Chapter of Solid state stability

PEG dispersions

Drugs dispersed in a semicrystalline carrier, polyethylene glycol (PEG 3350) or poly(ethylene oxide) (PEO, molecular weight about 100000) baird2011 M5; zhu2011 M7; zhu2012 M5; marsac2008b M7.

What this chapter covers

the phase behaviour of drug–PEG mixtures (eutectic and monotectic systems, the athermal Flory–Huggins prediction, the readings of drug–PEG interaction and the estimated solubility in PEG), the microstructure of the solidified dispersion (the lamellar long period and the location of the drug), the crystallization of drug and carrier after solidification (induction times, order of crystallization, nucleation on crystalline PEG, the effect of the drug on PEG), and the loss of drug crystallinity in PEO compacts under humidity. The papers and their findings are in sources.md and findings.md.

4 papers2008–201212 findings

01Findings map

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

02Which paper supports which finding

Show the table of papers and findings
Phase behaviour of drug–PEG mixturesMicrostructure of the solidified dispersionCrystallization of drug and carrier after solidificationStorage in humid air
paperF1F2F3F4F5F6F7F8F9F10F11F12
2008marsac2008bcrystalline drugs in PEO under humidity
2011baird2011eutectic composition and its prediction
2011zhu2011phase behaviour and microstructure over time
2012zhu2012crystallization kinetics of drug and carrier
other library papers2 papers outside the chapter

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

03Connections to other subcategories

Takes from

Solid state stability / Crystallization tendency

The heats of fusion and Tg values of the drugs, the idea that the neat-drug tendency combined with the interaction decides the outcome, and the benzocaine Tg zhu2011 R5, C16; zhu2012 C13, M3. The classes of the neat drugs sort haloperidol and benzocaine (class I-A) from ibuprofen, fenofibrate, ketoconazole and nilutamide (class III) (synthesis) baird2010 R1, R3, M9, M17, M38, M39, M42, M46. See F8 and the chapter Crystallization tendency.

Gives to

Solid state stability / Crystallization tendency

The neat-drug class did not carry over into PEG dispersions of slowly crystallizing drugs, because crystalline PEG apparently promotes their nucleation zhu2012 C41, C4. See F9 and F17 of that chapter.

Takes from

Solid state stability / Miscibility and drug-polymer interactions

The melting point depression route to the interaction parameter, developed for drugs in amorphous polymers, was used for PEG zhu2011 E1; marsac2006b R9, and the difficulty of measuring activity coefficients in viscous polymers led to the PEG 400 stand-in baird2011 C21. See F3.

Gives to

Solid state stability / Miscibility and drug-polymer interactions

The comparison of four readings of drug–polymer interaction and the finding that their sizes are not interchangeable baird2011 R9, R10; zhu2011 R5, R20. See F3.

Takes from

Solid state stability / Physical stability

The additive-spectrum procedure for infrared evidence of interaction came from a 2009 moisture-induced immiscibility paper baird2011 P4. Moisture as a second stress on the drug–polymer system appears there for PVP and here for PEO, where the same logic of an activity coefficient in an analogue solvent and in water is used marsac2008a C34, C37; marsac2008b C14. See F11.

Gives to

ASD process

The melting point depression and temperature–composition phase diagram used to set melt-extrusion temperatures for amorphous dispersions rest on the same liquidus thermodynamics that the PEG papers apply to crystalline dispersions moseson2018 R8, C22; baird2011 E1; zhu2011 E1; a compression-moulded probucol–PEO dispersion showed a melting point depression that the authors tie to close contact in the melt broman2001 R4.f, C46. See F1 and F4.

Dissolution and Bioperformance. None of the four papers measured dissolution or release; the authors state that drug location and crystallization are "likely" to affect delivery performance and that faster nucleation "could" change crystal size and dissolution zhu2011 C37; zhu2012 C42. These remain open questions for those subcategories.

Left to other subcategories: dispersions in amorphous polymers (Solid state stability / Physical stability and Solid state stability / Miscibility and drug-polymer interactions), the neat-drug crystallization tendency from which several drugs were chosen (Crystallization tendency), melt processing of dispersions (ASD process), and dissolution and absorption of PEG dispersions, which none of the four papers measured zhu2011 C37; zhu2012 C42. The other subcategories without a chapter page yet are named here without links.

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 4 · 4 findings · F1–F4

Phase behaviour of drug–PEG mixtures

F1

Topic 1Phase behaviour of drug–PEG mixtures1 of 4

Drugs dissolve in molten PEG to very different degrees, from almost nothing to about 40 wt% drug.

Mixtures of nine drugs with PEG 3350 were melted and their melting behaviour followed from 0 to 100 wt% drug. The eutectic composition (the maximum drug solubility in molten PEG at the lowest melting temperature) was below 1 wt% for haloperidol, which barely dissolves (monotectic), and 30–40 wt% for chlorpropamide, aceclofenac, benzocaine and ibuprofen baird2011 C1, R1.a, R1.b, R1.c, R1.d; zhu2011 R5.b, R5.d, R5.e, R5.f; zhu2012 R24.c, R24.d.

moderateModerate: three papers from one group used the same two melting methods, the eutectics were read from a 10 wt% grid, and the crystal forms of the drugs were not characterized baird2011 X7, X9, X14.

monotectic · below 1low to intermediatehigh · 30–40haloperidol, ketoconazole: monotecticloratadine ≈5nilutamide 10fenofibrate 15–20aceclofenac, benzocaine 30chlorpropamide 35ibuprofen 40010203040eutectic composition in PEG 3350, wt% drug

Eutectic composition of nine drugs in PEG 3350; the chlorpropamide value was not a tested composition. baird2011 R1.a, R1.b, R1.c, R1.d, X9; zhu2011 R5.b, R5.d, R5.e, R5.f; zhu2012 R24.c, R24.d

For your drug

  1. Measure the liquidus (the temperature at which the last solid melts) from 0 to 100 wt% drug by hot-stage microscopy at 1 °C/min on ground, fused samples, with steps finer than 10 wt% near the expected eutectic, and check with DSC.
  2. List the drug's hydrogen-bond donors, and treat the eutectic composition as an upper limit at roughly 50–58 °C, not as a storage-temperature solubility (F4).

baird2011 P1, P2, P3

How it works and key numbers
  1. A drug dissolves in molten PEG only up to a limit; in a monotectic system it hardly dissolves and hardly lowers the PEG melting point baird2011 C1.
  2. Weak crystal lattices (low melting point and heat of fusion) and strong drug–polymer interactions both raise the limit, so they "would be expected" to give high eutectics baird2011 C10.
  3. The four drugs with the highest eutectic compositions carry hydrogen-bond donor groups that can interact with the PEG ether oxygen baird2011 M1, M2, C30; zhu2011 C9.
  4. A donor group alone is not enough (synthesis: haloperidol has an OH group but is monotectic) baird2011 M4, R10, C32.
below 1 → 40 wt%range of the eutectic composition across drugs in PEG 3350baird2011 R1.d; zhu2011 R5.d
48.9–58.4 °Ceutectic temperatures of the mixtureszhu2011 R5.b, R5.c, R5.d, R5.e
9 drugssystems measured; the diagrams come from three papers of one groupbaird2011 R1.a; zhu2011 R5.b; zhu2012 R24.c

Connections to other chapters

Evidence: data, conditions and papers

Finding F1. The eutectic composition of drugs in PEG 3350 runs from monotectic to 40 wt% drug, and the highest values belong to drugs with hydrogen-bond donors

In short. Of nine drugs, haloperidol and ketoconazole were monotectic in PEG 3350 (haloperidol below 1 wt% drug), loratadine had its eutectic at about 5 wt%, nilutamide at 10, fenofibrate at 15–20, and chlorpropamide, aceclofenac, benzocaine and ibuprofen at 30–40 wt% baird2011 R1.a, R1.b, R1.c, R1.d; zhu2011 R5.b, R5.d, R5.e, R5.f; zhu2012 R24.c, R24.d. The four highest are drugs that the authors describe as carrying hydrogen-bond donor groups that can interact with the PEG ether oxygen, but a donor group alone did not decide the outcome baird2011 M1, M2, C30; zhu2011 C9. Eutectic temperatures lay between 48.9 and 58.4 °C zhu2011 R5.b, R5.c, R5.d, R5.e.

Type. observation in 9 systems Strength. the diagrams come from three papers of one group with the same two melting methods (the chlorpropamide and haloperidol diagrams of zhu2011 are those of baird2011, and zhu2012 repeats haloperidol as monotectic and benzocaine and ibuprofen as eutectic), but the eutectics were read from 10 wt% composition grids, the two melting methods differed by up to about 16 °C and the crystal forms of the drugs were not characterized (baird2011 K2: moderate, K3: moderate to strong; X7, X9, X14).

How it was shown

Baird and Taylor (2011) melted PEG 3350 mixtures of four drugs in 10 wt% steps from 0 to 100 wt% drug, cooled and ground them, and read the end of melting by DSC and by hot-stage microscopy at 1 °C/min baird2011 P1, P2, P3. Zhu and co-workers (2011) added benzocaine, ibuprofen, nilutamide and ketoconazole by hot stage, and Zhu and co-workers (2012) added fenofibrate zhu2011 P3, P4, R5; zhu2012 P9, P10, R24.

What the data show

Haloperidol and ketoconazole were monotectic, loratadine had its eutectic at about 5 wt% drug, nilutamide at 10, fenofibrate at 15–20, and chlorpropamide, aceclofenac, benzocaine and ibuprofen at 30–40 wt% baird2011 R1.a, R1.b, R1.c, R1.d; zhu2011 R5.b, R5.d, R5.e, R5.f; zhu2012 R24.c, R24.d.

groupsystem in PEG 3350eutectic compositionids
monotectichaloperidol; ketoconazolehaloperidol below 1 wt%; ketoconazole liquidus about 101 °C already at 5 wt%baird2011 R1.d, M4, C14; zhu2011 R4.b, R5.f
lowloratadine; nilutamideabout 5 wt%; 10 wt% at 58.4 °Cbaird2011 R1.c, M3; zhu2011 R5.e, R3.t
intermediatefenofibrate15–20 wt%, minimum about 58 °Czhu2012 R24.c, R24.d, R24.o, C48
highchlorpropamide; aceclofenac35 wt% at 55.0 °C (not a tested composition); 30 wt%baird2011 R1.a, R1.b, M1, M2, X9; zhu2011 R5.c
highbenzocaine; ibuprofen30 wt% at 48.9 °C; 40 wt% at 49.6 °Czhu2011 R5.b, R5.d, R1.t, R2.t
Fig. 4 of baird2011: predicted line and measured phase diagrams of four drugs with PEG 3350
Fig. 4 · baird2011predicted line and measured phase diagrams of four drugs with PEG 3350

Panels (a) chlorpropamide and (b) aceclofenac lie far below the predicted line, while (c) loratadine and (d) haloperidol lie on or above it baird2011 R5, R6, R7, R8.

Why

Baird and Taylor write that a drug's solubility in molten polymer depends mainly on crystal lattice energy and on specific drug–polymer interactions, so weak lattices or strong interactions "would be expected" to give high eutectics baird2011 C10. The four highest are drugs that the authors describe as carrying hydrogen-bond donors that can interact with the PEG ether oxygen baird2011 M1, M2, C30; zhu2011 C9. (synthesis: a donor group is not sufficient, since haloperidol has an OH group but is monotectic baird2011 M4, R10, C32.)

Limits and transfer

PEG 3350 only; eutectics were read from 5–10 wt% grids, and hot-stage and DSC liquidus values differ by up to about 16 °C baird2011 X9, X7. For a new drug, measure the liquidus from 0 to 100 wt% by hot stage at 1 °C/min with steps finer than 10 wt% near the expected eutectic, and treat the result as an upper limit at roughly 50–58 °C, not as a storage-temperature solubility (F4) baird2011 P1, P2, P3.

How it was shown

Baird and Taylor (2011) made fused dispersions of chlorpropamide, aceclofenac, loratadine or haloperidol with PEG 3350: 500 mg physical mixtures were melted on a hot plate, cooled slowly, ground and stored over P2O5 for 24 h, in 10 wt% steps from 0 to 100 wt% drug, with extra points at 5 wt% (loratadine) and 15 and 25 wt% (haloperidol) baird2011 P1, A2. They read the offset of melting in hermetic DSC pans at 1 °C/min and, separately, the temperature at which the last solid particle melted by hot-stage microscopy at 1 °C/min, 2–3 mg per sample baird2011 P2, P3. Zhu and co-workers (2011) used the hot-stage method at 1 °C/min on benzocaine, ibuprofen, nilutamide and ketoconazole with PEG 3350, mixtures stored a few days and lightly ground, with DSC only as a check for ibuprofen; their chlorpropamide and haloperidol diagrams were taken from Baird and Taylor zhu2011 P3, P4, R19, R5. Zhu and co-workers (2012) added fenofibrate, by the same two methods, in the supporting information zhu2012 P9, P10, R24.

What the data show

The measured eutectic or monotectic composition is given for each system in the table below. Near the eutectic a single endotherm appeared below both pure melting points, and away from it two endotherms, a low-temperature one from the eutectic or monotectic composition and a high-temperature one from excess PEG or drug baird2011 R4, C13. In haloperidol–PEG the PEG melting stayed near 59–61 °C and the liquidus rose steeply from 10 wt%; in chlorpropamide–PEG the liquidus stayed at about 55–60 °C from 10 to 40 wt% drug and in aceclofenac–PEG from 10 to 30 wt% baird2011 R5, R6, R8. The chlorpropamide value of 35 wt% was not a tested composition, since the lowest liquidus lay at 40 wt% baird2011 X9, R5.e. For benzocaine, ibuprofen and nilutamide the eutectic temperatures were 48.9, 49.6 and 58.4 °C, and chlorpropamide's was 55.0 °C zhu2011 R5.b, R5.d, R5.e, R5.c. Ketoconazole was monotectic, with its liquidus at about 101 °C already at 5 wt% drug zhu2011 R4.b, R5.f. Fenofibrate's liquidus fell from about 82.4 °C for the pure drug to about 58.0 °C at 15 and 20 wt% and rose again toward about 60.5 °C for PEG, so the 20/80 dispersion lay at the eutectic composition zhu2012 R24.o, R24.c, R24.d, R24.a, C40. The low-temperature endotherm of the chlorpropamide and aceclofenac dispersions drifted to about 39–49 °C in the drug-rich traces, which a simple eutectic would not show, so their eutectic temperatures are not established by those traces baird2011 R4, X8.

papersystemmethod and conditionsresultids
baird2011chlorpropamide–PEG 3350 (drug Tm 126.7 °C)fused, DSC and hot stage, 1 °C/mineutectic 35 wt% (not a tested composition)R1.a, M1, X9
baird2011aceclofenac–PEG 3350 (Tm 151.7 °C)as aboveeutectic 30 wt%R1.b, M2
baird2011loratadine–PEG 3350 (Tm 135.3 °C)as aboveeutectic about 5 wt%R1.c, M3
baird2011haloperidol–PEG 3350 (Tm 150.9 °C)as abovebelow 1 wt%, monotecticR1.d, M4, C14
zhu2011benzocaine–PEG 3350 (pure drug 92 °C)hot stage, 1 °C/mineutectic 30 wt% at 48.9 °CR5.b, R1.t
zhu2011ibuprofen–PEG 3350 (pure drug about 77.5 °C)as above, DSC checkeutectic 40 wt% at 49.6 °CR5.d, R2.t, R19
zhu2011nilutamide–PEG 3350 (pure drug about 160 °C)as aboveeutectic 10 wt% at 58.4 °CR5.e, R3.t
zhu2011ketoconazole–PEG 3350 (pure drug about 156 °C)as abovemonotecticR5.f, R4.t
zhu2011chlorpropamide; haloperidolphase diagrams cited from baird201135 wt% at 55.0 °C; monotecticR5.c, R5.a
zhu2012fenofibrate–PEG 3350 (pure drug about 82.4 °C)CPOM and DSC, 1 °C/min (SI)eutectic minimum about 58 °C at 15–20 wt%R24.c, R24.d, R24.o, C48

Figure

Fig. 4 of baird2011: predicted line and measured phase diagrams of four drugs with PEG 3350
Fig. 4 · baird2011predicted line and measured phase diagrams of four drugs with PEG 3350

Panels (a) chlorpropamide and (b) aceclofenac lie far below the predicted line between 20 and 60 wt% drug, while (c) loratadine and (d) haloperidol lie on or above it; squares are DSC offsets and triangles hot-stage values baird2011 R5, R6, R7, R8.

Why

Baird and Taylor define a eutectic dispersion as one in which the drug dissolves appreciably in the molten polymer and the eutectic point is the maximum drug solubility in the molten polymer at the eutectic temperature, against a monotectic system in which the drug barely dissolves and hardly lowers the PEG melting point baird2011 C1. They write that a drug's solubility in molten polymer depends mainly on the crystal lattice energy (melting point and heat of fusion) and on the strength of specific drug–polymer interactions relative to the pure liquids, so that weak lattices or strong interactions "would be expected" to give high eutectic compositions baird2011 C10. Zhu and co-workers repeat this, as described "previously", for their drugs zhu2011 C4. For the proposed interaction they point to hydrogen-bond donors: benzocaine, chlorpropamide and ibuprofen carry donors that can interact with the PEG ether oxygen and have moderate melting points, whereas nilutamide's lower solubility "can be explained by" its higher melting point zhu2011 C9, C12. Baird and Taylor consider it "likely" that the drug donates a hydrogen bond to the abundant ether oxygens of PEG (about 75 per chain against 2 hydroxyl end groups) baird2011 C30, R12. (synthesis: nilutamide and haloperidol show that a donor group is not sufficient: nilutamide, which the authors count among the interacting drugs, reaches only 10 wt%, and haloperidol, which has an OH group, is monotectic with no carbonyl shift zhu2011 R5.e, C12; baird2011 M4, R10, C32; the lattice term in F2 is the other half of the explanation.) A lower-melting drug without donors reached an intermediate eutectic: fenofibrate, with no sign of hydrogen bonding to PEG, has a eutectic at 15–20 wt% zhu2012 R24, R25, C49.

Conditions and limits

PEG 3350 only; fused and slowly cooled dispersions; eutectic compositions on a 5–10 wt% grid baird2011 X9. DSC and hot-stage liquidus values differ by up to about 16 °C at some compositions (haloperidol at 20 wt%: about 128 against 144 °C by DSC and hot stage) baird2011 X7, R8.d. The crystal forms of the drugs as received and after fusion are not stated, and pure chlorpropamide shows an extra event at about 121–122 °C before melting baird2011 X14, R4. Different PEG grades, cooling histories and drug loadings above the eutectic were not studied. The neat PEG 3350 melts at about 60.5 °C in the phase diagrams, against 55 °C used as a model input baird2011 R4, M5, X10.

Counterexamples and conflicts

None found in the library for the existence of the spread. Donor groups do not predict the eutectic alone (see the synthesis note above). The text of Zhu and co-workers says DSC confirmed the benzocaine, nilutamide and ketoconazole diagrams, but only the ibuprofen thermograms are shown zhu2011 C5, R19.

Transfer check

For a new drug in PEG 3350, record the drug's melting point and heat of fusion and list its hydrogen-bond donor groups. Then measure the liquidus from 0 to 100 wt% by hot-stage microscopy at 1 °C/min on ground, fused samples, with steps finer than 10 wt% near the expected eutectic and with DSC as a second method baird2011 P1, P2, P3. A drug that melts above about 100 °C and has no donors should be expected to give only a few wt% (F2). Treat the eutectic composition as an upper limit at the eutectic temperature of roughly 50–58 °C, not as a storage-temperature solubility (F4).

History

Baird and Taylor (2011) measured the first four phase diagrams and tied the eutectic to lattice energy and interaction baird2011 C10, C36. Zhu and co-workers (2011) added benzocaine, ibuprofen, nilutamide and ketoconazole and took the other two from Baird and Taylor zhu2011 R5, C3. Zhu and co-workers (2012) added fenofibrate and concluded that haloperidol–PEG is the only monotectic system among their four zhu2012 C40.

F2

Topic 1Phase behaviour of drug–PEG mixtures2 of 4

Without a drug–PEG interaction term the model fits two drugs and fails for two; higher-melting drugs require a stronger interaction.

The model assumes athermal mixing, with no specific interaction energy between drug and PEG. For four drugs it matched the measured eutectic of loratadine and haloperidol but predicted much lower values for chlorpropamide and aceclofenac baird2011 R1.a, R1.b, C14.

moderateModerate: the misses are large and the signs and ranking of the interaction energies hold in every recomputation, but the printed interaction-energy equation and the chlorpropamide prediction do not reproduce baird2011 X2, X3.

measuredpredicted with no interactionchlorpropamideback-calculated interaction energy: −6.85 kJ/mol12.835aceclofenacback-calculated interaction energy: −18.2 kJ/mol1.530loratadineback-calculated interaction energy: 0.34 kJ/mol≈56.5haloperidolback-calculated interaction energy: −0.11 kJ/mol0.5below 10510152025303540eutectic composition, wt% drug

The measured liquidus of chlorpropamide and aceclofenac lies far below the athermal prediction; the interaction energies are back-calculated to reproduce the measured eutectic. baird2011 R1.a, R1.b, R1.c, R1.d, R9.a, R9.b, R9.c, R9.d

I · high eutecticII · interaction requiredIII · very strongIV · not enoughno interaction needed up to ≈100≈ −5 kJ/mol up to ≈160≈ −10 kJ/mol up to ≈240the four real drugs80147.5215282.5350drug melting point, °C

Model map for an average drug: interaction energy required for a 10 wt% eutectic composition. baird2011 R2.c, R3, C11, C12, C19

For your drug

  1. Compute the athermal eutectic from the drug's melting point, heat of fusion and molar volume with the two liquidus equations, then measure the phase diagram.
  2. If the measured eutectic is more than about 2 times the prediction, treat a specific interaction as present and test it with the readings in F3. Do not use the map below 100 °C or above 160 °C without checking.

baird2011 R3, C12

How it works and key numbers
  1. The model builds a liquidus curve for the drug and one for PEG from heat of fusion, melting point and molar volume; the eutectic is where they intersect baird2011 E1, E2, C5.
  2. With no interaction only the lattice term is left: haloperidol and aceclofenac melt at 150.9 and 151.7 °C, but haloperidol's heat of fusion is higher (53.3 against 42.2 kJ/mol), so its predicted eutectic is lower baird2011 C9, M1, M2, M3, M4.
  3. A drug whose measured eutectic lies above the prediction is read as having a favourable interaction with molten PEG; the back-calculated energies of chlorpropamide and aceclofenac are −6.85 and −18.2 kJ/mol baird2011 C14, C15, C17.
  4. The higher the drug melting point, the stronger the interaction needed to keep a 10 wt% eutectic baird2011 R2.c, R3, C11, C12.
2.7× and 20×how far the measured eutectic exceeds the no-interaction prediction, chlorpropamide and aceclofenacbaird2011 R1.a, R1.b
−6.85 and −18.2 kJ/molinteraction energies needed to match chlorpropamide and aceclofenacbaird2011 C14, C15, C17
≈100 / 160 / 240 °Cdrug melting points up to which none / −5 / −10 kJ/mol keeps a 10 wt% eutecticbaird2011 R2.c, R3, C12

Connections to other chapters

Evidence: data, conditions and papers

Finding F2. An athermal Flory–Huggins model predicts the eutectic composition only for drugs without specific PEG interaction, and a higher melting point demands a stronger interaction

In short. The Lacoulonche model run with no drug–polymer interaction energy predicted eutectics of 12.8, 1.5, 6.5 and 0.5 wt% for chlorpropamide, aceclofenac, loratadine and haloperidol in PEG 3350, against measured 35, 30, about 5 and below 1 wt% baird2011 R1. It was close for loratadine and haloperidol and 2.7 and 20 times too low for chlorpropamide and aceclofenac (synthesis: 35/12.8 = 2.7 and 30/1.5 = 20), whose back-calculated interaction energies were negative (−6.85 and −18.2 kJ/mol) baird2011 R1, C14, C15, C17. In a model map for an average drug, a 10 wt% eutectic needs no interaction up to a drug melting point of about 100 °C, but about −5 kJ/mol up to about 160 °C and about −10 kJ/mol up to about 240 °C baird2011 R2.c, R3, C11, C12.

Type. model result with four measured comparisons Strength. the misses are large and signs and ranking of the interaction energies hold in every recomputation, but the printed interaction-energy equation and the chlorpropamide prediction do not reproduce (baird2011 K1, K2: moderate; K3: moderate to strong; X2, X3).

How it was shown

The model of Lacoulonche and co-workers applies Flory–Huggins lattice theory to the drug and PEG liquidus curves, with an interaction energy \Delta W_{d,p} baird2011 E1, E2, C5. Baird and Taylor set \Delta W_{d,p} = 0 (athermal mixing) for four drugs and back-calculated the energy that reproduces each observed eutectic baird2011 P6, P8, E4.

What the data show

With no interaction the predicted eutectics were 12.8, 1.5, 6.5 and 0.5 wt% against 35, 30, about 5 and below 1 measured baird2011 R1.a, R1.b, R1.c, R1.d. The model was 2.7 and 20 times too low for chlorpropamide and aceclofenac (synthesis: 35/12.8 = 2.7 and 30/1.5 = 20), and agreed for loratadine and haloperidol in eutectic composition only baird2011 R1.a, R1.b, C14, X6. In the map a drug melting at 100 °C has an athermal eutectic of about 10.0 wt%, one melting at 150 °C about 2.7 wt%, which an interaction energy of −5.0 kJ/mol raises to about 11.7 wt% baird2011 R2.c, R2.h.

systempredicted eutectic, \Delta W_{d,p}=0 (wt%)observed eutectic (wt%)\Delta W_{d,p} (kJ/mol); \chi_{dp}ids
chlorpropamide–PEG 335012.835−6.85; −2.53baird2011 R1.a, R9.a
aceclofenac–PEG 33501.530−18.2; −6.68baird2011 R1.b, R9.b
loratadine–PEG 33506.5about 50.34; 0.13baird2011 R1.c, R9.c
haloperidol–PEG 33500.5below 1−0.11; −0.04baird2011 R1.d, R9.d
Fig. 2 of baird2011: model map of eutectic composition against drug melting point at four interaction energies
Fig. 2 · baird2011model map of eutectic composition against drug melting point at four interaction energies

The higher the drug melting point, the stronger the interaction required for a eutectic composition above 10 wt% baird2011 R2, R3.

Why

With \Delta W_{d,p} = 0 only the lattice term is left: haloperidol and aceclofenac melt at 150.9 and 151.7 °C, but haloperidol's heat of fusion is higher (53.3 against 42.2 kJ/mol), so its predicted eutectic is lower baird2011 C9, M1, M2. A negative back-calculated energy is read as an extra driving force to mix with molten PEG baird2011 C18.

Limits and transfer

Only four drugs, all melting between 126.7 and 151.7 °C, were tested, and the printed interaction-energy equation does not reproduce, although signs and ranking hold baird2011 C19, M1, X3. Measure the phase diagram; if the eutectic is more than about 2 times the athermal prediction, treat a specific interaction as present and test it with the readings in F3.

How it was shown

The model of Lacoulonche and co-workers applies Flory–Huggins lattice theory to the liquidus curves of drug and polymer: one branch for crystalline drug and one for crystalline PEG, each depending on the heat of fusion, melting point and molar volume of that component and on an interaction energy \Delta W_{d,p} baird2011 E1, E2, C5. Baird and Taylor set \Delta W_{d,p} = 0 (athermal mixing), took heats of fusion, melting points and molar volumes from their Table 1, and called the drug volume fraction at which the two branches give the same temperature the eutectic, converted to weight percent baird2011 P6, E4, C6. To map the dependence on melting point they ran the model for a hypothetical drug (molar volume 250 cm³/mol, heat of fusion 35 kJ/mol, molecular weight 325 g/mol) with melting points from 80 to 350 °C and \Delta W_{d,p} of 0, −2.5, −5.0 and −10.0 kJ/mol baird2011 P7, R2. They then back-calculated the interaction energy that reproduces each observed eutectic and converted it to a Flory–Huggins parameter with \chi_{dp} = \Delta W_{d,p}/(R\,T_{eut,th}) baird2011 P8, P10, E3, E8.

What the data show

The predicted and observed eutectics, the back-calculated energies and the parameters are in the first table. The predicted lines start near 55 °C for PEG, dip to minima of about 52.5–54.5 °C and rise to each drug's melting point baird2011 R5, R6, R7, R8. At 40 wt% aceclofenac the measured liquidus was about 86–88 °C against about 135.5 °C predicted, and at 40 wt% chlorpropamide about 55–56 °C against about 98 °C baird2011 R6.e, R5.e. For loratadine and haloperidol the authors call the eutectic "comparable" and the abstract "accurately predicted", but the measured liquidus at intermediate compositions lay above the model line (loratadine at 20 wt%: about 103 °C by hot stage against about 90.5 °C predicted), so the agreement is one of eutectic composition only baird2011 C14, X6, R7.d. The model map gives, at a drug melting point of 100 °C, about 10.0, 18.9, 27.9 and 41.2 wt% for 0, −2.5, −5.0 and −10.0 kJ/mol, and at 150 °C about 2.7, 6.1, 11.7 and 24.9 wt% baird2011 R2.c, R2.h. The authors divide the melting-point axis into four regions at the 10 wt% crossings: region I below 100 °C (high eutectics even without interaction), region II 100–160 °C (appreciable loading only with significant interaction), region III 160–240 °C (very strong interaction needed) and region IV above 240 °C (even very strong interactions "are not enough") baird2011 R3, C12. All four real drugs melt in region II, between 126.7 and 151.7 °C baird2011 C19, M1, M2, M3, M4.

systempredicted eutectic, \Delta W_{d,p}=0 (wt%)observed eutectic (wt%)\Delta W_{d,p} (kJ/mol)\chi_{dp}ids
chlorpropamide–PEG 335012.835−6.85−2.53R1.a, R9.a
aceclofenac–PEG 33501.530−18.2−6.68R1.b, R9.b
loratadine–PEG 33506.5about 50.340.13R1.c, R9.c
haloperidol–PEG 33500.5below 1−0.11−0.04R1.d, R9.d
drug melting point (°C)0 kJ/mol−2.5 kJ/mol−5.0 kJ/mol−10.0 kJ/molids
80≈18.8≈30.4≈39.5≈50.7R2.a
100≈10.0≈18.9≈27.9≈41.2R2.c
150≈2.7≈6.1≈11.7≈24.9R2.h
200≈0.9≈2.1≈5.0≈15.0R2.l
240below ≈1≈1.1≈2.6≈10.0R2.n
350below ≈1below ≈1below ≈1≈3.6R2.q

Eutectic composition in wt% drug, read from the model map for an average drug in PEG 3350 baird2011 R2.

In the recomputation of the card, the chlorpropamide prediction comes out at 9.45 wt% instead of 12.8, while the other three predictions and the map reproduce baird2011 E1, X2. The printed expression for the interaction energy is not the rearrangement of the two liquidus equations, and solving them gives −7.35, −14.5, +0.71 and −1.60 kJ/mol for the four drugs instead of −6.85, −18.2, 0.34 and −0.11 baird2011 E3, X3. The ranking aceclofenac, chlorpropamide, haloperidol, loratadine holds in every variant, so only signs and ranking are robust baird2011 X3.

Figure

Fig. 2 of baird2011: model map of eutectic composition against drug melting point at four interaction energies
Fig. 2 · baird2011model map of eutectic composition against drug melting point at four interaction energies

Diamonds are 0, squares −2.5, triangles −5.0 and circles −10.0 kJ/mol; the horizontal line marks 10 wt% and the vertical lines the region borders at about 100, 160 and 240 °C. The higher the drug melting point, the stronger the interaction required for a eutectic composition above 10 wt% baird2011 R2, R3.

Why

The authors' account: with \Delta W_{d,p} = 0 only the lattice term is left, so the melting point and heat of fusion alone set the prediction: haloperidol and aceclofenac melt at nearly the same temperature (150.9 and 151.7 °C) but haloperidol's heat of fusion is higher (53.3 against 42.2 kJ/mol), so its predicted eutectic is lower, and both have higher lattice energies than loratadine and chlorpropamide ("it is clear") baird2011 C9, M1, M2, M3, M4. Molecular weight and molar volume are said to play an insignificant role, taken from earlier work and not tested here baird2011 C8. A negative back-calculated energy is read as an extra driving force to mix with molten PEG from a favourable enthalpy of mixing ("imply") baird2011 C18. In the conclusions the accuracy of the model is "delineated" by the presence or absence of specific interactions, "for the systems investigated", and the eutectic prediction is "interdependent" on the lattice energy and the nature of the interactions baird2011 C36, C37. The evidence for the interaction itself is in F3. The assumptions behind \chi_{dp} < 0 meaning exothermic mixing are on the Flory-Huggins interaction parameter page.

(synthesis: an independent check from another paper supports the athermal half of the model. Fenofibrate, whose pure-drug liquidus point is about 82.4 °C and whose molten mixture with PEG shows no spectral sign of interaction, has an observed eutectic of 15–20 wt%; the map gives about 18.8 wt% at 80 °C with no interaction zhu2012 R24.o, R24.c, R24.d, R25, C49; baird2011 R2.a. The map was drawn for a heat of fusion of 35 kJ/mol, and fenofibrate's is 33.03 kJ/mol baird2010 M38, so the agreement is approximate. In the same way, ibuprofen, melting at about 77.5 °C, reaches 40 wt%, about twice the athermal map value at 80 °C (synthesis: 40/18.8 = 2.1), and the authors list ibuprofen among the interacting drugs zhu2011 R2.t, R5.d, C9.)

Conditions and limits

Four real drugs, one polymer grade, all melting in region II; regions I, III and IV were not tested with real drugs, and the 200 °C condition for use of the model is stated differently in the abstract (compounds melting below 200 °C) and in the conclusions (above 200 °C), while the map has no boundary at 200 °C baird2011 R3, C12, C38, X5. Predictions and measurements are for the eutectic composition on a coarse grid baird2011 X9. Experimental eutectic temperatures were not reported baird2011 X8.

Counterexamples and conflicts

None found in the library for the existence of the upper limit of the eutectic composition under athermal mixing. The chlorpropamide value of 12.8 wt% does not follow from the printed inputs, and the gap to the observed 35 wt% remains under either value baird2011 X2. Loratadine is called close to ideal in PEG 400 although its measured solubility is about 0.42 of the ideal value (see F3) baird2011 C24, X13.

Transfer check

Compute the athermal eutectic from the drug's melting point, heat of fusion and molar volume with the two liquidus equations, or read it from the map by melting point. Measure the phase diagram. If the measured eutectic is more than about 2 times the prediction, treat a specific interaction as present and test it with the readings in F3. Do not apply the map to drugs melting below 100 °C or above 160 °C without checking, since no real drug outside 126.7–151.7 °C was measured in this paper (fenofibrate and ibuprofen in F1 add two low-melting cases from other papers) baird2011 R3, C12.

History

The model comes from Lacoulonche and co-workers (1997) and was tested for flurbiprofen and other organic compounds, with the cause of its errors "still debatable" baird2011 C5. Baird and Taylor (2011) tied the misses to specific interactions for four drugs baird2011 C36. Zhu and co-workers (2011) took over the view that the eutectic composition is set by the drug melting point and its ability to interact with PEG zhu2011 C4.

F3

Topic 1Phase behaviour of drug–PEG mixtures3 of 4

Different measures of drug–PEG interaction agree on which drugs interact, but not on its magnitude.

Four readings were compared: a parameter from melting point depression, the solubility in liquid PEG 400, a shift of the drug's infrared band in the melt, and an extrapolated solubility in PEG. They singled out chlorpropamide, aceclofenac, benzocaine and ibuprofen, and partly nilutamide, as interacting; loratadine, haloperidol and fenofibrate showed no sign baird2011 R9, R10; zhu2011 R5, R20; marsac2008b R14.d; zhu2012 R25.

moderateModerate: the sign agrees in most pairs of readings, but each reading rests on an assumption and the hydrogen bond to PEG was not observed directly baird2011 X15, C23.

Activity coefficient in PEG 400 at 25 °Cketoconazoleχ +0.02 · no solubility in PEG 33500.09aceclofenacχ −6.680.121chlorpropamideχ −0.50 / −2.530.614ibuprofenχ −0.190.64haloperidolχ +0.08 / −0.040.842loratadineχ +0.132.369

Below 1 means a solubility above the ideal value. Ketoconazole has the lowest coefficient but a positive χ and no solubility in PEG 3350; the readings do not agree on it. baird2011 R9.a, R9.b, R9.c, R9.d; marsac2008b R14.d, R14.f; zhu2011 R5.a, R5.c, R5.d, R5.e, R5.f

Readings indicate interaction with PEG
chlorpropamideaceclofenacbenzocaineibuprofennilutamide (partly)ketoconazole
Readings indicate no interaction
loratadinehaloperidolfenofibrateketoconazole

Ketoconazole appears on both sides: the PEG 400 reading indicates interaction, the other readings in PEG 3350 do not. baird2011 R9, R10; zhu2011 R5, R20; marsac2008b R14.f; zhu2012 R25

For your drug

  1. Use at least two readings: the liquidus against the athermal prediction (F2), the activity coefficient in PEG 400 at 25 °C, and the infrared carbonyl band of a 25:75 drug–PEG melt recorded 10–20 °C above the drug melting point against the additive spectrum.
  2. Compare a new drug only with drugs measured the same way and do not mix χ values across papers; if two readings disagree, record the drug as unresolved and test the real dispersion (F8).

baird2011 P4, P5, P6

How it works and key numbers
  1. A more negative interaction parameter χ is "consistent with" a negative enthalpy of mixing, that is, a favourable drug–PEG interaction zhu2011 C6.
  2. In the infrared, the large carbonyl shifts of chlorpropamide and aceclofenac are "indicative" of fewer drug–drug hydrogen bonds because the drug now bonds to PEG; with about 75 ether oxygens against 2 hydroxyl end groups per chain, the authors think it "likely" that the drug donates the bond to an ether oxygen baird2011 C29, C30, R12.
  3. An activity coefficient below 1 in PEG 400 "suggests" favourable interaction, but only if the entropy of mixing is close to ideal baird2011 C23, C24.
  4. No PEG band was analysed, so the bond to PEG is inferred; the abstract's "confirmed" is stronger than the shifts support baird2011 X15, C36.
1717 vs 1663 cm⁻¹chlorpropamide's carbonyl band in the melt against the additive spectrumbaird2011 R10.a
0.09ketoconazole's activity coefficient in PEG 400, yet a positive χ and no solubility in PEG 3350marsac2008b R14.f; zhu2011 R5.f
−2.53 vs −0.50χ of the same chlorpropamide phase diagram in two papersbaird2011 R9.a; zhu2011 R5.c

Connections to other chapters

6 more connections
Evidence: data, conditions and papers

Finding F3. Four measures of drug–PEG interaction agree in sign for most drugs, but their magnitudes are not interchangeable and they disagree for ketoconazole

In short. Negative interaction parameters from melting point depression, activity coefficients below 1 in liquid PEG 400, a shifted drug carbonyl band in the molten drug–PEG mixture and an estimated solubility above 20 wt% in supercooled PEG singled out the same drugs as interacting with PEG: chlorpropamide, aceclofenac, benzocaine and ibuprofen, and partly nilutamide baird2011 R9, R10; zhu2011 R5, R20; marsac2008b R14.d. Loratadine, haloperidol and fenofibrate gave no sign of interaction baird2011 R10.e, R10.g; zhu2012 R25. The magnitudes differ between papers even for the same phase diagram, the haloperidol sign flips, and ketoconazole has an activity coefficient of 0.09 in PEG 400 but a positive interaction parameter and no solubility in PEG 3350 baird2011 R9.d; zhu2011 R5.a, R5.f; marsac2008b R14.f.

Type. method comparison across 9 drugs Strength. the sign agrees in most pairs of readings, but each reading rests on an assumption (near-ideal mixing entropy, an additive reference spectrum, a PEG 400 stand-in) and the hydrogen bond to PEG was not observed directly (baird2011 K4: moderate; K6: weak to moderate).

How it was shown

Four readings were used: an interaction parameter from the phase diagram or from fitting the Flory–Huggins melting point depression equation baird2011 P8, E8; zhu2011 P5, E1; an activity coefficient from the drug solubility in liquid PEG 400 at 25 °C against its ideal solubility baird2011 P5, E7; marsac2008b P5, P9; the infrared carbonyl band of a molten drug–PEG 3350 mixture against the sum of the pure components baird2011 P4; zhu2011 P8; and the solubility in supercooled PEG at 25 °C (F4) zhu2011 R5.

What the data show

Chlorpropamide's carbonyl band sat at 1717 cm⁻¹ in the melt against 1663 cm⁻¹ in the additive spectrum, aceclofenac's at 1744 against 1728; loratadine and haloperidol showed no or only nominal shifts baird2011 R10.a, R10.c, R10.e, R10.g, R10.h. In PEG 400, chlorpropamide and aceclofenac gave activity coefficients of 0.614 and 0.121, loratadine and haloperidol 2.369 and 0.842 baird2011 R9.

drug\chiactivity coefficient in PEG 400carbonyl band, measured against additive (cm⁻¹)solubility in PEG at 25 °C (wt%)ids
chlorpropamide−0.50 (zhu2011); −2.53 (baird2011)0.6141717 against 166326zhu2011 R5.c; baird2011 R9.a, R10.a
aceclofenac−6.680.1211744 against 1728—baird2011 R9.b, R10.c
ibuprofen−0.190.64≈1735 against ≈170325zhu2011 R5.d, R20; marsac2008b R14.d
loratadine0.132.369no shift described—baird2011 R9.c, R10.e
haloperidol0.08 (zhu2011); −0.04 (baird2011)0.842no shift described0zhu2011 R5.a; baird2011 R9.d, R10.g
ketoconazole0.020.09superimposed0zhu2011 R5.f, R20; marsac2008b R14.f
Fig. 5 of baird2011: infrared spectra of 25:75 drug–PEG 3350 melts, measured and additive
Fig. 5 · baird2011infrared spectra of 25:75 drug–PEG 3350 melts, measured and additive

The carbonyl band moves for (a) chlorpropamide and (b) aceclofenac but not for (c) loratadine or (d) haloperidol baird2011 R10.

Why

The authors read the carbonyl shifts as "indicative" of fewer drug–drug hydrogen bonds because the drug now bonds to PEG, most "likely" by donating to one of its many ether oxygens baird2011 C29, C30. An activity coefficient below 1 "suggests" favourable interaction only if the entropy of mixing is near ideal baird2011 C23, C24. No PEG band was analysed, so the bond to PEG is inferred baird2011 X15.

Limits and transfer

Sizes differ between papers for the same phase diagram (chlorpropamide −2.53 against −0.50), and ketoconazole has an activity coefficient of 0.09 in PEG 400 but a positive \chi, 0 wt% solubility and no spectral shift baird2011 R9.a; zhu2011 R5.c, R5.f, R20; marsac2008b R14.f. Use at least two readings, compare only drugs measured in the same way, and test the real dispersion if readings disagree (F8).

How it was shown

Four kinds of reading were used. (1) Interaction energy or parameter from the phase diagram. Baird and Taylor back-calculated an interaction energy \Delta W_{d,p} that closes the gap between the athermal prediction and the observed eutectic (F2) and divided it by R\,T_{eut,th} to give \chi_{dp} baird2011 P8, P10, E3, E8. Zhu and co-workers fitted the Flory–Huggins melting point depression equation to the drug liquidus at 50–80% drug, with the drug volume as lattice site, and normalized the result per PEG segment zhu2011 P5, E1, E2. (2) Activity coefficient in PEG 400. Excess drug was stirred for 24 h at 25 °C in liquid PEG 400 (Baird and Taylor; Marsac and co-workers, with 0.45 µm and 0.2 µm filters respectively), assayed by UV, and the activity coefficient was taken as the ideal solubility divided by the measured mole-fraction solubility, the ideal solubility coming from the melting point and heat of fusion baird2011 P5, P9, E7; marsac2008b P5, P9, E2. PEG 400 was chosen because activity coefficients in viscous, semicrystalline PEG 3350 are hard to measure baird2011 C21. (3) Infrared spectra of the melt. ATR-FTIR spectra of 25:75 drug–PEG 3350 melts, taken at 130, 160, 140 and 155 °C for chlorpropamide, aceclofenac, loratadine and haloperidol, were compared with a spectrum calculated as the weighted sum of the pure molten components; Zhu and co-workers did the same for 20/80 melts of benzocaine, ibuprofen, nilutamide and ketoconazole (temperature not stated) and, in 2012, fenofibrate baird2011 P4; zhu2011 P8; zhu2012 P11. (4) Solubility in supercooled PEG at 25 °C, extrapolated from the liquidus (F4) zhu2011 R5.

What the data show

The table gives the readings per drug. For chlorpropamide the carbonyl band sat at 1717 cm⁻¹ in the melt against 1663 cm⁻¹ in the additive spectrum, and for aceclofenac at 1744 against 1728 cm⁻¹; loratadine and haloperidol showed no or only nominal shifts baird2011 R10.a, R10.c, R10.e, R10.g, R10.h. In PEG 400 at 25 °C, chlorpropamide (194 mg/mL) and aceclofenac (233 mg/mL) dissolved above their ideal solubility, with activity coefficients 0.614 and 0.121, while loratadine (49 mg/mL) and haloperidol (14 mg/mL) gave 2.369 and 0.842 baird2011 R9. Benzocaine, ibuprofen and nilutamide showed carbonyl bands at about 1700, 1735 and 1733 cm⁻¹ against 1686, 1703 and 1721 cm⁻¹ in the calculated spectra, read from the figure, whereas ketoconazole's measured and calculated spectra were superimposed zhu2011 R20. The fenofibrate spectrum had the same peak positions as its calculated spectrum zhu2012 R25, C49. Marsac and co-workers measured ibuprofen at 0.28 and ketoconazole at 0.02 mole fraction in PEG 400, with activity coefficients 0.64 and 0.09 marsac2008b R14.d, R14.f. The Flory–Huggins parameters and the 25 °C solubilities are in the table.

drug\chi (zhu2011) or \chi_{dp} (baird2011)activity coefficient in PEG 400, 25 °Ccarbonyl band, measured against additive spectrum (cm⁻¹)solubility in PEG at 25 °C (wt%)ids
chlorpropamide−0.50; −2.530.6141717 against 166326zhu2011 R5.c; baird2011 R9.a, R10.a
aceclofenac−6.680.1211744 against 1728—baird2011 R9.b, R10.c
benzocaine−0.23—≈1700 against ≈168628zhu2011 R5.b, R20
ibuprofen−0.190.64≈1735 against ≈170325zhu2011 R5.d, R20; marsac2008b R14.d
nilutamide−0.09—≈1733 against ≈172111zhu2011 R5.e, R20
loratadine0.132.369≈1693–1700, no shift described—baird2011 R9.c, R10.e
haloperidol0.08; −0.040.842≈1680 against 1677, no shift described0zhu2011 R5.a; baird2011 R9.d, R10.g
ketoconazole0.020.09measured and calculated superimposed0zhu2011 R5.f, R20; marsac2008b R14.f
fenofibrate——same peak positions as calculated6zhu2012 R25, M2

Carbonyl bands marked ≈ were read from the figures of the papers. The two entries in the χ column for chlorpropamide and haloperidol are zhu2011 first, baird2011 second, from the same published phase diagrams.

Figure

Fig. 5 of baird2011: infrared spectra of 25:75 drug–PEG 3350 melts, measured and additive
Fig. 5 · baird2011infrared spectra of 25:75 drug–PEG 3350 melts, measured and additive

Solid lines are the measured melts and dashed lines the additive spectra; the carbonyl band (left arrow) moves for (a) chlorpropamide and (b) aceclofenac but not for (c) loratadine or (d) haloperidol baird2011 R10. Table 3 of the same paper (figs/table03.png) lists the solubilities, activity coefficients and \chi_{dp} baird2011 R9.

Why

The authors' reading of the infrared result: the large carbonyl shifts of chlorpropamide and aceclofenac to higher wavenumber are "indicative" of fewer drug–drug hydrogen bonds because the drug now bonds to PEG; with about 75 ether oxygens against 2 hydroxyl end groups per chain, it is "likely" that the drug donates the hydrogen bond to an ether oxygen baird2011 C29, C30, R12. Haloperidol's absence of a carbonyl shift "may" be due to its tertiary nitrogen being the better acceptor baird2011 C32. For the activity coefficients, the reading holds only if the entropy of mixing is close to ideal: then a value below 1 "suggests" favourable drug–PEG interactions and a value near 1 supports their absence baird2011 C23, C24; Marsac and co-workers read their PEG 400 values below 1 the same way, as exothermic mixing, and the large values in water as endothermic mixing marsac2008b C14. A more negative \chi is "consistent with" a negative enthalpy of mixing zhu2011 C6. In the supporting information of Zhu and co-workers the carbonyl shifts are put down to changes in drug–drug hydrogen bonding caused by drug–polymer interactions, without a separate test zhu2011 C11. What was not measured: no PEG ether or hydroxyl band was analysed, so the bond to PEG is inferred baird2011 X15; the entropy of mixing was not measured baird2011 C23. The abstract of Baird and Taylor says the interactions were "confirmed" and "demonstrated" by infrared spectroscopy, which is stronger than the shifts support baird2011 C36, X15.

Conditions and limits

Nine drugs, PEG 3350 for the melts and PEG 400 for the solubility. The melts of Baird and Taylor were spectra at 130–160 °C, the PEG 400 solubilities at 25 °C, far below the eutectic temperatures of about 52–61 °C, so activity coefficients are comparable between drugs but are not values for molten PEG 3350 baird2011 P4, X16, R5, R6, R7, R8. PEG 400 has end groups that may make it a different solvent from PEG 3350 baird2011 C22, and Marsac and co-workers note that end-group effects would favour a higher solubility in PEO and entropy effects a lower one marsac2008b C19. The temperature of the infrared spectra of Zhu and co-workers is not stated, while the 20/80 liquidus ranges from about 54.5 to 133 °C zhu2011 X11. Each paper defines its own lattice site and normalization for \chi (drug volume and per PEG segment in zhu2011; interaction energy over R\,T_{eut,th} in baird2011; the volume of an ethyl-pyrrolidone analogue in marsac2009), so values should be compared within a paper only zhu2011 X10; baird2011 E8; marsac2009 E2.

Counterexamples and conflicts

(a) Ketoconazole: an activity coefficient of 0.09 in PEG 400, so a solubility above the ideal value, against a positive \chi of 0.02, a solubility of 0 wt% in PEG at 25 °C and an unshifted infrared spectrum in PEG 3350 marsac2008b R14.f; zhu2011 R5.f, R20. (synthesis: both can be true at once, since ketoconazole's ideal solubility is itself tiny (2.0 × 10⁻³ mole fraction) so a mole-fraction solubility of 0.02 is about ten times ideal while still only about 2.6 wt% of the PEG 400 solution, 0.02 × 531.43 / (0.02 × 531.43 + 0.98 × 400); but the two readings measure different quantities and do not agree on "interacts".) marsac2008b R14.f, M6, M8. (b) Haloperidol: \chi_{dp} −0.04 from one phase diagram and +0.08 from the other, the same published diagram; the sign is not robust near zero baird2011 R9.d; zhu2011 R5.a. (c) Chlorpropamide: −2.53 against −0.50 for the same system, a factor of about 5 (synthesis: 2.53/0.50) baird2011 R9.a; zhu2011 R5.c. (d) Loratadine is grouped with haloperidol as close to ideal in PEG 400 although its measured solubility is about 0.42 of the ideal value baird2011 C24, X13. (e) Haloperidol has an OH group but no carbonyl shift baird2011 M4, R10.g. (f) In the 2011 paper of Zhu and co-workers the text says the chlorpropamide interaction was confirmed by infrared spectroscopy but no chlorpropamide spectrum is shown zhu2011 X3. (g) All six drugs of Marsac and co-workers had activity coefficients below 1 in PEG 400 (0.02–0.64) although felodipine and ketoconazole kept their crystallinity in PEO at 94% RH, so this reading did not discriminate there (see F11) marsac2008b R14, R16.

Transfer check

Use at least two readings, not one, and compare a new drug only with drugs measured in the same way: (i) the liquidus from 0 to 100 wt% and the eutectic against the athermal prediction (F2); (ii) activity coefficient in PEG 400 at 25 °C, with the ideal solubility computed from the same melting point and heat of fusion; (iii) the infrared carbonyl and amine or hydroxyl bands of a 25:75 drug–PEG melt recorded 10–20 °C above the drug melting point against the additive spectrum baird2011 P4, P5, P6. Do not mix \chi values across papers. If two readings disagree, as for ketoconazole, record the drug as unresolved and test the real dispersion (F8).

History

Baird and Taylor build on earlier infrared work on drug–polymer hydrogen bonding, including Taylor and Zografi (1997) in the library, and take the additive-spectrum procedure from a 2009 library paper on moisture-induced immiscibility baird2011 C28, P4. Marsac and co-workers (2008) used PEG 400 solubility and activity coefficients first, to rank the driving force for drug dissolution into PEO marsac2008b C18. Baird and Taylor (2011) combined the melt phase diagram, PEG 400 solubility and infrared spectra for four drugs and proposed PEG 400 solubility as a screen baird2011 C25. Zhu and co-workers (2011) added \chi from melting point depression and the 25 °C solubility for four more drugs zhu2011 R5. Zhu and co-workers (2012) added a non-interacting drug, fenofibrate zhu2012 C49.

F4

Topic 1Phase behaviour of drug–PEG mixtures4 of 4

A drug's estimated solubility in PEG ranks drugs, but does not tell you whether a dispersion stays amorphous.

Below the PEG melting point the solubility cannot be measured, so it was extrapolated from higher temperatures or taken from liquid PEG 400. The estimates separate drugs that interact with PEG from those that do not, yet dispersions below the estimated solubility crystallized within hours zhu2011 R5; zhu2012 R23.a, X13; marsac2008b R16, C22.

weakWeak: these are extrapolations from 50–80 wt% drug data below the PEG melting point, and one value (nilutamide) is higher than its own eutectic content zhu2011 X4; zhu2012 X13.

Estimated solubility in PEG, 25 °C, wt%benzocaine20/80 crystallized after 120–180 min28chlorpropamideeutectic 35 wt%26ibuprofen20/80 crystallized after about 100 min25nilutamideabove its own 10 wt% eutectic11fenofibrate20/80 crystallized after 120–180 min6haloperidolcrystallized within seconds0

Dispersions at 20/80 lie below the estimates for benzocaine and ibuprofen, yet crystallized within hours. zhu2011 R5, X4; zhu2012 M1, M2, R23.a

Dissolvable by amorphous PEO, % of drugacetaminophenlost all crystallinity14ketoprofenlost part of it24naproxenlost part of it13ibuprofenlost part of it17felodipinehardly changed15ketoconazolehardly changed2

PEG 400 basis, six drugs in PEO 100000. Felodipine and acetaminophen have almost the same value and opposite outcomes. marsac2008b R14, R16, E4, C22

For your drug

  1. Treat an extrapolated or PEG 400-based solubility as a ranking between drugs measured the same way, not as a loading limit.
  2. To pick a loading, compute the drug concentration in the amorphous fraction of the polymer (this needs the polymer's crystallinity) and compare it with the estimate, then store the real dispersion at the intended loading and follow the drug by XRD or Raman over hours to days (F8).

marsac2008b E3; zhu2012 P5, P6

How it works and key numbers
  1. Zhu and co-workers fitted ln x against 1/T (the van't Hoff relation) to the drug liquidus and extended the line to 25 °C, below the PEG melting point, so the estimate refers to supercooled liquid PEG zhu2011 P6, E3, C8.
  2. Marsac and co-workers took the solubility in liquid PEG 400 as a stand-in and assumed that only the amorphous 9% of the PEO dissolves drug marsac2008b C18, C20, E4.
  3. The extractor suggests, and the authors do not discuss, that PEG crystallizes first within about 2 min, so the drug is concentrated in the remaining non-crystalline fraction zhu2012 X13, R23.c, R23.d.
  4. For the PEO compacts the authors relate the outcome instead to how well the drug dissolves in the water–amorphous PEO cosolvent (F11), and write that the true solubility in PEO "remains elusive" marsac2008b C22, C38, C19.
28 → 0 wt%estimated solubility in PEG at 25 °C, benzocaine highest; haloperidol and ketoconazole 0zhu2011 R5
120–180 minonset of benzocaine crystallization in the 20/80 dispersion, which lies below its estimated solubilityzhu2012 R23.a, X13
14% vs 15%amorphous-PEO capacity of acetaminophen (lost all) and felodipine (hardly changed)marsac2008b R16, C22

Connections to other chapters

Evidence: data, conditions and papers

Finding F4. The solubility of a drug in PEG at 25 °C is an estimate that ranks drugs but does not say whether a dispersion stays amorphous

In short. The solubility of a drug in PEG below the polymer's melting point cannot be measured directly, so it was extrapolated from the drug liquidus with a van't Hoff plot (benzocaine 28, chlorpropamide 26, ibuprofen 25, nilutamide 11, fenofibrate 6, haloperidol and ketoconazole 0 wt%) or replaced by the solubility in liquid PEG 400 zhu2011 R5; zhu2012 M2; marsac2008b C18. The estimates separate hydrogen-bonding from non-interacting drugs, yet 20/80 benzocaine and ibuprofen dispersions lie below the estimated solubilities and crystallized within hours, and PEG 400-based capacities of 2–24% did not predict which drugs lost crystallinity in PEO zhu2012 R23.a, X13; marsac2008b R16, C22.

Type. derived estimates (model result) compared with dispersion outcomes Strength. extrapolations from 50–80 wt% drug data below the PEG melting point, with one value (nilutamide) higher than its own eutectic content (zhu2011 X4; zhu2012 X13).

How it was shown

Zhu and co-workers extrapolated the drug liquidus with a van't Hoff plot (\ln x against 1/T) to 25 °C, below the PEG melting point, so the estimate refers to supercooled liquid PEG zhu2011 P6, E3, C8. Marsac and co-workers took the drug solubility in liquid PEG 400 as a stand-in and calculated how much of the drug in a compact the amorphous 9% of the PEO could dissolve marsac2008b C18, C20, E4.

What the data show

Estimated solubilities at 25 °C were 28 wt% (benzocaine), 26 (chlorpropamide), 25 (ibuprofen), 11 (nilutamide), 6 (fenofibrate) and 0 (haloperidol, ketoconazole) zhu2011 R5; zhu2012 M2, M1. Yet benzocaine and ibuprofen at 20/80 began to crystallize after 120–180 and about 100 min zhu2012 R23.a. The PEG 400 estimates of 2–24% did not predict which drugs lost crystallinity in PEO: felodipine (15%) hardly changed while acetaminophen (14%) lost all of it marsac2008b C22, R16.

papersystemestimate and conditionsresultids
zhu2011benzocaine, chlorpropamide, ibuprofen in PEG 3350van't Hoff extrapolation of the drug-rich liquidus to 25 °C28, 26, 25 wt% (eutectic 30, 35, 40 wt%)zhu2011 R5.b, R5.c, R5.d
zhu2011nilutamide; haloperidol, ketoconazoleas above11 wt% (eutectic 10 wt%); 0 wt%zhu2011 R5.e, R5.a, R5.f, X4
zhu201220/80 dispersions at 25 °CXRD and Ramanonset benzocaine 120–180 min, ibuprofen about 100 min, fenofibrate 120–180 min, haloperidol −100 szhu2012 R23.a
marsac2008bsix drugs, 10 wt% in PEO 100000solubility in PEG 400, 25 °C, amorphous 9% of PEOdissolvable 14, 24, 13, 17, 15, 2% of the drug; observed loss complete, moderate, moderate, moderate, negligible, negligiblemarsac2008b R14, R16, E4
Table 1 of zhu2011: interaction parameter, solubility in PEG and eutectic composition of six drugs
Table 1 · zhu2011interaction parameter, solubility in PEG and eutectic composition of six drugs

Negative \chi and 11–28 wt% for four drugs; positive \chi and zero for haloperidol and ketoconazole zhu2011 R5.

Why

The authors tie a solubility above 20% to a negative \chi, donors that can bind the PEG ether oxygen and moderate melting points zhu2011 C9, C12, C13. Marsac and co-workers relate the outcome instead to dissolving in the water–amorphous PEO cosolvent (F11), and write that the true solubility in PEO "remains elusive" marsac2008b C38, C19. The extractor adds that PEG crystallizes first, so the drug is concentrated in the remaining non-crystalline fraction zhu2012 X13.

Limits and transfer

The 25 °C values refer to supercooled liquid PEG, not to the largely crystalline polymer, and nilutamide's 11 wt% lies above its own 10 wt% eutectic zhu2011 C8, X4. Treat such a solubility as a ranking between drugs measured the same way, not as a loading limit, and follow the real dispersion by XRD or Raman over hours to days (F8) zhu2012 P5, P6.

How it was shown

Zhu and co-workers took the mole-fraction solubility x of each drug in liquid PEG at each temperature from its liquidus, fitted a straight line to \ln x against 1/T (the van't Hoff relation, d\ln x/dT = \Delta H_f/(R T^2)), extended it to 25 °C, below the PEG melting point, and converted the result to weight percent; the estimate therefore refers to supercooled liquid PEG zhu2011 P6, E3, C8. Zhu and co-workers used the same route for fenofibrate from the supporting-information diagram zhu2012 M2, E3. Marsac and co-workers could not measure the solubility in amorphous PEO because the transformation is too slow when dry, so they took the solubility in liquid PEG 400 at 25 °C as a stand-in, assumed that only the amorphous PEO dissolves drug, and calculated how much of the 50 mg of drug in a 500 mg compact the amorphous 9% of the 450 mg of PEO could dissolve marsac2008b C18, C20, E4, P10.

What the data show

The estimated solubilities at 25 °C were 28 wt% (benzocaine), 26 (chlorpropamide), 25 (ibuprofen), 11 (nilutamide) and 0 (haloperidol, ketoconazole) zhu2011 R5, and 6 for fenofibrate and under 1 for haloperidol zhu2012 M2, M1. For chlorpropamide, benzocaine and ibuprofen they lie below the eutectic content (35, 30 and 40 wt%), as a solubility that falls on cooling should; for nilutamide, 11 wt% at 25 °C is above the eutectic content of 10 wt% at 58.4 °C, which the extractor of the card notes as unexpected zhu2011 R5.c, R5.b, R5.d, R5.e, X4. (synthesis: at the 20/80 loading used in the dispersions, benzocaine and ibuprofen are below their estimated solubility and fenofibrate and haloperidol above it zhu2012 M3, M4, M2, M1.) Yet benzocaine started to crystallize after 120–180 min and ibuprofen after about 100 min, and haloperidol, which is insoluble, within seconds zhu2012 R23.a. The extractor suggests a reason that the authors do not discuss: PEG crystallizes first, within about 2 min, so the drug is concentrated in the remaining non-crystalline fraction zhu2012 X13, R23.c, R23.d. For Marsac and co-workers the PEG 400 mole fractions were 0.32 (acetaminophen and ketoprofen), 0.22 (naproxen), 0.28 (ibuprofen), 0.16 (felodipine) and 0.02 (ketoconazole), which translate to 14, 24, 13, 17, 15 and 2% of the drug dissolvable by amorphous PEO; for ketoprofen the card recomputes 0.09 × 450 mg × 0.299 = 12.1 mg of 50 mg, 24.2% marsac2008b R14, R16, E4. The authors find no clear correlation with the observed loss: felodipine (15%) hardly changed while acetaminophen (14%) lost all its crystallinity marsac2008b C22, R16.

papersystemestimate and conditionsresultids
zhu2011benzocaine / chlorpropamide / ibuprofen in PEG 3350van't Hoff extrapolation of the drug-rich liquidus to 25 °C28 / 26 / 25 wt% (eutectic 30 / 35 / 40 wt%)R5.b, R5.c, R5.d
zhu2011nilutamide; haloperidol, ketoconazoleas above11 wt% (eutectic 10 wt%); 0 wt%R5.e, R5.a, R5.f, X4
zhu2012fenofibrate; haloperidolas above; text6 wt%; below 1 wt%M2, M1
zhu201220/80 dispersions at 25 °CXRD and Ramanonset BZC 120–180 min, IBP about 100 min, FNB 120–180 min, HLP −100 sR23.a
marsac2008bsix drugs, 10 wt% in PEO 100000solubility in PEG 400, 25 °C, amorphous 9% of PEOdissolvable 14, 24, 13, 17, 15, 2% of the drug; observed loss complete, moderate, moderate, moderate, negligible, negligibleR14, R16, E4

Rows of the Marsac and co-workers estimate are in the order acetaminophen, ketoprofen, naproxen, ibuprofen, felodipine, ketoconazole marsac2008b R16.

The two estimates are not on the same scale: Zhu and co-workers give weight percent of drug in the saturated PEG solution, Marsac and co-workers the percent of the drug in a compact that a small amorphous polymer fraction could take up (synthesis: for ibuprofen, 25 wt% in supercooled PEG 3350 against 17% of the drug in a PEO compact zhu2011 R5.d; marsac2008b R16.d).

Figure

Table 1 of zhu2011: interaction parameter, solubility in PEG and eutectic composition of six drugs
Table 1 · zhu2011interaction parameter, solubility in PEG and eutectic composition of six drugs

Negative \chi and solubilities of 11–28 wt% for benzocaine, chlorpropamide, ibuprofen and nilutamide; positive \chi and zero solubility for haloperidol and ketoconazole zhu2011 R5.

Why

The authors link a solubility above 20% to a negative \chi, hydrogen-bond donors that can bind the PEG ether oxygen and moderate melting points (benzocaine, chlorpropamide, ibuprofen), and nilutamide's lower value to its higher melting point; positive \chi leaves haloperidol and ketoconazole "almost insoluble" zhu2011 C9, C12, C13. Marsac and co-workers find no clear correlation between the PEG 400-based estimate and the loss, relate the outcome instead to the drug's ability to dissolve in the water–amorphous PEO cosolvent (F11), and write that the true solubility in PEO "remains elusive" because end-group effects and mixing entropy act in opposite directions marsac2008b C22, C38, C19. For the dispersions, Zhu and co-workers do not use the solubilities to explain the crystallization times; they attribute benzocaine's delay to melting point depression and the early onset of ibuprofen and fenofibrate to nucleation on crystalline PEG (F8, F9) zhu2012 C32, C34.

Conditions and limits

The 25 °C values refer to supercooled liquid PEG, not to the largely crystalline polymer in a stored dispersion zhu2011 C8. The regression lines, heats of fusion and molar masses behind them are not printed zhu2011 E3. Nothing in these papers measured the crystallinity of PEG 3350 in the dispersions or the drug concentration in its amorphous fraction; Marsac and co-workers estimated PEO 100000 as about 91% crystalline from 197 against 216 J/g marsac2008b R15, E3. Only a 20/80 loading was studied for the dispersions.

Counterexamples and conflicts

The nilutamide value above its eutectic content zhu2011 X4. The dispersions of benzocaine and ibuprofen crystallized although nominally below saturation zhu2012 X13. In the PEO compacts, felodipine and acetaminophen had similar PEG 400 estimates and opposite outcomes marsac2008b R16.

Transfer check

Treat an extrapolated or PEG 400-based solubility as a ranking between drugs measured the same way, not as a loading limit. To decide a loading, compute the drug concentration in the amorphous fraction of the polymer (needs the polymer's crystallinity, for example from the melting enthalpy as in marsac2008b E3) and compare it with the estimate, then store the real dispersion at the intended loading and follow the drug by XRD or Raman over hours to days (F8) zhu2012 P5, P6.

History

Marsac and co-workers (2008) used the PEG 400 stand-in first and found no correlation with outcome marsac2008b C22. Zhu and co-workers (2011) applied the van't Hoff extrapolation, a method the card traces to the group's 2010 study, to six drugs zhu2011 E3, P6. Zhu and co-workers (2012) used the estimates to describe the four drugs of their kinetic study zhu2012 M1, M2, M3, M4.

Topic 2 of 4 · 2 findings · F5–F6

Microstructure of the solidified dispersion

F5

Topic 2Microstructure of the solidified dispersion1 of 2

Drugs that interact with PEG increase the PEG lamellar spacing by 3–5 nm while amorphous; on crystallization the spacing decreases again.

20/80 drug–PEG mixtures were followed by synchrotron X-ray scattering as they solidified at 25 °C. The repeat distance of the PEG layers, the long period L, was 14.7–16.5 nm with four drugs while they were still amorphous, against 11.6 nm for pure PEG, and fell to 11.4–11.9 nm once the drugs had partly crystallized zhu2011 R18, R8.

moderateModerate: the 3–5 nm change and its reversal are large and direct, but the drug's location is inferred from L alone and each system was run once zhu2011 X8, X9, X12.

30 min · drug amorphous24 h · drug partly crystallinepure PEG, no drugpure PEG11.211.6benzocaine11.416.5ibuprofen11.916.1nilutamide11.416.0chlorpropamide11.714.7101112131415161718long period L, nm

Long period of 20/80 drug–PEG blends quenched to 25 °C; pure PEG values at 30 min and 24 h. zhu2011 R7, R8, R18.b, R18.c, R18.d, R18.e

For your drug

  1. Quench the real dispersion at the intended ratio and record SAXS and WAXS together from seconds to 24 h, with a pure-PEG control made the same way and a second control at another crystallization temperature.
  2. An increase of L by 3 nm or more with no drug WAXS peaks is consistent with an amorphous drug between lamellae; confirm with a second method. A fall of L toward the pure-PEG value signals drug crystallization (F8).

zhu2011 X8

How it works and key numbers
  1. The long period is the repeat of one crystalline PEG layer plus the amorphous layer between layers zhu2011 X8, E4, C32.
  2. A drug that mixes with the amorphous PEG is located in that layer and thickens it, so L increases zhu2011 X8, C32.
  3. Pure PEG crystallized at 40 instead of 25 °C changed L by only about 1 nm, so lower PEG supercooling cannot explain the 4–5 nm increase with benzocaine, which "can be largely attributed" to the drug in the interlamellar region zhu2011 C21, R8.
  4. When the drug crystallizes it is excluded from the layer and L falls to near the pure-PEG value; for ibuprofen this came with new SAXS and WAXS peaks at about 111 min zhu2011 C26, R14, R15.
Analogy. A sandwich: slices of crystalline bread with a filling between them. A drug dissolved in the filling makes the filling thicker; when the drug turns into crystals it leaves the filling and the sandwich gets thin again.
16.5, 16.1, 16.0, 14.7 vs 11.6 nmL at 30 min with benzocaine, ibuprofen, nilutamide and chlorpropamide against pure PEGzhu2011 R18, R8
11.4–11.9 nmL at 24 h after the drugs partly crystallized; pure PEG 11.2zhu2011 R18, R8
≈111 minibuprofen's new SAXS peak and WAXS crystal peak appear togetherzhu2011 R14, R15
Evidence: data, conditions and papers

Finding F5. Drugs that interact with PEG enlarge the lamellar long period by 3–5 nm while they are amorphous, and crystallization returns it to the pure-PEG value

In short. Pure PEG 3350 quenched to 25 °C forms lamellae with a long period L of about 13.3 nm that thin to 11.6 nm within 30 min and 11.2 nm at 24 h zhu2011 R7, R8. In 20/80 blends with benzocaine, ibuprofen, nilutamide or chlorpropamide, L was 16.5, 16.1, 16.0 and 14.7 nm at 30 min while WAXS showed no drug crystals, 3–5 nm above pure PEG, and fell to 11.4–11.9 nm at 24 h when the drugs were partially crystalline zhu2011 R18, R8. For ibuprofen the fall coincided with a new SAXS peak and an ibuprofen WAXS peak at about 111 min zhu2011 R14, R15. The authors read the enlargement as drug held in the amorphous interlamellar region until it crystallizes; the location was inferred from L and not measured zhu2011 C21, C23, C26, X8.

Type. observation in 4 drugs with controls Strength. the 3–5 nm contrast and its reversal are large and direct, and the ibuprofen sequence was recorded in real time, but the location of the drug is inferred from L alone, each system was run once and the 24 h WAXS patterns are not shown (zhu2011 K1: strong; K2: moderate; K3: moderate to strong; X8, X9, X12).

How it was shown

Zhu and co-workers quench-cooled 20/80 drug–PEG 3350 melts to 25 °C in the synchrotron beam and recorded small- and wide-angle scattering together for about 30 min and at 24 h; pure PEG was quenched to 25 and 40 °C zhu2011 P2, A1, A2, A3. The long period L came from the SAXS peak, the drug state from the WAXS crystal peaks zhu2011 E4, R7.

What the data show

Pure PEG at 25 °C had L of about 13.3 nm, falling to 11.6 nm within 30 min and 11.2 nm at 24 h zhu2011 R7, R8. With benzocaine, ibuprofen, nilutamide or chlorpropamide, L was 16.5, 16.1, 16.0 and 14.7 nm at 30 min with no drug crystals by WAXS, and 11.4–11.9 nm at 24 h when the drugs were partially crystalline zhu2011 R18, R8. For ibuprofen the fall came with new SAXS and WAXS peaks at about 111 min zhu2011 R14, R15.

papersystemresultids
zhu2011pure PEG 3350, 25 °CL 13.3 nm at start, 11.6 at 30 min, 11.2 at 24 hzhu2011 R7, R8
zhu2011benzocaine/PEG 20/80L 16.5 nm at 30 min, amorphous; 11.4 nm at 24 h, partially crystallinezhu2011 R18.b, R12, R11
zhu2011ibuprofen/PEG 20/8016.1 nm at 30 min, amorphous; 11.9 nm at 24 h; new SAXS and WAXS peaks at about 111 minzhu2011 R18.d, R14, R15
zhu2011nilutamide/PEG 20/8016.0 nm at 30 min, amorphous; 11.4 nm at 24 hzhu2011 R18.e, R16
zhu2011chlorpropamide/PEG 20/8014.7 nm at 30 min, amorphous (WAXS not shown); 11.7 nm at 24 hzhu2011 R18.c, R13
Fig. 13 of zhu2011: long period of the ibuprofen/PEG 20/80 blend against time
Fig. 13 · zhu2011long period of the ibuprofen/PEG 20/80 blend against time

A plateau near 16 nm to about 110 min, then a fall to 11.9 nm at 24 h zhu2011 R14.

Why

The long period is the repeat of the crystalline lamella and the amorphous layer between lamellae; a drug that mixes into that layer thickens it zhu2011 X8, E4, C32. Pure PEG crystallized at 40 °C changed L by only about 1 nm, so the 4–5 nm increase with benzocaine "can be largely attributed" to the drug in the interlamellar region zhu2011 C21, R8. When the drug crystallizes it is excluded and L falls zhu2011 C26.

Limits and transfer

The drug's location is inferred from L alone, each system was run once, and the 24 h WAXS patterns are not shown zhu2011 X8, X9, X12. An increase of L by 3 nm or more with no drug WAXS peaks is consistent with an amorphous drug between lamellae; confirm with a second method.

How it was shown

Zhu and co-workers mixed each drug with PEG 3350 at 20/80 w/w, put the physical mixture in an aluminium DSC pan on a Linkam stage in the beam of the Advanced Photon Source (17 keV), heated it above the drug melting point and quench-cooled it to 25 °C; pure PEG was quenched to 25 and 40 °C zhu2011 P2, A1, A2. Small-angle (q 0.0085–0.23 Å⁻¹) and wide-angle (q 0.6–4.6 Å⁻¹) scattering were recorded together for about 30 min (about 116 min for chlorpropamide, about 131 min for ibuprofen) and once more at 24 h zhu2011 P2, A3. The long period was taken from the SAXS peak position as L = 2n\pi/q zhu2011 E4. The drug phase state came from WAXS: PEG shows crystal peaks at q about 1.36 and 1.65 Å⁻¹ zhu2011 R7.

What the data show

On quenching pure PEG to 25 °C the WAXS crystal peaks appeared at once and did not move, while the SAXS peak, first seen at q about 0.047 Å⁻¹, shifted to larger q; L fell from around 13.3 nm to 11.6 nm within 30 min and to 11.2 nm at 24 h zhu2011 R7, R8. At 40 °C L rose slightly, then fell to 12.6 nm after 40 min, about 1 nm above the 25 °C value at 30 min, and reached 11.2 nm at 24 h zhu2011 R8. The authors assign the first structure to nonintegral folded lamellae and the 11.2 nm period to once-folded lamellae zhu2011 C14.

In the blends, benzocaine raised L to about 16.5 nm within about 1.5 min, and the value remained there to 28.2 min, with no benzocaine crystals by WAXS although pure benzocaine crystallizes at once zhu2011 R12, R11, R6. Ibuprofen raised L to about 16.5 nm within about 3 min, and the value remained at about 16.1 nm until about 110 min, 4.9 nm above pure PEG at 20 min zhu2011 R14. With nilutamide the long period overshot to about 17.3 nm at 2–3 min and then remained at about 16.5, later 16.1 nm zhu2011 R16. With chlorpropamide the long period remained at about 14.7 nm from about 18 to 85 min, more than 3 nm above pure PEG at about 28 min, with no crystallization by WAXS (data not shown) zhu2011 R13. The ibuprofen change was followed through: at 100 min one SAXS peak at q about 0.039 Å⁻¹ and an amorphous drug; at 111 min a second SAXS peak at about 0.047 Å⁻¹ and a crystalline ibuprofen WAXS peak; at 116 min the 0.047 Å⁻¹ peak dominated; two long periods coexisted for a few minutes (about 15.9–15.5 and 13.7–13.5 nm) and L settled near 13.3 nm before reaching 11.9 nm at 24 h zhu2011 R14, R15. At 24 h L was 11.4, 11.7, 11.9 and 11.4 nm with benzocaine, chlorpropamide, ibuprofen and nilutamide, which Table 2 lists as partially crystalline, while the text says benzocaine "crystallized" and "most" of the chlorpropamide did zhu2011 R18, C22, C24, X12.

papersystemmethod and conditionsresultids
zhu2011pure PEG 3350, 25 °CSAXS/WAXS after quench, one runL 13.3 nm at start, 11.6 at 30 min, 11.2 at 24 hR7, R8
zhu2011pure PEG 3350, 40 °Cas aboveL 12.6 nm at 40 min, about 1 nm above 25 °C at 30 min, 11.2 at 24 hR8
zhu2011benzocaine/PEG 20/80, 25 °Cas aboveL 16.5 nm at 30 min, amorphous; 11.4 nm at 24 h, partially crystallineR18.b, R12, R11
zhu2011ibuprofen/PEG 20/80as above16.1 nm at 30 min, amorphous; 11.9 nm at 24 h; new SAXS and WAXS peaks at about 111 minR18.d, R14, R15
zhu2011nilutamide/PEG 20/80as above16.0 nm at 30 min, amorphous; 11.4 nm at 24 hR18.e, R16
zhu2011chlorpropamide/PEG 20/80as above14.7 nm at 30 min, amorphous (WAXS not shown); 11.7 nm at 24 hR18.c, R13

Figure

Fig. 11 of zhu2011: long period of the benzocaine/PEG 20/80 blend and of pure PEG against time
Fig. 11 · zhu2011long period of the benzocaine/PEG 20/80 blend and of pure PEG against time

L sits at about 16.5 nm from 1.5 to 28 min against about 11.6 nm for pure PEG, and drops at 24 h; the 24 h point is plotted at about 11.7 nm while text and Table 2 give 11.4 nm zhu2011 R12, X1.

Fig. 13 of zhu2011: long period of the ibuprofen/PEG 20/80 blend against time
Fig. 13 · zhu2011long period of the ibuprofen/PEG 20/80 blend against time

About 16.5 then 16.1 nm to about 110 min, then a second, smaller L and a fall to 11.9 nm at 24 h zhu2011 R14.

Why

The authors' explanation, step by step: the long period is the repeat of the crystalline lamella and the amorphous layer between lamellae; a drug that mixes with the amorphous PEG and is located in that layer thickens it and enlarges L zhu2011 X8, E4, C32. For benzocaine, the alternative that the drug lowers the PEG melting point and so the supercooling of PEG, which could also enlarge L, was weighed: pure PEG crystallized at 40 instead of 25 °C changed L by only about 1 nm at 30 min, so the 4–5 nm increase "can be largely attributed" to benzocaine in the interlamellar region zhu2011 C21, R8. For chlorpropamide, "suggesting interlamellar incorporation" zhu2011 C23. When the drug crystallizes it is removed from the interlamellar region and L falls: "crystallization of the drug results in its exclusion from the interlamellar regions" zhu2011 C26. In the wording of the general conclusion, "This suggests that interlamellar incorporation is favored" for molecules that interact strongly with PEG, and "the location of the API could thus be inferred" from L zhu2011 C32, C33. From the polymer-blend literature the authors expect exclusion from PEG crystals to depend on the PEG crystallization rate, the additive's mobility through the blend Tg and specific interactions zhu2011 C2. What was not measured: the thicknesses of crystalline and amorphous layers were not separated, a change of chain folding in the blends was not examined, and the drug was not located by any other method zhu2011 X8. (synthesis: the 24 h values with a crystallized drug, 11.4–11.9 nm, are still 0.2–0.7 nm above the 11.2 nm of pure PEG at 24 h, the same kind of residual that the extractor notes for ketoconazole zhu2011 R18, R8, X6.)

Conditions and limits

One drug/PEG ratio (20/80), PEG 3350, quench to 25 °C; one run per system and no replicates reported; the storage between the last time-resolved frame and the 24 h measurement is not stated zhu2011 X9. The interaction parameters were fitted at 50–80% drug, not at 20/80 zhu2011 X10. The 24 h crystallinity rests on WAXS patterns that are not shown, and chlorpropamide WAXS is not shown at any time zhu2011 X12. The drug content in the amorphous layer and its time dependence are not known.

Counterexamples and conflicts

The size of the increase does not follow the size of the interaction or the solubility: chlorpropamide has the most negative \chi (−0.50) and 26 wt% solubility but the smallest L at 30 min (14.7 nm), while nilutamide (\chi −0.09, 11 wt%) gives 16.0 nm, so only the sign of \chi separates interacting from non-interacting drugs zhu2011 R5.c, R5.e, R18, X5. The BZC 24 h value differs between figure and table zhu2011 X1. None found in the cards of this chapter, since no other card measured the long period.

Transfer check

Prepare the dispersion at the intended ratio and quench under the production conditions; record SAXS and WAXS together from seconds to 24 h, with a pure-PEG control made the same way and a second control at another crystallization temperature to bound the effect of supercooling. An increase of L by 3 nm or more with no drug WAXS peaks is consistent with an amorphous drug between lamellae; confirm with a second method before relying on it, since L alone does not locate the drug zhu2011 X8. A fall of L toward the pure-PEG value signals drug crystallization, as in F8.

History

The group had probed drug/PEG microstructure after 24 h only in an earlier study that is not part of the PEG dispersions set, and the polymer-blend literature on additive exclusion is outside the library zhu2011 C2, C7. Zhu and co-workers (2011) introduced the time-resolved SAXS/WAXS view in this library. Zhu and co-workers (2012) later followed the crystallization of the same ibuprofen and benzocaine dispersions by XRD and Raman and found onsets consistent with the SAXS/WAXS result (F8) zhu2012 R14, R11.

F6

Topic 2Microstructure of the solidified dispersion2 of 2

Weakly interacting drugs leave the PEG lamellar spacing unchanged, whether they crystallize at once or stay amorphous.

Haloperidol crystallized at once in the PEG blend and ketoconazole stayed amorphous for 24 h, yet the long period of both stayed close to the pure-PEG value zhu2011 R9, R10, R17, R18.a, R18.f, R8. A drug glass-transition temperature (Tg) above the 25 °C solidification temperature, up to 44 °C, did not change the pattern zhu2011 C28, C31.

weakWeak to moderate: the contrast with F5 is clear, but ketoconazole's exclusion is inferred and the Tg test rests on two drugs that also differ in interaction and crystallization zhu2011 X7, X13.

30 min24 h or after crystallizationpure PEG, no drugpure PEG11.211.6haloperidolcrystalline from the first frame11.212.0ketoconazoleamorphous to 24 h · Tg 4411.811.8nilutamideinteracts · Tg about 3311.416.011121314151617long period L, nm

The two weakly interacting drugs stay at the pure-PEG value; nilutamide, which interacts, first enlarges L, which returns to near the pure-PEG value on crystallization. zhu2011 R8, R9, R10, R16, R17, R18.a, R18.e, R18.f, M5

For your drug

  1. For a drug with a positive \chi or no sign of interaction, do not expect the long period to show its amorphous state: ketoconazole was amorphous but did not change the long period.
  2. Check the drug's state directly by WAXS or XRD over 24 h and look for separate amorphous drug domains by another method; do not extend the Tg result beyond about 44 °C at a 25 °C solidification.

zhu2011 X7, X13

How it works and key numbers
  1. Haloperidol's lack of influence "most likely results from its rapid removal from the PEG phase" by crystallization on cooling zhu2011 C19.
  2. Ketoconazole stays amorphous but has a positive interaction parameter, which "may indicate a low tendency to mix with PEG and a large extent of exclusion from the interlamellar region" zhu2011 C30.
  3. A drug Tg above the 25 °C solidification temperature (nilutamide about 33 °C, ketoconazole 44 °C) did not stop phase separation; "clearly" the higher Tg did not prevent it zhu2011 C28, C31.
  4. (synthesis: haloperidol (class I-A) and ketoconazole (class III) belong to opposite ends of the neat-drug classes yet behave alike here, so the interaction, not the drug's own crystallization tendency, decides incorporation) baird2010 R1, M17, M42.
12.0 and 11.8 nmL at 30 min with haloperidol and ketoconazole, close to the 11.6 nm of pure PEGzhu2011 R18.a, R18.f, R8
44 °Chighest drug Tg tested (ketoconazole), above the 25 °C solidification temperature, with no effectzhu2011 C28, C31
2 drugsweakly interacting drugs tested, with opposite crystallization behaviour and the same Lzhu2011 R9, R17

Connections to other chapters

Evidence: data, conditions and papers

Finding F6. Weakly interacting drugs leave the long period at the pure-PEG value whether they crystallize at once or stay amorphous, and a drug Tg up to 44 °C did not change this

In short. Haloperidol crystallized at once in the PEG blend (a haloperidol WAXS peak from the first frame) and the long period was 12.0 nm at 30 min and 11.2 nm at 24 h; ketoconazole stayed amorphous for 24 h and the long period was 11.8 nm at both times, close to the 11.6 and 11.2 nm of pure PEG zhu2011 R9, R10, R17, R18.a, R18.f, R8. The authors attribute haloperidol's lack of effect to its fast removal by crystallization and ketoconazole's to its positive interaction parameter, and state that a drug Tg above the 25 °C solidification temperature (nilutamide about 33 °C, ketoconazole 44 °C) did not change the pattern zhu2011 C19, C30, C28, C31.

Type. observation in 2 weakly interacting drugs plus a Tg comparison on 2 drugs Strength. to moderate — the contrast with F5 is clear, but ketoconazole's exclusion is inferred and the Tg test rests on two drugs that also differ in interaction and crystallization (zhu2011 K4: moderate; K6: weak to moderate; X7, X13).

How it was shown

The SAXS/WAXS protocol of F5 was used for haloperidol (rapid crystallizer, weak interaction with PEG) and ketoconazole (slow crystallizer, weak interaction, Tg of 44 °C) at 20/80 and 25 °C, with a pure-PEG control zhu2011 P2, A1, C16, M5, M6. Zhu and co-workers (2012) later followed haloperidol/PEG by synchrotron XRD zhu2012 P4, R7.

What the data show

Haloperidol's WAXS peak was present from the first frame; L settled near 11.95 nm and was 11.2 nm at 24 h, "essentially the same" as pure PEG zhu2011 R9, R10, C18. In ketoconazole/PEG L was about 11.8 nm from about 2 min to 24 h, with no drug crystals by WAXS zhu2011 R17. Nilutamide (Tg about 33 °C) behaved like the low-Tg drugs: L rose to 16–17 nm while amorphous and fell to 11.4 nm once crystallized zhu2011 R16, R18.e, C28.

papersystemresultids
zhu2011haloperidol/PEG 20/80, 25 °C (Tg below 25 °C)drug crystalline from the first frame; L 12.0 nm at 30 min, 11.2 nm at 24 hzhu2011 R9, R10, R18.a
zhu2011ketoconazole/PEG 20/80 (Tg 44 °C)amorphous to 24 h; L 11.8 nm at 30 min and at 24 hzhu2011 R17, R18.f, X9
zhu2011pure PEG 3350L about 11.6 nm at 15–28 min, about 11.3 nm at 1440 min (read from the figure)zhu2011 R8, R17
zhu2011nilutamide/PEG 20/80 (Tg about 33 °C)L 16.0 nm while amorphous, 11.4 nm after crystallizationzhu2011 R16, R18.e, M5
Fig. 16 of zhu2011: long period of the ketoconazole/PEG 20/80 blend against time
Fig. 16 · zhu2011long period of the ketoconazole/PEG 20/80 blend against time

L is about 11.8 nm from 2 min to 24 h, close to the PEG control; the drug stays amorphous zhu2011 R17.

Why

The authors say haloperidol's lack of influence "most likely results from its rapid removal from the PEG phase" by crystallization, and ketoconazole's is "likely due to the positive interaction parameter", and "clearly" its higher Tg did not prevent phase separation zhu2011 C19, C30, C31. (synthesis: haloperidol (class I-A) and ketoconazole (class III) belong to opposite ends of the neat-drug classes, so the interaction, not the drug's own crystallization tendency, decides incorporation baird2010 R1, M17, M42.)

Limits and transfer

Two drugs, one ratio and one PEG grade; ketoconazole's exclusion is inferred from L, and the Tg test rests on two drugs that also differ in \chi and crystallization zhu2011 X7, X13. For a drug with a positive \chi, do not expect the long period to show its amorphous state; check the drug directly by WAXS or XRD over 24 h.

How it was shown

The same SAXS/WAXS protocol as in F5 was used for haloperidol and ketoconazole at 20/80 and 25 °C, with the pure-PEG control zhu2011 P2, A1. The drugs were chosen for differing crystallization tendency, interaction with PEG and Tg: haloperidol rapidly crystallizing and weakly interacting, ketoconazole slowly crystallizing, weakly interacting, with a Tg of 44 °C; the Tg values are cited from the 2010 classification paper zhu2011 C16, M5, M6. Zhu and co-workers (2012) later followed haloperidol/PEG by synchrotron XRD at 20/80 and 25 °C, recording the order of crystallization zhu2012 P4, R7.

What the data show

In haloperidol/PEG the haloperidol WAXS peak at q about 1.40 Å⁻¹ was present from the 0 min frame and persisted as a shoulder of the 1.36 Å⁻¹ PEG peak zhu2011 R9. L started at about 13.9 nm, settled near 11.95 nm from about 11.5 to 35 min, about 0.4 nm above pure PEG, and was 11.2 nm at 24 h; the authors call this "essentially the same" as pure PEG zhu2011 R10, C17, C18. In ketoconazole/PEG L dropped to about 11.8 nm within about 2 min and stayed there to 24 h, with no ketoconazole crystals by WAXS after 24 h zhu2011 R17. At 24 h ketoconazole's L is 0.6 nm above pure PEG (11.8 against 11.2 nm), a residual similar to that of crystallized chlorpropamide (11.7) and ibuprofen (11.9) and not discussed by the authors zhu2011 X6, R18. For nilutamide, L rose to about 16–17 nm and fell to 11.4 nm once the drug had crystallized by 24 h, like the low-Tg drugs zhu2011 R16, R18.e, C28. In the 2012 paper haloperidol began to crystallize before PEG and was completely crystalline within a few seconds, and PEG crystallization began immediately afterwards zhu2012 R7, C2.

papersystemmethod and conditionsresultids
zhu2011haloperidol/PEG 20/80, 25 °C (Tg below 25 °C)SAXS/WAXSdrug crystalline from the first frame; L 12.0 nm at 30 min, 11.2 nm at 24 hR9, R10, R18.a
zhu2011ketoconazole/PEG 20/80 (Tg 44 °C)as aboveamorphous to 24 h; L 11.8 nm at 30 min (last frame about 15 min) and at 24 hR17, R18.f, X9
zhu2011pure PEG 3350as aboveL about 11.6 nm at 15–28 min, about 11.3 nm at 1440 min (read from the figure)R8, R17
zhu2011nilutamide/PEG 20/80 (Tg about 33 °C)as aboveL 16.0 nm while amorphous, 11.4 nm after crystallizationR16, R18.e, M5
zhu2012haloperidol/PEG 20/80synchrotron XRD, 25 °Chaloperidol crystallized first, within seconds; PEG afterR7, R23.a

Figure

Fig. 16 of zhu2011: long period of the ketoconazole/PEG 20/80 blend against time
Fig. 16 · zhu2011long period of the ketoconazole/PEG 20/80 blend against time

L is about 11.8 nm from 2 min to 24 h, close to the PEG control; the drug stays amorphous zhu2011 R17.

Why

The authors' explanation: haloperidol's lack of influence "most likely results from its rapid removal from the PEG phase" by crystallization on cooling zhu2011 C19. Ketoconazole's lack of effect is "likely due to the positive interaction parameter", which "may indicate a low tendency to mix with PEG and a large extent of exclusion from the interlamellar region"; "clearly" its higher Tg did not prevent phase separation zhu2011 C30, C31. In the polymer-blend literature the additive's mobility, through the blend Tg, is one of three factors that decide exclusion, which is why Tg was examined zhu2011 C2. (synthesis: with the neat-drug classes of the chapter Crystallization tendency, the two drugs belong to opposite ends of the classification, haloperidol in class I-A (crystallizes on cooling, even in liquid N2) and ketoconazole in class III, yet both leave the long period unchanged, so the drug's own crystallization tendency does not decide incorporation; the interaction does baird2010 R1, M17, M42.)

Conditions and limits

Two weakly interacting drugs, one ratio, one PEG grade and one solidification temperature. Ketoconazole's exclusion and phase separation are inferred from L; the amorphous ketoconazole was not imaged and no separate domain was observed zhu2011 X7. The Tg conclusion rests on nilutamide and ketoconazole, whose Tg lie 8 and 19 °C above the 25 °C solidification temperature, which also differ in \chi and crystallization; the Tg values of the other four drugs are given only as below 25 °C zhu2011 X13. (The card gives haloperidol's Tg as below 25 °C, while the classification paper lists 33 °C calculated from the molecular weight; see card-issues.md zhu2011 M1; baird2010 M17.)

Counterexamples and conflicts

None found in the library.

Transfer check

For a drug with a positive \chi or no sign of interaction, do not expect the long period to show its amorphous state: ketoconazole was amorphous but did not change the long period. Check the drug's state directly by WAXS or XRD over 24 h and look for separate amorphous drug domains by another method zhu2011 X7. Do not extend the Tg result beyond about 44 °C at a 25 °C solidification zhu2011 X13.

History

Zhu and co-workers (2011) showed the contrast between F5 and F6 in one study. Zhu and co-workers (2012) confirmed that haloperidol crystallizes ahead of PEG and is unaffected by it zhu2012 R7, C2.

Topic 3 of 4 · 4 findings · F7–F10

Crystallization of drug and carrier after solidification

F7

Topic 3Crystallization of drug and carrier after solidification1 of 4

PEG 3350 turns solid within about two minutes, long before most drugs begin to crystallize.

Pure PEG and 20/80 drug–PEG mixtures were cooled quickly to 25 or 40 °C in a synchrotron beam. At 25 °C PEG was half crystalline after about 22–24 s and complete within 2 min; only haloperidol crystallized before PEG, and benzocaine, ibuprofen and fenofibrate began hours after PEG crystallization was complete zhu2012 R4, C18, R7, R9, R14, R17, C1, C26, C28.

moderateModerate: synchrotron XRD with second resolution, backed by a second synchrotron study, but the replicates are not stated and the cooling rate is not printed zhu2012 X1, X6; zhu2011 R7.

PEG time to 50% crystallinity, shaloperidol/PEG, 25 °C15fenofibrate/PEG, 25 °C21benzocaine/PEG, 25 °C22pure PEG, 25 °Cabout 22–24ibuprofen/PEG, 25 °C26pure PEG, 40 °Cabout 64

At 25 °C PEG is half crystalline within 15–26 s in every dispersion and complete within 2 min. zhu2012 R4, C18, R23.d

Drug crystallizes first, within seconds
haloperidol
PEG first, drug hours later
benzocaineibuprofenfenofibrate

Order of crystallization in the 20/80 dispersions at 25 °C. zhu2012 R7, R9, R14, R17, C1, C26, C28

For your drug

  1. Measure the relative crystallinity of the carrier alone and in the dispersion after the cooling used for manufacture.
  2. If carrier crystallization is complete within minutes, ask whether the drug crystallizes first or stays amorphous, and follow the drug for hours to days (F8); other cooling rates and PEG grades are untested.

zhu2012 P4, R4

How it works and key numbers
  1. At 25 °C PEG crystallizes so fast that its kinetics look alike in different dispersions: the authors speak of the "extremely fast crystallization of PEG" zhu2012 C27.
  2. By about 2 min PEG crystallization is essentially complete, and the authors conclude that PEG crystallizes within a few minutes in all systems zhu2012 C46.
  3. Haloperidol crystallizes before PEG, within seconds, and PEG follows immediately zhu2012 R7, C2.
  4. In benzocaine/PEG the drug "did not begin to crystallize until PEG had completely crystallized"; in ibuprofen/PEG PEG was "much faster" than the drug, and fenofibrate/PEG solidified like ibuprofen/PEG zhu2012 R9, C26, C28.
  5. (synthesis: a drug that is still amorphous when PEG crystallization is complete crystallizes later in a mostly crystalline matrix, the setting of F8 and F9) zhu2012 X13.
Analogy. Like plaster that sets in two minutes: whatever has not crystallized by then is left in the narrow gaps of an already solid framework.
15–26 sPEG time to 50% crystallinity in four dispersions at 25 °Czhu2012 R23.c, R23.d
2 minPEG crystallization complete at both 25 and 40 °Czhu2012 R4, C18
≈15 suncertainty of pure PEG's 40 °C time scale between figures (about 64 against 48 s)zhu2012 X1
Evidence: data, conditions and papers

Finding F7. PEG 3350 solidifies within about two minutes, so a drug that does not crystallize first must crystallize inside an already crystalline carrier

In short. Pure PEG 3350 passed 50% relative crystallinity at about 22–24 s at 25 °C and about 64 s at 40 °C and was complete within 2 min at both temperatures; in 20/80 dispersions at 25 °C the PEG time to 50% was 15 s with haloperidol, 22 s with benzocaine, 26 s with ibuprofen and 21 s with fenofibrate zhu2012 R4, C18, R23.d. In the other synchrotron study the PEG crystal peaks were present from the second frame, 0.2 min after the quench zhu2011 R7. Only haloperidol crystallized before PEG; benzocaine, ibuprofen and fenofibrate began to crystallize hours after PEG crystallization was complete zhu2012 R7, R9, R14, R17, C1, C26, C28.

Type. observation in 5 systems (pure PEG and four dispersions) Strength. synchrotron XRD with seconds resolution, supported by a second synchrotron study, but the replicates are not stated, the cooling rate is not printed and the pure-PEG curve at 40 °C differs by about 15 s between figures (zhu2012 X1, X6; P4).

How it was shown

Zhu and co-workers quench-cooled pure PEG 3350 or 20/80 mixtures to 25 or 40 °C in the synchrotron beam and integrated the PEG crystal peaks to give the relative crystallinity X(t), with time zero at the start of PEG crystallization zhu2012 P4, E1.

What the data show

Pure PEG at 25 °C reached about 47% at 22 s and about 96% at 40 s; at 40 °C it reached about 51% at 64 s zhu2012 R4. In 20/80 dispersions at 25 °C the PEG time to 50% was 15, 22, 26 and 21 s with haloperidol, benzocaine, ibuprofen and fenofibrate zhu2012 R23.c, R23.d. Haloperidol crystallized before PEG, whereas in benzocaine/PEG the drug "did not begin to crystallize until PEG had completely crystallized", and in ibuprofen/PEG and fenofibrate/PEG PEG crystallized much faster than the drug zhu2012 R7, C2, R9, C26, C28.

papersystemresultids
zhu2012pure PEG 3350, 25 °CX 50% at about 22–24 s; about 96% at 40 s; induction −10 szhu2012 R4, R5
zhu2012pure PEG 3350, 40 °CX 51% at about 64 s (Fig. 2); induction 16 szhu2012 R4, R5, X1
zhu2012PEG in haloperidol, benzocaine, ibuprofen, fenofibrate 20/80, 25 °Ct_{50} of PEG 15, 22, 26, 21 s; induction −12, 0, 8, 1 szhu2012 R23.c, R23.d
zhu2012haloperidol/PEG 20/80drug crystallized before PEG, within secondszhu2012 R7
zhu2011pure PEG 3350, 25 °CPEG crystal peaks at q 1.36 and 1.65 Å⁻¹ from 0.2 minzhu2011 R7
Fig. 2 of zhu2012: relative crystallinity of pure PEG against time at 25 and 40 °C
Fig. 2 · zhu2012relative crystallinity of pure PEG against time at 25 and 40 °C

Both curves complete in under 2 min, the 40 °C curve about 41 s later at the midpoint (synthesis: 64 − 23 s) zhu2012 R4.

Why

The authors attribute the similar PEG kinetics in different dispersions at 25 °C to the "extremely fast crystallization of PEG" there, and conclude that PEG crystallizes within a few minutes in all systems zhu2012 C27, C46. (synthesis: a drug that is still amorphous when PEG crystallization is complete crystallizes later in a mostly crystalline matrix, the setting of F8 and F9 zhu2012 X13.)

Limits and transfer

Cooling rate, hold time and replicates are not stated, and pure PEG at 40 °C reaches 51% at about 64 s in one figure but at about 48 s in two others zhu2012 P4, X6, X1. Measure the relative crystallinity of the carrier alone and in the dispersion after the manufacturing cooling; if carrier crystallization is complete within minutes, ask whether the drug crystallizes first, and follow it for hours to days (F8).

How it was shown

Zhu and co-workers melted pure PEG 3350 or 20/80 physical mixtures in aluminium DSC pans in a Linkam stage in the synchrotron beam (17 keV), held them above the drug melting point until all diffraction peaks had disappeared and quench-cooled them to 25 or 40 °C zhu2012 P4. The two PEG crystal peaks (q 1.35 and 1.65 Å⁻¹) were integrated against the total area by curve fitting to give an apparent crystallinity, normalized to its final value to give the relative crystallinity X(t) = \Phi_{peg}(t)/\Phi_{peg}(\infty), with time zero at the start of PEG crystallization zhu2012 P4, E1. The induction time is the time to the first detected crystals and is negative when crystallization began before the set temperature was reached zhu2012 R5. The Avrami equation X(t) = 1 - \exp(-z\,t^{n}) was fitted to the pure-PEG curves zhu2012 E2, R6. In the SAXS/WAXS study the same beamline was used at 25 °C with frames from 0.2 min zhu2011 P2, R7.

What the data show

Pure PEG at 25 °C reached about 13% at 10 s, about 47% at 22 s, about 88% at 30 s, about 96% at 40 s and about 99% at 80–120 s; at 40 °C it stayed near zero for about 12 s, reached about 51% at 64 s and about 89% at 90 s, and about 95% by 120–150 s zhu2012 R4. The induction time was −10 s at 25 °C, meaning that PEG began to crystallize before 25 °C was reached, and 16 s at 40 °C zhu2012 R5. The fitted Avrami exponent was below 1 at both temperatures (values not printed), read by the authors as one-dimensional growth ("This suggested"), as reported for very fast growth zhu2012 R6, C19. In the dispersions at 25 °C PEG started within seconds (induction times −12, 0, 8 and 1 s for haloperidol, benzocaine, ibuprofen and fenofibrate) and reached 50% in 15, 22, 26 and 21 s zhu2012 R23.c, R23.d. The curves still differ somewhat: PEG in haloperidol/PEG reached 50% sooner than pure PEG, PEG in benzocaine/PEG followed pure PEG to about 58% and levelled off lower (about 94% against about 99% at 120 s), and PEG in ibuprofen/PEG lagged slightly zhu2012 R8, R12, R16, R20, X3, X4. In the SAXS/WAXS study the PEG crystal peaks appeared immediately after the quench and did not move, and the crystalline haloperidol peak was already present in the first frame zhu2011 R7, R9.

The order of crystallization differs by drug. Haloperidol began to crystallize before PEG and was completely crystalline within a few seconds, with PEG following immediately zhu2012 R7, C2. In benzocaine/PEG the drug "did not begin to crystallize until PEG had completely crystallized", in ibuprofen/PEG PEG crystallization was "much faster" than the drug's, and fenofibrate/PEG solidified like ibuprofen/PEG zhu2012 R9, C26, C28.

papersystemmethod and conditionsresultids
zhu2012pure PEG 3350, 25 °Csynchrotron XRD, quenchX 50% at about 22–24 s; about 96% at 40 s; induction −10 sR4, R5
zhu2012pure PEG 3350, 40 °Cas aboveX 51% at about 64 s (Fig. 2); induction 16 sR4, R5, X1
zhu2012PEG in haloperidol, benzocaine, ibuprofen, fenofibrate 20/80, 25 °Cas abovet_{50} of PEG 15, 22, 26, 21 s; induction −12, 0, 8, 1 sR23.c, R23.d
zhu2012haloperidol/PEG 20/80as abovedrug crystallized before PEG, within secondsR7
zhu2011pure PEG 3350, 25 °CSAXS/WAXSPEG crystal peaks at q 1.36 and 1.65 Å⁻¹ from 0.2 minR7
zhu2011haloperidol/PEG 20/80as abovehaloperidol peak in the first frameR9

Figure

Fig. 2 of zhu2012: relative crystallinity of pure PEG against time at 25 and 40 °C
Fig. 2 · zhu2012relative crystallinity of pure PEG against time at 25 and 40 °C

Diamonds are 25 °C and squares 40 °C; both curves complete in under 2 min, the 40 °C curve about 41 s later at the midpoint (synthesis: 64 − 23 s) zhu2012 R4.

Why

The authors take the similarity of PEG kinetics at 25 °C in different dispersions to arise from the "extremely fast crystallization of PEG" at that temperature, with larger differences at 40 °C (F10) zhu2012 C27, C43. They conclude that in practice PEG crystallizes within a few minutes in all systems, and that how a changed PEG crystallization rate influences the dispersion microstructure is not known zhu2012 C46. (synthesis: since PEG crystallization is nearly complete within one to two minutes, a drug that is still amorphous at that point remains in the non-crystalline volume of PEG, so its later crystallization at 25 °C takes place in a mostly crystalline matrix, which is the setting of F8 and F9. The card's extractor notes that the drug was concentrated in the remaining non-crystalline fraction zhu2012 X13.)

Conditions and limits

PEG 3350, 20/80 w/w, quench to 25 or 40 °C; the cooling rate, hold time above the melting point, frame exposure and sample mass are not printed zhu2012 P4; zhu2011 P2. The fitted Avrami exponent and constant are not printed, and the reading of n < 1 as one-dimensional growth is qualitative, since on the authors' own scheme n = 1 is already the lowest value zhu2012 R6, X9. In Fig. 2 pure PEG at 40 °C reaches 51% at about 64 s, while in Figs. 11 and 15, with the same legend, it reaches 51% at about 48 s, so the 40 °C time scale of pure PEG is uncertain by about 15 s zhu2012 X1. The number of replicate runs is not stated zhu2012 X6. Slower cooling, other PEG grades and bulk samples were not studied.

Counterexamples and conflicts

None found in the library for the speed of PEG solidification. The text calls PEG kinetics in haloperidol/PEG "essentially the same" as pure PEG although PEG in haloperidol/PEG reaches 50% at about 15 s against about 23 s zhu2012 C21, X3.

