c M1, M2, M4, M3]
indoprofen, nilutamide, loratadine, clofoctol, probucol	log P 2.84, 2.14, 4.13, 8.19, 10.0	drugs of PVP films	[rumondor2011 R15.e, R15.s, R15.t, R15.f, R15.g]
resveratrol against felodipine	log P 3.1 against 4.5 (cited)	contrast of PVP dispersions in humid storage	[wegiel2013b R20]
pimozide with HPMCAS	the only HPMCAS dispersion that separated; attributed to hydrophobicity	94% RH, dried	[rumondor2010c C35, R3.e]
clofoctol–PVP (≥ 70% drug), probucol–PVP (90% drug)	no separation up to 94% RH; "it is thought" too little water sorbed	22 °C films	[rumondor2011 C36, R14]

Pitfalls and disagreements

The direction of the effect is disputed within the library: pimozide's high log P is used to explain separation even with HPMCAS [rumondor2010c C35], while in the 20-system study the two most hydrophobic drugs were the only ones that resisted at some compositions and log P was dropped from the discriminant model as insignificant [rumondor2011 X14, R16]. Calculated and cited log P values differ between papers for the same drug: felodipine 2.24 [rumondor2010c M1] against 4.5 [wegiel2013b R20].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
HPMC E3	3.22, 1.517, 0.48% w/w	40, 20, 7% RH	mugheirbi2017 R2.a
AFFINISOL	2.03, 0.89, 0.19% w/w; about 63% of E3 at 40% RH	same	mugheirbi2017 R2.d, C21
PVP, HPMC, HPMCAS (outside)	PVP absorbs more water than HPMC, HPMC more than HPMCAS, at the same RH and temperature	25 °C	[rumondor2010a C6, R1]
ritonavir ASDs (outside)	PVP and PVPVA are more hygroscopic than HPMCAS, so their ASDs are expected to be more prone to moisture-induced AAPS	argument	purohit2017b C45
polymer hygroscopicity and AAPS (outside)	the water–drug contribution to the free energy of mixing depends on the water sorbed, which depends on polymer hygroscopicity	felodipine, indomethacin and others in PVP, PVPVA, HPMCAS	[rumondor2010c C30]
PVP, HPMC, HPMCAS, felodipine	≈33.5, 10.9, 6.2, 0.7 g/100 g	75% RH, 25 °C	konno2008 R8
felodipine with 25% PVP, HPMC, HPMCAS	≈4.7, 2.3, 1.7 g/100 g	75% RH	konno2008 R9.d
nifedipine vs felodipine with 25% PVP	≈5.5 vs 4.6 g/100 g	75% RH	[marsac2008a R2]
felodipine–PVP vs HPMCAS dispersions	PVP dispersions more hygroscopic (cited)	93% RH	rumondor2009b R25
75:25 felodipine and quinidine with PVP, PVPVA, HPMCAS	6.4/3.6/2.4 and 5.3/3.4/2.4 g per 100 g	25 °C/85% RH	[rumondor2010c R18]
PVP, PVPVA, HPMCAS alone	≈50, ≈24, ≈8 g per 100 g at ≈85% RH	cited isotherms, 25 °C	[rumondor2010c R19]
40% resveratrol–PVP dispersion against its physical mixture	≈12.8 against ≈36.5% at 95% RH	25 °C	[wegiel2013b R19]
PVP K29/32, K12, PVPVA, HPMC, HPMCAS; amorphous celecoxib	≈68, 67, 48, 31, 12; ≈2.2 g/100 g at 95% RH	DVS, 25 °C	[xie2016b R12]
six tacrolimus capsule fills	1.6–12.8% at 95% RH, most with the most croscarmellose	DVS, 25 °C	trasi2017 R4, C16
PVP, PVPVA, HPMC, EUDS, HPMCAS	≈34, ≈20, ≈9, ≈7.8, ≈5.9% at 75% RH; ≈71, ≈47, ≈28, ≈12.7, ≈10.2% at 95% RH	37 °C	saboo2020a R3
amorphous felodipine	≈1.3% at 75% RH	37 °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 Amorphous solid dispersions: the whole picture

ideal mixing

Entropy-driven mixing of two amorphous components in the drug-rich phase with no heat of mixing, so that the chemical potential of each falls by RT\ln x and its amorphous solubility becomes the pure-drug value times its mole fraction in that phase trasi2015a C37, E2, E3, E4. Ritonavir and lopinavir are said to mix "nearly ideally" trasi2015a C40. The papers of 2017–2022 add the polymer case: in the ideal-mixing form S_a = S_a^{0}\,x_{drug} a polymer in the drug-rich phase lowers the amorphous solubility, but the authors note that a polymer's large molar volume and specific interactions make mixing non-ideal, and the volume-fraction Flory–Huggins form over-predicts the measured solubility of ibuprofen with PVP-VA and HPMC 603 [ueda2021 E2, C28, C33]. New aspect (Supersaturation from ASD dissolution): ideal mixing (cited) is applied to dissolving films and dispersions of two drugs: each drug reaches its amorphous solubility times its mole fraction in the amorphous mixture trasi2015b C38, E1. Li and Taylor draw the amorphous solubility scaled by drug weight fraction as "ideal behavior" for lopinavir mixed with an undissolved polymer; HPMCAS lay slightly above it, CAP near it at 15–50% and EC near it at 50–85% drug, HPMCP below it [li2018 E7, C20].

Findings

Amorphous solubility and LLPS: F11, F19, F20, F21. Supersaturation from ASD dissolution: F11, F18.

Related concepts

lowers the chemical potential in the drug-rich phase; consequence for the amorphous solubility. Papers of 2017–2022: extended by the interaction term in the Flory-Huggins interaction parameter; requires drug-drug miscibility.

Formulas

ideal-mixing reduction of amorphous solubility.

How it is measured or obtained

The mole fraction in the drug-rich phase follows from mass balance of bulk concentrations after ultracentrifugation; a melting point depression of ritonavir by lopinavir greater than the Schröder–van Laar prediction is offered as confirmation (data not shown) trasi2015a P12, R17. For dissolving two-drug films and dispersions: film plateaus and ultracentrifuged dispersion concentrations against Eq. 1, with amorphous solubilities from the antisolvent study trasi2015b P6, P9, M1, M2.

Values in the library

material	value or class	conditions	paper ids
ritonavir–lopinavir	bulk ritonavir 3.0 → 21.4 µg/mL and lopinavir 15.2 → 4.6 µg/mL for x = 0.06–0.70; ritonavir 2–4 µg/mL above the line	25 °C	trasi2015a R16
ritonavir–lopinavir, 30 + 30 µg/mL	predicted about 10.8 and 10.1 µg/mL against 13.3 and 9.1 measured	extractor check	trasi2015a X9, R13
ibuprofen with PVP-VA, HPMC 603	ideal Flory–Huggins: about 129 and 127 µg/mL at polymer ratio 1.0; measured about 89–106 µg/mL	37 °C	[ueda2021 R12, R5]
ibuprofen with PVP, PVP-VA, HPMC	ideal per-chain mole fraction of drug 0.97 or more at the highest ratios, against Sa/Sa0 of 0.52–0.54 (extractor calculation)	15–60 °C	[ueda2022 X3, R17]
RTV:LPV films 7:3 / 5:5 / 3:7	RTV 15.2 / 11.4 / 6.3 against 16.7 / 11.6 / 6.8 µg/mL	pH 6.8	trasi2015b R5
HPMCAS dispersions, three ratios	RTV on the line; LPV on or up to about 15% below it	ultracentrifuged	trasi2015b R17, X8
lopinavir, ideal line at 50% drug	17.4 × 0.50 = 8.7 µg/mL	pH 3, 25 °C	[li2018 E7]
lopinavir with HPMCAS at 50% drug	≈12.3 µg/mL	pH 3, 25 °C, 48 h	[li2018 R3]

Pitfalls and disagreements

Tested for one pair; no fit statistic; other pairs "are likely" to be non-ideal trasi2015a X9, C43. Later work draws the same ideal-mixing line for lopinavir–polymer dispersions [li2018 E7]. Used only qualitatively for polymers; the mole basis of the polymer is not stated [ueda2022 X3]. In the two-drug dissolution study the predictions use cited amorphous solubilities, and the pure films reached about 8% less trasi2015b X14; one nearly ideal pair was tested trasi2015b C39. The diagonal of the lopinavir–polymer study is proportional dilution by weight, not the χ = 0 case of the Flory–Huggins term, which with a large polymer would lie above it [li2018 X2].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
eight delamanid sulfonate salts, neat	seven 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 storage	2 weeks at 40 °C/75% RH	duong2022a R20
delamanid edisylate 1:1 with excess acid	Tg 53.9 °C and 59% water uptake, against 117.8 °C and 11.6% for the 2:1 salt	95% RH	duong2022a R21
salt dispersions at 20% drug with HPMCAS	Tg 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 shift	tablets, 100 µg/mL = complete	duong2022a R26
delamanid edisylate dispersions with HPMCP, 10–40% drug	≈99 / ≈98 / ≈95 / ≈59 / ≈21 µg/mL of 100	PBS 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 base	pH 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 Amorphous solid dispersions: the whole picture

in vitro–in vivo correlation

The relation between an in vitro test and in vivo performance. The papers up to 2018 state expectations only raina2015c C44; elkhabaz2017 C2, C60; purohit2018 C58, C65. Four later papers set an in vitro measure against exposure in rats, dogs or monkeys; they rank formulations and do not give a quantitative relation (F25, F26, F30) wilson2018 C51, C57; wilson2020 C44; purohit2019 C40; nguyen2023a C57, C73.

Findings

F11, F17, F25, F26, F27, F30, F31.

Related concepts

relates biorelevant media and oral bioavailability to virtual bioequivalence.

Formulas

non-compartmental AUC, relative bioavailability, absolute bioavailability.

How it is measured or obtained

(1) The mass flow of the dissolved formulation across a dialysis membrane plotted against Cmax and AUC in rats wilson2018 R17; wilson2020 R8, R6. (2) A comparison of the same formulations in compendial or low-volume dissolution, an absorptive test and dogs (F31) purohit2019 C40. (3) Release in biorelevant media against monkey exposure, fasted and fed (F26, F27) nguyen2023a R17, R19, R23. (4) The PBPK route, with the dissolution profile as release input purohit2018 P10, P12.

Values in the library

material	value or class	conditions	paper ids
tacrolimus capsules	simulated bioequivalence lost from 20% (100 mL input) or 40% (900 mL input)	virtual trials	purohit2018 R17
posaconazole, atazanavir (Elkhabaz 2021)	in vitro onset about 80 min against 93 min in human jejunum; atazanavir about 2 h against 1.25 h	FaHIF	elkhabaz2021 C34, C36
enzalutamide, five ASD and slurry formulations	mass flow 0.632 to 0.063 µg/min in the order of rat Cmax and AUC0–48, except the crystallizing 10% HPMCAS ASD	rats, 10 mL/kg	wilson2018 R15, R17, C51
enzalutamide, four formulations	mass flow about 0.53, 0.49, 0.068, 0.063 µg/min against AUC0–inf 516, 305, 45, 43.1 µg·h/mL	rats, 50 mg/kg	wilson2020 R8, R6
tacrolimus capsule	fully crystalline capsule 51% of the fresh generic's AUC in dogs; 17–22% in the absorptive test; 8% or 55% in simulation (100 or 900 mL input)	dogs, 1 mg	purohit2019 R9, C40; hate2019 R13; purohit2018 R14, R16
pretomanid HPMCAS-HF ASD	in vitro release to the crystalline solubility below FeSSIF pH 5.8; monkey fed exposure 72.2% of fasted (crystalline reference 163%; printed, dose-normalized)	cynomolgus monkeys, 30 mg	nguyen2023a R19, R23, C73, C85

Pitfalls and disagreements

Solubilizing components of biorelevant media, if ignored, "may explain" poor correlations raina2015c C44. The tacrolimus human study was pending purohit2018 C58. Non-sink closed dissolution did not rank the rat exposures, and the dissolution AUC ranked the ASDs differently over 0–2 h and 0–4 h (F25) wilson2018 C57, R7. In vitro gains from a surfactant or a base did not carry over to monkeys, and standard media missed the food effect on an enteric-polymer ASD (F26, F27) nguyen2023a C57, C73, C85. The in vivo dose-to-fluid volume ratio is unknown, so the choice among the low-volume and large-volume in vitro results decides how a dog result is read (F31) purohit2019 C40.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

incomplete drug release

Release that stops below the dose although the drug has not crystallized; in the library it is the defining problem of drug-loaded mesoporous silica under supersaturating conditions dening2018 C2, C1; dening2019 C1. The papers attribute it to adsorption of dissolved drug back onto the silica, in a dynamic and partly irreversible equilibrium dening2018 C4, C63; dening2019 C32; mccarthy2020 C52; hate2020a C5, with loading, wetting and pore filling as further causes dening2018 C60; hate2020a C44, C45.

Findings

F7, F8, F9, F10, F11, F12, F13, F14, F15.

Related concepts

caused by drug adsorption onto silica in a dynamic adsorption-desorption equilibrium; contrasts with desupersaturation by crystallization; assessed by absorptive dissolution testing and membrane flux; depends on drug loading.

Formulas

supersaturation ratio, total release by mass balance.

How it is measured or obtained

Closed non-sink dissolution dosed at the amorphous solubility of the medium, with centrifuged or filtered samples over 1–4 h, against the nominal or assayed dose dening2018 P6; mccarthy2020 P14; hate2020a P7; hate2020b P5. Free drug by membrane flux against amorphous drug at the same concentration dening2018 P12. Recovery, XRPD and assay of the solid after release dening2018 P9; mccarthy2020 P14. Release with an absorptive compartment, by mass balance hate2020a P9, E4.

Values in the library

material	value or class	conditions	paper ids
ritonavir–SBA-15	about 50% (dose at amorphous solubility), 70% (half)	pH 6.8, 75 mL, 120 min	dening2018 R6
ritonavir–SBA-15	about 67 → 9% at 50 → 1000% of the amorphous solubility	pH 6.8	dening2018 R23
ritonavir–SBA-15	60–65% after dilution to S about 1; about 71% in FaSSIF	pH 6.8; FaSSIF	dening2018 R18, R21
lopinavir–SBA-15	40–50%	pH 6.8	dening2018 R19
indomethacin; methyl ester, 50% monolayer	S 7.2 of 15.3; 7.0 of 21.4; 58.8 and 61.8% retained	pH 2.2, HPMC	mccarthy2020 R20, R21, R23
atazanavir–SBA-15, 20% w/w	about 46.5% closed; about 89.5% with an absorptive sink (240 min)	pH 6.8, HPMC	hate2020a R20
atazanavir–SBA-15, 5–50% w/w	about 73 / 80.5 / 66.5 / 52 / 36% in 90 min	absorptive, pH 6.8	hate2020a R15
ketoconazole; clozapine; atazanavir, 20% w/w	about 55; 73.5; 40% at pH 6.8; 92; 93; 70% at pH 1 (60 min)	HPMC	hate2020b R7, R8, R9
ketoconazole; clozapine after pH 1 → 6.8	about 64–69%; 68–69%	HPMC	hate2020b R10, R11
itraconazole–SBA-15 (outside the library)	plateau about 55%	simulated gastric fluid	dening2018 R28

Evidence table: incomplete drug release.

Pitfalls and disagreements

Percent release depends on dose, medium volume and the drug content assumed: the ritonavir percentages rest on a nominal 28 µg/mL, and the dose masses imply about 22% instead of 25% w/w dening2018 X5; the indomethacin percentages do not reconcile across text, axes and dose mccarthy2020 X5. "Sink" in the dilution test means a total dose equal to the crystalline solubility dening2018 X7. "Complete release" with an absorptive sink was about 90% hate2020a X10. Release is not incomplete for every drug and medium: charged, soluble bases released 87–97% at pH 1–4.5 hate2020b R7, R8. The isotherm accounted for only about a twentieth of the atazanavir held back hate2020a X14.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

incongruent release

Polymer and drug leave the dispersion at different rates; above the limit of congruency the polymer leaves first, the undissolved solid becomes drug-rich and release slows moseson2021 C34, C58. For bicalutamide–PVPVA at 30% DL, PVPVA reached about 90% of its dose within 20 min while only about 30–60% of the drug dissolved in 4 h, and the undissolved solid went from PVPVA:BCL 7:3 to 1:1 within 5 min (computed from solution data) moseson2021 R25, R26, R17. Incongruent release can also come from a coating: in tablets of coated ritonavir–PVPVA particles slower hydration let phase separation outpace dissolution, which the authors describe as a lower effective limit of congruency [benson2025 C34]. New aspect (Release mechanism and LoC): above the limit of congruency the polymer leaves faster than the drug, and the ritonavir tablets show a transition loading (30%) that starts congruent and turns incongruent after about 40 min indulkar2019a R5, C3, C32. Humidity can make a congruent dispersion incongruent saboo2019 R9, C41. The papers of 2020–2022 add drug release that starts only after a lag while PVPVA dissolves from the start: from 30% lumefantrine benzoate about 20% of the polymer and almost no drug had been released at 30 min, "indicative of" incongruent release hiew2022b R13, C18; and incongruent release that develops after minutes when crystals cover the surface of a congruent compact saboo2020 R8, C17. Partly connected drug-rich domains at 40% MePHPH gave release that was not fully congruent: drug lagged polymer by 30 min and accumulated in the gel [deac2023a C61, R1, R3].

Findings

ASD process: F27, F38, F40, F48. Release mechanism and LoC: F3, F6, F7, F8, F12, F19, F22, F25.

Related concepts

above the limit of congruency; produces surface drug enrichment; precedes matrix crystallization; with a drug-rich barrier layer.

Formulas

surface-normalized release rate.

How it is measured or obtained

Polymer by size-exclusion chromatography and drug by UV or HPLC against time; surface by SEM, IR, XPS or EDX after short exposures moseson2021 P14, R24; indulkar2019a R16, R17. In the release-mechanism papers: as for congruent release, from separately assayed drug and polymer saboo2019 R8.

Values in the library

material	value or class	conditions	paper ids
BCL–PVPVA S/180 (crystal-free)	PVPVA about 36 µg/mL at 2.5 min, about 58.8 µg/mL at 60 min (of 70)	30 µg/mL BCL dose	moseson2021 R25
BCL–PVPVA M/155 (3.5% crystals)	PVPVA about 54.6 µg/mL at 2.5 min, levelling at about 64	same	moseson2021 R25
undissolved solid after 5 min	PVPVA:BCL 1:1 (crystal-free), 1:2 (with residual crystals)	computed	moseson2021 R26
ritonavir–PVPVA 50% DL tablet (outside)	surface drug-rich after 5 min	IR, SEM	indulkar2019a C18, C41
nilvadipine and cilnidipine–PVPVA compacts (outside)	XPS shows surface drug enrichment of incongruently releasing compacts, none for congruent ones	10 min	saboo2019 C25
BCL–PVPVA 20 / 30% DL	polymer about 82 / 68% against drug about 33 / 18% at 10 min; ends about 88 / 86%	dose of at most 30 µg/mL	moseson2022b R6, R7
BCL–PVPVA 50% DL	polymer about 18% at 10 min and 80% at 2 h; drug plateau about 73% from about 120 min	same	moseson2022b R6, R7
BCL–PVPVA 30% DL with 1.5% TPGS	incongruent; about 54% (106–250 µm) at 30 min, about 93–94% at 4 h	same	moseson2022b R11, R13
coated RTV–PVPVA 20% DL tablets	connected drug-rich regions along particle boundaries; about 35–75% at 60 min at pH 6.8	tablets	[benson2025 R10, R14]
ritonavir–PVPVA 30%	lag ~15 min; together to ~40 min; then PVPVA ≈96 against drug ≈48.5% at 120 min	pH 6.8, 37 °C	indulkar2019a R5, R3
ritonavir–PVPVA 35%	PVPVA ≈49 against drug ≈11% at 300 min	same	indulkar2019a R6
nilvadipine 15:85, 20:80; cilnidipine 20:80, 25:75 in PVPVA	polymer/drug rate ratio about 20, 40, 40, 105	same	saboo2019 R5, R6
nilvadipine 10:90 compact after 12 h at 97% RH	≈0.34% drug against ≈2.6% polymer in 15 min	same	saboo2019 R9
felodipine 15–30% in PVP	drug ≈0.005–0.020 against PVP ≈1.7–1.9 mg/min/cm²	same	saboo2020a R14
indomethacin–PVPVA 15, 20, 25%	drug ≈0.04, 0.02, 0.01 against PVPVA ≈0.72, 0.64, 0.50 mg/min/cm²	5-min rates, pH 2.1, 37 °C	saboo2020 R3, M5
clopidogrel–PVPVA 60%	drug ≈0.2 against PVPVA ≈4.1 mg/min/cm²	compacts	correasoto2022a R18
atazanavir–PVPVA 10%	drug ≈0.07 against PVPVA ≈0.24 mg/min/cm²	pH 6.8, 37 °C	correasoto2022b R3, P5
lumefantrine benzoate–PVPVA 30%	≈0 drug and ≈20% PVPVA released at 30 min; ≈8.5 and ≈50% at 90 min	compacts, 37 °C	hiew2022b R13

Pitfalls and disagreements

The drug-rich layer is inferred from the shape of the PVPVA release curve and pitted surfaces, "presumably drug-rich"; its composition was not measured moseson2021 C32, C58. Incongruent release does not by itself doom a dispersion: a TPGS dispersion released incongruently yet completely because little solid was left when nucleation began moseson2022b C50. Polymer release was not measured in the ritonavir tablets, so the shift of the limit is inferred [benson2025 X18]. The 35% ritonavir tablet is placed with 30% in one passage and with 40–50% in another indulkar2019a X13.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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 Å³ 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

material	value or class	conditions	paper ids
felodipine crystal edge	γ 3.9 × 10⁻²⁰ J/nm (contact angles, not printed); ρc 3.98 nm at S 4	25 °C	[schram2016 R13, R14, X10]
atazanavir in lecithin media; with lecithin, lyso-PC and oleate	lecithin "possibly" lowers the interfacial energy between solute and emerging crystal; proposed to be lowered, more by the digests; not measured	3 mM STC, pH 6.5; bile salt media, pH 6.5	[indulkar2018 C40, E6; enright2020 C26]
felodipine with polymer	a polymer-rich layer at the nucleus "may also increase" the surface penalty	argument	konno2006 C39
felodipine solution with SDS	faster growth explained by a lower interfacial energy	S = 4	[schram2016 C36]
felodipine–PVPVA–TPGS	TPGS lowering the energy between separated phases slows coarsening	ASD hydration	saboo2021 C40
flutamide prenuclei	unfavourable interfacial term outweighs the volume term below a critical radius	framework	[trasi2012b C46]
posaconazole, PBS pH 6.5	3.52 mJ/m²	37 °C, fit of the high-supersaturation induction times	[duong2022b R16]
posaconazole, FaSSIF V1, FaSSIF V2, FeSSIF V1	2.61, 2.73, 3.24 mJ/m²; FeSSIF V2 not fittable	as above	[duong2022b R16, R15]
naproxen, acetaminophen, tolazamide, lovastatin, cefodizime sodium, prasugrel hydrochloride, spironolactone (cited)	0.60–2.80 mJ/m²	literature	[duong2022b R18]
atazanavir with SDS hemimicelles	proposed to be lowered; not measured	0.075–0.3 mg/mL SDS	[indulkar2019b C33, X4]
felodipine–HPMC	γ, a and L of eq 7 not given	Kubota–Mullin	alonzo2012 C27
surfactants on ritonavir	growth about twice as fast with TPGS or Tween 80 at 5 µg/mL	seeded, S 7.6	ilevbare2012a R17, C51
paclitaxel critical radius 5–7 nm	from literature surrogates of γ	S 88	que2018 R15, C37
supersaturated drugs in surfactant media	surfactants should lower γ and speed nucleation; human fluid slowed it instead	classical nucleation theory, 37 °C	elkhabaz2021 C20, C21

Pitfalls and disagreements

The interfacial energy in SDS or HPMCAS solution was not measured [schram2016 X8]. The solid-state papers use homogeneous theory although nucleation in the films is "most likely heterogeneous" konno2006 C33. The papers disagree on whether γ carries the medium effect: the posaconazole fits find no trend of induction time with γ and assign the effect to the pre-exponential factor, whereas the lecithin, SDS and digest papers assume a lower γ [duong2022b C51, C52; indulkar2018 C40; indulkar2019b C33]. The fits rest on 3–9 points per medium, and γ also falls in the induction-time order for three of four media, so a γ contribution is not excluded [duong2022b X11, X12]. The human-fluid paper notes that surfactants that lower γ should speed nucleation, while human fluid slowed it, and adds an attachment-rate term elkhabaz2021 C20, C22. In the celecoxib work on polymer combinations the differences between polymers were not attributed to interfacial tension, because polymer adsorption on the nucleus would lower it and raise the nucleation rate, the opposite of what was observed; the point is argued, not measured xie2015 C43. This is opposite in sign to the felodipine argument that a polymer-rich layer at the nucleus "may also increase" the surface penalty konno2006 C39 (synthesis: two papers assume opposite effects of polymer on γ; neither measured it). The lower interfacial tension in droplets is an expectation, not a measurement ilevbare2013d C40. Interfacial tension with and without polymer was not measured, and the text cites the wrong equation for it xie2015 C43, X1. The same γ is reported per area (mJ/m²) for three-dimensional nuclei and per length (J/nm) for the step edge of a two-dimensional nucleus, so the two kinds of value are not comparable [schram2016 R13; duong2022b R16] (synthesis: different units and geometry).

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
nimesulide	NH 3345 cm⁻¹ at 1–100 mg/ml in dichloromethane; unchanged with added acid or lactam	IR, 100 µm cell	[kestur2011 R11, R17]
nimesulide	NH ≈3288 (crystal), ≈3276 cm⁻¹ (amorphous)	KBr; spin-coated film	[kestur2011 R12]
flufenamic acid	N···O 2.682 Å (form III), 2.646 Å (form I)	crystal structures	vaneerdenbrugh2010b R12
flutamide; curcumin (other chapters)	intramolecular CH···O leaves a poor acceptor; intramolecular bond limits polymer bonding	calculation; IR, stability	[trasi2012b C35; wegiel2014 C3]
naringenin, quercetin	5-OH to keto O (both); 3-OH to keto O (quercetin); PVP still bonds the free OH (OH band 3138 and 3135 cm⁻¹)	structure; IR	wegiel2013a M1, M2, R2
anthranilic acid	energy 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 bond	DFT dihedral scan	[vaneerdenbrugh2011a R6, C18]
lumefantrine	OH···N bond in the crystal; no PVPVA carbonyl shift	crystal structures (cited); IR	hiew2022a R33, R17
flutamide	planar lowest-energy conformer with the carbonyl next to C(5)–H; second minimum ≈2.7 kJ/mol higher; barriers ≈23 kJ/mol	DFT, vacuum	[trasi2012b R23, R24]
flutamide crystal	amide carbonyl in a bifurcated bond, one contact intramolecular	cited structure	[trasi2012b R26]
amorphous curcumin	keto–enol band at 1626 cm⁻¹ as in the crystal; no carbonyl band near 1700 cm⁻¹	IR	[wegiel2014 R2, C11]
curcumin against resveratrol with PVP	bonded PVP carbonyl dominant only at 60% curcumin, already at 50% resveratrol	IR of films	[wegiel2014 R8, R9, C32]

Evidence table: intramolecular hydrogen bonding.

Pitfalls and disagreements

For the amorphous state the evidence is that a broad band lies near the crystal's, and the crystal contains an intermolecular NH bond too [kestur2011 R19, R12]. The NH maximum shifts as much with PVAc as with PVP in the films, which weakens the argument that the intramolecular bond alone sets the polymer ranking [kestur2011 X16]. The treatment of flufenamic acid as purely acidic is an assumption supported by crystal geometry, not by a spectrum in the films vaneerdenbrugh2010b C12. An intramolecular bond limits but does not exclude polymer bonding when other donors remain (naringenin and quercetin bonded PVP strongly) wegiel2013a R2, R4. Whether the lumefantrine OH bond persists in the dispersion was not measured hiew2022a C61. No curcumin analogue without the intramolecular bond was tested, and within the curcumin paper PVP still gave the largest shifts [wegiel2014 X13]. For flutamide the bond in the glass is inferred from a vacuum calculation, and PAA's failure may reflect poor mixing instead [trasi2012b C35, X12].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

intrinsic dissolution rate

Evidence table: intrinsic dissolution rate. Content from the release-mechanism chapter (2018–2022) and two papers of the ASD process and Peptide permeability chapters.

The dissolution rate per unit area of a compact of one pure material, with one face of fixed area exposed; for a dispersion each component's rate divided by its weight fraction gives the rate per area "as if it were the pure material" [bhardwaj2018 R4; saboo2020a E3]. Bhardwaj and co-workers equate the ratio of the intrinsic dissolution rates of two solid forms with the ratio of their solubilities, carried over from polymorphs to amorphous against crystalline ITZ ("should be the same") [bhardwaj2018 E3, C45].

Findings

Release mechanism and LoC: F1, F2, F11, F15, F18, F24.

Related concepts

basis of congruent release read-outs; related to the Noyes-Whitney equation; sets the ceiling of polymer-controlled release.

Formulas

surface-normalized release rate, ratio of intrinsic dissolution rates and of solubilities.

How it is measured or obtained

Compacts of 25–100 mg in an 8 mm die (face ~0.5 cm²), Wood's apparatus or a backed die, rate from the initial linear slope [bhardwaj2018 P6, P7; saboo2019 P9, E4; saboo2020a P6]. In the papers of 2020–2022 the neat PVPVA compact is run beside every series as the reference rate saboo2020 R3; correasoto2022a R18; correasoto2022b R3. The same surface-normalized rotating-disk method gave the dissolution rates of the enteric polymer HP-50, its salts and its miconazole dispersions [qi2022 P10].

Values in the library

material	value or class	conditions	paper ids
crystalline ITZ; melt-quenched ITZ	2.8 ± 0.2; 51 ± 2 µg/min/cm² (ratio ≈18)	0.1 N HCl, 37 °C, 300 rpm	[bhardwaj2018 R4, R5]
PVPVA as received	10.4 mg/min/cm² over 4.5 min (8.1 cited)	same	[bhardwaj2018 R9, R10]
PVPVA; amorphous nilvadipine	3.49 ± 0.07; 0.002 mg/min/cm²	pH 6.8, 100 rpm, 37 °C	saboo2019 R5
PVP, PVPVA, HPMC, HPMCAS, EUDS; amorphous felodipine	≈3.6, ≈3.4, ≈0.37, ≈0.77, ≈0.23; ≈0.0008 mg/min/cm²	pH 6.8 (EUDS 7.4)	saboo2020a R13
OCA, SNAC, PVPVA (Peptide permeability)	OCA about twice SNAC; neat OCA above neat PVPVA	pH 6.8, 0.5 cm²	bapat2025b C2, C12
amorphous ritonavir against 20% ritonavir–PVPVA (ASD process, cited)	amorphous drug significantly slower	as cited	[benson2025 R24]
neat PVPVA (indomethacin; ester series)	≈3.4; ≈3.8 mg/min/cm²	5-min rates, 37 °C	saboo2020 R3
neat PVPVA	≈2.6–2.7 mg/min/cm²	compacts	correasoto2022a R18
neat PVPVA at 37 and 55 °C	≈2.7; ≈3.7 mg/min/cm²	compacts	correasoto2022b R7
neat PVPVA at 37 and 5 °C	≈3.45; ≈1.68 mg/min/cm²	compacts	[yang2021 X16, R21]
HP-50; nine HP-50 salts	≈0.92; ≈2.35–3.09 mg/min/cm²	compacts, 50 mM pH 6.8 phosphate, 37 °C	[qi2022 R10]
HP-50-BIS-TRIS, 20–100 mol% base	≈1.22 → 2.93 mg/min/cm²	same	[qi2022 R13, X9]

Pitfalls and disagreements

The neat PVPVA values differ with medium, paddle speed and compact mass (10.4, 3.49 and ≈3.4 mg/min/cm²), and an extractor check of the 2020 curve gives ≈1.7 [bhardwaj2018 R9; saboo2019 R5; saboo2020a X10]. The visible part of the 2018 PVPVA curve corresponds to about 8 mg/min/cm² [bhardwaj2018 X8]. The amorphous-to-crystalline ITZ solubility ratio behind the rate ratio was not measured [bhardwaj2018 C45]. Packed particles present a renewed surface, so the rate reflects layers of particles [bhardwaj2018 C64]. Ueda 2024 (p. 44) exclude these rate methods from measuring the amorphous solubility: intrinsic dissolution rates of multicomponent systems do not reflect it, because of their phase behavior, and those of crystalline poorly soluble drugs are typically inaccessible.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ketoconazole on SBA-15, pH 6.8	about 66 → 8.6 mg/g with 50 mM triethylamine; about 47.7 with 0.5 M urea	37 °C, HPMC	hate2020b R14
clozapine on SBA-15, pH 6.8	about 53 → 25 mg/g with triethylamine; about 54 with urea	same	hate2020b R14
ketoconazole; clozapine, pH 1 → 6.8 with triethylamine	about 93 → 88%; 85 → 80% released, against about 64–69% without	50 mL, 37 °C	hate2020b R15, R16
ritonavir; lopinavir on SBA-15	release about 50%; 40–50%, read as no ion exchange	pH 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
clotrimazole	98.7% ionized at pH 4; 0.8% at pH 8	pKa 5.89	indulkar2015 R18
atazanavir	90.9% ionized at pH 3.5 (91.3% recalculated); 0.0% at pH 9	pKa 4.52	indulkar2015 R18, X4
nicardipine	94.1% at pH 6; 0.9% at pH 9 (1.6% recalculated)	pKa 7.2	indulkar2015 R18, X4
ritonavir	un-ionized at pH above 7.0	pKa 1.8 and 2.6	ilevbare2013a C13
diclofenac	ionized at pH 6.8; did not mix with the ritonavir-rich phase	pKa 4.2	trasi2015a M5, R11
CRH1	un-ionized and ionized equal at equilibrium at pH 4.6	pKa 4.6	[almeidaesousa2016 C13]
pazopanib	dissolves in SGF (pH 1.2); essentially un-ionized at pH 8.4	pKa 6.4	sugihara2018 C9, C19
felodipine, nifedipine	ionization term set to 1	pH 6.8	raina2014a C9
clotrimazole	about 99% unionized	pH 8	indulkar2016 C8
ezetimibe	buffer solubility measured at pH 2 because of degradation at neutral pH		elkhabaz2017 C9, X5
atazanavir, clotrimazole	amorphous solubility rises as pH falls toward the pKa; ratio constant		indulkar2015 C46
atazanavir	pH 3 receiver acts as a sink like 2% SDS	PAMPA, pKa 4.48	hate2022 C52, R15
bifonazole; carvedilol; clotrimazole; clozapine; dipyridamole	pKa 6.22; 7.75; 5.89; 3.83 and 7.54; below 1 and 6.08	37 °C, 0.15 M KCl	hsieh2012 M1–M5
droperidol; ketoconazole; loratadine; papaverine; pyrimethamine	pKa below 2, 7.38 and 10.96; 3.16 and 6.13; 5.26; 6.29; 7.07	same	hsieh2012 M6–M10
papaverine; dipyridamole; glyburide; warfarin	pKa 6.4; 6.2 and 0.8; 4.9; 5.3	25 °C	hsieh2014 M1–M4
final pH of the 2014 pH shifts	8.4–9.0 (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 1	18%, 9%, 20% ionized (extractor arithmetic)	pH 3.5, 3.5, 4	chen2015 X3
posaconazole	pKa 3.6 and 4.6 (cited); unionized at pH 5.5–7.5; crystalline 0.31–0.34 µg/mL	FaSSIF-V2 buffer, 37 °C	shah2025 M1, R1, C9
posaconazole	fitted pKa 3.53 and 1.24 at 37 °C, 0.14 M; crystalline 0.27 (pH 7.0) to 347 µg/mL (pH 1.0)	phosphate buffers pH 1.0–7.0	[duong2022b R2, R1]
HP-50-BIS-TRIS, 20–100 mol% base	rate ≈1.22 → 2.93 mg/min/cm²	50 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% dispersion	4, 55, 52% protonated	XPS N 1s	kaur2025 R20
HPMCAS and bedaquiline at pH 6.0 and 5.8	91.5 / 88.1% and above 99% ionized	Henderson–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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
itraconazole, HPMC	Tg 60 and 140 °C, both glassy at room temperature	DSC, midpoint	purohit2015a M1, M2, C46
itraconazole–HPMC 10:90 to 50:50	domains removed by 2 min at 165 °C; pyrene I/III 1.39–1.42 → 1.50–1.53	spin-coated films	purohit2015a R1, R12, C38
itraconazole–HPMC, dry against water-containing solvent	miscible as a dry binary; trapped separated state with water	films, spray-dried particles	mugheirbi2017 C39
evacetrapib–HPMC	drug droplets stay trapped when the water has gone	ternary diagram argument	li2017 C38
felodipine–PVP	dry glass as a trapped one-phase mixture that water plasticises enough to separate	argument	rumondor2009c C36
delamanid free-base ASDs	solvent evaporation rate decides whether material is trapped before nucleation and growth	rotary 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 Amorphous solid dispersions: the whole picture

light scattering by particles

Particles suspended in a solution remove light from a beam by scattering and, if they absorb, by absorption; the sum is the extinction. Small particles scatter more at short wavelength (Tyndall effect), larger ones give a flatter, wavelength-independent baseline vaneerdenbrugh2011b C28, C16, C37. Extinction measured where the drug does not absorb is used as a read-out for a new phase, which may be crystals or a liquid raina2015a C9.

Findings

F1, F2, F3, F11.

Related concepts

part of extinction; contrasts with particle absorption of light; related to liquid-liquid phase separation and Mie theory.

Formulas

attenuation coefficient from particle cross-sections, extinction cross-section as sum, Mie theory, scattering baseline correction of UV absorbance.

How it is measured or obtained

Fiber-optic UV/Vis spectra (200–700 nm, 1 cm transflectance dip probes) of suspensions vaneerdenbrugh2011b P9; extinction at 450 nm by a dip probe during drug addition or dissolution raina2015a P6; tres2018 P8; Mie calculation of the extinction of spheres vaneerdenbrugh2011b P11.

Values in the library

material	value or class	conditions	paper ids
felodipine nanosuspension	absorbance at 425 nm ≈0.10, 0.26, 0.45, 0.55	10, 25, 40, 50 µg/mL total, 25 °C	vaneerdenbrugh2011b R3
felodipine, jetmilled	absorbance at 425 nm ≈0.011 to ≈0.046	10 to 50 µg/mL total	vaneerdenbrugh2011b R4
nonabsorbing spheres	extinction at 276 nm ≈0.01 (30 nm) to ≈0.93 (300 nm)	Mie, 50 µg/mL, 1 cm	vaneerdenbrugh2011b R13
ritonavir, 10% and 50% dispersions	extinction at 450 nm ≈0.51 (3 min) against ≈0.01–0.02	non-sink dissolution	tres2018 R7
lopinavir, 10% and 50% dispersions	≈0.70 (54 min) against ≈0.01	same	tres2018 R15

Pitfalls and disagreements

Scattering depends on particle size and number, so extinction is not a measure of the amount or composition of the new phase (synthesis: the ritonavir and lopinavir curves differ in time course) tres2018 R7, R15. For spheres of 600–1000 nm nonabsorbing particles lose the Tyndall shape and may upset the usual corrections vaneerdenbrugh2011b C33, C34.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir–PVPVA	25% DL; 30% initially congruent then incongruent	tablets, pH 6.8, 37 °C	indulkar2019a C2, C32
felodipine, five polymers	PVP 10, PVPVA 15, HPMC 10% DL; HPMCAS and EUDS no limit to 50%	30% DL test set	saboo2020a R15
ledipasvir–PVPVA	5% DL (between 5 and 7.5%); 30% with 5 wt% SDS (5 parts per 100 parts drug and polymer); 7.5% with poloxamer 407	compacts	que2019 C10, R9, C12
atazanavir–PVPVA	5% DL; 10–15% with surfactants (10% with SDS or CTAB, 15% with Span 80)	compacts	correasoto2022b C12
clopidogrel–PVPVA	about 40% DL; 50% with SDS	compacts	correasoto2022a C46, C55
lumefantrine–PVPVA	35% DL	compacts	hiew2022a C31
loratadine	HPMCAS 20% at 37 °C, 5% at 5 °C; PVPVA 30% and 2%	compacts	[yang2021 R22]
BCL–PVPVA	between 10 and 20% DL (not located)	powders, polymer by size-exclusion chromatography	moseson2022b R6, R7, X15
coated RTV–PVPVA tablets	effective limit described as below the 10 and 20% DL studied	confocal, tablets	[benson2025 C34]
ITZ–PVPVA	switch between 25 and 20% (spray-dried), 20 and 10% (melt-extruded)	0.1 N HCl, compacts	[bhardwaj2018 X6, R4]
ritonavir films with PVP; PVPVA	LLPS up to 20%; only at 10%	25 °C, 100 mM pH 6.8	purohit2017b R10, R11
nilvadipine; cilnidipine in PVPVA	10% (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 PVPVA	10%; at least 25% (5-min rates)	37 °C	saboo2020 C14, P5
indomethacin–PVPVA	10% (25–57 °C), 5% (17 °C), below 5% (10 °C)	temperature series	saboo2020 R29
PHPH, TIPP, Me-TIPP, Me-PHPH in PVPVA	5, 10, 30, 40%; 0.016, 0.012, 0.035, 0.115 mol per 100 g	pH 6.8 (TIPP 2.5)	[que2021 R19, R20, P9]
felodipine–PVPVA with 0, 2, 5, 10% TPGS	15, 25, 35, 45%	pH 6.8	saboo2021 R12, P6
lumefantrine free base; eight salts in PVPVA	at least 35%; 2–25%	drug release only	hiew2022b R20, X7
atazanavir–PVPVA with 5 g plasticizer per 100 g	5 → 7.5–25% (citrate esters 20–25%)	compacts, pH 6.8, 37 °C	[correasoto2023 R1, C12]
ledipasvir–PVPVA with 10 g TEAC, TBC; GTB	5 → 15; 20%	same	[correasoto2023 R11, C17]
ritonavir–PVPVA with 5 g GTB or TBC	complete release at 30%, not at 35% (cited limit 25%)	same	[correasoto2023 R14, R16]
MePHPH–PVPVA 40%; 50%	gel drug content 40 → 49%; 50 → 59.5% over 30 min	scraped gel, dry basis	[deac2023a R3]
PHPH, TIPP, MeTIPP, MePHPH–PVPVA	limit 5 / 10 / 30 / 40% (cited) against PVPVA in nanoparticles ≈77 / 36.5 / 9 / 5 wt%	nanoparticles at 60 °C	deac2023b 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 PVPVA	cited 5, 10, 30, 40% against critical-point loadings ≈3.7, 13.7, 32.6, 33.2%	PC-SAFT phase diagrams, 37 °C	deac2024b R37
ritonavir–PVPVA + 10 parts Span 20 or Span 85	between 30 and 40% (cited 25% without)	compacts, pH 6.8	yang2023 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
indomethacin mixtures, Raman	LOD 0.6% (3 × 0.2%); about 1% judged reasonable	pure-form SD, 10 measurements	taylor1998a R14, C21
naproxen–HPMCAS blends, PXRD	no peaks below 5 wt%	whole-pattern OPLS	kestur2012 R8
naproxen–HPMCAS, SHG	10^{-3} % (10 ppm), calculated; lowest imaged 0.1%	single voxel at S/B 3	kestur2012 R7, R6, X10
griseofulvin and chlorpropamide films, SHG	90 and 125 nm; 3.4\times10^{-9} and 9\times10^{-9} % by volume	size back-calculated	wanapun2010 R10, R11
flutamide and ezetimibe in HPMCAS, SHG	0.03 and 0.047%; 0.005% visible	regression residual	correasoto2017 R8, R5
flutamide and ezetimibe, XRPD	about 0.4 and 0.7%; none seen below 1%	peak-window area ratio	correasoto2017 R8, R7
posaconazole HME ASD (PCZ–HPMCAS), pXRD	LOD 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, XRPD	LOD about 1%, LOQ about 3%	S/N 3:1 and 10:1	moseson2021 P2
tacrolimus capsule contents, XRPD	about 1% (LOQ about 5%); 10% crystallinity (0.38% w/w)	spiked standards	hate2019 R2; purohit2018 R2
IDM in PVPVA (XRPD), extrudates	LOD 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 °C	XRD may lose the crystals earlier than PLM or TEM show them; loss is also consistent with a small fraction below the limit	variable-temperature XRD	moseson2019 R4, C11, C54, X7
30% BCL in PVPVA (XRPD), 2022 paper	limit 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 standards	correasoto2017 R7
cited	laboratory 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 Amorphous solid dispersions: the whole picture

limit of quantitation

The smallest content that can be measured with acceptable precision, taken as ten standard deviations of a pure-form reading taylor1998a E8, from the residual standard deviation of a regression correasoto2017 E5 or at a signal-to-noise ratio of 10:1 moseson2021 P2. Taylor and Zografi call their estimate of about 2% "too low", because the variation of the mixture data is larger than the pure-form SD suggests taylor1998a C21.

Findings

F1, F4, F7.

Related concepts

pairs with limit of detection; depends on signal-to-noise ratio.

Formulas

limit of detection and quantification.

How it is measured or obtained

As for the limit of detection: from spiked standards or a pure-form SD. Quantitative XRPD analysis in the dispersions of Correa-Soto and co-workers was only possible for samples with more extensive crystallization than the SHG could quantify correasoto2017 C18.

Values in the library

material	value or class	conditions	paper ids
indomethacin, Raman	about 2% (10 × 0.2%)	pure-form SD	taylor1998a R14
flutamide, ezetimibe in HPMCAS, SHG	0.08%; 0.14%	regression residual	correasoto2017 R8
flutamide, ezetimibe in HPMCAS, XRPD	1%; about 2%	same	correasoto2017 R8
posaconazole HME ASD, pXRD	1.2 wt%	spiked standards	shah2024 P6
BCL–PVPVA extrudates, XRPD	about 3%	S/N 10:1	moseson2021 P2
tacrolimus capsule contents, XRPD	about 5%; 15% crystallinity (0.57% w/w)	spiked standards	hate2019 R2; purohit2018 R2

Pitfalls and disagreements

For ezetimibe the basis of the limits (powder or drug) is not stated; if on a powder basis, the 75% RH SHG values before 53 days lie below the quantitation limit correasoto2017 X6. A quantitation limit measured on a pure form does not include sampling error (F2).

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
enzalutamide	2.98 (cLogP, cited from a regulatory report) and 4.75 (MarvinSketch)	neutral species	wilson2018 M1; wilson2020 M1, P4
atazanavir	about 4.5	pKa 4.3–4.52	elkhabaz2019b M1; alkalla2026 M1; hate2022 M1
posaconazole	4.6	pKa 3.6 and 4.6	elkhabaz2019b M2
darunavir	2.8	pKa 2.4	alkalla2026 M2
acetaminophen	0.46 and 0.51 as printed	hydrophilic comparator	hate2022 M6, X5
lumefantrine	8.34; good release to 35% in PVPVA	base form, cited	hiew2022b C35, M1, R20
ritonavir; efavirenz; celecoxib	Log P 5.6 (5.98 in the 2012 paper); 4.7; 3.5	SP 20.03; 21.89; 23.38 MPa^1/2	[ilevbare2013b M1–M3; ilevbare2012c M1]
growth-inhibiting window	cellulose polymers of SP 20.56–23.28 for drugs of Log P 3.5–5.6	5 µg/mL	[ilevbare2013b C43]
13 bile salts	LogP'A of the ionized acid from 2.65 (SDC) to −0.50 (STC); none for STDC, STCDC, SLC	literature	[li2016a M4–M16]
posaconazole	log P 4.6 (cited); phase-separates at about 10 µg/mL	pH 6.5	shah2025 M1, C48
nifedipine	log P 3.17 (cited)	model drug	indulkar2017b M1
nilvadipine; cilnidipine	ClogP 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; ledipasvir	log P 4.3, LoC 25%; LoC 5% for ledipasvir	cited; PVPVA	que2019 R28, R27, C10
nilvadipine, felodipine, cilnidipine at 40% in HPMCAS	log P 4.06, 4.46, 5.40; rates 0.42, 0.34, 0.26 mg/min/cm²	pH 6.8	saboo2020a R16
TIPP, Me-TIPP, PHPH, Me-PHPH	log 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, ivacaftor	log P 4.4, 5.69, 3.8, 5.33, 3.96, 5.68; PVPVA drops at 25, 40, 5, 10, 5–10, 5–10%	cited	[yang2021 M1, M2, M3, M4, M5, M6, R7, R8, R9, R10, R11, R12]
clopidogrel	cLogP 3.8; limit about 40%	cited	correasoto2022a 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir droplets	about 345 nm at 1 min, about 842 nm at 64 min	water, 37 °C, single addition at the onset	ilevbare2013a R3
ritonavir drug-rich phase	94.85–95.97% drug, 4.03–5.15% water, Tg 0.4 °C	10–50 °C, ultracentrifuged	ilevbare2013a R5, R6
weak-base droplets	Z-average about 116–387 nm	clotrimazole, atazanavir, nicardipine, 37 °C	indulkar2015 R14
telaprevir	species about 300 nm	pH 6.8, 37 °C	mosqueragiraldo2015 R5
ritonavir droplets	about 360 nm at 30 µg/mL	100 mM pH 6.8, 25 °C	trasi2015a R15
pazopanib colloids	495.9 nm without, 145.4 nm with 50 µg/mL HPMC (DLS); NTA about 50–650 nm	pH 6.5 after pH shift, 37 °C	sugihara2018 R15, R16
ibuprofen droplets	3182–5313 nm (buffer); 272–345 (HPMC); 268–320 (PVP-VA); 472–808 nm (EUD-E)	pH 2.0 (D2O), 37 °C, fresh	ueda2020b R5
felodipine	onset 5.70–13.4 µg/mL	20–45 °C, buffer	raina2014a R1
nifedipine	LLPS only with 1 mg/mL HPMC: 30.86–88.89 µg/mL	20–45 °C	raina2014a R1, R5
clotrimazole	onset 7.5 µg/mL; droplets 111–257 nm	pH 8	indulkar2016 R2, R4
atazanavir	78 µg/mL; droplets 204–226 nm	pH 6.8	hate2018 R2, R6
ritonavir	onset about 38 µg/mL in water	UV extinction	ilevbare2013a R2
enzalutamide	onset about 42 µg/mL	pH 6.5, 37 °C	wilson2018 R2, C16
atazanavir, darunavir	93.1 and 363.8 µg/mL (antisolvent, 450 nm)	pH 6.8, 37 °C	alkalla2026 R3, C16
pretomanid	about 166 µg/mL in buffer, 308 in FaSSIF	pH 6.5, 37 °C	nguyen2023a P2, R2
danazol dispersions (eight)	onset about 6.0–10.4 µg/mL against 8 µg/mL	pH 6.8, 25 °C	jackson2015 R5, M1
ritonavir–PVP dispersion, stepwise	onset between 10 and 20 µg/mL	37 °C	ilevbare2013d R1, X8
ritonavir, 180 µg/mL PVP / PAA / HPMC / HPMCAS / CAAdP 0.85	18.3 / 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
BCL–PVPVA 30:70, crystal-free	form 2 begins at 20–30 min (half conversion about 36 min); plateau about 37–38 µg/mL against an amorphous solubility of 150 µg/mL	60 and 150 µg/mL doses, pH 6.8	moseson2021 R12, R13, R19
BCL–PVPVA with residual or added form 1 crystals	form 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 route	buffer, 25 °C	raina2014b C10, C11
celecoxib dispersions (outside)	polymers dissolved in solution cannot inhibit crystal formation in the matrix	high drug loading	xie2015 C35
telaprevir 50% HPMCAS (outside)	slow, incongruent release; HPMCAS leaves about twice as fast as the drug, leaving a drug-rich layer	optical micrographs	mosqueragiraldo2018b C40, C43
enzalutamide 10:90 HPMCAS (outside)	rapid matrix crystallisation on contact with water	dissolution	wilson2018 C56
posaconazole ASDs in acid (outside)	matrix crystallisation about 68% at 50% DL, about 0.05% at 25% DL	SHG over TPE-UVF, 30 min	elkhabaz2019a R20, C38
BCL–PVPVA 5 / 10 / 20 / 30 / 50% DL powders	end level about 91 / 96 / 88 / 86 / 73% of the dose; polymer ahead of drug from 20% DL	dose of at most 30 µg/mL, pH 6.8	moseson2022b R6, R7
30% and 50% DL compacts, 1 h	drug-rich boundary layer of 94 ± 8 µm with crystals (F/F0 1.41 ± 0.10); 5–10 µm crust of crystals	SEM-EDX	moseson2022b R15
30% DL cryomilled 2 and 5 min	about 50 and 49% of the dose, plateau about 15 µg/mL	same	moseson2022b R4
10% DL after 10 min of cryomilling or extrusion and 30 s of milling	about 93% of the dose	same	moseson2022b R8
30% DL with 3% TPGS, cryomilled 5 min	stops at about 60% (about 18 µg/mL)	same	moseson2022b R12
50% PCZ–HPMCAS, small particles, uncoated against 12 nm Al2O3	SHG 126.7 against 3.7; about 3.35 against 5.1 µg/mL at 3 h	single stage, pH 6.5	[moseson2023 R18, R15]
telaprevir 50% HPMCAS ASD	birefringent domains in the particle at 20 min; 0.65 µg/min	pH 6.8	mosqueragiraldo2018b R16, R18
telaprevir 47.5:47.5:5 SDS ASD	none visible; 1.07 µg/min	same	mosqueragiraldo2018b R16, R18
ezetimibe PAA ASD	crystals within minutes, inferred from the matrix	buffer, 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 ASDs	50% DL final crystallinity about 250 times that of 25% DL		elkhabaz2019a R18
enzalutamide 10:90 HPMCAS-MF ASD	peak about 10 µg/mL, crystals in the medium	pH 6.5, 100 µg/mL total	wilson2018 R6, C56
pretomanid HPMCAS-HF ASD tablets	crystalline drug in the particles after FeSSIF at pH 5.5 and below, and after a 1 h gastric stage	PXRD and SEM, 30 mg in 150 mL	nguyen2023a R20, R22
neat amorphous felodipine	≈54% crystalline at 1 min (37 °C); 50% after about 8 min (25 °C)	pH 6.8 slurry	alonzo2010 R2
felodipine with 500 µg/mL PVP, HPMC, HPMC-AS in the medium	50% crystalline at ≈20.5, ≈18.5, ≈13.5 min	37 °C	alonzo2010 R6
neat amorphous indomethacin	α form present at 90 min, like pure α at 120 min	pH 2, 37 °C	alonzo2010 R12
nifedipine 50:50 dispersions (PVP shown)	particles not birefringent; crystals form in the solution	pH 6.8	raina2014b R13, X18
nifedipine–HPMCAS 50:50 at pH 2	matrix amorphous for 3 h	polymer barely soluble	raina2014b R15
celecoxib–HPMCAS 33.3% particles in pH 3 suspension	crystals on or in particles after about 7 days (Triton X100), none in 48 h	25 °C	[chen2015a R20, R14]
resveratrol 35% with HPMC / HPMCAS / CMCAB	Raman ratio ≈0.87 / ≈0.84 / ≈0.81 (crystal 0.76) within hours	pH 6.8, 37 °C	[wegiel2015 R9]
resveratrol, minimum polymer to prevent it	80% HPMC, 85% HPMCAS, 95% CMCAB	pH 6.8, 37 °C	[wegiel2015 R14]
neat amorphous celecoxib	complete within an hour; crystals on the particles from 2 min	pH 6.8, 37 °C	xie2015 R4, R8
celecoxib–PVP-K12 50%	crystalline within 4 h in a slurry	pH 6.8, 37 °C	xie2015 R4
celecoxib–PAA 5:5 and 1:9, HPMCAS in the medium	release stopped at about half; needles in the residue	pH 6.8, 37 °C	xie2016a R9, R10
lopinavir 50% with EUD, CAP / HPMCP	crystals by 8–16 h / none at 48 h	pH 3, 25 °C	[li2018 R7]
delamanid salt dispersions, films after 1 h in acid	clear at pH 1.6 (HPMCP); crystals at pH 3.0 on all but HPMCP-55; small crystals on every film at pH 5.0	25% drug, 37 °C	nguyen2023c R19
same, powders	pitted, porous HPMCAS surfaces with agglomerates increasing with pH; HPMCP-50 covered at pH 5.0	1 h in acid	nguyen2023c R18
delamanid dispersions in HPMCP, films with and without a 2 µm Eudragit L 100-55 layer	star- and needle-shaped crystals on every uncoated film; none under the layer	pH 3.0, 1 h	nguyen2023b R3, R6
posaconazole–HPMCAS dispersions	crystals by SHG in every system after 30 min in FaSSGF, more numerous after transfer	37 °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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
benzamide	2.86 × 10⁻³ Pa·s, the lowest	at Tm	baird2012 R1.b
ritonavir	1.99 Pa·s, the highest	at Tm	baird2012 R1.ah
felodipine; nifedipine	154.0 and 36.20 × 10⁻³ Pa·s	at Tm	baird2012 R1.u, R1.q
class I-A; class III averages	≈0.005 and ≈0.11 Pa·s at Tm; ≈0.014 and ≈0.53 Pa·s at 20 °C undercooling	class averages	baird2012 R8
17 drugs	\eta(T_m) falls linearly with Tm − Tg, R^2 = 0.7368	data of baird2012	[trasi2014a R9]
indomethacin with 10% PVP	higher viscosity than with HPMC or HPMCAS at 80–105 °C; pure indomethacin crystallized during measurement	rheometry	[tian2017 R13, C19]
indomethacin in a polymer	matrix viscosity falls quickly as the drug plasticizes the polymer	hot 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
benzocaine in PEG 3350	melting around 89 °C neat, eutectic around 48 °C; text of the other paper: 92 °C neat and about 55 °C for the 20/80 blend	fused dispersions	zhu2012 C32, M3; zhu2011 R1
ibuprofen; fenofibrate in PEG 3350	about 30 °C; about 20 °C by the text, about 24 °C by the plot	eutectic depression	zhu2012 C34, X11, R24
chlorpropamide, aceclofenac in PEG 3350	liquidus at 40 wt% drug about 55–56 and 86–88 °C against about 98 and 135.5 °C predicted	DSC and hot stage	[baird2011 R5.e, R6.e]
nifedipine, felodipine in PVP K12	decreased linearly over 0–25 wt% polymer; \chi −3.8 and −4.2	1 °C/min, small particles	marsac2006b R7, R9
indomethacin in PVP K12	\chi −6.16 (onset), −1.94 (midpoint), −0.82 (offset)	1 °C/min	marsac2009 R6
indomethacin in PVPVA	about 30 °C at 50% drug loading; 1–4 °C below 30% polymer	DSC offsets	moseson2018 R6
probucol in PEO	melting point 101 °C, Form II only, "may be due to" depression	compression-moulded dispersion	broman2001 R4.f, C20
nifedipine in PVP K12	onset ≈171 → ≈156.5 °C; ≈144.5 °C at Φ ≈ 0.383	1 °C/min	marsac2006b R6
felodipine in PVP K12	onset ≈141 → ≈122 °C; ≈115.5 °C at Φ ≈ 0.383	1 °C/min	marsac2006b R6
indomethacin in PVP K12	offset ≈161.5 → ≈155 °C; onset ≈160 → ≈135.5 °C	Φ ≈ 0.23	marsac2009 R2
ketoconazole in PVP K12	offset ≈150.0 → ≈147.5 °C	Φ ≈ 0.23	marsac2009 R3
itraconazole with Eudragit E100	offset ≈168.0 → ≈167.4 °C	polymer fraction up to ≈0.54	marsac2009 R4
felodipine with 3% PVP, PVP/VA, HPMCAS, PVAc	140.7, 142.9, 141.4, 142.6 °C against 141.5 °C: none	offset, 1 °C/min	kestur2010a R1
indomethacin (IDM) with PVPVA, 90/10 to 40/60	Tc 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 °C	offset 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–PVP	DSC	mosqueragiraldo2014 C18
IDM with copovidone (1:5)	solubility temperature about 78 °C (cited)	phase diagram	moseson2019 R21
bicalutamide with PVPVA, 30–90% BCL	Tc 145 °C at 30% BCL to about 192.3 °C at 90%; drug about 193.8 °C	offset extrapolated to 0 °C/min	[moseson2022c R8, R9]
posaconazole with HPMCAS MF, PCZ fractions 0.4–1.0	Tc about 161.7 °C at 0.4 to about 168.6 °C for neat PCZ; calculated 135 / 155 / 165 °C at 10 / 25 / 50% DL	same	shah2024 R1, R4, R5, X7
felodipine with 3 wt% PVP K-12	140.7 vs 141.5 °C, within the ±1 °C SD	1 °C/min	[kestur2010b R1.e, M1, X11]
indomethacin–PVP (cited)	χ23 from melting point depression used as input to the ternary sorption model	literature	[rumondor2010a P5]
acetaminophen with 10% w/w polymers	166.7–168.6 against 169 °C	physical mixtures, DSC	trasi2012a R9
flutamide with 10 mol% polymers	108–110 °C	DSC	[trasi2012b R7]
six compounds with 1–20% PHB	0–2 °C (1–10% PHB), up to 4 °C (20%)	DSC of physical mixtures	[sato2016 R7, X11]
indomethacin with 10% polymer	named as a possible reason for the steep inhibition above the growth maximum; not measured	argument	[tian2017 C36]

