How the viscosity of a drug melt relates to whether it crystallizes or forms a glass on cooling

Background and motivation

Many new drug candidates are poorly soluble in water (Lipinski 2000, ref 1), and amorphous formulations are increasingly used to raise their oral bioavailability (Leuner 2000, ref 2). Melt extrusion, in which the drug is co-melted with polymers and other excipients and extruded into a homogeneous amorphous dispersion, has become common (refs 3–5). Solid dispersions have been studied for more than 40 years (Chiou 1971, ref 6), yet relatively few products had reached the market (Sinha 2009, ref 7); the authors name scale-up and crystallization of the drug during shelf life as the main obstacles. For melt extrusion they add a third concern: crystallization during the cooling step after the melt leaves the extruder, which they call "particularly important" to understand. C1

The paper builds directly on a classification published by the same group (Baird 2010, ref 8). There, a large set of organic molecules was cooled and reheated in a differential scanning calorimeter (DSC) and sorted by when, if ever, it crystallized. Class I compounds crystallize on cooling from the melt; class I-A crystallize even when quenched in liquid nitrogen, and class I-B crystallize on cooling at 20 °C/min but can be trapped as glasses by quenching. Class II compounds do not crystallize on cooling (below 5 °C/min in this paper's wording) but do crystallize when the glass is reheated. Class III compounds crystallize neither on cooling at 2 °C/min nor on reheating at 2 °C/min. Principal component analysis then linked molecular and thermal properties to class. C2·P2 One property that was not examined was viscosity.

Viscosity matters twice in melt processing. It is a processing parameter for melt extrusion, and it is a transport property, tied to molecular rotation time and so to mobility above the glass transition temperature Tg, that governs how fast molecules can rearrange between the melting temperature Tm and Tg, the range the authors call the undercooled melt regime. Viscosity can be measured by rheometry, dynamic mechanical analysis or thermomechanical analysis, but only a few studies had measured it for pharmaceutical amorphous materials or dispersions in this range (Andronis 1997, ref 9; Hancock 1999, ref 10; Kestur 2010, ref 11), and these had paid little attention to crystallization tendency. C3

Theory gives viscosity a central place. In classical nucleation theory and in the screw-dislocation model of crystal growth (both introduced below), the kinetic part of each rate is tied to viscous flow, so the authors expect viscosity to be "likely" one of the key attributes of crystallization tendency from the melt. C4 The study therefore sets out to measure the steady-shear viscosity of 34 of the 51 compounds of ref 8 from Tm downward, to look for links between the measured viscosities and the crystallization classes, and to fit the data to the Vogel–Tamman–Fulcher (VTF) equation so as to compare the kinetic fragility of the compounds through the strength parameter D. A1·P1·P5

Background concepts

The undercooled melt. A crystalline compound melts at Tm. If the melt is cooled below Tm without crystallizing, it is undercooled (or supercooled); the temperature difference Tm − T is the degree of undercooling. Cooled far enough without crystallizing, the liquid becomes a glass at Tg. The paper describes each compound's melt by three quantities: the viscosity at Tm, written ηmelt; the viscosity η at a given undercooling; and the viscosity ratio η/ηmelt, which says how many times thicker the melt has become since Tm. P3·E7

Classical nucleation theory. Crystallization needs two steps, nucleation and growth. For steady-state homogeneous nucleation from the undercooled melt the paper writes (Eq. 1; the paper uses square brackets for the outer bracket):

Here $I_{SS}$ is the nucleation rate per unit volume, $I_0$ a pre-exponential factor, $k_B$ the Boltzmann constant and $T$ the temperature. $W^{*}$ is the thermodynamic barrier to forming a critical nucleus, and $\Delta G_{\eta }$ is the activation free energy for viscous flow, the kinetic barrier for moving a molecule from the melt to the nucleus surface. In plain terms: nuclei appear exponentially less often as either the thermodynamic barrier or the barrier to molecular motion grows. E1 For a spherical nucleus the thermodynamic barrier is (Eq. 2):

where ${\sigma }_{cm}$ is the specific free energy (interfacial tension) of the crystal-nucleus–melt interface and $\Delta G_v$ the free-energy difference between undercooled melt and crystal per unit volume. In plain terms: the barrier rises steeply with interfacial tension and falls steeply as the driving force grows; at Tm the driving force is zero and the barrier infinite. E2