Transfer check

Measure the relative crystallinity of the carrier alone and in the dispersion after the cooling used for manufacture; if carrier crystallization is complete within minutes, ask whether the drug crystallizes first (a fast crystallizer in the sense of the neat-drug classes) or remains amorphous, and then follow the drug for hours to days (F8). For other cooling rates or PEG grades, the time scale is untested.

History

Zhu and co-workers (2011) saw the PEG crystal peaks in the first seconds and the haloperidol peak in the first frame zhu2011 R7, R9. Zhu and co-workers (2012) quantified the PEG kinetics at 25 and 40 °C, alone and with four drugs, and found the same order for haloperidol zhu2012 R4, R7, R23.

F8

Topic 3Crystallization of drug and carrier after solidification2 of 4

PEG can delay, leave unchanged or accelerate a drug's crystallization, depending on the drug.

Each pure drug and its 20/80 melt with PEG 3350 were held at 25 °C and watched for the first crystals. Benzocaine crystallized in seconds as a pure melt but only after 120–180 min in PEG; haloperidol crystallized as fast as the neat drug; ibuprofen and fenofibrate, which mostly did not crystallize within weeks as neat melts, began after about 100 and 120–180 min in PEG zhu2012 R23.a, R1, R2, R3.

moderateModerate to strong: two methods in each paper agree on the onsets, but the replicate number is unstated and the neat-drug tests stop at 3 weeks zhu2012 X5, X6, X7.

Onset in 20/80 PEG 3350 at 25 °C, minibuprofenneat: 10 of 50 in 3 weeks · soonerabout 100benzocaineneat: seconds · delayed120–180fenofibrateneat: 17 of 50 in 3 weeks · sooner120–180

Haloperidol is not shown: it crystallized within seconds in PEG, as the neat drug does. Benzocaine is delayed; ibuprofen and fenofibrate start sooner than most neat samples. zhu2012 R1, R2, R3, R23.a

Neat melts: started after 3 weeks, of 50ibuprofen10 of 50fenofibrate17 of 50

In the dispersions the same two drugs start within hours. zhu2012 R2, R3

For your drug

  1. Time the neat drug at the storage temperature on many samples (the 2012 study used 50), then quench the dispersion at the intended ratio and follow the drug by XRD and two Raman bands, or by SAXS/WAXS, from minutes to at least 24 h, noting whether PEG crystallization is complete before the drug begins to crystallize.
  2. Compare the drug melting point in the dispersion with that of the neat drug to see how much PEG lowers the supercooling, and test for nucleation on crystalline PEG as in F9; do not assume that a slowly crystallizing neat drug stays amorphous in PEG.

zhu2012 P2, P3, P5, P6, C32

How it works and key numbers
  1. Haloperidol crystallizes faster than PEG and is practically insoluble in it, so PEG has no effect on its crystallization zhu2012 C2, C39, M1.
  2. Benzocaine's delay "is thought to be caused by the entropic mixing effects" and by melting point depression: at 20:80 it melts around 48 °C against around 89 °C for the pure drug, so supercooling and driving force at 25 °C are much smaller; both values are cited and the supercooling in the dispersion was not measured zhu2012 C32, C33, M3.
  3. For ibuprofen and fenofibrate the earlier onset, despite melting point depressions of about 30 and 20 °C, is attributed to nucleation on crystalline PEG (F9) zhu2012 C34, C4.
  4. In their summary the link between the crystallization rate of the pure drug and in the dispersion "was found to break down for the slowly crystallizing compounds" zhu2012 C41.
To feel the numbers. With the cited melting points, the supercooling of benzocaine at 25 °C falls from 89 − 25 = 64 K to 48 − 25 = 23 K, about 36% of the neat value (23 ÷ 64 = 0.36).
120–180 min vs secondsbenzocaine in 20/80 PEG against the neat drugzhu2012 R23.a, R1
10 of 50neat ibuprofen samples started after 3 weeks; in PEG the onset is about 100 minzhu2012 R2, R23.a
111 minibuprofen turns crystalline in the SAXS/WAXS study (amorphous at 100 min)zhu2011 R15

Connections to other chapters

Evidence: data, conditions and papers

Finding F8. PEG can delay, leave unchanged or bring forward the crystallization of a drug, and the amorphous drug in the dispersion crystallizes over minutes to hours at 25 °C

In short. In 20/80 comelts at 25 °C, benzocaine began to crystallize after 120–180 min although the neat drug crystallizes within seconds; haloperidol crystallized within seconds, as neat; ibuprofen and fenofibrate began after about 100 and 120–180 min, whereas only 10 of 50 neat ibuprofen and 17 of 50 neat fenofibrate samples had started after 3 weeks zhu2012 R23.a, R1, R2, R3. The SAXS/WAXS study of the same ratio gave consistent times: ibuprofen crystalline at 111 min and amorphous at 100 min, benzocaine amorphous at 30 min, chlorpropamide and nilutamide partially crystalline at 24 h, ketoconazole still amorphous at 24 h zhu2011 R15, R18. The authors conclude that PEG "can delay, promote or have no influence" on drug crystallization zhu2012 C6.

Type. observation in 7 drugs, with four drugs followed by kinetics and three drugs in both papers Strength. to strong — two methods in each paper (XRD and two Raman bands; SAXS and WAXS) agree on the onsets, but the number of replicate runs is unstated, the haloperidol values have no stated method and the neat-drug statistics stop at 3 weeks (zhu2012 K1: strong; K2: moderate; K3: moderate to strong; X5, X6, X7).

How it was shown

Zhu and co-workers (2012) held pure drug melts at 25 °C under a polarized light microscope, following 50 samples each of ibuprofen and fenofibrate for about 500 h, and measured 20/80 comelts at intervals by XRD and Raman marker bands zhu2012 P2, P3, P5, P6. Zhu and co-workers (2011) followed six drugs at 20/80 by SAXS/WAXS for about 30 min and at 24 h zhu2011 P2, P7.

What the data show

Neat haloperidol and benzocaine crystallized within seconds, whereas neat ibuprofen and fenofibrate had started in only 10 and 17 of 50 samples after 3 weeks zhu2012 R1, R2, R3. In the comelts benzocaine began after 120–180 min, ibuprofen after about 100 min and fenofibrate after 120–180 min, while haloperidol was crystalline within seconds zhu2012 R23.a. The authors conclude that PEG "can delay, promote or have no influence" on drug crystallization zhu2012 C6.

drugneat melt at 25 °C20/80 PEG 3350 at 25 °Cids
haloperidolcrystalline within secondsonset −100 s, t_{50} 7 s (method not stated); crystalline from first SAXS/WAXS framezhu2012 R1, R23.a, R23.b, X7; zhu2011 R9
benzocainecrystalline within secondsonset 120–180 min, t_{50} 110–170 minzhu2012 R1, R23.a, R23.b
ibuprofen2/50 started within 1 h; 10/50 after 3 weeksonset about 100 min, t_{50} about 70 min; above 90% at 4 hzhu2012 R2, R23.a, R23.b, R14
fenofibrate4/50 started within 1 h; 17/50 after 3 weeksonset 120–180 min, t_{50} 140–200 minzhu2012 R3, R23.a, R23.b
chlorpropamidewithin a few hoursamorphous at 30 min; partially crystalline at 24 hzhu2011 R6, R13, R18.c
ketoconazoleamorphous, not crystallized at 24 hamorphous at 30 min and at 24 hzhu2011 R6, R17, R18.f
Fig. 6 of zhu2012: relative crystallinity of benzocaine in the benzocaine/PEG 20/80 dispersion against time, from Raman bands at 1573 and 1680 cm-1
Fig. 6 · zhu2012relative crystallinity of benzocaine in the benzocaine/PEG 20/80 dispersion against time, from Raman bands at 1573 and 1680 cm-1

Onset after about 150–200 min, 50% at about 290 min and near-complete crystallinity after 600 min zhu2012 R11.

Why

Haloperidol crystallizes faster than PEG and is practically insoluble in it, so PEG has no effect on its crystallization zhu2012 C2, C39, M1. Benzocaine's delay "is thought to be caused by the entropic mixing effects" and by melting point depression: at 20:80 it melts around 48 °C against around 89 °C for the pure drug, so supercooling and driving force are much smaller zhu2012 C32, C33, M3. For ibuprofen and fenofibrate the earlier onset is attributed to nucleation on crystalline PEG (F9) zhu2012 C34, C4.

Limits and transfer

One composition and temperature; replicates are not stated, and the neat-drug tests stop at 504 h with 40 of 50 ibuprofen and 33 of 50 fenofibrate samples uncrystallized zhu2012 X6, X5, C3. Do not assume that a drug that is slow as a neat melt stays amorphous in PEG; follow the real dispersion by XRD and Raman for at least 24 h.

How it was shown

Zhu and co-workers (2012) melted each pure drug on a hot plate and held it at 25 °C under a polarized light microscope; for ibuprofen and fenofibrate 50 samples each were followed for about 500 h, recording P(t), the fraction that had started to crystallize by time t, because their induction times varied widely zhu2012 P2, P3. The 20/80 comelts were stored over phosphorus pentoxide and measured at intervals by laboratory XRD (Cu Kα, 2θ 4–30°) and by Raman spectroscopy, with marker bands at 1573 and 1680 cm⁻¹ (benzocaine), 746 and 784 cm⁻¹ (ibuprofen) and 1419 and 1648 cm⁻¹ (fenofibrate); haloperidol was too fast for XRD zhu2012 P5, P6, R7. The induction time and t_{50} (time from onset to 50% relative crystallinity, induction not included) of each drug are in Table 1 zhu2012 R23. Zhu and co-workers (2011) followed six drugs at 20/80 and 25 °C by SAXS/WAXS for about 30 min (about 116 and 131 min for chlorpropamide and ibuprofen) and once at 24 h, and observed the pure melts under the microscope after cooling to room temperature zhu2011 P2, P7, R6.

What the data show

Neat haloperidol and benzocaine crystallized before the samples reached 25 °C and were fully crystalline within a few seconds zhu2012 R1. Neat ibuprofen stepped from 2/50 within 1 h to 10/50 (0.20) after 3 weeks, neat fenofibrate from 4/50 within 1 h to 17/50 (0.34), then stayed at 0.34 to 504 h zhu2012 R2, R3. In the dispersions, benzocaine showed no XRD peak at 30 min and a peak at 180 min; the Raman band at 1680 cm⁻¹ appeared at 180 min; crystallinity was about 20% at 200 min, about 50% at 290 min and about 92% at 530 min (text: about 10 h to 90%; plot: about 8 h) zhu2012 R9, R10, R11, X12. Ibuprofen's XRD peak was absent at 20 min and present from 120 min; Raman gave about 100 min induction, about 57–61% at 180 min and about 91–94% at 240 min zhu2012 R13, R14. Fenofibrate's XRD peaks appeared from 240 min and Raman crystallinity rose from about 8% at 180 min to about 54% at 330 min and about 92% at 510 min zhu2012 R17, R18. In the SAXS/WAXS study the neat melts of chlorpropamide, nilutamide and ibuprofen crystallized within a few hours and ketoconazole not within 24 h, and in the blends benzocaine and chlorpropamide were amorphous at 30 min (chlorpropamide WAXS not shown, its long period unchanged to about 115 min), ibuprofen for about 100 min, nilutamide at 30 min and ketoconazole at 24 h zhu2011 R6, R11, R13, R14, R16, R17. Haloperidol was crystalline from the first frame zhu2011 R9.

paperdrugneat melt at 25 °C20/80 PEG 3350 at 25 °Cids
zhu2012haloperidolcrystalline within secondsonset −100 s, t_{50} 7 s (method not stated); crystalline from first SAXS/WAXS frameR1, R23.a, R23.b, X7; zhu2011 R9
zhu2012benzocainecrystalline within secondsonset 120–180 min, t_{50} 110–170 min; 90% at about 8–10 hR1, R23.a, R23.b, R11, X12
zhu2012ibuprofen2/50 started within 1 h; 10/50 after 3 weeksonset about 100 min, t_{50} about 70 min; above 90% at 4 hR2, R23.a, R23.b, R14
zhu2012fenofibrate4/50 started within 1 h; 17/50 after 3 weeksonset 120–180 min, t_{50} 140–200 min; 90% at about 8–9 hR3, R23.a, R23.b, R18, X12
zhu2011benzocainecrystallized at onceamorphous at 30 min; partially crystalline at 24 hR6, R11, R18.b
zhu2011chlorpropamidewithin a few hoursamorphous at 30 min (WAXS not shown; long period unchanged to about 115 min); partially crystalline at 24 hR6, R13, R18.c
zhu2011ibuprofenwithin a few hoursamorphous at 100 min; crystalline peak at 111 minR6, R15
zhu2011nilutamidenot at once; within a few hoursamorphous at 30 min; partially crystalline at 24 hR6, R16, R18.e
zhu2011ketoconazoleamorphous, not crystallized at 24 hamorphous at 30 min and at 24 hR6, R17, R18.f

(synthesis: ibuprofen was followed in both papers, at the same 20/80 ratio and 25 °C, by Raman (onset about 100 min) and by SAXS/WAXS (amorphous at 100 min, crystalline at 111 min), so two methods give the same time scale zhu2012 R14; zhu2011 R15.) (synthesis: relative to the neat drug, PEG therefore delayed benzocaine from seconds to hours, did not change haloperidol and advanced ibuprofen and fenofibrate from weeks, for most samples, to hours zhu2012 R1, R2, R3, R23.a.)

(synthesis: the neat-drug classes of the chapter Crystallization tendency sort the first two outcomes but not the third. Haloperidol and benzocaine are class I-A and chlorpropamide class I-B; ibuprofen, fenofibrate, ketoconazole and nilutamide are class III. The class III drugs behave differently in PEG: ibuprofen and fenofibrate began after about 100 and 120–180 min, nilutamide was partially crystalline and ketoconazole not crystalline at 24 h baird2010 R1, R3, M9, M17, M12, M39, M38, M42, M46; zhu2012 R23.a; zhu2011 R18.e, R18.f. See F17 of that chapter.)

Figure

Fig. 6 of zhu2012: relative crystallinity of benzocaine in the benzocaine/PEG 20/80 dispersion against time, from Raman bands at 1573 and 1680 cm-1
Fig. 6 · zhu2012relative crystallinity of benzocaine in the benzocaine/PEG 20/80 dispersion against time, from Raman bands at 1573 and 1680 cm-1

Onset after about 150–200 min, 50% at about 290 min and near-complete crystallinity after 600 min; both Raman bands give the same curve zhu2012 R11, C23.

Fig. 9 of zhu2012: relative crystallinity of ibuprofen in the ibuprofen/PEG 20/80 dispersion against time
Fig. 9 · zhu2012relative crystallinity of ibuprofen in the ibuprofen/PEG 20/80 dispersion against time

Onset at about 100 min and more than 90% at 240 min zhu2012 R14.

Why

The authors set out to test whether the crystallization tendency of the pure drug, combined with its ability to interact with the polymer, decides the outcome zhu2012 C13. Haloperidol crystallizes faster than PEG and is practically insoluble in it, so PEG has no effect on its crystallization, in the authors' account zhu2012 C2, C39, M1. For benzocaine the delay "is thought to be caused by the entropic mixing effects" and favourable benzocaine–PEG interactions that depress the benzocaine melting point: at 20:80, below the eutectic composition, it melts at the eutectic, around 48 °C, against around 89 °C for the pure drug, so the supercooling at 25 °C and the driving force are much smaller; with a Tg of −31 °C the authors find the supposition that the cause is thermodynamic rather than kinetic "reasonable" zhu2012 C32, C33, M3. (synthesis: with the cited values the supercooling at 25 °C falls from 89 − 25 = 64 K to 48 − 25 = 23 K, to about 36% of the neat value zhu2012 M3.) Both values are cited from earlier work and the supercooling and mobility in the dispersion were not measured zhu2012 C32, C33. For ibuprofen and fenofibrate the earlier onset despite melting point depressions of about 30 and 20 °C is attributed to nucleation on crystalline PEG (F9) zhu2012 C34, C4. In their summary the link between the crystallization rate of the pure drug and in the dispersion "was found to break down for the slowly crystallizing compounds" zhu2012 C41. Benzocaine in the SAXS/WAXS study stayed amorphous for 30 min in the blend although the neat drug crystallizes at once; the authors relate this "most likely" to the lower supercooling of benzocaine in the blend, 55 against 92 °C zhu2011 C20, R1.

Conditions and limits

One composition (20/80 w/w), PEG 3350, solidification at 25 °C, comelts; the number of replicate kinetic runs is not stated and Table 1 gives ranges zhu2012 X6. Neat-drug statistics stop at 504 h, when 40 of 50 ibuprofen and 33 of 50 fenofibrate samples had not crystallized, so the abstract's "hours to months" is not measured zhu2012 X5, C3. The haloperidol values of Table 1 have no stated method although the text says the kinetics were too fast for XRD zhu2012 X7. The instrument of Figs. 4, 8 and 12 is not stated zhu2012 X8. The 24 h states in the SAXS/WAXS study rest on WAXS patterns that are not shown, and chlorpropamide WAXS is not shown at all zhu2011 X12. Lower loadings, other PEG grades and storage temperatures were not tested zhu2012 A1, A3.

Counterexamples and conflicts

The 2011 paper says that the neat melts of chlorpropamide, nilutamide and ibuprofen crystallized within a few hours, whereas the 2012 statistics of 50 samples show neat ibuprofen starting in only 2 of 50 samples within 1 h and 10 of 50 within 3 weeks zhu2011 R6; zhu2012 R2. (synthesis: the 2012 authors read the spread as the stochastic nature of nucleation, with the chance of starting low over hours to days zhu2012 C16, C17; a single melt observed in 2011 is then not decisive, so whether PEG advances ibuprofen rests on the 50-sample statistics.) (synthesis: without a statistic of the same kind for the neat drugs, nilutamide and ketoconazole cannot be said to be advanced or delayed zhu2011 R6, R16, R17.) The text times to 90% (about 10 h for benzocaine, about 9 h for fenofibrate) are longer than the plots (about 8.3 h) zhu2012 X12.

Transfer check

For a new drug in a PEG comelt: (1) time the neat drug at the storage temperature on many samples (the 2012 study used 50) because the spread is large; (2) quench the dispersion at the intended ratio and follow the drug by XRD and by two Raman bands, or by SAXS/WAXS, from minutes to at least 24 h, noting whether PEG crystallization is complete before the drug begins to crystallize; (3) compare the drug melting point in the dispersion with that of the neat drug to see how much PEG lowers the supercooling; (4) test for nucleation on crystalline PEG as in F9. Until then do not assume that a drug which is slow as a neat melt will stay amorphous in PEG; the authors state that the drug should be fully amorphous or fully crystalline at administration, not a mixture zhu2012 C37.

History

Zhu and co-workers (2011) gave the first time courses, over 30 min and 24 h, for six drugs and showed which stayed amorphous zhu2011 R18. Zhu and co-workers (2012) followed four of them over hours by two methods and compared them with neat-drug statistics, concluding that PEG can delay, promote or have no influence zhu2012 C6. The finding that the neat-drug class does not predict the behaviour of slow crystallizers in PEG dispersions is taken up in the chapter Crystallization tendency.

F9

Topic 3Crystallization of drug and carrier after solidification3 of 4

A crystal of PEG can seed drug crystals: ibuprofen and fenofibrate crystallize at its surface within minutes.

A small piece of crystalline PEG was dropped into supercooled liquid ibuprofen or fenofibrate at 25 °C. A drug crystal appeared at the PEG surface within a few minutes and none in the bulk liquid zhu2012 R15, R19. The authors conclude that crystalline PEG is a favourable nucleation site ("it appears"), which would explain why the dispersions begin to crystallize earlier than most neat samples zhu2012 C4, C34, R23.a.

moderateModerate: the seeding images and the shorter onsets are direct, but seeding was done in pure drug, nucleation inside the dispersion was not observed and the alternative route was not tested zhu2012 X13.

Neat melts: share of 50 startedibuprofen · 1 h2 of 500.04ibuprofen · 3 weeks10 of 500.20fenofibrate · 1 h4 of 500.08fenofibrate · 3 weeks17 of 500.34

Share of 50 neat melt samples at 25 °C that had started to crystallize; even after 3 weeks most had not. zhu2012 R2, R3

Onset in 20/80 PEG dispersion, minibuprofenmelting point depression about 30 °Cabout 100fenofibratemelting point depression about 20 °C120–180

The dispersions start within hours although the melting point is depressed, which lowers the driving force. zhu2012 R23.a, C34

For your drug

  1. Test a crystalline carrier directly: place a small piece in the supercooled neat drug at the storage temperature and look for crystals at the interface under a polarized light microscope.
  2. Run enough dispersion samples to see the spread (the neat-drug tests used 50). If crystals form at the interface, treat the neat-drug class as a risk flag, not a prediction, and measure the actual dispersion.

zhu2012 P7, P3

How it works and key numbers
  1. Seeding test: a drug crystal formed at the PEG interface within minutes, and none in the bulk supercooled liquid zhu2012 R15, R19.
  2. The authors write "it appears that crystalline PEG acted as a favorable heterogeneous nucleation site", and made the seeding tests "to further confirm this hypothesis" zhu2012 C4.
  3. They read the wide spread of induction times in the neat drugs as the stochastic nature of nucleation zhu2012 C16, C17.
  4. The extractor's reservation: PEG crystallized first, so the drug was concentrated in the remaining non-crystalline fraction, and seeding in pure supercooled drug cannot separate the two routes zhu2012 X13, M3, M4.
Analogy. Sugar crystals appear first on a string dipped into syrup, not in the clear syrup: a ready-made surface makes the formation of the first crystal (nucleation) easy.
a few mintime for a drug crystal to appear at the PEG surface, none in the bulkzhu2012 R15, R19
about 100 minibuprofen onset in the dispersion; only 10 of 50 neat samples started in 3 weekszhu2012 R23.a, R2
about 30 and 20 °Cmelting point depression of ibuprofen and fenofibrate with PEG, which lowers the driving forcezhu2012 C34

Connections to other chapters

Evidence: data, conditions and papers

Finding F9. Crystalline PEG nucleates slowly crystallizing drugs: ibuprofen and fenofibrate crystallize at a PEG particle, and their onset in the dispersion is earlier than for the neat drug

In short. A small piece of crystalline PEG placed in supercooled liquid ibuprofen or fenofibrate at 25 °C produced a drug crystal at the PEG interface within a few minutes and none in the bulk liquid zhu2012 R15, R19. The authors conclude that crystalline PEG acts as a favourable heterogeneous nucleation site ("it appears") and that this is why the dispersions began to crystallize after about 100 and 120–180 min, earlier than most neat samples, although melting point depression of about 30 °C (ibuprofen) and about 20 °C (fenofibrate) lowers their driving force zhu2012 C4, C34, R23.a. The seeding was done in pure supercooled drug, not in the dispersion, and another route, enrichment of the drug in the residual melt, is not excluded zhu2012 X13.

Type. single-system observations in 2 drugs Strength. the seeding images and the shorter onsets are direct, but nucleation inside the dispersion was not observed and the alternative route was not tested (zhu2012 K4: moderate; K3: moderate to strong; X13).

How it was shown

Zhu and co-workers placed a small piece of crystalline PEG into supercooled liquid ibuprofen or fenofibrate at 25 °C and watched it under a polarized light microscope zhu2012 P7. For comparison they used the fraction of 50 neat-drug melts that had started to crystallize over about 500 h and the onset in 20/80 comelts (F8) zhu2012 P3, P5, P6.

What the data show

An ibuprofen crystal formed at the PEG interface after a few minutes with none in the bulk liquid, and fenofibrate crystallized "immediately adjacent to the PEG particle" zhu2012 R15, R19. Neat ibuprofen and fenofibrate had started in 10 and 17 of 50 samples after 3 weeks, but in the dispersions the onset was at about 100 min and 120–180 min, although melting point depressions of about 30 and 20 °C lower the driving force zhu2012 R2, R3, R23.a, C34.

papersystemresultids
zhu2012neat ibuprofen, 50 melt samples at 25 °C2/50 within 1 h; 10/50 (0.20) after 3 weekszhu2012 R2
zhu2012neat fenofibrate, as above4/50 within 1 h; 17/50 (0.34) after 3 weekszhu2012 R3
zhu2012supercooled ibuprofen with a crystalline PEG piececrystal at the PEG interface after a few minutes, none in the bulkzhu2012 R15
zhu2012supercooled fenofibrate with a crystalline PEG piececrystal next to the PEG particle within minutes, none elsewherezhu2012 R19
zhu2012ibuprofen and fenofibrate in 20/80 PEG 3350onset about 100 min and 120–180 minzhu2012 R23.a
zhu2011ibuprofen in 20/80 PEG 3350amorphous at 100 min, crystalline at 111 minzhu2011 R15
Fig. 10 of zhu2012: an ibuprofen crystal growing from a crystalline PEG particle in supercooled liquid ibuprofen
Fig. 10 · zhu2012an ibuprofen crystal growing from a crystalline PEG particle in supercooled liquid ibuprofen

The dashed circle marks the ibuprofen crystal at the PEG edge; the surrounding supercooled ibuprofen contains no visible crystals zhu2012 R15.

Why

The authors write "it appears that crystalline PEG acted as a favorable heterogeneous nucleation site" and ran the seeding tests "to further confirm this hypothesis" zhu2012 C4. The extractor's reservation: PEG crystallized first, so the drug was concentrated in the remaining non-crystalline fraction, and seeding tests in pure supercooled drug cannot separate the two routes zhu2012 X13.

Limits and transfer

Two drugs, one PEG grade, one composition; the number of seeding tests is not stated and nucleation inside the dispersions was not observed zhu2012 P7, X6. Whether other class III drugs are nucleated by PEG was not tested: nilutamide was partially crystalline and ketoconazole amorphous at 24 h zhu2011 R18.e, R18.f; baird2010 R1, M46, M42. Test a crystalline carrier by placing a piece in the supercooled neat drug and looking for interface crystals; if crystals form there, measure the actual dispersion rather than relying on the neat-drug class.

How it was shown

Zhu and co-workers placed a small piece of crystalline PEG into supercooled liquid ibuprofen or fenofibrate at 25 °C and watched it under a polarized light microscope zhu2012 P7. For the comparison with the neat drugs they recorded P(t), the fraction of 50 melt samples that had started to crystallize by time t at 25 °C, for about 500 h zhu2012 P3. The onset in the dispersions came from laboratory XRD and Raman on 20/80 comelts stored at 25 °C (F8) zhu2012 P5, P6.

What the data show

In the seeding test, an ibuprofen crystal formed at the interface between molten ibuprofen and crystalline PEG after a few minutes, with no nuclei visible in the bulk supercooled liquid; fenofibrate crystallized "immediately adjacent to the PEG particle" within a few minutes with no crystallites elsewhere (scale bars 200 µm) zhu2012 R15, R19. For the neat drugs, P(t) of ibuprofen was about 0.04 (2 of 50) from about 1 to about 62 h, about 0.12 from about 72 to about 134 h, about 0.14 from about 168 to about 315 h and about 0.20 from about 336 to about 504 h; fenofibrate's was about 0.08 at about 1 h, about 0.20 at about 8–14 h and about 0.34 from about 96 to about 504 h zhu2012 R2, R3. In the 20/80 dispersions the onset was consistently earlier: about 100 min for ibuprofen and 120–180 min for fenofibrate, with more than 90% crystallinity at 4 h and 9 h zhu2012 R23.a, R14, R18, C3. The two drugs form eutectics with PEG, with melting point depressions of about 30 and 20 °C (the plot of fenofibrate shows about 24 °C), which would lower the driving force zhu2012 C34, X11, R24. In the SAXS/WAXS study the ibuprofen dispersion crystallized at about 111 min zhu2011 R15.

papersystemmethod and conditionsresultids
zhu2012neat ibuprofen50 melt samples at 25 °C, microscopy, to 504 h2/50 within 1 h; 10/50 (0.20) after 3 weeksR2
zhu2012neat fenofibrateas above4/50 within 1 h; 17/50 (0.34) after 3 weeksR3
zhu2012supercooled ibuprofen with a crystalline PEG piecemicroscopy, 25 °Ccrystal at the PEG interface after a few minutes, none in the bulkR15
zhu2012supercooled fenofibrate with a crystalline PEG pieceas abovecrystal next to the PEG particle within minutes, none elsewhereR19
zhu2012ibuprofen and fenofibrate in 20/80 PEG 3350XRD and Raman, 25 °Conset about 100 min and 120–180 minR23.a
zhu2011ibuprofen in 20/80 PEG 3350SAXS/WAXS, 25 °Camorphous at 100 min, crystalline at 111 minR15

Figure

Fig. 10 of zhu2012: an ibuprofen crystal growing from a crystalline PEG particle in supercooled liquid ibuprofen
Fig. 10 · zhu2012an ibuprofen crystal growing from a crystalline PEG particle in supercooled liquid ibuprofen

The dashed circle marks the ibuprofen crystal at the PEG edge; the surrounding supercooled ibuprofen contains no visible crystals zhu2012 R15.

Fig. 1 of zhu2012: probability that pure ibuprofen (top) and fenofibrate (bottom) have started to crystallize against time at 25 °C
Fig. 1 · zhu2012probability that pure ibuprofen (top) and fenofibrate (bottom) have started to crystallize against time at 25 °C

Ibuprofen steps to 0.2 and fenofibrate levels at 0.34 over about 500 h zhu2012 R2, R3.

Why

The authors' account: "it appears that crystalline PEG acted as a favorable heterogeneous nucleation site", thought to explain the shorter induction times, and the seeding tests were made "to further confirm this hypothesis" zhu2012 C4. Polymers have been shown to act as heteronuclei for organic molecules and even to select the polymorph, though in solution rather than melt crystallization (a study outside the library), and most studies of drugs in polymers find that the polymer retards crystallization, which makes the promotion by PEG of particular interest zhu2012 C35, C36. Because the induction times of the neat drugs vary widely between samples, the authors read the spread as the stochastic nature of nucleation zhu2012 C16, C17. The extractor's reservation: PEG crystallized first in every system, within about 2 min, so the drug was concentrated in the remaining non-crystalline fraction, and by the table of estimated solubilities benzocaine (28%) and ibuprofen (25%) exceed the 20% loading in supercooled PEG yet crystallized; local enrichment of the residual melt could shorten the induction as well, and the seeding tests, run in pure supercooled drug, cannot separate the two routes zhu2012 X13, M3, M4. The authors add that faster nucleation could change crystal size distribution and so the dissolution of the dispersion; nothing was measured on this zhu2012 C42.

Conditions and limits

Two drugs, one PEG grade, 25 °C, one composition. The size of the PEG pieces and the number of seeding tests are not stated, and the number of replicate dispersion runs is not stated zhu2012 P7, X6. Pure-drug induction was followed only to 504 h, so "hours to months" for the neat drugs is not measured zhu2012 X5. Nucleation inside the dispersions was not observed. Whether other class III drugs are nucleated by crystalline PEG was not tested; in the same PEG at the same ratio nilutamide, also class III, was partially crystalline and ketoconazole, class III, amorphous at 24 h zhu2011 R18.e, R18.f; baird2010 R1, M46, M42.

Counterexamples and conflicts

A single melt of ibuprofen observed in 2011 crystallized within a few hours zhu2011 R6, whereas 50 samples in 2012 gave 2 starting within 1 h and 10 after 3 weeks zhu2012 R2. (synthesis: the spread is read by the 2012 authors as stochastic nucleation zhu2012 C16, C17, so one melt is not decisive; see F8.) None found in the library for the seeding result itself.

Transfer check

Test a crystalline carrier by placing a piece of it in the supercooled neat drug at the storage temperature and looking for crystals at the interface zhu2012 P7. Run enough dispersion samples to see the spread (the neat-drug tests used 50). If crystals form at the interface, a slow crystallizer cannot be assumed to remain amorphous in the carrier; read the neat-drug class (the chapter Crystallization tendency) as a risk flag, not as a prediction, and prefer to measure the actual dispersion.

History

The idea that the neat-drug tendency, combined with the interaction with the polymer, decides the outcome in a dispersion was the hypothesis of Zhu and co-workers (2012); they found that it holds for the fast crystallizers and breaks down for the slow ones, with nucleation by crystalline PEG as the added factor zhu2012 C13, C38, C41. The same group's 2011 SAXS/WAXS study had shown ibuprofen crystallizing in PEG at about 111 min zhu2011 R15.

F10

Topic 3Crystallization of drug and carrier after solidification4 of 4

Drugs that hydrogen-bond with PEG slow its crystallization at 40 °C, yet PEG crystallization is still complete within minutes.

The speed of PEG crystallization was followed by X-ray diffraction and the growth of PEG spherulites (round crystal clusters) under the microscope. At 40 °C PEG with ibuprofen took 114 s to reach 50% crystallinity against 52 s with fenofibrate, and spherulites grew at 1 µm/s with benzocaine and 3 µm/s with ibuprofen against about 8 µm/s with haloperidol and fenofibrate zhu2012 R23.d, R22, R4, C31.

weakWeak to moderate: bulk kinetics at 40 °C were measured for only two drugs, the hydrogen bonds of ibuprofen and benzocaine are cited from earlier work, and the pure-PEG reference rates differ between text and figures zhu2012 X1, X2, X14.

PEG spherulite growth rate at 40 °C, µm/spure PEGtext value10haloperidolno hydrogen bond with PEG (cited)about 8fenofibrateno hydrogen bond with PEGabout 8ibuprofenhydrogen bond with PEG (cited)3benzocainehydrogen bond with PEG (cited)1

The two drugs that can hydrogen-bond with PEG slow its spherulite growth most. zhu2012 R22, R22.a, R22.b, R22.c, R22.d, R22.e, M1, M2, M3, M4, R25

PEG time to 50% crystallinity, 40 °C, spure PEG (Figs. 11, 15)about 48fenofibrate/PEG52pure PEG (Fig. 2)about 64ibuprofen/PEG114

Ibuprofen lengthens the PEG half-time at 40 °C; fenofibrate hardly does. zhu2012 R4, R16, R20, R23.d, X1

For your drug

  1. To see whether your drug slows PEG crystallization, measure the PEG relative crystallinity with and without the drug in the same run at 40 °C, where PEG is slow enough to resolve.
  2. Measure the PEG melting point in the blend to separate a supercooling effect from an interaction effect; the result matters only if the dispersion microstructure affects release, which this chapter does not show.

zhu2012 P4, P8

How it works and key numbers
  1. The authors say the difference between ibuprofen and fenofibrate "is probably due to the differing ability of the two APIs to interact with PEG": ibuprofen can hydrogen-bond with PEG, whereas fenofibrate lacks donor groups zhu2012 C44.
  2. In polymer blends a second component that interacts favourably with PEG reduces its spherulite growth rate; the spherulite rates are taken as "further confirmed" zhu2012 C14, C45.
  3. At 25 °C PEG crystallization is so fast that the dispersions show similar kinetics; the differences appear at 40 °C zhu2012 C27, C30.
  4. (synthesis: an alternative the authors do not weigh is reduced PEG supercooling: the last crystal melts at about 54.5, 57 and 58.0 °C with benzocaine, ibuprofen and fenofibrate against about 60.5 °C for PEG, the same order as the spherulite rates, so the two explanations are not separated) zhu2011 R1.g, R2.g, R1.a; zhu2012 R24.d; baird2011 R4.
To feel the numbers. The melting point depression of PEG is 60.5 − 54.5 = 6.0 K with benzocaine, 60.5 − 57 = 3.5 K with ibuprofen and 60.5 − 58.0 = 2.5 K with fenofibrate.
1 vs 10 µm/sPEG spherulite growth with benzocaine against pure PEG (text value) at 40 °Czhu2012 R22, C31
114 vs 52 sPEG time to 50% crystallinity with ibuprofen and with fenofibrate at 40 °Czhu2012 R23.d
about 2 minPEG crystallization is still complete within minutes in every dispersionzhu2012 C43, C46

Connections to other chapters

Evidence: data, conditions and papers

Finding F10. Drugs that hydrogen-bond with PEG slow PEG crystallization and spherulite growth, most at 40 °C, but PEG crystallization is still complete within minutes

In short. At 40 °C the PEG time to 50% crystallinity was 114 s in ibuprofen/PEG and 52 s in fenofibrate/PEG, against about 48–64 s for pure PEG, and PEG spherulites grew at 1 µm/s with benzocaine and 3 µm/s with ibuprofen, about 8 µm/s with haloperidol and fenofibrate and 10 µm/s without drug (text value) zhu2012 R23.d, R22, R4, C31. At 25 °C the differences are small and PEG crystallization is complete in about 2 min in every dispersion zhu2012 C43, C46. The authors attribute the slowing to hydrogen bonding of the drug with PEG ("probably due to"); a drug that lowers the PEG melting point and so its supercooling is an alternative that the paper does not weigh zhu2012 C44, C45.

Type. observation in 4 drugs, bulk kinetics for 2 Strength. to moderate — bulk kinetics at 40 °C were measured for two drugs only, hydrogen bonding of ibuprofen and benzocaine is cited, not measured here, and the pure-PEG reference rates differ between text and figures (zhu2012 K6: moderate; X1, X2, X14).

How it was shown

PEG relative crystallinity was measured by synchrotron XRD as in F7 for pure PEG and four 20/80 dispersions at 25 °C and for ibuprofen/PEG and fenofibrate/PEG at 40 °C zhu2012 P4, R8, R12, R16, R20. Spherulite growth was timed by following the front of a PEG spherulite under the polarized light microscope at 40 °C zhu2012 P8, C30.

What the data show

At 25 °C the PEG time to 50% was 15–26 s in all four dispersions zhu2012 R23.d. At 40 °C it was 114 s in ibuprofen/PEG and 52 s in fenofibrate/PEG, against about 48–64 s for pure PEG zhu2012 R23.d, R16, R20, R4, X1. Spherulites grew at 1 µm/s with benzocaine, 3 with ibuprofen, about 8 with haloperidol and fenofibrate and 10 µm/s (text value) without drug zhu2012 R22, R22.a, X2.

systemPEG t_{50} at 25 °C (s)PEG t_{50} at 40 °C (s)spherulite growth rate at 40 °C (µm/s)hydrogen bond with PEGids
pure PEGabout 23about 48 (Figs. 11, 15) or about 64 (Fig. 2)10 (text); about 20 (Fig. 17 slope)—zhu2012 R4, R16, R20, R22.a, X1, X2
haloperidol/PEG15not measuredabout 8no (cited)zhu2012 R23.d, R22.b, M1
benzocaine/PEG22not measured1yes (cited)zhu2012 R23.d, R22.e, M3
ibuprofen/PEG261143yes (cited)zhu2012 R23.d, R22.d, M4
fenofibrate/PEG2152about 8no (SI Fig. S2)zhu2012 R23.d, R22.c, R25, M2
Fig. 17 of zhu2012: PEG spherulite length against time at 40 °C in pure PEG and in four drug/PEG dispersions
Fig. 17 · zhu2012PEG spherulite length against time at 40 °C in pure PEG and in four drug/PEG dispersions

The slopes fall from pure PEG to haloperidol and fenofibrate, then ibuprofen, then benzocaine zhu2012 R22.

Why

The authors say the difference between ibuprofen and fenofibrate "is probably due to the differing ability of the two APIs to interact with PEG": ibuprofen can hydrogen-bond with PEG, fenofibrate lacks donor groups zhu2012 C44. (synthesis: an alternative the authors do not weigh is reduced PEG supercooling: the last crystal melts at about 54.5, 57 and 58.0 °C with benzocaine, ibuprofen and fenofibrate against about 60.5 °C for PEG, the same order as the spherulite rates zhu2011 R1.g, R2.g, R1.a; zhu2012 R24.d; baird2011 R4.)

Limits and transfer

Bulk kinetics at 40 °C exist for two drugs only, the hydrogen bonds of ibuprofen and benzocaine are cited and not measured, and the pure-PEG reference rates differ between text and figures zhu2012 X14, C20, X1, X2. PEG still crystallizes within minutes in all systems, so the practical effect is small zhu2012 C46. To separate interaction from supercooling, also measure the PEG melting point in the blend at 40 °C.

How it was shown

PEG relative crystallinity versus time was measured by synchrotron XRD as in F7 for pure PEG, haloperidol/PEG, benzocaine/PEG, ibuprofen/PEG and fenofibrate/PEG at 25 °C and for ibuprofen/PEG and fenofibrate/PEG at 40 °C zhu2012 P4, R8, R12, R16, R20. The spherulite growth rate was measured by following the front of a PEG spherulite under the polarized light microscope at 40 °C, the temperature at which growth is slow enough, in pure PEG and the four 20/80 dispersions zhu2012 P8, C30. Hydrogen bonding with PEG was taken from earlier infrared work for benzocaine and ibuprofen and measured in the supporting information for fenofibrate zhu2012 C20, R25, M1, M2, M3, M4.

What the data show

At 25 °C PEG's time to 50% was 15 s with haloperidol, 22 s with benzocaine, 26 s with ibuprofen and 21 s with fenofibrate, and the induction times were −12, 0, 8 and 1 s zhu2012 R23.c, R23.d. At 40 °C PEG in ibuprofen/PEG began after 40 s and reached about 62% at 132 s, the last point, with t_{50} 114 s; PEG in fenofibrate/PEG began after 7 s, reached 50% at about 52 s and 96% at about 135 s, close to pure PEG zhu2012 R23.c, R23.d, R16, R20. In the same figures pure PEG at 40 °C reached 51% at about 48 s and about 89% at about 67 s, while in the pure-PEG curve of Fig. 2 these points come at about 64 s and about 90 s zhu2012 R16, R20, R4, X1. The spherulite front advanced about 205 µm in 10 s in pure PEG and the text gives 10 µm/s; the plotted pure-PEG length reaches about 470 µm at about 24 s, a slope near 20 µm/s by the extractor's calculation zhu2012 R21, R22.a, X2.

systemPEG t_{50} at 25 °C (s)PEG t_{50} at 40 °C (s)spherulite growth rate at 40 °C (µm/s)hydrogen bond with PEGids
pure PEGabout 23about 48 (Figs. 11, 15) or about 64 (Fig. 2)10 (text); about 20 (Fig. 17 slope)—R4, R16, R20, R22.a, X1, X2
haloperidol/PEG15not measuredabout 8no (cited)R23.d, R22.b, M1
benzocaine/PEG22not measured1yes (cited)R23.d, R22.e, M3
ibuprofen/PEG261143yes (cited)R23.d, R22.d, M4
fenofibrate/PEG2152about 8no (SI Fig. S2)R23.d, R22.c, R25, M2

The pure-PEG value at 25 °C is the interpolated half point of the curve (about 47% at 22 s and about 55% at 24 s) zhu2012 R4.

Figure

Fig. 17 of zhu2012: PEG spherulite length against time at 40 °C in pure PEG and in four drug/PEG dispersions
Fig. 17 · zhu2012PEG spherulite length against time at 40 °C in pure PEG and in four drug/PEG dispersions

The slopes fall from pure PEG to haloperidol and fenofibrate, then ibuprofen, then benzocaine zhu2012 R22.

Fig. 11 of zhu2012: PEG relative crystallinity in ibuprofen/PEG and in pure PEG at 25 and 40 °C
Fig. 11 · zhu2012PEG relative crystallinity in ibuprofen/PEG and in pure PEG at 25 and 40 °C

At 40 °C PEG crystallization with ibuprofen (triangles) is much slower than in pure PEG (squares); at 25 °C the curves are close zhu2012 R16.

Why

The authors write that the different behaviour of PEG with ibuprofen and fenofibrate "is probably due to the differing ability of the two APIs to interact with PEG": ibuprofen can hydrogen-bond with PEG, whereas fenofibrate lacks donor groups and PEG has mainly acceptor groups; the spherulite growth rates, slowest with benzocaine and ibuprofen, are taken as "further confirmed" zhu2012 C44, C45. The expectation comes from a polymer-blend study outside the library, in which a second component that interacts favourably with PEG reduces its spherulite growth rate zhu2012 C14. They explain the similar PEG rates at 25 °C by the extremely fast crystallization of PEG there zhu2012 C27. (synthesis: an alternative the authors do not weigh is the supercooling of PEG. The 15 K step from 40 to 25 °C shortens pure PEG's t_{50} from about 48–64 s to about 23 s zhu2012 R4, R16. A dissolved drug lowers the melting point of PEG: the temperature at which the last crystal melts at 20 wt% drug is about 54.5 °C with benzocaine, about 57 °C with ibuprofen and about 58.0 °C with fenofibrate against about 60.5 °C for PEG, a depression of 6.0, 3.5 and 2.5 K (synthesis: 60.5 − 54.5, 60.5 − 57, 60.5 − 58.0), while PEG melting stays near 59–61 °C with haloperidol zhu2011 R1.g, R2.g, R1.a; zhu2012 R24.d; baird2011 R4. That order, benzocaine, ibuprofen, fenofibrate, haloperidol, is the order of the spherulite rates (1, 3, about 8, about 8 µm/s), so hydrogen bonding and reduced supercooling are not separated by these data. The numbers are read from plots.)

Conditions and limits

Bulk PEG kinetics at 40 °C only for ibuprofen/PEG and fenofibrate/PEG; the spherulite ranking covers four drugs at one temperature zhu2012 X14. The hydrogen bonding of ibuprofen and benzocaine with PEG is cited from earlier work and was not measured here zhu2012 X14, C20. The number of replicate runs is not stated zhu2012 X6. "Slightly slower" spherulite growth with haloperidol and fenofibrate holds only with the text value of 10 µm/s for pure PEG zhu2012 X2. The authors note that the practical effect is small because PEG still crystallizes within a few minutes in all systems and that the influence of a changed PEG rate on the dispersion microstructure is not known zhu2012 C46.

Counterexamples and conflicts

The text says PEG kinetics at 25 °C show negligible differences, but benzocaine/PEG levels off lower (about 94% against about 99% at about 120 s), haloperidol/PEG starts sooner and ibuprofen/PEG lags zhu2012 C43, X3, X4. Pure PEG's reference curve and spherulite rate are inconsistent between figures and text zhu2012 X1, X2.

Transfer check

To see whether a drug slows PEG crystallization, measure the PEG relative crystallinity with and without the drug in the same run at 40 °C, where PEG is slow enough to resolve, and measure the PEG melting point in the blend to separate a supercooling effect from an interaction effect. Treat the result as relevant only if the microstructure of the dispersion matters for release, which this chapter does not show.

History

A polymer-blend study outside the library had found that an interacting second component slows PEG spherulites zhu2012 C14. Zhu and co-workers (2011) showed in the library that the drug changes the PEG lamellar structure (F5) zhu2011 R18. Zhu and co-workers (2012) measured the effect on PEG crystallization kinetics and spherulite growth for four drugs zhu2012 C5.

Topic 4 of 4 · 2 findings · F11–F12

Storage in humid air

F11

Topic 4Storage in humid air1 of 2

In humid PEO, the extent of crystallinity loss follows the drug's activity coefficient in water, not its solubility in PEG.

Tablets of six crystalline drugs (10 wt%) in PEO were stored at 94% RH (relative humidity) for up to 28 days. Acetaminophen lost all detectable crystallinity within about 14–17 days, ketoprofen, naproxen and ibuprofen lost part of it, and felodipine and ketoconazole changed little; the loss followed the drug's activity coefficient in water marsac2008b R2, R4, R5, R6, R7, R8, R10, R14, R16.

moderateModerate: Raman and XRPD agree and the contrast between drugs is large, but the loss was graded, not measured, the key controls are "data not shown", and the correlation rests on six drugs in three groups marsac2008b X7, X8.

acetaminophen 1.2 × 10¹ · lost allnaproxen 3.8 × 10³ · lost partketoprofen, ibuprofen ≈10⁴ · lost partfelodipine, ketoconazole ≈10⁵ · little12345water activity coefficient, power of ten

The lower the activity coefficient of the drug in water, the more crystallinity it loses. marsac2008b R14.a, R14.c, R14.d, R14.e, R14.f, R10, R16

Dissolvable by amorphous PEO, % of drugacetaminophenlost all crystallinity14ketoprofenlost part of it24naproxenlost part of it13ibuprofenlost part of it17felodipinehardly changed15ketoconazolehardly changed2

Calculated on a PEG 400 basis; this stand-in does not rank the drugs. marsac2008b R14, R16

For your drug

  1. For a crystalline drug in a PEG or PEO matrix, compute the activity coefficient in water from the melting point, heat of fusion and aqueous solubility at the storage temperature (ideal solubility divided by the measured solubility).
  2. Test first a drug near 10¹; drugs near 10⁵ stayed crystalline here. Store compacts at 75% and 94% RH for weeks, follow the drug by Raman and XRPD against references and weigh the compacts for water; do not extrapolate from 10 wt% and PEO 100000 to other loadings or to PEG 3350.

marsac2008b R14, R16, R13

How it works and key numbers
  1. Compaction brings crystalline drug into contact with the amorphous regions of PEO, which "can be dissolved by PEO" (a hypothesis); the process is too slow to see when dry marsac2008b C16, C17, R8.
  2. Water is sorbed in the amorphous PEO and lowers the driving force for dissolution, because every drug is far less soluble in water than in PEG 400 marsac2008b C24.
  3. Water still speeds the loss by "two potential mechanisms": it plasticizes the amorphous PEO, and it slowly deliquesces PEO, enlarging the disordered volume (F12) marsac2008b C25, C26, C30.
  4. The larger volume of water–PEO cosolvent dissolves drugs with a favourable interaction with water; those with an activity coefficient near 10⁵ stay crystalline marsac2008b C33, C35, C38.
14–17 daysacetaminophen lost all detectable crystallinity at 94% RHmarsac2008b R2, R10
10¹ vs 10⁵activity coefficient in water of the drug that lost all crystallinity against the two that remained crystallinemarsac2008b R14, R16, C35
0.02–0.64activity coefficients of all six drugs in PEG 400, including the two unchanged: this reading did not discriminatemarsac2008b R14, R16

Connections to other chapters

Evidence: data, conditions and papers

Finding F11. Crystalline drugs compacted with PEO lose crystallinity at 94% RH, and the extent follows the drug's activity coefficient in water, not its solubility in PEG 400

In short. In 10 wt% physical-mixture compacts of six crystalline drugs in PEO 100000 stored at 94% RH, acetaminophen lost all detectable crystallinity within about 14–17 days, ketoprofen, naproxen and ibuprofen lost part of it in 28 days, and felodipine and ketoconazole changed little; compacts kept dry and the pure drugs at 94% RH were reported unchanged marsac2008b R2, R4, R5, R6, R7, R8, R10. The extent of loss followed the activity coefficient in water (about 10¹ for acetaminophen, 10³–10⁴ for the three drugs with partial loss, about 10⁵ for the two unchanged drugs), whereas the share of each drug that the amorphous PEO could dissolve if it behaved like PEG 400 (2–24%) and the melting properties did not rank the drugs marsac2008b R14, R16, C22, C34, C35.

Type. observation in 6 drugs Strength. Raman and XRPD agree on the grade of each drug and the contrast between drugs is large, but the loss was graded as complete, moderate or negligible and not quantified, the key controls are "data not shown", and the correlation rests on six drugs in three groups (marsac2008b K1: moderate to strong; K2: moderate; K6: moderate; X7, X8).

How it was shown

Marsac and co-workers pressed 500 mg compacts of PEO (molecular weight about 100000) with 10 wt% of a crystalline drug and stored them at 0% and 94% RH for up to 28 days marsac2008b P1, P2, M7. Drug crystallinity was followed by FT-Raman and XRPD; activity coefficients came from the ideal solubility and the solubility in PEG 400 and in water marsac2008b P3, P4, P5, P8, P9, E2.

What the data show

At 94% RH acetaminophen lost all detectable crystallinity within about 14–17 days, ketoprofen, naproxen and ibuprofen lost part of it in 28 days, and felodipine and ketoconazole changed little marsac2008b R2, R4, R5, R6, R7, R10. The loss followed the activity coefficient in water, from 10¹ to 10⁵, whereas all six drugs had coefficients of 0.02–0.64 in PEG 400, including the two that stayed crystalline marsac2008b R14, R16.

drug (Tm, °C)grade at 94% RH\gamma in water\gamma in PEG 400drug dissolvable by amorphous PEO, PEG 400 basis (%)ids
acetaminophen (169.02)complete1.2 × 10¹0.0614marsac2008b R2, R10, R14.a, R16.a
ketoprofen (121.70)moderate1.4 × 10⁴0.3124marsac2008b R4, R10, R14.b, R16.b
naproxen (155.21)moderate3.8 × 10³0.0213marsac2008b R5, R10, R14.c, R16.c
ibuprofen (74.61)moderate3.1 × 10⁴0.6417marsac2008b R6, R10, R14.d, R16.d
felodipine (141.77)negligible2.4 × 10⁵0.1415marsac2008b R7, R10, R14.e, R16.e
ketoconazole (147.93)negligible5.3 × 10⁵0.092marsac2008b R7, R10, R14.f, R16.f
Fig. 4 of marsac2008b: XRPD of the compacts with arrows on the drug peaks before and after storage
Fig. 4 · marsac2008bXRPD of the compacts with arrows on the drug peaks before and after storage

Acetaminophen (a) is gone at 6 days and a halo at 17 days; felodipine and ketoconazole (e, f) persist marsac2008b R10.

Why

Compaction brings crystalline drug into contact with amorphous PEO, which "can be dissolved by PEO" (a hypothesis) marsac2008b C16, C17. Water lowers the driving force because every drug is far less soluble in water than in PEG 400, yet it speeds the loss by plasticizing the amorphous PEO and slowly deliquescing it (F12) marsac2008b C24, C25, C26, C30. The authors conclude that the transformation "was related to the ability of the drug to dissolve in the water-amorphous PEO" cosolvent marsac2008b C38.

Limits and transfer

One loading, one PEO grade (not PEG 3350), one high humidity and up to 28 days; the controls that make water necessary are "data not shown" and the loss was graded, not quantified marsac2008b X7, X6, X8. For a crystalline drug in a PEG or PEO matrix, compute its activity coefficient in water: near 10¹ is the case to test first, near 10⁵ stayed crystalline here marsac2008b R14, R16.

How it was shown

Marsac and co-workers sieved drugs and PEO (Polyox WSR N-10, average molecular weight about 100000, dried over phosphorus pentoxide for at least a week) to 45–75 µm, made 500 mg physical mixtures with 10 wt% drug by geometric mixing and pressed them in a 16 mm die at 2040 psi for 1 s marsac2008b P1, M7. The compacts were stored at 0% and 94% RH (saturated potassium nitrate, 22 °C as stated for the moisture work; acetaminophen also at 75% RH) for up to 28 days marsac2008b P2, X6. Drug crystallinity was followed by FT-Raman (1064 nm, 4 cm⁻¹ resolution, at least 256 scans, compact rotating) against two references, the crystal and the drug at its solubility limit in PEG 400 (amorphous for ketoconazole), and by XRPD (Cu Kα, 5–35° 2θ) at 0, 6 and 17 days (acetaminophen) or 0 and 28 days marsac2008b P3, P4, P2. Pure amorphous acetaminophen, naproxen and ibuprofen could not be made as references because they crystallized on cooling marsac2008b R1, C9. Solubility in PEG 400 was measured by UV after 24 h at 25 °C, and activity coefficients were calculated from the ideal solubility (from the DSC melting data) and from the measured or cited solubility in PEG 400 and in water marsac2008b P5, P8, P9, E2.

What the data show

For acetaminophen the crystalline Raman bands at 1610 and 1648 cm⁻¹ shrank and the dissolved-state bands at 1619 and 1661 cm⁻¹ grew, with no crystalline drug detected after 14 days; the XRPD drug peaks (15.5, 18.2, 20.4, 24.3 and 26.6° 2θ) showed little sign after 6 days and a completely X-ray amorphous halo after 17 days marsac2008b R2, R10. Ketoprofen's Raman band moved from 1655 to 1657 cm⁻¹ (1658 in PEG 400) and stayed narrower than in PEG 400, naproxen's from 1630 to 1631 cm⁻¹ (1633 in PEG 400) with significant broadening, and ibuprofen's from 1608 to 1609 cm⁻¹ (1613 in PEG 400); their XRPD peaks became weak, though some ibuprofen peaks may remain; the shifts are below the 4 cm⁻¹ resolution, so the grade rests on the broadening and the XRPD marsac2008b R4, R5, R6, R10, X11. Felodipine and ketoconazole compacts after 28 days were very similar to the crystalline spectra and several drug XRPD peaks persisted; for felodipine, Raman barely distinguishes the crystal from the PEG 400 solution, so its grade rests mainly on XRPD marsac2008b R7, R10, X21. Compacts of acetaminophen became gelatinous within a few days, those of ketoprofen, naproxen and ibuprofen noticeably softer, and those of felodipine and ketoconazole lost a little integrity; the acetaminophen compact took up about 0.46 g water per g dry solid after 28 days against about 0.16–0.215 for the others marsac2008b R17, R13. Acetaminophen compacts also lost crystallinity "significantly", to a lesser extent, at 75% RH (data not shown) marsac2008b R3.

drug (Tm, °C)grade at 94% RH, from Raman and XRPD\gamma in water\gamma in PEG 400drug dissolvable by amorphous PEO, PEG 400 basis (%)ids
acetaminophen (169.02)complete1.2 × 10¹0.0614R2, R10, R14.a, R16.a, M1
ketoprofen (121.70)moderate1.4 × 10⁴0.3124R4, R10, R14.b, R16.b, M2
naproxen (155.21)moderate3.8 × 10³0.0213R5, R10, R14.c, R16.c, M3
ibuprofen (74.61)moderate3.1 × 10⁴0.6417R6, R10, R14.d, R16.d, M4
felodipine (141.77)negligible2.4 × 10⁵0.1415R7, R10, R14.e, R16.e, M5
ketoconazole (147.93)negligible5.3 × 10⁵0.092R7, R10, R14.f, R16.f, M6

The aqueous solubilities behind the water coefficients range from 1.7 × 10⁻³ (acetaminophen) to 3.0 × 10⁻⁹ mole fraction (ketoconazole), cited from the literature marsac2008b R14. Several Table 2 rows are not internally consistent if \gamma = S^{ideal}/S, so the printed coefficients serve as order-of-magnitude values marsac2008b X5, X18.

Figure

Fig. 4 of marsac2008b: XRPD of the compacts with arrows on the drug peaks before and after storage
Fig. 4 · marsac2008bXRPD of the compacts with arrows on the drug peaks before and after storage

The bottom trace in each panel is the fresh compact with arrowed drug peaks; the large off-scale peaks are PEO. Acetaminophen (a) is gone at 6 days and a halo at 17 days, ketoprofen, naproxen and ibuprofen (b–d) are weak at 28 days, felodipine and ketoconazole (e, f) persist marsac2008b R10.

Table 2 of marsac2008b: solubilities and activity coefficients in PEG 400 and in water
Table 2 · marsac2008bsolubilities and activity coefficients in PEG 400 and in water

Similar solubility in PEG 400 for all drugs; activity coefficients in water from 10¹ to 10⁵ in the same order as the crystallinity loss marsac2008b R14.

Why

The authors' account, with their hedges: compaction brings crystalline drug into contact with amorphous PEO regions, which "can be dissolved by PEO" (a hypothesis); the process is too slow to see when dry at 25 °C marsac2008b C16, C17, R8. Water, which is most likely located in the amorphous PEO, lowers the driving force for dissolution because every drug is far less soluble in water than in PEG 400 marsac2008b C24. Water nevertheless speeds the loss by "two potential mechanisms": it plasticizes the amorphous PEO (water Tg −136 °C against about −67 °C for PEO), lowering its viscosity, and it slowly deliquesces PEO, enlarging the disordered volume (F12) marsac2008b C25, C26, C30. The larger volume of water–PEO cosolvent dissolves drugs with a favourable interaction with water, and those with an activity coefficient of about 10⁵ stay crystalline marsac2008b C33, C35, C38. Dissolved drug "will most likely anti-plasticize" the amorphous PEO, since the drug Tg values (−43.6 to 44.4 °C) are above that of PEO marsac2008b C27, M1, M2, M3, M4, M5, M6. The authors conclude that the degree of transformation "was related to the ability of the drug to dissolve in the water-amorphous PEO" cosolvent and that "the thermodynamics of the binary systems were useful in describing the dynamic nature of the ternary system" marsac2008b C38, C39. What was not measured: where the drug is located (in amorphous PEO, in sorbed water or as amorphous drug), the mobility of the wet PEO, a PEO solution phase and the crystalline fraction lost marsac2008b X17, C26, X9, X8. The extractor adds that acetaminophen lost crystallinity at 75% RH, below the cited deliquescence point of PEO, and that its compacts took up about twice the water, which could reflect the drug dissolving in the sorbed water; neither point is discussed marsac2008b X10, R3, R13.

Conditions and limits

One loading (10 wt%), one PEO grade (about 100000, not PEG 3350), one high humidity (94% RH; 75% for acetaminophen only) and up to 28 days; the storage temperature of the spectroscopy compacts is not printed marsac2008b X7, X6. The controls that make water and PEO necessary (0% RH compacts, pure drugs at 94% RH, pure-drug water uptake) and the 75% RH result are "data not shown" marsac2008b X7. The aqueous solubilities come from three cited sources at unstated temperatures marsac2008b X18. Whether the drugs recrystallize on drying, and the effect on release, were not examined marsac2008b C8.

Counterexamples and conflicts

The liquid analogue PEG 400 sorted the drugs in the melt study of F3 but not here: all six drugs had \gamma between 0.02 and 0.64 in PEG 400, including the two that kept their crystallinity baird2011 C25; marsac2008b R14, R16. (synthesis: the two studies ask different questions, a molten dispersion at 50–160 °C and a humid compact at about 22 °C with water as a third component, so a PEG 400 stand-in is not a general proxy for the polymer.) The authors' wording differs between sections: the discussion calls the trend with aqueous solubility "a clear trend", the abstract and conclusions "qualitatively correlate" marsac2008b C35. None found in the cards read for this chapter; no other card of the chapter exposed a PEG dispersion to humidity.

Transfer check

For a crystalline drug in a PEG or PEO matrix, compute the activity coefficient in water from the melting point, heat of fusion and aqueous solubility at the storage temperature (ideal solubility from the melting data, then the ratio to the measured solubility). A drug in the range of acetaminophen (about 10¹) is the case to test first; drugs near 10⁵ stayed crystalline here marsac2008b R14, R16. Store compacts at ≥75% RH and 94% RH for weeks and follow the drug by Raman and XRPD against references, quantify the crystalline fraction, and weigh the compacts for water: a jump in water uptake coincided with the largest loss in this study (synthesis: 0.46 against 0.16–0.215 g/g marsac2008b R13). Do not extrapolate from 10 wt% and PEO 100000 to other loadings or PEG 3350.

History

A study outside the library (Schachter and co-workers, 2004) had shown that ketoprofen in PEO lost crystallinity on heating below the PEO melting point, with the drug thought to reside in the amorphous regions marsac2008b R19, C4. Marsac and co-workers (2008) added water as the stress and the activity coefficient in water as the discriminating property, in the earliest paper of this chapter. The later PEG papers of the chapter studied melts and dispersions at 25 °C without humidity (F1–F10).

F12

Topic 4Storage in humid air2 of 2

PEO keeps absorbing water for months at 94% RH and loses its crystal peaks, so short tests understate the change.

PEO took up about 10 wt% water at 94% RH after several hours but about 37 wt% after 5 months. In tablets held 28 days at 94% RH its two main diffraction peaks lost intensity, broadened and shifted, and with acetaminophen they disappeared after 17 days marsac2008b R11, R9, R17.

weakWeak to moderate: the uptake and peak changes are measured, but no PEO solution phase was observed, the sorption method is not stated and the long-term difference is clear only at 94% RH marsac2008b X9, X20.

Water taken up by PEO 100000, weight change %75% RH · hours1.775% RH · 5 months2.185% RH · hours3.885% RH · 5 months4.994% RH · hours9.894% RH · 5 months37.3

Below 85% RH the two series differ little; at 94% RH the 5-month value is almost four times the several-hours value. marsac2008b R11.a, R11.b

For your drug

  1. For a PEG or PEO product, follow water uptake and polymer diffraction over weeks to months at the storage humidities of interest, not for hours.
  2. Expect states at 94% RH that do not exist at moderate humidity; the authors warn that partially crystalline polymers "may" not allow Arrhenius extrapolation in accelerated tests.

marsac2008b R9, R11, C40

How it works and key numbers
  1. Water sorbs mostly into the amorphous regions of PEO and increases the disordered fraction, "as evidenced by" the decrease of the PEO peaks marsac2008b C28, C29.
  2. The authors suggest that PEO "may slowly deliquesce": the crystalline polymer dissolves in the sorbed water, which keeps lowering water activity and drawing in more water; the slowness "most likely" reflects the large polymer molecules marsac2008b C30, R22.
  3. The softening and gel-like state of the tablets is "qualitatively consistent" with the loss of PEO crystallinity marsac2008b C32, R17.
  4. The abstract states that deliquescence occurred; the discussion only suggests it, and no PEO solution phase was observed marsac2008b X9.
To feel the numbers. At 94% RH the 5-month uptake is 37.3 ÷ 9.8 = 3.8 times the several-hours value; at 75–76% RH it is only 2.1 ÷ 1.7 = 1.2 times.
10% vs 37%water in PEO at 94% RH after several hours against 5 monthsmarsac2008b R11
0.46 vs 0.16–0.215 g/gwater in acetaminophen tablets against the other tablets after 28 days at 94% RHmarsac2008b R13
17 daysthe two main PEO peaks are absent in the acetaminophen tabletmarsac2008b R9, R17

Connections to other chapters

Evidence: data, conditions and papers

Finding F12. PEO keeps taking up water for months at 94% RH and loses its own diffraction peaks, so hours-long equilibrations and short stress tests understate the change

In short. PEO 100000 held about 10 wt% water at 94% RH after several hours but about 37 wt% after 5 months, while at 75–85% RH the two series differ little (about 1.7 against 2.1% at 75–76%, 3.8 against 4.9% at 84–85%) marsac2008b R11. In the compacts the two main PEO diffraction peaks (19.2 and 23.4° 2θ) lost intensity, broadened and shifted after 28 days at 94% RH, and disappeared with acetaminophen after 17 days; the authors read this as growth of the disordered fraction and "suggest" that PEO slowly deliquesces, a conclusion stated more firmly in the abstract marsac2008b R9, C28, C30, X9. They warn that partially crystalline polymers "may" not allow Arrhenius extrapolation in accelerated tests marsac2008b C40.

Type. single-system observation (PEO 100000) Strength. to moderate — the uptake and the peak changes are measured, but no PEO solution phase was observed, the sorption method is not stated and the long-term difference is clear only at 94% RH (marsac2008b K3: moderate; K4: weak to moderate; X9, X20).

How it was shown

Pure PEO 100000 was equilibrated at each RH for several hours and for 5 months and the weight change recorded; instrument, temperature and sample form are not printed marsac2008b P7, X6. Compacts were weighed after 28 days at 94% RH, and the PEO peaks were followed by XRPD before and after storage marsac2008b P6, P4.

What the data show

PEO held about 10 wt% water at 94% RH after several hours but about 37 wt% after 5 months, while at 75–85% RH the two series differ little marsac2008b R11. After 28 days at 94% RH the compacts held about 0.16–0.215 g water per g dry solid, acetaminophen compacts about 0.46 marsac2008b R13. The two main PEO XRPD peaks lost intensity, broadened and shifted to slightly higher angles, and with acetaminophen were absent after 17 days marsac2008b R9, R17.

RH (%)water uptake after several hours (weight change, %)water uptake after 5 months (weight change, %)ids
≈33–35≈0.3≈0.3marsac2008b R11.a, R11.b
≈64–65≈0.8≈0.9marsac2008b R11.a, R11.b
≈75–76≈1.7≈2.1marsac2008b R11.a, R11.b
≈84–85≈3.8≈4.9marsac2008b R11.a, R11.b
≈94–95≈9.8≈37.3marsac2008b R11.a, R11.b
Fig. 5 of marsac2008b: water uptake of PEO 100000 against relative humidity after several hours and after 5 months
Fig. 5 · marsac2008bwater uptake of PEO 100000 against relative humidity after several hours and after 5 months

The curves diverge at 94% RH, about 10 against 37% marsac2008b R11.

Why

Water sorbs mostly into the amorphous regions of PEO and increases the disordered fraction, "as evidenced by" the decrease of the PEO peaks marsac2008b C28, C29. "It is suggested that PEO may slowly deliquesce," with a cited deliquescence point of water activity 0.93 at 20 °C, but no PEO solution phase was observed and the abstract states it more firmly than the discussion marsac2008b C30, R22, X9.

Limits and transfer

PEO 100000 only; the isotherm method and temperature are not printed, and the PEO crystallinity after storage was not measured marsac2008b X6, C28. The cited deliquescence point lies above 75% RH, yet acetaminophen lost crystallinity at 75% RH marsac2008b R22, R3, X10. Follow water uptake and polymer diffraction over weeks to months, not hours: at 94% RH the short equilibration understated uptake almost fourfold (synthesis: 37.3/9.8 = 3.8) marsac2008b R11.

How it was shown

Pure PEO 100000 was equilibrated at each RH for several hours and for 5 months, and the weight change recorded (instrument, temperature and sample form not printed) marsac2008b P7, X6. Whole compacts were weighed after 28 days at 94% RH over saturated potassium nitrate at 22 °C, and the water was given per dry mass (a dry-basis fraction, which the text reports as wt%) marsac2008b P6, X15. The PEO peaks were followed by XRPD in the compacts before and after storage marsac2008b P4. The crystallinity of the PEO used was estimated from its enthalpy of fusion, 197 J/g against 216 J/g for perfectly crystalline PEO marsac2008b M7, E3.

What the data show

The isotherm points are in the table below. The authors write that PEO takes up significantly more water after 5 months at 75% RH and above; in the plot the large gap is at 94% RH marsac2008b C12, X20. After 28 days at 94% RH pure PEO and the compacts held about 0.16–0.215 g water per g dry solid, acetaminophen compacts about 0.46, which the text gives as roughly 20 and 45 wt% and, normalized to PEO, about 22 and 50 wt% (synthesis: 20/0.9 = 22.2 and 45/0.9 = 50) marsac2008b R13, E6. In XRPD, after 28 days at 94% RH the compacts with ketoprofen, naproxen, ibuprofen, felodipine and ketoconazole showed a decrease in the intensity of the two main PEO peaks (called "dramatic"), a shift to slightly higher angles and clear broadening; with acetaminophen the peaks were weak at 6 days and absent at 17 days, and the compact was a gelatinous mass marsac2008b R9, R17. The PEO used was about 91% crystalline (197/216 = 0.912; the text calls 91% the "amorphous fraction", a misprint, since Table 3 uses 9% amorphous) marsac2008b E3, R15, X1.

seriesRH (%) and water uptake (weight change, %)ids
several hours≈1: ≈0; ≈35: ≈0.3; ≈65: ≈0.8; ≈75: ≈1.7; ≈85: ≈3.8; ≈95: ≈9.8R11.a
5 months≈33: ≈0.3; ≈64: ≈0.9; ≈76: ≈2.1; ≈84: ≈4.9; ≈94: ≈37.3R11.b

Values are read from Fig. 5; the two series were measured at slightly different RH values marsac2008b R11.

Figure

Fig. 5 of marsac2008b: water uptake of PEO 100000 against relative humidity after several hours and after 5 months
Fig. 5 · marsac2008bwater uptake of PEO 100000 against relative humidity after several hours and after 5 months

Diamonds are after several hours and circles after 5 months; the curves diverge at 94% RH, about 10 against 37% marsac2008b R11.

Why

The authors' account: water sorbs mostly into the amorphous regions of PEO and increases the disordered fraction, "as evidenced by" the decrease of the PEO peaks, and the very slow equilibration shows that equilibrium states are hard to reach experimentally marsac2008b C28, C29, C7. In the discussion "it is suggested that PEO may slowly deliquesce": the crystalline polymer dissolves in the sorbed water, which keeps lowering water activity and drawing in more water, and the slowness "most likely" reflects the large polymer molecules; support is the peak loss and a cited deliquescence point of water activity 0.93 at 20 °C from a study outside the library marsac2008b C30, R22. The reduced and broadened peaks are "consistent with" deliquescence even if the drug may alter its thermodynamics marsac2008b C31. The softening of the compacts is "qualitatively consistent" with the loss of PEO crystallinity marsac2008b C32. The abstract states that PEO "undergoes a very slow deliquescence" and concludes that it did so, which the discussion's wording does not support; no PEO solution phase was observed marsac2008b X9. The statement that partially crystalline polymers may not allow Arrhenius extrapolation in accelerated stress testing is offered with "may" and without temperature-dependent data marsac2008b C40.

Conditions and limits

PEO 100000 only, not PEG 3350; the isotherm method, temperature and sample form are not printed, nor is the DSC method for the PEO enthalpy of fusion marsac2008b X6, X19. Water contents are given as wt%, weight change and dry-basis fractions in different places, and the type of the error bars and the number of replicates are not stated marsac2008b X15, X16. The traces for day 0 and day 28 are not labelled in panels b–f of the XRPD figures, so the peak changes cannot be checked quantitatively marsac2008b X13. The PEO crystallinity after storage was not measured marsac2008b C28.

Counterexamples and conflicts

The cited deliquescence point (water activity 0.93 at 20 °C) lies above 75% RH, yet acetaminophen lost crystallinity at 75% RH, so deliquescence of PEO is not a precondition of the drug loss marsac2008b R22, R3, X10.

Transfer check

For a PEG or PEO product, follow water uptake and polymer diffraction over weeks to months at the storage humidities of interest, not for hours; a short equilibration at 75–85% RH understates uptake only slightly here, but at 94% RH it understated it almost fourfold (synthesis: 37.3/9.8 = 3.8) marsac2008b R11. (synthesis: expect states at 94% RH that do not exist at moderate humidity, and read high-RH stress data with the polymer's own change in mind marsac2008b R9, R11.)

History

A deliquescence point of PEO and the destruction of polymer crystals by water in poly(vinyl alcohol) were known from studies outside the library marsac2008b R22, C6. Marsac and co-workers (2008) are the only paper of this chapter to have followed PEO under humidity.

01Development line

One entry per paper in year order: what the library already knew, what the paper added, and how it relates to earlier entries.

  1. 2008
    marsac2008bcrystalline drugs in PEO under humidityfirst proposed

    Spontaneous Crystallinity Loss of Drugs in the Disordered Regions of Poly(Ethylene Oxide) in the Presence of Water

    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.
    SupportsF11F12F3F4
  2. 2011
    baird2011eutectic composition and its predictionfirst proposed

    Evaluation and modeling of the eutectic composition of various drug-polyethylene glycol solid dispersions

    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.
    SupportsF1F2F3
  3. 2011
    zhu2011phase behaviour and microstructure over timeextends

    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.
  4. 2012
    zhu2012crystallization kinetics of drug and carrierconfirmsextendscontradicts

    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.
    SupportsF1F7F8F9F10
For the authors: coverage of each paper card's main findings
paperfinding of section 0.3used in
marsac2008bF1. Acetaminophen loses all its crystallinity within about two weeksF11
marsac2008bF2. Ketoprofen, naproxen and ibuprofen lose part of their crystallinity in 28 daysF11
marsac2008bF3. Felodipine and ketoconazole hardly change, and nothing changes without water or without PEOF11
marsac2008bF4. Water erodes PEO's own crystallinity, and PEO keeps taking up water for monthsF12
marsac2008bF5. Solubility in PEG 400 does not explain which drugs lose crystallinityF11, F3, F4
marsac2008bF6. The extent of loss follows the drugs' affinity for waterF11
baird2011F1. With no interaction term, the model predicts little drug in molten PEG 3350F2
baird2011F2. The higher the drug's melting point, the stronger the interaction it needsF2
baird2011F3. Measured phase diagrams: two drugs match the model, two do notF1, F2
baird2011F4. Back-calculated interaction energies are negative only for the two missesF2, F3
baird2011F5. Solubility in PEG 400 sorts the drugs the same wayF3
baird2011F6. In molten PEG, only the two misses show shifted carbonyl bandsF3
zhu2011F1. Four drugs interact favourably with PEG and dissolve in it; HLP and KET do notF1, F3, F4
zhu2011F2. Pure PEG lamellae thin within minutes, and crystallizing at 40 °C changes the long period by only about 1 nmF5, F7
zhu2011F3. Drugs that interact with PEG enlarge the long period by 3–5 nm while they stay amorphousF5
zhu2011F4. When the drug crystallizes, the long period falls back toward pure PEGF5, F8
zhu2011F5. Weakly interacting drugs leave the long period as in pure PEG, whether they crystallize or notF6
zhu2011F6. A drug Tg above 25 °C did not change the patternF6
zhu2012F1. Two drugs crystallize in seconds, two slowly and erraticallyF8, F9
zhu2012F2. PEG alone crystallizes within 2 minutes, more slowly at 40 °CF7
zhu2012F3. PEG delays and slows benzocaineF8
zhu2012F4. PEG leaves haloperidol unchangedF7, F8
zhu2012F5. PEG brings forward ibuprofen and fenofibrate, and their crystals start at PEG surfacesF8, F9
zhu2012F6. The drugs slow PEG, most where they hydrogen-bondF10

01Concepts

eutecticthe composition and temperature at which drug and PEG melt togethermonotectic systemdrugs that barely dissolve in molten PEG (haloperidol, ketoconazole)temperature-composition phase diagramthe liquidus curves from which eutectics and solubility were readmelting point depressionlowering of the drug and PEG melting points in the mixtureFlory-Huggins interaction parameter\chi from melting point depression and from the interaction energyenthalpy of mixingexothermic or athermal mixing inferred from \chi and \gammaactivity coefficientsolubility in PEG 400 and water against ideal solubilityideal solubilityreference for the activity coefficientsdrug solubility in polymereutectic content, extrapolated 25 °C solubility and PEG 400 stand-invan't Hoff equationextrapolation of solubility along the liquidushydrogen bondingdonor to the PEG ether oxygen, read from carbonyl shiftsdrug-polymer interactionsthe four readings and what they predictpolymer crystallizationcrystallization of PEG itself within minutesnucleation induction timeonset of drug and PEG crystallization in the comeltsheterogeneous nucleationcrystalline PEG as a nucleating surfacecrystallization tendencythe neat-drug property whose carry-over into PEG dispersions was testeddegree of supercoolingreduced by melting point depression; PEG at 25 against 40 °Cthermodynamic driving force for crystallizationthe argument for benzocaine's delayglass transition temperaturedrug Tg against the solidification temperature; Tg of water and PEOwater sorptionuptake of PEO and compacts at high RHplasticizationwater as plasticizer of amorphous PEO

02Formulas

5 more formulas printed by one paper (table only)
formularole hereexpression
ideal solubilitymole-fraction ideal solubility of the six drugsrelation not printed marsac2008b E1
Tg/Tm ratio ruleTg of naproxenT_g/T_m = 0.7 marsac2008b E5
water uptake normalized to polymer contentwater per PEO in the compacts\text{water per PEO} = \frac{\text{water uptake of the compact}}{0.9} marsac2008b E6
simplified solubility equationlink of solubility and free energy of fusion\ln\left[\gamma_d x_d\right] = -\frac{\Delta G_{fus}}{R\,T} baird2011 E5
normalization of the interaction parameter per PEG segment\chi of zhu2011\chi times the molar volume ratio of PEG to API, divided by the number of chain segments of a PEG molecule; segment number not printed zhu2011 E2

Sources: PEG dispersions

Every paper cited in the chapter PEG dispersions (category Solid state stability) and in the concept and formula drafts written from it. Keys are first-author surname plus year; a, b separate papers of the same author and year, assigned as in the chapter Crystallization tendency (marsac2008a is the PVP–nifedipine–felodipine paper, marsac2008b the PEO paper). The first four rows are the papers of the subcategory.

keyyeartitleslugcategory / subcategory
marsac2008b2008Spontaneous Crystallinity Loss of Drugs in the Disordered Regions of Poly(Ethylene Oxide) in the Presence of Water2008-marsac-peo-water-spontaneous-drug-crystallinity-lossSolid state stability / PEG dispersions
baird20112011Evaluation and modeling of the eutectic composition of various drug-polyethylene glycol solid dispersions2011-baird-drug-peg-eutectic-composition-modeling-solid-dispersionsSolid state stability / PEG dispersions
zhu20112011Time-Resolved SAXS/WAXS Study of the Phase Behavior and Microstructural Evolution of Drug/PEG Solid Dispersions2011-zhu-time-resolved-saxs-waxs-drug-peg-solid-dispersionsSolid state stability / PEG dispersions
zhu20122012Modification of Crystallization Behavior in Drug/Polyethylene Glycol Solid Dispersions2012-zhu-api-peg-solid-dispersion-crystallization-behaviorSolid state stability / PEG dispersions
baird20102010A Classification System to Assess the Crystallization Tendency of Organic Molecules from Undercooled Melts2010-baird-classification-crystallization-tendency-undercooled-meltsSolid state stability / Crystallization tendency
broman20012001A comparison of alternative polymer excipients and processing methods for making solid dispersions of a poorly water soluble drug2001-broman-polymer-excipients-processing-probucol-solid-dispersionsASD process / ASD process
marsac2006b2006Theoretical and Practical Approaches for Prediction of Drug–Polymer Miscibility and Solubility2006-marsac-drug-polymer-miscibility-solubilitySolid state stability / Miscibility and drug-polymer interactions
vaneerdenbrugh2010b2010Small Scale Screening To Determine the Ability of Different Polymers To Inhibit Drug Crystallization upon Rapid Solvent Evaporation2010-van-eerdenbrugh-polymer-crystallization-inhibition-spin-coating-screenSolid state stability / Miscibility and drug-polymer interactions
marsac2008a2008Recrystallization of Nifedipine and Felodipine from Amorphous Molecular Level Solid Dispersions Containing Poly(vinylpyrrolidone) and Sorbed Water2008-marsac-nifedipine-felodipine-pvp-sorbed-water-recrystallizationSolid state stability / Physical stability
marsac20092009Estimation of Drug–Polymer Miscibility and Solubility in Amorphous Solid Dispersions Using Experimentally Determined Interaction Parameters2009-marsac-drug-polymer-miscibility-solubility-asd-interaction-parametersSolid state stability / Miscibility and drug-polymer interactions
moseson20182018The application of temperature-composition phase diagrams for hot melt extrusion processing of amorphous solid dispersions to prevent residual crystallinity2018-moseson-temperature-composition-phase-diagrams-hme-asd-residual-crystallinityASD process / ASD process
For the authors: card issues found while writing

Card issues: PEG dispersions

Material problems found in cards while writing this chapter. The four subcategory cards were also scanned for ids cited in square brackets that no row or heading of the same card defines; none were found.

paperidproblem
2011-zhu-time-resolved-saxs-waxs-drug-peg-solid-dispersionsM1 (and the Tg statements of section 0.2, C16)The card gives the Tg of haloperidol as "below 25 °C", citing the classification paper. The card of that paper (2010-baird-classification-crystallization-tendency-undercooled-melts, M17) lists 33 °C for haloperidol, calculated from the molecular weight. The two cards disagree on whether haloperidol's Tg lies below the 25 °C solidification temperature, which matters for the Tg comparison of F6. The extractor of the Zhu card or of the Baird card (or the cited source) may be wrong; it could not be settled from the cards.
← Concepts and formulas

concept · as used in PEG dispersions

acid-base interaction

The transfer of a proton, or the formation of an ion pair, between an acidic and a basic group of drug and polymer, instead of a neutral hydrogen bond. In the papers of this chapter: the basic dimethylamino group of E100 with the weakly acidic OH groups of naringenin and quercetin (also resveratrol and curcumin); the carboxylic acids of HPMCAS, HPMCP, CAP and Eudragit L 100 with the tertiary amine of lumefantrine; and the strongly acidic sulfonic acid of PSSA with the amine or ring nitrogen of anthranilic acid, lidocaine and dibucaine [wegiel2013a C16, C17, C33; hiew2022a C25, C48; vaneerdenbrugh2011a C22, C38, C44]. The authors take ionic interactions to be "typically stronger" than hydrogen bonds, an assumption, and ascribe the unusual stability of E100 dispersions to them ("appear to be the reason") [wegiel2013a C16, C35]. For the enteric polymers the same contact is held to reduce hydration of the polymer carboxylates and so to slow release ("are postulated"; "is thought to") [hiew2022a C53].

Findings

Miscibility and drug-polymer interactions: F21, F23, F24, F25, F26. Physical stability: F24, F34.

Related concepts

depends on pKa; contrasts with hydrogen bonding, halogen bonding and hydrogen-bond donor and acceptor groups; part of drug-polymer interactions; acts on crystallization inhibition and physical stability; an alternative where intramolecular hydrogen bonding limits hydrogen bonds [wegiel2014 C44].

Formulas

free carboxylate fraction after ion pairing, Fox equation.

How it is measured or obtained

By the loss of the E100 amine bands at 2820 and 2770 cm⁻¹ with rising drug content [wegiel2013a R6]; by a protonated component of the N 1s XPS peak and by carboxylate bands at 1594–1560 and 1410–1343 cm⁻¹ in subtraction IR spectra [hiew2022a R19, R20]; by ATR-FTIR of melts at equimolar functional groups (spectra not shown) [vaneerdenbrugh2011a R8, R15, R17]; by colour change (curcumin with E100) [wegiel2014 R10, C20]: dark red for curcumin–E100 against orange for the others, read as a change of the drug's ionization state; by a dispersion Tg above both components [wegiel2014 C41]. For the weak base lumefantrine with acidic enteric polymers in the physical-stability papers, XPS of the N 1s signal gives the share of protonated drug, and ATR-FTIR shows the polymer carbonyl band moving up and a band near 1560 cm⁻¹ read as carboxylate ("likely") [trasi2020 P15, R9, C11, C12; bhujbal2021 P6, R6]. The pKa of each group is calculated or titrated to judge whether a proton can move [vaneerdenbrugh2011a P7; hiew2022a P17].

Values in the library
materialvalue or classconditionspaper ids
quercetin–E100amine bands gone at 50% quercetinIR, films[wegiel2013a R6]
resveratrol–E100; curcumin–E100bands absent at 50% resveratrol; eradicated at 60% curcuminIR, films[wegiel2013b R7, C15; wegiel2014 R7, C16]
lumefantrine, 25% drug loadingprotonated 19% (HPMCAS), 46% (HPMCP), 55% (CAP), 49% (Eudragit L 100); 0% with PVPVAXPS, dry compacts[hiew2022a R20]
same, after 2 h in pH 6.8 buffer3, 21, 54, 12%XPS[hiew2022a R20]
anthranilic acid, lidocaine, dibucaine with PSSAproton transfer reported; not with PAAATR-FTIR of melts (not shown)[vaneerdenbrugh2011a R8, R15, R17]
cationic drugs with HPMCAS-MF, 1:1 drug to carboxyl, pH 6.0≥70% of the polymer complexedco-precipitation[bapat2024 C19]
curcumin–E100 (basic monomer pKa 8.4; curcumin pKa 10.51, 9.88, 8.38)dark red; Tg 62 °C, about 19 °C above the Fox line after recalculation75:25 powder[wegiel2014 M5, M1, R10, X1, C41]
resveratrol–E100highest amorphous loading of six polymers (60%); "could be responsible" for better manufacturabilityrotary evaporation[wegiel2013b R2, C16, C43]
curcumin–E100; resveratrol–E100amorphous > 350 and > 400 days at 84% RHstorage, 25 °C[wegiel2014 R13; wegiel2013b R12.g]
lumefantrine 40:60 with HPMCAS, Eudragit L100, HPMCP, CAP16, 33, 48, 61% protonated; neat drug 7%rotary-evaporated powders, XPS[trasi2020 R11, C14]
lumefantrine with HPMCP, HPMCAS (20–40% drug), CAP, Eudragit L100 (40%)14–42% protonated; amorphous drug 3%powders precipitated into dilute HCl, XPS[bhujbal2021 R8]
fluorescein in miconazole–PVPVA filmslocated in the drug-rich phase, read as a possible acid–base contact with the weakly basic drug ("may arise")confocal dye screen[saboo2017 C36]

Evidence table: acid-base interaction.

Pitfalls and disagreements

The strength of the contact was not measured, and the causal role of the E100 contact in stability was not separated from other properties of E100 [wegiel2013a X10]. The naringenin–E100 spectra are described but not shown, and no polyphenol-side marker is reported [wegiel2013a C17, X10]. The melt spectra behind the PSSA reactions are not shown, and no acid–base reaction was seen for bifonazole [vaneerdenbrugh2011a X13, R16]. The lumefantrine values come from dry compacts and fall after dissolution, except for CAP; an earlier XPS study found no protonation with HPMCAS where this one found 19% [hiew2022a R20, R30, X14]. An ion pair does not guarantee stability: the 50% HPMCAS dispersion, with 1.61 mol drug per mol acid groups, crystallized within a week [hiew2022a R26, C63]. For curcumin the extent of proton transfer was not measured, and no polymer with the same backbone without amine groups was tested [wegiel2014 C37]. For resveratrol the IR-based ranking that put E100 first did not hold in storage, where PVP outperformed it [wegiel2013b X10]. In the lumefantrine powder studies the share of protonated drug ordered the stability of powders made without water but not of powders precipitated into water, where residual water and drying time decided [trasi2020 C36; bhujbal2021 C50, C51]. The polymer that protonated the drug most, CAP, released the least drug at 40% loading [trasi2020 R14; bhujbal2021 R15].

← Concepts and formulas

concept · as used in PEG dispersions

activity coefficient

The ratio of the ideal solubility to the real solubility of a drug in a solvent, \gamma_d; a value below 1 means that the drug dissolves better than ideal, far above 1 that it mixes much worse baird2011 E7, C23; marsac2008b E2, C14. If the entropy of mixing is close to ideal, \gamma < 1 points to exothermic mixing and favourable drug–solvent interactions and \gamma > 1 to endothermic mixing baird2011 C23; marsac2008a C34. New aspect (C. Amorphous solubility and LLPS): the activity coefficient γ of the drug in the dilute aqueous solution links concentration to activity, a = C\gamma or a = x\gamma; the amorphous solubility estimate assumes that γ in the bulk is the same at the crystalline and at the amorphous solubility, a "reasonable assumption" for dilute solutions of poorly soluble compounds [ilevbare2013a E7, C55; indulkar2015 C43; mosqueragiraldo2015 E5]. Micelles break the assumption of equal activity coefficients at the crystalline and the amorphous concentration: for atazanavir in 3.6 mg/mL SDS the slope of free against total drug, labelled γ, was 0.047, so the concentration ratio is about half the activity ratio [indulkar2017a R11, E8, C44]. For telaprevir the ratio of flux slopes below the plateau gives the ratio of activity coefficients (Eq. 7) [lu2017b E7]. New aspects (Miscibility and drug-polymer interactions): For a drug in a polymer the activity coefficient γ carries any non-ideal entropy or heat of mixing, and the mole-fraction solubility of the crystal is its ideal value divided by γ marsac2009 E1, C4. It splits into a combinatorial (entropy) part and a residual (enthalpy) part; exothermic mixing lowers γ and endothermic mixing raises it marsac2009 C10. In a polymer γ is much higher than in a small-molecule analogue because the polymer contributes less mixing entropy marsac2006b C50; marsac2009 C33. Estimating the solubility of a drug in a liquid is essentially the problem of determining γ, which is exceedingly difficult for drugs in viscous glassy polymers marsac2009 C4. New aspect (Bioperformance): γ appears in a = \gamma C for the donor and as γm for the membrane in the flux equation, and additives change the donor value [raina2015c E3, E4, C35]. The concentration-based supersaturation ratio assumes \gamma/\gamma_{eq} = 1; this holds in simple buffers, where the dilute solution is nearly ideal, and fails in media with micelles, where the solubilized fraction differs between the saturated and the supersaturated solution [elkhabaz2019b E2, C28, C42]. New aspect (Physical stability): the activity coefficient of water in an amorphous drug, from water uptake by Raoult's law a_{water} = \gamma_{water} X_{water}, and of the drug in water, from aqueous solubility; both were tested as predictors of moisture-induced separation and showed no trend [rumondor2009c E1, E2, C29].

Findings

PEG dispersions: F3, F11. C. Amorphous solubility and LLPS: F5, F12, F16. Miscibility and drug-polymer interactions: F8, F9. Bioperformance: F3, F6, F18. Physical stability: F2, F13.

Related concepts

depends on ideal solubility; measured by drug solubility in polymer; indicates enthalpy of mixing; related to Flory-Huggins interaction parameter and drug-polymer interactions, and chemical potential; part of thermodynamic activity; depends on combinatorial entropy of mixing.

Formulas

activity coefficient from solubility, Flory-Huggins melting point depression, activity from concentration, binodal condition, solid-liquid equilibrium solubility equation; Flory-Huggins activity equation.

How it is measured or obtained

From the mole-fraction solubility in a liquid analogue of the polymer, PEG 400, after 24 h at 25 °C with a UV assay, and the ideal solubility from the melting point and heat of fusion, \gamma_d = \frac{1}{x_d}\exp\left(\frac{-\Delta H_{fus}(T_m - T)}{R\,T_m^{2}}\right) baird2011 P5, P9, E7; marsac2008b P5, P9. PEG 400 is used because activity coefficients in viscous, semicrystalline PEG 3350 are hard to determine baird2011 C21. In the amorphous solubility papers it is not measured; in the liquid–liquid equilibrium form x_{L_1}\gamma_{L_1} = x_{L_2}\gamma_{L_2} it links the water-phase and drug-rich-phase compositions [ilevbare2013a E12]. For the PVP dispersions, from the solubility of the crystalline drug in 1-ethyl-2-pyrrolidone (excess drug, 25 °C, at least 24 h, UV–Vis, or HPLC with refractive-index detection for sucrose) and the ideal solubility from the melting point, heat of fusion and heat capacities; Eq. 8 then scales γ to PVP, assuming ideal entropy with EP, equal contacts and equal γ at both solubility limits marsac2009 P2, P7, E1, E8, C11. In the Bioperformance papers it was not measured; the slope of free against total drug is taken from atazanavir–SDS work [indulkar2017a R11, E8], and the solubility split into a crystal term and an activity-coefficient term was used to compare ritonavir and atazanavir [alhalaweh2016 E3, E4, E5]. In the moisture study, the water activity coefficient from the uptake of the amorphous drug at 95% RH and the drug activity coefficient from mole-fraction solubility [rumondor2009c P13].

Values in the library
materialvalue or classconditionspaper ids
chlorpropamide; aceclofenac; loratadine; haloperidol in PEG 4000.614; 0.121; 2.369; 0.84225 °Cbaird2011 R9.a, R9.b, R9.c, R9.d
acetaminophen, ketoprofen, naproxen, ibuprofen, felodipine, ketoconazole in PEG 4000.06, 0.31, 0.02, 0.64, 0.14, 0.0925 °Cmarsac2008b R14.a, R14.b, R14.c, R14.d, R14.e, R14.f
the same six drugs in water1.2 × 10¹, 1.4 × 10⁴, 3.8 × 10³, 3.1 × 10⁴, 2.4 × 10⁵, 5.3 × 10⁵cited aqueous solubilitiesmarsac2008b R14
nifedipine; felodipine in water1.89 × 10³; 2.43 × 10⁵25 °Cmarsac2008a R10.c, R10.d
five compounds in an ethyl-pyrrolidone analogue of PVPbelow 1 for all25 °Cmarsac2009 C23, R9
felodipine, nifedipine, ketoconazole, sucrose, indomethacin in EP0.89, 0.26, 0.68, 0.37, 0.1525 °Cmarsac2009 R9
same five in PVP K123.94, 1.18, 5.04, 1.76, 0.50scaled with Eq. 8marsac2009 R9
same five in PVP K29/324.34, 1.30, 5.92, 1.93, 0.54scaled with Eq. 8marsac2009 R9
nifedipine, felodipineχ-based activity from melting depression; no direct γFlory–Hugginsmarsac2006b E6
ritonavir, atazanavirlog γ ordering RTV > ATV (recomputed 4.65 against 3.01)pH 6.8[alhalaweh2016 X1, X2]
felodipine / nifedipine fluxγ/γ* assumed 1 for dilute solutionsbuffer[raina2015c C32]
atazanavir, posaconazoleconcentration-based and activity-based ratios agree in the two buffers and differ in the four micellar mediasix media, 37 °C[elkhabaz2019b R8, R9, C42]
water in nifedipine, felodipine, droperidol, pimozide, indomethacin, ketoprofen3.19, 4.13, 3.00, 4.65, 2.54, 3.3525 °C, 95% RH[rumondor2009c R24]
same drugs in water4.95 × 10⁵ to 8.88 × 10⁶; ketoprofen 9.85 × 10⁴from solubility[rumondor2009c R24]

The amorphous solubility chapter prints no activity coefficient value.

Pitfalls and disagreements

The conversion from mg/mL to mole fraction is not printed in Baird and Taylor; the printed values equal moles of drug per mole of PEG 400 in 1 mL, and a true mole fraction would give 0.766, 0.149, 2.49 and 0.856 instead of 0.614, 0.121, 2.369 and 0.842, leaving the split at 1 unchanged baird2011 X4. Loratadine, grouped with haloperidol as close to ideal, dissolves at about 0.42 of its ideal solubility baird2011 X13. Several rows of the Marsac and co-workers table are not internally consistent, aqueous solubilities come from three cited sources at unstated temperatures and the ideal solubility temperature is not stated, so the coefficients in water serve only as orders of magnitude marsac2008b X5, X18. Activity coefficients in PEG 400 were measured at 25 °C, far below the 52–61 °C of the molten dispersions, and are not values for molten PEG 3350 baird2011 X16. A value below 1 in PEG 400 did not separate the crystalline from the transforming drugs in PEO under humidity: all six were below 1 marsac2008b R14, R16. Ketoconazole has 0.09 in PEG 400 but a positive interaction parameter in PEG 3350 marsac2008b R14.f; zhu2011 R5.f. In the amorphous solubility papers the constancy of γ underlies the claim that a solubilizer leaves the maximum supersaturation unchanged, while a later study found the concentration ratio falling [ilevbare2013a C54; raina2015c C29]. There γ is estimated with the ideal dilute solution as standard state, from a buffer calibration [indulkar2017a R11], and is the factor in a = C\gamma; the PEG dispersions chapter defines \gamma_d instead as the ratio of ideal to real solubility in a liquid polymer analogue, so the values tabulated above are not those of the aqueous solutions. The predicted γ in PVP exceeds 1 for four of five compounds (1.18–5.97), so the compounds that dissolve better than ideal in the analogue are predicted to dissolve worse than ideal in the polymer; only indomethacin stays below 1 marsac2009 R9. Lattice volume, heat capacities, ideal solubilities and the mole-fraction basis in PVP are not printed marsac2009 X4, X13. The value of indomethacin in K29/32 differs between table and text marsac2009 X2. In the Bioperformance papers γ/γ* = 1 breaks down with solubilizers [raina2015c C36]; the plotted log γ in the ritonavir–atazanavir figure does not match the recomputation [alhalaweh2016 X1, X2]. The value of \gamma/\gamma_{eq} is not measured; its departure from 1 is read from the gap between the flux ratio and the concentration ratio (F18) [elkhabaz2019b C21, C28]. In the 2009 moisture study the drug-in-water column of the table equals the inverse mole-fraction solubility rather than the printed equation, so it ranks drugs by solubility alone [rumondor2009c X1]; two text rankings disagree with the table [rumondor2009c X2, X3].

← Concepts and formulas

concept · as used in PEG dispersions

amorphous-amorphous phase separation

The separation of an amorphous drug–polymer mixture into two amorphous phases of different composition, a drug-rich and a polymer-rich one, shown by two glass transitions or by imaging. In the miscibility papers it is the outcome of a miscibility test: solvent-cast films of itraconazole–HPMC (10–50% drug) and telaprevir with HPMC, PVPVA or HPMCAS carried discrete drug-rich domains in a polymer-rich matrix, and blends of long dextran and PVP chains split into a PVP-rich and a dextran-rich phase [purohit2015a C36, C37; li2016c C54; vaneerdenbrugh2012a C16, C17]. Both phases usually hold some of the other component, by partial miscibility or spectral mixing [li2016c C14]. The papers expect the drug-rich phase to crystallize faster, because less polymer surrounds the drug, and a polymer-rich phase to dissolve first [purohit2015a C51; li2016c C41]. Outside the subcategory it is produced by humidity (felodipine–PVP, miconazole–PVPVA, evacetrapib–HPMC) and by water or alcohol in the casting solvent (itraconazole–HPMC) [marsac2010 C14, C27; saboo2017 C42; li2017 C32; mugheirbi2017 C39; mugheirbi2018 R1]. New aspects (ASD process): it arises either because the pair is not miscible at the composition and temperature (thermodynamic) or because the solvent path through a miscibility gap, or later water, traps a separated state (kinetic) [mugheirbi2017 C3; li2017 C1]. The drug-rich phase can crystallize more readily and phase separation can lower the maximum concentration on dissolution [li2017 C1]. In spray-dried ritonavir–PVPVA powders it is read by aged DSC, a pyrene probe and XPS, and it lowered the 25% DL dissolution rate where the baseline release was fast [li2020 R4, R6, R7, R10]. In hydrating ritonavir–PVPVA tablets the drug-rich phase appears as small discrete droplets in a polymer- and water-rich gel (uncoated) or as connected drug-rich regions along particle boundaries (coated), imaged by confocal fluorescence microscopy [benson2025 R14, R16]. New aspect (Physical stability): the moisture-induced form in drug–PVP dispersions, its signatures (IR toward a non-interacting physical mixture, a second Tg near the drug's Tg, near-additive water uptake) and its consequence: crystallization then proceeds from a polymer-poor drug-rich phase [rumondor2009c C15, C24, C5, C6; marsac2010 C49]. New aspect (Release mechanism and LoC): water-induced AAPS of the hydrating dispersion is the authors' explanation of the limit of congruency. Two roles were proposed. As a source of nanodroplets (mechanism II, cited), drug-rich domains formed in the hydrated matrix would be released as droplets; the 2017 nifedipine and ritonavir papers found no evidence for this, the matrix domains being micron-sized against droplets an order of magnitude smaller [indulkar2017b C7, C26; purohit2017b C56]. As a cause of incongruent release, AAPS at the surface leaves a drug-rich layer once the polymer-rich domains dissolve; films above the limit separated on contact with water and films below it did not [indulkar2019a C8, C33; que2019 C35; saboo2020a C43]. If a drug-rich layer forms by AAPS, the drug controls release and the carrier effect of the polymer is lost [indulkar2017b C33]. Papers of 2020–2022 distinguish the morphology of the separated phase: discrete drug-rich domains went with congruent release and contiguous ones with incongruent release [saboo2021 C30, C53; correasoto2022a C53], while release of two high-Tg drug forms failed without visible separation [correasoto2022b R9; hiew2022b R19]. In dissolving compacts the high water content of the gel layer makes water-induced separation possible, favoured close to the solution where water is highest [yang2022a C44].

Findings

Miscibility and drug-polymer interactions: F18, F19, F22, F3, F23, F26. ASD process: F1, F6, F7, F14, F3, F20, F21, F48. Physical stability: F7, F12, F13, F14, F15, F23. Release mechanism and LoC: F5, F8, F12, F20, F22, F25, F27.

Related concepts

contrasts with drug-polymer miscibility; characterized by phase-separated domain size and spectral mixing; persists through kinetic trapping; lowers physical stability. Caused by moisture-induced phase separation or solvent-induced phase separation. Reversed by remixing of separated amorphous phases; driven in humid storage by the Δχ effect; set by drug-polymer-water miscibility. Its rate against dissolution is phase separation kinetics; produces surface drug enrichment; favoured by hygroscopicity; its morphology is phase separation morphology.

Formulas

Gibbs free energy of mixing, additive moisture sorption, multicomponent Flory-Huggins free energy of mixing, Δχ effect.

How it is measured or obtained

Two Tg events by DSC (one Tg is read as miscible, with the limits in single-Tg miscibility criterion) [vaneerdenbrugh2012a P3, C3]; pyrene and prodan fluorescence and fluorescence imaging, AFM-nanoIR, nanoTA, Lorentz contact resonance and AFM topography [purohit2015a P3, P4, P9, P10; li2016c P2, P4, P7, P8]; for polymer pairs also the hydrogen-bonded fraction of PVP carbonyls by FTIR [vaneerdenbrugh2012a P5]. In the later process papers: two Tgs by DSC, AFM with LCR or nanoTA, fluorescence microscopy and the drug's autofluorescence, TEM with EDX or HAADF [li2017 P9, P10, P13; mugheirbi2017 P8, P9; li2019 P10]. In the moisture papers: IR against a physical-mixture spectrum built from C–C band ratios; DSC wet and re-dried; sorption against additivity; AFM and TEM [rumondor2009c P7, E7, P9, P12; marsac2010 P14, P15]. In the release-mechanism papers: Pyrene I/III ratio, nile red or prodan confocal fluorescence, AFM and DSC of films and powders after 97–100% RH, or of films dipped in buffer for seconds [purohit2017b R2, R3, R4, R5, R6; indulkar2019a R18; que2019 R14; saboo2019 R19; saboo2020a R23]; pyrene and TEM of spray-dried particles [bhardwaj2018 R15, R16].

