Crystallization tendency

How it was shown

Kestur and Taylor (2010) grew metastable form II felodipine from melt-quenched films about 30–50 µm thick between cover glasses: the films were nucleated over P2O5 at 40 °C, then the spherulites were grown on a hot stage at 70–110 °C, the slope of diameter against time giving the rate, in triplicate kestur2010a P2, P3, P4, R3. A second 2010 paper used the same two-step protocol on neat felodipine and PVP mixtures kestur2010b P2, P3. Kestur and Taylor (2011) applied it to bifonazole (18–100 °C) and nimesulide (18–80 °C), moving slow samples into ovens or coolers when growth was too slow for one microscopy session kestur2011 P2, P3. Trasi and co-workers (2014) then compared 31 chemically diverse drugs with one method: 3–5 mg of powder was melted between coverslips, quenched, seeded at the edge with the starting crystals so that the polymorph of interest grows, and the front was filmed on a hot stage from about 30 to 90 °C above Tg trasi2014a P1, A1. The highest rate of each drug, its MCV, was used to sort the drugs into fast (10 µm/s or more), intermediate (1–10) and slow (0.01–1 µm/s) growers trasi2014a P6, X2. No replicates or uncertainties are reported, and how the MCVs were obtained is not stated trasi2014a X17, X3. Trasi and Taylor (2014) measured seeded growth of stable and metastable nilutamide in triplicate at 30–100 °C trasi2014b P2, P3, R8. Lu and Taylor (2016) held vemurafenib glass at fixed temperatures from 120 to 270 °C on a hot stage and identified each growing crystal by Raman microscopy lu2016 P2, P4. Tian and co-workers (2017) measured three indomethacin polymorphs from 80 °C to near their melting points, with at least three samples per point tian2017 P3, P4.

What the data show

In the 31-drug set, plotted bulk rates covered about 4 × 10⁻⁵ to 100 µm/s, at T/Tg of about 1.03–1.36 and undercoolings of about 15–120 K trasi2014a R2. MCVs ran from 216 µm/s for nimesulide to 0.02 µm/s for clotrimazole, a ratio of about 10⁴ trasi2014a R1.a, R1.ae, X14. Thirteen drugs had MCVs of 20.6 µm/s or more, ten lay between 1.1 and 8.2 µm/s and eight between 0.02 and 0.86 µm/s trasi2014a R1. Compared at equal T/Tg, the fastest and slowest drugs differed by about four orders of magnitude, with griseofulvin fastest; compared at equal undercooling the spread was about five orders, with acetaminophen and pimozide fastest, so the rank order depends on the normalization trasi2014a R3, C7. Within single drugs the temperature dependence is steep kestur2011 C6; trasi2014b R8. Felodipine form II peaked near 105 °C at about 1.8 × 10⁻⁷ m/s and fell to about 3.5 × 10⁻⁹ m/s at 70 °C, about 51-fold, although the text speaks of 3 orders of magnitude kestur2010a R5.a, C10, X1. The second felodipine study placed the peak at 105 ± 5 °C with a fall of about 2 orders from 110 to 70 °C kestur2010b R7, C9. Bifonazole growth fell about 5.5 orders from 100 to 18 °C and nimesulide 5–6 orders from 80 to 18 °C kestur2011 R7, R9. Stable-form nilutamide grew at about 0.00015 µm/s at 30 °C and about 40 µm/s at 100 °C trasi2014b R8.a, R8.j. Vemurafenib α-needles peaked at about 106 µm/s at 250 °C and β reached about 110 µm/s at 230 °C, while γ, δ and α-brown feathers grew at about 4 µm/s or less lu2016 R12. The α maximum matches the preliminary 106 ± 4 µm/s quoted from the 2014 work lu2016 R25. Indomethacin γ had an MCV of 4.07 × 10⁻⁷ m/s, about an order of magnitude below α at 4.34 × 10⁻⁶ m/s tian2017 R7. (synthesis: where the same drug appears in two papers the values mostly agree: bifonazole at 100 °C, about 4.7 × 10⁻⁶ m/s or 4.7 µm/s kestur2011 R7, against an MCV of 4.0 µm/s trasi2014a R1.s; nimesulide at 80 °C, about 8.5 µm/s kestur2011 R9, against about 8.6 µm/s as the highest plotted bulk rate in 2014 but 216 µm/s as its MCV trasi2014a R5.f, R1.a, which supports the extractor's doubt about that MCV trasi2014a X3.)

Figure

The rates span about six decades on a log axis; compare panel (a), against T/Tg, with panel (b), against undercooling, to see the order of drugs change trasi2014a R2, R3. Blue symbols (class III glass formers) sit at both the top and the bottom of the plot, the point taken up in F15 trasi2014a R1.

Why

The authors place growth between two opposing factors: near Tm molecules are mobile but the driving force is small, and on cooling the driving force rises while mobility falls, so the rate passes through a maximum (see F2) trasi2014a C22. In Jackson's growth law, 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), mobility enters as 1/\eta, the bracket is the driving force and the last term the fraction of correctly oriented molecules trasi2014a E1, C31. They assume that the Stokes–Einstein relation holds in their temperature range, so that viscosity describes interfacial diffusion, and note that it fails close to Tg trasi2014a C20, C21. Differences in melt viscosity and melting entropy "could explain much" of the spread between drugs, while other factors "clearly play a role" (see F5 and F6) trasi2014a C38. The steep fall within one drug on cooling is the mobility side of the same balance: for nilutamide the authors read growth over the measured range as under kinetic rather than thermodynamic control ("appears") trasi2014b C6. A cited 1993 study had found a spread of about five decades in MCV among organic compounds trasi2014a R13. The formula behind the maximum is on the Jackson interface-kinetics growth rate page.

Conditions and limits

Neat drugs, seeded or nucleated growth in confined films above Tg, mostly 30–90 °C above Tg trasi2014a P1, A2. The 31-drug set has no replicates or error bars, the MCV derivation is not stated, and several MCVs lie far above (nimesulide, salicin, griseofulvin) or below (felodipine, indomethacin) the plotted rates trasi2014a X17, X3. The polymorph of the growing crystal is assumed from the seed, not checked trasi2014a C6. Felodipine was grown as form II in 2010 but seeded with its starting form in 2014, so the values are not directly comparable kestur2010a R3; trasi2014a P1. Bulk growth below Tg, surface growth (see F21) and growth in dispersions at formulation loadings were not part of the 31-drug comparison trasi2014a C35, C8.

Counterexamples and conflicts

None found in the library for the size of the spread. Surface growth near Tg ranks the drugs differently from bulk growth trasi2014a C8. The 216 µm/s MCV of nimesulide is not supported by the plotted bulk rates of the same paper or by the 2011 nimesulide data (see above) trasi2014a X3; kestur2011 R9.

Transfer check

Measure seeded growth of the polymorph of interest at three or more temperatures between Tg and Tm, confirm the form of the growing crystal by Raman or XRPD, and place the highest rate against the fast (10 µm/s or more), intermediate (1–10) and slow (0.01–1 µm/s) groups trasi2014a P6, X2, C6; lu2016 P4. Compare drugs on the same temperature scale, preferably T/Tg, because the order changes with the normalization trasi2014a C7. Report replicates, since the 2014 values carry no stated uncertainty trasi2014a X17.

History

Kestur measured in 2010 how steeply felodipine growth falls on cooling and in 2011 extended this to bifonazole and nimesulide over 18 °C to 100 °C kestur2010a R5; kestur2010b R7; kestur2011 R7, R9. Trasi in 2014 compared 31 drugs under one method and grouped them by MCV trasi2014a R1, C37. Lu in 2016 confirmed vemurafenib as a fast grower, matching the preliminary 2014 value lu2016 R12, R25. Tian in 2017 showed an order-of-magnitude difference between two polymorphs of one drug tian2017 R7.

How it was shown

Locating a maximum needs isothermal growth rates on both sides of it (synthesis: only the papers below measured on both sides or reported the position). Kestur and Taylor (2010) grew felodipine form II spherulites from films nucleated at 40 °C, at 70, 80, 90, 95, 100, 105 and 110 °C, in triplicate kestur2010a P4, R3. A second 2010 felodipine study used the same temperatures kestur2010b P3. Trasi and co-workers (2014) measured 31 drugs from about 30 to 90 °C above Tg, reported one MCV per drug, cited the 0.94 Tm rule and did not tabulate the temperature of each maximum trasi2014a P1, R1, E8, X4. Lu and Taylor (2016) measured vemurafenib growth isothermally at 17 temperatures from 120 to about 270 °C, close to the melting point of 271 °C, identifying each crystal type by Raman lu2016 A1, P2, P4, R19. Tian and co-workers (2017) measured the δ, α and γ polymorphs of indomethacin from 80 °C to close to each melting point in 5 or 10 °C steps, with at least three samples per point tian2017 P4. Sato and co-workers (2016) cited 0.94 Tm to place their measurement temperatures, all of which lay below the maximum sato2016 E2, C14.

