How polymers slow the growth of indomethacin polymorphs from the undercooled melt

Background and motivation

Many new drug candidates are poorly soluble in water. Making the drug amorphous raises its apparent solubility because the amorphous form has a higher free energy than the crystal, but the same excess free energy drives it back to the crystal and can erase the gain (Hancock and Parks 2000; Tian et al. 2014, refs 8–9) C1. The usual protection is an amorphous solid dispersion (ASD), in which the drug is dispersed molecularly in a polymer. Crystallization from such a system has two steps, nucleation and growth, and polymers act on both. Earlier work, much of it from the Taylor group, showed that a polymer can speed up or slow down either step and that its effects on nucleation and on growth are not correlated: a good growth inhibitor need not be a good nucleation inhibitor (Trasi and Taylor 2012; Powell et al. 2013, refs 12–13) C2. Growth at the free surface of a glass is much faster than in the bulk and can be suppressed by a thin coating (refs 14–16) C2.

For growth from an undercooled liquid, several factors "have been suggested" to decide how well a polymer inhibits: how readily the drug crystallizes and how mobile it is, the polymer's concentration, molecular weight and glass transition temperature, and the strength of drug–polymer interactions (refs 17–25) C3. How these factors combine was not understood. Two studies of polymorphs pointed in different directions. Kestur and Taylor (2013, ref 26) found that PVP slowed the growth of two felodipine polymorphs to a similar extent and placed the polymer's action in the liquid phase R17·C38. Zhang et al. (2017, ref 27) found that PVPVA64 and HPMCAS slowed itraconazole polymorphs to different extents and attributed this to changes in the crystal–melt interfacial free energy R18·C38. The authors also note that polymer selection for ASDs is "still empirical" C4.

Indomethacin (IDM) is a convenient test case because it has many crystal forms: seven polymorphs are known, and the structures of the stable γ form and the metastable α form have been solved (refs 28–32) C5. In γ IDM, pairs of molecules linked through their carboxylic acid groups sit inside a shell of indole and phenyl rings, so the crystal faces are mainly hydrophobic. In α IDM, three molecules form a trimer, and both the hydrophobic rings and the polar carboxylic acid groups are exposed on the faces R19. Because all the polymorphs can grow from one and the same liquid, a polymer that only changes the liquid (for example its viscosity) should slow all of them in a similar way, while a polymer that acts on the growing surface could treat them differently.

The paper therefore measures the bulk growth rates of the δ, α and γ polymorphs from the IDM melt, without polymer and with 10% w/w hydroxypropyl methylcellulose (HPMC), HPMC acetate succinate (HPMCAS) or polyvinylpyrrolidone (PVP), over the whole temperature range from 80 °C to close to each melting point. It compares the polymorphs with each other, compares the three polymers, and asks whether one polymer acts in the same way on all polymorphs A1·A2·A3.

Background concepts

Crystal growth from an undercooled melt. To add a layer to a crystal, molecules must diffuse across the crystal–liquid interface and attach at growth sites C22. Two factors set the rate. The kinetic factor is molecular mobility, usually described by the viscosity or the self-diffusion coefficient of the liquid. The thermodynamic factor is the driving force, the free energy difference $\Delta G$ between liquid and crystal, which for one polymorph is proportional to the degree of undercooling (p.16) E4:

In plain terms: $T_m$ is the melting point of the polymorph and $T$ the growth temperature; the further below its own melting point a polymorph is held, the larger its driving force to grow. Just below $T_m$ the driving force is close to zero, so growth is slow although the liquid is mobile. On cooling the driving force rises but mobility falls. The growth rate therefore passes through a maximum, giving a bell-shaped curve against temperature. The authors call the peak the maximum crystal velocity (MCV) and its temperature $T_{max}$; above $T_{max}$ growth is "under thermodynamic control", below it "under kinetic control" C22.

Where the peak lies. The authors state in words that the MCV occurs at about 0.95 of the melting temperature for every polymorph, in line with earlier observations (ref 37) E3·C10:

In plain terms: with temperatures in kelvin, each polymorph grows fastest a little below its melting point. With the melting onsets used in the paper (127, 152 and 160 °C) this rule gives about 107, 131 and 138 °C, against the observed 110, 135 and 135 °C, which is within the 5 °C spacing of the measurements E3·R15.