Pitfalls and disagreements

Onset, midpoint and offset of the melting event give different depressions and different \chi marsac2009 R6. DSC and hot-stage values differ by up to about 16 °C at some compositions [baird2011 X7]. The low-temperature endotherm of the chlorpropamide and aceclofenac dispersions drifts to 39–49 °C in drug-rich traces, which a simple eutectic would not show [baird2011 R4, X8]. Very slow scans and controlled particle size were needed to see substantial depression with PVP K12, and with PVP K29/32 at 10 °C/min there was essentially none marsac2006b C30, R11. For PEG, the depression of the drug is the cited reason for a smaller driving force and delayed crystallization of benzocaine, but the supercooling in the dispersion was not measured zhu2012 C32, C33. The felodipine premix test read as slow mixing has an unverified direction marsac2009 X6, R8. The linear plot has a small non-zero intercept and the fit range is stated two ways marsac2006b X4. At 3 wt% polymer no depression is measured, and the melting point used there is that of form I in physical mixtures while form II grows kestur2010a R1, X7. Sucrose degrades on melting marsac2009 C14. A polymer with Tg near the drug melting point can hide the depression marsac2009 C22. In the extrusion work, mixtures with little polymer show only 1–4 °C of depression and the extent depends on interaction strength moseson2018 C16, C42. The 40/60 mixture scattered by about ±6 °C and lay above the model line, attributed to viscosity, and was left out of the fit moseson2018 R5.g, C17. In the probucol study depressions of a few °C compare dispersion melts at 20 °C/min with reference melts at 10 °C/min, and the table does not say whether values are onsets or peaks broman2001 X4, X5. The same low melting of probucol in moulded PEO is read as depression "may be due to" broman2001 C20. The depression of bicalutamide at 30% loading is large (about 49 °C from 193.8 °C to 145 °C, arithmetic on the cited values); that of posaconazole measured at 40% PCZ is about 7 °C (168.6 against 161.7 °C), and the values at 10–25% loading are extrapolations from the fitted line [moseson2022c R8, R9; shah2024 R1, X7]. The felodipine growth test used one composition and one grade only; the conclusion that the driving force is unchanged rests on a 0.8 °C difference inside the error [kestur2010b X11]. The celecoxib text gives 3–4 °C for one additive while the table gives 1.68–4.49 °C mosqueragiraldo2014 X3, and the depression does not order the celecoxib ternaries mosqueragiraldo2014 X13.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
telaprevir	about 0.068 µg/min at 5 µg/mL; about 0.97 at 90; about 1.07 at 130 µg/mL donor	37 °C	mosqueragiraldo2015 R12
ritonavir; lopinavir; paclitaxel	plateaus about 0.21–0.22; 0.13–0.14; 0.25–0.27 µg/min	25 °C	trasi2015a R2
ritonavir, lopinavir, paclitaxel in 30 + 30 µg/mL mixtures	flux of each drug lower than from the single-drug donor	25 °C	trasi2015a R12
atazanavir	about 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·cm²	buffer, 37 °C	indulkar2017a R10
telaprevir	slope 0.009 µg/min per µg/mL; about 1.32 µg/min at 150 µg/mL; plateau 1.25–1.27	50 mM pH 6.5, 37 °C	lu2017b R6
telaprevir with 12 mM STDC	about 0.43 against 0.83 µg/min at 90 µg/mL	37 °C	lu2017b R12, R6
felodipine	plateau 63–71 (25 °C) and 136–149 × 10⁻³ µg/min (37 °C)	buffer + HPMC	raina2014a R11, R12
nifedipine	about 1.7–1.9 µg/min	37 °C, 1 mg/mL HPMC	raina2014a R14
clotrimazole	Jmax 0.686–0.693 µg/(h·cm²)	flow-through, pH 8	indulkar2016 R9
telaprevir	1.05–1.18 µg/min above 90 µg/mL	ASD dose series	mosqueragiraldo2018b R1
atazanavir, ritonavir	(10.5 / 9.1) × 10⁻⁵ mg/min/cm² alone; about half in 1:1	Caco-2	alhalaweh2016 R17
telaprevir, antisolvent	plateau about 18-fold the saturated solution	side-by-side	mosqueragiraldo2015 R12, C40
tacrolimus	about 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/min	pH 4.5, 37 °C	trasi2016 R14
danazol, no polymer, 25 °C	flux 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]
enzalutamide	about 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 0.76	side-by-side, 5 µg/mL HPMCAS	wilson2018 R13, R14
enzalutamide formulations after 1 h of dissolution	0.632, 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 formulations	about 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, posaconazole	J_{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, PAMPA	about 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/mL	lipid-impregnated PVDF	hate2022 R1, R19
atazanavir alone and with darunavir hydrate	plateau about 9.5 × 10⁻⁵ against 2.9 × 10⁻⁵ µg/(min·cm²); Caco-2 about 0.083 against 0.053	pH 6.8, 400 µg/mL HPMCAS	alkalla2026 R9, R13
danazol, PVP, HPMC, HPMC-AS 1–1000 µg/mL	maximum flux about 0.0126–0.0175 against about 0.0153	donor 15 µg/mL	[jackson2016 R11]
celecoxib, nevirapine, 0.1% STC or SGC	0.44, 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 solubility	0.027–0.031 and 0.0014–0.0018 µg/min·cm² in buffer, FaSSIF-V1, Composite-SIF; flux at the crystalline solubility not measurable	37 °C, 7.07 cm², regenerated cellulose 6–8 kD	indulkar2018 R12, R13
telaprevir, bile salt mixtures	mass flow unchanged at 1.86 mM, lower at 3.72 and 5.58 mM	50 mM phosphate pH 6.5	[lu2018 R2, X2]
felodipine controls 10 and 5 µg/mL	ratios 10.0 ± 3.4 and 4.8 ± 0.39 to the crystal	37 °C	alonzo2011 R14
felodipine 90:10, 50:50, pure amorphous	10.5 ± 1.2, 9.5 ± 1.8, 8.5 ± 1.8	37 °C	alonzo2011 R14
danazol dispersions PVP, HPMC, HPMCAS	14.0–18.3 × 10⁻⁵ µg/(min·mm²) with LLPS; 10.3 × 10⁻⁵ without (50:50 HPMCAS)	25 °C	jackson2015 R9
tacrolimus products dissolved in 30 mL	0.0048–0.0054 µg/min	pH 4.5, 37 °C	trasi2016 R15
resveratrol–HPMCAS solutions; saturated crystal	≈4.4 → ≈2.6 µg/min; 2.0 µg/min	pH 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 Amorphous solid dispersions: the whole picture

membrane mass transfer coefficient

The overall coefficient K_in (cm/s) of a hollow-fibre module, the sum of three resistances in series; independent of the donor concentration in theory hate2017 C11, E3. For tacrolimus the fitted coefficient of the absorption profiles was 1.09 × 10⁻⁴ cm/s hate2019 R16, E3.

Findings

F13, F14, F15, F28, F29.

Related concepts

composed of the resistance-in-series permeability model; affected by the unstirred water layer.

Formulas

hollow-fibre donor depletion, resistances-in-series model.

How it is measured or obtained

Fitting the donor-depletion equation to donor profiles hate2017 P10, E9.

Values in the library

material	value or class	conditions	paper ids
nevirapine	(9.07 ± 1.06) × 10⁻⁵ cm/s mean; 4.9 × 10⁻⁵ to 1.54 × 10⁻⁴ over 0.5–4 mL/min	hollow fibre	hate2017 R12, R14
atazanavir	a changed coefficient above the amorphous solubility is inferred, not measured		hate2018 C25, X11
tacrolimus	1.09 × 10⁻⁴ cm/s	hollow fibre, 2 mL/min inside and outside	hate2019 R16, E3

Pitfalls and disagreements

The model curve used a value above the mean hate2017 X8. The absorption line of the absorption-versus-growth model cannot be reproduced from the printed coefficient, area and flow rates (F29) hate2019 X4.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

membrane transport

Passive transfer of dissolved drug across a membrane; in these papers a measure of free drug or activity alhalaweh2016 C2; hate2017 C36. Includes diffusion cells, Caco-2 monolayers and a hollow-fibre module.

Findings

F2, F6, F13, F21.

Related concepts

quantified as membrane flux; depends on membrane mass transfer coefficient.

Formulas

membrane flux in terms of solute activity.

How it is measured or obtained

See membrane flux; percentage transferred, receiver Cmax and AUC in the hollow fibre hate2017 R3, R6.

Values in the library

material	value or class	conditions	paper ids
nevirapine	41.5% in 60 min (hollow fibre) against 1.50% (flat sheet)	100 µg/mL	hate2017 R3
ritonavir, atazanavir	Caco-2 flux about halved in a 1:1 solution	HBSS pH 6.5	alhalaweh2016 R17
telaprevir, bile salts	trihydroxy salts on the buffer curve; dihydroxy at 12 mM about 2-fold lower		lu2017b R10, R12

Pitfalls and disagreements

Only passive diffusion; active transport and P-gp are not covered raina2014a C42.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

metastable equilibrium

The state in which the drug-rich and the drug-lean phases coexist with equal activity while both remain supersaturated with respect to the crystal raina2014a C33; alhalaweh2016 C1; indulkar2016 C23. The Crystallization from solution papers extend it to amorphous precipitates and add cases: type 2 bases precipitate when the concentration is close to the amorphous solubility and keep a metastable equilibrium between solution and amorphous precipitate hsieh2012 C29; after danazol separates, the supersaturation stays constant because the drug-lean solution is in equilibrium with the droplets jackson2014 C28; the dihydropyridine precipitates are taken to be in metastable equilibrium with a supersaturated water-rich phase, so that crystallization can start in either, and for danazol the binodal compositions are x = 4.27 × 10⁻⁷ (water-rich) and 0.92 (droplet) mole fraction [raina2015b C24, C39; jackson2016 R22].

Findings

Bioperformance: F1, F5, F10. Crystallization from solution: F1, F2, F4, F21, F22.

Related concepts

the state of liquid-liquid phase separation; related to chemical potential; characterizes amorphous precipitation; related to amorphous solubility.

Formulas

none.

How it is measured or obtained

Not measured as such; concentration or flux staying constant while two phases coexist raina2014a C36. In the pH-shift and danazol papers it is inferred from a concentration plateau at the amorphous solubility while the precipitate remains amorphous (Bjerrum data following the curve for the supernatant concentration, a pyrene ratio held at about 1.5), and by the later fall to the crystalline solubility hsieh2012 R8, R9; jackson2014 R8, R15.

Values in the library

material	value or class	conditions	paper ids
telaprevir	a 130 µg/mL solution has the same flux as a 90 µg/mL solution; added drug increases the amount of drug-rich phase while the drug-lean concentration stays constant	37 °C	mosqueragiraldo2015 C35, C36
danazol ASDs	all except 50:50 HPMCAS exceed the amorphous solubility only briefly		jackson2015 C31
felodipine	amorphous precipitates are probably viscous supercooled liquids in metastable equilibrium		raina2015b C24
loratadine	plateau 9.6–10.3 µg/mL to about 91 min against crystalline 1.6 µg/mL	pH shift, 37 °C	hsieh2012 R8, R10
danazol above 13 µg/mL	pyrene about 1.5 for 9 min, then crystallization	25 °C	jackson2014 R15
atazanavir (Bioperformance)	metastable equilibrium until crystal nucleation, drug activity equal in both phases	ASD-coupled dissolution and membrane transfer	hate2018 C5
danazol–water, 25 °C	binodal 4.27 × 10⁻⁷ and 0.92 mole fraction danazol	from the onset and moisture sorption	[jackson2016 R22]

Pitfalls and disagreements

It lasts only until crystals nucleate (F10). The phase was not observed or analysed in the type 2 bases, and phase separation was "believed" to explain them hsieh2012 C34. For danazol, how LLPS affects subsequent crystallization is "not well understood" jackson2014 C45.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir with 500 µg/mL Tween 80	crystalline 1.3 → 3.5 µg/mL; LLPS 18.8 → 46.1 µg/mL	37 °C	ilevbare2013a R16
felodipine with 0.04% vitamin E TPGS	crystalline solubility up almost 40-fold; concentration ratio 9.2 → 4.5	37 °C	raina2015c C29
atazanavir with SDS	crystalline 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 salts	crystalline 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
felodipine	1.1 to 35.3–49.0 µg/mL with six additives above CMC / 0.1–1%	37 °C	raina2015c R2
nifedipine	10.3 to 53.4–90.7 µg/mL	37 °C	raina2015c R3
atazanavir + SDS	constant 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/mL	pH 6.8	indulkar2017a R7, R8
celecoxib Form III	SDS 0.25% 14.5, STC 0.75% 5.8 µg/mL	25 °C	[chen2015a R5]
posaconazole	crystalline 0.23 (buffer) to 3.2 µg/mL (FaSSIF-V1); amorphous 8.1 to 43.3	six media, 37 °C	elkhabaz2019b R1, R2
atazanavir	crystalline 1.4 to 7.1 µg/mL; amorphous 79 to about 99–102	six media, 37 °C	elkhabaz2019b R1, R2
pretomanid	equilibrium solubility about 3-fold (FaSSIF V1) and 6-fold (FeSSIF V2) the buffer value	37 °C	nguyen2023a R1, C33
11 drugs, 0.1% STC and SDS	STC 1.1–3.5-fold; SDS 1.2–266-fold	25 °C (telaprevir 37 °C)	chen2015 R1
celecoxib, 0.1% STC, SGC, HPMCAS	solubility 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, STCDC	about 140 against 60 µg/mL for the same δ 11.5	pH 6.5, 37 °C	[lu2017 R1]
ritonavir, cilnidipine; buffer, FaSSIF-V1, Composite-SIF	amorphous/crystalline ratio 12 → 8.4, 7.8 and 36.5 → 12.9, 13.7; ritonavir SRamorph 9.2–10 throughout	pH 6.5, 37 °C, 3 mM bile salt	indulkar2018 R8, R12
telaprevir, 3.72 and 5.58 mM bile salt mixtures	δ 11.5 at about 72–77 against 60 µg/mL in buffer	50 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 65	50 mM phosphate pH 6.8, 37 °C	[indulkar2019b R1, R2, X6]
posaconazole, five biorelevant media	concentration 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 solubility	37 °C, pH 1.6–6.5	[duong2022b R8, R14]
atazanavir, posaconazole in aspirated human fluid	concentration ratio about 15 and 5.4 against cited activity ratios 54 and 30	pH 7.3, 37 °C	elkhabaz2021 R1, R4, X14
ritonavir, 28 µg/mL SDS; 28 and 500 µg/mL Vit E TPGS	crystalline 3.6 → 6.6; 11.8; 14.9 µg/mL; amorphous 27.9 → 26.8; 27.7; 76.6 µg/mL	pH 6.8, 37 °C	dening2019 R1
ritonavir–SBA-15 in micellar Vit E TPGS	69% at 30 min against 50% in buffer; bound drug 72 against 146 mg/g; crystallized about 45 min	dose 77 µg/mL	dening2019 R18, R19
ritonavir in FaSSIF	crystalline 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/mL	pH 3, 25 °C	[chen2015a R6]
STC 0.10 → 1.50%	1.8 → 26.0 µg/mL	pH 3	[chen2015a R7]
polysorbate 80 0 → 1%	1.2 → 198.4 µg/mL	pH 3	[chen2015a R8]
Triton X100 0 → 0.15%	1.2 → 59.6 µg/mL	pH 3	[chen2015a R9]
Poloxamer 188 0.002 → 3%	1.4 → 2.5 µg/mL	pH 3	[chen2015a R10]
lopinavir with HPMCAS-HF, + SDS / Poloxamer 188 / polysorbate 80 / STC	3.3 / 3.0 / 4.5 / 7.2 against 1.9 µg/mL	pH 3, 25 °C	[li2016b R5]
lopinavir with HPMCAS-HF, PVPVA and SDS	11.4 µg/mL	pH 3, 25 °C	[li2016b R5]
lopinavir with HPMCAS-HF and SDS at pH 5	6.3 µg/mL	25 °C	[li2016b R5]
delamanid, crystalline	0.52 (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 5.5	37 °C	nguyen2023b R13, R18
praziquantel, amorphous and crystalline	amorphous 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 6.5	37 °C	alvarenga2025 R1
delamanid, amorphous	69.9 (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 TPGS	crystalline solubility ≈1.3 µg/mL, as in buffer; slope change near 48 (buffer) and 40 µg/mL TPGS (with PVPVA)	37 °C	saboo2021 R2, C8, P1
clopidogrel in buffer; with 50 µg/mL TPGS; with 50 µg/mL Tween 80	LLPS concentration 23 ± 3; 29 ± 2; 30 ± 2 µg/mL	37 °C	correasoto2022a R3
clopidogrel with 5 µg/mL TPGS, CTAB or 50 µg/mL SDS	20 ± 1 µg/mL	37 °C	correasoto2022a R3
neat HPMCAS-MF in FaSSIF; in blank FaSSIF buffer	≈0.56; ≈0.57 mg/min/cm²	pH 6.5, 12 mM/ΔpH	[bapat2023 R7]
bedaquiline in FaSSIF-V1, FeSSIF-V2, FeSSIF-V1	crystalline solubility 7.8, 258.8, 628 µg/mL	37 °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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
HP-50 films (cited)	surface pH ≈0.4 units below bulk	phosphate of similar capacity	[qi2022 R18]
HPMCAS-MF gel at 13, 26, 51 mM/ΔpH; pH 7.5 phosphate	apparent pH 5.6, 6.0, 6.2; 6.3, against rates ≈0.60–1.09 mg/min/cm²	bulk pH 6.8 or 7.5	[bapat2023 R15, R16]
HPMCAS-TEA gel	apparent pH 6.7, rate ≈1.62 mg/min/cm²	50 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 7.6–7.9	biorelevant media	fagan2025 C36, C8
HPMCAS LF, MF, HF slurries in water	pH 4.52, 4.61, 4.73	overnight stirring	bapat2025a M3, M4, M5
25% loratadine–HPMCAS-MF on a cited gel-pH axis 6.0, 6.2, 6.3	release ≈0.12, 0.29, 0.68 mg/min/cm²	three 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
telaprevir, single bile salts	systems with micelles and a drug-rich phase are called probably the most relevant in vivo and need lecithin mixed micelles	pH 6.5, 37 °C	[lu2017 C42]
FaSSIF-V1, Composite-SIF	unimodal 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 lecithin	induction time about 595 → 43 min; amorphous solubility 38 → about 82 µg/mL	pH 6.5, 37 °C	indulkar2018 R16, R6
atazanavir, volunteer media with 350 µM phospholipid	bile salt:phospholipid 1.6–14.7; 23–33 against 112–144 min	pH 6.5, 37 °C	[enright2020 R18, E2]
posaconazole, FaSSIF-V1 against FaSSIF-V2	more lecithin gives higher amorphous solubility and Km/w for posaconazole, not for atazanavir	biorelevant 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
amorphous felodipine film	nucleation ≈1.4 × 10⁵ → 2.9 × 10⁶ m⁻³ s⁻¹	0 → 75% RH, 22 °C	konno2008 R1.a, R3.a
amorphous nifedipine film	nucleation ≈4.7 × 10⁵ → 6.8 × 10⁶ m⁻³ s⁻¹	0 → 75% RH	[marsac2008a R1.a]
amorphous felodipine film	growth ≈0.030 → 0.066 mm/min (13–80% RH), 2.3–2.8 mm/min at 87–93% RH, with needles	humidity stage, 25 °C	[rumondor2010 R1, C9]
felodipine–PVP 25% powder	1.2% (0% RH) to 82.1% (93% RH) crystallized after ≈494 days	22–25 °C	rumondor2009b R9.a, R9.g
felodipine–HPMCAS 50% powder	9.2–16.6% at every RH after ≈490 days	22–25 °C	rumondor2009b R9
felodipine–PVP 50% film	crystals by 4 h at 94% RH, after phase separation	AFM, polarized light	marsac2010 R19, C24
FTM–HPMCAS spray-dried dispersion (outside)	faster crystallization at 82% than at 75% RH	40 °C, SHG	correasoto2017 C15
Accord tacrolimus capsules (outside)	rapid crystallization in the powder blend	40 °C/75% RH	purohit2019 C33
resveratrol with HPMC, HPMCAS, CMCAB, PAA	crystalline at the first sampling at 84% RH, then fully; PVP and E100 not	25 °C	[wegiel2013b R12, R14, R16]
curcumin dispersions	at 84% RH: E100 > 350, cellulosics 75, PVP 22, neat 14 days	25 °C	[wegiel2014 R13]
indoprofen–PVP	separation at 54% RH, crystals from 75% (30% PVP) or 84% RH (50% PVP)	22 °C films	[rumondor2011 R11, R14]
lumefantrine–CAP 40:60 precipitated into water (9% water)	crystalline from the first day at 40 °C/75% RH; amorphous 3 months under vacuum	PXRD	[bhujbal2021 R4.a, R5, R10, C17]
tacrolimus generic capsule contents	≈36, 68 and 84.5% at 30, 35 and 40 °C/75% RH, ≈11% at 40 °C/54% RH, 4 weeks	open dish	trasi2017 R14
felodipine dispersions with PVP, HPMC, HPMCAS (cited)	no difference dry; HPMCAS ≈ HPMC > PVP at high RH	storage	konno2008a R18
flutamide and ezetimibe HPMCAS dispersions (Solid-state methods)	first storage time with detected crystallinity, by method	storage	correasoto2017 R1
tacrolimus capsules (Bioperformance)	% crystallized against storage time	storage	purohit2019 R1
resveratrol dispersions (storage, cited)	PVP, E100 stable; HPMC, HPMCAS, CMCAB crystallized at high RH	storage	[wegiel2015 R21]
indomethacin 60% with HPMC; EPO; EPO–HPMC	crystals within 5 days; within 5 days; amorphous beyond 100 days	40 °C/75% RH	xie2017 R26

Evidence table: moisture-induced crystallization.

Pitfalls and disagreements

The growth jump of felodipine above 80% RH has no counterpart in water uptake or Tg, and its cause is "currently unknown" [rumondor2010 C31, C33]. Bulk powder of pure amorphous felodipine crystallized within 12 days at 0% as well as at 93% RH, so at that resolution water made no difference rumondor2009b R12, X8. Whether crystallization follows the wet one-phase route or the phase-separated route changes how polymer content acts (no effect of PVP level at 93% RH) rumondor2009b C20, C21. For resveratrol the authors "do not fully understand" why humidity acted more than heat, and the contrast fails at 120 °C [wegiel2013b C40, X8]. In the precipitated lumefantrine series water content varies with the polymer, so the water effect is inferred [bhujbal2021 C51, C56]. A solid-state ranking under moisture need not hold in dissolution: HPMCAS and HPMC were alike in humid solids but HPMCAS dispersions gave far more supersaturation, and the authors suggest the inhibition mechanisms "may vary" with the amount of water konno2008a C33, C34.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ECP–HPMC / PVPVA films	featureless at 18% RH; domains at 35–50% RH; 20 µL water per mL of stock splits a 50% film	spin coated	li2017 R3, R5, R12
ECP–PVPVA after 97% RH, 7 days	net-like structures at 10–80% DL; F/N 0.10 (continuous) against 0.06	TEM-EDX	li2017 R19, R22
ECP–PVPVA powders after 24 h at 97% RH	two Tgs at 10–50% DL, one at 60–90%	modulated DSC	li2017 R24
ITZ–HPMC E3 films	domains at 40% and 20% RH, none at 7% RH; network after 24 h at 40 °C/75% RH	spin coated	mugheirbi2017 P13, R1, R3, R17
LPV–HPMC E5 films after 97% RH	irregular discrete and semi-continuous domains; continuous phase 173 ± 13 °C	nanoTA	li2019 R8, R14
felodipine–PVP at about 75% RH and above	drug-rich and polymer-rich amorphous phases	cited	rumondor2009b R24
telaprevir ASD films	dry nitrogen (RH below 18%) eliminates water-vapour-induced separation	cited	mosqueragiraldo2018b C11
LPV ASD powders with EC, HPMCAS, HPMCP	stayed one phase after 48 h at 97% RH	Tg	[li2018 R9, C40]
nifedipine-, pimozide-, droperidol–PVP	separated within 1 h at 94% RH; pimozide from 54% RH	dried films	rumondor2009c R7, R9, R10, R12
indomethacin-, ketoprofen–PVP	one phase for 40 and 68 days at 94% RH	same	rumondor2009c R14, R16
felodipine–PVP	small change at 33–58% RH, distinct at 75% RH, amorphous-felodipine-like after 94% RH	1 day–1 week	marsac2010 R7, R11
felodipine with 25% HPMCAS or HPMC	no change after 7 weeks at 75% RH	dried films	konno2008 R11
same drugs with PVP, PVPVA, HPMCAS	extent follows polymer hygroscopicity, PVP > PVPVA > HPMCAS	IR band loss, DSC	[rumondor2010c C38, C33]
20 drug–polymer systems	HPMCAS dispersions less susceptible in general; PVP highly vulnerable	classes	[rumondor2011 C29]
miconazole–PVPVA 50:50	1–3 µm drug-rich domains after 7 days at 75% RH; 4–25 µm domains within 5–30 min in buffer	confocal, AFM-IR	[saboo2017 R15, R18, R19]
celecoxib–PVP 6:4	two Tg events after 3 days at 94% RH, not after 75% RH	DSC	[xie2016b R18, R19]
ritonavir–PVPVA 30:70 with surfactants	SDS and Tween 80 delay visible separation; Spans speed it and coarsen the domains	confocal at high RH, 37 °C	[yang2022b R5, R6, R7, R8, C7]

Pitfalls and disagreements

The water content of films and solutions was not measured in the film studies, so "moisture" is inferred from humidity and added water li2017 X14; mugheirbi2017 X4. The water-uptake explanation of the DL effect on storage separation rests on powders after 24 h, not on films li2017 X8. Whether a dry film is miscible or kinetically trapped is open li2017 C43. The effect of water reverses with PrOH and BuOH mugheirbi2018 C12. In the drug–PVP storage study, two-phase evidence in the wet state exists only for pimozide; for nifedipine and droperidol it rests on IR of re-dried films and sorption rumondor2009c X10. Donor type, carbonyl red shift and drug–water χ split the drugs the same way rumondor2009c X13. Class labels per system ignore that resistance depended on drug loading [rumondor2011 X13, C38]. The pattern depends on how water arrives: humid air gives drug-rich droplets in a polymer-rich matrix, bulk water a coarser connected structure [saboo2017 C46].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
amorphous nifedipine, felodipine	τ 6.3 and 4.2 h at 23.5 °C; nucleation 2–4 times faster for nifedipine	dry	[marsac2006a R4.n, C13]
felodipine with 3 wt% PVP K-12, K-29/32, K-90	melt viscosity ≈58, 156, 690 Pa·s vs ≈44 Pa·s alone	100 °C	[kestur2010b R10.c]
amorphous felodipine films	growth follows AGV mobility to the power 0.5	13–75% RH	[rumondor2010 R7, C27]
pimozide–PVP	moisture-induced separation much slower at 4 °C than at 22 °C	75% RH	rumondor2009c R11, C41
ketoprofen–PVP	wet Tg −23 °C, mobile, yet no separation	94% RH	rumondor2009c R25, C38
coated ASD powders (outside)	crystallization onset linked to Tg − T at the storage condition	40 °C	moseson2022a C24, C25
ritonavir ASDs (outside)	Tg only a crude indicator of mobility	degradation study	alvarenga2022 C21
celecoxib with miscible surfactants	main effect "most likely" on mobility	Tg-scaled growth	mosqueragiraldo2014 C30
felodipine free surface	faster growth "may be attributed" to mobile surface molecules	films	kestur2013a C16

Evidence table: molecular mobility.

Pitfalls and disagreements

Bulk mobility measures did not rank crystallization: DSC relaxation may not describe "the motion involved in nucleation", viscosity "cannot be used as a precise measure" of drug mobility, and growth outran AGV mobility [marsac2006a C37; kestur2010b C24; rumondor2010 C26]. Mobility sets the rate of moisture-induced separation but does not cause it rumondor2009c C35, C41; li2017 C44. Tg did not rank polymers for acetaminophen, flutamide, resveratrol or curcumin [trasi2012a C18; trasi2012b C33; wegiel2013b C33; wegiel2014 C22].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

monolayer coverage

The amount of adsorbate that covers a surface with one layer

Two meanings are used in the library, and the papers say they must be told apart dening2019 C44. The geometric (theoretical) monolayer is the drug that would cover the whole specific surface area of a carrier with flat-lying molecules, each occupying the area of its two largest dimensions dening2018 E3, C17; hate2020a E2, C20; mccarthy2020 E3, P11. The BET monolayer Q_m is the first-layer capacity fitted to an isotherm measured from water; Dening and co-workers read it as the silanol sites occupied in the presence of co-adsorbed water ("it is feasible") dening2019 R6, C41. Outside silica the same geometric idea gives the surfactant needed to cover the surface of drug-rich nanodroplets correasoto2022a E2.

Findings

F2, F1, F10, F11.

Related concepts

obtained from an adsorption isotherm through the BET isotherm; contrasts with multilayer adsorption; sets the scale for drug loading of silica; related to nanoconfinement.

Formulas

theoretical monolayer adsorption capacity, liquid-phase BET isotherm.

How it is measured or obtained

Geometric: specific surface area (586 m²/g for SBA-15, as supplied) times 10^{20} times the molar mass, divided by the contact area and Avogadro's number, with the contact area from molecular dimensions measured with Mercury on a crystal structure dening2018 E3, P3, M3; hate2020a P15; mccarthy2020 P11. BET: nonlinear fit of a liquid-phase BET equation to an isotherm by solution depletion dening2019 P12; mccarthy2020 P17; hate2020a P16.

Values in the library

material	value or class	conditions	paper ids
ritonavir on SBA-15	geometric 0.253 g/g (printed "25.3% w/w"); BET 103 mg/g	18.2 × 15.2 Å; pH 6.8 phosphate, 37 °C	dening2018 R4; dening2019 R6
atazanavir on SBA-15	geometric 278 mg/g (about 28% w/w); BET 4.5 mg/g	17.53 × 14.07 Å; 300 µg/mL silica, HPMC	hate2020a R1, R3
indomethacin on SBA-15	geometric 0.287 g/g; BET 29 mg/g	13.0 × 9.4 Å; pH 2.2, HPMC	mccarthy2020 R16, R10
indomethacin methyl ester on SBA-15	geometric 0.269 g/g (0.260 recomputed); BET 31 mg/g	13.9 × 10.0 Å	mccarthy2020 R16, R10, X19
ketoconazole, clozapine, atazanavir on SBA-15	BET Qm 0.006–0.275, unit printed "mg/mol"	pH 1–6.8, HPMC	hate2020b R21, X9
clopidogrel nanodroplets, nonionic surfactants	calculated monolayer agrees reasonably with the effective concentration	phosphate buffer, 37 °C	correasoto2022a R24, C41

Evidence table: monolayer coverage.

Pitfalls and disagreements

The BET values from water are 2.5 to about 60 times below the geometric values (synthesis: 253/103 and 278/4.5) dening2018 R4; dening2019 R6; hate2020a R1, R3. Whether adsorption is "multilayer" depends on which monolayer is meant: indomethacin exceeded its BET value tenfold but its geometric value only at the top points mccarthy2020 X10. The geometric value is quoted in g/g silica and as % w/w of the formulation as if equal; 0.253 g/g is about 20.2% w/w on a drug-plus-silica basis dening2018 X4; mccarthy2020 X4; hate2020a X4. The geometric value assumes the whole surface accessible and a flat orientation; no paper measured coverage directly dening2018 C17, C38. The BET form assumes a homogeneous surface without lateral interactions, which silica is not dening2019 C14, C15. The geometric monolayer marked where ritonavir flux fell with loading, and the BET value matched the ritonavir release floor dening2018 C38; dening2019 C32.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

multilayer adsorption

Adsorption beyond one layer of adsorbate on the surface

In the mesoporous-silica papers it is inferred when the isotherm exceeds a monolayer and models that allow more than one layer fit better than Langmuir; it is read as driven by supersaturation and as ending in partial pore filling near the amorphous solubility dening2019 C11, C13, C45; mccarthy2020 C43, C44; hate2020a C25.

Findings

F2, F3.

Related concepts

contrasts with monolayer coverage; modelled by the BET isotherm and Freundlich isotherm; read from an adsorption isotherm; related to nanoconfinement through pore filling near the amorphous solubility.

Formulas

liquid-phase BET isotherm, Freundlich isotherm.

How it is measured or obtained

Comparison of the isotherm with the geometric or BET monolayer; fit quality of BET and Freundlich against Langmuir; the pyrene I_1/I_3 ratio of a solution in contact with silica below the LLPS concentration dening2019 R2, R3, R6, R7; mccarthy2020 R7, R8, R10, R6.

Values in the library

material	value or class	conditions	paper ids
ritonavir on SBA-15	up to 424 mg/g against 253 (geometric) and 103 mg/g (BET)	pH 6.8, 37 °C	dening2019 R2, R3, R6
ritonavir + SBA-15	pyrene I_1/I_3 1.83 against 1.91 in buffer (p = 0.054)	30 µg/mL drug, 12.5 µg/mL silica	dening2019 R7
indomethacin; methyl ester on SBA-15	about 289; 342 mg/g against 287; 269 (geometric) and 29; 31 mg/g (BET)	pH 2.2, HPMC	mccarthy2020 R7, R8, R16, R10
indomethacin; methyl ester + SBA-15	pyrene I_1/I_3 1.72; 1.88 against 2.00 with silica alone	sub-LLPS drug	mccarthy2020 R6
atazanavir on SBA-15	"possibly" beyond the 4.5 mg/g BET monolayer	300 µg/mL silica	hate2020a C25, R3

Evidence table: multilayer adsorption.

Pitfalls and disagreements

Whether the top points are multilayers depends on the monolayer used: against the geometric value indomethacin and its ester are at or only modestly above one layer mccarthy2020 X10. The pyrene test was not significant and would also give a drop if pyrene entered a single adsorbed layer dening2019 X11; the indomethacin test lacks drug-alone controls at the same concentrations mccarthy2020 X11. The proposed change of mechanism at Q_m is not supported by the adsorbed fraction, which is already constant below it dening2019 C31, X10.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

nanoconfinement

The state of drug held in pores a few nanometres wide, where in the literature view it resists crystallization, especially below the critical nucleus size, has a lower melting temperature and is held by the pore wall hate2020a C38; hate2020b C2; dening2018 C7. In the papers it is inferred from the absence of a glass transition, melting and diffraction in drug-loaded SBA-15 (7.1 nm pores) hate2020a C4; hate2020b C15. Dening and co-workers also invoke confinement for adsorption from solution: by analogy with capillary condensation, filling the pores is expected to be more favourable than LLPS in the bulk ("we believe") dening2019 C45.

Findings

F1, F3, F11.

Related concepts

limited by drug loading relative to monolayer coverage; read from the absence of a glass transition temperature and of crystallization; related to drug-silanol hydrogen bonding at the pore wall.

Formulas

theoretical monolayer adsorption capacity (sets the loadings).

How it is measured or obtained

PXRD of loaded silica against a crystalline physical-mixture control; modulated DSC for a glass transition and melting; TGA degradation temperature; ATR-FTIR of carbonyl and isolated-silanol bands; a series of loadings around the calculated monolayer hate2020a P3, P4, P5, P6, M10; mccarthy2020 P12, P13; dening2018 P4, P5.

Values in the library

material	value or class	conditions	paper ids
atazanavir in SBA-15, 5–20% w/w	no glass transition or melting	MDSC 2 °C/min	hate2020a R9
atazanavir in SBA-15, 30 and 50% w/w	glass transition near 105 °C and melting near 208 °C; 50% crystalline after 1 week	MDSC; storage dry, room temperature	hate2020a R9, R8
ketoconazole, clozapine, atazanavir, 20% w/w	X-ray halo, no thermal events	PXRD, DSC	hate2020b R6
ritonavir in SBA-15, up to 38.1% w/w	no crystalline peaks	XRPD	dening2018 R26
indomethacin; methyl ester in SBA-15	amorphous at 25–50% of monolayer; peaks from 75% and 100%	PXRD	mccarthy2020 R19

Evidence table: nanoconfinement.

Pitfalls and disagreements

Confinement is inferred from absences: the location of the drug inside or outside the pores was not measured hate2020a C39. The XRPD control with 5% crystalline drug showed only one weak peak, so low levels of crystals are missed hate2020a X5. The degradation temperatures did not fall in order of loading hate2020a X6. Broad DSC rises near 100 °C in two 20% w/w traces were not discussed hate2020b X13. Atazanavir at 30 and 50% w/w was X-ray amorphous but showed a glass transition and melting hate2020a R7, R9.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

nanodroplet agglomeration

Evidence table: nanodroplet agglomeration (names merged there: droplet agglomeration, nanodroplet agglomeration). Content from the release-mechanism chapter (2023–2024), with a row from the Bioperformance chapter.

The joining of drug-rich droplets into clusters or networks

In the 2024 PVP molecular-weight paper droplets that formed in the gel of short-chain PVP dispersions joined into strands anchored in the gel near the gel–solution boundary and stayed there while the polymer left, a release failure the authors name "Failure Mode I", distinct from phase inversion [deac2024a R10, C26, C38]. In the 2023 surfactant study Tween 80 let ritonavir droplets agglomerate at the gel surface and leave as chunks, which "could potentially explain" slower release yang2023 R10, C20. In the Bioperformance chapter atazanavir droplets with PVPVA agglomerated in solution during a dissolution–absorption run hate2018 C27.

Findings

Release mechanism and LoC: F29, F31, F16, F20, F25.

Related concepts

prevented, in the authors' hypothesis, by polymer chain entanglement above the critical entanglement molecular weight; not prevented by steric stabilization in dilute solution; contrasts with phase inversion as a cause of the limit of congruency; acts on drug-rich nanodroplets.

Formulas

none.

How it is measured or obtained

Confocal imaging of dye-labelled humid films and of the edge of dissolving compacts [deac2024a P10, P8; yang2023 P7, P8]; DLS size and PDI in solution hate2018 R20.

Values in the library

material	value or class	conditions	paper ids
clotrimazole–PVP K12 10%	droplet strands by 11 h; network at the gel–solution boundary within 2 min	100% RH films; in situ compact edge	[deac2024a R7, R10]
clotrimazole–PVP K29/32 10%	no agglomeration (films, 11 h; compact, >7 min)	same	[deac2024a R7, R10]
ritonavir–PVPVA + Tween 80, 30%	droplets agglomerated in the gel, released as chunks	compacts, confocal	yang2023 R10
atazanavir solution with PVPVA (Bioperformance chapter)	≈245 nm to ≈10000 nm over 105 min	DLS	hate2018 R20

Pitfalls and disagreements

Agglomeration in the gel was imaged for one short grade, at a loading other than the one released, and inferred for two others [deac2024a X7, X11]. Droplet growth in dilute solution did not differ with the PVP grade, so solution tests do not predict agglomeration in the gel [deac2024a R5, C44].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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.

material	value or class	conditions	paper ids
clotrimazole 10 / 15 / 20 µg/mL	steady period 1 / 5 / at least 13 h	16 h flow-through	indulkar2016 R6, X5
clotrimazole + 7.5 mg/mL 150–250 µm particles	no reservoir (0.63 to 0.42 µg/mL)	5 h	indulkar2016 R7
atazanavir 90:10 ASDs	receiver above AS level 120 min; 4 h: about 200 min	hollow fibre	hate2018 R13, R21
posaconazole ASDs (FaSSGF)	longer supersaturation at higher dose, "most likely" reservoir	two doses	elkhabaz2019a C48
ritonavir on SBA-15	no reservoir at the amorphous solubility without excess drug		dening2018 C44
ritonavir–SBA-15, 400 and 1000% dose	about 24 µg/mL, about 85% of the amorphous solubility; no drug-rich phase by dissolution	pH 6.8	dening2018 R22, C32
10% atazanavir–SBA-15 against 10% HPMC ASD	donor about 48–57 against up to about 207 µg/mL with LLPS; receiver about 4.3–5.2 against 10.2–11.6 µg/mL	200 µg/mL, absorptive	hate2020a R24, R25
atazanavir, clozapine, two HPMCAS grades	Cmax keeps rising above the amorphous solubility with approximately parallel slopes	hollow fibre, 37 °C	ueda2020a R10, C26, C27
atazanavir, PAMPA with 2% SDS receiver	mass flow 5.0 to 8.8 µg/min between 80 and 1000 µg/mL; estimated interface concentration near a plateau at 400 µg/mL	lipid-impregnated hydrophobic PVDF	hate2022 R19, C61
enzalutamide in rats	aggregate-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 LLPS	same maximum flux, read as the maximum transport rate	25 °C	jackson2015 C39, C32
indomethacin EPO–HPMC 3:5:2 dispersion	apparent ≈93.5 → ≈43 µg/mL within ≈2 min of the shift; 39.1 of 40 µg/mL at 3 h	pH 2.2 → 5, 37 °C	xie2017 R10, R20
posaconazole–HPMCAS 10% dispersion, two doses	the same peak near 20 µg/mL; desupersaturation about an hour earlier at one-fifth of the dose, with fewer droplets	FaSSGF → FaSSIF, 37 °C	elkhabaz2019a R12, R6, R14
delamanid salt dispersions during release	stable drug-rich nanodroplets, smaller with HPMCP than with HPMCAS	PBS pH 6.5, 37 °C	duong2022a R25
ledipasvir–PVPVA 5%; with poloxamer 407; 7.5% with SDS	≈225–257; ≈96–130; ≈60–63 nm	DLS, 10–60 min	que2019 R12
TIPP, Me-TIPP; PHPH, Me-PHPH	colloids 179–193; 348–364 nm	DLS, 30 min	[que2021 R22]
clopidogrel droplets	stable with 4–50 µg/mL SDS, TPGS or Tween 80 for 4 h	DLS	correasoto2022a R6

Pitfalls and disagreements

The claim that a colloidal drug-rich phase is favourable for absorption rests on literature and argument ("likely") indulkar2015 C55, X15. A plateau of flux shows constant activity but not resupply trasi2015a C14. The Amorphous solubility papers of 2013–2016 treat the effect as untested, whereas the flow-through experiments of indulkar2016 follow resupply by the length of the steady receiver period indulkar2016 R5, R6; so it is untested only in the former. In the Bioperformance papers depletion times were back-calculated in a way that does not match a mass balance indulkar2016 X3; droplet dissolution speed was estimated, not measured indulkar2016 R18; with mesoporous silica the effect "may not occur" hate2020a C54. The interface concentration of the PAMPA study is derived from mass flow anchored at 75 µg/mL, so the 1000 µg/mL point equals 75 by construction and the plotted values still rise from about 64 at 400 to 75 at 1000; no interface concentration, layer thickness or droplet dissolution rate was measured, so the mechanism is an interpretation (F22) hate2022 X7, X8. The rat difference rests on one aggregate-forming ASD that also dissolved fastest (F23) wilson2018 X14. Mesoporous silica: at the tenfold ritonavir dose, flux equalled that of amorphous ritonavir while dissolution through a filter that passes the droplets gave about 85% of the amorphous solubility, so whether the LLPS concentration was reached is unresolved dening2018 X14, C33. The method used to look for nanodroplets in the acid-first atazanavir run is not described and its data are not shown hate2020a C54, R23. In the ASD dissolution papers, for ritonavir the droplets "appear" to promote crystallization, the opposite of a stabilizing role ilevbare2013d C41. Danazol transport was measured across a dialysis-type membrane only, without absorption data jackson2015 X12. The posaconazole reservoir was inferred from the dose effect; neither the undissolved amorphous drug nor the droplet mass was measured over time elkhabaz2019a X8. The three colloid-forming formulations differ in loading and release rate, so the size difference cannot be assigned to the surfactant alone que2019 X11. No flux or absorption was measured in these papers [que2019 C54; que2021 C37].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

NMR chemical exchange broadening

The widening of the NMR peaks of a species that moves between two environments, here ibuprofen exchanging between the aqueous phase and the drug-rich phase. The dissolved-ibuprofen peaks stay sharp in saturated polymer solutions and in buffer with droplets, and broaden only when a drug-rich phase that contains polymer is present [ueda2021 R1, R9, C9]. The authors attribute this to lifetime broadening by exchange with a mobility-suppressed, polymer-loaded phase with faster spin–spin relaxation, and not to solution viscosity [ueda2020b C24; ueda2021 C9; ueda2022 C14].

Findings

F15.

Related concepts

used to read the drug-rich phase and polymer partitioning into the drug-rich phase.

Formulas

none.

How it is measured or obtained

Line shape of the aqueous-phase peaks of the drug (H4, H5 or H5, H6) after Lorentzian decomposition at 37 °C or at 15–60 °C; widths are described qualitatively and were not tabulated [ueda2020b P4; ueda2021 P3; ueda2022 P4].

Values in the library

material	value or class	conditions	paper ids
dissolved ibuprofen with HPMC, PVP-VA	sharp below the amorphous solubility, broad above it; narrower and resolved again during stirring as PVP-VA droplets leave	pH 2.0 (D2O), 37 °C	ueda2020b R3, R10, R14
dissolved ibuprofen with six polymers	broadened most with HPMC and PVP-VA; positions unchanged	1000 µg/mL polymer, 400 µg/mL drug	[ueda2021 R3]
dissolved ibuprofen, 15–60 °C	broader in PVP-VA and HPMC solutions than in PVP solution	1000 µg/mL polymer	[ueda2022 R5]

Pitfalls and disagreements

The exchange rate and the relaxation rates were not measured; the authors say the mobility suppression "also appears to contribute" [ueda2020b C24; ueda2021 C17]. The polymer-induced downfield shift of the drug-rich peaks reduces the shift difference, and mobility suppression in the drug-rich phase strengthens the lifetime broadening, so both enter the explanation [ueda2021 C9].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

non-centrosymmetric crystal structure

A crystal whose structure has no inversion centre

Only such crystals, surfaces and interfaces produce coherent second harmonic generation; liquids, glasses, solutions and centrosymmetric crystals do not kestur2012 C4; correasoto2017 C7. Chirality of the molecule is not required: flutamide is not chiral but crystallizes as form I in the non-centrosymmetric space group Pna2₁ correasoto2017 C8, M1.

Findings

F5, F9, F11.

Related concepts

required for second harmonic generation; related to polymorphism and preferred orientation.

Formulas

none.

How it is measured or obtained

From the crystal structure or literature (space group); indirectly, by the presence of SHG from a known crystalline sample correasoto2017 M1; wanapun2010 R13. SHG is a selection criterion for model drugs correasoto2017 M1, M2.