What the data show

Vemurafenib α-needles grew at about 41, 60, 85, 98, 106 and 92 µm/s at 210, 220, 230, 240, 250 and 260 °C and at about 14 µm/s near 270 °C, a bell-shaped curve with its maximum at 250 °C lu2016 R12. Naito's rule gives 240 °C for α, 10 °C below the observed maximum lu2016 R24, C18. In kelvin the observed maximum is 0.96 Tm (synthesis: 523.15/544.15) lu2016 R12.o, R19.a. Indomethacin δ, α and γ each gave a bell-shaped curve, with maxima at 110, 135 and 135 °C against onset melting points of 400.15, 425.15 and 433.15 K; the authors write "approximately 0.95" of the melting temperature tian2017 R7, E3. The ratios are 0.96, 0.96 and 0.94 (synthesis: 383.15/400.15, 408.15/425.15, 408.15/433.15) tian2017 E3. Felodipine form II peaked near 105 °C and grew more slowly at 110 °C kestur2010a R5, C10; kestur2010b R7, C9. Against the 147 °C melting point of the stable form, that is 0.90 Tm (synthesis: 378.15/420.15) baird2010 M37, but the crystals that grew were metastable form II, whose own melting point is not given kestur2010a R3, X7. For the 31 drugs no maximum temperatures were reported; the extractor notes that the printed ΔG and ΔSm columns, read with \Delta G \approx \Delta S_m\,\Delta T, imply maxima between 0.90 and 0.99 Tm trasi2014a X4, E3. In nilutamide the stable form's growth was still rising at 100 °C, the highest temperature measured, against a melting point near 153 °C trasi2014b R8.j, M1.

Figure

Follow the purple α-needle series: it rises from 210 °C, peaks at 250 °C and drops steeply toward the melting point; the blue β series is faster below 230 °C but was not measured through a maximum lu2016 R12.

Why

The authors' explanation is the same in each paper: near Tm molecules are mobile but the driving force for crystallization is small, while on cooling the driving force rises, roughly in proportion to the undercooling, and mobility falls, so the product of the two passes through a maximum trasi2014a C22; lu2016 C17; tian2017 C22. Above the maximum growth is under thermodynamic control, below it under kinetic (viscosity) control trasi2014a C22; tian2017 C22. The authors call the bell shape "readily explained" but did not measure the mobility of the liquid lu2016 C17. Driving force and mobility are combined in growth laws of the form u = \frac{k}{\eta}\left[1 - \exp\left(-\frac{\Delta G}{RT}\right)\right], used in the felodipine studies kestur2010a E1. Normalizing growth for the driving force removed the maximum for indomethacin α, whose normalized rate kept rising up to 150 °C tian2017 R11. The 0.94 factor itself is an empirical observation cited from Naito, not derived in the library trasi2014a E8, X5. Trasi and co-workers use it to argue that a drug with a small Tm − Tg reaches its maximum closer to Tg and so in a more viscous liquid (see F5) trasi2014a C27. (synthesis: the four measured forms lie within 0.94–0.96 Tm and felodipine form II lower; a fixed ratio of this kind is consistent with growth curves that scale with Tm, but the five forms are too few to test the rule.) The relation is written out on the temperature of maximum crystal growth rate page.

Conditions and limits

Neat melts; maxima located on 5–10 °C temperature steps, so a ratio is uncertain by about ±0.01 (synthesis: half of a 5–10 K step divided by 400–550 K) tian2017 P4; lu2016 A1. The rule is cited, and the 31-drug MCVs come without the temperature at which they occurred trasi2014a X5, X4. Growth with polymers can move the maximum: with 3% polymer the felodipine maximum appeared at 110 °C instead of 105 °C, except with PVAc kestur2010a R5, C11. For vemurafenib, thermal stability was checked only for the 1 min melt-quench step at 285 °C lu2016 P1, R2.

Counterexamples and conflicts

The vemurafenib maximum lay 10 °C above the rule's prediction lu2016 R24, R12.o. The 0.90–0.99 range implied by the 2014 table rests on an unstated ΔG method trasi2014a X4.

Transfer check

Use 0.94 Tm (in kelvin) only to place the window of fastest growth, for example on the cooling path after melt extrusion, where slow cooling leaves the product in the undercooled range trasi2014a C34, E8. Measure growth on both sides of the predicted maximum before relying on it, and identify the polymorph, since polymorphs of one drug peak at different temperatures tian2017 R7; lu2016 R12.

History

The rule enters the library through the 2014 papers trasi2014a E8; trasi2014b C3. The felodipine maximum had been measured in 2010 kestur2010a R5; kestur2010b R7. Vemurafenib in 2016 and indomethacin polymorphs in 2017 gave maxima close to the rule lu2016 R24; tian2017 R7. Sato in 2016 used the rule to place measurement temperatures sato2016 C14.

How it was shown

Baird and co-workers (2010) proposed the framework for their DSC classes on a time–temperature–transformation diagram adapted from Angell: class I melts cross overlapping nucleation and growth curves and crystallize, class II melts form nuclei that cannot grow before the glass forms, and class III melts pass both curves too fast baird2010 C51, C52. The diagram is a schematic baird2010 X5. Trasi and Taylor (2012) tested the idea on acetaminophen trasi2012a C9. To find the nucleation zone, about 5 mg of melt in a pin-holed pan was cooled at 15 °C/min to successively lower end temperatures, held 1 min and reheated at 10 °C/min: the highest end temperature that gave a recrystallization exotherm on reheating marks the upper limit of the zone, and the end temperature below which the exotherm stops moving marks the lower limit trasi2012a P6. Growth rates were measured separately on a hot stage, and nuclei were counted on a hot stage after one cooling–reheating cycle (mean of 5) trasi2012a R6, P7. The same group applied the DSC zone search to flutamide in 2012 and to nilutamide in 2014, adding for nilutamide 30 min holds of open glass surfaces at −30 to 60 °C followed by 1 min at 65 °C to grow the nuclei for counting trasi2012b R10; trasi2014b P1, P7. Baird and co-workers (2013) inferred the overlap for 25 compounds from the asymmetry between critical cooling and reheating rates in a rapid calorimeter baird2013 C35, R9. Lu and Taylor (2016) inferred a separate nucleation zone for each vemurafenib polymorph from where each form appeared in isothermal crystallization, judging nucleation by eye lu2016 C42, C43, X8.

What the data show

Pure acetaminophen (Tg 24 °C) had a very narrow nucleation zone of 50–60 °C: it had to be cooled to 60 °C or lower to crystallize on reheating trasi2012a C22, R12; baird2010 M24. Its growth rate fell by nearly two orders of magnitude from 110 to 70 °C, so the nuclei formed at 50–60 °C can grow only once reheating reaches about 80 °C ("It is thus possible") trasi2012a R6, C38. The authors conclude that the separated-zone hypothesis "appears to be reasonable" for acetaminophen trasi2012a C39. Flutamide's nucleation zone lay between 10 and 40 °C, and its growth was measured at 40–70 °C, falling nearly two orders of magnitude from 70 to 40 °C trasi2012b R10, R3. Nilutamide crystallized on DSC reheating only after its melt had been cooled to −30 °C, around 60 °C below its Tg of 32 °C trasi2014b R5, M1. Its surface nuclei counts after 30 min holds were about 12.6 at −30 °C, 0.8–2.5 between −10 and 40 °C and about 6 at 50–60 °C, while its stable-form crystals grew at about 1.5 µm/s at 70 °C and about 40 µm/s at 100 °C trasi2014b R9, R8. The authors call this a "large separation" between the temperature ranges favouring nucleation and growth trasi2014b C36. In the rapid calorimeter, class II glasses needed reheating rates far above the cooling rates that formed them, which the authors read as little overlap between the curves; class I-A crystallized even at 1000 °C/min, read as strong overlap baird2013 R9, C35, C33. For vemurafenib the authors place the α nucleation zone at "approximately" 170–270 °C because α never appeared at 165 °C or below ("it appears") lu2016 C43, R10.a. Indomethacin polymorphs likewise nucleated preferentially at different temperatures: δ fastest at 60 °C, α favoured at 80 °C, γ not readily tian2017 R1.

Figure

Nucleation rate J (dark) and growth rate U (hatched) are drawn between Tg and Tm: overlapping curves for class I, separated curves for class II, small or widely separated curves for class III; it is a schematic, not data trasi2012a C7.

Panel (b), for acetaminophen with 10% PVPVA, shows the method: no exotherm on reheating after cooling to 70 °C, a recrystallization peak that moves down as the cooling end point is lowered to 30 °C, and no further change below that trasi2012a R11.