Crystal growth. For growth by screw dislocations the paper gives (Eq. 3; again printed with square brackets):

where $U$ is the growth rate, $f$ the fraction of interface sites where molecules can attach or detach, $\lambda$ the distance the interface advances in one kinetic step (taken as the molecular diameter) and $\eta$ the viscosity of the undercooled melt (Simmons 1982, ref 13). In plain terms: the growth rate is inversely proportional to viscosity, multiplied by a thermodynamic factor that is zero at Tm and grows on cooling. E3 Note by the AI writer (not discussed in the paper): as printed, the exponent divides $\Delta G_v$, defined per unit volume for Eq. 2, by a per-molecule thermal energy $k_{B}T$; a molecular-volume factor is implied but not printed. X17 The authors' point from Eqs. 1–3 is that both nucleation and growth depend on viscosity, which stands for the diffusion or rearrangement needed to build nuclei or add molecules to a crystal face. C4

Glass-forming ability and its usual predictors. Glass-forming ability (GFA) is the ease with which a melt can be cooled to a glass without crystallizing. Three rules of thumb from glass science appear in the paper. First, only liquids with a sufficient viscosity at Tm and/or a rapidly rising viscosity on cooling form glasses at attainable cooling rates (Uhlmann 1972, ref 16); the empirical rule that molecular compounds whose boiling-to-melting temperature ratio Tb/Tm is 2 or more vitrify easily is read as describing liquids viscous enough at Tm (refs 16–21). C28 From liquids slow enough to be measured below Tm, Angell concluded that a good glass former generally needs a viscosity at Tm no lower than 0.01–1 Pa·s (Angell 2008, ref 22). C29 Second, the reduced glass transition temperature Tg/Tm (Kauzmann 1948, ref 23; Turnbull 1969, ref 24) is the most common metric of GFA for organic molecules: a higher Tg/Tm means a narrower undercooled range Tm − Tg, and is expected to mean greater resistance to crystallization. C36 Third, kinetic fragility.

Kinetic fragility and the VTF equation. Fragility describes how sensitive the structure of an undercooled liquid is to temperature. In Angell's strong/fragile scheme (refs 25–28), strong liquids show an Arrhenius temperature dependence of viscosity, change little in structure with temperature and are good glass formers, whereas fragile liquids show a non-Arrhenius dependence, reorganise structurally with temperature and have higher crystallization tendencies. C37 The non-Arrhenius dependence is described by the VTF equation (Eq. 4):

where ${\eta }_0$ is the viscosity of the "unrestricted" material, $D$ the strength parameter and $T_0$ the zero-mobility temperature, which for some systems coincides with the Kauzmann temperature (Tanaka 2005, ref 29). In plain terms: viscosity grows without limit as $T$ approaches $T_0$, and the smaller $D$ is, the more sharply it bends upward near Tg. E4 The paper relates $T_0$ to $D$ through Tg (Eq. 5):

with ${\eta }_g$ the viscosity at Tg and $\log ({\eta }_g/{\eta }_0)\approx 17$ (refs 19, 30). In plain terms: once Tg and D are fixed, $T_0$ follows, so a liquid's whole viscosity curve between its high-temperature limit and the glass is set by one number, D. Strong liquids have D above 30 and fragile liquids D below 10 (refs 31–33). E5·C37 Plotting log viscosity against Tg/T, an "Angell plot", puts all liquids on one scale ending at Tg, where strong liquids give nearly straight lines and fragile ones strongly curved lines; the paper's Figure 4 draws such curves for a hypothetical liquid with Tg = 273 K and D = 100, 50, 20, 10 and 5. P6·C41

Table A. The four crystallization classes and the 34 compounds measured. Class definitions as described in the paper (from ref 8); melt viscosities from Tables 1–4. P2·M1–M34·R1

Methods in detail

The study has one experimental core, a stepwise viscosity measurement of each melt, and three ways of reading the results: comparing compounds by their melt viscosity, by how fast their viscosity rises on undercooling, and by their VTF fragility. The thermodynamic properties of the compounds are tabulated alongside but, apart from Tm − Tg and Tg/Tm, are not analysed.