Values in the library
materialvalue or classconditionspaper ids
itraconazole–HPMC 10:90 to 50:50drug-rich domains at every loading by four film methods; one broad Tg by DSC of powderssolvent-cast from methanol–dichloromethane[purohit2015a R1, R11, R13, R7]
telaprevir–HPMC, –PVPVAdomains from 10% drugspin-coated films[li2016c R4, R6]
telaprevir–HPMCASregular domains only from about 30–40% drugspin-coated films, humidity not controlled[li2016c R5, C17, X2, X9]
dextran–PVP, 20 pairsphase separated at 0, 0–5, 5–7, 5–9 of nine compositions for DEX1, DEX6, DEX40, DEX450DSC, freeze-dried[vaneerdenbrugh2012a R13]
felodipine–PVP, 30–50% PVPdrug-rich and polymer-rich phases after 94% RHIR, TEM[marsac2010 C14, C27]
miconazole–PVPVA 50:50domains after film formation at 60% RH and after 75% RH storageAFM, confocal[saboo2017 R13, R15, C42]
telaprevir–PVPVA, 70% PVPVAtwo overlapping Tgs; "may have partially phase separated"mDSC[mosqueragiraldo2018b R23, C53]
ECP–polymerdrug-rich spheres (preparation) or drug-rich network (storage)TEM-EDX[li2017 R18, R19, R22]
ITZ–HPMCdiscrete drug-rich domains with self-associated ITZ (extra emission near 381 nm)FLOM, AFM, UV, emission[mugheirbi2017 R1, R22]
LPV–HPMCdiscrete drug-rich domains 50–500 nm high in a polymer-rich matrix; faster release at 33–85% DLAFM, nanoTA, release[li2019 R8, R2]
ritonavir–PVPVA spray-driedsecond non-reversing DSC event after ageing in 50% DL powders from 10:90 to 40:60; drug-rich surfaces (XPS) from 60:40; SNDR at 25% DL about 3.5 → 2.27 → 0.90 mg·min⁻¹·cm⁻¹BLD-35 dryer[li2020 R4, R7, R10]
pimozide–PVP 50:50Tgs −21/44 °C wet, 61/112 °C re-dried94% RH, 42 h[rumondor2009c R17]
felodipine–PVP 46.5 wt%event at ≈45–50 °C instead of one Tg near 80 °Cafter 75–94% RH[marsac2010 R14]
felodipine–PVP 50% filmislands of about 300–500 nm (TEM, AFM)94% RH[marsac2010 C41]
felodipine–PVP at 93% RHcrystallization independent of PVP level; plateau 70–80%powders[rumondor2009b R21, R11, C20]
felodipine, quinidine, pimozide with PVPVA; pimozide with HPMCAStwo Tgs after 94% RH50:50 powders, dried[rumondor2010c R3.a, R3.c, R3.d, R3.e]
indoprofen, clofoctol, probucol, nilutamide, loratadine with PVPseparation at 70–90% PVP for all; at every composition for nilutamide and loratadineIR, 54–94% RH[rumondor2011 R14]
ritonavir with PVP, PVPVA; HPMCASall PVP and PVPVA dispersions separated, from about 1 h; HPMCAS stayed miscible97% RH, films and powders[purohit2017b C1, C22]
ritonavir 50:50 PVP filmdark domains of about 1–3 µm in a drug-rich continuous phase after 10 s in buffer; 10:90 uniformdried after immersion[purohit2017b R4]
ritonavir–PVPVA films 20, 30, 40%uniform; sparse bright domains; dense domains (LoC 25%)seconds in water[indulkar2019a R18, C20]
ledipasvir–PVPVA films 5, 10, 50%mostly homogeneous; small domains; ≈10–20 µm domains100% RH, 37 °C, 3 days[que2019 R14, C16]
nilvadipine 10:90 film and compactdrug-rich circles and rings of roughly 5–15 µm; rough surface gone after 15 min of dissolution ("superficial")97% RH, 12 h[saboo2019 R19, R17, C24]
felodipine 30% films with PVP, PVPVA, HPMC; HPMCAS, EUDSdiscrete domains; uniform97% RH, 24 h[saboo2020a R23, C23]
ITZ–PVPVA 20% spray-dried particlesno separate drug-rich and polymer-rich phases by pyrene or TEM, also with water in the solventbefore dissolution[bhardwaj2018 C35, C37]
felodipine 30% films with 0–10% TPGSall separated after 12 h; semi-continuous (0, 2%) against discrete (5, 10%) drug-rich domains≈100% RH[saboo2021 R21]
clopidogrel 40, 50, 60% filmsuniform; bicontinuous; drug-continuous5 min, 100% RH[correasoto2022a R20]
atazanavir 10% filmuniform for 3 h at 37 °C; separated within 10 min at 50 °C100% RH[correasoto2022b R9, R12]
lumefantrine free base, benzoate; sulfate filmsseparated; homogeneoushigh RH, 37 °C[hiew2022b R19]
ritonavir–PVPVA 30:70:5 with Tween 80; Span 20Tg onset of surface material 66.01 → 40.25 and 67.85 → 42.18 °C after dissolution, read as a ritonavir-rich phaseDSC, scraped after dissolution[indulkar2022 R19, C19]
ritonavir–PVPVA 10–40% compactsdroplets near the gel–solution boundary (10–20%); continuous drug-rich layer at the interface (30–40%)real-time confocal, pH 6.8[yang2022a R10, R11, R12, R13]
MePHPH–PVPVA; PHPH–PVPVA compactsseparation in the gel layer of most compacts; segregative (MePHPH) and associative (PHPH)in situ confocal with two dyes[deac2023a R6, R7, C25, C28, C71]

Evidence table: amorphous-amorphous phase separation.

Pitfalls and disagreements

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

← Concepts and formulas

concept · as used in PEG dispersions

amorphous-crystalline free energy difference

The Gibbs free energy of converting the crystal to the amorphous drug (supercooled liquid or glass) at the test temperature; it fixes the factor e^{\Delta G/RT} of the amorphous solubility [almeidaesousa2015 E1, E11]. It is estimated from Tm and ΔHf by the Hoffman equation or from temperature-dependent heat capacities by a thermodynamic cycle (the Cp method), to the supercooled liquid or, below Tg, to the glass [almeidaesousa2015 E2, E9, E10, E14].

Findings

F5, F7.

Related concepts

estimated by the Hoffman equation; depends on degree of supercooling; sets the amorphous solubility advantage; reference state discussed under structural relaxation.

Formulas

Hoffman equation, amorphous-crystalline free energy difference from heat capacity, Gibbs free energy relation.

How it is measured or obtained

DSC melting data and modulated-DSC reversing heat capacities fitted linearly in T for crystal, glass and supercooled liquid; the Cp method needs an un-ionized, non-solvated crystal that melts without degradation [almeidaesousa2015 P5, P6, C11; mosqueragiraldo2015 P3].

Values in the library
materialvalue or classconditionspaper ids
ibuprofen, phenylbutazone, tolnaftate3.24/3.56; 4.84/4.59; 5.69/6.13 kJ/mol (Hoffman / Cp, to supercooled liquid)25 °C[almeidaesousa2015 R11]
diclofenac; sorafenib; griseofulvin8.51/9.99; 10.33/10.34; 9.69/9.39 kJ/mol25 °C[almeidaesousa2015 R11]
sorafenib; griseofulvin, to the glass11.37; 10.38 kJ/mol25 °C[almeidaesousa2015 R12]
CRH15.68 (Hoffman); 5.85 (Cp, supercooled liquid); 5.95 kJ/mol (Cp, glass)25 °C[almeidaesousa2016 M1]
telaprevir, Hoffman13.31 kJ/mol (extractor recomputation)37 °C[mosqueragiraldo2015 E1]
atazanavir14.55 kJ/mol, Hoffman, recomputed from the printed Table I inputs (ratio about 62, as printed, with 0.22 read as exp[−I(a)]; about 228 read as I(a))310 K[indulkar2017a E2, X1; indulkar2015 M2]
Pitfalls and disagreements

The Cp parameters are not printed, so the Cp values cannot be recomputed [almeidaesousa2015 E9, E10]. The claim that the Cp method is more accurate presupposes that the onset equals the supercooled-liquid solubility [almeidaesousa2015 X4]. The glass carries more free energy than the supercooled liquid below Tg [almeidaesousa2015 C29]. For atazanavir (undercooling 171 K, synthesis: 481 − 310 K) the Hoffman inputs printed give the printed ratio of 62 only with 0.22 read as exp[−I(a)], not I(a) as Table I heads the column (synthesis) [indulkar2017a X1; indulkar2015 M2]; for pazopanib the cycle cannot be run because it degrades on melting [sugihara2018 C17].

← Concepts and formulas

concept · as used in PEG dispersions

amorphous salt

The amorphous form of a drug salt; salt formation adds an ionic interaction between the protonated base and the counterion, taken to dominate over hydrogen bonding in setting Tg [towler2008 C23]. Combining salt formation and amorphization "may be desirable", for example for a lyophilized product [towler2008 C18].

Findings

F20.

Related concepts

depends on glass transition temperature; related to crystallization tendency and physical stability.

Formulas

none in this chapter (counterion descriptors listed in the chapter table).

How it is measured or obtained

Prepared by freeze-drying or melt quenching and checked by DSC [towler2008 P3, P5, R1]; Tg, recrystallization on heating, moisture sorption and storage at high humidity are then measured [towler2008 P6, P8, P9]; later by open-dish storage at 40 °C/75% RH [hiew2022b R7; duong2022a C32].

Values in the library
materialvalue or classconditionspaper ids
propranolol saltsTg 9.0–35.9 °C against −9.3 °C for the baseDSC[towler2008 R4]
nicardipine saltsTg 28.5–81.0 °C against 3.2 °C for the baseDSC[towler2008 R5]
20 salts of both bases11 amorphous after freeze-dryingDSC[towler2008 R1]
propranolol salts0.39–61.90% water uptake at 75% RHvapour sorption[towler2008 R8]
lumefantrine saltsbenzoate, PEG 250 diacid, besylate crystallized within 4 weeks; HCl and sulfate not for at least 16 weeks40 °C/75% RH[hiew2022b R7]
delamanid saltsstable 2 weeks; salt formation raised Tg40 °C/75% RH[duong2022a C32, C47]
Pitfalls and disagreements

Stoichiometry and ionization state of the amorphous salts were not reported [towler2008 X8]. Crystallization and moisture uptake did not follow counterion pKa [towler2008 C14, C34]; drug or salt Tg appeared an important predictor for lumefantrine [hiew2022b C37], yet the highest-Tg propranolol salt crystallized [towler2008 R12]. Salt formation did not change delamanid crystallization in dispersion films at pH 3.0 [nguyen2023b C17].

← Concepts and formulas

concept · as used in PEG dispersions

amorphous solid dispersion

A drug dispersed in a polymer in the amorphous state to raise dissolution rate and supersaturation. In the amorphous solubility and LLPS papers an ASD matters as a route to supersaturation: dissolved beyond the amorphous solubility it gives a drug-rich phase and a cap on the free drug (F8, F13) [ilevbare2013a C52, C5; almeidaesousa2016 C6]. The ASDs tested were ritonavir:PVP 1:9 and CRH1:HPMC 20:80 [ilevbare2013a P13; almeidaesousa2016 M7]. The ueda2020b, ueda2021 and ueda2022 studies add that the polymer of an ASD, once dissolved, enters the drug-rich phase and lowers the amorphous solubility, so a higher polymer:drug ratio in the ASD can "conceivably" reduce the supersaturation advantage further; the studies used dissolved polymers, melt-made ibuprofen ASDs for DVS and solid-state NMR, and no dissolving ASD [ueda2020b C37, C55; ueda2021 P6; ueda2022 P5]. New aspects (Miscibility and drug-polymer interactions): A molecularly mixed, single-phase, homogeneous mixture of drug and polymer, in older wording a "glass solution" in which a solute is dissolved in a glassy solvent [kestur2010b C4; taylor1997 C1]. Amorphous dispersions are used to raise apparent solubility and dissolution, but the amorphous phase is metastable and may crystallize during storage or dissolution [taylor1997 C1, C2; vaneerdenbrugh2010b C6, C7]. The miscibility papers hold that the polymer must be in the same amorphous phase as the drug to be effective ("it is generally accepted") and that maximum stabilization "can only be realized" with intimate mixing, so that a physical mix does not inhibit crystallization [kestur2010a C2; rumondor2009a C3]. Dispersions made by solvent evaporation were not always molecularly mixed: itraconazole–HPMC and telaprevir films carried drug-rich domains [purohit2015a C36; li2016c C54], and neat naringenin and quercetin could not be made amorphous by rotary evaporation, so a polymer was needed to make the dispersion at all [wegiel2013a R7, C46]. Ionizable polymers (E100, HPMCAS, HPMCP, CAP, Eudragit L 100, PAA) add acid–base contacts [wegiel2013a M4, M8; hiew2022a M3, M4, M5, M6]. New aspects (ASD process): the earliest paper of that chapter asks which carrier and process give a useful solid form of an extremely poorly soluble drug and finds that the carrier set whether probucol stayed amorphous broman2001 C1, C14. (synthesis: the paper's "solid dispersions" include samples that are not amorphous, since the probucol–PEO and probucol–PAA dispersions are mainly crystalline Form II broman2001 R4.c–f.) The ASDs of the process papers were also made by solvent granulation of drug and polymer onto lactose and cellulose [trasi2019 C50], by spray drying from water-containing methanol [li2020 P1] and by extrusion of physical mixtures of drug and polymer [moseson2020 P4]. New aspect (Bioperformance): the ASD is a drug dispersed amorphously in a polymer (or, in alhalaweh2016, in a mix with a second drug) that releases drug into supersaturation. Rotary-evaporated dispersions were used in alhalaweh2016, hate2018, mosqueragiraldo2018b and elkhabaz2017, and commercial capsules in purohit2018 [alhalaweh2016 P3; hate2018 P5; mosqueragiraldo2018b P1; elkhabaz2017 P6; purohit2018 M2]. Later papers dose such dispersions to animals: rotary-evaporated enzalutamide dispersions to rats, spray-dried pretomanid tablets to monkeys, and generic and innovator tacrolimus capsules to dogs, the generic being a mainly physical mixture of amorphous drug with HPMC and the innovator an intimate dispersion [wilson2018 P10; wilson2020 P1; nguyen2023a P4, P5; purohit2019 C21]. New aspect (Physical stability): the physical-stability papers call the drug–polymer glass a molecular (one-phase) dispersion when it shows a single Tg and drug–polymer hydrogen bonds by IR [konno2006 C8, R5; rumondor2009c C1], and stress that a polymer can inhibit crystallization only while it stays intimately mixed with the drug [marsac2010 C31]. In the study of marketed tacrolimus capsules the term is used strictly: a product that contains the polymer but holds the drug as an amorphous coating on lactose, not mixed with HPMC, is in the authors' belief not an amorphous solid dispersion, and molecular-level mixing is "considered to be essential" for stabilization [trasi2017 C47, C50].

Findings

C. Amorphous solubility and LLPS: F8, F13, F14, F19, F20, F21. Miscibility and drug-polymer interactions: F1, F3, F9, F15, F16, F18, F19, F23, F26. ASD process: F17, F18, F19, F22, F23, F24. Bioperformance: F6, F8, F9, F11, F16, F23, F24. Physical stability: F1, F12, F14, F23, F24, F26, F27, F28, F29, F30, F33, F35.

Related concepts

produces a drug-rich phase above the amorphous solubility; relieved by crystallization unless a polymer is present (F14); requires drug-polymer miscibility; stabilized by drug-polymer interactions and kinetic stabilization; related to crystallization inhibition and supercooled liquid. Processed in the HME operating design space. Sets drug loading effects; related to non-sink dissolution. Can undergo amorphous-amorphous phase separation; stabilized by crystallization inhibition by polymers.

Formulas

Gordon-Taylor equation.

How it is measured or obtained

Rotary evaporation from methanol (ritonavir) or methanol/dichloromethane (CRH1) and incremental or single-dose non-sink dissolution [ilevbare2013a P13, P14; almeidaesousa2016 P2, P11]. The dispersions of the miscibility papers were made by dissolving drug and polymer in a common solvent and removing it: rotary evaporation from methanol, ethanol, chloroform or dichloromethane–ethanol, followed by vacuum drying [taylor1997 P3; rumondor2009a P1; vaneerdenbrugh2010b P6]; spin coating on coverslips, ZnSe or KRS5 for films vaneerdenbrugh2010b P1; marsac2009 P4; cryomilling of a 10% w/w dispersion with crystalline drug and melt-quenching for the low-polymer growth samples [kestur2010a P1, P2]. A physical mix of amorphous drug and polymer is the control without molecular mixing [taylor1997 C24, C26]. Amorphous state is checked by XRPD or polarized light [taylor1997 R1; vaneerdenbrugh2010b P2]. Further preparations: rotary evaporation at 45–60 °C with 24 h vacuum drying and cryomilling [wegiel2013a P1; hiew2022a P5]; spin coating on KRS-5, ZnSe or quartz [purohit2015a P2, P9]; freeze-drying of aqueous polymer blends [vaneerdenbrugh2012a P2]; 50 mg compacts for release [hiew2022a P9]. In the process papers the solid form was read by Raman and DSC (single Tg between those of the components; polymer-free marker band) broman2001 P1, P2, R1, R4. In the Bioperformance papers the dispersions were made by rotary evaporation from methanol and cryomilling, and checked by PXRD, DSC, PLM and SHG [hate2018 P5, P10; elkhabaz2017 R8]. In the physical-stability papers: spin-coated films (dichloromethane:ethanol, ethanol or chloroform, heated to 90 °C) for nucleation, growth and IR; rotary-evaporated and, for low polymer contents, cryomilled powders for DSC, sorption and PXRD [konno2006 P1, P3; rumondor2009c P1; rumondor2009b P1; kestur2010b P1]. Spin-coated films and rotary-evaporated powders of nine 50:50 drug–polymer pairs [rumondor2010c P1, P5]; rotary evaporation in 5% steps to find the highest amorphous loading [wegiel2013b P1]; rotary evaporation followed by cryomilling [wegiel2014 P2, P3]; a 10% PVP dispersion diluted with crystalline drug by cryomilling, then melted, to reach 3% PVP [kestur2013a P4; kestur2013b P2].

Values in the library
materialvalue or classconditionspaper ids
ritonavir:PVP 1:96.4, 11.8, 18.3, 18.0 µg/mL with 6.0, 12.0, 18.0, 24.0 added100 mM pH 6.8, 37 °C[ilevbare2013a R17]
CRH1:HPMC 20:80about 12.9 µg/mL without polymer in the medium; HPLC maximum about 13.2pH 4.6, 25 °C[almeidaesousa2016 R8, R12]
indomethacin–PVP-K90, 5–70 wt% PVPamorphous by XRPD; interactions in dispersions, none in physical mixesmethanol, rotary evaporation[taylor1997 R1, R10, R11, R12]
felodipine–PVP, nifedipine–PVPone amorphous phaseIR, PXRD[rumondor2009a C38]
8 drugs × 7 polymers392 spin-coated compositions scored over 7 daysethanol or ethanol–dichloromethanevaneerdenbrugh2010b R2
50/50 drug–PAA, drug–PVP powderscrystalline with PAA for acidic drugs, amorphous with PVProtary evaporation, 7 daysvaneerdenbrugh2010b R9
felodipine, 0.5–4.5% w/w polymermade by diluting a 10% dispersion by cryomillingmelt-quenched films[kestur2010a P1, C5]
naringenin, quercetin with six polymershighest X-ray amorphous polyphenol content about 20–85%; E100 highest, PAA lowestrotary evaporation at 60 °C, cryo-milled[wegiel2013a R8]
lumefantrine with PVPVA and four enteric polymersall X-ray amorphous with one Tg, except 50% HPMCAS (melted at 126.3 °C on heating)rotary evaporation at 45 °C, sieved below 250 µm[hiew2022a R4, R6]
itraconazole–HPMC, telaprevir–polymersdrug-rich domains in the filmsspin-coated from methanol–dichloromethane[purohit2015a R11; li2016c R4, R5, R6]
probucol–PVP K30 50:50amorphous; Tg 95 °C (solvent), 129 °C (moulded)Raman, DSCbroman2001 R4.a, R4.b
probucol–PAA, –PEOmainly Form IIsamebroman2001 R4.c–f
probucol–PVP–PAA 50:25:25mainly amorphousboth routesbroman2001 R4.g, R4.h
ritonavir and lopinavir with PVPVA 1:1 on lactose:MCCX-ray amorphous granules, unchanged for one month at 40 °C/75% RHsolvent granulation[trasi2019 R1, R2]
ritonavir–PVPVA spray-dried, 25–75% DLX-ray amorphous (methanol powders); one Tg of 91, 75 and 63 °Cspray drying[li2020 R1, R2]
ritonavir/atazanavir/lopinavir in PVP K29/3290% polymer, Tg 139–160 °C10% drug[alhalaweh2016 R4]
atazanavir in HPMCAS, HPMC, PVPVA10, 30, 50%X-ray amorphous[hate2018 R10]
telaprevir in HPMCAS, HPMC, PVPVA, CA Sub10, 30, 50%one Tg for HPMCAS 50%[mosqueragiraldo2018b R15, R23]
ezetimibe in PAA, PVP, HPMC-AS50:50no crystals by PLM or SHG[elkhabaz2017 R8]
tacrolimus capsulestacrolimus:HPMC 1:1; drug about 4% of fillgeneric[purohit2018 M2, R2]
enzalutamide in PVPVA or HPMCAS-MF10 and 50 wt% drug, rotary-evaporated, amorphous by XRPD and FTIRused within 2 weeks[wilson2018 P10, P11]
enzalutamide in CA Sub or CPHPC-106CA Sub 50%; CPHPC-106 10 and 50% drugrotary evaporation[wilson2020 P1, A3]
atazanavir in AS-LF or AS-HF1:9, spray-drieddissolution and transport[ueda2020a P1, M14]
pretomanid in HPMCAS-HF, MF, LF blends20% drug in the monkey tablets, spray-dried; screening powders rotary-evaporatedwith TPGS or tris in two tablets[nguyen2023a P4, P5]
felodipine with PVP, HPMCAS, HPMC 0–100%single Tg at every compositionrotary-evaporated, DSC[konno2006 R5, C8]
five drugs with PVPdry dispersions one phase by IR; single Tg for droperidol and pimozidespin-coated and rotary-evaporated[rumondor2009c R3, R5, C1]
felodipine with 0.5–4.5 wt% PVPmade by cryomilling a 10% dispersion with crystalline drug, then meltingto avoid partial crystallization on rotary evaporation[kestur2010b P1]
resveratrol with E100, PVP, HPMC, HPMCAS, CMCAB, PAAhighest X-ray amorphous loading 60, 45, 40, 35, 35, 15%rotary evaporation[wegiel2013b R2]
curcumin with five polymers75:25 dispersionsrotary evaporation, cryomilling[wegiel2014 P2, P3]
tacrolimus–HPMC 1:1 (solvent cast) and six marketed capsulesdispersion amorphous 4 weeks at 40 °C/75% RH; one generic 57–95% crystalline at 4 weeksopen dish[trasi2017 R16, R13]
ATP enantiomers with 5% w/w polymermelt-quenched films from solvent-evaporated mixturesgrowth at 40–90 °C[sato2015 P1, P3]
indomethacin with 10% w/w HPMC, HPMCAS or PVPsolvent-evaporated dispersion, then melt-quenchedgrowth from 80 °C to near Tm[tian2017 P2]
Pitfalls and disagreements

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

← Concepts and formulas

concept · as used in PEG dispersions

amorphous solubility advantage

The factor by which the amorphous drug is more soluble than the crystal, e^{\Delta G/RT} from the crystal–amorphous free-energy difference, reduced by the activity of the water-saturated amorphous drug [ilevbare2013a E1, C60; almeidaesousa2015 E1]. In the amorphous solubility and LLPS papers the measured counterpart is the supersaturation ratio at the LLPS onset (F6). The papers of 2017–2022 add measured values of the ceiling ratio of 63.6 (atazanavir, synthesis: 70 ÷ 1.1), 28.5 (telaprevir, synthesis: 148 ÷ 5.2), about 600 (pazopanib) and 2.5–5.9 (ibuprofen, falling with temperature), and that micelles lower the concentration-based advantage (atazanavir 65 → 33) without lowering the activity-based one [indulkar2017a R4, R6, R13; lu2017b R2, R1; sugihara2018 R4; ueda2022 R16]. New aspect (ASD process): it is the supersaturation an ASD can reach if it stays amorphous and dissolves; crystals in the dispersion "directly" lose their share of it ("potency") and may also consume what is generated [moseson2020a C3]. For bicalutamide the maximum advantage over the stable form is 35-fold [moseson2021 R2]. In the pH-shift test of posaconazole the dose was set at about 10 times the amorphous solubility in the intestinal medium (19.1 µg/mL), that is about 191 µg/mL, and 200 µg/mL at full release [shah2024 P11, X9]. New aspect (Bioperformance): the ratio is computed by the Hoffman estimate with water correction or taken as the LLPS onset over the crystalline solubility [raina2014a R7; raina2015c E8]. New aspect (Crystallization from solution): in the solution-crystallization papers the advantage fixes the highest supersaturation tested: the calculated amorphous solubility over the crystalline solubility gives S 15.3–15.4 for ritonavir and about 14.7 for celecoxib, and the "amorphous benchmark" S of about 10 for felodipine [ilevbare2012b R3; ilevbare2013c E1, R2; alonzo2012 C42]. The measured counterpart is the plateau after a pH shift or the onset of phase separation (F2). For six dihydropyridines the estimated ratios of amorphous to crystalline solubility in buffer were 16.1 (cilnidipine), 9.03, 8.42, 23.0, 11.7 and 22.9, not reproducible from the printed inputs (felodipine 5.93 recomputed against 6.68 µg/mL); for danazol the recalculated estimate of 7.8 µg/mL is a ratio of 8.7 against the earlier 19.6 [raina2015b X2; jackson2016 R3, R4]. New aspect (Supersaturation from ASD dissolution): the calculated advantage is the yardstick for what a dissolving amorphous solid or dispersion should reach, and the question is whether a dispersion can exceed that of the pure amorphous drug: by flux it did not for felodipine, and the authors add that thermodynamics gives "no reason to expect" the two to be equal [alonzo2011 C22, C45]. The advantage is "rarely achieved" because the solid or the solution crystallizes [konno2008a C4; alonzo2010 C2]. For six marketed tacrolimus capsules the advantage of about 35-fold was "sustained throughout" a 2 h non-sink test [trasi2016 C44, C16]; mixing the drug with a polymer that does not dissolve lowers the advantage a dispersion can realize [li2018 C67].

Findings

Amorphous solubility and LLPS: F5, F6, F7, F12, F14, F16, F21. ASD process: F23, F26, F27, F28, F39, F41. Bioperformance: F1, F4, F18. Crystallization from solution: F2, F9, F14, F19, F21, F22, F34. Supersaturation from ASD dissolution: F1, F5, F7, F18, F22, F23, F28, F29.

Related concepts

same as the ceiling supersaturation ratio; built from amorphous-crystalline free energy difference and water sorption correction of amorphous solubility; gives the amorphous solubility. Realised in non-sink dissolution; lost to residual crystallinity and matrix crystallization; lowered by mutual amorphous solubility reduction. Depends on Hoffman equation; estimated with the Gibbs-Duhem equation water correction; depends on crystalline solubility; related to free drug concentration.

Formulas

amorphous solubility advantage with water-sorption correction, amorphous solubility advantage from free energy difference, supersaturation ratio. Amorphous-to-crystalline solubility ratio, Hoffman equation.

How it is measured or obtained

By calculation (Hoffman or heat-capacity free energy, sorption isotherm) and by the onset [almeidaesousa2015 P9, P10]; also by dissolving an amorphous film [ilevbare2013a P4]. In the ASD process papers: crystalline solubility by 72 h shake flask; amorphous solubility as the onset of light scattering during solvent-shift addition (liquid–liquid phase separation), in some cases only with a polymer present because the drug crystallised too fast without it [moseson2020a P7, P8; moseson2021 R1, R27]. In the Bioperformance papers it is estimated from melting data or as onset ÷ crystalline solubility [raina2015c P3, P6]. In the crystallization-from-solution papers: calculated with the Hoffman equation and a water-sorption correction; measured by dissolving a spin-coated film (ritonavir), by pH-induced precipitation, and by the onset of phase separation of a solvent-shifted solution [ilevbare2012b P4–P6; hsieh2012 P11; jackson2014 P6, P7]. In the ASD dissolution papers: calculated from melting data with the Hoffman equation and the measured crystalline solubility [konno2008a P7; alonzo2010 P12; alonzo2011 P8]; tested against flux relative to the crystal [alonzo2011 R14].

Values in the library
materialvalue or classconditionspaper ids
ibuprofen to griseofulvinpredicted 3.7/4.2, 7.0/6.4, 9.8/11.7, 28.9/52.5, 48.4/48.6, 34.8/30.9 (Hoffman / Cp method)25 °C[almeidaesousa2015 R13]
clotrimazole; atazanavirpredicted about 9.2 and 62; measured about 13 and about 6337 °C[indulkar2015 R3, R10]
felodipine, buffer; with 0.04% vitamin E TPGS; in FaSSIFabout 9.2; 4.5; 5.0 (concentration-based)37 °C[raina2015c C29]
tacrolimusabout 35 (49/1.4), about 33–36 by method; other drugs 5–65amorphous solubility by ultracentrifugation, pH 4.5, 37 °C[trasi2016 R16, R17, X9]
IDM, pH 4.5 acetatecrystalline about 8, amorphous about 80 µg/mL (about 10-fold, synthesis); unchanged by 50 µg/mL PVPVA37 °C[moseson2020a R1]
BCL, pH 6.8 phosphateform 1 4.3, form 2 15, amorphous 150 µg/mL; 35-fold37 °C[moseson2021 R1, R2]
RTV and LPV, pH 6.8crystalline 1.8 and 2.9, amorphous 31 and 19 µg/mL10 mM phosphate, 37 °C[trasi2019 M1, M2]
IDM–PVPVA with 25% residual crystalsC720 about 28.8 against about 43.1 µg/mL: the share of the advantage lost with the crystals50 µg/mL total dose[moseson2020a R6]
posaconazole in FaSSGF and FaSSIF V2LLPS concentration (taken as the amorphous solubility) 2326 and 19.1 µg/mL against crystalline 86.5 and 1.2 µg/mL, ratios about 27 and 16 (arithmetic on the cited values)37 °C[shah2024 R11, C14]
ritonavir / atazanavir / lopinavirabout 14 / 83 / 6pH 6.8[alhalaweh2016 R6]
clotrimazole15pH 8[indulkar2016 R3]
atazanavirobserved ratio in SDS about half that in buffer, with unchanged activity[indulkar2017a C64, C45]
atazanavir, posaconazoleconcentration ratio about 55 and 36 in the buffers, about 14 and 5 in pooled human fluid; flux ratio 50–56 and 29–37six media[elkhabaz2019b R8, R9]
atazanavir, darunavir58 and 1.37 from the printed solubilities (printed "almost 82-fold" and "1.30")pH 6.8, 37 °C[alkalla2026 R3, R6, X1]
pretomanid8–10 in buffers37 °C[nguyen2023a R1]
tacrolimusabout 33pH 4.5[purohit2019 C30]
enzalutamideabout 14.5 (42/2.9); S "approximately 13" is the theoretical 39/2.9pH 6.5[wilson2018 R1, R3, X2]
felodipineS of about 10 over the crystal (theoretical and measured)benchmark for the supersaturation range S 3–12[alonzo2012 M1, C42]
ritonavir20.6 µg/mL calculated, 19.8 measured; S 15.3–15.4 over 1.3 µg/mL37 °C[ilevbare2012b R1, R2, R3]
efavirenz; celecoxib19.8 and 22.6 µg/mL calculated against 12.3 and 2.5 measured37 °C[ilevbare2013c R2]
five weak basesratios 22.2, 11.9, 20.4, 54.6, 7.0 without and 12.3, 9.8, 16.7, 15.3, 4.3 with water correction37 °C[hsieh2012 R10]
glyburide; warfarinabout 60 and 4825 °C[hsieh2014 R16]
danazol19.6 printed (15.4 recomputed); earlier estimates 13.7 and 26.525 °C[jackson2014 R2, R3, X1]
six dihydropyridinesestimated amorphous solubility 0.5, 6.68, 48, 20, 6.3, 19.0 µg/mLbuffer, Hoffman with water correction[raina2015b R10]
danazol7.8 µg/mL with heat-capacity data and the water correction; onset 8 µg/mL25 °C, pH 6.8[jackson2016 R3, R8]
posaconazolemeasured amorphous/crystalline 33.6 at pH 7.0 (32.4–37.3 from pH 2.0 to 7.0); estimate 37.9 printed37 °C[duong2022b R1, R6, R7, X5]
felodipineabout 10 times the crystal, about 9.5 µg/mL37 °C, pH 6.8 test fluid[konno2008a R17]
felodipineabout 9.1 µg/mL at 37 °C; 5–6 µg/mL at 25 °CpH 6.8[alonzo2011 M1]
felodipine, flux ratio to the crystal8.5 (pure amorphous), 9.5 (50:50), 10.5 (90:10 HPMC dispersion)dialysis, 37 °C[alonzo2011 R14]
indomethacinabout 21 µg/mL (crystal about 1.2 µg/mL)pH 2.0[alonzo2011 M2]
ritonavir; lopinavir (cited)25 and 17 µg/mL against 1.7 and 2.7 µg/mL crystallinepH 6.8[trasi2015b M1, M2]
lopinavirabout 5.6 (17.4/3.1)pH 3, 25 °C[li2018 E2, R1]
indomethacin with 100 µg/mL HPMC36 µg/mL against 1.61 (γ) and 2.8 µg/mL (α)pH 2.2, 37 °C[xie2017 R3, R1]
paclitaxel31.6 against 0.36 µg/mL, a ratio of about 88pH 6.8, 37 °C, three methods[que2018 R1, R2]
delamanid0.76 against 0.018 µg/mL at pH 6.5, a measured ratio of 42.3 against 31.8 from the Hoffman free energy37 °C[duong2022a R1, R27]
praziquantel, racemate and R-enantiomerratios 5.6–7.7 and 4.0–5.8 across nine media; amorphous 1.17–1.74 and 1.20–1.70 mg/mL37 °C[alvarenga2025 R1]
posaconazoleabout 20 against 1.69 µg/mL in FaSSIF; 115.1 µg/mL crystalline in FaSSGF37 °C[elkhabaz2019a R2, R1]
Pitfalls and disagreements

The calculated advantage fails for high-melting drugs when the Hoffman free energy is used (F7) [mosqueragiraldo2015 C23, C24]. When additives raise crystalline solubility more than the LLPS concentration, the concentration-based ratio falls (felodipine, about 9.2 in buffer to 4.5 in 0.04% vitamin E TPGS and 5.0 in FaSSIF), while the maximum flux stays in the buffer band, so the advantage in activity is retained [raina2015c R9, R11, C29]. In dispersions, a dose below the amorphous solubility (IDM 50 against about 80 µg/mL) can still lose most of the advantage to crystals; a crystal-free bicalutamide dispersion never reached 40 µg/mL against 150 µg/mL [moseson2020a X17; moseson2021 C41]. The amorphous solubility of ritonavir alone is reduced to about 4 µg/mL in a co-amorphous granule [trasi2019 R4]. In the Bioperformance papers the ratio from concentrations falls with solubilizers although the flux advantage does not [raina2015c C43]; the atazanavir ratio differs between cards because the crystalline solubility differs (F1). In human fluid the flux of a solution at the amorphous solubility was about 30 times that of a crystalline suspension for posaconazole, so the advantage was not lost although the concentration ratio fell to about 5 (F18) [elkhabaz2019b C30, C45]. The printed atazanavir and darunavir ratios do not follow from the printed solubilities [alkalla2026 X1]. With a polymer in the medium the same ratio applied to the polymer-containing solubility overestimates the ceiling (danazol: 43 against an onset of 8–9 µg/mL) [jackson2014 X9]. Celecoxib's measured 2.5 µg/mL is far below the calculated value and is not discussed [ilevbare2013b X9]. The efavirenz run started at S about 2.3, the ratio of calculated amorphous to crystalline solubility being 2.4 [ilevbare2013c X4]. The printed estimates for the dihydropyridines differ between media in ways the equation does not allow [raina2015b X2]. Felodipine dispersion and solution readings of 14.1 and about 11 µg/mL exceed the 9.5 µg/mL estimate of the 2008 paper, measured by UV through a 70-µm filter [konno2008a X5]. The 25 °C indomethacin range (17–25 µg/mL) does not reproduce from its printed inputs (15.8–23.6) [alonzo2010 X2]. That a dispersion reached the same activity as the pure amorphous drug "may be purely coincidental" [alonzo2011 C48]. The tacrolimus ratio uses an ultracentrifugation value measured with 10 µg/mL HPMC in the buffer [trasi2016 X9]. For praziquantel the ratio is lower for the enantiomer because its crystal is more soluble, not because its amorphous solubility is lower [alvarenga2025 R1].

← Concepts and formulas

concept · as used in PEG dispersions

antiplasticization

The rise of the Tg of a drug on mixing in a polymer of higher Tg, and with it a lower mobility, proposed as a reason for the stabilization of amorphous dispersions [taylor1997 C4; kestur2011 M3]. PVP, with a Tg of 177 °C, "has been suggested" to raise the Tg of the mixture and lower the mobility [taylor1997 C4, M4]. For indomethacin, inhibition by PVP at relatively low levels was already known to be too large to be explained by antiplasticization alone [taylor1997 C5]. In the growth studies of this chapter, antiplasticization is ruled out as the cause at 3–5 wt% polymer, since the dispersion Tg changes by 2.2 °C or less [kestur2010a C32; kestur2011 C12]. New aspect (Physical stability): water undoes it: after 75% RH every felodipine dispersion with up to 25% polymer had a Tg below the dry drug [konno2008 C16].

Findings

Miscibility and drug-polymer interactions: F11, F1. Physical stability: F5, F6.

Related concepts

depends on and is measured by glass transition temperature; contrasts with drug-polymer interactions as an explanation of crystallization inhibition; related to supercooled liquid; contrasts with plasticization and plasticization by water.

Formulas

Gordon-Taylor equation.

How it is measured or obtained

By onset Tg of dispersions by DSC at 10 °C/min after erasing thermal history, against the drug alone and the pure polymer [kestur2010a P8; kestur2011 P5]. Growth rates may be normalized to Tm − T and T − Tg to separate driving force and mobility [kestur2010a C31, E2]. DSC Tg against polymer content, dry and after humid storage [konno2008 P6; marsac2006a R17].

Values in the library
materialvalue or classconditionspaper ids
felodipine with 3% PVP, PVP/VA, HPMCAS, PVAcTg 44.1, 43.7, 42.7, 43.5 °C against 43.3 °Conset DSC[kestur2010a R1]
bifonazole with 5% polymersTg 16.4–17.4 °C against 15.2 °Conset DSC[kestur2011 R6]
nimesulide with 5% polymersTg 19.9–20.8 °C against 19.5 °Conset DSC[kestur2011 R6]
felodipine with PVP, HPMC, HPMCAS (other chapter)PVP raised Tg by 10 °C at 25 wt%; HPMC and HPMCAS no change up to 25 wt%onset DSC[konno2006 R6, C25]
felodipine with PVP (other chapter)Tg largely unaffected (43.4–44.1 °C against 43.3 °C at 0.5–4.5 wt% PVP); antiplasticization not the cause, yet growth slowedPVP grades, 3–4.5 wt%; dry[kestur2010b R1, C34]
felodipine–PVP 10 wt%Tg 40.5 °C, below pure felodipine 43.1 °Cdry[marsac2006a R8, C22]
felodipine with ≤ 25% polymerTg ≈30–35 °C after 75% RH25 °C[konno2008 R7, C16]
celecoxib with 40% PVP K12 or PVPVA vs HPMCAS or HPMCdry Tg 84.4 and 81 °C vs 64 and 71 °C, although neat PVP K12 and PVPVA have lower Tg (97, 102 °C) than HPMCAS and HPMC (117, 140 °C)DSC, 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 PEG dispersions

Barandiaran-Colmenero method

A DSC method from inorganic glass science to estimate the critical cooling rate: the natural logarithm of the cooling rate is regressed on 1/\Delta T^2, where ΔT is the undercooling at the crystallization peak, and Rcrit is taken as \exp(A), the extrapolated rate at which no crystallization would be seen [baird2010 E1, E2; baird2013 E1, E3]. The Cabral variant subtracts B/T_m^2 from the intercept baird2010 E3.

Findings

F11.

Related concepts

estimates critical cooling rate; uses degree of supercooling; related to glass-forming ability.

Formulas

Barandiaran-Colmenero critical cooling rate, Cabral critical cooling rate.

How it is measured or obtained

Crystallization peak temperatures at several cooling rates, 5–20 °C/min in a conventional DSC baird2010 P2, P9 or 5 to about 800–1100 °C/min with rapid heat–cool DSC [baird2013 P3].

Values in the library
materialvalue or classconditionspaper ids
carbamazepineRcrit 118 K/min, r² 0.995–20 °C/minbaird2010 R13.j
griseofulvin588 K/min, r² 0.975–20 °C/minbaird2010 R13.m
4-biphenylmethanol3.28 × 10⁴ K/min, r² 0.745–20 °C/minbaird2010 R13.b
12 of 19 class I moleculesr^2 < 0.55, no estimate5–20 °C/minbaird2010 R13
phenacetin; benzocaine2.7 × 10³; 6.2 × 10³ K/min5 to ≈1000 °C/min[baird2013 R7.h, R7.d]
benzamide, lidocaine, indoprofenr^2 < 0.555 to ≈1000 °C/min[baird2013 R7]
Pitfalls and disagreements

The method needs undercooling to rise steadily with cooling rate, which often failed because of scattered crystallization temperatures [baird2010 C18; baird2013 C17]. Estimates from 5–20 °C/min contradicted liquid-N2 quench results baird2010 C21; accurate predictions are said to need rates at least two orders of magnitude below Rcrit baird2010 R31.

← Concepts and formulas

concept · as used in PEG dispersions

binding constant

The equilibrium constant of the association of a drug molecule with a polymer group, here the indomethacin–PVP carbonyl species. In the indomethacin–PVP paper the constant is never given a value: the authors reason that spectral changes continue above the composition at which PVP monomer equals drug in moles, "which suggests" a low equilibrium constant and/or a stoichiometry below 1:1, so that dimers, PVP-bonded drug and free PVP coexist and "dimers may still be present depending on" the constant [taylor1997 C37, C38]. In the halogen-bond study K_F is the equilibrium constant of the 1:1 complex between a halogenated compound (donor D) and a monomer analogue of the polymer carbonyl (acceptor A), K_F = [AD]/([A][D]) [que2020 E1]. Unlike the indomethacin–PVP case it is measured: 0.56–1.11 M⁻¹ in cyclohexane and 0.21–0.39 M⁻¹ in toluene [que2020 R12, R13].

Findings

F1, F20.

Related concepts

measured by hydrogen bonding; related to self-association and drug-polymer interactions; measures halogen bonding.

Formulas

none (the weight-fraction conversion is named in plain text only).

How it is measured or obtained

It was not measured. The stoichiometric compositions were computed from the weight fraction of PVP with a monomer molecular weight of 111: 1:1 at 24 wt% PVP, and 12 wt% printed for two hydrogen bonds per carbonyl, which the card recomputes as 13.6 wt% [taylor1997 E1, R18, X2]. The evidence for incomplete binding is a visual reading of overlapping bands, with no intensities, areas or fits [taylor1997 X5]. By ¹H and ¹³C NMR titration at 25 °C: 11 to 1219 mM 1-ethyl-2-pyrrolidone added to a 14.5 mM solution of the compound, fitted to a 1:1 hyperbolic model; three titrations each; a carbonyl-free titrant (1-ethylpyrrolidine) as control [que2020 P6, E1, C4, R15].

Values in the library
materialvalue or classconditionspaper ids
indomethacin–PVP-K901:1 monomer:drug at 24 wt% PVP; changes continue aboveIR, 5–70 wt% PVP[taylor1997 R18, R11, R12]
indomethacin–PVP-K90two bonds per carbonyl: 12 wt% printed, 13.6 wt% recomputedsame[taylor1997 E1, X2]
clotrimazole0.63 ± 0.05 (¹H), 0.97 ± 0.04 (¹³C) M⁻¹ in cyclohexane; 0.32, 0.35 in tolueneNMR, 25 °C[que2020 R12, R13]
loratadine0.65 ± 0.05, 1.11 ± 0.07 M⁻¹ in cyclohexane; 0.35, 0.39 in toluenesame[que2020 R12, R13]
brotrimazole0.56 ± 0.06, 0.81 ± 0.04 M⁻¹ in cyclohexane; 0.30, 0.21 in toluenesame[que2020 R12, R13]

Evidence table: binding constant.

Pitfalls and disagreements

The incomplete binding is qualitative: the growing PVP band overlaps the same region [taylor1997 X5]. The two-bond threshold is a halved weight fraction, not a halved mole ratio [taylor1997 X2]. The authors' "low equilibrium constant" is one reading; a stoichiometry below 1:1 is the other, and the data do not separate them [taylor1997 C37]. The ¹³C values are 1.45–1.71 times the ¹H values, which the authors call similar, and the tracked ¹³C peak of loratadine crosses a neighbour [que2020 C13, X8]. K_F belongs to a monomer analogue in a non-polar solvent, not to the solid dispersion [que2020 C4]. The lower constants in toluene are read as competition from π electrons, not tested [que2020 C15].

← Concepts and formulas

concept · as used in PEG dispersions

chemical potential

The partial molar free energy of the drug in a phase

The amorphous drug, treated as a supercooled liquid, has a higher chemical potential than the crystal, so its solubility is higher by \exp(\Delta\mu/RT); in an equilibrated two-phase system the chemical potential of the drug is the same in both phases, so transport driven by chemical potential responds non-linearly to total concentration and peaks where the drug-rich phase first forms [trasi2015a E1, C36, C5]. With ideal mixing in the drug-rich phase the chemical potential of each component falls by RT\ln x [trasi2015a E2, E3]. The papers of 2017–2022 add that a dissolved polymer which enters the drug-rich phase lowers the chemical potential of the drug there by dilution (and, for PVP-VA, by interaction), so the drug in the water is lowered to match: ibuprofen 154 → 89–131 µg/mL [ueda2021 R5, C11, C42]; and the fundamental supersaturation is defined by \ln\delta = (\mu - \mu^{\circ})/RT [lu2017b E3]. New aspect (Bioperformance): it is the driving quantity of passive transport; it is higher in a supersaturated solution than in a saturated one, and lowered by solubilizers and by a second component in the drug-rich phase [raina2014a C6, E8; raina2015c C7; alhalaweh2016 C25, C26]. Polymer or a second drug in the drug-rich phase dilutes the drug and lowers its chemical potential, and with it the amorphous solubility: HPMCAS-HF for four drugs, darunavir for atazanavir [ueda2020a C36; alkalla2026 C7, C12, C37]. The Crystallization from solution papers add that solubilization raises the solubility without raising the chemical potential, whereas supersaturation raises it, and derive the activity-based supersaturation δ = a/a° from the same relation [jackson2016 C31; raina2015b C2; lu2017 E1]. New aspect (Supersaturation from ASD dissolution): once a drug-rich phase forms in metastable equilibrium with the water-rich phase, the free drug is fixed at the amorphous solubility, so dispersions cannot raise it further [jackson2015 C31, C32]; mixing two drugs in the drug-rich phase lowers the chemical potential of each and with it each amorphous solubility, "as long as" they are miscible there [trasi2015b C36, C53]. Membrane flux into a sink follows the activity of the free drug, so the tacrolimus flux levelling off at the amorphous solubility marks the maximum chemical potential, which six marketed capsules reached [trasi2016 C23, C36, C38]. Complexed drug raises the total concentration without raising the free drug, so complexed solutions are thermodynamically "quite different" from supersaturated ones [wegiel2015 C23, C44]. Mixing an amorphous drug with a polymer that stays undissolved, and the water the dispersion takes up, lower the drug's chemical potential and with it the maximum concentration the dispersion can reach [li2018 C1, C2, C43].

Findings

Amorphous solubility and LLPS: F8, F11, F12, F15, F17, F19, F20, F21. Bioperformance: F6, F7, F19, F20. Crystallization from solution: F22, F31, F37, F44. Supersaturation from ASD dissolution: F7, F11, F17, F18, F25.

Related concepts

related to thermodynamic activity; lowered by ideal mixing in the drug-rich phase; determines the amorphous solubility advantage. Related to drug–drug miscibility and polymer partitioning into the drug-rich phase; related to supersaturation; related to amorphous solubility; lowered by mixing in solubility suppression.

Formulas

amorphous solubility advantage from free energy difference, ideal-mixing reduction of amorphous solubility, activity-based supersaturation ratio, Huang model of drug solubility in an ASD, Flory-Huggins activity equation.

How it is measured or obtained

Not measured; derived from solubility ratios and used to reason about the effect of a second component on the amorphous solubility (F11) [trasi2015a E1, E4]. In the Bioperformance papers it is inferred from flux or from the shift of the LLPS concentration [alhalaweh2016 R12, R13; mosqueragiraldo2018b C37]. Through the membrane flux ratio, which follows the activity [lu2017 E2]. In the ASD dissolution papers it is inferred from flux plateaus and from the fit of ideal mixing [jackson2015 R9; trasi2015b R5].

Values in the library

None printed in the amorphous solubility and LLPS chapter; the Bioperformance, Crystallization from solution and ASD dissolution papers give the following.

materialvalue or classconditionspaper ids
telaprevir with CA Sublowered in the drug-rich phase by polymer (fraction 0.90)inferred[mosqueragiraldo2018b C37, R14]
ritonavir, atazanavir mixtureeach drug's amorphous solubility times its mole fractionideal mixing[alhalaweh2016 E7]
ritonavir, lopinavir, paclitaxelmax flux drops with a second componentdiffusion cell[trasi2015a C35, E3]
ibuprofenpolymer dilution, extra water and interactions lower itdrug-rich phase[ueda2021 C42]
atazanavir, clozapine, ketoconazole, nifedipine with AS-HFamorphous solubility lowered by a quarter to well over half; AS-LF by under a tenth for threebuffer, 37 °C[ueda2020a R1, C36]
atazanavir with darunaviratazanavir ceiling and flux plateau lowered, darunavir partitioning into the atazanavir-rich phaseinferred from supernatant depletion and flux[alkalla2026 R9, R11, C37]
telaprevir with six bile saltsδ 11.5 and 28.8 set from the flux ratiopH 6.5, 37 °C[lu2017 R1]
enzalutamide above 42 µg/mLequal chemical potential in droplets and water; crystals can start in either phase or at the interfacepH 6.5[wilson2021 C3]
posaconazole droplets with HPMCASpolymer mixed into the droplets "serves to" lower the drug's chemical potential (not measured)pH 6.5[shah2025 C46]
ritonavir + lopinavir mixed drug-rich phasesfree RTV 14.2–15.8 and LPV 7.0–7.5 µg/mL at once and twice the single-drug onsets5 h[trasi2015b R16]
ritonavir with 180 µg/mL PVP, PAA, HPMC, HPMCASLLPS concentration unchanged, read as no change of the phase's activity37 °C[ilevbare2013d R10, C22]
tacrolimus solutions, 20–100 µg/mLflux plateau ≈0.0050–0.0055 µg/min from 60 µg/mLpH 4.5, 37 °C[trasi2016 R14]
resveratrol–HPMCAS solutionsup to ≈1610 µg/mL with flux ≈2.6–4.4 against 2.0 µg/min for the crystalpH 6.8, 37 °C[wegiel2015 R19, R20]
lopinavir with undissolved HPMCP, 15–85% drug≈0.6–10.5 against 17.4 µg/mLpH 3, 25 °C, 48 h[li2018 R3]
delamanid edisylate in HPMCP-55 against HPMCP-50, pH 1.6release ≈9% against ≈30% of the dose, polymer release ≈1–2% in both25% drug, 37 °C[nguyen2023c R11, R12]
Pitfalls and disagreements

A polymer mixing into the drug-rich phase is later reported to lower the drug's chemical potential and hence the amorphous solubility, as does a second drug in a co-amorphous system [ueda2020a C36; trasi2015b C36; alkalla2026 C12]. Ideal mixing was tested for one pair only [trasi2015a X9]. The chemical potential of the drug in the polymer-containing droplets was not measured in any of the polymer papers [ueda2020b X4; ueda2021 X5, X6]. The activity of telaprevir in the CA Sub-rich phase was not measured, so mixing and complexation are not separated [mosqueragiraldo2018b X12]. For the darunavir case the mixing is inferred; the centrifuged drug-rich phase was not analysed and the light-scattering onset with darunavir present was not measured (F20) [alkalla2026 X6]. A higher concentration is not a higher chemical potential in micellar media [jackson2016 C31]. In the two-drug dispersions the lower chemical potential is inferred, not measured [trasi2015b C36]. CAAdP 0.85 raised the ritonavir LLPS concentration by about 17%, unlike the other polymers [ilevbare2013d X7]. The lower chemical potential in the lopinavir dispersions is inferred from concentrations; χ was not measured and the model is used qualitatively [li2018 C46]. For delamanid in HPMCP-55 the authors invoke stronger or more extensive drug–polymer interactions lowering the chemical potential of the drug, which were not measured [nguyen2023c C41, C42].

← Concepts and formulas

concept · as used in PEG dispersions

classical nucleation theory

The theory that writes the nucleation rate as a pre-exponential factor times \exp\left[-\frac{W^* + \Delta G_\eta}{kT}\right], with a thermodynamic barrier W^* = \frac{16\pi\sigma^3}{3\,\Delta G_v^2} for a spherical nucleus and an activation energy for viscous flow [baird2012 E1, E2; vaneerdenbrugh2010a E3]. Its main factors are driving force, interfacial energy and mobility, and the library adds molecular recognition [trasi2012a C48; konno2006 C33]. In this chapter it is used qualitatively; solution papers fit it to induction times. New aspect (Crystallization from solution): For nucleation from supersaturated aqueous solution the papers use the form J = A\exp(-\Delta G_{crit}/kT) with a barrier that falls steeply with supersaturation, \Delta G^{*} \propto 1/(\ln S)^{2} (a pre-exponential factor A that depends on molecular mobility); the induction time is then inversely proportional to J if growth is fast [hsieh2012 E7, E8; ilevbare2013c E3, E4]. Two further elements are added: the polymer's effect through the interfacial tension or the cluster reorganization, and the two-step picture in which a disordered solute cluster forms first and then reorganizes, the reorganization being taken as rate-limiting ("we assume") [ilevbare2013c C5, C15]. The acetaminophen study prints J = A\exp[-16\pi\gamma^3 v^2/(3k^3T^3(\ln S)^2)] to say that temperature, supersaturation and interfacial tension set J, and fits a Poisson model to induction-time distributions for J [trasi2015 E6, C20, E5]. From 2018 the theory is also used to read medium effects: a lower interfacial energy for lecithin, SDS hemimicelles and phospholipid digests, a lower attachment rate in the pre-exponential factor for human fluid, and a fit of \ln(J/S) = \ln A - B/\ln^{2}S to posaconazole induction times in buffer and four media [indulkar2018 C40; indulkar2019b C33; enright2020 C26; elkhabaz2021 C22; duong2022b E7]. New aspect (Physical stability): the physical-stability papers use the theory to sort possible polymer effects into the thermodynamic barrier (driving force, interfacial energy) and the kinetic barrier, and conclude that a few percent of polymer acts on the kinetic barrier [konno2006 C34, C36, C40; marsac2006a C44, C48]. New aspect (Supersaturation from ASD dissolution): used qualitatively for dissolving dispersions: nucleation rises steeply with supersaturation, so amorphous–crystalline systems with a high theoretical solubility ratio are expected to nucleate readily [konno2008a C20]; at equal supersaturation in two coexisting phases nucleation is favoured in the drug-rich droplets, where the drug concentration is higher and the crystal–liquid interfacial tension lower [ilevbare2013d C40, E1]. A celecoxib paper of 2015 prints the classical rate with (\ln S)^2 and argues from it that the polymer differences come neither from supersaturation, taken as similar in all polymer solutions, nor from interfacial tension, which adsorbed polymer would lower and so speed nucleation; the theory therefore "does not readily allow for obvious mechanistic insights", and two-step nucleation through dense liquid clusters is offered instead (cited) [xie2015 E3, C43, C44, C45]. The longer celecoxib induction time at 11 than at 22 µg/mL is read as in agreement with the theory [xie2016a C13].

Findings

Crystallization tendency: F3, F6. Crystallization from solution: F1, F5, F13, F14, F27, F34, F39, F42. Physical stability: F2, F4, F17. Supersaturation from ASD dissolution: F4, F5, F9, F13, F22.

Related concepts

models nucleation; depends on thermodynamic driving force for crystallization and melt viscosity; contrasts with heterogeneous nucleation; related to prenucleation clusters; governs nucleation rate and nucleation induction time; depends on interfacial tension; related to crystal-solution interfacial free energy; includes kinetic barrier to nucleation and interfacial free energy; depends on supersaturation.

Formulas

classical nucleation barrier, critical cooling rate to avoid nucleation, classical nucleation theory, induction time decomposition.

How it is measured or obtained

Not fitted for melts in this subcategory: the classes are read through it, a more negative ΔGv giving a lower barrier baird2010 C61, interfacial energy differences being assumed small [vaneerdenbrugh2010a C39], and a steeper viscosity rise lowering the rate [baird2012 C32]. In solution, the barrier and interfacial energy are fitted from induction times against supersaturation [duong2022b E7, E8]. Most of the solution-crystallization papers do not fit it; they use it qualitatively to explain why induction times fall with rising supersaturation and why a polymer gains more at a lower one (celecoxib 27.5 min at S 7.3 against 2.4 min at S 14.7) [ilevbare2013c R15, R9.a, C45]. The posaconazole paper converted induction times into nucleation rates (conversion not stated) and fitted the high-supersaturation points of each medium with ν = 920 ų and T = 310 K [duong2022b P15, X10]. In the 2006 felodipine and nifedipine film papers it is used as a framework only; no parameter was fitted [konno2006 E8; marsac2006a E9]. In the ASD dissolution papers no rate was computed; the expression is printed in two papers and stated in words in a third [konno2008a E3; alonzo2010 E4; ilevbare2013d E1].

Values in the library
materialvalue or classconditionspaper ids
posaconazoleinterfacial energy 3.52 mJ/m²; ΔG* ≈2.73 × 10⁻²¹ JPBS, 310 K, fit to induction times[duong2022b E7, E8]
classes I against IIIlower barrier inferred for class I from more negative ΔGvmelt classes, γ assumed similarbaird2010 C61
felodipine filmsrate described by driving force, kinetic barrier and molecular recognition; nucleation most likely heterogeneous0% RH films[konno2006 C33]
celecoxibinduction time 27.5 ± 0.7 min at S 7.3; about 2.4 min at S 14.737 °C[ilevbare2013c R15, R9.a]
danazol with HPMC-AS516, 365, 277 min at 10, 15, 20 µg/mL25 °C[jackson2014 R17]
type 1 weak basesprecipitate only after a supersaturation of 1.4–26.7 times the titration solubilitypH shift, 37 °C[hsieh2012 R5, C3]
celecoxib dispersions (ASD dissolution chapter)nucleation-rate expression with \ln S and interfacial tension \gamma used to read induction times37 °C[xie2015 E3, C42]
acetaminophen, S 1.5, 20 °CJ 1465 (none), 3820 (PAA), 81.86 (HPMCAS), 40.68 (HPMC) # m⁻³ s⁻¹ for V = 1.2 mL10 µg/mL polymer[trasi2015 R3, X1]
posaconazole, PBS, FaSSIF V1, FaSSIF V2, FeSSIF V1γ 3.52, 2.61, 2.73, 3.24 mJ/m²; A 2.44, 5.14, 4.98, 9.87; R² 0.84–0.9737 °C, high-S points (3–9 per medium)[duong2022b R15, R16, X11]
posaconazole, PBS, S 13 → 33.6ΔG* about 5.11 → 2.72 × 10⁻²¹ J; r* about 5.89 → 4.29 × 10⁻¹⁰ m310 K[duong2022b R17]
seven other drugs (cited)γ 0.60–2.80 mJ/m²literature[duong2022b R18]
felodipine with 3–25% polymerthermodynamic route "probably cannot account" for the drop; kinetic barrier speculatedargument[konno2006 C35, C40]
nifedipine vs felodipinelarger enthalpic driving force and lower barrier below Tg for the faster nucleatorTable II, Table I[marsac2006a C49]
flutamideprenuclei redissolve unless they exceed a critical radius, the volume free energy against the interfacial termframework[trasi2012b C46]
felodipine (argument)dissolution of the amorphous drug "will be accompanied by rapid crystallization"37 °C[konno2008a C21]
felodipine 90:10 dispersion (argument)almost all drug enters a highly supersaturated state that immediately crystallizes ("We speculate")37 °C[alonzo2011 C29]
celecoxib, no polymer, 22 against 11 µg/mLonset within 5 min against about 20 minpH 6.8, 37 °C[xie2016a R2]
celecoxib 22 µg/mL, 5 µg/mL PVP-K12 / PVP-K29/32 / HPMCAS or HPMConset ≈1 h / ≈2 h / more than 8 hpH 6.8, 37 °C[xie2015 R1]
paclitaxel, critical radius of a two-dimensional nucleus5.4–7.0 nm at S = 88 with three stand-in interfacial tensions; ≈6.8–8.8 nm at the residual supersaturation after 16 hpH 6.8, 37 °C[que2018 R15, R17]
Pitfalls and disagreements

Pharmaceutical films are not completely described by homogeneous nucleation theory, which ignores stresses and heterogeneous nucleation [marsac2006a C32]. It does not readily explain polymer effects on nucleation or encompass molecular recognition [trasi2012a C49; xie2015 C44]. In the melt papers neither γ nor nucleation rates were measured, so the barrier argument is an inference [vaneerdenbrugh2010a C39; baird2010 C61]. The proportionality of induction time to 1/J assumes nucleation is much slower than growth to detectable size, which was not tested [ilevbare2013c X14]. The two-step model is assumed, not shown, for these systems [ilevbare2013c C5]. The critical supersaturation at which precipitation is seen depends on the compound and the conditions and is somewhat variable [hsieh2012 C3]. The printed sample volume (0.0012 m³) and the sign of the exponent in Eq. 5 are misprints [trasi2015 X1, X2]. The human-fluid paper prints the rate equation without the minus sign in the exponent [elkhabaz2021 X1]. In the posaconazole fits γ and A both differ between media and the critical free energy in the FaSSIF media is less than half the buffer value at equal S, so the assignment of the medium effect to A alone is not secure [duong2022b X12]. In the felodipine films the homogeneous theory is applied to nucleation that is "most likely heterogeneous" [konno2006 C33; marsac2006a C32]. The reduced-temperature form printed for acetaminophen has typesetting errors (r³ for γ³, a positive kinetic term) [trasi2012a X1]. The 2008 and 2010 dissolution papers print ln S without the square of the classical form [konno2008a X8; alonzo2010 X3]. The celecoxib supersaturation argument uses crystalline solubilities measured with 22 µg/mL polymer, not the 5 µg/mL of the induction tests, and these differ by 26–43% from the polymer-free value [xie2015 X9]; the text refers to the wrong equation for interfacial tension [xie2015 X1]. The paclitaxel values use interfacial tensions of other compounds, and with the printed units the equation gives a dimensionless number [que2018 C37, X7].

← Concepts and formulas

concept · as used in PEG dispersions

cold crystallization

Crystallization on heating a glass into its supercooled liquid (devitrification), as opposed to melt crystallization on cooling [lu2016 C2]. In the DSC classification it separates class II (crystallizes on reheating) from class III baird2010 R1.

Findings

F7, F15.

Related concepts

process in supercooled liquid; contrasts with crystallization from the supercooled melt; measured by critical heating rate; related to glass stability and polymorphism.

Formulas

none.

How it is measured or obtained

As an exotherm on DSC reheating of a quenched glass, or by isothermal holds above Tg on a hot stage [lu2016 P2, P3; baird2010 P1]; the slowest heating that avoids it is the critical heating rate [baird2013 R9].

Values in the library
materialvalue or classconditionspaper ids
vemurafenib glassexotherms peaking at 157 and 217 °C, then α melting at 271.5 °CDSC at 10 °C/min[lu2016 R3]
11 class II moleculescrystallize on reheating at 10 °C/minDSCbaird2010 R1
nifedipine glasscrystallized to a metastable form at 87 °C; felodipine did notheating at 2 °C/min[marsac2006a R5]
delamanid glassdevitrified just above Tgliquid-N2 quenched[duong2022a R3]
propranolol saltsrecrystallization at 46.5–105.4 °C for four salts; none for nicardipine saltsDSC[towler2008 R4, C10]
rotary-evaporated drug–polymer powdersno exotherm on heatingDSCvaneerdenbrugh2010b R10
Pitfalls and disagreements

The polymorph formed on heating is often metastable and may convert later [lu2016 C54]. The rate at which the glass was made changes cold crystallization on reheating [baird2013 C28].

← Concepts and formulas

concept · as used in PEG dispersions

combinatorial entropy of mixing

The entropy part of the Flory–Huggins activity coefficient and free energy, set by molecular size alone. The activity coefficient of a drug splits into a combinatorial (entropy) part and a residual (enthalpy) part; exothermic mixing lowers and endothermic mixing raises the residual part, and the two are linked because order imposed by exothermic interactions lowers the entropy of mixing marsac2009 C10. For the drug in the liquid analogue (1-ethyl-2-pyrrolidone) the combinatorial part is taken as ideal, so only the residual part remains; in PVP it is larger by the factor that the chain length gives, and with equal residual parts the whole difference of ln γ between PVP and the analogue is the combinatorial part marsac2009 E3, E4, E5, E6, E7, C11. Per lattice site and for two polymers the term is kT[(\phi_1/N_1)\ln\phi_1 + (\phi_2/N_2)\ln\phi_2], which shrinks as the chains grow [vaneerdenbrugh2012a E5, C35].

Findings

F5, F8, F9, F22.

Related concepts

part of entropy of mixing; contrasts with the residual part carried by enthalpy of mixing; used in activity coefficient; part of Flory-Huggins theory.

Formulas

Flory-Huggins activity equation, Flory-Huggins combinatorial entropy of mixing.

How it is measured or obtained

By calculation (Eqs. 3–8 of the 2009 paper): ln γ in PVP = (MV_drug/MV_lattice)[(1/m_drug) ln(Φ_drug/x_drug) + (1/m_drug − 1/m_PVP) Φ_PVP] + ln γ in EP, with the lattice volume equal to that of EP marsac2009 E8, P7. As the chain grows, 1/m_polymer vanishes and the term approaches 1/m_drug, which explains the drop of predicted solubility from EP to PVP K12 and its saturation beyond K29/32 marsac2009 C24. The inputs (lattice volume, mole-fraction basis in PVP) are not printed marsac2009 X4, X13.

Values in the library
materialvalue or classconditionspaper ids
five compounds, γ in PVP K123.94, 1.18, 5.04, 1.76, 0.50 (felodipine, nifedipine, ketoconazole, sucrose, indomethacin)scaled from EP with Eq. 8marsac2009 R9
same, PVP K29/324.34, 1.30, 5.92, 1.93, 0.54as abovemarsac2009 R9
same, EP at 25 °C0.89, 0.26, 0.68, 0.37, 0.15measured solubilitymarsac2009 R9
dextran–PVP, 20 pairsminimum from about −27 × 10⁻²³ J (DEX1–PVP12) to about 0 (DEX450–PVP90)25 °C, PVP monomer as lattice site[vaneerdenbrugh2012a R15]

Evidence table: combinatorial entropy of mixing.

Pitfalls and disagreements

The scaling assumes ideal entropy of mixing with EP, identical drug–EP and drug–PVP contacts, and equal γ at the solubility limit in the polymer; none of these was tested against a measured solubility in a polymer marsac2009 C11, X17. The γ of indomethacin in K29/32 is 0.134 in Table III but 0.144 in the text of the paper marsac2009 X2.

← Concepts and formulas

concept · as used in PEG dispersions

conformational flexibility

The ability of a molecule to take different shapes by rotation about single bonds, counted in the library as the number of rotatable bonds baird2010 P8. More flexible molecules exist in the melt as many similar conformers, lowering the probability of the orientation needed to nucleate or grow, which is argued to raise glass-forming ability [baird2010 C59; vaneerdenbrugh2010a C37]. New aspect (Crystallization from solution): in solution crystallization the argument is turned around from the melt picture, as molecules with several low-energy forms (conformers or tautomers) are said to crystallize more slowly because only the right form joins a nucleus, which lowers the effective supersaturation of that form [hsieh2014 C31]. Ilevbare and co-workers attribute the slow nucleation of ritonavir, the largest molecule (720.9 g/mol), "most likely" to its higher molecular weight and greater conformational flexibility [ilevbare2013c C25, M1]. Among six dihydropyridines, rotatable bonds (6–11), molecular weight and polar surface area did not track the order of crystallization from the precipitate, and only cilnidipine stands out as larger and more flexible [raina2015b C31, M1–M6].

Findings

Crystallization tendency: F7, F13. Crystallization from solution: F3, F16, F21.

Related concepts

related to entropy of fusion and polymorphism; contributes to crystallization tendency; related to polymer chain stiffness.

Formulas

none.

How it is measured or obtained

Rotatable-bond counts from software or databases [baird2010 P8; baird2012 P7]; single-molecule conformer energy scans for one drug [trasi2014b P10]. In the solution papers not measured; rotatable-bond and tautomer counts are quoted: dipyridamole 12 rotatable bonds, warfarin 4; tautomers 6 (glyburide) and 9 (warfarin) [hsieh2014 X12, R19].

Values in the library
materialvalue or classconditionspaper ids
class I against class IIIrotatable bonds ≈−0.54 against ≈+0.66 SD51 moleculesbaird2010 R22.a
solvent classes I against III≈−0.42 against ≈+0.57 SD40 drugs[vaneerdenbrugh2010a R20.b]
ritonavir18 rotatable bonds, class IIImelt[baird2012 M34]
nilutamideone rotatable bond; crystal conformer at 54.4° against a computed minimum near 30°DFT, crystal structure[trasi2014b M1, R19, R24]
ritonavir in solution, against celecoxib and efavirenzslow nucleation attributed to higher MW and flexibility; induction time about 120 against 2.4 and 5.1 minaqueous buffer, 37 °C[ilevbare2013c R8, C25]
glyburide, warfarinseveral tautomers may explain slow crystallization; amorphous precipitates for at least 6 h with most polymerspH shift, 1 mg/mL polymer[hsieh2014 R4, R19, C31, C32]
papaverine, dipyridamolereduced conformational freedom proposed; crystalline with every polymer; papaverine adopts its crystal conformation in solutionpH shift[hsieh2014 R4, R19, C33]
six dihydropyridinesno correlation of rotatable bonds with the first crystalline time (0.25–12 h)10 mg/mL solvent shift[raina2015b R6, C31]
Pitfalls and disagreements

Conformer populations were never measured; the argument is inferred from class averages baird2010 C59. Nilutamide, with a single rotatable bond, is nonetheless a good glass former [trasi2014b C36]. In one solution study the rotatable-bond counts did not follow the conformational-freedom ranking used for dipyridamole and papaverine, and the argument rests on cited data [hsieh2014 X12]. Neither the ritonavir explanation nor the tautomer explanation was tested [ilevbare2013c C25; hsieh2014 C31]. Prediction from structure is called extremely difficult by the authors of the dihydropyridine study [raina2015b C6].

← Concepts and formulas

concept · as used in PEG dispersions

cosolvency

The change of a solute's solubility in a mixture of two solvents with their ratio; in this chapter water is an anti-solvent for hydrophobic drugs, and polymer plus sorbed water is treated as the drug's co-solvent inside a humid dispersion [marsac2008a C39, C26, C33; rumondor2009c C37].

Findings

F2, F10.

Related concepts

related to solid-liquid equilibrium solubility equation via activity coefficient; feeds supersaturation; related to Δχ effect.

Formulas

the log-linear cosolvency model of the 2008 paper is listed on the chapter page as table only.

How it is measured or obtained

Shake-flask solubility of the crystalline drug in a liquid analogue of the polymer (NMP for PVP), in water and in their mixtures at 25 °C, fitted with a log-linear cosolvency line; the water fraction of the polymer–water co-solvent is computed from sorption data marsac2008a P8, E5, E6.

Values in the library
materialvalue or classconditionspaper ids
nifedipine, felodipine in NMP–watermole fraction 0.05 and 0.10 at 0% water; ≈0.015 and ≈0.017 at ≈24 wt% water25 °Cmarsac2008a R12
nifedipine with 10 and 25% PVPco-solvent 23 and 18 wt% water75% RH, 25 °Cmarsac2008a R13
felodipine with 10 and 25% PVP≈16 wt% water75% RHmarsac2008a R13.c, R13.d
drug–PVP–water (argument)water–PVP "cosolvent" mixes less well with the drug as it takes up waterhumid dispersions[rumondor2009c C37, C44]
drugs in PEO compacts (outside)water lowers solubility in the water–PEO co-solvent but enlarges the solvent volume94% RHmarsac2008b C33

Evidence table: cosolvency.

Pitfalls and disagreements

The printed cosolvency fits do not reproduce their own points and cross at 16.5 rather than about 25 wt% water; the crossover rests on three water contents marsac2008a X2, X3. NMP stands in for PVP by assumption marsac2008a C33, X4.

← Concepts and formulas

concept · as used in PEG dispersions

critical cooling rate

Rcrit (Rcrit,cool) is the slowest cooling of a melt that avoids detectable crystallization; the rate that avoids any nucleation, RNcrit, is faster still, and cooling between the two leaves nuclei in the glass [baird2010 C50; baird2013 C2]. It is the classical measure of glass-forming ability baird2010 C49.

Findings

F10, F11, F16.

Related concepts

measures glass-forming ability; estimated by Barandiaran-Colmenero method; contrasts with critical heating rate; related to quenched-in nuclei.

Formulas

Barandiaran-Colmenero critical cooling rate, Cabral critical cooling rate, critical cooling rate to avoid nucleation.

How it is measured or obtained

By cooling at progressively slower rates in a rapid heat–cool DSC until crystallization appears [baird2013 P2, R5]; by extrapolation with the Barandiaran–Colmenero or Cabral methods [baird2010 P9; baird2013 P3]; bounded by the fastest rate at which crystallization was still seen [baird2013 R1, X6].

Values in the library
materialvalue or classconditionspaper ids
8 class I-A moleculesabove the fastest rate reached, 800–1100 °C/minrapid heat–cool DSC[baird2013 R1, X6]
antipyrin, chlorpropamide, flufenamic acid, tolbutamide25 °C/minrapid heat–cool DSC[baird2013 R9]
10 class II molecules5 °C/min or lessDSC[baird2013 R9]
7 class I molecules (extrapolated)20 to 3.26 × 10⁴ K/minBC and Cabral, 5–20 °C/minbaird2010 R13
delamanidabove 50 °C/min (no glass at 50 °C/min)DSC[duong2022a R3]
Pitfalls and disagreements

Extrapolated values from narrow rate ranges are unreliable baird2010 C20. The authors advise that knowing Rcrit,cool exceeds 500 °C/min is "probably sufficient" to flag a difficult drug [baird2013 C21]. A low Rcrit,cool does not imply a stable glass, since reheating rates needed are far higher [baird2013 C24].

← Concepts and formulas

concept · as used in PEG dispersions

crystal growth inhibition

Reduction of the crystal growth rate by an additive, here dissolved PVPVA or HPMCAS, expressed as the effectiveness ratio E_G=R_{G,np}/R_{G,p}, the growth rate without polymer over the rate with it [moseson2020a E2; moseson2021 E1]. The mechanism proposed is surface poisoning: polymer globules adsorb on the crystal face and the adsorbed network "appears to limit the sites available for molecular integration" [moseson2020a C48, C50]. HPMCAS at nine times the drug concentration slowed seeded growth of posaconazole in FaSSIF V2 but did not stop it at 100 µg/mL drug: 10 µg/mL seeds left 43.5% at 30 min against 4.5% without polymer [shah2024 R22]. New aspect (Crystallization from solution): The slowing of the growth of drug crystals in a supersaturated aqueous solution by a dissolved additive, usually a polymer, expressed as the ratio of the initial growth rate without additive to that with it, E_g = R_{g0}/R_{gp}; above 1 the additive inhibits growth, below 1 it accelerates it [ilevbare2013b E5; ilevbare2012a E3, E4]. In these papers it is a kinetic effect at constant solubility, shown by solubility controls with the polymer [ilevbare2012c R1, C16]. It is the solution counterpart of the growth inhibition in supercooled liquids described below and is one of two steps of crystallization inhibition, the other being nucleation inhibition. Seeded growth ratios now include HPMCAS on felodipine (2.29 at pH 6.8, 1.28 at pH 3, and 2.7 to 12 depending on how the seeds were made) and bile salts on telaprevir seeds (E_G 1.0–4.6; complete stop with monomeric STCDC) [schram2015 R4; schram2016 R2; lu2017a R7, R10]. New aspect (Supersaturation from ASD dissolution): the 2008 felodipine study reads a flat concentration after an initial drop as growth inhibition: the drop takes the solution from the labile into the metastable zone ("it appears"), where only growth could lower the concentration further, so a plateau "strongly suggests" inhibited growth [konno2008a C27, C26]. The 2011 study reads slower growth of particles with HPMC than with PVP the same way [alonzo2011 C18]. For celecoxib, seeded desupersaturation with HPMCAS gave growth ratios R_0/R_p of about 70–158, less inhibition at the higher supersaturation, against an estimated nucleation ratio of ~4000, so both steps were slowed but nucleation far more ("it can be surmised") [xie2016a R12, R13, C37, C40]; the slow growth explains why crystals formed in dissolving PAA particles did not empty a medium holding HPMCAS [xie2016a C36]. In the supercooled liquid (formerly the page "crystal growth inhibition by polymers", from Crystallization tendency and Miscibility and drug-polymer interactions): the reduction of the crystal growth rate of a drug by a polymer dissolved in its supercooled liquid; the extent is thought to depend on specific drug–polymer interactions such as hydrogen bonding, and at higher levels on the polymer's effect on mobility [trasi2014a C33; trasi2014b C19]. The inhibition depends on the chemistry of the polymer at low levels, where it changes neither the Tg nor the melting point of the drug: at 3% w/w felodipine growth was slowed in the order PVP > PVP/VA > HPMCAS > PVAc [kestur2010a C17, C32, C36]. The factor is not a constant of the polymer: it grows as the temperature falls toward Tg and with polymer content [kestur2010a C12, R6, R8], and the best polymer depends on the drug (PAA for bifonazole, PVP and PVP/VA for nimesulide at low temperature) [kestur2011 C9, C10, C29]. The authors tie the order to the strength or extent of drug–polymer hydrogen bonding and propose, as a "speculation", that crystal growth needs the drug to demix from the polymer at the growth front [kestur2010a C40, C42].

Findings

ASD process: F25, F27, F29, F41. Crystallization from solution: F5, F6, F7, F8, F9, F10, F11, F12, F17, F18, F20, F23, F24, F27, F33. Supersaturation from ASD dissolution: F4, F5, F16, F22. Crystallization tendency: F19. Miscibility and drug-polymer interactions: F10, F11, F12, F13, F14, F17.

Related concepts

part of crystallization inhibition by polymers; acts on crystal seeding; slows desupersaturation; related to crystal growth rate; part of crystallization inhibition; contrasts with nucleation inhibition and with polymer effects on nucleation; related to polymer adsorption on crystal surfaces, step pinning and physical stability; contrasts with the polymer's effect on antiplasticization and thermodynamic driving force for crystallization; depends on hydrogen bonding and intramolecular hydrogen bonding.

Formulas

crystal growth inhibition effectiveness ratio, power-law crystal growth rate, initial growth rate from the desupersaturation slope, Kubota-Mullin model, overall mass crystal growth rate, relative nucleation rate from seeded and unseeded induction times, viscosity-limited normal growth law.

How it is measured or obtained

Seeded growth from a supersaturated solution at a stated supersaturation and polymer concentration, with the growth rate from the desupersaturation profile; adsorption by AFM in liquid (globule spacing) and crystal habit by SEM [moseson2020a P10, P15, P16; moseson2021 P12]. In the crystallization-from-solution papers: Seeded desupersaturation: a fixed mass of seed crystals (0.010 g in 50 mL for ritonavir, celecoxib and efavirenz; about 2.5 mg in 18 mL for felodipine) is placed in buffer with predissolved polymer, supersaturation is created by adding drug in methanol, and a fibre-optic UV probe on second-derivative spectra gives the slope of the first 2 min (5 min for felodipine) as the growth rate [ilevbare2013b P10; alonzo2012 P4]. Eg is the ratio of slopes, in triplicate [ilevbare2012c P12]. Rates can be normalized by seed mass and BET area [ilevbare2013b E6]. Unseeded controls and turbidity checks test that the slope is growth [ilevbare2012a R9; ilevbare2013b R5]. Rotating-disc seeds (felodipine) and seeds grown in situ in the vessel (telaprevir); the ratio is R_0/R [schram2015 P2; schram2016 P5; lu2017a P1, P2]. In the ASD dissolution papers: initial slopes of desupersaturation curves with equal crystal surface areas assumed (Eq. 5) [konno2008a E5, P6, C28]; particle size against time by light scattering [alonzo2011 P5]; seeded desupersaturation with 7 mg seeds in 50 mL, initial slope without polymer against the slope over 16 h with polymer [xie2016a P4, P11]. In the supercooled liquid: by comparing seeded growth rates of the neat drug and of drug with a low polymer level at the same temperatures [trasi2014a P3; trasi2014b P2], with FTIR to assess drug–polymer hydrogen bonding [trasi2014b P4]. For the felodipine, bifonazole and nimesulide dispersions: a 10% w/w polymer dispersion made by rotary evaporation is diluted with crystalline drug in a cryogenic mill to 0.5–4.5% w/w, melted between cover glasses, nucleated over P2O5 at 40 °C (or at ambient temperature) and grown on a hot stage at 70–110 °C (or 18–100 °C), the slope of spherulite diameter against time being the rate [kestur2010a P1, P2, P3, P4; kestur2011 P1, P2, P3]. Whether the slope is a diameter or radius rate is not always stated, and the felodipine Fig. 3 slopes are about twice the Fig. 4 rates [kestur2010a X3; kestur2011 X12]. Hydrogen bonding is read separately by IR on films with 20–50 wt% polymer [kestur2010a P6, C6].

Values in the library
materialvalue or classconditionspaper ids
IDM, PVPVAE_G 18 (5 µg/mL) and 56 (50 µg/mL polymer)50 µg/mL seeds, S = 6[moseson2020a R5]
BCL, PVPVA 70 µg/mL and HPMCAS 1 mg/mLE_G 8.6 and 158150 µg/mL, form 1 seeds[moseson2021 R5]
felodipine seeds, HPMCAS 5 µg/mL (outside)E_G about 2 to 12 depending on how the seed crystals were preparedS = 4[schram2016 R2, C13]
celecoxib, HPMCAS (outside)E_G about 130, 70 and 158 (R_0/R_p at 11/11, 22/5 and 22/22 µg/mL drug/polymer)11 and 22 µg/mL drug, pH 6.8, 37 °C[xie2016a R12]
ritonavir with cellulose polymers (outside)inhibition large at low supersaturation, marginal at the amorphous "solubility"seeded growth[ilevbare2012b C56]
felodipine in buffer, PVP, HPMC, HPMCAS (outside)initial slopes about 0.1399, 0.0398, 0.0044 and 0.0021 µg/mL·min⁻¹9.5 µg/mL start, 150 µg/mL polymer[konno2008a R16]
PCZ 100 µg/mL in FaSSIF V2, HPMCAS 0 / 3 / 9 times the drug; seeds 0 / 10 µg/mL% left at 30 min about 13 / 4.5; 66 / 10.5; 95 / 43.5seeded solution[shah2024 R22]
ritonavir, 34 polymersE_g 0.83–3.25; Pn-IPAAmd 3.25, CAP Adp 0.85 2.98, CAB Adp 0.81 2.70, HPMCAS about 2.545 µg/mL polymer, S 7.6, 37 °C[ilevbare2012c R9]
ritonavir, CA 320S Sub 0.90; 0.6312.6; 10.8same[ilevbare2013b R9]
celecoxib, HPMC; HPMCAS; PVPVA10.2; 8.5; 7.45 µg/mL polymer, S 6.6[ilevbare2013b R9]
efavirenz, PVPVA; CA 320S Sub 0.90about 4.9S 1.2[ilevbare2013b R9]
ritonavir, CAP Adp 0.856.40, 2.99, 1.56S 3.8, 7.6, 15.3[ilevbare2012b R5]
ritonavir, CAP Adp 0.85 + Pn-IPAAmdabout 12.1 (S 7.6); 3.3 (S 15.4)5 + 5 µg/mL[ilevbare2012a R11, R16]
felodipine, 1 µg/mL HPMCgrowth ratio 0.607S 10, 25 °C[alonzo2012 R5]
felodipine, HPMCAS-LF 5 µg/mLE_g 2.29 (pH 6.8), 1.28 (pH 3); 2.7 to 12 by seed route (pH 6.8)S 8 and S 4, 25 °C[schram2015 R4; schram2016 R2]
acetaminophen, 20 µg/mL polymerconcentration at 24 h 16.1 (HPMC), 15.8 (PVP), 13.4 (PAA), 13.0 (none) mg/mLS 1.5, 20 °C[trasi2015 R11]
telaprevir, 1.86 mM bile salts, δ 2.4E_G 3.2 (STC), 1.5, 1.4, 1.2; STCDC no desupersaturationpH 6.5, 37 °C[lu2017a R7, R10]
telaprevir seeds, 1:1 STDC–STCDC (binary-L, 1.86 mM; binary-H, 3.72 mM)E_G about 35.5 and 7.4, between STDC (3.8) and STCDC (>60)δ 7.9, 50 mM phosphate pH 6.5, 37 °C, first 10 min[lu2018 R5]
felodipine particles: none; 90:10 PVP dispersion; HPMC936 nm at 7 min; ≈218 → ≈459 nm (10–90 min); ≈280–307 nm at 90 min25 °C[alonzo2011 R10, R8]
felodipine particles at 37 °C, PVP against HPMC dispersions≈441 nm by 20 min against ≈287–307 nm37 °C[alonzo2011 R11]
paclitaxel seeds with 20 µg/mL HPMCASgrowth continued at S = 88 and left ≈7.9–25.3 µg/mL after 16 h; seeds grew dendritic fingers ≈10.5–16.8 nm widepH 6.8, 37 °C[que2018 R14, R12]
praziquantel with HPMCAS-MF against HPMC E5 LVno concentration drop with HPMCAS outside fed media; HPMC lost dissolved drug at 1.5 mg/mL37 °C[alvarenga2025 R14, C28]
five drugs with 10 mol% PVPgrowth reduced about 3- to 14-fold (authors: "around 5−10"), one point about 50-foldsupercooled liquid, 40–120 °C[trasi2014a R6, X6, C10]
nilutamide≈5 (alone), ≈3.8 (PAA), ≈1.1 µm/s (PVP)supercooled liquid, 80 °C[trasi2014b R3]
felodipine with PVP K-29/322- and 6-fold at 110 °C, 3- and 35-fold at 70 °C (1.5 and 4.5 wt%)supercooled liquid, melt[kestur2010b R13]
bifonazole with PAA5-fold at 100 °C, 15-fold at 18 °Csupercooled liquid, 5 wt%[kestur2011 R7]
flutamide with PVPabout one order of magnitudesupercooled liquid, 10 mol%[trasi2012b R3]
celecoxib with PVP; with TPGSmore than one order slower; about two orders faster at 70 °Csupercooled liquid, 10% w/w[mosqueragiraldo2014 R1, C9]
felodipine with 3% PVP, PVP/VA, HPMCAS, PVAcrate ratios at 70 °C ≈10.0, 6.5, 4.4, 1.2; at 110 °C ≈2.9, 1.1, 1.1, 1.1supercooled liquid, form II, hot stage, triplicate[kestur2010a R6]
felodipine, 4.5% w/w at 90 °C≈4.7 × 10⁻⁹ (PVP), 6.4 × 10⁻⁹ (PVP/VA), 1.7 × 10⁻⁸ (HPMCAS), 3.8 × 10⁻⁸ m/s (PVAc) against 6.7 × 10⁻⁸ m/ssupercooled liquid, log-linear in polymer content[kestur2010a R8]
bifonazole with 5% PAA; PVP; HPMCASratios ≈15, 5.9, 4.0 at 18 °C; ≈5.1, 2.1, 1.7 at 100 °Csupercooled liquid, melt-quenched films[kestur2011 R7]
nimesulide with 5% PVP; PVP/VA; PVAcratios ≈21, 16, 3.4 at 18 °C; ≈4.7, 3.1, 2.0 at 80 °Csupercooled liquid, melt-quenched films[kestur2011 R9]
Pitfalls and disagreements

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

← Concepts and formulas

concept · as used in PEG dispersions

crystal growth rate

The speed at which a crystal front advances into the surrounding supercooled liquid or glass, taken as the slope of crystal size (length, radius or diameter) against time [trasi2014a P1; trasi2014b E1]. Its temperature dependence is bell-shaped, with a maximum crystal growth velocity between Tg and Tm [trasi2014a C22]. This draft comes from the crystallization-tendency chapter (growth from melts); growth from supersaturated solution, measured by desupersaturation, is covered by other chapters [ilevbare2013b R7]. New aspects (Miscibility and drug-polymer interactions): Growth of felodipine from the supercooled liquid is expected to depend on a thermodynamic part (the free energy difference between liquid and crystal) and a kinetic part (viscosity), as in u = (k/\eta)[1 - \exp(-\Delta G/RT)], and also on molecular recognition at the crystal surface [kestur2010a C30, E1]. The growth rate of felodipine peaks at about 105 °C and a polymer at 3% shifts the apparent maximum to 110 °C (not for PVAc) [kestur2010a R5, C11]. The polymer effect, expressed as the ratio of growth rates without and with polymer, is not constant but grows toward the glass transition [kestur2010a R6; kestur2011 C8, C10]. New aspect (Crystallization from solution): growth from supersaturated aqueous solution is measured as the initial bulk growth rate of seed crystals, the slope of the dissolved drug amount against time over the first 2 min (5 min for felodipine), in µg/mL/min or µg/min, and normalized by seed mass and BET area (mg min⁻¹ m⁻²) to compare drugs [ilevbare2013b E6, E8; alonzo2012 P4]. It follows the empirical law R_G = k_G S^{g} with order g between 1 (diffusion control) and 2 (integration control) [alonzo2012 C3, E2]. New aspect (Physical stability): in the physical-stability papers the growth rate is the slope of crystal diameter (melt films) or radius (thin films at fixed RH) against time, of existing crystals nucleated first, so that growth is measured apart from nucleation [kestur2010b P3; rumondor2010 P1, P5, C7]. New aspect (Supersaturation from ASD dissolution): in the ASD dissolution papers a growth rate from solution is the mass gained by crystals per unit surface area and time, R_G = \frac{1}{A_c}\frac{dM_c}{dt}; with equal surface areas assumed, the slope of the falling concentration ranks growth rates [konno2008a E5, C28].

Findings

Crystallization tendency: F1, F2, F3, F5, F6, F7, F15, F19, F21. Miscibility and drug-polymer interactions: F10, F11, F12, F13. Crystallization from solution: F3, F5, F7, F9, F10, F23, F24, F33, F42. Physical stability: F3, F9, F11, F15, F17, F18, F19, F21, F22, F27, F28, F29, F35. Supersaturation from ASD dissolution: F5.

Related concepts

part of crystal growth; includes maximum crystal growth velocity; depends on melt viscosity and thermodynamic driving force for crystallization; contrasts with nucleation; related to crystal growth inhibition by polymers and surface crystallization; includes spherulitic growth; depends on supercooled liquid; lowered by crystal growth inhibition by polymers; inhibited in crystal growth inhibition; limited at high supersaturation by kinetic roughening; related to integration-controlled crystal growth. Regime diffusion-controlled crystal growth; modified by crystallization inhibition by polymers and moisture-induced crystallization; related to surface-enhanced crystal growth; faster mode near Tg: glass-crystal growth mode; split from nucleation and crystal growth; related to desupersaturation.

Formulas

temperature of maximum crystal growth rate, Jackson interface-kinetics growth rate, linear fit of melt viscosity on Tm − Tg, linear fit of normalized growth rate on melting entropy; viscosity-limited normal growth law, power-law crystal growth rate, initial growth rate from the desupersaturation slope; empirical log-linear growth-rate equation, linear crystal growth rate from size-time slope, crystal growth inhibition effectiveness ratio, overall mass crystal growth rate.

How it is measured or obtained

Hot-stage polarized light microscopy of melt-quenched films seeded at the edge with the form of interest, triplicate where stated [trasi2014a P1; trasi2014b P3]; with the top coverslip removed for surface growth [trasi2014a P2]; from the crystallized area when the front is irregular [trasi2014b P3]; the size–time plot is linear [trasi2012a R4; kestur2011 R4]. In the felodipine, bifonazole and nimesulide studies: the slope of spherulite diameter against time on a hot stage at 70–110 °C (felodipine) or 18–100 °C (bifonazole, nimesulide), triplicate; slower growth below 40 °C was followed in ovens or coolers with periodic pictures [kestur2010a P4; kestur2011 P3]. Whether the slope is a diameter or a radius rate is not always clear: the felodipine Fig. 3 slopes are about twice the Fig. 4 rates [kestur2010a X3; kestur2011 X12]. From solution, by seeded desupersaturation with a fibre-optic UV probe on second-derivative spectra, in triplicate (F5) [ilevbare2013b P10; ilevbare2012a P8]. In the physical-stability papers: melt-quenched felodipine between cover glasses, nuclei formed at 40 °C, grown on a hot stage at 70–110 °C, with crystals 5.5 ± 2 µm thick so that diameter slopes can be compared [kestur2010b P2, P3, R19, C5]. Uncovered spin-coated films, spherulites nucleated on a 90 °C hot plate, radius read from photomicrographs at four or more times for three or more crystals at each RH [rumondor2010 P1, P5]. Seeded edge growth of melt-quenched films of flutamide, acetaminophen and celecoxib, triplicate where stated; the flutamide paper reports diameter, the acetaminophen paper radial growth rates [trasi2012b P2, R3; trasi2012a P2, R6; mosqueragiraldo2014 P3]. Felodipine form I at a free surface or seeded in the bulk, form II unseeded between two cover glasses [kestur2013a P2, P3]. In the ASD dissolution papers: the initial linear slope of solvent-shift desupersaturation curves (felodipine from 9.5 µg/mL with 150 µg/mL polymer) [konno2008a P6].

Values in the library
materialvalue or classconditionspaper ids
nimesulideMCV 216 µm/s, the fastest of 31 drugsbulk melt[trasi2014a R1.a]
clotrimazoleMCV 0.02 µm/s, the slowestbulk melt[trasi2014a R1.ae]
vemurafenib α-needles; β≈106 µm/s at 250 °C; ≈110 µm/s at 230 °Csupercooled liquid[lu2016 R12.o, R12.m]
nilutamide stable form≈0.00015 µm/s at 30 °C to ≈40 µm/s at 100 °Cseeded films[trasi2014b R8]
felodipinemaximum near 105 °C, 3 orders lower at 70 °Cmelt films[kestur2010a R5, C10]
felodipine form Iabout 6 times faster at the surface than in the bulk30 °C, 0% RH[kestur2013b R12]
felodipine filmsabout 2-fold rise over 13–80% RH (≈0.030 → 0.066 mm/min), 40-fold at 87% RH (2.3–2.8 mm/min at 87–93% RH)25 °C[rumondor2010 R1]
bifonazoleabout 5.5 orders lower from 100 to 18 °Cmelt-quenched films[kestur2011 R7]
flutamidenearly 2 orders lower from 70 to 40 °Cfilms[trasi2012b R3]
acetaminophennearly 2 orders lower from 110 to 70 °Cfilms[trasi2012a R6]
indomethacin γ; α; δMCV 4.07 × 10⁻⁷; 4.34 × 10⁻⁶; ≈1.5 × 10⁻⁷ m/s, at 135, 135 and 110 °Cpure melt[tian2017 R7, R8, R9, R10]
celecoxib with TPGSabout two orders faster than celecoxib alone at 70 °C10% w/w[mosqueragiraldo2014 C9]
felodipine form II≈3.5 × 10⁻⁹ (70 °C), ≈6.9 × 10⁻⁸ (90 °C), ≈1.8 × 10⁻⁷ m/s (105 °C)neat, hot stage[kestur2010a R5.a]
felodipine, 3% PVP; PVP/VA; HPMCAS; PVAcat 70 °C ≈3.5 × 10⁻¹⁰, 5.4 × 10⁻¹⁰, 7.9 × 10⁻¹⁰, 3.0 × 10⁻⁹ m/sform II[kestur2010a R5.e, R5.d, R5.c, R5.b]
bifonazole neat; with 5% PAA≈1.7 × 10⁻¹² and ≈1.1 × 10⁻¹³ m/s at 18 °C; ≈4.7 × 10⁻⁶ and ≈9.2 × 10⁻⁷ m/s at 100 °Cmelt-quenched films[kestur2011 R7.a, R7.i]
nimesulide neat; with 5% PVP≈3.7 × 10⁻¹¹ and ≈1.8 × 10⁻¹² m/s at 18 °C; ≈8.5 × 10⁻⁶ and ≈1.8 × 10⁻⁶ m/s at 80 °Cmelt-quenched films[kestur2011 R9.a, R9.g]
ritonavir; celecoxib; efavirenznormalized 0.20; 0.91; 2.97 mg min⁻¹ m⁻² at S 1.2–1.3seeded, 37 °C[ilevbare2013b R7]
celecoxib; ritonavir at S 6.6; 7.66.23; 6.14 mg min⁻¹ m⁻²same[ilevbare2013b R7]
celecoxib; ritonavir at S 14.7; 15.419.08; 14.32 mg min⁻¹ m⁻² (217.5 and 181.5 µg min⁻¹)same[ilevbare2013b R7]
ritonavir without additive, 10 µg/mL1.56 µg mL⁻¹ min⁻¹ (text), about 1.4 (figure)100 mM buffer, S 7.6[ilevbare2012a R10, X5]
ritonavir without additive, S 3.8; 7.6; 15.4about 0.72; 1.4; 3.63 µg mL⁻¹ min⁻¹same[ilevbare2012a R15]
felodipine without HPMC, S 3 to 12about 0.078 to 0.62 µg mL⁻¹ min⁻¹; g about 1.5025 °C[alonzo2012 R4, R13]
telaprevir seeds, no bile salt5.4, 58.6, 89.2 µg/min at δ 2.4, 7.9, 12.5 (per 50 mL vessel)pH 6.5, 37 °C[lu2017a R2, X12]
felodipine seeds, no polymerconcentration 4.0 → 1.7 µg/mL in 50 minS 8, 25 °C, 1000 rpm[schram2015 R1]
atazanavir, posaconazole, six mediaSHG size growth about 2–55 (atazanavir) and 20–156 nm/min (posaconazole); highest in blank buffers37 °C, relative per field[elkhabaz2021 R15, X13]
felodipine form II (PVP grade study)3.5 × 10⁻⁹ m/s (70 °C) to 1.7 × 10⁻⁷ m/s (105 °C, maximum)melt films[kestur2010b R7, C9]
felodipine with 3 wt% PVP K-12, K-29/32, K-9011-, 15-, 21-fold slower at 70 °C; 3-, 3-, 6-fold at 110 °Cmelt films[kestur2010b R8]
felodipine with 0.5–4.5 wt% PVP K-29/32ln rate linear in concentration; slope −0.82 (70 °C) to −0.49 per wt% (105 °C)melt films[kestur2010b R15, E1]
felodipine with 10% PVP vs 10% HPMCAS5.8 × 10⁻⁵ vs 1.3 × 10⁻³ mm/min (13% RH); 7.3 × 10⁻² vs 2.4 × 10⁻³ (93% RH)room temperature[rumondor2010 R5, R3]
flutamide with 10 mol% PVP≈0.13 against ≈1.4 µm/s at 40 °Cmelt films, diameter rate[trasi2012b R3.a, R3.h]
acetaminophen with 10% w/w PAA≈0.43 against ≈5.3 µm/s at 80 °Cmelt films, radial rate[trasi2012a R6.a, R6.h]
celecoxib≈0.002 (70 °C) to ≈12 µm/s (120 °C); 19–38-fold slower with 10% PVPseeded melt films[mosqueragiraldo2014 R1.a, R1.b]
felodipine form I against form II, bulkform I faster at 40–100 °C: ≈4700-fold at 40 °C, 7–9-fold at 80–100 °Cmelt films[kestur2013a R8, X5]
felodipine form I with 3% PVPsurface 1.45 × 10⁻⁹, bulk 6.37 × 10⁻¹¹ m/s (ratio 22.8)30 °C, 0% RH[kestur2013b R12]
ATP(S), ATP(R)0.022–0.032 µm/s (40 °C) to 21–34 µm/s (90 °C); S 1.2–1.6 times fastermelt films[sato2015 R5.a, R5.b, X2]
griseofulvin with 5% PHB≈0.015 → ≈0.15 µm/s at 120 °C (diameter rate)melt films[sato2016 R4.a, R4.c]
celecoxib, alone and with 10% PVP K29/32≈0.010 and ≈0.00003 µm/s at 80 °Cmelt films[xie2016b R21]
felodipine, buffer / PVP / HPMC / HPMCASdMc/dt ~0.1399 / ~0.0398 / ~0.0044 / ~0.0021 µg/mL-minpH 6.8, 37 °C[konno2008a R16]
Pitfalls and disagreements

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

← Concepts and formulas

concept · as used in PEG dispersions

crystallization from the supercooled melt

Crystallization of a drug melt as it is cooled below Tm, or while it is held below Tm; it is the route probed by the DSC classification and the one relevant to melt extrusion and melt quenching [baird2013 C1; vaneerdenbrugh2010a P10].

Findings

F9, F14.

Related concepts

contrasts with cold crystallization; measured by crystallization tendency classification; depends on degree of supercooling and melt viscosity; occurs in supercooled liquid.

Formulas

Barandiaran-Colmenero critical cooling rate.

How it is measured or obtained

DSC cooling at fixed rates baird2010 P1; rapid heat–cool DSC [baird2013 P2]; isothermal holds of the undercooled melt [moseson2020 R7]; rheometry while cooling [baird2012 P1].

Values in the library
materialvalue or classconditionspaper ids
51 molecules23 crystallize on cooling at 20 °C/minDSCbaird2010 R1
vemurafenibcrystallized from 248.9 °Ccooling at 10 °C/min[lu2016 R1]
posaconazole, bicalutamide; indomethacincrystallization within 1 h; none in 4 hisothermal holds at 130–180 °C[moseson2020 R7]
acetaminophen with polymersrank orders for nucleation and growth inhibition differ, and differ from solutionundercooled melt (cited)[trasi2015 R14, C28]
Pitfalls and disagreements

Solid-state polymer rankings need not hold in solution [trasi2015 C28]. Melt and solvent classes agree only for rapid solidification [vaneerdenbrugh2010a X7].

← Concepts and formulas

concept · as used in PEG dispersions

crystallization inhibition

The delay or slowing of crystallization of an amorphous drug by a polymer mixed with it. Several explanations are in circulation and none is accepted: reduced molecular mobility through a higher Tg (antiplasticization), a lower driving force through a lower chemical potential, a higher barrier, and drug–polymer specific interactions that disrupt the drug's self-association [taylor1997 C3, C4, C5; marsac2006b C2, C5; kestur2010a C29; rumondor2009a C2]. For indomethacin and PVP the proposal is that a nucleus of the stable γ form is built of acid dimers, so that nucleation "would require" breaking the PVP–drug hydrogen bond [taylor1997 C43]. The effect is measured on different quantities: the overall crystallinity of a film over days (the amorphicity index), the growth rate of crystals into the supercooled liquid, or nucleation separately [vaneerdenbrugh2010b E1; kestur2010a P4]. In later designs the effect is read as the amorphicity index of 105 spin-coated pairs of 15 drugs and 7 polymers [vaneerdenbrugh2011a R3], as the highest polyphenol content that stays X-ray amorphous and the days to crystals at five storage conditions [wegiel2013a R8, R9], and as the weeks to crystals of lumefantrine dispersions [hiew2022a R6]. The ranking of polymers follows complementary groups of drug and polymer (see F24). In the glass, melt and solution (formerly the page "crystallization inhibition by polymers", from ASD process, Crystallization from solution, Physical stability and Supersaturation from ASD dissolution): delay of nucleation and slowing of growth of a drug by a polymer in the glass, melt or solution. Two settings matter here. In solution, dissolved PVPVA prevented nucleation of indomethacin for more than 12 h and HPMCAS prevented that of bicalutamide for 8 h [moseson2020a C11; moseson2021 R3]. In the solid or melt, a polymer can stabilise the amorphous drug against recrystallisation and let degradation be tested on a dispersion [moseson2020 C32, C55]. A polymer inhibits in the solid only when intimately mixed with the drug in one phase, usually inferred from a single Tg [rumondor2009c C26; marsac2010 C31]. The polymer's help in solution does not carry into the hydrating solid or across drugs: HPMCAS slowed seeded growth of posaconazole in FaSSIF [shah2024 R22], but in the hydrating solid cryomilled and high-loading bicalutamide–PVPVA dispersions still crystallized [moseson2022b R4, R6]; and coated erlotinib–HPMCAS held 48 weeks at 43% RH where coated erlotinib–PVPVA failed at 6 weeks, a difference the authors attribute to the polymer [moseson2022a R11, R12, C31]. New aspect (Crystallization from solution): the delay of crystallization from a supersaturated aqueous drug solution by a dissolved polymer, through slowing nucleation, growth or both; for felodipine and HPMC both were slowed at µg/mL levels and nucleation far more [alonzo2012 C46]. The papers separate it into crystal growth inhibition and nucleation inhibition because polymers rank differently in the two (F6) [ilevbare2013c C40]. The solid-state version, in amorphous dispersions, is described at the start of this definition. New aspect (Physical stability): in dry felodipine films a few percent of polymer lowered nucleation by orders of magnitude, independent of polymer type and of any Tg rise, and the authors speculate that it raises the kinetic barrier to nucleation [konno2006 C13, C14, C40]. With water present the polymer still inhibits, competing with the water it brings, but the polymers then differ [konno2008 C13, C10]. New aspect (Supersaturation from ASD dissolution): one polymer can act differently on the two routes by which an amorphous solid loses supersaturation: PVP delayed crystallization of the wetted felodipine solid at least as well as HPMC and HPMC-AS but held felodipine solutions poorly [alonzo2010 C38]; the authors therefore "speculate" that some drugs "might" be formulated better with two polymers, one per route [alonzo2010 C46]. Because 1 mg/mL of each polymer left the crystalline solubility of felodipine unchanged, the higher concentrations from the dispersions are read as kinetically maintained supersaturation, not solubilization [konno2008a R1, C17, C22]. The papers of 2015–2018 add that a fast-releasing polymer can be paired with a minor inhibitor that then works in solution [xie2015 C6; xie2016a C69], that against matrix crystallization the inhibitor must stay in contact with the drug in the particle [xie2016a C54], and that the polymer content needed to stop matrix crystallization depends on the polymer [wegiel2015 C11].

Findings

Miscibility and drug-polymer interactions: F1, F9, F10, F11, F12, F13, F15, F16, F17, F23, F24, F25, F26. ASD process: F25, F27, F31, F38, F41, F44. Crystallization from solution: F6, F7, F8, F13, F14, F15, F16, F20, F25, F26, F27, F36, F37, F41, F43, F44. Physical stability: F1, F3, F4, F10, F11, F15, F17, F18, F19, F21, F22, F24, F26, F27, F28, F29, F33, F35. Supersaturation from ASD dissolution: F2, F3, F4, F5, F6, F12, F16, F20.

Related concepts

includes crystal growth inhibition and nucleation inhibition; depends on drug-polymer interactions, drug-polymer miscibility, antiplasticization and thermodynamic driving force for crystallization; contrasts with crystallization tendency of the neat drug; limited by matrix crystallization; related to nucleation, crystal growth rate, kinetic stabilization, polymer hydrophobicity and supersaturation. Acts through kinetic barrier to nucleation and polymer rejection at the crystal growth front (proposed); not through antiplasticization at low content; lost by moisture-induced phase separation; decided by hydrogen-bond donor and acceptor groups and acid-base interaction; related to drug-polymer complexation.

Formulas

amorphicity index, viscosity-limited normal growth law, crystal growth inhibition effectiveness ratio, relative nucleation rate from seeded and unseeded induction times, induction time decomposition, empirical log-linear growth-rate equation, classical nucleation theory, supersaturation ratio, overall mass crystal growth rate.

How it is measured or obtained

Spin-coated films of drug and polymer at several ratios, scored by polarized light microscopy at day 0, 1, 3 and 7 and expressed as an amorphicity index vaneerdenbrugh2010b P1, P2, E1; hot-stage growth of spherulites in melt-quenched films with low polymer levels after nucleation at 40 °C [kestur2010a P2, P3, P4]; rotary-evaporated bulk powders by DSC crystallinity vaneerdenbrugh2010b P8, E5. Only growth, not nucleation, was measured in the felodipine and bifonazole–nimesulide studies [kestur2010a X10; kestur2011 P3]. Induction time and seeded desupersaturation in solution; DSC of undercooled melts for the dispersion (a melting peak on reheating means nucleation during the hold); matrix crystallisation by microscopy and Raman of particles in buffer [moseson2021 P12, P15, P16; moseson2020 P7]. In the crystallization-from-solution papers: seeded growth rates and unseeded induction times with and without predissolved polymer under identical conditions, combined into a relative nucleation rate (F5, F6) [alonzo2012 P10, E9, E10]; induction times by UV extinction or absorbance [ilevbare2013c P9]; pH-shift precipitation followed by polarized light, WAXS and HPLC [hsieh2014 P2–P7]; fluorescence and SHG for droplet and crystal read-outs [jackson2014 P7, P10]. In the physical-stability papers: nucleation-site counts in films [konno2006 P2; marsac2006a P4; konno2008 P4], melt or film growth rates [kestur2010b P3; rumondor2010 P5], PXRD crystallinity of stored powders [rumondor2009b P5]. In the ASD dissolution papers: non-sink dissolution of dispersions or of amorphous drug with polymer in the medium; solvent-shift solutions with predissolved polymer; induction times by extinction or pyrene; Raman of slurries for the solid [konno2008a P3, P5; alonzo2010 P2, P4, P5; jackson2015 P3; ilevbare2013d P6].