Why

Classical crystallization theory gives both rates a maximum between Tg and Tm, nucleation being favoured at larger undercooling and growth closer to the melting point trasi2012a C35; trasi2014b C3. The nucleation maximum arises because the driving force rises and the mobility falls on cooling; near Tg, viscosity "can restrict" diffusion baird2010 C49; trasi2012a C48. To avoid any nucleus, the melt must pass the temperature of shortest nucleation time quickly, R_{Ncrit} \sim \frac{1}{\tau_{Nmin}} with \tau_N = \frac{1}{J_N V}, and nucleation is faster and on a shorter length scale than growth, so the rate that avoids nuclei exceeds the rate that avoids detectable crystals baird2010 E21, E22, C50. In the authors' reading, a melt forms a glass easily when the cooling path crosses the growth window while few nuclei exist and forms nuclei only where growth is slow baird2013 C36. Ready glass formation could therefore come from a low nucleation rate, a low growth rate, both, or poor overlap of the two windows, which a cooling–reheating test alone cannot tell apart trasi2014a C13, C2. For nilutamide the authors attribute the separation to slow nucleation of the stable form, which they link "may be due to" a scarce high-energy conformer in the liquid; conformer populations were not measured (see F7) trasi2014b C51, X15. Each polymorph of a compound may have its own nucleation profile, as for indomethacin γ and α ("it is possible") trasi2014b C38, R32. (synthesis: in all three measured drugs the nucleation window lies at lower temperatures than the range of fast growth, as the class II and class III schemes assume; zones were measured only for drugs that form glasses, because class I melts crystallize before the zones can be separated.) The argument is written out on the critical cooling rate to avoid nucleation and classical nucleation barrier pages.

Conditions and limits

Zones were measured for three neat drugs, from DSC and hot-stage protocols with holds of 1–30 min trasi2012a P6; trasi2012b R10; trasi2014b P1, P7. In the acetaminophen protocols the nucleation zone is passed both on cooling and on reheating, so nuclei from the two steps were not separated trasi2012a X9. Nilutamide nuclei counts are counts per sample from an open surface after 30 min, not rates, and the polymorph of the counted nuclei was not identified trasi2014b X7, X6. Vemurafenib nucleation was judged by eye lu2016 X8. Polymer effects on the zones are a separate topic (acetaminophen's zone broadened with polymers) trasi2012a C22.

Counterexamples and conflicts

None found in the library against separated windows where both were measured. Acetaminophen and flutamide nucleate above Tg, nilutamide mainly far below it, so the separation can lie on either side of Tg (see F4) trasi2014b C37.

Transfer check

Locate the nucleation zone by cooling the melt to successively lower end points and reheating, extending the end points well below Tg, and measure growth separately on seeded films trasi2012a P6; trasi2014b P1, R5. Well separated windows predict glass formation on cooling but not stability on reheating or in storage, because nuclei formed on the way down can grow later (see F15, F16) baird2010 C55; trasi2012a C41.

History

Separated zones were proposed for class II by Baird in 2010 baird2010 C51. Trasi in 2012 tested the idea on acetaminophen and found it reasonable, and measured the flutamide zone trasi2012a C9, C39; trasi2012b R10. Baird in 2013 inferred little overlap for many compounds from the cooling–heating asymmetry baird2013 C35. Trasi in 2014 found an extreme separation in nilutamide and pointed out that the classes cannot separate nucleation from growth trasi2014b C36; trasi2014a C2. Lu in 2016 and Tian in 2017 applied the idea to individual polymorphs lu2016 C42; tian2017 R1.

How it was shown

Trasi and Taylor (2014) asked why nilutamide, a small drug with a single rotatable bond, forms a glass so readily, and at which temperatures and into which forms its liquid or glass nucleates trasi2014b M1, A1. In a DSC screen, about 5 mg in a pin-holed hermetic pan was heated to 160 °C, cooled at 15 °C/min to a chosen end temperature, held 1 min and reheated at 10 °C/min; the end temperature was lowered run by run until crystallization appeared on reheating trasi2014b P1. For nucleation counts, about 3 mg was melted and cooled between a slide and a coverslip, the coverslip was removed to expose the surface (where nucleation is much faster than in the bulk), the glass was held 30 min at a temperature between −30 and 60 °C, then 1 min at 65 °C to grow the nuclei to visible size, and the nuclei were counted (mean of 5) trasi2014b P7, R1. To identify what nucleates, about 50 DSC runs per temperature were held 30 min at −30 or 60 °C and reheated at 10 °C/min, and the product was identified by Raman trasi2014b P8. Growth rates of the stable form and of the new form I were measured on seeded films at 30–100 °C trasi2014b P2, P3. Comparison data came from the same group's earlier zone measurements on acetaminophen and flutamide trasi2012a C22; trasi2012b R10.

What the data show

In the DSC screen only the run cooled to −30 °C showed an exotherm on reheating (onset about 88 °C, peaks about 97 and 104 °C), followed by melting at 141 °C, the melting point of a polymorph different from the starting material trasi2014b R5, R6. A run cooled only to 0 °C gave a glass that did not crystallize on reheating up to melting trasi2014b R2. The surface counts traced a U shape: about 12.6 nuclei at −30 °C, 2.3 at −20 °C, 0.8–2.5 between −10 and 40 °C, and about 5.8 and 6.0 at 50 and 60 °C; above 60 °C the film flowed trasi2014b R9. The DSC holds agreed: at −30 °C, 88% of runs gave form I, 2% form II, 5% the stable form and 5% no crystallization, while at 60 °C 94% did not crystallize and the rest gave the stable form trasi2014b R16. The 5% stable-form outcomes at −30 °C came from samples that had already nucleated and partly crystallized during cooling, at about 100–115 °C trasi2014b R16. Form I melts at 141 °C with about 66 J/g, against about 153 °C and 98 J/g for the stable form, and is about 3.4 kJ/mol less stable at 25 °C trasi2014b R6, M1, R7. Samples kept a few hours at room temperature nucleated both metastable and stable forms trasi2014b R17. The authors read the counts as two nucleation zones, a strong one far below Tg and a weaker one beginning about 30 °C above Tg, "likely" belonging to form I and the stable form trasi2014b C41. In contrast, acetaminophen (Tg 24 °C) nucleated at 50–60 °C and flutamide (Tg 271 K) between 10 and 40 °C, both above Tg trasi2012a C22; baird2010 M24; trasi2012b R10; trasi2014a M2. The paper cites two indomethacin results: glass stored 55 °C below Tg gave a small melting endotherm on reheating, while the nucleation maxima of its γ and α forms lie at about Tg and about 20 °C higher; a metastable ibuprofen form nucleates when held around 60 °C below Tg trasi2014b R34, R32, R33.

Figure

Read the blue series (nilutamide): many nuclei at −30 °C, few from −20 to 40 °C and a smaller rise at 50–60 °C; the values are counts per sample after a 30 min hold and 1 min at 65 °C, not nucleation rates trasi2014b R9, X7.

Only the last run, cooled to −30 °C, shows a crystallization exotherm on reheating, followed by melting of form I trasi2014b R5.

Why

The usual expectation is that the low molecular mobility of a glass protects it, and storage about 50 °C below Tg has been proposed as a good way to prevent crystallization trasi2014b C2, C4. The authors' reading is that nilutamide has two nucleation zones, one per polymorph, as each polymorph may have its own nucleation profile ("it is possible") trasi2014b C38, C41. They name three possible causes for favoured nucleation of the metastable form at low temperature: cracks and mechanical stress formed on cooling (postulated for ibuprofen), control of nucleation far below Tg by β-relaxation rather than viscosity (Oguni), and different conformers or tautomers in the liquid trasi2014b C45, C43, C46. Only the tautomer idea was tested, and a 1H–15N correlation showing the NH intact in form I ruled it out trasi2014b C48, R26. They favour the conformer route: the stable crystal holds a higher-energy conformer (rings at 54.4°) that "would be expected" to become scarcer in the liquid on cooling, so the stable form nucleates slowly and form I, assumed to hold a lower-energy conformer, nucleates at low temperature ("may be due to") trasi2014b C51, C34, C55. Conformer populations in the liquid were not measured at any temperature, and the explanation is one of several untested ones trasi2014b X15. They also reject Ostwald's rule of stages as the source of the stable-form nuclei above Tg, because form I needs about 24 h to convert at 70 °C, far longer than the growth step ("somewhat unlikely") trasi2014b C44, R23. (synthesis: whatever the cause, the nilutamide data show that the minimum of nucleation counts lay between −20 and 40 °C, that is from about 50 °C below to 10 °C above Tg, so the "50 °C below Tg" rule sits at the edge of the deep-cold nucleation zone for this drug trasi2014b R9, M1, C4.) For ASDs, Moseson and Taylor 2023 (p. 6) give the same rule as a rule of thumb for a stability period of years and note reported ASDs with long-term physical stability under much less stringent conditions.

Conditions and limits

One neat drug; 30 min holds; counts per sample without a stated area, from an open surface, compared with sealed DSC pans trasi2014b X7. The low counts between −20 and 40 °C hold for the 30 min time scale only, since longer room-temperature storage nucleated both forms trasi2014b X16, R17. The polymorph of the counted nuclei was not identified trasi2014b X6. Only two polymers at low levels were studied, and the effect of PVP on nucleation could not be measured trasi2014b C22. No amorphous solid dispersion at a formulation drug loading was tested trasi2014b A4.