Normalized growth rate. Polymorphs with different melting points have different driving forces at the same temperature. To compare their intrinsic ability to grow, the authors divided the pure-IDM growth rates by a driving-force term, following Wu and Yu (2006, ref 34) E5·R11. The procedure itself is not printed in the paper.

Growth-rate ratio. To compare polymers, the paper uses the growth rate without polymer divided by the growth rate with polymer at the same temperature. A ratio of 1 means no effect; a ratio of 10 means growth is ten times slower with the polymer R12.

The indomethacin polymorphs used. Table A collects what the paper gives for the three forms.

Table A. The three indomethacin polymorphs (Results, p.7; Introduction, p.4; Discussion, p.16). α and γ melting data were measured by DSC in this study; δ data are from refs 34–35 M1·R1·P3.

Viscosity and its temperature dependence. The authors assume that over small temperature ranges the viscosity of the melt "may follow" an Arrhenius-type relation (Eq. 1, ref 38) C20·E1:

In plain terms: $\eta$ is the viscosity, ${\eta }_0$ a constant, $E_{\eta }$ the activation energy for viscous flow, $R$ the gas constant and $T$ the absolute temperature. A plot of $\log \eta$ against $1/T$ is a straight line whose slope, multiplied by $2.303R$, gives $E_{\eta }$; a larger $E_{\eta }$ means the viscosity climbs faster on cooling.

Free energy of mixing. To argue that a polymer can also lower the driving force for growth, the authors quote the Flory–Huggins expression for a binary drug–polymer mixture (Eq. 2, ref 42) E2·C30:

In plain terms: $\Phi$ is the volume fraction of drug, $m$ the number of lattice sites one polymer chain occupies and $\chi$ the drug–polymer interaction parameter. The first two terms are the entropy of mixing, the last the interaction. The authors reason that systems with stronger drug–polymer interactions "would have lower free energy, and hence a reduced driving force for crystal growth" C30. They do not evaluate the equation for any of the three systems.

Methods in detail

The study has three experimental strands: growth rates of three polymorphs in four systems, identification of the polymorphs, and melt viscosity of the three polymer systems. The flow below shows how they connect.

Samples and the choice of polymorph

Indomethacin was bought as the γ form (Letco Medical) and used as received; HPMC (Methocel E5, Dow), HPMCAS (MF grade, Shin-Etsu) and PVP (K30, BASF) were dried in a vacuum oven for 24 h M1·M2·M3·M4. For pure IDM, 3–5 mg of γ crystals was melted at 170 °C for 1 min between two 18 × 18 mm² coverslips and the liquid cooled to room temperature on an aluminum block; the film was checked to be amorphous under polarized light P1. For the polymer systems, an IDM ASD containing 10% w/w polymer was first made by rotary evaporation, following the group's earlier paper (Tian et al. 2016, ref 33), and then melted and quenched in the same way P2. The solvents used for the ASDs are not stated here, although methanol and dichloromethane are listed among the materials M5·M6.

Which polymorph grows depends on where the glass is stored. Stored over desiccant at 60 °C, amorphous IDM crystallized mostly as δ, which had the fastest nucleation rate; storage at 80 °C favoured α; γ did not nucleate readily, so γ crystals were placed against the edge of the glass and the film was stored at 80 °C until γ had grown into the bulk R1·P3. The polymers slowed nucleation as well as growth, and a higher temperature was needed to start crystallization in the polymer films; the paper does not give that temperature R5·C7·X8.

Measuring the growth rate

Isothermal growth was followed on a Linkam THMS 600 hot stage under a polarized light microscope with a Nikon DS-Fi1 camera, which took time-lapse images at set intervals. The position of the growth front, measured in a direction perpendicular to it with NIS-Elements software, was plotted against time, and the slope was taken as the growth rate. Temperatures ran from 80 °C to close to the melting point of each polymorph, in 5 or 10 °C steps, and each value is the mean of at least three independently prepared samples P4. The figures carry error bars, but the paper does not say what they represent X10.

Identifying the polymorphs

The forms were identified in three ways. Raman spectra (DXR confocal Raman microscope, 532 nm laser at 8.0 mW, 10 scans averaged, 2000–200 cm⁻¹ collected) of crystals grown from the melt were compared with α IDM recrystallized from ethanol and with the γ IDM as received P6·M7. A film containing all three forms was heated from 80 °C at 5 °C/min on the hot stage and photographed, so that each form could be recognized by its melting P5. X-ray diffraction (Rigaku SmartLab, Cu Kα, 2θ 5–40°) was recorded on fully crystallized films after removing the top coverslip P7. The melting points and enthalpies of fusion of α and γ were measured by DSC; the DSC settings are not given P8·X11.