Contribution 1: one viscosity protocol for 34 melts

Problem. To compare melts that crystallize within seconds with melts that never crystallize, every compound has to be measured the same way, and each reading must be taken before crystals form and spoil it. What they did. About 0.5 g of each powder was loaded at room temperature onto the lower plate of an Anton Paar MCR 301 rheometer (25 mm parallel plates, Peltier temperature control inside a heating hood) and heated at 10 °C/min to 10 °C above Tm. The upper plate was lowered to a 0.4 mm gap, excess melt was trimmed, and the melt was cooled rapidly to Tm and equilibrated. A shear rate of 30 s^-1 was applied and the viscosity recorded once the reading was steady. The sample was then reheated to Tm + 10 °C and held for 5 min to melt any nuclei, cooled rapidly to Tm − 5 °C and measured again, and so on at successively lower temperatures (5 °C steps; Figure 1a shows 1 °C steps close to Tm for some class I-A compounds). A run ended when the viscosity rose with time at fixed temperature and shear rate, the sign of crystallization. P1 For three class II compounds (bifonazole, cinnarizine, dibucaine) the run ended instead when the shear rate no longer stayed constant, and no class III compound crystallized at all. R2·R7 Why it works. Remelting between steps resets each measurement, so every temperature is approached from the melt in the same way, and viscosity is read at the moment the melt is still free of crystals. What is not stated. The number of replicate runs, the equilibration time at each temperature, the criterion for a steady reading and whether the viscosity was independent of shear rate are not given; each curve appears to be a single run. X12

The shear itself influences crystallization. The authors note that the applied shear "will" promote heterogeneous nucleation at the interface between the upper plate and the sample, so the class I-A compounds crystallized at uniformly higher temperatures in the rheometer than in the DSC experiments of ref 8. C8·R5 The classes, in other words, come from one experiment (DSC, no shear) and the viscosities from another (shear, plate contact). X13

Contribution 2: three viscosity descriptors and class averages

For each compound the authors compare the absolute viscosity at Tm (ηmelt), the viscosity at a given undercooling, and the viscosity ratio η/ηmelt as a function of undercooling (Figures 1 and 2). P3 They then average viscosity and viscosity ratio over all compounds of a class at 0, 5, 10, 15 and 20 °C of undercooling (Figure 3); the error bars, they write, reflect the large variation between compounds within each class. P4·C24 Because the undercooled range Tm − Tg differs from compound to compound, they also compare compounds with similar Tm − Tg at a fixed undercooling of 35–45 °C, so that the two melts are at similar distances from their glass transitions. R3·C20

Note by the AI writer (not discussed in the paper): the class III average plotted at Tm in Figure 3a (about 0.11 Pa·s, with an error bar to about 0.21) matches the mean and standard deviation of the 15 class III melt viscosities without ritonavir (0.108 ± 0.101 Pa·s) and not with it (0.226 Pa·s); the paper does not say that ritonavir was left out, nor what the error bars are. The class I-A averages at 10–20 °C can only include the compounds still liquid there, because 4-biphenylmethanol and phenacetin crystallized after about 5 and 7 °C. X6·R2

Contribution 3: VTF fragility and the Angell plot

Each viscosity curve of classes I-B, II and III was fitted to Eq. 4 by varying D and T₀ together until the best fit was reached (Table 5). P5 Following Stickel et al. (ref 35), who found the VTF equation valid from Tm down to about 0.4Tg on a scale on which Tg = 0 and Tm = 1, the data were cut at that point for bifonazole, cinnarizine, tolazamide and all class III compounds except clotrimazole and ritonavir. C38·P5 Class I-A could not be fitted, because too few points could be measured before crystallization. P5 All data were then plotted as log viscosity against Tg/T (Figure 5), with Tg taken from ref 8, together with the curves for D = 100 and D = 5 from Figure 4. P6

Note by the AI writer (not discussed in the paper): the fitted pairs of D and T₀ do not satisfy Eq. 5 with log(η_g/η₀) = 17. For ritonavir, Eq. 5 with D = 5.6 and Tg = 49 °C gives T₀ = 8.7 °C, against the fitted 0 °C; for chlorpropamide it gives −29.4 °C against −54 °C. This is not a misprint: Table 5 comes from a free two-parameter fit, while Eq. 5 is used only to draw the model curves of Figures 4 and 5. The fitted curves therefore do not end at the viscosity at Tg assumed for those model curves, and D values are best compared within this paper's procedure. The truncation temperatures, η₀ and the quality of the fits are not reported. E5·X5·X14