Values in the library

material	value or class	conditions	paper ids
griseofulvin	intrinsically chiral, "strongly favours" an SHG-active space group	melt-quenched films	wanapun2010 C23
chlorpropamide	α (P2₁2₁2₁) and γ (P2₁) SHG-active; β (Pbcn) and δ (Pbca) SHG-inactive	four known polymorphs	wanapun2010 R13
flutamide	form I Pna2₁; metastable form II converts to form I as soon as it forms	cited	correasoto2017 M1, C8
ezetimibe	three stereocentres, expected to crystallize in an SHG-active space group; crystals less bright than flutamide (laser raised from 50 to 250 mW)	HPMCAS dispersions	elkhabaz2017 C8; correasoto2017 R17
crystalline chiral excipients	can interfere with the drug signal		kestur2012 C37

Pitfalls and disagreements

A dark SHG image means no SHG-active crystals above the limit, not no crystals; polymorphs of one drug can differ in activity (chlorpropamide), and the ezetimibe crystal form and space group are not printed in the SHG paper wanapun2010 X11; correasoto2017 M2.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
IDM–PVPVA extrudates	C720 about 43.1 → 28.8 µg/mL with 0 → 25% crystalline drug	50 µg/mL total dose, pH 4.5, 12 h	moseson2020a P9, R6
BCL–PVPVA 30:70	fraction 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 granules	RTV about 4 µg/mL in the co-granule against about 30 alone	250 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 solubility	pH 4.5, 37 °C, 300 rpm	trasi2017 R3, C12
tacrolimus generic capsules (outside)	the more non-sink tests (100 and 40 mL) discriminate crystallinity better than larger volumes	USP and non-pharmacopeial media	purohit2018 C57
BCL–PVPVA 5 / 10 / 20 / 30 / 50% DL powders	end level about 91 / 96 / 88 / 86 / 73% of the dose	dose of at most 30 µg/mL, pH 6.8, 4 h	moseson2022b R6
BCL–PVPVA 30% DL, cryomilled 2 and 5 min	about 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 min	pH shift at 60 min, dose about 200 µg/mL	shah2024 R12, R14
PCZ–HPMCAS 25% DL coated 11–39 nm, pH 6.5	about 90% of the dose in 10–20 min	dose 8 µg/mL	[moseson2023 R9]
ezetimibe–HPMCAS 50% DL, uncoated / thin / thick	peak about 14.0 / 12.5 / 10.1 µg/mL fresh; at 12 months about 5.6 against 12.4 and 11.1 µg/mL	10 mg in 50 mL, pH 6.5	duong2022c R13, R23
ezetimibe ASDs	7.5 mg in 15 mL, about 500 µg/mL	buffer, FeSSIF, Ensure Plus	elkhabaz2017 P7
ritonavir, atazanavir PVP ASDs	150 mg in 15 mL, 120 min	pH 6.8	alhalaweh2016 P10
atazanavir ASDs	200 µg/mL in 50 mL	closed vessel	hate2018 P8
tacrolimus capsules	5 mg in 900 / 450 / 100 / 40 mL	medium I	purohit2018 P7, P8
tacrolimus (Accord)	maximum 45 µg/mL within 40 min, about 25 µg/mL at 2 h	one capsule in 100 mL	trasi2017 R3, C12
tacrolimus 5 mg in 240 / 100 / 40 mL	maximum donor concentration about 21 / 50 / 125 µg/mL; sink index against the amorphous solubility 2.4 / 1 / 0.4	absorptive hollow-fibre test	hate2019 R7
tacrolimus capsule contents	5 mg in 100 mL, pH 4.5, 50 µg/mL HPC, 300 rpm	USP-type test 1 medium	purohit2019 P5, E3, C35
enzalutamide ASDs	100 µg/mL total in 12.5 mL, pH 6.5, 300 rpm	closed vessel	wilson2018 R6
felodipine dispersions, 10–75% PVP, HPMC or HPMCAS	30 mg in 600 mL (50 µg/mL nominal); maxima 0.8–14.1 µg/mL	pH 6.8, 37 °C, 50 rpm	konno2008a P3, R10, X15
neat amorphous felodipine	100, 500 and 1,000 µg/mL; plateau ≈0.9–1.1 µg/mL, like the crystal	pH 6.8, 37 °C	alonzo2010 P2, R1
neat amorphous indomethacin	300 µg/mL; peak ≈14.9 (25 °C) and ≈11.2 µg/mL (37 °C)	pH 2	alonzo2010 P3, R7
HPMC–felodipine 90:10 and 50:50	30 and 150 µg/mL nominal; UV ≈27 and ≈8.9 µg/mL	18 mL, 37 °C	alonzo2011 R1
danazol films, three polymers, three loadings	20–30 µg/mL nominal; free drug 5.4–9.1 µg/mL	pH 6.8, 25 °C	jackson2015 P1, R9
ritonavir and lopinavir 20% dispersions	20 mg in 40 mL	pH 6.8, 25 °C	trasi2015b P5
celecoxib dispersions with PVP, HPMCAS, HPMC, PAA, 10–60% drug	22 µg/mL nominal (= amorphous solubility) in 400 mL	pH 6.8, 37 °C, 16 h	xie2015 P5; xie2016a P5
six marketed tacrolimus capsules	5 mg in 40 mL (125 µg/mL nominal); plateau ≈46–50 µg/mL	pH 4.5, 37 °C	trasi2016 P11, R10
indomethacin dispersions and crystals	4 mg in 50 mL (80 µg/mL), then 100 mL (40 µg/mL)	pH 2.2 → 5	xie2017 P7
lopinavir films, 15–85% drug	2 mg solids in 10 mL, 48 h	pH 3, 25 °C	[li2018 P4, P5]
paclitaxel–HPMCAS 49/51 dispersion	dose set to reach the amorphous solubility (31.6 µg/mL) in 15 mL	pH 6.8, 37 °C, 16 h	que2018 P8, R1
posaconazole–HPMCAS dispersions and Noxafil powder	400 µg/mL in the gastric stage, 200 µg/mL after transfer, ten times the amorphous solubility	FaSSGF pH 1.6 → FaSSIF pH 6.5, 37 °C	elkhabaz2019a P6
delamanid dispersions and tablets	100 µg/mL at full release, about 100 times the amorphous solubility at pH 6.5	PBS pH 6.5 or pH 1.6 → 6.5, 37 °C	duong2022a P16
praziquantel dispersions	667 µg/mL and 1.5 mg/mL against an amorphous solubility of 1.1–1.4 mg/mL	PBS pH 6.5, 37 °C	polyzois2024 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
acetaminophen	nucleation zone 50–60 °C, where growth is ≈0.04–0.23 µm/s against ≈45 µm/s at 100 °C	DSC and hot stage	trasi2012a R12.a, R8.a, C39
acetaminophen with PAA or HPMCAS	PAA slows growth most but gives most nuclei; HPMCAS the reverse	10% w/w	trasi2012a C46
flutamide with PVP or nilutamide	PVP slows growth about tenfold without a nucleation effect; nilutamide nearly stops nucleation	10 mol%	[trasi2012b C7, R11.e, R12]
felodipine powders with 3% PVP	early crystallization 60–77-fold slower; surface and bulk growth ≈2- and ≈7-fold	30 °C	[kestur2013b R15, R12, C34]
miconazole–PVPVA films after humid casting or storage	discrete drug-rich domains in a polymer-rich matrix, read as separation by nucleation and growth ("may occur")	confocal, AFM	[saboo2017 C40]
ritonavir–PVPVA films with SDS or Tween 80 vs binary and Spans	nucleation and growth vs spinodal decomposition, read from the first morphology	confocal	[yang2022b C55]
tacrolimus generic	fall in concentration after 40–50 min read as growth on seeds present before storage ("some evidence")	dissolution, 100 mL	trasi2017 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
celecoxib; efavirenz; ritonavir, no polymer	about 2.4; 5.1; 120 min	at the calculated amorphous solubility, 37 °C	ilevbare2013c R8, R9.a
ritonavir, CAB Adp 0.81; efavirenz, CAB Adp 0.81; celecoxib, HPMC	about 244; 28.0; 12.6 min	5 µg/mL polymer	ilevbare2013c R9
celecoxib at 11 µg/mL, none against HPMC	27.5 ± 0.7 against 855.5 ± 6.0 min	S 7.3	ilevbare2013c R15
felodipine, none against 1 µg/mL HPMC	15.3 against 136.5 min	S 10, 25 °C	alonzo2012 R16
danazol, none; PVP; HPMC; HPMC-AS	6–10; 88–162; 111–285; 250–516 min	10–20 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 4,000	37 °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 HPMCAS	37 °C	que2018 R3
indomethacin S 6 (ASD process chapter)	about 40 min; more than 12 h with 5–50 µg/mL PVPVA	pH 4.5, 37 °C	moseson2020a R3
11 drugs, 0.1% STC and SDS, matched C/Ceq	buffer 7–87 min; STC 15 to >1000; SDS shorter for 7 of 9	25 °C, telaprevir 37 °C	chen2015 R3
acetaminophen, S 1.5	95% of vials 26 min; first crystals 150–785 s	20 °C	[trasi2015 R1, R10]
celecoxib, nevirapine, flibanserin, 13 bile salts	3 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 polymers	HPMC >700 and 243; none 14–15 min	pH 6.8, 37 °C	[mosqueragiraldo2016 R4]
telaprevir δ 11.5 and 28.8, six bile salts	30 min and immediate in buffer; >960 min with 1.86 mM	pH 6.5, 37 °C	[lu2017 R3, R4]
danazol 15 µg/mL, PVP, HPMC, HPMC-AS 1–1000 µg/mL	about 5 min; 26–412 min	25 °C	[jackson2016 R17]
atazanavir without additive, five protocols	about 40, 92–102, 170, 200, 253 ± 65 min	near the amorphous solubility, 37 °C	[mosqueragiraldo2018a R1; elkhabaz2021 R6; indulkar2018 R19; indulkar2019b R3; enright2020 R2]
posaconazole without additive, three protocols	about 5–8, 8.4, 29 ± 5 min	pH 6.5, 37 °C	[elkhabaz2021 R7; duong2022b R10; shah2025 R3]
enzalutamide without polymer	about 5–15 min, 30–120 µg/mL	pH 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
felodipine, 1 µg/mL HPMC	J/J_0 7.05 × 10⁻⁴ ("more than a thousand fold"); induction 15.3 → 136.5 min	S 10, 25 °C	alonzo2012 R16, R17, C38
ritonavir; efavirenz; celecoxib, best polymer	120 → 244; 5.1 → 28.0; 2.4 → 12.6 min	5 µg/mL	ilevbare2013c R9, R12
celecoxib at S 7.3, HPMC	27.5 → 855.5 min (31-fold)	5 µg/mL	ilevbare2013c R15
celecoxib, 5 µg/mL HPMCAS (ASD dissolution chapter)	J_0/J_p about 4,000	22 µg/mL drug	xie2016a R13
paclitaxel, HPMCAS (ASD dissolution chapter)	"highly effective" at S 88	20 µg/mL polymer	que2018 R3, C13
indomethacin, PVPVA 5–50 µg/mL (ASD process chapter)	"highly effective" at S 6; stays supersaturated more than 12 h	pH 4.5	moseson2020a R3, C11
11 drugs, 0.1% STC	induction time lengthened for all, eight by more than 10-fold	25 °C	chen2015 R3, X6
telaprevir, 1.86 mM STC, SGC	relative 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 1.5	J lowered 18-fold (HPMCAS) and 36-fold (HPMC); raised 2.6-fold by PAA	10 µg/mL	[trasi2015 R3]
telaprevir, 1.86 mM binary and ternary bile salt mixtures	>960 min against about 30 in buffer; 3.72–5.58 mM mixtures about 255 min	δ 11.5, 37 °C	[lu2018 R3, R4]
nine drugs, 5 µg/mL A5a	atazanavir 40 → >300, telaprevir 15 → 91 min	pH 6.8, 37 °C	[mosqueragiraldo2018a R1]
celecoxib 22 µg/mL: no polymer; 5 µg/mL PVP-K12; PVP-K29/32; HPMCAS or HPMC	within 5 min; ≈1 h; ≈2 h; more than 8 h	pH 6.8, 37 °C	xie2015 R1
delamanid at 0.76 µg/mL with 300 µg/mL polymer	more than 1000 min with PVPVA, HPMCP and HPMCAS; about 50 min with HPMC; 10.2 min with Eudragit L100 against 10.7 min without polymer	PBS pH 6.5, 37 °C	duong2022a R4, R2
racemic praziquantel at 1.1 mg/mL with 300 µg/mL polymer	10.9 (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 run	PBS pH 6.5, 37 °C	polyzois2024 R3
R-praziquantel at 1.4 mg/mL	37 min (HPMCAS-MF) and 15.5 min (HPMC E5 LV)	PBS pH 6.5, 37 °C	polyzois2024 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
felodipine, 1 µg/mL HPMC	J/J_0 7.05 × 10⁻⁴ (text: more than thousand-fold; conclusions: factor of 1000)	S 10, 25 °C	alonzo2012 R17, C38, C46
celecoxib, 5 µg/mL HPMCAS	J_0/J_p about 4,000 (unseeded time taken as 960 min)	22 µg/mL drug, 37 °C	xie2016a R13
acetaminophen, S 1.5	J 1465 (none), 3820 (PAA), 81.86 (HPMCAS), 40.68 (HPMC) # m⁻³ s⁻¹	1.2 mL vials, 20 °C	[trasi2015 R3]
telaprevir with STC, SGC	J/J₀ 2.5 × 10⁻³, 2.9 × 10⁻⁶	δ 11.5	[lu2017 R10]
atazanavir, posaconazole, six media	SHG count rate about 0.1–1.6 and 0.05–48 counts/min	37 °C, relative per field	elkhabaz2021 R14, E5, X13
posaconazole, PBS and three media	J from induction times, fitted for A and γ	37 °C, S above about 7–13	[duong2022b R15, X10]
amorphous felodipine	≈1.3 × 10⁵ m⁻³ s⁻¹; ≈2–3 × 10³ with 3% PVP, HPMCAS or HPMC	0% RH, 22 °C	konno2006 R4
amorphous nifedipine vs felodipine	0.39 vs 0.17 × 10¹⁰ m⁻³ day⁻¹	0% RH, 22 °C	[marsac2006a R4.a]
nifedipine and felodipine with 7% PVP	≈1.4 × 10³ and ≈2.7 × 10² m⁻³ s⁻¹	0% RH	[marsac2006a R16.b]
felodipine with 3% PVP vs HPMCAS	≈8.6 × 10⁵ vs ≈1.3 × 10⁴ m⁻³ s⁻¹	75% RH, 22 °C	konno2008 R3.b
nifedipine vs felodipine with 25% PVP	≈4.3 × 10⁵ vs ≈2.3 × 10³ m⁻³ s⁻¹	75% RH	[marsac2008a R1.f, R1.l]
felodipine (activation energy)	145 kJ/mol below Tg; 201 with 3% PVP	Arrhenius, ≈25–75 °C	[marsac2006a R3]
griseofulvin melt (SHG imaging)	number density ≈45 → ≈600 mm⁻³ over ≈62–285 min	125 °C, SHG	wanapun2010 R17

Pitfalls and disagreements

The ratio rests on one pair of induction times without uncertainty and on a seeded ratio standing in for a seeded induction-time ratio; a 10% change in the polymer-case time changes J/J_0 about 1.5-fold alonzo2012 X7, C11. The printed inverse of 0.607 is 1.643 against 1.647, with J/J_0 7.05 or 7.06 × 10⁻⁴ alonzo2012 X6. The celecoxib value is a lower bound because no desupersaturation occurred within the experiment xie2016a R13. In the film papers absolute rates are per depth-of-field volume and comparable only within one counting method; in one paper Table II and two figures disagree about fourfold, and the felodipine-alone rate of that paper's Fig. 9 (≈3 × 10⁴) is about fourfold below the other papers' ≈1.3–1.4 × 10⁵ (synthesis) [marsac2006a X1; konno2006 R4.a]. The 2006 methods describe the area-to-volume conversion as multiplication where division is meant konno2006 X6. Site density rose roughly linearly, but early points can lie below the fitted line, so a short lag is not excluded konno2006 X8.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
nilutamide	strong zone near −30 °C; weaker rise from about 50 °C, about 30 °C above Tg	DSC; surface counts	[trasi2014b R5, R9, C41]
acetaminophen	50–60 °C	DSC	trasi2012a C22
flutamide	10–40 °C	DSC	[trasi2012b R10]
acetaminophen with 10% w/w HPMC, HPMCAS, E100, PVPh, PVPVA, PVP, PAA	10–60, 10–45, 40–60, 40–70, 30–60, 30–50, −10–30 °C	DSC cool–reheat	trasi2012a R12
acetaminophen with 15% w/w PVP, PAA, HPMCAS	no crystallization in the test	same	trasi2012a R12
flutamide with 10 mol% PDMA, PVAc, PVPH, PIPA, PVP	10–30, 20–40, 30–40, 20–30, 20–40 °C	same	[trasi2012b R10]
vemurafenib α	approximately 170–270 °C (inferred)	hot stage	[lu2016 C43]
indomethacin γ; α (cited)	maxima at about Tg and about 20 °C higher	literature	[trasi2014b R32]

Pitfalls and disagreements

The method passes the zone on both cooling and reheating, so the two contributions are not separated trasi2012a X9; the polymorph of the counted nuclei was not identified for nilutamide [trasi2014b X6]. Storage inside the zone gives high nucleation; a polymer that lowers the zone (HPMCAS for acetaminophen) "could potentially" still give more nuclei at room temperature than another polymer trasi2012a C47.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
nilutamide glass	≈12.6 nuclei per sample at −30 °C; ≈0.8–2.5 at −20 to 40 °C	30-min hold, open surface, 1 min growth at 65 °C	[trasi2014b R9]
acetaminophen	nucleation zone 50–60 °C	DSC cool–reheat	trasi2012a C22
acetaminophen with polymers	HPMCAS reduces nuclei to about a third; PAA gives nearly three times more	10% w/w	trasi2012a C23
flutamide	nucleation zone 10–40 °C	DSC cool–reheat	[trasi2012b R10]
nifedipine against felodipine	faster nucleation for nifedipine	pure films, 22 °C, 0% RH	[marsac2006a R1]
felodipine films	rate rises with storage RH; drug alone fastest	22 °C, with polymers	konno2008 C11
indomethacin polymorphs	δ fastest at 60 °C; α favoured at 80 °C; γ not readily (only from seeds); polymers retarded nucleation	amorphous films, storage at 60 and 80 °C	[tian2017 R1, R5, C7]
celecoxib	samples "quite hard to nucleate"	hot stage	mosqueragiraldo2014 R15
vemurafenib β	nucleation the limiting step above 150 °C (qualitative)	hot stage	[lu2016 C46]
pure nifedipine, felodipine against dispersions	nucleation much faster for the pure drugs	cited from a companion study	marsac2006b R16
indomethacin–PVP	nucleus requires breaking the PVP–drug bond (proposed, untested)	no crystallization data	[taylor1997 C43, X8]
flufenamic acid–PSSA, chlorpropamide–PSSA, lidocaine–PVP films	fully crystalline within 30 min of coating	spin coating	vaneerdenbrugh2010b R2.an, R2.s, R2.as
celecoxib; efavirenz; ritonavir	induction time about 2.4; 5.1; 120 min	at the calculated amorphous solubility	ilevbare2013c R8
felodipine, HPMC 1 µg/mL	J/J_0 7.05 × 10⁻⁴	S 10	alonzo2012 R17
danazol	6–10 min without polymer; 88–516 min with 10 µg/mL polymer	25 °C	jackson2014 R17
nine drugs with carboxylated cellulose derivatives	contact with the emerging nucleus "clearly a prerequisite" for disruption	5 µg/mL, pH 6.8	[mosqueragiraldo2018a C44]
amorphous felodipine	rate ≈1.4 × 10⁵ → 2.9 × 10⁶ m⁻³ s⁻¹	0 → 75% RH, 22 °C	konno2008 R1.a, R3.a
nifedipine vs felodipine	faster at every PVP level and RH	0–75% RH	[marsac2008a R1, C7]
felodipine with 50% HPMCAS	negligible crystals for 35–120 days at 52–93% RH, read as delayed nucleation	PXRD of powders	rumondor2009b R17, C29
flutamide with 10 mol% PVAc, PIPA	growth rate at the DSC exotherm maximum 7.7 and 7.0 against 4.4 µm/s, read as fewer nuclei	DSC and growth curve	[trasi2012b R11.b, R11.d, R11.f, C18]
flutamide with 10 mol% nilutamide	one nucleus in the imaged region	cooled to −30 °C, reheated	[trasi2012b R12, C16]
felodipine with 3% PVP	≈150-fold lower rate (cited)	30 °C	[kestur2013b R22, C35]
ritonavir 17 against 20 µg/mL (below and above LLPS)	induction about 284 against 119.3 min	pH 6.8, 37 °C	ilevbare2013d R16, R12
felodipine methanol shift with HPMC, S about 60	precipitation not completely suppressed	25 °C	alonzo2011 C30
nifedipine α in γ slurries with polymer	lag lengthened at similar slopes, read as α nucleation inhibition	25 °C	raina2014b C32

Pitfalls and disagreements

Nucleation is stochastic and often heterogeneous, which scatters crystallization temperatures [baird2010 C19; baird2013 C18]. Nuclei counts are not rates unless area and time are controlled [trasi2014b X7]. Polymers can act oppositely on nucleation and growth: HPMCAS was the best nucleation inhibitor but the weakest growth inhibitor for acetaminophen trasi2012a C46, and drug–additive hydrogen bonding correlated with growth inhibition but not with nucleation for flutamide [trasi2012b C45]. Classical nucleation theory does not capture molecular recognition or polymer effects trasi2012a C49. The role of the hydrogen bond in nucleation is argued, not tested [taylor1997 X8]. The growth-rate ranking of polymers says nothing about nucleation, which was not measured [kestur2010a X10; kestur2011 P3]. The film screen cannot separate crystallization during coating from crystallization during storage except through the day-0 score vaneerdenbrugh2010b R2. In solution, how additives slow nucleation is "more speculative" than how they slow growth, because the molecular events cannot be observed ilevbare2013c C9; the papers do not separate nucleation from early growth inside the induction time ilevbare2013c X14. The delayed-nucleation reading of the HPMCAS lag in stored felodipine powders assumes that growth below and above the detection limit follows the same factors rumondor2009b C28. Nucleation counts separated polymers at 33% RH that PXRD crystallinity could not separate within 490 days (synthesis) konno2008 R2.b; rumondor2009b R19. The flutamide nucleation verdicts rest on two Tmax values per sample and an unnamed test [trasi2012b X4]. Nuclei per cycle are not rates when the zones differ in width trasi2012a X8. The felodipine "nucleation then growth" reading rests on curves alone konno2008a X4; the ritonavir 17 µg/mL comparison has no n or SD and mixes droplets with a higher bulk supersaturation ilevbare2013d X18.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

oral bioavailability

The fraction of the dose reaching the circulation, F = F_a F_{gut} F_H purohit2018 E6. The papers up to 2018 measured none; the claims were expectations alhalaweh2016 C37; indulkar2016 C47; mosqueragiraldo2018b C58. Later papers give exposure in animals as AUC and Cmax (dogs, rats, monkeys) and, for pretomanid, a bioavailability relative to a reference product (F23, F26, F30) purohit2019 R9; wilson2018 R16; nguyen2023a R23.

Findings

F17, F23, F24, F25, F26, F30, F31.

Related concepts

assessed by virtual bioequivalence; related to in vitro–in vivo correlation. Also related to food effect (fed and fasted exposure) and endogenous crystallization (exposure of crystals formed in the product).

Formulas

F = F_a F_{gut} F_H is printed in words purohit2018 E6; see non-compartmental AUC, relative bioavailability and absolute bioavailability.

How it is measured or obtained

Simulated by a PBPK model for tacrolimus purohit2018 R12. Measured as AUC0–24 and Cmax in six beagle dogs after 1 mg of tacrolimus, with whole-blood LC-MS/MS purohit2019 R9; as AUC0–48 in rats wilson2018 R16; and in cynomolgus monkeys, fasted and fed, after 30 mg of pretomanid nguyen2023a R23.

Values in the library

material	value or class	conditions	paper ids
tacrolimus	simulated F 20.2% (observed 14.4–25%); Fa·Fgut 20.8% (14%); FH 97.1% (96.8%)	GastroPlus	purohit2018 R12
grazoprevir	about 1.8-fold AUC with hierarchical cPAD in dogs		[hiew2023 R16, C32]
tacrolimus capsules, dogs	AUC0–24 42.1 (fresh generic), 22.9 (50% crystalline), 21.6 (100%), 5.29 (reference crystals) ng·h/mL	1 mg, n = 6	purohit2019 R9, R11, C56
enzalutamide, rats	AUC0–48 about 770, 575, 575, 61, 91 µg·h/mL (10% copovidone, 50% copovidone, 50% HPMCAS, 10% HPMCAS ASDs, crystalline)	10 mL/kg gavage	wilson2018 R16
pretomanid, monkeys	relative bioavailability of the 20% HPMCAS-HF tablet 155% (fasted); fed exposure 72.2% of fasted for the ASD and 163% for the crystalline product (printed, dose-normalized)	30 mg, n = 4, crossover	nguyen2023a R23, R33, C50, C53

Pitfalls and disagreements

The simulated Fa·Fgut exceeds the observed value purohit2018 X3. The dog Cmax unit is printed as "(ng)" and the whole-blood concentration is not a plasma concentration purohit2019 R9. The exposure of the endogenously crystallized drug lay about four times above that of purchased reference crystals, so exposure depends on how the crystals were made (F30) purohit2019 R11, C56.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

particle breakage

Mechanical break-up of drug particles under the stresses of mixing, for example in the dispersive or kneading elements of an extruder; the authors expect it to add defects and dissolution surface, and suggest that defect stress fields may be the sites where breakage starts moseson2019 C45, C56. Clusters of randomly oriented 5–10 nm domains in an extrudate were first read as a "mechanical origin" moseson2018a R9, C14. In the bicalutamide population balance model breakage is a size-dependent selection function (critical size 5 µm, two equal-volume daughters, Gaussian spread 12.5%) scaled by each lot's percentage of agglomerates, and the fit needs it: dissolution alone left 26–73% crystallinity at 20 min [moseson2022c E7, E11, E17, R12, R16]. Mechanical stress at the screw elements is held to break the same weak sites as fragmentation by dissolution [moseson2022c C45, C51].

Findings

F12, F36, F37.

Related concepts

contrasts with fragmentation-based dissolution (a dissolution-driven source of fragments).

Formulas

population balance equation, breakage selection function.

How it is measured or obtained

Not measured directly in the ASD process papers; inferred from TEM clusters of similar fragments and from the absence of mechanical input in still films moseson2018a R11; moseson2019 R16.

Values in the library

material	value or class	conditions	paper ids
IDM extrudate	clusters of 5.8 ± 1.2 nm domains (n = 20)	TEM	moseson2018a R11
IDM crystals in still films	fragmentation without mechanical input	130 °C	moseson2019 R5, R16, C43
BCL in PVPVA at Tc, population balance model	breakage rate constant 0.355 ± 0.111 with breakage scaled by % agglomerates; dissolution only leaves 26–73% crystallinity at 20 min	four lots, 20 min	[moseson2022c R16, R12]

Pitfalls and disagreements

The 2018 TEM paper noted that "other explanations are also possible" given the high mechanical input of HME moseson2019 C5. Breakage in the extruder was not observed, and the supporting images are quiescent PLM at 170 °C [moseson2022c X9, X18].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

peptide-enhancer co-release

The release of an oral peptide and its permeation enhancer from one dosage form at the same rate, so that the two reach the epithelium together and at the same relative amounts as in the solid. Two names are used for it in the library: congruent or synchronous release, borrowed from amorphous dispersion work and judged by equal surface-normalized release rates of every component bapat2025b C3, C15, E1, and corelease or temporal synchronicity, judged by the times at which peptide and enhancer reach their maximum release from a tablet fagan2025 C44, C46, R20. The motive is cited rather than measured in both papers: a high local enhancer concentration is needed, the absorption window after the enhancer acts is short, and co-localization of peptide and enhancer at the absorption site is considered important and hard to achieve with a solid oral form, especially in the small intestine bapat2025b C8, C10. Co-release is a release property only; neither paper that measures it measured permeability, transport or absorption, so the benefit remains an expectation ("may improve co-localization at the epithelial membrane", "would likely result in incongruous presentation") bapat2025b C6; fagan2025 C45. Evidence table: peptide-enhancer co-release.

Findings

F4, F5, F6, F1.

Related concepts

the same criterion as congruent release applied to three components; ends at the loading boundary of limit of congruency and its failure is incongruent release; achieved here through polymer-controlled release from an eroding gel layer; depends on drug loading and on pH-dependent solubility of the peptide; intended to serve membrane transport and oral bioavailability, neither of which was measured.

Formulas

surface-normalized release rate is the test for co-release in the compact route; equal values for every component are the criterion bapat2025b E1, C15.

How it is measured or obtained

Two routes, one per paper. (1) Surface-normalized release from a constant-area compact in a Wood's rotating die (100 mg, 0.5 cm² exposed face, 100 rpm, 100 mL of 50 mM pH 6.8 phosphate buffer, 37 °C, n = 3), with each component assayed in the same run by reversed-phase HPLC or aqueous size-exclusion chromatography and each profile converted to a rate per unit area and per weight fraction by surface-normalized release rate; equal rates mean the dissolved mixture has the composition of the solid bapat2025b P4, P2, E1. (2) Paddle dissolution of minitablets (40 mL, 75 rpm, samples to 120 min, n = 3) with peptide and enhancer assayed in the same samples by size-exclusion HPLC, compared by their times to maximum release fagan2025 P4, P7, R20. Both routes need every component to be assayable: sodium decanoate could not be quantified in the first study, so its co-release is inferred, and in the second the same enhancer was below detection in the two gastric media until the vessel was made basic bapat2025b R6, C19, X1; fagan2025 R14, R16.

Values in the library

material	value or class	conditions	paper ids
octreotide : SNAC : copovidone, 1.6% peptide	co-release; ≈8.1 / ≈8.4 / ≈8.9 mg min⁻¹ cm⁻²; complete 25–30 min	pH 6.8, 0.5 cm² compact, 37 °C	bapat2025b R2.f–h, R5
octreotide : sodium decanoate : copovidone, 1.6% peptide	co-release of the two assayable components; ≈23 / ≈25 mg min⁻¹ cm⁻²; complete in about 10 min; enhancer inferred	same	bapat2025b R2.j–k, R9, C19
SNAC : copovidone 50:50 (no peptide)	≈7.9 / ≈8.7 mg min⁻¹ cm⁻², about 4.4 and 2.7 times the neat rates	same	bapat2025b R2.d–e, X18
cyclosporine : copovidone ± enhancer, 1.6% peptide	peptide follows the polymer: complete in about 50 min (binary), about 10 min (decanoate), ≈95% at 60 min (SNAC)	same	bapat2025b R10, C21
cyclosporine ternaries, 5–20% peptide	co-release lost: polymer complete while peptide stalls at ≈54.5% and ≈16% (decanoate), all components slowed (SNAC)	same	bapat2025b R11.i, R12.i, R13.i
insulin with 72% sodium caprate or SNAC, minitablet	staggered: enhancer maximum at about 10–20 min, insulin at about 30 min	six simulated fluids, 40 mL, 75 rpm	fagan2025 R20, R14, R15
neat peptide and neat enhancer, no release-controlling excipient	rates differ: ≈4.5 (octreotide) against ≈1.8 (SNAC) mg min⁻¹ cm⁻²; amorphous cyclosporine below 0.1% in 6 h	pH 6.8, 0.5 cm² compact	bapat2025b R2.a–c, R14

Pitfalls and disagreements

The criterion is only as good as the assay: a component that cannot be quantified turns co-release into an inference, as for sodium decanoate in every dispersion of the first study, which also carries its extension "to different types of PEs" bapat2025b X1, C43. Overlapping profiles are not the same as equal rates: the cyclosporine dispersions are called congruent although no normalized rate was computed for any of them, and at 1.6% loading with SNAC the peptide in fact lagged the enhancer and polymer (≈75.5% against ≈85% and ≈89.5% at 30 min) bapat2025b X2, R10.f, C21. In the minitablet study the enhancer's apparent incompleteness is partly an artefact of the centrifugation step, since almost all of it was recovered once the medium was made basic, which makes the measured stagger an upper bound fagan2025 C28, R16, X9. Release above 100% in both papers bounds the precision to a few percentage points bapat2025b X9; fagan2025 X11. Co-release says nothing about the state of the released enhancer: it may sit in colloidal self-assemblies or a second phase rather than as free monomers or micelles, "which may restrict their efficacies", and SNAC quenched the octreotide fluorescence in solution, an interaction that was not followed up fagan2025 C43, C32; bapat2025b C31. No paper in the library relates any co-release measurement to a permeability, cell, tissue or in vivo result; the optimal release timeframe "remains to be elucidated" bapat2025b C37, C6; fagan2025 C45.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

pH-dependent polymer solubility

Evidence table: pH-dependent polymer solubility. Content from the ASD dissolution chapter (2014, 2015) and from papers of the release-mechanism and crystallization-from-solution chapters.

The change of a polymer's aqueous solubility with pH through ionization of its acidic or basic groups. HPMCAS, an enteric polymer, is a weak acid (pKa about 5), insoluble when un-ionized and soluble when sufficiently ionized kaur2025 C27. In the ASD dissolution chapter this is used twice: an HPMCAS dispersion of nifedipine placed at pH 2 keeps its matrix in place because the polymer is not very soluble there (cited) raina2014b C25, and celecoxib–HPMCAS particles are dosed as an acidified suspension because the polymer stays largely undissolved at pH 3 [chen2015a R18]. The papers of 2015–2018 add further uses: a resveratrol–HPMCAS dispersion crystallized about equally at pH 6.8 and at pH 1.2, where HPMCAS is "essentially insoluble", which placed the crystallization in the matrix [wegiel2015 M4, C16]; enteric dispersions of lopinavir at pH 3 leached less than 5 µg/mL of polymer [li2016b R3, C8]; at pH 3 HPMCAS, HPMCP and CAP stay undissolved, which keeps a mixed dispersion's composition and lets the polymer lower the drug's maximum concentration [li2018 C12, C45]; and the cationic EPO dissolves by ionization at pH 2.2 but is "soluble up to pH 5" xie2017 M3, C29. New aspect (Release mechanism and LoC, 2024–2025): the HPMCAS grades differ in how much they need to ionize: the more succinoylated LF dissolved about three times faster than HF at pH 6.8 and 7.5, and the authors propose that it needs less ionization to dissolve bapat2025a R1, C25. HPMCAS alone stays dissolved at pH 5.8 and above at 0.5 mg/mL, while about 77% ionization is estimated to be needed for it to start dissolving kaur2025 C11, R3, C28. A drug that complexes the polymer lowers its solubility at a pH where it would otherwise dissolve (insoluble drug-polymer complex) bapat2024 C29. Co-precipitation into acidified water uses the low solubility of HPMCAS at low pH to make high-loading particles [hiew2025 C6].

Findings

Supersaturation from ASD dissolution: F2, F15, F1, F15, F16, F18, F19, F21, F24, F25, F27. Release mechanism and LoC: F23, F33, F34, F35.

Related concepts

related to polymer ionization, drug leaching and polymer-controlled release. Set by critical ionization for polymer dissolution; lowered at the surface by microenvironmental pH and by an insoluble drug-polymer complex.

Formulas

Henderson-Hasselbalch equation.

How it is measured or obtained

By polarized light of the undissolved matrix raina2014b P5, by colorimetric assay of dissolved polymer [chen2015a P12], or by polymer solubility at fixed pH kaur2025 R4.

Values in the library

material	value or class	conditions	paper ids
nifedipine–HPMCAS 50:50 at pH 2	matrix undissolved and amorphous for 3 h	polarized light, Raman	raina2014b R15
HPMCAS-LF from celecoxib particles at pH 3	about 1.5–3.5 µg/mL in the liquid over 24 h without surfactant	25 °C	[chen2015a R18]
HPMCAS LF and MF at pH 5.0 (Release mechanism and LoC)	about 250 and 110 µg/mL	blank FeSSIF-V1 pH	kaur2025 R4
HPMCAS grades with posaconazole (Crystallization from solution)	incomplete release where the grade is less soluble	pH 5.5–7.5	shah2025 C16
HPMCAS at gastric pH (Release mechanism and LoC)	insoluble, so exposed surface area mattered only in the FaSSIF stage	two-stage release	[hiew2025 C32]
HPMCAS LF / MF / HF / HPMCP, spray-dried alone	≈15 / ≈19 / ≈68 / below 5 µg/mL	pH 3, 25 °C, 1–3 h	[li2016b R2]
the same from 33% lopinavir dispersions	below 5 µg/mL	pH 3	[li2016b R3]
HPMCAS-HF from lopinavir dispersions with SDS at pH 5	≈74.5–134 µg/mL	25 °C	[li2016b R13]
cellulosic polymers in lopinavir release tests	mostly below detection, estimated 3–25 µg/mL	pH 3, 25 °C	[li2018 R5]
HPMCP-50; HPMCP-55	893 ± 95 and 189 ± 18 µg/mL at pH 5.0; insoluble below pH 4.5	48 h, 37 °C	nguyen2023c R4
HPMCAS-LF; -MF; -HF	1687 ± 47 and 1401 ± 69 µg/mL at pH 5.5; HF only from about pH 6.0	48 h, 37 °C	nguyen2023c R4
Eudragit L 100-55 coat on tablets	intact 15 to more than 17 h at pH 1.6–3.0; failed after ≈130 min at pH 4.5 and ≈150 min at pH 5.0; dissolved within 10–15 min at pH 6.0	500 mL, 37 °C	nguyen2023b R7
neat HPMCAS LF, MF, HF	≈1.50 / 0.90 / 0.45 (pH 6.8) and ≈1.73 / 1.09 / 0.63 mg/min/cm² (pH 7.5)	compacts, 50 mM phosphate, 37 °C	bapat2025a R1
HPMCAS LF, MF slurries in water	pH 4.52, 4.61 (HF 4.73)	overnight stirring	bapat2025a M3, M4, M5
HPMCAS with ≈5 mg/mL solubility at pH 6.0	lowered by lipophilic weak bases through complexation	spike test	bapat2024 C29
bedaquiline–HPMCAS 20% in FeSSIF-V1 (pH 5.0)	≈22.5–25% released	powder, 120 min	kaur2025 R16, C51

Pitfalls and disagreements

A surfactant can dissolve the polymer at low pH and undo the effect (SDS raised dissolved HPMCAS to about 860 µg/mL at pH 3) [chen2015a R18]. The low dissolved levels at pH 3 lie far below the printed calibration range of the assay [chen2015a X8]. HPMCAS-HF, the grade with the highest pKa, leached most of the three grades at pH 3, "somewhat counterintuitive", perhaps from a small low-pH-soluble fraction ("may") [li2016b C9, C10]; the dispersion polymer values lie below the detection limit or near the quantitation limit [li2016b X7]. Dissolved polymer does not guarantee released drug: delamanid release from an HPMCAS-HF dispersion stayed near zero at pH 6.5 while about 30% of the polymer dissolved nguyen2023c R11, R12. The printed polymer solubilities above about 3.3 mg/mL exceed what the stated amounts allow nguyen2023c X1. The MF slurry pH has no stated source bapat2025a X4; raising the bulk pH speeds the neat polymer as well as reducing drug ionization, so the two effects are not separated in the grade comparison bapat2025a K2.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
clotrimazole	crystalline 0.55 (pH 8) to about 62 µg/mL (pH 4); LLPS 7.7 to 490.2 µg/mL	37 °C	indulkar2015 R4, R5, R18
atazanavir	crystalline 1.04 (pH 9) to about 40 µg/mL (pH 3); LLPS about 65 to about 1970 µg/mL	37 °C	indulkar2015 R4, R6
nicardipine	LLPS 5.5 (pH 9) to about 355 µg/mL (pH 5.5); no crystalline value	37 °C	indulkar2015 R7, R1
CRH1	un-ionized onset about 12 µg/mL at pH 6.8 and pH 4.6	25 °C	[almeidaesousa2016 R24]
pazopanib	crystalline 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 6.4	37 °C, 0.1 M buffers + 5 µg/mL HPMC	sugihara2018 R1, R2, R4
loratadine	Bjerrum 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
dipyridamole	data left the ionization curve at pH about 5.1 and met the crystal curve at pH about 4.0	37 °C	hsieh2012 R4
papaverine, dipyridamole, glyburide, warfarin	crystalline solubility in pH 10 or pH 2 buffer: 12.2, 5.4, 0.2 (titration), 3.7 µg/mL	25 °C, no polymer	hsieh2014 R4
posaconazole	crystalline 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 fit	phosphate buffers, 0.14 M, 37 °C	[duong2022b R1, R2, E4]
indomethacin (cited)	1.5 µg/mL at pH 1.2 to 105 µg/mL at pH 7.4; pKa 4.42	literature	xie2017 M1
indomethacin γ; α	1.61; 2.8 µg/mL at pH 2.2; α 15 µg/mL at pH 5	37 °C, no polymer	xie2017 R1, R2
delamanid, amorphous and crystalline	154.5 → 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
praziquantel	amorphous 1.17–1.43 mg/mL across six buffers; calculated pKa 1.14, so the drug is neutral above about pH 3	37 °C	alvarenga2025 R1, R4
ritonavir from the marketed tablet	about 84 µg/mL in acid falling to about 4.6 after the shift to pH 6.8	200 mL acid, 30 min, then NaOH and buffer	trasi2019 R8
ritonavir solution without excipients	about 97 → 16 µg/mL after neutralisation; precipitate not birefringent	ultracentrifuged 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 acid	biorelevant media	elkhabaz2019a C11, C40
delamanid (outside)	pH-solubility profile of a weak base by the Henderson–Hasselbalch equation	buffers and media	nguyen2023b E1, R13
posaconazole form I	crystalline 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/mL	37 °C	shah2024 R11, C14
PCZ–HPMCAS extruded at 125 °C against 175 °C, 10 / 25 / 50% DL	about 38 / 43 / 73.5 against 30 / 28.5 / 39.5 µg/mL after 60 min at pH 1.6	two-stage test	shah2024 R12, R15, R18
coated and uncoated 20% DL RTV–PVPVA tablets in 0.1 N HCl	about 87–91% at 60 min	tablets	[benson2025 R12]
delamanid in biorelevant media, crystalline; amorphous	17.6 / 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, crystalline	115.1 ± 9.4 µg/mL in FaSSGF against 1.69 ± 0.06 µg/mL in FaSSIF	48 h, 37 °C	elkhabaz2019a R1
posaconazole, amorphous	about 20 µg/mL in FaSSIF with 20 µg/mL HPMCAS; 8 µg/mL in plain buffer pH 6.5	37 °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 Amorphous solid dispersions: the whole picture

pH-shift dissolution

Two-stage dissolution in which the dose dissolves in acid and the pH is raised, creating supersaturation of a weak base hate2017 C8, C41. Two-stage tests were also used for the enteric-polymer pretomanid ASD: a gastric stage, then fasted or fed intestinal medium nguyen2023a P11, P12, C63.

Findings

F10, F14, F26, F27.

Related concepts

related to non-sink dissolution and ionization.

Formulas

none.

How it is measured or obtained

30 min in 0.1 N HCl, then an equal volume of 0.17 M Na2HPO4, giving pH 6.5 hate2017 P7.

Values in the library

material	value or class	conditions	paper ids
nevirapine powder (100 mL) and tablet (400 mL)	nominal S 3.9; donor 475–500 µg/mL after the shift	37 °C	hate2017 R7, R18
ketoconazole, clozapine on silica	dissolved amount decreased by 30–35% on shifting	pH 1 to 5.5/6.8	hate2020b R10, R11
pretomanid ASD tablets	1 h gastric stage, then intestinal medium: all three tablets crystallized	30 mg in 150 mL	nguyen2023a R22, P12

Pitfalls and disagreements

The PVPVA run used another route to supersaturation hate2017 X15.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
MePHPH–PVPVA 5–30%; 40%; 50%	discrete particles below 1 µm; networks; inverted, hydrophobic continuous	in situ confocal of the dissolving compact edge	[deac2023a R6, C26]
MePHPH–PVPVA 30%; 50% compact surfaces	50% surface the inverse of the 30% surface	after partial dissolution	[deac2023a R9, C35]
dextran–PVP blends DEX450-PVP12, DEX40-PVP12; DEX40-PVP90, DEX6-PVP90 (Solid-state methods chapter)	dextran-rich continuous phase; phase inversion	AFM-IR, dry films	[vaneerdenbrugh2012c C43, R15, R17]
clotrimazole–PVP K12, K29/32 films	droplets 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, confocal	deac2024b R18
PHPH–PVPVA films 5–20%	droplets 5–10%; continuous 15–20%	same	deac2024b 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
itraconazole–HPMC 10:90 to 50:50, solvent-cast films	domains 500–1000 nm (authors); about 0.4–1.4 µm in the images; 1.5–2.5 µm in the chemical map of 30:70	AFM-nanoIR, spin-coated	purohit2015a C37, R10, R14, X8
telaprevir–HPMC	below 50 nm at 10:90; around 100–200 nm in the other films	AFM height	[li2016c R7]
telaprevir–HPMCAS	about 120 nm wide and 50 nm high at 40% drug; 122 × 13 nm at 50:50, gaps 21 and 25 nm	AFM height	[li2016c R5, R7]
telaprevir–PVPVA	about 280 nm wide and 20 nm high at 10%; about 380 nm and 100 nm at 50%	AFM height	[li2016c R6]
itraconazole–HPMC 40:60, outside the subcategory	about 3–5 µm in slowly cast films; about 0.4–1 µm, D50 0.9 µm, in spin-coated films	confocal 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir 50:50 PVP, PVPVA films	separated within 10 s in buffer; 10:90 did not	25 °C	purohit2017b R4, R9
ritonavir PVP, PVPVA films	AAPS from about 1 h at 97% RH	pyrene I/III	purohit2017b C22
felodipine dispersions ≤ 10%	dissolution thought to outpace AAPS with every polymer	argument	saboo2020a C41
atazanavir–PVPVA 10% films	binary uniform for 3 h at 37 °C, separated within 10 min at 50 °C; surfactant films within 10 min	100% RH	correasoto2022b R9, R12, R10, R11

Pitfalls and disagreements

Neither the rate of AAPS nor that of dissolution was measured on the same sample; the competition is the authors' inference from films plus release data indulkar2019a X6. At low loading too little drug for a contiguous layer may keep release congruent as well as slower AAPS saboo2020a C42.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
felodipine–PVPVA 30% with 0, 2% TPGS; 5, 10% TPGS	irregular semi-continuous domains; circular, discrete domains	AFM, 12 h at ≈100% RH	saboo2021 R21
felodipine–PVPVA 30% with 0; 10% TPGS	contiguous, elongated drug-rich regions; round, separated drug-rich domains in a continuous drug-lean phase	AFM-nanoIR	saboo2021 R23
clopidogrel–PVPVA 40, 50, 60%	uniform; bicontinuous; continuous drug-rich phase with discrete polymer-rich domains	5 min at 100% RH	correasoto2022a R20
clopidogrel–PVPVA with 5 g SDS per 100 g at 50%	homogeneous within the ≈500 nm detection limit	same	correasoto2022a R21
clopidogrel–PVPVA with TPGS; with Tween 80, at 50 and 60%	bicontinuous, then large irregular structures; fine-scale heterogeneous pattern	same	correasoto2022a R22, R23
ritonavir–PVPVA 30% binary; with SDS or Tween 80; with Span 85 (Physical stability chapter)	bicontinuous; discrete circular drug-rich domains; continuous drug-rich phase	films, time-lapse	[yang2022b R4, R22, C9]
ritonavir–PVPVA 10–20%; 30%; 40%	discrete droplets 0.5–2 µm; porous continuous layer; continuous layer	confocal of dissolving compacts	yang2022a R6, R10, R12, R13
MePHPH–PVPVA 5–30%; 40%; 50%	discrete particles below 1 µm; networks; inverted morphology	in situ confocal of the dissolving edge	[deac2023a R6, C26]
PHPH–PVPVA 10–20%	network	same	[deac2023a R7]

Pitfalls and disagreements

Morphology was imaged in films or humidified compacts, not in the dissolving gel layer; the contiguous network "likely also forms" there saboo2021 C39. Morphology and release did not track in every system: with TPGS the 50% clopidogrel film was bicontinuous correasoto2022a R22, and Correa Soto and co-workers (2022) find kinetics and morphology changed by the surfactant with a significance for release "if any" unknown correasoto2022a C61.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
indoprofen; droperidol, nifedipine; clotrimazole, felodipine	crystalline in 1 day; by 3 months; edges only at 3 months	quenched glasses, 0% RH, 14–20 °C below Tg	baird2010 R23, R24, R25
felodipine with 3% PVP	not completely crystallized after 24 weeks	30 °C, dry	[kestur2013b C11]
indomethacin–PVP dispersions, 10–90% drug	amorphous over 3 months (all compositions)	40 °C, desiccant	tian2016 R16, C35
indomethacin with HPMC or HPMCAS, 10–90% drug	above the miscibility limit crystalline in 2–15 days; at or below it amorphous 13–14 months	40 °C, desiccant	tian2016 R17, C53
pretomanid–HPMCAS dispersions	stable several months; neat glass crystallized within minutes	ambient	nguyen2023a C62
lumefantrine HCl and sulfate salts	no recrystallization for at least 16 weeks	40 °C/75% RH	hiew2022b R7
delamanid salts	no PXRD peaks after 2 weeks	40 °C/75% RH	duong2022a C32
naringenin, quercetin with E100 and PVP	no crystals for >200 to >450 days	five conditions, 40–50% polymer	wegiel2013a R9
naringenin, quercetin with HPMCAS, HPMC, CMCAB, PAA	first crystals after 1–3 days	84% RH/25 °C and 75% RH/40 °C, 30–80% polymer	wegiel2013a R9
lumefantrine–PVPVA at 50, 25, 10 and 5% drug loading	first crystals after 1, 2, 4 and 8 weeks	40 °C/75% RH, open dish	hiew2022a R6
lumefantrine at 50% drug loading with HPMCAS, Eudragit L 100, HPMCP, CAP	first drug crystals after 1, 8, 32 and 40 weeks	same	hiew2022a R6
resveratrol with PVP K29/32, E100, HPMC, HPMCAS, CMCAB, PAA	PVP never crystallized (> 400 days); E100 > 400 days at 84% RH; the others crystalline at day 1 at 84% RH	25 °C	[wegiel2013b R12]
curcumin with E100, cellulosics, PVP; neat	> 350, 75, 22 and 14 days at 84% RH	25 °C	[wegiel2014 R13]
curcumin dispersions	all > 350 days at 0% RH/25 °C; all crystalline within 1 day at 90 °C/0% RH and 60 °C/98% RH	storage	[wegiel2014 R13, C23]
indomethacin 60% with HPMC; EPO; EPO–HPMC 6:2.9:1.1	crystals within 5 days; within 5 days, slower growth; amorphous beyond 100 days	40 °C/75% RH, open vials	xie2017 R26
indomethacin 30%, EPO–HPMC against HPMC	ternary more stable (text only)	40 °C/75% RH	xie2017 R27
lopinavir 50% HPMCP dispersion in suspension	≈2.5–3.0 µg/mL over 48 h; no crystals at 48 h	pH 3, 25 °C, no inhibitor	[li2018 R6, R7]
lopinavir 50% EC; CA dispersions in suspension	≈4.3–5.0 µg/mL to 12 h, then ≈1.6–3.4; ≈10.5–11.2 µg/mL to 12 h, then ≈2.3–3.9	same	[li2018 R6]
delamanid sulfonate salts, neat	seven 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 liquefied	open dish	duong2022a R20
delamanid salt dispersions at 20% drug with HPMCAS	Tg 100.4–117.0 °C against 86.7 °C; water uptake ≈10–13.6% against ≈8.2% at 95% RH	37 °C	duong2022a R23, R22
praziquantel dispersions at 20% drug	HPMC E5 LV amorphous at 23 weeks; HPMCAS-MF small crystalline peaks by 21 weeks	40 °C/75% RH	polyzois2024 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
clotrimazole; atazanavir; nicardipine	5.89 (cited); 4.52 (measured); 7.2 (cited)	37 °C	indulkar2015 M1, M2, M3
ritonavir	1.8 and 2.6	cited	ilevbare2013a M1
loratadine; efavirenz	5.0; 10.2	cited	ilevbare2013a M3, M2
telaprevir	acid 11.8; base 0.31	cited	mosqueragiraldo2015 M1
CRH1	4.6 (base)	method not printed	[almeidaesousa2016 M1]
ibuprofen; phenylbutazone; diclofenac	4.35; 4.35; 4.03 (acids)	cited	almeidaesousa2015 M1, M2, M4
pazopanib	6.4 (strongest basic group)	stated without a source; used for the 37 °C curves	sugihara2018 M1, C9
flurbiprofen; flufenamic acid; chlorpropamide	4.37; 3.88; 4.33 (acidic)	computed	vaneerdenbrugh2010b M3, M4, M5
chlorzoxazone	9.39 (weakly acidic)	computed	vaneerdenbrugh2010b M6
bifonazole; lidocaine	6.69; 7.75 (basic)	computed	vaneerdenbrugh2010b M7, M8
indoprofen against other carboxylic acids (other chapter)	a somewhat weaker acid, with the smallest phase separation	PVP dispersions with moisture	[rumondor2011 C33]
PAA; PSSA; E100 amine	4.5; −1.5; 8.5	computed	[vaneerdenbrugh2011a R2]
anthranilic acid; flufenamic acid (basic pKa)	2.0; −2.1	computed	[vaneerdenbrugh2011a R1, R9]
HPMCAS, HPMCP, CAP, Eudragit L 100	4.97, 4.32, 4.57, 6.21 (acid content 1.19, 1.69, 2.94, 4.48 mmol/g)	titration, n = 2	hiew2022a R22
lumefantrine (tertiary amine)	8.73	cited	hiew2022a M1
indomethacin, ketoprofen, indoprofen in PVP	pKa 4.5, 5.02, 5.8; resist, resist, separate slightly	20-system table	[rumondor2011 R15.a, R15.d, R15.e]
20 drug–polymer systems	OPLS-DA loading of pKa ≈ −0.35: lower pKa goes with no separation	discriminant model	[rumondor2011 R17, C40]
curcumin against E100	pKa 10.51, 9.88, 8.38 against an average 8.4 for the basic monomer	acid–base pairing	[wegiel2014 M1, M5, C16]
HP-50 in BIS-TRIS, phosphate, Tris, TEA buffers	buffer pKa 6.5, 7.2, 8.1, 10.2; ≈44.8, 28.4, 6.6, 1.8% HP-50 dissolved at 60 min	50 mM, pH 6.8	[qi2022 R2, C27]
HP-50; HPMCAS-MF	pKa 4.2; 4.92 or 5.0 (cited)		[qi2022 C23; bapat2023 M3]
HPMCAS LF, MF, HF	4.91, 4.97 (cited), 5.06	back-titration, half-neutralization	bapat2025a M3, M4, M5
bedaquiline	8.5 (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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir	Tg 50.4 → 0.4 °C with 4.03–5.15% water	isolated phase, 10–50 °C	ilevbare2013a R5, R6
clotrimazole; atazanavir	Tg 28 → about 14 °C (1.4% water); 104 → about 51 °C (5.2%)	precipitates, 37 °C	indulkar2015 R22, M1, M2
telaprevir	Tg 103 → 52 °C; 4.31% water at 95% RH	pellet, 37 °C	mosqueragiraldo2015 R2, M1
sorafenib; griseofulvin	Tg 88.2 → 49 °C; 90.8 → 88 °C at 97% RH	amorphous drug	almeidaesousa2015 M5, M6, R9
erlotinib–HPMCAS 60% DL	wet Tg − T about −8.8 °C (75% RH) and −2.3 ± 1.1 °C (43% RH)	24 h at RH, T = 40 °C	moseson2022a R12
erlotinib–PVPVA 50% DL	−0.5 ± 1.2 °C	43% RH	moseson2022a R12
naproxen–HPMCAS 10% DL; lumefantrine–PVPVA 40% DL	about +11.3 °C (75% RH); +10.7, +14.3, +11.3 and +11.4 °C (43% and 31% RH)	same	moseson2022a R12
rule of thumb for stability	more than 50 °C between storage temperature and Tg (cited); the authors state the benefit of the coating holds at about 0 to +15 °C		moseson2022a E3, C45, R17
felodipine with 25% PVP, HPMCAS, HPMC	Tg 54.9 → 31.1, 44.2 → 35.6, 43.1 → 34.4 °C	0 → 75% RH	konno2008 R5
felodipine dispersions ≤ 25% polymer	Tg ≈30–35 °C after 75% RH, below dry felodipine ≈43 °C	25 °C	konno2008 R7, C16
nifedipine pure; 25% PVP	≈43 → 26 °C; ≈54 → 29 °C	0 → 76% RH	[marsac2008a R6]
amorphous felodipine (cited)	Tg ≈45.7 → 29.6 °C, smooth	0 → 94% RH	[rumondor2010 R10]
pimozide–PVP 50:50	wet Tgs −21 and 44 °C	94% RH	rumondor2009c R17
ketoprofen–PVP 70:30	wet Tg −23 °C	94% RH	rumondor2009c R25
celecoxib 6:4 dispersions	Tg 64–103 → 22–42.1 °C after 3 days at 94% RH	DSC	[xie2016b R17, R20]
tacrolimus; tacrolimus–HPMC 1:1	63.6 → 51.4 °C; 77.2 → 49.0 °C after 3 days at 75% RH	DSC	trasi2017 R15
lumefantrine dispersions precipitated into water	4–6% water (HPMCP, HPMCAS), 9% (CAP); Tg 45–112 °C	TGA; DSC	[bhujbal2021 R10]
felodipine (cited)	Tg about 45 °C dry, just below 35 °C after 75% RH	storage data	alonzo2010 M1
ritonavir drug-rich phase from a PVP dispersion	Tg inflection 1.05 °C against 50 °C for the amorphous drug	water, 37 °C, DSC at 20 °C/min	ilevbare2013d R2, M1
indomethacin (cited)	Tg falls rapidly with water content, as for felodipine	literature	alonzo2010 R24
nifedipine	dry Tg 42 °C; wet Tg approximately 17 °C (estimated)	2.5% water (estimated)	indulkar2017b M1, C16
ritonavir	Tg 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% water	37 °C, 100% RH	saboo2020 M1, R30
loratadine, miconazole, danazol, elbasvir	wet Tg 13.8 (DSC), −4.7, 73.3, 129.1 °C (rule)	37 °C	[yang2021 M1, M2, M3, M4]
atazanavir	dry 105 °C, wet 55 °C	cited	correasoto2022b M1