Counterexamples and conflicts

Acetaminophen and flutamide nucleate above Tg trasi2012a C22; trasi2012b R10. The nucleation maxima of two indomethacin polymorphs lie at or above Tg trasi2014b R32. With 10% molar PAA the nilutamide count at −20 °C was about 9.0 against 2.3, so the polymer effect on nucleation is unresolved rather than absent trasi2014b X5, R9.

Transfer check

Before cold storage, freeze-drying, cryomilling or cold shipment of an amorphous drug, hold glass samples at the lowest temperature they will meet, then reheat or warm them, and identify any crystals by polymorph (synthesis: the nilutamide DSC-hold protocol applied to a process question) trasi2014b P8. Use holds longer than 30 min where the product will spend days or months in the cold, because the 2014 counts cover 30 min only trasi2014b X16. A drug inside the evidence is a small glass-former that nucleates slowly above Tg; a drug that nucleates readily above Tg, like flutamide, falls outside it trasi2014b C37.

History

The rule of storing about 50 °C below Tg is cited in the library trasi2014b C4. Trasi and Taylor in 2014 reported nilutamide as a counterexample, nucleating a previously unreported metastable polymorph far below Tg, and placed it beside earlier indomethacin and ibuprofen reports trasi2014b C10, C13, R33, R34. No later library paper revisited the question.

How it was shown

Baird and co-workers (2012) asked whether the viscosity of a drug's undercooled melt, at Tm and in its rise on cooling, follows its crystallization class baird2012 A1. They measured 34 of the 51 compounds of the 2010 DSC screen (6 class I-A, 5 I-B, 7 II, 16 III) in an Anton Paar MCR 301 rheometer with 25 mm parallel plates and a 0.4 mm gap baird2012 A1, P1. About 0.5 g of powder was melted at 10 °C above Tm, cooled rapidly to Tm and sheared at 30 s⁻¹; before each lower temperature, in 5 °C steps, the sample was remelted at Tm + 10 °C for 5 min to remove nuclei, and a run ended when viscosity rose with time at constant temperature, the sign of crystallization baird2012 P1. Replicates and equilibration times are not stated baird2012 X12. Viscosity at Tm (ηmelt), the ratio \eta/\eta_{melt} and class averages over 0–20 °C of undercooling were compared baird2012 P3, P4, E7. Trasi and co-workers (2014) took the viscosities of 17 of their 31 drugs from the 2012 study, grouped the drugs by maximum growth velocity, and expressed each group's mean property as a deviation from the overall mean in standard deviations trasi2014a P7, P6, E5. For nine drugs with viscosity–temperature data they divided the growth rate by the driving-force factor, U_{kin} = \frac{U}{1 - e^{-\Delta G/RT}} with \Delta G \approx \Delta S_m\,\Delta T, and plotted it against viscosity trasi2014a E2, E3, P8.

What the data show

Melt viscosities spanned almost three orders of magnitude baird2012 R1. Class I-A ran from 2.86 × 10⁻³ (benzamide) to 8.62 × 10⁻³ Pa·s (haloperidol), class III from 13.34 × 10⁻³ (ibuprofen) to 1.99 Pa·s (ritonavir) baird2012 R1. Taking 10⁻² Pa·s as a benchmark, no class I-A compound lay above it and every class III compound did baird2012 C22. Classes I-B and II were mostly above it, with antipyrin, 4-biphenylcarboxaldehyde (I-B) and tolazamide (II) below baird2012 R11, C22. By the tables, 9 of 34 compounds are below 0.01 Pa·s and 3 of these form glasses on quenching baird2012 X3, R11. Class-average viscosity at Tm was about 0.005, 0.032, 0.040 and 0.11 Pa·s for classes I-A, I-B, II and III, and over 20 °C of undercooling it rose about 2.0-, 2.4-, 2.7- and 4.7-fold baird2012 R8, R9. The difference between classes I-B and II was "small and not statistically significant" baird2012 R10, C24. At 40 °C of undercooling, five class III compounds had risen 35- to 87-fold (felodipine 71, ketoprofen 61, loratadine 87, probucol 82, procaine 35), against about 29 for dibucaine, the highest in class II, and about 10 for chlorpropamide (I-B) baird2012 R3, C25. Within classes the ranking failed: benzamide, the least viscous class I-A melt, undercooled further than 4-biphenylmethanol before crystallizing, and tolazamide (6.61 × 10⁻³ Pa·s) reached about 105 °C of undercooling while the more viscous celecoxib (51.30 × 10⁻³ Pa·s) crystallized at about 45 °C baird2012 R4, R2, R1, C11, C16. In the growth data, the slow group lay about +0.95 standard deviations above average in viscosity and −0.99 in Tm − Tg, the fast group −0.73 and +0.49 trasi2014a R8. Across 17 drugs, viscosity at Tm followed \eta = -0.0028\,(T_m - T_g) + 0.3989 Pa·s with R² 0.7368 trasi2014a R9, E6. Bifonazole, aceclofenac and tolazamide grow at intermediate rates although their melt viscosities (0.0101, 0.0143 and 0.0066 Pa·s) and Tm − Tg (134, 143 and 154) sit with the fast growers trasi2014a R9, M16, M17, M19. Corrected for driving force, near \log \eta \approx 1 nilutamide grew at about 20 µm/s and miconazole at about 0.019 µm/s, two sets about 2–3 orders apart trasi2014a R10, C30.

Figure

Panel (a) keeps the order class III above II above I-B above I-A at every step from 0 to 20 °C, and panel (b) shows class III rising fastest; the bars are the spread between compounds of a class, not measurement error baird2012 R8, R9.

Each drug falls steeply as its melt becomes more viscous, but nilutamide, nimesulide and felodipine lie 2–3 decades above the other six at the same viscosity trasi2014a R10.

Why

In classical nucleation theory the nucleation rate falls exponentially with the sum of a thermodynamic barrier and the activation free energy for viscous flow, I_{SS} = I_0 \exp\left[-\frac{W^* + \Delta G_\eta}{k_B T}\right], and screw-dislocation growth is inversely proportional to viscosity baird2012 E1, E3, C4. The authors therefore expect a faster viscosity rise to lower the nucleation rate "all other factors being equal", and read the probucol–chlorpropamide pair as a faster rise that "thus hindered" diffusion of molecules to form nuclei baird2012 C32, C33. For class I-A they read crystallization near Tm as "primarily under thermodynamic control", mobility being high and the driving force small baird2012 C9. Angell's critical melt viscosity of 0.01–1 Pa·s for a good glass former is cited, and the authors find it a "good predictor" for these compounds baird2012 C29, C31. For growth, Trasi and co-workers argue that if all melts had the same viscosity at Tg, a drug with high viscosity at Tm and a short range to Tg would be more viscous at its MCV temperature, near 0.94 Tm, and so grow more slowly ("This makes sense") trasi2014a C27. The three intermediate growers with fluid melts are "most likely" more fragile, and tolazamide "could be" slowed by its structure; neither was measured trasi2014a C29, X18. Nucleation and growth rates, through which viscosity is argued to act, were not measured in the 2012 study baird2012 X15. Competing explanations are in the library: the probucol–chlorpropamide comparison is not controlled for driving force, since probucol's Hoffman ΔGv at 298 K is −13.2 against −26.4 J/cm³ baird2012 X9. Melting entropy accounts for part of the spread left at equal viscosity (see F6) trasi2014a C32. The authors conclude that viscosity is "indeed one critical attribute", while an exact correlation "is not to be expected in all cases" baird2012 C48, C34. The fitted relation is on the linear fit of melt viscosity on Tm − Tg page and the temperature dependence of viscosity on the Vogel-Tammann-Fulcher equation page.

Conditions and limits

Neat melts at one shear rate, with single runs of unstated reproducibility; classes and Tg values come from unsheared DSC, and Tg is estimated for all class I-A compounds baird2012 X12, X13. Shear raised class I-A crystallization temperatures above the DSC values baird2012 R5, C8. The class III average at Tm leaves out ritonavir without saying so baird2012 X6. The 2014 viscosity bars rest on 17 drugs, only 5 of the 13 fast growers trasi2014a X9. Diffusion to nuclei or crystal faces was not measured baird2012 X15.

Counterexamples and conflicts

Antipyrin, 4-biphenylcarboxaldehyde and tolazamide lie below 0.01 Pa·s yet form glasses, and bifonazole sits at the threshold baird2012 X8. Bifonazole, aceclofenac and tolazamide grow at intermediate rates although their melt viscosities are as low as those of fast growers trasi2014a R9, C29. At similar viscosity, growth corrected for driving force differs by 2–3 orders of magnitude, and the upper set includes felodipine, a slow grower by MCV trasi2014a C30, X15.

Transfer check

Measure the viscosity at Tm and its rise over the first 20–40 °C of undercooling in a parallel-plate rheometer, remelting between steps baird2012 P1. A melt below about 0.01 Pa·s at Tm flags rapid crystallization on cooling, and one above it whose viscosity rises 35-fold or more over 40 °C resembles the class III compounds compared in 2012 (synthesis: the named class III values were 35–87, against at most about 29 in class II) baird2012 C46, R3, C25. Confirm by DSC, and compare the driving force before concluding from viscosity alone baird2012 X9. Tm − Tg from one DSC run is a cheap proxy at class level only trasi2014a R9, C26.