Values in the library
materialvalue or classconditionspaper ids
8 drugs, 7 polymersmean amorphicity index PVP = PVPVA 70 > E100 67 > HPMC 66 > HPMCAS 62 > PAA 49 > PSSA 48spin-coated films, 7 days dryvaneerdenbrugh2010b R5
amides, bases against acids with PAA and PSSAhighest for amides (64–78) and bases; lowest for acids (8–31)as abovevaneerdenbrugh2010b R3, C3
felodipine, 3% PVP, PVP/VA, HPMCAS, PVAcgrowth ratio at 70 °C 10.0, 6.5, 4.4, 1.2hot stage[kestur2010a R6]
bifonazole with 5% PAA5-fold at 100 °C, 15-fold at 18 °Chot stage[kestur2011 R7]
nimesulide with 5% PVP, PVP/VA, PVAcabout 21-, 16-, 3-fold at 18 °Chot stage[kestur2011 R9, X7]
50/50 powders, acidic drugs with PAA against PVPabout 64–117% against at most about 3% crystallinerotary evaporation, DSCvaneerdenbrugh2010b R9
acids, acidic N–H drugs, alcohols (13 drugs)AI with E100, PVP, PVPVA about 54–100; with PAA, PSSA mostly about 4–31spin-coated films, 7 days dry[vaneerdenbrugh2011a R3, C20, C25]
naringenin, quercetinhighest X-ray amorphous content: E100 about 85 and 70%, PAA about 30 and 20%rotary evaporation, PXRD[wegiel2013a R8]
naringenin, quercetin with E100 and PVPno crystals for >200 to >450 days at five conditionsPXRD[wegiel2013a R9]
lumefantrine–PVPVA; –enteric polymerscrystals at 1–8 weeks; only at 50% drug loading (1–40 weeks)40 °C/75% RH[hiew2022a R6]
IDM, PVPVA in solutionno nucleation for more than 12 h at 5–50 µg/mL; about 40 min withoutS = 6[moseson2020a R3, C11]
BCL, PVPVA 70 µg/mL and HPMCAS 1 mg/mL in solutioninduction above 1 h; none in 8 h; without polymer under 30 min37 °C[moseson2021 R3]
BCL–PVPVA dispersion in the slurryHPMCAS in the medium delays crystallisation by about 10 min and leaves form 2 growth unchangedRaman[moseson2021 R19, R20, C51]
neat PCZ and BCL meltsnucleate within 1 h between Tg and Tm; IDM did not in 4 hDSC holds[moseson2020 R7]
twenty commercial polymers on ritonavir growth (outside)five effective: Pn-IPAAmd > HPMCAS > HPMC > CAPh > CMCABseeded growth[ilevbare2012c C22]
bifonazole in melt-quenched films (outside)PAA the most effective polymer; PAA ineffective on acetaminophen in solution5 wt%[kestur2011 C9; trasi2015 C26]
erlotinib–HPMCAS against erlotinib–PVPVA, coated, 43% RHnone at 48 weeks against about 6 weeks40 °C, SEM[moseson2022a R11, R12]
felodipine, 1 µg/mL HPMCgrowth ratio 0.607; induction time 15.3 → 136.5 min; J/J_0 7.05 × 10⁻⁴S 10, 25 °C[alonzo2012 R5, R16, R17]
ritonavir, CAB Adp 0.81induction time ≈120 → ≈244 min5 µg/mL, 20 µg/mL drug[ilevbare2013c R9]
celecoxib, HPMC2.4 → 12.6 min (22 µg/mL); 27.5 → 855.5 min (11 µg/mL)5 µg/mL, 37 °C[ilevbare2013c R9, R15]
danazol, HPMC-AS6–10 → 250–516 min10 µg/mL polymer, 25 °C[jackson2014 R17]
warfarin, six polymersamorphous precipitate ≥ 6 h; 103–224 µg/mL1 mg/mL, pH shift[hsieh2014 R4]
celecoxib, 5 µg/mL HPMCASsupersaturation held 16 h; J_0/J_p about 4,00022 µg/mL drug[xie2016a R3, R13]
six dihydropyridines, 4.5 mg/mL polymerPVPVA = HPMC = HPMCAS > PVP > CMCAB = CAPAdp > P2VP = PAAnominal 10 mg/mL[raina2015b C16, R9]
telaprevir 150 µg/mL, 5 µg/mL polymerHPMC 243, HPMCAS 175–226, CA-Sub-090 106 min against 14–15 withoutpH 6.8, 37 °C[mosqueragiraldo2016 R4, R5]
acetaminophen S 1.5, 10 µg/mL95% of vials: none 26, PAA 11, HPMCAS 470, HPMC 1043 min20 °C[trasi2015 R1]
atazanavir, volunteer media V5 and V6, 1 mg/mL HPMC134 ± 23 and 45 ± 7 → >360 minpH 6.5, 37 °C[enright2020 R28]
telaprevir δ 28.8, 150 µg/mL HPMCAS-MF, four lecithin mediaabout 357–474 min, no difference37 °C[lu2018 R7]
enzalutamide 120 µg/mL, 50–100 µg/mL HPMCASabout 431–530 min; P177 about 71–125 minpH 6.5[wilson2021 R3]
felodipine with 3% PVP, HPMCAS or HPMCnucleation ≈1.3 × 10⁵ → ≈2–3 × 10³ m⁻³ s⁻¹, equal for all three0% RH, 22 °C[konno2006 R4, C14]
nifedipine and felodipine with 7 wt% PVPabout two orders of magnitude lower; 3–4-fold more to 25 wt%0% RH[marsac2006a R16, C18]
felodipine with 3% PVP vs HPMCAS≈8.6 × 10⁵ vs ≈1.3 × 10⁴ m⁻³ s⁻¹75% RH[konno2008 R3.b, C10]
felodipine with 3 wt% PVP K-90growth 21-fold slower at 70 °C, 6-fold at 110 °Cmelt[kestur2010b R8]
felodipine with 25–50% PVP vs HPMCAS51–82% vs 9–28% crystallized after ≈490 days75–93% RH[rumondor2009b R9, C13]
acetaminophen with PAA or HPMCASPAA the best growth inhibitor but most nuclei; HPMCAS the reverse10% w/w[trasi2012a C46, C53]
flutamide with acceptor or donor polymersacceptor polymers (PVP, PDMA, PIPA) slow growth; donor polymers do not10 mol%[trasi2012b C8, C50]
felodipine forms I and II with 3% PVPrate ratios ≈15.8 and ≈18.7 at 60 °C, ≈3.5 and ≈6.5 at 100 °Cmelt growth[kestur2013a R15]
celecoxib with PVP and TPGSslower than PVP alone at 70–120 °C at 10% PVPmelt growth[mosqueragiraldo2014 R2.b, C13]
resveratrol and curcumin dispersionsPVP and E100 best for resveratrol; E100 best, PVP worst for curcuminstorage at 84% RH[wegiel2013b R12; wegiel2014 R13]
ATP(S) vs ATP(R) with 5% HPMCAS-HF or -LFS 1.9–2.5 times faster than R (HF); R 1.5–1.9 times faster than S (LF)melt growth, 50–80 °C[sato2015 R5.i–l]
six compounds with 5% PHBratio with/without polymer ≈0.42–10, rising with compound Tgmelt growth[sato2016 R11]
indomethacin α vs γ with 10% HPMCratio without/with polymer ≈2900 vs ≈2.9 at 120 °Cmelt growth[tian2017 R12.i]
tacrolimus–HPMC 1:1 vs pure amorphous drugamorphous at 4 weeks vs crystalline after 2 weeks at 40 °C/75% RHopen dish[trasi2017 R16, C40]
felodipine dispersions 75% HPMCAS / HPMC / PVPmaxima 14.1 / 4.9 / 2.3 µg/mLpH 6.8, 37 °C[konno2008a R7]
felodipine 9.5 µg/mL, 150 µg/mL polymer8.5–9.1 (HPMCAS), 7.8–8.9 (HPMC) µg/mL held; PVP to ≈2.8solvent shift[konno2008a R14]
amorphous indomethacin, 250 µg/mL PVP≈23.8 µg/mL held 4 h at 25 °CpH 2[alonzo2010 R14]
indomethacin solvent shift, 37 °Cnone ≈42 → ≈7.3 µg/mL in 30 min; HPMC ≈39 held about 2.5 hpH 2[alonzo2010 R17]
danazol dispersions PVP / HPMC / HPMCASinduction ≈56–70 / ≈188–200 / ≈284–319 minpH 6.8, 25 °C[jackson2015 R5]
ritonavir 20 µg/mL, 5 µg/mL of 15 additivesinduction 23.6 to 242.8 against 119.3 minpH 6.8, 37 °C[ilevbare2013d R12]
nifedipine γ → α, 1 mg/mL polymerγ intact ≈20 (PVP), ≈60 (HPMC), ≈110 min (HPMCAS) against ≈1325 °C[raina2014b R9]
celecoxib 22 µg/mL, 5 µg/mL PVP-K12 / PVP-K29/32 / HPMCAS, HPMC / PAAonset ≈1 h / ≈2 h / more than 8–16 h / as no polymerpH 6.8, 37 °C[xie2015 R1; xie2016a R3]
tacrolimus 50 µg/mL with 50 µg/mL HPMConset 6–8 h against within 3 hpH 4.5, 37 °C[trasi2016 R9]
indomethacin, 100 µg/mL HPMC against EPOheld ≈1.5 h against crystals during the titrationpH 2.2, 37 °C[xie2017 R5, R8]
resveratrol dispersionsno matrix crystallization from 80% HPMC, 85% HPMCAS, 95% CMCABpH 6.8, 37 °C[wegiel2015 R14]

Evidence table: crystallization inhibition.

Pitfalls and disagreements

Inhibition of growth, of nucleation and of overall crystallinity need not coincide: the best growth inhibitor of acetaminophen promoted nucleation [trasi2012a C46]. Polymers rank differently for different drugs [vaneerdenbrugh2010b C20; kestur2011 C29]. No polymer property tested at low levels (Tg, melting point, molecular weight) explained the order [kestur2010a C32, C34, C35]. The hydrogen-bond mechanism is a rank correlation over four polymers, and the demixing step is the authors' "speculation" [kestur2010a C38, C42]. Film results carried over to bulk powders for six of seven drugs vaneerdenbrugh2010b C42, C43, C44. The IR ranking of the polyphenol polymers separated the best and worst but not the middle ones, and polymer content differed from 30 to 80% in the stability comparison [wegiel2013a X4, X3]. The same ionic contact that protected lumefantrine dispersions slowed the dissolution of the enteric polymers [hiew2022a C53]. A polymer that inhibits in solution does not necessarily inhibit in the hydrating solid (HPMCAS and bicalutamide; polymers predissolved with amorphous nifedipine) [moseson2021 C51; raina2014b C11]. The mixing condition fails when the dispersion has phase separated, so water-induced separation can remove the benefit of the polymer [rumondor2009c C6]. Celecoxib with HPMC or HPMCAS at 22 µg/mL and 5 µg/mL polymer gave induction times of about 10–13 min in one laboratory and more than 8–16 h in another [ilevbare2013c R9; xie2015 R1; xie2016a R3]. Growth and nucleation data for the same polymers are often measured at different supersaturations [ilevbare2013b X15]. A polymer that raises the crystalline solubility or lowers the onset of phase separation changes the supersaturation it is credited with (F19) [jackson2014 X9]. In the solid state, equal effectiveness holds for felodipine nucleation when dry, not for growth (polymers differed several-fold) or in humid air [konno2006 C14; kestur2010a R6; konno2008 C10]. After moisture-induced phase separation the PVP level stopped mattering for crystallization at 93% RH [rumondor2009b C20]. The mechanism (barrier at the nucleus, hydrogen-bond coupling, polymer encaged in the crystal) was argued, not measured [konno2006 C40; kestur2010b C35, C42]. A polymer's effects on nucleation and on growth need not agree [trasi2012a C53]. Equal inhibition of two polymorphs is read as action in the liquid, unlike adsorption in solution [kestur2013a C6, C28]. PVP slowed felodipine bulk growth about sevenfold but surface growth only twofold [kestur2013b C32]. A polymer can also speed growth (PHB with high-Tg compounds) [sato2016 C29]; the factor depends on the polymorph and on the side of the growth maximum [tian2017 C37, C35]; and two grades of one polymer can favour opposite enantiomers [sato2015 C28]. PAA, the most effective polymer for bifonazole in melt-quenched films and the best growth inhibitor for acetaminophen melts, was ineffective on acetaminophen in solution (synthesis: contrast between papers) [kestur2011 C9; trasi2012a C46; trasi2015 C26]. In the ASD dissolution papers the ranking depends on the drug (PVP worked for indomethacin, not for felodipine, danazol or ritonavir) [alonzo2010 C22; konno2008a R7; jackson2015 R5; ilevbare2013d R12]. Solution screens predict only the rank order, and HPMC was misranked for felodipine [konno2008a C31; jackson2015 X8]. An additive can stabilize droplet size yet promote crystallization [ilevbare2013d R14].

← Concepts and formulas

concept · as used in PEG dispersions

crystallization tendency classification

A sorting of neat drugs by when, if ever, they crystallize under a fixed protocol. From the melt: class I crystallizes on cooling (split into I-A, which still crystallizes on liquid-N2 quenching, and I-B, which vitrifies), class II only on reheating, class III on neither baird2010 R1, C10; the labels very high, high, moderate and low tendency are used for I-A, I-B, II and III [baird2013 P5]. After rapid solvent evaporation: rapid, intermediate and slow crystallizers [vaneerdenbrugh2010a P9]. An extended scheme combines nucleation behaviour and growth rate into classes IA, IB, II, III and IV [trasi2014a C17].

Findings

Crystallization tendency: F5, F9, F10, F14, F17, F18. Physical stability: F17, F24.

Related concepts

measures crystallization tendency; extended by extended nucleation and growth classification; related to glass-forming ability, glass stability, critical cooling rate and nucleation and crystal growth.

Formulas

none specific; the critical-rate formulas refine the classes: Barandiaran-Colmenero critical cooling rate.

How it is measured or obtained

DSC heat–cool–heat at 20 and 10 °C/min plus liquid-N2 quench baird2010 P1, P6; spin coating and polarized light microscopy over 7 days [vaneerdenbrugh2010a P8, P9]; growth rates for the extended scheme [trasi2014a P1].

Values in the library
materialvalue or classconditionspaper ids
51 molecules23 class I, 11 class II, 17 class IIImelt DSCbaird2010 R1
93 drug–solvent combinations39 class I, 23 class II, 31 class IIIspin coating[vaneerdenbrugh2010a R9]
felodipineclass III (melt and solvent)both routes[baird2010 M37; vaneerdenbrugh2010a R8.ag]
nifedipineclass IImelt DSC[baird2010 M32; raina2015b C12]
celecoxibclass II (melt); class III (solvent)both routes[baird2010 M26; vaneerdenbrugh2010a R8.ae]
atenololclass I (melt); class III (solvent)both routes[vaneerdenbrugh2010a R17]
cilnidipine, nisoldipine, nitrendipineclass IIImelt DSC[raina2015b C12]
curcumin; resveratrolintermediate; rapid crystallizersolvent scheme[wegiel2014 R21; wegiel2013b C6]
naringenin; quercetinintermediate; rapidsolvent scheme[wegiel2013a C19]
lumefantrineclass 3melt DSC[trasi2020 R5]
pretomanid, delamanidclass Imelt DSC[nguyen2023a C59]
nimesulide, nilutamide, celecoxibextended class II (fast growth, low nucleation)extended scheme[trasi2014a C17]
celecoxibslow crystallizer by the cited scheme, yet growth "quite fast"; "quite hard to nucleate"melt films[mosqueragiraldo2014 R17, R16, R15, C7]
acetaminophenforms a glass because nucleation and growth zones barely overlapDSC and hot stage[trasi2012a C39]
Pitfalls and disagreements

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

← Concepts and formulas

concept · as used in PEG dispersions

crystallization tendency

The propensity of an amorphous or supercooled drug to crystallize, expressed as a class from the melt or after solvent evaporation, as a growth rate, or as a time to crystallize in storage or solution [baird2010 C8; vaneerdenbrugh2010a C33; trasi2014a R1]. The inherent crystallization tendency is called the most important parameter of physical instability and is said to depend on conformational flexibility, configurational entropy, driving force, viscosity and hydrogen bonding, factors "not fully elucidated" [trasi2017 C6]. New aspect (PEG dispersions): the tendency can also be read in a dispersion, relative to the neat drug; in 20/80 comelts with PEG 3350 at 25 °C PEG delayed benzocaine, left haloperidol unchanged and brought forward ibuprofen and fenofibrate, so the authors conclude that PEG "can delay, promote or have no influence" on drug crystallization and that both the neat-drug tendency and the interaction with PEG matter zhu2012 C6, C38, C39. New aspect (solution methods): in solution work the tendency decides whether a supersaturated drug first phase-separates or first crystallizes; very fast crystallizers (nifedipine; nimodipine at 37 °C) crystallize just below the LLPS concentration unless a polymer slows nucleation, slow crystallizers form a drug-rich phase first [raina2015a R17, C11, C37; ilevbare2013a C27]. New aspect (Miscibility and drug-polymer interactions): the tendency of the neat drug carries into polymer dispersions. In a spin-coating screen of eight drugs with seven polymers, drugs whose pure amorphous form crystallizes rapidly (class I) "tended to be" more difficult to stabilize and, the authors say, needed more polymer; the overall crystallization tendency of a drug in the dispersions is related to that of the pure amorphous drug prepared in a similar way vaneerdenbrugh2010b C1, C15. Class I compounds are therefore "ideal model compounds" for telling polymers apart, whereas the compounds usually used as models in solid-dispersion work are often class III vaneerdenbrugh2010b C16, C17. Knowledge of the pure drug's tendency is called "extremely important" early in development and a guide to whether a dispersion is feasible vaneerdenbrugh2010b C18. Further cases: naringenin (intermediate crystallizer) and quercetin (rapid crystallizer) could not be made amorphous by rotary evaporation, naringenin only as a spin-coated film, and needed 15–80% polymer to give an amorphous dispersion [wegiel2013a C19, R7, R8]; the 15 model drugs of the donor–acceptor screen all have an intermediate to rapid tendency [vaneerdenbrugh2011a C16]; lumefantrine is a class III glass former (no crystallization on heat–cool–heat; Tg 19.7 °C) whose PVPVA dispersions crystallized in 1–8 weeks [hiew2022a R3, R6]. New aspect (ASD process): in process papers the tendency is a precondition: a drug must resist crystallization while the solvent leaves in granulation, so slowly crystallizing, larger and more complex molecules are "most suitable" for solvent granulation [trasi2019 C35]; ritonavir crystallizes slowly, so amorphous phase separation can be studied without crystallization interfering [li2020 C15]. Bicalutamide is "a fast-crystallizing compound in solution" and also crystallizes inside the hydrating solid; the authors name its low Tg, high crystallization tendency, high loading and fast polymer dissolution as the reasons for its susceptibility to matrix crystallization [moseson2021 C6, C60]. The tendency decides whether a residual-crystal level is tolerable: posaconazole, a fast crystallizer, lost supersaturation with 0.3% crystals, whereas indomethacin–PVPVA, a slow crystallizer, was little affected (cited) [shah2024 C56, R26]. Spray-dried ezetimibe–HPMCAS crystallized within 12–19 days at 40 °C/75% RH uncoated [duong2022c R16, R17]. New aspect (Bioperformance): the tendency is used as a descriptor to explain why felodipine reaches LLPS and nifedipine crystallizes first [raina2014a C31, R20]. Pretomanid is a low-Tg, class I rapid crystallizer (reduced glass transition temperature 0.67): its melt-quenched glass crystallized on heating just above Tg and within minutes at room temperature, and its solution crystallized within 2 min near the amorphous solubility [nguyen2023a C10, C59, C61, R1, R3, R4]. New aspect (Crystallization from solution): the solution counterpart of the class from the melt, that is how fast a drug crystallizes from a supersaturated aqueous solution, read as the type 1 or type 2 behaviour of a pH shift, as the precipitate form (crystalline against amorphous), or as an induction time at a defined supersaturation [hsieh2012 C42; ilevbare2013c R8; hsieh2014 R4]. It is only partly predicted by the melt class (see Crystallization tendency F18). The synchrotron WAXS ranking of six dihydropyridine precipitates (nifedipine 0.25 h to cilnidipine 12 h) is wider than their melt classes (two Class II, four Class III) [raina2015b R1, R6]. New aspect (Physical stability): the relative crystallization tendency of drugs from dispersions "may be dependent" on that of the pure drugs: nifedipine stayed the faster nucleator over felodipine in PVP at every content, dry and humid [marsac2006a C52; marsac2008a C7]. New aspect (Supersaturation from ASD dissolution): behaviour of neat amorphous drugs on wetting: nifedipine, a "relatively fast crystallizer" (cited), crystallized in the particle within minutes even with polymer in the medium, and its faster inherent crystallization than felodipine "appears" to carry over to water [raina2014b M1, C10, C28]; Tg alone did not rank felodipine and indomethacin [alonzo2010 C42]. Resveratrol, classed as a rapid crystallizer (cited), crystallized in or at the matrix of cellulosic dispersions within the first hour of slurrying, and its high melting point and rapid crystallization make effective polymeric inhibitors "essential" [wegiel2015 R22, C27, C16]; lopinavir, a slow crystallizer from solution, was chosen so that leaching and solubility could be measured over hours without crystals [li2016b C5; li2018 C11].

Findings

Crystallization tendency: F9, F13, F14, F17, F18, F20. PEG dispersions: F8, F9. Solution methods: F8, F9. Miscibility and drug-polymer interactions: F15, F16, F23, F24, F26. ASD process: F22, F25, F27, F29, F31, F41, F43, F44. Bioperformance: F1, F10, F27. Crystallization from solution: F1, F3, F16, F21, F35, F36. Physical stability: F2, F17, F24, F33, F34. Supersaturation from ASD dissolution: F1, F2, F16, F23, F29.

Related concepts

measured by crystallization tendency classification; depends on nucleation, crystal growth rate, melt viscosity and thermodynamic driving force for crystallization; related to glass-forming ability, glass stability, physical stability, stochastic nucleation, nucleation induction time, heterogeneous nucleation, semicrystalline solid dispersion, liquid-liquid phase separation, crystallization and crystallization inhibition. Governs matrix crystallization; moderated by crystallization inhibition by polymers. Related to solution crystallization and reduced glass transition temperature. Measured in solution by chaser and non-chaser behaviour; related to conformational flexibility and nucleation rate; related to glass transition temperature.

Formulas

Hoffman equation, classical nucleation barrier; amorphicity index. Reduced glass transition temperature, printed in words for pretomanid (0.67; recomputed 0.673) [nguyen2023a E2, M1].

How it is measured or obtained

By the DSC cooling–reheating classification baird2010 P1; by spin coating and dry storage [vaneerdenbrugh2010a P9]; by seeded growth rates [trasi2014a P1]; by induction times or precipitate crystallinity in supersaturated solution [ilevbare2013c R8; raina2015b R6]; by storage of neat glasses [baird2010 P7; nguyen2023a R4]. In dispersions: the fraction P(t) of 50 neat melts that had started to crystallize at 25 °C, followed for about 500 h zhu2012 P3; onset and t_{50} of the drug in the comelt by XRD and by two Raman bands zhu2012 P5, P6, R23; simultaneous SAXS/WAXS of the blend from 0.2 min to 24 h zhu2011 P2; crystallization of each neat melt cooled to room temperature under polarized light zhu2011 P7, R6. In solution: by the order of extinction onset and visible crystals, with and without a nucleation inhibitor [raina2015a R4, R5], and by how long a drug-rich phase persists before the probe signal returns to the aqueous value (lopinavir 94 min; ritonavir not within 213 min) [tres2018 R20, R21]. For drug–polymer films of the spin-coating screen, by scoring crystalline area over 7 days and expressing it as an amorphicity index, averaged over drug/polymer ratios, polymers or drugs vaneerdenbrugh2010b P2, P3, E1, E2, E3, E4. The class of the pure drug is cited from the group's melt and spin-coating classifications vaneerdenbrugh2010b R11. In the process papers: isothermal DSC holds of the undercooled melt between Tg and Tm followed by reheating (a melting peak means nucleation during the hold): posaconazole 1 h at 130–160 °C and bicalutamide 1 h at 130–180 °C nucleated, indomethacin did not in 4 h at 130–150 °C [moseson2020 P7, R7]; in solution by induction time and seeded growth [moseson2021 P12, R3]. In raina2014a the tendency is cited, not measured: felodipine a slow and nifedipine a faster crystallizer [raina2014a R20]. The crystallization-from-solution papers cite the classes from cooling the melt (Baird 2010) and from rapid solvent evaporation (Van Eerdenbrugh 2010), and measure the solution tendency by the pH-shift titration or the unseeded induction time [hsieh2012 P7; ilevbare2013c P9]. In the physical-stability papers, by nucleation in films and crystallization on heating of melt-quenched glasses [marsac2006a P4, P10]. In the ASD dissolution papers: by time to crystallize in aqueous slurry (Raman) and by microscopy of wetted particles [alonzo2010 P5; raina2014b P4, P6].

Values in the library
materialvalue or classconditionspaper ids
31 drugsMCV 216 to 0.02 µm/smelt growth[trasi2014a R1]
haloperidol, benzocainecrystallized within seconds after quench coolingpure meltszhu2012 R1
ibuprofen; fenofibratecrystallization probability 0.20 and 0.34 after 3 weekspure melts at 25 °Czhu2012 R2, R3
ketoconazoleamorphous after 24 h at room temperaturepure meltzhu2011 R6
nifedipine against felodipinegreater tendency for nifedipinemelt-quenched, heated at 2 °C/min[marsac2006a R5, C11]
propranolol against nicardipine saltspropranolol salts more prone to crystallizeamorphous salts[towler2008 C32]
dihydropyridinescilnidipine slowest, nifedipine fastest in solution; for six drugs the ranking is cilnidipine < felodipine = nisoldipine < nitrendipine = nimodipine < nifedipinesupersaturated buffer; synchrotron[raina2015b C13, C28]
nifedipine; nimodipinenifedipine a very fast crystallizer; nimodipine faster than the other four dihydropyridinesaqueous media (cited)[raina2015a R17]
felodipinerelatively slow; nifedipine fastercited[raina2014a R20, C31]
ritonavir, efavirenz (class III); celecoxib (class II)induction times about 120, 5.1 and 2.4 minsupersaturated buffer, 37 °C, calculated amorphous solubility[ilevbare2013c M1–M3, R8]
ritonavirlow tendency; drug-rich phase persists for 213 minno polymer, 24 °C[tres2018 P5, M1, C29, R20]
lopinavirdrug-rich phase lost after an induction period of 94 minno polymer, 24 °C[tres2018 P5, R21]
papaverine, warfarin, glyburide (slow); dipyridamole (rapid)slow from the melt but crystalline on rapid supersaturation; all crystallized without polymer within about 15–30 minpH shift, 25 °C[hsieh2014 R1, R18, C30]
pretomanidneat glass crystallized within minutesroom temperature[nguyen2023a R4, C10]
drugs with polymerspure-drug tendency related to that in dispersionsspin coatingvaneerdenbrugh2010b C1
haloperidol in PEG 3350onset −100 s, t_{50} 7 s; crystalline from the first SAXS/WAXS frame20/80, 25 °Czhu2012 R23.a, R23.b; zhu2011 R9
benzocaine in PEG 3350onset 120–180 min, t_{50} 110–170 min20/80, 25 °Czhu2012 R23.a, R23.b
ibuprofen in PEG 3350onset about 100 min, t_{50} about 70 min20/80, 25 °Czhu2012 R23.a, R23.b
fenofibrate in PEG 3350onset 120–180 min, t_{50} 140–200 min20/80, 25 °Czhu2012 R23.a, R23.b
chlorpropamide; nilutamide in PEG 3350partially crystalline at 24 h20/80, 25 °Czhu2011 R18.c, R18.e
ketoconazole in PEG 3350amorphous at 24 h20/80, 25 °Czhu2011 R18.f
phenacetin, chlorzoxazone, benzamide, lidocaine, flufenamic acid (class I)mean AI over 7 polymers 47, 47, 48, 55, 59%spin-coated films, 7 days dryvaneerdenbrugh2010b R4
flurbiprofen (class I/II); chlorpropamide, bifonazole (class II)mean AI 68, 73, 97%as abovevaneerdenbrugh2010b R4
class I films with every polymer at 75/25 drug/polymeralmost all fully crystalline (AI 0)as abovevaneerdenbrugh2010b R2
naringenin; quercetinintermediate; rapid crystallizerneat films, rotary evaporation and spin coating[wegiel2013a C19, R7]
lumefantrineclass III; melting onset 127.9 °C, Tg 19.7 °CDSC heat–cool–heat[hiew2022a R3]
bicalutamide in pH 6.8 buffernucleation in under 30 min without polymer, under 5 min at the highest supersaturation; seeded growth near zero at 30 µg/mL, extremely rapid at 150 µg/mL37 °C[moseson2021 R3, R4]
posaconazole and bicalutamide neat meltsmelting endotherm on reheating after 1 h holds below TmDSC[moseson2020 R7]
indomethacin neat meltonly Tg after 4 h at 130–150 °CDSC[moseson2020 R7]
ritonavir and lopinaviramorphous granules unchanged for one month at 40 °C/75% RHXRPD[trasi2019 R2]
uncoated spray-dried ezetimibe–HPMCAS 50 and 70% DLcrystals by SEM at 19 and 12 daysopen dish, 40 °C/75% RH[duong2022c R16, R17]
uncoated ASD powders of four drug–polymer systemscrystals within about 1–2 weeks40 °C, 31–75% 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 / 43.5seeded solution[shah2024 R22]
nevirapineinduction about 5 min at S 3.9 (fast without polymer)pH 6.5[hate2017 R2]
atazanavirrelatively slow; crystallization inhibited more than 4 h with enough polymercited[hate2018 C13]
pretomanidinduction time under 2 min at 160 µg/mL in seven media; melting onset of the crystals 147 °CDSC, 37 °C[nguyen2023a R1, R3, R4]
carvedilol, clotrimazole, clozapine, ketoconazoleclass III (melt) and III (solvent evaporation); type 2pH shift[hsieh2012 M2, M3, M4, M7, R1]
loratadineIII and II/III; type 2same[hsieh2012 M8, R1]
bifonazole; dipyridamole; droperidol; papaverine; pyrimethamineII/II; I/III; II/III; III/II; not classed; all type 1same[hsieh2012 M1, M5, M6, M9, M10, R1]
six dihydropyridinesmelt: nifedipine, nimodipine Class II; others Class III; solution: 0.25–12 hDSC; solvent shift[raina2015b R1, R6]
nine drugs (griseofulvin, celecoxib, ezetimibe, danazol fast; telaprevir, nifedipine, nevirapine intermediate; ritonavir, atazanavir slow)induction time without polymer about 1 to 66 min100 mM phosphate pH 6.8, 37 °C; basis of the classes not given[mosqueragiraldo2018a R1, M1–M9, X11]
nifedipine vs felodipine glass0.39 vs 0.17 × 10¹⁰ m⁻³ day⁻¹; only nifedipine crystallized on heating (87 °C)22 °C; 2 °C/min[marsac2006a R4.a, R5]
nifedipine vs felodipine with 25% PVP≈4.3 × 10⁵ vs ≈2.3 × 10³ m⁻³ s⁻¹75% RHmarsac2008a R1.f, R1.l
resveratrolrapid crystallizer; a polymer is needed to make it amorphousspin coating, rotary evaporation, cryomilling[wegiel2013b R1, C6, C27]
curcuminintermediate crystallizer, relatively high tendencysolvent evaporation[wegiel2014 C9, C1]
celecoxibgrows fast but nucleates poorlymelt films[mosqueragiraldo2014 C7]
tacrolimus in a marketed generic capsulecrystallized within days at 40 °C/75% RH, faster than the pure amorphous drugopen dish[trasi2017 R12, R16, C28]
lumefantrine; artemetherclass 3; class 1DSC heat–cool–heat[trasi2020 R5, R6, C7]
felodipine, neat amorphous≈54% crystalline at 1 minpH 6.8 slurry, 37 °C[alonzo2010 R2]
indomethacin, neat amorphousamorphous for at least 4 hpH 2 slurry, 25 °C[alonzo2010 R11]
nifedipine, neat glasscrystalline (γ) by ≈6 min with or without dissolved polymerpH 6.8, 25 °C[raina2014b R6, R2]
resveratrolrapid crystallizer (cited); Tm 262 °Cstorage and solvent-evaporation class[wegiel2015 R22, M1]
celecoxib, 22 µg/mL without polymercrystallization within 5 minpH 6.8, 37 °C[xie2016a C13]
lopinavirslow crystallization from aqueous solutionpH 3[li2016b C5]
delamanidinduction time 2.4 min at pH 1.6 and 10.7 min at pH 6.5 at the amorphous solubility; no glass on cooling the melt at 50 °C/min; Tg 43.3 °C37 °C[duong2022a R2, R3]
praziquantel, racemate and R-enantiomerabout 5.5 and 5 min without polymer at their amorphous solubilities; 83 min and 37 min with HPMCAS-MFPBS pH 6.5, 37 °C[polyzois2024 R3, R4]
paclitaxelunseeded crystallization within 6 min at S = 88 without polymerpH 6.8, 37 °C[que2018 R3]
Pitfalls and disagreements

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

← Concepts and formulas

concept · as used in PEG dispersions

crystallization

In this chapter, the formation of crystals from a supersaturated solution or from a drug-rich phase; it depletes the supersaturation, unlike a drug-rich phase, which keeps it [tres2017 C42].

Findings

F3, F8, F9.

Related concepts

contrasts with drug-rich phase and liquid-liquid phase separation; related to crystallization inhibition, crystallization tendency and nucleation induction time.

Formulas

none.

How it is measured or obtained

By visual particles and birefringence under polarized light [raina2015a P7]; by the return of a probe signal toward its aqueous value (pyrene I1/I3, PRODAN lifetime) [raina2015a R16; tres2018 R21]; by a long lifetime component of the drug itself [tres2017 R1.g]; in outside work by PXRD of compacts [bhardwaj2018 R3].

Values in the library
materialvalue or classconditionspaper ids
nifedipinecrystals in buffer at ≈38 (25 °C) and ≈58 µg/mL (37 °C)extinction onset with visible crystals[raina2015a R4, R5]
nimodipinecrystals at ≈21.5 µg/mL (37 °C)same[raina2015a R4, R5]
nifedipine with HPMCpyrene I1/I3 back to ≈1.60 at 400 µg/mL after ≈0.76 at 200 µg/mL25 °C[raina2015a R16]
felodipine 108 µM, no HPMClifetime component 9.04 ns (17%) after 15 hpH 7.4[tres2017 R1.g]
lopinavir, no polymerlifetime 1.31 ns at 94 min to 1.06 ns at 213 minpH 7.4, 24 °C[tres2018 P5, R21]
itraconazole dispersionsno crystallinity in compacts after dissolutionPXRD[bhardwaj2018 R3, C14]
Pitfalls and disagreements

Crystallization of a drug-rich phase was inferred from fluorescence in three papers and confirmed by an independent test in none of them [raina2015a X15; tres2017 X6; tres2018 X5]. Extinction cannot tell crystals from a liquid phase [raina2015a C9].

← Concepts and formulas

concept · as used in PEG dispersions

degree of supercooling

\Delta T = T_m - T, how far below its melting point a liquid is held or crystallizes; "undercooling" and "supercooling" are used as synonyms [baird2013 E4; tian2017 E4]. It sets the driving force, which is proportional to ΔT [tian2017 C22]. New aspect (PEG dispersions): in a dispersion the supercooling of each component is set by the melting point of that component in the mixture, which the other component depresses. For benzocaine the authors cite a melting point of around 89 °C for the neat drug and around 48 °C at the eutectic, so the supercooling at 25 °C is much smaller in the PEG dispersion zhu2012 C32, M3. PEG's own supercooling falls when a drug lowers its melting point zhu2011 C21, R1. New aspect (C. Amorphous solubility and LLPS): in the amorphous solubility papers the undercooling is T_m - T at the temperature of the solution experiment (25 or 37 °C), together with T_g - T_\infty, where T_\infty is the temperature at which crystal and supercooled liquid would have equal enthalpy; both are used to judge whether the Hoffman free-energy estimate is reliable [almeidaesousa2015 C34, C35, R16].

Findings

Crystallization tendency: F2, F7, F10, F11. PEG dispersions: F5, F8, F10. C. Amorphous solubility and LLPS: F7. Physical stability: F18, F28, F29.

Related concepts

related to thermodynamic driving force for crystallization; used by Barandiaran-Colmenero method and critical cooling rate; part of crystallization from the supercooled melt; reduced by melting point depression; governs the accuracy of the Hoffman equation and the amorphous-crystalline free energy difference; related to kinetic versus thermodynamic control of crystal growth.

Formulas

Barandiaran-Colmenero critical cooling rate, Hoffman equation, temperature of maximum crystal growth rate.

How it is measured or obtained

As Tm minus the crystallization peak temperature on cooling at a given rate [baird2010 P2; baird2013 R1]; as the temperature scale for growth data [trasi2014a P5]; in dispersions it shrinks when the polymer depresses the drug's melting point zhu2011 C20. In the PEG dispersions it was not measured: the supercooling is inferred from the liquidus of the drug–PEG phase diagram zhu2012 C32; zhu2011 R1. The 25 versus 40 °C solidification of pure PEG was used as a control of how much a change of PEG supercooling moves the lamellar long period (about 1 nm) zhu2011 R8, C21. In the amorphous solubility papers Tm comes from DSC and T∞ from the enthalpy of conversion with ΔH(c → sl) set to zero in the heat-capacity cycle [almeidaesousa2015 E9, R16]. In the polymer growth papers, from the onset melting temperature of 10% physical mixtures at 10 °C/min [trasi2012a P5, R9].

Values in the library
materialvalue or classconditionspaper ids
caffeine3.0 °CDSC cooling at 20 °C/minbaird2010 R12.j
tolbutamide80.8 °CDSC cooling at 20 °C/minbaird2010 R12.v
4-biphenylmethanol; haloperidol15.1; 90.8 °Crapid cooling at 500 °C/min[baird2013 R1.a, R1.f]
class I-A meltscrystallized after about 5–35 °Crheometer[baird2012 R4]
vemurafenibabout 25 °C before crystallizationDSC cooling at 10 °C/min[lu2016 R1]
benzocaine in PEG 20:80melting point 55 against 92 °C for the pure drugdispersionzhu2011 C20
felodipine growth runsΔT 71.4–31.4 °C over 70–110 °Cmelt growth[kestur2010b R17]
benzocaine in PEG 3350supercooling at 25 °C: 89 − 25 = 64 K neat against 48 − 25 = 23 K at the eutectic (synthesis)cited melting pointszhu2012 M3, C32
PEG 3350 with 20 wt% benzocaine; ibuprofen; fenofibrateliquidus about 54.5, 57, 58.0 °C against about 60.5 °C for PEG, a depression of 6.0, 3.5, 2.5 K (synthesis)read from the phase diagramszhu2011 R1.g, R2.g, R1.a; zhu2012 R24.d
pure PEG 335025 °C: t_{50} about 23 s; 40 °C: about 48–64 ssynchrotron XRDzhu2012 R4, R16
ibuprofen, phenylbutazone, tolnaftateTm − T 51, 82, 86 K; Tg − T∞ 81, 42, 143 K25 °C[almeidaesousa2015 R16]
diclofenac, sorafenib, griseofulvinTm − T 147, 180, 192 K; Tg − T∞ 145, 107, 122 K25 °C[almeidaesousa2015 R16]
telaprevirTm 238 °C against 37 °C, a gap of about 200 KHoffman estimate 2.7 times the onset[mosqueragiraldo2015 M1, C23, C24]
CRH1Tm 141.7 °C, so Tm − T = 116.7 K (synthesis: 141.7 − 25)all three free-energy routes agree within 1.3 µg/mL[almeidaesousa2016 M1, R2]
acetaminophen with 10% w/w of seven polymersTm 166.7–168.6 against 169 °C; supercooling similar for allDSC[trasi2012a R9, C19]
flutamide with 10 mol% polymersTm 108–110 °C; supercooling hardly changedDSC[trasi2012b R7, C33]
celecoxib with TPGS and PVPTm 151.49 °C, 12 °C below the drugDSC[mosqueragiraldo2014 R5.f, C18]
six compounds with 1–20% PHBTm of physical mixtures 0–4 °C lower, so supercooling taken as unchangedDSC[sato2016 R7, C18]
indomethacin δ, α, γTm 127 (cited), 152 and 160 °CDSC[tian2017 M1]
Pitfalls and disagreements

Undercooling did not always rise with cooling rate and scattered between runs baird2010 R12, C18. Hoffman estimates lose accuracy at large undercooling [almeidaesousa2015 C34; mosqueragiraldo2015 C24]. Low polymer levels barely shift Tm, so the supercooling is similar with and without polymer [trasi2012a C19; sato2016 C18]. In the PEG dispersions the supercooling and the mobility of benzocaine were not measured, and the two cited melting points differ between the two PEG papers (89 and 48 °C against 92 and 55 °C for the 20/80 blend) zhu2012 C32, C33; zhu2011 R1. The authors do not weigh reduced PEG supercooling as a cause of slower PEG crystallization, only hydrogen bonding zhu2012 C44. In the amorphous solubility papers Table 10 does not predict the size of the Hoffman error drug by drug: sorafenib has 180 K undercooling and equal Hoffman and Cp ratios [almeidaesousa2015 X8]. Small melting-point shifts were used to rule the driving force out as the cause of growth differences between polymers [trasi2012a C19; trasi2012b C33].

← Concepts and formulas

concept · as used in PEG dispersions

Δχ effect

Demixing of two miscible components caused by a third component, a solvent, that interacts very differently with each of them; the larger the difference between the solvent–component interaction parameters, the stronger the tendency to separate [marsac2010 C36, E1; purohit2017b E4]. In the library the solvent is water, the components a hydrophobic drug and a hydrophilic polymer [marsac2010 C43].

Findings

F12, F13, F14, F31.

Related concepts

mechanism of moisture-induced phase separation; depends on Flory-Huggins interaction parameter; related to cosolvency and enthalpy of mixing.

Formulas

Δχ effect, multicomponent Flory-Huggins free energy of mixing.

How it is measured or obtained

From the absolute difference of the water–drug and water–polymer Flory–Huggins parameters, each obtained from water sorption [marsac2010 E1, R22, E3].

Values in the library
materialvalue or classconditionspaper ids
felodipine–PVP–waterχ water–felodipine ≈3.3, water–PVP ≈0.5 (difference 2.8 by subtraction); felodipine–PVP slightly negativecited values[marsac2010 R22, E1]
six drugs in PVP–waterseparating drugs had water–drug χ 2.84–3.58, non-separating 2.50–2.7125 °C sorption[rumondor2009c R24, C46]
ritonavir with PVP, PVPVA, HPMCAS (outside)larger Δχ, higher tendency to phase separation (argument)stated in words[purohit2017b E4, C43]
loratadine-type ASDs (outside)separation predicted when the difference is large even if drug–polymer χ is negativeargument[yang2021 E2]
miconazole–PVPVA 50:50no separation dry at 100 °C; separation with water during casting, storage and immersion, read as a water-driven change of the thermodynamics ("evidence is provided")films and powders[saboo2017 R22, C41, C43]

Evidence table: Δχ effect.

Pitfalls and disagreements

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

← Concepts and formulas

concept · as used in PEG dispersions

dipole-dipole interactions

Electrostatic interaction between permanent dipoles, proposed in this chapter as the contact of ketoconazole with PVP, since ketoconazole has no hydrogen-bond donor and its PVP carbonyl does not shift: "it seems reasonable to speculate" that the two interact through dipole–dipole forces, helped by the large size of ketoconazole and its van der Waals contacts marsac2009 C40, C41, R14. The slight changes in the ketoconazole carbonyl band in PVP dispersions are also "speculated" to come from dipole–dipole interactions, by analogy with ion–dipole interactions reported for PVP with another drug [rumondor2009a C23].

Findings

F2, F4.

Related concepts

contrasts with hydrogen bonding; part of drug-polymer interactions; related to drug-polymer miscibility.

Formulas

none.

How it is measured or obtained

Not measured as an interaction: only the dipole moments of single molecules were computed by DFT (B3LYP/6-311++G(2d,p)) marsac2009 P5, R12, and the IR changes were compared with calculated physical mixtures [rumondor2009a R10].

Values in the library
materialvalue or classconditionspaper ids
ketoconazole6.03 D; no donor; PVP C=O shift 0DFT; FTIRmarsac2009 R12.h, R14
nifedipine; felodipine; sucrose9.58; 5.30; 5.40 DDFTmarsac2009 R12.a, R12.b, R12.d
indomethacin; ibuprofen; vinyl pyrrolidone2.68; 1.76; 3.91 DDFTmarsac2009 R12.c, R12.e, R12.g

Evidence table: dipole-dipole interactions.

Pitfalls and disagreements

The dipole moment does not rank the carbonyl shift (nifedipine has the largest moment and no shift entry, indomethacin a small moment and the largest shift) marsac2009 R12. No dipole–dipole interaction was demonstrated in the mixture [marsac2009 C41; rumondor2009a C23]. The PXRD and DSC results on ketoconazole–PVP leave its phase state open [rumondor2009a X1].

← Concepts and formulas

concept · as used in PEG dispersions

drug-polymer interactions

The contacts between drug and polymer in an amorphous dispersion, relative to the contacts in the pure components: strong adhesive (drug–polymer) interactions formed at the expense of weak cohesive (self) interactions make mixing exothermic, adhesive interactions that require breaking strong cohesive ones do not marsac2009 C3, C36. The interactions are hydrogen bonds where the drug has a donor and the polymer an acceptor, and, for a drug without donors, perhaps dipole–dipole forces and van der Waals contacts [taylor1997 C35; marsac2009 C41; rumondor2009a C23]. Specific interactions have been postulated as one way polymers stabilize amorphous drugs, and as a condition of single-phase dispersions [kestur2010a C3; marsac2009 C3]. In this chapter they are the common thread of the miscibility papers (whether the pair mixes) and the inhibition papers (whether the polymer slows crystallization). The later papers add ionic (acid–base) contacts of E100, enteric polymers and PSSA with basic or acidic drugs [wegiel2013a C16, C35; hiew2022a C25, C48; vaneerdenbrugh2011a C22] and a weak halogen bond between compounds with Cl, Br or I but no donor and the PVP carbonyl [que2020 C1, C25]. A polymer can also bond to itself (PAA, dextran), which competes with the drug [rumondor2009a C45; vaneerdenbrugh2012a C36].

Findings

F1, F2, F3, F4, F7, F8, F12, F13, F14, F15, F17, F20, F21, F23, F24, F25, F26.

Related concepts

includes hydrogen bonding and dipole-dipole interactions; measured by Flory-Huggins interaction parameter and activity coefficient; determines drug-polymer miscibility and crystal growth inhibition by polymers; related to enthalpy of mixing; includes acid-base interaction and halogen bonding.

Formulas

Flory-Huggins melting point depression, Flory-Huggins activity equation.

How it is measured or obtained

Spectroscopically, by shifts of IR bands of the drug and the polymer carbonyl in dispersions against physical mixes and amorphous references [taylor1997 C24, C26; marsac2009 P4]; by a second principal component of the IR spectra beyond calculated physical mixtures [rumondor2009a P5, C9]; thermodynamically, by the melting point depression of the crystalline drug in the polymer (χ) and by the solubility of the drug in a liquid analogue of the polymer (activity coefficient) marsac2009 P6, P7; by DSC and PXRD for the resulting phase state [rumondor2009a P2, P8, P9]. Interactions are not measured at the temperature and polymer level of the growth studies [kestur2010a X5]. Further methods: IR band shifts of the polyphenol OH and the polymer C=O in films [wegiel2013a P4]; XPS of N 1s and of halogen core levels [hiew2022a P16; que2020 P5]; solution NMR titration with a monomer analogue for a binding constant [que2020 P6]; crystal-structure statistics of competing groups [vaneerdenbrugh2011a P5].

Values in the library
materialvalue or classconditionspaper ids
indomethacin–PVPacid OH bonded to PVP carbonyl; dimers opened; incomplete bindingIR, 5–70 wt% PVP; physical mixes show none[taylor1997 C35, C26, C37]
felodipine–PVP, nifedipine–PVPone phase over 10–90% and 25–70% PVP; hydrogen bonding "presumably" behind the second PCIR, PXRD[rumondor2009a C38, C20]
felodipine–PAAlittle mixing at 30–70% PAA; competition from PAA self-association "speculated"DSC, IR, PXRD[rumondor2009a C44, C45]
ketoconazole–PVPnear-athermal mixing, no carbonyl shift; dipole–dipole forces "speculated"melting, FTIRmarsac2009 C40, C41, R12.h
felodipine with PVP, PVP/VA, HPMCAS, PVAcstrength PVP > PVP/VA > HPMCAS ≥ PVAcNH shifts at 50 wt% polymer[kestur2010a C26, R9]
nimesulide with PVP, PVP/VA, PVAcpresent but small; limited by the intramolecular bondIR, 20–50 wt% polymer[kestur2011 C23, C24, C27]
amide and basic drugs with PAA, PSSAhighest crystallization resistance; acidic drugs lowestspin-coated films, 7 daysvaneerdenbrugh2010b C23, C24, C27
indomethacin–PVP K12χ −0.82 (melting), −1.83 (EP solubility)most favourable of five pairsmarsac2009 R7.e, R9.e, C42
naringenin, quercetin with PVP; with E100hydrogen bonding strongest with PVP; acid–base contact with E100 (amine bands lost at 50% quercetin)IR, films[wegiel2013a R2, R4, R6]
lumefantrine with enteric polymers and PVPVAprotonated 19–55% with HPMCAS, HPMCP, CAP, Eudragit L 100; 0% with PVPVAXPS, 25% drug loading[hiew2022a R20]
clotrimazole, loratadine, brotrimazole, Me-DIBF with PVPVAhalogen bond: K_F 0.56–1.11 M⁻¹, carbonyl shift 2–6 cm⁻¹NMR, IR[que2020 R12, R11]
15 drugs, 7 polymerscomplementary donor and acceptor groups give the highest amorphicity indexspin-coated films[vaneerdenbrugh2011a R3, C20, C33]

Evidence table: drug-polymer interactions.

Pitfalls and disagreements

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

← Concepts and formulas

concept · as used in PEG dispersions

drug-polymer miscibility

A single amorphous phase formed by liquid–liquid mixing of amorphous drug and amorphous polymer, a description the authors themselves call "clearly" an oversimplification below Tg, where the system is not at equilibrium marsac2006b C3. A molecularly mixed system has one amorphous phase; more than one phase means regions of different drug:polymer ratio [rumondor2009a C4]. Three behaviours follow from the free energy of mixing: complete miscibility (one minimum), complete immiscibility (positive ΔGmix) and partial miscibility (two minima), with strict immiscibility rare, because some of each component always dissolves in the other [rumondor2009a C35, C36, C37]. Miscibility is not solubility: crystals in a dispersion after manufacture or storage do not necessarily mean the two liquids are immiscible, since the solubility limit of the crystal in the polymer may have been exceeded marsac2006b C43. Maximum stabilization of an amorphous drug "can only be realized" when drug and polymer are intimately mixed [rumondor2009a C3]. The concept also applies to pairs of polymers, whose miscibility falls with the molecular weights of both: from one phase at every composition for a 783 Da maltodextrin with all PVP grades to two phases at all nine compositions for a 450 kDa dextran with PVP K 90 [vaneerdenbrugh2012a C6, C23, C24, C38]. Solvent-cast films of itraconazole–HPMC (10–50% drug) and of telaprevir with HPMC, PVPVA or HPMCAS were not miscible at the loadings tested, with the onset of separation at 10% drug for HPMC and PVPVA and at about 30–40% for HPMCAS [purohit2015a C36; li2016c C17, C52]. New aspect (ASD process): mixing of drug and polymer at the molecular level in one amorphous phase, judged by a single Tg, featureless AFM and TEM images and spectroscopy, is considered essential for solid-state stability and for supersaturation on dissolution [li2017 C2, C30; broman2001 C14]. In the hot-melt extrusion context it is also the condition for melting point depression: miscible pairs show it, immiscible pairs do not moseson2018 C8, C15.

Findings

Miscibility and drug-polymer interactions: F3, F4, F5, F6, F7, F17, F18, F19, F22. ASD process: F1, F5, F8, F17.

Related concepts

measured by single-Tg miscibility criterion, melting point depression and Flory-Huggins interaction parameter; depends on enthalpy of mixing, entropy of mixing and drug-polymer interactions; described by free energy of mixing; contrasts with drug solubility in polymer; required for an amorphous solid dispersion; contrasts with amorphous-amorphous phase separation. In films, miscibility is lost in amorphous-amorphous phase separation.

Formulas

Gibbs free energy of mixing, Flory-Huggins free energy of mixing, Flory-Huggins melting point depression, Flory-Huggins combinatorial entropy of mixing.

How it is measured or obtained

By counting glass transitions by DSC, with its limits [rumondor2009a C5, C6]; by IR with PCA against calculated physical mixtures [rumondor2009a C9]; by PXRD with PDF fitting and pure curve resolution [rumondor2009a C10, C11]; by the melting point depression of the crystalline drug in the polymer marsac2009 C12; by Flory–Huggins free energy curves from χ marsac2006b C17. A pair is classed miscible, partially miscible or immiscible from Tg, FTIR and microscopy in the earlier literature marsac2009 R1. Further methods: pyrene and prodan fluorescence, fluorescence imaging, AFM-nanoIR, nanoTA and Lorentz contact resonance on films [purohit2015a P3, P4, P9, P10; li2016c P4, P7, P8]; DSC together with the hydrogen-bonded fraction of PVP carbonyls for polymer blends [vaneerdenbrugh2012a P3, P5]. In the later process papers: a single Tg between those of the components (probucol–PVP 95 or 129 °C between 26 and 163 °C) broman2001 R4.a, R4.b, C14, M1, M2; featureless films at the 40 nm AFM resolution [li2017 C8]; melting point depression across the range moseson2018 R5; itraconazole's own UV and fluorescence [mugheirbi2017 C30].

Values in the library
materialvalue or classconditionspaper ids
nifedipine, felodipine, ketoconazole, sucrose, indomethacin with PVPmiscible (cited Tg, FTIR)classification used for χmarsac2009 R1.a, R1.b, R1.c, R1.d, R1.e
sucrose–dextranmiscible; ibuprofen–dextran, indomethacin–dextran immisciblecited and this study (Tg data not shown)marsac2009 R1.f, R1.g, R1.h, X10
itraconazole–Eudragit E100partially misciblecitedmarsac2009 R1.i
felodipine–PVP, nifedipine–PVPone amorphous phase over the compositions studiedIR, PXRD, DSC (cited)[rumondor2009a C38, X5]
felodipine–PAA"practically immiscible" at 30–70% PAA; some mixing at 10 and 90%DSC, IR, PXRD[rumondor2009a C44, C46]
ketoconazole–PVP"suspected" partially miscible, one phase at higher PVP onlyone Tg; IR; PXRD[rumondor2009a C40, X1]
nifedipine–PVP K29/32predicted miscible at all compositions from χ −3.8Flory–Hugginsmarsac2006b R2, C33
itraconazole–HPMC 10:90 to 50:50phase separated at every loading in solvent-cast films; one broad Tg of powdersfluorescence, AFM-nanoIR, nanoTA; mDSC[purohit2015a C36, R7]
telaprevir with HPMC, PVPVA, HPMCASdomains from 10% drug (HPMC, PVPVA); from about 30–40% (HPMCAS)AFM, AFM-IR, nanoTA, LCR[li2016c C17, C52]
dextran–PVP, 20 pairsmiscible at all compositions for 783 Da maltodextrin; phase separated at all nine for DEX450–PVP90DSC, FTIR[vaneerdenbrugh2012a R13, R14]
probucol–PVP K30 50:50single Tg, "seemed" one-phase; carbonyl shiftsolvent, mouldedbroman2001 R4, R5, C14
ECP–HPMC / PVPVAmiscible over 10–90% DL when dry18% RH[li2017 R3.a, C33]
ITZ–HPMCthermodynamically miscible when dry, trapped as two phases when wet ("suggest")7% RH vs 20–40% RH[mugheirbi2017 R1, C39]
IDM–PVPVAmelting point depression confirms miscibility at elevated temperatureDSCmoseson2018 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 PEG dispersions

drug-polymer-water miscibility

Evidence table: drug-polymer-water miscibility. Content from the release-mechanism chapter (2017–2025).

Whether drug and polymer stay mixed once water enters the dispersion. Indulkar and co-workers (2017) state that AAPS depends on drug–polymer miscibility in the presence of water, set by the balance of drug, polymer and water interactions, and varies with drug, polymer type and composition; drug–PVPVA dispersions that dissolve rapidly while staying miscible in water "are expected" to form nanospecies by dissolution followed by LLPS [indulkar2017b C38]. Saboo and co-workers (2020) add that water can impair the miscibility of a dispersion on hydration, which "is expected" to harm dissolution [saboo2020a C39]. In the Flory–Huggins description a hydrophobic drug and a hydrophilic polymer interact very differently with water, which drives separation [purohit2017b C43]. Measured in 2023 as the water content at which 30% ritonavir–PVPVA films separated within 12 h: 14.0% without surfactant, 24.5% with SDS, 10.5–16.0% with Span 20, Span 85 or Tween 80; the authors read the SDS shift as a larger miscible region ("suggesting"), "likely responsible" for its better release [yang2023 R21, C9, C10].

Findings

Release mechanism and LoC: F5, F8, F31.

Related concepts

lost through amorphous-amorphous phase separation; expressed by the Flory-Huggins interaction parameter and the Δχ effect; its loss in time is phase separation kinetics.

Formulas

multicomponent Flory-Huggins free energy of mixing, Δχ effect.

How it is measured or obtained

From films or powders exposed to water or high humidity, imaged by fluorescence or tested by DSC (see amorphous-amorphous phase separation) [purohit2017b R3, R6; saboo2020a R23].

Values in the library
materialvalue or classconditionspaper ids
ritonavir–HPMCASmiscible after 97% RH; PVP and PVPVA dispersions separatedfilms and powders[purohit2017b C1]
felodipine 30% with HPMCAS, EUDS; PVP, PVPVA, HPMCuniform; separated97% RH, 24 h[saboo2020a C23]
ritonavir–PVPVA 30% films ± 10 parts surfactant14.0 / 16.0 / 10.5 / 12.5 / 24.5% water (none / Span 85 / Span 20 / Tween 80 / SDS)saturated-salt RH, 12 h, 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 PEG dispersions

drug-rich nanodroplets

The dispersed drug-rich phase formed by LLPS, usually of 100–300 nm, which dissolves fast and is expected to replenish absorbed drug [indulkar2016 C4, C25]. Droplets are too large to cross the 3–4 nm (regenerated cellulose, 12–14 kDa) or 15 nm (hollow fibre) pores of the membranes used [indulkar2016 C11; hate2018 C52]. In enzalutamide dispersions the same species is called amorphous aggregates, about 100 nm; in simulated and pooled human intestinal fluids spheres of 0.1–0.5 µm were found [wilson2018 R11, C45; elkhabaz2019b R4, C19, C24]. New aspect (Supersaturation from ASD dissolution): fast-releasing dispersions put drug above the amorphous solubility into a submicron colloid within minutes, and additives decide its size and how soon it crystallizes [ilevbare2013d C59, C60; jackson2015 C29]. New aspect (Release mechanism and LoC): from dissolving dispersions, nanodroplets formed only where release was congruent or close to congruent, so that the drug concentration exceeded the amorphous solubility [purohit2017b C52; indulkar2019a C5; saboo2019 C30]. The 2017 isotope study concludes that they form from drug that has first dissolved, followed by LLPS ("strongly suggest"), not by release of drug-rich domains from the hydrated matrix [indulkar2017b C26]; Purohit and Taylor reach the same reading for ritonavir films ("likely") [purohit2017b C57]. When drug release is controlled by polymer dissolution, colloid formation is "highly dependent" on drug loading [que2019 C55]. Their size and life after release depend on the drug, the polymer and small amounts of surfactant: HPMCAS kept elbasvir and loratadine droplets small, and SDS, TPGS or Tween 80 at 4–50 µg/mL kept clopidogrel droplets stable for 4 h while CTAB agglomerated them [yang2021 C4; correasoto2022a C12, C38]. Built into ritonavir–PVPVA at 30%, the Spans kept the released droplets near 1 µm, while TPGS and Tween 80 let them grow to several micrometres, which the authors suggest "could possibly" come from these surfactants partitioning into the droplets and lowering their Tg [indulkar2022 C47, C48]. In dissolving ritonavir–PVPVA compacts at 10 and 20% droplets formed near the gel–solution interface and entered the solution with the dissolving polymer, which the authors explain by a water content needed to cross the binodal [yang2022a C34, C35, R10, R11].

Findings

Bioperformance: F5, F8, F15, F19, F22, F23. Supersaturation from ASD dissolution: F8, F9, F12, F13. Release mechanism and LoC: F4, F5, F12, F13, F16, F25, F27.

Related concepts

produced by liquid-liquid phase separation; act as nanodroplet reservoir effect; part of the drug-rich phase; related to droplet coalescence and particle absorption of light; form under congruent release above the amorphous solubility. Coarsen by drug-rich phase coarsening.

Formulas

Stokes-Einstein equation.

How it is measured or obtained

NTA (scattering or fluorescence mode with Nile red), DLS, the 369 nm band of atazanavir [indulkar2016 P4; hate2018 P3, P4, P6]. Nile Red fluorescence of the pellet against aggregate mass, and DLS [wilson2018 R8, R11]; SEM of a centrifuged pellet with the drug's own fluorescence in human fluid [elkhabaz2019b R3, R4]; Z-average by DLS under agitation [ueda2020a R5, R6]; size and zeta potential with polymer or surfactant additives [hate2022 R17]. In the ASD dissolution papers: light scattering in a flow-through cell, nanoparticle tracking of samples or 0.45 µm filtrates, SEM of dried samples [ilevbare2013d P3, P8; jackson2015 P5; trasi2015b P8]. In the release-mechanism papers: NTA, DLS, visible turbidity, environment-sensitive probes in solution and free drug after ultracentrifugation [indulkar2017b R6, R7; purohit2017b R7, R8; indulkar2019a R9; que2019 R5, R12; saboo2019 R11, R12].

Values in the library
materialvalue or classconditionspaper ids
clotrimazole111 / 223 / 246 / 257 nm at 8 / 10 / 15 / 20 µg/mL; 1.2 × 10⁸ to 12.5 × 10⁸ per mLpH 8, NTA[indulkar2016 R4]
atazanavir, solvent shift204–226 nm, PDI 0.08–0.15100–500 µg/mL, DLS[hate2018 R6]
atazanavir 90:10 HPMCAS and HPMC ASDs294–326 nmclosed and absorptive[hate2018 R12]
atazanavir with PVPVAabout 245 nm rising to about 700 nm at 75 min and 10 µm at 105 minagglomeration[hate2018 R20]
telaprevir 90% HPMCAS ASDabout 300 nmDLS (data not shown)[mosqueragiraldo2018b R3]
ritonavir ASD (Tres 2018)696 / 294 nm (ritonavir / lopinavir)NTA[tres2018 R18]
enzalutamide 10:90 and 50:50 copovidone ASDsabout 100 nm; about 50 against about 3 µg/mL of 100 as aggregatespH 6.5, 1 h dissolution[wilson2018 R10, R11]
atazanavir, posaconazole in pooled human fluidspheres of 0.1–0.5 µm, no needlesSEM of pellet, 100 µg/mL HPMC-AS[elkhabaz2019b R4]
atazanavir, clozapine with HPMCAS-LF and -HFAS-LF droplets below 300 nm over 3 h; AS-HF kept the initial size; clozapine about 100 nm (AS-HF) against 250 (AS-LF)300 rpm, 37 °C[ueda2020a R6]
atazanavir 150 µg/mL with polymer or surfactant additivesdroplets of about 280 and about 1000 nm gave the same mass flowPAMPA, 2% SDS receiver[hate2022 R17]
ritonavir–PVP dispersion at 20 µg/mLabout 350 nm at onset; ≈5590 nm by 120 min100 mM buffer, 37 °C[ilevbare2013d R1, R5]
ritonavir 20 µg/mL with 5 µg/mL CAAdP 0.33210−214 nm before crystallizationsolvent shift[ilevbare2013d R12]
danazol 90:10 dispersions246–284 nm25 °C[jackson2015 R6]
ritonavir; ritonavir + lopinavir, HPMCAS dispersionsabout 500 nm; about 160 nm in 0.45 µm filtrates1 h[trasi2015b R7]
felodipine 90:10 HPMC dispersion≈185 → ≈300 nm, read as crystalline25 °C[alonzo2011 R8, C33]
nifedipine 10, 20% with HPMC-E5 or PVPVA≈190–222 nmNTA, 5 °C, D2O[indulkar2017b R7]
ritonavir 10:90 films with PVPVA, HPMCAS, PVP200, 250, 315 nmNTA, fresh films[purohit2017b R8]
ritonavir–PVPVA 10% tablet218 ± 15 nm; media of 10–25% turbidDLS at 30 min[indulkar2019a R9]
ledipasvir–PVPVA 2, 5%cloudy medium; ≈225–257 nm at 5%DLS[que2019 R5, R12]
nilvadipine 5, 10%; cilnidipine 5, 10, 15%237 ± 8, 246 ± 3; 255 ± 1, 300 ± 2, 366 ± 7 nm; none at higher loadingsDLS, about 1 h[saboo2019 R11]
indomethacin–PVPVA 5, 10%250–350 nmNTA, 30 min[saboo2020 R7]
felodipine with 5% TPGSZ-average ≈237–279 nmDLS, 60 min[saboo2021 R17]
elbasvir 2.5%; loratadine 10%PVPVA ≈670 → 1190; ≈820 → 2120 nm; HPMCAS ≈280 → 390; ≈420 → 570 nmDLS, 60 min[yang2021 R3, R6]
clopidogrel≈520 nm in buffer; stable with SDS, TPGS or Tween 80; ≈12-fold growth with CTABDLS, 4 h[correasoto2022a R5, R6]
four phenolphthalein analogues179–364 nmDLS, 30 min[que2021 R22]
ritonavir–PVPVA 30:70:5 with Span 85; Span 20; none; SDS; TPGS; Tween 80≈330–960; ≈550–1410; ≈940–2200; ≈2400; ≈3840 nm; ≈10 µmDLS of the medium during release[indulkar2022 R11, R13]
plasticized dispersions (systems not specified)500–1500 nm after 90 minDLS[correasoto2023 R5]
MePHPH–PVPVA 5–30%; PHPH–PVPVA 5%nanoparticles formed within the gel; onset 601 ± 68 µm beyond the 356 ± 18 µm gelin situ confocal[deac2023a C27, R8, C31]
drug-rich phase released from 30% MePHPH; from 5% PHPH98.8 against 26.2 wt% drug; Tg 16.8 against −5.8 °CHPLC, DSC[deac2023a R12]
PHPH; MePHPH nanoparticles with PVPVAPVPVA 71.4–78.0; 0.5–7.5 wt%37 °C, two preparation 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 PEG dispersions

drug-rich surface layer

A polymer-depleted, drug-enriched layer at the surface of a dissolving ASD, left when the polymer dissolves ahead of the drug above the limit of congruency. Moseson (2022) shows it on bicalutamide–PVPVA compacts and says that this layer, hydrated and mobile, crystallizes within 20–30 min, which "could prevent release, promote surface crystallization, and prevent or slow continued hydration" [moseson2022b C46, C43]. In the 2021 paper it was inferred from the shape of the PVPVA release curve and pitted surfaces, "presumably drug-rich" [moseson2021 C32, C58]. It is the general case of surface drug enrichment applied to dissolution. New aspect (Release mechanism and LoC): the layer is the drug-controlled surface of the older two-component literature (sulfathiazole–PVP, cited) [purohit2017b R23], and the nifedipine study states that if water-induced phase separation forms such a layer, the drug controls release and the carrier effect of the polymer is lost [indulkar2017b C33]. For ritonavir the authors add that drug molecules "can" move laterally on the dissolving surface and that drug-rich nanodomains "can" coalesce into contiguous regions, ritonavir being a supercooled liquid at 37 °C [indulkar2019a C28, C40]. Saboo and co-workers (2021) model it as what a contiguous drug-rich network leaves once the polymer-rich phase dissolves ("likely") [saboo2021 C39]; for clopidogrel, faster polymer loss leaves a drug-enriched compact that "likely accounts for" incomplete release [correasoto2022a C25].

Findings

ASD process: F27, F38, F48. Release mechanism and LoC: F3, F7, F20.

Related concepts

forms above the limit of congruency during incongruent release; sits on the gel layer; leads to matrix crystallization and surface crystallization. Its barrier role is the drug-rich barrier layer; sets drug-controlled release; mobile where the drug is a supercooled liquid.

Formulas

None.

How it is measured or obtained

SEM-EDX of exposed compacts: fluorine occurs only in the drug, so F/F0 above 1 means drug enrichment; confocal fluorescence with a drug-rich dye; SEM of the surface for crystals [moseson2022b P14, P15, P16, P17, C8]. In the release-mechanism papers: IR of the tablet surface, micro-CT and SEM of dried compacts [indulkar2019a P7, P8; que2019 P5; saboo2019 P14].

Values in the library
materialvalue or classconditionspaper ids
30% BCL–PVPVA compact surfaceF/F0 = 1.23 ± 0.07 (about 20% enrichment)30 min in buffer[moseson2022b R14]
same, cross-sectiondrug-rich boundary layer 94 ± 8 µm with crystals, F/F0 = 1.41 ± 0.10; gel layer below F/F0 = 0.93 ± 0.061 h[moseson2022b R15]
same, confocalred layer 55 ± 6 µm at 5 min, 103 ± 9 µm at 30 minNile red[moseson2022b R16]
50% BCL–PVPVA compact5–10 µm crust of crystals; red regions of 8 ± 2 µm at 5 min, a continuous layer of 1.9 ± 0.3 µm at 30 min, gone at 60 minSEM-EDX, confocal[moseson2022b R15, R17]
10% BCL–PVPVA compactsurface smooth at 30 minSEM[moseson2022b R14]
coated ritonavir–PVPVA tablet edgeconnected drug-rich regions along particle boundariesconfocal[benson2025 R14]
ritonavir–PVPVA 50%amorphous-ritonavir IR spectrum from 5 min; flaky at 15 minpH 6.8, 37 °C[indulkar2019a R16, R17]
ledipasvir–PVPVA 10%distinct top layer at 10 min; bulging, porous top by 30 minmicro-CT, dried[que2019 R13]
nilvadipine 15:85porous layer within 10 min, growing to 30 minmicro-CT[saboo2019 R13]
felodipine 30% in PVP, PVPVA, HPMCporous layer at the dissolving facemicro-CT, 10 min[saboo2020a R19]
felodipine 30% with 0, 2% TPGS; 5, 10% TPGSporous surface layer after 10 min; homogeneousmicro-CT, 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 PEG dispersions

drug solubility in polymer

The amount of crystalline drug that a polymer can hold in solution at a given temperature. In the PEG papers it appears in three forms: the eutectic composition, "the maximum drug solubility at the eutectic temperature" of the molten polymer baird2011 C1; an extrapolated value at 25 °C, which refers to supercooled liquid PEG because 25 °C is below the PEG melting point zhu2011 C8; and the solubility in a liquid low-molecular-weight analogue, PEG 400, used as a stand-in for amorphous PEO because the true value cannot be measured when the transformation is too slow marsac2008b C18. For amorphous polymers it is predicted from the heat of fusion, the melting point and the sign of the mixing enthalpy, so that drugs with a high heat or temperature of fusion are less soluble marsac2006b C52. New aspects (Miscibility and drug-polymer interactions): For amorphous polymers, the solubility of the crystal in the polymer is the quantity that separates a thermodynamically stable dispersion from a supersaturated one; knowing it would allow the supersaturation, a measure of the driving force, to be evaluated, but it had been measured only in a low-Tg polymer marsac2006b C44. It depends on the melting temperature, the heat of fusion and the sign of the mixing enthalpy: high-melting, high-ΔHfus drugs without substantial polymer interaction have very low solubility, and a negative mixing enthalpy raises it marsac2006b C52, C53. Miscibility and solubility are different: crystals in a dispersion do not by themselves mean immiscibility marsac2006b C43. New aspect (ASD process, extrusion): the depressed melting point at a given composition is the temperature at which the polymer holds that amount of crystalline drug in solution; the authors treat the value from DSC melting point depression (heating a fixed composition until the last crystal dissolves) as thermodynamically equivalent to the solubility that isothermal dissolution during extrusion approaches from the under-saturated side moseson2018 C10, C43. New aspect (Physical stability): with water present, the solubility that matters is that in the polymer–water co-solvent, which falls as water is added, and the dispersion's supersaturation rises accordingly (reasoned from NMP–water) marsac2008a C33, C46.

Findings

ASD process: F8, F9, F11. PEG dispersions: F1, F3, F4, F11. Miscibility and drug-polymer interactions: F4, F8, F9. Physical stability: F10, F15.

Related concepts

depends on melting point depression, crystal lattice energy and drug-polymer interactions; measured by van't Hoff equation and activity coefficient; related to eutectic, ideal solubility and semicrystalline solid dispersion; depends on ideal solubility and activity coefficient for the predicted values; contrasts with drug-polymer miscibility; related to kinetic stabilization. Expressed as formulation critical temperature. Related to cosolvency and supersaturation.

Formulas

van't Hoff equation, activity coefficient from solubility, drug mass solubilized by the amorphous polymer fraction, Flory-Huggins melting point depression; solid-liquid equilibrium solubility equation, Flory-Huggins activity equation.

How it is measured or obtained

From the drug-rich liquidus of the temperature–composition phase diagram: a straight line of \ln x against 1/T, extended to 25 °C and converted to weight percent zhu2011 P6, E3; by shake-flask in liquid PEG 400 (excess drug, 24 h at 25 °C, UV assay) baird2011 P5; marsac2008b P5; for amorphous PEO as the PEG 400 value times the amorphous volume of PEO in the compact, assuming that crystalline PEO dissolves no drug marsac2008b E4, C20; from melting point depression with the Flory–Huggins relation, or from the solubility in an analogue solvent scaled to the polymer, for drugs in PVP marsac2006b R8, R17; marsac2009 R9. For drugs in PVP it was not measured in the polymer. It is predicted by solving the solid–liquid equilibrium equation together with the Flory–Huggins activity coefficient and the melting-route χ (2006), checked against the measured solubility in methyl pyrrolidone at 25 °C marsac2006b P9, P3, E5, E6; or by measuring the activity coefficient in a liquid analogue (1-ethyl-2-pyrrolidone) and scaling it to PVP K12, K29/32 or K90 with Eq. 8 (2009) marsac2009 P7, E8. Estimates made by measuring solubility in a low-molecular-weight analogue "need to be corrected" for the smaller mixing entropy of the polymer marsac2006b C51. The fraction of drug in excess of the predicted solubility, at each polymer content, is the fraction "available for crystallization" marsac2009 P9, R11. In the extrusion papers it is read from the offset temperature extrapolated to 0 °C/min of cryomilled mixtures, or in a hot-stage test at constant temperature, where complete dissolution within about 8 h below Tc was read as a thermodynamic rather than kinetic limit moseson2018 P2, R13, C35; for IDM in copovidone at 1:5 a solubility temperature of about 78 °C is cited from the phase diagram [moseson2019 R21]. In the moisture papers it was not measured in PVP; NMP and NMP–water were used as stand-ins, and a dry-PVP value was cited for the plateau estimate [marsac2008a P8; rumondor2009b R26].

Values in the library
materialvalue or classconditionspaper ids
benzocaine; chlorpropamide; ibuprofen in PEG 335028; 26; 25 wt%extrapolated to 25 °C from the liquiduszhu2011 R5.b, R5.c, R5.d
nilutamide in PEG 335011 wt% (eutectic 10 wt% at 58.4 °C)as abovezhu2011 R5.e, X4
haloperidol; ketoconazole in PEG 33500 wt%as above; text for haloperidol: under 1% w/wzhu2011 R5.a, R5.f; zhu2012 X10
fenofibrate in PEG 33506 wt%as above, from the supporting-information diagramzhu2012 M2
chlorpropamide; aceclofenac; loratadine; haloperidol in PEG 400194; 233; 49; 14 mg/mL24 h, 25 °Cbaird2011 R9
acetaminophen, ketoprofen, naproxen, ibuprofen, felodipine, ketoconazole in PEG 4000.32, 0.32, 0.22, 0.28, 0.16, 0.02 mole fraction24 h, 25 °Cmarsac2008b R14
the same six drugs in amorphous PEO (9% of 450 mg PEO)14, 24, 13, 17, 15, 2% of the 50 mg of drug dissolvablePEG 400 value usedmarsac2008b R16
nifedipine in PVPmore than 90% polymer needed for no crystallization on a thermodynamic basispredicted with \chi = −3.8marsac2006b R18, R17
most drugs in polymeric matriceslikely low at room temperature unless cohesive interactions are extremely favourablesolubility in an ethyl-pyrrolidone analoguemarsac2009 C46, R9
nifedipine in PVP K29/32; K120.06; 0.07 g/g (0.001 g/g with χ = 0.5)χ −3.8, predictedmarsac2006b R17.a, R17.b
felodipine in PVP K29/32; K120.25; 0.31 g/gχ −4.2, predictedmarsac2006b R17.a, R17.b
nifedipine; felodipine in methyl pyrrolidonepredicted 0.15 and 0.48; measured 0.21 ± 0.02 and 0.45 ± 0.07 g/g25 °Cmarsac2006b R17.c, R17.d
felodipine, nifedipine, ketoconazole, sucrose, indomethacin in PVP K29/320.065, 0.049, 0.010, 0.015, 0.134 weight fractionscaled from EPmarsac2009 R9
same five in EP0.268, 0.215, 0.079, 0.074, 0.396 weight fractionmeasured, 25 °Cmarsac2009 R9
same fivefraction above solubility reaches zero at polymer 0.93, 0.95, 0.99, 0.99, 0.86PVP K29/32marsac2009 R11
IDM in PVPVA, 50% DL132.3 ± 0.8 °C (predicted 131.0 °C)DSC offset, 0 °C/minmoseson2018 R5
IDM in copovidone, 1:5about 78 °Ccited[moseson2019 R21]
felodipine in dry PVP (cited)about 0.25 g/g; taken as at most 0.025 g/g in PVP–waterused for the plateau estimate[rumondor2009b R26, C31]
felodipine–PVP 50% at 93% RHresidual ≈0.1 g drug per 0.86 g PVP–water, above that boundmass balance in words[rumondor2009b E4]
all dispersions studied (cited)supersaturated with respect to the estimated solubility in PVPnifedipine and felodipinemarsac2008a C47
Pitfalls and disagreements

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

← Concepts and formulas

concept · as used in PEG dispersions

enthalpy of fusion

The heat absorbed when a crystal melts (ΔHfus, heat of fusion), measured by DSC; with Tm it gives the entropy of fusion and the Hoffman estimate of the crystallization driving force [vaneerdenbrugh2010a E1, E2], and with the melting points of two polymorphs it decides monotropy by the heat-of-fusion rule [lu2016 C50].

Findings

F6, F7, F13.

Related concepts

used by entropy of fusion, Hoffman equation and Burger-Ramberger rules; part of thermodynamic driving force for crystallization.

Formulas

Hoffman equation, entropy of fusion, Burger-Ramberger heat-of-fusion rule.

How it is measured or obtained

By DSC melting endotherms, in kJ/mol or J/g, and per volume with the crystal density [baird2010 P1, P8; lu2016 R20].

Values in the library
materialvalue or classconditionspaper ids
ritonavir; haloperidol65.34; 54.26 kJ/molDSCbaird2010 M51, M17
caffeine20.81 kJ/molDSCbaird2010 M10
vemurafenib α; β53.8; 33.3 kJ/molDSC[lu2016 R20]
nilutamide stable form; form I~98; around 66 J/gDSC[trasi2014b M1, R6]
class I against class III≈+0.45 against ≈−0.63 SDper volumebaird2010 R22.b
nifedipine against felodipinehigher ΔHf and Tm, read as a higher intrinsic crystallization tendencyDSCmarsac2008a C35
Pitfalls and disagreements

One paper gives three different values for the α-vemurafenib heat of fusion, and its virtual transition temperature depends on the choice [lu2016 X1]; a melting endotherm overlapped by recrystallization can understate ΔHm [lu2016 X12]. Fusion properties did not correlate with crystallinity loss of drugs in PEO marsac2008b C34.

← Concepts and formulas

concept · as used in PEG dispersions

enthalpy of mixing

The heat effect of mixing drug and solvent or polymer, set by the strength of the cross (adhesive) interactions relative to the interactions in the pure components. Exothermic mixing is read from a Flory–Huggins parameter below zero baird2011 C26, C27 or from an activity coefficient below 1, provided the entropy of mixing is close to ideal baird2011 C23; marsac2008b C14. In the library it is never measured calorimetrically in the PEG papers; it is inferred. Outside this chapter the entropy of mixing is taken as always favourable, so the enthalpy decides miscibility marsac2009 C29. New aspects (Miscibility and drug-polymer interactions): The sign and size of the enthalpy of mixing follow the strength and number of interactions in the mixture relative to the pure materials: exothermic only if the cross-interactions are stronger or more numerous, endothermic if a component self-associates more strongly, athermal if they are similar; hydrogen bonds, dipolar forces and van der Waals contacts all contribute, and van der Waals-only systems are expected to mix endothermically marsac2009 C36, C37. Since the entropy of mixing with a polymer is always favourable and nearly the same for any pair, the enthalpy, through χ, decides miscibility marsac2006b C13; marsac2009 C26. A pair can tolerate a certain maximum unfavourable enthalpy marsac2009 C26. In dextran–PVP blends the enthalpy of mixing is inferred to be positive because many blends phase separate, with dextran–dextran hydrogen bonds assumed to be stronger or more numerous than dextran–PVP ones; it was not measured [vaneerdenbrugh2012a C32, C36, X7]. For itraconazole–HPMC, which has no donor, any miscibility is "likely" entropy-driven with little favourable enthalpy [purohit2015a C42]. New aspect (Physical stability): moisture-induced separation "must" come from a positive mixing enthalpy of the ternary system, because the entropy of mixing favours mixing; it is expected when water, polymer and drug interact very differently [rumondor2009c C42, C43]. Miscibility of the dry pair is set by the balance of cohesive and adhesive interactions [marsac2010 C4].

Findings

PEG dispersions: F2, F3, F11. Miscibility and drug-polymer interactions: F2, F5, F6, F7, F18, F22. Physical stability: F13, F23.

Related concepts

depends on Flory-Huggins interaction parameter and activity coefficient; related to hydrogen bonding, drug-polymer interactions and athermal mixing; part of free energy of mixing; contrasts with entropy of mixing; part of Flory-Huggins theory; drives Δχ effect.

Formulas

Flory-Huggins melting point depression, Flory-Huggins interaction parameter from interaction energy; Gibbs free energy of mixing; multicomponent Flory-Huggins free energy of mixing.

How it is measured or obtained

Inferred from the sign of \chi (melting point depression), of \gamma in PEG 400 or water, or from the interaction energy back-calculated from an eutectic composition baird2011 E3, E8, E7; zhu2011 C6; marsac2008b C14. Not by calorimetry in the miscibility papers. It is inferred from the sign of χ obtained by melting point depression or from the solubility of the drug in a liquid analogue, which assumes ideal entropy of mixing in that liquid marsac2009 C29, C11; marsac2006b C35. The papers on dispersions also define the quantity from component enthalpies: Rumondor and co-workers print ΔHmix as the pure-component minus the mixture enthalpy, so that a positive value is exothermic, but use the conventional sign elsewhere [rumondor2009a E4, X8]. In the moisture papers it is inferred from activity coefficients above or below 1 and from interaction parameters, assuming ideal mixing entropy [marsac2008a C34, C37; rumondor2009c C28].

Values in the library
materialvalue or classconditionspaper ids
chlorpropamide; aceclofenac with PEG 3350exothermic mixing implied by \chi_{dp} −2.53 and −6.68 and interaction energies −6.85 and −18.2 kJ/molback-calculatedbaird2011 C18, C27, R1.a, R1.b, R9.a, R9.b
loratadine; haloperidol with PEG 3350athermal mixing implied by \chi_{dp} 0.13 and −0.04back-calculatedbaird2011 C27, R9.c, R9.d
six drugs with PEG 400; with waterexothermic with PEG 400 (\gamma 0.02–0.64); endothermic with water (\gamma 10¹–10⁵)if mixing entropy is near idealmarsac2008b C14
nifedipine, felodipine with NMP and waterexothermic with NMP (γ 0.09, 0.30), endothermic with water (γ 1.89 × 10³, 2.43 × 10⁵)assuming near-ideal mixing entropy; 25 °Cmarsac2008a R10, C37
six drugs in waterγ water 2.54–4.65; unfavourable drug–water contacts95% RH[rumondor2009c R24, C28]
felodipine and quinidine with HPMCASless sorbed water gives a less positive mixing enthalpy, which "may explain" no separationqualitative[rumondor2010c C31]
indomethacin with PVPVAstronger drug–polymer bonds give a more favourable mixing enthalpyqualitative[rumondor2010c C28]
miscible pairs with PVP\chi near or below zero: athermal or slightly exothermic, miscibility largely driven by entropymelting point depressionmarsac2009 C29
indomethacin–PVPmost exothermic of five PVP pairs (χ −0.82 melting, −1.83 solubility route)melting at 1 °C/min; EP at 25 °Cmarsac2009 R7.e, R9.e, C29
felodipine, ketoconazole, nifedipine, sucrose with PVP K12athermal or slightly exothermic, miscibility "largely driven by entropy"offset meltingmarsac2009 R7.a, R7.b, R7.c, R7.d, C29
nifedipine, felodipine with PVP K12exothermic mixing indicated by χ −3.8 and −4.2melting at 1 °C/minmarsac2006b C35, R9
dextran with ibuprofen or indomethacinadhesive interactions not more favourable than cohesive ones, "speculated"no depressionmarsac2009 C43
dextran–PVPpositive enthalpy inferred where blends separate; dextran–dextran bonds assumed stronger or more numerousphase map; OH band shift[vaneerdenbrugh2012a C36, C37, R13, R16]
itraconazole–HPMCentropy-driven mixing with little favourable enthalpyargument in 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 PEG dispersions

entropy of fusion

The entropy gained on melting, \Delta S_{fus} = \frac{\Delta H_{fus}}{T_m} with Tm in kelvin [baird2010 E26; vaneerdenbrugh2010a E1]. It is read in two ways in the library: as part of the driving force for crystallization baird2010 C60 and, following Jackson, as a measure of how few melt molecules are correctly oriented to join the crystal [trasi2014a C31]. A related reading takes the entropy of crystallization as the probability that a molecule has the right conformation or orientation for nucleation [marsac2006a C34].

Findings

F6, F13.

Related concepts

depends on enthalpy of fusion; part of thermodynamic driving force for crystallization; related to conformational flexibility.

Formulas

entropy of fusion, linear fit of normalized growth rate on melting entropy.

How it is measured or obtained

From DSC heat of fusion and melting temperature, per mole or, with the crystal density, per volume [baird2010 P8; trasi2014a M1].

Values in the library
materialvalue or classconditionspaper ids
caffeine; haloperidol; ritonavir4.08, 12.8 and 16.4 × 10⁻² kJ mol⁻¹ K⁻¹DSCbaird2010 M10, M17, M51
felodipine; nifedipine74.4 and 89.6 J mol⁻¹ K⁻¹DSC[marsac2006a E11]
nilutamide; cinnarizineΔSm/R ≈8.7; ≈12.5growth analysis[trasi2014a R11.a, R11.i]
class I against class III≈+0.41 against ≈−0.59 SDper volumebaird2010 R22.c
spin-coat class I against III≈+0.46 against ≈−0.33 SDper volume[vaneerdenbrugh2010a R20.d]
fast growers (group 1)≈−0.38 SDper mole[trasi2014a R8.f]
Pitfalls and disagreements

Fast melt crystallizers score high on ΔSfus per volume while fast growers score low on ΔSm per mole (synthesis: different bases and read-outs, see F6). For felodipine and nifedipine an entropy-dominated view would predict felodipine to crystallize more easily, which it does not; the enthalpy dominates there [marsac2006a C35]. Fusion properties did not correlate with crystallinity loss of drugs in PEO marsac2008b C34.

← Concepts and formulas

concept · as used in PEG dispersions

entropy of mixing

The entropy gained when drug and polymer mix

For a drug with a polymer it is much smaller than with a small solvent, because the configurational entropy of the polymer is reduced by the connectivity of its repeat units, and it is nearly the same for any polymer grade marsac2006b C10, C11. For typical drugs (molecular weight 200–600) and polymers (10,000 and above) the contribution is "predicted to be relatively constant" and always favourable, so the enthalpy of mixing decides miscibility marsac2006b C12, C13; marsac2009 C26. In the ideal case the entropy of mixing of two components is ΔS = −R(X_u ln X_u + X_v ln X_v), printed without its minus sign in one paper [rumondor2009a E3, X7]. Where an entropy of mixing is not measured, readings of the activity coefficient and of χ as enthalpy rest on the assumption that it is close to ideal marsac2009 C11. For two polymers the entropy per lattice site falls with the chain length of both, from about −27 × 10⁻²³ J for a 783 Da maltodextrin with PVP K 12 to about zero for a 450 kDa dextran with PVP K 90, so the grade-independence found for a small drug does not hold between polymers [vaneerdenbrugh2012a R15, C34, C35].

Findings

F5, F9, F22.

Related concepts

part of free energy of mixing; includes combinatorial entropy of mixing; contrasts with enthalpy of mixing; related to Flory-Huggins theory.

Formulas

Flory-Huggins free energy of mixing, Gibbs free energy of mixing.

How it is measured or obtained

Not measured: it is computed from the Flory–Huggins expression with χ = 0, for a lattice whose site is one drug molecule marsac2006b P6, R1; for a small analogue liquid such as methyl pyrrolidone or 1-ethyl-2-pyrrolidone it is taken as ideal marsac2006b C46; marsac2009 C11.

Values in the library
materialvalue or classconditionspaper ids
nifedipine with methyl pyrrolidoneminimum near Φ ≈ 0.44χ = 0marsac2006b R1
nifedipine with PVP K12, K29/32, K90minimum near Φ ≈ 0.6; K29/32 and K90 virtually identical, K12 slightly lowerχ = 0marsac2006b R1
typical molecular weightsAPIs 200–600; polymers 10,000–1,000,000citedmarsac2009 R13
indomethacin, EP → PVP K12 → K29/32 → K90predicted solubility 0.396 → 0.144 → 0.134 → 0.134entropy term scaled with chain lengthmarsac2009 R9.e, C24
maltodextrin (783 Da) with PVP K 12 to K 90minimum about −27 to −21.5 × 10⁻²³ J per site25 °C, no enthalpy term[vaneerdenbrugh2012a R15]
6 kDa dextran with PVP K 12 to K 90−9.1 to −2.8 × 10⁻²³ Jsame[vaneerdenbrugh2012a R15]
450 kDa dextran with PVP K 90about 0same[vaneerdenbrugh2012a R15, C35]

Evidence table: entropy of mixing.

Pitfalls and disagreements

The generalization to all drugs and polymers rests on one simulated drug, with an unscaled axis, and on a PVP grade (K12, 2,500) below the stated polymer range marsac2006b X7, X8. The ideal-entropy assumption for the analogue liquid and for equal contacts in analogue and polymer was not tested marsac2009 C11, X17. In ternary systems with absorbed water the entropy still favours mixing, and demixing is expected only when the enthalpy of mixing is positive enough [rumondor2010c C27]. Two of the 20 plotted curves (PVP K 12 with 40 kDa and 450 kDa dextran) do not follow from the stated inputs [vaneerdenbrugh2012a X1].

← Concepts and formulas

concept · as used in PEG dispersions

Etter's hydrogen-bond rules

Empirical rules from crystal engineering on which donors and acceptors pair in a crystal: all good proton donors and acceptors are used in hydrogen bonding; intramolecular hydrogen bonds that close a six-membered ring form in preference to intermolecular ones; and the best donors and acceptors left after intramolecular bonding pair with one another [vaneerdenbrugh2011a C11; wegiel2013a C29]. The library applies them to drug–polymer pairs: the free group of the drug with the highest donor or acceptor strength is matched to the polymer group that can compete with the drug's own self-association, which gives the expectation that acceptor-only polymers suit donor drugs and acidic donor polymers suit amide and basic drugs [vaneerdenbrugh2011a C19, C32, C33, C53]. The authors say the rules should be used as "a set of tools providing guidance, rather than a strict set of rules" [vaneerdenbrugh2011a C53].

Findings

F24, F25, F14, F17.

Related concepts

uses hydrogen-bond basicity and intramolecular hydrogen bonding; predicts crystallization inhibition by polymers; part of hydrogen bonding; related to steric hindrance and pKa.

Formulas

none.

How it is measured or obtained

By classifying every functional group of drug and polymer: donor strength from the bonding atom (O–H, N–H) and its acidity, adjusted by substituents, pKa and short contacts in crystal structures; acceptor strength from the pKBHX scale of a model compound; possible intramolecular rings from ring size, published surveys, crystal structures and DFT; and competition between groups from crystal-structure statistics [vaneerdenbrugh2011a P5, P6, P7, P8, C13, C14, C15]. The resveratrol paper used the same scheme for the polymers of its set [wegiel2013b P10, C30], and the polyphenol paper for naringenin and quercetin [wegiel2013a P8, C29].

Values in the library
materialvalue or classconditionspaper ids
carboxylic acid groups of the drugsvery strong donors, medium acceptors (ethyl acetate 1.07)Table 1 classes[vaneerdenbrugh2011a R1]
PVP, PVPVA pyrrolidonevery strong acceptor (1-methyl-2-pyrrolidone 2.38), no donorTable 2[vaneerdenbrugh2011a R2]
amide carbonyl of benzamide, phenacetinstrong acceptor (1.81, 1.69); amide N–H medium donorTable 1[vaneerdenbrugh2011a R1]
benzamide, phenacetin crystalsamide–amide only: 100 and 94% alone; 0% with COOH; 14 and 33% with C(O)NC2CSD survey[vaneerdenbrugh2011a R14]
naringenin, quercetinfree phenolic OH donors (two and three) after intramolecular bondsstructure[wegiel2013a M1, M2, C30]

Evidence table: Etter's hydrogen-bond rules.

Pitfalls and disagreements

The rules come from crystals and are applied to amorphous mixtures; the hydrogen bonds in the films were not measured and the melt spectra for acid–base reactions are not shown [vaneerdenbrugh2011a C50, X13]. The abstract speaks of an ab initio rank order that "agreed well", but no predicted order per drug was tabulated or scored, and the exceptions were explained afterwards [vaneerdenbrugh2011a C55, X5]. Footnotes of the group tables call the acceptor classes "donor strength" and cite two different references for the pKBHX values [vaneerdenbrugh2011a X2].

← Concepts and formulas

concept · as used in PEG dispersions

eutectic

The composition (the eutectic composition) and temperature at which a mixture of two components that mix fully as liquids and not as solids melts at its lowest temperature. In drug–polymer dispersions the eutectic point is the most drug the molten polymer can hold at the eutectic temperature; dispersions with an appreciable drug solubility are eutectic, those in which the drug barely dissolves and hardly lowers the polymer melting point are monotectic baird2011 C1. Zhu and co-workers state that eutectic compositions are determined by the pure drug's melting point together with its ability to interact with PEG zhu2011 C4.

Findings

F1, F2, F8.

Related concepts

part of temperature-composition phase diagram; contrasts with monotectic system; depends on melting point depression, crystal lattice energy and drug-polymer interactions; predicted by semi-empirical eutectic prediction model.

Formulas

Lacoulonche liquidus model.

How it is measured or obtained

From the temperature–composition phase diagram: liquidus by hot-stage microscopy and DSC at 1 °C/min over 0–100 wt% drug; near the eutectic one endotherm appears below both pure melting points, away from it two baird2011 P2, P3, C13. The eutectic can also be predicted with a Flory–Huggins model baird2011 E1, E2, E4.

Values in the library
materialvalue or classconditionspaper ids
chlorpropamide–PEG 335035 wt% drug, 55.0 °Cobserved; predicted 12.8 wt%baird2011 R1.a; zhu2011 R5.c
aceclofenac–PEG 335030 wt%observed; predicted 1.5 wt%baird2011 R1.b
loratadine–PEG 3350about 5 wt%observed; predicted 6.5 wt%baird2011 R1.c
haloperidol–PEG 3350below 1 wt%, monotecticobserved; predicted 0.5 wt%baird2011 R1.d
benzocaine; ibuprofen; nilutamide–PEG 335030 wt% at 48.9 °C; 40 wt% at 49.6 °C; 10 wt% at 58.4 °Cobservedzhu2011 R5.b, R5.d, R5.e
fenofibrate–PEG 3350minimum about 58 °C at 15–20 wt%CPOM and DSCzhu2012 R24.c, R24.d, C48
Pitfalls and disagreements

Observed eutectics were read on a 5–10 wt% grid, and the chlorpropamide value of 35 wt% was not a tested composition baird2011 X9. The eutectic temperatures of the chlorpropamide and aceclofenac systems are not established by the drifting low-temperature endotherm baird2011 X8. The eutectic composition is a ceiling at the eutectic temperature, not a solubility at storage temperature (see drug solubility in polymer). The 20/80 dispersions of the kinetic study lie at or near the eutectic composition for ibuprofen and fenofibrate and below it for benzocaine zhu2012 C40, C32.

← Concepts and formulas

concept · as used in PEG dispersions

Flory-Huggins interaction parameter

The parameter \chi of Flory–Huggins lattice theory that expresses the energy of drug–polymer contacts relative to the contacts in the pure components. In the PEG papers \chi > 0, \chi = 0 and \chi < 0 mean endothermic, athermal and exothermic mixing baird2011 C26, and more negative values are "consistent with" a negative enthalpy of mixing and favourable drug–polymer interactions zhu2011 C6. The three PEG papers that report it define it differently: Baird and Taylor divide a back-calculated interaction energy by R\,T_{eut,th}, Zhu and co-workers take the drug volume as lattice site and normalize per PEG segment baird2011 E8; zhu2011 E1, E2. Marsac and co-workers take the volume of a low-molecular-weight analogue as lattice site for polymers such as PVP marsac2009 E2. New aspects (Miscibility and drug-polymer interactions): χ reflects the relative strength of cohesive (drug–drug, polymer–polymer) and adhesive (drug–polymer) interactions and has an entropic part; it can vary with temperature and composition marsac2006b C15. A negative χ describes strong, numerous adhesive interactions that favour miscibility, a positive χ stronger cohesive interactions marsac2006b C16. In the simulations the χ needed for miscibility over the whole composition range of nifedipine–PVP is about 0.6 or less, and the critical value depends on the lattice definition and is system specific marsac2006b R3, C18. Because the entropy of mixing with a polymer is small and almost the same for any pair, differences between compounds come from the magnitude of χ marsac2009 C26, C31. A larger negative χ reflects a greater driving force for mixing near the drug's melting temperature marsac2009 C18. For dextran–PVP blends χ was not determined and was assumed independent of molecular weight so that only the combinatorial term differs between the 20 pairs [vaneerdenbrugh2012a C33]; for itraconazole–HPMC no χ was measured, and a positive χ is inferred from the lack of hydrogen-bond donors [purohit2015a C41, C42, C47]. New aspect (ASD process): in the 2018 hot-melt extrusion study the lattice volume is the drug's molecular volume (molecular weight divided by true density: IDM 273 cm³/mol, PVPVA 46,610 cm³/mol), \phi is the drug volume fraction from true densities and m the polymer-to-drug volume ratio (170.7 at 50/50) moseson2018 M1, M2, E2, E6. The same theory applied to water gives large positive water–drug parameters and a small water–polymer parameter; the asymmetry is the reason cited for moisture-induced demixing [marsac2010 C43; rumondor2009c C45, C46]. In the four-component drying model χ is estimated for each pair from vapour-sorption fits (Flory–Huggins sorption isotherm), a solubility or a heat of mixing: ritonavir–methanol 0.8, ritonavir–water 2.8, PVPVA–methanol 0.73, PVPVA–water 1.13, methanol–water −0.002, ritonavir–PVPVA 0.5 (assumed in the SI) [li2020 R15, E12]. In the later HME papers the same linearized fit gave a negative value for bicalutamide–PVPVA and a positive one for posaconazole–HPMCAS, so the sign differs between pairs [moseson2022c R8; shah2024 R4]. New aspect (Physical stability): water–component parameters from sorption isotherms rank drugs and polymers by their dislike of water, and the drug–water value split six drugs by moisture-induced separation in PVP [rumondor2010a R11; rumondor2009c R24, C46]. New aspect (Supersaturation from ASD dissolution): in an argument about dissolution, the enthalpy of solution of pure amorphous drug contains the water–drug term χ12, whereas a dispersion adds water–polymer (χ13) and drug–polymer (χ23) terms, so there is "no reason to expect" the two to give the same solution activity [alonzo2011 E7, E8, C43, C45]. In the lopinavir work χ enters the drug's chemical potential in a polymer that stays undissolved: a more negative χ, a stronger drug–polymer attraction, lowers the maximum concentration more than dilution alone, a χ above zero lowers it less, and a large χ gives phase separation with little suppression [li2018 C44, C51]. χ was not measured; the model is "probably best applied in a qualitative manner" [li2018 C46]. New aspect (Release mechanism and LoC): in the water–drug–polymer free energy of mixing, three pairwise parameters enter: \chi_{DP} is negative or small for a molecular dispersion, \chi_{WD} of a hydrophobic drug is large and positive, and \chi_{WP} is smaller because the polymer hydrogen-bonds with water; a large difference between \chi_{WD} and \chi_{WP} gives a tendency to phase separate on hydration [purohit2017b C43, E2, E4]. Yang and co-workers (2021) use the Δχ form to explain why log P fails: drugs have much larger χ with water than polymers (cited), so water–drug against water–polymer interactions, drug–polymer interactions and hygroscopicity, not one descriptor, decide separation [yang2021 C21, C22, E2].

Findings

PEG dispersions: F2, F3, F5, F6. Miscibility and drug-polymer interactions: F2, F5, F6, F7, F8, F9, F18, F22. ASD process: F8, F1, F20, F41. Physical stability: F4, F8, F13, F23, F29. Supersaturation from ASD dissolution: F7, F18. Release mechanism and LoC: F8, F9.

Related concepts

depends on enthalpy of mixing and melting point depression; derived from drug-polymer interaction energy; contrasts with athermal mixing; related to drug-polymer interactions and activity coefficient; part of Flory-Huggins theory. Relates to drug solubility in polymer. Basis of Δχ effect; measured from water sorption isotherm; linked to water through hydrophobicity; related to drug-polymer miscibility and amorphous solubility advantage. Related to drug-polymer-water miscibility.

Formulas

Flory-Huggins melting point depression, Flory-Huggins interaction parameter from interaction energy, Lacoulonche liquidus model; Flory-Huggins interaction parameter from solubility parameters, Flory-Huggins free energy of mixing, Flory-Huggins activity equation. Extrusion work: molar volume from molecular weight and density, multicomponent Flory–Huggins free energy of mixing. Water sorption: Flory-Huggins water sorption isotherm, ternary Flory-Huggins water sorption isotherm. Dissolution of dispersions: Flory–Huggins enthalpy of mixing for two and three components (named, no shared page) [alonzo2011 E7, E8]; Huang model of drug solubility in an ASD, Δχ effect.

How it is measured or obtained

From the melting point depression of the drug: the slope of the linearized relation against the squared polymer volume fraction, at 50–80% drug in the PEG study zhu2011 P5, E1; from the interaction energy that closes the gap between the athermal and the observed eutectic baird2011 P8, P10, E3, E8; for PVP, from the slope of the melting-point plot at 0–25 wt% polymer, or from group-contribution solubility parameters marsac2006b R8, R9, R4. In the Marsac studies of drugs in PVP and other polymers, three routes appear. (1) Group-contribution solubility parameters, Eq. 2, which always give a non-negative χ marsac2006b E2, R4. (2) The slope of the linearized melting point depression against Φ_polymer², over 0–25 wt% polymer, with the lattice site set to the drug (2006) or to a liquid analogue (2009), using the offset of the melting peak in 2009 marsac2006b E10, R8, R9; marsac2009 P6, C16. (3) From the activity coefficient of the drug in a liquid analogue (1-ethyl-2-pyrrolidone, 25 °C), scaled to the polymer with Eq. 8 marsac2009 P7, E8, E9. A fourth route, the ternary Flory–Huggins fit to moisture sorption, was unable to give unambiguous values [rumondor2010a C30]. In the extrusion work χ is the slope of the linearized melting point depression plot A=\chi B, with A=\left(-\Delta H/R\right)(1/T_c-1/T_m)-[\ln\phi+(1-1/m)(1-\phi)] and B=(1-\phi)^2, fitted through 90/10 to 50/50 IDM:PVPVA; the printed value is reproduced only with a free intercept of about +0.02 (a line through the origin gives −1.86) moseson2018 E4, R4, X7. For water: binary Flory–Huggins sorption fits of pure amorphous components, and the drug–water χ from the 95% RH uptake [rumondor2010a P4; rumondor2009c P13, E5]. In the ASD dissolution papers no values were measured; binary parameters cannot simply be carried into the ternary model (cited) [alonzo2011 C44, R27]. In the release-mechanism papers: not measured in the release-mechanism papers; used in argument [purohit2017b E2, E4].