Pitfalls and disagreements

The griseofulvin Tg falls only 2.8 °C with an estimated 2.7% water, against 39 °C for sorafenib with 1.8%, and storage time and water content are not stated almeidaesousa2015 X11. The water content of the telaprevir pellet was not measured mosqueragiraldo2015 X3. For the coated powders the wet Tg values are not printed, only Tg − T bars, and the definition in words is the reverse of the sign used moseson2022a R12, X24, E2. Uncoated powders failed in about 1–2 weeks across the whole range of Tg − T, so Tg − T orders the coated failures only in part moseson2022a X15. The 0 to +15 °C statement applies to coated powders only moseson2022a C45, R11. The rule of 10 °C per 1% water given in the Definition fits the pure drugs but not the 25% polymer dispersions of the felodipine study, which drop about 5 °C per 1% (synthesis: 23.7 °C with 4.68% water konno2008 R6). Plasticization did not by itself cause phase separation or rank nucleation rumondor2009c C38; konno2008 C26. Plasticization by water did not rank celecoxib dispersions at 94% RH: four Tgs within about 5 °C, very different stability [xie2016b C46]. The water content of the ritonavir phase was not measured ilevbare2013d C8. Plasticization does not rank crystallization: indomethacin, with a similar Tg drop, crystallized much more slowly than felodipine during dissolution alonzo2010 C42. The 17 °C nifedipine value is an estimate from a rule taken from indomethacin; no Tg of water-saturated nifedipine was measured indulkar2017b X8. The 70% indomethacin dispersion is a model of the surface layer saboo2020 X16, and most wet Tgs are rule estimates [yang2021 P9].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
felodipine with 25% PVP, HPMCAS, HPMC	Tg 54.9 → 31.1, 44.2 → 35.6, 43.1 → 34.4 °C	0 → 75% RH, 25 °C	konno2008 R5
felodipine–PVP 0–100%	ΔTg ≈15 °C (7% PVP) to ≈158 °C (pure PVP)	dry minus 75% RH	konno2008 R9
25% polymer dispersions	Tg drop ≈13.3 °C at ≈1.1% water (PVP) vs ≈6.2 °C (HPMCAS)	25 °C	konno2008 R6, C14
nifedipine, pure and 25% PVP	≈43 → 31 °C with ≈1.15 g/100 g water; ≈54 → 43 °C with ≈2 g/100 g	25 °C	[marsac2008a R7, C19]
pimozide–PVP 50:50	two Tgs −21 and 44 °C wet against one at 94 °C dry	94% RH	rumondor2009c R17
PTM–HPMCAS–TPGS (outside)	Tg ≈79 → 63 °C with TPGS at 20% loading	DSC	nguyen2023a R13, C22
atazanavir and ledipasvir ASDs with plasticizers (outside)	lower Tg than the binary ASD	DSC	[correasoto2023 C30]
celecoxib with 10% TPGS or sucrose palmitate	Tg 55.34 → 44.81 and 44.46 °C; growth faster	DSC	mosqueragiraldo2014 R5, C16
pretomanid–HPMCAS with TPGS (other chapter)	Tg falls as TPGS rises	DSC	nguyen2023a R13, C22
ritonavir–PVPVA with Span 20 or Span 85	Spans in the drug-rich phase, read as plasticizing it and speeding separation ("likely")	O-PTIR, NMR, confocal	[yang2022b C58, X13]
griseofulvin, DPB, celecoxib with 5% PHB	Tg −5 to −12 °C; growth up to ≈10-fold faster	DSC; melt growth	[sato2016 R7, R11, X6]
delamanid sulfonate salts, neat	water 5.8–7.1% (aromatic), 8.1–11.6% (camsylate, edisylate), 16.2–21.1% (esylate, mesylate); four liquefied	95% RH; 2 weeks at 40 °C/75% RH	duong2022a R20
delamanid edisylate 1:1 with excess acid	59% water uptake and Tg 53.9 °C against 11.6% and 117.8 °C for the 2:1 salt	95% RH	duong2022a R21
delamanid salt dispersions at 20% drug with HPMCAS	water ≈10–13.6% against ≈8.2% for the free-base dispersion; Tg 100.4–117.0 against 86.7 °C	95% RH	duong2022a R22, R23
delamanid free-base dispersions, 0 to 20% drug	Tg 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-enantiomer	Tg about 37 and 34 °C, used to place the extrusion temperatures at 150 and 120 °C	DSC	alvarenga2025 M2, M1
felodipine–PVPVA 30% with 0, 2, 5, 10% TPGS	Tg 89.2, 86.0, 80.8, 71.1 °C (felodipine 44.7, PVPVA 105.4 °C)	DSC, dry	saboo2021 R5
atazanavir–PVPVA 10% with SDS, CTAB, TPGS, Tween 80, Span 20, Span 80, Span 85, VP	Tg lowered by 16, 9, 14, 14, 11, 13, 7, 16 °C from the binary	DSC, dry	correasoto2022b R20
clopidogrel–PVPVA 40–60%	PVPVA ≈4.1–6.7 against ≈2.6–2.7 mg/min/cm² for neat PVPVA	compacts, 37 °C	correasoto2022a R18, C48
loratadine–HPMCAS 5%	HPMCAS released faster than from neat HPMCAS, "feasible" plasticization by a low-Tg drug	compacts	[yang2021 C31, R18]
ritonavir–PVPVA 30:70 with 5 parts Tween 80, TPGS, Span 20, Span 85, SDS	Tg midpoint 70.90, 72.84, 73.24, 77.51, 84.93 °C against 82.24 °C	DSC, dry	indulkar2022 R18
8:1 atazanavir and ledipasvir glasses with nine plasticizers	Tg lowered by 30.4–43.3 and 47.6–53.1 °C	modulated DSC	[correasoto2023 R17, R18]
ledipasvir–PVPVA 10% with 5 and 10 g TEAC	Tg 99.1 → 85.8 °C; release 20 → 94% by 90 min	DSC; compacts, pH 6.8	[correasoto2023 R9]
amorphous ritonavir with Span 20 (80–20, 60–40)	onset Tg 14.8, 7.7 °C (46.8 °C neat)	DSC	yang2023 R22
amorphous ritonavir with Span 85 (80–20, 60–40)	27.8, 12.7 °C	DSC	yang2023 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 Amorphous solid dispersions: the whole picture

polymer adsorption

The attachment of a dissolved polymer to a surface, here the drug crystal (and, for danazol, the droplet interface). Every explanation of crystal growth inhibition in these papers assumes that the polymer must adsorb on the crystal to act, and "there is a general consensus" that it must (Mullin 2001, outside the library) [ilevbare2012c C3, C35; ilevbare2013b C47]. Adsorption can be physical (van der Waals, electrostatic, usually reversible) or chemical, and is driven by hydrophobic interaction, electrostatic attraction and hydrogen bonding [ilevbare2012c C4]. On crystal surfaces (formerly the page "polymer adsorption on crystal surfaces", from Crystallization from solution): the binding of a dissolved polymer to the faces of a growing drug crystal, which blocks growth sites and slows or shapes growth; it is usually face-selective, because molecular crystals are anisotropic, and changes habit when it slows the fast faces [ilevbare2012c C3, C5, R18]. It is the central assumed mechanism of crystal growth inhibition: the polymer occupies growth sites as a mechanical barrier and pins advancing steps [alonzo2012 C9; ilevbare2012c R19]. HPMCAS-LF was seen by AFM on three faces of felodipine, (1 1 −1), (1 −2 −2) and (1 −1 1), with no visible difference in density, taken as nonspecific adsorption, and AFM-IR identified the adsorbed material on a dried film [schram2015 R23, R25, R20, R21].

Findings

Crystallization from solution: F7, F8, F10, F11, F12, F23, F24, F27, F36, F38, F42, F44.

Related concepts

related to surface coverage, step pinning, polymer conformation, crystal habit and BFDH morphology prediction; mechanism of crystal growth inhibition.

Formulas

adsorbed amount by solution depletion, Langmuir-Freundlich isotherm, Kubota-Mullin model, Cabrera-Vermilyea step pinning.

How it is measured or obtained

By depletion: seeds equilibrated with polymer solution for 16–24 h, the amount adsorbed per area from the polymer lost from the supernatant, C_a = (C_i - C_f)\,V/(m \times A), with the polymer assayed by the phenol–sulfuric acid method at 490 nm, or by surface tension for HPMC [ilevbare2012b P9, E10; alonzo2012 P6]. In the ritonavir screen and the 2013 growth paper adsorption was not measured [ilevbare2012c C35; ilevbare2013b X14]. Adsorption on crystal faces is also read indirectly by growth-rate ratios against polymer concentration, by crystal habit and PXRD of the grown crystals, and by FTIR shifts of the drug bands after exposure to polymer [alonzo2012 R8; ilevbare2012c R4, R6; ilevbare2013b R12].

Values in the library

material	value or class	conditions	paper ids
HPMC on felodipine seeds	about 60–167 µg/mL/m² up to 0.38 µg/mL equilibrium; 285–534 at 0.62–1.12 µg/mL	surface tension, 16–24 h	alonzo2012 R6
CAP Adp 0.85 on ritonavir seeds	plateau about 41 mg/m² (pH 3.8); about 27 mg/m² (pH 6.8)	depletion, 4.0 mg seeds in 20 mL	[ilevbare2012b R9, R10]
PVPVA on indomethacin crystals	globule spacing 160 ± 50 nm (5 µg/mL); 70 ± 20 nm (50 µg/mL)	AFM	moseson2020a R12
HPMCAS on paclitaxel dendrites	adsorption-site spacing about 10–16.8 nm	SEM finger width	que2018 R12
HPMCAS-LF pre-adsorbed on felodipine seeds	overgrown by fresh drug in polymer-free solution (growth ratio about 1.8, then 1.08 in a second run)	S 4, 25 °C	[schram2016 R2, R3]
A5a, A5b, ECA, ECB, ECD on amorphous atazanavir	A5a even, no globules; ECA, ECB small even globules; ECD larger; A5b large uneven globules	5 µg/mL, 1 h, tapping-mode AFM in buffer	[mosqueragiraldo2018a R4]
HPMCAS L, M, H on posaconazole droplets	polymer on every droplet surface from the ζ-potential ("is expected to delay surface crystallization")	pH 6.5	shah2025 R15, C43, C44
HPMC, felodipine seeds	inhibition plateau (ratio about 0.55) where fitted coverage reaches about 1 (1 µg/mL)	S 8, 25 °C	alonzo2012 R7, R8
Pn-IPAAmd, ritonavir	aspect ratio 4.4 against 8.8; (200) PXRD peak about 245 against 150 counts	S 7.6, 37 °C	[ilevbare2012c R4, R6]
PVPVA, celecoxib and efavirenz seeds	N–H bands 3331 → 3321, 3225 → 3217; 3316 → 3308 cm⁻¹	overnight in 100 µg/mL	[ilevbare2013b R12]
HPMCAS on paclitaxel seeds	polymer slows but does not block growth at S 88	seeded ASD dissolution	que2018 C30, C38
HPMCAS, earlier felodipine work	"may adsorb at the crystal surface and block growth sites"	dilute supersaturated solution	[rumondor2010 C38]
felodipine, HPMCAS-LF, pH 3	adsorption on three faces exposing methyl/oxygen, chlorine/methyl and methyl/amine/oxygen groups	AFM in liquid	[schram2015 R23, R25]
HPMC-606, HPMCAS-MF on atazanavir with SDS	strong adsorption keeps SDS off the crystal ("we can speculate"), not measured	1 mg/mL polymer, 0.1 mg/mL SDS	[indulkar2019b C43]
bile salts on atazanavir needles	blocking of the needle sides "hypothesized" from aspect ratios 41–83 against 12.4	biorelevant media	elkhabaz2021 C47, R21

Pitfalls and disagreements

Adsorption by depletion has no crystal-free control, so loss by aggregation or on vessel walls would count as adsorption [ilevbare2012b X15]. The amount adsorbed did not predict the effect: more adsorbed at pH 3.8 and less inhibition [ilevbare2012b R9, R7]. Maximal adsorption did not stop growth at S 7.6 with 100 µg/mL polymer [ilevbare2012b R17]. Isotherm fits missed adsorption at low concentration alonzo2012 C21. The adsorbed amount was not measured in either felodipine–HPMCAS paper [schram2015 X7]. The AFM coverage ranking is qualitative, one image per polymer [mosqueragiraldo2018a X16]. The face-specific binding of Pn-IPAAmd rests on means of 50 crystals with overlapping spreads and PXRD relative intensities, with no adsorption or face-specific rate measured [ilevbare2012c X12]. The BFDH fast faces are assumed to be the fast faces of the real crystals [ilevbare2012c C45]. The PVPVA hydrogen bond is proposed from N–H shifts alone [ilevbare2013b X13]. Nonspecific adsorption is a visual judgement and the (1 −1 1) region shows streaks [schram2015 X8]. Face-selective adsorption is the stated general case for ritonavir [ilevbare2012c C5], whereas HPMCAS-LF on felodipine showed no visible difference in density between three faces [schram2015 R23, R25]; neither paper measured face-specific adsorbed amounts (synthesis: contrast between papers).

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

polymer chain stiffness

How rigid a polymer backbone is

The authors attribute the advantage of cellulose derivatives over most synthetic polymers of similar hydrophobicity "most likely" to their semirigid, bulky backbones, which adsorb flat with more contact, against flexible chains that adsorb in loops with little contact [ilevbare2012c C39]. For nucleation the same property is given as a "perhaps" reason why bulky cellulose esters disrupt solute packing more than flexible chains ilevbare2013c C39.

Findings

F8, F13.

Related concepts

Formulas

none.

How it is measured or obtained

Not measured. The argument rests on the classification of the polymer chemistry (cellulose against vinyl-type chains) and on a molecular-dynamics result from the literature that stiffer chains adsorb more easily [ilevbare2012c R16, C39].

Values in the library

material	value or class	conditions	paper ids
synthetic polymers on ritonavir growth	about 0.9–1.4 except Pn-IPAAmd (3.25)	5 µg/mL	[ilevbare2012c R9]
cellulose-based polymers on ritonavir growth	up to 2.98	5 µg/mL	[ilevbare2012c R9]
PAlAmn (SP 20.70) and Pn-IPAAmd (22.64) on ritonavir and efavirenz induction times	about 112 and 119 min (ritonavir), 4.4 and 5.0 min (efavirenz), against 172–244 and 21.6–28.0 min for adipate esters of similar SP	induction time	ilevbare2013c R9, K4

Pitfalls and disagreements

Only two synthetic polymers fall in the matching SP range for the nucleation argument, and for celecoxib the synthetic Pn-IPAAmd was among the best ilevbare2013c K4, X11. Rigidity was not measured, and the SP values of the synthetic polymers are not printed in the growth paper [ilevbare2012c X11]. Pn-IPAAmd is flexible yet the best growth inhibitor, attributed to a specific interaction [ilevbare2012c C44, C47].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

polymer conformation

The spatial arrangement of a polymer chain in solution and when adsorbed on a crystal: extended or condensed (globular), and, on a surface, trains lying on it, loops bulging into solution and tails [ilevbare2012c C39]. In these papers conformation is invoked to explain why the amount of polymer adsorbed does not predict how well it inhibits growth [ilevbare2012b C29, C30]. Simulated conformations of cellulose oligomers: short-spacer side chains stay extended (Rg 1.12–1.14 nm) and long-spacer charged ones fold (A5b Rg 0.92 nm); in-liquid AFM shows HPMCAS as globules at pH 3 and a flat layer at pH 6.8 [mosqueragiraldo2016 R18, R19; schram2015 R12, R10].

Findings

F8, F10, F11, F23, F25, F36, F37.

Related concepts

related to adsorbed polymer conformation, polymer chain stiffness, polymer ionization, polymer adsorption and conformational flexibility.

Formulas

Kubota-Mullin model, Langmuir-Freundlich isotherm.

How it is measured or obtained

It was not measured in any of these papers. It is inferred from the pH dependence of the growth ratio, adsorption isotherms, the zeta potential of seeds with polymer, and the Kubota–Mullin factor α, and by analogy with poly(acrylic acid), whose chains stretch as pH and ionization rise (pyrene-labelled chains, mean square radius of gyration) [ilevbare2012b R7, R9, R8, R16, R20].

Values in the library

material	value or class	conditions	paper ids
CAP Adp 0.85 on ritonavir	extended at pH 6.8 (α 4.35, plateau about 27 mg/m²); condensed at pH 3.8 (α 1.25, plateau about 41 mg/m²)	σ 0.99	[ilevbare2012b R9, R16, C46]
seeds with CAP Adp 0.85	zeta potential −52.6 mV (pH 6.8); −27.2 mV (pH 3.8)	10 mM citrate	[ilevbare2012b R8]
cellulose esters against synthetic polymers	semirigid backbones lie flat in trains; flexible chains form loops, which fits the synthetic polymers' ratios of about 0.9–1.4	ritonavir growth	[ilevbare2012c C39, R9]
ionized adipate esters	extended adsorbed chains block drug attachment better	celecoxib, pH 6.8 against 3.8	[ilevbare2013b C59, R13]
PVPVA on indomethacin	adsorbed chains described as a flatter train at lower concentration, a thicker layer at higher	AFM	moseson2020a C51
cellulose oligomers A5a and A5b	Rg 1.12 and 0.92 nm; SASA 0.088 and 0.0705 nm² per atom	MD 40 ns	[mosqueragiraldo2016 R19]
A5a, A5b chains, alone and next to 25 telaprevir or atazanavir molecules	Rg 3.58 and 3.16 nm alone; A5b 2.86 and 2.64 nm next to the drug	MD, 310 K, 10 ns	[mosqueragiraldo2018a R7]
HPMCAS against Eudragit E PO beside 10 enzalutamide molecules	Rg about 1.38 against 0.69 nm (extended against globular)	MD, 15 ns	wilson2021 R21

Pitfalls and disagreements

The extended-against-condensed reading rests on the pH effect, higher depletion at pH 3.8 (which includes any loss other than adsorption) and α derived from a single point [ilevbare2012b X15, X8]. Other "plausible" explanations are a changed interaction with incoming drug molecules or with the surface energy of the crystal face [ilevbare2012b C32]. The cellulose-against-synthetic rigidity argument cannot be checked from the paper because the SP and rigidity of the synthetic polymers are not printed [ilevbare2012c X11]. Each simulation was run once and the chains are idealized (fully ionized, average substitution) [mosqueragiraldo2018a X9, X10; wilson2021 X14].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

polymer-controlled release

Dissolution paced by the dissolving polymer, fast and typical of low drug loading, at which the drug can exceed its amorphous solubility and form drug-rich droplets li2019 C48. In a phase-separated film the polymer-rich phase plays this role as "glue" that dissolves quickly and frees drug-rich domains li2019 C50. For ritonavir–PVPVA below 25% DL the polymer controls release; a single-phase spray-dried powder at 25% DL dissolved at about 3.5 mg·min⁻¹·cm⁻¹, and phase separation by water in the spray solvent lowered it to about 2.27 and 0.90 li2020 C63, R10. The marketed lopinavir–ritonavir tablet "appears" polymer-controlled because it forms a milky dispersion at pH 6.8 trasi2019 C44. New aspect (Supersaturation from ASD dissolution): the polymer-controlled regime (cited) is connected with what happens in solution: at 10% drug there is too little drug to form a dissolution-limiting layer, the drug dissolves at a fraction of the polymer rate, and it can reach "very high local supersaturations", "most likely local", that are depleted by rapid precipitation alonzo2011 C37, C39, C47, E4. In acid, where HPMCAS barely dissolves, release of celecoxib from a 33.3% drug dispersion "appears" to follow the polymer [chen2015a C31]. Release from HPMC dispersions of indomethacin and HPMCAS or HPMC dispersions of celecoxib became faster as drug loading fell, "indicative of" polymer-controlled dissolution, HPMC gelling and releasing "probably" by matrix-regulated diffusion xie2017 C31, C64; xie2016a C20; a carrier that dissolves fast by ionization (PAA at pH 6.8, EPO at pH 2.2) releases a burst that crystallizes unless an inhibitor is present xie2016a C24; xie2017 C29. New aspect (Release mechanism and LoC): the polymer carries the drug into the medium because there is too little drug to form an intact surface layer ("is thought to occur"), so drug and polymer leave at the polymer's normalized rate and drug release can far exceed that of the neat amorphous drug indulkar2019a C25, C26. Release that continues into a medium already at the amorphous solubility is the authors' test of it indulkar2017b C35; indulkar2019a C43. The two-component Higuchi model does not predict it: its critical mixture ratio is far below any practical loading, about 1.7 × 10⁻³ for felodipine–PVPVA saboo2020a R27, C36, C37. The polymer itself is slowed by the drug, "most likely" by the hydrophobicity of the formulation or by drug–polymer interactions [saboo2019 C13; bhardwaj2018 C49]. At the limit four phenolphthalein analogues released at the neat-polymer rate, so the system is "agnostic" to the compound and drug release "can be predicted" from polymer release [que2021 C39, C41]. The polymer rate in a dispersion need not be the neat rate: clopidogrel made PVPVA dissolve about twice as fast, which the authors attribute to plasticization ("is thought to") correasoto2022a C30, C48. For a binary dispersion of non-interacting components at low loading the soluble polymer carries the drug at the same relative rate, and congruent, complete release is "generally" observed indulkar2022 C20, E1. For HPMCAS-MF dispersions of indomethacin and its methyl ester at 10%, drug and polymer followed each other across buffer capacities and media, and the authors conclude that drug release from HPMCAS dispersions of model acidic or neutral drugs is controlled by polymer release [bapat2023 C16, C49]; in this regime Noyes–Whitney type equations "fail" to describe drug release [bapat2023 C2]. Hiew and co-workers (2023) restate the transition for copovidone dispersions and found release of grazoprevir particles drug-dominated once the surface drug reached about 50% [hiew2023 C35, C53]. For HPMCAS the 2024–2025 papers take polymer solubility at the gel–solution interface as the rate-limiting step, through the flux J_p = (D_p/\delta)\,C_p, so that a drug that lowers this solubility by forming an insoluble complex slows both components bapat2024 C31, E3, C32; kaur2025 C41. Kaur and co-workers support polymer control by low release at acidic pH and in FeSSIF-V1, where the drug is far more soluble but HPMCAS does not dissolve kaur2025 C40, C51. For PVP, congruent dispersions released like the neat polymer and more slowly with higher molecular weight [deac2024a C19, C31].

Findings

ASD process: F14, F15, F21, F23, F38, F48. Supersaturation from ASD dissolution: F9, F10, F15, F20, F25. Release mechanism and LoC: F1, F2, F4, F11, F14, F15, F23, F28, F29, F32, F34.

Related concepts

contrasts with drug-controlled release; related to drug-rich nanodroplets, drug leaching and congruent release. Contradicts the Higuchi two-component dissolution model at low loading; tested with the Nernst-Brunner equation; capped by the polymer's intrinsic dissolution rate; its rate is set by polymer chain disentanglement in the gel layer; slowed by insoluble drug-polymer complex formation with enteric polymers.

Formulas

congruent release relation, Noyes-Whitney equation, Higuchi-Corrigan critical mixture ratio, saturated-medium condition.

How it is measured or obtained

Release against drug loading: LPV concentration at 10 min fell from about 16.9 µg/mL at 15% DL to about 1.2 µg/mL at 100% DL for miscible films li2019 R2. In the ASD dissolution papers: by particle disintegration under polarized light, by the speed of release in UV and by dissolved polymer measured by colorimetry [alonzo2011 P6, P2; chen2015a P12]. In the release-mechanism papers: equal normalized drug and polymer rates from constant-area compacts, and release into presaturated medium saboo2019 R8; indulkar2019a R12; integrated over time, (dC/dt)_{drug} = (dC/dt)_{polymer}\,m_{drug}/m_{polymer} gave ≈7.4 against ≈7.6 mg ritonavir at 20 min from a 10% tablet indulkar2019a E3, R1, R2.

Values in the library

material	value or class	conditions	paper ids
LPV–HPMC E5 miscible, 15% DL	about 25 µg/(mL·min) peak rate; about 16.9 µg/mL at 10 min	30 µg/mL dose	li2019 R2.a
ritonavir ASDs	high-DL PVP and PVPVA lose polymer-controlled release by rapid AAPS	outside	purohit2017b C3, C54
ritonavir ASDs	LLPS was seen only for ASDs whose release was polymer-controlled and that stayed miscible during the initial phase	outside	purohit2017b C6
ledipasvir–PVPVA at 2 and 5% DL	release polymer-controlled and congruent	outside	que2019 C9
indomethacin–PVPVA at 10% DL or less	drug and polymer release rates resemble the neat polymer rate	outside	saboo2020 C11
10% DL ritonavir and lopinavir ASDs	dissolution polymer-controlled, driven by the polymer's aqueous solubility	outside	tres2018 C23
ritonavir–PVPVA, spray-dried, 25% DL	about 3.5 mg·min⁻¹·cm⁻¹ from methanol; about 2.27 from 10:90 and about 0.90 from 60:40 water:methanol	pH 6.5, 100 rpm	li2020 R10
marketed lopinavir/ritonavir tablet (Aluvia)	milky dispersion at pH 6.8, read as nanodroplets; drug loading inferred at 25% or lower	not measured	trasi2019 R20, C44, C45
BCL–PVPVA 5 and 10% DL	drug and polymer released together; about 91 and 96% of the dose within 10 min	dose of at most 30 µg/mL	moseson2022b R6, R7, C17
felodipine 90:10 HPMC dispersion	particle gone within 5 min; 80–100% of the drug in solution within about 10 min	37 °C	alonzo2011 R4, R2
ritonavir and lopinavir 20% HPMCAS against PVP dispersions	maximum within 20 min against about 2 h	pH 6.8, 25 °C	trasi2015b R14
celecoxib–HPMCAS 33.3% particles, pH 3	HPMCAS ≈3.5 (none) to ≈860 µg/mL (SDS) at 24 h, drug following it in absolute terms	suspension, 25 °C	[chen2015a R18, X9]
celecoxib–HPMCAS 10 / 30 / 50 / 60% drug	≈18.3 / ≈10.5 / ≈5.0 / ≈2.0 µg/mL at 1 h (22 nominal)	pH 6.8, 37 °C	xie2016a R4
celecoxib 50%, PVP-K12 against HPMCAS	≈16.1 against ≈9.0 µg/mL at 2 h	pH 6.8, 37 °C	xie2015 R6
indomethacin–HPMC 10 / 30 / 50% drug	≈39.5 / ≈24.5 / ≈18.5 µg/mL at 60 min (80 nominal)	pH 2.2, 37 °C	xie2017 R10
delamanid salt dispersions, polymer release against drug release	at pH 5.0 HPMCP-55 released ≈65% of its polymer and no drug; HPMCAS-LF released ≈92% of its polymer after pH 1.6 with ≈47.5% drug	25% drug, 37 °C	nguyen2023c R12, R11
praziquantel–HPMCAS-MF 20 / 30 / 40% drug	≈100 / ≈94 / ≈83% released at 1.5 mg/mL, a gradual decline without a release cliff	PBS pH 6.5, 37 °C	polyzois2024 R9
nifedipine 10, 20% with HPMC-E5 or PVPVA	release continued to ≈214–218 µg/mL in medium presaturated at 110 µg/mL	5 °C, D2O	indulkar2017b R8, R9
ITZ–PVPVA 10%	199 µg/min/cm², about 4 times amorphous ITZ; polymer at 0.22–0.29 of neat PVPVA	0.1 N HCl, 37 °C	[bhardwaj2018 R4, R12]
ritonavir–PVPVA 10% tablet	≈67 mg PVPVA by 20 min against ≈46 mg for neat PVPVA	pH 6.8, 37 °C	indulkar2019a R2
nilvadipine 10% in PVPVA	2.13 mg/min/cm² against 0.002 for amorphous nilvadipine (synthesis: about 1100-fold)	pH 6.8, 37 °C	saboo2019 R5
felodipine 10% in PVP, PVPVA, HPMC, HPMCAS, EUDS	≈3.8, ≈2.4, ≈0.14, ≈0.82, ≈0.16 mg/min/cm² (amorphous drug ≈0.0008)	pH 6.8; EUDS 7.4	saboo2020a R14, R13
four phenolphthalein analogues at their limits	drug and PVPVA ≈2.8–3.7 against neat ≈3.0 mg/min/cm²	compacts	[que2021 R21]
clopidogrel–PVPVA 40–60%	PVPVA ≈4.1–6.7 against neat ≈2.6–2.7 mg/min/cm²	compacts	correasoto2022a R18
lumefantrine free base 5–35%	drug ≈3.15–3.9 mg/min/cm²	compacts	hiew2022b R12
indomethacin–HPMCAS-MF 10%	drug = polymer, ≈0.12 → 0.82 mg/min/cm², following the neat polymer	pH 6.8 phosphate 3–51 mM/ΔpH	[bapat2023 R9, R10]
bedaquiline–HPMCAS 20% in FeSSIF-V1 (pH 5.0)	≈22.5–25% in 120 min despite 628 µg/mL crystalline solubility	powder, in situ UV	kaur2025 R16, R2, C51
clotrimazole–PVP congruent dispersions	slower with higher PVP grade, like neat PVP	compacts, pH 8.0	[deac2024a C19, R3]

Pitfalls and disagreements

The boundary between polymer- and drug-control was not located for LPV–HPMC here li2019 C48. Phase separation can lower as well as raise polymer-controlled release depending on where the drug-rich phase ends up li2020 C64. Polymer release was not measured in the 2011 felodipine study, and the local supersaturation at the dissolving particles "cannot be discounted" but was not measured alonzo2011 C28. In the celecoxib suspensions the polymer–drug link holds for absolute concentration in four media, not for supersaturation [chen2015a X9]. Polymer release was not measured in the celecoxib and indomethacin papers either, so the regime is inferred from drug release xie2015 C50; xie2017 C31. For praziquantel the gradual decline with loading is read as polymer-controlled release, although polymer release was not measured polyzois2024 C17. Polymer-controlled does not mean fast, against the general description of the regime as fast in the Definition: 10% felodipine–HPMC released at ≈0.14 mg/min/cm², about a sixth of HPMCAS saboo2020a R14. The persisting drug–polymer interaction proposed for low-loading ritonavir was not measured indulkar2019a C36. The 10% ITZ profiles were non-linear (R² 0.957–0.983), which "might" reflect polymer hydration and swelling [bhardwaj2018 R4, C20]. Drugs and surfactants change the polymer rate itself, so the neat-polymer rate bounds polymer-controlled release only roughly correasoto2022a R18; correasoto2022b R22. Kaur and co-workers did not measure polymer release, so polymer control is inferred from the pH dependence of drug release kaur2025 X14. In PVP the coupled rates of different grades were compared at different loadings [deac2024a R1].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
CA Sub / HPMCAS / HPMC / PVPVA	3.3 / 20.5 / 37.1 / 45.9 mg/mL; 23.18 / 21.47 / 23.93 / 23.59 MPa^1/2	pH 6.8	mosqueragiraldo2018b M2, M3, M4, M5
ezetimibe in Ensure Plus	opposite polymer ranking in the aqueous and oily phases "raises questions" about hydrophilicity		elkhabaz2017 C52
ritonavir, cellulose esters	solubility parameter 20.56–23.28 inhibited growth; more hydrophobic ones did not		[ilevbare2012c C25, C30]
PVP / HPMCAS films	contact angle 11.8° / 45°	spin-coated	saboo2020a R4
CPHPC-106 / cellulose acetate suberate	dissolves (cited 43.5 mg/mL) / does not (3.0 mg/mL); the better solution inhibitor was the insoluble one	enzalutamide	wilson2020 M2, M3, C35
14 new cellulose esters	SP 19.62–23.28 MPa^1/2; effective (ratio 1.64–2.98) at 20.56–23.28, ineffective (0.83–1.01) at 19.62–20.41	ritonavir growth, 5 µg/mL	[ilevbare2012c R10]
OPLS-DA of 19 cellulose-based polymers	SP loading about 0.70, R²Ycum 0.713, Q²Y 0.512	ritonavir growth	[ilevbare2012c R12, R14]
effective polymers, ritonavir; efavirenz; celecoxib	mean SP 20.87; 21.73; 24.28 against drug SP 20.03; 21.89; 23.38	induction time at 5 µg/mL	ilevbare2013c R13
16 polymers on three drugs	window 20.56–23.28 for drugs of SP 20.03–23.38	seeded growth	[ilevbare2013b R9, M1–M3]
pH-shift precipitation, nine polymers	PAA (very hydrophilic) and CMCAB failed for warfarin; CAP-adipate (most hydrophobic) failed for both acids	1 mg/mL	hsieh2014 R4, C39
celecoxib, HPMCAS; PAA	HPMCAS and HPMC effective, very hydrophilic PAA not	22 µg/mL drug	xie2016a C18
PVPVA, HPMC, HPMCAS; PAA, P2VP	beyond 24 h for four drugs; as buffer	nominal 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 effective	5 µg/mL, nine drugs	[mosqueragiraldo2018a R6, R2]
HPMCAS L, M, H	more acetyl, less succinoyl: longer posaconazole induction times, more polymer in droplets	pH 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 Amorphous solid dispersions: the whole picture

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

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

material	value or class	conditions	paper ids
adipate, suberate, sebacate substituents	pKa about 4.43; about 100% ionized at pH 6.8; less than 25% at pH 3.8	literature	[ilevbare2012c R15; ilevbare2013c R18]
CAP Adp 0.85; HPMC on ritonavir	growth ratio 2.98 → 1.12; 2.19 → 2.31 from pH 6.8 to 3.8	S 7.6	[ilevbare2012b R7]
CA 320S Sub 0.63 on celecoxib	6.1 → 1.5 (75% lower)	S 6.6	[ilevbare2013b R13]
CAP Adp 0.85 on efavirenz	induction time 24.9 → 12.6 min	19 µg/mL	ilevbare2013c R14
HPMCAS, Eudragit E100 in the pH-shift study	HPMCAS unionized at the acidic final pH 1.9–3.3; E100 cationic	1 mg/mL	hsieh2014 C36, R4
PAA in celecoxib dispersions (ASD dissolution chapter)	pKa 4.28, completely ionized at pH 6.8	pH 6.8	xie2016a C24
CAP-Adp-085, CA-Sub-090, telaprevir	68 → 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 5	drug about 13 → about 36 µg/mL; polymer about 21 → about 120 µg/mL	25 °C	[li2016b C24]
EPO in indomethacin dispersions	highly soluble at pH 2.2 owing to ionization	37 °C	xie2017 C29

Pitfalls and disagreements

The pH arm changes the buffer species (acetate against phosphate) and sometimes the polymer-free rate or time [ilevbare2013b X11; ilevbare2013c X9]. The size of the loss at pH 3.8 does not follow the carboxyl content in the middle of the ranking [ilevbare2012b X17]. PAA, fully ionized at pH 6.8, did not inhibit any of the three drugs [ilevbare2013b R9.b]. The degree of ionization was not measured in these papers [schram2015 C4; mosqueragiraldo2016 X24]. Ionization and hydrophobicity of HPMCAS change together with pH and were not measured; the pH effect on the induction time is measured, its route is not shah2025 X8. The degree of ionization of the HPMCAS grades at pH 3 and pH 5 was not measured, and how a small degree of ionization raises SDS-driven leaching is "currently unclear" [li2016b C24, C27, C49].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ibuprofen with six polymers	polymer: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/mL	1000 µg/mL polymer, 400 µg/mL drug, pH 2.0 (D2O), 37 °C	[ueda2021 R5]
ibuprofen with PVP K25, PVP-VA, HPMC 603	ratio 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-E	polymer still in solution at S_a + 300 µg/mL: about 141, 85, 289 of 300 µg/mL	37 °C	ueda2020b R13
ibuprofen, 15–60 °C	ratio 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 phase	ΔG −12 to −19 kJ/mol; ΔH of HPMC 58 → 12, PVP-VA 25 → 5 kJ/mol	15–60 °C, quadratic van't Hoff fit	[ueda2022 R22, R23]
telaprevir ASDs, 150 µg/mL drug	polymer 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, H	polymer weight fraction in the phase about 0.05, 0.14, 0.31, water ignored	100 µg/mL drug, 900 µg/mL polymer, pH 6.5, 37 °C	shah2025 R16, R17, C30, E3
enzalutamide droplets	Eudragit E PO associates with the droplets more than HPMCAS	pH 6.5, 37 °C	wilson2021 R7, C19
telaprevir, CA Sub / HPMCAS / 70% HPMCAS / PVPVA	polymer fraction 0.90 / 0.21 / 0.27 / 0.22	150 µg/mL	mosqueragiraldo2018b R14
felodipine	PVPVA and HPMCAS distributed; PAA in the supernatant; P2VP with the drug	precipitates	raina2015b C20, R12
ibuprofen, polymers	polymer ratio falls with total drug	37 °C	[ueda2021 R10]
atazanavir, nifedipine, clozapine, ketoconazole droplets with 1000 µg/mL AS-LF / AS-HF	NMR-detected polymer about 975 / 880, 955 / 480, 920 / 415, 990 / 600 µg/mL	37 °C	ueda2020a R8, C20
felodipine 100 mg, PVPVA 45 mg	precipitate 6.8 mg, supernatant 36.7 mg	10% DMSO, pH 6.8	raina2015b R12
felodipine, HPMCAS	7.1 mg and 34.2 mg	same	raina2015b R12
felodipine, PAA; P2VP (18 mg)	0.9 and 46.6 mg; 17.7 mg and not detected	same	raina2015b R12
enzalutamide droplets, HPMCAS, Eudragit E PO	12.7–24.7 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 Amorphous solid dispersions: the whole picture

polymer salt formation

Evidence table: polymer salt formation. Content from the release-mechanism chapter (2022–2023), with rows from the Bioperformance chapter.

Pre-ionizing an acidic dispersion polymer by reacting its acid groups with a base (sodium or an amine) before the dispersion is made. Pre-ionization removes the generation and transport of protons during dissolution; the comparisons of HP-50 with HP-50-Na (faster in 50 mM phosphate, independent of buffer capacity, soluble in water) "confirm" that proton generation and removal hinder dissolution of the protonated polymer [qi2022 C31]. Polymer salts dissolved about 3-fold faster than HP-50 at pH 6.8, and pre-ionization via salt formation is called a successful strategy for designing polymers for better dispersion performance [qi2022 C3, C6]. The triethylamine salt of HPMCAS, which releases no protons, had a gel pH close to the bulk and released faster than protonated HPMCAS [bapat2023 C41]. In the Bioperformance chapter base was added at one mole per mole of HPMCAS-HF acid groups to pretomanid dispersions, which "likely" forms a polymer salt nguyen2023a E7, C67.

Findings

Release mechanism and LoC: F23, F24.

Related concepts

removes the dependence on buffer capacity and on the microenvironmental pH; exceeds the critical ionization for polymer dissolution before dissolution; a form of polymer ionization of enteric polymers.

Formulas

none.

How it is measured or obtained

Acid–base reaction of the polymer with the base, then dispersion preparation [bapat2023 P4, M4]; the sodium content of HP-50-Na by ICP-OES and ¹H NMR [qi2022 R3]; rotating-disk dissolution of neat and drug-loaded compacts [qi2022 R10, R15].

Values in the library

material	value or class	conditions	paper ids
HP-50-Na	3.38–3.52 wt% sodium, 91–95% of acid groups	ICP-OES, ¹H NMR	[qi2022 R3]
HP-50 and nine salts	≈0.92 against ≈2.35–3.09 mg/min/cm²	50 mM pH 6.8 phosphate, 37 °C	[qi2022 R10]
HP-50-Na; HP-50	≈2.80 → 2.45; ≈0.92 → 0.14 mg/min/cm² from 29 to 3 mM/ΔpH	pH 6.8 phosphate	[qi2022 R12]
miconazole 20% on HP-50, HP-50-Na, PTEA	drug ≈0.22 / 3.15 / 2.70 mg/min/cm²	50 mM pH 6.8 phosphate	[qi2022 R15]
HPMCAS-TEA against HPMCAS-MF	≈1.62 against ≈0.89 mg/min/cm²; gel pH 6.7 against 6.0	50 mM pH 6.8 phosphate	[bapat2023 R16, R15]

Pitfalls and disagreements

Water uptake does not rank the salts: the sodium salt took up most water without dissolving faster than the amine salts [qi2022 X17, C35]. The amounts used to prepare the partial salts are not printed [qi2022 X9]. The salts change the dry dispersion as well: Tg ranged from 55 °C for the tris salt to 231 °C for the sodium salt [qi2022 R8].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

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

material	value or class	conditions	paper ids
efavirenz with CAP Adp 0.85; CAB Adp 0.81	induction time 24.9 → 12.6 min; 27.9 → 13.6 min from pH 6.8 to 3.8	19 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 ritonavir	5 µg/mL	[ilevbare2013b R9]
A5b; A6 oligomers	Rg 0.92 and 1.02 nm; SASA 0.0705 and 0.077 nm² per atom	MD 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 atazanavir	MD 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 Amorphous solid dispersions: the whole picture

polymer-surfactant complexation

Evidence table: polymer-surfactant complexation. Content from the ASD dissolution chapter (celecoxib, 2015).

Association of surfactant molecules with polymer chains in solution, which can raise the solubility of the polymer. SDS is proposed to raise the solubility of HPMCAS at pH 3 "most likely" by forming polymer–surfactant complexes, as reported for HPMC with SDS and during release from solid dispersions (cited) [chen2015a C32]. With lopinavir, PVPVA and SDS "may be able to form a complex" with a higher solubilizing capacity than either alone, and slight ionization of HPMCAS at pH 5 raised SDS-driven leaching of drug and polymer by a mechanism the authors call "currently unclear" [li2016b C31, C42, C24, C49]; surfactant–polymer complexation "can also enhance" polymer solubility [li2016b C44].

Findings

F15, F19.

Related concepts

Formulas

None.

How it is measured or obtained

Not detected directly; inferred from dissolved polymer in suspension liquids [chen2015a P12, R18].

Values in the library

material	value or class	conditions	paper ids
HPMCAS-LF from celecoxib particles, 0.25% SDS	≈73 µg/mL at 0.5 h, ≈420 at 4 h, ≈860 at 24 h	pH 3, 25 °C	[chen2015a R18]
same, 0.75% STC; no surfactant	≈43 and ≈3.5 µg/mL at 24 h	pH 3	[chen2015a R18]
HPMCAS-HF from lopinavir dispersions, SDS at pH 3 / pH 5	≈19–24 / ≈105–134 µg/mL	25 °C	[li2016b R8, R13]
lopinavir with HF, PVPVA and SDS	crystalline solubility 11.4 against 3.3 µg/mL with HF and SDS	pH 3	[li2016b R5]

Pitfalls and disagreements

No complex was detected in this system; the mechanism is by analogy with HPMC–SDS [chen2015a C32]. Polymer was not measured in the polysorbate 80 and Poloxamer 188 media [chen2015a X9]. Neither complex was characterized [li2016b C31, C44].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
Tween 80 with CAP Adp 0.33; 0.85	growth ratio 0.70; 0.83 against 1.64; 2.97 for the esters alone	5 µg/mL each, ritonavir, S 7.6	ilevbare2012a R17
TPGS with and without 900 µg/mL PVPVA	CMC about 50 µg/mL; about 40 µg/mL with PVPVA, "little-to-no" interaction	pH 6.8, 37 °C	saboo2021 R1, C7
surfactants with a crystallization-inhibiting polymer	the polymer can be rendered fully or partly ineffective, particularly when surfactant and polymer interact extensively	ritonavir–PVPVA ASD (argued)	indulkar2022 C42
felodipine, HPMCAS + SDS	growth ratio 1.07 against 2.7 (HPMCAS)	S 4, 25 °C	[schram2016 R16]
SDS with PVPVA, HPMC-606, HPMCAS-MF	CAC 0.1, 0.2, 0.2 mg/mL; with 0.1 mg/mL SDS atazanavir induction time 350, >1000, >1000 min	1 mg/mL polymer, pH 6.8	[indulkar2019b R8, R4]
ritonavir–PVPVA 30:70:5 with SDS against binary 25:75	PVPVA ≈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 Amorphous solid dispersions: the whole picture

preferred orientation

A non-random orientation of crystals in a powder, which changes the relative intensity of reflections in PXRD and the total signal in orientation-dependent methods such as SHG. SONICC crystallinity assumes uniformly distributed crystallite orientations and "might not" hold for very sparse early crystals kestur2012 C33; a habit with a different orientation distribution "could" give a quite different SHG signal for the same polymorph correasoto2017 C24.

Findings

F9, F11.

Related concepts

affects second harmonic generation and degree of crystallinity; related to non-centrosymmetric crystal structure.

Formulas

none.

How it is measured or obtained

Not measured in the chapter: neither single-crystal SHG nor an orientation analysis was done correasoto2017 X14. In PXRD, unusual relative reflection intensities signal it: peaks at 6.1° and 12.3° 2θ more intense than the reference pattern for BCL form 1 were read as consistent with the elongated tabular habit [moseson2022c R6, C21].

Values in the library

material	value or class	conditions	paper ids
flutamide, ASD-grown against as-received crystals	SHG ratio up to about 3 against the fully crystalline standard; needles against blades	40 °C, 82% RH	correasoto2017 R9, R15, R16, C24
naproxen–HPMCAS	random orientation assumed	cryomilled blends	kestur2012 C33
BCL lots	6.1° and 12.3° peaks stronger than reference	PXRD	[moseson2022c R6]

Pitfalls and disagreements

The explanation of the flutamide SHG excess by habit and orientation is "assumed" and untested correasoto2017 C38, X14.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
class I (23 molecules)	0.69 ± 0.02	DSC	baird2010 R14
class III (17 molecules)	0.73 ± 0.04, not significantly different from class I	DSC	baird2010 R14
classes II and III	0.65–0.76 and 0.65–0.81	DSC	baird2010 F5
ritonavir	0.81	DSC	baird2010 R18.ab
class II compounds	0.65–0.76, not the constant 2/3	DSC	baird2012 R14
pretomanid; delamanid	0.67; 0.64, both class I	DSC	nguyen2023a C59
35 compounds	T_{rg} = 0.00021\,\mathrm{MW} + 0.64433,\quad R^2 = 0.44	regression	baird2010 E27, R19

Pitfalls and disagreements

Trg did not separate the classes, nor class I-A from I-B baird2010 C23, C37, and compounds with similar Tm − Tg had very different tendencies baird2012 C36. Trg of the 16 class I molecules without measured Tg is a function of molecular weight alone baird2010 X17. A small Tm − Tg (high Trg) did go with slow growth [trasi2014a R8.h].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
felodipine–PVP 50% film after 94% RH	band ratio ≈0.70 (5 min) → ≈1.41 (1500 min) vs ≈1.47 never exposed	125 °C	marsac2010 R17
felodipine–PVP 46.5 wt% powder	thermal event moves up with each DSC cycle; single Tg ≈80 °C on second scans	DSC to 60–110 °C	marsac2010 R15, R14
felodipine–PVP film at room temperature	no remixing after 1 week of drying	0% RH	marsac2010 R8
celecoxib–PVP 6:4 after 94% RH	two Tg events on first heating, one on reheating; remixing during the scan a "possible explanation"	DSC	[xie2016b R18, C34]
indomethacin–HPMC, 50–90% drug	single Tg above the miscibility limit, which remixing during heating "might" explain	DSC	tian2016 C31
miconazole–PVPVA 50:50 powder	one Tg after 60 min at 100 °C	DSC	[saboo2017 R22]

Evidence table: remixing of separated amorphous phases.

Pitfalls and disagreements

Remixing was still incomplete after 25 h, and the extrapolated 39 h has no stated method; a straight extension of the last points gives about 2.5–3 days marsac2010 X8.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
griseofulvin film (b)	several submicrometre SHG crystals at 0 min; dense field by 12 min	120 °C	wanapun2010 R4
naproxen–HPMCAS 75/25, fresh	SONICC about 24% of the drug, about 6 wt% of the powder; PXRD halo	rotary-evaporated, cryomilled	kestur2012 R16, X9
IDM–PVPVA extrudate	discrete 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 domains	HME at 131 °C, 20 min (1:1, at Tc)	moseson2018a R5, R9, C10, P1, R6, R7, R11
BCL–PVPVA extrudates	below 1%: TEM only; 3.5%: PLM and TEM; 30%: DSC, SEM too	XRPD LOD about 1%	moseson2021 R6
posaconazole HME ASD, 125 °C	0.3, 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 °C	HME 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 min	XRPD	moseson2018 R10
IDM crystals in copovidone	last XRD peak gone by about 135 min; crystals by PLM at 120 min and TEM at 3 h	130 °C, still	moseson2019 R4, R5.h, R15
paclitaxel–HPMCAS with seeds	seed mass is not the relevant parameter; growth area and interface structure are	dissolution	que2018 C5, C54, C58
tacrolimus	PXRD limit of detection about 1%, of quantification about 5%	—	hate2019 R2
delamanid free-base ASDs	residual 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 extrudates	S/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/mL	about 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 capsules	no detectable crystallinity but seeds below 5% of the drug	non-sink, 100 mL	purohit2018 C44, C46
30% BCL–PVPVA at Tc = 145 °C, lots of D50 3.51 / 37.0 / 38.0 µm	below the limit of detection at 2 / 5 / 6 min	PXRD, triplicate	[moseson2022c R10, R1]
same, lots of D50 42.2 µm (D90/D50 4.14) and 92.7 µm	about 2.5% and 15.0% at 20 min	PXRD	[moseson2022c R10, R1]
PCZ–HPMCAS MF 10 / 25 / 50% DL, after 60 min at pH 1.6	SHG 0.3 → 0.4, 3 → 4, 19 → 26%	37 °C	shah2024 R21
PCZ–HPMCAS 10% DL, 0.3% crystals against none	about 14.5 against 125 µg/mL at 300 min after the pH shift	two-stage test	shah2024 R12, R14
tacrolimus generic capsule, 0 / 20 / 50 / 100% crystalline	donor maximum about 40 / 38 / 15 / 5 µg/mL and receiver AUC0–120 about 682 / 583 / 272 / 117 µg/mL·min	hollow-fibre absorptive test, 100 mL	hate2019 R9, R12
same capsule	AUC0–24 in dogs 42.1 (fresh), 22.9 (50%), 21.6 (100%) ng·h/mL	1 mg, n = 6	purohit2019 R9
same capsule	release 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 tests	purohit2018 R5, R7
same capsule	virtual bioequivalence lost at 20% with 100 mL input and at 40% with 900 mL input	GastroPlus, 24 subjects	purohit2018 R17
felodipine, seeded against unseeded with 1 µg/mL HPMC	5.1 → 2.17 µg/mL in 58 min against 5.4 → 5.03 over 198 min	S 10, 25 °C	alonzo2012 R18
ritonavir, best single polymer	growth only 1.56-fold slower at S 15.3	37 °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 it	pH 6.8, 37 °C, 16 h, HPLC	que2018 R14, C30
indomethacin, PVPVA (ASD process chapter)	growth ratio 18 and 56 at the highest seed level	S 6, pH 4.5	moseson2020a R5
felodipine seeds from the HPMCAS melt	growth ratio 8.4 (no polymer in solution) and 12.0 (with)	S 4, pH 6.8	[schram2016 R2]
paclitaxel seeds: long needles grown at S 16 and S 80	end area ≈0.00024 and ≈0.00023 m²/g, mean aspect ratio ≈23.6 and ≈20.1	SEM, 100 crystals	que2018 R6, R9
the same, sonicated 10 min	≈0.0021 and ≈0.0017 m²/g, aspect ratio ≈7.3 and ≈4.7	SEM	que2018 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 100	PBS pH 6.5, 37 °C	duong2022a R14
delamanid free base 25% with HPMCP-50, spray-dried against rotary-evaporated	amorphous 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 Amorphous solid dispersions: the whole picture

second harmonic generation

Conversion of laser light into light of twice the frequency (800 → 400 nm; 1064 nm light gives 532 nm shah2024 P7) by material that lacks inversion symmetry. Crystals of many drugs emit it; liquids, glasses and amorphous polymers do not, so the image of a mixed sample shows only the crystals (SONICC, second-order nonlinear optical imaging of chiral crystals) wanapun2010 C4; kestur2012 C4; correasoto2017 C7. SHG reports the presence of certain crystal structures, not molecular information correasoto2017 C7; kestur2012 C37.

Findings

F5, F6, F7, F8, F9, F10, F11.

Related concepts

requires a non-centrosymmetric crystal structure; scales as in coherent and incoherent SHG scaling; limited by SHG coherence length and preferred orientation; detects residual crystallinity.

Formulas

SHG relative crystallinity.

How it is measured or obtained

Beam-scanning microscopes with a femtosecond laser, forward (transmission) and backward (epi) detection by photon counting; powders between cover glasses; images thresholded at signal-to-background 3 or averaged for relative crystallinity (F8).