History

Angell's critical melt viscosity of 0.01–1 Pa·s is cited baird2012 C29. Baird in 2012 first measured melt viscosities against crystallization class in the library baird2012 R1. Trasi in 2014 linked the same viscosities and Tm − Tg to growth rates and showed the residual spread trasi2014a R9, R10.

How it was shown

The driving force for crystallization of an amorphous drug is the free energy difference between the supercooled liquid and the crystal, estimated in the library almost always with the Hoffman equation, \Delta G_v = -\frac{\Delta H_{fus}\,(T_m - T)\,T}{T_m^2}, from DSC melting data baird2010 E25; vaneerdenbrugh2010a E2. Marsac and co-workers (2006) compared amorphous nifedipine and felodipine, two dihydropyridines of nearly equal Tg (45.5 and 46.4 °C midpoint), measuring nucleation in films at 22 °C and 0% RH and the free energy difference by modulated DSC from 0 to 100 °C marsac2006a R4, R1, R11. Baird and co-workers (2010) and Van Eerdenbrugh and co-workers (2010) included ΔHfus, ΔSfus and ΔGv at 293.15 K, all per unit volume, among seven descriptors in principal component analyses of 51 and 40 compounds, and reported each class's mean as a deviation from the overall mean in standard deviations baird2010 P8, R22; vaneerdenbrugh2010a P11, R20. Trasi and co-workers (2014) tested melting entropy against growth: for nine drugs they divided the growth rate by the driving-force factor (\Delta G \approx \Delta S_m\,\Delta T) and by \tau_\alpha/a, with \tau_\alpha = \frac{C\eta}{G}, to remove viscosity, and plotted the result against ΔSm/R trasi2014a E2, E3, E4, R11. Lu and Taylor (2016) computed Hoffman free energies for vemurafenib α and β from their melting data lu2016 P7, E1.

What the data show

Nifedipine nucleated faster than felodipine at 22 °C (0.39 against 0.17 × 10¹⁰ nuclei per m³ per day) and crystallized on heating at 87 °C, while felodipine did not crystallize on heating marsac2006a R4.a, R1, R5. Nifedipine's free energy difference was larger at every temperature (about −30 against −18 J/g at 0 °C; 9.6 against 6.2 kJ/mol at 25 °C by MDSC), and MDSC agreed well with the Hoffman estimate (8.8 and 6.2 kJ/mol) marsac2006a R11, R4.k, R4.l, C14. Nifedipine also had the larger heat (39.9 against 30.8 kJ/mol) and entropy of fusion (89.6 against 74.4 J/mol/K), so its larger driving force is enthalpic and in spite of a larger entropy loss marsac2006a R4.g, R4.h, C15. In the 2010 melt classes, class I averaged about +0.45 SD in ΔHfus, +0.41 in ΔSfus and −0.40 in ΔGv, class III about −0.63, −0.59 and +0.57 baird2010 R22. In the 2010 solvent classes, the ΔGv contributions were about −0.29, +0.29 and +0.13 for classes I, II and III, so class II, not class III, had the smallest driving force vaneerdenbrugh2010a R20, X10. For growth, \log(U_{kin}\,\tau_\alpha/a) fell with ΔSm/R as y = -0.6\,x - 0.95 (R² 0.61), from about −5.1 for nilutamide at ΔSm/R ≈ 8.7 to about −8.2 for miconazole at ≈10.9 trasi2014a R11, E7. The fast-growth group had a lower melting entropy than average (about −0.38 SD) and the slow group a higher one (about +0.30) trasi2014a R8.f. In 2012, probucol and chlorpropamide, compared for their viscosity rise, differed twofold in ΔGv at 298 K (−13.2 against −26.4 J/cm³) baird2012 X9. For vemurafenib, α had the larger Hoffman driving force at every temperature (about −11.0 against −6.3 kJ/mol near 115 °C), yet metastable β dominated crystallization between 120 and 190 °C lu2016 R22, C51, C52.

Figure

The nifedipine points (circles) lie below the felodipine points (triangles) at every temperature, and the Hoffman lines run close to the MDSC points, which is why the Hoffman estimate is used as the driving force elsewhere in the library marsac2006a R11, C14.

A falling trend with considerable scatter (R² 0.61); drugs at similar ΔSm/R still differ by more than a decade trasi2014a R11, C32.

Why

The authors' nucleation argument uses the classical barrier W^* = \frac{16\pi\gamma^3}{3\,\Delta G_v^2}: a more negative ΔGv "would result", for a similar interfacial energy γ, in a lower barrier and faster homogeneous nucleation baird2010 E24, C61. Van Eerdenbrugh and co-workers call the class correlation "consistent with theory" and infer ("suggests") that differences in γ between compounds are small compared with those in ΔGv; γ was not measured and is "difficult to either measure or estimate" vaneerdenbrugh2010a C39. Baird and co-workers add that lower ΔHfus and ΔSfus imply, for equal ΔCp, a smaller driving force at lower temperature, and that a higher melting point means more energy to disrupt the lattice baird2010 C60, C62, E23. For growth, the Jackson factor \exp(-\Delta S/k_B) represents the fraction of molecules with the right orientation to join the crystal, so a larger melting entropy means slower growth at equal mobility and driving force; entropy "certainly plays a role", but other factors, "could include" interactions in the melt and at the interface trasi2014a C31, C32. Marsac and co-workers cite the same orientation view of the entropy of crystallization, but note that it would predict felodipine to crystallize more easily, which it did not; for that pair the enthalpy dominates marsac2006a C34, C35. (synthesis: the two screens express ΔHfus and ΔSfus per volume and find the rapid crystallizers high in both, while the 2014 growth analysis uses ΔSm per mole and finds the fast growers low in it; the opposite signs come from different bases and read-outs, and show that melting entropy is not a dependable single predictor baird2010 R22; trasi2014a R8.f.) The Hoffman estimate itself becomes less accurate at large undercooling, because it assumes a constant heat-capacity difference and a temperature close to Tm, and the screens evaluate it at 293.15 K for drugs melting up to 272 °C almeidaesousa2015 C8; mosqueragiraldo2015 C24; baird2010 P8, M21. The formulas are on the Hoffman equation, classical nucleation barrier, entropy of fusion and linear fit of normalized growth rate on melting entropy pages.

Conditions and limits

ΔGv is a Hoffman estimate, not a measurement, except for the MDSC values of nifedipine and felodipine; interfacial energy, ΔCp(T) and nucleation rates were not measured in the screens marsac2006a R11; baird2010 C60, C61; vaneerdenbrugh2010a C39. Per-compound descriptor values are not printed for the solvent classes, and the class bars are read from plots vaneerdenbrugh2010a R20. The entropy fit rests on nine drugs, with constants whose units are not given trasi2014a X11. Felodipine and nifedipine are not matched in mobility: felodipine's melt viscosity at Tm is about four times nifedipine's (synthesis: 154 against 36.2 × 10⁻³ Pa·s) baird2012 R1.u, R1.q.

Counterexamples and conflicts

Indomethacin has the larger driving force than felodipine yet crystallizes much more slowly during dissolution alonzo2010 C42. Vemurafenib β dominates although α has the larger driving force (see F7) lu2016 C52. ΔGv is least favourable for the intermediate, not the slow, solvent class vaneerdenbrugh2010a X10. A molecular dispersion in PVP lowers nifedipine's driving force less than the difference between nifedipine and felodipine, so the drug itself sets the larger part of the driving force marsac2006b C41.

Transfer check

Compute the Hoffman ΔGv at the storage or process temperature from DSC Tm and ΔHfus (per volume with the crystal density), and use it to compare drugs of otherwise similar viscosity and Tg, not as a stand-alone predictor baird2010 E25, P8; marsac2006a C15. Where the storage temperature lies far below Tm, check the estimate by MDSC as in the nifedipine–felodipine study marsac2006a C14; almeidaesousa2015 C8. For polymorphic drugs, do not expect the form with the larger driving force to appear first lu2016 C52.

History

Marsac in 2006 tied the faster crystallization of nifedipine to its larger, enthalpic driving force marsac2006a C15. Baird and Van Eerdenbrugh in 2010 found the same direction across many compounds baird2010 C40; vaneerdenbrugh2010a C38. Alonzo in 2010 recorded a pair where the driving force pointed the wrong way during dissolution alonzo2010 C42. Trasi in 2014 added melting entropy as an orientation factor for growth trasi2014a C31. Lu in 2016 showed a polymorphic case where the form with the smaller driving force dominates crystallization lu2016 C52.