Values in the library
materialvalue or classconditionspaper ids
chlorpropamide; haloperidol with PEG 3350−0.50 and 0.08; −2.53 and −0.04zhu2011 (per PEG segment); baird2011 (\Delta W/RT), same phase diagramszhu2011 R5.c, R5.a; baird2011 R9.a, R9.d
aceclofenac; loratadine with PEG 3350−6.68; 0.13\Delta W_{d,p}/(R\,T_{eut,th})baird2011 R9.b, R9.c
benzocaine, ibuprofen, nilutamide, ketoconazole with PEG 3350−0.23, −0.19, −0.09, 0.02melting point depression at 50–80% drugzhu2011 R5.b, R5.d, R5.e, R5.f
nifedipine; felodipine with PVP K12−3.8; −4.2 near the melting point; solubility-parameter estimates 2.0 and 0.5slope of the linearized plotmarsac2006b R9, R4
indomethacin with PVP K12−6.16 (onset), −1.94 (midpoint), −0.82 (offset)melting point depressionmarsac2009 R6
indomethacin with PVPVA−1.97 (R² = 0.9895); reproduces all predicted Tc of Table III within 0.05 °Cused to predict Tc; slope with free intercept, 50–90% DLmoseson2018 R4, R5, E2
PVP-miscible pairsnegative or near zero; immiscible pairs larger positive values, from −0.82 to 0.72offset meltingmarsac2009 C17
indomethacin, felodipine, nifedipine, ketoconazole, sucrose with PVP K12offset χ −0.82, −0.08, 0.00, −0.08, 0.021 °C/minmarsac2009 R7.a, R7.b, R7.c, R7.d, R7.e
same five compoundssolubility-route χ −1.83, −0.08, −0.81, −0.12, −0.5325 °C, EPmarsac2009 R9
sucrose–dextran; ibuprofen–dextran; indomethacin–dextran; itraconazole–Eudragit E1000.20; ≥ 0.38; ≥ 0.72; ≥ 0.11 (lower limits for the last three)offset meltingmarsac2009 R7.f, R7.g, R7.h, R7.i, C19
felodipine–PVP; indomethacin–PVP−9.6 to 26.9; −20.4 to 22.0 (ranges only)ternary sorption fit[rumondor2010a R14]
IDM–PVPVA in four other studies−0.64, −2.06, −2.9, −4.5 (assignment to studies not printed)citedmoseson2018 R7
water–felodipine, water–PVPabout 3.3 and about 0.5 (Δχ large)sorption isotherms, Flory–Huggins fits[marsac2010 C43]
water with amorphous felodipine, PVP, HPMC and HPMCAS3.27 for felodipine; above 0.5 for HPMC and HPMCAS; the PVP value close to but slightly below other authors' valueswater sorption isotherms, 25 °C[rumondor2010a R11, C19, C20]
BCL–PVPVA 30% DL−1.57, read as favourable miscibilityphase diagram, SI not supplied[moseson2021 M1, C10]
RTV–PVPVA (drying model)0.5 assumed in the SI; "likely <0.5, and possibly close to zero" in the text; varied −0.5 to 0.5sensitivity moved mainly the drug–polymer side[li2020 R15, R16, C72, X10]
water–ritonavir and water–PVPVA (drying model)2.8 and 1.13fitted to dynamic vapour sorption, room temperature[li2020 R15]
BCL–PVPVA 30–90% BCL−1.57 (R² 0.994); Tc 145 °C at 30% BCLDSC offsets extrapolated to 0 °C/min[moseson2022c R8, R9]
PCZ–HPMCAS MF, PCZ fractions 0.4–1.0+0.43 (R² 0.991); the fitted line meets B = 0 at A of about −0.05same[shah2024 R1, R4]
water with nifedipine, felodipine, droperidol, pimozide, indomethacin, ketoprofen2.84, 3.18, 2.85, 3.58, 2.50, 2.7125 °C, 95% RH[rumondor2009c R24]
nifedipine–PVP, felodipine–PVP (cited)−3.8 and −4.2 from melting point depressionused for activity[marsac2006a R18]
indomethacin–PVP vs nifedipine–PVP (cited)−0.8 vs 0.0used for susceptibility[rumondor2009c R26]
indomethacin against felodipine, quinidine, pimozide with PVPVAlarger carbonyl red shift (42–44 against 19–22 cm⁻¹) "would result" in a lower \chi_{DP}IR of dry films[rumondor2010c R20, C28]
hydrophobic drugs with water\chi_{WD} expected positive from log Pqualitative[rumondor2010c C30]
indomethacin with HPMC, HPMCAS, PVPχ not measured; stronger interaction "would" lower the driving force for growthargument with the free energy of mixing[tian2017 E2, C30, X13]
lopinavir with HPMCP, EC, HPMCASranked HPMCP > EC > HPMCAS in suppression, read as interaction strengthpH 3, 25 °C[li2018 C54]
lopinavir with CA, EUDtwo Tgs, sorption on the additive line; little suppressionpH 3, 25 °C[li2018 C56]
ritonavir with PVP, PVPVA, HPMCASno values; the argument explains AAPS of PVP and PVPVA films at 97% RH25 °C[purohit2017b C43, C1]
six drugs with PVPVA and HPMCASno χ measured; argument—[yang2021 E2, C21]
Pitfalls and disagreements

The values of one paper are not comparable with those of another: for the same published diagram of chlorpropamide the two PEG papers give −2.53 and −0.50, and for haloperidol −0.04 and 0.08, so the sign near zero is not robust baird2011 R9; zhu2011 R5. The printed expression for the interaction energy in Baird and Taylor does not reproduce, and only signs and ranking are robust baird2011 X3. Zhu and co-workers fitted \chi at 50–80% drug, not at the 20/80 composition of the SAXS/WAXS samples, and the normalization cannot be reproduced from printed inputs zhu2011 X10. In the PEG study the size of \chi did not rank the size of the long-period increase: chlorpropamide has the most negative \chi and the smallest increase zhu2011 X5. The reading as exothermic mixing assumes a near-ideal entropy of mixing baird2011 C23. The printed solubility-parameter values (2.0, 0.5) were not reproduced from the inputs (2.36 and 0.70 at 298.15 K) marsac2006b X1. The melting-route χ of one pair spans 7.5-fold with the point of the melting peak read (synthesis: 6.16/0.82) marsac2009 R6. The two experimental routes differ by up to 1.01 and rank the compounds differently marsac2009 X7. The positive values for non-depressing pairs are lower limits marsac2009 C19, X11. The nifedipine volume fractions of the 2006 fit may use felodipine's density marsac2006b X2. A χ determined near the drug melting point is applied at storage temperature without correction marsac2006b C32. The χ of one pair differs between studies (indomethacin–PVPVA −1.97 against −0.64 to −4.5) moseson2018 R4, R7. The positive mixing enthalpy of dextran–PVP is inferred from the existence of phase separation, not measured [vaneerdenbrugh2012a C32, X7]. In the extrusion work a single \chi neglects temperature and composition dependence moseson2018 C18. Differences between studies "can be attributed" to sample preparation, DSC method or onset versus offset moseson2018 C21; the nature of the fit (with or without intercept) also shifts the value moseson2018 X7. For ritonavir–PVPVA the main text and the SI disagree on χ, and the basis of the other χ values (vapour sorption or solubility, room temperature or 37 °C) is described differently in the two; the DVS and solubility data are not shown [li2020 X10, X11]. For posaconazole–HPMCAS χ is a slope with a free intercept, and Tc below 40% PCZ are extrapolations from it [shah2024 R4, X7, X8]. Two values cited in the physical-stability papers for the same pair differ by an order of magnitude: −3.8 and −4.2 (melting onset route, used in 2006) against −0.8 and 0.0 (offset route, used in 2009) for nifedipine–PVP, which reflects the choice of melting-peak point (synthesis; see the onset, midpoint and offset values above) [marsac2006a R18; rumondor2009c R26]. The drug–water χ split rests on approximated densities and a gap of 0.13 [rumondor2009c X4]. No χ was computed in the 2010 polymer comparison: \chi_{DP} is ranked by red shift and \chi_{WD} by calculated log P [rumondor2010c X13]. In the dispersion-dissolution argument, with 90% polymer, fewer drug–drug contacts "would lead to a reduction in the barrier" to dissolution, an argument without χ values [alonzo2011 C43]. The "ideal" line of the lopinavir figure is proportional dilution, not χ = 0 of the equation [li2018 X2]. No χ values were measured or cited for the ritonavir systems [purohit2017b E4].

← Concepts and formulas

concept · as used in PEG dispersions

Flory-Huggins theory

Lattice solution theory for a small molecule and a polymer, used here with the amorphous drug treated as the solvent and one lattice site set equal to the molecular volume of the drug (or, in the 2009 paper, of a liquid analogue of PVP) marsac2006b C9, E1; marsac2009 P6. For a large and a small molecule the free energy of mixing is better written in volume fractions than in mole fractions, because the large molecule has far fewer configurations; the first terms of the expression are the entropy of mixing and the last carries the interaction parameter χ marsac2006b C7, E1. The authors call it "still considered" an excellent starting point despite documented limits and more advanced models marsac2006b C8. In the library the same lattice picture gives four quantities: the free energy of mixing and miscibility, the melting point depression, the activity coefficient of the drug and the solubility of the crystal in the polymer marsac2006b E1, E3, E6; marsac2009 E2, E8, E10. Two later uses: for two polymers the chain lengths enter through the lattice sites per chain, N_1 and N_2, in the combinatorial term [vaneerdenbrugh2012a E5, C31]; and for itraconazole–HPMC the equation is used in words to say that, without hydrogen-bond donors, any miscibility is entropy-driven [purohit2015a E1, C41, C42]. New aspect (ASD process): written for a small molecule and a polymer as \Delta G=RT[\phi\ln\phi+\frac{1-\phi}{m}\ln(1-\phi)+\chi\phi(1-\phi)], with the two entropy terms always favouring mixing and the \chi term carrying the enthalpy [moseson2018 E1; purohit2015a C41]. In the hot-melt extrusion papers it is used through the melting point depression relation to build the solubility line for HME moseson2018 E2. It was extended to four components in the drying model of a spray droplet, with volume fractions of methanol, water, ritonavir and PVPVA and six pairwise χ values, to locate the drug solubility along the drying path [li2020 P12, E11]. New aspect (Physical stability): extended to the ternary water–drug–polymer system, where separation requires the interaction terms to outweigh the entropy of mixing, and to water sorption of blends, where the drug–polymer term is too small to be fitted [rumondor2009c E4, C42; rumondor2010a C25].

Findings

Miscibility and drug-polymer interactions: F5, F6, F7, F8, F9, F18, F22. ASD process: F8, F20. Physical stability: F4, F8, F13, F23, F29.

Related concepts

gives Flory-Huggins interaction parameter, entropy of mixing, combinatorial entropy of mixing, free energy of mixing and activity coefficient; used for drug-polymer miscibility and drug solubility in polymer. Predicts melting point depression. Explains Δχ effect and moisture-induced phase separation.

Formulas

Flory-Huggins free energy of mixing, Flory-Huggins melting point depression, Flory-Huggins activity equation, Gibbs free energy of mixing, Flory-Huggins combinatorial entropy of mixing. Four-component form: multicomponent Flory–Huggins free energy of mixing. Water sorption: Flory-Huggins water sorption isotherm, ternary Flory-Huggins water sorption isotherm.

How it is measured or obtained

It is a model; its inputs are densities (helium pycnometry or cited), molecular volumes (molecular weight over density), heats of fusion and melting points from DSC, and χ from experiment marsac2006b P4, P5, P6; marsac2009 P6, P7, P8. Outside the binary case, a ternary water–drug–polymer form is used to discuss moisture [rumondor2010c E1, C26]. In the extrusion work χ is fitted to melting point depression data (see Flory–Huggins interaction parameter); the free energy itself is not evaluated there moseson2018 E1, E4. In the moisture papers the ternary free energy of mixing is used in words, and binary, ternary and pseudobinary sorption equations are fitted to isotherms [rumondor2009c E4; rumondor2010a E1, E2, E4].

Values in the library
materialvalue or classconditionspaper ids
nifedipine with PVP K12, K29/32, K90entropy minimum near Φ ≈ 0.6, against ≈ 0.44 with methyl pyrrolidoneχ = 0marsac2006b R1
nifedipine–PVP K29/32miscible over the whole range for χ ≲ 0.6; single deep minimum at χ −3.8, −4.2five χ valuesmarsac2006b R2, R3
five compounds with PVPΔG/RT minima at polymer fractions ≈ 0.5–0.6; indomethacin deepestmelting-route and solubility-route χmarsac2009 R10
nifedipine, felodipine in PVPlittle activity lowering below polymer volume fraction ≈ 0.5χ from melting depression[konno2006 R20, C35; marsac2006a R19]
indomethacin–PVPVAχ −1.97 from the linearized melting relation; one χ describes Tc from 50 to 90% DL (HME phase diagram)offset extrapolated to 0 °C/minmoseson2018 R4, C19
dextran–PVP, 20 pairscombinatorial entropy per site from about −27 × 10⁻²³ J (783 Da maltodextrin, PVP K 12) to about 0 (450 kDa dextran, PVP K 90)25 °C, no enthalpic term[vaneerdenbrugh2012a R15, E5]
itraconazole–HPMCentropy-driven miscibility, limited at room temperature (UCST-type); no χ measuredargument in words[purohit2015a C42, C47, E1]
ternary water–drug–polymer systemswater lowers the free energy entropically; large positive \chi_{WD} favours drug-rich separationstored ASDs[purohit2017b C43]
drug in polymer, melting point depression and activityfree energy of mixing and melting point depression from Flory–Hugginsfelodipine, nifedipine with PVP[marsac2006b E1, E3; marsac2006a E10]
ritonavir–PVPVA–methanol–waterthe computed solubility boundary is crossed from about 12.5:87.5 initial water:methanol at 25% DLfour-component model[li2020 R17, C50]
indomethacin–PVP, felodipine–PVPdrug–polymer term 0.029–0.160% of the ternary adjustment25 °C sorption[rumondor2010a R13]
felodipine–PVP, indomethacin–PVPfitted χ23 −9.6 to 26.9 and −20.4 to 22.0same[rumondor2010a R14]
four blend seriesmean water–blend χ1,23 falls with polymer contentsame[rumondor2010a R15]
felodipine, quinidine, pimozide, indomethacin with PVP, PVPVA, HPMCASternary free energy of mixing used to explain why less hygroscopic polymers separate lessqualitative[rumondor2010c E1, C26, C31, C39]
indomethacin–polymer meltsfree energy of mixing used to argue a lower driving force with stronger interactiongrowth, 80–135 °C[tian2017 E2, C30, C31]

Evidence table: Flory-Huggins theory.

Pitfalls and disagreements

The glasses are non-equilibrium, χ is assumed independent of composition and temperature, and the critical χ for miscibility depends on how the lattice is defined and is system specific marsac2006b C3, C18; marsac2009 P8. The melting relation is linear only at low polymer content, so the fitted χ is a composite marsac2009 C7. The entropy curves exist for nifedipine only and carry no ordinate scale marsac2006b X7, X8. The hydrogen-bond picture cannot be represented by solubility parameters inside the theory marsac2006b C24. The ternary form fitted to moisture sorption gave ambiguous χ values [rumondor2010a C30]. The comparison of the 20 dextran–PVP pairs rests on a χ that is independent of molecular weight, which was assumed and not measured, and two of the 20 plotted entropy curves do not follow from the stated inputs [vaneerdenbrugh2012a C33, X1]. For itraconazole–HPMC no χ, n or φ was given [purohit2015a E1]. In the extrusion work the theory neglects the temperature and composition dependence of \chi and treats the polymer as a chain on a lattice; for IDM–PVPVA a single \chi fits 50–90% DL but not 40% DL, where viscosity hindered the measurement moseson2018 R4, C18, C17. The printed SI equation of the four-component model lacks the operator joining the combinatorial and χ sums and leaves the chain length undefined, so it is not directly implementable [li2020 X15]. The ternary sorption model assumes that binary interactions carry over unchanged into the blend, which the authors consider "unlikely" [rumondor2010a C26, C27]. χ in the ternary free energy also holds non-ideal entropy, so a positive χ term need not be enthalpic [rumondor2009c X14]. In the three-polymer moisture study it is applied without parameter values, and the data do not separate the thermodynamic from the mobility reading [rumondor2010c X13, X12].

← Concepts and formulas

concept · as used in PEG dispersions

formulation critical temperature

The formulation critical temperature (Tc, also called the solubility temperature) is the lowest temperature at which a homogeneous molecular dispersion of a given drug–polymer composition can in theory form, because all drug crystals can dissolve; for 1:1 IDM–PVPVA it is 131 °C by the Flory–Huggins prediction and 132.3 ± 0.8 °C measured [moseson2018 R5.f, X2; moseson2018a R2, C4]. It is the depressed melting point of the drug at that composition, not an upper or lower critical solution temperature moseson2018 P2. For 30:70 BCL–PVPVA Tc is 145 °C and for PCZ–HPMCAS MF 135, 155 and 165 °C at 10, 25 and 50% loading (calculated) [moseson2022c R9; shah2024 R5].

Findings

F8, F9, F36, F41.

Related concepts

obtained from melting point depression; defines the lower edge of the HME operating design space; related to drug solubility in polymer.

Formulas

Flory–Huggins melting point depression.

How it is measured or obtained

DSC melting point offsets of cryomilled physical mixtures at several heating rates extrapolated to 0 °C/min, and a Flory–Huggins fit to extend the line over the composition range moseson2018 P2, E2.

Values in the library
materialvalue or classconditionspaper ids
IDM–PVPVA 50:50132.3 ± 0.8 °C measured; 131.0 °C predicted; "131 ± 2 °C" usedoffset extrapolationmoseson2018 R5.f, X2
IDM–PVPVA 1:1 extrudateprocessing at 131 °C melt temperature, 20 min, left nanometre crystalsHME, TEM[moseson2018a R2, R9]
BCL–PVPVA 30:70Tc = 145 °C; extruded at 145 °C the 3.5–38 µm lots were below the PXRD limit within 2–6 min, the 42.2 and 92.7 µm lots held about 2.5 and 15.0% at 20 min5 mL micro-extruder[moseson2022c R9, R10]
PCZ–HPMCAS MF 10 / 25 / 50% DLcalculated 135 / 155 / 165 °C; extruded at 125 °C they held 0.3 / 3.2 / 19.3 wt% crystals2 min, SHG[shah2024 R5, R10]
Pitfalls and disagreements

Processing at Tc gives no margin: 20 min at 131 °C passed XRPD, DSC and (by the phase-diagram paper) PLM, yet TEM found residual crystals [moseson2018 C59; moseson2018a C31]. The measured product temperature can differ from what the melt experiences moseson2018 C43. Processing at Tc is not practical for most products and was used as the slowest case [moseson2022c C56]. The low-loading posaconazole values are extrapolations [shah2024 X7].

← Concepts and formulas

concept · as used in PEG dispersions

fragility

How steeply molecular mobility or viscosity changes as a liquid approaches Tg: strong liquids follow Arrhenius behaviour, fragile ones depart from it [baird2012 C37]. It is expressed by the fragility index m (strong below 40, fragile above 75) or by the VTF strength parameter D (strong above 30, fragile below 10) baird2010 R30. Good glass formers were expected to be strong liquids baird2010 C3.

Findings

F5, F12.

Related concepts

measured by melt viscosity; depends on glass transition temperature; proposed predictor of glass-forming ability; related to reduced glass transition temperature.

Formulas

Vogel-Tammann-Fulcher equation.

How it is measured or obtained

m from the heating- and cooling-rate dependence of Tg (Moynihan) and D from m, or D from the VTF equation with T0 set to the Kauzmann temperature baird2010 P10, E14, E15, E18; D also by fitting the VTF equation to melt viscosity [baird2012 P5, E4].

Values in the library
materialvalue or classconditionspaper ids
tolazamidem 18DSC rate dependencebaird2010 R18.k
itraconazolem 731DSC rate dependencebaird2010 R18.r
nifedipinem 33, D 36 from m, D 9 from VTF with TKDSCbaird2010 R18.i
28 compounds of classes I-B to IIID 4.3–8.7VTF fit of melt viscosity[baird2012 R12]
Pitfalls and disagreements

The category depends on the estimate used: aceclofenac, tolazamide and nifedipine are strong by m but fragile by the VTF-based D baird2010 X14. Fitted T0 values do not satisfy the paper's own T0–D–Tg relation [baird2012 X5]. Fragility did not separate good from poor glass formers [baird2012 C43], and invoking it for outliers in growth data is untested [trasi2014a X18].

← Concepts and formulas

concept · as used in PEG dispersions

free energy of mixing

The free energy change on mixing drug and polymer, ΔGmix = ΔHmix − TΔSmix: a negative ΔGmix with one minimum versus composition means complete miscibility, a positive ΔGmix complete immiscibility, and two minima (the binodal points) with a metastable region between them and an unstable region bounded by the spinodal points partial miscibility; this liquid-mixture theory is extended by the authors to amorphous solids [rumondor2009a C35]. In Flory–Huggins form the first terms are the entropy of mixing, small for a polymer, and the last the interaction term χ marsac2006b E1, C10. Large positive χ gives a positive ΔGmix and immiscibility, small χ a negative ΔGmix with one minimum marsac2006b C17. In the dextran–PVP paper ΔGmix = ΔHmix − TΔSmix is used to argue that a blend mixes only when the combinatorial entropy outweighs a positive enthalpy [vaneerdenbrugh2012a E3, C32]; the itraconazole–HPMC paper writes the Flory–Huggins form for the same argument [purohit2015a E1, C41].

Findings

F5, F6, F3, F18, F22.

Related concepts

made of enthalpy of mixing and entropy of mixing; gives drug-polymer miscibility; part of Flory-Huggins theory.

Formulas

Flory-Huggins free energy of mixing, Gibbs free energy of mixing.

How it is measured or obtained

By calculation from χ, volume fractions and molecular volumes (Eq. 1 of the 2006 paper, Eq. 10 of the 2009 paper); no calorimetric ΔGmix is measured in these papers marsac2006b E1, R2; marsac2009 E10, R10. The curves in the two papers carry no numbers on the vertical axis, so depths can be compared only within a panel marsac2006b X7; marsac2009 X12.

Values in the library
materialvalue or classconditionspaper ids
nifedipine–PVP K29/32positive at χ = 2.0 (maximum near Φ ≈ 0.37); shallow at 0.5 and 1.0; single deep minimum near Φ ≈ 0.54 at −3.8, −4.2Flory–Hugginsmarsac2006b R2
indomethacin–PVPminimum ≈2.4 times (melting χ) and ≈5 times (solubility χ) as deep as the athermal minimumΦ_polymer ≈ 0.5–0.6marsac2009 R10
felodipine, ketoconazole with PVPthree curves (athermal, melting χ, solubility χ) nearly coincideas abovemarsac2009 R10
sucrose–dextranmelting-route curve above the athermal curve (χ = 0.20)as abovemarsac2009 R10
Pitfalls and disagreements

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

← Concepts and formulas

concept · as used in PEG dispersions

Gibbs-Duhem equation

The relation between the changes of chemical potential of the components of a mixture; integrated with the measured water activity against composition from a sorption isotherm, it gives the activity of the drug in the water-saturated amorphous phase, the term e^{-I(a_2)} of the amorphous solubility estimate (the Murdande method) [almeidaesousa2015 E16, P7; ilevbare2013a P2]. In the solution-crystallization papers the factor lowers the Hoffman estimate of the amorphous solubility, and I(a2) is the sum of a Henry's-law term from zero water to the limit of linearity and a numerical integral \sum \langle (n_1/n_2)(1/a_1)\rangle\,\Delta a_1 over the sorption isotherm up to unit water activity [hsieh2012 E5, E6, P13; ilevbare2013c E6].

Findings

Amorphous solubility and LLPS: F5. Crystallization from solution: F2, F21.

Related concepts

yields the water sorption correction of amorphous solubility; input is water sorption; related to thermodynamic activity; corrects the Hoffman equation; used for the amorphous solubility advantage.

Formulas

Gibbs-Duhem equation, amorphous solubility advantage with water-sorption correction.

How it is measured or obtained

Numerical integration of moles of water per mole of drug against 1/a_1 over the sorption isotherm [hsieh2012 E5]. The papers of this chapter only name the method. The crystallization-from-solution papers measured the isotherm by dynamic vapour sorption of the amorphous solid at the test temperature (37 °C, 5–95% RH in 10% steps, three samples; 25 °C for danazol), with the water content extrapolated to water activity 1 [hsieh2012 P8, P13; jackson2014 P3, P4].

Values in the library

The resulting factors are listed under water sorption correction of amorphous solubility [ilevbare2013a M1; almeidaesousa2015 M6]. Values printed in the crystallization-from-solution papers:

materialvalue or classconditionspaper ids
danazol\exp[-I(a_2)] = 0.935DVS 5–95% RH, 25 °C[jackson2014 E1, R2]
five weak baseswater correction lowers the estimate for every base, for ketoconazole from 202 to 56.6 µg/mLDVS, 37 °C[hsieh2012 R10.d]
ritonavir, efavirenz, celecoxibI(a2) values not printed; theoretical amorphous solubilities 20.6, 19.8, 22.6 µg/mL37 °C[ilevbare2012b E8; ilevbare2013c E6, R2]
six dihydropyridinese^(−I(a2)) 0.74–0.91moisture sorption, TA Q5000[raina2015b M1–M6]
Pitfalls and disagreements

The expression is not printed in the 2015 and 2016 papers (named only) and the integral is not shown in any paper of 2013–2016 [almeidaesousa2015 E16; almeidaesousa2016 E4]. The sorption isotherms, the values of I(a2) and the preparation of the amorphous samples are not printed in the 2012 paper, so the estimates cannot be recomputed [hsieh2012 X14]. The amorphous solids for sorption (melt-quenched) and for dissolution (solvent-evaporated) differ in preparation [ilevbare2013c X17]. The sorption conditions and water contents are not printed [raina2015b P3].

← Concepts and formulas

concept · as used in PEG dispersions

glass-forming ability

In the library, glass-forming ability (GFA) is the ease with which a melt vitrifies on cooling instead of crystallizing; a compound that crystallizes during a controlled DSC cooling (class I) has a low GFA [baird2010 C8; trasi2014a R14]. It is kept apart from glass stability, the resistance of the glass to crystallization on reheating or storage [baird2010 C4, C47; trasi2014a R14]. The definition above comes from the crystallization-tendency papers, where GFA is measured on neat drugs from the melt. New aspect (ASD process): in the thermogravimetry study of 2020, indomethacin, posaconazole and bicalutamide were chosen as class III molecules of high glass-forming ability so that degradation could be tested in both the crystalline and the amorphous state; the class comes from the cooling and reheating classification of the library [moseson2020 C5; baird2010 C8]. Class III glass formers can still nucleate when held for an hour between Tg and Tm.

Findings

Crystallization tendency: F3, F9, F10, F11, F12, F15, F17. ASD process: F31. Physical stability: F17, F24, F34. Supersaturation from ASD dissolution: F7, F23.

Related concepts

contrasts with glass stability; measured by crystallization tendency classification and critical cooling rate; depends on nucleation temperature zone; related to melt viscosity and reduced glass transition temperature; see crystallization tendency; related to crystallization inhibition by polymers and nucleation and crystal growth; related to physical stability.

Formulas

Barandiaran-Colmenero critical cooling rate, Cabral critical cooling rate, critical cooling rate to avoid nucleation, reduced glass transition temperature.

How it is measured or obtained

By whether the melt crystallizes on DSC cooling at 20 °C/min, with liquid-N2 quenching to separate class I-A (still crystallizes) from I-B (vitrifies) baird2010 P1, P6, R3; by slow cooling at 1 °C/min baird2010 R7; by the critical cooling rate from rapid heat–cool DSC [baird2013 R5, R9]; and, as a proxy, by the melt viscosity at Tm [baird2012 C31]. A drug's GFA is also reported from DSC cooling in later formulation papers [trasi2020 R5; duong2022a R3]. In the 2020 thermogravimetry study the class was cited, not measured; what was measured is nucleation of the neat undercooled melt during isothermal holds below Tm: posaconazole (130–160 °C, 1 h) and bicalutamide (130–180 °C, 1 h) melted on reheating, indomethacin (130–150 °C, 4 h) showed only a glass transition [moseson2020 P7, R7]. When the melt route is excluded by degradation, by attempting amorphization by spin coating, rotary evaporation and cryomilling [wegiel2013b P2, R1]. In the study of commercial tacrolimus capsules: DSC of crystalline tacrolimus monohydrate, with a first heating (broad endotherm between 60 and 120 °C, then melting of the anhydrate), cooling of the melt to an amorphous solid, and reheating through the glass transition without crystallization; the high Tg and the absence of recrystallization on reheating "suggest" good glass-forming ability and stability [trasi2016 R3, M1, C13].

Values in the library
materialvalue or classconditionspaper ids
51 drug-like molecules23 crystallize on cooling (low GFA)DSC, 20 °C/minbaird2010 R1
23 class I molecules8 vitrify on liquid-N2 quench (I-B)melt plunged into liquid N2baird2010 R3
antipyrin, chlorpropamide, flufenamic acid, tolbutamideglass already at 25 °C/minrapid heat–cool DSC[baird2013 R5]
8 class I-A moleculescrystallize even at 800–1100 °C/minrapid heat–cool DSC[baird2013 R1, R3]
acetaminophenforms a glass even at slow coolingcited DSC data[trasi2012a R1]
nilutamidegood glass former; attributed to low nucleationDSC at 15 °C/min[trasi2014b R2, C9]
vemurafenib"relatively poor glass former", about 25 °C supercoolingDSC at 10 °C/min[lu2016 R1, C5]
tacrolimusgood GFA and stability; melting onset 121 °C, Tg onset 75 °C, no crystallization on reheatingDSC heat–cool–reheat[trasi2016 R3, C13, M1]
lumefantrine; artemetherclass 3 (Tg ≈18 °C, no crystallization on reheating); class 1 (crystallized on cooling from about 60 °C)DSC heat–cool–heat[trasi2020 R5, R6, C7]
acetaminophenglass because nucleation (50–60 °C) and growth barely overlapDSC cool–reheat, hot stage[trasi2012a C39, R12.a, R8.a]
resveratrolnot made amorphous by spin coating from four solvents, rotary evaporation or 6 h of cryomillingneat drug[wegiel2013b R1, C6]
curcuminamorphous by spin coating, not in larger amounts by rotary evaporation; cryomilling gave a larger amorphous massneat drug[wegiel2014 C9]
celecoxibeasily made amorphous by cooling the melthot stage[mosqueragiraldo2014 R15]
delamanidno glass at up to 50 °C/min; class I; a glass quenched in liquid nitrogen recrystallized just above its Tg of 43.3 °CDSC; liquid-N2 quench[duong2022a R3, C44]
bicalutamidehigh GFA but rapid crystallization above Tgcited[moseson2022b R26]
posaconazole, indomethacin, bicalutamideclass III (high glass-forming ability)cited[moseson2020 C5]
posaconazole, bicalutamide neat meltsnucleated within 1 h between Tg and TmDSC holds[moseson2020 R7]
Pitfalls and disagreements

A high GFA says nothing about stability on reheating: class II and some class III drugs form glasses easily yet crystallize on reheating or grow fast once nucleated [baird2013 C24; trasi2014a C14]. The judgement depends on the cooling rate and on the unknown liquid-N2 quench rate baird2010 C17, C21. Standard predictors (Tg/Tm, glass-stability parameters, fragility) did not rank GFA of organic molecules [baird2010 C38; baird2012 C43]. The amount of polymer needed for a stable dispersion is expected to depend on GFA and glass stability [trasi2012a C4]. A high glass-forming ability also says nothing about stability of the glass on holding near Tm; the dispersion, not the neat glass, was used for isothermal degradation tests for that reason [moseson2020 C17, C55]. Easy glass formation said nothing about growth once nucleated: celecoxib forms a glass easily yet grows fast [mosqueragiraldo2014 R15, R16]. Good glass-forming ability of lumefantrine, read as making it "a good candidate" for a stable dispersion, did not keep its PVPVA dispersion amorphous beyond 1 week at 40 °C/75% RH [trasi2020 C27, R3]. The tacrolimus result rests on one cooling run, at 15 °C/min with reheating at 10 °C/min [trasi2016 P1]; the class is inferred from it, not measured by the cooling-rate criteria of the crystallization-tendency papers [trasi2016 C13]. Rotary evaporation was too slow to trap delamanid, a poor glass former, above about 10–15% drug, whereas spray drying gave an amorphous dispersion at 25% drug [duong2022a C45; nguyen2023c R5].

← Concepts and formulas

concept · as used in PEG dispersions

glass stability

The resistance of a glass, or of the liquid formed when it is reheated above Tg, to crystallization; the authors of the 2010 classification call the term "somewhat of a misnomer" because it is usually judged by reheating rather than by the glass itself baird2010 C4. In the classification, glass stability means no crystallization on reheating [trasi2014a R14].

Findings

F9, F15, F16, F17.

Related concepts

contrasts with glass-forming ability; measured by glass-stability parameters and critical heating rate; depends on quenched-in nuclei; part of physical stability.

Formulas

critical cooling rate to avoid nucleation.

How it is measured or obtained

By DSC reheating after cooling (class II against III) baird2010 R1; by glass-stability parameters from crystallization onsets on reheating baird2010 E5; by critical heating rates [baird2013 R9]; by storage of glasses below Tg baird2010 P7.

Values in the library
materialvalue or classconditionspaper ids
class IImuch lower glass stability than class IIIDSC reheating and storagebaird2010 C47
class IIIhigh glass-forming ability and high stability on reheatingDSCbaird2010 C34
indoprofen glassfully crystalline after 1 day30 °C, 0% RHbaird2010 R23
class II glassesRcrit,heat 12.5 to above 1910 °C/minrapid heat–cool DSC[baird2013 R9]
acetaminophenquenched-in nuclei may matter for stability over longer timesargument[trasi2012a C41]
Pitfalls and disagreements

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

← Concepts and formulas

concept · as used in PEG dispersions

glass transition temperature

The temperature that separates the glass from the supercooled liquid [lu2016 C2]; it is a kinetic transition where the system falls out of equilibrium [trasi2014b C2]. Tg is called "probably" one of the most important properties of an amorphous solid, because storage temperature relative to Tg affects stability [towler2008 C20]. This draft is written from the crystallization-tendency chapter; the evidence table covers far more papers that later chapters will add. New aspect (PEG dispersions): the Tg of the drug relative to the solidification temperature as a possible determinant of whether an amorphous drug is excluded from the crystalline carrier. In polymer blends the additive's mobility, through the blend Tg, is one of three factors that decide exclusion zhu2011 C2. In the drug/PEG study a drug Tg above the 25 °C solidification temperature (nilutamide about 33 °C, ketoconazole 44 °C) did not change the pattern zhu2011 C28, C31. For water in PEO, Tg describes plasticization (water −136 °C, PEO about −67 °C) marsac2008b M12, M7, C26.

Findings

Crystallization tendency: F4, F12, F20. PEG dispersions: F6, F11.

Related concepts

used in reduced glass transition temperature and Tm − Tg temperature gap; bounds the supercooled liquid; related to fragility, amorphous salt, plasticization and interlamellar incorporation.

Formulas

reduced glass transition temperature, Vogel-Tammann-Fulcher equation.

How it is measured or obtained

By DSC on reheating a melt-quenched or freeze-dried sample, as onset or midpoint [baird2010 P1; trasi2014b M1; towler2008 P6]; for fast crystallizers that give no Tg, estimated from a Tg/Tm ratio or a Trg–molecular-weight fit [vaneerdenbrugh2010a E7; baird2010 E27]. In the PEG papers the Tg values of the drugs were cited from the crystallization-tendency classification, or measured by DSC (acetaminophen) or estimated with a Tg/Tm ratio (naproxen) zhu2011 M5, M6; marsac2008b M1, M3, E5.

Values in the library
materialvalue or classconditionspaper ids
propranolol base; hydrochloride−9.3; 35.9 °CDSC[towler2008 R4]
nicardipine base; hydrochloride3.2; 81.0 °CDSC[towler2008 R5]
nilutamide32 °C (onset)DSC[trasi2014b M1]
vemurafenib108 °CDSC at 10 °C/min[lu2016 M1]
felodipine; nifedipine; indomethacin45 °C eachDSC midpointbaird2010 M37, M32, M40
lumefantrineabout 18 °C; 19.7 °C (onset)DSC[trasi2020 R5; hiew2022a R3]
five drugs with 10 mol% PVPraised by about 2–3 °CDSC[trasi2014a R7]
nilutamide; ketoconazoleabout 33 °C; 44 °Ccitedzhu2011 M5, M6
benzocaine−31 °Ccitedzhu2012 M3
acetaminophen; ketoprofen; naproxen; ibuprofen; felodipine; ketoconazole22.1; −3.0; 24 (estimated); −43.6; 43.1; 44.4 °CDSC and citedmarsac2008b M1, M2, M3, M4, M5, M6
amorphous PEO; waterabout −67 °C (reported −67 to −55 °C); −136 °Ccitedmarsac2008b M7, M12
Pitfalls and disagreements

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

← Concepts and formulas

concept · as used in PEG dispersions

halogen bonding

Evidence table: halogen bonding. Content from the release-mechanism chapter (2021–2025), with rows from the Miscibility and drug-polymer interactions chapter.

A non-covalent interaction between a halogen atom (Cl, Br, I) of a drug and an electron donor, in PVP and PVPVA the amide carbonyl oxygen of the vinylpyrrolidone unit (I···O=C) [que2020 C1; que2021 C15]. On combined XPS, NMR and IR evidence four model compounds with halogens and no hydrogen-bond donors are proposed to form such bonds in PVPVA dispersions [que2020 C1]. Que and co-workers (2021) find that the methyl ether of the iodinated phenol TIPP can form only halogen bonds with the VP carbonyl, and its smaller carbonyl shift "suggests" this halogen bond is weaker than the hydrogen bond formed by the phenolic group [que2021 C7]. Yang and co-workers (2021) note that their two low-Tg drugs lack hydrogen-bond donors but contain chlorine and can halogen-bond with polymer carbonyls (not measured) [yang2021 C8]. Of the four analogues TIPP forms hydrogen and halogen bonds and MeTIPP halogen bonds only; the halogen-bonded MeTIPP took about 9 wt% PVPVA into its drug-rich phase against about 36.5 for TIPP [deac2023b C2, R3]. The 2024 phase-diagram paper treats the halogen bonding of the iodinated analogues TIPP and MeTIPP as weak hydrogen bonding in PC-SAFT, with fitted association sites and energy [deac2024b P19].

Findings

Release mechanism and LoC: F17, F27, F30.

Related concepts

the weaker alternative to drug-polymer hydrogen bonding in donor-free analogues; a kind of drug-polymer interactions; went with a higher limit of congruency than hydrogen bonding in the analogue pairs.

Formulas

molar amount of halogen at the lower XPS binding energy.

How it is measured or obtained

XPS of the halogen core level, where a second doublet at lower binding energy marks more electron-rich halogen atoms, and the shift of the VP carbonyl IR band [que2021 R9, R7; que2020 R7, R11]; the share of halogen atoms at the lower binding energy converted to a molar amount per 100 mg dispersion [que2021 R11, R12, E4].

Values in the library
materialvalue or classconditionspaper ids
TIPP, Me-TIPP neat; in PVPVAI 3d5/2 620.7 eV; additional doublet at 618.1 eVXPS, compacts[que2021 R9]
Me-TIPP–PVPVA 10, 20, 30, 40%60.8, 53.3, 29.9, 22.2% of iodine at the lower binding energyXPS[que2021 R11]
TIPP–PVPVA 10, 20, 30, 40%55.9, 26.5, 15.6, 8.9%XPS[que2021 R11]
TIPP; Me-TIPP in PVPVA, 10–40%≈0.017–0.027; ≈0.029–0.050 mmol lower-binding-energy iodine per 100 mgderived[que2021 R12]
Me-TIPP–PVPVAVP carbonyl shift at most 7 cm⁻¹IR, films[que2021 R7]
clotrimazole, brotrimazole; Me-DIBF in PVPVA (Miscibility chapter)VP carbonyl 1684 → 1682 cm⁻¹ from 10 to 90%; 6 cm⁻¹ downshiftIR, films[que2020 R11]
Pitfalls and disagreements

Bond energies or association constants were not measured; the weaker strength is read from the size of the IR shift [que2021 C7]. The XPS share of Me-TIPP is cited from the authors' earlier study [que2021 R11].

← Concepts and formulas

concept · as used in PEG dispersions

heterogeneous nucleation

Nucleation at an interface (a foreign particle, a container wall, a second phase), which lowers the nucleation barrier, so nucleation there proceeds more readily [wilson2021 C44]. New aspect (PEG dispersions): a crystalline carrier as the nucleating surface. Zhu and co-workers conclude that crystalline PEG acts as a favourable heterogeneous nucleation site for the slowly crystallizing ibuprofen and fenofibrate, which explains why the drugs began to crystallize in the dispersion (after about 100 and 120–180 min) earlier than most neat samples, despite a smaller thermodynamic driving force ("it appears") zhu2012 C4, C34, R23.a. New aspect (Crystallization from solution): In solution, impurities in large volumes at high supersaturation may induce heterogeneous nucleation, which the authors give as a reason for the small scatter (below 15%) of induction times ("it is reasonable to expect") [ilevbare2013c R17, C16]. For danazol the interface of the drug-rich droplets is a candidate site: crystals could form from the drug-rich or the drug-lean phase, the change to a two-phase solution can alter nucleation, and polymer at the droplet–water interface is "likely" to disrupt nucleation there [jackson2014 C45, C53]. Micelles of dihydroxy bile salts "may" offer interfaces for heterogeneous nucleation, and the surfaces of drug-rich telaprevir particles are expected to enable it; adsorbed bile salt is expected to modify it [lu2017 C34, C36, C39]. New aspect (Supersaturation from ASD dissolution): the ASD dissolution papers invoke it three times: polymer adsorbed on parent γ nifedipine crystals could reduce heterogeneous nucleation of α on them, and many small solution-grown crystals offer more surface for it [raina2014b C31, C36]; the interfaces of a drug-rich phase "may" act as heterogeneous nucleation sites [trasi2015b C31]; surfactants promoted ritonavir crystallization only when the ritonavir–water interface of droplets was present [ilevbare2013d C43].

Findings

Crystallization tendency: F10, F17. PEG dispersions: F9. Crystallization from solution: F14, F15, F25, F32, F34, F37, F38. Supersaturation from ASD dissolution: F3, F11, F13.

Related concepts

part of nucleation; contrasts with classical nucleation theory (homogeneous form); related to surface crystallization, stochastic nucleation, nucleation induction time and semicrystalline solid dispersion; related to secondary nucleation and polymer adsorption to drug-rich droplets; related to drug-rich nanodroplets and surfactant-induced crystallization.

Formulas

classical nucleation theory.

How it is measured or obtained

Rarely measured directly; inferred from scatter of crystallization temperatures in DSC pans baird2010 C19, from crystals forming at a seeded interface zhu2012 R15, R19, from the effect of shear in a rheometer [baird2012 C8] or from the change of slope of induction time against supersaturation [duong2022b C28]. In the seeding test a small piece of crystalline PEG is placed in the supercooled neat drug at 25 °C and observed by polarized light microscopy for where the first crystals form; crystals formed at the PEG edge within minutes and none in the bulk zhu2012 P7, R15, R19. In the crystallization-from-solution papers it is not measured; the site of nucleation (droplet, interface or bulk) was not determined [jackson2014 X15]. Seeds added on purpose test the related seeded growth (F5, F20) [alonzo2012 P4]. In the ASD dissolution papers it is not measured either, but argued from conversion kinetics and induction times [raina2014b C32; ilevbare2013d R16].

Values in the library
materialvalue or classconditionspaper ids
ibuprofen; fenofibratecrystals form at a crystalline PEG interface within minutes, none in the bulk25 °Czhu2012 R15, R19, C4
neat ibuprofen; fenofibrate0.20 and 0.34 of 50 samples crystallized after 3 weeks25 °C, no carrierzhu2012 R2, R3
ibuprofen; fenofibrate in 20/80 PEG 3350onset about 100 min; 120–180 min25 °Czhu2012 R23.a
class I-A meltscrystallization temperatures higher in the rheometer than in DSC, ascribed to the upper plateshear 30 s⁻¹[baird2012 R5, C8]
class I moleculesscatter of crystallization temperatures ascribed to stochastic and heterogeneous nucleationDSC pans[baird2010 C19; baird2013 C18]
felodipine filmsnucleation "most likely heterogeneous"spin-coated films[konno2006 C33]
posaconazolehomogeneous at high supersaturation, heterogeneous at low; shallow slope of log t against 1/log²S below S about 12 read as heterogeneous ("has been attributed")PBS pH 6.5, 37 °C[duong2022b R10, C28]
enzalutamide with drug-rich dropletsdroplets enhance crystallization; droplet/water interface "likely" a favourable site; induction times fall on crossing 42 µg/mLpH 6.5, 2.5–100 µg/mL polymer[wilson2021 C45, C46, R3]
bicalutamidefractures of mechanically activated samples favour heterogeneous nucleationdispersions[moseson2022b C45]
induction-time replicates, 50–80 mL, S 2.4–15.4scatter below 15%triplicate[ilevbare2013c R17]
danazol, HPMC-ASinduction time 516 → 277 min as drug concentration rises from 10 to 20 µg/mL25 °C[jackson2014 R17]
telaprevir δ 28.8, buffercrystallizes immediately with a drug-rich phase presentpH 6.5, 37 °C[lu2017 R4]
atazanavir ASD particlesdissolving ASD did not seed nucleation (about 300 against 350 min)PVPVA + SDS, pH 6.8[indulkar2019b R5, C25]
ritonavir with SDS; Tween 80, below and above LLPSabout 262 against 34.7 min; about 289 against 23.6 min37 °C[ilevbare2013d R16, R12]
nifedipine dispersions against glassγ → α complete in ≈5–40 min against ≈40–145 min with dissolved polymer25 °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 PEG dispersions

HME operating design space

A map of product melt temperature against residence time for hot melt extrusion with regimes: thermal degradation at the top, melting above the drug's melting point, dissolution between Tc and Tm (the drug dissolves into the softened polymer, not melts) and suspension below Tc, plus an inaccessible zone below the polymer's minimum processing temperature [moseson2018a R1; moseson2018 C40, C48]. Higher temperature and longer residence time raise the risk of thermal degradation; lower temperature and shorter residence time the risk of residual crystallinity moseson2018 C65. The 2018 map put thermal degradation at the top as a schematic region; the thermogravimetry and assay studies of the ASD process papers give it a measured form, time–temperature contour maps of mass loss and assays of drug after exposure, and show that the lower boundary also moves with the input crystal size [moseson2020 R15, R18; moseson2021 R6]. For 30% bicalutamide–PVPVA, with Tc = 145 °C as the slowest dissolution case, the residence time needed to reach a crystal-free extrudate ranged from 2 min for micronized crystals to more than 20 min for large or broad-distribution crystals [moseson2022c R10].

Findings

F9, F10, F35, F36, F37, F41.

Related concepts

bounded by formulation critical temperature and temperature-composition phase diagram; governs residual crystallinity and crystal dissolution into a polymer melt; the chemical-stability side is the HME processing window.

Formulas

Noyes–Whitney equation.

How it is measured or obtained

By extruding one composition at several melt temperatures and residence times, reading crystallinity with several methods and placing each run on the plane; the zone lines are drawn by the authors between data points and could instead be set by XRPD thresholds (<1%, <2%, <5%) with performance tests moseson2018 R15, C60.

Values in the library
materialvalue or classconditionspaper ids
50% IDM–PVPVA15 runs; 117–161 °C; 2–20 min; amorphous by all techniques first at 131 °C 20 min, 141 °C 10 min, 161 °C 2 min5 mL recirculating extrudermoseson2018 R10, R15
1:1 IDM–PVPVAextrudate at 131 °C and 20 min on the lower edge of the dissolution regionschematic from earlier work[moseson2018a R1]
30:70 BCL–PVPVAdissolution regime between Tc = 145 °C and Tm = 195 °C; at 155 °C small input crystals left crystals visible only by TEM, medium and large ones 3.5% and 30%; at 180 °C small crystals left none5 mL extruder[moseson2021 M1, P1, R6]
50/50 IDM/PVPVA and 30/70 BCL/PVPVA, chemical sideIDM/PVPVA under 1% mass loss for short times to 200 °C; BCL/PVPVA 1% within 10 min at 180 °C, after 40 min at 165 °C, after more than 100 min at 155 °Cisothermal TGA, 4 h[moseson2020 R15, C44, C45]
20% RTV with PVPVA 64, HPMCAS MF, HPMCextrusion at 130–160 °C, 5 min: assay 95.7–100.5%, polymer-dependent2 mL extruder[alvarenga2022 R22]
30% BCL–PVPVA at Tc = 145 °C, lots of D50 3.51 / 37.0 / 38.0 / 42.2 / 92.7 µmbelow the limit of detection at 2 / 5 / 6 min; about 2.5% and 15.0% at 20 min for the last two5 mL micro-extruder, PXRD[moseson2022c R10]
PCZ–HPMCAS MF, 10 / 25 / 50% DLcrystals 0.3 / 3.2 / 19.3 wt% at 125 °C, none at 175 °C2 min, 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 PEG dispersions

Hoffman equation

An approximation for the free-energy difference between the supercooled liquid and the crystal at a temperature T below Tm, needing only Tm and the heat of fusion [vaneerdenbrugh2010a E2; lu2016 E1]. It assumes that the enthalpies of crystal and supercooled liquid vary linearly with temperature, that is a constant heat-capacity difference, and applies above Tg [marsac2006b C37; ilevbare2013a C58]. In this chapter it supplies the crystallization driving force; most other library papers use it to estimate the amorphous solubility advantage. New aspect (solution methods): in the solution-methods papers the Hoffman equation supplies the free-energy advantage of the amorphous form in the amorphous solubility estimate, printed with a positive sign and \Delta T = T_m - T: \Delta G = \frac{\Delta H_f\,\Delta T}{T_m}\cdot\frac{T}{T_m} [raina2015a E2]. New aspect (C. Amorphous solubility and LLPS): those papers print it as the free-energy term of Eq. 1, \Delta G = \Delta H_f\,(T_m - T)\,T/T_m^{2}, and list its assumptions: a constant, temperature-independent ΔCp, small undercooling and Tg close to T∞; it also does not address the crystal-to-glass conversion [ilevbare2013a E2, C58; almeidaesousa2015 E2, C8; mosqueragiraldo2015 E2; almeidaesousa2016 E2]. For atazanavir Eq. 2 is printed with DSC Tm 208 °C and ΔHf 90.1 J/g, and the paper's own ratio of 62 follows from them when 0.22 is read as exp[−I(a)], although Table I heads that column I(a) (synthesis) [indulkar2017a E2, E3, X1; indulkar2015 M2]. New aspect (Bioperformance): the equation estimates the amorphous-to-crystalline solubility ratio \sigma_a/\sigma_c = e^{\Delta G/RT} and is combined with a water-sorption correction [raina2014a E3, E5; raina2015c E1, E2]. New aspect (Crystallization from solution): in the solution-crystallization papers \exp(\Delta G_c/RT) is the activity ratio taken as the solubility ratio before a water-sorption correction, evaluated at 25 or 37 °C, and the ratio times the measured crystalline solubility is compared with plateaus after pH shifts and with onsets of phase separation (F2) [hsieh2012 E3, E4, R10; hsieh2014 E2, E3; jackson2014 E2, R5]. New aspect (Supersaturation from ASD dissolution): the ASD dissolution papers use it to estimate the amorphous solubility advantage of felodipine and indomethacin; the felodipine inputs of 2008 come from earlier work, which found the equation estimated felodipine's free-energy difference well (cited) [konno2008a E2, R20].

Findings

Crystallization tendency: F6, F7, F13. Solution methods: F5. C. Amorphous solubility and LLPS: F5, F7. Bioperformance: F1, F23. Crystallization from solution: F2, F16, F21. Supersaturation from ASD dissolution: F5, F7.

Related concepts

measures thermodynamic driving force for crystallization; depends on enthalpy of fusion and degree of supercooling; related to entropy of fusion, amorphous-crystalline free energy difference and amorphous solubility; compared with the heat-capacity route in amorphous-crystalline free energy difference; accuracy set by degree of supercooling. Related to amorphous solubility advantage; corrected by the Gibbs-Duhem equation route.

Formulas

Hoffman equation, amorphous solubility advantage from free energy difference.

How it is measured or obtained

Calculated from DSC Tm and ΔHfus at the temperature of interest, per mole, per gram or, with the crystal density, per volume [baird2010 E25; vaneerdenbrugh2010a P11]. Its agreement with MDSC-based free energies was checked for felodipine and nifedipine [marsac2006a C14]. In solution work it enters \exp\left(\frac{\Delta G}{RT}\right) as the amorphous-to-crystalline solubility ratio [alonzo2010 R3; duong2022a R27]. ΔHf and Tm were measured by DSC at 10 °C/min in pinhole aluminum pans; the values are not printed [raina2015a P4, E2]. With a heat-capacity term it becomes \frac{\Delta G_{a\to c}}{RT} = \frac{\Delta H_f}{RT}\left(1 - \frac{T}{T_m}\right) + \frac{1}{RT}\int_{T_m}^{T}\Delta C_p\,dT - \frac{1}{R}\int_{T_m}^{T}\frac{\Delta C_p}{T}\,dT [mosqueragiraldo2015 E3]. In the amorphous solubility papers ΔHf and Tm are DSC values at 10 °C/min (5 °C/min in one paper), evaluated at 25 or 37 °C [almeidaesousa2015 P5; indulkar2015 P6, P5; almeidaesousa2016 P9]. In the Bioperformance papers ΔHf and Tm come from DSC melting onset and enthalpy, and the water sorption from gravimetric moisture sorption [raina2014a P3, P4]. The DSC method is not given in the 2014 pH-shift paper and the heats of fusion are not printed in the 2012 paper [hsieh2012 P13, X14; hsieh2014 X11]. In the ASD dissolution papers: from the DSC enthalpy of fusion and melting temperature (felodipine 30.12 kJ/mol, 143.41 °C; indomethacin 32.48 kJ/mol, 153.4 °C) and the crystalline solubility [alonzo2010 P10, P12, M1, M2]; inputs not printed in the 2008 and 2011 papers [konno2008a E2; alonzo2011 E3].

Values in the library
materialvalue or classconditionspaper ids
felodipine; nifedipine6.2 and 8.8 kJ/mol25 °C[marsac2006a E3, R4]
34 drugsΔGv −8.6 (lidocaine) to −54.7 J/cm³ (acetaminophen)298 K[baird2012 M5, M12]
vemurafenib α against βα lower in free energy up to a virtual transition at 319 °CTm and ΔHm of both forms[lu2016 R22, E1]
felodipineestimated amorphous solubility about 9 µg/mL37 °C[alonzo2010 R3]
delamanidsolubility ratio 31.8 calculated against 42.3 measured37 °C[duong2022a R27]
ritonavir, efavirenz, celecoxib≈10.2, ≈2.70, ≈7.74 kJ/mol (extractor calculation)37 °C[ilevbare2013c E7]
six dihydropyridinesused for the yardstick of F5; no ΔG value printed25 and 37 °C[raina2015a E2, R11]
diverse drugsCp method closer to the measured LLPS onsets than the Hoffman equation25 °C[almeidaesousa2015 R11, C43]
ritonavir10.1 kJ/mol (extractor recomputation from Table 2 inputs)37 °C[ilevbare2013a E2]
ibuprofen to griseofulvin3.24, 4.84, 5.69, 8.51, 10.33, 9.69 kJ/mol25 °C[almeidaesousa2015 R11]
telaprevir13.31 kJ/mol (recomputed); amorphous solubility 245 ± 5 µg/mL, 2.7 times the onset37 °C[mosqueragiraldo2015 E1, R13, R17]
clotrimazole6.26 kJ/mol with a molar mass not printed in the paper (extractor)310 K[indulkar2015 E3]
CRH15.68 kJ/mol; estimate 11.2 µg/mL at pH 4.625 °C[almeidaesousa2016 M1, R2]
atazanavir14.55 kJ/mol (recomputed from Table I); ratio about 62, as printed, with 0.22 read as exp[−I(a)]; about 228 read as I(a)310 K[indulkar2017a E2, X1; indulkar2015 M2]
felodipineHoffman ratio 10.92 (25 °C), 8.64 (37 °C); water factor 0.74, 0.83Tm 147 °C, ΔHf 28.67 kJ/mol[raina2014a R7]
nifedipineprinted ratio 8.78; recomputed 14.45Tm 173 °C, ΔHf 32.5 kJ/mol[raina2014a R7, X3]
atazanavirratio 62, predicted 68 µg/mL310 K[indulkar2017a R5]
indomethacin17–25 µg/mL (25 °C), about 37 µg/mL (37 °C)Hoffman estimate[alonzo2010 R8]
enzalutamideprinted estimate about 39 µg/mL (13-fold); the printed inputs give 27.737 °C, Tm 470 K[wilson2018 E1, R3, X1]
ritonavirΔHf 60.4 kJ/mol, Tm 121 °C, 37 °C: ΔG = 10.1 kJ/mol and exp(ΔG/RT) = 50.8 (extractor calculation); calculated amorphous solubility 20.6 µg/mL with the water term37 °C[ilevbare2012b E8, E9, R1]
glyburide; warfarinabout 60-fold and 48-fold (59.9 and 47.7 recomputed) from Tm 175.6 °C, ΔHf 45.5 kJ/mol and Tm 169.2 °C, 43.6 kJ/mol25 °C (assumed)[hsieh2014 R16, E3, M3, M4]
danazolTm 225.4 °C, ΔHf 28.9 kJ/mol: ΔG = 6.95 kJ/mol; ratio with the 0.935 water factor 15.4 recomputed against 19.6 printed25 °C[jackson2014 E1, E2, X1]
five weak basesratios 22.2, 11.9, 20.4, 54.6, 7.0 without water correction (carvedilol, clotrimazole, clozapine, ketoconazole, loratadine)37 °C[hsieh2012 R10]
felodipine (six-dihydropyridine study)e^(ΔG/RT) recomputed 10.84 at 298.15 K from 74.6 J/g and 147 °CDSC data of the paper[raina2015b E1, R1.b]
posaconazoleTm 169.1 °C, ΔHf 76.95 J/g; printed amorphous/crystalline ratio 37.9 with water factor 0.33, estimate 10.22 against 9.08 µg/mL measured310 K; the extractor obtains ΔG = 16.13 J/g and a ratio of about 26.5[duong2022b R7, E3, X2]
felodipineratio about 10; about 9.5 µg/mL37 °C[konno2008a R17]
felodipineΔG 5729 J/mol, ratio 9.22 (recomputed) against "around 9"37 °C[alonzo2010 E1]
felodipineabout 9.1 µg/mL (37 °C); 5–6 µg/mL (25 °C)pH 6.8[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 PEG dispersions

hydrogen-bond basicity

The strength of a group as a hydrogen-bond acceptor

In this chapter it is used qualitatively to rank polymer groups and drug groups: the more basic PVP amide is said to explain why PVP takes the OH from carboxylic acid dimers [taylor1997 C36]; PVP carries a better acceptor than the drug's own groups marsac2009 C39; the pyrrolidone groups of PVP and PVP/VA are stronger acceptors than the acetate groups of PVAc [kestur2010a C24, C25; kestur2011 C26]; and the imidazole nitrogen of bifonazole "would be expected" to be a better acceptor than the PAA carbonyl [kestur2011 C16]. A numerical scale (pKBHX) with classes weak < 0.75 < medium < 1.5 < strong < 2.25 < very strong is applied to polymer groups in another paper of the library [wegiel2013b E2, R17, C30]. The numerical pKBHX scale (weak < 0.75 < medium < 1.5 < strong < 2.25 < very strong, from the association of a model compound with 4-fluorophenol) is applied to all donor and acceptor groups of 15 drugs and 7 polymers, with the carbonyl of a COOH group taken as an ester because no value exists [vaneerdenbrugh2011a C14, R1, R2]; the polyphenol paper reuses it for its six polymers [wegiel2013a R12, P8].

Findings

F1, F12, F13, F24, F25.

Related concepts

part of hydrogen bonding; related to pKa and drug-polymer interactions.

Formulas

none.

How it is measured or obtained

Not measured in this chapter's papers; assigned from chemistry, from the drug NH shift in films with different polymers [kestur2010a R9] and from the cited scale [kestur2011 C26].

Values in the library
materialvalue or classconditionspaper ids
PVP, PVP/VA against PVAcstronger acceptor (pyrrolidone against acetate); PVP/VA has 40% acetate side chainspolymer chemistry[kestur2010a C24, M3; kestur2011 C26]
PVP amide against carboxylic acidthe amide is the more basiccited[taylor1997 C36]
polymer groups on the pKBHX scale (other chapter)classes from weak to very strongcited values[wegiel2013b R17, E2]
PVP, PVPVA pyrrolidonevery strong acceptor, 1-methyl-2-pyrrolidone 2.38, no donorpKBHX classes[vaneerdenbrugh2011a R2; wegiel2013a R12]
E100 amine; imidazole of bifonazolestrong 1.98 (triethylamine); very strong 2.72 (1-methylimidazole)same[vaneerdenbrugh2011a R1, R2]
ester, COOH carbonyl, ether, alcoholmedium: 1.07, 1.07, 1.01, 1.02same[vaneerdenbrugh2011a R2; wegiel2013a R12]
amide carbonyl of benzamide, phenacetinstrong 1.81, 1.69same[vaneerdenbrugh2011a R1]
PSSA sulfonic acidlow 0.71 (acceptor); very strong donorsame[vaneerdenbrugh2011a R2]

Evidence table: hydrogen-bond basicity.

Pitfalls and disagreements

The acceptor-strength explanation of the small edge of PVP and PVP/VA over PVAc for nimesulide is not resolved by the NH maxima, which move as far with PVAc as with PVP [kestur2011 X16]. PVP/VA is compared at equal weight, not at equal numbers of pyrrolidone groups, and the 40% acetate figure is not defined as mass or mole [kestur2010a X11]. The group tables call the acceptor classes "donor strength" in a footnote and cite two different references for the values [vaneerdenbrugh2011a X2]; the HPMCAS COOH acceptor mark is missing in the polyphenol paper's table [wegiel2013a X13]. The pKBHX predicted the PVP and E100 as best acceptors, but E100 formed no strong hydrogen bonds because its amine is ionized [wegiel2013a C32, C33].

← Concepts and formulas

concept · as used in PEG dispersions

hydrogen bonding

In the papers of this chapter, a bond between a donor group of the drug (the carboxylic acid OH of indomethacin, the NH of felodipine and nimesulide, hydroxyl groups of sucrose) and an acceptor group of the polymer (the lactam carbonyl of PVP, the acetate groups of PVAc and PVP/VA, the carboxyl of PAA, the groups of HPMCAS), or between molecules of the same kind (acid dimers of the drug, self-association of PAA) [taylor1997 C25, C35; kestur2010a C18; rumondor2009a C45]. A lower NH wavenumber means a stronger bond [kestur2010a C18]. PVP carries a better acceptor than the drug's own groups, so its bonds replace weaker drug–drug bonds marsac2009 C39; the more acidic carboxyl of indomethacin is expected to bond more strongly than the NH of felodipine or nifedipine or the OH of sucrose marsac2009 C42. A drug donor can also be bound within its own molecule (see intramolecular hydrogen bonding), which leaves little to bond to a polymer [kestur2011 C27]. Later papers add polyphenol OH groups bonding to the PVP carbonyl (a lower OH wavenumber and a larger carbonyl shift mean a stronger bond: OH band at 3138 and 3135 cm⁻¹ with PVP against 3329–3399 cm⁻¹ with the other polymers) [wegiel2013a C8, C9, C11, R2, R4]; dextran hydroxyls bonding to the PVP carbonyl in a polymer–polymer pair, where dextran–dextran bonds are assumed to be stronger or more numerous [vaneerdenbrugh2012a C10, C36]; and a donor and acceptor classification of the groups of 15 drugs and 7 polymers by bonding atom, acidity and the pKBHX scale [vaneerdenbrugh2011a C13, C14, C19]. Lumefantrine did not hydrogen-bond to PVPVA in dried films [hiew2022a C20, R17].

Findings

F1, F2, F3, F4, F12, F13, F14, F17, F20, F22, F24, F25.

Related concepts

part of drug-polymer interactions; includes intramolecular hydrogen bonding and self-association; contrasts with dipole-dipole interactions; related to hydrogen-bond basicity, pKa and binding constant; contrasts with halogen bonding and acid-base interaction; classified by Etter's hydrogen-bond rules.

Formulas

fraction of hydrogen-bonded carbonyl groups from band areas.

How it is measured or obtained

By IR and Raman. Cyclic acid dimers are found by the mutual exclusion rule: an acid band present in the IR and absent in the Raman [taylor1997 C14]. Drug–polymer bonds are read from shifts of the drug NH or acid C=O band and of the polymer carbonyl band, in spin-coated or solvent-cast films at one donor per polymer carbonyl or at 20–50 wt% polymer, always against the amorphous drug and a physical mix, not against the crystal [marsac2009 P4; kestur2010a P6, P7; taylor1997 C7, C24]. A dilution series in a non-polar solvent tests for intramolecular bonds [kestur2011 P9]. In dispersions, a second principal component of the IR spectra beyond a calculated physical mixture is read as "presumably" hydrogen bonding [rumondor2009a C20]. DFT gives the geometry of single molecules [kestur2011 P11]. Further methods: the fraction of PVP carbonyls bonded, from a free and a maximally bonded band fitted to the carbonyl region (fraction of hydrogen-bonded carbonyl groups from band areas) [vaneerdenbrugh2012a P5, E1]; the polyphenol OH band and the polymer C=O shift at 30% polyphenol [wegiel2013a P4]; crystal-structure statistics of competition between groups [vaneerdenbrugh2011a P5, R14]; DFT for intramolecular bonds [vaneerdenbrugh2011a P6].

Values in the library
materialvalue or classconditionspaper ids
indomethacin–PVP-K90PVP C=O at 1636 against 1679 cm⁻¹; drug acid C=O at 1726 cm⁻¹5–70 wt% PVP, solvent-evaporated[taylor1997 R5.l, R11, R12]
amorphous indomethacinacid dimer at 1710 cm⁻¹ (IR) with no Raman bandquench-cooled melt[taylor1997 R5.h, R6]
indomethacin, felodipine, sucrose, ketoconazole with PVP K12PVP C=O shift 45, 25, 25 and 0 cm⁻¹one donor per carbonyl, spin-coatedmarsac2009 R12
felodipine with PVP, PVP/VA, HPMCAS, PVAcNH at 3294, 3298, 3348, 3354 cm⁻¹ against 3341 cm⁻¹50 wt% polymer films[kestur2010a R9]
nimesulideNH at 3345 cm⁻¹ at every concentrationdichloromethane, 1–100 mg/ml[kestur2011 R11]
nimesulide with PVPPVP C=O ≈1684 → ≈1680 cm⁻¹, shoulder ≈1657 cm⁻¹20–50 wt% PVP[kestur2011 R14]
felodipine–PVP, nifedipine–PVPsecond PC with NH and carbonyl loadings10–90% and 25–70% PVP[rumondor2009a R7, R9]
naringenin, quercetin with PVPpolyphenol OH band 3138 and 3135 cm⁻¹; PVP C=O shift 21 and 24 cm⁻¹spin-coated films, 30% polyphenol[wegiel2013a R2, R4]
dextran–PVPPVP C=O 1680 → 1661 cm⁻¹; hydrogen-bonded fraction 1.00 (DEX1–PVP12) to about 0.09 (DEX450–PVP90) at 0.8 dextranspin-coated films[vaneerdenbrugh2012a R2, R14]
benzamide, phenacetin crystalsamide–amide only 100 and 94% alone; 0% with a COOH partner; 14 and 33% with C(O)NC2CSD survey[vaneerdenbrugh2011a R14]
lumefantrine–PVPVAcarbonyl bands fixed at 1736 and 1684 cm⁻¹ at 10, 25 and 50% drugdried spin-coated 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 PEG dispersions

hydrophobic effect

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

Findings

F20, F21.

Related concepts

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

Formulas

van't Hoff equation.

How it is measured or obtained

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

Values in the library
materialvalue or classconditionspaper ids
polymer transfer into the ibuprofen-rich phaseΔH of HPMC 58 → 12, PVP-VA 25 → 5, PVP 30 → 1 kJ/mol; −TΔS −71 → −31 (HPMC)15–60 °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 PEG dispersions

hydrophobicity

The tendency of a drug to avoid water, read in the library from its calculated log P; for the moisture-separation papers a hydrophobic drug is expected to have a positive water–drug interaction parameter, so that sorbed water makes the dispersion less favourable for it [rumondor2010c C30, M1, M2, M3, M4]. The same papers treat it as one of three factors, with dispersion hygroscopicity and drug–polymer interaction strength, behind moisture-induced amorphous–amorphous phase separation [rumondor2011 C1, C28].

Findings

F13, F23.

Related concepts

related to hygroscopicity (the two together set the water–drug term); part of the argument for moisture-induced phase separation; enters Flory-Huggins interaction parameter (\chi_{WD}); related to lipophilicity.

Formulas

multicomponent Flory-Huggins free energy of mixing, through the water–drug parameter \chi_{WD} [rumondor2010c E1, C30].

How it is measured or obtained

Calculated log P (ChemBioDraw Ultra) for the drugs [rumondor2010c M1; rumondor2011 P9]; cited log P for resveratrol and felodipine [wegiel2013b R20]. The water uptake of the hydrophobic films themselves was not measured [rumondor2011 X6].

Values in the library
materialvalue or classconditionspaper ids
felodipine, quinidine, indomethacin, pimozidecalculated log P 2.24, 2.48, 3.58, 5.34drugs of PVP, PVPVA and HPMCAS dispersions[rumondor2010c M1, M2, M4, M3]
indoprofen, nilutamide, loratadine, clofoctol, probucollog P 2.84, 2.14, 4.13, 8.19, 10.0drugs of PVP films[rumondor2011 R15.e, R15.s, R15.t, R15.f, R15.g]
resveratrol against felodipinelog P 3.1 against 4.5 (cited)contrast of PVP dispersions in humid storage[wegiel2013b R20]
pimozide with HPMCASthe only HPMCAS dispersion that separated; attributed to hydrophobicity94% RH, dried[rumondor2010c C35, R3.e]
clofoctol–PVP (≥ 70% drug), probucol–PVP (90% drug)no separation up to 94% RH; "it is thought" too little water sorbed22 °C films[rumondor2011 C36, R14]
Pitfalls and disagreements

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

← Concepts and formulas

concept · as used in PEG dispersions

hygroscopicity

How much water a material takes up at a given humidity

For HPMC grades at 21 °C: E3 3.22, E6 3.56, E50 3.43 and AFFINISOL 2.03% w/w at 40% RH; the polymer's hygroscopicity is held to set how much water a film takes up during formation and so the size of drug-rich domains [mugheirbi2017 R2, C23]. Solvents can be hygroscopic too: methanol takes up almost an equimolar amount of water at 50% RH [li2017 R26, C39]. In the coating papers hygroscopicity is a powder-level property read from dynamic vapour sorption of coated and uncoated particles; the abstract of the ezetimibe paper generalizes lower hygroscopicity to all coated powders, which only the thick coatings show [duong2022c C59, X6]. New aspect (Physical stability): for drug–polymer dispersions the polymer sets the hygroscopicity, because the drug is hydrophobic, so a dispersion takes up more water than the amorphous drug, the amount depending on polymer type and content [konno2008 C6, C18]. Nifedipine and its dispersions are more hygroscopic than felodipine's marsac2008a C12. New aspect (Release mechanism and LoC): since water-induced AAPS depends on the water absorbed, polymer hygroscopicity "likely" also matters for the limit of congruency; the congruent release of high-loading HPMCAS and EUDS dispersions "conceivably" reflects water uptake too low to induce AAPS [saboo2020a C44].

Findings

ASD process: F4, F2, F44, F45, F49. Physical stability: F6, F11, F16, F23, F33, F35. Release mechanism and LoC: F8, F11, F12.

Related concepts

measured as water sorption and by water sorption isotherm; sets moisture-induced phase separation; drives plasticization by water; acts with hydrophobicity in the water–drug term. Ranks with wettability; drives amorphous-amorphous phase separation on hydration; related to polymer hydrophobicity.

Formulas

Flory-Huggins water sorption isotherm.

How it is measured or obtained

Gravimetric moisture sorption (SGA-100; 42–44 mg of as-received powder dried at 60 °C, equilibrated at 21 °C at 5, 7, 20 and 40% RH, n = 3) [mugheirbi2017 P14]. Gravimetric sorption isotherms of bulk dispersions at 25 °C [konno2008 P7; marsac2008a P6]. In the release-mechanism papers: gravimetric water sorption of neat polymers and amorphous felodipine at 37 °C from 5 to 95% RH, single runs; uptake of 40% HPMCAS dispersions at 100% RH extrapolated from isotherms [saboo2020a R3, R18].

Values in the library
materialvalue or classconditionspaper ids
HPMC E33.22, 1.517, 0.48% w/w40, 20, 7% RH[mugheirbi2017 R2.a]
AFFINISOL2.03, 0.89, 0.19% w/w; about 63% of E3 at 40% RHsame[mugheirbi2017 R2.d, C21]
PVP, HPMC, HPMCAS (outside)PVP absorbs more water than HPMC, HPMC more than HPMCAS, at the same RH and temperature25 °C[rumondor2010a C6, R1]
ritonavir ASDs (outside)PVP and PVPVA are more hygroscopic than HPMCAS, so their ASDs are expected to be more prone to moisture-induced AAPSargument[purohit2017b C45]
polymer hygroscopicity and AAPS (outside)the water–drug contribution to the free energy of mixing depends on the water sorbed, which depends on polymer hygroscopicityfelodipine, indomethacin and others in PVP, PVPVA, HPMCAS[rumondor2010c C30]
PVP, HPMC, HPMCAS, felodipine≈33.5, 10.9, 6.2, 0.7 g/100 g75% RH, 25 °C[konno2008 R8]
felodipine with 25% PVP, HPMC, HPMCAS≈4.7, 2.3, 1.7 g/100 g75% RH[konno2008 R9.d]
nifedipine vs felodipine with 25% PVP≈5.5 vs 4.6 g/100 g75% RHmarsac2008a R2
felodipine–PVP vs HPMCAS dispersionsPVP dispersions more hygroscopic (cited)93% RH[rumondor2009b R25]
75:25 felodipine and quinidine with PVP, PVPVA, HPMCAS6.4/3.6/2.4 and 5.3/3.4/2.4 g per 100 g25 °C/85% RH[rumondor2010c R18]
PVP, PVPVA, HPMCAS alone≈50, ≈24, ≈8 g per 100 g at ≈85% RHcited isotherms, 25 °C[rumondor2010c R19]
40% resveratrol–PVP dispersion against its physical mixture≈12.8 against ≈36.5% at 95% RH25 °C[wegiel2013b R19]
PVP K29/32, K12, PVPVA, HPMC, HPMCAS; amorphous celecoxib≈68, 67, 48, 31, 12; ≈2.2 g/100 g at 95% RHDVS, 25 °C[xie2016b R12]
six tacrolimus capsule fills1.6–12.8% at 95% RH, most with the most croscarmelloseDVS, 25 °C[trasi2017 R4, C16]
PVP, PVPVA, HPMC, EUDS, HPMCAS≈34, ≈20, ≈9, ≈7.8, ≈5.9% at 75% RH; ≈71, ≈47, ≈28, ≈12.7, ≈10.2% at 95% RH37 °C[saboo2020a R3]
amorphous felodipine≈1.3% at 75% RH37 °C[saboo2020a R3]
40% HPMCAS dispersions of nilvadipine, felodipine, cilnidipine≈5.83, ≈5.67, ≈5.45% at 100% RH (extrapolated)37 °C[saboo2020a R18]
Pitfalls and disagreements

Sorption of dry powders at equilibrium is a proxy for uptake during a seconds-long coating; no water was measured during coating [mugheirbi2017 X4]. Plotted against water content the polymers' nucleation rates fell together within scatter, but at similar water content 7% PVP still nucleated faster than 7% cellulose polymer [konno2008 C30, X4]. The uptake used to explain the polymer order was measured on 75:25 powders at 85% RH, not on the 50:50 test samples [rumondor2010c X7]. Hygroscopicity is not a variable of the 20-system model [rumondor2011 X5]. Water uptake did not rank celecoxib dispersions at 94% RH: PVPVA, with about twice the uptake of HPMCAS, lasted longer [xie2016b R13, R23, C50]. In tacrolimus capsules extra croscarmellose raised sorption but did not destabilize the innovator product [trasi2017 C30]. Water uptake separated the hydrophilic from the hydrophobic polymers but did not rank the limits within the hydrophilic group: HPMC takes up less water than PVPVA yet had the lower limit [saboo2020a X7]. The uptake was measured on neat polymers [saboo2020a X7].

← Concepts and formulas

concept · as used in PEG dispersions

ideal solubility

The solubility a crystalline drug would have if it mixed ideally with the solvent; it is set by the melting temperature and the enthalpy of fusion alone marsac2008b E1. The real solubility differs from it by the activity coefficient, \ln[\gamma_d x_d] = -\Delta G_{fus}/(R\,T), with \Delta G_{fus} taken from the Hoffman relation in the PEG study baird2011 E5, E6, E7. Marsac and co-workers use it as the reference for the activity coefficients in PEG 400 and in water marsac2008b R14. New aspects (Miscibility and drug-polymer interactions): The mole-fraction solubility a crystal would have if it mixed ideally (γ = 1) is fixed by its heat of fusion, melting point and the heat-capacity difference between liquid and crystal, which enter the equation as integrals from the melting point to the temperature of interest; the real solubility is this value divided by the activity coefficient marsac2006b E5; marsac2009 E1, C4. High melting point and high heat of fusion lower the solubility in any solvent or polymer, so drugs with these properties and no strong polymer interaction "will display very low solubility" and "will most likely be harder to stabilize" marsac2006b C52, C53, C54. New aspects (Physical stability): the lattice term of the solubility equation separated the two dihydropyridines: nifedipine's larger term (higher heat of fusion and melting point) makes its crystal less soluble in NMP although both drugs mix exothermically with it marsac2008a R11, C35.

Findings

PEG dispersions: F3, F11. Miscibility and drug-polymer interactions: F8, F9. Physical stability: F2.

Related concepts

measured by enthalpy of fusion; part of activity coefficient; depends on crystal lattice energy; related to drug solubility in polymer and cosolvency.

Formulas

activity coefficient from solubility; solid-liquid equilibrium solubility equation.

How it is measured or obtained

Calculated from DSC melting data (heating at 10 °C/min in pin-holed pans; or the melting point and heat of fusion of Table 1) marsac2008b P8, P9; baird2011 E7. The mole-fraction values of Marsac and co-workers are printed without the relation or the temperature, and the extractor recomputed them at 25 °C from the melting data marsac2008b E1, X5. In the miscibility papers the heat-capacity terms are cited and not printed, and for ketoconazole the heat-capacity difference was approximated by its value at Tg, integrated between Tg and Tm; the ideal solubilities themselves are not printed marsac2009 P7, X4; marsac2006b X11. In the 2008 NMP study the lattice term is obtained from the measured mole-fraction solubility and the activity coefficient, as the first term of \ln x = -\frac{\Delta H_{fus}}{RT}\left(1 - \frac{T}{T_M}\right) - \ln\gamma marsac2008a E3.

Values in the library
materialvalue or classconditionspaper ids
acetaminophen, ketoprofen, naproxen, ibuprofen, felodipine, ketoconazole0.02, 0.10, 0.01, 0.18, 0.03, 2.0 × 10⁻³ mole fraction as printed; extractor's values at 25 °C 0.020, 0.097, 0.0047, 0.18, 0.023, 0.0016from melting datamarsac2008b R14, X5
loratadine in PEG 400about 0.109 ideal against 0.046 measured25 °C, Table 1 inputsbaird2011 X13, R9.c
nifedipine; felodipineΔHfus 39.89 and 30.83 kJ/mol; Tm 445.25 and 414.75 K (inputs)DSCmarsac2006b M1, M2
indomethacin; ketoconazole; sucroseΔHfus 39.68, 54.10, 44.70 kJ/mol; Tm 432.93, 421.25, 448.84 K (inputs)Table II of the 2009 papermarsac2009 M6, M3, M5
itraconazole; ibuprofenΔHfus 56.70 and 24.11 kJ/mol; Tm 438.35 and 347.88 K (inputs)as abovemarsac2009 M4, M7
nifedipine against felodipinethe lower-melting, lower-ΔHfus felodipine is predicted more soluble in PVP (0.25–0.31 against 0.06–0.07 g/g)with χ −4.2 and −3.8marsac2006b R17, C52
nifedipine; felodipinelattice term ≈−5.3; ≈−3.5 (natural-log units)25 °Cmarsac2008a R11
Pitfalls and disagreements

The temperature of the printed ideal solubilities is not stated, the naproxen row is not consistent with its coefficients (they fit about 0.0045, not 0.01), and the two coefficients printed for felodipine fit different ideal solubilities marsac2008b X5. The naproxen Tg used in the same paper does not follow from the Tg/Tm rule it cites marsac2008b X4. The temperature and the heat-capacity values of the 2006 Table II are not printed, and under recomputation with the heat-capacity terms set to zero one value (felodipine in PVP K29/32) does not match marsac2006b X11. The two-drug comparison of melting properties is confounded by the different χ of the two drugs marsac2006b X13. The melting temperatures of Table II lie 2–3 °C below the plotted pure offsets, so χ cannot be recomputed from the table alone marsac2009 X4. Melting data of the two dihydropyridines are not printed in the 2008 NMP paper; the lattice terms are derived from the solubility data marsac2008a E3.

← Concepts and formulas

concept · as used in PEG dispersions

in situ salt formation

Evidence table: in situ salt formation. Content from the ASD dissolution chapter (delamanid 2022–2023).

Forming the drug salt in the same solution and evaporation or drying step that forms the dispersion, so that drug, counterion and polymer are processed together and the dispersion contains the protonated drug. It was used to keep a fast-crystallizing weak base amorphous at a drug loading at which the free base left crystals behind: the salts have a much higher Tg, and the authors "speculate" that protonating the piperidine ring keeps the long, thin molecules from lining up into a crystal [duong2022a P8, C50]. Salts inside dispersions were rare before, with meloxicam–meglumine and naproxen–meglumine formed during melt extrusion [duong2022a C6]. The counterion is added at a 1:1 molar ratio to the spray-drying or evaporation solution, and alcohols are avoided with sulfonic acids to prevent sulfonate esters [nguyen2023b P1, C13; duong2022a C8].

Findings

F23, F25, F27.

Related concepts

raises the Tg of an amorphous salt; prevents residual crystallinity from preparation; limited by salt disproportionation and plasticization by water; read with crystallization tendency.

Formulas

none.

How it is measured or obtained

Salt formation is confirmed by the downfield shift of the protons at the basic nitrogen in the proton NMR spectrum and by a broad N+–H band in the infrared spectrum, with the free-base band gone; the solid is then characterized by PXRD, DSC and water sorption, and stored at 40 °C/75% RH [duong2022a R16, R17, P6, P13].

Values in the library
materialvalue or classconditionspaper ids
eight delamanid sulfonate salts, neatseven amorphous, Tg 83.7–117.8 °C against 43.3 °C for the free base; water uptake 5.8–21.1% at 95% RH; four liquefied on storage2 weeks at 40 °C/75% RH[duong2022a R20]
delamanid edisylate 1:1 with excess acidTg 53.9 °C and 59% water uptake, against 117.8 °C and 11.6% for the 2:1 salt95% RH[duong2022a R21]
salt dispersions at 20% drug with HPMCASTg 100.4–117.0 °C against 86.7 °C for the free base; water uptake ≈10–13.6% against ≈8.2%95% RH[duong2022a R23, R22]
four salt dispersions at 25% drug with HPMCP against the free base≈95–97 against ≈20 µg/mL at pH 6.5; ≈85–91 against ≈55 µg/mL after a pH shifttablets, 100 µg/mL = complete[duong2022a R26]
delamanid edisylate dispersions with HPMCP, 10–40% drug≈99 / ≈98 / ≈95 / ≈59 / ≈21 µg/mL of 100PBS pH 6.5, 37 °C[duong2022a R24]
chloride and edisylate dispersions with HPMCP-50, uncoated tablets≈86 and ≈93 µg/mL after a pH 1.6 stage against ≈62 µg/mL for the free basepH 1.6 → 6.5[nguyen2023b R2]
Pitfalls and disagreements

No PXRD of any salt dispersion and no storage data for salt dispersions appear in the main text, so the crystal-free state is asserted rather than shown, and the free-base and salt dispersions were cast from different solvents with an unstated drug-loading basis [duong2022a X8, X7, X6]. The salt does not stop crystallization where the polymer stays undissolved: salt dispersion films crystallized at pH 3.0 like the free base, and the salt "only partially remediated" the pH dependence [nguyen2023b C17; nguyen2023c C20]. Three of the four salts chosen for their stability liquefied at 40 °C/75% RH, and release of several salt dispersions was lower after an acid stage than in a single stage [duong2022a X19, C63].

← Concepts and formulas

concept · as used in PEG dispersions

intramolecular hydrogen bonding

A hydrogen bond between two groups of the same molecule

It matters for polymer selection because it removes a donor or acceptor from the pool available to the polymer: the sulfonamide NH of nimesulide bonds to its own ether oxygen, which the authors say "considerably diminished" its capacity to bond to polymers and "most likely" explains why the polymers differ less than anticipated [kestur2011 C20, C27, C28]. Flufenamic acid holds its aniline N–H in a resonance-assisted hydrogen bond (N···O 2.682 Å in form III and 2.646 Å in form I, against a range of 2.66–2.74 Å for such bonds) and is therefore regarded as interacting only through its acid group vaneerdenbrugh2010b R12, C12. Further cases: the 5-OH and keto group of naringenin and the 5-OH and 3-OH of quercetin, which leave two and three phenolic OH groups free for the polymer [wegiel2013a M1, M2, C30]; the aniline N–H of flufenamic acid (DFT) and the energy profile of anthranilic acid, where one aniline hydrogen stays free [vaneerdenbrugh2011a R5, R6, C18]; and the OH of lumefantrine, bonded to its own nitrogen in the crystal [hiew2022a R33, C61].

Findings

Miscibility and drug-polymer interactions: F14, F15, F17, F24, F25, F26. Physical stability: F18, F24.

Related concepts

part of hydrogen bonding; limits drug-polymer interactions and hydrogen-bond donor and acceptor groups; contrasts with self-association; makes acid-base interaction the alternative [wegiel2014 C44].

Formulas

none.

How it is measured or obtained

By a donor band that stays at the same wavenumber on a 100-fold dilution in a non-polar solvent (nimesulide NH at 3345 cm⁻¹, 1–100 mg/ml); by no change on adding a strong acceptor or donor (1-ethyl-2-pyrrolidinone, acetic acid); by comparing the band of the amorphous and crystalline forms; by crystal structure and DFT geometry [kestur2011 R10, R11, R12, R17, R19]. For flufenamic acid, from N···O distances in two crystal structures vaneerdenbrugh2010b P11, R12. By a conformer energy profile of the single molecule in vacuum [trasi2012b P9, R24]; by an IR band of the amorphous drug that matches the intramolecularly bonded form of the crystal [wegiel2014 R2, C11].

Values in the library
materialvalue or classconditionspaper ids
nimesulideNH 3345 cm⁻¹ at 1–100 mg/ml in dichloromethane; unchanged with added acid or lactamIR, 100 µm cell[kestur2011 R11, R17]
nimesulideNH ≈3288 (crystal), ≈3276 cm⁻¹ (amorphous)KBr; spin-coated film[kestur2011 R12]
flufenamic acidN···O 2.682 Å (form III), 2.646 Å (form I)crystal structuresvaneerdenbrugh2010b R12
flutamide; curcumin (other chapters)intramolecular CH···O leaves a poor acceptor; intramolecular bond limits polymer bondingcalculation; IR, stability[trasi2012b C35; wegiel2014 C3]
naringenin, quercetin5-OH to keto O (both); 3-OH to keto O (quercetin); PVP still bonds the free OH (OH band 3138 and 3135 cm⁻¹)structure; IR[wegiel2013a M1, M2, R2]
anthranilic acidenergy about 31–33 kJ/mol up to 30° (acid O–H to N), about 50 at 80–90°, about 0 at 180° (N–H to carbonyl O); no bifurcated bondDFT dihedral scan[vaneerdenbrugh2011a R6, C18]
lumefantrineOH···N bond in the crystal; no PVPVA carbonyl shiftcrystal structures (cited); IR[hiew2022a R33, R17]
flutamideplanar lowest-energy conformer with the carbonyl next to C(5)–H; second minimum ≈2.7 kJ/mol higher; barriers ≈23 kJ/molDFT, vacuum[trasi2012b R23, R24]
flutamide crystalamide carbonyl in a bifurcated bond, one contact intramolecularcited structure[trasi2012b R26]
amorphous curcuminketo–enol band at 1626 cm⁻¹ as in the crystal; no carbonyl band near 1700 cm⁻¹IR[wegiel2014 R2, C11]
curcumin against resveratrol with PVPbonded PVP carbonyl dominant only at 60% curcumin, already at 50% resveratrolIR of films[wegiel2014 R8, R9, C32]

Evidence table: intramolecular hydrogen bonding.

Pitfalls and disagreements

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

← Concepts and formulas

concept · as used in PEG dispersions

kinetic barrier to nucleation

The activation energy for moving molecules across the nucleus–matrix interface, \Delta G_a in classical nucleation theory, related to diffusivity or reciprocal viscosity; distinct from the thermodynamic barrier set by interfacial energy and driving force [konno2006 E8, C33; marsac2006a E9, C31]. Experimentally the Arrhenius activation energy of the nucleation rate is used as its measure [marsac2006a R3, E2].

Findings

F1, F2, F4.

Related concepts

part of classical nucleation theory; contrasts with thermodynamic driving force for crystallization; related to molecular mobility and polymer rejection at the crystal growth front.

Formulas

classical nucleation theory, Arrhenius equation.

How it is measured or obtained

Not measured directly; nucleation rates at several temperatures give an Arrhenius slope, taken separately above and below Tg [marsac2006a P5, R2, R3]; otherwise argued from the size of a polymer effect at low content [konno2006 C40, C41].

Values in the library
materialvalue or classconditionspaper ids
nifedipine, felodipineactivation energy below Tg 122 (11) and 145 (3) kJ/mol; above Tg 78 and 95Arrhenius, ≈25–75 °C[marsac2006a R3]
with 3 wt% PVPbelow Tg 127 and 201; above Tg 103 and 111 kJ/molsame[marsac2006a R3.c, R3.d]
felodipine with 3–25% PVP, HPMCAS, HPMCspeculated rise of ΔGa, set by amount rather than type of polymer22 °C, dry[konno2006 C40, C41]

Evidence table: kinetic barrier to nucleation.

Pitfalls and disagreements

The Arrhenius plot carries no rate unit and its temperatures are given only by the axis; the activation-energy difference between the two drugs is significant only below Tg, a restriction the abstract drops [marsac2006a X2, X6]. The polymer-raised barrier is speculation ("it seems reasonable to speculate") [konno2006 C40].

← Concepts and formulas

concept · as used in PEG dispersions

kinetic stabilization

Stabilization of an amorphous drug against crystallization by slowing the process (molecular mobility, nucleation, interfacial factors) while the thermodynamic driving force stays large. Marsac and co-workers conclude from a small predicted reduction of the driving force, a low predicted solubility in PVP and the faster nucleation of the pure drugs that inhibition "can therefore be attributed predominantly to a kinetic stabilization"; molecular-level miscibility is "of critical importance" because it alters "thermodynamics and, more importantly, dynamics" marsac2006b C41, C42, C55, C56, C59. The same group states that thermodynamically stable dispersions are hard to achieve and that apparent stability is "most likely achieved through modification of the kinetics" marsac2009 C34. For the growth of felodipine with PVP the effect "is believed to be kinetic rather than thermodynamic" [kestur2010b C28].

Findings

F9.

Related concepts

contrasts with thermodynamic driving force for crystallization; depends on drug solubility in polymer; related to crystallization inhibition and amorphous solid dispersion.

Formulas

Hoffman equation.

How it is measured or obtained

Not measured directly in this chapter. It is inferred by elimination: the thermodynamic estimates (Hoffman driving force, predicted solubility) are small or low, while the dispersions stay amorphous marsac2006b R12, R17, X12; marsac2009 R11, X17. Kinetic quantities (nucleation rates, mobility) are cited from a companion study or not measured marsac2006b R16, C59.

Values in the library
materialvalue or classconditionspaper ids
nifedipine with 40% PVPdriving force −7.95 against −9.0 kJ/mol pure at 20 °CHoffmanmarsac2006b R12
nifedipine, felodipine in PVPpredicted solubility 0.06–0.07 and 0.25–0.31 g/gFlory–Hugginsmarsac2006b R17
five compounds in PVP K29/3282–99% of the drug above solubility at 0.50 polymerpredictedmarsac2009 R11
pure nifedipine and felodipine against their dispersionsnucleation much faster for the pure drugscitedmarsac2006b R16

Evidence table: kinetic stabilization.

Pitfalls and disagreements

The kinetic reading is an inference: no crystallization, nucleation or mobility data are reported in either paper marsac2006b X12; marsac2009 X17. Being below the estimated solubility did not make PEG dispersions stable, which points to nucleation by the carrier as another route zhu2012 X13. A small dissolved fraction may explain why crystallization of a dispersion is not always complete marsac2009 C35.

← Concepts and formulas

concept · as used in PEG dispersions

kinetic versus thermodynamic control of crystal growth

Growth of a crystal from a supercooled liquid needs both mobility and a driving force: near Tm mobility is high and the driving force low (thermodynamic control), and on cooling the driving force rises while mobility falls (kinetic control) [mosqueragiraldo2014 C25]. Felodipine growth that slowed on cooling over 70–110 °C was read as transport-limited [kestur2010b C22, C23]. In the indomethacin polymorph paper mobility limits growth below the temperature of fastest growth and the driving force above it, and the steep rise of polymer inhibition above that temperature is placed in the second region [tian2017 C22, C35, C36].

Findings

F3, F22, F29.

Related concepts

depends on thermodynamic driving force for crystallization and molecular mobility; related to melting point depression and degree of supercooling; contrasts with Tg-scaled crystal growth rate.

Formulas

temperature of maximum crystal growth rate.

How it is measured or obtained

From where growth peaks between Tg and Tm and from how an additive's effect changes with temperature [trasi2012a C35; mosqueragiraldo2014 C36].

Values in the library
materialvalue or classconditionspaper ids
celecoxib with 10% TPGS and 10% PVPcelecoxib Tm 151.49 °C (12 °C depressed); growth about 0.03 of PVP alone at 120 °C, 0.6 at 70 °Cseeded melt growth[mosqueragiraldo2014 R5.f, R2.b, X5]
celecoxib with 3, 5, 7% PVP, with and without TPGSpaired curves cross at 110, 100, 90 °Csame[mosqueragiraldo2014 R3, R4, C14]
felodipine form IIgrowth falls on cooling from 105 to 70 °C although the driving force risesmelt films[kestur2010b C22, C23]
acetaminophengrowth maximum closer to Tm, nucleation at larger supercoolingclassical picture[trasi2012a C35]
indomethacin α with 10% HPMCfastest growth moved from 135 to 100 °C; ratio without/with polymer ≈11 (100 °C) → ≈2900 (120 °C)melt growth[tian2017 R15, R12]
Pitfalls and disagreements

The driving force was not calculated for the celecoxib mixtures, and melting-point depression alone does not order them [mosqueragiraldo2014 C33, X13]. The celecoxib growth temperatures were assumed to lie in the mobility-controlled range [mosqueragiraldo2014 C26].

← Concepts and formulas

concept · as used in PEG dispersions

liquid-liquid phase separation

The splitting of a highly supersaturated aqueous drug solution into a water-rich continuous phase and a dispersed, non-crystalline drug-rich phase, before crystals form; the authors call it glass–liquid phase separation when the drug-rich phase is a glass [ilevbare2013a C2; indulkar2015 C38]. The concentration at which it starts is called the LLPS concentration, CL-L or coexistence concentration, and in this chapter equals the amorphous solubility within the accuracy of the methods [ilevbare2013a C14, C3]. It was earlier discussed as "promiscuous aggregation" in screening assays and as "oiling out" in crystallization [ilevbare2013a C7, C9, C35]. The papers of 2017–2022 add a weak base shifted from simulated gastric fluid to pH 6.5: pazopanib gave a milky, bluish solution at once, with particles of 495.9 nm (145.4 nm with 50 µg/mL HPMC) and no particles at a dose below its amorphous solubility [sugihara2018 R14, R15, R20], and ibuprofen droplets that measured 3182–5313 nm in buffer and 268–345 nm with HPMC or PVP-VA [ueda2020b R5]. New aspect (Bioperformance): the two phases are in metastable equilibrium with equal activity [raina2014a C3, C4, C33; indulkar2016 C1; hate2018 C5]. For high-Tg drugs such as telaprevir the term glass–liquid phase separation is used [mosqueragiraldo2018b M1]. Drug-rich spheres were also found by SEM in pooled human intestinal fluid, the first such demonstration according to the authors [elkhabaz2019b R4, C24]; a crystalline co-drug lowers the concentration at which atazanavir separates [alkalla2026 C2]. New aspect (Supersaturation from ASD dissolution): dispersion dissolution, unlike dissolution of a neat amorphous drug, can push the concentration past the amorphous solubility, so that LLPS follows dissolution and precedes crystallization [jackson2015 C7, C29]; the colloids of rapidly dissolving ritonavir dispersions "highly likely" originate from LLPS [ilevbare2013d C33].

Findings

Amorphous solubility and LLPS: F1, F2, F3, F4, F5, F8, F9, F11, F13, F15, F16, F22, F23. Bioperformance: F1, F2, F4, F5, F10, F18, F19, F27. Supersaturation from ASD dissolution: F7, F9, F10.

Related concepts

produces the drug-rich phase; special case glass-liquid phase separation; sets the amorphous solubility; described by the binodal and spinodal decomposition; grows by droplet coalescence; precedes crystallization (a precursor, F3). Produces drug-rich nanodroplets; related to metastable equilibrium.

Formulas

binodal condition, amorphous solubility advantage with water-sorption correction, ideal-mixing reduction of amorphous solubility.

How it is measured or obtained

By extinction at a non-absorbing wavelength during slow addition of a drug stock, by a polarity-sensitive probe or the drug's own fluorescence, by DLS or NTA sizing of the droplets, by ultracentrifugation of the phases, by NMR of dissolved drug, by a flux break, and by a solvent-free pH-shift titration for weak bases [ilevbare2013a P5, P10, P11; almeidaesousa2015 P1, P2; mosqueragiraldo2015 P10; trasi2015a P6; indulkar2015 P10] (F4). In the Bioperformance papers: rise of extinction on solvent shift; turbidity without birefringence under polarized light [raina2014a R4, C12]; droplet size and number by NTA or DLS [indulkar2016 P4; hate2018 R6, R7]; the 369 nm fluorescence band of atazanavir [hate2018 P6, C18]; the flux plateau; antisolvent titration read by 450 nm extinction [alkalla2026 P7, C16]; the drug's own fluorescence intensity and SEM of the centrifuged pellet [elkhabaz2019b R3, R4, C17]. During dispersion dissolution: the pyrene ratio, with the onset read as the UV concentration at the pyrene drop; stepwise dissolution with dilution; turbidity titration with polymer present [jackson2015 P3; ilevbare2013d P4, P2].

Values in the library
materialvalue or classconditionspaper ids
ritonavir dropletsabout 345 nm at 1 min, about 842 nm at 64 minwater, 37 °C, single addition at the onset[ilevbare2013a R3]
ritonavir drug-rich phase94.85–95.97% drug, 4.03–5.15% water, Tg 0.4 °C10–50 °C, ultracentrifuged[ilevbare2013a R5, R6]
weak-base dropletsZ-average about 116–387 nmclotrimazole, atazanavir, nicardipine, 37 °C[indulkar2015 R14]
telaprevirspecies about 300 nmpH 6.8, 37 °C[mosqueragiraldo2015 R5]
ritonavir dropletsabout 360 nm at 30 µg/mL100 mM pH 6.8, 25 °C[trasi2015a R15]
pazopanib colloids495.9 nm without, 145.4 nm with 50 µg/mL HPMC (DLS); NTA about 50–650 nmpH 6.5 after pH shift, 37 °C[sugihara2018 R15, R16]
ibuprofen droplets3182–5313 nm (buffer); 272–345 (HPMC); 268–320 (PVP-VA); 472–808 nm (EUD-E)pH 2.0 (D2O), 37 °C, fresh[ueda2020b R5]
felodipineonset 5.70–13.4 µg/mL20–45 °C, buffer[raina2014a R1]
nifedipineLLPS only with 1 mg/mL HPMC: 30.86–88.89 µg/mL20–45 °C[raina2014a R1, R5]
clotrimazoleonset 7.5 µg/mL; droplets 111–257 nmpH 8[indulkar2016 R2, R4]
atazanavir78 µg/mL; droplets 204–226 nmpH 6.8[hate2018 R2, R6]
ritonavironset about 38 µg/mL in waterUV extinction[ilevbare2013a R2]
enzalutamideonset about 42 µg/mLpH 6.5, 37 °C[wilson2018 R2, C16]
atazanavir, darunavir93.1 and 363.8 µg/mL (antisolvent, 450 nm)pH 6.8, 37 °C[alkalla2026 R3, C16]
pretomanidabout 166 µg/mL in buffer, 308 in FaSSIFpH 6.5, 37 °C[nguyen2023a P2, R2]
danazol dispersions (eight)onset about 6.0–10.4 µg/mL against 8 µg/mLpH 6.8, 25 °C[jackson2015 R5, M1]
ritonavir–PVP dispersion, stepwiseonset between 10 and 20 µg/mL37 °C[ilevbare2013d R1, X8]
ritonavir, 180 µg/mL PVP / PAA / HPMC / HPMCAS / CAAdP 0.8518.3 / 18.3 / 18.7 / 18.2 / 21.3 µg/mL (18.2 without)titration, 37 °C[ilevbare2013d R10]
Pitfalls and disagreements

Extinction alone cannot tell droplets from crystals, and a fast crystallizer may crystallize before it phase separates (griseofulvin without polymer) [almeidaesousa2015 C16, C18]. The ritonavir phase diagram rests on four binodal points between about 11 and 29 °C [ilevbare2013a X17]. Droplet size grows with time by coalescence and varies with drug and technique [ilevbare2013a R3, C18]. In SDS the 369 nm band that marks the atazanavir drug-rich phase in buffer appears from about 200 µg/mL, far below the amorphous solubility of about 1450 µg/mL, so a spectral marker has to be checked in the micellar medium [indulkar2017a R17, R18, C27]; extinction rose on the first addition to STCDC and SGCDC without visible turbidity [lu2017b R4]. LLPS is seen only if nucleation is slow compared with phase separation; the metastable zone for LLPS is "small" by the authors' reading [raina2014a C30, C32]. Turbidity does not tell LLPS from crystallization without a crystal-specific method [elkhabaz2017 C30]. Above the onset an inhibitor can still fail: pretomanid with HPMCAS-HF crystallized within minutes in the presence of droplets (F27) [nguyen2023a R7, C13]. A polymer in the droplets lowers the onset (F19) [ueda2020a R1, C13]. In the danazol dispersion study the overshoot above the amorphous solubility before LLPS was inferred from UV, which is unreliable there [jackson2015 X12]; a slowly releasing dispersion (50:50 HPMCAS danazol) never reached it [jackson2015 C33].

← Concepts and formulas

concept · as used in PEG dispersions

matrix crystallization

Crystallisation of the amorphous solid itself while it is in contact with the medium, before the drug has dissolved (also called solid-mediated crystallisation), in competition with dissolution and with crystallisation from solution [moseson2021 C1, C27]. Bicalutamide–PVPVA is the case in point of the ASD process papers: a hydrated, polymer-depleted, drug-rich solid that is "likely" below its Tg at 37 °C becomes mobile enough to crystallise in place, a surface-driven reaction triggered by hydration and polymer loss [moseson2021 C55, C56, C59]. Moseson (2022) tested the route across loadings: bicalutamide–PVPVA at 5 and 10% loading released drug and polymer together and escaped it, whereas 20–50% loading, cryomilling and cryomilled surfactant-containing powders raised the risk. The authors call it surface-mediated: a polymer-depleted, drug-rich boundary layer forms, crystallizes and "could prevent release" [moseson2022b C36, C39, C43, R6, R7]. In posaconazole–HPMCAS at 50% loading a 12 nm coating went with a much lower SHG signal after 3 h and higher release, which the authors suggest is a delay of matrix crystallization [moseson2023 R15, R18, C40]. New aspect (Bioperformance): crystallization inside the undissolved ASD particle during dissolution, as against crystallization from solution [mosqueragiraldo2018b C40; elkhabaz2017 C34]. The poor exposure of the 10% enzalutamide–HPMCAS dispersion was attributed to rapid matrix crystallization on contact with water; the printed evidence is crystals in the medium and a 10 µg/mL maximum [wilson2018 C56, X11]. New aspect (Supersaturation from ASD dissolution): in the first study of the two routes it is called "crystallization from matrix": the amorphous particle converts to crystal on contact with the medium, against nucleation and growth from the supersaturated solution [alonzo2010 C43, C47]. If it is faster than dissolution, no concentration above that of the crystal can be reached, because the crystal is what dissolves [alonzo2010 C33]. The papers of 2015–2018 show that the dispersion polymer and its share decide it: resveratrol dispersions needed 80–95% cellulosic polymer to stay amorphous in buffer, PAA failed for celecoxib "irrespective of the drug loading", and an inhibitor dissolved in the medium cannot reach it [wegiel2015 R14; xie2016a C33, C31; xie2015 C35].

Findings

ASD process: F27, F28, F29, F38, F39, F40, F41, F46. Bioperformance: F9, F11, F12, F23, F26, F27, F30. Supersaturation from ASD dissolution: F1, F2, F3, F16, F24, F27.

Related concepts

contrasts with desupersaturation; accelerated by residual crystallinity; not blocked by crystallization inhibition by polymers in solution; accompanies incongruent release and surface drug enrichment; related to surface crystallization; avoided by congruent release; fed by the drug-rich surface layer; delayed by an atomic layer coating in one posaconazole system. Contrasts with solution crystallization; favoured by drug loading; part of crystallization during dissolution; related to plasticization by water.

Formulas

None specific; the competition with dissolution is set out with the Noyes-Whitney equation [alonzo2010 E3].

How it is measured or obtained

Time-lapse polarised light microscopy of particles in buffer, in-line Raman of a slurry resolved by MCR-ALS, XRPD and SEM of recovered solids, polymer release by size-exclusion chromatography, and dissolution at several doses read for plateaus below the amorphous solubility and a falling fraction dissolved [moseson2021 P14, P15, P16, R17, R18, R19]. SEM, SEM-EDX (fluorine occurs only in the drug, F/F0) and confocal fluorescence of compacts exposed face down to medium for 5–60 min; Raman slurries resolved by MCR-ALS for the form 2 time course [moseson2022b P12, P14, P15, P16, P17]. SHG of particles after 3 h in buffer [moseson2023 R18]. Polarized light microscopy of particles in buffer [mosqueragiraldo2018b R18]; SHG [elkhabaz2017 P10]; indirectly, a flux ceiling not reached [mosqueragiraldo2018b R16]. In the ASD dissolution papers: in situ Raman of aqueous slurries with a PLS model for crystallinity or marker bands, PXRD of wetted powder after 15 min, and polarized light microscopy of wetted particles [alonzo2010 P5, P6, P8; raina2014b P4, P6, P10]; the 1630/1605 cm−1 Raman ratio of resveratrol slurries, also in a medium where the enteric polymer does not dissolve (pH 1.2) [wegiel2015 P7, A3]; the amorphous Raman shoulder near 1598 cm−1 of celecoxib slurries [xie2015 P3, R3]; polarized light of residues retrieved after the release peak [xie2016a P6].