Melt viscosity

Steady-shear viscosity was measured on an AR2000ex rheometer with 20 mm parallel plates and a 0.34 mm gap. Each sample, 130 mg of IDM ASD with 10% w/w polymer, was melted at 175 °C for 3 min, then held for 10 min at each test temperature between 80 and 130 °C before a steady reading at a shear rate of 1 s⁻¹; measurements were done in duplicate P9. The pure IDM melt crystallized during the measurement, so no viscosity is available for it R13. The logarithm of viscosity was regressed against $1/T$ to obtain the activation energy for viscous flow (Eq. 1) P10·E1.

Experimental analysis

The three forms can be told apart

Grown from the pure melt, δ and α form spherulites with sharp boundaries to the amorphous phase and can be distinguished by eye under polarized light; γ grows as a polycrystalline fan from the added seeds (Figure 2A–C) R2. The α and γ morphologies did not change with temperature, whereas δ changed from smooth spherulites at 40 °C to spherulites with needle-like protrusions and a fine-grained texture at 80 °C (Figure 2G, H) R2. In the Raman spectra (Figure 3) the carbonyl region separates the forms: about 1689 and 1677 cm⁻¹ for δ, about 1691, 1680 and 1649 cm⁻¹ for α, one sharp band near 1698 cm⁻¹ for γ, and one broad band near 1681 cm⁻¹ for the amorphous form (positions read from the figure); the melt-grown α and γ spectra match the reference α and γ R3·C6. On the hot stage (Figure 4), the δ region of a mixed film had largely melted by 135 °C, α by about 159 °C, while γ persisted to 164–166 °C R4.

With HPMCAS, γ looked the same as from pure IDM, δ resembled pure δ grown at the lower temperature of 40 °C, and α had a different texture that became a densely branched spherulite with a rough, fibre-like interface at higher temperature (Figure 2D–F, I) R5. The text places the rough δ interface at 115 °C, while the Figure 2 caption gives 105 °C for panel I X3. XRD patterns of the three forms grown with HPMCAS (Figure 5) match the α and γ references and the literature R6. For HPMC and PVP the paper states only that the crystals looked like those grown with HPMCAS; no Raman, melting or XRD data are shown for these two systems C8·X6.

Pure indomethacin: three polymorphs, three growth curves

Figure 6A shows bell-shaped growth curves for all three polymorphs. α grows fastest, with an MCV of 4.34 × 10⁻⁶ m/s at 135 °C; γ reaches 4.07 × 10⁻⁷ m/s at the same temperature, about an order of magnitude slower R7·C9. δ grows slightly faster than α at 80–90 °C (about 1.2 × 10⁻⁸ against 7.2 × 10⁻⁹ m/s at 80 °C) but peaks early, at about 1.5 × 10⁻⁷ m/s at 110 °C, and at 120 °C has fallen to about 6.3 × 10⁻⁸ m/s, below both other forms R7·R8·R9. The authors explain the early δ peak by its lower melting point ("as a result of their different melting characteristics") C23.

Table 2 of the paper lists the pure-IDM MCVs as 40.72 for δ and 14.95 for γ, in units of 10⁻⁸ m/s. These two cells disagree with the text and with Figures 6A, 7A and 7C, which put δ at about 1.5 × 10⁻⁷ m/s and γ at about 4.1 × 10⁻⁷ m/s; the two values appear to have been interchanged R15·X1. Read as printed, Table 2 would even show HPMCAS raising the γ MCV (24.01 against 14.95), which Figure 7C does not show X1. This article uses the values from the text and the figures. The column heading "MCV (×10⁸ m/s)" also has to be read as "in units of 10⁻⁸ m/s" for the α value to match the text X2.

Table B. Growth of the pure polymorphs. MCV of α and γ from the text, δ read from Figure 6A; Tmax from Table 2; normalized rates read from Figure 6B (approximate) R7·R8·R11·R15.