How it was shown

Baird and co-workers (2010) identified the forms obtained after quenching class I melts in liquid N2 by Raman spectra taken in liquid N2 and, for the DSC runs, by the melting profile of the recrystallized material baird2010 P5, R3, R11. Kestur and Taylor (2013) measured the bulk growth rates of felodipine forms I and II over a range of temperatures, in triplicate kestur2013a R8. Trasi and Taylor (2014) held nilutamide melts for 30 min at −30 or 60 °C in about 50 DSC runs each and identified the product by Raman; they characterized the forms by XRPD, FTIR, Raman and 13C solid-state NMR and measured seeded growth of the stable form and form I at 30–100 °C in triplicate trasi2014b P8, P3, R15, R20, R25, R8. Conversion of form I to the stable form was followed by Raman at 70–90 °C trasi2014b P5, R23. Lu and Taylor (2016) crystallized vemurafenib glass isothermally at fixed temperatures from 120 to 270 °C on a hot stage, identified every crystal type in place by Raman microscopy with a 2.1 µm spot, ran PXRD on isothermal samples, and measured the growth rate of each form lu2016 P2, P4, P5, R12. They related α and β thermodynamically by the heat-of-fusion rule and the Hoffman equation lu2016 P7, E3, E1. Tian and co-workers (2017) stored amorphous indomethacin films at 60 and 80 °C to obtain δ and α, and seeded γ tian2017 R1, P3.

What the data show

Vemurafenib produced four polymorphs in six morphologies lu2016 R7, C41. At 120 °C only β and δ nucleated; at 170–190 °C β, γ and α diamond spherulites crystallized together; α needles appeared at 200 °C and took over above 210 °C; above 250 °C only α grew lu2016 R10, R11. β grew fastest up to 230 °C, from about 12 µm/s at 170 °C to about 110 µm/s at 230 °C, faster than α below that temperature lu2016 R12, C21. α melts at 271 °C with 114 J/g and β at 248 °C with 68 J/g, so by the heat-of-fusion rule the pair is monotropic, with α the stable form; the Hoffman curves give α the larger driving force at every temperature and a virtual transition at 319 °C lu2016 R19, C50, R22, C51. Metastable forms then converted toward α: γ to β above 200 °C, δ to β near 220 °C, and β to α slowly in the solid state, only where it touched α, and fast once β melted (DSC endotherm near 252 °C at 100 °C/min) lu2016 R15, R17, R13, C14, R21. Nilutamide held 30 min at −30 °C gave form I in 88% of runs, form II in 2% and the stable form in 5%, while holds at 60 °C gave the stable form when they crystallized at all trasi2014b R16. The stable form grew 3–4 times faster than form I at 70–100 °C (about 40 against 11 µm/s at 100 °C), while form I was faster at 60 °C and below (about 0.14 against 0.034 µm/s at 60 °C, about 0.005 against 0.00015 µm/s at 30 °C) trasi2014b R8, C12. Form I is monotropic to the stable form and about 3.4 kJ/mol less stable at 25 °C trasi2014b C11, R7. Felodipine shows the other pattern: stable form I grew 1–2 orders of magnitude faster than metastable form II over the whole range studied kestur2013a C4. Of the class I molecules of the 2010 screen, eight (4-biphenylmethanol, anthranilic acid, benzamide, caffeine, carbamazepine, chlorpropamide, haloperidol, tolbutamide) gave a different polymorph by Raman after quenching, and the authors call recrystallization to a metastable form from the undercooled melt "not unexpected" baird2010 R3, C16. Amorphous indomethacin nucleated δ fastest at 60 °C, favoured α at 80 °C and nucleated γ poorly tian2017 R1.

Figure

Read the bars against the Tg–Tm axis: δ grows only near Tg, γ in a narrow middle band, β over most of the range and α from about 170 °C to Tm; the arrows show the conversions δ to β, γ to β and β to α lu2016 R9.

The two curves cross between 60 and 70 °C: the stable form (blue) is faster at 70 °C and above, form I (red) at 60 °C and below trasi2014b R8, X3.

Why

Lu and Taylor explain the vemurafenib pattern by different nucleation and growth zones for each polymorph, whose overlap and magnitudes at the crystallization temperature set which forms appear ("This can be explained") lu2016 C42. In their reading, β is nucleation-limited above 150 °C but grows fast into large regions below 200 °C; γ "nucleates rapidly but grows slowly"; δ nucleates densely near Tg but grows extremely slowly and is engulfed by β; above 200 °C β nucleation becomes unfavourable and α predominates owing to "more favorable nucleation" lu2016 C46, C47, C48. Since β dominates although α has the larger driving force, "these observations indicate" that cold crystallization is controlled by factors other than the thermodynamic driving force, consistent with metastable forms being more probable at larger undercooling lu2016 C52, C53. Nucleation was judged from microscope impressions rather than measured, and γ and δ were never isolated pure lu2016 X8, X6. They cite Ostwald's rule of stages and Yu's point that a fast-nucleating, slow-growing form can be overtaken by a slow-nucleating, fast-growing one lu2016 C37. For nilutamide the authors propose, with "may be due to", that the stable crystal's higher-energy conformer (rings at 54.4°) becomes scarce in the cold liquid, so form I nucleates and grows faster at low temperature trasi2014b C51, C34. Conformer populations were not measured trasi2014b X15. They find Ostwald's rule "somewhat unlikely" as the source of the stable form above Tg, because form I converts too slowly at 70 °C (about 24 h) to be an unobserved intermediate step trasi2014b C44, R23. (synthesis: the four drugs give two patterns: in felodipine the stable form grows faster at all temperatures studied, while in nilutamide and vemurafenib a metastable form grows faster in the colder part of the range; which form appears then depends on where in the undercooled range the material spends its time kestur2013a C4; trasi2014b R8; lu2016 R12.) Monotropy is assigned with the heat-of-fusion rule on the Burger-Ramberger heat-of-fusion rule page, and the driving forces with the Hoffman equation.

Conditions and limits

Neat drugs in thin films lu2016 P1; trasi2014b P2. Vemurafenib growth rates come without a stated number of crystals, and temperature ranges for the same form differ by about 10 °C between figures and text lu2016 X9, X3. γ and δ rest on morphology and Raman only, without PXRD patterns, melting points or structures lu2016 X6. The structure of nilutamide form I was not solved trasi2014b R29. The 2010 polymorph calls disagree between two tables for five compounds baird2010 X2.

Counterexamples and conflicts

Close to Tm the stable form prevails: vemurafenib above 250 °C and nilutamide held at 60 °C lu2016 R10; trasi2014b R16. In felodipine the stable form grows faster at all temperatures studied, so no crossover occurs there kestur2013a C4. The 2016 conclusion orders γ and δ although the paper states their relationship could not be established lu2016 X7.

Transfer check

Identify crystals formed during processing or stability stress by Raman or XRPD before assuming the stable form; a metastable product can convert later, slowly in the solid state (vemurafenib β to α only at α contacts; nilutamide form I about 24 h at 70 °C) lu2016 C14; trasi2014b R23. Map growth rates of the known polymorphs at two or more temperatures in the range the product will meet, because the faster form can change with temperature trasi2014b R8. A minor form can be invisible by PXRD and visible by Raman microscopy, as γ vemurafenib was lu2016 C47.

History

Baird in 2010 noted metastable forms from undercooled melts baird2010 C16. Kestur in 2013 found the stable felodipine form faster at all temperatures kestur2013a C4. Trasi and Taylor in 2014 found a new nilutamide polymorph at low temperature and a growth crossover, reported as unusual trasi2014b C10, C12. Lu and Taylor in 2016 mapped four vemurafenib polymorphs against temperature lu2016 C41. Tian in 2017 saw temperature-dependent nucleation of indomethacin polymorphs tian2017 R1.

How it was shown

Towler and Taylor (2007) asked whether the hydrogen-bonding motifs that molecules form in solution, as seen by vibrational spectroscopy, foretell which polymorph crystallizes first towler2007 A1. They chose two polymorphic carboxylic acids whose forms differ in hydrogen bonding towler2007 A1. Indomethacin (99%) has a metastable α form, with three molecules in the asymmetric unit of which two form a carboxylic acid dimer and the third an acid–amide hydrogen bond, and a more stable γ form built only of cyclic acid dimers towler2007 M1. Anthranilic acid (≥98%) has form I with a zwitterion and a neutral molecule, metastable form II and high-temperature form III, both of acid dimers towler2007 M2. Indomethacin was dissolved in ethanol (a hydrogen-bond donor and acceptor; solubility 25 mg/mL at 25 °C) and nitromethane (acceptor only; 11 mg/mL) at concentrations up to a supersaturation c/c* of 5.5, with eight and six spectra shown but their concentrations not given towler2007 P1, M3, M4, E1. Anthranilic acid was dissolved in acetonitrile (150 and 52 mg/mL), DMSO (175), ethanol (200), toluene (25) and methanol (25 mg/mL; benzyl alcohol in the Fig. 5 caption), at levels that usually give form II, after heating with excess solid so that each solution was at least saturated at the crystallization temperature towler2007 P2, P3, X2. Raman spectra were recorded with a 785 nm laser at 150 mW (5 s integration, 10 scans) and ATR-IR spectra on a ZnSe accessory at 4 cm⁻¹ resolution with 64 scans; solvent subtraction is not stated towler2007 P4, P5. Solution bands were set against published solid-state assignments of α, γ and amorphous indomethacin from a 1997 library study and against reference spectra of the anthranilic acid forms towler2007 R3, P6. The polymorph crystallized first is stated for each system, but no crystallization procedure or identification method is described towler2007 P7, X5.