The tabulated properties

Tables 1–4 list, for each compound, molecular weight, Tm, Tg, Tm − Tg, heat and entropy of fusion per unit volume, the free-energy difference ΔG_v at 298 K from the Hoffman equation, ηmelt and the number of rotatable bonds. Tg comes from ref 8, and is an estimate for all class I-A compounds and for 4-biphenylcarboxaldehyde. P7·M1–M34 Note by the AI writer: three entries cannot be reproduced from the paper's own numbers. The dibucaine row of Table 3 repeats the molecular weight (234.3 g/mol), Tm (68 °C) and Tg (−39 °C) of lidocaine in Table 1, and its Tm − Tg of 100 °C does not equal 68 − (−39) = 107 °C. X1 The ΔG_v of ritonavir (−37.6 J/cm³, the same number as tolazamide's) is about −21.4 J/cm³ by the standard Hoffman form with the table's own ΔH_fus and Tm, which reproduces all other rows. X2 Two Tm − Tg entries (felodipine, fenofibrate) differ by 2 °C from Tm − Tg computed from the printed temperatures. X4

Experimental analysis

Melt viscosity separates the extreme classes

As expected, the viscosity of every compound rose as the melt was cooled below Tm, and the viscosity ratio grew faster the further the melt was undercooled, a non-linear temperature dependence. C5 Melt viscosities at Tm span almost three orders of magnitude, from 2.86 × 10^-3 Pa·s for benzamide to 1.99 Pa·s for ritonavir, which the authors note is almost an order of magnitude above any other compound. R1·C22 Within each class the spread is large: more than tenfold in class I-B (antipyrin 4.18 × 10^-3 to chlorpropamide 9.32 × 10^-2 Pa·s), in class II (tolazamide 6.61 × 10^-3 to dibucaine 1.31 × 10^-1 Pa·s) and in class III. R1·C14·C17·C22 The authors conclude that compounds with similar crystallization behaviour "can exhibit quite different viscosities". C6

Table B. Melt viscosity at Tm by class, from Tables 1–4. The paper's text counts "31 compounds" with 22 above 0.01 Pa·s; the tables list 34 compounds with 25 above. R1·R11·X3

The split at 10^-2 Pa·s is complete between the extreme classes: no class I-A compound lies above it and every class III compound does; class I-B and class II compounds are mostly above it, except antipyrin and 4-biphenylcarboxaldehyde (I-B) and tolazamide (II). R1·R11·C22 The class averages of Figure 3a keep the same order at every step from 0 to 20 °C of undercooling, class III highest and class I-A lowest; the authors write that "it seems that there is some trend" in which compounds with higher crystallization tendency have lower viscosity, and they note that the class I-B and class II averages differ only slightly and "not statistically significant[ly]". R8·C23·C24 No statistical test is named. R10

Viscosity of the slow crystallizers rises faster

Table C. Class-average viscosity and viscosity ratio at 0, 10 and 20 °C undercooling, read from Figure 3a and 3b (approximate). Error bars, very wide for class III, are not reproduced. R8·R9

On average class I-A has the weakest and class III the strongest temperature dependence of viscosity (Figure 3b). R9·C25 The individual curves show the same picture. Class I-A curves run nearly parallel, and when crystallization ended the runs the viscosity had risen less than twofold for every compound except lidocaine, which reached about 4.9 times its melt viscosity at about 35 °C of undercooling. R2.a–f·R4·C12 In class I-B the ratio stays small below 15 °C of undercooling and then rises rapidly, which the authors say "most likely explains" why these compounds can be captured as glasses when cooled fast enough. R6·C15 Most class III compounds exceed a ratio of 100 at large undercooling, and the steepest, ritonavir and miconazole, are already at about 240 and 220 at 40 °C. R7·R3.q–r

How far each class could be undercooled

Table D. Extent of the viscosity runs, read from Figure 1 (approximate), with the end of each run as stated in the text. Final class III viscosities were roughly 10³–10⁴ Pa·s. R2·R4·R7·X12

Class I-A crystallized close to Tm, in a regime the authors describe as "primarily under thermodynamic control": the melt is mobile, with viscosities at crystallization typically below 10^-2 Pa·s, but the driving force is small so close to Tm. R4·C9 From the spread of crystallization temperatures within the class they infer that the temperature of maximum nucleation and/or growth rate "most likely" lies at smaller undercooling for 4-biphenylmethanol than for lidocaine. C10