After normalization for driving force (Figure 6B) the polymorphs still differ: δ levels off at about 5–6 × 10⁻⁷ m/s near 110–120 °C, γ at about 9 × 10⁻⁷ m/s near 135–140 °C, and α keeps rising up to about 6 × 10⁻⁵ m/s at 150 °C, so that above about 100 °C α is by far the fastest form, while δ is the fastest at 80–95 °C R11. The authors summarize that the differences "persisted when differences in the extent of undercooling were accounted for" and that α "has the highest MCV" C24. Strictly, the normalized α curve has no maximum within the measured range, so the "highest MCV" refers to the raw values of Table 2 X17.

The authors then ask why. A rule proposed for glasses says the densest polymorph grows fastest (ref 41), and the denser felodipine polymorph did grow faster from its glass (ref 26); but for itraconazole the less dense form grew faster above $T_g$ (ref 27) R17·R18. Here the denser α (1.427 g/cm³) does grow faster than γ (1.377 g/cm³), yet the authors judge the density rule "unlikely to be applicable to crystals growing from liquids" C25·M1. Instead, the differences "may arise" from how fast molecules integrate at the crystal–liquid interface, which depends on the structure of that interface C26.

Every polymer slows every polymorph, but the ranking changes with temperature

Figure 7A–C plots the growth rates with and without polymer for each polymorph. All three polymers lowered the growth rate of all three polymorphs at every temperature measured R8·R9·R10·C11. The ranking depends on the polymorph and on the temperature:

• δ: PVP was the best inhibitor at 80–105 °C (at 80 °C about 4.5 × 10⁻¹⁰ m/s with PVP, 2.0 × 10⁻⁹ with HPMC and 4.4 × 10⁻⁹ with HPMCAS, against 1.2 × 10⁻⁸ m/s without polymer), HPMC at 115–120 °C, and HPMCAS was the least effective at all temperatures R8·C12.
• α: PVP was the most effective at 80–100 °C and HPMC at 105–120 °C, with HPMCAS the least effective; at 130 °C, however, α grew more slowly with HPMCAS (about 1.1 × 10⁻⁸ m/s) than with PVP (about 5.8 × 10⁻⁸ m/s) R9·C13·X4.
• γ: HPMCAS was again the least effective; PVP inhibited better than HPMC at 80–115 °C and about as well at 120–150 °C R10·C14.

The authors condense this into the abstract's statement that at lower temperatures the effectiveness "decreased in the order of PVP > HPMC > HPMCAS", and in the results that "in general" PVP is better at lower temperatures, HPMC at higher temperatures, and HPMCAS least effective C15. In numbers: at 80–100 °C, below the temperature of fastest growth, PVP reduced growth 5–25-fold, HPMC 2–12-fold and HPMCAS 2–3-fold C28·R12.

The same polymer treats the polymorphs differently

Figure 7D–F plots, for each polymer, the ratio of growth without and with polymer for the three polymorphs. This is the central result of the paper. Table C gives the ratios at four temperatures.

Table C. Ratio of growth rate without polymer to growth rate with polymer, read from Figure 7D–F (approximate); "—" = no data point R12.

Three patterns stand out. First, every polymer slows γ the least over most of the range: the γ ratio stays between about 1.5 and 11 up to 130 °C for all polymers R12·C16·C17. Second, α is slowed most at high temperature: the α ratio climbs to about 2900 with HPMC at 120 °C, about 283 with HPMCAS at 130 °C and about 558 with PVP at 135 °C R12. Third, at the low end δ is slowed more than α: with HPMC at 80–90 °C the ratios are about 5.9–7.3 for δ against 3.5–4.7 for α (the authors quote "7.5 times vs. 5 times"), while above 95 °C α is slowed more R12·C16. The authors summarize that all three polymers were more effective on δ at lower temperatures and on α at higher temperatures, had the least effect on γ, and were "generally relatively more effective at higher temperatures" C18.

The plotted ratios contain two exceptions to these summary statements. At 80 °C, HPMC and HPMCAS slow γ slightly more than α (about 4.7 against 3.5, and 2.2 against 1.8), so "least effect on γ" holds for these two polymers only from about 90 °C upward X5. And for α at 130 °C HPMCAS is the stronger inhibitor (about 283 against 52 for PVP) X4. The very largest ratios also rest on single, very slow points: the HPMC α rate at 120 °C is only about 5.1 × 10⁻¹⁰ m/s, and the PVP α point at 135 °C has a wide error bar X16.

Above the temperature of fastest growth

The polymers also move the growth maximum. Table D combines the printed values of Table 2 with the corrected pure-IDM MCVs.