What the data show

For anthranilic acid, the Raman spectra in the five solvents differed from one another in band positions and intensities, with no common feature, yet form II was stated to crystallize from every solvent towler2007 R6, R19. The NH2 stretches proved the most useful bands to tell the forms apart: form III near 3495 and 3381 cm⁻¹, form II near 3474 and 3373, form I near 3324 and 3238 towler2007 R5, C12. In toluene the solution doublet sat at about 3497 and 3383 cm⁻¹, on the form III bands (about 3494 and 3380) and not on form II (about 3471 and 3370), at every concentration and temperature measured that leads to form II towler2007 R9. In acetonitrile a carbonyl band at 1670 cm⁻¹, a shoulder at 52 mg/mL and a distinct peak at 150 mg/mL, coincided with a band of solid form II and was assigned to the acid dimer; on the plot it reads near 1678 cm⁻¹ towler2007 R10, C18, X11. For indomethacin, dilute ethanol solutions gave one broad band near 1660 cm⁻¹, assigned to both carbonyls hydrogen bonded to solvent and as broad as the band of amorphous indomethacin towler2007 R12, C19. As concentration rose, a shoulder developed at 1711 cm⁻¹, the asymmetric stretch of an acid dimer, and the main band moved from 1660 to 1680 cm⁻¹ towler2007 R13, C20. In nitromethane, dilute solutions showed free benzoyl (1685) and acid (1740 cm⁻¹) carbonyls, and a dimer band at 1713 cm⁻¹ appeared with concentration towler2007 R15, C23. A band near 920 cm⁻¹, typical of acid dimers, grew with concentration in both solvents, and dimer bands were present in undersaturated as well as supersaturated solutions towler2007 R16, R17, C24. At supersaturations where α crystallizes, solid α showed Raman bands near 1688, 1679 and 1648 cm⁻¹, but neither the ethanol solution (one broad maximum near 1681) nor the nitromethane solution (maximum near 1682) had a band at 1650 cm⁻¹ towler2007 R18.

Figure

Look at the bottom trace: solid α has a strong band near 1648 cm⁻¹, which is missing from the ethanol and nitromethane solutions above it, although both give α towler2007 R18.

The broad solution doublet sits on the form III bands, not on those of form II, the form that crystallizes towler2007 R9.

Why

The authors' starting idea was that molecules must cluster before nuclei form, and that if the cluster motif matched a polymorph it could determine the outcome ("might") towler2007 C1, C2. In their interpretation, at low concentration the solute interacts mainly with the solvent ("appears"): in ethanol both indomethacin carbonyls are hydrogen bonded to solvent, and for anthranilic acid solute–solvent interactions "appear to dominate" the spectra in every solvent towler2007 C19, C25, C13. As concentration rises, solute–solute dimers form, and the 1660 → 1680 cm⁻¹ shift is linked to molecules gathering into solute-rich clusters that exclude solvent ("We can link") towler2007 C21, C25. In ethanol these clusters "appear" to become more γ-like, yet α crystallizes; the authors propose that the few carbonyls freed inside dimer clusters "seem" sufficient to provide a pathway to α, and that free amide carbonyls in nitromethane "might facilitate" α nucleation towler2007 C22, C28, C27. For anthranilic acid they conclude that solvent "seems" to act on crystal growth (form II morphology) but not on nucleation towler2007 C15. None of these steps was measured: cluster size and composition, the free-carbonyl population and nucleation rates were not determined towler2007 C21, C27, C28. The extractor notes two competing readings: the toluene band position, which did not change with concentration, fits solvated single molecules as well as clusters, and a bulk spectrum cannot exclude a minority population of α-like clusters towler2007 X9, X10. The ethanol "γ-like" reading is also loose, since the solution dimer band (1711–1712 cm⁻¹) lies nearer the amorphous (1710) than the γ position (1718) towler2007 X12. The authors cite competing pictures of the nucleus, including clusters without long-range order and a two-step route through a dense liquid that need not resemble the crystal towler2007 C4. (synthesis: the polymorphs obtained here are the ones the cited supersaturation and temperature rules predict, α above a supersaturation of 4 in ethanol and form II below 50 °C, so the outcome is explained by known conditions without any role for the solution motif towler2007 R1, R2, X5.)

Conditions and limits

Two carboxylic acids only, examined only under conditions that give their metastable forms (α; form II) towler2007 R19, A1. The concentrations, supersaturations and temperatures of the individual spectra are not printed, so which spectra are undersaturated cannot be checked towler2007 X6. Solvent subtraction is not stated, so part of the differences between the anthranilic acid Raman spectra may be solvent bands towler2007 X7. Bulk solution spectra, not time-resolved measurements during nucleation, were used towler2007 P4, P5, X10. Water gave no solute signal for anthranilic acid towler2007 R7, C11.

Counterexamples and conflicts

In acetonitrile the growing dimer band matched form II, the form crystallized towler2007 C18; however, form III contains the same dimer and no form III carbonyl spectrum is shown, so this match is evidence of dimers, not of form II specifically towler2007 X8. A cited earlier study matched dimers in some supersaturated tetrolic acid solutions to the dimers of the polymorph crystallized towler2007 C3. The authors note agreement with a cited 2006 study that solution motifs need not indicate the polymorph towler2007 C33. No other library paper revisited the question.

Transfer check

Do not choose a crystallization solvent for a target polymorph from solution IR or Raman spectra alone; in this study the forms obtained followed the known supersaturation and temperature rules (α above a supersaturation of 4 in ethanol, γ below about 3.5; anthranilic acid form II below 50 °C) towler2007 R1, R2, X5. If solution spectra are used, record the concentration and supersaturation of each spectrum, subtract the solvent, include conditions that give each polymorph, and identify the crystallized form on the same solutions by XRPD or Raman (synthesis: the gaps listed in X5–X7 turned into steps) towler2007 X5, X6, X7. A dimer band in a supersaturated solution of a carboxylic acid drug does not by itself indicate which form will appear, because dimers occur in α and γ alike and even below saturation towler2007 C26, R17.

History

Solid-state IR and Raman assignments of α, γ and amorphous indomethacin came from a 1997 library study of PVP–indomethacin dispersions towler2007 R3. A 2005 study cited in the paper had matched tetrolic acid dimers in solution to the crystallizing polymorph towler2007 C3. Towler and Taylor in 2007 tested the idea on two acids and found the relationship "generally" limited towler2007 C35; no later library paper revisited it.

How it was shown

Baird, Van Eerdenbrugh and Taylor (2010) asked whether a single DSC heat–cool–heat cycle can classify how easily an organic molecule forms a glass from its melt baird2010 A1. The test set was 51 neat drug-like molecules, described as randomly selected, with melting points from 59 to 272 °C and molecular weights from 121 to 721 g/mol baird2010 A1, M3, M21, M8, M51. Each sample was sealed in a hermetic pan in a TA Q2000 DSC under nitrogen, heated at 10 °C/min to about 10 °C above Tm, held 3 min, cooled at 20 °C/min to −75 °C and reheated at 10 °C/min to just above Tm, in triplicate baird2010 P1. Class I meant crystallization on cooling before the glass transition, class II no crystallization on cooling but crystallization on reheating above Tg, and class III crystallization on neither step baird2010 R1. For class I, 1–2 mg melts on glass slides were plunged into liquid N2 and examined for birefringence under crossed polarizers, and Raman spectra were taken with the sample still immersed so that the laser could not warm and crystallize it baird2010 P5, P6. Baird and co-workers (2013) re-tested eight class I-A and seven class I-B molecules in a prototype rapid heat/cool calorimeter on 30–50 µg single crystals, cooling at 100 and 500 °C/min and at the maximum rate obtainable, 687–1220 °C/min baird2013 P2, A1. Later papers ran the same heat–cool–heat cycle on new drugs, citing the 2010 scheme: six dihydropyridines, lumefantrine and artemether, delamanid, pretomanid and vemurafenib raina2015b R1; trasi2020 R5, R6; duong2022a R3; nguyen2023a C59; lu2016 R1.