Values in the library
materialvalue or classconditionspaper ids
BCL–PVPVA 30:70, crystal-freeform 2 begins at 20–30 min (half conversion about 36 min); plateau about 37–38 µg/mL against an amorphous solubility of 150 µg/mL60 and 150 µg/mL doses, pH 6.8[moseson2021 R12, R13, R19]
BCL–PVPVA with residual or added form 1 crystalsform 1 first detectable at about 15 min (S/155), 7 min (M/155), from the first spectrum (10% seeds)Raman slurry, 10 mg/mL[moseson2021 R21]
amorphous nifedipine (outside)crystallises mainly by the matrix route within about 10 min; PVP, HPMC or HPMCAS in solution do not change onset or routebuffer, 25 °C[raina2014b C10, C11]
celecoxib dispersions (outside)polymers dissolved in solution cannot inhibit crystal formation in the matrixhigh drug loading[xie2015 C35]
telaprevir 50% HPMCAS (outside)slow, incongruent release; HPMCAS leaves about twice as fast as the drug, leaving a drug-rich layeroptical micrographs[mosqueragiraldo2018b C40, C43]
enzalutamide 10:90 HPMCAS (outside)rapid matrix crystallisation on contact with waterdissolution[wilson2018 C56]
posaconazole ASDs in acid (outside)matrix crystallisation about 68% at 50% DL, about 0.05% at 25% DLSHG over TPE-UVF, 30 min[elkhabaz2019a R20, C38]
BCL–PVPVA 5 / 10 / 20 / 30 / 50% DL powdersend level about 91 / 96 / 88 / 86 / 73% of the dose; polymer ahead of drug from 20% DLdose of at most 30 µg/mL, pH 6.8[moseson2022b R6, R7]
30% and 50% DL compacts, 1 hdrug-rich boundary layer of 94 ± 8 µm with crystals (F/F0 1.41 ± 0.10); 5–10 µm crust of crystalsSEM-EDX[moseson2022b R15]
30% DL cryomilled 2 and 5 minabout 50 and 49% of the dose, plateau about 15 µg/mLsame[moseson2022b R4]
10% DL after 10 min of cryomilling or extrusion and 30 s of millingabout 93% of the dosesame[moseson2022b R8]
30% DL with 3% TPGS, cryomilled 5 minstops at about 60% (about 18 µg/mL)same[moseson2022b R12]
50% PCZ–HPMCAS, small particles, uncoated against 12 nm Al2O3SHG 126.7 against 3.7; about 3.35 against 5.1 µg/mL at 3 hsingle stage, pH 6.5[moseson2023 R18, R15]
telaprevir 50% HPMCAS ASDbirefringent domains in the particle at 20 min; 0.65 µg/minpH 6.8[mosqueragiraldo2018b R16, R18]
telaprevir 47.5:47.5:5 SDS ASDnone visible; 1.07 µg/minsame[mosqueragiraldo2018b R16, R18]
ezetimibe PAA ASDcrystals within minutes, inferred from the matrixbuffer, FeSSIF[elkhabaz2017 C34, R12, R16]
posaconazole ASDs 10 / 25 / 50%SHG crystallinity 0.3–0.4 / 3–4 / 19–26%60 min FaSSGF[shah2024 R21]
posaconazole ASDs50% DL final crystallinity about 250 times that of 25% DL[elkhabaz2019a R18]
enzalutamide 10:90 HPMCAS-MF ASDpeak about 10 µg/mL, crystals in the mediumpH 6.5, 100 µg/mL total[wilson2018 R6, C56]
pretomanid HPMCAS-HF ASD tabletscrystalline drug in the particles after FeSSIF at pH 5.5 and below, and after a 1 h gastric stagePXRD and SEM, 30 mg in 150 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 medium50% crystalline at ≈20.5, ≈18.5, ≈13.5 min37 °C[alonzo2010 R6]
neat amorphous indomethacinα form present at 90 min, like pure α at 120 minpH 2, 37 °C[alonzo2010 R12]
nifedipine 50:50 dispersions (PVP shown)particles not birefringent; crystals form in the solutionpH 6.8[raina2014b R13, X18]
nifedipine–HPMCAS 50:50 at pH 2matrix amorphous for 3 hpolymer barely soluble[raina2014b R15]
celecoxib–HPMCAS 33.3% particles in pH 3 suspensioncrystals on or in particles after about 7 days (Triton X100), none in 48 h25 °C[chen2015a R20, R14]
resveratrol 35% with HPMC / HPMCAS / CMCABRaman ratio ≈0.87 / ≈0.84 / ≈0.81 (crystal 0.76) within hourspH 6.8, 37 °C[wegiel2015 R9]
resveratrol, minimum polymer to prevent it80% HPMC, 85% HPMCAS, 95% CMCABpH 6.8, 37 °C[wegiel2015 R14]
neat amorphous celecoxibcomplete within an hour; crystals on the particles from 2 minpH 6.8, 37 °C[xie2015 R4, R8]
celecoxib–PVP-K12 50%crystalline within 4 h in a slurrypH 6.8, 37 °C[xie2015 R4]
celecoxib–PAA 5:5 and 1:9, HPMCAS in the mediumrelease stopped at about half; needles in the residuepH 6.8, 37 °C[xie2016a R9, R10]
lopinavir 50% with EUD, CAP / HPMCPcrystals by 8–16 h / none at 48 hpH 3, 25 °C[li2018 R7]
delamanid salt dispersions, films after 1 h in acidclear at pH 1.6 (HPMCP); crystals at pH 3.0 on all but HPMCP-55; small crystals on every film at pH 5.025% drug, 37 °C[nguyen2023c R19]
same, powderspitted, porous HPMCAS surfaces with agglomerates increasing with pH; HPMCP-50 covered at pH 5.01 h in acid[nguyen2023c R18]
delamanid dispersions in HPMCP, films with and without a 2 µm Eudragit L 100-55 layerstar- and needle-shaped crystals on every uncoated film; none under the layerpH 3.0, 1 h[nguyen2023b R3, R6]
posaconazole–HPMCAS dispersionscrystals by SHG in every system after 30 min in FaSSGF, more numerous after transfer37 °C[elkhabaz2019a R16]
Pitfalls and disagreements

The hydrated-solid mobility mechanism was not measured (the wet Tg of amorphous bicalutamide could not be determined) and the kinetics come from slurries far above the dose concentrations [moseson2021 R27, X8, X11]. Attribution to the matrix route is often inferred: crystals could instead nucleate in the concentrated boundary layer around the dissolving particles, or the evidence is crystals in the medium and a low maximum without a solid-state analysis [xie2016a X6; wilson2018 X11]. Solution-mediated growth is not absent at high dose [moseson2021 X4]. The results and the discussion of the 2022 study disagree on whether 20–30% loading crystallized, the crystals of the compacts were identified by shape and not by diffraction, and the polymer-depleted state of the crust is inferred from a dye [moseson2022b X14, X16, X18]. The Tg and composition of the hydrated layer were not measured [moseson2022b C60]. One micrograph without XRPD supports the telaprevir case [mosqueragiraldo2018b X13]. Matrix and solution crystallization were not separated for enzalutamide: no solid-state analysis of the wetted dispersion is shown (F9) [wilson2018 X11]. In the ASD dissolution papers, slurries held far more solid per unit of polymer than dissolution vessels (about 500–750-fold for felodipine), so their lag times rank systems but do not give the time scale in dissolution [alonzo2010 X5]. The proposal that crystallization starts at the particle surface and that dissolved polymer delays it there was not tested [alonzo2010 C36]. For felodipine at 25 °C the fall after the peak may come from the matrix as well as from solution [alonzo2010 X6]. The PVP-K12 celecoxib dispersion crystallized in a slurry yet released fully in dissolution [xie2015 R4, R6]. PXRD found no crystals in delamanid dispersion powders after 1 h in acid, a method that detects about 1–5% crystallinity, so the crystal mass that harmed release was small [nguyen2023c R15, R16, C46].

← Concepts and formulas

concept · as used in PEG dispersions

melt viscosity

The steady-shear viscosity of a drug melt at Tm (ηmelt) and below it in the undercooled range; its rise on cooling is expressed as the ratio \eta/\eta_{melt} [baird2012 P1, E7]. It stands for the molecular mobility that nucleation and growth need [baird2012 C4].

Findings

F5, F12.

Related concepts

measures molecular mobility for crystal growth rate and nucleation; used to obtain fragility; related to Tm − Tg temperature gap and glass-forming ability.

Formulas

Vogel-Tammann-Fulcher equation, linear fit of melt viscosity on Tm − Tg.

How it is measured or obtained

Parallel-plate rheometry at 30 s⁻¹, stepwise from Tm downward with remelting between steps [baird2012 P1]; fitted with the VTF equation [baird2012 P5]; in drug–polymer melts by the same method [tian2017 R13].

Values in the library
materialvalue or classconditionspaper ids
benzamide2.86 × 10⁻³ Pa·s, the lowestat Tm[baird2012 R1.b]
ritonavir1.99 Pa·s, the highestat Tm[baird2012 R1.ah]
felodipine; nifedipine154.0 and 36.20 × 10⁻³ Pa·sat Tm[baird2012 R1.u, R1.q]
class I-A; class III averages≈0.005 and ≈0.11 Pa·s at Tm; ≈0.014 and ≈0.53 Pa·s at 20 °C undercoolingclass averages[baird2012 R8]
17 drugs\eta(T_m) falls linearly with Tm − Tg, R^2 = 0.7368data of baird2012[trasi2014a R9]
indomethacin with 10% PVPhigher viscosity than with HPMC or HPMCAS at 80–105 °C; pure indomethacin crystallized during measurementrheometry[tian2017 R13, C19]
indomethacin in a polymermatrix viscosity falls quickly as the drug plasticizes the polymerhot melt extrusionmoseson2018 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 PEG dispersions

melting point depression

The lowering of the melting temperature of a crystalline component by the second component of a miscible mixture. Marsac and co-workers describe it as a manifestation of the reduced thermodynamic activity of the drug in the polymer: the dispersed drug reaches the chemical potential of the crystal at a lower temperature marsac2006b C39. In drug–PEG dispersions both branches of the liquidus are depressed, the drug's by dissolving in molten PEG and PEG's by dissolved drug, until they meet at the eutectic baird2011 E1, E2. Whether a pair shows depression separates miscible from immiscible pairs marsac2009 C12. New aspects (Miscibility and drug-polymer interactions): For drugs in amorphous polymers the depression is the visible sign of a miscible pair and the route to χ: pairs reported miscible lower the melting point of the drug, immiscible or partially miscible pairs show little or none, and a depression beyond the entropy-only (athermal) prediction means negative χ marsac2009 C5, C12. The offset of the melting endotherm is used because it gives the melting point at the final composition if mixing is complete marsac2009 C16. New aspect (ASD process): for an amorphous polymer the depressed melting point at a fixed composition is called the critical temperature Tc (the temperature at which the last drug crystal has dissolved in the polymer); it is the crystalline solubility temperature of that composition and the lowest product melt temperature at which a crystal-free extrudate is possible in theory, but it is not an upper or lower critical solution temperature moseson2018 P2, C43. A negative Flory–Huggins \chi adds depression beyond the combinatorial entropy moseson2018 C9. New aspect (Physical stability): used as the test of whether a few percent of polymer lowers the driving force for crystallization: no depression means no thermodynamic route [kestur2010b C25, C26].

Findings

PEG dispersions: F1, F2, F3, F4, F8, F10. Miscibility and drug-polymer interactions: F6, F7, F8, F9, F11. ASD process: F8, F9, F17, F19, F35, F36, F41. Physical stability: F4, F18, F22, F28, F29.

Related concepts

part of temperature-composition phase diagram; measured by liquidus temperature; depends on enthalpy of mixing and Flory-Huggins interaction parameter; reduces degree of supercooling; related to eutectic; measures Flory-Huggins interaction parameter through the Flory–Huggins relation; depends on drug-polymer miscibility and on the glass transition temperature of the polymer; related to thermodynamic driving force for crystallization. Measured to give formulation critical temperature; sets the lower bound of the HME operating design space.

Formulas

Flory-Huggins melting point depression, Lacoulonche liquidus model.

How it is measured or obtained

By hot-stage polarized light microscopy as the temperature at which the last crystal melts (1 °C/min) and by DSC offset melting (1 °C/min), on fused or physical mixtures that are ground and stored dry baird2011 P2, P3; zhu2011 P3, P4; zhu2012 P9, P10. For amorphous polymers the offset is extrapolated to 0 °C/min moseson2018 R5. An interaction parameter follows from the slope of the Flory–Huggins relation at 50–80% drug zhu2011 P5. In the PVP studies: physical mixtures of sieved crystalline drug and polymer (45–75 µm or 45–90 µm), dried for a week over phosphorus pentoxide or nitrogen, geometric mixing, modulated DSC at 1 °C/min under nitrogen, onset (marsac2006b) or offset (marsac2009) of the melting endotherm marsac2006b P1; marsac2009 P1. Only polymers that are liquid-like at the drug melting point work: PVP K12 (Tg 100 °C) gave depression, PVP K29/30 (Tg 168 °C) at 10 °C/min essentially none marsac2006b C29, R11, M3, M4. The fit uses data over 0–0.25 polymer fraction marsac2006b R8. In the extrusion work: cryomilled physical mixtures at 40–90% drug loading (DL), triplicate preparations, 3–5 mg scanned from 25 to 180 °C at six heating rates (0.5, 1, 2, 3, 5, 10 °C/min); the melting point offset temperature is fitted with a second-order polynomial against heating rate and extrapolated to 0 °C/min to give Tc moseson2018 P1, P2, E7. The offset rises with heating rate, for 50/50 IDM:PVPVA from about 133.2 °C at 0.5 °C/min to about 146.1 °C at 10 °C/min moseson2018 R3.f. In the felodipine growth work: DSC offset of the bulk melting endotherm at 1 °C/min of crystalline felodipine cryomilled with 3% PVP K-12; not possible for higher PVP grades, whose Tg lies above the drug melting point [kestur2010b P6].

Values in the library
materialvalue or classconditionspaper ids
benzocaine in PEG 3350melting around 89 °C neat, eutectic around 48 °C; text of the other paper: 92 °C neat and about 55 °C for the 20/80 blendfused dispersionszhu2012 C32, M3; zhu2011 R1
ibuprofen; fenofibrate in PEG 3350about 30 °C; about 20 °C by the text, about 24 °C by the ploteutectic depressionzhu2012 C34, X11, R24
chlorpropamide, aceclofenac in PEG 3350liquidus at 40 wt% drug about 55–56 and 86–88 °C against about 98 and 135.5 °C predictedDSC and hot stagebaird2011 R5.e, R6.e
nifedipine, felodipine in PVP K12decreased linearly over 0–25 wt% polymer; \chi −3.8 and −4.21 °C/min, small particlesmarsac2006b R7, R9
indomethacin in PVP K12\chi −6.16 (onset), −1.94 (midpoint), −0.82 (offset)1 °C/minmarsac2009 R6
indomethacin in PVPVAabout 30 °C at 50% drug loading; 1–4 °C below 30% polymerDSC offsetsmoseson2018 R6
probucol in PEOmelting point 101 °C, Form II only, "may be due to" depressioncompression-moulded dispersionbroman2001 R4.f, C20
nifedipine in PVP K12onset ≈171 → ≈156.5 °C; ≈144.5 °C at Φ ≈ 0.3831 °C/minmarsac2006b R6
felodipine in PVP K12onset ≈141 → ≈122 °C; ≈115.5 °C at Φ ≈ 0.3831 °C/minmarsac2006b R6
indomethacin in PVP K12offset ≈161.5 → ≈155 °C; onset ≈160 → ≈135.5 °CΦ ≈ 0.23marsac2009 R2
ketoconazole in PVP K12offset ≈150.0 → ≈147.5 °CΦ ≈ 0.23marsac2009 R3
itraconazole with Eudragit E100offset ≈168.0 → ≈167.4 °Cpolymer fraction up to ≈0.54marsac2009 R4
felodipine with 3% PVP, PVP/VA, HPMCAS, PVAc140.7, 142.9, 141.4, 142.6 °C against 141.5 °C: noneoffset, 1 °C/min[kestur2010a R1]
indomethacin (IDM) with PVPVA, 90/10 to 40/60Tc 159.9 ± 0.3, 157.2 ± 0.4, 151 ± 3, 141 ± 3, 132.3 ± 0.8, 129 ± 6 °C; IDM 160.64 °C; depressions 0.7, 3.4, 9.6, 19.6, 28.3, 31.6 °Coffset extrapolated to 0 °C/minmoseson2018 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 referencesbroman2001 R4.c, R4.d, C17, X5
polymers and surfactants with celecoxib (10% additive)3–4 °C with one additive; 12 °C for TPGS–PVPDSC[mosqueragiraldo2014 C18]
IDM with copovidone (1:5)solubility temperature about 78 °C (cited)phase diagram[moseson2019 R21]
bicalutamide with PVPVA, 30–90% BCLTc 145 °C at 30% BCL to about 192.3 °C at 90%; drug about 193.8 °Coffset extrapolated to 0 °C/min[moseson2022c R8, R9]
posaconazole with HPMCAS MF, PCZ fractions 0.4–1.0Tc about 161.7 °C at 0.4 to about 168.6 °C for neat PCZ; calculated 135 / 155 / 165 °C at 10 / 25 / 50% DLsame[shah2024 R1, R4, R5, X7]
felodipine with 3 wt% PVP K-12140.7 vs 141.5 °C, within the ±1 °C SD1 °C/min[kestur2010b R1.e, M1, X11]
indomethacin–PVP (cited)χ23 from melting point depression used as input to the ternary sorption modelliterature[rumondor2010a P5]
acetaminophen with 10% w/w polymers166.7–168.6 against 169 °Cphysical mixtures, DSC[trasi2012a R9]
flutamide with 10 mol% polymers108–110 °CDSC[trasi2012b R7]
six compounds with 1–20% PHB0–2 °C (1–10% PHB), up to 4 °C (20%)DSC of physical mixtures[sato2016 R7, X11]
indomethacin with 10% polymernamed as a possible reason for the steep inhibition above the growth maximum; not measuredargument[tian2017 C36]
Pitfalls and disagreements

Onset, midpoint and offset of the melting event give different depressions and different \chi marsac2009 R6. DSC and hot-stage values differ by up to about 16 °C at some compositions baird2011 X7. The low-temperature endotherm of the chlorpropamide and aceclofenac dispersions drifts to 39–49 °C in drug-rich traces, which a simple eutectic would not show baird2011 R4, X8. Very slow scans and controlled particle size were needed to see substantial depression with PVP K12, and with PVP K29/32 at 10 °C/min there was essentially none marsac2006b C30, R11. For PEG, the depression of the drug is the cited reason for a smaller driving force and delayed crystallization of benzocaine, but the supercooling in the dispersion was not measured zhu2012 C32, C33. The felodipine premix test read as slow mixing has an unverified direction marsac2009 X6, R8. The linear plot has a small non-zero intercept and the fit range is stated two ways marsac2006b X4. At 3 wt% polymer no depression is measured, and the melting point used there is that of form I in physical mixtures while form II grows [kestur2010a R1, X7]. Sucrose degrades on melting marsac2009 C14. A polymer with Tg near the drug melting point can hide the depression marsac2009 C22. In the extrusion work, mixtures with little polymer show only 1–4 °C of depression and the extent depends on interaction strength moseson2018 C16, C42. The 40/60 mixture scattered by about ±6 °C and lay above the model line, attributed to viscosity, and was left out of the fit moseson2018 R5.g, C17. In the probucol study depressions of a few °C compare dispersion melts at 20 °C/min with reference melts at 10 °C/min, and the table does not say whether values are onsets or peaks broman2001 X4, X5. The same low melting of probucol in moulded PEO is read as depression "may be due to" broman2001 C20. The depression of bicalutamide at 30% loading is large (about 49 °C from 193.8 °C to 145 °C, arithmetic on the cited values); that of posaconazole measured at 40% PCZ is about 7 °C (168.6 against 161.7 °C), and the values at 10–25% loading are extrapolations from the fitted line [moseson2022c R8, R9; shah2024 R1, X7]. The felodipine growth test used one composition and one grade only; the conclusion that the driving force is unchanged rests on a 0.8 °C difference inside the error [kestur2010b X11]. The celecoxib text gives 3–4 °C for one additive while the table gives 1.68–4.49 °C [mosqueragiraldo2014 X3], and the depression does not order the celecoxib ternaries [mosqueragiraldo2014 X13].

← Concepts and formulas

concept · as used in PEG dispersions

moisture barrier effect

Reduction of the uptake of water, or of its rate, by a particle coating. It was offered as one of two reasons why an alumina shell stabilizes an ASD powder, the other, "perhaps more importantly", being lower surface molecular mobility [duong2022c C53, C54]; alumina nanoshells blocked water uptake of amorphous lactose in earlier work (cited) [duong2022c C6]. In the ASD process papers it is measured as equilibrium uptake and as uptake kinetics, and the two do not agree: thin coatings leave equilibrium uptake unchanged, thick or slow-deposited coatings lower or slow it [moseson2022a C20; duong2022c C59; moseson2023 C13].

Findings

F43, F45, F47.

Related concepts

measured as water sorption and hygroscopicity; set by coating defect density and thickness; proposed beside surface molecular mobility as a stabilizing mechanism of the atomic layer coating.

Formulas

none.

How it is measured or obtained

Dynamic vapour sorption of coated and uncoated powder: isotherms at 40 °C (0–95% RH) or 37 °C (5–95% RH in 5% steps, n = 3), or kinetics after drying at 0% RH and a step to 90% RH for 2–3 h [moseson2022a P12, R8, R9; duong2022c P9, R9; moseson2023 P10, R7, R8; benson2025 P8, R3].

Values in the library
materialvalue or classconditionspaper ids
erlotinib–HPMCAS, 5–25 nmabout 5.7% uncoated against about 5.4% coatedDVS 40 °C, 75% RH[moseson2022a R8, R9, C20]
ezetimibe–HPMCAS 50% DL, uncoated / thin / thickabout 5.65 / 5.83 / 3.17%DVS 37 °C, 95% RH[duong2022c R9]
ezetimibe–HPMCAS 70% DL, uncoated / thin / thickabout 4.88 / 5.21 / 4.35%same[duong2022c R9]
posaconazole–HPMCAS 25% DL, 0 / 11 / 23 / 39 nmabout 4.7 / 4.3 / 3.7 / 1.2% at 30 minDVS 37 °C, 90% RH[moseson2023 R7]
posaconazole–HPMCAS 50% DL, slow-deposited 26 nmabout 0.33% at 2 h against about 4.2–4.5%same[moseson2023 R8]
ritonavir–PVPVA 20% DL, slow-coated 20.5 nmabout 15.1% against about 20% at 3 hsame[benson2025 R3]
Pitfalls and disagreements

The thin 50% ezetimibe coating protected for two years without lowering uptake, so equilibrium uptake is not a measure of protection [duong2022c X7; moseson2023 C52]. The abstract of the ezetimibe paper generalizes lower hygroscopicity to all coated powders, which only the thick coatings show [duong2022c C59, X6]. Sorption was measured on dry powders, not on powders in storage, and the slow-sorbing posaconazole samples had not levelled off within 2 h [moseson2023 X17]. Moseson (2022) read the unchanged bulk uptake as a coating that "would block water adsorption to the particle surface", which was not measured [moseson2022a C42, C43].

← Concepts and formulas

concept · as used in PEG dispersions

moisture-induced phase separation

Splitting of an initially miscible drug–polymer dispersion into drug-rich and polymer-rich amorphous phases because of water, either taken up during storage or present during preparation. Two routes are distinguished: water carried into a drying solution, which gives drug-rich spheres in a polymer-rich matrix, and water absorbed by a dry film, which gives a drug-rich network with polymer-rich holes (evacetrapib) [li2017 C24, C28, C32]. Water acts as an antisolvent for hydrophobic drugs [li2017 C32; saboo2017 C42]. New aspect (Physical stability): in the physical-stability papers, sorbed water splits an initially one-phase drug–PVP dispersion into drug-rich and polymer-rich amorphous phases before crystals appear; the authors hold it to be thermodynamically driven, with mobility setting its rate [rumondor2009c C2, C35, C41; marsac2010 C14].

Findings

ASD process: F1, F2, F4, F6. Physical stability: F12, F13, F14, F15, F16, F23, F31, F32.

Related concepts

a case of solvent-induced phase separation; a form of amorphous-amorphous phase separation; depends on hygroscopicity and water sorption; trapped by kinetic trapping; explained by Δχ effect; followed by moisture-induced crystallization; reversed by remixing of separated amorphous phases; driven also by hydrophobicity.

Formulas

Δχ effect, multicomponent Flory-Huggins free energy of mixing.

How it is measured or obtained

AFM topography and roughness, TEM with EDX, AFM-LCR and nanoTA, fluorescence microscopy and, for powders, modulated DSC for the number of Tgs [li2017 P8, P10, P13; mugheirbi2017 P8, P9, P11; li2019 P9, P10]. In the drug–PVP storage papers: IR of re-dried films against a calculated physical-mixture spectrum, DSC for two Tgs wet and re-dried, near-additive water uptake, AFM phase contrast and TEM without diffraction rings [rumondor2009c P7, P9, R22; marsac2010 R19, R20].

Values in the library
materialvalue or classconditionspaper ids
ECP–HPMC / PVPVA filmsfeatureless at 18% RH; domains at 35–50% RH; 20 µL water per mL of stock splits a 50% filmspin coated[li2017 R3, R5, R12]
ECP–PVPVA after 97% RH, 7 daysnet-like structures at 10–80% DL; F/N 0.10 (continuous) against 0.06TEM-EDX[li2017 R19, R22]
ECP–PVPVA powders after 24 h at 97% RHtwo Tgs at 10–50% DL, one at 60–90%modulated DSC[li2017 R24]
ITZ–HPMC E3 filmsdomains at 40% and 20% RH, none at 7% RH; network after 24 h at 40 °C/75% RHspin coated[mugheirbi2017 P13, R1, R3, R17]
LPV–HPMC E5 films after 97% RHirregular discrete and semi-continuous domains; continuous phase 173 ± 13 °CnanoTA[li2019 R8, R14]
felodipine–PVP at about 75% RH and abovedrug-rich and polymer-rich amorphous phasescited[rumondor2009b R24]
telaprevir ASD filmsdry nitrogen (RH below 18%) eliminates water-vapour-induced separationcited[mosqueragiraldo2018b C11]
LPV ASD powders with EC, HPMCAS, HPMCPstayed one phase after 48 h at 97% RHTg[li2018 R9, C40]
nifedipine-, pimozide-, droperidol–PVPseparated within 1 h at 94% RH; pimozide from 54% RHdried films[rumondor2009c R7, R9, R10, R12]
indomethacin-, ketoprofen–PVPone phase for 40 and 68 days at 94% RHsame[rumondor2009c R14, R16]
felodipine–PVPsmall change at 33–58% RH, distinct at 75% RH, amorphous-felodipine-like after 94% RH1 day–1 week[marsac2010 R7, R11]
felodipine with 25% HPMCAS or HPMCno change after 7 weeks at 75% RHdried films[konno2008 R11]
same drugs with PVP, PVPVA, HPMCASextent follows polymer hygroscopicity, PVP > PVPVA > HPMCASIR band loss, DSC[rumondor2010c C38, C33]
20 drug–polymer systemsHPMCAS dispersions less susceptible in general; PVP highly vulnerableclasses[rumondor2011 C29]
miconazole–PVPVA 50:501–3 µm drug-rich domains after 7 days at 75% RH; 4–25 µm domains within 5–30 min in bufferconfocal, AFM-IR[saboo2017 R15, R18, R19]
celecoxib–PVP 6:4two Tg events after 3 days at 94% RH, not after 75% RHDSC[xie2016b R18, R19]
ritonavir–PVPVA 30:70 with surfactantsSDS and Tween 80 delay visible separation; Spans speed it and coarsen the domainsconfocal at high RH, 37 °C[yang2022b R5, R6, R7, R8, C7]
Pitfalls and disagreements

The water content of films and solutions was not measured in the film studies, so "moisture" is inferred from humidity and added water [li2017 X14; mugheirbi2017 X4]. The water-uptake explanation of the DL effect on storage separation rests on powders after 24 h, not on films [li2017 X8]. Whether a dry film is miscible or kinetically trapped is open [li2017 C43]. The effect of water reverses with PrOH and BuOH [mugheirbi2018 C12]. In the drug–PVP storage study, two-phase evidence in the wet state exists only for pimozide; for nifedipine and droperidol it rests on IR of re-dried films and sorption [rumondor2009c X10]. Donor type, carbonyl red shift and drug–water χ split the drugs the same way [rumondor2009c X13]. Class labels per system ignore that resistance depended on drug loading [rumondor2011 X13, C38]. The pattern depends on how water arrives: humid air gives drug-rich droplets in a polymer-rich matrix, bulk water a coarser connected structure [saboo2017 C46].

← Concepts and formulas

concept · as used in PEG dispersions

molecular mobility

How fast molecules of an amorphous solid move and rearrange, the kinetic side of crystallization next to the driving force [marsac2006a C4; vaneerdenbrugh2010a C3]. In the library it is read from Tg (higher Tg, lower mobility at a given temperature), from enthalpy relaxation times, from melt viscosity and from model relaxation times, and water raises it by plasticization [konno2006 C2; marsac2006a R4.n; kestur2010b R10; rumondor2010 E1; marsac2008a C1].

Findings

F5, F9, F13, F14, F21, F22.

Related concepts

indicated by glass transition temperature; measured by enthalpy relaxation and structural relaxation time; raised by plasticization by water; related to kinetic barrier to nucleation.

Formulas

Kohlrausch-Williams-Watts equation, Stokes-Einstein equation; the AGV equation is listed on the chapter page as table only.

How it is measured or obtained

Enthalpy recovery after ageing fitted with the KWW function [konno2006 P6; marsac2006a P9]; zero-shear melt viscosity [kestur2010b P4]; Adam–Gibbs–Vogel relaxation time from Tg [rumondor2010 P8]; Tg and Tg − T as indicators marsac2008a R8.

Values in the library
materialvalue or classconditionspaper ids
amorphous nifedipine, felodipineτ 6.3 and 4.2 h at 23.5 °C; nucleation 2–4 times faster for nifedipinedry[marsac2006a R4.n, C13]
felodipine with 3 wt% PVP K-12, K-29/32, K-90melt viscosity ≈58, 156, 690 Pa·s vs ≈44 Pa·s alone100 °C[kestur2010b R10.c]
amorphous felodipine filmsgrowth follows AGV mobility to the power 0.513–75% RH[rumondor2010 R7, C27]
pimozide–PVPmoisture-induced separation much slower at 4 °C than at 22 °C75% RH[rumondor2009c R11, C41]
ketoprofen–PVPwet Tg −23 °C, mobile, yet no separation94% RH[rumondor2009c R25, C38]
coated ASD powders (outside)crystallization onset linked to Tg − T at the storage condition40 °C[moseson2022a C24, C25]
ritonavir ASDs (outside)Tg only a crude indicator of mobilitydegradation study[alvarenga2022 C21]
celecoxib with miscible surfactantsmain effect "most likely" on mobilityTg-scaled growth[mosqueragiraldo2014 C30]
felodipine free surfacefaster growth "may be attributed" to mobile surface moleculesfilms[kestur2013a C16]

Evidence table: molecular mobility.

Pitfalls and disagreements

Bulk mobility measures did not rank crystallization: DSC relaxation may not describe "the motion involved in nucleation", viscosity "cannot be used as a precise measure" of drug mobility, and growth outran AGV mobility [marsac2006a C37; kestur2010b C24; rumondor2010 C26]. Mobility sets the rate of moisture-induced separation but does not cause it [rumondor2009c C35, C41; li2017 C44]. Tg did not rank polymers for acetaminophen, flutamide, resveratrol or curcumin [trasi2012a C18; trasi2012b C33; wegiel2013b C33; wegiel2014 C22].

← Concepts and formulas

concept · as used in PEG dispersions

monotectic system

A crystalline dispersion in which drug and polymer mix fully as liquids and not as solids, and the drug has minimal solubility in the molten polymer and causes a negligible depression of the polymer melting point; the liquidus of the drug rises steeply from the PEG side baird2011 C1; zhu2011 R4. It is the counterpart of the eutectic system.

Findings

F1, F2, F6.

Related concepts

contrasts with eutectic; part of temperature-composition phase diagram; related to drug-polymer interactions.

Formulas

Lacoulonche liquidus model.

How it is measured or obtained

From the liquidus over 0–100 wt% drug by hot-stage microscopy and DSC: the PEG melting stays near 59–61 °C and the liquidus climbs toward the drug melting point from low drug contents baird2011 R8, R4.

Values in the library
materialvalue or classconditionspaper ids
haloperidol–PEG 3350monotectic; observed eutectic below 1 wt% (predicted 0.5 wt%); liquidus about 122 °C by hot stage at 10 wt%fused, 1 °C/minbaird2011 R1.d, R8.b, C7
haloperidol–PEG 3350monotectic, interaction parameter 0.08, solubility 0cited phase diagramzhu2011 R5.a
ketoconazole–PEG 3350monotectic; liquidus about 101 °C at 5 wt% drug; \chi 0.02, solubility 0hot stage, 1 °C/minzhu2011 R4.b, R5.f
four drugs of the kinetic studyhaloperidol is the only monotectic system; the others are eutectic20/80 near the eutectic compositionzhu2012 C40
Pitfalls and disagreements

The observation for haloperidol (below 1 wt%) has no tested composition between 0 and 10 wt% baird2011 X9. Ketoconazole is monotectic with PEG 3350 and has a positive interaction parameter zhu2011 R4.b, R5.f, while its activity coefficient in PEG 400 is 0.09, below 1 marsac2008b R14.f; see activity coefficient.

← Concepts and formulas

concept · as used in PEG dispersions

nucleation induction time

The time from creating a supersaturation until crystals are first detected, t_{ind} = t_n + t_g: the time to form stable nuclei plus the time for them to grow to a detectable size; if growth is quick, t_{ind} \propto J^{-1} and a longer time means a slower nucleation rate [ilevbare2013c E2, E3, C14]. It depends on the detection method, since crystals are seen earlier by SHG than by a probe ratio or light scattering [jackson2014 R25, R17].

Findings

F3, F4, F5, F6, F13, F14, F15, F25, F27, F28, F29, F32, F34, F35, F37, F38, F39, F40, F41, F42, F43, F44.

Related concepts

part of nucleation; gives nucleation rate; modified by nucleation inhibition; measured on supersaturation.

Formulas

induction time decomposition, relative nucleation rate from seeded and unseeded induction times, classical nucleation theory.

How it is measured or obtained

A methanol stock of drug is pumped or injected into stirred buffer with or without predissolved polymer and the signal is followed: extinction at a wavelength where the drug does not absorb (280 or 350 nm) or the fall in UV absorbance, taking the crossing of regression lines through the flat and rising (or falling) parts as the time; pyrene fluorescence and SHG as second read-outs; triplicate [alonzo2012 P5; ilevbare2013c P9, P10; jackson2014 P8]. The stated supersaturation uses a methanol-free solubility; the methanol fraction is about 0.5% v/v [ilevbare2013c X16].

Values in the library
materialvalue or classconditionspaper ids
celecoxib; efavirenz; ritonavir, no polymerabout 2.4; 5.1; 120 minat the calculated amorphous solubility, 37 °C[ilevbare2013c R8, R9.a]
ritonavir, CAB Adp 0.81; efavirenz, CAB Adp 0.81; celecoxib, HPMCabout 244; 28.0; 12.6 min5 µg/mL polymer[ilevbare2013c R9]
celecoxib at 11 µg/mL, none against HPMC27.5 ± 0.7 against 855.5 ± 6.0 minS 7.3[ilevbare2013c R15]
felodipine, none against 1 µg/mL HPMC15.3 against 136.5 minS 10, 25 °C[alonzo2012 R16]
danazol, none; PVP; HPMC; HPMC-AS6–10; 88–162; 111–285; 250–516 min10–20 µg/mL, 25 °C[jackson2014 R17]
celecoxib 22 µg/mL, 5 µg/mL HPMCAS (ASD dissolution chapter)held for 16 h; J_0/J_p about 4,00037 °C[xie2016a R3, R13]
paclitaxel 30.7 µg/mL (S 88) (ASD dissolution chapter)within 6 min; more than 16 h with 20 µg/mL HPMCAS37 °C[que2018 R3]
indomethacin S 6 (ASD process chapter)about 40 min; more than 12 h with 5–50 µg/mL PVPVApH 4.5, 37 °C[moseson2020a R3]
11 drugs, 0.1% STC and SDS, matched C/Ceqbuffer 7–87 min; STC 15 to >1000; SDS shorter for 7 of 925 °C, telaprevir 37 °C[chen2015 R3]
acetaminophen, S 1.595% of vials 26 min; first crystals 150–785 s20 °C[trasi2015 R1, R10]
celecoxib, nevirapine, flibanserin, 13 bile salts3 min to >16 h (celecoxib); 0–577 (nevirapine); 0–623 min (flibanserin)pH 6.5, 37 °C[li2016a R6]
telaprevir, 80 and 150 µg/mL, 26 polymersHPMC >700 and 243; none 14–15 minpH 6.8, 37 °C[mosqueragiraldo2016 R4]
telaprevir δ 11.5 and 28.8, six bile salts30 min and immediate in buffer; >960 min with 1.86 mMpH 6.5, 37 °C[lu2017 R3, R4]
danazol 15 µg/mL, PVP, HPMC, HPMC-AS 1–1000 µg/mLabout 5 min; 26–412 min25 °C[jackson2016 R17]
atazanavir without additive, five protocolsabout 40, 92–102, 170, 200, 253 ± 65 minnear the amorphous solubility, 37 °C[mosqueragiraldo2018a R1; elkhabaz2021 R6; indulkar2018 R19; indulkar2019b R3; enright2020 R2]
posaconazole without additive, three protocolsabout 5–8, 8.4, 29 ± 5 minpH 6.5, 37 °C[elkhabaz2021 R7; duong2022b R10; shah2025 R3]
enzalutamide without polymerabout 5–15 min, 30–120 µg/mLpH 6.5[wilson2021 R1]
Pitfalls and disagreements

The assumption t_n \gg t_g was not tested; strong inhibitors give gradual onsets whose fitted times depend on where the lines are drawn (rise above baseline at about 25 min against a fitted 31.5 min; about 180 against 260 min) [ilevbare2013c C14, X14]. Methods differ by up to about 40% for single conditions [jackson2014 X5]. The same polymer, drug and concentration gave 10–13 min in one laboratory and more than 8–16 h in another [ilevbare2013c R9; xie2015 R1; xie2016a R3]. The efavirenz run was at S about 2.3, not 15 [ilevbare2013c X4]. Replicate scatter is below 15% [ilevbare2013c R17]. Values above 960 or 720 min are lower bounds set by the run length [lu2017 X16; chen2015 X7]. The control induction time of one drug differs up to about sixfold between protocols, so effects compare only as ratios to a control in the same protocol [mosqueragiraldo2018a R1.b; enright2020 R2]. Several papers do not identify the scattering particles at the induction time [indulkar2018 X14; enright2020 X15].

← Concepts and formulas

concept · as used in PEG dispersions

nucleation inhibition

The slowing of crystal nucleation from a supersaturated solution by an additive, measured as a longer nucleation induction time or a lower nucleation rate. Ilevbare and co-workers propose that a polymer inhibits nucleation by joining clusters of solute molecules and hindering their reorganization into an ordered nucleus, which needs a polymer with more affinity for the solute than for water or for itself ("we assume", "would be expected") [ilevbare2013c C4, C5, C35]. How additives slow nucleation is more speculative than how they slow growth, because the molecular events cannot be observed [ilevbare2013c C9]. New aspect (Supersaturation from ASD dissolution): for celecoxib released from dispersions, the authors take the polymer effect on nucleation as "of paramount importance" to the desupersaturation profile, because growth needs nuclei [xie2015 C40]. Extended induction times with polymers indicate a decreased nucleation rate, PVP-K12 being the least effective and HPMCAS or HPMC showing no discernible nucleation or growth for 8 h [xie2015 C42, R1]; the greater effect of the cellulose derivatives "may relate" to a greater ability to interact with a dense liquid cluster of celecoxib than the more hydrophilic PVP, which also interacts with the solvent [xie2015 C46]. With 5 µg/mL HPMCAS the relative effect on nucleation (~4000) was far larger than on growth (70) ("it can be surmised") [xie2016a C40, R13].

Findings

Crystallization from solution: F6, F13, F14, F15, F20, F27, F28, F31, F32, F33, F36, F40. Supersaturation from ASD dissolution: F4, F5, F20, F29.

Related concepts

contrasts with crystal growth inhibition; part of crystallization inhibition by polymers; measured by nucleation induction time and nucleation rate; related to polymer hydrophobicity; related to interfacial tension.

Formulas

relative nucleation rate from seeded and unseeded induction times, induction time decomposition, classical nucleation theory.

How it is measured or obtained

Unseeded induction times with and without polymer under identical conditions (see nucleation induction time), optionally combined with seeded growth rates into the nucleation-rate ratio J/J_0 [alonzo2012 P10, E10]. In the celecoxib dispersion papers: solvent shift to 22 µg/mL celecoxib in pH 6.8 phosphate buffer at 37 °C with 5 µg/mL dissolved polymer, the onset read from a rise in 350 nm extinction with a fall in 249 nm absorbance [xie2015 P4, R1].

Values in the library
materialvalue or classconditionspaper ids
felodipine, 1 µg/mL HPMCJ/J_0 7.05 × 10⁻⁴ ("more than a thousand fold"); induction 15.3 → 136.5 minS 10, 25 °C[alonzo2012 R16, R17, C38]
ritonavir; efavirenz; celecoxib, best polymer120 → 244; 5.1 → 28.0; 2.4 → 12.6 min5 µg/mL[ilevbare2013c R9, R12]
celecoxib at S 7.3, HPMC27.5 → 855.5 min (31-fold)5 µg/mL[ilevbare2013c R15]
celecoxib, 5 µg/mL HPMCAS (ASD dissolution chapter)J_0/J_p about 4,00022 µg/mL drug[xie2016a R13]
paclitaxel, HPMCAS (ASD dissolution chapter)"highly effective" at S 8820 µg/mL polymer[que2018 R3, C13]
indomethacin, PVPVA 5–50 µg/mL (ASD process chapter)"highly effective" at S 6; stays supersaturated more than 12 hpH 4.5[moseson2020a R3, C11]
11 drugs, 0.1% STCinduction time lengthened for all, eight by more than 10-fold25 °C[chen2015 R3, X6]
telaprevir, 1.86 mM STC, SGCrelative nucleation rate J/J₀ 2.5 × 10⁻³ and 2.9 × 10⁻⁶ (recomputed 2.58 × 10⁻³ and 3.06 × 10⁻⁶)δ 11.5[lu2017 R10, X1]
acetaminophen, S 1.5J lowered 18-fold (HPMCAS) and 36-fold (HPMC); raised 2.6-fold by PAA10 µg/mL[trasi2015 R3]
telaprevir, 1.86 mM binary and ternary bile salt mixtures>960 min against about 30 in buffer; 3.72–5.58 mM mixtures about 255 minδ 11.5, 37 °C[lu2018 R3, R4]
nine drugs, 5 µg/mL A5aatazanavir 40 → >300, telaprevir 15 → 91 minpH 6.8, 37 °C[mosqueragiraldo2018a R1]
celecoxib 22 µg/mL: no polymer; 5 µg/mL PVP-K12; PVP-K29/32; HPMCAS or HPMCwithin 5 min; ≈1 h; ≈2 h; more than 8 hpH 6.8, 37 °C[xie2015 R1]
delamanid at 0.76 µg/mL with 300 µg/mL polymermore than 1000 min with PVPVA, HPMCP and HPMCAS; about 50 min with HPMC; 10.2 min with Eudragit L100 against 10.7 min without polymerPBS pH 6.5, 37 °C[duong2022a R4, R2]
racemic praziquantel at 1.1 mg/mL with 300 µg/mL polymer10.9 (PVPVA), 14.3 (HPC), 15.7 (PVA), 24.5 (HPMC 603) and 50.5 min (HPMCAS-LF); HPMCAS-MF and HPMC E5 LV beyond the 83-min runPBS pH 6.5, 37 °C[polyzois2024 R3]
R-praziquantel at 1.4 mg/mL37 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 PEG dispersions

nucleation rate

The number of stable crystal nuclei formed per unit volume and time, J. Classical nucleation theory gives J = A\exp(-\Delta G_{crit}/kT) with a barrier that falls steeply with supersaturation, \Delta G^{*} \propto 1/(\ln S)^{2}; where the induction time is dominated by nucleation, t_{ind} \propto J^{-1} [ilevbare2013c E3, E4; hsieh2012 E7, E8]. The nucleation-rate ratio with and without a polymer is estimated from seeded and unseeded induction times [alonzo2012 E10]. New aspect (Physical stability): in the solid-state papers of the library it is the slope of the volume density of birefringent sites against time in amorphous films, in m⁻³ s⁻¹ [konno2006 C12, R3; marsac2008a E4]; in solution papers it is derived from induction times or counts of particles or SHG signals per time [alonzo2012 E10; elkhabaz2021 E5].

Findings

Crystallization from solution: F6, F14, F27, F32, F33, F34, F42. Physical stability: F1, F2, F9, F10, F11.

Related concepts

inverse of nucleation induction time; modified by nucleation inhibition; described by classical nucleation theory; measures nucleation; set by kinetic barrier to nucleation and thermodynamic driving force for crystallization; related to crystal growth rate.

Formulas

relative nucleation rate from seeded and unseeded induction times, classical nucleation theory, induction time decomposition, depth of field of a microscope objective, Arrhenius equation.

How it is measured or obtained

Not measured as an absolute rate in the papers of the crystallization-from-solution chapter. The ratio is J/J_0 = (t_s/t_{s,0})^{3}(t_{u,0}/t_u)^{4}, with the seeded induction-time ratio replaced by the growth-rate ratio R/R_0 at the same supersaturation and polymer level [alonzo2012 P10, E9, E10]. In the ASD dissolution chapter the same relation was applied to celecoxib [xie2016a R13]. In the solid-state papers: spin-coated films stored at a fixed RH and temperature; sites counted under polarized light in 12 areas per film, converted from area to volume with the depth of field of the objective (0.0144 mm at 10×), triplicate, film edges excluded [konno2006 P2, E1; marsac2006a P4; konno2008 P4]. Sites are counted once they reach about 1 µm [konno2008 C38]. In SHG images of griseofulvin the number density of crystal sites was followed over time with a 60 µm depth of field [wanapun2010 R17].

Values in the library
materialvalue or classconditionspaper ids
felodipine, 1 µg/mL HPMCJ/J_0 7.05 × 10⁻⁴ (text: more than thousand-fold; conclusions: factor of 1000)S 10, 25 °C[alonzo2012 R17, C38, C46]
celecoxib, 5 µg/mL HPMCASJ_0/J_p about 4,000 (unseeded time taken as 960 min)22 µg/mL drug, 37 °C[xie2016a R13]
acetaminophen, S 1.5J 1465 (none), 3820 (PAA), 81.86 (HPMCAS), 40.68 (HPMC) # m⁻³ s⁻¹1.2 mL vials, 20 °C[trasi2015 R3]
telaprevir with STC, SGCJ/J₀ 2.5 × 10⁻³, 2.9 × 10⁻⁶δ 11.5[lu2017 R10]
atazanavir, posaconazole, six mediaSHG count rate about 0.1–1.6 and 0.05–48 counts/min37 °C, relative per field[elkhabaz2021 R14, E5, X13]
posaconazole, PBS and three mediaJ from induction times, fitted for A and γ37 °C, S above about 7–13[duong2022b R15, X10]
amorphous felodipine≈1.3 × 10⁵ m⁻³ s⁻¹; ≈2–3 × 10³ with 3% PVP, HPMCAS or HPMC0% RH, 22 °C[konno2006 R4]
amorphous nifedipine vs felodipine0.39 vs 0.17 × 10¹⁰ m⁻³ day⁻¹0% RH, 22 °C[marsac2006a R4.a]
nifedipine and felodipine with 7% PVP≈1.4 × 10³ and ≈2.7 × 10² m⁻³ s⁻¹0% RH[marsac2006a R16.b]
felodipine with 3% PVP vs HPMCAS≈8.6 × 10⁵ vs ≈1.3 × 10⁴ m⁻³ s⁻¹75% RH, 22 °C[konno2008 R3.b]
nifedipine vs felodipine with 25% PVP≈4.3 × 10⁵ vs ≈2.3 × 10³ m⁻³ s⁻¹75% RHmarsac2008a R1.f, R1.l
felodipine (activation energy)145 kJ/mol below Tg; 201 with 3% PVPArrhenius, ≈25–75 °C[marsac2006a R3]
griseofulvin melt (SHG imaging)number density ≈45 → ≈600 mm⁻³ over ≈62–285 min125 °C, SHG[wanapun2010 R17]
Pitfalls and disagreements

The ratio rests on one pair of induction times without uncertainty and on a seeded ratio standing in for a seeded induction-time ratio; a 10% change in the polymer-case time changes J/J_0 about 1.5-fold [alonzo2012 X7, C11]. The printed inverse of 0.607 is 1.643 against 1.647, with J/J_0 7.05 or 7.06 × 10⁻⁴ [alonzo2012 X6]. The celecoxib value is a lower bound because no desupersaturation occurred within the experiment [xie2016a R13]. In the film papers absolute rates are per depth-of-field volume and comparable only within one counting method; in one paper Table II and two figures disagree about fourfold, and the felodipine-alone rate of that paper's Fig. 9 (≈3 × 10⁴) is about fourfold below the other papers' ≈1.3–1.4 × 10⁵ (synthesis) [marsac2006a X1; konno2006 R4.a]. The 2006 methods describe the area-to-volume conversion as multiplication where division is meant [konno2006 X6]. Site density rose roughly linearly, but early points can lie below the fitted line, so a short lag is not excluded [konno2006 X8].

← Concepts and formulas

concept · as used in PEG dispersions

nucleation

Nucleation is the formation of crystal nuclei, the first of two dependent steps of crystallization, each with its own rate and temperature dependence [baird2013 C32; kestur2010a C27]. In classical nucleation theory the barrier to a critical nucleus grows with the cube of the interfacial free energy and falls with the square of the driving force [vaneerdenbrugh2010a E3]; the library adds molecular recognition as a further factor [trasi2012a C48; konno2006 C33]. This draft comes from the crystallization-tendency chapter (supercooled melts and glasses); nucleation from solution is covered by other chapters. New aspects (Miscibility and drug-polymer interactions): For indomethacin and PVP the proposal is that a critical γ nucleus is built of acid dimers, so that "the formation of a critical nucleus of indomethacin would require the breaking of the PVP-indomethacin hydrogen bond"; the same logic is expected to hold for α, which hydrogen-bonds in chains [taylor1997 C43, C44]. During solvent removal nucleation and growth can occur once the drug's solubility in the drying solution is exceeded, and a polymer may alter the supersaturation reached vaneerdenbrugh2010b C29. Pure nifedipine and felodipine nucleate much faster than dispersions with even small amounts of polymer, which is the main argument that the polymer acts through kinetics marsac2006b R16, C42. New aspect (Crystallization from solution): nucleation from supersaturated aqueous solution differs from nucleation in a supercooled melt in that the driving force is the supersaturation S and the read-out is the induction time at fixed S; it is "energetically more demanding" than growth, so at some supersaturations crystals grow while new nuclei do not form [ilevbare2013c C10, E3]. Polymers can slow it several-fold at the supersaturation of amorphous dissolution and by much more at lower supersaturation (F13, F14), and for felodipine far more than they slow growth (F6) [alonzo2012 C46; ilevbare2013c R12, R15]. In a two-phase solution the droplet interface is a candidate site (see heterogeneous nucleation) [jackson2014 C45, C53]. New aspect (Physical stability): the physical-stability papers treat nucleation as the initiating event that a dispersion must suppress, framed by classical nucleation theory with a thermodynamic barrier and a kinetic barrier, while noting that nucleation in films is "most likely heterogeneous" [marsac2006a C5; konno2006 C33]. New aspect (Supersaturation from ASD dissolution): three readings from dissolving dispersions: a fast initial drop of a highly supersaturated felodipine solution as rapid nucleation, faster and giving more particles at higher concentration [konno2008a C24]; immediate crystallization of drug released at very high local supersaturation from a 10% drug dispersion [alonzo2011 C29]; and nucleation inside drug-rich droplets, favoured by the high drug concentration and an expected low crystal–liquid interfacial tension [ilevbare2013d C39, C40].

Findings

Crystallization tendency: F3, F4, F7, F15, F16, F18, F19, F21. Miscibility and drug-polymer interactions: F1, F9, F10, F15. Crystallization from solution: F3, F6, F13, F14, F20, F34, F36. Physical stability: F1, F2, F9, F10, F16, F17, F20, F29. Supersaturation from ASD dissolution: F3, F5, F13.

Related concepts

part of the process together with crystal growth rate (contrasts with); measured by nucleation temperature zone; modelled by classical nucleation theory; includes heterogeneous nucleation and sub-Tg nucleation; related to quenched-in nuclei and prenucleation clusters; depends on thermodynamic driving force for crystallization; related to crystallization inhibition and kinetic stabilization; includes secondary nucleation; inhibited by nucleation inhibition; quantified as nucleation rate; controlled by kinetic barrier to nucleation; see molecular recognition and nucleation and crystal growth; related to nucleation induction time and metastable zone.

Formulas

classical nucleation barrier, critical cooling rate to avoid nucleation, classical nucleation theory, induction time decomposition, relative nucleation rate from seeded and unseeded induction times, Arrhenius equation, depth of field of a microscope objective.

How it is measured or obtained

Directly, by the number of nuclei grown to visible size after a hold (two-step method) [trasi2014b P7] or by nucleation-site density over time in films [marsac2006a R1]; by locating a nucleation zone with DSC cooling to successive end points and reheating [trasi2014b P1; trasi2012a R12]; indirectly, from critical heating rates after slow and fast cooling [baird2013 C38] or from the absence of crystallization on reheating [trasi2014b C39]. In solution, induction times are used, which include a growth time [chen2015 C5]. In the felodipine, bifonazole and nimesulide growth studies nuclei are only formed and then grown: films are stored over P2O5 at 40 °C (or at ambient temperature) before the hot-stage growth runs, and nucleation with the polymers is not quantified [kestur2010a P3, X10; kestur2011 P2]. The spin-coating screen of vaneerdenbrugh2010b scores the crystalline area over 7 days, which mixes nucleation and growth vaneerdenbrugh2010b P2, C29. In the crystallization-from-solution papers by unseeded induction times (see nucleation induction time) and by the nucleation-rate ratio from seeded and unseeded runs [alonzo2012 P5, P10; ilevbare2013c P9]. In the physical-stability papers, by counting birefringent sites in films at fixed RH and temperature, and by the Arrhenius slope of the rate above and below Tg [konno2008 P4; marsac2006a P5]. A lag before detectable crystals in stored powders was read as delayed nucleation [rumondor2009b R17, C29]. In the ASD dissolution papers it is not measured directly but inferred from concentration curves, induction times, particle appearance and Raman lag times [konno2008a X4; ilevbare2013d R16; raina2014b C32].

Values in the library
materialvalue or classconditionspaper ids
nilutamide glass≈12.6 nuclei per sample at −30 °C; ≈0.8–2.5 at −20 to 40 °C30-min hold, open surface, 1 min growth at 65 °C[trasi2014b R9]
acetaminophennucleation zone 50–60 °CDSC cool–reheat[trasi2012a C22]
acetaminophen with polymersHPMCAS reduces nuclei to about a third; PAA gives nearly three times more10% w/w[trasi2012a C23]
flutamidenucleation zone 10–40 °CDSC cool–reheat[trasi2012b R10]
nifedipine against felodipinefaster nucleation for nifedipinepure films, 22 °C, 0% RH[marsac2006a R1]
felodipine filmsrate rises with storage RH; drug alone fastest22 °C, with polymers[konno2008 C11]
indomethacin polymorphsδ fastest at 60 °C; α favoured at 80 °C; γ not readily (only from seeds); polymers retarded nucleationamorphous films, storage at 60 and 80 °C[tian2017 R1, R5, C7]
celecoxibsamples "quite hard to nucleate"hot stage[mosqueragiraldo2014 R15]
vemurafenib βnucleation the limiting step above 150 °C (qualitative)hot stage[lu2016 C46]
pure nifedipine, felodipine against dispersionsnucleation much faster for the pure drugscited from a companion studymarsac2006b R16
indomethacin–PVPnucleus requires breaking the PVP–drug bond (proposed, untested)no crystallization data[taylor1997 C43, X8]
flufenamic acid–PSSA, chlorpropamide–PSSA, lidocaine–PVP filmsfully crystalline within 30 min of coatingspin coatingvaneerdenbrugh2010b R2.an, R2.s, R2.as
celecoxib; efavirenz; ritonavirinduction time about 2.4; 5.1; 120 minat the calculated amorphous solubility[ilevbare2013c R8]
felodipine, HPMC 1 µg/mLJ/J_0 7.05 × 10⁻⁴S 10[alonzo2012 R17]
danazol6–10 min without polymer; 88–516 min with 10 µg/mL polymer25 °C[jackson2014 R17]
nine drugs with carboxylated cellulose derivativescontact with the emerging nucleus "clearly a prerequisite" for disruption5 µg/mL, pH 6.8[mosqueragiraldo2018a C44]
amorphous felodipinerate ≈1.4 × 10⁵ → 2.9 × 10⁶ m⁻³ s⁻¹0 → 75% RH, 22 °C[konno2008 R1.a, R3.a]
nifedipine vs felodipinefaster at every PVP level and RH0–75% RHmarsac2008a R1, C7
felodipine with 50% HPMCASnegligible crystals for 35–120 days at 52–93% RH, read as delayed nucleationPXRD of powders[rumondor2009b R17, C29]
flutamide with 10 mol% PVAc, PIPAgrowth rate at the DSC exotherm maximum 7.7 and 7.0 against 4.4 µm/s, read as fewer nucleiDSC and growth curve[trasi2012b R11.b, R11.d, R11.f, C18]
flutamide with 10 mol% nilutamideone nucleus in the imaged regioncooled to −30 °C, reheated[trasi2012b R12, C16]
felodipine with 3% PVP≈150-fold lower rate (cited)30 °C[kestur2013b R22, C35]
ritonavir 17 against 20 µg/mL (below and above LLPS)induction about 284 against 119.3 minpH 6.8, 37 °C[ilevbare2013d R16, R12]
felodipine methanol shift with HPMC, S about 60precipitation not completely suppressed25 °C[alonzo2011 C30]
nifedipine α in γ slurries with polymerlag lengthened at similar slopes, read as α nucleation inhibition25 °C[raina2014b C32]
Pitfalls and disagreements

Nucleation is stochastic and often heterogeneous, which scatters crystallization temperatures [baird2010 C19; baird2013 C18]. Nuclei counts are not rates unless area and time are controlled [trasi2014b X7]. Polymers can act oppositely on nucleation and growth: HPMCAS was the best nucleation inhibitor but the weakest growth inhibitor for acetaminophen [trasi2012a C46], and drug–additive hydrogen bonding correlated with growth inhibition but not with nucleation for flutamide [trasi2012b C45]. Classical nucleation theory does not capture molecular recognition or polymer effects [trasi2012a C49]. The role of the hydrogen bond in nucleation is argued, not tested [taylor1997 X8]. The growth-rate ranking of polymers says nothing about nucleation, which was not measured [kestur2010a X10; kestur2011 P3]. The film screen cannot separate crystallization during coating from crystallization during storage except through the day-0 score vaneerdenbrugh2010b R2. In solution, how additives slow nucleation is "more speculative" than how they slow growth, because the molecular events cannot be observed [ilevbare2013c C9]; the papers do not separate nucleation from early growth inside the induction time [ilevbare2013c X14]. The delayed-nucleation reading of the HPMCAS lag in stored felodipine powders assumes that growth below and above the detection limit follows the same factors [rumondor2009b C28]. Nucleation counts separated polymers at 33% RH that PXRD crystallinity could not separate within 490 days (synthesis) [konno2008 R2.b; rumondor2009b R19]. The flutamide nucleation verdicts rest on two Tmax values per sample and an unnamed test [trasi2012b X4]. Nuclei per cycle are not rates when the zones differ in width [trasi2012a X8]. The felodipine "nucleation then growth" reading rests on curves alone [konno2008a X4]; the ritonavir 17 µg/mL comparison has no n or SD and mixes droplets with a higher bulk supersaturation [ilevbare2013d X18].

← Concepts and formulas

concept · as used in PEG dispersions

physical stability

The ability of an amorphous drug or dispersion to stay amorphous, and unseparated, during manufacture and storage [vaneerdenbrugh2010a C19; kestur2013b C46]. In this chapter it is approached through the crystallization tendency of the neat drug; dispersion stability is treated in other chapters. New aspects (Miscibility and drug-polymer interactions): For polymer dispersions, physical stability is read as the time to the first crystalline peaks under a stress condition, and it depends on whether the polymer bonds the drug. Naringenin and quercetin dispersions with E100 or PVP showed no crystals for more than 200 to more than 450 days at each of five storage conditions, whereas dispersions with HPMCAS, HPMC, CMCAB or PAA crystallized within 1–3 days at 84% RH/25 °C and at 75% RH/40 °C [wegiel2013a R9, C22]. Lumefantrine–PVPVA dispersions crystallized after 1 to 8 weeks at 40 °C/75% RH, while enteric-polymer dispersions showed drug crystals only at 50% drug loading [hiew2022a R6, C10]. Phase separation is expected to lower stability: a phase-separated dispersion "would be expected" to crystallize faster in storage and dissolution [purohit2015a C2, C35; li2016c C1, C41]. Dry storage, humidity and polymer content each change the ranking of polymers [wegiel2013a R9, X3; vaneerdenbrugh2011a C50]. New aspect (Physical stability): for the resveratrol and curcumin dispersions it is likewise read as days before crystals appear at a set storage condition, and it depended "greatly" on polymer and condition [wegiel2013b C23; wegiel2014 C21]. New aspect (Supersaturation from ASD dissolution): two settings in which physical stability decides dissolution performance. For dispersions with two polymers: at 60% indomethacin and 40 °C/75% RH the HPMC and the EPO binaries both crystallized within 5 days (growth much slower with EPO), whereas the EPO–HPMC ternary stayed amorphous for more than 100 days, contrary to the expectation that partly replacing EPO with HPMC would make it similar or slightly worse ("unexpected"); at 30% drug the ternary was also more stable than the HPMC binary [xie2017 R26, C51, R27]. For suspensions of dispersions dosed preclinically, the crystallization tendency "is expected" to depend on the extent of supersaturation, the polymer solubility in the medium and the polymer's ability to inhibit crystallization in solution and matrix [li2018 C60]. Lopinavir–HPMCP dispersions, with the strongest solubility suppression, were the most stable against crystallization ("correlates"), and where suppression brought the concentration to or below the crystalline solubility the authors see no driving force for crystallization, so that such dispersions "should remain" physically stable, dry and as suspensions [li2018 C61, C62, C63, C64].

Findings

Crystallization tendency: F17, F20, F21. Miscibility and drug-polymer interactions: F15, F17, F23, F24, F26. Physical stability: F24, F25, F26, F30, F33, F34, F35. Supersaturation from ASD dissolution: F18, F20, F23.

Related concepts

includes glass stability and surface crystallization; depends on crystallization tendency; related to amorphous salt; depends on drug-polymer interactions, acid-base interaction and amorphous-amorphous phase separation; includes crystallization inhibition; tested by accelerated stability testing; lost through moisture-induced crystallization; depends on solubility suppression in suspensions; related to ternary amorphous solid dispersion and matrix crystallization.

Formulas

none.

How it is measured or obtained

By storage at set temperature and humidity followed by PLM, XRPD or fluorescence [baird2010 P7; tian2016 R17; hiew2022b R7]; by Raman or PXRD crystallinity against time [kestur2013b R3]. For the lumefantrine and polyphenol dispersions: open-dish storage at 40 °C/75% RH with PXRD at times from 1 to 76 weeks [hiew2022a P8]; five conditions (22–25 °C over P2O5, 22–25 °C at 84% RH over potassium chloride, 40 °C at 75% RH over sodium chloride, 50 °C and 90 °C over Drierite) with PXRD for the first sharp peaks [wegiel2013a P3]; for thin films, polarized-light scoring of the crystalline area over 7 days of dry storage, expressed as an amorphicity index [vaneerdenbrugh2011a P2, P3, E1]. For resveratrol and curcumin, storage tables of first sampling times with crystals by XRPD at five or six temperature–humidity conditions [wegiel2013b P3, P4, R12; wegiel2014 P5, R13]. In the ASD dissolution papers: open-vial storage of 60% and 30% dispersions at 40 °C/75% RH with PXRD up to 100 days [xie2017 P16, R26]; in suspension, concentration over 48 h and polarized light microscopy of 50% dispersions in pH 3 buffer without a dissolved inhibitor [li2018 P6, P7].

Values in the library
materialvalue or classconditionspaper ids
indoprofen; droperidol, nifedipine; clotrimazole, felodipinecrystalline in 1 day; by 3 months; edges only at 3 monthsquenched glasses, 0% RH, 14–20 °C below Tgbaird2010 R23, R24, R25
felodipine with 3% PVPnot completely crystallized after 24 weeks30 °C, dry[kestur2013b C11]
indomethacin–PVP dispersions, 10–90% drugamorphous over 3 months (all compositions)40 °C, desiccant[tian2016 R16, C35]
indomethacin with HPMC or HPMCAS, 10–90% drugabove the miscibility limit crystalline in 2–15 days; at or below it amorphous 13–14 months40 °C, desiccant[tian2016 R17, C53]
pretomanid–HPMCAS dispersionsstable several months; neat glass crystallized within minutesambient[nguyen2023a C62]
lumefantrine HCl and sulfate saltsno recrystallization for at least 16 weeks40 °C/75% RH[hiew2022b R7]
delamanid saltsno PXRD peaks after 2 weeks40 °C/75% RH[duong2022a C32]
naringenin, quercetin with E100 and PVPno crystals for >200 to >450 daysfive conditions, 40–50% polymer[wegiel2013a R9]
naringenin, quercetin with HPMCAS, HPMC, CMCAB, PAAfirst crystals after 1–3 days84% RH/25 °C and 75% RH/40 °C, 30–80% polymer[wegiel2013a R9]
lumefantrine–PVPVA at 50, 25, 10 and 5% drug loadingfirst crystals after 1, 2, 4 and 8 weeks40 °C/75% RH, open dish[hiew2022a R6]
lumefantrine at 50% drug loading with HPMCAS, Eudragit L 100, HPMCP, CAPfirst drug crystals after 1, 8, 32 and 40 weekssame[hiew2022a R6]
resveratrol with PVP K29/32, E100, HPMC, HPMCAS, CMCAB, PAAPVP never crystallized (> 400 days); E100 > 400 days at 84% RH; the others crystalline at day 1 at 84% RH25 °C[wegiel2013b R12]
curcumin with E100, cellulosics, PVP; neat> 350, 75, 22 and 14 days at 84% RH25 °C[wegiel2014 R13]
curcumin dispersionsall > 350 days at 0% RH/25 °C; all crystalline within 1 day at 90 °C/0% RH and 60 °C/98% RHstorage[wegiel2014 R13, C23]
indomethacin 60% with HPMC; EPO; EPO–HPMC 6:2.9:1.1crystals within 5 days; within 5 days, slower growth; amorphous beyond 100 days40 °C/75% RH, open vials[xie2017 R26]
indomethacin 30%, EPO–HPMC against HPMCternary more stable (text only)40 °C/75% RH[xie2017 R27]
lopinavir 50% HPMCP dispersion in suspension≈2.5–3.0 µg/mL over 48 h; no crystals at 48 hpH 3, 25 °C, no inhibitor[li2018 R6, R7]
lopinavir 50% EC; CA dispersions in suspension≈4.3–5.0 µg/mL to 12 h, then ≈1.6–3.4; ≈10.5–11.2 µg/mL to 12 h, then ≈2.3–3.9same[li2018 R6]
delamanid sulfonate salts, neatseven of eight amorphous with Tg 83.7–117.8 °C against 43.3 °C for the free base; all amorphous after 2 weeks at 40 °C/75% RH, four liquefiedopen dish[duong2022a R20]
delamanid salt dispersions at 20% drug with HPMCASTg 100.4–117.0 °C against 86.7 °C; water uptake ≈10–13.6% against ≈8.2% at 95% RH37 °C[duong2022a R23, R22]
praziquantel dispersions at 20% drugHPMC E5 LV amorphous at 23 weeks; HPMCAS-MF small crystalline peaks by 21 weeks40 °C/75% 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 PEG dispersions

pKa

The pH at which half of an ionizable drug is protonated; two pH units above the pKa a weak base is almost fully un-ionized and two units below almost fully ionized, which set the pH range of the weak-base solubility studies [indulkar2015 C16]. New aspects (Miscibility and drug-polymer interactions): The acid dissociation constant is also used to classify the drugs of a polymer screen as acidic, weakly acidic or basic, and as a proxy of donor strength: a lower pKa means a stronger acid and a better hydrogen-bond donor [vaneerdenbrugh2010b M3, M4, M5, M6, M7, M8; rumondor2011 C30]. The values are computed, not measured. In the later papers the pKa decides whether a proton can move between drug and polymer: PSSA (−1.5) with the basic pKa of anthranilic acid (2.0), lidocaine (amine 7.8) and dibucaine (amine 9.8), and not PAA (4.5) or flufenamic acid (basic −2.1) [vaneerdenbrugh2011a R1, R2, R9, C22, C23]; lumefantrine (amine 8.73, cited) with enteric polymers of pKa 4.32–6.21 [hiew2022a M1, R22]. New aspect (Release mechanism and LoC): the pKa of the buffer species, relative to the surface and bulk pH, decides whether a buffer carries protons away from a dissolving enteric polymer. BIS-TRIS (pKa 6.5) and phosphate (7.2) bind protons at the lower surface pH and release them at the bulk pH, BIS-TRIS better because more of it is in the base form at a surface about 0.4 units below bulk; Tris (8.1) and TEA (10.2) are mostly protonated at both and cannot act as proton carriers, which slows HP-50 dissolution [qi2022 C27]. For HPMCAS-MF, pH 7.5 phosphate gave faster dissolution than pH 9.0 phosphate because the latter has a low buffer capacity [bapat2023 C15]. The polymer pKa values used were 4.2 for HP-50 and 4.92 or 5.0 for HPMCAS-MF, both cited [qi2022 C23; bapat2023 M3]. The 2025 grade paper titrated HPMCAS LF and HF, giving pKa 4.91 and 5.06 at the half-neutralization point against a cited 4.97 for MF [bapat2025a R8, C11, M3, M4, M5]; the 2024–2025 papers flag weak bases with pKa above about 5 as at risk of complexing HPMCAS at the gel pH [bapat2024 C45].

Findings

C. Amorphous solubility and LLPS: F10, F23. Miscibility and drug-polymer interactions: F15, F17, F21, F24, F26. Physical stability: F13, F24. Release mechanism and LoC: F23, F32, F33.

Related concepts

sets ionization and pH-dependent solubility; indicates donor strength in hydrogen bonding; related to drug-polymer interactions, hydrogen-bond basicity, acid-base interaction and hydrogen-bond donor and acceptor groups. Of buffer species, sets buffer capacity at a given pH and the microenvironmental pH; of the polymer, sets the critical ionization for polymer dissolution.

Formulas

Henderson-Hasselbalch equation.

How it is measured or obtained

UV-metric titration at 37 °C in 0.15 M NaCl (atazanavir), or taken from the literature or predicted by software (the other drugs) [indulkar2015 P2, M1, M3; almeidaesousa2015 M3]. In the polymer screens, calculated with the ChemAxon plugins of MarvinSketch 5.2.0 from the structures vaneerdenbrugh2010b P9. Functional-group densities of the polymers (mmol/g of COOH, amide, amine) were calculated from the structures in the same way vaneerdenbrugh2010b P10. For the enteric polymers the pKa was measured by potentiometric base-to-acid titration, as the pH at 50% neutralization, with the carboxylic acid content between the two end points (HPMCAS 1.19 mmol/g, pKa 4.97; HPMCP 1.69, 4.32; CAP 2.94, 4.57; Eudragit L 100 4.48, 6.21), giving 99, >99, >99 and 80% ionization at pH 6.8 [hiew2022a P17, R22]. In the 20-system moisture study, calculated with MarvinSketch unless marked otherwise in the table [rumondor2011 P9]. In the release-mechanism papers: buffer pKa values calculated or stated (table in the HP-50 paper) [qi2022 C27, X16]; polymer pKa cited [qi2022 C23; bapat2023 M3].

Values in the library
materialvalue or classconditionspaper ids
clotrimazole; atazanavir; nicardipine5.89 (cited); 4.52 (measured); 7.2 (cited)37 °C[indulkar2015 M1, M2, M3]
ritonavir1.8 and 2.6cited[ilevbare2013a M1]
loratadine; efavirenz5.0; 10.2cited[ilevbare2013a M3, M2]
telapreviracid 11.8; base 0.31cited[mosqueragiraldo2015 M1]
CRH14.6 (base)method not printed[almeidaesousa2016 M1]
ibuprofen; phenylbutazone; diclofenac4.35; 4.35; 4.03 (acids)cited[almeidaesousa2015 M1, M2, M4]
pazopanib6.4 (strongest basic group)stated without a source; used for the 37 °C curves[sugihara2018 M1, C9]
flurbiprofen; flufenamic acid; chlorpropamide4.37; 3.88; 4.33 (acidic)computedvaneerdenbrugh2010b M3, M4, M5
chlorzoxazone9.39 (weakly acidic)computedvaneerdenbrugh2010b M6
bifonazole; lidocaine6.69; 7.75 (basic)computedvaneerdenbrugh2010b M7, M8
indoprofen against other carboxylic acids (other chapter)a somewhat weaker acid, with the smallest phase separationPVP dispersions with moisture[rumondor2011 C33]
PAA; PSSA; E100 amine4.5; −1.5; 8.5computed[vaneerdenbrugh2011a R2]
anthranilic acid; flufenamic acid (basic pKa)2.0; −2.1computed[vaneerdenbrugh2011a R1, R9]
HPMCAS, HPMCP, CAP, Eudragit L 1004.97, 4.32, 4.57, 6.21 (acid content 1.19, 1.69, 2.94, 4.48 mmol/g)titration, n = 2[hiew2022a R22]
lumefantrine (tertiary amine)8.73cited[hiew2022a M1]
indomethacin, ketoprofen, indoprofen in PVPpKa 4.5, 5.02, 5.8; resist, resist, separate slightly20-system table[rumondor2011 R15.a, R15.d, R15.e]
20 drug–polymer systemsOPLS-DA loading of pKa ≈ −0.35: lower pKa goes with no separationdiscriminant model[rumondor2011 R17, C40]
curcumin against E100pKa 10.51, 9.88, 8.38 against an average 8.4 for the basic monomeracid–base pairing[wegiel2014 M1, M5, C16]
HP-50 in BIS-TRIS, phosphate, Tris, TEA buffersbuffer pKa 6.5, 7.2, 8.1, 10.2; ≈44.8, 28.4, 6.6, 1.8% HP-50 dissolved at 60 min50 mM, pH 6.8[qi2022 R2, C27]
HP-50; HPMCAS-MFpKa 4.2; 4.92 or 5.0 (cited)[qi2022 C23; bapat2023 M3]
HPMCAS LF, MF, HF4.91, 4.97 (cited), 5.06back-titration, half-neutralization[bapat2025a M3, M4, M5]
bedaquiline8.5 (measured)SI, not 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 PEG dispersions

plasticization by water

The lowering of the glass transition temperature of an amorphous drug by absorbed water, taken in these papers as about 10 °C per 1% water [ilevbare2013a C23, E15; indulkar2015 C39]. A water-saturated drug-rich phase therefore has a wet Tg far below that of the dry amorphous drug, and its state at the test temperature (supercooled liquid or glass) follows from it (F2). New aspect (ASD process): in the coating study of four drug–polymer systems, water sorbed at the storage humidity lowers the glass transition of the powder, and the wet Tg onset minus the storage temperature (Tg − T, negative when stored above Tg) is the number compared with crystallization onset [moseson2022a P6, E2, R12]. Nucleation and growth speed up with humidity because sorbed water raises mobility and lowers the wet Tg, so a coating that works on the surface cannot rescue a powder whose bulk is mobile [moseson2022a C41, C25]. In dissolution, hydration lowers the Tg of a drug-rich bicalutamide layer, and the authors list mobility above the wet Tg among the reasons why not every ASD is susceptible to matrix crystallization [moseson2022b C63]. For hydrating posaconazole–HPMCAS the gastric stage lets crystals grow inside the wetted matrix after water uptake and plasticization (the authors' reading) [shah2024 C45]. New aspect (Physical stability): in drug–polymer dispersions water erases the Tg gain of a high-Tg polymer: at 75–76% RH felodipine and nifedipine dispersions with up to 25% PVP fell below the Tg of the dry drug [konno2008 C16; marsac2008a C17]. Plasticization is "directly related to the hygroscopicity of polymer", yet per gram of water it lowers the Tg of the pure drug most [konno2008 C20; marsac2008a C19]. New aspect (Supersaturation from ASD dissolution): the ASD dissolution papers use it in two places: to explain why wetted amorphous felodipine crystallizes faster at 37 than at 25 °C (dry Tg about 45 °C, just below 35 °C at 75% RH, cited) [alonzo2010 M1, C34], and to read the low Tg of an isolated ritonavir drug-rich phase as a ritonavir-rich phase holding a few percent of water [ilevbare2013d C8]. New aspect (Release mechanism and LoC): the wet Tg of the drug-rich phase decides whether nanodroplets are glassy or liquid at the test temperature. Indulkar and co-workers (2017) estimate that water-saturated amorphous nifedipine droplets have a Tg near 17 °C (dry 42 °C, 2.5% water), which makes drug exchange between droplets and solution slow at 5 °C, the premise of their isotope test [indulkar2017b C16, M1, C13]. Ritonavir, with a wet Tg around 0 °C, is a supercooled liquid under release conditions [que2019 R28, C49; indulkar2019a M1]. For indomethacin the relevant wet Tg is "plausibly" that of the drug-enriched surface (a 70% dispersion with about 6% water, onset 18 °C) rather than that of the neat drug (estimated 29 °C) [saboo2020 C52, R30, M1]; by the same 10 °C per 1% rule every lumefantrine dispersion's wet Tg would lie below 37 °C [hiew2022b C44].

Findings

Amorphous solubility and LLPS: F2. ASD process: F44, F38, F41. Physical stability: F5, F6, F9, F12, F33, F34. Supersaturation from ASD dissolution: F1, F9. Release mechanism and LoC: F5, F9, F18.

Related concepts

lowers the glass transition temperature; measured with water sorption; decides glass-liquid phase separation against LLPS; related to supercooled liquid. Raises surface molecular mobility; lowers the Tg that decides surface crystallization; sets how long an atomic layer coating protects a powder. Special case of plasticization; set by hygroscopicity; raises molecular mobility; related to matrix crystallization, drug-rich phase and moisture-induced crystallization. Gives the wet glass transition temperature.

Formulas

water plasticization rule of thumb, Tg − T, Gordon-Taylor equation.

How it is measured or obtained

DSC of the isolated drug-rich phase or of amorphous drug stored at high humidity, with water from gravimetric sorption or from drying the pellet [ilevbare2013a P8, P9, P15; mosqueragiraldo2015 P4, P5; almeidaesousa2015 P8]. For stored ASD powders the wet Tg onset was read in hermetically sealed DSC pans after 24 h at the storage humidity, 5 °C/min, triplicate preparations [moseson2022a P6]. The Tg of hydrated bicalutamide could not be determined [moseson2021 R27, X8]. In the felodipine and nifedipine moisture papers, DSC of bulk samples equilibrated at each RH and sealed [konno2008 P6; marsac2008a P7], reported as ΔTg dry minus 75% RH [konno2008 R9]. In the ASD dissolution papers: by DSC of the phase isolated by ultracentrifugation [ilevbare2013d P9]; for felodipine the humid Tg is cited, not measured in the medium [alonzo2010 C34]. In the release-mechanism papers: dry Tg by DSC, water content extrapolated from a 25 °C sorption profile to 100% RH, and a rule of about 10 °C Tg depression per 1% water [indulkar2017b P3, P4, E6]. DSC of a 70% dispersion after 4 h at 100% RH [saboo2020 P23]; sorption at 37 °C extrapolated to 100% RH with the rule [yang2021 P9].

Values in the library
materialvalue or classconditionspaper ids
ritonavirTg 50.4 → 0.4 °C with 4.03–5.15% waterisolated phase, 10–50 °C[ilevbare2013a R5, R6]
clotrimazole; atazanavirTg 28 → about 14 °C (1.4% water); 104 → about 51 °C (5.2%)precipitates, 37 °C[indulkar2015 R22, M1, M2]
telaprevirTg 103 → 52 °C; 4.31% water at 95% RHpellet, 37 °C[mosqueragiraldo2015 R2, M1]
sorafenib; griseofulvinTg 88.2 → 49 °C; 90.8 → 88 °C at 97% RHamorphous drug[almeidaesousa2015 M5, M6, R9]
erlotinib–HPMCAS 60% DLwet Tg − T about −8.8 °C (75% RH) and −2.3 ± 1.1 °C (43% RH)24 h at RH, T = 40 °C[moseson2022a R12]
erlotinib–PVPVA 50% DL−0.5 ± 1.2 °C43% RH[moseson2022a R12]
naproxen–HPMCAS 10% DL; lumefantrine–PVPVA 40% DLabout +11.3 °C (75% RH); +10.7, +14.3, +11.3 and +11.4 °C (43% and 31% RH)same[moseson2022a R12]
rule of thumb for stabilitymore than 50 °C between storage temperature and Tg (cited); the authors state the benefit of the coating holds at about 0 to +15 °C[moseson2022a E3, C45, R17]
felodipine with 25% PVP, HPMCAS, HPMCTg 54.9 → 31.1, 44.2 → 35.6, 43.1 → 34.4 °C0 → 75% RH[konno2008 R5]
felodipine dispersions ≤ 25% polymerTg ≈30–35 °C after 75% RH, below dry felodipine ≈43 °C25 °C[konno2008 R7, C16]
nifedipine pure; 25% PVP≈43 → 26 °C; ≈54 → 29 °C0 → 76% RHmarsac2008a R6
amorphous felodipine (cited)Tg ≈45.7 → 29.6 °C, smooth0 → 94% RH[rumondor2010 R10]
pimozide–PVP 50:50wet Tgs −21 and 44 °C94% RH[rumondor2009c R17]
ketoprofen–PVP 70:30wet Tg −23 °C94% RH[rumondor2009c R25]
celecoxib 6:4 dispersionsTg 64–103 → 22–42.1 °C after 3 days at 94% RHDSC[xie2016b R17, R20]
tacrolimus; tacrolimus–HPMC 1:163.6 → 51.4 °C; 77.2 → 49.0 °C after 3 days at 75% RHDSC[trasi2017 R15]
lumefantrine dispersions precipitated into water4–6% water (HPMCP, HPMCAS), 9% (CAP); Tg 45–112 °CTGA; DSC[bhujbal2021 R10]
felodipine (cited)Tg about 45 °C dry, just below 35 °C after 75% RHstorage data[alonzo2010 M1]
ritonavir drug-rich phase from a PVP dispersionTg inflection 1.05 °C against 50 °C for the amorphous drugwater, 37 °C, DSC at 20 °C/min[ilevbare2013d R2, M1]
indomethacin (cited)Tg falls rapidly with water content, as for felodipineliterature[alonzo2010 R24]
nifedipinedry Tg 42 °C; wet Tg approximately 17 °C (estimated)2.5% water (estimated)[indulkar2017b M1, C16]
ritonavirTg 50 °C; wet Tg around 0 °C (cited)release conditions[que2019 R28]
indomethacin; indomethacin–PVPVA 70%wet Tg 29 °C (estimated); onset 62.64 → 18.48 °C with ≈6% water37 °C, 100% RH[saboo2020 M1, R30]
loratadine, miconazole, danazol, elbasvirwet Tg 13.8 (DSC), −4.7, 73.3, 129.1 °C (rule)37 °C[yang2021 M1, M2, M3, M4]
atazanavirdry 105 °C, wet 55 °Ccited[correasoto2022b M1]
Pitfalls and disagreements

The griseofulvin Tg falls only 2.8 °C with an estimated 2.7% water, against 39 °C for sorafenib with 1.8%, and storage time and water content are not stated [almeidaesousa2015 X11]. The water content of the telaprevir pellet was not measured [mosqueragiraldo2015 X3]. For the coated powders the wet Tg values are not printed, only Tg − T bars, and the definition in words is the reverse of the sign used [moseson2022a R12, X24, E2]. Uncoated powders failed in about 1–2 weeks across the whole range of Tg − T, so Tg − T orders the coated failures only in part [moseson2022a X15]. The 0 to +15 °C statement applies to coated powders only [moseson2022a C45, R11]. The rule of 10 °C per 1% water given in the Definition fits the pure drugs but not the 25% polymer dispersions of the felodipine study, which drop about 5 °C per 1% (synthesis: 23.7 °C with 4.68% water [konno2008 R6]). Plasticization did not by itself cause phase separation or rank nucleation [rumondor2009c C38; konno2008 C26]. Plasticization by water did not rank celecoxib dispersions at 94% RH: four Tgs within about 5 °C, very different stability [xie2016b C46]. The water content of the ritonavir phase was not measured [ilevbare2013d C8]. Plasticization does not rank crystallization: indomethacin, with a similar Tg drop, crystallized much more slowly than felodipine during dissolution [alonzo2010 C42]. The 17 °C nifedipine value is an estimate from a rule taken from indomethacin; no Tg of water-saturated nifedipine was measured [indulkar2017b X8]. The 70% indomethacin dispersion is a model of the surface layer [saboo2020 X16], and most wet Tgs are rule estimates [yang2021 P9].

← Concepts and formulas

concept · as used in PEG dispersions

plasticization

Lowering of the glass transition temperature of a mixture by a component with a lower Tg; in the library water is the usual plasticizer of drugs, polymers and dispersions, and drugs, surfactants and plasticizers lower the Tg of polymers [konno2008 C2, C14; marsac2008a C1; correasoto2022b C39]. The opposite, a higher-Tg component raising the Tg, is antiplasticization [konno2008 C16]. New aspect (Supersaturation from ASD dissolution): plasticization by water acts during dissolution as well as during storage. For delamanid salts, four of eight liquefied at 40 °C/75% RH, which the authors attribute "presumably" to plasticization by water, and the salts took up 5.8–21.1% water against far less for the free base [duong2022a R20, C27]. In the undissolved matrix of an enteric dispersion in acid, absorbed water lowers the Tg and raises molecular mobility, which the authors give as the reason why the drug can crystallize there although the medium is subsaturated; water content and Tg were not measured in that state [nguyen2023c C43]. In hot-melt extrusion the drug itself plasticizes the polymer, which the authors use to justify extruding a drug at the polymer's Tg ("would") [alvarenga2025 C46]. New aspect (Release mechanism and LoC): in the release papers of 2021–2022 plasticization of the dispersion by the drug or by an added surfactant is used to explain faster polymer release. Clopidogrel (Tg −9 °C) lowered the dispersion Tg, and the faster PVPVA release from its binary dispersions is called a plasticization effect, as for PMMA with 20 wt% PEO, whose dissolution rate rose by a factor of two (cited) [correasoto2022a C48, R30]. TPGS lowered the Tg of 30% felodipine–PVPVA dispersions and "could" raise the limit of congruency through higher molecular mobility [saboo2021 R5, C43]. Surfactants and VP lowered the Tg of 10% atazanavir–PVPVA dispersions, and improved release is "due, at least in part," to plasticization raising polymer-chain mobility [correasoto2022b R20, C40]. In the other direction, more low-polarity drug "would be anticipated" to reduce water penetration and water plasticization and so lower the polymer rate [yang2021 C32], and a drug–polymer interaction that persists in water is proposed to do the same [que2021 C44]. Surfactants can also promote crystallization by plasticizing the matrix (cited), and Tween 80 and TPGS "could possibly" plasticize ritonavir droplets so that they coalesce [indulkar2022 C40, C48]; except for SDS every surfactant lowered the single Tg of 30:70 ritonavir–PVPVA (midpoints 70.90–77.51 against 82.24 °C) [indulkar2022 R18]. Built into PVPVA dispersions of high-Tg drugs, plasticizers lowered the Tg and raised release and the limit; the authors suggest increased polymer chain mobility, that is a faster disentanglement rate, as one mechanism [correasoto2023 C30, C39]. Faster initial water entry from drug plasticization, together with phase separation moving most water into the hydrophilic phase, is a "possible explanation" for polymer release rising faster than water penetration in MePHPH–PVPVA up to 20% [deac2023a C51, C50]. The 2023 surfactant study attributes barrier disruption by non-ionic surfactants to plasticization: Span 20 and Span 85 lowered the Tg of amorphous ritonavir from 46.8 °C to 7.7–27.8 °C and, partitioning into the drug-rich phase, are taken to soften the drug-rich layer so that flow removes it [yang2023 R22, C11, C18, C35]. The 2025 high-loading particle study warns that SDS, also a plasticizer, may predispose amorphous formulations to phase separation and recrystallization [hiew2025 C58].

Findings

Physical stability: F6, F9, F22, F28, F32. Supersaturation from ASD dissolution: F23, F24. Release mechanism and LoC: F15, F18, F21, F26, F31.

Related concepts

special case plasticization by water; contrasts with antiplasticization; measured by glass transition temperature; raises molecular mobility; tested by Tg-scaled crystal growth rate; lowers physical stability and matrix crystallization; limits in situ salt formation. Speeds polymer chain disentanglement.

Formulas

Gordon-Taylor equation gives the ideal-mixing Tg that plasticization lowers.

How it is measured or obtained

DSC of samples equilibrated at a given RH and sealed hermetically, onset or midpoint Tg [konno2008 P6; marsac2008a P7]; the drop in Tg between the dry state and storage at 75% RH, ΔTg [konno2008 R9]. Outside the subcategory, Tg of drug–polymer–surfactant or plasticizer blends by DSC [correasoto2023 R17, C30; nguyen2023a R13]. In the ASD dissolution papers: water sorption at rising relative humidity with DSC of the same materials for Tg, and open-dish storage at 40 °C/75% RH with visual inspection and PXRD [duong2022a P12, P10, P13]; in extrusion, the drug Tg and the polymer Tg set the processing window [alvarenga2025 M1, M2, M3, E2]. In the release-mechanism papers: DSC of dispersions with and without the additive [saboo2021 R5; correasoto2022b R13].

Values in the library
materialvalue or classconditionspaper ids
felodipine with 25% PVP, HPMCAS, HPMCTg 54.9 → 31.1, 44.2 → 35.6, 43.1 → 34.4 °C0 → 75% RH, 25 °C[konno2008 R5]
felodipine–PVP 0–100%ΔTg ≈15 °C (7% PVP) to ≈158 °C (pure PVP)dry minus 75% RH[konno2008 R9]
25% polymer dispersionsTg drop ≈13.3 °C at ≈1.1% water (PVP) vs ≈6.2 °C (HPMCAS)25 °C[konno2008 R6, C14]
nifedipine, pure and 25% PVP≈43 → 31 °C with ≈1.15 g/100 g water; ≈54 → 43 °C with ≈2 g/100 g25 °Cmarsac2008a R7, C19
pimozide–PVP 50:50two Tgs −21 and 44 °C wet against one at 94 °C dry94% RH[rumondor2009c R17]
PTM–HPMCAS–TPGS (outside)Tg ≈79 → 63 °C with TPGS at 20% loadingDSC[nguyen2023a R13, C22]
atazanavir and ledipasvir ASDs with plasticizers (outside)lower Tg than the binary ASDDSC[correasoto2023 C30]
celecoxib with 10% TPGS or sucrose palmitateTg 55.34 → 44.81 and 44.46 °C; growth fasterDSC[mosqueragiraldo2014 R5, C16]
pretomanid–HPMCAS with TPGS (other chapter)Tg falls as TPGS risesDSC[nguyen2023a R13, C22]
ritonavir–PVPVA with Span 20 or Span 85Spans in the drug-rich phase, read as plasticizing it and speeding separation ("likely")O-PTIR, NMR, confocal[yang2022b C58, X13]
griseofulvin, DPB, celecoxib with 5% PHBTg −5 to −12 °C; growth up to ≈10-fold fasterDSC; melt growth[sato2016 R7, R11, X6]
delamanid sulfonate salts, neatwater 5.8–7.1% (aromatic), 8.1–11.6% (camsylate, edisylate), 16.2–21.1% (esylate, mesylate); four liquefied95% RH; 2 weeks at 40 °C/75% RH[duong2022a R20]
delamanid edisylate 1:1 with excess acid59% water uptake and Tg 53.9 °C against 11.6% and 117.8 °C for the 2:1 salt95% RH[duong2022a R21]
delamanid salt dispersions at 20% drug with HPMCASwater ≈10–13.6% against ≈8.2% for the free-base dispersion; Tg 100.4–117.0 against 86.7 °C95% RH[duong2022a R22, R23]
delamanid free-base dispersions, 0 to 20% drugTg 121.0 → 86.7 °C (HPMCAS) and 120.1 → 82.0 °C (HPMCP); water at 95% RH ≈10.8–11.6% → ≈7.9–8.2%DSC, sorption[duong2022a R9, R10]
praziquantel, racemate and R-enantiomerTg about 37 and 34 °C, used to place the extrusion temperatures at 150 and 120 °CDSC[alvarenga2025 M2, M1]
felodipine–PVPVA 30% with 0, 2, 5, 10% TPGSTg 89.2, 86.0, 80.8, 71.1 °C (felodipine 44.7, PVPVA 105.4 °C)DSC, dry[saboo2021 R5]
atazanavir–PVPVA 10% with SDS, CTAB, TPGS, Tween 80, Span 20, Span 80, Span 85, VPTg lowered by 16, 9, 14, 14, 11, 13, 7, 16 °C from the binaryDSC, dry[correasoto2022b R20]
clopidogrel–PVPVA 40–60%PVPVA ≈4.1–6.7 against ≈2.6–2.7 mg/min/cm² for neat PVPVAcompacts, 37 °C[correasoto2022a R18, C48]
loratadine–HPMCAS 5%HPMCAS released faster than from neat HPMCAS, "feasible" plasticization by a low-Tg drugcompacts[yang2021 C31, R18]
ritonavir–PVPVA 30:70 with 5 parts Tween 80, TPGS, Span 20, Span 85, SDSTg midpoint 70.90, 72.84, 73.24, 77.51, 84.93 °C against 82.24 °CDSC, dry[indulkar2022 R18]
8:1 atazanavir and ledipasvir glasses with nine plasticizersTg lowered by 30.4–43.3 and 47.6–53.1 °Cmodulated DSC[correasoto2023 R17, R18]
ledipasvir–PVPVA 10% with 5 and 10 g TEACTg 99.1 → 85.8 °C; release 20 → 94% by 90 minDSC; compacts, pH 6.8[correasoto2023 R9]
amorphous ritonavir with Span 20 (80–20, 60–40)onset Tg 14.8, 7.7 °C (46.8 °C neat)DSC[yang2023 R22]
amorphous ritonavir with Span 85 (80–20, 60–40)27.8, 12.7 °CDSC[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 PEG dispersions

polymer adsorption to drug-rich droplets

The accumulation of a dissolved polymer at the interface of the drug-rich droplets of a phase-separated solution, where it is thought to reduce droplet coalescence and to disturb heterogeneous nucleation at the droplet–water interface ("likely"); with the cellulosic polymers it is accompanied by some polymer mixing into the droplets [jackson2014 C33, C50, C53, C48]. The zeta potential of danazol droplets moved with the charge of the polymer over 1–1000 µg/mL (PVP −7.1 to −3.5, HPMC −2.9 to −2.2, HPMC-AS −8.9 to −18.6 mV against −8.1), and bile salts made telaprevir droplets about −40 to −53 mV against −9.2 mV [jackson2016 R18; lu2017 R8].

Findings

F15, F32.

Related concepts

part of liquid-liquid phase separation; related to droplet coalescence, zeta potential and polymer adsorption.

Formulas

none.

How it is measured or obtained

Indirectly: droplet size by DLS over hours, zeta potential of the droplets, and the lowered onset of phase separation; preliminary NMR gave the polymer content of the droplets (not shown) [jackson2014 R22, R23, R5, R26].

Values in the library
materialvalue or classconditionspaper ids
danazol droplets aloneabout 490 nm at once, about 9800 nm after 1 h25 °C[jackson2014 R22]
danazol droplets with HPMC; HPMC-ASabout 305–345 nm up to 2 h; about 230–250 nm up to 4 h10 µg/mL polymer[jackson2014 R22]
zeta potential: alone; PVP; HPMC; HPMC-AS−8.1; −5.3; −2.3; −13.7 mV25 °C[jackson2014 R23]
polymer in the dropletsaround 10–20% for HPMC, below about 10% for PVP, none for HPMC-ASpreliminary NMR[jackson2014 R26]
ritonavir nanodroplets (ASD dissolution chapter)charge repulsion between polymers adsorbed at the ritonavir–water interface "likely" stabilizes against coalescence37 °C[ilevbare2013d C38]
telaprevir droplets, 1.86 mM six bile saltszeta about −40 (SGC) to −53 mV (STCDC)180 µg/mL, pH 6.5[lu2017 R8]
Pitfalls and disagreements

The NMR is preliminary and not shown, with no value for HPMC-AS; the site of nucleation was not measured [jackson2014 X15]. The coalescence claim has no droplet size in the first minutes for danazol alone [jackson2014 X6]. Zeta potential was measured at 180 µg/mL, not in the induction-time solutions [lu2017 X6].

← Concepts and formulas

concept · as used in PEG dispersions

polymer chain disentanglement

Evidence table: polymer chain disentanglement. Content from the release-mechanism chapter (2020–2025), with rows from the Miscibility and drug-polymer interactions and ASD process chapters.

The step in which polymer chains leave the swollen, plasticized gel layer for the medium. A glassy polymer dissolves by solvent ingress, swelling, plasticization and gel-layer formation, chain disentanglement by reptation over a characteristic time and diffusion of the free chains; for high-molecular-weight neutral polymers such as PVPVA under stirring, solvent ingress or disentanglement is typically rate-limiting (cited) [correasoto2022b C33]. Polymer dissolution as a whole is controlled by water diffusion into the matrix, chain disentanglement from the plasticized gel and chain diffusion in the boundary layer; a polymer with Tg above the test temperature must take up a critical amount of solvent before its chains can disentangle, and the further the temperature lies below Tg, the more solvent is needed [hiew2022b C38, C39, E1]. Que and co-workers (2021) add from the literature that solvent quality (Flory–Huggins χ) matters, and that neat PVPVA at high water activity has its Tg below room temperature and gels and dissolves rapidly [que2021 C42]. Disentanglement is faster above Tg; below Tg the gel layer thins and dissolution changes from disentanglement to cracking (cited) [saboo2020 C54]. Enteric polymers must also ionize, which increases hydration and chain mobility and enables reptative disentanglement [qi2022 C10]; the higher hydration of HP-50 salts "likely" offsets the effect of a lipophilic drug on the water fraction of the gel [qi2022 C40]. A neat PVPVA compact first swelled and then shrank, read as chains that had not yet had time to disentangle and later disentangled and dissolved [yang2022a C32, R9]. Correa Soto and co-workers (2023) cite the Devotta free-volume model, in which the maximum chain mobility rises with the fractional free volume of the gel, and take the disengagement rate as proportional to chain mobility [correasoto2023 E2, E3, C39]. In low-loading MePHPH gels about as much water per polymer was needed to disentangle as in neat PVPVA, as expected if the hydrophilic phase controls gel erosion, and the congruent release rate is proposed to be controlled by water penetration and by disentanglement at the gel/solution surface [deac2023a C52, C73]. The 2024 phase-diagram paper takes the gel–solution boundary as the polymer concentration at which chains disentangle, which a strongly interacting drug such as phenolphthalein "may impact" [deac2024b C39]; below the limit droplets leave when the chains disentangle, above it a continuous drug-rich phase cannot [deac2024b C47].

Findings

Release mechanism and LoC: F15, F18, F22, F23, F24, F25, F26, F29, F30.

Related concepts

takes place in the gel layer; needs plasticization by water below the wet glass transition temperature; sets the rate of polymer-controlled release; faster with plasticization by the drug or a surfactant; needs chains above the critical entanglement molecular weight to be entangled in the first place.

Formulas

critical polymer volume fraction for glassy polymer dissolution; the disentanglement rate expression above is named and printed only by Hiew and Taylor (2022) [hiew2022b E2]. free-volume chain mobility (Devotta model).

How it is measured or obtained

Not measured directly in the library. It is inferred from polymer release rates of compacts [saboo2020 C55; correasoto2022b C40] and estimated through the critical polymer volume fraction and the Narasimhan–Peppas disentanglement rate k_d = B/(1 - v_p)^{1.9} [hiew2022b E1, E2].

Values in the library
materialvalue or classconditionspaper ids
PVPVA (Tg 102.9 °C, density 1.19 g/cm3)critical polymer volume fraction 0.89, so at least 11% water to start disentangling37 °C, estimated[hiew2022b R21]
lumefantrine salt–PVPVA dispersions35–55% water at 95% RH, more at lower loading40 °C[hiew2022b R5]
lumefantrine–PVPVA 5–35%; 40–50% (Miscibility chapter)PVPVA ≈4.49–4.91 against 4.58 neat; 0.21–0.004 mg/min/cm²pH 6.8, 37 °C[hiew2022a R13, C59]
ritonavir–PVPVA tablets (ASD process chapter)discrete drug-rich nanodroplets in the gel layer move into solution as the polymer disentanglesuncoated tablets, 37 °C[benson2025 C28]
Pitfalls and disagreements

The papers propose but do not measure how the drug changes disentanglement: a drug–polymer interaction that persists in water is proposed to occupy polymer solvation sites and so slow plasticization and disentanglement [que2021 C44], interaction of the hydrophobic drug with the polymer "is expected to" retard chain hydration [hiew2022a C49], and above a critical loading dilution by the drug "likely" prevents enough water uptake for disentanglement [hiew2022a C59]. A lower Tg from TPGS "should theoretically" let disentanglement start with less water [saboo2021 C43]. With 10 °C per 1% water, the wet Tg of every lumefantrine dispersion should lie below 37 °C, so the authors find release "difficult to rationalize" by wet Tg and the disentanglement model alone [hiew2022b C44]. PVPVA dissolves when a critical water concentration is reached at the gel–solution interface, at a steady state between water penetration and disentanglement [benson2025 C61]. For HPMCAS-MF (about 18 kDa, below the critical values estimated for other polysaccharides) the authors judge molecular entanglement "unlikely" and dissolution diffusion- rather than disentanglement-controlled, since the rate stayed linear in the square root of rotation speed with no plateau [bapat2023 C45, C30, R27].

← Concepts and formulas

concept · as used in PEG dispersions

polymer crystallization

The crystallization of the semicrystalline carrier itself, here PEG 3350, as it solidifies from the melt. In the PEG papers it is followed as the growth of PEG diffraction peaks (relative crystallinity), as the shift of the SAXS peak (long period) and as the advance of spherulites zhu2012 E1, R21; zhu2011 R7, R8. PEG crystallizes within seconds to minutes and the drug and the polymer affect each other's crystallization zhu2012 C5, C18.

Findings

F5, F7, F10, F12.

Related concepts

consists of relative crystallinity, spherulite growth rate and lamellar long period; described by Avrami equation; part of semicrystalline solid dispersion; related to polymer chain folding.

Formulas

relative crystallinity from XRD peak areas, Avrami equation, Bragg relation for the lamellar long period.

How it is measured or obtained

By synchrotron XRD with the PEG peaks at q 1.35 and 1.65 Å⁻¹ integrated against the total area, giving X(t) and an induction time; by an Avrami fit; by simultaneous SAXS/WAXS; by polarized light microscopy of the spherulite front at 40 °C, because growth is too fast at 25 °C zhu2012 P4, P8, E1, E2, C30; zhu2011 P2.

Values in the library
materialvalue or classconditionspaper ids
pure PEG 335050% at about 22–24 s (25 °C) and about 64 s (40 °C); complete within 2 minsynchrotron XRDzhu2012 R4, C18
PEG in haloperidol, benzocaine, ibuprofen, fenofibrate dispersions, 25 °Ct_{50} 15, 22, 26, 21 s20/80zhu2012 R23.d
PEG in ibuprofen/PEG; fenofibrate/PEG, 40 °Ct_{50} 114 s; 52 s20/80zhu2012 R23.d
PEG spherulites at 40 °C10 (text), 8, 8, 3, 1 µm/s for pure PEG, haloperidol, fenofibrate, ibuprofen, benzocaineCPOMzhu2012 R22
PEG lamellaelong period 13.3 nm falling to 11.2 nm in 24 h at 25 °CSAXSzhu2011 R8
Pitfalls and disagreements

The pure-PEG 40 °C curve differs by about 15 s between figures and the pure-PEG spherulite rate is 10 µm/s in the text but about 20 µm/s in the plot zhu2012 X1, X2. A fitted Avrami exponent below 1 is read as one-dimensional growth although n = 1 is the lowest value on the authors' scheme zhu2012 C19, X9. The polymer in the humidity study is PEO 100000, not PEG 3350 marsac2008b M7.

← Concepts and formulas

concept · as used in PEG dispersions

polymer partitioning into the drug-rich phase

The distribution of a dissolved polymer between the aqueous phase and the drug-rich phase that forms above the amorphous solubility, expressed as the polymer:drug weight ratio in the drug-rich phase or as the partition coefficient K = C_p/C_q (polymer in the drug-rich phase over polymer in water) [ueda2021 P4; ueda2022 E3]. For ibuprofen it is seen as the polymer that disappears from the solution NMR spectrum when droplets form, because polymer in the viscous droplets reorients too slowly to give a signal [ueda2020b C22; ueda2021 C7]. Polymer in the drug-rich phase lowers the chemical potential of the drug there and so the amorphous solubility (F19–F21) [ueda2021 C11]. New aspect (Bioperformance): a large share of polymer in the drug-rich phase lowers the chemical potential of the drug there and may lower the flux plateau [mosqueragiraldo2018b C34, C35, C37]. HPMCAS grade AS-HF distributed much more into the drug-rich phase than AS-LF for four drugs, which the authors say accounts for its lower amorphous solubility [ueda2020a C20, C33]; HPMCAS and PVP are not expected to enter the atazanavir–darunavir phase [alkalla2026 C38]. New aspect (Crystallization from solution): the share of a dissolved polymer found in the drug-rich precipitate against the solution, with PVPVA and HPMCAS in both (about 7% of the felodipine precipitate), PAA almost only in the water and P2VP in the precipitate [raina2015b R12, C20]; from 2021 the polymer share in the droplets was set against crystallization inhibition, and it did not rank HPMCAS against Eudragit E PO for enzalutamide but did rank three HPMCAS grades for posaconazole [wilson2021 C38; shah2025 C51].

Findings

Amorphous solubility and LLPS: F15, F19, F20, F21, F22. Bioperformance: F7, F19. Crystallization from solution: F19, F26, F37, F44.

Related concepts

lowers the amorphous solubility through the chemical potential of the drug in the drug-rich phase; driven by the hydrophobic effect and drug–polymer interaction (Flory-Huggins interaction parameter); measured with the help of NMR chemical exchange broadening; affects colloidal stability. Depends on polymer hydrophobicity. Related to amorphous precipitation.

Formulas

van't Hoff equation, Flory-Huggins reduction of amorphous solubility, ideal-mixing reduction of amorphous solubility. Drug-rich phase composition, polymer partitioning into the drug-rich phase by depletion.

How it is measured or obtained

Quantitative ¹H NMR of the dissolved polymer (peak at 2.0 ppm for PVP and PVP-VA, 3.1 ppm for HPMC) against TSP and a calibration line, compared with the polymer concentration before drug is added; the missing part is taken as being in the drug-rich phase and divided by the phase-separated drug [ueda2021 P3, P4]. Variable-temperature NMR gives K and, from a van't Hoff analysis, ΔG, ΔH and ΔS of transfer [ueda2022 P12]. Other methods in the library assay the polymer in the ultracentrifuged pellet or supernatant [mosqueragiraldo2018b R14; shah2025 R16]. Colorimetric assay of polymer in the centrifuged pellet and Nile red fluorescence for drug [mosqueragiraldo2018b P12–P14]. Solution NMR of the polymer with and without droplets (acetyl or hydroxypropyl peak), the lost signal being read as polymer in the droplets [ueda2020a R7, R8]. Ultracentrifugation of the suspension and ¹H NMR of precipitate and supernatant in d6-DMSO, masses scaled to 10 mL [raina2015b P8].