Within a class, viscosity does not rank the compounds

In class I-A, the viscosity of benzamide just before it crystallized was an order of magnitude lower than that of lidocaine at its crystallization temperature (about 3.9 × 10^-3 against 3.7 × 10^-2 Pa·s, read from Figure 1a), and benzamide was less viscous than 4-biphenylmethanol and phenacetin at every temperature, yet it could be cooled further below its Tm before it crystallized. The authors find "no direct correlation" between viscosity and crystallization within this class and take it as support for thermodynamic control. R4·C11 In class II, tolazamide has almost a tenfold lower melt viscosity than celecoxib or nifedipine but was measured to about 105 °C of undercooling, and bifonazole, also less viscous, was cooled more than 100 °C below its Tm without crystallizing, while celecoxib crystallized after about 45 °C. The authors conclude that differences in viscosity "cannot be used to explain" the variation in crystallization tendency within class II. R2.l–r·R1.l–r·C16

Class II also shows a wide spread of viscosity ratios. At 45 °C of undercooling acetaminophen, bifonazole and tolazamide reach ratios of about 5 (about 5, 6.5 and 2.8 in Figure 2c), while celecoxib, cinnarizine, dibucaine and nifedipine are at least ten times their melt viscosity. R3.d–j·C18 The authors explain this "in part" by the differing undercooled range: Tg/Tm of the class II compounds varies from 0.65 to 0.76 rather than being the often-assumed 2/3, so at 45 °C of undercooling the high-ratio compounds are closer to their Tg. R14·C19

Similar Tg/Tm, different behaviour

Table E. Compounds compared at a similar undercooled range. Tm − Tg, η_melt and ΔG_v from Tables 2–4; viscosity ratios at 40 °C undercooling as printed in the text (p.276–277, p.279). M9·M14·M26·M16·M33·M27·M21·M32·M28·R1·R3·X1

Chlorpropamide (class I-B, Tm − Tg = 108 °C) and celecoxib (class II, 105 °C) have similar melt viscosities and similar undercooled ranges, yet at 40 °C below Tm the viscosity of chlorpropamide has risen about 10-fold and that of celecoxib about 20-fold, "indicating celecoxib viscosity has a much stronger temperature dependence". The authors report the same for flufenamic acid against cinnarizine and tolbutamide against nifedipine. R3.a·R3.d·C20 Ketoconazole (class III), with a Tm − Tg similar to both, has the highest ratio of the three, 36. R3.p·C25 Dibucaine, the steepest class II compound at about 29, stays below five class III compounds with Tm − Tg near 100 °C (35 to 87). R3.j–o·C25 Within a class, compounds with the faster viscosity rise "tended" to have a smaller Tm − Tg, and the compound with the largest Tm − Tg had the lowest melt viscosity (antipyrin, tolazamide, aceclofenac) while the one with the smallest had the highest (chlorpropamide, dibucaine, ritonavir); across classes the mean Tm − Tg (123 ± 11, 119 ± 11, 126 ± 20 and 108 ± 16 °C for classes I-A, I-B, II and III) did not differ significantly. C35·C27·R10 Because compounds with similar melt viscosities and Tm − Tg can differ in the rate of viscosity change, as chlorpropamide and ketoconazole do, the authors conclude that Tg/Tm is "actually not a good predictor" of glass-forming ability. C36

Note by the AI writer (not discussed in the paper): in Figures 2b and 2c tolbutamide and nifedipine are about equal at 40 °C (about 10 each) and differ only at 45 °C (about 13 against 16), so that pair supports the stated trend only weakly. Ibuprofen's melt viscosity (13.34 × 10^-3 Pa·s) is slightly below aceclofenac's (14.30 × 10^-3 Pa·s), so aceclofenac is not quite the least viscous class III compound. X10·X11

Every fitted liquid is fragile

Table F. Ranges of the VTF parameters by class, from Table 5. Strong liquids have D above 30, fragile liquids D below 10. Itraconazole's printed |T₀ − Tg| of 59 °C differs from the 61 °C implied by its T₀ and Tg. R12·P5·X4