Values in the library

material	value or class	conditions	paper ids
griseofulvin and chlorpropamide films	800 nm, 100 fs, 80 MHz, 40 mW (about 0.5 nJ per pulse); 10× objective, N.A. 0.3; field 600 × 600 µm; frames 45 s and 25 s	forward and backward	wanapun2010 P4, P5
naproxen–HPMCAS powders	same laser at 20 mW; 4 × 4 × 20 µm³ resolution; frame 25 s; 3D image 3 min	epi	kestur2012 P6, P12
flutamide and ezetimibe spray-dried dispersions	1064 nm, 51 MHz, 166 fs; 50 mW (flutamide) and 250 mW (ezetimibe); fields 1925 × 1925 µm; about 1.5 min per sample	epi	correasoto2017 P3
posaconazole HME ASDs	1064 nm, 200 mW, 447 ms; standard curve linear, R² 0.999 at 0–25%	epi	shah2024 P7

Pitfalls and disagreements

Only non-centrosymmetric forms are seen; SHG-inactive polymorphs, crystals below about 100 nm and crystals of other orientation distributions give less or no signal (F11, F9). The detector can saturate (flutamide at 82% RH after 58 days) correasoto2017 R11. No chemical or structural information beyond percent crystallinity is given kestur2012 C37.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
tacrolimus seeded solutions	assumed minimal, so the desupersaturation rate gives the growth order (1.677)	hollow-fibre module, S 8–20	hate2019 C42, R18
ritonavir, celecoxib; efavirenz	no 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 formed	seeded, 37 °C; turbidity, size distribution	[ilevbare2013b R5, R6, C12, C13]
telaprevir	secondary 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 seeds	small needles on larger crystals in SEM; lower aspect ratio after growth	no polymer	que2018 R9, R10, C43
posaconazole 10 wt% ASD	fine-particle count rose after 15 min following the pH shift	FBRM and SHG	shah2024 R14, C28, C47
ritonavir seeds after growth	monomodal size distribution; unseeded 10 µg/mL no loss in 8 h	S 7.6	ilevbare2012a R7, R9
telaprevir seeds, δ 7.9	possible; bulk growth assumed dominant	50 mM phosphate pH 6.5, 37 °C	[lu2018 C8]
atazanavir needles from buffer	secondary growth and small needles on larger ones; none in human fluid	SEM, 300 min	elkhabaz2021 R17
posaconazole with 0.4–20 µg/mL nanocrystal seeds	induction period removed; immediate desupersaturation at 2 and 20 µg/mL	PBS pH 6.5, S 33.6	[duong2022b 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
paclitaxel, 18 wt% seeds, no polymer	31.6 → ≈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 min	pH 6.8, 37 °C	que2018 R7
paclitaxel–HPMCAS dispersion, 18 wt% seeds	≈7.9–25.3 µg/mL left at 16 h against ≈31.6 µg/mL unseeded	pH 6.8, 37 °C	que2018 R14
paclitaxel seeds grown with HPMCAS	dendritic fingers ≈10.5–16.8 nm wide at the needle ends	TEM, 20 measurements per sample	que2018 R12
felodipine seeds made four ways, 5 µg/mL HPMCAS (Crystallization from solution)	growth slowed ≈2.7-fold to ≈12-fold depending on seed origin	initial S 4, pH 6.8	[schram2016 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 HPMCAS	FaSSIF 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/mL	absorptive dissolution	hate2019 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 Amorphous solid dispersions: the whole picture

SHG coherence length

The thickness over which SHG generated along the beam adds in phase, set by the mismatch of the wave vectors of the fundamental (800 nm) and its harmonic (400 nm) wanapun2010 E1, E2:

L_C^{f}=\frac{2\pi}{\left|\vec k^{2\omega}-2\vec k^{\omega}\right|},\qquad L_C^{b}=\frac{2\pi}{\left|\vec k^{2\omega}+2\vec k^{\omega}\right|}

for forward (transmission) and backward (epi) detection wanapun2010 E1, E2. The backward length is about 40 times shorter than the forward one (synthesis: 4.8 µm/120 nm = 40) wanapun2010 R9.

Findings

F8, F11.

Related concepts

limits second harmonic generation detection size; underlies coherent and incoherent SHG scaling.

Formulas

none (the two coherence-length expressions have one paper in this chapter; see the evidence tables).

How it is measured or obtained

Calculated with an assumed 5% refractive-index mismatch between 800 and 400 nm; the sign of the mismatch is not stated, so L_C^b is uncertain by about 5% wanapun2010 R9, C16, X15. The forward-to-backward SHG ratio of a pixel stays near 1 until the crystal approaches L_C^b, which makes it an internal "ruler" wanapun2010 C15, R6, R7. Kestur and co-workers use about 100 nm for epi-detected SHG kestur2012 R17.

Values in the library

material	value or class	conditions	paper ids
griseofulvin, n = 1.65	L_C^f 4.8 µm; L_C^b 120 nm	5% index mismatch	wanapun2010 R9
chlorpropamide, n = 1.51	L_C^f 5.3 µm; L_C^b 136 nm	same	wanapun2010 R9
epi-detected SHG, general	about 100 nm along the beam; thicker pristine crystals add nothing	cited from Wanapun	kestur2012 R17, C5

Pitfalls and disagreements

The inputs of the simulated curves are not stated and their zeros do not sit at L_C^b wanapun2010 X16. Smaller nuclei are "unlikely" to be detected kestur2012 C34.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

signal-to-noise ratio

The size of a band or signal relative to the noise or background around it. The chapter uses it in four ways: the S/N of a PTIR band at 1625 cm⁻¹ for particles of different size [harrison2013 R13]; a signal-to-background of 3 as the threshold of an SHG image and the basis of the size-based limit wanapun2010 P7, P10; S/N 3:1 and 10:1 as detection and quantitation criteria in XRPD moseson2021 P2; and poor signal-to-noise as one possible cause of the large error of the area method in PXRD [rumondor2010b C18]. The SHG paper calls the same 3 threshold both signal-to-background and signal-to-noise and does not define background or noise wanapun2010 X17.

Findings

F3, F4, F7, F11, F14.

Related concepts

underlies limit of detection and limit of quantitation; related to spatial resolution.

Formulas

none.

How it is measured or obtained

The PTIR values are called "self-consistent" and their calculation is not stated; the spectra are drawn at different baselines without an absorbance scale [harrison2013 R13, X6]. The SHG limit scales the signal-to-background at the point where forward and backward signals separate down to 3, by a relation that is not printed wanapun2010 R10, X3. Raising PXRD signal-to-noise by slower scanning can itself crystallize the sample: Bragg peaks of amorphous–crystalline nifedipine mixtures grew between readings at 2 or 4°/min [rumondor2010b R11, C19].

Values in the library

material	value or class	conditions	paper ids
griseofulvin particles of about 100, 350, 800 nm in HPMC	S/N at 1625 cm⁻¹ 5:1, 9:1, 15:1; drug/HPMC signal 5, 8, 26	PTIR, 256 pulses per point, 6.5 min	[harrison2013 R13, R12, P7]
griseofulvin film, chlorpropamide film	S/B 30 and 5 at the forward/backward switch, scaled to 3	SONICC	wanapun2010 R10
BCL–PVPVA extrudates	LOD at S/N 3:1; LOQ at 10:1	XRPD	moseson2021 P2

Pitfalls and disagreements

Definitions of signal, background and noise are not given in the papers that use the term; the PTIR ratios cannot be recomputed from the figures [harrison2013 X6; wanapun2010 X17].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ketoconazole–PVP	one Tg at every composition, ≈7–10 °C below Couchman–Karasz at 10–30% PVP	0–100% PVP, 20 °C/min	[rumondor2009a R3, R4, X9]
felodipine–PAA	two Tgs at 10 and 30% PAA in both regimens; single Tgs 121/86 and 114/84 °C at 70 and 90% PAA	two heating regimens	[rumondor2009a R1]
felodipine–PVP, nifedipine–PVP	one Tg in earlier studies	cited	[rumondor2009a R5]
itraconazole–HPMC (other chapter)	one broad Tg (87 °C) although fluorescence found phase separation	mDSC	purohit2017a R3, C26
itraconazole–HPMC 10:90 to 50:50, powders	one Tg per composition, first-run midpoint 131 → 77 °C, step width 11–25 °C; second run 115 → 64 °C, width 6–16 °C	mDSC 2 °C/min, hold 2 min at 170 °C	purohit2015a R7, C25, C26
dextran–PVP, 20 pairs	none of the maltodextrin pairs phase separated; DEX450–PVP90 phase separated at all nine compositions	DSC 10 °C/min to 200–250 °C, second heating	[vaneerdenbrugh2012a R13]
telaprevir 102.7, PVPVA 108, HPMCAS 122, HPMC 140 °C	Tg of the pure components; no blend run by DSC	DSC midpoint, 20 °C/min	[li2016c M1, M2, M3, M4, X8]

Evidence table: single-Tg miscibility criterion.

Pitfalls and disagreements

Domains smaller than 15–30 nm may give one Tg; heating during the scan can change miscibility; a single Tg above the lowest component Tg may not show the number of phases at room temperature [rumondor2009a C6, R25]. Ketoconazole–PVP shows one Tg while PXRD suggests partial miscibility; the authors offer heating-driven mixing or poor detection [rumondor2009a C42]. Which of the three DSC cycles is reported, the sample mass and the number of replicates are not stated, and each Tg is a single determination [rumondor2009a X10]. The agreement with Couchman–Karasz is called "reasonable" but is approximate [rumondor2009a X9]. The first scan changes the sample: the itraconazole–HPMC step narrows and its midpoint falls by 13–26 °C on reheating, an effect the paper reports but does not explain purohit2015a R7, X14. A pair classed miscible by DSC showed domains of about 0.3–0.6 µm in films (DEX6–PVP90) [vaneerdenbrugh2012c R16].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

sink conditions

Two senses occur

In membrane cells the receiver stays far below saturation so that it does not slow transport; in dissolution the medium can dissolve the whole dose (sink index above 1) raina2014a C20; purohit2018 E1. A receiver can be made a sink for a lipophilic weak base by solubilizing it, with 2% SDS or at pH 3, which raised PAMPA mass flow by partitioning rather than by micelles as such hate2022 C30, C52. In diffusion cells it is the condition under which the flux depends only on the donor activity; in the danazol cell the receiver stayed below 0.3 µg/mL [jackson2016 P9, C9]. New aspect (Mesoporous silica): in the silica papers "sink" also means a total dose diluted to about the crystalline solubility, a test of whether drug held by the silica comes out when nothing in solution holds it back; release still stopped at 60–65% dening2018 P7, R18, C27, X7. In desorption tests, adsorbed drug was diluted to "33% of the crystalline saturated solubility" mccarthy2020 P8. In the diffusion cell, sink means receiver concentrations below the crystalline solubility dening2018 C12, R11.

Findings

Bioperformance: F2, F5, F13, F16, F21, F22. Crystallization from solution: F22, F31. Mesoporous silica: F8, F9, F14.

Related concepts

contrasts with non-sink dissolution; quantified by sink index; condition for membrane flux, absorptive sink (a membrane sink during dissolution), membrane asymmetry (a solubilizing receiver); reveals the partly irreversible part of the dynamic adsorption-desorption equilibrium; provided during release by absorptive dissolution testing.

Formulas

sink index, membrane flux from concentration difference, membrane flux in terms of solute activity.

How it is measured or obtained

Receiver concentration kept under one third of the crystalline solubility raina2014a P8; raina2015c P7; fresh receiver buffer flow indulkar2016 P5; hate2017 P4; sink index from solubility, volume and dose purohit2018 R4. Receiver with SDS at, below and above its CMC, or at pH 3 hate2022 R7, R13, R15; the sink effect is said to be available at 0.15% SDS, above the CMC of 0.05% hate2022 R13, X6. Receiver concentration followed with a UV dip probe and checked to stay far below the donor [jackson2016 P9]. Sequential dilution with fresh buffer every 30 min until the theoretical supersaturation reaches 1 dening2018 P7; dilution of an equilibrated suspension for 24 h mccarthy2020 P8; an absorptive receiver after a pH shift hate2020b P8.

Values in the library

material	value or class	conditions	paper ids
felodipine, 25 °C	receiver about 0.024–0.155 µg/mL at 60 min	under one third of crystalline solubility	raina2014a R10, C20
tacrolimus, 900 / 450 / 100 / 40 mL	SI amorphous 9 / 4.5 / 1 / 0.4	USP medium I	purohit2018 R4
tacrolimus	40 mL non-sink relative to the amorphous solubility; 100 mL needed for exact sink	5 mg dose	trasi2016 C29
telaprevir, bile salts	receiver always under one half of crystalline solubility	diffusion runs	lu2017b R25, C11
atazanavir, PAMPA	receiver with 2% SDS or pH 3 raised mass flow from about 0.65 to about 2 µg/min at 20 µg/mL and from about 3.2 to 8.6–9.0 at 1000 µg/mL	lipid-impregnated hydrophobic PVDF	hate2022 R15, C30
tacrolimus 5 mg in 240 / 100 / 40 mL	sink index against the amorphous solubility 2.4 / 1 / 0.4	dose-to-volume	hate2019 R7
danazol diffusion cell	receiver maximum below 0.3 µg/mL	regenerated cellulose 6–8 kDa, 25 °C	[jackson2016 P9]
four drugs in three media	receiver sink assumed so that flux tracks donor activity	side-by-side cell, 37 °C	indulkar2018 C9, E2
ritonavir–SBA-15, diluted to S about 1	release about 40 → 60–66%; 2.1 µg/mL against 3.6 µg/mL crystalline solubility	50 mL, 180 min	dening2018 R18
indomethacin; methyl ester on SBA-15, diluted to sink	73%; 57% desorbed; 0.98; 4.16 mg/g left	24 h, pH 2.2	mccarthy2020 R13
ritonavir diffusion cell	receiver linear (R² > 0.99) and below the crystalline solubility	30–120 min	dening2018 R11
ketoconazole–SBA-15 with absorptive sink	about 54–60.5% → 69.5% over 4 h	pH 1 → 6.8	hate2020b R17

Pitfalls and disagreements

"Sink" is relative to the crystalline or the amorphous solubility; a medium can be a sink for one and not the other purohit2018 C20. About 20% of the dose stayed in the hollow-fibre module hate2017 X12. A solubilizing receiver also changes membrane partitioning, so the same donor gives a different mass flow with and without it (F22) hate2022 C52, C53. The flux estimate also assumes a constant donor concentration [jackson2016 C9]. Mesoporous silica: "drug release was always incomplete, even under sink conditions" refers to a total dose equal to the crystalline solubility, not to excess dissolution capacity dening2018 C2, X7, which differs from the dissolution sense above (a medium that can dissolve the whole dose). The supersaturation assigned to the last dilution samples is uncertain dening2018 X6.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
griseofulvin film	first crystal 7.5 min by SHG, after 39 min optically	120 °C	wanapun2010 R2
chlorpropamide film	125 s by SHG, 500 s optically	30 °C	wanapun2010 R5
griseofulvin film	growth 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/mol	125 °C; five temperatures for ΔE	wanapun2010 R16, R17, R18, R19
naproxen–HPMCAS 75/25	SONICC about 24% of the drug at 0 h; about 48% at 48 h	60 °C	kestur2012 R16
flutamide–HPMCAS 15%	SHG at 11 d (75% RH), 8 d (82%); XRPD at 53 d and 29 d	40 °C	correasoto2017 R1
ezetimibe–HPMCAS 30%	SHG at 15 d; XRPD none in 60 d (75% RH), 48 d (82%)	40 °C	correasoto2017 R1
probucol–PVP 50:50	crystals by polarized light at 21 h; XRD peaks at 30 h	97% RH	purohit2015b R5, R21
felodipine–PVP dispersions	fast and extensive at 66–93% RH, extremely low at 0–52% RH	room temperature	rumondor2009b C7
tacrolimus capsule contents	fully crystallized in 5 weeks after an apparent lag; XRPD LOD 10% crystallinity	40 °C, 75% RH, open dish	purohit2018 C14, R2
70% drug-loaded spray-dried ASDs	crystallization in the fresh samples induced by DSC heating, consistent with fully amorphous starting material	DSC at 5 °C/min	duong2022c C21
felodipine with 25% PVP	1.2–2.8% (0–52% RH); 68.6–82.1% (75–93% RH) after ≈494 days	22–25 °C	rumondor2009b R9
felodipine with 50% HPMCAS	lag of 35–120 days at 52–93% RH, then 9.2–16.6%	same	rumondor2009b R17, R9
felodipine with 10% HPMCAS	two crystal forms, one Form II	93% RH, 491 days	rumondor2009b R13
felodipine powders, two sieve fractions	complete in 72–120 h alone; plateaus ≈45% and ≈17% with 3% PVP	30 °C, dry	[kestur2013b R5, R8]
felodipine–3% PVP powders	biphasic, early slope 13–14 times the late one	PXRD	[kestur2013b 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir; efavirenz; celecoxib	20.03; 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 esters	19.62 (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 0.85	20.05; 20.56; 20.86; 21.27	Fedors	ilevbare2013c R10
CA 320S Seb; HPMCAS; CAPh; CA 320S Sub; HPMC; CA 320S Adp; CMCAB; CP Adp	22.36; 22.44; 22.48; 22.62; 22.68; 22.95; 23.18; 23.28	Fedors	ilevbare2013c R10
Pn-IPAAmd; PAlAmn	22.64; 20.70	Fedors	ilevbare2013c R10
PVPVA; PAA; HPC; PVP; PVPdn-O	25.77; 25.92; 25.98; 28.39; 32.24	Fedors	ilevbare2013c R10
effective polymers, mean SP	20.87 (ritonavir); 21.73 (efavirenz); 24.28 (celecoxib)	induction time	ilevbare2013c R13
CAP-Adp-085, CA-Sub-090, CAP-Seb-024	22.46, 23.18, 23.04	Fedors, no ionization	[mosqueragiraldo2016 M12–M14]
A5a, A5b, ECA, ECB, ECC, ECD	25.5, 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 Amorphous solid dispersions: the whole picture

solubility-permeability interplay

The loss of membrane transport that accompanies a rise of apparent solubility when the rise comes from a solubilizer that lowers the free drug and its activity, in contrast to supersaturation from an amorphous formulation, which raises apparent solubility without lowering permeability indulkar2017a C1, C2; lu2017b C4. The same total concentration therefore gives a lower flux in micellar solution than in buffer (F16).

Findings

F16, F17.

Related concepts

consequence of micellar solubilization; read on the activity scale as thermodynamic activity and activity-based supersaturation; measured by membrane flux.

Formulas

membrane flux in terms of solute activity.

How it is measured or obtained

Flux across a 6–8 kDa membrane against donor concentration in buffer and in the surfactant or bile-salt medium, and apparent permeability with the donor concentration taken as activity or as total concentration indulkar2017a P7, P15; lu2017b P4.

Values in the library

material	value or class	conditions	paper ids
atazanavir in 3.6 mg/mL SDS	apparent permeability equal to buffer on an activity basis, 20-fold lower on a total basis (1/0.047 = 21, synthesis)	pH 6.8, 37 °C	indulkar2017a R27, E12
telaprevir with 12 mM STDC, SGDC	flux about half at a given concentration (0.43 against 0.83 µg/min at 90 µg/mL for STDC)	50 mM pH 6.5, 37 °C	lu2017b R12, R6
progesterone with cyclodextrins, surfactants, cosolvents (cited)	apparent permeability fell with higher apparent solubility; an ASD did not	cited work	indulkar2017a R30

Pitfalls and disagreements

Permeability calculated from total concentration is "implausible" because it is a property of the molecule for a given membrane, and permeability models that assume a constant micelle–drug association (the reciprocal permeability approach) "must be used with caution" if Km/w depends on concentration indulkar2017a C58, C59. The authors argue, without in vivo or permeation data for such formulations, that surfactant-containing ASDs ranked by dissolution may mislead indulkar2017a C57.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ezetimibe, buffer 21 µg/mL	induction about 1 min; PVP 100 µg/mL about 71 min; HPMC-AS about 50 min	37 °C	elkhabaz2017 R6
ezetimibe, FeSSIF 123 µg/mL	HPMC-AS 50 µg/mL more than 360 min; PVP about 10 min	37 °C	elkhabaz2017 R7
nevirapine 500 µg/mL	about 5 min; PVPVA about 60 min; HPMC-AS over 4 h	pH 6.5	hate2017 R2
telaprevir 90% PVPVA ASD	below 90 µg/mL from about 43 min; about 20 µg/mL at 100 min		mosqueragiraldo2018b R5
atazanavir 50:50 PVPVA ASD	crystals from about 80 min	hollow fibre	hate2018 R14
indomethacin–Eudragit EPO ASD	crystallization after 15–20 min; small α crystals within about 20 min	acid stage, pH 2.2, 37 °C	xie2017 R11, R23
celecoxib, no polymer or PAA	within 5 min at 22 µg/mL; ≈3.6 µg/mL at 1 h	pH 6.8, 37 °C	xie2016a R2, R3
enzalutamide 70 µg/mL	crystallized in about 15 min without polymer; held more than 16 h by four of 24 polymers added at 50 µg/mL	pH 6.5	wilson2020 R1, C32
pretomanid 80 µg/mL	1.6–3.1 min with most enteric polymers, 22–24 min with HPMCAS-MF or HPMC, over 1000 min with HPMCAS-HF	100 µg/mL polymer, pH 6.5	nguyen2023a R5
amorphous indomethacin	needles in the liquid within 60 min, solid amorphous ≥4 h; ≈14.9 → ≈2.7 µg/mL	pH 2, 25 °C	alonzo2010 R19, R11, R7
nifedipine 50:50 dispersions	crystals below 2 µm in solution against 1–300 µm by the matrix route	pH 6.8	raina2014b R13, R2
danazol dispersions PVP / HPMC / HPMCAS	induction ≈56–70 / ≈188–200 / ≈284–319 min	pH 6.8, 25 °C	jackson2015 R5
celecoxib–HPMCAS suspension with SDS; polysorbate 80	free needles at 0.5 h; 1 h	pH 3, 25 °C	[chen2015a R14, R15]
celecoxib–PVP-K12 50% dispersion	desupersaturation about 2 h after complete release	pH 6.8, 37 °C	xie2015 C20
tacrolimus 50 µg/mL	onset within 3 h; 6–8 h with HPMC	pH 4.5, 37 °C	trasi2016 R9
delamanid salt dispersions in acid	concentration did not generally fall during the acid stage, and 1 mg/mL predissolved PVPVA left release after a pH 3.0 stage unchanged	pH 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 Amorphous solid dispersions: the whole picture

solution-mediated phase transformation

Evidence table: solution-mediated phase transformation. Content from the ASD dissolution chapter (papers of 2010 and 2014) and two papers of the solid-state chapters.

Conversion of a metastable solid into a more stable one through the solution, in three stages: the metastable phase dissolves to a supersaturated solution, the new phase nucleates driven by that supersaturation, and its growth depletes the solution so that more metastable phase dissolves raina2014b C34. Alonzo and co-workers use the term for the loss of supersaturation by crystallization from solution after an amorphous solid dissolves alonzo2010 C44. When nucleation and growth are fast, dissolution controls the transformation raina2014b C35.

Findings

F1, F3.

Related concepts

related to polymorphic transformation, solution crystallization and heterogeneous nucleation; contrasts with matrix crystallization.

Formulas

multivariate curve resolution bilinear model.

How it is measured or obtained

In situ Raman of slurries resolved into the fractions of each form (MCR) raina2014b P10; solution concentration with crystals seen in the liquid alonzo2010 R19; elsewhere by solid-form analysis after slurrying [lu2016 R23].

Values in the library

material	value or class	conditions	paper ids
nifedipine γ → α, glass in buffer	γ half-life about 20 min; α complete at ≈40 min (25 °C), 30 min (37 °C)	pH 6.8 slurry	raina2014b R7, R6, R8
nifedipine γ → α, 1 mg/mL HPMCAS in buffer	γ intact to ≈110 min, α complete at 145 min	25 °C	raina2014b R9, R10
nifedipine 50:50 dispersions	α complete at ≈5 min (PVP), ≈40 min (HPMC, HPMCAS)	25 °C	raina2014b R12
amorphous indomethacin	dominant route of supersaturation loss; needles in the liquid	pH 2, 25 °C	alonzo2010 C44, R19
vemurafenib β → α (Crystallization tendency)	solvent-mediated conversion at room temperature, data not shown	slurry	[lu2016 R23]
hollow organic crystals (Solid-state methods)	reported cases arise from solvent-mediated phase transformation	literature	correasoto2017 C39

Pitfalls and disagreements

Whether a polymer slows the transformation by blocking nucleation of the new phase on the parent crystal, nucleation from solution or growth was not separated; the nucleation reading rests on curve shapes raina2014b C31, C32, X11. The faster conversion in dispersions is attributed to faster dissolution and higher supersaturation, neither measured in the slurries raina2014b C33, X10.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ITZ alone in DCM–MeOH	turbid by 120 min; DLS radius 168 ± 5 nm	evaporating solution	mugheirbi2017 R19, R20
ITZ–HPMC spray dried	homogeneous from dry solvents; domains with 1–12% water in methanol	Büchi B-290	mugheirbi2017 P3, R26, R27
ITZ–HPMC in five alcohol–DCM solvents	MeOH, EtOH, IPA separate at 50% RH; PrOH, BuOH mixed at 50% RH and separate at 20% and 7% RH	spin coated	mugheirbi2018 R1, R2, R4
pure DCM:MeOH with 4% water	evaporation about 12 → 40 min	TGA	mugheirbi2018 R9
ritonavir–PVPVA spray-dried from methanol, 10:90, 60:40 water:methanol	25% DL surface RTV by XPS 21% / 43% / 70%; aged DSC second phase at 50% DL from 10:90; pyrene ratio lower for 60:40	BLD-35 dryer, 4% solids	li2020 R4, R6, R7
same pair, droplet model	threshold about 12.5:87.5 at 25% DL; peak C/S about 2.4 and about 320 at 12.5:87.5 and 15:85	30 µm droplet	li2020 R17, R20

Pitfalls and disagreements

The composition path of the drying film was not measured; the azeotrope analysis ignores DCM and the solutes mugheirbi2018 C35, X8. Dried solvent at 20% RH reduced but did not remove the ITZ–HPMC domains mugheirbi2017 X21. The model keeps the 10:90 path single-phase although the powders show separation; its threshold "may move higher or lower" li2020 X12, C51.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

speciation

The split of total drug into free, micellar, complexed, droplet and crystalline species; only free unionized drug is thought to cross a membrane hate2018 C48; raina2015c C49. In enzalutamide dispersions the free drug at the amorphous solubility, amorphous aggregates and filtered-out drug were counted separately after 1 h of dissolution wilson2018 R10, R12.

Findings

F3, F15, F23, F25.

Related concepts

related to free drug concentration.

Formulas

none.

How it is measured or obtained

Mostly inferred from flux, ultracentrifugation and fluorescence hate2018 P6; raina2015c R13. In enzalutamide dispersions it was counted: the molecularly dissolved drug in the supernatant, the amorphous aggregates from Nile Red fluorescence calibrated against pellet mass, and the rest removed by filtration wilson2018 R8, R10, R12.

Values in the library

material	value or class	conditions	paper ids
atazanavir	total concentration not equal to drug available for permeation		hate2018 C48
felodipine with BSA	flux-based supersaturation 7.3 and 4.2 against 1.3 and 1.1 by total		raina2015c R13
enzalutamide 10:90 with copovidone	42 µg/mL molecularly dissolved, 50 µg/mL amorphous aggregates, 8 µg/mL removed by filtration (of 100)	pH 6.5, 22 °C	wilson2018 R10
enzalutamide 50:50 with copovidone	about 3 µg/mL as aggregates	pH 6.5, 22 °C	wilson2018 R10

Pitfalls and disagreements

Species were not separated in the hollow-fibre donor hate2018 X11. The aggregate count assumes that the free drug sits at the amorphous solubility, and the rat advantage of the aggregate-rich ASD (about 30% more exposure) was not tested statistically (F23) wilson2018 R12, C46, X6.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
DEX450–PVP12	boundary spectrum intermediate between domain and matrix spectra	single positions	[vaneerdenbrugh2012c R15, C23]
DEX6–PVP90	six spectra alike, pattern of pure PVP90	domains 0.3–0.6 µm	[vaneerdenbrugh2012c R20, C38, R19]
felodipine–PAA 50:50	other component's bands in both phases	four spectra per phase	[vaneerdenbrugh2012b R9, R10, C20]
telaprevir dispersions	apparent drug enrichment of the dispersed phase with loading judged more likely spectral mixing	AFM-IR	[li2016c C21]
telaprevir–HPMC 60:40, HPMCAS 80:20, PVPVA 50:50	bands of both components in both phases	local AFM-IR, 4–5 points per phase	[li2016c R8, R9, R10, C14]
telaprevir–HPMCAS 50:50	spectra of the two phases identical; IR imaging failed	domains 122 × 13 nm, gaps 21–25 nm	[li2016c R7, R11, C46]
telaprevir dispersed-phase spectra	drug band grows relative to polymer bands as loading rises	HPMC 2:8 → 5:5, HPMCAS 5:5 → 8:2, PVPVA 1:9 → 5:5	[li2016c R12, C21]

Pitfalls and disagreements

The stronger absorber (PVP against dextran) dominates mixed spectra; a strong PVP band in a dextran-rich spectrum does not show much PVP [vaneerdenbrugh2012c R6, C16]. The explanation was not tested: domain thickness and the composition of either phase were not measured, so spectral mixing and a kinetically trapped composition are not separated [li2016c X10]. A band in both phases cannot by itself give a phase composition, only a ranking of which phase is richer [li2016c C14, X3].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir	Tsp 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/min	ilevbare2013a R11
ITZ–HPMC E3 film, 40% RH	interconnected network of drug-rich and polymer-rich regions in the continuous phase; light HAADF regions about 2.9% N against 2.3%	HAADF, EDX	mugheirbi2017 R7, R8, C48
ITZ–HPMC from IPA–DCM above 30 °C	inhomogeneous fluorescence with spinodal-like microstructure	FLOM	mugheirbi2018 R1, C9
ritonavir–PVPVA films	binary and Span films may separate by spinodal decomposition, Tween 80 and SDS films by nucleation and growth	cited from outside	[yang2022b C55]
phenolphthalein analogue–PVPVA–water	separation assumed spinodal along the hydration path	argument only	deac2023b 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 Amorphous solid dispersions: the whole picture

step pinning

The mechanism (Cabrera and Vermilyea, outside the library) by which adsorbed impurity molecules hold back an advancing growth step: the step must bulge between adsorbed molecules, its radius of curvature is limited by their spacing, closer spacing means slower growth, and growth stops when the spacing equals twice the critical radius \rho_c of a two-dimensional nucleus; because \rho_c falls as supersaturation rises, the maximum effect of a fixed impurity spacing falls with S alonzo2012 C9, E8. Ilevbare and co-workers chose it among four mechanisms for adsorbed impurities (surfactant action, incorporation, kink blocking, step pinning) by argument, because large polymers adsorb irreversibly [ilevbare2012b C12]. AFM of felodipine seeds shows steps held at several points by dissolved HPMCAS (spacing 68.5 ± 9.4 nm on buffer-grown seeds, 15.8 ± 7.4 nm on dispersion-grown seeds, step height 0.8 nm) [schram2016 R5, R12].

Findings

F9, F10, F23, F24, F12, F42.

Related concepts

part of polymer adsorption on crystal surfaces; depends on critical radius of a two-dimensional nucleus; related to impurity effectiveness factor, Kubota-Mullin model and kinetic roughening.

Formulas

Cabrera-Vermilyea step pinning, Kubota-Mullin model, Kubota-Mullin impurity effectiveness factor.

How it is measured or obtained

Not observed directly in these papers. It is tested through the fall of the growth-rate ratio with coverage, the factor α of the Kubota–Mullin model and the rise of the growth order from about 1.5 to about 2 [alonzo2012 R9, R13; ilevbare2012b R16]. In the ASD dissolution chapter, SEM finger width of paclitaxel dendrites with HPMCAS gives the spacing of adsorption sites (about 10–16.8 nm), and the distance between step pinnings on indomethacin crystals with PVPVA was 270 ± 100 nm que2018 R12; moseson2020a R13.

Values in the library

material	value or class	conditions	paper ids
felodipine with HPMC	α 0.7, 0.5, 0.4, 0.6, 0.2; growth order 1.50 → 1.97 ± 0.12	S 3–12, 25 °C	alonzo2012 R9, R13
ritonavir with CAP Adp 0.85	α 4.35 (pH 6.8), 1.25 (pH 3.8); growth stopped at coverage 0.23	σ 0.99	[ilevbare2012b R16]
paclitaxel with HPMCAS	critical radius 5–7 nm at S 88, smaller than the site spacing of 10–20 nm, so seed growth is not prevented	seeded ASD dissolution	que2018 C38
HPMCAS on felodipine	l 68.5 and 15.8 nm; ρc 3.98 nm	S 4	[schram2016 R12, R14]
posaconazole plates in aspirated human fluid	finger-like ends; step pinning "may be occurring"	SEM, 37 °C	elkhabaz2021 R23, C39
telaprevir crystals with HPMCAS-MF	rough surfaces, related to HPMCAS step pinning on felodipine (cited)	SEM	[lu2018 R10, C48]

Pitfalls and disagreements

The spacing of adsorbed HPMC on felodipine, the central quantity, was not measured (for HPMCAS on felodipine it was imaged by AFM [schram2016 R12]); the statement that molecules sit "relatively far apart" is an inference from α alonzo2012 C28. The other mechanisms were excluded by argument [ilevbare2012b C12]. Step pinning applies only below the kinetic roughening transition and was not tested above it [ilevbare2012b X11].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
vemurafenib	supercooled liquid between Tg 108 °C and Tm 271 °C	melt-quenched glass	[lu2016 M1, R19.a]
34 drugs	viscosities at Tm from 2.86 × 10⁻³ to 1.99 Pa·s	rheometry	baird2012 R1
felodipine with 3% polymers	growth from the supercooled liquid substantially reduced	hot stage	kestur2010a C28
bifonazole, nimesulide	growth strongly temperature dependent	supercooled liquid	[kestur2011 C6]
ritonavir drug-rich phase	Tg 0.4 °C, so a supercooled liquid at 37 °C	aqueous LLPS	ilevbare2013a C22
clotrimazole; atazanavir precipitates	Tg ~14 °C (supercooled liquid at 37 °C); ~51 °C (glass)	water at 37 °C	indulkar2015 R22, C38
nicardipine drug-rich phase	supercooled liquid at 37 °C (dry Tg 15 °C); more viscous after 4 h at 2 °C	water	indulkar2015 M3, R23
griseofulvin; sorafenib new phase	onset matches the supercooled-liquid estimate although the dry drugs are glasses at 25 °C	25 °C	almeidaesousa2015 R11, C36
telaprevir	crystal-to-supercooled-liquid Cp estimate 97 ± 8 µg/mL against 90–92 µg/mL onset	37 °C	mosqueragiraldo2015 R13
felodipine	growth into the supercooled liquid peaks near 105 °C; 70–110 °C studied	form II, hot stage	kestur2010a R5, C10
bifonazole	growth falls by about 6.4 orders from 100 to 18 °C (plot)	melt-quenched films	[kestur2011 R7, X6]
nimesulide	growth falls by about 5.4 orders from 80 to 18 °C (plot)	melt-quenched films	[kestur2011 R9, X6]
indomethacin–PVP glass	non-equilibrium supercooled liquid; single Tg cited	solvent-evaporated	[taylor1997 C6, R17]
acetaminophen	Tg 21.2 °C, Tm 169 °C	DSC, 10 °C/min	trasi2012a R9.a
flutamide	Tg −3.1 °C; Tm 108–110 °C with 10 mol% additives	DSC	[trasi2012b R7]
celecoxib	Tg 55.34 °C, Tm 163.46 °C	DSC	mosqueragiraldo2014 R5.a
ATP enantiomers (Tg 16–17 °C)	growth from the supercooled liquid at 40–90 °C	melt films	[sato2015 R1, R5]
six compounds (Tg −1 to 90 °C) with PHB	growth from the supercooled liquid at 30–150 °C	melt films	[sato2016 A4, M1, M2, M3, M4, M5, M6]
ritonavir	wet Tg around 0 °C; supercooled liquid at 37 °C	release conditions	que2019 R28; indulkar2019a M1
ledipasvir	glass under release conditions	37 °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 °C	wet Tg onset 18 °C	saboo2020 C32, R30
loratadine	supercooled liquid at 37 °C, glass at 5 °C	wet Tg 13.8 °C	[yang2021 C16, M1]

Pitfalls and disagreements

Near Tg diffusion decouples from viscosity, so viscosity-based growth laws fail there [trasi2014a C21]. Polymer effects on growth from the supercooled liquid act on the liquid phase rather than at the crystal surface for felodipine kestur2013a C6. In the amorphous solubility papers a glass formed in water may behave as a supercooled liquid, which is inferred and not measured almeidaesousa2015 C37, C38. The text orders of magnitude (5.5 and 6 for bifonazole) are smaller than the plot readings (6.4 and 6.9) [kestur2011 X6]. Whether dilute dispersions made by cryomilling are molecularly mixed in the melt is assumed kestur2010a C5. In the acetaminophen and flutamide growth papers, interactions in the liquid were judged from spin-coated films at other compositions, not from the growth samples [trasi2012b X9; trasi2012a X15]. Two drugs only; the idea was not tested que2019 C49.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ibuprofen; tolnaftate; sorafenib	4.3; 20.0; 54.0 (fluorescence)	25 °C	almeidaesousa2015 R5
clotrimazole; atazanavir	about 13; about 63	37 °C	indulkar2015 R10
telaprevir	about 18 stated; 19.6 from 90 ÷ 4.6 (synthesis)	37 °C	mosqueragiraldo2015 R14, R13
CRH1	about 10	pH 6.8 and pH 4.6	[almeidaesousa2016 R24]
pazopanib	about 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
atazanavir	63.6 (synthesis: 70 ÷ 1.1); predicted 62; flux-derived 65	pH 6.8, 37 °C	indulkar2017a R4, R5, R6, R13
telaprevir	28.5 (synthesis: 148 ÷ 5.2)	50 mM pH 6.5, 37 °C	lu2017b R2, R1
ibuprofen	5.94 (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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ibuprofen to sorafenib	maximum ratio 4.3 to 54.0	25 °C, fluorescence onset	almeidaesousa2015 R5
telaprevir	maximum ratio about 18 (stated); flux gain about 18	pH 6.8, 37 °C	mosqueragiraldo2015 R14, R15
clotrimazole; atazanavir	about 13; about 63	37 °C	indulkar2015 R10
CRH1	about 10	pH 6.8 and pH 4.6	[almeidaesousa2016 R24]
atazanavir in 0–3.6 mg/mL SDS	concentration-based 64.8 → 33.0; activity-based 66.0 → 65.0 at the amorphous solubility	37 °C	indulkar2017a R13
telaprevir in bile salts	concentration-based value 3.9–6.7 at an activity-based 5.0	50 mM pH 6.5, 37 °C	lu2017b R17
felodipine, 25 °C	2.7–6.8 at 2–5 µg/mL; about 8 at the amorphous solubility	buffer	raina2014a R17
felodipine with BSA	S 1.3 and 1.1 by concentration ratio; 7.3 and 4.2 from flux	50 µg/mL	raina2015c R13
nevirapine	nominal 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; 3.9	3.6 µg/mL crystalline	dening2018 E6
atazanavir, six media	activity-based maximum about 50–56; concentration-based 56 in buffer to 14 in pooled human intestinal fluid	37 °C, side-by-side cell	elkhabaz2019b R8
posaconazole, six media	activity-based maximum about 29–37; concentration-based about 35–37 in buffer to 5 in human fluid	37 °C	elkhabaz2019b R9
tacrolimus	S 20 (5 mg in 100 mL) and S 8 (240 mL); maximum ratio about 33	solvent-shift solutions, hollow-fibre module	hate2019 R7, R14; purohit2019 C30
tacrolimus, fully crystalline capsule contents	concentration 2.5 times the crystalline solubility during 2 h	5 mg in 100 mL, pH 4.5	purohit2019 R5
atazanavir with darunavir	atazanavir in the drug-lean phase about 61–63 instead of 91–96 µg/mL	150 µg/mL atazanavir, about 196 µg/mL darunavir added	alkalla2026 R11, C1
felodipine	S 3–12; amorphous benchmark about 10	solubility about 0.5 µg/mL, 25 °C	alonzo2012 E1, C42
ritonavir	S 3.8, 7.6 (7.7), 15.3 (15.4) at 5, 10, 20 µg/mL; 4.3 in 50 mM buffer	solubility 1.3 µg/mL (100 mM), 2.3 µg/mL (50 mM), 37 °C	[ilevbare2012a R3; ilevbare2012b R3]
celecoxib; efavirenz	S 6.6, 14.7 at 10 and 22 µg/mL; 1.2 at 10 µg/mL	solubility 1.5 and 8.2 µg/mL	[ilevbare2013b R7]
type 1 weak bases	peak 1.4–26.7 times the titration solubility, lasting 3.1–14.7 min	pH shift, 37 °C	hsieh2012 R5
type 2 weak bases	7.2–20.7 times the crystalline solubility	pH shift	hsieh2012 R10
telaprevir with six bile salts	δ 11.5 and 28.8 need 60 and 150 µg/mL in buffer, 140 and 300–330 with 12 mM STDC/SGDC	pH 6.5, 37 °C	[lu2017 R1]
atazanavir, ritonavir in buffer, FaSSIF-V1, Composite-SIF	flux-based supersaturation at the amorphous solubility 63–65 and 9.2–10	pH 6.5, 37 °C	indulkar2018 R12
posaconazole	amorphous/crystalline about 34 from pH 2 to 7	phosphate buffers, 37 °C	[duong2022b R1, C19]

Pitfalls and disagreements

The ratio depends on the crystal form (a hydrate for paclitaxel) and the medium trasi2015a X12. A solubilizer raises total concentration without raising supersaturation in activity terms, and the concentration-based ratio can fall ilevbare2013a C54; raina2015c C29. Total UV concentration is not free drug once a drug-rich phase exists (F4) [almeidaesousa2016 R12]. Concentration ratios understate supersaturation where micelles solubilize the drug, and flux-based values assume that micelles do not cross the membrane indulkar2017a C42, X9; lu2017b X8. In the Bioperformance papers, with solubilizers the concentration ratio under-reads the activity-based supersaturation (F3) raina2015c C38. Concentration ratios are not valid above the amorphous solubility, where two phases coexist dening2018 E6. UV readings above the amorphous solubility include scattered light hate2018 X15. In six media of rising solubilizing capacity the concentration ratio fell several-fold while the flux ratio stayed about the same (F18) elkhabaz2019b R8, R9, C21. Which dose-to-volume ratio a test imposes decides whether absorption or growth on seeds dominates: S of 8 and S of 20 gave different results in the same module (F28, F29) hate2019 R14, R17. Polymer in the drug-rich phase lowers the achievable supersaturation although it inhibits crystallization (F19) ueda2020a C37. S for 10 µg/mL ritonavir is printed as 7.6 and 7.7, and for 20 µg/mL as 15.3 and 15.4, depending on rounding (10/1.3 = 7.69; 20/1.3 = 15.38) ilevbare2012a X1. The efavirenz induction-time runs state S 2.4, the ratio of the calculated amorphous solubility to the crystalline solubility, while the concentration used gives 2.3 ilevbare2013c X4. A polymer that raises the solubility lowers S for the same concentration (F19) ilevbare2013c X7. C/Cs understates the supersaturation of celecoxib in media where the mass flow does not change [li2016a X18].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
felodipine form I	about 6 times faster at the surface than in the bulk; about 23 times with 3% PVP	30 °C, 0% RH	[kestur2013b R12]
felodipine	≈0.06–0.42 µm/s at the surface	T/Tg ≈1.04–1.11	[trasi2014a R4.g]
loratadine	≈0.00005 µm/s at the surface, slowest of 14	near Tg	[trasi2014a R4.n]
nilutamide	much higher nucleation at the surface than in the bulk	melt-cooled films	[trasi2014b R1]
ezetimibe spray-dried dispersions	crystals after 19 days (50% DL) and 12 days (70% DL) uncoated	40 °C/75% RH	duong2022c C33
uncoated amorphous powders (erlotinib, naproxen and lumefantrine ASDs)	crystallization onset within 1–2 weeks	40 °C, open dish; 31–75% RH	moseson2022a R11
flutamide spray-dried dispersion	needle crystals growing from particle surfaces	40 °C/75% RH	correasoto2017 C26
indomethacin methyl ester compacts	surface crystals within 10 min of dissolution	PVPVA, 25% DL	saboo2020 R9
ritonavir–PVPVA–SDS compacts	needle-shaped surface crystals during dissolution	30% DL	indulkar2022 R15; yang2023 R16
delamanid dispersion films	rapid surface crystallization at pH 3.0	1 h	nguyen2023b R3, C37
ezetimibe–HPMCAS 50% DL, uncoated	needle-like crystals at 19 days; about 26% crystalline at 270 days	40 °C/75% RH	duong2022c R16, R19
ezetimibe–HPMCAS 70% DL, uncoated	plate-like crystals at 12 days; about 50% crystalline at 270 days	same	duong2022c R16, R19
ezetimibe–HPMCAS coated (50% thin and thick, 70% thick; about 12–40 nm)	no crystals by SEM, PXRD or DSC for 24 months	same	duong2022c R16, R17, R18, R20
ezetimibe–HPMCAS 70% thin coating (11.7–15.0 nm)	first crystals at 7 months; about 1.5% at 270 days	same	duong2022c R17, R19
erlotinib, naproxen and lumefantrine ASD powders, 13 coated arms	3–24 weeks, or none within 48 weeks in 7 arms	40 °C, 31–75% RH	moseson2022a R11
extruded and milled 30% and 50% DL BCL–PVPVA compacts	needle-like crystals on the surface at 30 min; a 5–10 µm crystal crust on the 50% compact at 1 h	pH 6.8, 37 °C	moseson2022b R14, R15
amorphous felodipine, polymer in the medium	lag of about 13–20 min before 50% crystallinity	pH 6.8, 37 °C slurry	alonzo2010 R6
celecoxib–HPMCAS spray-dried particles, Triton X100	birefringent regions on or in the particles after about 7 days, no free needles	pH 3, 25 °C	[chen2015a R20, C37]
same, no surfactant	crystallization only after more than 7 days, apparently from matrix or surface	pH 3	[chen2015a C33]
delamanid salt dispersions, five enteric grades	crystals on films and powders after 1 h in acid, more with HPMCAS and at higher pH; HPMCAS-HF also at pH 1.6	25% drug, 37 °C	nguyen2023c R19, R18
delamanid dispersions after the pH shift	undissolved particles covered with small crystals within 30 min	pH 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 min	SEM, pH 6.8	saboo2020 R22, M6
indomethacin methyl ester–PVPVA 10–25%	drug release levelled off after 7.5–20 min	30 min runs	saboo2020 R8
ritonavir–PVPVA 30:70:5 with SDS	smooth 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 30–70–10	birefringent needles at 30 min	PLM, SEM of the compact surface	yang2023 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
LPV–HPMC E5 33% DL, 50 / 70 / 100% water	continuous-phase local Tg 142 / 116 / 124 °C	nanoTA	li2019 R15, R16
ritonavir–PVPVA 50% DL tablet	surface enriched in drug after 5 min	IR, SEM (outside)	indulkar2019a C18, C41
felodipine ASDs 30% DL	incongruent 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% DL	surface RTV by XPS (C 1s) about 21% (methanol), 43% (10:90), 70% (60:40); at 50% DL 85–91% from 60:40	XPS, at least 4 spots	li2020 R7, R11
polymer-free 200:50 lopinavir:ritonavir melt after 1 h in 0.1 N HCl	1630/1718 cm⁻¹ band ratio 7.7 → 11.2, read as ritonavir loss from the surface	ATR-FTIR	trasi2019 R16, C29
BCL–PVPVA 30:70	PVPVA:BCL of the undissolved solid 7:3 → 1:1 within 5 min (computed); surfaces rough and pitted after 20 min	SEC, SEM	moseson2021 R24, R26, C32
30% BCL–PVPVA compact surface	F/F0 = 1.23 ± 0.07 (about 20% enrichment)	30 min in buffer, SEM-EDX	moseson2022b R14
same, cross-section	boundary layer F/F0 = 1.41 ± 0.10 over a gel layer of 0.93 ± 0.06	1 h	moseson2022b R15
ritonavir 50:50 PVP and PVPVA films	porous or granular surface after 10 s in buffer	SEM	purohit2017b R9
ledipasvir–PVPVA 20, 50%	17 → 54 and 40 → 61 wt% drug in 10 min	XPS	que2019 R15
nilvadipine 15:85; cilnidipine 20:80	2 → 32% and 20 → 60% in 10 min; rim N/O ≈0.50 against ≈0.35 inside a pit	XPS, 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 min	tablets and films, pH 2.1	saboo2020 R21, R28, R17, M5
ritonavir–PVPVA 40% compact	surface ritonavir ≈35 → 72 wt% after 30 min	XPS, pH 6.8	yang2022a R14
grazoprevir–HPMCAS co-precipitates and one solvent-evaporated dispersion, eight materials	surface drug ≤34% with ≈47–72% release; ≥53% with ≈8–17%	XPS; two-stage release at 90 min	[hiew2023 R14]
ritonavir–PVPVA–SDS 40–60–10	surface SDS ≈60 → 98 wt%; ritonavir ≈41 → 40% on a drug-plus-polymer basis	XPS; ATR-FTIR, before and after 30 min	yang2023 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% after	XPS	[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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
erlotinib–HPMCAS, 75% RH	wet Tg − T about −8.8 °C; coated onset about 3 weeks (uncoated about 2)	40 °C	moseson2022a R12, R11
erlotinib–HPMCAS, 43% RH	−2.3 ± 1.1 °C; coated none at 48 weeks	40 °C	moseson2022a R12, R11
erlotinib–PVPVA, 43% RH	−0.5 ± 1.2 °C; coated onset about 6 weeks	40 °C	moseson2022a R12, R11
naproxen–HPMCAS 75% RH; lumefantrine–PVPVA 43% and 31% RH	about +11.3, +10.7 and +14.3 °C; coated 24 weeks, 24 weeks and none at 48 weeks	40 °C	moseson2022a R12, R11
uncoated powders of all four systems	crystals within about 1–2 weeks whatever Tg − T	40 °C, 31–75% RH	moseson2022a 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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
70 µg/mL clopidogrel with 50 µg/mL TPGS	aqueous TPGS 50 → 33 ± 5.4 µg/mL; droplets ≈50:17 w/w drug:TPGS	qNMR	correasoto2022a R12
200 µg/mL atazanavir with PVPVA, VP, SDS, TPGS	additive in solution reduced by 1, 0, 7, 13%	¹H NMR, 37 °C	correasoto2022b R17
200 µg/mL atazanavir with 20 µg/mL Span 20, Span 85, Span 80	reduced by 65, 25, 68%; droplets ≈29:3, 60:4, 62:5 drug:Span by weight	same	correasoto2022b R17, R19
ritonavir–PVPVA films with SDS; Tween 80 and Spans (Physical stability chapter)	SDS only in the polymer-rich phase; Tween 80 and the Spans in the ritonavir-rich phase	O-PTIR	[yang2022b C46]

Pitfalls and disagreements

Partitioning did not predict release enhancement for atazanavir: SDS shows little affinity for the drug and Span 80 partitions into the droplets, and both enhance release correasoto2022b C45. With the Spans the amorphous solubility of atazanavir fell by about 28% (64 to 46 µg/mL) correasoto2022b R18. The temperature of the TPGS depletion measurement is not stated correasoto2022a R12.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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:

material	value or class	conditions	paper ids
felodipine	activity relative to crystal about 8 (5.99/0.74 = 8.09)	25 °C	raina2014a E10, R17
felodipine suspensions	same low flux at about 1 and 40 µg/mL dissolved	crystal fixes activity	raina2015c R4, C20
atazanavir + SDS	free drug about 1 to about 65 µg/mL with and without SDS	37 °C	indulkar2017a C19, R11
telaprevir, bile salts	deviation from the buffer slope gives the activity coefficient change	flux	lu2017b C41
atazanavir, posaconazole, six media	J_{amph}/J_{eq} about 50–56 and 29–37 while the concentration ratio fell to 14 and 5	37 °C, side-by-side cell	elkhabaz2019b R7, R8, R9
enzalutamide	mass flow rises up to about the amorphous solubility (42 µg/mL), then is roughly constant	5 µg/mL HPMCAS, side-by-side cell	wilson2018 R13, C25
atazanavir, nifedipine and three other drugs, PAMPA	break from a linear rise at about the amorphous solubility	lipid-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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
nifedipine	ΔG ≈−30, ≈−24, ≈−16 J/g at 0, 50, 100 °C	MDSC and Hoffman	[marsac2006a R11]
felodipine	ΔG ≈−18, ≈−13, ≈−7 J/g at 0, 50, 100 °C	MDSC and Hoffman	[marsac2006a R11]
34 drugs	ΔGv from −8.6 (lidocaine) to −54.7 J/cm³ (acetaminophen)	Hoffman, 298 K	baird2012 M5, M12
class I against class III	ΔGv ≈−0.40 against ≈+0.57 SD from the mean	per volume, 293.15 K	baird2010 R22.g
spin-coat classes I, II, III	≈−0.29, ≈+0.29, ≈+0.13 SD	per volume	vaneerdenbrugh2010a R20.e
vemurafenib α; β	≈−11.0; ≈−6.3 kJ/mol at about 115 °C	Hoffman, plotted as crystal minus liquid	[lu2016 R22, X17]
nifedipine with 40% PVP	reduction smaller than the nifedipine–felodipine difference	melting-point depression	marsac2006b C41
drugs in PVP	driving force remains at most practical polymer contents	interaction parameters	marsac2009 C34
benzocaine in PEG 3350	melting point depression from around 89 to around 48 °C at the eutectic	cited	zhu2012 C32, M3
ibuprofen; fenofibrate in PEG 3350	melting point depression of about 30 °C; about 20 °C (text), about 24 °C (plot)	eutectic	zhu2012 C34, X11
nifedipine, pure; 30% PVP; 40% PVP	−9.0, −8.4, −7.95 kJ/mol at 20 °C (zero at ≈171, ≈148, ≈128 °C)	Hoffman, plot readings	marsac2006b R12
nifedipine, pure; 30% PVP; 40% PVP	−5.45, −4.1, −2.7 kJ/mol at 100 °C	as above	marsac2006b R12
felodipine with 3% PVP, PVP/VA, HPMCAS, PVAc	melting point of physical mixtures unchanged (140.7–142.9 °C against 141.5 °C)	offset, 1 °C/min	kestur2010a R1
bifonazole, nimesulide with 5% polymers	Tg rise 0.4–2.2 °C	DSC onset	[kestur2011 R6, C12]
nifedipine, felodipine, droperidol, pimozide, indomethacin, ketoprofen	Hoffman ΔGc 8.2, 6.1, 9.2, 11.0, 8.1, 4.1 kJ/mol	25 °C	rumondor2009c M1, M6, M3, M2, M4, M5
nifedipine vs felodipine crystals	mole-fraction solubility 0.05 vs 0.10 in NMP: larger lattice term for nifedipine	25 °C	[marsac2008a R10, C35]
nifedipine and felodipine in PVP	Flory–Huggins activity ≈0.84 and ≈0.83 at Φ 0.2	χ −3.8, −4.2	[marsac2006a R19]
acetaminophen and flutamide with 10% polymer	Tm barely changed, so the driving force is similar for all polymers	DSC	[trasi2012a R9, C19; trasi2012b R7, C33]
celecoxib with TPGS and PVP	Tm 12 °C lower; a smaller driving force "could contribute" to slower growth near Tm	DSC, melt growth	mosqueragiraldo2014 R5.f, C33
six compounds with PHB	driving force inferred unchanged from Tm and IR ("can be inferred")	DSC; IR	[sato2016 C18, X11]
indomethacin polymorphs	differences in growth persist after a driving-force normalization	melt growth	[tian2017 R11, C24]

Pitfalls and disagreements

The class trend is not monotonic: class II, not class III, had the least negative ΔGv in the solvent screen vaneerdenbrugh2010a X10. Pair comparisons of viscosity can be confounded by driving force baird2012 X9. Indomethacin has a larger driving force than felodipine yet crystallizes more slowly during dissolution alonzo2010 C42, and metastable vemurafenib β outgrows α despite α's larger driving force [lu2016 C52]. Low polymer levels barely change it, so polymer effects on growth are read as kinetic [kestur2010b C28]; thermodynamically stable dispersions are hard to achieve marsac2009 C34. For ibuprofen and fenofibrate in PEG the depression should lower the driving force, yet the onset in the dispersion is earlier than for the neat drug; the authors explain it by nucleation on crystalline PEG, not by the driving force zhu2012 C34, C41. The estimated solubilities of benzocaine (28%) and ibuprofen (25%) exceed the 20% loading, which the card's extractor notes as not discussed zhu2012 X13, M3, M4. The 40% PVP curve rests on a melting temperature not shown among the measured data marsac2006b X5. The unchanged-driving-force conclusion for 3% polymer uses the melting point of form I in physical mixtures while form II grows kestur2010a X7. The size of the lowering differs between the polymers (synthesis: contrast between papers): in PEG 3350 the melting point depression (benzocaine from around 89 to around 48 °C at the eutectic) is taken to make supercooling and driving force much smaller zhu2012 C32, C33, whereas for PVP the predicted reduction is small marsac2006b C41. The driving force did not sort drugs by moisture-induced phase separation rumondor2009c C32. The supersaturation explanation of the nifedipine–felodipine ranking with water rests on NMP data and printed cosolvency fits that do not reproduce their points [marsac2008a X2, X4]. The celecoxib driving force was argued from Tm and not calculated mosqueragiraldo2014 C33.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir; tolazamide	77; 154 °C	DSC	baird2012 M34, M18
chlorpropamide; celecoxib; ketoconazole	108; 105; 105 °C, in classes I-B, II, III	DSC	baird2012 M9, M14, M26
slow and fast growth groups	85–117 and 121–146 for drugs with viscosity data	DSC	[trasi2014a R9]
class means I-A, I-B, II, III	123 ± 11, 119 ± 11, 126 ± 20, 108 ± 16 °C, not significantly different	DSC	baird2012 R10

Pitfalls and disagreements

The celecoxib Tm − Tg of 125 in one table conflicts with its own Tm and Tg (108) [trasi2014a X1], and the dibucaine row of another table repeats lidocaine baird2012 X1. The gap tracked growth groups but not the DSC classes (synthesis: compare R9 of trasi2014a with R10 of baird2012).