Values in the library
materialvalue or classconditionspaper ids
ibuprofen with six polymerspolymer:drug ratio 0.40 (PVP K12), 0.52 (K25, K90), 0.87 (PVP-VA), 0.95 (HPMC 603), 1.14 (HPMC 615); dissolved drug 131–89 µg/mL1000 µg/mL polymer, 400 µg/mL drug, pH 2.0 (D2O), 37 °C[ueda2021 R5]
ibuprofen with PVP K25, PVP-VA, HPMC 603ratio stops rising above 200 (K25) and 500 µg/mL polymer (PVP-VA); HPMC 603 keeps rising (about 0.08 → 0.95)25–1000 µg/mL polymer[ueda2021 R8]
ibuprofen with HPMC, PVP-VA, EUD-Epolymer still in solution at S_a + 300 µg/mL: about 141, 85, 289 of 300 µg/mL37 °C[ueda2020b R13]
ibuprofen, 15–60 °Cratio 0.24 → 0.62 (PVP), 0.46 → 1.32 (PVP-VA), 0.20 → 1.46 (HPMC, to 55 °C)1000 µg/mL polymer[ueda2022 R10]
polymer transfer into the ibuprofen-rich phaseΔG −12 to −19 kJ/mol; ΔH of HPMC 58 → 12, PVP-VA 25 → 5 kJ/mol15–60 °C, quadratic van't Hoff fit[ueda2022 R22, R23]
telaprevir ASDs, 150 µg/mL drugpolymer fraction of the pellet about 0.9 (cellulose acetate suberate), below 0.3 (PVPVA, HPMCAS)pH 6.8, 37 °C[mosqueragiraldo2018b R14, C35]
posaconazole with HPMCAS grades L, M, Hpolymer weight fraction in the phase about 0.05, 0.14, 0.31, water ignored100 µg/mL drug, 900 µg/mL polymer, pH 6.5, 37 °C[shah2025 R16, R17, C30, E3]
enzalutamide dropletsEudragit E PO associates with the droplets more than HPMCASpH 6.5, 37 °C[wilson2021 R7, C19]
telaprevir, CA Sub / HPMCAS / 70% HPMCAS / PVPVApolymer fraction 0.90 / 0.21 / 0.27 / 0.22150 µg/mL[mosqueragiraldo2018b R14]
felodipinePVPVA and HPMCAS distributed; PAA in the supernatant; P2VP with the drugprecipitates[raina2015b C20, R12]
ibuprofen, polymerspolymer ratio falls with total drug37 °C[ueda2021 R10]
atazanavir, nifedipine, clozapine, ketoconazole droplets with 1000 µg/mL AS-LF / AS-HFNMR-detected polymer about 975 / 880, 955 / 480, 920 / 415, 990 / 600 µg/mL37 °C[ueda2020a R8, C20]
felodipine 100 mg, PVPVA 45 mgprecipitate 6.8 mg, supernatant 36.7 mg10% DMSO, pH 6.8[raina2015b R12]
felodipine, HPMCAS7.1 mg and 34.2 mgsame[raina2015b R12]
felodipine, PAA; P2VP (18 mg)0.9 and 46.6 mg; 17.7 mg and not detectedsame[raina2015b R12]
enzalutamide droplets, HPMCAS, Eudragit E PO12.7–24.7 and 40.8–41.0 w/w% (NMR); about 19–23 w/w% both (colorimetry)120 and 70 µg/mL drug, pH 6.5[wilson2021 R7, R9, X4, X5]
Pitfalls and disagreements

The "polymer in the drug-rich phase" is the NMR-invisible polymer and would include polymer adsorbed at droplet surfaces; the droplet composition and the activity of the drug in it were not measured [ueda2021 X4; ueda2020b X4]. The molecular-weight rule fails between PVP K25 and K90, polymer hydrophobicity was not measured, and the ranking of HPMC 603 against PVP-VA reverses with polymer concentration [ueda2021 X7, X8]. Two papers state that polymers used in ASDs have minimal impact on the amorphous solubility or do not take part in the drug-rich phase, which the ibuprofen data contradict for PVP K25 (154 → 121 µg/mL) [trasi2016 C32; alkalla2026 C38; ueda2021 R5]. The transfer enthalpy is per polymer species of different molar masses and has no stated uncertainty [ueda2022 X9, X8]. In the telaprevir study HPMCAS and PVPVA fractions are equal although their solubilities differ twofold [mosqueragiraldo2018b X7]. For atazanavir only about 12% of AS-HF disappeared from the solution signal although the ceiling fell by more than half, and the signal does not separate polymer mixed into the droplet from polymer adsorbed at its surface (F19) [ueda2020a X4, X10]. The felodipine precipitate study used four polymers, one drug and single determinations, and its totals deviate from the stated amounts by up to about 8% [raina2015b X9, X12].

← Concepts and formulas

concept · as used in PEG dispersions

reduced glass transition temperature

T_{rg} = \frac{T_g}{T_m} with both temperatures in kelvin baird2010 E4. Assuming equal viscosity at Tg, a higher Trg means a more viscous liquid between Tg and Tm and so, it was expected, a better glass former; a typical value of 0.66 had been proposed baird2010 C1, R29.

Findings

F5, F12.

Related concepts

depends on glass transition temperature; related to Tm − Tg temperature gap; proposed predictor of glass-forming ability; contrasts with melt viscosity as a predictor.

Formulas

reduced glass transition temperature.

How it is measured or obtained

From DSC Tg (midpoint) and melting peak baird2010 P1; where Tg cannot be measured, Tg is estimated from a Trg–molecular-weight fit or a fixed Tg/Tm ratio [baird2010 E27; vaneerdenbrugh2010a E7].

Values in the library
materialvalue or classconditionspaper ids
class I (23 molecules)0.69 ± 0.02DSCbaird2010 R14
class III (17 molecules)0.73 ± 0.04, not significantly different from class IDSCbaird2010 R14
classes II and III0.65–0.76 and 0.65–0.81DSCbaird2010 F5
ritonavir0.81DSCbaird2010 R18.ab
class II compounds0.65–0.76, not the constant 2/3DSC[baird2012 R14]
pretomanid; delamanid0.67; 0.64, both class IDSC[nguyen2023a C59]
35 compoundsT_{rg} = 0.00021\,\mathrm{MW} + 0.64433,\quad R^2 = 0.44regressionbaird2010 E27, R19
Pitfalls and disagreements

Trg did not separate the classes, nor class I-A from I-B baird2010 C23, C37, and compounds with similar Tm − Tg had very different tendencies [baird2012 C36]. Trg of the 16 class I molecules without measured Tg is a function of molecular weight alone baird2010 X17. A small Tm − Tg (high Trg) did go with slow growth [trasi2014a R8.h].

← Concepts and formulas

concept · as used in PEG dispersions

secondary nucleation

The formation of new crystals in the presence of existing ones, from their surface or from fragments of them, with a lower energy barrier than primary nucleation [purohit2019 C3; duong2022b C35]. In the dissolution papers it enters in two ways: as the reason why seeds in an ASD speed crystallization and desupersaturation beyond their own growth [purohit2019 C3, C32], and as a process assumed to be small, so that the fall of the donor concentration reflects growth of the seeds alone [hate2019 C42]. New aspect (Crystallization from solution): it adds to the loss of dissolved drug in a seeded run and would confound a growth measurement [ilevbare2012a C14, C15; ilevbare2013b C12]; in seeded runs the authors judged it absent for celecoxib and ritonavir and present for efavirenz above 10 µg/mL [ilevbare2013b R5, C13]. Turbidity at 370 nm marks it in the telaprevir seeded runs (it rose at δ 7.9 and 12.5, not at 2.4), and STC and STCDC are said to inhibit it because no rise was seen (traces not shown); in acetaminophen PVPVA "does not appear" to stop it [lu2017a R4, R5, C22; trasi2015 C22].

Findings

Bioperformance: F29, F30. Crystallization from solution: F3, F5, F20, F27, F33, F42.

Related concepts

follows from crystal seeding; competes with crystal growth; part of desupersaturation; lowered by an absorptive sink; part of nucleation; a confounder of crystal growth rate; related to heterogeneous nucleation and residual crystallinity.

Formulas

power-law crystal growth rate (the fitted order assumes minimal secondary nucleation).

How it is measured or obtained

Not separated from growth in the Bioperformance papers. Elsewhere: turbidity in seeded runs, the size distribution of the seeds before and after growth, a mass balance of seed volume against solute removed, SEM of small crystals on larger ones, and the rise of a fine-particle count after a pH shift [ilevbare2012a R7, R8; ilevbare2013b R5, R6; que2018 R9, R10; shah2024 R14, C28]. In the seeded growth papers the turbidity is read at 280 or 350 nm, with an unseeded control at the same supersaturation and a volume balance on the seeds [ilevbare2013b P11, R5; ilevbare2012a R7, R8, R9].

Values in the library
materialvalue or classconditionspaper ids
tacrolimus seeded solutionsassumed minimal, so the desupersaturation rate gives the growth order (1.677)hollow-fibre module, S 8–20[hate2019 C42, R18]
ritonavir, celecoxib; efavirenzno significant secondary nucleation in seeded runs and no turbidity rise between 5 and 22 µg/mL (ritonavir also judged by size distribution and mass balance); efavirenz turbidity rose at every concentration above 10 µg/mL (S 1.2) once macroscopic crystals formedseeded, 37 °C; turbidity, size distribution[ilevbare2013b R5, R6, C12, C13]
telaprevirsecondary nucleation with growth at δ 7.9 and 12.5, none at 2.4; inhibited by 1.86 mM STC or STCDC; extinction without bile salt 0 (δ 2.4), about 0.047 (δ 7.9), about 0.061 (δ 12.5)370 nm extinction, pH 6.5, 37 °C[lu2017a R4, R5, C11, C22]
paclitaxel seedssmall needles on larger crystals in SEM; lower aspect ratio after growthno polymer[que2018 R9, R10, C43]
posaconazole 10 wt% ASDfine-particle count rose after 15 min following the pH shiftFBRM and SHG[shah2024 R14, C28, C47]
ritonavir seeds after growthmonomodal size distribution; unseeded 10 µg/mL no loss in 8 hS 7.6[ilevbare2012a R7, R9]
telaprevir seeds, δ 7.9possible; bulk growth assumed dominant50 mM phosphate pH 6.5, 37 °C[lu2018 C8]
atazanavir needles from buffersecondary growth and small needles on larger ones; none in human fluidSEM, 300 min[elkhabaz2021 R17]
posaconazole with 0.4–20 µg/mL nanocrystal seedsinduction period removed; immediate desupersaturation at 2 and 20 µg/mLPBS pH 6.5, S 33.6[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 PEG dispersions

self-association

Association of a molecule with its own kind, by hydrogen bonds between drug molecules or between polymer molecules. In the papers of this chapter: the cyclic carboxylic acid dimers that hold most of amorphous indomethacin, as in the γ crystal, with a few chain ends [taylor1997 C20]; the NH-to-carbonyl bond between neighbouring felodipine molecules [kestur2010a R15]; the weak C–H···N chains of crystalline bifonazole [kestur2011 R18]; and the multiple intra-species hydrogen bonds of PAA, which can compete with a drug [rumondor2009a R24, C45]. A polymer is thought to slow crystallization when it breaks the self-association needed for attachment to the crystal, for example by taking the acid OH of indomethacin or by bonding the imidazole nitrogen of bifonazole, and PAA self-association "is easily disrupted" by a better acceptor [taylor1997 C43, C45; kestur2011 C16, C19]. Further cases: dextran–dextran hydrogen bonds, assumed to be stronger or more numerous than dextran–PVP ones [vaneerdenbrugh2012a C36, C37]; amide self-association in benzamide and phenacetin crystals, broken more often by a carboxylic acid partner than by a tertiary amide [vaneerdenbrugh2011a C34, C35]; hydrogen-bonded sheets of naringenin and quercetin with a strong lattice energy [wegiel2013a C26]; and Br···C contacts of 3.373 and 3.425 Å in the brotrimazole crystal, which may compete with the polymer [que2020 R5, C27]. The bile-salt simulations of 2016 add a solution aspect, the tendency of a bile salt to contact itself instead of the drug: SUDC paired with itself during 73% of the trajectory of a nevirapine–SUDC tetramer and SDC during 5%, which the authors say "may indicate a lower tendency to interact with a nevirapine nucleus" for SUDC [li2016a R26, C60].

Findings

Miscibility and drug-polymer interactions: F1, F13, F14, F17, F20, F22, F24, F25. Crystallization from solution: F2, F30. Physical stability: F18, F24, F30.

Related concepts

part of hydrogen bonding; contrasts with drug-polymer interactions; related to intramolecular hydrogen bonding and binding constant; related to bile salt micelles and polymer self-association; competes with hydrogen-bond donor and acceptor groups; related to molecular recognition.

Formulas

none.

How it is measured or obtained

By IR and Raman of the amorphous drug against the crystal, with the dimer found by the mutual exclusion rule [taylor1997 C14, C15]; by the felodipine NH and carbonyl bands (3341 cm⁻¹, 1701 and 1682 cm⁻¹) [kestur2010a R10, R15]; from crystal structures [kestur2011 R18, R19]. In solution, by cluster analysis of 100 ns molecular-dynamics runs (molecules within 3.0 Å form one cluster) [li2016a P9, P10].

Values in the library
materialvalue or classconditionspaper ids
amorphous indomethacinacid dimers (IR 1710 cm⁻¹, no Raman band); chain-end shoulder 1735 cm⁻¹quench-cooled melt[taylor1997 R5.g, R5.h, R6, C20]
α-indomethacinacid bands in both IR and Raman, read as chainspolymorph reference[taylor1997 R5.e, R5.f, C16, C17]
amorphous felodipineNH 3341 cm⁻¹ bonded to a neighbouring carbonyl; carbonyls 1701 and 1682 cm⁻¹spin-coated film[kestur2010a R9.a, R10, R15]
bifonazoleweak C–H···N chains along the b axis; no traditional donorcrystal structure[kestur2011 R18]
PAAdimers and other self-associations, easily disruptedcited[kestur2011 R22]
felodipine–PAAPAA self-association "speculated" to limit mixing at 30–70% PAADSC, IR, PXRD[rumondor2009a C45, R24]
resveratrol, ledipasvir, itraconazole (other chapters)disrupting self-assembly by a polymer thought critical; drug–drug interactions seen by NMR; ITZ aggregates by fluorescencevarious[wegiel2013b C5; que2019 C23; mugheirbi2017 C31]
dextran–PVPdextran–dextran bonds assumed stronger or more numerous than dextran–PVP; OH band 3356–3358 → 3370–3383 cm⁻¹ with more PVPFTIR, DEX1–PVP12[vaneerdenbrugh2012a C36, C37, R16]
carboxylic acid drugs; benzamide, phenacetinacid dimers in crystals; amide–amide only 100 and 94% alone, 0% with COOHcrystal structures, CSD[vaneerdenbrugh2011a R7, R14]
naringenin, quercetinhydrogen-bonded sheets; two and three free OH after intramolecular bondsstructure[wegiel2013a C26, C30]
brotrimazoleBr···C 3.373 and 3.425 Å inside the 3.55 Å van der Waals sum150 K crystal[que2020 R5, C29]
SUDC-SUDC; SDC-SDC in NVP tetramerscontact 73%; 5% of 2000 snapshotsMD, 310 K[li2016a R26]
NVP-SUDC; NVP-SDC tetramersone cluster in 86% of snapshots; mostly two or three clustersMD, 310 K[li2016a R24]
posaconazole, ionized, below pH 2.5solubility above the calculated values, "probably" self-associationphosphate buffers, 37 °C[duong2022b C13, C14]
PAA with flutamidePAA forms hydrogen-bonded dimers and "very likely" prefers itself; no IR shift with the drug1:1 films[trasi2012b R28, C37, R18]
resveratrolthree OH groups in an extended network with flip-flop bonding; high crystallization tendencycrystal structure, cited[wegiel2013b C27, C28]
curcumin with donor-and-acceptor polymerscellulosics "may" disrupt curcumin self-association better than acceptor-only PVPstorage[wegiel2014 C31]
celecoxib with PVP, PVPVAstrong drug–polymer hydrogen bonds "may restrict" diffusion and self-associationargument from IR[xie2016b C44]
indomethacin in HPMC from 60% drug1709 cm⁻¹ acid-dimer band returns; an emission band near 480 nm "could be due to" dimersIR; fluorescence[tian2016 R10, C27, C46]

Evidence table: self-association.

Pitfalls and disagreements

The 1735 cm⁻¹ chain-end assignment rests on analogy with liquid acetic acid and α-indomethacin, and the evidence for dimers is the absence of a Raman band [taylor1997 K2, X4]. The α chain model depends on unpublished unit-cell data [taylor1997 X10]. PAA self-association is cited from the literature and was not measured in the felodipine dispersions [rumondor2009a C39, R24]. For bifonazole the statement that the imidazole nitrogen breaks PAA dimers is reasoning, not measurement [kestur2011 X9, C16]. The bile-salt simulations used one trajectory per system, nevirapine only, tetramers for SDC and SUDC only [li2016a X24]. In the physical-stability papers self-association in the dispersions was not measured either; the readings come from crystal structures, cited data and missing IR shifts [trasi2012b R28; wegiel2014 X7].

← Concepts and formulas

concept · as used in PEG dispersions

solution crystallization

Nucleation and growth of crystals from the supersaturated solution, as against crystallization inside the undissolved ASD (matrix crystallization) [elkhabaz2017 C38; mosqueragiraldo2018b C52]. Crystallization from solution decided the enzalutamide-PVPVA dispersions (fall after the maximum) and the pretomanid case, in which droplets present above the amorphous solubility defeated HPMCAS-HF within minutes [wilson2018 C18, C42; nguyen2023a C13]. New aspect (Supersaturation from ASD dissolution): crystals nucleate and grow in the supersaturated liquid after the amorphous solid has dissolved, the second route by which an amorphous solid loses its advantage [alonzo2010 C47]. Polymer in a dispersion can move crystallization from the matrix to this route (nifedipine) [raina2014b C21]. When dispersions release completely, the authors of a celecoxib study take matrix crystallization as suppressed and attribute the differences between polymers to crystallization from solution, which the induction time measures [xie2015 C39, C40].

Findings

Bioperformance: F9, F10, F11, F12, F14, F23, F27. Supersaturation from ASD dissolution: F1, F3, F4, F6, F14, F21, F24.

Related concepts

part of desupersaturation; contrasts with matrix crystallization; related to crystal growth and crystallization tendency; part of crystallization during dissolution; measured by nucleation induction time.

Formulas

supersaturation ratio, classical nucleation theory.

How it is measured or obtained

Fall of concentration with SHG, PLM or PXRD for the crystals; induction time by UV extinction [elkhabaz2017 P5, P8, P9, P10; hate2017 P2]. In the ASD dissolution papers: by a fall of the solution concentration together with crystals seen in the liquid rather than in the solid: needles between amorphous particles under polarized light [alonzo2010 R19], fine plate-shaped crystals in the solution around dissolving dispersion particles [raina2014b R13], free-floating needles in suspensions [chen2015a R15], or a rise of a pyrene ratio as crystals expel the probe [jackson2015 C14].

Values in the library
materialvalue or classconditionspaper ids
ezetimibe, buffer 21 µg/mLinduction about 1 min; PVP 100 µg/mL about 71 min; HPMC-AS about 50 min37 °C[elkhabaz2017 R6]
ezetimibe, FeSSIF 123 µg/mLHPMC-AS 50 µg/mL more than 360 min; PVP about 10 min37 °C[elkhabaz2017 R7]
nevirapine 500 µg/mLabout 5 min; PVPVA about 60 min; HPMC-AS over 4 hpH 6.5[hate2017 R2]
telaprevir 90% PVPVA ASDbelow 90 µg/mL from about 43 min; about 20 µg/mL at 100 min[mosqueragiraldo2018b R5]
atazanavir 50:50 PVPVA ASDcrystals from about 80 minhollow fibre[hate2018 R14]
indomethacin–Eudragit EPO ASDcrystallization after 15–20 min; small α crystals within about 20 minacid stage, pH 2.2, 37 °C[xie2017 R11, R23]
celecoxib, no polymer or PAAwithin 5 min at 22 µg/mL; ≈3.6 µg/mL at 1 hpH 6.8, 37 °C[xie2016a R2, R3]
enzalutamide 70 µg/mLcrystallized in about 15 min without polymer; held more than 16 h by four of 24 polymers added at 50 µg/mLpH 6.5[wilson2020 R1, C32]
pretomanid 80 µg/mL1.6–3.1 min with most enteric polymers, 22–24 min with HPMCAS-MF or HPMC, over 1000 min with HPMCAS-HF100 µg/mL polymer, pH 6.5[nguyen2023a R5]
amorphous indomethacinneedles in the liquid within 60 min, solid amorphous ≥4 h; ≈14.9 → ≈2.7 µg/mLpH 2, 25 °C[alonzo2010 R19, R11, R7]
nifedipine 50:50 dispersionscrystals below 2 µm in solution against 1–300 µm by the matrix routepH 6.8[raina2014b R13, R2]
danazol dispersions PVP / HPMC / HPMCASinduction ≈56–70 / ≈188–200 / ≈284–319 minpH 6.8, 25 °C[jackson2015 R5]
celecoxib–HPMCAS suspension with SDS; polysorbate 80free needles at 0.5 h; 1 hpH 3, 25 °C[chen2015a R14, R15]
celecoxib–PVP-K12 50% dispersiondesupersaturation about 2 h after complete releasepH 6.8, 37 °C[xie2015 C20]
tacrolimus 50 µg/mLonset within 3 h; 6–8 h with HPMCpH 4.5, 37 °C[trasi2016 R9]
delamanid salt dispersions in acidconcentration did not generally fall during the acid stage, and 1 mg/mL predissolved PVPVA left release after a pH 3.0 stage unchangedpH 1.6–5.0, 37 °C[nguyen2023c R23, R22]
Pitfalls and disagreements

In the telaprevir and nevirapine solutions crystallization is inferred from concentration, without solid-state analysis [mosqueragiraldo2018b X13; hate2017 C42]. Crystallization of the enzalutamide-PVPVA solutions is inferred from concentration, without a solid-state analysis [wilson2018 X12]. For felodipine with dissolved polymers this route was named dominant without monitoring the solid in the vessel [alonzo2010 X7]. In the felodipine solvent-shift tests of 2008 no precipitate was examined [konno2008a X4]. The danazol crystallization is inferred from UV and pyrene, without solid-state identification [jackson2015 C14]. Complete release was taken to exclude matrix crystallization although the HPMC-containing celecoxib dispersions neither released fully nor were checked [xie2015 X3]. Where the medium is subsaturated, as in the gastric stage of an enteric dispersion, the solution route is excluded and crystals must have formed in the wetted solid [elkhabaz2019a C34; nguyen2023c C39].

← Concepts and formulas

concept · as used in PEG dispersions

structural relaxation

The approach of a glass toward the equilibrium supercooled liquid, with loss of excess enthalpy and entropy. In the amorphous solubility papers a phase formed in water is argued to be "much more relaxed" than a melt-quenched glass, with a heat capacity close to that of the supercooled liquid, because water raises molecular mobility and speeds relaxation [almeidaesousa2015 C37]; telaprevir's glass formed in water is likewise assumed "highly relaxed" [mosqueragiraldo2015 C26, C25].

Findings

F2, F7.

Related concepts

concerns the supercooled liquid and glass-liquid phase separation; influenced by plasticization by water; enters the amorphous-crystalline free energy difference.

Formulas

amorphous-crystalline free energy difference from heat capacity.

How it is measured or obtained

Not measured in these papers; inferred from the match between the onset and the supercooled-liquid free-energy estimate, which was lower than the glass estimate for griseofulvin, sorafenib and telaprevir [almeidaesousa2015 R6, R11; mosqueragiraldo2015 R13].

Values in the library
materialvalue or classconditionspaper ids
sorafenibonset 0.532 µg/mL; supercooled-liquid estimate 0.479; glass estimate 0.72525 °C[almeidaesousa2015 R6, R11]
griseofulvinonset 355.96 µg/mL; supercooled-liquid 356.44; glass 531.4125 °C, HPMCAS-HF[almeidaesousa2015 R5, R11]
telaprevironset 90–92 µg/mL; supercooled-liquid Cp 97 ± 8; crystal-to-glass Cp 189 ± 1637 °C[mosqueragiraldo2015 R13]
Pitfalls and disagreements

The new phase could not be isolated, so its relaxation state is an inference; the reference state is justified by the agreement it produces [almeidaesousa2015 C38, X4; mosqueragiraldo2015 X11].

← Concepts and formulas

concept · as used in PEG dispersions

supercooled liquid

The amorphous state between Tg and Tm: mobile, but below the melting point; below Tg the same material is a glass [lu2016 C2]. "Undercooled melt" is used as a synonym [baird2012 A1]. A glass of a drug–polymer mixture can be regarded as a non-equilibrium supercooled liquid of high viscosity [taylor1997 C6]. New aspect (C. Amorphous solubility and LLPS): the amorphous reference state of the solubility calculation is the water-saturated supercooled liquid [ilevbare2013a C58; almeidaesousa2015 C39], and the drug-rich phase counts as one when its water-plasticized Tg lies below the experimental temperature [ilevbare2013a C22; indulkar2015 C38]. Ibuprofen, whose Tg of −45 °C makes its drug-rich phase a supercooled liquid at 37 °C, can be treated as an emulsion and seen by solution NMR [ueda2020b C38, M1, C7]. New aspects (Miscibility and drug-polymer interactions): The growth studies measure crystal growth into the supercooled liquid of drug or drug–polymer mixtures, 27–67 °C above the Tg of felodipine (70–110 °C against 43.3 °C), 3–85 °C above that of bifonazole (18–100 °C against 15.2 °C) and up to 61 °C above that of nimesulide (18–80 °C against 19.5 °C) (synthesis: temperature minus Tg) [kestur2010a P4, M1; kestur2011 P3, M1, M2]. Its lowest point, 18 °C, is at or just below the nimesulide onset Tg [kestur2011 X13]. Below Tg a binary drug–polymer glass can be regarded as a non-equilibrium, highly viscous supercooled liquid of "solvent" and "solute" molecules with homo- and hetero-associations, which makes the "solution" picture of the indomethacin–PVP dispersion reasonable "at least in terms of molecular interactions if not kinetics" [taylor1997 C6, C41, C42]. New aspect (Physical stability): in the physical-stability growth studies the supercooled liquid is the melt film, quenched and held between Tg and Tm, from which seeded crystals grow; the polymer effect on growth is placed in this liquid rather than at the crystal faces [kestur2013a C1, C6]. New aspect (Release mechanism and LoC): whether the drug-rich phase is a supercooled liquid or a glass at the release temperature is offered as a drug property that could matter for the limit of congruency. Que and co-workers (2019) name it "One interesting difference" between ritonavir (supercooled liquid under release conditions, LoC 25%) and ledipasvir (a glass, LoC 5%), and state that further investigation is "clearly" needed [que2019 C49, R28]. For ritonavir Indulkar and co-workers (2019) add that drug-rich nanodomains "can" coalesce into contiguous regions because the drug is a supercooled liquid at 37 °C [indulkar2019a C40]. Saboo and co-workers (2020) place the water-saturated indomethacin-rich phase in the supercooled-liquid state at 25–57 °C and in the glassy state at 10 °C, and find most PVPVA drugs studied "most likely" supercooled liquids at 37 °C in water (all but ledipasvir) [saboo2020 C32, C58]; at 5 °C loratadine behaves as a high-Tg compound [yang2021 C16].

Findings

Crystallization tendency: F1, F7. C. Amorphous solubility and LLPS: F2, F7, F15, F22. Miscibility and drug-polymer interactions: F1, F10, F13. Physical stability: F3, F18, F19, F27, F28. Release mechanism and LoC: F7, F9, F18.

Related concepts

bounded by glass transition temperature; property melt viscosity; process cold crystallization and crystallization from the supercooled melt; related to crystal growth rate, structural relaxation and plasticization by water; medium for crystal growth inhibition by polymers; related to amorphous solid dispersion; site of glass-crystal growth mode near Tg; related to kinetic versus thermodynamic control of crystal growth. Set by plasticization by water and the glass transition temperature; allows a contiguous drug-rich surface layer to form.

Formulas

Vogel-Tammann-Fulcher equation, Jackson interface-kinetics growth rate, amorphous-crystalline free energy difference from heat capacity; viscosity-limited normal growth law.

How it is measured or obtained

Made by melting and cooling (quench or controlled), then studied isothermally above Tg on a hot stage or in a rheometer [lu2016 P1, P2; baird2012 P1]. In solution work, a drug-rich phase is a supercooled liquid when its water-plasticized Tg lies below the experimental temperature [ilevbare2013a C22; indulkar2015 C38]. The drug-rich phase is examined by DSC of the isolated phase, and the free energy of conversion from the crystal to the supercooled liquid is obtained by the Hoffman or heat-capacity cycle [ilevbare2013a P9; almeidaesousa2015 E9, E10, E11]. In the kestur2010a and kestur2011 growth studies, films of 30–50 µm were made by melting 3–5 mg between cover glasses and cooling rapidly to about 50 K below Tg, with the absence of birefringence checked under crossed polarizers, then nucleated at 40 °C or at ambient temperature and grown on a hot stage [kestur2010a P2, P3, P4; kestur2011 P2, R1]. Melt-quenched films between cover slips, held on a hot stage, in the physical-stability growth papers [trasi2012a P2; trasi2012b P2; mosqueragiraldo2014 P3; kestur2013a P1]. In the release-mechanism papers: from the dry or wet Tg against the test temperature, cited or measured [que2019 R28, M1].

Values in the library
materialvalue or classconditionspaper ids
vemurafenibsupercooled liquid between Tg 108 °C and Tm 271 °Cmelt-quenched glass[lu2016 M1, R19.a]
34 drugsviscosities at Tm from 2.86 × 10⁻³ to 1.99 Pa·srheometry[baird2012 R1]
felodipine with 3% polymersgrowth from the supercooled liquid substantially reducedhot stage[kestur2010a C28]
bifonazole, nimesulidegrowth strongly temperature dependentsupercooled liquid[kestur2011 C6]
ritonavir drug-rich phaseTg 0.4 °C, so a supercooled liquid at 37 °Caqueous LLPS[ilevbare2013a C22]
clotrimazole; atazanavir precipitatesTg ~14 °C (supercooled liquid at 37 °C); ~51 °C (glass)water at 37 °C[indulkar2015 R22, C38]
nicardipine drug-rich phasesupercooled liquid at 37 °C (dry Tg 15 °C); more viscous after 4 h at 2 °Cwater[indulkar2015 M3, R23]
griseofulvin; sorafenib new phaseonset matches the supercooled-liquid estimate although the dry drugs are glasses at 25 °C25 °C[almeidaesousa2015 R11, C36]
telaprevircrystal-to-supercooled-liquid Cp estimate 97 ± 8 µg/mL against 90–92 µg/mL onset37 °C[mosqueragiraldo2015 R13]
felodipinegrowth into the supercooled liquid peaks near 105 °C; 70–110 °C studiedform II, hot stage[kestur2010a R5, C10]
bifonazolegrowth falls by about 6.4 orders from 100 to 18 °C (plot)melt-quenched films[kestur2011 R7, X6]
nimesulidegrowth falls by about 5.4 orders from 80 to 18 °C (plot)melt-quenched films[kestur2011 R9, X6]
indomethacin–PVP glassnon-equilibrium supercooled liquid; single Tg citedsolvent-evaporated[taylor1997 C6, R17]
acetaminophenTg 21.2 °C, Tm 169 °CDSC, 10 °C/min[trasi2012a R9.a]
flutamideTg −3.1 °C; Tm 108–110 °C with 10 mol% additivesDSC[trasi2012b R7]
celecoxibTg 55.34 °C, Tm 163.46 °CDSC[mosqueragiraldo2014 R5.a]
ATP enantiomers (Tg 16–17 °C)growth from the supercooled liquid at 40–90 °Cmelt films[sato2015 R1, R5]
six compounds (Tg −1 to 90 °C) with PHBgrowth from the supercooled liquid at 30–150 °Cmelt films[sato2016 A4, M1, M2, M3, M4, M5, M6]
ritonavirwet Tg around 0 °C; supercooled liquid at 37 °Crelease conditions[que2019 R28; indulkar2019a M1]
ledipasvirglass under release conditions37 °C[que2019 C49, M1]
indomethacin-rich phase (70% dispersion)supercooled liquid at 25–57 °C, slightly below its onset at 17 °C, glass at 10 °Cwet Tg onset 18 °C[saboo2020 C32, R30]
loratadinesupercooled liquid at 37 °C, glass at 5 °Cwet Tg 13.8 °C[yang2021 C16, M1]
Pitfalls and disagreements

Near Tg diffusion decouples from viscosity, so viscosity-based growth laws fail there [trasi2014a C21]. Polymer effects on growth from the supercooled liquid act on the liquid phase rather than at the crystal surface for felodipine [kestur2013a C6]. In the amorphous solubility papers a glass formed in water may behave as a supercooled liquid, which is inferred and not measured [almeidaesousa2015 C37, C38]. The text orders of magnitude (5.5 and 6 for bifonazole) are smaller than the plot readings (6.4 and 6.9) [kestur2011 X6]. Whether dilute dispersions made by cryomilling are molecularly mixed in the melt is assumed [kestur2010a C5]. In the acetaminophen and flutamide growth papers, interactions in the liquid were judged from spin-coated films at other compositions, not from the growth samples [trasi2012b X9; trasi2012a X15]. Two drugs only; the idea was not tested [que2019 C49].

← Concepts and formulas

concept · as used in PEG dispersions

supersaturation

A solution concentration above the crystalline solubility of the drug [almeidaesousa2016 C2; ilevbare2013a C21]. In this chapter the highest supersaturation a solution can hold without crystals is set by the amorphous solubility: above it the excess forms a drug-rich phase, and the concentration and activity of the continuous phase stay at that ceiling [mosqueragiraldo2015 C34, C35]. Taylor and Zhang 2016 (p. 10) add that the strict upper limit is the spinodal point: a one-phase solution can persist for a time between the binodal and the spinodal, and after phase separation the level is the binodal, which is the amorphous solubility (synthesis). Supersaturation can be generated by solvent shift, pH shift, or dissolution of a high-energy solid form (amorphous drug, dispersion, salt, co-crystal) [almeidaesousa2015 C4, C5; almeidaesousa2016 C2]. The papers of 2017–2022 add that in a micellar medium the supersaturation that matters is the activity ratio a/a^{*} and not the concentration ratio, the two differing about twofold for atazanavir in SDS at the amorphous solubility (65–70 against 33–38) [indulkar2017a R13, C21], and that after a pH shift of a weak-base salt the apparent concentration is held near the amorphous solubility if the dose exceeds it [sugihara2018 R8, R12]. New aspect (Bioperformance): a dissolved drug concentration above the crystalline solubility, with a solute activity above that of a solution saturated with the crystal; the supersaturation ratio is activity over crystal activity, and equals the concentration ratio c/c^* only if the activity coefficients are equal [raina2015c C7, E5, E6, C32]. The highest supersaturation a solution can hold as one phase is set by the amorphous solubility; above it LLPS or crystallization takes over [raina2014a C27, C30]. Its highest concentration-based value is the ratio of amorphous to crystalline solubility, and that ratio falls when a polymer, a second drug or micelles enter the drug-rich phase or the medium (F18, F19, F20) [ueda2020a E1, C17; alkalla2026 C1, C37; elkhabaz2019b C21, C25]. New aspect (Crystallization from solution): in the crystallization papers supersaturation is the ratio S = C/C_{eq} of the concentration to the crystalline solubility (concentration used in place of activity because the solutions are very dilute), with \sigma = \ln S for growth analyses; the amorphous solubility of ritonavir is S 15.3–15.4 and σ 2.7 [ilevbare2013b E4, C14; ilevbare2012b E1, E2, R3]. The reference solubility is that of the stable crystal, measured without methanol and, to be consistent, with the polymer present (F19) [hsieh2012 P4; ilevbare2013c P9, X16; hsieh2014 C18]. Other scales in these papers: C/Ceq in the medium of interest (1.5–15), S' = C/Cs with the solubility with additive, the activity ratio δ from membrane flux (2.4–28.8), S 1.5 for acetaminophen, and a nominal 10 mg/mL solvent shift [chen2015 E2; li2016a E1; lu2017 E1; trasi2015 P2; raina2015b P1].

Findings

Amorphous solubility and LLPS: F1, F5, F6, F8, F13, F14, F9, F10, F15, F16, F17, F19, F23. Bioperformance: F3, F10, F13, F14, F18, F19, F20, F28, F29. Crystallization from solution: F1, F2, F9, F14, F19, F21, F22, F27, F31, F34.

Related concepts

capped by amorphous solubility; measured against crystalline solubility; expressed as supersaturation ratio or via thermodynamic activity; relieved by crystallization. Papers of 2017–2022: activity-based supersaturation, maximum achievable supersaturation. Lost by desupersaturation; contrasts with solubilization; summarized by supersaturation factor.

Formulas

supersaturation ratio. Activity-based supersaturation ratio, supersaturation from membrane flux ratio, supersaturation factor, power-law crystal growth rate.

How it is measured or obtained

As concentration divided by the crystalline solubility in the same medium (the supersaturation ratio), or in terms of activity from the flux ratio; the concentration-based ratio at the ceiling is the amorphous-to-crystalline ratio (F6) [almeidaesousa2015 E15; mosqueragiraldo2015 R12]. In the Bioperformance papers: concentration ratio by UV or HPLC; activity-based ratio from membrane flux relative to the flux at the crystalline solubility [raina2015c E9, R13]; receiver-derived "effective" supersaturation from a Cmax calibration [hate2017 C49, R18]; generated by solvent shift, pH shift or ASD dissolution [raina2014a P7; hate2017 P7; hate2018 P9]. The activity-based maximum is the ratio of the flux from a solution at the amorphous solubility to the flux from a crystalline suspension in the same medium, J_{amph}/J_{eq} [elkhabaz2019b E2, R8, R9]. A dose is described by its ratio to the crystalline solubility: 5 mg of tacrolimus in 100 mL gives S = 20 and in 240 mL S = 8 [hate2019 R7, R14, E2]; pretomanid nucleation is compared at S = 5 [nguyen2023a E1, R5]. In the crystallization-from-solution papers: concentration by fibre-optic UV on second-derivative spectra or by HPLC; S from the crystalline solubility measured in the same buffer (48–72 h at 37 or 25 °C); the supersaturation factor integrates S over time [ilevbare2012a E2; ilevbare2013c E8].

Values in the library
materialvalue or classconditionspaper ids
ibuprofen to sorafenibmaximum ratio 4.3 to 54.025 °C, fluorescence onset[almeidaesousa2015 R5]
telaprevirmaximum ratio about 18 (stated); flux gain about 18pH 6.8, 37 °C[mosqueragiraldo2015 R14, R15]
clotrimazole; atazanavirabout 13; about 6337 °C[indulkar2015 R10]
CRH1about 10pH 6.8 and pH 4.6[almeidaesousa2016 R24]
atazanavir in 0–3.6 mg/mL SDSconcentration-based 64.8 → 33.0; activity-based 66.0 → 65.0 at the amorphous solubility37 °C[indulkar2017a R13]
telaprevir in bile saltsconcentration-based value 3.9–6.7 at an activity-based 5.050 mM pH 6.5, 37 °C[lu2017b R17]
felodipine, 25 °C2.7–6.8 at 2–5 µg/mL; about 8 at the amorphous solubilitybuffer[raina2014a R17]
felodipine with BSAS 1.3 and 1.1 by concentration ratio; 7.3 and 4.2 from flux50 µg/mL[raina2015c R13]
nevirapinenominal S 3.9; receiver-derived 2.8 (powder), 4.10 (powder + HPMC-AS)pH shift, 128 µg/mL crystalline[hate2017 R18]
ritonavir (mesoporous-silica study)S 7.8; 3.93.6 µg/mL crystalline[dening2018 E6]
atazanavir, six mediaactivity-based maximum about 50–56; concentration-based 56 in buffer to 14 in pooled human intestinal fluid37 °C, side-by-side cell[elkhabaz2019b R8]
posaconazole, six mediaactivity-based maximum about 29–37; concentration-based about 35–37 in buffer to 5 in human fluid37 °C[elkhabaz2019b R9]
tacrolimusS 20 (5 mg in 100 mL) and S 8 (240 mL); maximum ratio about 33solvent-shift solutions, hollow-fibre module[hate2019 R7, R14; purohit2019 C30]
tacrolimus, fully crystalline capsule contentsconcentration 2.5 times the crystalline solubility during 2 h5 mg in 100 mL, pH 4.5[purohit2019 R5]
atazanavir with darunaviratazanavir in the drug-lean phase about 61–63 instead of 91–96 µg/mL150 µg/mL atazanavir, about 196 µg/mL darunavir added[alkalla2026 R11, C1]
felodipineS 3–12; amorphous benchmark about 10solubility about 0.5 µg/mL, 25 °C[alonzo2012 E1, C42]
ritonavirS 3.8, 7.6 (7.7), 15.3 (15.4) at 5, 10, 20 µg/mL; 4.3 in 50 mM buffersolubility 1.3 µg/mL (100 mM), 2.3 µg/mL (50 mM), 37 °C[ilevbare2012a R3; ilevbare2012b R3]
celecoxib; efavirenzS 6.6, 14.7 at 10 and 22 µg/mL; 1.2 at 10 µg/mLsolubility 1.5 and 8.2 µg/mL[ilevbare2013b R7]
type 1 weak basespeak 1.4–26.7 times the titration solubility, lasting 3.1–14.7 minpH shift, 37 °C[hsieh2012 R5]
type 2 weak bases7.2–20.7 times the crystalline solubilitypH shift[hsieh2012 R10]
telaprevir with six bile saltsδ 11.5 and 28.8 need 60 and 150 µg/mL in buffer, 140 and 300–330 with 12 mM STDC/SGDCpH 6.5, 37 °C[lu2017 R1]
atazanavir, ritonavir in buffer, FaSSIF-V1, Composite-SIFflux-based supersaturation at the amorphous solubility 63–65 and 9.2–10pH 6.5, 37 °C[indulkar2018 R12]
posaconazoleamorphous/crystalline about 34 from pH 2 to 7phosphate buffers, 37 °C[duong2022b R1, C19]
Pitfalls and disagreements

The ratio depends on the crystal form (a hydrate for paclitaxel) and the medium [trasi2015a X12]. A solubilizer raises total concentration without raising supersaturation in activity terms, and the concentration-based ratio can fall [ilevbare2013a C54; raina2015c C29]. Total UV concentration is not free drug once a drug-rich phase exists (F4) [almeidaesousa2016 R12]. Concentration ratios understate supersaturation where micelles solubilize the drug, and flux-based values assume that micelles do not cross the membrane [indulkar2017a C42, X9; lu2017b X8]. In the Bioperformance papers, with solubilizers the concentration ratio under-reads the activity-based supersaturation (F3) [raina2015c C38]. Concentration ratios are not valid above the amorphous solubility, where two phases coexist [dening2018 E6]. UV readings above the amorphous solubility include scattered light [hate2018 X15]. In six media of rising solubilizing capacity the concentration ratio fell several-fold while the flux ratio stayed about the same (F18) [elkhabaz2019b R8, R9, C21]. Which dose-to-volume ratio a test imposes decides whether absorption or growth on seeds dominates: S of 8 and S of 20 gave different results in the same module (F28, F29) [hate2019 R14, R17]. Polymer in the drug-rich phase lowers the achievable supersaturation although it inhibits crystallization (F19) [ueda2020a C37]. S for 10 µg/mL ritonavir is printed as 7.6 and 7.7, and for 20 µg/mL as 15.3 and 15.4, depending on rounding (10/1.3 = 7.69; 20/1.3 = 15.38) [ilevbare2012a X1]. The efavirenz induction-time runs state S 2.4, the ratio of the calculated amorphous solubility to the crystalline solubility, while the concentration used gives 2.3 [ilevbare2013c X4]. A polymer that raises the solubility lowers S for the same concentration (F19) [ilevbare2013c X7]. C/Cs understates the supersaturation of celecoxib in media where the mass flow does not change [li2016a X18].

← Concepts and formulas

concept · as used in PEG dispersions

surface crystallization

Nucleation and growth of crystals at a free surface of an amorphous solid, reported to be faster than in the bulk by orders of magnitude because surface molecules are more mobile [duong2022c C2; trasi2014a C4]. It is a failure mechanism of amorphous solid dispersions in storage and during dissolution [duong2022c C2; saboo2020 C36]. New aspect (ASD process): in the coating papers the surface route is the target of the treatment, since crystal growth at the free surface of an amorphous solid is orders of magnitude faster than in the bulk, so a thin shell is expected to act where crystals start [duong2022c C2, C3; moseson2022a C6]. Uncoated powders stored open at 40 °C showed crystals by SEM within 1–2 weeks (ezetimibe–HPMCAS 12–19 days), coated ones later or not at all [moseson2022a R11; duong2022c R16, R17]. In a coated particle that did crystallize, crystals lay above an intact coating, "as is common for amorphous materials" [moseson2022a C26, R15]. In dissolution, a hydrated, drug-rich surface layer of bicalutamide–PVPVA crystallizes on the compact surface within 30–60 min (see drug-rich surface layer) [moseson2022b R14, R15]. New aspect (Supersaturation from ASD dissolution): a proposal for wetted amorphous particles: crystallization "probably" starts at the particle surface, is made worse by water plasticization, and dissolved polymer delays it by interacting with that surface, as a thin polymer film does for amorphous indomethacin (cited) ("reasonable to speculate") [alonzo2010 C36, R22, R23]. New aspect (Release mechanism and LoC): for indomethacin methyl ester–PVPVA, congruency was lost at a later time point above 5% loading: drug release ceased and polymer release slowed, which the authors attribute to drug crystallization at the compact surface, supported by XRD and PLM [saboo2020 C17, R8, R9]. A congruency read-out over the first minutes therefore misses this failure. A surfactant built into the dispersion can bring the same failure to a drug that does not crystallize on the binary tablet: ritonavir–PVPVA at 30% with SDS released fast and congruently, then stopped near 80% when needle crystals covered the tablet surface by 15 min, which "likely served as a barrier" [indulkar2022 R5, R15, R16, C38]. With 10 parts of SDS in ritonavir–PVPVA, needle crystals covered the 30% compact surface at 30 min, to which the authors attribute the release plateau ("can be attributed"); SDS covered about 98 wt% of the dissolved surface, which "conceivably" promotes crystallization through higher surface mobility [yang2023 R16, C24, R17, C50].

Findings

Crystallization tendency: F4, F21. ASD process: F43, F44, F38, F40. Supersaturation from ASD dissolution: F1, F2, F14, F24, F27. Release mechanism and LoC: F19, F31.

Related concepts

part of physical stability; related to crystal growth rate and nucleation; contrasts with bulk crystallization in crystallization from the supercooled melt. Targeted by the atomic layer coating through surface molecular mobility; sped up by plasticization by water; in dissolution follows the drug-rich surface layer and leads to matrix crystallization; related to crystallization inhibition by polymers. Ends congruent release after a delay; a form of crystallization during dissolution.

Formulas

none.

How it is measured or obtained

Growth on films with the top coverslip removed [trasi2014a P2]; nuclei counted on an exposed glass surface [trasi2014b P7]; SEM, SHG or PLM of particle and tablet surfaces in storage or dissolution [duong2022c R16; correasoto2017 R16; saboo2020 R9]. SEM was the primary detector of surface crystals on stored coated powder, with XRPD, DSC and SEM agreeing for ezetimibe and XRPD missing several arms of the four-system study [moseson2022a C22, X14; duong2022c R16, R18, R20]; SEM and SEM-EDX of exposed compacts [moseson2022b P14, P15]. In the ASD dissolution papers: by polarized light of suspended particles over days [chen2015a P10, R20] and indirectly by the lag in slurry crystallinity with polymer in the medium [alonzo2010 R6]. In the release-mechanism papers: SEM of the tablet surface at 5, 10 and 20 min, besides XRD, PLM and the 1607 cm⁻¹ IR band of crystalline ester [saboo2020 R22, R18, C23]. SEM of dried tablets and ATR-IR of blotted wet tablets against the crystalline drug [indulkar2022 P9, P11].

Values in the library
materialvalue or classconditionspaper ids
felodipine form Iabout 6 times faster at the surface than in the bulk; about 23 times with 3% PVP30 °C, 0% RH[kestur2013b R12]
felodipine≈0.06–0.42 µm/s at the surfaceT/Tg ≈1.04–1.11[trasi2014a R4.g]
loratadine≈0.00005 µm/s at the surface, slowest of 14near Tg[trasi2014a R4.n]
nilutamidemuch higher nucleation at the surface than in the bulkmelt-cooled films[trasi2014b R1]
ezetimibe spray-dried dispersionscrystals after 19 days (50% DL) and 12 days (70% DL) uncoated40 °C/75% RH[duong2022c C33]
uncoated amorphous powders (erlotinib, naproxen and lumefantrine ASDs)crystallization onset within 1–2 weeks40 °C, open dish; 31–75% RH[moseson2022a R11]
flutamide spray-dried dispersionneedle crystals growing from particle surfaces40 °C/75% RH[correasoto2017 C26]
indomethacin methyl ester compactssurface crystals within 10 min of dissolutionPVPVA, 25% DL[saboo2020 R9]
ritonavir–PVPVA–SDS compactsneedle-shaped surface crystals during dissolution30% DL[indulkar2022 R15; yang2023 R16]
delamanid dispersion filmsrapid surface crystallization at pH 3.01 h[nguyen2023b R3, C37]
ezetimibe–HPMCAS 50% DL, uncoatedneedle-like crystals at 19 days; about 26% crystalline at 270 days40 °C/75% RH[duong2022c R16, R19]
ezetimibe–HPMCAS 70% DL, uncoatedplate-like crystals at 12 days; about 50% crystalline at 270 dayssame[duong2022c R16, R19]
ezetimibe–HPMCAS coated (50% thin and thick, 70% thick; about 12–40 nm)no crystals by SEM, PXRD or DSC for 24 monthssame[duong2022c R16, R17, R18, R20]
ezetimibe–HPMCAS 70% thin coating (11.7–15.0 nm)first crystals at 7 months; about 1.5% at 270 dayssame[duong2022c R17, R19]
erlotinib, naproxen and lumefantrine ASD powders, 13 coated arms3–24 weeks, or none within 48 weeks in 7 arms40 °C, 31–75% RH[moseson2022a R11]
extruded and milled 30% and 50% DL BCL–PVPVA compactsneedle-like crystals on the surface at 30 min; a 5–10 µm crystal crust on the 50% compact at 1 hpH 6.8, 37 °C[moseson2022b R14, R15]
amorphous felodipine, polymer in the mediumlag of about 13–20 min before 50% crystallinitypH 6.8, 37 °C slurry[alonzo2010 R6]
celecoxib–HPMCAS spray-dried particles, Triton X100birefringent regions on or in the particles after about 7 days, no free needlespH 3, 25 °C[chen2015a R20, C37]
same, no surfactantcrystallization only after more than 7 days, apparently from matrix or surfacepH 3[chen2015a C33]
delamanid salt dispersions, five enteric gradescrystals on films and powders after 1 h in acid, more with HPMCAS and at higher pH; HPMCAS-HF also at pH 1.625% drug, 37 °C[nguyen2023c R19, R18]
delamanid dispersions after the pH shiftundissolved particles covered with small crystals within 30 minpH 6.5[nguyen2023c R21]
indomethacin methyl ester–PVPVA 25%smooth at 5 min; scattered needle-like crystals at 10 min; surface extensively covered at 20 minSEM, pH 6.8[saboo2020 R22, M6]
indomethacin methyl ester–PVPVA 10–25%drug release levelled off after 7.5–20 min30 min runs[saboo2020 R8]
ritonavir–PVPVA 30:70:5 with SDSsmooth at 2 min; needle crystals and crystalline-ritonavir IR bands at 15 min; release flat near 80%SEM, ATR-IR, pH 6.8[indulkar2022 R15, R16, R5]
ritonavir–PVPVA–SDS 30–70–10birefringent needles at 30 minPLM, SEM of the compact 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 PEG dispersions

temperature-composition phase diagram

A plot of the liquidus temperature, the temperature at which the last crystal melts, against the composition of a drug–polymer mixture. For a crystalline polymer such as PEG the diagram has a drug-rich and a PEG-rich branch that meet at the eutectic, or, for a monotectic system, only a steep drug branch baird2011 R5, R8; zhu2011 R4. Outside the PEG papers the same construction gives the solubility line of a drug in an amorphous polymer, whose crossing with the formulation Tg and the polymer's minimum melt temperature sets a minimum processing temperature moseson2018 R8, C22. New aspect (ASD process): for IDM:PVPVA the diagram plots the experimental and predicted critical (solubility) temperature Tc, falling from 160.6 °C for the pure drug to 131 °C at a drug weight fraction of 0.5, together with the formulation Tg line (Gordon–Taylor), the drug melting point, the polymer Tg and a dotted minimum processing temperature Tmin of 117 °C moseson2018 R5, R8, R9. Above the solubility line all crystals can dissolve at equilibrium; below it at 50% DL they cannot moseson2018 C43. The diagram guided the choice of the extrusion temperature for posaconazole–HPMCAS: 125 °C, below, and 175 °C, above the calculated solubility temperature at each loading [shah2024 R5, R10, C21].

Findings

PEG dispersions: F1, F2, F4. ASD process: F8, F9, F35, F36, F41.

Related concepts

consists of liquidus temperature; contains eutectic or monotectic system; depends on melting point depression; related to drug solubility in polymer. In extrusion work it consists of formulation critical temperature and is used in the HME operating design space.

Formulas

Lacoulonche liquidus model, Flory-Huggins melting point depression, Gordon–Taylor equation.

How it is measured or obtained

Physical mixtures or fused dispersions are heated at 1 °C/min on a hot stage under polarized light, and the temperature at which the last crystal or particle melts is recorded; DSC offset melting at 1 °C/min is used as a second method baird2011 P2, P3; zhu2011 P3, P4; zhu2012 P9, P10. For amorphous polymers the offset temperature is extrapolated to 0 °C/min moseson2018 R5. For IDM:PVPVA the model line comes from the Flory–Huggins equation with one \chi, and the Tg line from Gordon–Taylor with a density-based constant moseson2018 P2, E2, E3. Extrusion outcome is then placed on a plane of product melt temperature against residence time, coloured by the most sensitive method that still called a run amorphous moseson2018 R15.

Values in the library
materialvalue or classconditionspaper ids
chlorpropamide, aceclofenac, loratadine, haloperidol with PEG 3350predicted line against DSC and hot-stage points; two systems far below the line at 20–60 wt%0–100 wt%, 1 °C/minbaird2011 R5, R6, R7, R8
benzocaine, ibuprofen, nilutamide, ketoconazole with PEG 3350eutectic (30, 40, 10 wt%) or monotectichot stage, 1 °C/minzhu2011 R1, R2, R3, R4, R5
fenofibrate with PEG 3350eutectic minimum about 58 °C at 15–20 wt%CPOM and DSCzhu2012 R24
indomethacin–PVPVATc 131 °C ± 2 °C at 50% drug loadingoffset extrapolated to 0 °C/minmoseson2018 C22, R8
IDM–PVPVApredicted solubility line crosses Tmin near drug weight fraction 0.39 and the Tg line near 0.23 (about 88 °C); 50% DL point marked 131 ± 2 °CFig. 2, readingsmoseson2018 R8, X3
IDM–PVPVA process mapboundary of "amorphous by all techniques" from about 148 °C at 2 min to about 131 °C at 20 min; "X-ray and DSC amorphous" from about 136 °C at 2 min to about 131 °C at about 6 min15 extrusionsmoseson2018 R15
BCL–PVPVA, 30% DLTc = 145 °C and Tm = 195 °C bound the dissolution regime of the extrusion mapFlory–Huggins model, Fig. S2b not supplied[moseson2021 M1, P1]
BCL–PVPVA 30–90% BCLsolubility line from Tc 145 °C (30%) to about 192.3 °C (90%) with χ = −1.57DSC, Flory–Huggins[moseson2022c R8, R9]
PCZ–HPMCAS MFcalculated Tc 135 / 155 / 165 °C at 10 / 25 / 50% DL; extrusion at 125 °C left 0.3 / 3.2 / 19.3 wt% crystals, at 175 °C none2 min, SHG[shah2024 R5, R10, X7]
Pitfalls and disagreements

DSC and hot-stage liquidus values differ by up to about 16 °C at some compositions baird2011 X7. The PEG 3350 liquidus is about 61 °C in the diagrams and 55 °C in the model baird2011 R5, M5, X10. The diagram describes melting equilibria, not the state of the stored dispersion: a stored 20/80 dispersion has most of its PEG crystalline within minutes (see semicrystalline solid dispersion) zhu2012 R4. For amorphous polymers the experimental points depend on heating rate and the 40% drug-loading point deviated from the model line moseson2018 R3, C19. For IDM:PVPVA the 131 °C used is the predicted value, the experimental one is 132.3 ± 0.8 °C, and the origin of the "± 2 °C" is not stated moseson2018 X2. The switch from Tc to the polymer's Tmin as the lower bound is placed by the authors at 50% DL although the predicted line crosses Tmin near 39% DL moseson2018 C22, X3. The diagram gives thermodynamics only; the process map adds kinetics for one micro-extruder moseson2018 X15. The BCL diagram is known only through the two temperatures and χ = −1.57 in the text of the 2021 paper [moseson2021 M1].

← Concepts and formulas

concept · as used in PEG dispersions

Tg-scaled crystal growth rate

Crystal growth rate plotted against the distance from each system's own glass transition, T - T_g, so that the part of an additive's effect that comes from shifting Tg is removed and the remainder can be compared [mosqueragiraldo2014 P7, R12].

Findings

F5, F22, F28.

Related concepts

depends on glass transition temperature; used to test plasticization; contrasts with kinetic versus thermodynamic control of crystal growth; part of crystal growth rate.

Formulas

none.

How it is measured or obtained

Growth rates measured at fixed temperatures are shifted by the DSC Tg of each mixture [mosqueragiraldo2014 P7, R5, R12].

Values in the library
materialvalue or classconditionspaper ids
celecoxib alone and with 10% sucrose palmitate, SLS, TPGS≈0.020, ≈0.014, ≈0.039, ≈0.17 µm/s at T - T_g ≈25 °Cseeded melt growth[mosqueragiraldo2014 R12]
same≈12, ≈3.2, ≈13, ≈7.4 µm/s at T - T_g ≈65 °Csame[mosqueragiraldo2014 R12]
celecoxib with 10% PVP and with PVP plus TPGSTPGS–PVP about two orders of magnitude below PVP at T - T_g ≈26–28 °Csame[mosqueragiraldo2014 X4, R12]
DPB, griseofulvin, celecoxib with 5–10% PHBrates against T − Tg close to the pure compounds; 20% PHB and 5% PVAc belowmelt films[sato2016 R10, C21]
Pitfalls and disagreements

The authors call the corrected surfactant curves "fairly close", but they still span about 12-fold at 25 °C above Tg, against about 85-fold at equal temperature (70 °C), so the correction removes about half of the spread on a log scale (synthesis) [mosqueragiraldo2014 X4, C30, R1]. Tg differences below about 1 °C are unresolved [mosqueragiraldo2014 X7]. The scaling ignores the driving force, which falls with melting-point depression [mosqueragiraldo2014 C33].

← Concepts and formulas

concept · as used in PEG dispersions

thermodynamic activity

The activity of the drug in a phase, the product of its mole fraction and activity coefficient, a_i = x_i\gamma_i, or of concentration and activity coefficient, a = C\gamma; at phase equilibrium it is equal in all phases [ilevbare2013a E6, E7; mosqueragiraldo2015 E5]. In the LLPS picture the drug has the same activity in the water phase and in the drug-rich phase, which is why the water-phase concentration is capped and why added drug raises the amount of drug-rich phase and not the activity [ilevbare2013a C36, C48; mosqueragiraldo2015 C35]. Membrane flux is proportional to activity (F8) [mosqueragiraldo2015 C10]. The papers of 2017–2022 add that with micelles present the free drug sets the activity: in 3.6 mg/mL SDS the free atazanavir at the amorphous solubility was 65–70 µg/mL, the same as in buffer, although the total was about 1450 µg/mL (slope of free against total 0.047) [indulkar2017a R11], and that bile salts change the telaprevir activity at a given concentration (flux about halved with 12 mM STDC) while the activity at the phase boundaries stays [lu2017b R12, C49]. New aspect (Bioperformance): membrane flux is proportional to the activity, a = \gamma C, so equal concentrations need not give equal flux when additives change the activity coefficient [raina2015c C14, E4]. Relative to the crystal, the activity in a one-phase supersaturated solution is C/C_S and is about 8 for felodipine at 25 °C at the amorphous solubility; above it the activity stays constant [raina2014a E10, R17, C35]. The enzalutamide, posaconazole, atazanavir and darunavir papers use the same relation to infer activity from flux: with area, diffusion coefficient, thickness and membrane activity coefficient fixed, J = D a/(h\gamma_m) [wilson2018 E4, E5, C12; elkhabaz2019b E3; alkalla2026 E2, C10].

Findings

Amorphous solubility and LLPS: F5, F8, F11, F12, F16, F17, F18. Bioperformance: F2, F3, F4, F6, F15, F18, F19, F20, F22, F25.

Related concepts

defined with the activity coefficient; related to chemical potential; read from membrane flux; capped by the amorphous solubility. Papers of 2017–2022: expressed as activity-based supersaturation; partition between phases in micelles: micelle/water partition coefficient. Related to free drug concentration.

Formulas

activity from concentration, membrane flux in terms of solute activity, activity-based supersaturation ratio.

How it is measured or obtained

Not measured directly in these papers: it is inferred from the flux across a membrane when diffusion coefficient, area, thickness and membrane activity coefficient are constant, or argued from the phase equilibrium [mosqueragiraldo2015 C10; trasi2015a C14; ilevbare2013a X15]. Flux across a 6–8 kDa regenerated cellulose membrane calibrated in buffer, up to the amorphous solubility, where the activity coefficient is taken as one; flux of a crystal-saturated solution F° gives δ = F/F° [indulkar2017a P8, R10; lu2017b P6, E6]. In the Bioperformance papers it is not measured directly: it is inferred from flux (plateau = constant activity) [raina2014a C36], from flux relative to a reference [raina2015c E9], or from free drug after ultracentrifugation [alhalaweh2016 P10]. The activity-based maximum supersaturation is the ratio of the flux from a solution at the amorphous solubility to the flux from a crystalline suspension, J_{amph}/J_{eq} [elkhabaz2019b E4, R7]; the mass flow of a dissolved formulation gives its donor activity [wilson2018 C12]. Free monomeric drug is taken as the permeating species [ueda2020a C24; hate2022 C41].

Values in the library

None printed in this chapter; the activity of the water-saturated amorphous drug appears as the factor exp[−I(a2)] (0.22 for atazanavir to 0.999 for ibuprofen) [indulkar2015 M2; almeidaesousa2015 M1]. The papers of 2017–2022 add activity read from flux: free atazanavir 65–70 µg/mL at about 1450 µg/mL total in 3.6 mg/mL SDS (slopes of free against total 0.998, 0.181, 0.086 and 0.047 at 0, 1, 2 and 3.6 mg/mL SDS) at 37 °C [indulkar2017a R11], and telaprevir with δ = C/C° in buffer (slope 1.011) and bile-salt media off the 1:1 line in 50 mM pH 6.5 buffer at 37 °C [lu2017b R16, R17].

In the Bioperformance papers:

materialvalue or classconditionspaper ids
felodipineactivity relative to crystal about 8 (5.99/0.74 = 8.09)25 °C[raina2014a E10, R17]
felodipine suspensionssame low flux at about 1 and 40 µg/mL dissolvedcrystal fixes activity[raina2015c R4, C20]
atazanavir + SDSfree drug about 1 to about 65 µg/mL with and without SDS37 °C[indulkar2017a C19, R11]
telaprevir, bile saltsdeviation from the buffer slope gives the activity coefficient changeflux[lu2017b C41]
atazanavir, posaconazole, six mediaJ_{amph}/J_{eq} about 50–56 and 29–37 while the concentration ratio fell to 14 and 537 °C, side-by-side cell[elkhabaz2019b R7, R8, R9]
enzalutamidemass flow rises up to about the amorphous solubility (42 µg/mL), then is roughly constant5 µg/mL HPMCAS, side-by-side cell[wilson2018 R13, C25]
atazanavir, nifedipine and three other drugs, PAMPAbreak from a linear rise at about the amorphous solubilitylipid-impregnated PVDF[hate2022 R1, C11, X13]
Pitfalls and disagreements

Total concentration with micelles or with a second drug present is not activity; the maximum extent of supersaturation in activity terms is not raised by a solubilizer, whereas the concentration ratio can fall [ilevbare2013a C54; raina2015c C29]. The activity coefficient in the dilute solution is assumed constant between the crystalline and the amorphous concentration [ilevbare2013a C55]. The free-drug and δ read-outs assume that only dissolved drug crosses the membrane and that the additive does not change it [indulkar2017a X9; lu2017b X8]. Constant activity above the amorphous solubility is an inference from flux [raina2014a X12]; it fails in the hollow-fibre module, where transfer keeps rising (F15) [hate2018 C25]. With a sink receiver the PAMPA mass flow of atazanavir kept rising above the amorphous solubility, so a plateau is not guaranteed (F22) [hate2022 R19, X8]. A crystalline co-drug or a polymer mixed into the drug-rich phase lowers the activity of the drug in it, and with it flux (F19, F20) [alkalla2026 C37; ueda2020a C24].

← Concepts and formulas

concept · as used in PEG dispersions

thermodynamic driving force for crystallization

The free-energy difference between the supercooled liquid (amorphous form) and the crystal, written ΔGv per unit volume or ΔG per mole or gram; it is zero at Tm and grows on cooling [baird2012 C32; vaneerdenbrugh2010a E2]. A larger driving force lowers the classical nucleation barrier [vaneerdenbrugh2010a E3, C39]. This draft comes from the crystallization-tendency chapter; for drugs in polymers the same quantity is lowered by mixing [konno2006 C34]. New aspect (PEG dispersions): in a dispersion in a crystalline polymer the driving force of the drug is lowered by melting point depression, because the supercooling at the storage temperature falls. Zhu and co-workers attribute the delayed crystallization of benzocaine in PEG to entropic mixing and favourable benzocaine–PEG interactions that depress its melting point (around 48 °C at the eutectic against around 89 °C for the neat drug), so that supercooling and driving force at 25 °C are much smaller; with a Tg of −31 °C they consider a thermodynamic rather than a kinetic cause "reasonable" zhu2012 C32, C33. New aspects (Miscibility and drug-polymer interactions): In a miscible dispersion the chemical potential of the drug, and so the driving force for crystallization, must be lower than for the pure amorphous drug, through the entropy of mixing and, if adhesive interactions exceed cohesive ones, the enthalpy; melting point depression is its visible sign marsac2006b C38, C39. In the PVP dispersions the predicted reduction is small: the Hoffman estimate "does not forecast a large reduction", especially at lower temperature, and is "most likely underestimated" because equilibrium depression is hard to reach at high polymer content marsac2006b C41, C40. At low polymer levels, where the melting point and Tg of the drug are unchanged, there "does not appear" to be a macroscopic effect on ΔG, so polymer effects on growth are not read as thermodynamic [kestur2010a C36, C41]. New aspect (Physical stability): for dispersions holding water, the driving force is framed as the degree of supersaturation of the drug in the polymer–water co-solvent, \sigma = (\mu^{1} - \mu^{0})/RT, which water raises as an anti-solvent; it was reasoned, not computed marsac2008a E1, C26, C49, X4.

Findings

Crystallization tendency: F2, F6, F7, F13. PEG dispersions: F8, F9. Miscibility and drug-polymer interactions: F9, F10, F11. Physical stability: F2, F4, F18, F22, F28, F29.

Related concepts

measured by Hoffman equation; depends on enthalpy of fusion, entropy of fusion and degree of supercooling, which is reduced in a dispersion via melting point depression; part of classical nucleation theory; related to nucleation, crystal growth rate and heterogeneous nucleation; lowered by entropy of mixing; contrasts with kinetic stabilization; related to crystal growth inhibition by polymers, supersaturation, cosolvency and kinetic barrier to nucleation; balanced against mobility in kinetic versus thermodynamic control of crystal growth.

Formulas

Hoffman equation, classical nucleation barrier, entropy of fusion, solid-liquid equilibrium solubility equation, Flory-Huggins activity equation.

How it is measured or obtained

Mostly estimated with the Hoffman equation from Tm and ΔHfus [vaneerdenbrugh2010a E2; baird2010 E25; lu2016 E1]; from MDSC heat capacities, which agreed with the Hoffman estimate for felodipine and nifedipine [marsac2006a R11, C14]; as \Delta G \approx \Delta S_m\,\Delta T for growth analysis [trasi2014a E3]; for dispersions, from melting-point depression and Flory–Huggins mixing marsac2006b C41; marsac2009 C34. In the PEG dispersions it was not measured: the melting points are cited and the driving force is inferred from the phase diagram zhu2012 C32, M3. For the PVP dispersions, estimated with the Hoffman equation, for pure nifedipine from 0 to 180 °C and, with the depressed melting temperature, for 30 and 40% PVP marsac2006b P8, E4, R12; for the dispersions the melting temperature of the 40% PVP curve is not shown in the paper's own melting data marsac2006b X5. The unchanged offset melting point of physical mixtures with 3% polymer is taken as an unchanged driving force at a given temperature [kestur2010a R1, C36]. In the moisture papers: Hoffman estimates from Tm and heat of fusion for six drugs at 25 °C [rumondor2009c E3, M1]; crystal solubility in NMP and NMP–water as stand-ins for PVP and PVP–water marsac2008a P8.

Values in the library
materialvalue or classconditionspaper ids
nifedipineΔG ≈−30, ≈−24, ≈−16 J/g at 0, 50, 100 °CMDSC and Hoffman[marsac2006a R11]
felodipineΔG ≈−18, ≈−13, ≈−7 J/g at 0, 50, 100 °CMDSC and Hoffman[marsac2006a R11]
34 drugsΔGv from −8.6 (lidocaine) to −54.7 J/cm³ (acetaminophen)Hoffman, 298 K[baird2012 M5, M12]
class I against class IIIΔGv ≈−0.40 against ≈+0.57 SD from the meanper volume, 293.15 Kbaird2010 R22.g
spin-coat classes I, II, III≈−0.29, ≈+0.29, ≈+0.13 SDper volume[vaneerdenbrugh2010a R20.e]
vemurafenib α; β≈−11.0; ≈−6.3 kJ/mol at about 115 °CHoffman, plotted as crystal minus liquid[lu2016 R22, X17]
nifedipine with 40% PVPreduction smaller than the nifedipine–felodipine differencemelting-point depressionmarsac2006b C41
drugs in PVPdriving force remains at most practical polymer contentsinteraction parametersmarsac2009 C34
benzocaine in PEG 3350melting point depression from around 89 to around 48 °C at the eutecticcitedzhu2012 C32, M3
ibuprofen; fenofibrate in PEG 3350melting point depression of about 30 °C; about 20 °C (text), about 24 °C (plot)eutecticzhu2012 C34, X11
nifedipine, pure; 30% PVP; 40% PVP−9.0, −8.4, −7.95 kJ/mol at 20 °C (zero at ≈171, ≈148, ≈128 °C)Hoffman, plot readingsmarsac2006b R12
nifedipine, pure; 30% PVP; 40% PVP−5.45, −4.1, −2.7 kJ/mol at 100 °Cas abovemarsac2006b R12
felodipine with 3% PVP, PVP/VA, HPMCAS, PVAcmelting point of physical mixtures unchanged (140.7–142.9 °C against 141.5 °C)offset, 1 °C/min[kestur2010a R1]
bifonazole, nimesulide with 5% polymersTg rise 0.4–2.2 °CDSC onset[kestur2011 R6, C12]
nifedipine, felodipine, droperidol, pimozide, indomethacin, ketoprofenHoffman ΔGc 8.2, 6.1, 9.2, 11.0, 8.1, 4.1 kJ/mol25 °C[rumondor2009c M1, M6, M3, M2, M4, M5]
nifedipine vs felodipine crystalsmole-fraction solubility 0.05 vs 0.10 in NMP: larger lattice term for nifedipine25 °Cmarsac2008a R10, C35
nifedipine and felodipine in PVPFlory–Huggins activity ≈0.84 and ≈0.83 at Φ 0.2χ −3.8, −4.2[marsac2006a R19]
acetaminophen and flutamide with 10% polymerTm barely changed, so the driving force is similar for all polymersDSC[trasi2012a R9, C19; trasi2012b R7, C33]
celecoxib with TPGS and PVPTm 12 °C lower; a smaller driving force "could contribute" to slower growth near TmDSC, melt growth[mosqueragiraldo2014 R5.f, C33]
six compounds with PHBdriving force inferred unchanged from Tm and IR ("can be inferred")DSC; IR[sato2016 C18, X11]
indomethacin polymorphsdifferences in growth persist after a driving-force normalizationmelt growth[tian2017 R11, C24]
Pitfalls and disagreements

The class trend is not monotonic: class II, not class III, had the least negative ΔGv in the solvent screen [vaneerdenbrugh2010a X10]. Pair comparisons of viscosity can be confounded by driving force [baird2012 X9]. Indomethacin has a larger driving force than felodipine yet crystallizes more slowly during dissolution [alonzo2010 C42], and metastable vemurafenib β outgrows α despite α's larger driving force [lu2016 C52]. Low polymer levels barely change it, so polymer effects on growth are read as kinetic [kestur2010b C28]; thermodynamically stable dispersions are hard to achieve marsac2009 C34. For ibuprofen and fenofibrate in PEG the depression should lower the driving force, yet the onset in the dispersion is earlier than for the neat drug; the authors explain it by nucleation on crystalline PEG, not by the driving force zhu2012 C34, C41. The estimated solubilities of benzocaine (28%) and ibuprofen (25%) exceed the 20% loading, which the card's extractor notes as not discussed zhu2012 X13, M3, M4. The 40% PVP curve rests on a melting temperature not shown among the measured data marsac2006b X5. The unchanged-driving-force conclusion for 3% polymer uses the melting point of form I in physical mixtures while form II grows [kestur2010a X7]. The size of the lowering differs between the polymers (synthesis: contrast between papers): in PEG 3350 the melting point depression (benzocaine from around 89 to around 48 °C at the eutectic) is taken to make supercooling and driving force much smaller zhu2012 C32, C33, whereas for PVP the predicted reduction is small marsac2006b C41. The driving force did not sort drugs by moisture-induced phase separation [rumondor2009c C32]. The supersaturation explanation of the nifedipine–felodipine ranking with water rests on NMP data and printed cosolvency fits that do not reproduce their points marsac2008a X2, X4. The celecoxib driving force was argued from Tm and not calculated [mosqueragiraldo2014 C33].

← Concepts and formulas

concept · as used in PEG dispersions

Tm − Tg temperature gap

The span between the melting point and the glass transition, the range a melt must cross to become a glass [trasi2014a C27]. If viscosity at Tg is similar for all compounds, a small Tm − Tg with a high viscosity at Tm means a high viscosity at the temperature of fastest growth and so a low maximum growth rate [trasi2014a C27].

Findings

F5, F12.

Related concepts

related to reduced glass transition temperature; related to melt viscosity and crystal growth rate.

Formulas

linear fit of melt viscosity on Tm − Tg.

How it is measured or obtained

From DSC Tm and Tg [trasi2014a M1; baird2012 M1].

Values in the library
materialvalue or classconditionspaper ids
ritonavir; tolazamide77; 154 °CDSC[baird2012 M34, M18]
chlorpropamide; celecoxib; ketoconazole108; 105; 105 °C, in classes I-B, II, IIIDSC[baird2012 M9, M14, M26]
slow and fast growth groups85–117 and 121–146 for drugs with viscosity dataDSC[trasi2014a R9]
class means I-A, I-B, II, III123 ± 11, 119 ± 11, 126 ± 20, 108 ± 16 °C, not significantly differentDSC[baird2012 R10]
Pitfalls and disagreements

The celecoxib Tm − Tg of 125 in one table conflicts with its own Tm and Tg (108) [trasi2014a X1], and the dibucaine row of another table repeats lidocaine [baird2012 X1]. The gap tracked growth groups but not the DSC classes (synthesis: compare R9 of trasi2014a with R10 of baird2012).

← Concepts and formulas

concept · as used in PEG dispersions

van't Hoff equation

The relation d\ln x/dT = \Delta H_f/(R\,T^2) between the temperature dependence of a mole-fraction solubility x and the heat of solution; in the PEG papers it is used to extrapolate the solubility of a drug along its liquidus to 25 °C zhu2011 E3, P6; zhu2012 E3. This draft covers the solubility use; the evidence table lists a different use of the relation in another subcategory.

Findings

F4.

Related concepts

measures drug solubility in polymer; uses liquidus temperature; related to ideal solubility.

Formulas

van't Hoff equation.

How it is measured or obtained

\ln x is plotted against 1/T along the drug liquidus of the phase diagram (Figs. 2–5 of zhu2011), a straight line is fitted by linear regression and extended below the PEG melting point to 25 °C, and the result is converted to weight percent zhu2011 P6, E3. The same route was used for fenofibrate from the supporting-information diagram zhu2012 M2, E3.

Values in the library
materialvalue or classconditionspaper ids
benzocaine, chlorpropamide, ibuprofen, nilutamide, haloperidol, ketoconazole in PEG 335028, 26, 25, 11, 0, 0 wt% at 25 °Cextrapolated, supercooled liquid PEGzhu2011 R5
fenofibrate in PEG 33506 wt% at 25 °Cas abovezhu2012 M2
Pitfalls and disagreements

The regression lines, the heats of fusion and the molar masses behind the extrapolation are not printed zhu2011 E3. In the second paper the equation is named only zhu2012 E3. The nilutamide estimate (11 wt%) is above its eutectic content (10 wt%), although an extrapolation along the liquidus to a lower temperature would normally give a lower value zhu2011 X4. (synthesis: the relation assumes a constant heat of solution, while the extrapolation runs from liquidus temperatures well above the PEG melting point down to 25 °C zhu2011 R1, R2, R3, R4.)

← Concepts and formulas

concept · as used in PEG dispersions

water sorption correction of amorphous solubility

The factor e^{-I(a_2)} in Eq. 1, the activity of the amorphous drug once it has absorbed water to saturation; it is below 1 because water dilutes the amorphous drug, and lowers the predicted amorphous solubility [ilevbare2013a C59, E1]. The water-saturated supercooled liquid and the drug-rich phase made by LLPS have the same activity [ilevbare2013a C61]. The papers of 2017–2022 add that the water content of the ibuprofen-rich phase without polymer is negligible and has little impact on its amorphous solubility, and that the ibuprofen inputs of Eq. 1 come from H2O work while the measurements were in D2O [ueda2021 R20; ueda2022 X6].

Findings

F5, F6.

Related concepts

computed with the Gibbs-Duhem equation from water sorption; enters the amorphous solubility; related to plasticization by water.

Formulas

amorphous solubility advantage with water-sorption correction, Gibbs-Duhem equation.

How it is measured or obtained

From a gravimetric water sorption isotherm of the amorphous drug (0–95% RH at the test temperature) by integrating the Gibbs–Duhem equation (the Murdande method) [ilevbare2013a P2, P15; almeidaesousa2015 P7; indulkar2015 P7; mosqueragiraldo2015 P5; almeidaesousa2016 P8; hsieh2012 E5].

Values in the library
materialvalue or classconditionspaper ids
ritonavir; efavirenz; loratadine0.27; 0.44; 0.6037 °C[ilevbare2013a M1, M2, M3]
ketoconazole; indomethacin; felodipine0.28; 0.73; 0.8537 °C[ilevbare2013a M8, M7, M9]
ibuprofen to griseofulvin0.999, 0.997, 0.985, 0.932, 0.750, 0.69925 °C[almeidaesousa2015 M1, M2, M3, M4, M5, M6]
clotrimazole; atazanavir0.82; 0.2237 °C[indulkar2015 M1, M2]
telaprevir; CRH10.30; 0.75537 °C; 25 °C[mosqueragiraldo2015 M1; almeidaesousa2016 M1]
atazanavirexp[−I(a)] 0.22; 5.2% moisture37 °C[indulkar2017a M2]
Pitfalls and disagreements

The sorption isotherms and the integration are not shown, so the factor cannot be reproduced from the papers; only the ritonavir isotherm of the 2013 paper is shown [ilevbare2013a M1, R7; mosqueragiraldo2015 X3]. The griseofulvin and sorafenib water contents at water activity 1 are estimates with an unstated basis [almeidaesousa2015 R8]. For ibuprofen the predicted S0a/S0c lies below the measured one at every temperature, with D2O named as one possible reason [ueda2022 R16, C37].

← Concepts and formulas

concept · as used in PEG dispersions

water sorption isotherm

Equilibrium water content of a solid against relative humidity (water activity) at fixed temperature; for amorphous solids it can be treated as dissolution of water and fitted with Flory–Huggins theory [rumondor2010a C16, E1].

Findings

F6, F7, F8, F23.

Related concepts

measures water sorption and hygroscopicity; analysed with Flory-Huggins interaction parameter.

Formulas

Flory-Huggins water sorption isotherm, ternary Flory-Huggins water sorption isotherm, additive moisture sorption.

How it is measured or obtained

Gravimetric vapour sorption (VTI SGA-100) at 25 °C, either stepwise 5–95% RH with a weight criterion or a fixed time per step (PVP 1000 min), or one RH per experiment held to a plateau (about 600 min for amorphous drugs, about 1000 min for dispersions) [konno2008 P7; marsac2008a P6, R3; rumondor2010a P2; marsac2010 P10].

Values in the library
materialvalue or classconditionspaper ids
PVP K29/32≈33 (75% RH), ≈75 g/100 g (95% RH)25 °C[konno2008 R8.a; rumondor2010a R1]
HPMC, HPMCAS≈10.4–10.9 and ≈6.2–6.3 g/100 g at 75% RH25 °C[konno2008 R8; rumondor2010a R1]
amorphous felodipine, indomethacin≈1.1 and ≈1.55 g/100 g at 75% RH25 °C[rumondor2010a R1.h]
felodipine–PVP 70 wt% PVP≈10.3 (65% RH) turning up to ≈55.5 wt% (95% RH)25 °C[marsac2010 R9]
amorphous ritonavir (outside)≈1.55% at 50% RH, rising, extrapolated linearly to 100% RH37 °C[ilevbare2013a R7, E14]
PVP, PVPVA, HPMCASisotherms at 25 °C, PVP far above the others at high RHcited[rumondor2010c R19]
resveratrol–PVP dispersion and physical mixture0–95% RH, mixture above dispersion at every step25 °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 PEG dispersions

water sorption

The uptake of water vapor by an amorphous drug as a function of relative humidity; amorphous solids sorb more than their crystals, and the uptake sets both the activity of the water-saturated amorphous drug and the wet Tg [ilevbare2013a C23, C59]. The papers of 2017–2022 add dynamic vapor sorption of melt-made ibuprofen/PVP-VA and ibuprofen/HPMC 603 ASDs at 99% RH, used to test whether extra water explains the stronger effect of PVP-VA [ueda2021 P6, R17]. New aspect (ASD process): in the evacetrapib papers of 2017, low-DL dispersions are held to absorb more water because they contain more polymer, which is why they separate on storage while high-DL films stay miscible [li2017 C42, C52]. In the coating papers it is the uptake of coated and uncoated ASD powders in dynamic vapour sorption, as isotherms at 40 or 37 °C and as kinetics at 90% RH over 2–3 h (see moisture barrier effect) [moseson2022a R8, R9; duong2022c R9; moseson2023 R7, R8; benson2025 R3]. PVPVA ASDs sorb over three times as much water as HPMCAS ASDs [benson2025 C42, R23]. New aspect (Physical stability): one-phase drug–polymer blends sorb less water than the weighted sum of their components, while blends that have separated sorb close to additively [rumondor2010a C10; rumondor2009c C24]. New aspect (Release mechanism and LoC): in the release papers of 2021–2022 water sorption of the dispersion is read as a proxy for the water that enters the hydrating compact. Neat PVPVA sorbs much water at high water activity, its Tg falls below room temperature and it gels and dissolves rapidly (cited) [que2021 C42]; a drug–polymer interaction that persists in water is proposed to lower the water uptake and so the polymer dissolution rate [que2021 C44]. Surfactants slightly raised the water uptake of atazanavir–PVPVA [correasoto2022b C25], and salt formation changed the uptake of amorphous lumefantrine by counterion [hiew2022b C10]. For HPMCAS-MF dispersions the drug was proposed to lower polymer release at higher buffer capacity by reducing the amount and rate of water the polymer absorbs, leaving a more viscous gel [bapat2023 C46]. Plasticizers changed the rate and extent of water vapour uptake of atazanavir–PVPVA dispersions only slightly, against suggestions that additives act through solvent ingress [correasoto2023 C34, C35].

Findings

Amorphous solubility and LLPS: F2, F5, F20. ASD process: F6, F4, F43, F45, F47. Physical stability: F6, F7, F23. Release mechanism and LoC: F15, F22, F24, F26.

Related concepts

input to the Gibbs-Duhem equation and to plasticization by water; determines the water sorption correction of amorphous solubility. Governed by hygroscopicity; drives moisture-induced phase separation. Measured by water sorption isotherm; marker of amorphous-amorphous phase separation. Sets plasticization by water and so the wet glass transition temperature; needed for polymer chain disentanglement.

Formulas

Gibbs-Duhem equation, water plasticization rule of thumb, additive moisture sorption, Flory-Huggins water sorption isotherm.

How it is measured or obtained

Gravimetric vapor sorption (SGA-100) at the test temperature, 0–95% RH, equilibrium criterion about 0.01% weight change; the isotherm of ritonavir was extrapolated linearly from the high-water region to 100% RH [ilevbare2013a P15, E14; almeidaesousa2015 P7; mosqueragiraldo2015 P5]. In the ASD process papers: water absorbed by ASD powder in DSC pans after 24 h over saturated K2SO4 (procedure not printed), % w/w dry basis [li2017 P14]; equilibrium sorption of polymer powders by dynamic gravimetric sorption (see hygroscopicity) [mugheirbi2017 P14]. In the moisture-induced separation papers: plateau uptake at fixed RH (about 600 min for amorphous drugs, about 1000 min for dispersions) or isotherms at 25 °C [marsac2008a R3; rumondor2010a P2; rumondor2009c P11]. In the release-mechanism papers: dynamic vapour sorption at 37 °C up to 95% RH [correasoto2022b R16] and at 5–95% RH for the neat amorphous salts [hiew2022b R4].

Values in the library
materialvalue or classconditionspaper ids
ritonavirabout 4.98% at 95% RH; 5.21% extrapolated to 100% RH (slope 0.075, intercept −2.290)37 °C, melt-quenched[ilevbare2013a R7, E14]
telaprevir4.31% at 95% RH; about 4.6% estimated at 100% RHmelt-quenched glass[mosqueragiraldo2015 M1]
clotrimazole; atazanavir1.4%; 5.2%amorphous, 37 °C[indulkar2015 M1, M2]
griseofulvin; sorafenib2.7%; 1.8% at water activity 1 (estimated, basis not stated)25 °C[almeidaesousa2015 R8]
atazanavir5.2% moisture, exp[−I(a)] 0.22amorphous, 37 °C[indulkar2017a M2]
ibuprofen/HPMC 603 and ibuprofen/PVP-VA ASDs13.9 and 13.0% (1/1); 6.5 and 4.2% (4/1) after 200 min99% RH, 37 °C[ueda2021 R17]
ECP–PVPVA powdersabout 61% (PVPVA), 35% (10% DL), 4–7% (20–50% DL), 0.5–3.6% (60–100% DL)24 h, 97–98% RH[li2017 R25, X3]
felodipine, indomethacin, PVP, HPMC, HPMCASFlory–Huggins water parameters from isotherms25 °C[rumondor2010a R11]
clofoctol–PVP with 70% API or more; probucol–PVPresistance to moisture-induced separation attributed to too little moisture sorbed by the hydrophobic systems; no water content or sorption was reported for those filmsoutside[rumondor2011 C36, X6]
70 wt% PVP felodipine dispersionwater vapour sorption isotherm at 25 °Coutside[marsac2010 R9, R10]
erlotinib–HPMCAS 60% DL, uncoated against 5–25 nm coatedabout 5.7 against 5.4%DVS 40 °C, 75% RH[moseson2022a R8, R9]
ezetimibe–HPMCAS 50% DL, uncoated / thin / thickabout 5.65 / 5.83 / 3.17%DVS 37 °C, 95% RH[duong2022c R9]
PCZ–HPMCAS 25% DL, uncoated and coated 11 / 23 / 39 nmabout 4.7 / 4.3 / 3.7 / 1.2% at 30 minDVS 37 °C, 90% RH[moseson2023 R7]
PCZ–HPMCAS 50% DL, slow-deposited 26 nmabout 0.33% at 2 h against about 4.2–4.5%same[moseson2023 R8]
RTV–PVPVA 20% DL powdersabout 18.8–20.8% at 3 h; slow-coated 20.5 nm about 15.1%90% RH[benson2025 R3]
nifedipine; felodipine; with 25% PVP≈1.8; 1.1; 5.5; 4.6 g/100 g75% RH, 25 °Cmarsac2008a R2
felodipine–PVP 25%43–64% below additivity15–85% RH[rumondor2010a R7.b]
nifedipine-, pimozide-, droperidol–PVP5.9, 7.4, 0.2% from additivity (phase separated)95% RH[rumondor2009c R22]
indomethacin–PVP 75:254.9 vs 21.7 g/100 g predicted95% RH[rumondor2009c R22.g]
40% resveratrol–PVP dispersion≈1.8, ≈5.9, ≈8.7, ≈12.8% at 20, 60, 80, 95% RH, below its physical mixture at every step25 °C[wegiel2013b R19]
atazanavir–PVPVA 10%; with SDS or Span 8044%; 49% waterDVS, 37 °C, up to 95% RH[correasoto2022b R16]
amorphous lumefantrine salts≈6.6 (PEG 250 diacid 1:1), 3.3 (sulfate), below 2% (benzoate, besylate, tosylate, camsylate, HCl) at 95% RHDVS[hiew2022b R4]
lumefantrine salt–PVPVA dispersions35–55% water, higher at lower loading95% RH, 40 °C[hiew2022b R5]
HP-50-Na; amine salts of HP-50; HP-50≈42.4; ≈24.6–30.1; ≈9.7% water at 96 hpowders, 100% RH, 37 °C[qi2022 R11]
neat HPMCAS-MF; indomethacin and its methyl ester dispersionshighest extent and rate for the neat polymer; lower with indomethacin, lowest with the esterpowders, 95% RH, 37 °C, 12 h[bapat2023 R20, C31]
PVPVA; with 10% TBC; with 10% GTB≈41.8; ≈34.4; ≈32.0% water at 300 min95% RH, 37 °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

formula · as used in PEG dispersions

activity coefficient from solubility

Expression

\gamma_d = \frac{1}{x_d}\exp\left(\frac{-\Delta H_{fus,d}\,(T_{melt,d} - T)}{R\,T_{melt,d}^{2}}\right) baird2011 E7,

obtained by combining the simplified solubility equation

\ln\left[\gamma_d\,x_d\right] = -\frac{\Delta G_{fus}}{R\,T} baird2011 E5

with the Hoffman relation

\Delta G_{fus} = \frac{\Delta H_{fus,d}\,(T_{melt,d} - T)\,T}{T_{melt,d}^{2}} baird2011 E6.

Marsac and co-workers name the relation without printing it; the card's check finds the printed coefficients equal to the ideal solubility divided by the measured solubility within rounding for four drugs, that is \gamma = S^{ideal}/S marsac2008b E2, X5.

Variables and units

symbolmeaningunits
\gamma_dactivity coefficient of the drug in PEG 400 (or water)dimensionless baird2011 E7; marsac2008b E2
x_dmole-fraction solubility of the drugdimensionless; converted from mg/mL by a relation that is not printed baird2011 X4
\Delta H_{fus,d}heat of fusion of the drugkJ/mol (24.5 for chlorpropamide) baird2011 M1, E7
T_{melt,d}, Tmelting temperature and temperature of the measurementK (399.85 and 298.15 for chlorpropamide at 25 °C) baird2011 E7
S^{ideal}, Smole-fraction ideal and measured solubilitydimensionless marsac2008b E1, R14

Assumptions and valid domain

The solubility in liquid PEG 400 is used as a proxy for the polymer, because activity coefficients in viscous, semicrystalline PEG 3350 are hard to determine baird2011 C21. A coefficient below 1 is read as favourable drug–PEG interaction only if the entropy of mixing is close to ideal baird2011 C23; marsac2008b C14. The temperature of the ideal solubility in Marsac and co-workers is not stated and the aqueous solubilities are cited at unstated temperatures marsac2008b E1, X18. Tested for four drugs in PEG 400 at 25 °C baird2011 R9 and six drugs in PEG 400 and water marsac2008b R14.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
baird2011\gamma of chlorpropamide, aceclofenac, loratadine, haloperidol in PEG 4000.614, 0.121, 2.369, 0.842printed; reproduces for chlorpropamide (0.614 at T = 298.15 K, T_{melt,d} = 399.85 K, \Delta H_{fus,d} = 24.5 kJ/mol, x_d = 0.250) baird2011 E7, R9
marsac2008b\gamma of six drugs in PEG 400 and in water0.02–0.64 in PEG 400; 1.2 × 10¹ to 5.3 × 10⁵ in waternamed only; four rows equal S^{ideal}/S within rounding marsac2008b E2, R14, X5

Where it fails or is disputed

With the mole fraction defined as n_d/(n_d + n_{PEG}) instead of moles of drug per mole of PEG 400 in 1 mL, the four coefficients of Baird and Taylor become 0.766, 0.149, 2.49 and 0.856, with the split at 1 unchanged baird2011 X4. Loratadine is called close to ideal although its solubility is about 0.42 of the ideal value baird2011 X13. The Table 3 caption cites Equations 5 and 7 for γ and χ, while the text uses 7 and 8 baird2011 X12. In the Marsac and co-workers table, naproxen's coefficients fit an ideal solubility of about 0.0045 instead of the printed 0.01, and felodipine's two coefficients fit different ideal solubilities marsac2008b X5. The coefficient was measured at 25 °C, far below the eutectic temperatures of the dispersions baird2011 X16.

Concepts

activity coefficient, ideal solubility, drug solubility in polymer, enthalpy of mixing. Findings. F3, F11.

← Concepts and formulas

formula · as used in PEG dispersions

activity from concentration

Expression

a_{i1} = x_i\,\gamma_{i1} [ilevbare2013a E7];

a = C\,\gamma [mosqueragiraldo2015 E5].

The papers of 2017–2022 print the same relation as

a = \gamma\,c [indulkar2017a E8]

and as

a = C\,\gamma [lu2017b E2].

In the Bioperformance papers of 2014–2016 it is printed as

a = \gamma\,C [raina2014a E7; raina2015c E4; alhalaweh2016 E2].

Variables and units

symbolmeaningunits
athermodynamic activity of the drugdimensionless [mosqueragiraldo2015 E5]
x_imole fraction of the componentdimensionless [ilevbare2013a E7]
Cconcentration of the drug in the donor solutionµg/mL [mosqueragiraldo2015 E5]
\gammaactivity coefficient in the bulk (donor) solutiondimensionless [mosqueragiraldo2015 E5]

Assumptions and valid domain

None stated for the definition; the amorphous solubility treatment assumes a constant activity coefficient in the dilute solution between the crystalline and the amorphous concentration [ilevbare2013a C55; mosqueragiraldo2015 C10]. In the Bioperformance papers γ equals 1 in a dilute solution without solubilizers; with micelles or protein it does not [raina2015c C32, C36].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
ilevbare2013aactivity of a species equal in all phases at equilibriumnonenot applicable (no numerical output) [ilevbare2013a E6, E7]
mosqueragiraldo2015donor activity in the flux equationnone printedinputs not printed (γ) [mosqueragiraldo2015 E5]
indulkar2017afree atazanavir in SDS from the slope γ of free against total drugγ 0.998, 0.181, 0.086, 0.047 at 0, 1, 2, 3.6 mg/mL SDSreproduces (0.047 × 1450 µg/mL = 68 against about 70 plotted free) [indulkar2017a E8, R11]
lu2017bactivity of telaprevir in bile-salt medianone printedinputs not printed (γ) [lu2017b E2]
raina2014aflux proportional to activityγ not printednot applicable [raina2014a E7]
raina2015cwhy equal concentrations give different fluxγ not printednot applicable [raina2015c E4]
alhalaweh2016Caco-2 flux of ritonavir–atazanavir mixturesγ not printedinputs not printed [alhalaweh2016 E2]

Where it fails or is disputed

γ was not measured in either paper, so activity is only inferred, from the flux plateau [mosqueragiraldo2015 C10; ilevbare2013a X15]. γ in the micellar solutions is estimated with the ideal dilute solution as standard state and from a buffer calibration, not measured independently [indulkar2017a R11, C18]. In the Bioperformance papers γ was never measured directly. In the media study the activity-based and concentration-based supersaturation ratios agreed in buffers and diverged in micellar media, so γ/γ_eq departs from 1 there (F18) [elkhabaz2019b C28, C42].

Concepts

thermodynamic activity, activity coefficient, membrane flux, micellar solubilization. Findings. Amorphous solubility and LLPS: F8, F12, F16. Bioperformance: F3, F18.

← Concepts and formulas

formula · as used in PEG dispersions

additive moisture sorption

Expression

Printed in words in the two moisture papers (weight-averaged sum of the pure-component uptakes); written here in symbols:

\text{uptake}_{blend} = w_D\,\text{uptake}_D + w_P\,\text{uptake}_P [rumondor2009c E6; rumondor2010a E5]

as printed outside the subcategory:

M_{additive} = M_D w_D + M_P w_P [li2018 E1]

Variables and units

symbolmeaningunits
w_D, w_Pdry-basis weight fractions of drug and polymer– [rumondor2009c E6]
uptake, Mwater sorbed at the same RHg/100 g dry solid [rumondor2010a E5]

Assumptions and valid domain

The blend behaves like a physical mixture, every water-binding group keeping its ability [rumondor2010a C9]; components sorb independently [rumondor2009c E6].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
rumondor2009cmarker of moisture-induced separationwithin 0.2–7.4% of measured for separating dispersions; 121.7% and 341.5% off for mixed onesreproduces within 0.1 [rumondor2009c E6, R22]
rumondor2010ashortfall of one-phase blendsup to ≈64% (felodipine–PVP) below the sumreproduces from Fig. 1 readings [rumondor2010a E5, R7]
li2018 (outside)lopinavir dispersions with six polymersCA, EUD, CAP near additive; HPMCAS, HPMCP belowreproduces [li2018 E1, C33]

Where it fails or is disputed

It overestimates the uptake of one-phase blends by up to about two-thirds [rumondor2010a R7]. The two Rumondor papers express the deviation against different references (measured value, prediction) [rumondor2009c E6; rumondor2010a E6].

Concepts

water sorption, water sorption isotherm, amorphous-amorphous phase separation. Findings. F7.

← Concepts and formulas

formula · as used in PEG dispersions

amorphicity index

Expression

A score for a spin-coated film or a drug–polymer pair, built from the category codes assigned by polarized light microscopy at four time points. Each sample gets a four-letter code (AAAA completely amorphous to CCCC fully crystalline), and the amorphicity index counts its amorphous letters:

\mathrm{AI}\ (\%) = \frac{\text{number of A letters in the four category codes of a sample}}{16}\times 100 vaneerdenbrugh2010b E1

(printed in words; 16 is the number of A letters of a sample that is AAAA at all four time points). The scores are then averaged over the seven drug/polymer weight ratios of a pair, over all drugs for one polymer, and over all polymers for one drug (all printed in words):

\overline{\mathrm{AI}}_{\mathrm{pair}} = \frac{1}{7}\sum_{i=1}^{7}\mathrm{AI}_i vaneerdenbrugh2010b E2;

\overline{\mathrm{AI}}_{\mathrm{polymer}} = \frac{1}{N_{\mathrm{drugs}}}\sum_{\mathrm{drugs}}\overline{\mathrm{AI}}_{\mathrm{pair}} vaneerdenbrugh2010b E3;

\overline{\mathrm{AI}}_{\mathrm{drug}} = \frac{1}{N_{\mathrm{polymers}}}\sum_{\mathrm{polymers}}\overline{\mathrm{AI}}_{\mathrm{pair}} vaneerdenbrugh2010b E4.

The 2011 paper prints the same definition, with the index of a drug–polymer pair as the mean of the indices of its weight ratios [vaneerdenbrugh2011a E1, P3].

Variables and units

symbolmeaningunits
AIamorphicity index of one sample% vaneerdenbrugh2010b E1
A letteramorphous letter in the four-letter category, one for each of day 0, 1, 3 and 7count, 0 to 4 per sample vaneerdenbrugh2010b P2, E1
\overline{\mathrm{AI}}_{\mathrm{pair}}mean AI over the 7 drug/polymer ratios (90/10 to 10/90 w/w)% vaneerdenbrugh2010b E2, P1
N_{drugs}, N_{polymers}8 drugs and 7 polymerscount vaneerdenbrugh2010b R2

Assumptions and valid domain

The categories are semiquantitative and come from the extent of birefringence under polarized light, which is assumed to follow the amount of crystalline drug because the films are thin and crystallization extends over the full film height vaneerdenbrugh2010b C11, P2. The same weight is given to the four time points and to each ratio vaneerdenbrugh2010b E1, E2. Defined for dry-stored spin-coated films from ethanol, or from ethanol/dichloromethane for HPMC and HPMCAS vaneerdenbrugh2010b P1.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
vaneerdenbrugh2010bamorphicity of 392 spin-coated drug–polymer films (synthesis: 8 drugs × 7 polymers × 7 ratios)BD-E100 25/75 = 44; FFA-PAA mean 13; PVP mean 70; BD mean 48reproduces (4 + 1 + 1 + 1 = 7 A letters, 7/16 = 43.75%; FFA-PAA mean 12.5; PVP mean 70.0; BD mean 47.6) vaneerdenbrugh2010b E1, E2, E3, E4
vaneerdenbrugh2010bper-drug rankingPH 47, CZ 47, BD 48, LI 55, FFA 59, FB 68, CP 73, BI 97derived vaneerdenbrugh2010b R4
vaneerdenbrugh2010bper-polymer rankingPVP 70, PVPVA 70, E100 67, HPMC 66, HPMCAS 62, PAA 49, PSSA 48derived vaneerdenbrugh2010b R5
vaneerdenbrugh2011aamorphicity of 105 spin-coated pairs (15 drugs × 7 polymers; ratios 75/25, 50/50, 25/75 and five more for the drugs of the first screen)PH–PSSA 78; FFA–PAA 13; the 8 repeated drugs equal the first screenreproduces: a sample scored AAAA at all four time points has 4 × 4 = 16 A letters, AI 100%; per-sample categories not printed [vaneerdenbrugh2011a E1, R3, X9]

Where it fails or is disputed

One entry of the supplementary table (FFA–PSSA 60/40, printed 94 where the category codes give 6) does not reproduce, and the averages for FFA–PSSA, FFA and PSSA reproduce only with the printed value vaneerdenbrugh2010b X1. The averages hide the drug-by-drug reversal of the acidic polymers: PAA and PSSA are the best polymers for basic drugs and the worst for acidic drugs, yet their polymer means (49, 48) are the lowest of the seven vaneerdenbrugh2010b R5, C3. Film thickness, total solids concentration and storage temperature are not stated, so scores can be compared with other papers only qualitatively vaneerdenbrugh2010b X10. The cellulosic polymers were cast from a different solvent, which confounds their scores with solvent vaneerdenbrugh2010b X12. The paper reports only averaged scores, not the polymer fraction needed for each drug vaneerdenbrugh2010b X13. In the 2011 screen the number of ratios averaged per drug is not stated, there are no error bars, and one changed letter moves a three-ratio mean by about 2.1% [vaneerdenbrugh2011a X9, X10].

Concepts

crystallization inhibition, crystal growth inhibition by polymers, drug-polymer interactions, crystallization tendency. Findings. F15, F16, F24.

← Concepts and formulas

formula · as used in PEG dispersions

amorphous-crystalline free energy difference from heat capacity

Expression

With linear reversing heat capacities C_p^{sl} = aT + b and C_p^{c} = cT + d [almeidaesousa2015 E6, E7], the crystal-to-supercooled-liquid change at T is

\Delta H_{c\to sl} = \Delta_{fus}H + \frac{aT^2 + 2bT}{2} - \frac{aT_m^2 + 2bT_m}{2} + \frac{cT_m^2 + 2dT_m}{2} - \frac{cT^2 + 2dT}{2} [almeidaesousa2015 E9],

\Delta S_{c\to sl} = \frac{\Delta_{fus}H}{T_m} + (T_m - T)(c - a) + \ln\left(\frac{T_m}{T}\right)(d - b) [almeidaesousa2015 E10],

\Delta G_{c\to sl} = \Delta H_{c\to sl} - T\,\Delta S_{c\to sl} [almeidaesousa2015 E11].

A glass version uses C_p^{g} = eT + f below Tg [almeidaesousa2015 E8, E12, E13, E14]. The integral form printed for telaprevir is

\frac{\Delta G_{a\to c}}{RT} = \frac{\Delta H_f}{RT}\left(1 - \frac{T}{T_m}\right) + \frac{1}{RT}\int_{T_m}^{T}\Delta C_p\,dT - \frac{1}{R}\int_{T_m}^{T}\frac{\Delta C_p}{T}\,dT [mosqueragiraldo2015 E3].

Variables and units

symbolmeaningunits
a, b; c, d; e, flinear fit parameters of the reversing Cp of supercooled liquid, crystal, glassJ mol⁻¹ K⁻¹ and J mol⁻¹ K⁻² [almeidaesousa2015 E6, E7, E8]
\Delta_{fus}H, T_menthalpy of fusion, melting temperaturekJ/mol, K [almeidaesousa2015 E9]
\Delta H, \Delta S, \Delta Gconversion enthalpy, entropy, free energy at TkJ/mol, J mol⁻¹ K⁻¹, kJ/mol [almeidaesousa2015 R12]

Assumptions and valid domain

Cp linear in temperature over the range of interest (shown for tolnaftate only); un-ionized, non-solvated crystal that melts without degradation; only the reversing Cp is used because the entropy change is the reversibly exchanged heat divided by T [almeidaesousa2015 C10, C11, E17]. For much larger undercooling the form with a 1/T^2 term is better [almeidaesousa2015 E5, C10].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
almeidaesousa2015six drugs at 25 °C; sorafenib and griseofulvin also to the glassΔG 3.56–10.34 kJ/mol (to supercooled liquid); 11.37 and 10.38 kJ/mol (to glass)ΔG = ΔH − TΔS reproduces from Table 7 (9.39 kJ/mol for griseofulvin); parameters a–f not printed [almeidaesousa2015 E11, R11, R12]
mosqueragiraldo2015telaprevir at 37 °C97 ± 8 and 189 ± 16 µg/mL through Eq. 1ΔCp values not printed [mosqueragiraldo2015 E3, R13]
almeidaesousa2016CRH15.85 and 5.95 kJ/molmethod named only, parameters not printed [almeidaesousa2016 E5, M1]

Where it fails or is disputed

The method's superiority is concluded on the hypothesis that the onset is governed by the supercooled liquid, and neither ΔG nor the amorphous solubility was determined independently [almeidaesousa2015 X4]. Eq. 4 is printed with a symbol clash with Eqs. 5–7 and is not used [almeidaesousa2015 X13].