All strength parameters lie below 10, "indicating the compounds evaluated are kinetically fragile liquids". R12·C39 Non-Arrhenius viscosity is, the authors note citing Angell and others, a hallmark of organic glass formers, whose molecules are held by hydrogen bonds or dispersive interactions much weaker than the covalent network of a strong liquid such as SiO₂, and it had been reported for pharmaceuticals from relaxation studies. C40 In the Angell plot (Figure 5) the measured points cover Tg/T of about 0.65–0.93 and log viscosity of about −2.6 to 4, around the D = 5 curve and far from the D = 100 line, and the authors see "essentially no observable difference between the different classes". Large absolute differences in viscosity shrink to small ones on the logarithmic scale. R13·C42 They conclude that "Angell" plots "give minimal information" on crystallization tendency or GFA, and in the abstract that kinetic fragility "may not accurately assess" GFA from the undercooled melt. C43 Note by the AI writer: the abstract and conclusions describe "all" compounds as fragile, but D was fitted only for the 28 compounds of classes I-B, II and III; class I-A appears only in the Angell plot. X7

Discussion

How the authors connect viscosity to crystallization

The authors' argument runs from nucleation theory to their two viscosity descriptors. At Tm the free-energy difference between crystal and liquid is zero, so there is no driving force for crystallization. As the melt cools, the nucleation rate is set by three things: the free-energy difference, the interfacial free energy between nucleus and melt, and the fluidity (or viscosity) of the liquid (Eqs. 1 and 2). A faster rise in viscosity therefore lowers the nucleation rate "all other factors being equal", and they "might predict" that compounds with a steeper rise are more resistant to crystallization, provided melt viscosities and nucleation barriers are similar. C32 The chain below sets out the two outcomes as the paper describes them.

Their worked example is chlorpropamide against probucol. The two melts have similar viscosities at Tm (9.33 × 10^-2 against 8.03 × 10^-2 Pa·s), but at 40 °C of undercooling the viscosity of probucol has risen about 82-fold and that of chlorpropamide about 10-fold; chlorpropamide crystallized during the measurement, probucol did not. The authors write that the faster rise for probucol "thus hindered the diffusion of molecules together to form nuclei", contributing to its much lower crystallization tendency, and that other class I-B and class III pairs with similar melt viscosities behave alike. C33·R1.i·R1.af·R3.a·R3.n They add that an exact correlation between viscosity and crystallization tendency "is not to be expected in all cases", because the thermodynamic parameters vary between compounds, but that the results "clearly indicate" viscosity is a very important parameter, as theory predicts. C34

For the melt viscosity itself they return to the glass-science literature. Angell's critical values, a melt viscosity of at least 0.01–1 Pa·s for a good glass former, "appear to be good predictors" of glass-forming ability for these compounds: all class I-A melts lie below 0.01 Pa·s, all class II melts except tolazamide and all class III melts above it, and most class I-B melts above it. C29·C31 Why some crystals melt into a viscous liquid and others into a runny one, they argue, goes back to the melting point itself: since Tm is where liquid and crystal free energies are equal, compounds with lower melting points have either poor packing in the crystal or a high cohesive energy of the liquid relative to the lattice energy. C30 Their closing statement is that viscosity "is indeed one critical attribute governing the crystallization tendency" on cooling through the undercooled melt, and in the abstract "a critical parameter to fully understand crystallization tendency". C48

Why the usual predictors fail here

The paper's two negative results matter as much as the positive one. Tg/Tm fails because the undercooled range Tm − Tg says nothing about how fast the viscosity climbs across it: chlorpropamide, celecoxib and ketoconazole have nearly the same Tm − Tg but belong to three different classes and thicken at clearly different rates. C36·R3 Kinetic fragility fails for the opposite reason: every compound, good or poor glass former, has the same strongly non-Arrhenius curve on the Tg-scaled plot, so the strong/fragile scale, built to distinguish silica from molecular liquids, has no resolution within a set of organic drugs. The authors' own summary is that crystallization depends "not only on viscosity, but also on thermodynamic properties" and other factors, so a single kinetic index should not be expected to predict it. C42·C43·C44

What it suggests for formulation

The authors frame the work in terms of amorphous formulations, and specifically the cooling step after a melt extruder, where a drug that crystallizes readily from its own melt is a risk. C1·C3 Note by the AI writer (not discussed in the paper): read as a screen, the data suggest that a single rheometer reading at Tm is informative at the extremes: all nine melts below about 0.01 Pa·s crystallized during their viscosity runs, although three of them can be quenched to a glass, and for melts above that value the rise of viscosity over the first 30–40 °C of undercooling separated intermediate from slow crystallizers better than Tg/Tm or D did for this set. R1·R2·X8 Three cautions apply. The data are for neat drugs at one shear rate, whereas in melt extrusion a polymer raises the viscosity and the shear is much higher. The comparisons are not controlled for driving force, which the paper tabulated but did not use. And the result is a class-level association, not a calibrated threshold.