Table D. Maximum crystal velocity (in units of 10⁻⁸ m/s) and its temperature. Polymer rows and all Tmax values from Table 2; pure-IDM δ and γ MCVs from the text and Figures 6A and 7, since Table 2 prints them interchanged R15·R7·X1·X2.

HPMC lowers $T_{max}$ for every polymorph, most strikingly for α, from 135 to 100 °C; HPMCAS lowers the α peak to 110 °C and PVP to 125 °C, while PVP raises the δ peak slightly, from 110 to 115 °C R15·C34. Above each $T_{max}$, where growth is limited by the driving force, the growth-rate ratios rise sharply, and the authors call this region "particularly intriguing" because few, if any, studies have looked at it C35·C33. They offer two "possible reasons": the polymer depresses the melting point of the IDM crystals and so lowers the driving force C36. The authors add that the MCV values of Table 2 show the same polymorph dependence as the ratios C37. Note by the AI writer (a calculation from Table D, not given in the paper): dividing the pure-IDM MCV by the MCV with polymer gives about 280-fold (HPMC), 29-fold (HPMCAS) and 70-fold (PVP) for α, but only about 4.4-, 1.7- and 4.5-fold for γ, using the corrected γ value R15·X1.

Melt viscosity

Figure 8 plots $\log \eta$ of the three IDM–polymer melts against ${10}^3/T$. The viscosity of all three falls with temperature; IDM–HPMC and IDM–HPMCAS are similar throughout, while IDM–PVP is higher at 80–105 °C and comparable at higher temperatures R13·C19. At 80 °C, $\log \eta$ is about 4.9 for PVP against about 4.3 for HPMC and 4.1 for HPMCAS; at 130 °C all three lie near 1.4–1.5 (the unit of η is not printed) R13·X9.

Table E. Arrhenius regressions of melt viscosity (Table 1 of the paper) R14.

The activation energy for viscous flow increases in the order IDM–HPMCAS < IDM–HPMC < IDM–PVP C21. The printed slopes reproduce the printed activation energies: for IDM–HPMC, 8340.7 K × 2.303 × 8.314 J mol⁻¹ K⁻¹ gives 159.7 kJ/mol, with the gas constant taken as 8.314 J mol⁻¹ K⁻¹ because its value is not printed E1.

Discussion

How the authors connect the results

The authors build their explanation in steps, moving from the liquid to the crystal surface.

Mobility-controlled growth. Below $T_{max}$, where mobility limits growth, the most viscous melt, IDM–PVP, goes with the strongest inhibitor: the authors say the viscosity "correlates" with the generally stronger effect of PVP where mobility controls growth C28. Viscosity cannot be the whole story, however, because IDM–HPMC and IDM–HPMCAS have similar viscosities while HPMC inhibits more; the authors write that "clearly" viscosity cannot explain this C29. They turn to the free energy of mixing (Eq. 2): stronger drug–polymer interaction should lower the driving force. An earlier fluorescence study by the same group ranked the interactions IDM–PVP > IDM–HPMC > IDM–HPMCAS (ref 33) R16. On that basis the improved inhibition by PVP at low temperature is "most likely" due to both reduced molecular mobility and a smaller thermodynamic driving force, and the weaker effect of HPMCAS compared with HPMC "can perhaps be attributed to the reduced extent of drug-polymer interactions" C31·C32.

Driving-force-controlled growth. Above $T_{max}$ the polymers become very effective and HPMC in particular lowers $T_{max}$ C34·C35. The authors suggest that melting point depression of the IDM crystals by the polymer, and the resulting smaller driving force, "may be possible reasons" C36. They stress that this region is likely to matter for hot melt extrusion, in which drug–polymer blends are processed close to the drug's melting point and residual crystals can grow depending on the temperature regimen C33.

The polymorph dependence. The decisive observation is that one polymer slows polymorphs that grow from the same liquid by very different amounts C37. If a polymer acted only through the liquid, by raising viscosity or by lowering the free energy of the melt, the effect on every polymorph would be similar, as Kestur and Taylor proposed for felodipine C38. Because it is not, the authors conclude: "Rather, it appears that the polymers impact the crystal-melt interface of the various polymorphs differently" C39. This sides with the interfacial explanation that Zhang et al. gave for itraconazole C38. It also fits the authors' own reading of the pure-IDM data, where the remaining polymorph differences "may arise" from the kinetics of integration at the crystal–liquid interface C26.