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
nevirapine	transfer rises with flow rate then falls	0.5–9 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, acetaminophen	atazanavir 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 lipid	PAMPA, buffer receiver	hate2022 R5, R16
Caco-2 and donor stirring	300 rpm donor and 500 rpm insert shaking to minimise the layer	side-by-side and Caco-2	alkalla2026 C15
neat HPMCAS-MF and HPMCAS-TEA	rate linear in √rpm, ≈2.9–3.3 times the 100 rpm rate at 700 rpm, no plateau	rotating 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 Amorphous solid dispersions: the whole picture

virtual bioequivalence

A simulated crossover study in a population of virtual subjects; a level passes when the 90% confidence interval of the test-to-reference ratio of Cmax, AUCt and AUC lies within 80.00–125.00% purohit2018 E10, P12. An absorptive dissolution test gives a second route: the test-to-reference ratio of receiver AUC with the 80–125% limits, at three volumes hate2019 R13, E6, C25.

Findings

F17, F28, F31.

Related concepts

assesses oral bioavailability; input from non-sink dissolution, residual crystallinity and absorptive sink.

Formulas

none.

How it is measured or obtained

24 virtual healthy fasted subjects, 5 mg, 50% CV on CYP3A parameters, Phoenix average bioequivalence purohit2018 P12.

Values in the library

material	value or class	conditions	paper ids
generic vs Prograf, 100 mL input	fails from 20% crystallinity (AUC ratio about 70%)		purohit2018 R13, R17
generic vs fresh generic, 100 mL input	fails from 10% (about 79.5%)		purohit2018 R14, R17
generic vs both, 900 mL input	fails from 40% (about 69% and 74.5%)		purohit2018 R15, R16, R17
tacrolimus (generic with residual crystallinity against Prograf), absorptive test	20% crystallinity bioequivalent at 100 mL, not at 40 mL; 50% and 100% not at any volume; fresh generic above the limit at 240 mL	hollow-fibre module, 240, 100, 40 mL	hate2019 R13, C25

Pitfalls and disagreements

Two-way crossover with fixed limits, not the replicated reference-scaled design now required for narrow-therapeutic-index drugs purohit2018 C13, X14. Only the mean ratio was evaluated in the absorptive test, and the outcome depends on the volume, so a pass at one volume is not a pass at all (F28) hate2019 R13, C41.

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir; efavirenz; loratadine	0.27; 0.44; 0.60	37 °C	ilevbare2013a M1, M2, M3
ketoconazole; indomethacin; felodipine	0.28; 0.73; 0.85	37 °C	ilevbare2013a M8, M7, M9
ibuprofen to griseofulvin	0.999, 0.997, 0.985, 0.932, 0.750, 0.699	25 °C	almeidaesousa2015 M1, M2, M3, M4, M5, M6
clotrimazole; atazanavir	0.82; 0.22	37 °C	indulkar2015 M1, M2
telaprevir; CRH1	0.30; 0.755	37 °C; 25 °C	[mosqueragiraldo2015 M1; almeidaesousa2016 M1]
atazanavir	exp[−I(a)] 0.22; 5.2% moisture	37 °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 Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
PVP K29/32	≈33 (75% RH), ≈75 g/100 g (95% RH)	25 °C	[konno2008 R8.a; rumondor2010a R1]
HPMC, HPMCAS	≈10.4–10.9 and ≈6.2–6.3 g/100 g at 75% RH	25 °C	[konno2008 R8; rumondor2010a R1]
amorphous felodipine, indomethacin	≈1.1 and ≈1.55 g/100 g at 75% RH	25 °C	[rumondor2010a R1.h]
felodipine–PVP 70 wt% PVP	≈10.3 (65% RH) turning up to ≈55.5 wt% (95% RH)	25 °C	marsac2010 R9
amorphous ritonavir (outside)	≈1.55% at 50% RH, rising, extrapolated linearly to 100% RH	37 °C	ilevbare2013a R7, E14
PVP, PVPVA, HPMCAS	isotherms at 25 °C, PVP far above the others at high RH	cited	[rumondor2010c R19]
resveratrol–PVP dispersion and physical mixture	0–95% RH, mixture above dispersion at every step	25 °C	[wegiel2013b R19]

Evidence table: water sorption isotherm.

Pitfalls and disagreements

Equilibration protocols differ between polymers and papers (5 h at fixed RH gives about half the plateau value for 50% PVP; synthesis from 4.8 against ≈9.4 g/100 g [marsac2010 R10.b; rumondor2010a R2.d]). One paper reports different PVP water contents in two figures konno2008 X2. Isotherms appear to be single runs [rumondor2010a X12].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
ritonavir	about 4.98% at 95% RH; 5.21% extrapolated to 100% RH (slope 0.075, intercept −2.290)	37 °C, melt-quenched	ilevbare2013a R7, E14
telaprevir	4.31% at 95% RH; about 4.6% estimated at 100% RH	melt-quenched glass	mosqueragiraldo2015 M1
clotrimazole; atazanavir	1.4%; 5.2%	amorphous, 37 °C	indulkar2015 M1, M2
griseofulvin; sorafenib	2.7%; 1.8% at water activity 1 (estimated, basis not stated)	25 °C	almeidaesousa2015 R8
atazanavir	5.2% moisture, exp[−I(a)] 0.22	amorphous, 37 °C	indulkar2017a M2
ibuprofen/HPMC 603 and ibuprofen/PVP-VA ASDs	13.9 and 13.0% (1/1); 6.5 and 4.2% (4/1) after 200 min	99% RH, 37 °C	[ueda2021 R17]
ECP–PVPVA powders	about 61% (PVPVA), 35% (10% DL), 4–7% (20–50% DL), 0.5–3.6% (60–100% DL)	24 h, 97–98% RH	li2017 R25, X3
felodipine, indomethacin, PVP, HPMC, HPMCAS	Flory–Huggins water parameters from isotherms	25 °C	[rumondor2010a R11]
clofoctol–PVP with 70% API or more; probucol–PVP	resistance to moisture-induced separation attributed to too little moisture sorbed by the hydrophobic systems; no water content or sorption was reported for those films	outside	[rumondor2011 C36, X6]
70 wt% PVP felodipine dispersion	water vapour sorption isotherm at 25 °C	outside	marsac2010 R9, R10
erlotinib–HPMCAS 60% DL, uncoated against 5–25 nm coated	about 5.7 against 5.4%	DVS 40 °C, 75% RH	moseson2022a R8, R9
ezetimibe–HPMCAS 50% DL, uncoated / thin / thick	about 5.65 / 5.83 / 3.17%	DVS 37 °C, 95% RH	duong2022c R9
PCZ–HPMCAS 25% DL, uncoated and coated 11 / 23 / 39 nm	about 4.7 / 4.3 / 3.7 / 1.2% at 30 min	DVS 37 °C, 90% RH	[moseson2023 R7]
PCZ–HPMCAS 50% DL, slow-deposited 26 nm	about 0.33% at 2 h against about 4.2–4.5%	same	[moseson2023 R8]
RTV–PVPVA 20% DL powders	about 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 g	75% RH, 25 °C	[marsac2008a R2]
felodipine–PVP 25%	43–64% below additivity	15–85% RH	[rumondor2010a R7.b]
nifedipine-, pimozide-, droperidol–PVP	5.9, 7.4, 0.2% from additivity (phase separated)	95% RH	rumondor2009c R22
indomethacin–PVP 75:25	4.9 vs 21.7 g/100 g predicted	95% RH	rumondor2009c R22.g
40% resveratrol–PVP dispersion	≈1.8, ≈5.9, ≈8.7, ≈12.8% at 20, 60, 80, 95% RH, below its physical mixture at every step	25 °C	[wegiel2013b R19]
atazanavir–PVPVA 10%; with SDS or Span 80	44%; 49% water	DVS, 37 °C, up to 95% RH	correasoto2022b R16
amorphous lumefantrine salts	≈6.6 (PEG 250 diacid 1:1), 3.3 (sulfate), below 2% (benzoate, besylate, tosylate, camsylate, HCl) at 95% RH	DVS	hiew2022b R4
lumefantrine salt–PVPVA dispersions	35–55% water, higher at lower loading	95% 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 h	powders, 100% RH, 37 °C	[qi2022 R11]
neat HPMCAS-MF; indomethacin and its methyl ester dispersions	highest extent and rate for the neat polymer; lower with indomethacin, lowest with the ester	powders, 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 min	95% RH, 37 °C	[correasoto2023 R22]

Pitfalls and disagreements

The relative humidity to which the % moisture of the weak-base table refers is not stated indulkar2015 M1, M2. Linear extrapolation to 100% RH is an approximation ilevbare2013a E14. In the film papers, uptake was measured on bulk powders, not on the films imaged by TEM, and the values at 20–50% and 60–80% DL differ by only a few per cent although separation was seen to 80% DL li2017 X8, R19. The same explanation (too little moisture sorbed at high loading) is given for other hydrophobic drug–PVP systems without sorption data [rumondor2011 C36, X6]. The thin 50% ezetimibe coating protected for two years without lowering uptake duong2022c X7. The slow-sorbing posaconazole samples had not levelled off within 2 h [moseson2023 X17]. The two moisture papers normalise the deviation from additivity differently (against the prediction, against the measured value) [rumondor2010a E6; rumondor2009c E6]. No sorption was measured on the films in which nucleation and growth were counted [marsac2008a X12]. The lower uptake of the resveratrol dispersion is read as hydrogen bonds suppressing sorption, but bonding in the wet dispersion was not measured [wegiel2013b C37, X18]. The dispersion sorption curves of both papers are in SI not supplied correasoto2022b R16; hiew2022b R5. The excess-acid PEG 250 diacid (1:1) salt liquified at 95% RH hiew2022b C10. Among the HP-50 salts the sodium salt took up the most water without dissolving faster, which weakens hydration as the explanation of the salt effect [qi2022 X17, C35].

← Concepts and formulas

concept · as used in Amorphous solid dispersions: the whole picture

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

material	value or class	conditions	paper ids
probucol–PEO tablets	gel formation in the medium; highest release	29 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 better	dissolution medium	[hiew2023 R9, C20]
uncoated 70% ezetimibe–HPMCAS powder	floated; peak about 7.6 µg/mL against about 11.9 and 10.9 for the coated powders	10 mg in 50 mL, pH 6.5	duong2022c R13, R14
slow-coated 20.5 nm ritonavir–PVPVA particles	part unhydrated after 10 min; almost no further hydration after 3 h in acid; sonic sieving restores it	confocal	[benson2025 R7, R8, R9]
30% BCL–PVPVA, binary powder with 3 µg/mL SDS in the medium	about 46% at 30 min against about 42% without	dose of at most 30 µg/mL	moseson2022b R9
PVPVA; HPMCAS (cited)	water contact angle 30.6°; 58.6°	literature	[yang2021 M7, M8]
grazoprevir–HPMCAS 75:25 particles with SDS; with 10 mg/mL HPMC	0° from 1 s; ≈30° and 51–52° at 10 s	FaSSIF, 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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
a, a^{*} (or a^{\circ})	activity of the drug in the solution and in a solution saturated with the crystal	dimensionless indulkar2017a E9; lu2017b E3; dening2019 E5
\gamma, \gamma^{*}	activity coefficients at the two states	dimensionless indulkar2017a E9; dening2019 E5
c, c^{} (or C, C^{})	concentrations at the two states	µg/mL indulkar2017a E9; dening2019 E5
F, F^{\circ}	mass flow rate of the solution and of the crystal-saturated solution	µg/min lu2017b E6
\delta	fundamental (activity-based) supersaturation	dimensionless lu2017b E3
\mu, \mu^*	chemical potential in the solution and at saturation with the crystal	J/mol raina2015c E5; dening2018 E5
C_i, C_S	concentration and crystalline solubility	µg/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_i	free drug concentration (from flux); supersaturation, equal to a	µg/mL; dimensionless jackson2015 E2
R, T	gas constant, temperature	J/(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

paper	used for	values or fitted parameters	status / recomputed
indulkar2017a	SRactivity and SRconc of atazanavir in 0–3.6 mg/mL SDS	SRactivity about 65–70 at the amorphous solubility; SRconc 33–38 in SDS	reproduces (1450 ÷ 45.6 = 31.8 against about 31.0 and 33.0 in Figs. 7a, 7b) indulkar2017a E9, R12, R13
lu2017b	δ of telaprevir from flux	buffer 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
lu2017b	activity-coefficient ratio from flux slopes	slopes not printed	inputs not printed lu2017b E7
other chapters	the same relation printed as an activity ratio or a chemical-potential difference	none	printed; not recomputed here [raina2014a E10; raina2015c E5; jackson2015 E2; lu2017 E1; wilson2018 E7; elkhabaz2019b E2; indulkar2019b E1]
raina2014a	activity of felodipine	5.99/0.74 = 8.09 (text about 8); 2/0.74 = 2.70	reproduces raina2014a E10
raina2015c	defining S	none	not applicable raina2015c E5
jackson2015	danazol activity	8.1/0.9 = 9.0 against about 8.9	reproduces jackson2015 E2
wilson2018	enzalutamide	S printed "approximately 13" from the Table 2 ratio	mismatch: 42/2.9 = 14.5; 13 matches the theoretical 39/2.9 wilson2018 E7, X2
elkhabaz2019b	atazanavir and posaconazole in six media	read as J_{amph}/J_{eq}; \gamma not determined	inputs not printed elkhabaz2019b E2, C28
li2016a	apparent S' = C/C_s with γ ratio set to 1, tested against mass flow	nevirapine S' 7.1–8.7; celecoxib printed 13.6 against 16.7 recomputed	inputs not printed for γ; mismatch for celecoxib [li2016a E1, X1, X18]
lu2017	δ 11.5 and 28.8 for telaprevir with six bile salts	see the flux-ratio formula	calibrated from flux [lu2017 E1, R1]
indulkar2018	supersaturation in lecithin and SIF media	SR = a/a^{*}, crystalline standard state	inputs not printed indulkar2018 E1
indulkar2019b	atazanavir in SDS	as above	stated about 65, flux not shown [indulkar2019b E1, X6]
elkhabaz2021	cited for atazanavir and posaconazole in six media	named only	54; 36 and 30 elkhabaz2021 E8, R4
duong2022b	posaconazole in micellar media	estimated from the concentration ratio with Km/w falling linearly	inputs not printed [duong2022b E11]
dening2018	falling released fraction with dose from silica	none	inputs not printed dening2018 E5
dening2019	adsorption onto silica rising with supersaturation	none	inputs not printed dening2019 E5
jackson2015	maximum supersaturation of danazol dispersions	eight bars equal free drug over 0.9 µg/mL; 90:10 HPMCAS and 50:50 HPMC do not	reproduces in part jackson2015 R10, X3
xie2015	definition of the driving force for celecoxib nucleation	none	not 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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
a	thermodynamic activity of the drug	dimensionless mosqueragiraldo2015 E5
x_i	mole fraction of the component	dimensionless ilevbare2013a E7
C	concentration of the drug in the donor solution	µg/mL mosqueragiraldo2015 E5
\gamma	activity coefficient in the bulk (donor) solution	dimensionless 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

paper	used for	values or fitted parameters	status / recomputed
ilevbare2013a	activity of a species equal in all phases at equilibrium	none	not applicable (no numerical output) ilevbare2013a E6, E7
mosqueragiraldo2015	donor activity in the flux equation	none printed	inputs not printed (γ) mosqueragiraldo2015 E5
indulkar2017a	free atazanavir in SDS from the slope γ of free against total drug	γ 0.998, 0.181, 0.086, 0.047 at 0, 1, 2, 3.6 mg/mL SDS	reproduces (0.047 × 1450 µg/mL = 68 against about 70 plotted free) indulkar2017a E8, R11
lu2017b	activity of telaprevir in bile-salt media	none printed	inputs not printed (γ) lu2017b E2
raina2014a	flux proportional to activity	γ not printed	not applicable raina2014a E7
raina2015c	why equal concentrations give different flux	γ not printed	not applicable raina2015c E4
alhalaweh2016	Caco-2 flux of ritonavir–atazanavir mixtures	γ not printed	inputs 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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
w_D, w_P	dry-basis weight fractions of drug and polymer	– rumondor2009c E6
uptake, M	water sorbed at the same RH	g/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

paper	used for	values or fitted parameters	status / recomputed
rumondor2009c	marker of moisture-induced separation	within 0.2–7.4% of measured for separating dispersions; 121.7% and 341.5% off for mixed ones	reproduces within 0.1 rumondor2009c E6, R22
rumondor2010a	shortfall of one-phase blends	up to ≈64% (felodipine–PVP) below the sum	reproduces from Fig. 1 readings [rumondor2010a E5, R7]
li2018 (outside)	lopinavir dispersions with six polymers	CA, EUD, CAP near additive; HPMCAS, HPMCP below	reproduces [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 Amorphous solid dispersions: the whole picture

adsorbed amount by solution depletion

Expression

Q_a = \frac{(C_i - C_e)\,V}{m} dening2019 E1.

Q_a = \frac{(C_i - C_e)\,V}{m} mccarthy2020 E1.

Q = \frac{(C_{\mathrm{initial}} - C_{\mathrm{equilibrium}})\,V}{m_{\mathrm{SBA\text{-}15}}} (restated; printed in words) hate2020a E3.

The electrostatics paper prints it in words as the amount at the initial concentration minus the amount at the equilibrium concentration hate2020b E4. Outside silica, the polymer adsorbed per area of seed crystals is

C_a = \frac{(C_i - C_f)\,V}{m\,A} [ilevbare2012b E10].

Variables and units

symbol	meaning	units
Q_a, Q	amount adsorbed at equilibrium per mass of silica	mg/g dening2019 E1; mccarthy2020 E1
C_i, C_e	initial and equilibrium solution concentration	µg/mL dening2019 E1
V	solution volume	mL; 40 mL dening2019 P3; mccarthy2020 P7
m	mass of silica	0.5 mg dening2019 P3; 5 mg mccarthy2020 P7
C_a, A	polymer adsorbed per area; BET area of the seeds	mg/m²; 1.265 m²/g [ilevbare2012b E10]

Assumptions and valid domain

Above the crystalline solubility the "equilibrium" is a metastable, transient one, held while nothing crystallizes dening2019 C7; mccarthy2020 C9; methanol from the stock (0.01–0.3% or below 0.5%) is taken as negligible dening2019 C8; hate2020a C18. Used from below the crystalline solubility to about the amorphous solubility at 37 °C dening2019 P3; mccarthy2020 P7; hate2020a P13.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
dening2019	ritonavir isotherm on SBA-15	39–424 mg/g	reproduces: C_i 30 µg/mL, V/m 80 mL/mg and 424 mg/g give C_e 24.7 µg/mL dening2019 E1
mccarthy2020	indomethacin and methyl ester isotherms	up to about 289 and 342 mg/g	mismatch: with 40 mL and 5 mg the methyl ester cannot exceed 112 mg/g at C_i 14 µg/mL mccarthy2020 E1, X2
hate2020a	atazanavir isotherms at 300 and 25 µg/mL silica	about 1.6–20.8 and 7.5–193 mg/g	reproduces approximately: 9% of 60 µg/mL on 300 µg/mL gives 18 against about 16.2 mg/g hate2020a E3
hate2020b	isotherms of three bases at four pH values	up to about 66 mg/g	inputs not printed hate2020b E4
ilevbare2012b	HPMC on ritonavir seed crystals	up to about 40.8 mg/m²	reproduces [ilevbare2012b E10]

Where it fails or is disputed

When only a few percent of the drug is removed, as with 25 µg/mL silica, the amount rests on concentration differences near the assay precision hate2020a X15. The indomethacin values exceed the mass balance for the stated volume and silica mass mccarthy2020 X2. Repeated runs near the top of the ritonavir isotherm differed by about 90 mg/g dening2019 X4. The silica concentration changed the per-gram result for atazanavir, which a single isotherm should not do hate2020a X15.

Concepts

adsorption isotherm, drug adsorption onto silica. Findings. F3, F5, F6, F9, F10.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
AI	amorphicity index of one sample	% vaneerdenbrugh2010b E1
A letter	amorphous letter in the four-letter category, one for each of day 0, 1, 3 and 7	count, 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 polymers	count 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

paper	used for	values or fitted parameters	status / recomputed
vaneerdenbrugh2010b	amorphicity 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 48	reproduces (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
vaneerdenbrugh2010b	per-drug ranking	PH 47, CZ 47, BD 48, LI 55, FFA 59, FB 68, CP 73, BI 97	derived vaneerdenbrugh2010b R4
vaneerdenbrugh2010b	per-polymer ranking	PVP 70, PVPVA 70, E100 67, HPMC 66, HPMCAS 62, PAA 49, PSSA 48	derived vaneerdenbrugh2010b R5
vaneerdenbrugh2011a	amorphicity 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 screen	reproduces: 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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
a, b; c, d; e, f	linear fit parameters of the reversing Cp of supercooled liquid, crystal, glass	J mol⁻¹ K⁻¹ and J mol⁻¹ K⁻² almeidaesousa2015 E6, E7, E8
\Delta_{fus}H, T_m	enthalpy of fusion, melting temperature	kJ/mol, K almeidaesousa2015 E9
\Delta H, \Delta S, \Delta G	conversion enthalpy, entropy, free energy at T	kJ/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

paper	used for	values or fitted parameters	status / recomputed
almeidaesousa2015	six drugs at 25 °C; sorafenib and griseofulvin also to the glass	ΔG 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
mosqueragiraldo2015	telaprevir at 37 °C	97 ± 8 and 189 ± 16 µg/mL through Eq. 1	ΔCp values not printed mosqueragiraldo2015 E3, R13
almeidaesousa2016	CRH1	5.85 and 5.95 kJ/mol	method 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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
x_{SL,L_1}, x_{C,L_1}	mole-fraction solubility of the supercooled liquid and of the crystal in water	dimensionless ilevbare2013a E3, E4
\Delta G_{a\to c}	free-energy difference amorphous–crystal	ilevbare2013a E2
\mu_1^{\circ}, \mu_{1c}^{\circ}	chemical potential of pure amorphous (supercooled liquid) and crystalline drug	trasi2015a E1
S_a, S_c	amorphous and crystalline solubility	µg/mL trasi2015a E1, R1
S_{amorphous}, S_{crystalline}	solubility of the amorphous and crystalline forms	µg/mL hsieh2012 E4
a_{amorphous}, a_{crystalline}	thermodynamic activity of the solid form	dimensionless hsieh2012 E4
\Delta G_c	free-energy difference between the forms (Hoffman equation)	kJ/mol hsieh2014 E3
R, T	gas constant; temperature	J mol⁻¹ K⁻¹; K
\sigma^{\mathrm{amorph}}, \sigma^{\mathrm{crystal}}	solubility of each form (2011 notation)	µg/mL alonzo2011 E2
S_A, S_C	amorphous and crystalline solubility (2018 notation)	µg/mL [li2018 E2]
\mu_A, \mu_C	chemical potential of the drug in the amorphous and the crystalline solid	J/mol [li2018 E2]
\Delta G; C_a, C_s	free-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

paper	used for	values or fitted parameters	status / recomputed
ilevbare2013a	first approximation of the amorphous solubility, ritonavir	none printed	not applicable (no numerical output) ilevbare2013a E5
trasi2015a	defines the amorphous-to-crystalline solubility ratio	ritonavir 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
hsieh2012	uncorrected amorphous solubility of five bases	ratios 22.2, 11.9, 20.4, 54.6, 7.0	ratios reproduce from printed solubilities (24.4/1.1 = 22.2) hsieh2012 E4, R10
hsieh2014	glyburide and warfarin	about 60 and 48	reproduces 59.9 and 47.7 at 25 °C hsieh2014 E3, R16
konno2008a	felodipine at 37 °C	ratio about 10: 10 × 0.94 = 9.4 against printed about 9.5 µg/mL	reproduces within rounding konno2008a E1
alonzo2011	felodipine at 37 °C	ratio about 9 implies ΔG = RT ln 9 ≈ 5.67 kJ/mol	inputs not printed alonzo2011 E2
alonzo2011	flux of pure amorphous felodipine against crystal	ratio 8.5	close to the estimate alonzo2011 R14, C40
li2018	lopinavir, pH 3, 25 °C	measured S_A/S_C = 17.4/3.1 = 5.6; \mu_A - \mu_C not printed	inputs not printed [li2018 E2, R1] (synthesis: RT\ln 5.6 ≈ 4.3 kJ/mol at 298 K)
duong2022a	turning a Hoffman free-energy estimate into a delamanid solubility ratio	measured ratio 42.3 at pH 6.5 against 31.8 estimated	the 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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
C_{amorphous}	predicted amorphous solubility	µg/mL ilevbare2013a E1
C_{eq}, C_T	crystalline solubility in the test medium	µg/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 isotherm	dimensionless, 0.22–0.999 indulkar2015 M2; almeidaesousa2015 M1
\Delta G	free-energy difference between amorphous (supercooled liquid or glass) and crystal	kJ/mol, from the Hoffman or heat-capacity route almeidaesousa2015 E2, E11, E14
R, T	gas constant (8.314 J mol⁻¹ K⁻¹ in the checks), temperature	298.15 or 310.15 K almeidaesousa2015 E1; ilevbare2013a E1
\sigma_a, \sigma_c	amorphous and crystalline solubility	µg/mL raina2014a E5
e^{-I(a_2)} for felodipine, nifedipine	factor for the activity lowered by absorbed water	0.74–0.83 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 solid	dimensionless 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

paper	used for	values or fitted parameters	status / recomputed
ilevbare2013a	eight drugs, 37 °C	4.0–133.3 µg/mL; ritonavir 39.2 in water, 20.6 in buffer	reproduces within about 5% for ketoconazole, clotrimazole, felodipine, clozapine, not for ritonavir (32.9 against 39.2), efavirenz, loratadine, indomethacin ilevbare2013a E1, X1
almeidaesousa2015	six drugs, 25 °C	Hoffman 0.272–402.29, Cp supercooled liquid 0.325–356.44 µg/mL	reproduces (ibuprofen, Hoffman: 29.29 × 0.999 × exp(3240/(8.314 × 298.15)) = 108.1 against 108.16) almeidaesousa2015 E1, R11
indulkar2015	clotrimazole, atazanavir	ratios about 9.2 and 62; 4.9 and 64.9 µg/mL	printed sign mismatch: exp[−ΔG/RT] gives 0.072 for clotrimazole; exp[+ΔG/RT] gives 9.30 and 62.2 indulkar2015 E2, X1
mosqueragiraldo2015	telaprevir, 37 °C	245 ± 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
almeidaesousa2016	CRH1, pH 6.8 and pH 4.6 + HPMC	9.0–10.0 and 11.2–12.5 µg/mL	reproduces for all six values [almeidaesousa2016 E1, R2]
indulkar2017a	atazanavir, 37 °C	ratio 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
ueda2021	ibuprofen, pH 2.0 (D2O), 37 °C	151 µg/mL against 154 µg/mL measured	inputs 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]
ueda2022	ibuprofen in buffer, 25–60 °C	predicted ratio about 3.7 → 1.3 (20 → 65 °C); measured 5.8 → 2.5	inputs not printed; predicted below measured at every temperature [ueda2022 E1, R16]
raina2014a	felodipine, nifedipine	0.74 × 10.92 × 0.74 = 5.98 (printed 5.99); 10.00 × 8.78 × 0.82 = 72.0	reproduces raina2014a E5
raina2015c	same drugs, FaSSIF	FaSSIF estimate assumes the buffer ratio	inputs not printed raina2015c E2
indulkar2016	clotrimazole	factor in square brackets in the paper	inputs not printed indulkar2016 E15
wilson2018	enzalutamide	printed 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
hsieh2012	five type 2 bases	ratios 12.3, 9.8, 16.7, 15.3, 4.3	inputs not printed; ratios reproduce from printed solubilities hsieh2012 E6
ilevbare2012b	ritonavir	20.6 µg/mL from Ceq 1.3, ΔHf 60.4 kJ/mol, Tm 121 °C	inputs not printed (I(a2)) [ilevbare2012b E8, R1]
ilevbare2013b	celecoxib, efavirenz, ritonavir	22.6, 19.8, 20.6 µg/mL	inputs not printed [ilevbare2013b E2]
ilevbare2013c	same, starting concentrations	same	inputs not printed ilevbare2013c E6, R2
jackson2014	danazol	exp[−I(a2)] 0.935; ratio 19.6 printed	mismatch: 15.4 recomputed jackson2014 E1, X1
raina2015b	e^(−I(a2)) e^(ΔG/RT) for six dihydropyridines	e^(−I(a2)) 0.74–0.91; estimates 0.5–48 µg/mL in buffer	mismatch: felodipine 5.93 recomputed against 6.68 µg/mL raina2015b E2, X2
jackson2016	amorphous solubility of danazol from crystalline solubility, DSC data with heat capacity and moisture sorption	7.8 µg/mL (earlier 16)	named only; thermal inputs not printed [jackson2016 E3, R3]
duong2022b	posaconazole at pH 7.0	C_A = \exp[-\Delta G/RT]\exp(-I_a)C_T as printed; ratio 37.9 with activity factor 0.33	estimate 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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
LLPS onset	concentration of the extinction rise (the amorphous solubility)	µg/mL
crystalline solubility	shake-flask value in the same medium	µg/mL
\sigma^{\mathrm{amorph}}, \sigma^{\mathrm{crystal}}	solubility of amorphous and stable crystalline form	µg/mL alonzo2010 E1
\Delta G	free-energy difference, from the Hoffman equation	J/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

paper	used for	values or fitted parameters	status / recomputed
raina2015c	felodipine in three media	177.3/39.3 = 4.51; 214.6/42.8 = 5.01; 10.4/1.1 = 9.45 (printed 9.2)	reproduces except buffer raina2015c E8, X2
alonzo2010	felodipine 37 °C	ΔG 5729 J/mol, ratio 9.22	reproduces alonzo2010 E1
trasi2016	tacrolimus monohydrate	49/1.4 = 35.0	reproduces: 35.0 against printed approximately 35 trasi2016 E1, R16
lu2017b	telaprevir	148/5.2 = 28.5	reproduces lu2017b E5
purohit2019	tacrolimus, maximum supersaturation	printed about 33	mismatch: 50/1.4 = 35.7 with the text value, 50/1.5 = 33.3 with the figure-caption value purohit2019 E2, X1
ueda2020a	atazanavir, nifedipine, clozapine, ketoconazole with HPMCAS grades	twelve ratios in Table 1	eleven reproduce; clozapine with AS-LF printed 5.9, recomputed 219.0/22.0 = 9.95 ueda2020a E1, X1
nguyen2023a	pretomanid in seven media	printed 6.0 in FaSSIF V1	mismatch: 308/53.8 = 5.72; buffer pH 6.5 reproduces (166.1/16.2 = 10.25, printed 10.2) nguyen2023a E3
alonzo2010	indomethacin, 37 °C	ratio 12.17 × 3 µg/mL = 36.5 against about 37 µg/mL	reproduces alonzo2010 E2
alonzo2010	indomethacin, 25 °C	ratio 15.75 gives 15.8–23.6 against printed 17–25 µg/mL	mismatch alonzo2010 X2
que2018	paclitaxel, pH 6.8, 37 °C	31.6/0.36	reproduces: 87.8 against printed 88 que2018 R1, R2
duong2022a	delamanid at pH 6.5	0.76/0.018	reproduces: 42.2 against printed 42.3 duong2022a R1, R27
nguyen2023c	delamanid at pH 1.6 and 6.5	154.5/10.2 and 0.76/0.018	reproduces: 15.1 and 42.2 against printed 42 at pH 6.5 nguyen2023c R1, R2
alvarenga2025	praziquantel in nine media, racemate and R-enantiomer	5.6–7.7 and 4.0–5.8	reproduces for PBS pH 6.5: 1.17/0.16 ≈ 7.3 and 1.39/0.23 ≈ 6.0 alvarenga2025 R1, E1
polyzois2024	praziquantel at pH 6.5	1.4/0.2826 and 1.1/0.1964	reproduces: ≈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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
\text{rate}	cooling rate	K min⁻¹ baird2010 E1
\Delta T	undercooling at the crystallization peak on cooling, T_m - T_{crys,max}	K [baird2010 E1; baird2013 E4]
A, B	intercept and slope of the regression	B in K² baird2010 E1
R_{crit}	critical cooling rate, ΔT extrapolated to infinity	K 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

paper	used for	values or fitted parameters	status / recomputed
baird2010	Rcrit of 19 class I molecules	r² 0.74–0.99 for 7 and below 0.55 for 12; Rcrit from 20 K/min (haloperidol) upward	reproduces (carbamazepine B 701 against 708, A 4.75 against 4.8; haloperidol \exp(3.0) = 20.1) baird2010 R13, E1, E2
baird2013	Rcrit,cool of class I-A from 5–800 °C/min	2.7 × 10³ (phenacetin) to 8.1 × 10³ K/min (4-biphenylmethanol), r² 0.89–0.99	reproduces 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 Amorphous solid dispersions: the whole picture

boundary-layer diffusion flux (film model)

Evidence table: boundary-layer diffusion flux (film model). Content from the release-mechanism chapter (2023–2025), with a row from the Bioperformance chapter.

Expression

J_p = \frac{D_p}{\delta}\,C_p [bapat2023 E2]

The Bioperformance chapter printed the steady-state form across an unstirred water layer:

C_b - C_{m1} = \frac{J \times d_{UWL}}{D} hate2022 E6

J_p = \frac{D_p}{\delta}\, C_p bapat2024 E3

J_p = \frac{D_p}{\delta}\, C_p kaur2025 E1

Variables and units

symbol	meaning	unit
J_p	polymer flux	not printed
D_p	polymer diffusion coefficient	not printed
\delta	boundary-layer thickness	not printed
C_p	polymer solubility at the polymer–solution interface	not printed
C_b, C_{m1}	bulk donor concentration; aqueous concentration at the layer–membrane interface (Bioperformance form)	not printed
J, d_{UWL}, D	mass flow rate; layer thickness; solute diffusion coefficient (Bioperformance form)	not printed

Assumptions and valid domain

Diffusion-controlled regime at a rotating disk under laminar flow (cited) [bapat2023 E2]; in the Bioperformance form, steady state with mass flow across the layer equal to that across the membrane (cited) hate2022 E6.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
bapat2023	HPMCAS-MF release across media, gel pH and rotation speed	none	inputs not printed (D_p, C_p) [bapat2023 E2, R5, R16, R18]
hate2022 (Bioperformance)	transport of supersaturated solutions across PAMPA membranes	none	inputs not printed hate2022 E6, R19
bapat2024	lower interfacial HPMCAS solubility from an insoluble drug complex slows polymer and drug release	none	used in argument bapat2024 E3, C32
kaur2025	the same for bedaquiline–HPMCAS	none	used in argument kaur2025 E1, C41

Where it fails or is disputed

The interfacial polymer solubility C_p is not measured; a lower interfacial pH, inferred from gel measurements, stands in for it [bapat2023 C38]. The rate rose above the \omega^{1/2} proportionality expected with the Levich thickness at 700 rpm [bapat2023 X10]. The interfacial polymer solubility was not measured in either paper bapat2024 X10; kaur2025 X14.

Concepts

unstirred water layer, microenvironmental pH, buffer capacity, diffusion boundary layer. Findings. Release mechanism and LoC: F23, F32, F34.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

Cabrera-Vermilyea step pinning

Expression

\frac{V_\rho}{V_\infty} = 1 - \frac{\rho_c}{\rho} alonzo2012 E8

Growth is arrested when the spacing of adsorbed impurity molecules equals 2\rho_c alonzo2012 C9.

Variables and units

symbol	meaning	unit
V_ρ	growth rate of a two-dimensional nucleus (step) of radius ρ	m/s
V_∞	step growth rate at infinite radius	m/s
ρ_c	critical radius of a two-dimensional nucleus	nm
ρ	radius of curvature of the step between pinning points	nm

Assumptions and valid domain

The spacing L of adsorbed impurities does not depend on supersaturation; ρc falls as supersaturation rises, so the maximum effect of an additive falls with S alonzo2012 C9. Not tested numerically in the chapter papers (no use of eq 8 in a calculation).

Use in the library

paper	used for	values or fitted parameters	status / recomputed
alonzo2012	argument for the fall of HPMC's effect with S	none	inputs not printed alonzo2012 E8, C9
ilevbare2012b	step pinning chosen among four mechanisms	α 4.35, 1.25	argument only [ilevbare2012b C12, E7]
que2018	critical radius 5–7 nm against site spacing 10–20 nm at S 88 (ASD dissolution chapter)	ρc from γ surrogates	derived que2018 R15, C38
schram2015	R_P/R_0 = 1 − ρc/l applied qualitatively to the AFM globule spacing	l about 44 nm at pH 3; ρc not estimated	inputs not printed [schram2015 E3, X7]
schram2016	V_P/V_0 = 1 − ρc/l with measured l and computed ρc	l 68.5 and 15.8 nm; ρc 3.98 nm; V_P/V_0 0.94 and 0.75	recomputed; predicts rate ratios of 1.06 and 1.34 against 2.7 and about 12 [schram2016 E4, R12, R14, X3]

Where it fails or is disputed

The spacing of adsorbed HPMC on felodipine, the quantity the equation needs, was not measured alonzo2012 C28. The model's mechanism is chosen by argument against three others [ilevbare2012b C12]. The arrest criterion is l ≤ ρc in one place and l ≤ 2ρc in another [schram2016 X1].

Concepts

step pinning, critical radius of a two-dimensional nucleus. Findings. F9, F10, F23, F24.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
W^*	free energy to form a nucleus of critical size	not stated baird2010 E24
\gamma, \sigma_{cm}	interfacial free energy of the nucleus–liquid (or nucleus–matrix) interface per area	not stated vaneerdenbrugh2010a E3; baird2012 E2
\Delta G_v	free energy difference per volume between crystal and liquid	J/cm³ vaneerdenbrugh2010a E2, E5
\Delta G^{*}	free energy of forming the critical nucleus	J hsieh2012 E8
S	supersaturation ratio	dimensionless
\gamma, v	interfacial 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

paper	used for	values or fitted parameters	status / recomputed
baird2010	argument that a more negative ΔGv of class I lowers the barrier	none	inputs not printed baird2010 E24, C61
vaneerdenbrugh2010a	reading the ΔGv–class link	none	inputs not printed vaneerdenbrugh2010a E3, C39
baird2012	argument that viscosity enters nucleation and growth	none	inputs not printed baird2012 E2, C4, C32
duong2022b	posaconazole 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 33.6	reproduces [duong2022b E8, R17]
hsieh2012	why type 1 bases precipitate only after reaching a supersaturation of 1.4–26.7 times the titration solubility	none	not applicable (no numerical output) hsieh2012 E8, R5
xie2015	reading polymer effects on celecoxib induction times (ASD dissolution chapter)	γ, v not fitted	printed 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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	unit
J	nucleation rate	m⁻³ s⁻¹
A	pre-exponential kinetic factor, depends on molecular mobility	m⁻³ s⁻¹
ΔG*, ΔG_crit	free energy of forming a critical nucleus	J
k, k_B	Boltzmann constant	J/K
T	absolute temperature	K
γ	interfacial tension (free energy) between nucleus and solution	J/m² (mJ/m² in the posaconazole fits)
ν, v, ν_o	molecular volume	m³ (920 Å³ for posaconazole)
S	supersaturation	dimensionless
v*, z, n	monomer attachment rate, Zeldovich factor, number density of molecules	as printed
I	nucleation rate in the film papers	m⁻³ s⁻¹ konno2006 R4
\Delta G^{}, W^{}	thermodynamic barrier, from interfacial term against bulk driving force	J konno2006 E8
\Delta G_{a}, \Delta G_{\eta}	kinetic barrier for transport onto the nucleus	J konno2006 E8
T_r, \Delta T_r	reduced temperature T/T_m and 1 - T_r	– trasi2012a E1
\Delta H_f; \Delta G'	heat of fusion; activation energy for molecular motion	not 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

paper	used for	values or fitted parameters	status / recomputed
hsieh2012	why type 1 bases precipitate only above a certain supersaturation	none	not applicable (no numerical output) hsieh2012 E7
ilevbare2013c	why a polymer gains more at lower supersaturation (celecoxib 31-fold at S 7.3)	none	inputs not printed ilevbare2013c E4, C45
xie2015	celecoxib 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 PVP	γ, v not fitted; γ, v, A not printed	printed; inputs not printed xie2015 E3, C42, C43
trasi2015	J = A exp[−16πγ³v²/(3k³T³(ln S)²)] to state that T, S and γ set J	acetaminophen S 1.5, 20 °C	inputs (A, γ, v) not printed [trasi2015 E6]
li2016a	named only: nucleation rate depends highly on supersaturation	bile-salt series	named only [li2016a E5]
indulkar2018	why lecithin might accelerate nucleation through γ	none	inputs not printed indulkar2018 E6, C40
elkhabaz2021	why surfactants should lower γ, and why human fluid does not fit	none	printed without minus sign elkhabaz2021 E2, X1
duong2022b	linearized fit of posaconazole induction times in buffer and three media	γ 3.52, 2.61, 2.73, 3.24 mJ/m²; A 2.44, 5.14, 4.98, 9.87	reproduces from the printed slopes and intercepts [duong2022b E7, R16]
konno2006	sorting polymer effects into driving force and kinetic barrier	none	inputs not printed konno2006 E8
marsac2006a	framework for the nifedipine–felodipine comparison	none	framework only [marsac2006a E9]
baird2012	role of viscosity in class differences	none	inputs not printed baird2012 E1
trasi2012a	framework for polymer effects on acetaminophen nucleation	none	inputs not printed; printed form has misprints trasi2012a E1, X1
konno2008a	felodipine nucleates readily at a high solubility ratio	none	not applicable konno2008a E3
alonzo2010	scheme of dissolution against crystallization	none	not applicable alonzo2010 E4
ilevbare2013d	nucleation favoured in drug-rich droplets	none	printed 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 Amorphous solid dispersions: the whole picture

competitive solvent-drug adsorption equilibrium

Expression

\text{adsorbed drug} + \text{solvent} \rightleftharpoons \text{adsorbed solvent} + \text{drug in solution} dening2018 E4.

\text{adsorbed drug} + \text{solvent in solution} \rightleftharpoons \text{adsorbed solvent} + \text{drug in solution} dening2019 E9.

\text{adsorbed drug} + \text{solvent in solution} \rightleftharpoons \text{adsorbed solvent} + \text{drug in solution} mccarthy2020 E5.

The same group writes the analogous exchange with a surfactant and a three-way equilibrium with micelles (see the chapter's formula table) dening2019 E10, E11.

Variables and units

symbol	meaning	units
adsorbed drug, drug in solution	drug on the silica surface and dissolved drug	qualitative dening2018 E4
solvent	water	qualitative dening2018 E4

Assumptions and valid domain

Polar water displaces adsorbed drug; a higher dose and theoretical supersaturation shift the equilibrium to the left (toward adsorbed drug) dening2018 E4, C53. With supersaturated solutions the equilibrium is metastable dening2019 C2, C7. Proposed for ritonavir, indomethacin and its methyl ester on SBA-15 dening2018 C4; mccarthy2020 C47.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
dening2018	explaining the fall of released fraction with dose	qualitative	not applicable dening2018 E4
dening2019	the hypothesis behind the isotherm study	qualitative	not applicable dening2019 E9
mccarthy2020	explaining renewed release of the recovered solid	qualitative	not applicable mccarthy2020 E5

Where it fails or is disputed

Loaded silica kept about 50% of its ritonavir, blank silica took up only about 20%, so retention "may therefore depend only in part on the adsorption equilibrium" dening2018 C47. Release on dilution stopped at about one BET monolayer, read as partly irreversible adsorption dening2019 C32. Slow diffusion of drug in the pores that is not adsorbed would respond to the bulk concentration in the same way hate2020a X16.

Concepts

dynamic adsorption-desorption equilibrium, competitive adsorption, drug adsorption onto silica. Findings. F9, F12, F14.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

congruent release relation

Evidence table: congruent release relation. Content from the ASD dissolution chapter (2011) and from papers of the release-mechanism chapter.

Expression

G_D = \frac{G_C\,A_D}{A_C} alonzo2011 E4

\left(\frac{dC}{dt}\right)_{drug} = \left(\frac{dC}{dt}\right)_{polymer}\frac{m_{drug}}{m_{polymer}} indulkar2019a E3

G_B = \frac{N_B}{N_A}\,G_A xie2016a E1

Printed with weight fractions in the 2020 felodipine study:

\left(\frac{dC}{dt}\right)_{drug} = \left(\frac{dC}{dt}\right)_{polymer}\frac{N_{drug}}{N_{polymer}} saboo2020a E2

Printed in the 2022 ritonavir surfactant study:

\left(\frac{dC}{dt}\right)_{\mathrm{drug}} = \frac{\left(\frac{dC}{dt}\right)_{\mathrm{polymer}} m_{\mathrm{drug}}}{m_{\mathrm{polymer}}} indulkar2022 E1

Variables and units

symbol	meaning	unit
G_D, G_C	dissolution rate of drug and of carrier	as measured
A_D, A_C	proportion of drug and of carrier in the solid	w/w
(dC/dt)_{drug}, (dC/dt)_{polymer}	release rates of drug and polymer	µg/(mL min)
m_{drug}, m_{polymer}	masses in the dispersion	mg
G_A, G_B	dissolution rates of components A and B	as measured
N_A, N_B	proportion of each component	w/w
N_{drug}, N_{polymer}	weight fractions of drug and polymer	–

Assumptions and valid domain

High polymer loading, so that no drug-rich layer limits dissolution alonzo2011 C37. Holds when Corrigan's condition N_A/N_B > D_A C_{SA}/(D_B C_{SB}) is met (cited), which the 2016 paper takes as the basis of polymer-controlled release at low and drug-controlled release at moderate to high drug loading xie2016a E2, C4. Release controlled by polymer dissolution saboo2020a E2; the polymer dissolves and brings the drug into solution because there is too little drug to form an intact surface layer indulkar2019a E3. In the normalized form of the surface-normalized release rate it predicts equal drug and polymer rates saboo2020a E2, E3.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
alonzo2011	why 90:10 dispersions dissolve much faster than 50:50	none	inputs not printed alonzo2011 E4
indulkar2019a	ritonavir–copovidone release at low drug loading (10% ritonavir–PVPVA at 20 min)	integrated over time at 10% drug: ≈67 mg PVPVA × 10/90 = ≈7.4 mg ritonavir against ≈7.6 mg read from the release curve	reproduces (inputs read from plots) indulkar2019a E3, R1, R2
saboo2020a	normalized drug and polymer release rates; nilvadipine, felodipine, cilnidipine at 40% in HPMCAS	equal normalized rates predicted; drug/polymer 0.42/0.42, 0.34/0.32, 0.26/0.24 mg/min/cm²	reproduces in the normalized form, equal within SD saboo2020a E2, R16
indulkar2022	cited regime, the good regime for 30:70 ritonavir–PVPVA with surfactants	none	not applicable (not fitted) indulkar2022 E1
xie2016a	why celecoxib release slows at high drug loading	none	not applicable xie2016a E1, C4

Where it fails or is disputed

In the 2011 study neither rate was measured, so the regime is inferred from particle disintegration and UV speed alonzo2011 C38, C28. Above the limit of congruency the polymer leaves first and the relation no longer holds saboo2020a R14; indulkar2019a R5. It fixes the ratio of the two rates, not their size: in congruent dispersions the polymer rate itself was below that of a neat polymer compact saboo2019 R8; saboo2020a C19.

Concepts

polymer-controlled release, congruent release. Findings. Supersaturation from ASD dissolution: F10, F20. Release mechanism and LoC: F1, F2.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

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

symbol	meaning	unit	ids
E_G	effectiveness ratio	dimensionless	moseson2020a E2
R_{G,np}	crystal growth rate without polymer	µg/s (vessel mass rate)	moseson2020a E2, X12
R_{G,p}	crystal growth rate with polymer	µg/s	moseson2020a E2
R_{g0}	initial growth rate without polymer	µg mL⁻¹ min⁻¹ or µg min⁻¹	ilevbare2012a E3
R_{gp}	initial growth rate with polymer or additive	same	ilevbare2012a E3
E_g	effectiveness ratio; 3 means growth three times slower	dimensionless	[ilevbare2013b E5]
bulk growth rates (felodipine melt)	linear growth rates without and with 3% PVP, read from plots	m/s	kestur2013a E2, R8, R13

Assumptions and valid domain

Evaluated at the highest seed level (50 µg/mL) at S = 6 for indomethacin; for bicalutamide from seeded growth at 150 µg/mL moseson2020a E2, P20; moseson2021 R5. The growth rates are vessel mass rates not normalised to seed surface area and the extraction method is not printed moseson2020a X12. In the seeded-growth papers a ratio above 1 is taken as effective and below 1 as accelerating; the rate is the slope of the dissolved drug over the first 2 min at fixed seed mass and supersaturation [ilevbare2013b C17; ilevbare2012a E3, E4]. Tested for ritonavir, celecoxib and efavirenz at 37 °C, pH 6.8, 5 µg/mL polymer. In the felodipine polymorph work it is applied to growth from the supercooled melt at 60–100 °C, not from solution kestur2013a R15, C28.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
moseson2020a	indomethacin with 5 and 50 µg/mL PVPVA	E_G 18 and 56	reproduces from the figure readings: 0.99 / 0.055 = 18 and 0.99 / 0.018 = 55 moseson2020a R5, E2
moseson2021	bicalutamide with PVPVA 70 µg/mL and HPMCAS 1 mg/mL	E_G 8.6 and 158	inputs not printed (growth rates are in a supplement that was not supplied) moseson2021 R5, E1
ilevbare2012c	34 polymers on ritonavir	0.83–3.25	absolute rates not printed [ilevbare2012c E5, R9]
ilevbare2012b	polymers against S and pH	6.40, 2.99, 1.56; 2.98 → 1.12	not applicable (definition) [ilevbare2012b E12]
ilevbare2012a	14 polymers, 13 pairs, surfactants	up to 12.1; 0.49 for TPGS	reproduces (3.6/1.1 = 3.27, printed 3.3) ilevbare2012a E3
ilevbare2013b	16 polymers on three drugs	up to 12.6	reproduces (69.80/11.88 = 5.88, text about 6.0) [ilevbare2013b E5]
schram2015	E_g = R_0/R_P of felodipine with HPMCAS-LF	2.29 (pH 6.8), 1.28 (pH 3)	slopes not tabulated; end-point estimate gives 2.3 and 1.3 [schram2015 E4, R4]
schram2016	same, R_0 of buffer-grown seeds without polymer	2.7, 5.5, 8.0, 12.0 with HPMCAS in solution; 1.8, 3.0, 8.4 without	plot readings [schram2016 E5, R2]
lu2017a	E_G at δ 2.4 and E_C at δ 7.9 or 12.5 for telaprevir with bile salts	E_G 1.0–4.6; STCDC no desupersaturation	plot readings [lu2017a E2, E3, R7, R8]
lu2018	telaprevir seeds with bile salt mixtures, δ 7.9	E_G = R_0/R over the first 10 min	STDC 3.8; STCDC >60; binary-L 35.5; binary-H 7.4; inputs not printed [lu2018 E3, R5]
kestur2013a	whether PVP acts in the liquid or at the crystal faces of felodipine forms I and II	form 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
kestur2013b	surface 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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	unit
\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

paper	used for	values or fitted parameters	status / recomputed
marsac2010 (Physical stability)	felodipine–PVP–water	χ water–felodipine ≈3.3, water–PVP ≈0.5	no Δχ printed; the inputs give 3.3 − 0.5 = 2.8 marsac2010 E1, R22
purohit2017b	why ritonavir–PVP and –PVPVA separate with water	none	not applicable (no χ values) purohit2017b E4, C43
yang2021	why log P does not predict water-induced separation of six drugs	none	inputs 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 Amorphous solid dispersions: the whole picture

Fedors group-contribution solubility parameter

Expression

\delta = \sqrt{\frac{\sum_i \Delta e_i}{\sum_i \Delta v_i}} = \sqrt{\frac{\Delta E_v}{V}} [ilevbare2012c E1; ilevbare2013c E5; ilevbare2013b E1; ilevbare2012a E1]

Molar-volume correction for glassy polymers (Tg above 25 °C):

\Delta v_i = 4n \quad (n < 3), \qquad \Delta v_i = 2n \quad (n \geq 3) [ilevbare2012c E2, E3]

Variables and units

symbol	meaning	unit
δ	solubility parameter; lower means more hydrophobic	MPa^1/2
Δe_i	group contribution to the energy of vaporization	J/mol
Δv_i	group contribution to the molar volume	cm³/mol
ΔE_v, V	energy of vaporization and molar volume	J/mol; cm³/mol
n	number of main-chain skeletal atoms in the smallest repeating unit	integer

Assumptions and valid domain

Group contributions at 25 °C; only the structural formula is needed; for glassy polymers the estimated molar volume deviates from the measured one, hence the correction [ilevbare2012c E1, E2]. Applied to drugs and to cellulosic, vinyl and acrylic polymers; no uncertainty is stated.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
ilevbare2012c	14 new cellulose esters	19.62–23.28 MPa^1/2	inputs not printed (group contributions are in the reference) [ilevbare2012c E1]
ilevbare2012a	14 polymers	20.05–32.24 MPa^1/2	inputs not printed ilevbare2012a E1
ilevbare2013b	16 polymers and 3 drugs	drugs 20.03, 21.89, 23.38	inputs not printed [ilevbare2013b E1]
ilevbare2013c	21 polymers and 3 drugs	19.62–32.24; drugs as above	inputs not printed ilevbare2013c E5
mosqueragiraldo2016	Fedors SP of 18 new cellulose derivatives (ionization not allowed for)	SP 22.08–25.54 MPa^1/2 for the telaprevir polymers	not recomputed [mosqueragiraldo2016 P5, M10–M27]
mosqueragiraldo2018a	six carboxylated cellulose derivatives, neutral structures	named only	19.9–25.5 MPa^1/2 [mosqueragiraldo2018a E2, R6]

Where it fails or is disputed

The SP values of the commercial and synthetic polymers are not printed in the 2012 growth paper [ilevbare2012c X11]. The SP window explains ritonavir and efavirenz but not PVPVA on celecoxib and efavirenz or Pn-IPAAmd and PAA on celecoxib [ilevbare2013c X11; ilevbare2013b C51]. Hydrophobicity (SP) and carboxyl content are confounded in the new esters [ilevbare2012c X10]. The SP of A5a (25.54) and A5b (24.29) differ by more than the span of the effective acids, and the calculated SP did not predict effectiveness across chemistries [mosqueragiraldo2016 X8, C25]. The method cannot include ionized substituents, while the simulations of the same paper treat the chains as fully ionized [mosqueragiraldo2018a P12, X9].