Limitations

Limitations stated by the authors. The authors are explicit that viscosity does not explain everything. Within class I-A they find "no direct correlation" between viscosity and crystallization, and within class II differences in viscosity "cannot be used to explain" the differences in crystallization tendency. C11·C16 The class I-B and class II averages are not significantly different, and the error bars reflect large variation within each class. C24 They do not expect an exact correlation, because the thermodynamic parameters vary between compounds. C34 The shear in the rheometer promotes heterogeneous nucleation, so crystallization temperatures under shear are higher than in DSC. C8 Class I-A could not be fitted to the VTF equation, and the fits for the other classes used only the part of each curve where the VTF form is expected to hold. P5·C38

The AI writer's own judgement (1): association, not mechanism. The central claim, that viscosity governs crystallization tendency, rests on a class-level association: class averages with wide spreads, one pair of classes that cannot be told apart, and a handful of hand-picked pairs. The step from viscosity to nucleation ("thus hindered the diffusion of molecules") was argued from theory; no nucleation or growth rate was measured. X15 The best-known pair, probucol against chlorpropamide, is not controlled for the thermodynamic term that the authors themselves put next to viscosity: probucol's ΔG_v at 298 K (−13.2 J/cm³) is half of chlorpropamide's (−26.4 J/cm³), so a smaller driving force could also lower its crystallization tendency. The ketoconazole–chlorpropamide pair, with similar ΔG_v (−29.0 against −26.4 J/cm³), is the cleaner comparison. X9

The AI writer's own judgement (2): how sharp the threshold is. The 0.01 Pa·s line separates class I-A from class III without exception, but three of the nine compounds below it still form glasses on quenching, bifonazole (10.07 × 10^-3 Pa·s) sits right at it, and class I-B compounds above it still crystallized in the rheometer. It is better read as a boundary between the two extreme classes than as a glass-forming criterion. The paper's own count ("31 compounds", 22 above the line) also does not match its tables (34 compounds, 25 above). X8·X3

The AI writer's own judgement (3): data quality. Each curve appears to be a single run, with replicates, equilibration times and the steady-state criterion unstated. X12 The classes and all Tg values come from the earlier DSC study, and Tg is an estimate for class I-A, so Tg/Tm, Tm − Tg and the Tg-scaled positions of class I-A rest on estimates. X13 The VTF fits cannot be re-derived: the truncation temperatures, η₀ and the fit quality are not reported, and the fitted T₀ values do not satisfy the paper's own Eq. 5. X14·X5 Figure 3 appears to leave ritonavir out of the class III average without saying so. X6 Several table entries are inconsistent: the dibucaine row repeats lidocaine's molecular weight, Tm and Tg; ritonavir's ΔG_v cannot be reproduced; and a few differences Tm − Tg and |T₀ − Tg| are off by 2 °C. X1·X2·X4 None of these changes the class-level picture, but they matter for anyone reusing individual values. The ketoconazole ratio of 36 is printed as "(36)", formatted like a reference to ref 36; the plot confirms it is a ratio. X16

Conclusion

This paper adds a kinetic property, the viscosity of the undercooled melt, to the group's earlier crystallization-tendency classification. Measured the same way for 34 drug-like compounds, the melt viscosity at Tm and its rise on cooling line up with crystallization class: the compounds that crystallize even on quenching all have melts below about 0.01 Pa·s that barely thicken before crystals appear, and the compounds that never crystallize are all more viscous and, on average, thicken fastest. R1·R9·R2 The same data show the limits of two popular predictors: Tg/Tm does not capture how fast viscosity climbs, and the VTF strength parameter is low (fragile) for every fitted compound, so it cannot tell good from poor glass formers. C36·C43·R12 Within a class viscosity does not rank compounds, and the authors expect no exact correlation because thermodynamics varies between compounds; the link from viscosity to nucleation remains an argument from theory. C11·C16·C34·X15