Note by the AI writer (not discussed in the paper): the paper cites the different face chemistry of γ (hydrophobic faces, carboxylic acid dimers shielded inside) and α (hydrophobic rings and polar carboxylic acid groups both exposed) in the introduction R19, and the pattern "least effect on γ, most on α" is what one would expect if the polymers interact with exposed polar groups on the growing faces. The paper itself does not draw this link in its discussion, and no measurement of polymer adsorption or face-specific growth supports it.

What it suggests for formulation

The authors state that their observations matter for the crystallization of amorphous formulations "in particular at higher temperatures, such as those that might be encountered during processing" C41, and that polymer effects near the melting point are "likely of great importance in the context of hot melt extrusion" C33. The AI writer's reading (not stated in the paper): a ranking of polymers by growth inhibition is not a property of the polymer alone. In this data set PVP leads below about 105 °C and HPMC above, HPMCAS outperforms PVP for α at 130 °C, and the stable γ form, the form most likely to survive as residual crystals in a melt process, is the one every polymer slows least R12·X4. A screen at one temperature, or on the polymorph that happens to crystallize first, may therefore rank polymers differently from what matters in processing. All measurements were made at 80 °C and above with 10% w/w polymer, so they do not speak directly to growth during storage at room temperature.

Limitations

Stated by the authors

The authors call the mechanism of polymeric growth inhibition from the melt "still not well understood" C27, note that few, if any, studies have examined the region above $T_{max}$ C33, and that the effect of polymers on the growth of different polymorphs "has not been studied extensively" C38. Their explanations are hedged: "may arise" for the interface kinetics of the pure polymorphs, "most likely" and "perhaps" for the role of drug–polymer interactions, "may be possible reasons" for melting point depression, and "it appears" for the action on the crystal–melt interface C26·C31·C32·C36·C39.

The AI writer's own judgement

• Table 2. The pure-IDM δ and γ MCVs are interchanged relative to the text and the figures, and the unit heading must be read as 10⁻⁸ m/s X1·X2.
• Summary rankings with exceptions. HPMCAS is not the weakest inhibitor of α at 130 °C, and at 80 °C HPMC and HPMCAS slow γ slightly more than α X4·X5.
• Mechanisms not measured. The drug–polymer interaction ranking is cited from ref 33, Eq. 2 is not evaluated, and neither melting point depression nor any interfacial property (interfacial free energy, polymer adsorption on the growing faces) was measured; the interface explanation is reached by excluding a liquid-phase explanation X13·X14.
• Viscosity baseline. The pure IDM melt crystallized during rheometry, so how much each polymer raises the viscosity is unknown, and the rheometer samples had a different thermal history from the growth films X12.
• Documentation gaps. Polymorph identity in the HPMC and PVP systems is not shown, the temperature used to nucleate the polymer films is not given, the error bars are not defined, and the δ melting data are cited while α and γ were measured with an undescribed DSC method X6·X8·X10·X11.
• Extreme ratios. The ratios of several hundred to about 2900 for α rest on single, very slow points X16.
• Scope. One drug, one polymer content (10% w/w) and temperatures from 80 °C upward.

Overall, the AI writer rates the evidence as moderate: the growth-rate measurements are direct, replicated and internally consistent, so the observation that polymer effects depend on the growing polymorph is well supported, but the explanations offered for it remain untested R8·R9·R10·R12·X13·X14.

Conclusion

The paper shows, for one drug, that crystal growth inhibition by polymers is not only a property of the liquid. From the same undercooled indomethacin melt, the δ, α and γ polymorphs grow at rates that differ by up to about thirty-fold at their maxima, and the differences remain after correcting for driving force R7·R11. HPMC, HPMCAS and PVP at 10% w/w slow all three polymorphs; at lower temperatures PVP is the strongest and HPMCAS the weakest inhibitor, and above the temperature of fastest growth inhibition rises steeply, with HPMC moving that temperature down by as much as 35 °C for α R12·R15·C15·C34. Most strikingly, each polymer slows the stable γ least and the fast-growing α most R12·C37. Viscosity accounts for PVP's strength at low temperature but not for the HPMC–HPMCAS difference, and the authors conclude that "it appears" the polymers act on the crystal–melt interface of each polymorph differently, a hypothesis that later work would need to test with interfacial measurements C28·C29·C39·X14.