Concepts

solubility parameter, polymer hydrophobicity. Findings. F8, F13, F25, F36.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
\Delta G_M, \Delta G	free energy of mixing	divided by RT in the 2006 and 2009 forms marsac2006b E1; marsac2009 E10
n_{drug}, n_{polymer}	moles of drug and polymer	mol marsac2006b E1
\Phi	volume fraction	dimensionless; from weight fraction and true density marsac2006b P5, E8
m, m_{drug}, m_{polymer}	ratio of the molecular volume to that of the lattice site	dimensionless marsac2009 E10; moseson2018 E1
\chi	interaction parameter	dimensionless marsac2006b E1
R, T	gas constant, absolute temperature	marsac2006b E1

Assumptions and valid domain

The amorphous drug is treated as a solvent and one lattice site equals the molecular volume of the drug marsac2006b E1, C9; χ is independent of composition marsac2009 P8; the entropy curves are computed with χ = 0 for nifedipine with methyl pyrrolidone and three PVP grades marsac2006b R1. The temperature and the PVP grade of the 2009 curves are not printed marsac2009 X12. The critical χ for miscibility depends on how the lattice is defined marsac2006b C18. The indomethacin polymorph paper uses it for drug–polymer melts at 80–135 °C, above Tg, with 10% w/w polymer, as an argument only [tian2017 E2, A2].

Use in the library

paper	used for	values or fitted parameters	status / recomputed
marsac2006b	entropy of mixing of nifedipine with methyl pyrrolidone and PVP; ΔG/RT for χ −4.2 to 2.0	χ = 0, −4.2, −3.8, 0.5, 1.0, 2.0; miscibility needs about 0.6 or less	printed; not applicable, curves carry no ordinate scale marsac2006b E1, R1, R2, R3
marsac2009	ΔG/RT of five PVP pairs and sucrose–dextran from two sets of χ	indomethacin minimum ≈2.4 and ≈5 times the athermal one	printed; not applicable, no numerical axis marsac2009 E10, R10
tian2017	argument that stronger drug–polymer interactions lower the driving force, so that PVP acts "most likely" through both mobility and driving force	none	printed; Φ, m and χ not given; interactions cited from another paper [tian2017 E2, C30, C31, X13]
moseson2018	framework for the melting depression of the drug in PVPVA	none directly	printed; no numerical output moseson2018 E1
purohit2015a	argument that, without hydrogen-bond donors, itraconazole–HPMC mixing is entropy-driven and may be limited at room temperature	none (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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
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 drug	kJ/mol (39.89 and 30.83 for nifedipine and felodipine) marsac2006b M1, M2
\Phi_{drug}, \Phi_{polymer}	volume fractions	dimensionless marsac2006b E8
m	ratio of the polymer volume to the lattice-site (drug) volume	7.80 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
\chi	interaction parameter	dimensionless marsac2006b R9
T_c, T_m	depressed melting point of the mixture; melting point of the pure drug (extrusion papers)	K moseson2018 E2
R, \Delta H	gas constant; enthalpy of fusion of the drug (IDM 37.8 ± 0.6 kJ/mol)	J/(mol K); J/mol moseson2018 E2, M1
\phi	drug volume fraction from true densities	dimensionless moseson2018 E2
m	ratio 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

paper	used for	values or fitted parameters	status / recomputed
marsac2006b	χ 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
marsac2009	χ 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, 0.11	inputs not printed (depressed melting temperatures only plotted, lattice volume not printed) marsac2009 E2, R7, X4
marsac2009	indomethacin–PVP K12 from three points of the peak	−6.16, −1.94, −0.82	as above marsac2009 R6
zhu2011	χ of drugs with PEG 3350	see the PEG chapter	inputs not printed zhu2011 E1
moseson2018	χ of indomethacin–PVPVA	−1.97; Tc 131.0 °C predicted at 50/50 against 132.3 ± 0.8 °C measured	reproduces within 0.05 °C for all nine predicted Tc (φ = 0.4739, m = 170.7, Tm = 433.79 K) moseson2018 E2, R4, R5
moseson2022c	χ of BCL–PVPVA from the heating-rate-extrapolated melting offset, 30–90% BCL	−1.57 (R² 0.994); Tc 145 °C at 30% BCL	reproduces (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]
shah2024	χ 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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
p/p_0	water activity (RH/100)	– [rumondor2010a E1]
\phi_1, \phi_2	volume fractions of water and solid	– [rumondor2010a E1]
x_{12}	molecular volume of the solid relative to water	16.7 (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

paper	used for	values or fitted parameters	status / recomputed
rumondor2010a	χ with water of five amorphous solids	felodipine 3.27, indomethacin 2.86, PVP 0.36, HPMC 1.33, HPMCAS 1.62	point values bracket the stated averages except PVP (≈0.47–0.75 against 0.36) [rumondor2010a R11, E1, X5]
rumondor2009c	drug–water χ of six drugs from 95% RH uptake	2.50–3.58	extractor check reproduces 2.84, 3.58, 2.71 rumondor2009c R24, E5
marsac2010	water–felodipine χ from the 2008 sorption data	about 3.3	named 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 Amorphous solid dispersions: the whole picture

flux definition

Expression

J = \frac{dm}{A\,dt} indulkar2016 E11.

The same expression is printed for the side-by-side diffusion cell [indulkar2018 E4; indulkar2019b E4].

Variables and units

symbol	meaning	units
m	mass transferred	µg
A	membrane area	1.77 cm² indulkar2016 P5
J	flux	µg/(h·cm²)
A	membrane area of the side-by-side cell	7.07 cm² [indulkar2018 P8; indulkar2019b P3]
J	flux, from the slope of receiver concentration against time with receiver volume and area	µg/(min·cm²) indulkar2018 R12

Assumptions and valid domain

Receiver concentration of each interval converted to mass; the outflow is non-cumulative indulkar2016 P10, P5. Sink conditions on the receiver side, so that the flux follows the donor activity; donor at the amorphous or the crystalline solubility of each medium, runs of about 40–60 min without crystallization indulkar2018 C9, P8, R15.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
indulkar2016	Jmax of clotrimazole donors	0.720 µg/mL × 1.8 mL/h / 1.77 cm² = 0.732 µg/(h·cm²)	reproduces indulkar2016 E11
indulkar2017a	atazanavir flux	A 7.07 cm²	slopes not printed indulkar2017a E4
wilson2018	enzalutamide mass flow	no flux value printed; the 30 mm orifice would give A = 7.07 cm²	not applicable wilson2018 E3, R13, R15
indulkar2018	flux at the amorphous solubility of tacrolimus and cilnidipine in three media; ratio to the crystalline flux for atazanavir and ritonavir	0.027–0.031 and 0.0014–0.0018 µg/(min·cm²); flux at the crystalline solubility not measurable for these two drugs	slopes not printed indulkar2018 E4, R12, R13
indulkar2019b	supersaturation at the amorphous solubility of atazanavir in SDS media	stated about 65; no flux values printed	inputs not printed [indulkar2019b E4, R2, X6]

Where it fails or is disputed

None found in the Bioperformance papers. For tacrolimus and cilnidipine the flux at the crystalline solubility was below what the method could measure, so the supersaturation ratio could not be formed and equality across media was assumed indulkar2018 R13, X4.

Concepts

membrane flux, sink conditions. Findings. Bioperformance: F2, F25. Crystallization from solution: F31, F38, F40.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
\Delta G_{mix}, \Delta H_{mix}, \Delta S_{mix}	free energy, enthalpy and entropy of mixing	not printed [rumondor2009a E3, E4, E5]
X_u, X_v	mole fractions of the two components	dimensionless [rumondor2009a E3]
H_{ii}, H_{jj}, H_{ij}	enthalpies of the pure components and of the mixture	not printed [rumondor2009a E4]
x_A, x_B	mole fractions of drug and buffer solution	dimensionless raina2014a E8
\mu, \mu^{*}	chemical potential and its standard-state value	raina2014a E8
T, R	temperature and gas constant	[rumondor2009a E3, E5]

Assumptions and valid domain

Ideal mixing entropy with mole fractions is assumed in the 2009 form [rumondor2009a E3]. Positive \Delta G_{mix} is read as unfavourable mixing and negative as favourable; one minimum is read as a single phase, two minima as partial miscibility, and a positive curve as immiscibility [rumondor2009a C35, C37]. The scheme is liquid-mixture theory extended to amorphous solids [rumondor2009a C35]. The drug–buffer form is used for a partially miscible system at constant temperature raina2014a E8.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
rumondor2009a	framework for the three miscibility behaviours of felodipine, nifedipine and ketoconazole dispersions	none	printed; not applicable, no numerical output (E3 is a misprint of sign) [rumondor2009a E3, E4, E5, C35]
rumondor2009a	argument that a favourable drug–polymer interaction gives one minimum and a one-phase dispersion; competition with intra-polymer hydrogen bonds makes mixing less favourable	none	not applicable [rumondor2009a C37, C39, C45]
raina2014a	framework for the onset of liquid–liquid phase separation as binodal points	none	printed; not applicable raina2014a E8, C27
vaneerdenbrugh2012a	argument that a blend mixes only if the combinatorial entropy outweighs a positive enthalpy	none (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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	unit	ids
T_g	glass transition temperature of the miscible blend	K	moseson2018 E3
w_1, w_2	weight 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 K	K	moseson2018 M1, M2; li2019 E1
K	constant from true densities (0.932 with Tg in K) or fitted (0.628)	–	moseson2018 E3; li2019 E1
\rho, \Delta C_P	densities 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/K	g/cm³; J/g/K	konno2006 M1, M2, M3, M4
T_{g,mix}	Tg of the homogeneous film (indomethacin release study)	°C	saboo2020 E3
w_1, T_{g1}	weight fraction and Tg of indomethacin (53 °C by nanoTA)	–, °C	saboo2020 E3
w_2, T_{g2}	weight fraction and Tg of PVPVA (130 °C by nanoTA)	–, °C	saboo2020 E3
k	fitted 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

paper	used for	values or fitted parameters	status / recomputed
moseson2018	formulation Tg line of IDM–PVPVA	72.9 °C predicted against 72.2 ± 0.5 °C at 50/50	reproduces within 0.05 °C for all predicted Tg (K = 0.932 with Tg in K) moseson2018 E3, R5
li2019	local drug content from nanoTA softening	K = 0.628, Tg1 = 367 K, Tg2 = 482 K	reproduces (110 °C → 0.794; 180 °C → 0.174; 150 and 105 °C → 0.40 and 0.85) li2019 E1, R16
moseson2022c	Tg line of BCL–PVPVA	K = 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]
shah2024	Tg line of PCZ–HPMCAS	Tg of PCZ 61 °C and HPMCAS 122 °C, densities 1.28 and 1.27 g/mL	mismatch: 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
konno2006	ideal-mixing Tg lines for felodipine with PVP, HPMCAS, HPMC	K 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
trasi2012a	Tg rises of 1.7–4.2 °C with 10% polymer read as miscibility	none	printed in words; polymer Tg values not printed trasi2012a E2, R9, C17
trasi2017	context for the Tg drop of amorphous tacrolimus and its HPMC dispersion after 75% RH	none	named only trasi2017 E7, R15
saboo2020	inverting the local Tg of a dissolving 25% indomethacin–PVPVA film into its drug content	111, 95, 88, 82 °C → 23, 44, 52, 60 wt% at 0–20 min	reproduces: 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
deac2024b	dry MePHPH–PVPVA Tg; Tg against water for the glass–gel boundary	K = 0.65; fitted water Tg 197.6–297.1 K	reproduces 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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
\Delta G_v	free energy difference between crystal and amorphous or liquid state	J/cm³ after conversion with crystalline density vaneerdenbrugh2010a E2, E5; baird2010 E25; kJ/mol [lu2016 E1]
\Delta H_{fus}, \Delta H_m	enthalpy of fusion	kJ/mol or J/cm³ baird2010 E26; vaneerdenbrugh2010a E1
T_m, T_{melt,ons}	melting temperature (onset)	K [vaneerdenbrugh2010a E1; lu2016 E1]
T	temperature of evaluation	293.15 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_f	molar heat of fusion	not printed raina2015a E2
\Delta T	T_m - T	K 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_C	free-energy difference between amorphous (supercooled liquid) and crystal	kJ/mol [hsieh2012 E3; ilevbare2013b E3]
\Delta H_f, T_m, T in the moisture paper	heat of fusion; melting and evaluation temperatures	kJ/mol; K rumondor2009c E3
\Delta G_c, \Delta G (ASD dissolution papers)	free-energy difference between amorphous and crystalline drug	J/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

paper	used for	values or fitted parameters	status / recomputed
baird2010	ΔGv descriptor in the class PCA	class I contribution −0.40 (more negative ΔGv)	inputs not printed baird2010 E25, R22.g
vaneerdenbrugh2010a	ΔGv descriptor in the class PCA	contributions −0.29, +0.29, +0.13 for classes I, II, III	inputs not printed vaneerdenbrugh2010a E2, R20.e
baird2012	ΔGv 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
lu2016	driving force of α and β vemurafenib; virtual transition	α 11.0 kJ/mol at 115 °C; transition 319 °C	reproduces [lu2016 E1, R22]
marsac2006a	felodipine and nifedipine driving force	6.22 and 8.83 kJ/mol at 25 °C	reproduces [marsac2006a E3]
ilevbare2013c	driving force at 37 °C (extractor calculation)	ritonavir ≈10.2, efavirenz ≈2.70, celecoxib ≈7.74 kJ/mol	inputs not printed for a stated output ilevbare2013c E7
baird2011	\Delta G_{fus} inside the activity coefficient of four drugs in PEG 400 at 25 °C	no \Delta G_{fus} value printed	not applicable; checked through the activity coefficient (0.614 for chlorpropamide, reproduces) [baird2011 E6, E7]
raina2015a	ΔG in the amorphous solubility estimate of six dihydropyridines	ΔHf and Tm not printed	inputs not printed raina2015a E2
ilevbare2013a	ΔG inside Eq. 1 for eight drugs	ritonavir 10.1 kJ/mol at 37 °C from Table 2 inputs	no ΔG printed; recomputed ilevbare2013a E2
almeidaesousa2015	comparator of the Cp method	3.24–10.33 kJ/mol for six drugs	reproduces (ibuprofen 3.25 against 3.24 kJ/mol) almeidaesousa2015 E2, R11
indulkar2015	ΔG at 310 K for clotrimazole and atazanavir	6.26 kJ/mol (clotrimazole, with an unprinted molar mass)	inputs not printed indulkar2015 E3
mosqueragiraldo2015	telaprevir	13.31 kJ/mol; amorphous solubility 245 ± 5 µg/mL	reproduces mosqueragiraldo2015 E1, E2
almeidaesousa2016	CRH1	5.68 kJ/mol	reproduces (5.685) [almeidaesousa2016 E2]
indulkar2017a	ΔG of atazanavir inside Eq. 3	14.55 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
hsieh2012	amorphous solubility of five bases	ΔHf, Tm not printed	inputs not printed hsieh2012 E3
ilevbare2012b	ritonavir	ΔHf 60.4 kJ/mol, Tm 121 °C, 37 °C	ΔG 10.1 kJ/mol, exp(ΔG/RT) 50.8 (extractor) [ilevbare2012b E9]
hsieh2014	glyburide, warfarin	175.6 °C and 45.5 kJ/mol; 169.2 °C and 43.6 kJ/mol	reproduces: 59.9 and 47.7 at 25 °C hsieh2014 E2, E3
jackson2014	danazol	ΔHf 28.9 kJ/mol, Tm 225.4 °C	ΔG 6.95 kJ/mol; ratio 15.4 against 19.6 printed jackson2014 E1, E2
duong2022b	posaconazole, 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]
rumondor2009c	driving force of six drugs tested as a predictor of moisture-induced separation	4.1 (ketoprofen) to 11.0 kJ/mol (pimozide); nifedipine 8.2, felodipine 6.1	reproduces (nifedipine 8.23, pimozide 10.97, ketoprofen 4.14) rumondor2009c E3, M1, M2, M5
rumondor2009b	named as the pure-drug driving force	none	named only rumondor2009b E1
konno2008a	felodipine amorphous solubility, 37 °C	ratio about 10, about 9.5 µg/mL	inputs not printed konno2008a E2, R17
alonzo2010	felodipine, 37 °C	30.12 kJ/mol, 143.41 °C: ΔG 5729 J/mol, ratio 9.22 against about 9	reproduces alonzo2010 E1
alonzo2010	indomethacin, 37 °C; 25 °C	32.48 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/mL	reproduces; mismatch at 25 °C alonzo2010 E2, X2
alonzo2011	felodipine, 37 and 25 °C	about 9.1 and 5–6 µg/mL	inputs not printed alonzo2011 E3, M1
duong2022a	delamanid amorphous-to-crystalline solubility ratio at 37 °C, against the measured 42.3	ratio 31.8; Tm 196.1 °C	inputs 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 Amorphous solid dispersions: the whole picture

hollow-fibre donor depletion

Expression

\ln\frac{c_{in}^{0}(t)}{c_{in}^{0}(0)} = \frac{t\,Q_{in}}{V_{in}\left(1+\frac{Q_{in}}{Q_{out}}\right)}\left[\exp\!\left(-\frac{K_{in}A}{Q_{in}}\left(1+\frac{Q_{in}}{Q_{out}}\right)\right)-1\right] hate2017 E8, and the exponential form for c_{in}^0(t) hate2017 E9.

Variables and units

symbol	meaning	units
Q_{in}, Q_{out}	lumen and shell flow rates	mL/min; 2 mL/min hate2017 P4
V_{in}	donor volume	50 mL (calibration), 100 mL (powder), 400 mL (tablet) hate2017 P7
A	membrane area	115 cm² hate2017 M10
K_{in}	overall mass transfer coefficient	cm/s

Assumptions and valid domain

Steady state, no adsorption once steady state is reached, uniform pores, no partitioning, no crystallization hate2017 C9, C10, C30.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
hate2017	donor depletion at 2 mL/min, 50 mL	removed 42.8% of the donor in 60 min against 41.5% printed	reproduces approximately hate2017 E8
hate2017	powder + HPMC-AS model curve	491 to 139 µg/mL at 270 min against about 144	reproduces hate2017 E9
hate2019	tacrolimus absorption rate in the absorption-versus-growth model	Kin 1.09 × 10⁻⁴ cm/s, A 100 cm², 2 mL/min inside and outside; initial time point only	mismatch: recomputed dC/dt 0.012, 0.0048, 0.0020 µg/mL/s for 40, 100, 240 mL; the plotted line needs a donor volume near 5 mL hate2019 E3, X4

Where it fails or is disputed

The curve ends about 20% below the data; the K_in used is not the fitted mean hate2017 X7, X8. The absorption line of the tacrolimus model cannot be reproduced from the printed constants (F29) hate2019 X4.

Concepts

membrane mass transfer coefficient. Findings. F13, F14, F28, F29.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
S_a(x_1)	amorphous solubility of drug 1 at mole fraction x_1 in the drug-rich phase	µg/mL trasi2015a E4
S_a^{\circ}	amorphous solubility of the pure drug	µg/mL, ultracentrifuge values 26.2 and 17.1 trasi2015a R1, X14
x_1	mole fraction of drug 1 among the drug molecules in the drug-rich phase	dimensionless trasi2015a E4
S_1	free concentration of drug 1 with a drug-rich phase containing other drugs	M alhalaweh2016 E7
S_{A1}	amorphous solubility of drug 1 alone	M alhalaweh2016 E7
X_1	mole fraction of drug 1 in the drug-rich phase	– alhalaweh2016 E9
J_1, J_{A1}	flux with and without the other drugs	mg/min/cm² alhalaweh2016 E8
C_{max}	maximum bulk concentration of one drug	µg/mL [trasi2015b E1; li2018 E7]
S_a	amorphous solubility of that drug alone (25 µg/mL ritonavir, 17 µg/mL lopinavir)	µg/mL trasi2015b E1
x_d	mole fraction of the drug in the amorphous mixture or drug-rich phase	dimensionless trasi2015b E1
w_d	drug weight fraction (drug loading) of the dispersion	dimensionless [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

paper	used for	values or fitted parameters	status / recomputed
trasi2015a	bulk ritonavir and lopinavir against the ritonavir mole fraction	lines 0 to about 20.8 µg/mL (ritonavir) and about 16.8 to about 3.4 µg/mL (lopinavir) for x = 0 to 0.8	reproduces (26.2 × 0.8 = 20.96; 17.1 × 0.2 = 3.42) trasi2015a E4, R16
ueda2021	dilution argument for polymer in the ibuprofen-rich phase	none (not evaluated numerically)	not applicable [ueda2021 E2]
ueda2022	qualitative link of Sa/Sa0 with the polymer content	no x_drug values printed	the 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 chapters	ideal-mixing line for binary amorphous mixtures and polymer dispersions	none	printed; not recomputed here [trasi2015b E1; alhalaweh2016 E7; li2018 E7]
alhalaweh2016	binary and ternary ceilings; Caco-2 flux	clinical 1:3 ratio: X_RTV = 0.246; 0.5 × 10.5 × 10⁻⁵ = 5.25 × 10⁻⁵	reproduces alhalaweh2016 E7, E8, E9
li2018	lopinavir ASD films	17.4 × 0.50 = 8.7 µg/mL	reproduces [li2018 E7]
trasi2015b	film plateaus at 7:3, 5:5, 3:7	five of six within 0.5 µg/mL; RTV 7:3 15.2 against 16.7 µg/mL	printed comparison trasi2015b R5
trasi2015b	5:5 film with literature molecular weights	x_RTV 0.466: 11.6 and 9.1 µg/mL against printed 11.6 and 9.0	reproduces trasi2015b E1
trasi2015b	HPMCAS dispersions against the line	RTV on the line; LPV up to about 15% below	approximate trasi2015b R17, X8
li2018	positions of the polymers against the line	HPMCAS slightly above; CAP at 15–50% and EC at 50–85% drug near it; HPMCP below	printed 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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	unit
t_ind	measured induction time, from creating the supersaturation until crystals are detected	min
t_n	time to form stable nuclei	min
t_g	time for nuclei to grow to detectable size	min
J	nucleation rate	m⁻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

paper	used for	values or fitted parameters	status / recomputed
ilevbare2013c	reading polymer effects on induction time as nucleation-rate effects	induction times about 2.4–855.5 min	inputs not printed ilevbare2013c E2, E3
xie2015	celecoxib dispersions (ASD dissolution chapter); celecoxib 22 µg/mL with 5 µg/mL polymers, pH 6.8, 37 °C	decomposition 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, HPMC	printed xie2015 E1, E2; no t_n or t_g printed xie2015 E1, R1
xie2016a	celecoxib with PAA and cellulose derivatives; with HPMCAS	decomposition printed; 960 min taken as the induction time with HPMCAS, an underestimate	printed xie2016a E4; no component times printed xie2016a E4, C39
chen2015	t_ind = t_n + t_g, not separated	11 drugs	printed chen2015 E1, C5
li2016a	same, with t_n >> t_g assumed	three drugs, 13 bile salts	printed in words [li2016a E4]
mosqueragiraldo2016	T_ind = T_n + T_growth	telaprevir, 26 polymers	printed [mosqueragiraldo2016 E1]
lu2017	t_ind = t_n + t_g, read as nucleation when t_n dominates	telaprevir, six bile salts	printed [lu2017 E3, C9]
trasi2015	t_j = t − t_g with t_g fitted	acetaminophen: t_g 7.8–928 s	fitted [trasi2015 E4, R3]
indulkar2018	lecithin, bile salt and SIF media, four drugs	induction time as first scattering rise; components not separated	not applicable indulkar2018 E5
lu2018	telaprevir in bile salt mixtures and complete media	t_{ind} = t_n + t_g	not applicable [lu2018 E2]
indulkar2019b	atazanavir in SDS	additive may act on either part	not applicable [indulkar2019b E5, C29]
enright2020	atazanavir in phospholipid-digest and volunteer media	printed in words	not applicable [enright2020 E1]
elkhabaz2021	atazanavir, posaconazole in six media	T_{ind} = T_{crit} + T_{grow}, read as nucleation onset	not applicable elkhabaz2021 E1
que2018	unseeded paclitaxel at S ≈88 with and without 20 µg/mL HPMCAS	within 6 min against more than 16 h	no 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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	unit
R_g	initial bulk crystal growth rate	µg mL⁻¹ min⁻¹ or µg min⁻¹
C, C_t	dissolved drug concentration or amount (in 50 mL) at time t	µg/mL or µg
t	time after seeding	min
b	intercept (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

paper	used for	values or fitted parameters	status / recomputed
ilevbare2012a	ritonavir growth rates and ratios	1.56 µg mL⁻¹ min⁻¹ at 10 µg/mL (text), about 1.4 (figure)	concentration–time curves not printed ilevbare2012a E4, X5
ilevbare2013b	celecoxib at 10 µg/mL, no polymer and with CA 320S Sub 0.63	−69.80 t + 487.46; −11.88 t + 482.40 µg	reproduces (≈488 to ≈348 µg in 2 min gives ≈70 µg min⁻¹) [ilevbare2013b E8, R8]
schram2015	slope of concentration against time over 1 h taken as the growth rate	felodipine S 8	[schram2015 C5, E4]
lu2017a	initial slope over 30 min (δ 2.4) or 10 min (higher δ), in µg/min for 50 mL	5.4, 58.6, 89.2 µg/min in buffer	plot 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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
U	crystal growth rate	not stated [trasi2014a E1]
\lambda	average diffusion jump distance	not stated
\eta	viscosity	Pa·s (cited data) [trasi2014a P7]
f	fraction of interface sites that are active growth sites	dimensionless
\Delta H, \Delta S	enthalpy and entropy difference between liquid and crystal	not stated
T, T_m, \Delta T	temperature, melting temperature, undercooling	K

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

paper	used for	values or fitted parameters	status / recomputed
trasi2014a	framework for the driving-force correction and the entropy fit	none fitted directly	inputs 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 Amorphous solid dispersions: the whole picture

Kubota-Mullin model

Expression

\frac{R}{R_0} = 1 - \alpha\,\theta_{eq} [alonzo2012 E5; ilevbare2012b E7]

A model of growth inhibition by an adsorbed impurity based on step pinning: the growth rate with impurity relative to that without falls linearly with the surface coverage, where α is an effectiveness factor that depends on the surface energy, the molecular area, the supersaturation and the spacing of adsorption sites, \alpha = \gamma a/(kT\,(\ln S)\,L) [alonzo2012 E5, E7; ilevbare2012b E7]. It was developed for inorganic systems; Alonzo and co-workers state that, to their knowledge, it had not been used for polymers on organic pharmaceutical crystals alonzo2012 C10. The authors extend its proportionality between step, face and mass growth-rate ratios to bulk de-supersaturation rates alonzo2012 C4, E4. Both felodipine–HPMCAS papers print V_P/V_0 = 1 - \rho_c/l and apply it to AFM spacings: with l 68.5 nm and ρc 3.98 nm it gives 0.94, and with l 15.8 nm it gives 0.75, against measured rate ratios of 2.7 and about 12 [schram2015 E3; schram2016 E4, R12, R14, X3]. (This page also holds the former concept page "Kubota-Mullin model", whose content is about the same equation.)

Variables and units

symbol	meaning	unit
R, R_0	overall mass growth rate with and without polymer	µg mL⁻¹ min⁻¹
α	impurity effectiveness factor	dimensionless
θ_eq	equilibrium surface coverage by adsorbed polymer	dimensionless

Assumptions and valid domain

Langmuir-type adsorption (isotherm fit, here shifted by hand for felodipine); the proportionality between step, face and overall mass growth-rate ratios extends to bulk de-supersaturation rates; constant seed surface area and face-area ratios; applies only below the kinetic roughening transition [alonzo2012 C4, C5, C6, C23; ilevbare2012b E7]. How the parameters are obtained: seeded growth rates with and without polymer at several polymer concentrations give R/R_0; the coverage \theta_{eq} comes from an adsorption isotherm fit (modified Langmuir, Langmuir–Freundlich); α is chosen so that the line fits the measured ratios at one supersaturation [alonzo2012 P9; ilevbare2012b P11, E6].

Use in the library

paper	used for	values or fitted parameters	status / recomputed
alonzo2012	felodipine with HPMC at S 8	α 0.4 (text, table) or 0.45 (Fig. 5 caption)	reproduces with 0.45: 1 − 0.45 × 0.631 = 0.716 against 0.71 plotted; mismatch with 0.4 alonzo2012 E5, X1
alonzo2012	felodipine with HPMC, α at S 3, 5, 8, 10, 12	0.7, 0.5, 0.4, 0.6, 0.2 (25 °C)	as printed alonzo2012 R9
alonzo2012	plateaus of R/R0	0.65 (S 5) and 0.55 (S 10) quoted	mismatch: 1 − α at θ = 1 from Table 1 gives 0.5 and 0.4 alonzo2012 E5, X2
ilevbare2012b	ritonavir with CAP Adp 0.85, σ 0.99, 37 °C	α = (1 − 0.80)/0.16 = 1.25, θ 0.16, R/R0 0.80 (pH 3.8); α = 1/0.23 = 4.35, θ 0.23, R/R0 0 (pH 6.8)	reproduces [ilevbare2012b E7, R16]
ilevbare2012b, alonzo2012	reading of α	α about 1: adsorbed molecules one critical-nucleus diameter apart at full coverage; above 1: closer, so growth can stop below full coverage	interpretation [ilevbare2012b E13; alonzo2012 C25]
schram2015	R_P/R_0 = 1 − ρc/l with l the globule spacing	pH 3 l 44 nm	qualitative [schram2015 E3, C18]
schram2016	same with measured spacing and critical radius, HPMCAS on buffer-grown and dispersion-grown felodipine seeds (S 4, 25 °C); see the pinning formula	l 68.5 and 15.8 nm; ρc 3.98 nm; predicted rate ratios about 1.06 and 1.34	recomputed [schram2016 E4, R12, R14, X3]

Where it fails or is disputed

α at pH 6.8 was derived from the point it is compared with and is a lower bound; the low-concentration points disagree (0.44–0.09 measured against 1.00–0.96 calculated) [ilevbare2012b X8, R15]. The coverage of the felodipine fit is model-dependent alonzo2012 X12. The model was not tested above σ_c [ilevbare2012b X11]. With the printed l and ρc the model gives much smaller effects than measured [schram2016 X3]. The felodipine α at S 8 is 0.4 in text and table and 0.45 in the Fig. 5 caption; the plateaus quoted "from the alpha estimates" do not follow from Table 1; the coverage was shifted by hand alonzo2012 X1, X2, X12. The ln S in eq 7 replaces the low-supersaturation approximation S − 1 of the original alonzo2012 C7. The arrest criterion is stated as l ≤ ρc and as l ≤ 2ρc, and ρc was not estimated in the 2015 paper [schram2016 X1; schram2015 X7].

Concepts

impurity effectiveness factor, surface coverage; based on step pinning; related to polymer adsorption. Related formulas. Kubota-Mullin impurity effectiveness factor, Langmuir-Freundlich isotherm, proportionality of step velocity and growth rate ratios. Findings. Crystallization from solution: F9, F10, F11, F23, F24.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

limit of detection and quantification

Expression

Three standard deviations of the reading on a pure form taylor1998a E7:

\mathrm{LOD}=3\times\mathrm{SD}_{\text{pure form}}

Ten standard deviations for the quantitation limit taylor1998a E8:

\mathrm{LOQ}=10\times\mathrm{SD}_{\text{pure form}}

From the residual standard deviation of a calibration regression, "ICH Q2(R1)"; the expression is named and not printed in the paper correasoto2017 E5. In its common slope form, as printed in an HPLC validation outside the chapter alvarenga2022 E2:

\mathrm{LD}=3\times\frac{\mathrm{std}}{S},\qquad \mathrm{LQ}=10\times\frac{\mathrm{std}}{S}

Variables and units

symbol	meaning	unit	ids
SD	standard deviation of the crystallinity (Eq. 5) from 10 measurements of a pure form	% crystallinity	taylor1998a E7, E8
std	standard deviation of the blank (n = 10)	concentration	alvarenga2022 E2
S	slope of the calibration curve	signal per concentration	alvarenga2022 E2
LOD, LOQ	detection and quantitation limits	% crystallinity (Raman, SHG, XRPD papers)	correasoto2017 R8

Assumptions and valid domain

Taylor and Zografi take the criteria from a statistics text and apply them to ten readings of each pure form; the SD of a pure form excludes mixing error taylor1998a E7, R13. Correa-Soto and co-workers apply the residual standard deviation of fits over 0.005–0.1% and 0.5–5% (SHG) and 1–5% or 1–10% (XRPD); the residual SDs are not printed correasoto2017 P8, R6, R8, P6.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
taylor1998a	Raman limits of indomethacin mixtures	SD 0.2%: LOD 0.6%, LOQ about 2%	reproduces (3 × 0.2 = 0.6; 10 × 0.2 = 2) taylor1998a R14
correasoto2017	SHG and XRPD limits of flutamide and ezetimibe	LOD 0.03 / 0.047% (SHG), about 0.4 / 0.7% (XRPD); LOQ 0.08 / 0.14%, 1 / about 2%	named only correasoto2017 R8
alvarenga2022	HPLC of ritonavir (outside the chapter)	LD 7.2 × 10⁻³ µg/mL; LQ 2.4 × 10⁻² µg/mL	reproduces as ratio LQ/LD = 3.33 = 10/3 alvarenga2022 E2

Where it fails or is disputed

The Raman authors judge the 2% quantitation limit "too low" given the variation of mixtures taylor1998a C21. Other limits in the chapter follow different recipes (single-voxel signal-to-background 3 kestur2012 E9; size-based wanapun2010 E3) and are not comparable (F4, F7).

Concepts

limit of detection, limit of quantitation, signal-to-noise ratio. Findings. F1, F2, F4, F7.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
G	linear (radial or diameter) growth rate	m/s or µm/s [kestur2013b E2; trasi2014b E1]
L	crystal size (radius, diameter or length)	m or µm [trasi2014b E1]
t	time	s [trasi2014b E1]
crystallization slope	% crystallinity per unit time, printed as day⁻¹ or h⁻¹	[kestur2013b 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

paper	used for	values or fitted parameters	status / recomputed
kestur2013b	form I growth at the free surface and in the bulk, 30 °C	2.7 × 10⁻⁹ and 0.47 × 10⁻⁹ m/s; 1.45 × 10⁻⁹ and 6.37 × 10⁻¹¹ m/s with 3% PVP	single values, no uncertainty [kestur2013b R12, X11]
kestur2013b	early and late crystallization slopes of powders	0.905 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]
kestur2013b	early slope, pure drug against 3% PVP	2.21 against 0.037 h⁻¹; 1.41 against 0.018 h⁻¹	PVP values equal Table 2 divided by 24 [kestur2013b R15, X4]
trasi2014b (outside)	radial growth of nilutamide and other drugs	rates per temperature	inputs not printed [trasi2014b E1]
sato2015	growth of ATP enantiomers with five polymers	size–time lines through the origin, e.g. at 60 °C with HPMCAS-HF	linear in time [sato2015 R4, R7, R8]
sato2016	growth of six compounds with PHB	diameter rates; griseofulvin with 5% PHB about tenfold faster at 120 °C	diameter 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 Amorphous solid dispersions: the whole picture

liquid-phase BET isotherm

Expression

Q_a = \frac{Q_m K_S C_e}{\left(1 - K_L C_e\right)\left(1 - K_L C_e + K_S C_e\right)} dening2019 E4.

\frac{1}{K_L} = C_0 (restated; printed in words) dening2019 E7.

Q_a = Q_m \frac{K_S C_e}{(1 - K_L C_e)(1 - K_L C_e + K_S C_e)} mccarthy2020 E8.

Q_a = Q_m \frac{K_{BET} X}{(1 - X)\left(1 + (K_{BET} - 1) X\right)}, \qquad X = \frac{C_e}{C_s} hate2020a E1.

Variables and units

symbol	meaning	units
Q_a	amount adsorbed	mg/g dening2019 E4
Q_m	first-layer (monolayer) capacity	mg/g dening2019 E4
K_S, K_L	equilibrium constants of the first and upper layers	printed "µg/mL⁻¹", dimensionally mL/µg dening2019 X1; mccarthy2020 E8
C_e	equilibrium concentration	µg/mL dening2019 E4
C_0	saturation concentration of the liquid drug phase, proposed equal to the amorphous solubility	µg/mL dening2019 E7
K_{BET}, X, C_s	constant of adsorption and desorption; relative concentration; saturation concentration taken as the amorphous solubility	hate2020a E1

Assumptions and valid domain

Multilayer adsorption with the strongest interaction in the first layer, no lateral interactions, a homogeneous surface and an infinite number of layers dening2019 C14; hate2020a C23. The form of Ebadi and co-workers is taken as suitable for liquid-phase data mccarthy2020 E8. Fitted to isotherms of ritonavir, indomethacin, its methyl ester and atazanavir on SBA-15 at 37 °C up to about 80–90% of the amorphous solubility dening2019 R2; mccarthy2020 R7, R8; hate2020a R2.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
dening2019	ritonavir isotherm	R² 0.94; Q_m 103 mg/g; K_S 1.169; K_L 0.031; 1/K_L 32.7 µg/mL	reproduces: 430–436 mg/g at C_e about 24.6–24.7 against 424 measured; 1/0.031 = 32.3 dening2019 E4, E7
mccarthy2020	indomethacin and methyl ester isotherms	R² 0.94, 0.98; Q_m 29, 31 mg/g; K_L 0.025, 0.118	1/K_L reproduces (40 and 8.47 µg/mL); K_S not printed mccarthy2020 E8, R11
hate2020a	atazanavir isotherm, 300 µg/mL silica	Q_m 4.5 mg/g	inputs not printed (K_{BET}) hate2020a E1, R3

Where it fails or is disputed

The heterogeneous silica surface is expected to cause deviations at low concentration, seen for atazanavir dening2019 C15; hate2020a C24. 1/K_L for ritonavir lies 17% above the measured amorphous solubility, from one fit without points at or above it dening2019 X9, X8. The Q_m values are far below the geometric monolayers dening2019 R3; hate2020a R1; mccarthy2020 R16. The electrostatics paper names a BET fit without printing its form and gives Q_m in "mg/mol" hate2020b E2, X9.

Concepts

BET isotherm, multilayer adsorption, monolayer coverage, adsorption isotherm, amorphous solubility. Findings. F2, F3, F10.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

mass flow rate from receiver concentration slope

Expression

J = \frac{dC_r}{dt}\times V_r with V_r the receiver volume; printed in words raina2014a E11; mosqueragiraldo2018b E2.

Variables and units

symbol	meaning	units
dC_r/dt	slope of the linear region of receiver concentration	µg/mL per min
V_r	receiver volume	30 mL raina2014a P9; 32 mL mosqueragiraldo2018b E2
J	mass flow	µg/min

Assumptions and valid domain

Sink receiver, linear region, time window chosen after the donor maximum (and before crystallization for PVPVA) mosqueragiraldo2018b P4.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
raina2014a	felodipine and nifedipine flux	2 µg/mL: about 0.0004 µg/mL/min × 30 mL ≈ 0.012 µg/min	reproduces from plot reading raina2014a E11
mosqueragiraldo2018b	telaprevir mass flow	windows 10–60 to 800–1000 min	slopes not printed mosqueragiraldo2018b E2, X18
hate2022	PAMPA mass flow of five drugs	slope of receiver concentration against time up to 90 min, normalized by volume, in µg/min	inputs not printed hate2022 E2

Where it fails or is disputed

One paper cites it as "Eq. (8)", which is the free energy of mixing raina2014a X2. Time windows differ between systems mosqueragiraldo2018b X18.

Concepts

membrane flux. Findings. F2, F7, F9, F21, F22.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

mass transferred from receiver AUC

Expression

M_{total} = \mathrm{AUC}_{total}\times Q_{out} hate2017 E10; for the atazanavir study, amount transferred = AUC × receiver flow rate of 4 mL/min hate2018 E5.

Variables and units

symbol	meaning	units
\mathrm{AUC}	area under the receiver concentration–time curve	µg·min/mL
Q_{out}	receiver flow	2 mL/min hate2017 P4; 4 mL/min hate2018 P7

Assumptions and valid domain

Single-pass, non-cumulative receiver profile hate2018 C22.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
hate2017	mass balance	AUC about 830 × 2 = 1.7 mg against 1.89–2.14 mg found	inputs from plot, 10–20% gap hate2017 E10, X11
hate2018	amount transferred; total release	50:50 HPMCAS: 75 µg/mL × 50 mL + 660 × 4 = 6390 µg against about 6200	reproduces hate2018 E5, E6

Where it fails or is disputed

Fig. 6G of the atazanavir paper plots AUC, not amount hate2018 X6; the apparatus does not close the mass balance hate2018 X14.

Concepts

membrane mass transfer coefficient. Findings. F8, F13, F14, F15.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

membrane flux from concentration difference

Expression

J = \frac{D_{eff}}{l}\left(C_d - C_r\right) indulkar2016 E1; with the receiver washed continuously, J = (D_{eff}/l)\,C_d indulkar2016 E4. A form with the membrane partition coefficient is printed for the PAMPA cell: C_{m1} - C_{m2} = \dfrac{J\,K\,d_m}{D}, with C_{m2} \ll C_{m1} under a receiver sink hate2022 E7.

For the dialysis membrane of the ASD dissolution papers it is printed with a sorption coefficient,

J_i = \frac{D_i K_i}{l}\,(c_{io} - c_{il}) alonzo2011 E1.

Variables and units

symbol	meaning	units
D_{eff}	effective diffusion coefficient in the membrane	not printed
l	diffusion path length	not printed
C_d, C_r	donor and receiver concentration	µg/mL
J_i	flux of component i across the dialysis membrane	as measured
D_i, K_i	diffusion coefficient; sorption coefficient between liquid and membrane	not given
c_{io} - c_{il}	concentration difference across the membrane	µg/mL

Assumptions and valid domain

Pseudo-steady state in the membrane indulkar2016 C9; receiver concentration neglected when washed indulkar2016 C10. For the dialysis set-up of the ASD dissolution papers the flux is taken as directly proportional to the concentration difference, so that a difference in dissolved drug between donors shows as a difference in receptor slope alonzo2011 C9; particles do not cross.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
indulkar2016	flow-through model of clotrimazole	K = A D_eff/(V_d l) fitted	inputs not printed indulkar2016 E1, E4, E6
hate2022	donor-side interface concentration in a PAMPA cell	K, membrane thickness and D not given	inputs not printed hate2022 E7, R19
alonzo2011	dissolved felodipine from dispersions	slope ratios 10.5, 9.5, 8.5 (90:10, 50:50, pure amorphous)	proportionality check 0.0816/0.0394 = 2.07 against 2.0 alonzo2011 R14, E1

Where it fails or is disputed

Droplets are assumed not to contribute to the flux indulkar2016 C11, X4. All ratios share one crystalline slope (n = 1), and the membrane cutoff is given as 6–8 kDa and as 10 kDa alonzo2011 X4, X1.

Concepts

membrane flux, sink conditions, free drug concentration. Findings. Bioperformance: F5. Supersaturation from ASD dissolution: F7, F8.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

membrane flux from permeability and concentration

Expression

J = P\,C elkhabaz2019b E5, printed as J = pc in the enzalutamide study wilson2018 E6. In the supplement of the media study the apparent permeability is the normalized flux divided by the donor concentration, in cm/min elkhabaz2019b E5.

Variables and units

symbol	meaning	units
J	flux across the membrane	µg/(min·cm²) elkhabaz2019b R7
P	membrane permeability	cm/min elkhabaz2019b E5
C	concentration available for permeation	µg/mL, taken as µg/cm³ elkhabaz2019b E5; wilson2018 E6

Assumptions and valid domain

None stated in either paper; the concentration is meant to be the one available for permeation, that is the free drug wilson2018 E6.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
wilson2018	relation of flux to concentration for enzalutamide	not used numerically	printed; no numerical output wilson2018 E6
elkhabaz2019b	apparent permeability of atazanavir and posaconazole in six media	atazanavir in buffer-V1 at J_{amph}: 1.19 × 10⁻¹/79 = 1.51 × 10⁻³ cm/min	reproduces Table S2 elkhabaz2019b E5, R12

Where it fails or is disputed

With total concentration as C the apparent permeability fell in the micellar media, because only free drug crosses; multiplied by the ratio of total to buffer solubility it was the same at both solid phases in every medium (1.33–1.77 × 10⁻³ cm/min for atazanavir, 2.36–3.03 × 10⁻³ for posaconazole) (F18) elkhabaz2019b R12, R13.

Concepts

membrane flux, Fick's first law, free drug concentration, micellar solubilization. Findings. F18, F25.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

membrane flux in terms of solute activity

Expression

J = \frac{dM}{dt} = \frac{D\,S\,a}{h\,\gamma_m} mosqueragiraldo2015 E4.

The papers of 2017–2022 print the relation per unit area,

J = \frac{D\,a}{h\,\gamma_{m}} indulkar2017a E7,

with the flux defined as

J = \frac{dm}{A\,dt} indulkar2017a E4, and as the mass flow rate

F = \frac{dM}{dt} = \frac{D\,S\,a}{h\,\gamma_m} lu2017b E1.

In the Bioperformance papers the relation is printed with the area outside the numerator,

J = \frac{dM}{dt\,S} = \frac{D\,a}{h\,\gamma_m} alhalaweh2016 E1,

as J = dM/dt = D S a/(h \gamma_m) with the area S inside the numerator raina2014a E6; raina2015c E3, and as J = (1/A)(dM/dt) = D a/(h \gamma_m) hate2017 E1.

The crystallization-from-solution papers print it per area,

J = \frac{dM}{S\,dt} = \frac{D\,a}{h\,\gamma_m} [jackson2016 E1];

J = \frac{dM}{A\,dt} = \frac{D\,a}{h\,\gamma_m} [li2016a E2],

with the activity written as

a = C\,\gamma [jackson2016 E2].

In the Mesoporous silica papers it is printed as

J = \frac{dM}{A\,dt} = \frac{D\,a}{h\,y_{m}} dening2018 E1,

with the membrane activity coefficient written y_m and the activity a = C\,y dening2018 E2.

In the ASD dissolution papers it is printed per membrane area,

J = \frac{dM}{dt}\cdot\frac{1}{S} = \frac{D\,a}{h\,\gamma_m} jackson2015 E1,

and with the supersaturation as the activity,

J = S_i\,\frac{D}{h\,\gamma_m} jackson2015 E3;

the tacrolimus paper prints \frac{dM}{dt} \propto a in words: the rate of transport into sink conditions is proportional to the thermodynamic activity of the solute in the donor, not to its concentration trasi2016 E2.

Variables and units

symbol	meaning	units
J	flux across the membrane	µg/min in the telaprevir figure mosqueragiraldo2015 E4, R12
M, t	mass transported, time	mosqueragiraldo2015 E4
D, S, h	diffusion coefficient, membrane area, membrane thickness	mosqueragiraldo2015 E4
a	solute activity in the donor	mosqueragiraldo2015 E5
\gamma_m (printed as italic y_m in the Mesoporous silica paper)	activity coefficient of the drug in the membrane	mosqueragiraldo2015 E4; dening2018 E1
J in the Bioperformance papers	flux (or mass flow rate when S is inside)	µg/min; µg/(h·cm²); mg/min/cm² raina2014a E6; indulkar2016 E11; alhalaweh2016 R17
S or A	membrane area	7.065 cm² raina2014a P8; 1.77 cm² indulkar2016 P5; 115 cm² hate2017 M10; 7.07 cm² dening2018 P12
J in the crystallization-from-solution papers	mass crossing the membrane per time and area	µg min⁻¹ cm⁻² (the printed danazol axis lacks the time) [jackson2016 E1]
S or A in the danazol cell	membrane area (orifice)	7.065 cm²
D, h	diffusion coefficient of the solute in the membrane; membrane thickness	cm² s⁻¹; cm
C, \gamma	concentration and activity coefficient in solution	µg mL⁻¹, dimensionless [jackson2016 E2]
J in the ASD dissolution papers	flux	µg/(min·mm²) jackson2015 E1
S in the danazol cell of 2015	membrane cross-sectional area (not the supersaturation)	mm² jackson2015 E1
S_i	supersaturation, free drug over crystalline solubility	dimensionless jackson2015 E3
dM/dt	mass flow rate into the receiver	µg/min trasi2016 E2

Assumptions and valid domain

D, S, h and γm are constant across experiments, so differences in flux reflect differences in activity; sink conditions (receiver below half the crystalline solubility) mosqueragiraldo2015 C10, R11. In the Bioperformance papers: sink receiver, nearly constant donor concentration, and constant D, S, h and γm raina2014a C11; alhalaweh2016 C2. It was tested in a side-by-side cell with a regenerated cellulose membrane, a flow-through cell, a hollow-fibre module and Caco-2 monolayers. Sink conditions in the receiver, constant donor concentration, and S (or A), D, γ_m and h constant for a given set-up and solute, so that mass flow is proportional to the donor activity [jackson2016 C9; li2016a E2]. Tested for danazol (receiver below 0.3 µg/mL) and for celecoxib and nevirapine [jackson2016 P9; li2016a P8]. In the Mesoporous silica papers D, A, y_m and h are constant in all diffusion experiments, so mass flow follows donor activity; receiver concentrations stayed below the crystalline solubility dening2018 C11, C12. There it is used to read free drug released from drug-loaded silica, where dissolution sampling cannot tell free from held drug dening2018 C22. In the danazol dispersion study D, S, \gamma_m and h are constant in the cell, so flux is proportional to free drug, not total drug jackson2015 C11; in the tacrolimus study the receiver is under sink conditions and the relation is cited trasi2016 E2.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
mosqueragiraldo2015	telaprevir flux against donor concentration	about 0.068 µg/min at 5 µg/mL, about 0.97 at 90, about 1.07 at 130	inputs not printed (D, h, γm) mosqueragiraldo2015 E4, R12
trasi2015a	flux of ritonavir, lopinavir, paclitaxel as a measure of activity	plateaus 0.13–0.27 µg/min	read-out, relation not printed trasi2015a R2, C14
indulkar2017a	atazanavir flux in buffer, calibration of free drug in SDS	slope 0.0017 mL/min·cm² (R² 0.998) up to the amorphous solubility	inputs not printed (D, h, γm) indulkar2017a E7, R10
lu2017b	telaprevir mass flow rate against concentration	0.009 µg/min per µg/mL (R² 0.9932)	inputs not printed (D, h, γm; S not stated as a value) lu2017b E1, R6
raina2014a	felodipine and nifedipine flux plateau	D, h, γm not printed	printed; inputs not printed raina2014a E6
raina2015c	solubilizer effect on flux	same	printed raina2015c E3
alhalaweh2016	Caco-2 flux of drug mixtures	A, D, γm assumed constant	printed alhalaweh2016 E1
hate2017	hollow-fibre transfer	not applied numerically	printed hate2017 E1
jackson2015	danazol ASD flux; free danazol from dissolving dispersions	17.5 × 10⁻⁵ µg/(min·mm²) printed; free drug 7.1–9.1 µg/mL with LLPS, 5.4 µg/mL without	mismatch: recomputed 1.28 × 10⁻³ jackson2015 E1; flux and concentration columns not proportional jackson2015 R9, X5
trasi2016	tacrolimus mass flow; solutions and dissolved marketed products, pH 4.5, 37 °C	stated in words; plateau ≈0.0050–0.0055 µg/min from 60–100 µg/mL, products 0.0048–0.0054 µg/min	no constants printed trasi2016 E2, R14, R15
wilson2018	enzalutamide, ASD solutions and drug with polymer	D, h and γm constant; donor activity inferred from mass flow	no numerical output wilson2018 E4, E5, C12
elkhabaz2019b	atazanavir, posaconazole in six media	constants not printed	inputs not printed elkhabaz2019b E3
ueda2020a	atazanavir, clozapine with two HPMCAS grades	flux proportional to the extent of supersaturation, in words	not applicable ueda2020a E2
alkalla2026	atazanavir and darunavir in diffusion cells and Caco-2	A, D, γm and h assumed constant	inputs not printed alkalla2026 E2
jackson2016	maximum free-drug concentration of danazol from the flux plateau at 8 µg/mL; maximum flux with 1–1000 µg/mL polymer	flux about 0.0152–0.0159 (plateau); 0.0126–0.0175 with polymer (units as printed)	plot readings [jackson2016 R10, R11, X9]
li2016a	check that 0.1% STC and SGC leave the activity of celecoxib and nevirapine unchanged	0.44, 0.46, 0.41 and 20.9, 23.4, 21.0 µg/min	measured [li2016a R15]
lu2017	activity ratio δ = F/F° from the mass flow of telaprevir (calibration from an earlier study)	δ 11.5 and 28.8 (concentrations 60–330 µg/mL)	plot readings [lu2017 E2, R1]
indulkar2018	flux as a measure of donor activity in micellar media	J = Da/(h\gamma_m)	inputs not printed indulkar2018 E2
indulkar2019b	same, in SDS	as above	inputs not printed [indulkar2019b E2]
dening2018	free ritonavir from SBA-15 at 50–1000% of the amorphous solubility	3.80–9.12 ng/min against 9.20 for amorphous ritonavir; free drug about 19 and 23 µg/mL at 200 and 400%	inputs not printed; printed "ng/min" equal receiver slopes in ng/mL per min dening2018 E1, R8, R9, R10, X3
dening2018	ritonavir loadings 4.9–38.1% w/w; lopinavir	5.1–5.4 against 4.37 and 4.10 ng/min; lopinavir 51.4 and 70.9%	inputs not printed dening2018 R27, R20

Where it fails or is disputed

The plateau still rises by about 10% mosqueragiraldo2015 X6; replicates and the slope window are not stated mosqueragiraldo2015 X13; trasi2015a X10. The relation needs a membrane that passes only dissolved drug; the telaprevir paper explains the same flux drop with bile-salt micelles both by lower activity and by slower diffusion of drug-loaded aggregates, and does not separate them lu2017b X8; indulkar2017a X9. Flux of nifedipine at about 10 µg/mL, near its crystalline solubility, was about zero, which proportionality to activity does not predict raina2014a X11. In the hollow-fibre module transfer keeps rising above the amorphous solubility, where activity should be constant hate2018 C25. One paper uses γ for both the membrane and the donor coefficient raina2015c X8. With a sink receiver the PAMPA mass flow of atazanavir kept rising above the amorphous solubility, where activity should be constant (F22) hate2022 R19. A crystalline co-drug lowered the flux plateau by lowering the activity of the drug-rich phase (F20) alkalla2026 C37, and flux and total concentration decouple in micellar media (F18) elkhabaz2019b C25. The flux axes of the danazol paper have no time unit and no replicates are stated; the crystalline reference flux differs between figures (0.0011 and 0.0008) and the plateau-to-crystal flux ratio (about 14 to 19) exceeds the concentration ratio (about 9), which is not discussed [jackson2016 X9, X10, X11]. For celecoxib the ratio of concentration to solubility disagrees with the unchanged flux [li2016a X18]. The formula is also printed by 14 papers outside the crystallization-from-solution chapter (see the evidence table). With ritonavir on SBA-15 at the 1000% dose the flux equalled that of amorphous ritonavir while filtered dissolution gave about 85% of the amorphous solubility, unresolved dening2018 X14. The membrane of that paper is regenerated cellulose in the methods and "cellulose acetate" in one section dening2018 X2. The percent of reference depends on whether the reference is dose-matched dening2018 X15. For one danazol system the example profile gives 128 × 10⁻⁵ against a printed 17.5 × 10⁻⁵ µg/(min·mm²), unresolved jackson2015 E1, X4; the standard curve has an intercept jackson2015 X5. Below 50 µg/mL the tacrolimus flux rose with concentration but did not extrapolate to zero trasi2016 X8.