Concepts

amorphous-crystalline free energy difference, supercooled liquid, structural relaxation. Findings. F7.

← Concepts and formulas

formula · as used in PEG dispersions

Barandiaran-Colmenero critical cooling rate

Expression

\ln(\text{rate}) = A - \frac{B}{(\Delta T)^2},\quad \Delta T = T_m - T_{crys,max} baird2010 E1;

R_{crit} = \exp(A) [baird2010 E2; baird2013 E1], with A the intercept of \ln(\text{cooling rate}) regressed on 1/(\Delta T)^2 [baird2013 E3].

Variables and units

symbolmeaningunits
\text{rate}cooling rateK min⁻¹ baird2010 E1
\Delta Tundercooling at the crystallization peak on cooling, T_m - T_{crys,max}K [baird2010 E1; baird2013 E4]
A, Bintercept and slope of the regressionB in K² baird2010 E1
R_{crit}critical cooling rate, ΔT extrapolated to infinityK min⁻¹ [baird2010 E2; baird2013 E1]

Assumptions and valid domain

Undercooling must rise by an experimentally significant amount with cooling rate baird2010 E1; a higher cooling rate must lower the crystallization temperature [baird2013 C17]. Fitted over 5–20 °C/min baird2010 R13 and over about 5 to above 500 °C/min [baird2013 X16].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
baird2010Rcrit of 19 class I moleculesr² 0.74–0.99 for 7 and below 0.55 for 12; Rcrit from 20 K/min (haloperidol) upwardreproduces (carbamazepine B 701 against 708, A 4.75 against 4.8; haloperidol \exp(3.0) = 20.1) baird2010 R13, E1, E2
baird2013Rcrit,cool of class I-A from 5–800 °C/min2.7 × 10³ (phenacetin) to 8.1 × 10³ K/min (4-biphenylmethanol), r² 0.89–0.99reproduces for phenacetin; haloperidol 6.6 × 10³ does not follow from A = 6.5 (6.65 × 10²); felbinac not reproducible [baird2013 R7, X2, X13]

Where it fails or is disputed

Over 5–20 °C/min the estimates contradicted experiment: haloperidol and phenacetin, with the lowest estimates, crystallized on liquid-nitrogen quench, whereas carbamazepine and griseofulvin, with higher estimates, quenched amorphous baird2010 C21; the approach "may be of limited utility" for organic molecules baird2010 C20, and accurate estimates need rates far below Rcrit and spanning several orders baird2010 R31, C22. A wider rate range seems to improve fits [baird2013 C20], but the method is clearly inappropriate where undercooling rises and falls with rate (benzamide, lidocaine, indoprofen) [baird2013 C16]. Knowing that Rcrit,cool exceeds 500 °C/min is "probably sufficient" for pharmaceutical use [baird2013 C21].

Concepts

Barandiaran-Colmenero method, critical cooling rate, degree of supercooling, glass-forming ability. Findings. F11.

← Concepts and formulas

formula · as used in PEG dispersions

classical nucleation barrier

Expression

W^* = \frac{16\pi\gamma^3}{3\,\Delta G_v^2} [baird2010 E24; vaneerdenbrugh2010a E3];

W^* = \frac{16\pi\,\sigma_{cm}^3}{3\,\Delta G_v^2} [baird2012 E2], which enters the steady-state rate I_{SS} = I_0 \exp\left[-\frac{W^* + \Delta G_\eta}{k_B T}\right] [baird2012 E1].

\Delta G^{*} \propto \frac{1}{(\ln S)^{2}} [hsieh2012 E8]. The same dependence appears in the nucleation-rate expression used for celecoxib, J = A\exp[-16\pi\gamma^{3}v^{2}/(3k^{3}T^{3}(\ln S)^{2})] [xie2015 E3].

Variables and units

symbolmeaningunits
W^*free energy to form a nucleus of critical sizenot stated baird2010 E24
\gamma, \sigma_{cm}interfacial free energy of the nucleus–liquid (or nucleus–matrix) interface per areanot stated [vaneerdenbrugh2010a E3; baird2012 E2]
\Delta G_vfree energy difference per volume between crystal and liquidJ/cm³ [vaneerdenbrugh2010a E2, E5]
\Delta G^{*}free energy of forming the critical nucleusJ [hsieh2012 E8]
Ssupersaturation ratiodimensionless
\gamma, vinterfacial tension and molecular volume (in the full expression)J/m²; m³ [xie2015 E3]

Assumptions and valid domain

Homogeneous nucleation and a similar interfacial energy for the compared classes baird2010 E24; spherical nuclei [baird2012 E2]. Neither γ nor σcm was measured or estimated in any of the three papers [baird2010 E24; vaneerdenbrugh2010a E3; baird2012 E2]. In the supersaturation form the barrier falls steeply as S rises, so crystals nucleate only above a certain supersaturation, which depends on compound and conditions [hsieh2012 C3]; no numerical output is stated in the pH-shift paper.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
baird2010argument that a more negative ΔGv of class I lowers the barriernoneinputs not printed baird2010 E24, C61
vaneerdenbrugh2010areading the ΔGv–class linknoneinputs not printed [vaneerdenbrugh2010a E3, C39]
baird2012argument that viscosity enters nucleation and growthnoneinputs not printed [baird2012 E2, C4, C32]
duong2022bposaconazole barrier in buffer and nucleus size from fitted γ\Delta G^{*} = 16\pi\gamma^{3}\nu^{2}/(3k^{2}T^{2}\ln^{2}S); 2.73 × 10⁻²¹ J against ≈2.72 × 10⁻²¹ J read from the figure; PBS 2.72 × 10⁻²¹ J at S 33.6reproduces [duong2022b E8, R17]
hsieh2012why type 1 bases precipitate only after reaching a supersaturation of 1.4–26.7 times the titration solubilitynonenot applicable (no numerical output) [hsieh2012 E8, R5]
xie2015reading polymer effects on celecoxib induction times (ASD dissolution chapter)γ, v not fittedprinted [xie2015 E3]

Where it fails or is disputed

W* depends on γ³ but only on ΔGv²; the authors read the ΔGv–class correlation as suggesting that γ differences between compounds are small [vaneerdenbrugh2010a C39], an inference that rests on a ΔGv ranking that is not monotonic across classes [vaneerdenbrugh2010a X10]. In the pans and films used, nucleation may be heterogeneous [baird2010 C19; baird2012 C8], which the homogeneous form does not cover. Precipitation was seen at widely different supersaturations (1.4 for pyrimethamine to 26.7 for droperidol) [hsieh2012 R5, C22]. (synthesis: the barrier expression alone does not predict this spread without the interfacial energies of the compounds, which the paper does not give.)

Concepts

classical nucleation theory, nucleation, thermodynamic driving force for crystallization, heterogeneous nucleation. Findings. Crystallization tendency: F3, F6. Crystallization from solution: F1, F14, F34.

← Concepts and formulas

formula · as used in PEG dispersions

classical nucleation theory

Expression

J \propto \exp\left(-\frac{\Delta G^{*}}{k_B T}\right) [hsieh2012 E7]

J = A\exp\left(\frac{-\Delta G_{crit}}{kT}\right) [ilevbare2013c E4]

J_{N} = v^{*} z n \exp\left(\frac{-16\pi\gamma^{3}v^{2}}{3k_{B}^{3}T^{3}(\ln S)^{2}}\right) [indulkar2018 E6]

J = A\exp\left(\frac{16\pi \nu_o^{2} \gamma^{3}}{3 (k_B T)^{3} (\ln S)^{2}}\right) [elkhabaz2021 E2] (printed without the minus sign)

J = A\,S\,\exp\left(\frac{-16\pi\gamma^{3}\nu^{2}}{3k^{3}T^{3}\ln^{2}S}\right) [duong2022b E6]

\ln(J/S) = \ln A - \frac{B}{\ln^{2}S}, \qquad B = \frac{16\pi\gamma^{3}\nu^{2}}{3k^{3}T^{3}} [duong2022b E7]

J = A\exp\left(-\frac{16\pi\gamma^{3}v^{2}}{3k^{3}T^{3}(\ln S)^{2}}\right) [trasi2015 E6; xie2015 E3]

Nucleation rate with a thermodynamic and a kinetic barrier, as printed in the solid-state papers of the physical-stability chapter:

I = A\exp\left(\frac{-\left(\Delta G^{*} + \Delta G_{a}\right)}{kT}\right) [konno2006 E8]

I = A\exp\frac{-\left(\Delta G^{*} + \Delta G_{a}\right)}{kT} [marsac2006a E9]

and for the undercooled melt:

I_{SS} = I_0\exp\left(-\frac{W^{*} + \Delta G_{\eta}}{k_B T}\right) [baird2012 E1]

In the reduced-temperature form printed for acetaminophen, with its typesetting as printed:

J = A\exp\left[-\frac{16\pi r^{3}}{3kT_m\Delta H_f^{2}T_r(\Delta T_r)^{2}} + \frac{\Delta G'}{KT}\right] [trasi2012a E1]

where the card reads r as the interfacial energy \gamma and the kinetic term as -\Delta G'/kT, as the text describes [trasi2012a X1].

The ASD dissolution papers of 2008 and 2010 print it with ln S unsquared,

J = A\exp\left(-\frac{16\pi\gamma^{3}v^{2}}{3k^{3}T^{3}\,(\ln S)}\right) [konno2008a E3],

J \propto \exp\left[-\frac{1}{\ln S}\right] [alonzo2010 E4];

the ritonavir dispersion paper states the dependence in words only: the relative nucleation rate rises with the drug concentration in a phase and falls with the crystal–solution interfacial tension [ilevbare2013d E1].

Variables and units

symbolmeaningunit
Jnucleation ratem⁻³ s⁻¹
Apre-exponential kinetic factor, depends on molecular mobilitym⁻³ s⁻¹
ΔG*, ΔG_critfree energy of forming a critical nucleusJ
k, k_BBoltzmann constantJ/K
Tabsolute temperatureK
γinterfacial tension (free energy) between nucleus and solutionJ/m² (mJ/m² in the posaconazole fits)
ν, v, ν_omolecular volumem³ (920 ų for posaconazole)
Ssupersaturationdimensionless
v*, z, nmonomer attachment rate, Zeldovich factor, number density of moleculesas printed
Inucleation rate in the film papersm⁻³ s⁻¹ [konno2006 R4]
\Delta G^{*}, W^{*}thermodynamic barrier, from interfacial term against bulk driving forceJ [konno2006 E8]
\Delta G_{a}, \Delta G_{\eta}kinetic barrier for transport onto the nucleusJ [konno2006 E8]
T_r, \Delta T_rreduced temperature T/T_m and 1 - T_r– [trasi2012a E1]
\Delta H_f; \Delta G'heat of fusion; activation energy for molecular motionnot given [trasi2012a E1]

Assumptions and valid domain

Clusters grow by sequential molecular additions; the barrier rises with the cube of the interfacial energy and falls with (\ln S)^{2} (see classical nucleation barrier) [ilevbare2013c E4, C14; hsieh2012 E8]. Used qualitatively; no fit to induction times is printed. The solid-state papers assume homogeneous nucleation, although nucleation in the films is "most likely heterogeneous"; stresses from the volume change are ignored [konno2006 C33; marsac2006a C32]. In the ASD dissolution papers of 2008–2013 it is used only qualitatively: higher supersaturation, faster nucleation [konno2008a C20; alonzo2010 C43; ilevbare2013d C40]. The 2015 celecoxib paper prints the classical form with (\ln S)^{2} and uses it to argue that neither supersaturation nor interfacial tension explains the polymer differences in induction time [xie2015 E3, C43].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
hsieh2012why type 1 bases precipitate only above a certain supersaturationnonenot applicable (no numerical output) [hsieh2012 E7]
ilevbare2013cwhy a polymer gains more at lower supersaturation (celecoxib 31-fold at S 7.3)noneinputs not printed [ilevbare2013c E4, C45]
xie2015celecoxib dispersions: J = A\exp[-16\pi\gamma^{3}v^{2}/(3k^{3}T^{3}(\ln S)^{2})]; longer induction times with polymers read as lower nucleation rate; why HPMCAS and HPMC lengthen celecoxib induction times more than PVPγ, v not fitted; γ, v, A not printedprinted; inputs not printed [xie2015 E3, C42, C43]
trasi2015J = A exp[−16πγ³v²/(3k³T³(ln S)²)] to state that T, S and γ set Jacetaminophen S 1.5, 20 °Cinputs (A, γ, v) not printed [trasi2015 E6]
li2016anamed only: nucleation rate depends highly on supersaturationbile-salt seriesnamed only [li2016a E5]
indulkar2018why lecithin might accelerate nucleation through γnoneinputs not printed [indulkar2018 E6, C40]
elkhabaz2021why surfactants should lower γ, and why human fluid does not fitnoneprinted without minus sign [elkhabaz2021 E2, X1]
duong2022blinearized fit of posaconazole induction times in buffer and three mediaγ 3.52, 2.61, 2.73, 3.24 mJ/m²; A 2.44, 5.14, 4.98, 9.87reproduces from the printed slopes and intercepts [duong2022b E7, R16]
konno2006sorting polymer effects into driving force and kinetic barriernoneinputs not printed [konno2006 E8]
marsac2006aframework for the nifedipine–felodipine comparisonnoneframework only [marsac2006a E9]
baird2012role of viscosity in class differencesnoneinputs not printed [baird2012 E1]
trasi2012aframework for polymer effects on acetaminophen nucleationnoneinputs not printed; printed form has misprints [trasi2012a E1, X1]
konno2008afelodipine nucleates readily at a high solubility rationonenot applicable [konno2008a E3]
alonzo2010scheme of dissolution against crystallizationnonenot applicable [alonzo2010 E4]
ilevbare2013dnucleation favoured in drug-rich dropletsnoneprinted in words [ilevbare2013d E1]

Where it fails or is disputed

Induction times include growth to detectable size, so a rate from them is nucleation plus early growth [ilevbare2013c X14]. The two-step picture (disordered cluster, then reorganization) is assumed to be rate-limiting but not shown [ilevbare2013c C5, C15]. The critical supersaturation at which precipitation is seen depends on compound and conditions [hsieh2012 C3]. The Poisson fit uses the printed volume 0.0012 m³ and a positive exponent, both misprints (V = 1.2 mL and a minus sign reproduce the 95% times within about 12%) [trasi2015 X1, X2, E5]. In the posaconazole fits the high-supersaturation sets hold 3–9 points (R² 0.84–0.97, FeSSIF V2 not fittable), and the conversion of induction time into J is not stated [duong2022b X10, X11]. No parameter was fitted in the solid-state papers; the theory serves to exclude a driving-force route and to frame a kinetic one [konno2006 C35, C40]. The polymer effects on acetaminophen nucleation were "not particularly straightforward" to explain with it, and it does not contain molecular recognition [trasi2012a C49]. The 2008 and 2010 dissolution papers print ln S without the square of the classical expression; use the squared form to compute rates [konno2008a X8; alonzo2010 X3]. The 2015 celecoxib form carries the square; in its argument the supersaturation is not the same with and without polymer (about 14.7 against 10.3–11.6), and the text refers to Eq. 2 where interfacial tension appears in Eq. 3 [xie2015 X9, X1].

Concepts

classical nucleation theory, nucleation rate, crystal-solution interfacial free energy, kinetic barrier to nucleation, interfacial free energy, nucleation, interfacial tension. Findings. Crystallization from solution: F1, F14, F27, F29, F5, F34, F39, F42. Physical stability: F1, F4, F17. Supersaturation from ASD dissolution: F1, F4, F5, F13.

← Concepts and formulas

formula · as used in PEG dispersions

Δχ effect

Evidence table: Δχ effect. Content from the release-mechanism chapter (2017–2021), with a row from the Physical stability chapter.

Expression

\left|\Delta\chi\right| = \left|\chi_{12} - \chi_{13}\right| [marsac2010 E1]

Stated in words as the magnitude of the difference between the water–drug and water–polymer parameters; the larger it is, the higher the tendency to phase separate [purohit2017b E4]. Written in that paper's symbols (synthesis: transcription of the words):

\Delta\chi = \left|\chi_{WD} - \chi_{WP}\right|

Printed with absolute-value bars in the drug-property study [yang2021 E2]:

\left|\Delta\chi\right| = \left|\chi_{12} - \chi_{13}\right| [yang2021 E2]

Variables and units

symbolmeaningunit
\chi_{12}, \chi_{WD}Flory–Huggins interaction parameter water–drug–
\chi_{13}, \chi_{WP}Flory–Huggins interaction parameter water–polymer–

Assumptions and valid domain

Phase separation is promoted when the two components interact asymmetrically with the solvent (cited) [marsac2010 E1]; the named effect of a cited paper [purohit2017b E4].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
marsac2010 (Physical stability)felodipine–PVP–waterχ water–felodipine ≈3.3, water–PVP ≈0.5no Δχ printed; the inputs give 3.3 − 0.5 = 2.8 [marsac2010 E1, R22]
purohit2017bwhy ritonavir–PVP and –PVPVA separate with waternonenot applicable (no χ values) [purohit2017b E4, C43]
yang2021why log P does not predict water-induced separation of six drugsnoneinputs not printed [yang2021 E2, C21]

Where it fails or is disputed

No χ values were stated for the ritonavir systems, so the argument is qualitative [purohit2017b E4].

Concepts

Δχ effect, Flory-Huggins interaction parameter, amorphous-amorphous phase separation. Findings. Release mechanism and LoC: F8, F9.

← Concepts and formulas

formula · as used in PEG dispersions

entropy of fusion

Expression

\Delta S_{fus} = \frac{\Delta H_{fus}}{T_{melt,ons}} baird2010 E26;

\Delta S_{fus} = \frac{\Delta H_{fus}}{T_m} [vaneerdenbrugh2010a E1].

Variables and units

symbolmeaningunits
\Delta S_{fus}entropy of fusionkJ mol⁻¹ K⁻¹ baird2010 E26; J cm⁻³ K⁻¹ after volume conversion [vaneerdenbrugh2010a E1]
\Delta H_{fus}heat of fusion from DSCkJ mol⁻¹ baird2010 E26; J cm⁻³ [vaneerdenbrugh2010a E1]
T_m, T_{melt,ons}melting point (onset)K [baird2010 E26; vaneerdenbrugh2010a E1]

Assumptions and valid domain

None stated beyond DSC inputs [baird2010 E26; vaneerdenbrugh2010a E1]. The 31-drug growth study uses the melting entropy ΔSm per mole in \Delta G \approx \Delta S_m\,\Delta T, an approximation [trasi2014a E3].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
baird2010descriptor tables and class PCAhaloperidol 12.8 × 10⁻² kJ mol⁻¹ K⁻¹; class I contribution +0.41reproduces: 54.26/425.15 = 0.1276 baird2010 E26, R22
vaneerdenbrugh2010aclass PCAcontributions +0.46, −0.27, −0.33 for classes I, II, IIIinputs not printed [vaneerdenbrugh2010a E1, R20]
marsac2006afelodipine and nifedipine74.3 and 89.6 J mol⁻¹ K⁻¹reproduces [marsac2006a E11]

Where it fails or is disputed

On a volume basis the fast class I has the higher entropy of fusion [baird2010 R22; vaneerdenbrugh2010a R20], while on a molar basis the fastest growers had lower melting entropy and the normalized growth rate fell with ΔSm/R [trasi2014a R8, R11]. (synthesis: the two bases and the two outcomes, class and growth rate, differ, so the signs need not conflict; class I molecules are small, which raises per-volume values.)

Concepts

entropy of fusion, enthalpy of fusion, thermodynamic driving force for crystallization. Findings. F6, F13.

← Concepts and formulas

formula · as used in PEG dispersions

Flory-Huggins activity equation

Expression

Activity coefficient of the drug in a polymer, with the amorphous drug as the solvent (2006):

\ln\gamma_{\mathrm{drug}} = \ln\frac{\Phi_{\mathrm{drug}}}{x_{\mathrm{drug}}} + \left(1-\frac{1}{m}\right)\Phi_{\mathrm{polymer}} + \chi\,\Phi_{\mathrm{polymer}}^{2} marsac2006b E6;

the same quantity scaled from a liquid analogue (1-ethyl-2-pyrrolidone, EP) to PVP (2009):

\ln\gamma_{\mathrm{drug}}^{PVP} = \frac{MV_{\mathrm{drug}}}{MV_{\mathrm{lattice}}}\left[\frac{1}{m_{\mathrm{drug}}}\ln\frac{\Phi_{\mathrm{drug}}}{x_{\mathrm{drug}}} + \left(\frac{1}{m_{\mathrm{drug}}}-\frac{1}{m_{PVP}}\right)\Phi_{PVP}\right] + \ln\gamma_{\mathrm{drug}}^{EP} marsac2009 E8;

\ln\gamma_{\mathrm{drug}}^{PVP} = \frac{MV_{\mathrm{drug}}}{MV_{\mathrm{lattice}}}\left[\frac{1}{m_{\mathrm{drug}}}\ln\frac{\Phi_{\mathrm{drug}}}{x_{\mathrm{drug}}} + \left(\frac{1}{m_{\mathrm{drug}}}-\frac{1}{m_{PVP}}\right)\Phi_{PVP} + \chi\,\Phi_{PVP}^{2}\right] marsac2009 E9.

As the activity of the drug in the library's other papers:

\ln a = \ln\Phi_1 + \left(1-\frac{1}{x_{12}}\right)\Phi_2 + \chi\,\Phi_2^{2} [konno2006 E9];

\ln a_{\mathrm{drug}} = \ln\Phi_{\mathrm{drug}} + \left(1-\frac{1}{m}\right)\Phi_{PVP} + \chi\,\Phi_{PVP}^{2} [marsac2006a E10].

The ASD dissolution papers print it as the change of the drug chemical potential in an undissolved polymer:

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

Variables and units

symbolmeaningunits
\gamma_{drug}, aactivity coefficient and activity of the drugdimensionless [marsac2006b E6; konno2006 E9]
\Phivolume fractiondimensionless marsac2006b E6
x_{drug}mole fraction of the drugdimensionless; mole-fraction basis in PVP not printed marsac2009 X13
mratio of polymer to lattice-site volumedimensionless marsac2006b E6
MVmolar volumecm³/mol (e.g. 288.62 for nifedipine) marsac2006b M1; marsac2009 E8
\chiinteraction parameterdimensionless marsac2006b E6
\Delta\mu_{\mathrm{drug}}change of the drug chemical potential on mixingJ/mol [li2018 E4]
\Phi_{\mathrm{drug}}, \Phi_{\mathrm{poly}}volume fractions of drug and polymer (2018 notation)dimensionless [li2018 E4]
rV_{\mathrm{poly}}/V_{\mathrm{drug}}, volume ratio of polymer to drug (2018 notation for m)dimensionless [li2018 E4]

Assumptions and valid domain

In the analogue liquid the first two terms vanish when the mixing entropy is ideal (minimal size difference) marsac2006b C46. The 2009 scaling assumes ideal mixing entropy with EP, identical contacts of the drug with EP and with the PVP repeat unit, Flory–Huggins combinatorial entropy for PVP, and equal γ at the solubility limits in EP and in PVP marsac2009 E6, E7, C11. In the ASD dissolution use: a drug–polymer dispersion that is one phase and stays one phase on hydration, with a polymer largely insoluble in the medium; the change of χ with water is not included [li2018 C45, C46].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
marsac2006bsolubility of the crystalline drug in PVP and methyl pyrrolidonewith χ −3.8 and −4.2reproduces for felodipine in PVP K12 with m = 7.50 (Φ_drug 0.210, 0.31 g/g against 0.31); felodipine in K29/32 gives 0.29 against 0.25 marsac2006b E6, R17
marsac2009γ of five compounds in PVP K12, K29/32, K90 from γ in EPγ in PVP 0.50–5.97inputs not printed (lattice volume of EP, mole-fraction basis) marsac2009 E8, E9, R9
marsac2006adrug activity against PVP content with χ of the melting routeactivity ≈0.84 (nifedipine) and ≈0.83 (felodipine) at Φ_PVP 0.2reproduces approximately (0.839, 0.826 with 1/m ≈ 0) [marsac2006a E10, R19]
marsac2006aargument that PVP lowers the driving force alike and little for nifedipine and felodipine, so the ranking persistsactivity ≈0.96, 0.84, 0.67 at Φ 0.1, 0.2, 0.3same calculation as the row above [marsac2006a R19, C47]
konno2006argument that Flory–Huggins gives little activity loweringnoneχ and x₁₂ for felodipine–polymer not given [konno2006 E9, C35]
li2018qualitative ranking of the suppression of lopinavir concentration by insoluble polymersχ and r not determinedinputs not printed [li2018 E4, C44, C51]

Where it fails or is disputed

The values in PVP are predictions under the stated assumptions; none was checked against a solubility measured in a polymer, and the one check (methyl pyrrolidone) is about 30% low for nifedipine marsac2006b X10; marsac2009 X17. The 2009 relation has no printed lattice volume, so it cannot be recomputed from the paper marsac2009 X4, X13. The combinatorial and residual parts are linked, because order imposed by exothermic interactions lowers the entropy of mixing marsac2009 C10. The conclusion drawn from it in the physical-stability papers, that a few percent of polymer acts kinetically, was not tested by any measured activity [konno2006 C35; marsac2006a C46]. For lopinavir, χ was not measured for any lopinavir–polymer pair, so the use is qualitative [li2018 C46, C51]. With χ = 0 and a large r the equation gives a drug activity of about 0.82 at a drug volume fraction of 0.5, above the proportional-dilution line that the paper calls ideal (extractor calculation) [li2018 X2].

Concepts

activity coefficient, combinatorial entropy of mixing, Flory-Huggins theory, drug solubility in polymer, thermodynamic driving force for crystallization, Flory-Huggins interaction parameter, chemical potential, solubility suppression. Findings. Miscibility and drug-polymer interactions: F8, F9. Physical stability: F4. Supersaturation from ASD dissolution: F18.

← Concepts and formulas

formula · as used in PEG dispersions

Flory-Huggins free energy of mixing

Expression

In mole numbers, as printed in the 2006 paper:

\frac{\Delta G_M}{RT} = n_{\mathrm{drug}}\ln\Phi_{\mathrm{drug}} + n_{\mathrm{polymer}}\ln\Phi_{\mathrm{polymer}} + n_{\mathrm{drug}}\,\Phi_{\mathrm{polymer}}\,\chi marsac2006b E1;

per lattice site, with the size ratios m of the 2009 paper:

\frac{\Delta G}{RT} = \frac{\Phi_{\mathrm{drug}}}{m_{\mathrm{drug}}}\ln\Phi_{\mathrm{drug}} + \frac{\Phi_{\mathrm{polymer}}}{m_{\mathrm{polymer}}}\ln\Phi_{\mathrm{polymer}} + \chi\,\Phi_{\mathrm{drug}}\Phi_{\mathrm{polymer}} marsac2009 E10;

and for a drug (volume fraction \Phi) and a polymer of m lattice sites, as printed in two later papers of the library:

\Delta G_{mix} = RT\left[\Phi\ln\Phi + \frac{1-\Phi}{m}\ln(1-\Phi) + \chi\,\Phi\,(1-\Phi)\right] [tian2017 E2];

\Delta G = RT\left[\varphi\ln\varphi + \frac{1-\varphi}{m}\ln(1-\varphi) + \chi\,\varphi\,(1-\varphi)\right] moseson2018 E1.

A form is named but not printed in [rumondor2009b E2].

The itraconazole–HPMC paper prints the same form for a drug D and a polymer P,

\frac{\Delta G_{mix}}{RT} = n_D\ln\phi_D + n_P\ln\phi_P + n_D\,\phi_P\,\chi [purohit2015a E1],

and uses it in words only.

Variables and units

symbolmeaningunits
\Delta G_M, \Delta Gfree energy of mixingdivided by RT in the 2006 and 2009 forms marsac2006b E1; marsac2009 E10
n_{drug}, n_{polymer}moles of drug and polymermol marsac2006b E1
\Phivolume fractiondimensionless; from weight fraction and true density marsac2006b P5, E8
m, m_{drug}, m_{polymer}ratio of the molecular volume to that of the lattice sitedimensionless marsac2009 E10; moseson2018 E1
\chiinteraction parameterdimensionless marsac2006b E1
R, Tgas constant, absolute temperaturemarsac2006b E1

Assumptions and valid domain

The amorphous drug is treated as a solvent and one lattice site equals the molecular volume of the drug marsac2006b E1, C9; χ is independent of composition marsac2009 P8; the entropy curves are computed with χ = 0 for nifedipine with methyl pyrrolidone and three PVP grades marsac2006b R1. The temperature and the PVP grade of the 2009 curves are not printed marsac2009 X12. The critical χ for miscibility depends on how the lattice is defined marsac2006b C18. The indomethacin polymorph paper uses it for drug–polymer melts at 80–135 °C, above Tg, with 10% w/w polymer, as an argument only [tian2017 E2, A2].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
marsac2006bentropy of mixing of nifedipine with methyl pyrrolidone and PVP; ΔG/RT for χ −4.2 to 2.0χ = 0, −4.2, −3.8, 0.5, 1.0, 2.0; miscibility needs about 0.6 or lessprinted; not applicable, curves carry no ordinate scale marsac2006b E1, R1, R2, R3
marsac2009ΔG/RT of five PVP pairs and sucrose–dextran from two sets of χindomethacin minimum ≈2.4 and ≈5 times the athermal oneprinted; not applicable, no numerical axis marsac2009 E10, R10
tian2017argument that stronger drug–polymer interactions lower the driving force, so that PVP acts "most likely" through both mobility and driving forcenoneprinted; Φ, m and χ not given; interactions cited from another paper [tian2017 E2, C30, C31, X13]
moseson2018framework for the melting depression of the drug in PVPVAnone directlyprinted; no numerical output moseson2018 E1
purohit2015aargument that, without hydrogen-bond donors, itraconazole–HPMC mixing is entropy-driven and may be limited at room temperaturenone (no χ, n or φ given)printed; not applicable [purohit2015a E1, C41, C42, C47]

Where it fails or is disputed

The notation differs between papers (mole numbers against size ratios against polymer segments), so a χ from one convention is not directly usable in another marsac2006b E1; marsac2009 E10; moseson2018 E1. The first two terms are the entropy of mixing and are small for a polymer; the curves depend on the lattice and on χ's constancy, while the melting-route χ refers to temperatures near the drug melting point marsac2006b C11, C32. The same function applied to a ternary water–drug–polymer system needs three χ values that cannot be transferred from the binary ones [alonzo2010 C44]. The driving-force argument of the indomethacin polymorph paper cannot explain why HPMC beat HPMCAS at high temperature, and χ was not measured for any of the three polymers [tian2017 C29, X13].

Concepts

free energy of mixing, entropy of mixing, Flory-Huggins theory, Flory-Huggins interaction parameter, drug-polymer miscibility, thermodynamic driving force for crystallization. Findings. Miscibility and drug-polymer interactions: F5, F6, F18. Physical stability: F4, F29.

← Concepts and formulas

formula · as used in PEG dispersions

Flory-Huggins melting point depression

Expression

For a crystalline drug in an amorphous polymer, extended from polymer–solvent equations (2006):

\frac{1}{T_M^{mix}} - \frac{1}{T_M^{pure}} = \frac{-R}{\Delta H_{fus}}\left[\ln\Phi_{\mathrm{drug}} + \left(1-\frac{1}{m}\right)\Phi_{\mathrm{polymer}} + \chi\,\Phi_{\mathrm{polymer}}^{2}\right] marsac2006b E3;

rearranged so that the slope of a plot against \Phi_{\mathrm{polymer}}^{2} is χ:

\left(\frac{1}{T_M^{mix}}-\frac{1}{T_M^{pure}}\right)\frac{\Delta H_{fus}}{-R} - \ln\Phi_{\mathrm{drug}} - \left(1-\frac{1}{m}\right)\Phi_{\mathrm{polymer}} = \chi\,\Phi_{\mathrm{polymer}}^{2} marsac2006b E10;

with the lattice volume set by a liquid analogue (2009):

\left(\frac{1}{T_M^{mix}}-\frac{1}{T_M^{pure}}\right) = \frac{-R}{\Delta H_{fus}}\left(\frac{MV_{\mathrm{drug}}}{MV_{\mathrm{lattice}}}\right)\left[\frac{\ln\Phi_{\mathrm{drug}}}{m_{\mathrm{drug}}} + \left(\frac{1}{m_{\mathrm{drug}}}-\frac{1}{m_{\mathrm{polymer}}}\right)\Phi_{\mathrm{polymer}} + \chi\,\Phi_{\mathrm{polymer}}^{2}\right] marsac2009 E2.

The relation is also printed for drugs in PEG 3350 and for PVPVA:

\frac{1}{T_M^{mix}} - \frac{1}{T_M^{pure}} = -\frac{R}{\Delta H_{fus}}\left[\ln\varphi_{API} + \left(1-\frac{1}{m}\right)\varphi_{\mathrm{polymer}} + \chi\,\varphi_{\mathrm{polymer}}^{2}\right] zhu2011 E1;

\frac{1}{T_c} - \frac{1}{T_m} = -\frac{R}{\Delta H}\left[\ln\varphi + \left(1-\frac{1}{m}\right)(1-\varphi) + \chi\,(1-\varphi)^{2}\right] moseson2018 E2.

In the extrusion work T_c is the depressed melting point of the mixture and T_m that of the pure drug moseson2018 E2. The linearised form used there to fit \chi as a slope (printed as A=\chi B with B=(1-\phi)^2):

\left(-\frac{\Delta H}{R}\right)\left(\frac{1}{T_c}-\frac{1}{T_m}\right)-\left[\ln\phi+\left(1-\frac{1}{m}\right)(1-\phi)\right]=\chi(1-\phi)^2

moseson2018 E4.

Variables and units

symbolmeaningunits
T_M^{mix}, T_M^{pure}melting temperature of the drug with polymer and pure (onset in 2006, offset in 2009)K marsac2006b E3, P1; marsac2009 C16
\Delta H_{fus}heat of fusion of the pure drugkJ/mol (39.89 and 30.83 for nifedipine and felodipine) marsac2006b M1, M2
\Phi_{drug}, \Phi_{polymer}volume fractionsdimensionless marsac2006b E8
mratio of the polymer volume to the lattice-site (drug) volume7.80 for PVP K12 with nifedipine (synthesis: 2252.25/288.62) marsac2006b M3, M1
MV_{drug}/MV_{lattice}molar volume of the drug over that of the lattice site (EP)dimensionless; not printed marsac2009 X4, P6
\chiinteraction parameterdimensionless marsac2006b R9
T_c, T_mdepressed melting point of the mixture; melting point of the pure drug (extrusion papers)K moseson2018 E2
R, \Delta Hgas constant; enthalpy of fusion of the drug (IDM 37.8 ± 0.6 kJ/mol)J/(mol K); J/mol moseson2018 E2, M1
\phidrug volume fraction from true densitiesdimensionless moseson2018 E2
mratio of the polymer molecular volume to the drug's (170.7 at 50/50 IDM:PVPVA)dimensionless moseson2018 E2

Assumptions and valid domain

The drug and polymer must be chemically stable over the temperature range and interact enough for a depression to appear; the polymer must be liquid-like at the drug melting point, so Tg should lie well below it marsac2006b C27; marsac2009 C6. The equation is linear only at low polymer fractions (fit range 0–0.25) and gives χ at temperatures close to the drug melting point marsac2006b R8, C32; marsac2009 C7. The offset is used because it gives the melting point at the final composition, assuming complete mixing marsac2009 C16. In the extrusion work: one \chi independent of temperature and composition; the drug's molecular volume as lattice volume; offset temperature extrapolated to 0 °C/min; fitted through 90/10 to 50/50 IDM:PVPVA with 40/60 excluded for high variability moseson2018 C18, P2, R4. Later papers use the same form with the drug's molecular volume as lattice volume: bicalutamide–PVPVA with m = 46,610/319 = 146.1, φ from amorphous densities of 1.35 and 1.18 g/mL, ΔH = 45.9 kJ/mol and Tm = 467.25 K [moseson2022c E5, E21, R9]; posaconazole–HPMCAS with m = 25.95, ΔH = 50,323.87 J/mol and Tm = 441.78 K, φ from densities of 1.28 and 1.27 g/mL [shah2024 E1, E4].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
marsac2006bχ of nifedipine and felodipine with PVP K12−3.8 (r² 0.99); −4.2 (r² 0.92)reproduces (T_M^mix 430.2 K = 157.1 °C at Φ_polymer 0.278, against ≈157 °C on the curve) marsac2006b E3, R9, R10
marsac2009χ of five PVP pairs, three dextran pairs, itraconazole–Eudragit E100−0.82, −0.08, 0.00, −0.08, 0.02; 0.20, 0.38, 0.72, 0.11inputs not printed (depressed melting temperatures only plotted, lattice volume not printed) marsac2009 E2, R7, X4
marsac2009indomethacin–PVP K12 from three points of the peak−6.16, −1.94, −0.82as above marsac2009 R6
zhu2011χ of drugs with PEG 3350see the PEG chapterinputs not printed zhu2011 E1
moseson2018χ of indomethacin–PVPVA−1.97; Tc 131.0 °C predicted at 50/50 against 132.3 ± 0.8 °C measuredreproduces within 0.05 °C for all nine predicted Tc (φ = 0.4739, m = 170.7, Tm = 433.79 K) moseson2018 E2, R4, R5
moseson2022cχ of BCL–PVPVA from the heating-rate-extrapolated melting offset, 30–90% BCL−1.57 (R² 0.994); Tc 145 °C at 30% BCLreproduces (30 wt% BCL: 144.3 °C against 145 °C measured); the linearized form gives A/B = −1.53 against the fitted −1.57 [moseson2022c E5, E20, R8, R9]
shah2024χ of posaconazole–HPMCAS MF, PCZ fractions 0.4–1.0+0.43 (R² 0.991)reproduces within about 1 °C (135.9, 155.3 and 165.2 °C at 10, 25 and 50 wt% against printed 135, 155 and 165 °C) [shah2024 E1, E3, R4, R5]

Where it fails or is disputed

The nifedipine volume fractions of the 2006 fit appear to use felodipine's density, and the felodipine plot behind −4.2 is not shown marsac2006b X2, X4. The positive χ of non-depressing pairs are lower limits marsac2009 C19, X11. A high-Tg polymer hides the depression (PVP K29/30 at 10 °C/min) marsac2006b R11, C29. The choice of onset, midpoint or offset changes χ 7.5-fold (synthesis: 6.16/0.82) marsac2009 R6. Differences between laboratories for one pair are attributed to preparation, heating rate and onset against offset moseson2018 C21. In the extrusion work, written as A=\chi B (a line through the origin) the printed \chi is not reproduced: a fit through the origin gives −1.86 and only a free intercept of about +0.02 gives −1.97; using the drug weight fraction in place of \phi would give 133.9 °C instead of 131.0 °C moseson2018 E2, E4, X7. The 40/60 mixture lies well above the line (129 ± 6 against 118.5 °C) because viscosity hindered the offset moseson2018 R5.g, C17. Values of \chi for one pair differ between studies and with onset, midpoint or offset moseson2018 R7, C21; marsac2009 R6. The posaconazole line has a free intercept (it meets B = 0 at A of about −0.05) and its values below 40% PCZ are extrapolated [shah2024 R4, X7, X8]. The basis of φ (weight or volume fraction) is not stated in the bicalutamide paper [moseson2022c E5]; for posaconazole, setting φ equal to the weight fraction changes the result by only about 0.2 °C [shah2024 E1].

Concepts

melting point depression, Flory-Huggins interaction parameter, drug-polymer miscibility, enthalpy of mixing, Flory–Huggins theory, formulation critical temperature. Findings. Miscibility and drug-polymer interactions: F6, F7, F8. ASD process: F8, F35, F41.

← Concepts and formulas

formula · as used in PEG dispersions

Flory-Huggins water sorption isotherm

Expression

Binary form, water (1) in one amorphous solid (2):

\ln\left(\frac{p}{p_0}\right) = \ln\phi_1 + \left(1 - \frac{1}{x_{12}}\right)\phi_2 + \chi_{12}\phi_2^{2} [rumondor2010a E1]

with the molar volume ratio written explicitly (outside the subcategory):

\ln(a_{1,g}) = \ln\phi_1 + \phi_2\left(1 - \frac{v_1}{v_2}\right) + \chi_{12}\phi_2^{2} [li2020 E12]

The 2009 and 2010 moisture papers name it for the drug–water parameter without printing it [rumondor2009c E5; marsac2010 E3].

Variables and units

symbolmeaningunits
p/p_0water activity (RH/100)– [rumondor2010a E1]
\phi_1, \phi_2volume fractions of water and solid– [rumondor2010a E1]
x_{12}molecular volume of the solid relative to water16.7 (felodipine), 14.9 (indomethacin) [rumondor2010a P4]
\chi_{12}water–solid interaction parameter– [rumondor2010a E1]

Assumptions and valid domain

Water uptake by an amorphous solid treated as dissolution [rumondor2010a C16]; fitted at p/p0 0.15–0.85 or 0.95 at 25 °C [rumondor2010a P4].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
rumondor2010aχ with water of five amorphous solidsfelodipine 3.27, indomethacin 2.86, PVP 0.36, HPMC 1.33, HPMCAS 1.62point values bracket the stated averages except PVP (≈0.47–0.75 against 0.36) [rumondor2010a R11, E1, X5]
rumondor2009cdrug–water χ of six drugs from 95% RH uptake2.50–3.58extractor check reproduces 2.84, 3.58, 2.71 [rumondor2009c R24, E5]
marsac2010water–felodipine χ from the 2008 sorption dataabout 3.3named only [marsac2010 R22, E3]

Where it fails or is disputed

The stated water–PVP value cannot be recovered from the plotted PVP isotherm; the x12 for the polymers and the averaging are not stated [rumondor2010a X5]. The 2009 χ values rest on densities partly approximated as 0.9 × crystal density [rumondor2009c X4].

Concepts

Flory-Huggins interaction parameter, water sorption isotherm, Δχ effect. Findings. F6, F8, F13.

← Concepts and formulas

formula · as used in PEG dispersions

Gibbs-Duhem equation

Expression

I(a_2) = \left(\frac{n_1}{n_2}\right)_{Henry} + \int_{\bar{a}_1^{H}}^{\bar{a}_1^{S}} \frac{n_1}{n_2}\,\frac{1}{a_1}\,da_1 [hsieh2012 E5]

The integral is evaluated numerically as \sum \langle (n_1/n_2)(1/a_1)\rangle (a_1^{i+1} - a_1^{i}) over the sorption isotherm [hsieh2012 E5]. The other chapter papers name the Gibbs–Duhem equation without printing it [ilevbare2013b E7; jackson2014 E3].

Variables and units

symbolmeaningunit
n_1, n_2moles of water and of solute in the amorphous solidmol
a_1water activitydimensionless
ā_1^Hwater activity at the limit of Henry's-law linearitydimensionless
ā_1^Swater activity of the solid in equilibrium with a dilute solution (extrapolated to unit water activity)dimensionless
I(a_2)integral entering \exp[-I(a_2)], the activity of the water-saturated amorphous drugdimensionless

Assumptions and valid domain

A Henry's-law region from zero water up to the limit of linearity plus a "high water" region from the sorption isotherm (Murdande 2010, outside the library) [hsieh2012 E5, P13]. Applied to amorphous drugs at 37 °C (5–95% RH) and 25 °C (danazol).

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
hsieh2012water correction of five amorphous basesI(a2) not printedinputs not printed [hsieh2012 E5]
ilevbare2013bamorphous solubility of three drugs−I(a2) not printednamed only [ilevbare2013b E7]
jackson2014danazolexp[−I(a2)] = 0.935named only [jackson2014 E3, E1]

Where it fails or is disputed

The sorption isotherms and I(a2) values are not printed, so the corrected amorphous solubilities cannot be recomputed [hsieh2012 X14].

Concepts

Gibbs-Duhem equation, water sorption correction of amorphous solubility. Findings. F2.

← Concepts and formulas

formula · as used in PEG dispersions

Gibbs free energy of mixing

Expression

The general relation between the free energy, enthalpy and entropy of mixing, as printed in the 2009 study of drug–polymer miscibility:

\Delta G_{mix} = \Delta H_{mix} - T\,\Delta S_{mix} [rumondor2009a E5];

with the ideal (combinatorial) entropy of mixing, printed without the leading minus sign:

\Delta S_{mix} = R\,(X_u\ln X_u + X_v\ln X_v) [rumondor2009a E3];

the form that is positive for all compositions, as the text requires (synthesis: the minus sign restored, as the card's note X7 reads it):

\Delta S_{mix} = -R\,(X_u\ln X_u + X_v\ln X_v) [rumondor2009a E3, X7];

and the enthalpy of mixing, written as the pure-component enthalpies minus the mixture enthalpy:

\Delta H_{mix} = (H_{ii}+H_{jj}) - H_{ij} [rumondor2009a E4].

For a drug (A) and a buffer solution (B) in a partially miscible system, the free energy of mixing is written with chemical potentials:

\Delta G_{mix} = x_A(\mu_A - \mu_A^{*}) + x_B(\mu_B - \mu_B^{*}) [raina2014a E8].

The conditions for the two points of phase separation are given in words only: the binodal points are the two minima of \Delta G_{mix} against composition, and the spinodal points are the inflection points, found by setting the second derivative to zero [rumondor2009a E6, E7].

The dextran–PVP paper prints the same relation for a polymer blend,

\Delta G_{mix} = \Delta H_{mix} - T\,\Delta S_{mix} [vaneerdenbrugh2012a E3],

and splits it into a Flory–Huggins enthalpy \Delta H_{mix} = kT\chi\phi_1\phi_2 per lattice site [vaneerdenbrugh2012a E4] and the combinatorial entropy of Flory-Huggins combinatorial entropy of mixing.

Variables and units

symbolmeaningunits
\Delta G_{mix}, \Delta H_{mix}, \Delta S_{mix}free energy, enthalpy and entropy of mixingnot printed [rumondor2009a E3, E4, E5]
X_u, X_vmole fractions of the two componentsdimensionless [rumondor2009a E3]
H_{ii}, H_{jj}, H_{ij}enthalpies of the pure components and of the mixturenot printed [rumondor2009a E4]
x_A, x_Bmole fractions of drug and buffer solutiondimensionless [raina2014a E8]
\mu, \mu^{*}chemical potential and its standard-state value[raina2014a E8]
T, Rtemperature and gas constant[rumondor2009a E3, E5]

Assumptions and valid domain

Ideal mixing entropy with mole fractions is assumed in the 2009 form [rumondor2009a E3]. Positive \Delta G_{mix} is read as unfavourable mixing and negative as favourable; one minimum is read as a single phase, two minima as partial miscibility, and a positive curve as immiscibility [rumondor2009a C35, C37]. The scheme is liquid-mixture theory extended to amorphous solids [rumondor2009a C35]. The drug–buffer form is used for a partially miscible system at constant temperature [raina2014a E8].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
rumondor2009aframework for the three miscibility behaviours of felodipine, nifedipine and ketoconazole dispersionsnoneprinted; not applicable, no numerical output (E3 is a misprint of sign) [rumondor2009a E3, E4, E5, C35]
rumondor2009aargument that a favourable drug–polymer interaction gives one minimum and a one-phase dispersion; competition with intra-polymer hydrogen bonds makes mixing less favourablenonenot applicable [rumondor2009a C37, C39, C45]
raina2014aframework for the onset of liquid–liquid phase separation as binodal pointsnoneprinted; not applicable [raina2014a E8, C27]
vaneerdenbrugh2012aargument that a blend mixes only if the combinatorial entropy outweighs a positive enthalpynone (χ not determined)printed; not applicable, no numerical output [vaneerdenbrugh2012a E3, E4, C32]

Where it fails or is disputed

Equation 3 of the 2009 paper is printed without the minus sign and as printed would give a negative entropy of mixing [rumondor2009a X7]. The sign convention of \Delta H_{mix} in E4 is the reverse of the conventional one, and the text mixes the two conventions [rumondor2009a X8]. Taking the binodal points as the minima of \Delta G_{mix} holds only for a symmetric curve, so E6 cannot locate the binodal compositions of an asymmetric drug–polymer system [rumondor2009a X15]. The paper applies none of the relations to data. The Flory–Huggins form of the same quantity, with its size-ratio terms, is a separate page: Flory-Huggins free energy of mixing.

Concepts

free energy of mixing, enthalpy of mixing, entropy of mixing, drug-polymer miscibility. Findings. F3, F4, F22.

← Concepts and formulas

formula · as used in PEG dispersions

Gordon-Taylor equation

Expression

As printed with a density-based constant:

T_g=\frac{w_1T_{g1}+Kw_2T_{g2}}{w_1+Kw_2},\qquad K=\frac{\rho_1T_{g1}}{\rho_2T_{g2}}

moseson2018 E3. As printed with the drug weight fraction w_1 and a fitted constant:

T_g=\frac{w_1T_{g1}+K(1-w_1)T_{g2}}{w_1+K(1-w_1)}

[li2019 E1].

As printed in the felodipine nucleation paper:

T_{g12} = \frac{w_1 T_{g1} + K w_2 T_{g2}}{w_1 + K w_2} [konno2006 E2]

K = \frac{T_{g1}\rho_1}{T_{g2}\rho_2} [konno2006 E3]

with a Couchman–Karasz constant:

K = \frac{\Delta C_{P1}}{\Delta C_{P2}} [konno2006 E4]

In the acetaminophen paper the Gordon–Taylor-type rule is cited in words only: the Tg of a miscible blend varies with the weight fraction and Tg of each component [trasi2012a E2].

As printed in the indomethacin release study, with a fitted constant:

T_{g,mix} = \frac{w_1 T_{g1} + k\,w_2 T_{g2}}{w_1 + k\,w_2} [saboo2020 E3]

As printed in the 2024 phase-diagram study of the phenolphthalein analogues:

T_{g,ASD} = \frac{w_d T_{g,d} + K\,w_p T_{g,p}}{w_d + K\,w_p} [deac2024b E14]

Variables and units

symbolmeaningunitids
T_gglass transition temperature of the miscible blendKmoseson2018 E3
w_1, w_2weight fractions of drug and polymer–moseson2018 E3
T_{g1}, T_{g2}Tg of drug (IDM 43.7 °C) and polymer (PVPVA 104.2 °C); nanoTA: 367 K and 482 KK[moseson2018 M1, M2; li2019 E1]
Kconstant from true densities (0.932 with Tg in K) or fitted (0.628)–[moseson2018 E3; li2019 E1]
\rho, \Delta C_Pdensities 1.33 (felodipine), 1.25 (PVP), 1.29 (HPMCAS), 1.19 g/cm³ (HPMC); heat capacity steps 0.33, 0.20, 0.31, 0.25 J/g/Kg/cm³; J/g/K[konno2006 M1, M2, M3, M4]
T_{g,mix}Tg of the homogeneous film (indomethacin release study)°C[saboo2020 E3]
w_1, T_{g1}weight fraction and Tg of indomethacin (53 °C by nanoTA)–, °C[saboo2020 E3]
w_2, T_{g2}weight fraction and Tg of PVPVA (130 °C by nanoTA)–, °C[saboo2020 E3]
kfitted constant, 0.91–[saboo2020 E3]

Assumptions and valid domain

A miscible, ideally mixing blend; K from the Simha–Boyer rule with Tg in kelvin (the temperature unit of K is not stated in the paper); for nanoTA the fit to softening temperatures of miscible rotary-evaporated films from 0 to 100% DL [moseson2018 E3; li2019 P10, R13]. The felodipine paper states that the components are miscible and their free volumes additive [konno2006 E2]. In the indomethacin release study: homogeneous films; Tg from nanoTA; k by partial least squares to films of 10–90% drug [saboo2020 E3, R27].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
moseson2018formulation Tg line of IDM–PVPVA72.9 °C predicted against 72.2 ± 0.5 °C at 50/50reproduces within 0.05 °C for all predicted Tg (K = 0.932 with Tg in K) moseson2018 E3, R5
li2019local drug content from nanoTA softeningK = 0.628, Tg1 = 367 K, Tg2 = 482 Kreproduces (110 °C → 0.794; 180 °C → 0.174; 150 and 105 °C → 0.40 and 0.85) [li2019 E1, R16]
moseson2022cTg line of BCL–PVPVAK = 0.987 with Tg in K (BCL 52.3 °C, 1.35 g/mL; PVPVA 104.2 °C, 1.18 g/mL)reproduces: 88.5 °C at 30% BCL against about 89.6 °C read from the figure; the density choice is not stated [moseson2022c E6, R9]
shah2024Tg line of PCZ–HPMCASTg of PCZ 61 °C and HPMCAS 122 °C, densities 1.28 and 1.27 g/mLmismatch: printed line about 81.5 °C at 0.5 PCZ; 89.1 °C with K = 0.852 (Tg in K); 81.4 °C with K = 0.504 (Tg in °C), which matches the line at 0.1–0.9 within about 0.5 °C [shah2024 E2, R6]
konno2006ideal-mixing Tg lines for felodipine with PVP, HPMCAS, HPMCK 0.280, 0.398, 0.351 (Tg in °C)reproduces the plotted lines only with Tg in °C; with kelvin K 0.767, 0.845, 0.858 and all systems fall below [konno2006 E3, X3]
trasi2012aTg rises of 1.7–4.2 °C with 10% polymer read as miscibilitynoneprinted in words; polymer Tg values not printed [trasi2012a E2, R9, C17]
trasi2017context for the Tg drop of amorphous tacrolimus and its HPMC dispersion after 75% RHnonenamed only [trasi2017 E7, R15]
saboo2020inverting the local Tg of a dissolving 25% indomethacin–PVPVA film into its drug content111, 95, 88, 82 °C → 23, 44, 52, 60 wt% at 0–20 minreproduces: at 82 °C w_1 = k(T_{g2} - T_g)/(T_g(1 - k) - T_{g1} + k T_{g2}) = 0.601 against 60 ± 5; 111 °C gives 23 wt% [saboo2020 E3, R28]
deac2024bdry MePHPH–PVPVA Tg; Tg against water for the glass–gel boundaryK = 0.65; fitted water Tg 197.6–297.1 Kreproduces 349.3 against 349.1 K [deac2024b E14, X11]

Where it fails or is disputed

With Tg in °C, K = 0.466 and 50/50 would give 62.9 °C moseson2018 E3. nanoTA softening temperatures lie 20–60 °C above DSC Tg, so a nanoTA calibration is a separate fit, and a miscible 33% DL film (about 145–154 °C) reads as about 40% LPV on the curve [li2019 C25, X17]. Some drug-rich values lie below the pure-LPV calibration point [li2019 X16]. In the posaconazole paper the printed line matches K computed from Tg in °C, whereas in the indomethacin paper it matches K computed from Tg in K, and the unit of K is not stated in either [shah2024 E2; moseson2018 E3]. In the felodipine nucleation paper the temperature scale of the constant is not stated either and the plotted lines need °C [konno2006 X3]; the Couchman–Karasz constant as printed reproduces neither orientation [konno2006 X4]. The nanoTA method probes about 50 nm of a film, while FTIR and EDX of the same study probed tablets more deeply, so at 20 min the three estimates span about 60–72 wt% [saboo2020 X15]. Could not describe dry PHPH–PVPVA, whose Tg lay above both components [deac2024b E14, R31].

Concepts

Gordon–Taylor equation, temperature-composition phase diagram, glass transition temperature, Couchman-Karasz equation, surface drug enrichment. Findings. ASD process: F7, F8, F15. Physical stability: F5, F18, F33. Release mechanism and LoC: F7, F30.

← Concepts and formulas

formula · as used in PEG dispersions

Hoffman equation

Expression

\Delta G_v = -\frac{\Delta H_{fus}\,(T_{melt,ons} - T)\,T}{T_{melt,ons}^{2}} baird2010 E25;

\Delta G_v = -\frac{\Delta H_{fus}\,(T_{m} - T)\,T}{T_{m}^{2}} [vaneerdenbrugh2010a E2];

\Delta G_v = \frac{\Delta H_{m}\,(T_{m} - T)\,T}{T_{m}^{2}} [lu2016 E1].

Named but not printed in [baird2012 E6]. The sign differs between papers: the two 2010 papers print a leading minus sign, the 2016 paper does not and plots the negative of its own expression [lu2016 X17].

Two more printed forms. In the PEG dispersions paper the expression is printed without a leading sign and used inside the simplified solubility equation \ln[\gamma_d x_d] = -\Delta G_{fus}/(R\,T) baird2011 E5:

\Delta G_{fus} = \frac{\Delta H_{fus,d}\,(T_{melt,d} - T)\,T}{T_{melt,d}^{2}} baird2011 E6.

In the solution-methods paper it is printed with a positive sign and \Delta T = T_m - T:

\Delta G = \frac{\Delta H_f\,\Delta T}{T_m}\cdot\frac{T}{T_m} [raina2015a E2],

which equals \Delta H_f\,(T_m - T)\,T/T_m^{2} and is the amorphous-minus-crystal free energy that enters e^{\Delta G/RT} of the amorphous solubility estimate.

The papers of the amorphous solubility chapter print the relation with a positive sign, as the amorphous-minus-crystal free energy that enters e^{\Delta G/RT}:

\Delta G_{a\to c} = \frac{\Delta H_f\,(T_m - T)\,T}{T_m^{2}} [ilevbare2013a E2; indulkar2015 E3; mosqueragiraldo2015 E2; almeidaesousa2016 E2];

the 2015 Almeida e Sousa paper writes \Delta_{fus}H for the heat of fusion and \Delta G_{c\to a} for the direction [almeidaesousa2015 E2]. For atazanavir it is printed again,

\Delta G = \frac{\Delta H_f\,(T_m - T)\,T}{T_m^{2}} [indulkar2017a E2].

The papers of the crystallization-from-solution chapter print it with a positive sign as well:

\Delta G_c = \Delta H_f\,\frac{(T_m - T)\,T}{T_m^{2}} [hsieh2012 E3; hsieh2014 E2];

\Delta G_{a \to c} = \frac{\Delta H_{fus}\,(T_m - T)\,T}{T_m^{2}} [ilevbare2012b E9; ilevbare2013c E7];

\Delta G_C = \frac{\Delta H_f\,(T_m - T)\,T}{T_m^{2}} [ilevbare2013b E3];

\Delta G = \frac{\Delta H_f\,\Delta T\,T}{T_m^{2}}, \qquad \Delta T = T_m - T [jackson2014 E2].

The moisture-induced separation paper of the physical-stability chapter prints it with a positive sign,

\Delta G_c = \Delta H_f\frac{\left(T_m - T\right)T}{T_m^{2}} [rumondor2009c E3],

and the felodipine kinetics paper names it without an expression [rumondor2009b E1].

The ASD dissolution papers print it as

\Delta G_c = \Delta H_f\,\frac{(T_m - T)\,T}{T_m^{2}} [konno2008a E2],

\Delta G = \frac{\Delta H_f\,\Delta T\,T}{T_m^{2}} [alonzo2010 E2; alonzo2011 E3],

and, with the sign that makes \Delta G negative,

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

Variables and units

symbolmeaningunits
\Delta G_vfree energy difference between crystal and amorphous or liquid stateJ/cm³ after conversion with crystalline density [vaneerdenbrugh2010a E2, E5; baird2010 E25]; kJ/mol [lu2016 E1]
\Delta H_{fus}, \Delta H_menthalpy of fusionkJ/mol or J/cm³ [baird2010 E26; vaneerdenbrugh2010a E1]
T_m, T_{melt,ons}melting temperature (onset)K [vaneerdenbrugh2010a E1; lu2016 E1]
Ttemperature of evaluation293.15 K [baird2010 E25; vaneerdenbrugh2010a E2], 298 K [baird2012 E6], crystallization temperature [lu2016 E1]; 25 or 37 °C [hsieh2014 E2; ilevbare2012b E9]
\Delta G_{fus}, \Delta H_{fus,d}, T_{melt,d}free energy difference between crystalline and liquid drug at T (298.15 K in the check); heat of fusion of the drug in kJ/mol; its melting temperature\Delta H_{fus,d} in kJ/mol; temperatures in K; unit of \Delta G_{fus} not printed baird2011 E5, E7
\Delta H_fmolar heat of fusionnot printed [raina2015a E2]
\Delta TT_m - TK [raina2015a E2]
\Delta G_{a\to c}amorphous-minus-crystal free energy that enters e^{\Delta G/RT} in the amorphous solubility papers (\Delta G_{c\to a} in the 2015 Almeida e Sousa paper)kJ/mol in the use table below [ilevbare2013a E2; almeidaesousa2015 E2]
\Delta G_c, \Delta G_Cfree-energy difference between amorphous (supercooled liquid) and crystalkJ/mol [hsieh2012 E3; ilevbare2013b E3]
\Delta H_f, T_m, T in the moisture paperheat of fusion; melting and evaluation temperatureskJ/mol; K [rumondor2009c E3]
\Delta G_c, \Delta G (ASD dissolution papers)free-energy difference between amorphous and crystalline drugJ/mol [konno2008a E2; alonzo2010 E2]

Assumptions and valid domain

Lu et al. call it an approximation [lu2016 E1]. Papers outside this chapter state that it assumes enthalpies of crystal and supercooled liquid linear in temperature and applies above Tg [marsac2006a E3; marsac2006b E4], that it assumes a constant heat-capacity difference and small undercooling [almeidaesousa2015 E2], and that it may not suit large undercoolings [mosqueragiraldo2015 E2]. In this chapter it is evaluated at room temperature, far below Tm and below Tg for many compounds [baird2010 E25; baird2012 E6]. In the PEG dispersions paper it is used as an estimate of \Delta G_{fus} from thermal properties, with the drug solubility in PEG 400 as a proxy for the polymer baird2011 E6, C20, C21. In the solution-methods paper no assumptions are stated beyond the reference; ΔHf and Tm come from DSC at 10 °C/min [raina2015a E2, P4]. In the amorphous solubility papers the assumptions are a constant, temperature-independent ΔCp, small undercooling and Tg close to T∞ [almeidaesousa2015 C8], and a temperature of interest "reasonably close to Tm", which is violated for telaprevir (Tm 238 °C, 37 °C) [mosqueragiraldo2015 C24, M1]. The pH-shift and crystal-growth papers state that the enthalpies of crystal and supercooled liquid vary linearly with temperature, "to a first approximation" [hsieh2014 E2; jackson2014 E2]; ΔHf and Tm come from DSC of the crystalline material and temperatures must be in kelvin [hsieh2012 E3]. The felodipine kinetics paper states that it applies to a pure amorphous drug; with polymer and sorbed water a reasonable estimate is "extremely difficult" [rumondor2009b C17]. In the ASD dissolution papers it is called increasingly approximate far below Tg (cited) [alonzo2011 C5] and was judged a good estimate for felodipine in earlier work (cited) [konno2008a R20].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
baird2010ΔGv descriptor in the class PCAclass I contribution −0.40 (more negative ΔGv)inputs not printed baird2010 E25, R22.g
vaneerdenbrugh2010aΔGv descriptor in the class PCAcontributions −0.29, +0.29, +0.13 for classes I, II, IIIinputs not printed [vaneerdenbrugh2010a E2, R20.e]
baird2012ΔGv column at 298 K−8.6 (lidocaine) to −54.7 J/cm³ (acetaminophen)named only; the standard form reproduces the other 33 rows within about 0.6 J/cm³, ritonavir printed −37.6 against about −21.4 [baird2012 E6, M5, M12, X2]
lu2016driving force of α and β vemurafenib; virtual transitionα 11.0 kJ/mol at 115 °C; transition 319 °Creproduces [lu2016 E1, R22]
marsac2006afelodipine and nifedipine driving force6.22 and 8.83 kJ/mol at 25 °Creproduces [marsac2006a E3]
ilevbare2013cdriving force at 37 °C (extractor calculation)ritonavir ≈10.2, efavirenz ≈2.70, celecoxib ≈7.74 kJ/molinputs not printed for a stated output [ilevbare2013c E7]
baird2011\Delta G_{fus} inside the activity coefficient of four drugs in PEG 400 at 25 °Cno \Delta G_{fus} value printednot applicable; checked through the activity coefficient (0.614 for chlorpropamide, reproduces) baird2011 E6, E7
raina2015aΔG in the amorphous solubility estimate of six dihydropyridinesΔHf and Tm not printedinputs not printed [raina2015a E2]
ilevbare2013aΔG inside Eq. 1 for eight drugsritonavir 10.1 kJ/mol at 37 °C from Table 2 inputsno ΔG printed; recomputed [ilevbare2013a E2]
almeidaesousa2015comparator of the Cp method3.24–10.33 kJ/mol for six drugsreproduces (ibuprofen 3.25 against 3.24 kJ/mol) [almeidaesousa2015 E2, R11]
indulkar2015ΔG at 310 K for clotrimazole and atazanavir6.26 kJ/mol (clotrimazole, with an unprinted molar mass)inputs not printed [indulkar2015 E3]
mosqueragiraldo2015telaprevir13.31 kJ/mol; amorphous solubility 245 ± 5 µg/mLreproduces [mosqueragiraldo2015 E1, E2]
almeidaesousa2016CRH15.68 kJ/molreproduces (5.685) [almeidaesousa2016 E2]
indulkar2017aΔG of atazanavir inside Eq. 314.55 kJ/mol from Table I (ΔHf 90.1 J/g, Tm 208 °C, 310 K)not printed; with 0.22 read as exp[−I(a)] it gives the printed 62, and about 228 read as I(a) (synthesis) [indulkar2017a E2, X1; indulkar2015 M2]
hsieh2012amorphous solubility of five basesΔHf, Tm not printedinputs not printed [hsieh2012 E3]
ilevbare2012britonavirΔHf 60.4 kJ/mol, Tm 121 °C, 37 °CΔG 10.1 kJ/mol, exp(ΔG/RT) 50.8 (extractor) [ilevbare2012b E9]
hsieh2014glyburide, warfarin175.6 °C and 45.5 kJ/mol; 169.2 °C and 43.6 kJ/molreproduces: 59.9 and 47.7 at 25 °C [hsieh2014 E2, E3]
jackson2014danazolΔHf 28.9 kJ/mol, Tm 225.4 °CΔG 6.95 kJ/mol; ratio 15.4 against 19.6 printed [jackson2014 E1, E2]
duong2022bposaconazole, 310 K\Delta G = \Delta H_f(T_m - T)T/T_m^{2}Tm 442.25 K, ΔHf 76.95 J/g; ΔG 16.13 J/g by the extractor [duong2022b E3, X2]
rumondor2009cdriving force of six drugs tested as a predictor of moisture-induced separation4.1 (ketoprofen) to 11.0 kJ/mol (pimozide); nifedipine 8.2, felodipine 6.1reproduces (nifedipine 8.23, pimozide 10.97, ketoprofen 4.14) [rumondor2009c E3, M1, M2, M5]
rumondor2009bnamed as the pure-drug driving forcenonenamed only [rumondor2009b E1]
konno2008afelodipine amorphous solubility, 37 °Cratio about 10, about 9.5 µg/mLinputs not printed [konno2008a E2, R17]
alonzo2010felodipine, 37 °C30.12 kJ/mol, 143.41 °C: ΔG 5729 J/mol, ratio 9.22 against about 9reproduces [alonzo2010 E1]
alonzo2010indomethacin, 37 °C; 25 °C32.48 kJ/mol, 153.4 °C: ΔG 6445 J/mol, ratio 12.17, 36.5 against about 37 µg/mL; 15.8–23.6 against printed 17–25 µg/mLreproduces; mismatch at 25 °C [alonzo2010 E2, X2]
alonzo2011felodipine, 37 and 25 °Cabout 9.1 and 5–6 µg/mLinputs not printed [alonzo2011 E3, M1]
duong2022adelamanid amorphous-to-crystalline solubility ratio at 37 °C, against the measured 42.3ratio 31.8; Tm 196.1 °Cinputs partly printed; (synthesis: a ratio of 31.8 at 310 K needs ΔG ≈ 8.9 kJ/mol, so ΔHf ≈ 39.8 kJ/mol) [duong2022a E2, R27, M1]

Where it fails or is disputed

The ΔGv term does not rank the classes monotonically: class II, not class III, has the most positive contribution [vaneerdenbrugh2010a X10]. A printed ΔGv in one table does not follow from its own inputs [baird2012 X2]. Similar viscosity with a twofold different ΔGv weakens a viscosity-only comparison [baird2012 X9]. For vemurafenib the larger driving force of α did not make α dominate at 120–190 °C [lu2016 C52]. Outside this chapter, errors at large undercooling are reported [almeidaesousa2015 E2; mosqueragiraldo2015 E2]. In the PEG dispersions paper the relation is evaluated at 25 °C, far below the melting points of 126.7–151.7 °C, and the result is the activity coefficient of F3 of the PEG dispersions chapter baird2011 E7, M1, M2, M3, M4. In the solution-methods papers, for diverse drugs the heat-capacity method gave estimates much closer to measured LLPS onsets [almeidaesousa2015 C43]; the Hoffman-based danazol estimate (16 µg/mL) was above the measured 13 µg/mL [jackson2014 R5]. In the amorphous solubility papers it lacked accuracy for diclofenac (28.9 against 52.2 measured ratio) and telaprevir (2.7 times the onset) [almeidaesousa2015 R13, R5; mosqueragiraldo2015 R17]; Table 10 of the six-drug paper does not predict the size of the error [almeidaesousa2015 X8]. The DSC method and some inputs are not stated [hsieh2014 X11; hsieh2012 X14]. The danazol ratio of 19.6 cannot be reproduced [jackson2014 X1]. The temperature of the warfarin and glyburide calculation is not printed (25 °C assumed) [hsieh2014 E2]. In the physical-stability papers the driving force did not sort the six drugs by moisture-induced separation [rumondor2009c C32]; for nifedipine against felodipine it pointed the right way for nucleation (F2 of the physical stability chapter) [marsac2006a R4.l]. The 25 °C indomethacin range of the 2010 dissolution paper does not reproduce from its inputs [alonzo2010 X2]. Felodipine concentrations of 14.1 µg/mL measured by UV exceed the 9.5 µg/mL estimate of the same 2008 paper [konno2008a X5]. For delamanid the estimate lies about a quarter below the measured ratio (42.3), which the authors call "reasonable agreement" [duong2022a R27, C43].

Concepts

Hoffman equation, thermodynamic driving force for crystallization, enthalpy of fusion, degree of supercooling, activity coefficient, amorphous-crystalline free energy difference, amorphous solubility advantage. Findings. Crystallization tendency: F6, F7, F13. PEG dispersions: F3. Solution methods: F5. C. Amorphous solubility and LLPS: F5, F7. Crystallization from solution: F2, F16. Physical stability: F2, F13. Supersaturation from ASD dissolution: F5, F7, F23.

← Concepts and formulas

formula · as used in PEG dispersions

induction time decomposition

Expression

t_{ind} = t_n + t_g [ilevbare2013c E2]

t_{ind} \propto J^{-1} [ilevbare2013c E3]

Both relations are printed in the same form in the celecoxib dispersion papers [xie2015 E1, E2; xie2016a E4].

Variables and units

symbolmeaningunit
t_indmeasured induction time, from creating the supersaturation until crystals are detectedmin
t_ntime to form stable nucleimin
t_gtime for nuclei to grow to detectable sizemin
Jnucleation ratem⁻³ s⁻¹

Assumptions and valid domain

The proportionality holds if steady-state nucleation is reached quickly and t_n \gg t_g; nuclei are detectable only after growth [ilevbare2013c C14, E2]. The relation was not tested for the three drugs or the polymers [ilevbare2013c X14]. In the celecoxib papers the proportionality is stated as an assumption ("If it is assumed") [xie2015 C41]; the onset is read from the abrupt rise of extinction at 350 nm together with the fall of absorbance at 249 nm [xie2016a C9].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
ilevbare2013creading polymer effects on induction time as nucleation-rate effectsinduction times about 2.4–855.5 mininputs not printed [ilevbare2013c E2, E3]
xie2015celecoxib dispersions (ASD dissolution chapter); celecoxib 22 µg/mL with 5 µg/mL polymers, pH 6.8, 37 °Cdecomposition printed as E1; proportionality as E2; induction within 5 min without polymer, ≈1 h PVP-K12, ≈2 h PVP-K29/32, more than 8 h HPMCAS, HPMCprinted [xie2015 E1, E2]; no t_n or t_g printed [xie2015 E1, R1]
xie2016acelecoxib with PAA and cellulose derivatives; with HPMCASdecomposition printed; 960 min taken as the induction time with HPMCAS, an underestimateprinted [xie2016a E4]; no component times printed [xie2016a E4, C39]
chen2015t_ind = t_n + t_g, not separated11 drugsprinted [chen2015 E1, C5]
li2016asame, with t_n >> t_g assumedthree drugs, 13 bile saltsprinted in words [li2016a E4]
mosqueragiraldo2016T_ind = T_n + T_growthtelaprevir, 26 polymersprinted [mosqueragiraldo2016 E1]
lu2017t_ind = t_n + t_g, read as nucleation when t_n dominatestelaprevir, six bile saltsprinted [lu2017 E3, C9]
trasi2015t_j = t − t_g with t_g fittedacetaminophen: t_g 7.8–928 sfitted [trasi2015 E4, R3]
indulkar2018lecithin, bile salt and SIF media, four drugsinduction time as first scattering rise; components not separatednot applicable [indulkar2018 E5]
lu2018telaprevir in bile salt mixtures and complete mediat_{ind} = t_n + t_gnot applicable [lu2018 E2]
indulkar2019batazanavir in SDSadditive may act on either partnot applicable [indulkar2019b E5, C29]
enright2020atazanavir in phospholipid-digest and volunteer mediaprinted in wordsnot applicable [enright2020 E1]
elkhabaz2021atazanavir, posaconazole in six mediaT_{ind} = T_{crit} + T_{grow}, read as nucleation onsetnot applicable [elkhabaz2021 E1]
que2018unseeded paclitaxel at S ≈88 with and without 20 µg/mL HPMCASwithin 6 min against more than 16 hno component times printed; growth on seeds continued in the same system [que2018 R3, C30]

Where it fails or is disputed

A polymer that slows early growth also lengthens t_{ind}, and for strong inhibitors the extinction rises above the baseline before the fitted onset (about 25 against 31.5 min; about 180 against 260 min), so values depend on where the lines are drawn [ilevbare2013c X14, R6]. The detection method changes the time (SHG earlier than a probe ratio) [jackson2014 R25]. The seeded and unseeded comparison shows that for STC and SGC the nucleation part dominates but for STCDC and SGCDC growth does [lu2017 R10; lu2017a R14, C37]; in the acetaminophen study the induction time is the time to massive nucleation [trasi2015 C32]. In the SDS study crystal size and agglomeration change across the same threshold as the induction time, so a change in the growth term cannot be excluded [indulkar2019b X7, X5]. Neither celecoxib paper separates t_n from t_g [xie2015 E1; xie2016a E4] (synthesis: growth was slowed about 70-fold with HPMCAS [xie2016a R12], so part of the longer induction time may come from t_g). For paclitaxel the polymer that lengthened the unseeded induction time beyond 16 h only slowed growth on seeds, so the induction time of an unseeded test says little about a dispersion that carries crystals [que2018 R3, R14].

Concepts

nucleation induction time, nucleation rate, nucleation inhibition. Findings. Crystallization from solution: F3, F5, F13, F14, F27, F28, F29, F31, F32, F33, F35, F38, F39. Supersaturation from ASD dissolution: F4, F6, F20, F22.

← Concepts and formulas

formula · as used in PEG dispersions

Jackson interface-kinetics growth rate

Expression

U = \frac{2 k_B T}{\pi \lambda^2 \eta}\, f \left[1 - \exp\left(-\frac{\Delta H\,\Delta T}{k_B T\,T_m}\right)\right] \exp\left(-\frac{\Delta S}{k_B}\right) [trasi2014a E1].

Variables and units

symbolmeaningunits
Ucrystal growth ratenot stated [trasi2014a E1]
\lambdaaverage diffusion jump distancenot stated
\etaviscosityPa·s (cited data) [trasi2014a P7]
ffraction of interface sites that are active growth sitesdimensionless
\Delta H, \Delta Senthalpy and entropy difference between liquid and crystalnot stated
T, T_m, \Delta Ttemperature, melting temperature, undercoolingK

Assumptions and valid domain

Stokes–Einstein holds and viscosity describes diffusion at the interface in the studied range [trasi2014a C20]; not near Tg, where diffusion decouples from viscosity [trasi2014a C21]. The entropy term reflects the fraction of molecules with the right orientation to join the crystal [trasi2014a C31].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
trasi2014aframework for the driving-force correction and the entropy fitnone fitted directlyinputs not printed (λ, f and η(T) not given) [trasi2014a E1, R10, R11]

Where it fails or is disputed

At similar viscosity the drugs fell into two sets whose corrected growth rates differ by about 2–3 orders of magnitude, so factors beyond viscosity and driving force contribute [trasi2014a C30]. The 2012 viscosity study used a related screw-dislocation form without the entropy term [baird2012 E3].

Concepts

crystal growth rate, melt viscosity, entropy of fusion, thermodynamic driving force for crystallization. Findings. F2, F6.

← Concepts and formulas

formula · as used in PEG dispersions

molar volume from molecular weight and density

Expression

Printed in words as "molecular volume = molecular weight / true density":

V_m=\frac{M}{\rho}

moseson2018 E6.

Variables and units

symbolmeaningunitids
V_mmolecular (molar) volumecm³/molmoseson2018 E6
Mmolecular weightg/molmoseson2018 E6
\rhotrue densityg/mLmoseson2018 E6

Assumptions and valid domain

None stated; densities of amorphous IDM (1.31 g/mL) and PVPVA (1.18 g/mL) were taken from the literature, and the PVPVA molecular weight (55,000 g/mol) is an estimate from the manufacturer's range moseson2018 M1, M2.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
moseson2018volume fractions and the ratio m of the Flory–Huggins melting point depressionIDM 273 cm³/mol; PVPVA 46,610 cm³/molreproduces (357.8 / 1.31 = 273.1; 55,000 / 1.18 = 46,610) moseson2018 E6, M1, M2
moseson2022cm of bicalutamide–PVPVABCL 318.8 cm³/mol (printed 319); PVPVA 46,610; m = 146.1reproduces (430.37/1.35 = 318.8; 55,000/1.18 = 46,610) [moseson2022c E21, M1, M2]
shah2024m of posaconazole–HPMCASPCZ 546 and HPMCAS 14,164 cm³/mol; m = 25.95reproduces within rounding (701/1.28 = 547.7 against 546; 18,000/1.27 = 14,173 against 14,164; 14,164/546 = 25.94) [shah2024 E4, E1]

Where it fails or is disputed

The polymer molar volume depends on an estimated molecular weight, so m is approximate moseson2018 M2.

Concepts

Flory–Huggins interaction parameter. Findings. F8, F41.

← Concepts and formulas

formula · as used in PEG dispersions

multicomponent Flory-Huggins free energy of mixing

Expression

Water–drug–polymer system:

\frac{\Delta G_{mix}}{RT} = n_W\ln\phi_W + n_D\ln\phi_D + n_P\ln\phi_P + n_W\phi_D\chi_{WD} + n_W\phi_P\chi_{WP} + n_D\phi_P\chi_{DP} [rumondor2009c E4; rumondor2010c E1; purohit2017b E2]

Variables and units

symbolmeaningunits
n_W, n_D, n_Pamounts of water, drug, polymer (stated as mole fractions)– [rumondor2009c E4]
\phivolume fractions– [rumondor2009c E4]
\chi_{WD}, \chi_{WP}, \chi_{DP}pair interaction parameters, also holding non-ideal entropy– [rumondor2009c E4]

Assumptions and valid domain

First three terms the combinatorial entropy, last three the pair interactions [rumondor2009c E4; purohit2017b E2]. Used in words only: separation needs the interaction terms to outweigh the entropy, so a very unfavourable water–drug term next to a favourable water–polymer term can push the drug out [rumondor2009c C42, C37].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
rumondor2009cthermodynamic origin of moisture-induced separationnoneargument only [rumondor2009c E4]
purohit2017b (outside)AAPS of ritonavir dispersions on hydrationnoneargument only [purohit2017b E2]
rumondor2010cwhy the same drugs separate more with PVP than with PVPVA and HPMCASnoneargument only; χ ranked by red shift and log P [rumondor2010c E1, C26, C31, X13]

Where it fails or is disputed

No χ values for the ternary systems were measured; the conclusion that separation needs a positive mixing enthalpy treats χ terms as purely enthalpic although they also carry entropy [rumondor2009c X13, X14]. The same data allow a mobility reading (less plasticized HPMCAS dispersions), which the free-energy argument does not exclude [rumondor2010c C32, X12].

Concepts

Flory-Huggins theory, enthalpy of mixing, Δχ effect, moisture-induced phase separation. Findings. F8, F12, F13, F23.

← Concepts and formulas

formula · as used in PEG dispersions

reduced glass transition temperature

Expression

T_{rg} = \frac{T_g}{T_{melt}} baird2010 E4.

Variables and units

symbolmeaningunits
T_{rg}reduced glass transition temperaturedimensionless baird2010 E4
T_g, T_{melt}glass transition and melting temperaturesK baird2010 E4

Assumptions and valid domain

Viscosity is taken as constant at Tg baird2010 E4; a value of 0.66 was proposed in the cited literature baird2010 R29. For 16 class I molecules without a measured Tg, Tg was estimated from a fit T_{rg} = 0.00021\,\mathrm{MW} + 0.64433 with R² 0.44 baird2010 E27, X17.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
baird2010testing Trg against classI-A 0.69, I-B 0.7; class I 0.69 ± 0.02, class III 0.73 ± 0.04, not significantly differentreproduces: acetaminophen 297.15/443.15 = 0.671 baird2010 E4, R14
nguyen2023apretomanid0.67reproduces: (10 + 273.15)/(147.3 + 273.15) = 0.673 [nguyen2023a E2]

Where it fails or is disputed

Trg did not differ between class I-A and I-B, indicating no correlation with the ability to quench amorphous baird2010 C23. Tg/Tm was not a reliable indicator; class II alone spans Tg/Tm 0.65–0.76 [baird2012 C36, R14]. The class I values rest partly on estimated Tg baird2010 X17.

Concepts

reduced glass transition temperature, glass transition temperature, glass-forming ability, Tm − Tg temperature gap. Findings. F12.

← Concepts and formulas

formula · as used in PEG dispersions

relative nucleation rate from seeded and unseeded induction times

Expression

\frac{R}{R_0} = \frac{t_{s,0}}{t_s} [alonzo2012 E9]

\frac{J}{J_0} = \left(\frac{t_s}{t_{s,0}}\right)^{3}\left(\frac{t_{u,0}}{t_u}\right)^{4} [alonzo2012 E10]

\frac{J}{J_0} = \left(\frac{R_0}{R}\right)^{3}\left(\frac{t_{u,0}}{t_u}\right)^{4}, \qquad E_J = \frac{J_0}{J} [lu2017 E4; lu2017a E4, E5]

With the polymer case in the denominator:

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

Variables and units

symbolmeaningunit
J, J_0nucleation rate with and without inhibitorm⁻³ s⁻¹
t_s, t_s,0seeded induction times with and without inhibitormin
t_u, t_u,0unseeded induction times with and without inhibitormin
R/R_0seeded growth-rate ratio, used for t_{s,0}/t_sdimensionless
J_0, J_pnucleation rate without and with polymerm⁻³ s⁻¹
R_0, R_pmass growth rate without and with polymer, from seeded desupersaturation slopesµg/(mL min)
t_{u,0}, t_{u,p}unseeded induction times without and with polymermin

Assumptions and valid domain

Seeded and unseeded runs under identical conditions; the seeded induction-time ratio is replaced by the growth-rate ratio of the de-supersaturation curves (Verdoes 1992, outside the library) [alonzo2012 C11, E9]. Used for one drug, one polymer level and one supersaturation. For celecoxib R_0 is the slope of the linear region over the first 5 min without polymer; R_p is, for simplicity, the slope over the whole 16 h with HPMCAS [xie2016a C38]. t_{u,p} = 960 min because no sharp slope change was seen, which underestimates the induction time [xie2016a C39].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
alonzo2012felodipine, 1 µg/mL HPMC, S 10t_{u,0} 15.3 min, t_u 136.5 min, R/R_0 0.607; J/J_0 = 7.05 × 10⁻⁴reproduces: 7.06 × 10⁻⁴ with 1.647; 7.00 × 10⁻⁴ with the printed 1.643 [alonzo2012 E10, X6]
xie2016acelecoxib with HPMCAS (ASD dissolution chapter): 22 µg/mL with 5 µg/mL HPMCAS, pH 6.8, 37 °Ct_{u,p} 960 min, R_0/R_p = 70; J_0/J_p about 4,000derived [xie2016a R13]; reproduces with t_{u,0} = 5 min from the text: (1/70)^{3}(960/5)^{4} = 3962; the t_{u,0} used by the authors is not printed [xie2016a E6, R13]
lu2017telaprevir, 1.86 mM STC and SGC, δ 11.5; t_u,0 about 30 min, t_u 960 minJ/J_0 2.5 × 10⁻³ and 2.9 × 10⁻⁶recomputed 2.58 × 10⁻³ and 3.06 × 10⁻⁶ [lu2017 E4, R10, X1]
lu2017asame with bile salts at 1.86 and 12 mM; rate ratio set to 100 for STCDC and SGCDCE_J about 360 to 3 × 10⁵; about 1 for STCDCreproduced for the 1.86 mM values [lu2017a E4, E5, R14]

Where it fails or is disputed

Rests on one pair of induction times with no stated uncertainty entering to the fourth power; a 10% change in t_u changes J/J_0 about 1.5-fold [alonzo2012 X7]. The exponents are not derived in the paper. The induction times enter capped at 960 min, so E_J is a bound; the rate ratios used are the δ 12.5 values while the text speaks of growth; the 12 mM inputs are not printed [lu2017 X2; lu2017a X13, X14]. For celecoxib the slopes and t_{u,0} are not printed, and R_p was taken over 16 h while the figure covers 4 h, so the ratio cannot be reproduced from the printed data [xie2016a X8]. With t_{u,p} capped at 960 min the ratio is a lower bound [xie2016a C39, C40]. t_{u,0} enters to the fourth power (synthesis: with t_{u,0} of 4 or 6 min the ratio is about 9,700 or 1,900).

Concepts

nucleation rate, nucleation inhibition, crystal growth inhibition. Findings. Crystallization from solution: F5, F6, F20, F32, F33. Supersaturation from ASD dissolution: F5.

← Concepts and formulas

formula · as used in PEG dispersions

solid-liquid equilibrium solubility equation

Expression

\ln x_{C,L_1} = -\frac{\Delta G_{a\to c}}{RT} - \ln\gamma_{L_1} [ilevbare2013a E3];

\ln C_B = -\frac{\Delta G}{RT} - \ln\gamma [indulkar2015 E7];

and for the supercooled liquid \ln x_{SL,L_1} = -\ln\gamma_{L_1} [ilevbare2013a E4]. As printed, \Delta G_{a\to c} and \Delta G are positive magnitudes; with the signed quantity \mu^{(c)}-\mu^{0(a)}, which is negative, the term carries a plus sign, as in Taylor and Zhang 2016 (Eqs. 2 and 6).

New forms (Miscibility and drug-polymer interactions). With the heat-capacity terms, as printed for the solubility of a crystalline drug in a polymer (2006):

\ln\gamma_{\mathrm{drug}}\,x_{\mathrm{drug}} = -\frac{\Delta H_{fus}}{RT}\left[1-\frac{T}{T_m}\right] - \frac{1}{RT}\int_{T_m}^{T}\Delta C_P^{\mathrm{config}}\,dT + \frac{1}{R}\int_{T_m}^{T}\frac{\Delta C_P^{\mathrm{config}}}{T}\,dT marsac2006b E5;

and in the 2009 paper, where the left side is written as the free energy of fusion:

\ln\gamma_{\mathrm{drug}}\,x_{\mathrm{drug}} = \frac{-\Delta G_{fus}}{RT} = -\frac{\Delta H_{fus}(T_m)}{RT}\left[1-\frac{T}{T_m}\right] - \frac{1}{RT}\int_{T_m}^{T}\Delta C_P\,dT + \frac{1}{R}\int_{T_m}^{T}\frac{\Delta C_P}{T}\,dT marsac2009 E1.

Simpler forms in other papers of the library:

\ln x_{actual} = -\frac{\Delta H_{fus}}{RT}\left(1-\frac{T}{T_M}\right) - \ln\gamma marsac2008a E3;

\ln\left[\gamma_d\,x_d\right] = -\frac{\Delta G_{fus}}{RT} baird2011 E5;

\ln x = -\frac{\Delta H_f}{R}\left(\frac{1}{T}-\frac{1}{T_m}\right) - \frac{\Delta C_p}{R}\left(1-\frac{T_m}{T}+\ln\frac{T_m}{T}\right) - \ln\gamma [raina2014a E1].

The ritonavir–atazanavir paper writes \log\chi = \log X_{ideal} - \log\gamma with \log X_{ideal} = -\frac{\Delta H_m}{2.303R}\frac{T_m - T}{T_m T} [alhalaweh2016 E4, E5].

Variables and units

symbolmeaningunits
x_{C,L_1}, C_Bsolubility of the crystalline drug in watermole fraction; µg/mL [ilevbare2013a E3; indulkar2015 E7]
\Delta Gfree-energy difference between supercooled liquid and crystal[indulkar2015 E7]
\gamma_{L_1}, \gammaactivity coefficient of the drug in the aqueous solutiondimensionless [ilevbare2013a E3]
\gamma_{drug}activity coefficient of the drug at the solubility limitdimensionless marsac2009 E1
\chi, X_{ideal}mole-fraction solubility and ideal solubility in the ritonavir–atazanavir paper– [alhalaweh2016 E4, E5]
x_{drug}mole-fraction solubilitydimensionless marsac2009 E1
\Delta H_{fus}, T_mheat of fusion and melting temperature of the drugkJ/mol, K (Table I and II values) marsac2006b M1, M2; marsac2009 M1, M2
\Delta C_P^{config}, \Delta C_Pheat-capacity difference between liquid and crystalvalues cited, not printed marsac2006b X11; marsac2009 P7
TtemperatureK; not stated for the Table II predictions marsac2006b X11

Assumptions and valid domain

The solvent is not present in the crystal; the first term is the lattice contribution and the second the solute–solvent interaction [indulkar2015 E7]; γ is constant over the crystalline and amorphous concentration range [ilevbare2013a C55]. For a drug in a polymer, the polymer assumes the role of a solvent, so the equation describes solubility of a crystalline drug in a polymer, with \gamma from Flory–Huggins theory marsac2006b C45. For the analogue liquid the entropy of mixing is assumed ideal marsac2006b C46. For ketoconazole the heat-capacity difference was approximated by its value at Tg, integrated between Tg and Tm marsac2009 P7. In the 2009 route the same γ is assumed at the solubility limits in the analogue and in PVP marsac2009 C11. The amorphous form removes the fusion terms, so \ln x = -\ln\gamma [raina2014a E2]. The ritonavir–atazanavir paper sets ΔCp to zero [alhalaweh2016 E5].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
ilevbare2013aappendix derivation of the amorphous solubilitynoneγ not printed [ilevbare2013a E3, E4]
indulkar2015argument that the un-ionized amorphous and crystalline solubility differ by a constant factornoneγ not printed [indulkar2015 E7, C42]
marsac2006bsolubility of nifedipine and felodipine in PVP K12, PVP K29/32 and methyl pyrrolidone0.06–0.07 g/g and 0.25–0.31 g/g in PVP; 0.15 and 0.48 g/g in methyl pyrrolidonereproduces with ΔC_P terms set to zero at 298.15 K for nifedipine in PVP K12 (0.071 against 0.07); one felodipine value in K29/32 does not match (≈0.29 against 0.25) marsac2006b E5, E6, R17, X11
marsac2009γ in EP from the measured solubility; ideal solubilityγ 0.15–0.89inputs not printed (heat capacities, ideal solubilities) marsac2009 E1, R9, X4
baird2011activity coefficient in PEG 400see the PEG chapterreproduces (through its E7) baird2011 E5
marsac2008aactivity coefficient of nifedipine and felodipine in water from the solubility in methyl pyrrolidoneγ in water 1.89 × 10³ and 2.43 × 10⁵reproduces within the stated SD with the lattice terms implied by the printed data (−5.40 and −3.51); ΔH_fus and T_M not printed marsac2008a E3, R10, R11
raina2014abackground to the amorphous solubility predictionnoneinputs not printed (ΔC_p and γ not printed) [raina2014a E1, R7]
alhalaweh2016crystal and solvation contributions to the solubility of ritonavir and atazanavir at 310 Klog γ about 4.45 and 3.88 (read)mismatch: recomputed 4.65 and 3.01 from the card's ideal solubility and the Table 2 crystalline solubility [alhalaweh2016 E4, R7]
alhalaweh2016ideal-solubility term of ritonavir and atazanavirplotted log X_ideal −1.07, −1.97; recomputed −2.59, −4.53mismatch [alhalaweh2016 E5, X1, X2]
marsac2008anifedipine and felodipine in methyl pyrrolidone and water (second reading)γ in water 1.73 × 10³ and 2.31 × 10⁵reproduces within SD marsac2008a E3

Where it fails or is disputed

The appendix prints its first equation as "(1)" but cites it as Eq. 3 [ilevbare2013a X4]. The temperature and the heat-capacity values of the 2006 Table II are not printed, the methyl pyrrolidone check is about 30% low for nifedipine, and the polymer-phase values are predictions, not measurements marsac2006b X10, X11; marsac2009 X17. Solubility measured in a small analogue overestimates solubility in the polymer unless corrected for the smaller mixing entropy marsac2006b C51. The plotted terms of the ritonavir–atazanavir paper mix concentration scales; the ordering of the terms survives the recomputation [alhalaweh2016 X2]. For marsac2008a the γ in water is given as 1.89 × 10³ and 2.43 × 10⁵ in one reading and as 1.73 × 10³ and 2.31 × 10⁵ in another; both are reported as reproducing within the stated SD marsac2008a E3, R10, R11.

The ratio form of the same relation for liquid PEG is on the page activity coefficient from solubility.

Concepts

crystalline solubility, activity coefficient, ideal solubility, drug solubility in polymer, micellar solubilization, amorphous solubility. Findings. C. Amorphous solubility and LLPS: F5, F10, F12. Miscibility and drug-polymer interactions: F8, F9. Bioperformance: F1, F6.

← Concepts and formulas

formula · as used in PEG dispersions

temperature of maximum crystal growth rate

Expression

T_{cryst,max} \approx 0.94\,T_m [trasi2014a E8];

T(\text{max growth}) \approx 0.94\,T_m, printed in words as Naito's rule [lu2016 E2].

The physical-stability papers give about 0.94 Tm [sato2016 E2] and about 0.95 Tm:

T_{max} \approx 0.95\,T_m [tian2017 E3].

Variables and units

symbolmeaningunits
T_{cryst,max}temperature of the maximum crystal growth velocityK [trasi2014a E8]
T_mmelting temperature (of the α-form for vemurafenib)K [trasi2014a E8; lu2016 E2]
T_{max}temperature of fastest growthK, for the ratio [tian2017 E3]

Assumptions and valid domain

A cited empirical observation (ref 26) [trasi2014a E8], a typical value (ref 21) [lu2016 E2]. The ratio holds only in kelvin: in °C the vemurafenib product would be 254.7 °C instead of 238.4 °C [lu2016 E2]. The rule refers to the pure drug. With 10% polymer the temperature of fastest growth of indomethacin moved, for α from 135 to 100 °C (HPMC), 110 °C (HPMCAS) and 125 °C (PVP), and for δ to 105–115 °C, so the rule does not give the maximum of a drug–polymer melt [tian2017 R15]. In the PHB paper all growth temperatures were placed below 0.94 Tm to read growth as transport-limited [sato2016 E2, C15].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
trasi2014agrouping 31 drugs by maximum growth rateTcryst,max not tabulated; ΔG and ΔSm columns imply 0.90–0.99 Tminputs not printed [trasi2014a E8, X4]
lu2016expected maximum for α-vemurafenib240 °C predicted against 250 °C observedreproduces: 0.94 × 544.15 K = 511.5 K = 238.4 °C [lu2016 E2, R24, C18]
sato2016position of measured temperatures below the maximum0.94 Tm above all highest growth temperaturesreproduces [sato2016 E2]
tian2017indomethacin polymorphs≈0.95 Tm, within the 5 °C step of the datareproduces [tian2017 E3]
tian2017maxima of indomethacin polymorphs with and without polymerpure drug 110, 135, 135 °C (δ, α, γ); with polymer 100–130 °Cthe rule holds for the pure drug (row above); with polymer the maximum is lower [tian2017 R15, E3]

Where it fails or is disputed

The 0.94 Tm in the conclusions of the 31-drug study is a cited rule, not a result of that paper [trasi2014a X5]. The observed vemurafenib maximum of 250 °C corresponds to 523.15/544.15 = 0.96\,T_m (synthesis, from [lu2016 R12.o, E2]). Inhibition ratios rise steeply above the polymer-lowered maximum (indomethacin α with HPMC about 11 at 100 °C and 2900 at 120 °C), so a ratio taken between the two maxima compares growth in different regimes [tian2017 R12, C35].

Concepts

maximum crystal growth velocity, crystal growth rate, degree of supercooling, kinetic versus thermodynamic control of crystal growth. Findings. Crystallization tendency: F1, F2. Physical stability: F3, F28, F29.

← Concepts and formulas

formula · as used in PEG dispersions

van't Hoff equation

Expression

\frac{d\ln x}{dT} = \frac{\Delta H_f}{R\,T^{2}} zhu2011 E3.

Zhu and co-workers (2012) name the van't Hoff equation for the same extrapolation without printing it zhu2012 E3.

The amorphous solubility chapter uses the van't Hoff analysis for the partition coefficient of a polymer between the drug-rich phase (p) and water (q),

K_{p/q} = \frac{C_p}{C_q} [ueda2022 E3],

\Delta G_{q\to p} = -RT\ln K_{p/q} [ueda2022 E4],

\ln K_{p/q} = -\frac{\Delta H_{q\to p}}{RT} + \frac{\Delta S_{q\to p}}{R} [ueda2022 E5],

and, when the straight line fits poorly, with a quadratic term that lets ΔH and ΔS vary with temperature,

\ln K_{p/q} = A + \frac{B}{T} + \frac{C}{T^{2}} [ueda2022 E6],

\Delta H_{q\to p} = -R\left(B + \frac{2C}{T}\right),\qquad \Delta S_{q\to p} = R\left(A - \frac{C}{T^{2}}\right) [ueda2022 E7, E8].

Variables and units

symbolmeaningunits
xmole-fraction solubility of the drug in liquid PEGdimensionless zhu2011 E3
\Delta H_fheat of solution (named "heat of solution" in the card)not printed zhu2011 E3
R, Tgas constant; temperatureK zhu2011 E3
K_{p/q}, C_p, C_qpartition coefficient of the polymer between the drug-rich phase (p) and water (q), and its concentrations in themdimensionless; C_p computed with 0.99 g/cm³ (amorphous ibuprofen) [ueda2022 E3, X2]
\Delta G_{q\to p}, \Delta H_{q\to p}, \Delta S_{q\to p}free energy, enthalpy and entropy of transfer from water into the drug-rich phasekJ/mol for ΔG and ΔH (see the use table); unit of ΔS not stated in the notes [ueda2022 E4, E5]
A, B, Cconstants of the quadratic fit of \ln K_{p/q} against 1/Tnot stated [ueda2022 E6]

Assumptions and valid domain

\ln x against 1/T along the drug liquidus (Figs. 2–5) is fitted by linear regression and extrapolated to 25 °C, below the PEG melting point, so the result refers to supercooled liquid PEG, and is converted to weight percent zhu2011 E3, C8. The second paper uses it to extrapolate solubilities from the binary phase diagrams to 25 °C zhu2012 E3. Tested on four liquidus series measured here (benzocaine, ibuprofen, nilutamide, ketoconazole) and on the cited chlorpropamide and haloperidol diagrams zhu2011 R1, R2, R3, R4, R5. In the amorphous solubility chapter the linear form assumes ΔH and ΔS independent of temperature; the linear fit gave R² of 0.817 (PVP), 0.962 (HPMC) and 0.961 (PVP-VA) and the quadratic fit 0.971 (PVP), 0.996 (HPMC) and 0.994 (PVP-VA) [ueda2022 C47, R20, R21]. The concentration in the drug-rich phase is computed with 0.99 g/cm³ (amorphous ibuprofen), a basis that ignores water in that phase and is not written out [ueda2022 E3, X2]. Valid at 15–60 °C (HPMC 15–55 °C), pH 2.0 in D2O [ueda2022 P12, R3].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
zhu2011solubility of six drugs in PEG 3350 at 25 °C28, 26, 25, 11, 0, 0 wt% (benzocaine, chlorpropamide, ibuprofen, nilutamide, haloperidol, ketoconazole)printed; inputs not printed (liquidus points only plotted; regression lines and molar masses not printed) zhu2011 E3, R5
zhu2012solubility of haloperidol, benzocaine, ibuprofen, fenofibrate at 25 °Cbelow 1, 28, 25, 6 wt%named only zhu2012 E3, M1, M2, M3, M4
ueda2022ΔG, ΔH, ΔS of transfer of PVP, PVP-VA and HPMC from water into the ibuprofen-rich phaselinear: HPMC ln K = −4.23 × 10³ (1/T) + 19.9; PVP-VA −1.79 × 10³ (1/T) + 12.2; PVP −1.44 × 10³ (1/T) + 10.5; ΔG −12 to −19 kJ/mol; ΔH of HPMC 58 → 12 kJ/molreproduces (HPMC at 288.15 K: ΔH = −8.314 × (38700 − 45740) J/mol = 58.5 kJ/mol; −TΔS = −70.8 kJ/mol; ΔG = −RT ln K = −12.3 kJ/mol) [ueda2022 E4, E5, E7, E8, R20, R21]

Where it fails or is disputed

The nilutamide estimate (11 wt%) is above its eutectic content (10 wt% at 58.4 °C), whereas an extrapolation to a lower temperature would normally give a lower value zhu2011 X4. The regression lines and inputs are not printed in either paper, so the estimates cannot be recomputed zhu2011 E3; zhu2012 E3. The relation assumes a constant heat of solution over the extrapolated range (synthesis: the extrapolation runs from liquidus temperatures well above the PEG melting point down to 25 °C zhu2011 R1, R2, R3, R4). In the amorphous solubility chapter ΔH, ΔS and ΔG are derivatives of three-parameter fits to 9–10 points with no propagated uncertainty, so the temperature slopes of ΔH and ΔS rest on the curvature term; for PVP ΔH is negative at 55 and 60 °C [ueda2022 X8, X1]. The linear fits give temperature-independent ΔH of about 35 (HPMC), 15 (PVP-VA) and 12 kJ/mol (PVP) (extractor calculation), close to the quadratic values at mid-range [ueda2022 X8]. The two chapters apply the relation to different quantities (drug solubility along the liquidus in PEG; polymer partition coefficient between two liquid phases), so their values are not comparable.

Concepts

van't Hoff equation, drug solubility in polymer, liquidus temperature, polymer partitioning into the drug-rich phase, hydrophobic effect. Findings. PEG dispersions: F4. C. Amorphous solubility and LLPS: F21.

← Concepts and formulas

formula · as used in PEG dispersions

Vogel-Tammann-Fulcher equation

Expression

\tau = \tau_0 \exp\left(\frac{D\,T_0}{T - T_0}\right) baird2010 E12;

\eta = \eta_0 \exp\left(\frac{D\,T_0}{T - T_0}\right) [baird2012 E4].

Variables and units

symbolmeaningunits
\tau, \etamean molecular relaxation time, or viscositys; Pa·s [baird2010 E12; baird2012 E4]
\tau_0, \eta_0value for the unrestricted materialτ0 ≈ 10⁻¹⁴ s baird2010 E12
Dstrength parameterdimensionless [baird2012 E4]
T_0zero-mobility temperature, for some systems the Kauzmann temperatureK [baird2012 E4]

Assumptions and valid domain

For the strength parameter D^b: T_0 = T_K, τ(Tg) ≈ 10² s, τ0 ≈ 10⁻¹⁴ s baird2010 E12. Valid from Tm down to about 0.4 Tg on a scale with T_g = 0 and T_m = 1, with D and T0 fitted together [baird2012 E4]. Strong liquids have D above 30, fragile ones below 10 baird2010 R30.

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
baird2010D^b from Tg and Kauzmann temperature for class II and IIIindomethacin D^b 5reproduces: \ln(10^{16}) \times (318.15 - 282.15)/282.15 = 4.70 baird2010 E12, R18
baird2012fits of melt viscosity for 28 compoundsD 4.3–8.7, all below 10inputs not printed (η0 not reported) [baird2012 E4, R12]

Where it fails or is disputed

The fitted T0 and D do not satisfy the paper's own relation between T0, D and Tg [baird2012 X5]. The six class I-A compounds were not fitted, though the abstract calls all compounds fragile [baird2012 X7]. Whether a compound counts as strong or fragile depends on using m or D baird2010 X14. Good and poor glass formers showed the same non-Arrhenius behaviour, so kinetic fragility "may not accurately assess" glass-forming ability [baird2012 C43]; fragility was also invoked, untested, for two growth-rate outliers [trasi2014a C29, X18].

Concepts

fragility, melt viscosity, glass transition temperature, supercooled liquid. Findings. F5, F12.

← Concepts and formulas

formula · as used in PEG dispersions

water plasticization rule of thumb

Evidence table: water plasticization rule of thumb. Content from the release-mechanism chapter (2017–2022), with a row from the amorphous solubility and LLPS chapter.

Expression

Stated in words: the wet Tg equals the dry Tg less about 10 °C for each 1% of water sorbed [indulkar2017b E6]; Tg falls by about 10 °C for each 1% of water sorbed [ilevbare2013a E15]. Written as an expression (synthesis: transcription of the words):

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

Variables and units

symbolmeaningunit
T_{g,\mathrm{wet}}, T_{g,\mathrm{dry}}glass transition temperature with and without sorbed water°C
wwater content% (w/w)

Assumptions and valid domain

A typical observation, taken from indomethacin (cited) [indulkar2017b E6]; cited from earlier work [ilevbare2013a E15].

Use in the library

paperused forvalues or fitted parametersstatus / recomputed
indulkar2017bwet Tg of water-saturated nifedipine dropletsdry 42 °C, 2.5% water, approximately 17 °Creproduces: 42 − 10 × 2.5 = 17 [indulkar2017b E6, M1, C16]
ilevbare2013a (LLPS chapter)Tg of a water-saturated drug-rich phasedry 50.4 °C, 0.4 °C with 4.87% waterreproduces within rounding: 50.0 / 4.87 = 10.3 °C per 1% [ilevbare2013a E15]
saboo2020wet Tg of amorphous indomethacin from 37 °C sorption29 °Cinputs not printed [saboo2020 E6, M1]
yang2021wet Tg of miconazole, danazol, elbasvir from 37 °C sorption−4.7, 73.3, 129.1 °Cinputs not printed [yang2021 E3, M2, M3, M4]
hiew2022bwet Tg of lumefantrine dispersions with 35–55% waterall below 37 °Creproduces: 105.5 − 10 × 35 lies far below 37 [hiew2022b E3, C44, R5]

Where it fails or is disputed

The nifedipine water content was extrapolated from a 25 °C sorption profile to 100% RH and no Tg of water-saturated nifedipine was measured [indulkar2017b X8]. For lumefantrine dispersions the rule puts every wet Tg below 37 °C, so it cannot by itself explain release [hiew2022b C44]; a measured 70% indomethacin dispersion fell from 62.64 to 18.48 °C with about 6% water, about 7 °C per 1% (synthesis: 44.2/6) [saboo2020 R30].

Concepts

plasticization by water, glass transition temperature, supercooled liquid. Findings. Release mechanism and LoC: F5, F18, F22.