Concepts

membrane flux, thermodynamic activity, chemical potential, Fick's first law, sink conditions, incomplete drug release, free drug concentration. Findings. Amorphous solubility and LLPS: F8, F11, F16, F17. Bioperformance: F2, F3, F18, F19, F20, F22, F25. Crystallization from solution: F22, F31, F32, F38. Mesoporous silica: F8, F11, F15. Supersaturation from ASD dissolution: F7, F8.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

molar amount of halogen at the lower XPS binding energy

Evidence table: molar amount of halogen at the lower XPS binding energy. Content from the release-mechanism chapter (2019–2021).

Expression

n_{F,\mathrm{low}} = \frac{100\,\mathrm{mg} \times DL}{889\,\mathrm{g\,mol^{-1}}} \times 2 \times f_{\mathrm{low}} que2019 E4

Variables and units

symbol	meaning	unit
n_{F,\mathrm{low}}	moles of fluorine at the lower F 1s binding energy in a compact	mmol
100 mg	compact mass	mg
DL	drug loading	–
889 g/mol	molecular weight of ledipasvir	g/mol
2	fluorine atoms per ledipasvir molecule	–
f_{\mathrm{low}}	share of F 1s at 684.0 eV (73.4% at 10% loading)	–

Assumptions and valid domain

The composition of the whole compact is used que2019 E4. For iodine: four iodine atoms per molecule and the share of lower-binding-energy I 3d, homogeneous within the 10 nm XPS depth [que2021 E4].

Use in the library

paper	used for	values or fitted parameters	status / recomputed
que2019	amount of drug–polymer-bonded fluorine against loading (secondary axis of Fig. 16)	10% loading: printed 0.165 mmol	mismatch: 10 mg / 889 g/mol × 2 × 0.734 = 0.0165 mmol, the value plotted que2019 E4, R25, X3
que2021	halogen-bonded iodine of TIPP and Me-TIPP, 10–40%	0.017–0.050 mmol per 100 mg	reproduces: 10 mg / 821.91 × 4 × 0.559 = 0.0272 mmol; 20 mg / 849.97 × 4 × 0.533 = 0.0502 [que2021 E4, R11, R12]

Where it fails or is disputed

The printed example is a factor-10 misprint que2019 X3. XPS samples the top ~10 nm, so the whole-compact composition is an assumption que2019 P7, E4.

Concepts

drug-polymer interactions, surface drug enrichment. Findings. Release mechanism and LoC: F7, F10, F17.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
n_W, n_D, n_P	amounts of water, drug, polymer (stated as mole fractions)	– rumondor2009c E4
\phi	volume 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

paper	used for	values or fitted parameters	status / recomputed
rumondor2009c	thermodynamic origin of moisture-induced separation	none	argument only rumondor2009c E4
purohit2017b (outside)	AAPS of ritonavir dispersions on hydration	none	argument only purohit2017b E2
rumondor2010c	why the same drugs separate more with PVP than with PVPVA and HPMCAS	none	argument 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 Amorphous solid dispersions: the whole picture

non-compartmental AUC

Expression

AUC_{0-\infty} = AUC_{0-t} + \frac{C_t}{\beta} wilson2018 E9, with AUC_{0-t} by the linear trapezoidal rule. The rule is only named as the linear trapezoidal rule in the enzalutamide study of polysaccharide ASDs and as the linear-up/log-down trapezoidal rule in the pretomanid study wilson2020 E5; nguyen2023a E6.

Variables and units

symbol	meaning	units
AUC_{0-t}, AUC_{0-\infty}	area under the plasma concentration–time curve to the last point and to infinity	µg·h/mL (rats); ng·h/mL (monkeys) wilson2020 R6; nguyen2023a R23
C_t	final measured plasma concentration	same concentration unit wilson2018 E9
\beta	terminal elimination rate constant	1/h wilson2018 E9
t	time of the last measurable concentration	h

Assumptions and valid domain

Non-compartmental analysis with WinNonlin; nominal sampling times; values below the limit of quantification set to zero before the first quantifiable concentration and treated as missing thereafter wilson2020 E5; nguyen2023a E6.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
wilson2018	rat Cmax and AUC0–48 against in vitro mass flow	AUC0–∞ not reported	printed in words; not applicable wilson2018 E9, R17
wilson2020	rat AUC0–inf of four formulations	516, 305, 45 and 43.1 µg·h/mL	named only wilson2020 E5, R6
nguyen2023a	monkey AUC0–inf, fasted and fed	reference 7846 fasted and 11,663 fed ng·h/mL	expression not printed nguyen2023a E6, R23

Where it fails or is disputed

The window is not stated alike: the enzalutamide AUC is called AUC0–48 in the methods and AUC0–72 h on the mass-flow axis of the same paper, and AUC0–inf is used for bioavailability wilson2020 E5, R6, R8. The dog and monkey studies use few animals (six and four), and the sampling and the handling of values below quantification affect the area nguyen2023a E6, R23; purohit2019 R9.

Concepts

oral bioavailability, in vitro–in vivo correlation. Findings. F23, F24, F25, F26, F30.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

Noyes-Whitney equation

Expression

As printed for crystals dissolving in a polymer melt (concentration C of dissolved drug in the liquid phase):

\frac{dC}{dt}=\frac{DA}{hV}\left(C_s-C\right)

moseson2018 E5, and with a Nernst–Brunner diffusion layer in the same form moseson2019 E2.

The ASD dissolution papers print a proportional form for aqueous dissolution,

\frac{dc}{dt} \propto A\,(C - C_{\mathrm{eq}}) alonzo2010 E3,

and name the equation for indomethacin precipitates without an expression xie2017 E1.

New printed forms (Release mechanism and LoC):

\frac{dm}{dt} = A\,\frac{D}{h}\left(C_s - C_b\right) indulkar2017b E4

\frac{dx}{dt} = C\left(S - x\right) purohit2017b E3

\frac{dC}{dt} = k\left(C_s - C\right) indulkar2019a E1

\frac{dC}{dt} = \frac{DA}{Vh}\left(C_s - C\right) indulkar2019a E2

\frac{dM}{dt} = \frac{DA}{h}\left(C_s - C\right) que2019 E1

\frac{dC}{dt} = k\left(C_s - C_t\right) saboo2020a E1

Stated in words as the Nernst–Brunner relation, the dissolution rate proportional to the saturation solubility under sink conditions correasoto2022b E4.

\left(\frac{dC}{dt}\right)_{\mathrm{drug}} = \frac{D A}{V h}\left(C_s - C\right) indulkar2022 E2

Variables and units

symbol	meaning	unit	ids
C, C_s	concentration of dissolved drug; solubility of the crystalline drug in the molten polymer	–	moseson2018 E5
D	diffusion coefficient	–	moseson2018 E5
A	surface area available for dissolution	–	moseson2018 E5
h	boundary-layer thickness at the solid–liquid interface	–	moseson2018 E5
V	volume of the liquid phase	–	moseson2018 E5
dc/dt	dissolution rate in aqueous medium	µg/(mL min)	alonzo2010 E3
C, C_{\mathrm{eq}}	solution concentration; equilibrium concentration (aqueous form)	µg/mL	alonzo2010 E3
dm/dt, dM/dt	mass of drug dissolved per unit time (release-mechanism forms)	–	indulkar2017b E4; que2019 E1
A	surface area exposed to the medium	–	indulkar2017b E4
D, h	drug diffusion coefficient; boundary or diffusion layer thickness	–	indulkar2019a E2
C_s, S	solubility of the dissolving solid form (the amorphous solubility for an amorphous surface)	µg/mL	indulkar2019a E1, E2; purohit2017b E3
C_b, C, C_t, x	drug concentration in the bulk medium at time t	µg/mL	indulkar2017b E4; saboo2020a E1; purohit2017b E3
V	volume of the dissolution medium	mL	indulkar2019a E2
k, C (purohit2017b)	rate constant	–	indulkar2019a E1; purohit2017b E3

Assumptions and valid domain

Applied to crystal dissolution in the polymer melt, with viscosity not constant but falling as drug dissolves; no numerical output is stated in either paper moseson2018 E5; moseson2019 E2. Named the "modified Noyes and Whitney equation" (cited) and used as one arm of the scheme in which dissolution competes with crystallization of the solid and of the solution alonzo2010 E3, C43. Used to argue that EPO, by raising the crystalline solubility of indomethacin, "may" raise its dissolution rate xie2017 C47. Describes drug-controlled dissolution indulkar2017b E4; dissolution governed by the amorphous drug at high loading purohit2017b E3; C_s is the solubility of the solid form at the dissolving surface, and the rate approaches zero as C approaches it indulkar2019a E1, E2; D, A and h fixed, not applicable to dispersions whose release exceeds the amorphous solubility que2019 E1.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
moseson2018	argument that temperature, plasticisation and shear speed up dissolution	none	inputs not printed moseson2018 C52
moseson2019	the diffusion-only model that fragmentation extends	none	inputs not printed moseson2019 C39, C40
moseson2020	why a physical mixture with large crystals lags a dispersion in thermogravimetry (crystal size sets dissolution in the molten polymer)	none	named only moseson2020 E1, C33
moseson2022c	framework for dissolution of bicalutamide crystals in PVPVA; the population balance model uses it through a size-dependent shrinkage rate with a fitted rate constant	kd 0.1002 ± 0.0511 µm/s against assumed 0.5 and 4 µm/s	inputs not printed (D, h and V not given) [moseson2022c E18, E9, R16]
alonzo2010	scheme of Fig. 16	none	not applicable alonzo2010 E3
xie2017	redissolution of indomethacin precipitates at pH 5	α solubility 15 µg/mL, 27 µg/mL with 100 µg/mL EPO	named only xie2017 E1, R2, C47
indulkar2017b	release into medium saturated at the amorphous solubility	none	not applicable indulkar2017b E4, C35
purohit2017b	why drug-controlled release cannot pass the amorphous solubility	none	inputs not printed purohit2017b E3, C50
indulkar2019a	release from a drug-rich surface into saturated medium	none	inputs not printed indulkar2019a E1, E2, C42
que2019	the amorphous solubility as the ceiling of free drug	none	inputs not printed que2019 E1, C2
saboo2020a	rate advantage of an amorphous form similar to its solubility advantage	none	not applicable saboo2020a E1, C1
correasoto2022b	introduction: why the amorphous form dissolves faster	none	not applicable correasoto2022b E4
indulkar2022	drug-controlled release of high-loading ritonavir–PVPVA (cited 50% result)	none	inputs not printed indulkar2022 E2, R3
bapat2023	named only, as the form that fails in the polymer-controlled regime	none	named only [bapat2023 E4, C2]

Where it fails or is disputed

It neglects crystal defects, particle breakage and a changing particle number, which is the gap the 2019 paper addresses moseson2019 C2, C55. The 2022 paper replaces the diffusion-only picture by a model in which breakage is needed to finish within 20 min, and calls the equation a framework with unlikely sink conditions in HME [moseson2022c E18, R12]. As printed, A(C - C_{\mathrm{eq}}) is negative while a solid dissolves below C_{\mathrm{eq}}; read it as a direction only alonzo2010 X3. The solubility effect "alone cannot explain" the faster redissolution of the precipitate; crystal size, not tested with size-matched crystals, is the authors' main explanation xie2017 C47, C48. It does not describe polymer-controlled release, which continues into medium already at the amorphous solubility indulkar2017b C35; indulkar2019a C43. The 2017 ritonavir paper prints the label "(2)" for this equation, the same as for its Flory–Huggins equation, and calls it eq. 3 in the text purohit2017b X2.

Concepts

Noyes–Whitney equation, diffusion boundary layer, crystal dissolution into a polymer melt, crystallization during dissolution, Nernst-Brunner equation, drug-controlled release, amorphous solubility. Findings. ASD process: F9, F11, F12, F31, F36, F37. Supersaturation from ASD dissolution: F1, F10, F21. Release mechanism and LoC: F1, F2, F3, F4.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

pH-solubility profile

Expression

C_T = C_B\left(1 + 10^{\,\mathrm{p}K_a - \mathrm{pH}}\right) indulkar2015 E8.

The paper of 2018 prints the same relation as

C_T = \left(\frac{1 + X}{X}\right)C_U,\qquad X = 10^{\mathrm{pH} - \mathrm{p}K_a} sugihara2018 E1,

which equals C_B\,(1 + 10^{\mathrm{p}K_a-\mathrm{pH}}) (synthesis: (1+X)/X = 1 + 1/X).

Two delamanid papers use the relation without printing it, one to fit the drug's pKa from measured solubilities and one to draw the predicted curve of a cited pKa nguyen2023c E1; nguyen2023b E1. The posaconazole paper prints it in the same form,

C_T = C_B\left(1 + 10^{\,\mathrm{p}K_a - \mathrm{pH}}\right) [duong2022b E1],

as cited by the delamanid work nguyen2023c E1.

Variables and units

symbol	meaning	units
C_T	total solubility at the pH	µg/mL indulkar2015 E8
C_B	crystalline free-base solubility (the amorphous free-base solubility is substituted for the amorphous form)	µg/mL indulkar2015 E8, C46
\mathrm{p}K_a, \mathrm{pH}	pKa of the base, medium pH	indulkar2015 E8
C_T (delamanid papers)	total solubility of the drug at that pH, crystalline or amorphous	µg/mL nguyen2023c R1
\mathrm{p}K_a (delamanid)	pKa of the base: fitted 3.94 ± 0.04, 4.3 cited	nguyen2023c R3; nguyen2023b E1

Assumptions and valid domain

The solution is in equilibrium with the neutral form, not the salt indulkar2015 E8. Tested for clotrimazole, atazanavir and nicardipine at 37 °C over about ±2 pH units of the pKa indulkar2015 A2. In the delamanid papers it is applied to a monoprotic weak base in equilibrium with the neutral form, over pH 1.6 to 6.5 at 37 °C, to the crystalline and to the amorphous solubility alike nguyen2023c P1, P2, E1. For the coated-tablet paper the intrinsic solubility behind the printed curve is not given, so the curve is a reference line rather than a fit nguyen2023b E1.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
indulkar2015	predicted crystalline and amorphous solubility at each pH; oral-dose scenarios	atazanavir at pH 1.5: 1090 µg/mL	reproduces (1.04 µg/mL, pKa 4.52; printed 1.1 mg/mL) indulkar2015 E8, R26
sugihara2018	pazopanib crystalline and amorphous solubility against pH	pKa 6.4; amorphous points fall below the curve at pH 5 and 5.5	reproduces for the crystalline curve sugihara2018 E1, R3, C11
nguyen2023c	fitting the delamanid pKa to crystalline and amorphous solubility between pH 1.6 and 6.5	pKa 3.94 ± 0.04; crystalline 10.2 → 0.018 and amorphous 154.5 → 0.76 µg/mL	the fitted curve follows the amorphous data but gives about 3.7 instead of 10.2 µg/mL for the crystal at pH 1.6 nguyen2023c R3, R1
nguyen2023b	drawing the predicted buffer solubility of delamanid against the measured buffer and biorelevant values	pKa 4.3 cited; about 10.3 µg/mL at pH 1.6, below 0.02 µg/mL above pH 5.5	inputs not printed; the biorelevant values lie far above the curve nguyen2023b E1, R13, R18

Where it fails or is disputed

The predicted amorphous curve is the crystalline curve times one factor, so its overlap with the LLPS data does not test the relation; the constancy of the un-ionized concentration does indulkar2015 X14. At the lowest pH a salt may limit solubility, not examined indulkar2015 X7. It covers the drug only: in the dispersions of the ASD dissolution papers the polymer's own pH-dependent solubility decides release, and the worst gastric pH for delamanid dispersions lay where neither drug nor polymer dissolved well nguyen2023c C14, C15. It does not apply to a neutral drug: praziquantel, with a calculated pKa of 1.14, kept an amorphous solubility of 1.17–1.43 mg/mL across six buffers and still lost release after gastric stages at pH 3.0 and 5.0 alvarenga2025 R4, R1, R10. Food components raised delamanid solubility far above the curve (13.10 and 57.97 µg/mL in a fed gastric medium) nguyen2023b R13.

Concepts

pH-dependent solubility, ionization, pKa, pH-dependent solubility of weak bases, enteric polymer. Findings. Amorphous solubility and LLPS: F10, F23. Supersaturation from ASD dissolution: F24, F25, F28.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

polymer partitioning into the drug-rich phase by depletion

Expression

Printed in words in both papers; written here as the stated balances.

c_{p,\,\mathrm{droplets}} = c_{p,\,\mathrm{total}} - c_{p,\,\mathrm{solution}} wilson2021 E3

c_{p,\,\mathrm{droplets}} = c_{p,\,\mathrm{before}} - c_{p,\,\mathrm{supernatant}} shah2025 E2

w_{p} = \frac{c_{p,\,\mathrm{droplets}}}{c_{p,\,\mathrm{droplets}} + c_{d,\,\mathrm{droplets}}}, \qquad c_{d,\,\mathrm{droplets}} = c_{d,\,\mathrm{total}} - c_{d,\,\mathrm{solution}} shah2025 E3; wilson2021 X4

Variables and units

symbol	meaning	units
c_{p,\,\mathrm{total}}, c_{p,\,\mathrm{before}}	polymer added	µg/mL
c_{p,\,\mathrm{solution}}, c_{p,\,\mathrm{supernatant}}	polymer left dissolved (solution ¹H NMR, or HPLC–ELSD after ultracentrifugation)	µg/mL
c_{d,\,\mathrm{solution}}	drug left dissolved (NMR, or the LLPS concentration)	µg/mL
w_{p}	polymer weight fraction of the droplets, water ignored	dimensionless

Assumptions and valid domain

NMR sees only dissolved species, and the drug-rich phase is fully sedimented by ultracentrifugation; the water content of the droplets is ignored wilson2021 C22; shah2025 E2, E3. Tested for enzalutamide (25–100 µg/mL HPMCAS or Eudragit E PO, 70 or 120 µg/mL drug) and posaconazole (900 µg/mL HPMCAS L, M or H, 100 µg/mL drug) wilson2021 R7; shah2025 R16.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
wilson2021	share of HPMCAS and Eudragit E PO in enzalutamide droplets	HPMCAS 12.7–24.7, Eudragit E PO 40.8–41.0 w/w%	reproduces with plot-read drug values (HPMCAS 100 µg/mL: 100 − 67.4 = 32.6 µg/mL in droplets) wilson2021 E3, R7, X4
shah2025	share of HPMCAS L, M, H in posaconazole droplets	895, 886, 861 µg/mL left of 900; fractions about 0.05, 0.14, 0.31	reproduces (H: 39/(39 + 87.5) = 0.31) shah2025 E3, R16, R17
raina2015b	polymer in felodipine precipitate and supernatant (direct NMR of both phases, not depletion)	PVPVA 6.8 and 36.7, HPMCAS 7.1 and 34.2 mg	single determinations raina2015b R12

Where it fails or is disputed

The two enzalutamide polymers were compared at different drug totals (70 against 120 µg/mL), and a colorimetric pellet assay gave about 19–23 w/w% for both, so the ranking rests on NMR alone wilson2021 X4, X5. For posaconazole the L and M depletions (5 and 14 µg/mL) lie within one to two standard deviations of zero shah2025 X7.

Concepts

polymer partitioning into the drug-rich phase, drug-rich nanodroplets. Findings. F26, F37, F44.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
R_G	crystal growth rate	–
k_G	growth rate coefficient	not determined
A	crystal surface area	not determined
C_b, C^*	bulk concentration, crystal solubility	µg/mL
g	overall growth order, typically 1 to 2	–
R_G (supersaturation form)	overall crystal growth rate	µg mL⁻¹ min⁻¹ alonzo2012 E2
k_g	growth rate constant against σ	as R_G [ilevbare2012b E3]
S, \sigma	supersaturation ratio and its logarithm	dimensionless

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

paper	used for	values or fitted parameters	status / recomputed
purohit2018	why 450 mL shows growth and 900 mL not	none fitted	inputs not printed purohit2018 E3, C52, C55
alonzo2012	growth order of felodipine without and with HPMC	g 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 0.080	reproduces (1 µg/mL HPMC, S 5: 0.080 against 0.087 µg mL⁻¹ min⁻¹ in Fig. 3) alonzo2012 E2, E3
hate2019	tacrolimus on seeds	dC/dt = k_g A (C_{in}(0) - C^*)^n with constant area; fit y = 1.677x - 3.136, R² 0.9896	E4 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
ilevbare2012b	growth against σ; linear above σ_c	no k_g or g reported	not applicable [ilevbare2012b E3]
schram2015	R_G = k_G S^g, held at fixed disc speed	S 8; no k_G or g reported	not fitted [schram2015 E2, X7]
schram2016	R_G = A k_G S^g, area factor in the argument against area as the cause	S 4; no k_G or g reported	not 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 Amorphous solid dispersions: the whole picture

reduced glass transition temperature

Expression

T_{rg} = \frac{T_g}{T_{melt}} baird2010 E4.

Variables and units

symbol	meaning	units
T_{rg}	reduced glass transition temperature	dimensionless baird2010 E4
T_g, T_{melt}	glass transition and melting temperatures	K 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

paper	used for	values or fitted parameters	status / recomputed
baird2010	testing Trg against class	I-A 0.69, I-B 0.7; class I 0.69 ± 0.02, class III 0.73 ± 0.04, not significantly different	reproduces: acetaminophen 297.15/443.15 = 0.671 baird2010 E4, R14
nguyen2023a	pretomanid	0.67	reproduces: (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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	unit
J, J_0	nucleation rate with and without inhibitor	m⁻³ s⁻¹
t_s, t_s,0	seeded induction times with and without inhibitor	min
t_u, t_u,0	unseeded induction times with and without inhibitor	min
R/R_0	seeded growth-rate ratio, used for t_{s,0}/t_s	dimensionless
J_0, J_p	nucleation rate without and with polymer	m⁻³ s⁻¹
R_0, R_p	mass growth rate without and with polymer, from seeded desupersaturation slopes	µg/(mL min)
t_{u,0}, t_{u,p}	unseeded induction times without and with polymer	min

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

paper	used for	values or fitted parameters	status / recomputed
alonzo2012	felodipine, 1 µg/mL HPMC, S 10	t_{u,0} 15.3 min, t_u 136.5 min, R/R_0 0.607; J/J_0 = 7.05 × 10⁻⁴	reproduces: 7.06 × 10⁻⁴ with 1.647; 7.00 × 10⁻⁴ with the printed 1.643 alonzo2012 E10, X6
xie2016a	celecoxib with HPMCAS (ASD dissolution chapter): 22 µg/mL with 5 µg/mL HPMCAS, pH 6.8, 37 °C	t_{u,p} 960 min, R_0/R_p = 70; J_0/J_p about 4,000	derived 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
lu2017	telaprevir, 1.86 mM STC and SGC, δ 11.5; t_u,0 about 30 min, t_u 960 min	J/J_0 2.5 × 10⁻³ and 2.9 × 10⁻⁶	recomputed 2.58 × 10⁻³ and 3.06 × 10⁻⁶ [lu2017 E4, R10, X1]
lu2017a	same with bile salts at 1.86 and 12 mM; rate ratio set to 100 for STCDC and SGCDC	E_J about 360 to 3 × 10⁵; about 1 for STCDC	reproduced 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 Amorphous solid dispersions: the whole picture

SHG relative crystallinity

Expression

Relative crystallinity as the background-subtracted field-averaged SHG intensity over that of a crystalline reference, in words in the paper kestur2012 E8:

X_c=\frac{\bar I_{\text{sample}}-\bar I_{\text{HPMCAS}}}{\bar I_{\text{ref}}-\bar I_{\text{HPMCAS}}}

and the ratio of the stored sample to the 15% crystalline standard, taken as fully crystalline correasoto2017 E2:

R=\frac{I_{\text{sample}}}{I_{\text{std},15\%}}

Variables and units

symbol	meaning	unit	ids
\bar I	average SHG intensity integrated over the field of view	photon counts	kestur2012 E8
\bar I_{\text{HPMCAS}}	background from pure HPMCAS (near zero, value not printed)	counts	kestur2012 P7, X10
\bar I_{\text{ref}}	100% crystalline naproxen (blends) or a 75/25 HPMCAS–crystalline naproxen mixture (dispersion)	counts	kestur2012 P7
R	ratio to the standard of fully crystalline drug (flutamide 15%)	dimensionless	correasoto2017 E2

Assumptions and valid domain

Linear scaling of SHG with crystallinity, uniformly distributed crystal orientations, and standards matching the particle size of the samples kestur2012 C26, C33. A fully crystallized sample gives R=1 correasoto2017 E2. Tested for naproxen–HPMCAS blends over 0–100% and flutamide standards at 0.005–5%.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
kestur2012	calibration, prediction set and storage kinetics	slope 0.98, R² 0.998, RMSEE 2.68 (0–100%); SONICC about 24 to 48% over 0–48 h	printed in words; inputs not printed kestur2012 R5, R16
correasoto2017	flutamide time courses	R about 1.0 (75% RH) and about 3.1 (82% RH) at 60 days	printed in words; inputs not printed correasoto2017 R9

Where it fails or is disputed

R>1 shows that the calibration crystals do not represent the crystals grown in the sample, and the 82% RH values lie at detector saturation correasoto2017 C20, X10. The 75/25 reference for the dispersion was never compared with dispersion-based standards kestur2012 X15. The blend and dispersion values use different crystallinity bases kestur2012 X11.

Concepts

second harmonic generation, coherent and incoherent SHG scaling, degree of crystallinity. Findings. F8, F9, F10.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

sink index

Expression

\mathrm{SI} = \frac{C_s\,V}{\mathrm{Dose}} purohit2018 E1.

Variables and units

symbol	meaning	units
C_s	solubility (crystalline or amorphous)	µg/mL
V	medium volume	mL
Dose	total drug	5000 µg purohit2018 R4

Assumptions and valid domain

SI above 1: enough medium to dissolve the dose; sink in the compendial sense is three times the solubility needed purohit2018 E1. Ueda 2024 (Eqs. 15–16, p. 54) write the two forms separately, SI_{cr}=S_c/(Dose/V) and SI_{am}=S_a/(Dose/V): the criterion of 3 applies to SI_{cr}, and SI_{am}=1 marks the dose that just reaches the maximum activity.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
purohit2018	five dissolution conditions	1.8 × 900/5000 = 0.324; 14.9 × 900/5000 = 2.68	reproduces purohit2018 E1, R4
hate2019	tacrolimus 5 mg in 240, 100, 40 mL	50 × 240/5000 = 2.4 (printed 2.4); 1 and 0.4	reproduces hate2019 E1, R7

Where it fails or is disputed

The amorphous solubility is cited and approximate purohit2018 R4.

Concepts

sink index, sink conditions. Findings. F16, F17, F28, F31.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
x_{C,L_1}, C_B	solubility of the crystalline drug in water	mole fraction; µg/mL ilevbare2013a E3; indulkar2015 E7
\Delta G	free-energy difference between supercooled liquid and crystal	indulkar2015 E7
\gamma_{L_1}, \gamma	activity coefficient of the drug in the aqueous solution	dimensionless ilevbare2013a E3
\gamma_{drug}	activity coefficient of the drug at the solubility limit	dimensionless marsac2009 E1
\chi, X_{ideal}	mole-fraction solubility and ideal solubility in the ritonavir–atazanavir paper	– alhalaweh2016 E4, E5
x_{drug}	mole-fraction solubility	dimensionless marsac2009 E1
\Delta H_{fus}, T_m	heat of fusion and melting temperature of the drug	kJ/mol, K (Table I and II values) marsac2006b M1, M2; marsac2009 M1, M2
\Delta C_P^{config}, \Delta C_P	heat-capacity difference between liquid and crystal	values cited, not printed marsac2006b X11; marsac2009 P7
T	temperature	K; 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

paper	used for	values or fitted parameters	status / recomputed
ilevbare2013a	appendix derivation of the amorphous solubility	none	γ not printed ilevbare2013a E3, E4
indulkar2015	argument that the un-ionized amorphous and crystalline solubility differ by a constant factor	none	γ not printed indulkar2015 E7, C42
marsac2006b	solubility of nifedipine and felodipine in PVP K12, PVP K29/32 and methyl pyrrolidone	0.06–0.07 g/g and 0.25–0.31 g/g in PVP; 0.15 and 0.48 g/g in methyl pyrrolidone	reproduces 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
marsac2009	γ in EP from the measured solubility; ideal solubility	γ 0.15–0.89	inputs not printed (heat capacities, ideal solubilities) marsac2009 E1, R9, X4
baird2011	activity coefficient in PEG 400	see the PEG chapter	reproduces (through its E7) [baird2011 E5]
marsac2008a	activity coefficient of nifedipine and felodipine in water from the solubility in methyl pyrrolidone	γ in water 1.89 × 10³ and 2.43 × 10⁵	reproduces 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]
raina2014a	background to the amorphous solubility prediction	none	inputs not printed (ΔC_p and γ not printed) raina2014a E1, R7
alhalaweh2016	crystal and solvation contributions to the solubility of ritonavir and atazanavir at 310 K	log 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
alhalaweh2016	ideal-solubility term of ritonavir and atazanavir	plotted log X_ideal −1.07, −1.97; recomputed −2.59, −4.53	mismatch alhalaweh2016 E5, X1, X2
marsac2008a	nifedipine and felodipine in methyl pyrrolidone and water (second reading)	γ in water 1.73 × 10³ and 2.31 × 10⁵	reproduces 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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
D_{NMR}	self-diffusion coefficient of the micelle	m²/s indulkar2017a E5
k_B, T	Boltzmann constant; temperature (25 °C)	indulkar2017a E5
\eta	viscosity of water at 25 °C	indulkar2017a C9
r	hydrodynamic radius	nm indulkar2017a R25
r in NTA sizing	hydrodynamic radius of nanodroplets	nm (111–257 nm) indulkar2016 R4
D	diffusion coefficient	–
k_B, T	Boltzmann constant; absolute temperature	K
\eta	dynamic viscosity of the medium	–
r	particle (hydrodynamic) radius	nm

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

paper	used for	values or fitted parameters	status / recomputed
indulkar2017a	radius of SDS micelles with 0, 0.4 and 7 mg/mL atazanavir	D 10^−10.3, 10^−10.3, 10^−10.42 m²/s; r 4.61, 4.61, 6.08 nm	reproduces 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
lu2017b	explanation of the lower flux of drug carried in bile-salt aggregates	none	named only, no numerical output lu2017b E8, C46
other chapters	sizing of drug-rich nanodroplets by NTA	none	printed; not recomputed here trasi2016 E4; purohit2017b E1; indulkar2016 E18; hate2018 E7; tres2018 E3
moseson2019	explaining why dissolution of IDM crystals in copovidone took hours and fragments stayed in place	none	inputs not printed moseson2019 C39, C51, E3
moseson2022c	framework for the low fitted dissolution rate of bicalutamide crystals in the viscous melt	none	inputs not printed [moseson2022c E19, C37]
indulkar2016	NTA sizing of clotrimazole droplets; constancy of the effective diffusion coefficient in the membrane	none	named only indulkar2016 E18
hate2018	NTA sizing	none	named only hate2018 E7
hate2022	colloid size against PAMPA mass flow	diffusion coefficient inversely proportional to particle size, in words	named only hate2022 E3, C56
indulkar2017b	NTA sizing of nifedipine nanodroplets	≈190–222 nm	named only indulkar2017b E7, R7
saboo2019	NTA of nilvadipine and cilnidipine media	none printed from NTA	named only saboo2019 E5, R12
saboo2020a	diffusion-coefficient ratio of felodipine and PVPVA	D_{drug}/D_{polymer} = 10	reproduces (10 nm / 1 nm at equal viscosity) saboo2020a E6, R27
saboo2020	NTA of indomethacin and ester media	250–350 nm stated	named 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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
J	flux of the test solution	µg/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 drug	µg min⁻¹ cm⁻² [lu2017 E2]
a, a^{\circ}	activity of the drug in the solution and at crystalline saturation	dimensionless
\delta	activity-based supersaturation	dimensionless

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

paper	used for	values or fitted parameters	status / recomputed
raina2015c	BSA solutions	S 7.3 and 4.2 from flux	inputs not printed; plot readings give about 16 and 9 raina2015c E9, X5
lu2017b	telaprevir with bile salts	δ ≈ 26.5 at 140 µg/mL	reproduces lu2017b E6
elkhabaz2019b	atazanavir and posaconazole in six media	SR_{max} = J_{amph}/J_{eq}; atazanavir buffer-V1 0.119/0.00217 = 54.8 (figure about 55), six-medium mean 53.6	reproduces elkhabaz2019b E4, R8, R9
lu2017	set δ 11.5 and 28.8 in buffer and with six bile salts at 1.86 and 12 mM	concentration 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]
lu2017a	set δ 2.4, 7.9, 12.5; read the free drug after 15 h of growth	residual 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]
indulkar2018	atazanavir, ritonavir in buffer, FaSSIF-V1, Composite-SIF and the lecithin series	SR = J/J^{}; SR_{amorph} = J_{amorph}/J^{}	63–65; 9.2–10; about 40 in STC alone indulkar2018 E3, R12, R10
lu2018	telaprevir in bile salt mixtures and complete media	F/F^{\circ} = a/a^{\circ} = \delta with buffer calibration	δ 11.5 and 28.8 set per medium [lu2018 E1, R1]
indulkar2019b	atazanavir in SDS	SR = 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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
C_{LLPS}	concentration at the onset of phase separation	µg/mL almeidaesousa2015 R5
C_{eq}	crystalline equilibrium solubility in the same medium	µg/mL almeidaesousa2015 R5
S	degree of supersaturation (relative)	dimensionless li2019 E2; trasi2019 E1; moseson2020a E3
C	measured, 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 S	concentration if the whole dose dissolved, over the crystalline solubility	dimensionless dening2019 E6; dening2018 P6
C/S	drug concentration over its solubility along the drying path	dimensionless li2020 E14
c, c^*	solution concentration; crystalline solubility in the same medium	µg/mL; 128 µg/mL for nevirapine at pH 6.5 hate2017 R1
C_{eq}, c_{eq}, c^{*}, C_0, c_0	equilibrium (crystalline) solubility at the test temperature and medium (crystallization-from-solution notation)	µg/mL [ilevbare2012b E1; ilevbare2012a E2; ilevbare2013b E4]
\sigma	natural logarithm of S, used for growth analyses	dimensionless [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 medium	µg/mL [konno2008a E4; chen2015a E1]
C_{\mathrm{eq}} (lopinavir)	crystalline solubility in a medium with the same excipients at the same temperature	µg/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

paper	used for	values or fitted parameters	status / recomputed
almeidaesousa2015	six drugs	4.3–54.0 (fluorescence), 4.7–64.5 (extinction)	eleven of twelve ratios reproduce; diclofenac extinction printed 51.6, recomputed 54.3 almeidaesousa2015 E15, R5
indulkar2015	weak bases	about 13 and about 63	stated in words (amorphous over crystalline solubility) indulkar2015 R10, C46
sugihara2018	pazopanib, pH 5.0 to 8.4	about 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
li2019	degree of supersaturation of lopinavir release	none printed	printed li2019 E2
trasi2019	compare single-drug and co-granulated dissolution at pH 6.8	RTV about 17 alone and about 3 co-granulated; LPV about 7 and 5; C^{*} 1.8 and 2.9 µg/mL	reproduces: 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
moseson2020a	the test condition of 50 µg/mL indomethacin	S = 6 (crystalline solubility about 8 µg/mL)	reproduces: 50 / 8 = 6.25 moseson2020a E3, R1
li2020	supersaturation of a drying droplet	peak about 2.4 (12.5:87.5 water:methanol) and about 320 (15:85) at 25% DL	model output li2020 R20
raina2015c	test of c/c* against flux	BSA 0.1%: 50/39.0 = 1.28; 1%: 50/47.8 = 1.05	reproduces raina2015c E6
hate2017	nominal supersaturation after the pH shift	500/128 = 3.91 (printed 3.9)	reproduces hate2017 E11
alonzo2012	felodipine S 3–12	Ceq about 0.5 µg/mL; S 10 = 5 µg/mL	reproduces alonzo2012 E1
ilevbare2013c	induction-time starts for celecoxib, ritonavir, efavirenz	S 14.7, 15.4, 2.4; 22/1.5 = 14.67	efavirenz printed 2.4 against recomputed 2.32 from 19/8.2 ilevbare2013c E1, X4
li2016a	S' = C/Cs with the solubility measured with 0.1% bile salt	nevirapine 7.1–8.7; celecoxib 13.6 printed, 16.7 recomputed	mismatch for celecoxib [li2016a E1, X1]
elkhabaz2019b	concentration-based maximum in six media	atazanavir buffer-V1 79/1.4 = 56.4; posaconazole human fluid 13.2/2.6 = 5.1	reproduces elkhabaz2019b E1, R8, R9
hate2019	tacrolimus dose levels	5 mg in 100 mL: 50/2.5 = 20; in 240 mL: S 8	reproduces hate2019 E2, R7
purohit2019	crystallized capsule contents against the crystalline solubility	about 3.7/1.5 = 2.5; with text values 4/1.4 = 2.9	reproduces purohit2019 E1, R5, X1
nguyen2023a	pretomanid nucleation	80/16.2 = 4.9 (stated 5); 160/16.2 = 9.9 (stated about 10)	reproduces nguyen2023a E1, R5, R6
ilevbare2012c	ritonavir S 7.6	10 µg/mL over 1.3 µg/mL	printed 7.6, recomputed 7.7 (10/1.3 = 7.69) [ilevbare2012c E4]
ilevbare2012b	ritonavir S 3.8, 7.6, 15.3; σ_c 1.37	c_eq about 1.31 µg/mL fits the printed set	reproduces within rounding; σc 1.37 gives 5.13 µg/mL [ilevbare2012b E1, E2]
ilevbare2012a	ritonavir 100 and 50 mM buffer	S 7.6/7.7 and 4.3	10/2.3 = 4.35 reproduces 4.3 ilevbare2012a E2
ilevbare2013b	celecoxib, efavirenz, ritonavir	S 6.6, 1.2, 7.6, 14.7, 15.4	10/1.5 and 10/1.3 printed as 6.6 and 7.6 (truncated) [ilevbare2013b E4]
hsieh2012	degree of supersaturation	dipyridamole 71.3/5.7 = 12.5	reproduces hsieh2012 E9
chen2015	ratio of drug concentration to the crystalline solubility in the medium of interest, fixed per drug	1.5–15 for 11 drugs; Ceq 0.2–81.3 µg/mL	printed in words; reproduces (13 × 19.0 = 247 µg/mL) chen2015 E2, R1
schram2015	S = C/Ceq of felodipine, 4 µg/mL over about 0.5 µg/mL	S 8	reproduces [schram2015 E1]
schram2016	same, 2 µg/mL	S 4 (ln S 1.39)	reproduces [schram2016 E1, R13]
dening2018	ritonavir doses and the dilution schedule	S 7.8 (27.9/3.6) and 3.9; stepwise to 1	reproduces (27.9/3.6 = 7.75; 14/3.6 = 3.9) dening2018 E6, M1
dening2019	theoretical S of the dilution steps	7.8, 3.9, 2.6, 1.9, 1.3, 1.0	reproduces (28/3.6 = 7.8) dening2019 E6, R16
mccarthy2020	theoretical and achieved S of indomethacin and methyl ester	15.3 and 21.4 theoretical; 7.2 and 7.0 achieved	reproduces (35.1/2.29 = 15.3; 9.0/0.42 = 21.4; 16.6/2.29 = 7.2) mccarthy2020 E4, R21, R20
konno2008a	qualitative: nucleation rate rises with S	none	not applicable konno2008a E4
chen2015a	S = 5 start in eight media; S of suspension liquids	SDS 107/14.5	reproduces, 7.38 against printed 7.4 [chen2015a E1, R17]
alonzo2011	supersaturation ratio about 60 of methanol-shift solutions	crystalline solubility at 25 °C not printed	approximate alonzo2011 C30, X9
li2016b	lopinavir leached from HPMCAS-HF and HPMCP suspensions into surfactant media, pH 3	about 3.3–3.9 (HF) and 1.6–1.8 (HPMCP) across surfactants	reproduces nine of ten bars; HF without surfactant ≈7.3/1.9 = 3.8 against ≈3.9 [li2016b E1, R20, X2]
xie2015	celecoxib 22 µg/mL with and without polymer	none printed	extractor calculation: 22/1.5 ≈ 14.7 without polymer, ≈10.3–11.6 with 22 µg/mL polymer xie2015 E5, X9
xie2016a	celecoxib 22 µg/mL	none printed	extractor calculation: 22/1.5 ≈ 15 without polymer xie2016a E3
que2018	paclitaxel at the amorphous solubility	31.6/0.36 ≈ 88	reproduces, 87.8 against printed 88 que2018 E1, R1, R2
nguyen2023c	delamanid 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 solubility	reproduces 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 Amorphous solid dispersions: the whole picture

surface-normalized release rate

Evidence table: surface-normalized release rate. Content from the release-mechanism chapter (2018–2025), with rows from the ASD process and Peptide permeability chapters.

Expression

A = \frac{k \times V}{S \times N} saboo2020a E3

R = \frac{k \times V}{S \times x} bapat2025b E1

Stated in words: the release rate is "normalized (to account for differences in drug and polymer content)" [bhardwaj2018 E4]; the slope of the initial linear part of percent release against time, normalized to each component's content and to the exposed area saboo2019 E4; the slope of drug concentration against time normalized by the area of the dissolving front and by the drug loading li2020 E13.

Printed in the papers of 2020–2022:

R = \frac{k \times V}{S \times x} saboo2020 E1

R = \frac{k\,V}{A\,x} [yang2021 E1]

R = \frac{k}{S \times x} correasoto2022a E1

R = \frac{k}{S \times x} correasoto2022b E1

In the last two forms k is the slope of cumulative mg released, so the medium volume drops out correasoto2022a E1.

Printed in the papers of 2022–2023:

R = \frac{k\,V}{A\,x} yang2022a E1

R = \frac{k \times V}{S \times x} [bapat2023 E1]

R = \frac{k}{S \times x} [correasoto2023 E1]

Printed in the papers of 2023–2025:

R = \frac{k\,V}{A\,x} yang2023 E1

R = \frac{k \times V}{S \times x} bapat2024 E1

R = \frac{k \times V}{S \times x} bapat2025a E1

Variables and units

symbol	meaning	unit
A, R	normalized release rate of one component	mg/min/cm² (µg/min/cm² in the 2018 paper)
k	slope of the regression line of concentration against time, not including the origin	mg/(mL min)
V	volume of medium	100 mL
S	exposed compact area	0.5 cm²
N, x	weight fraction of the component	–
A (2022 ritonavir form)	exposed surface area of the compact	units not printed

Assumptions and valid domain

The weight fraction is used on the assumption that the component densities are similar saboo2020a E3; the exposed area stays constant saboo2019 E4; the slope is taken from the linear part of the release curve bapat2025b E1. Used for compacts of 25–100 mg in an 8 mm die [bhardwaj2018 P6; saboo2019 P9; saboo2020a P6]. Slope from the linear region, the first 30 min when the profile is not linear [yang2021 E1]; from the initial linear points with the exposed area assumed constant correasoto2022a E1; slope window not stated correasoto2022b X19. The 2023 plasticizer paper took the slope after a lag time, from 30 to 60 min, where a lag occurred [correasoto2023 E1, P6].

Use in the library

paper	used for	values or fitted parameters	status / recomputed
bhardwaj2018	loading-normalized ITZ and PVPVA rates of spray-dried compacts	≈100, ≈250, ≈555, ≈2000 µg/min/cm² at 50, 25, 20, 10%	reproduces if the rate is divided by the weight fraction: 106, 256, 565, 1990 [bhardwaj2018 E4, R11]
saboo2019	nilvadipine, cilnidipine and PVPVA rates	0.002–3.49 mg/min/cm²	inputs not printed saboo2019 E4, R5, R6
saboo2020a	felodipine and polymer rates, five polymers; 40% HPMCAS analogues	≈0.0008–3.8 mg/min/cm²	inputs not printed; plot-based check in X10 saboo2020a E3, R13, R14, R16
li2020 (ASD process)	spray-dried ritonavir–PVPVA	surface-normalized dissolution rate	inputs not printed li2020 E13
bapat2025b (Peptide permeability)	release of OCA, SNAC and PVPVA	neat PVPVA ≈3.2; OCA ≈8.1 mg/min/cm²	reproduces within plot reading (≈3.1 and ≈8.6) bapat2025b E1, R2
saboo2020	indomethacin and its methyl ester with PVPVA over 5 min	≈0.01–4.2 mg/min/cm²; neat PVPVA ≈3.4	plot check reproduces neat PVPVA ≈3.4 saboo2020 E1, R3
yang2021	loratadine compacts with PVPVA and HPMCAS at 37 and 5 °C	≈0–3.45 mg/min/cm²	inputs not printed [yang2021 E1, R18, R21]
correasoto2022a	clopidogrel and PVPVA, 40–60% ± surfactant	≈0.2–6.7 mg/min/cm²	inputs not printed correasoto2022a E1, R18
correasoto2022b	atazanavir and PVPVA with additives, 37 and 55 °C	≈0.07–5.6 mg/min/cm²	inputs not printed correasoto2022b E1, R3, R7
yang2022a	ritonavir and PVPVA rates, 10–50%	congruency judged on normalized rates	inputs not printed yang2022a E1, R1, R2
bapat2023	HPMCAS-MF, its salt, indomethacin and its methyl ester by medium and rotation speed	≈0.12–1.62 mg/min/cm² at 100 rpm	inputs not printed [bapat2023 E1, R5, R9, R10, R16]
correasoto2023	atazanavir, ledipasvir and PVPVA with plasticizers	atazanavir ≈2.0–5.1; PVPVA with plasticizer ≈4.8–6.1; neat PVPVA ≈2.7 mg/min/cm²	inputs not printed [correasoto2023 E1, R6, R7, R13]
yang2023	PVPVA release from surfactant blends; Tween 80 dispersion at 30 against 40%	≈3.6–6.9 mg/min/cm² (blends)	inputs not printed yang2023 E1, R5
bapat2024	drug and HPMCAS rates of eight drugs, 5–60%	≈0.01–0.85 mg/min/cm²	bapat2024 E1, R2
bapat2025a	loratadine and cinnarizine in three HPMCAS grades	≈0.01–0.73 mg/min/cm²	bapat2025a E1, R2, R3

Where it fails or is disputed

For neat PVPVA an extractor check of the 2020 release curve gives ≈1.7 mg/min/cm² against ≈3.4 plotted, while the same check reproduces the other neat polymers; the compact mass of the neat polymers is not stated saboo2020a X10. The visible part of the 2018 PVPVA curve corresponds to about 8 against the stated 10.4 mg/min/cm² [bhardwaj2018 X8]. The neat PVPVA compact of the ledipasvir study weighed 250 mg against 100 mg for the dispersions que2019 X13. The basis of the felodipine–TPGS rates is not stated and they appear to be per total dispersion mass saboo2021 X4; the rates of the analogue study were derived in an unstated way [que2021 X6]; for ternary dispersions whether x uses the drug:polymer ratio or the weight fraction is not stated correasoto2022a X9. The basis of x (with or without surfactant) is not stated in the 2023 surfactant study yang2023 X10; in the 2025 grade paper the cinnarizine concentrations after 1 h do not match the plotted rates bapat2025a X8.

Concepts

intrinsic dissolution rate, congruent release, limit of congruency. Findings. Release mechanism and LoC: F1, F2, F3, F6, F11, F13, F14, F15, F17, F19, F21, F23, F26, F31, F32, F33.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

theoretical monolayer adsorption capacity

Expression

X_m = \frac{\mathrm{SSA} \times 10^{20} \times \mathrm{MW}}{S_c \times N_A} dening2018 E3.

X_m = \frac{\mathrm{SSA}_{\mathrm{adsorbent}} \times 10^{20} \times MW_{\mathrm{adsorbate}}}{S_c \times N_A} mccarthy2020 E3.

Q_{\mathrm{mono}} = \frac{\mathrm{SSA} \times M_{\mathrm{drug}}}{A_{\mathrm{molecule}} \times N_A} (restated; printed in words) hate2020a E2.

Outside silica, the minimum surfactant to cover drug-rich nanodroplets is calculated in the same way from the droplet surface area and the surfactant's molecular area (printed in words) correasoto2022a E2.

Variables and units

symbol	meaning	units
X_m, Q_{mono}	adsorbate needed for monolayer coverage	g/g silica dening2018 E3
SSA	specific surface area of the adsorbent	m²/g; 586 for SBA-15 dening2018 M3
10^{20}	conversion of m² to Å²	dening2018 E3
MW, M_{drug}	molar mass of the adsorbate	g/mol; not printed in the three papers dening2018 E3; hate2020a E2; mccarthy2020 E3
S_c, A_{molecule}	contact area of one molecule, the product of its two largest dimensions	Å² dening2018 P15; hate2020a P15; mccarthy2020 P11
N_A	Avogadro's number	mol⁻¹

Assumptions and valid domain

The whole surface is accessible and the drug adsorbs in the orientation that maximizes its contact with the surface, so the two largest dimensions give the contact area; the estimate is geometric only dening2018 C17; hate2020a C20. Applied to SBA-15 with 7.1 nm pores dening2018 M3.

Use in the library

paper	used for	values or fitted parameters	status / recomputed
dening2018	ritonavir loadings at 25–150% of the monolayer	0.253 g/g ("25.3% w/w"); 18.2 × 15.2 Å	reproduces: 0.2536 g/g with molar mass 720.94 g/mol dening2018 E3, R4
hate2020a	atazanavir	278 mg/g (about 28% w/w); 17.53 × 14.07 Å	inputs not printed; implies a molar mass of about 705 g/mol hate2020a E2, R1
mccarthy2020	indomethacin and methyl ester loadings	0.287 and 0.269 g/g	indomethacin 0.285 against 0.287; methyl ester 0.260 against 0.269 g/g mccarthy2020 E3, X19
correasoto2022a	surfactant on clopidogrel nanodroplets	agrees reasonably for nonionic surfactants	inputs in the supporting information, not supplied correasoto2022a E2, C41

Where it fails or is disputed

The result is in g/g silica but is quoted and used as % w/w of the formulation; 0.253 g/g is about 20.2% w/w on a drug-plus-silica basis dening2018 X4; mccarthy2020 X4; hate2020a X4. BET monolayers fitted to adsorption from water are 2.5 to about 60 times lower (synthesis: 253/103; 278/4.5) dening2019 R6; hate2020a R3. The ritonavir flux drop placed at the calculated monolayer lies between 20.1 and 29.8% w/w, with no batch in between dening2018 X16.

Concepts

monolayer coverage, drug loading, nanoconfinement. Findings. F2, F1, F11.

← Concepts and formulas

formula · as used in Amorphous solid dispersions: the whole picture

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

symbol	meaning	units
x	mole-fraction solubility of the drug in liquid PEG	dimensionless zhu2011 E3
\Delta H_f	heat of solution (named "heat of solution" in the card)	not printed zhu2011 E3
R, T	gas constant; temperature	K zhu2011 E3
K_{p/q}, C_p, C_q	partition coefficient of the polymer between the drug-rich phase (p) and water (q), and its concentrations in them	dimensionless; 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 phase	kJ/mol for ΔG and ΔH (see the use table); unit of ΔS not stated in the notes [ueda2022 E4, E5]
A, B, C	constants of the quadratic fit of \ln K_{p/q} against 1/T	not 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

paper	used for	values or fitted parameters	status / recomputed
zhu2011	solubility of six drugs in PEG 3350 at 25 °C	28, 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
zhu2012	solubility of haloperidol, benzocaine, ibuprofen, fenofibrate at 25 °C	below 1, 28, 25, 6 wt%	named only zhu2012 E3, M1, M2, M3, M4
ueda2022	ΔG, ΔH, ΔS of transfer of PVP, PVP-VA and HPMC from water into the ibuprofen-rich phase	linear: 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/mol	reproduces (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 Amorphous solid dispersions: the whole picture

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

symbol	meaning	unit
T_{g,\mathrm{wet}}, T_{g,\mathrm{dry}}	glass transition temperature with and without sorbed water	°C
w	water 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

paper	used for	values or fitted parameters	status / recomputed
indulkar2017b	wet Tg of water-saturated nifedipine droplets	dry 42 °C, 2.5% water, approximately 17 °C	reproduces: 42 − 10 × 2.5 = 17 indulkar2017b E6, M1, C16
ilevbare2013a (LLPS chapter)	Tg of a water-saturated drug-rich phase	dry 50.4 °C, 0.4 °C with 4.87% water	reproduces within rounding: 50.0 / 4.87 = 10.3 °C per 1% ilevbare2013a E15
saboo2020	wet Tg of amorphous indomethacin from 37 °C sorption	29 °C	inputs not printed saboo2020 E6, M1
yang2021	wet Tg of miconazole, danazol, elbasvir from 37 °C sorption	−4.7, 73.3, 129.1 °C	inputs not printed [yang2021 E3, M2, M3, M4]
hiew2022b	wet Tg of lumefantrine dispersions with 35–55% water	all below 37 °C	reproduces: 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.