What the data show

Of the 51 molecules, 23 were class I, 11 class II and 17 class III baird2010 R1. Four class I molecules (4-biphenyl carboxaldehyde, chlorpropamide, flufenamic acid, tolbutamide) crystallized both on cooling and on reheating, which the authors read as "an indication" that part of each sample had been trapped amorphous baird2010 R2, C9. After liquid-N2 quenching, 15 class I molecules were birefringent and 8 were not, and Raman peak broadening, the sign of amorphous material, appeared for the same 8 baird2010 R3. Quenched griseofulvin, for example, gave a broader carbonyl band reaching about 1725 cm⁻¹, against about 1706–1708 cm⁻¹ for the crystalline references, while benzocaine kept its starting crystal form baird2010 R6, R4. The class I-B glasses crystallized rapidly when reheated above Tg in the Raman experiments baird2010 R15, C24. In the rapid calorimeter all eight class I-A molecules still crystallized at their maximum rates of 800–1100 °C/min; faster cooling only moved the exotherm lower, for phenacetin from about 113 to 107 °C between 100 and 1026 °C/min baird2013 R1, R3, R2. Undercooling at 500 °C/min ranged from 15.1 °C (4-biphenylmethanol) to 90.8 °C (haloperidol) baird2013 R1, C10. The later applications reproduce the 2010 assignments where a compound recurs: felodipine class III and nifedipine class II in both 2010 and 2015, and lumefantrine class III in two papers baird2010 M37, M32; raina2015b C12; trasi2020 C7; hiew2022a R3. Vemurafenib melts crystallized on cooling from 248.9 °C, about 25 °C below Tm, which the authors read as a "relatively poor glass former" lu2016 R1, C5. Delamanid gave no glass at cooling rates up to 50 °C/min, and its liquid-N2 glass devitrified just above Tg, so it was placed in class I with pretomanid duong2022a R3, C44; nguyen2023a C59.

Figure

Compare the blue trace (quenched sample in liquid N2) with the black and dashed crystalline references: it overlaps for benzocaine (still crystalline, class I-A), shifts to about 1350 cm⁻¹ for anthranilic acid (a new polymorph) and broadens for griseofulvin (amorphous, class I-B) baird2010 R4, R5, R6.

Why

The authors read the classes on a time–temperature–transformation diagram, which they draw as a schematic, not from data baird2010 C51, X5. A glass forms only if the melt is cooled below Tg faster than crystallization can proceed; avoiding any nucleus needs roughly R_{Ncrit} \sim \frac{1}{\tau_{Nmin}}, where τNmin is the shortest nucleation time, which falls as the nucleation rate JN or the sample volume V rises (\tau_N = \frac{1}{J_N V}) baird2010 C49, E21, E22. Because nucleation is faster and acts on a shorter length scale than growth, the rate that avoids detectable crystals (Rcrit) is slower than RNcrit baird2010 C50. Class I molecules "clearly" have rapid nucleation and growth at overlapping temperatures, so 20 °C/min, and for many even liquid N2, is too slow baird2010 C52. Class II melts are cooled faster than Rcrit but slower than RNcrit and so, in the authors' reading, keep nuclei that grow on reheating ("most likely") baird2010 C51, C55. Class III melts are cooled faster than both, giving a nuclei-free glass, although "it is possible" that some nuclei form and grow very slowly baird2010 C51, C56. None of this was measured: nuclei were not detected, and nucleation and growth rates were not determined baird2010 C58, K8. The rapid-calorimetry results were read the same way, as strongly overlapping rate curves for class I-A ("indicate") and less overlap for classes I-B and II baird2013 C33, C35. A 2012 library paper restated the scheme as overlapping (class I), separated (class II) and widely separated or low-rate (class III) nucleation and growth zones trasi2012a C7. (synthesis: each class is a readout of where the screen's fixed cooling and heating rates fall relative to the drug's own nucleation and growth rates, so the class is a rate-specific kinetic property, not a material constant; see F10 baird2010 C51; trasi2012a C7.) The formula behind the argument is on the critical cooling rate to avoid nucleation page.

Conditions and limits

Neat crystalline drugs in hermetic pans at 20 °C/min cooling and 10 °C/min reheating; no polymer, solvent or humidity baird2010 P1, A1. The liquid-N2 cooling rate was not measured, so the I-A/I-B boundary is tied to that one method baird2010 C21. The starting crystal forms are not reported, and niclosamide is listed in the materials without a result baird2010 X11. The Tg values of 16 class I molecules are estimates from molecular weight baird2010 X17. DSC polymorph calls for five compounds differ between two tables baird2010 X2. Class membership near the boundaries depends on the scan rates (see F10) baird2010 X12.

Counterexamples and conflicts

Indoprofen is labelled class I-A in the storage test but class I-B by its own quench data baird2010 X3. Rapid calorimetry moved four class I-B molecules to borderline I-B/II and two class II molecules to borderline II/III baird2013 C13, C31. One later paper calls celecoxib a "slow crystallizer" on the authority of the 2010 scheme, whereas the 2010 paper places it in class II and another later paper lists it as class II mosqueragiraldo2014 R17; baird2010 M26; ilevbare2013c C24 (synthesis: a labelling conflict between papers, not a new measurement). The same molecule can fall in opposite classes by different routes: atenolol is melt class I but spin-coat class III, and dipyridamole is class I from the melt and class III on solvent evaporation vaneerdenbrugh2010a R17; hsieh2012 M5.

Transfer check

Run the cycle on the neat crystalline drug exactly as published: heat at 10 °C/min to about 10 °C above Tm, hold 3 min, cool at 20 °C/min well below Tg, reheat at 10 °C/min, in triplicate baird2010 P1. If it crystallizes on cooling, quench a 1–2 mg melt in liquid N2 and check for birefringence or broadened Raman bands to separate I-A from I-B baird2010 P5, P6. Report the class with the rates used, because the class can change with them trasi2012a C7. A drug inside the evidence is a small neat organic molecule that is thermally stable on melting; a drug that crystallizes even at the fastest cooling available should be treated as class I-A, for which the authors write that knowing Rcrit,cool exceeds 500 °C/min is "probably sufficient" to flag difficulty baird2013 C21.

History

Baird and co-workers introduced the screen in 2010 and offered it as "a useful tool" for early development baird2010 C8, C64. Van Eerdenbrugh and co-workers built a solvent-evaporation analogue the same year vaneerdenbrugh2010a R9. Baird refined the classes with melt viscosity in 2012 and with rapid calorimetry in 2013, which confirmed class I-A and split class I-B baird2012 P2; baird2013 C2, C13. Trasi in 2014 extended the scheme with crystal growth rates into classes IA to IV trasi2014a C17. From 2015 to 2023 the screen was used to classify new drugs and to choose model compounds raina2015b C12; trasi2020 C7; moseson2020 C5; nguyen2023a C59.

How it was shown

Because the 20 and 10 °C/min rates of the 2010 screen had been chosen arbitrarily, Baird and co-workers re-tested its classes at other rates baird2010 P4. Class II and III molecules were cooled at 1 °C/min; class II glasses were reheated at 20 °C/min, and class III glasses at 2 °C/min (triplicate) and 10 °C/min baird2010 P4. For the 23 class I molecules the undercooling at crystallization was measured at cooling rates of 5, 10, 15 and 20 °C/min baird2010 P2, R12. In 2013 the same group used a prototype rapid heat/cool calorimeter, calibrated at 10–1700 °C/min, on 30–50 µg crystals of 8 class I-A, 7 class I-B and 10 class II molecules baird2013 P2, A1. Class I-B molecules that did not crystallize at the fastest cooling were cooled at progressively slower rates to find the slowest rate that still gave a glass, the critical cooling rate Rcrit,cool baird2013 P2, R5. Class II glasses made by cooling at 20 °C/min were reheated at 10–200 °C/min in a conventional DSC or at up to about 2000 °C/min in the rapid calorimeter, and the slowest reheating that avoided crystallization was recorded as the critical heating rate Rcrit,heat baird2013 P1, P4. In a separate 2012 study the melts were also sheared at 30 s⁻¹ in a rheometer while cooled stepwise below Tm baird2012 P1.

What the data show

On 1 °C/min cooling, four class II molecules (celecoxib, dibucaine, flurbiprofen, nifedipine) crystallized partly or fully, and none of the 17 class III molecules did baird2010 R7. On 20 °C/min reheating, bifonazole and celecoxib did not recrystallize, while the other nine class II glasses did baird2010 R8. On 2 °C/min reheating, nilutamide and nimesulide (class III) crystallized, each in two of three runs, while the other 15 did not; none of the 17 crystallized at 10 °C/min baird2010 R9. Counted by compound, 7 of the 28 class II and III molecules behaved unlike their class in at least one test, although the authors call the assignments "robust and reasonably independent" of the rates baird2010 X12, C13. Class I crystallization temperatures scattered: at 20 °C/min undercooling ranged from 3.0 °C (caffeine) to 80.8 °C (tolbutamide), antipyrin undercooled by 80.1 °C and the thermally similar 4-biphenylmethanol by 10.1 °C, and for 4-phenylphenol the undercooling was 19.5, 28.4, 27.9 and 23.7 °C at 5, 10, 15 and 20 °C/min, not rising steadily with rate baird2010 R12, C15, X18. In the rapid calorimeter, antipyrin, chlorpropamide, flufenamic acid and tolbutamide (class I-B) did not crystallize at the maximum rate nor at progressively slower rates down to 25 °C/min, while 4-biphenylcarboxaldehyde (687 °C/min) and carbamazepine (1220 °C/min) still crystallized partly and indoprofen fully at the fastest cooling baird2013 R5, R9. Class II glasses needed Rcrit,heat of 12.5 (bifonazole), 15 (celecoxib), 35 (tolazamide), below 50 (D(−) salicin), 175 (droperidol), 300 (cinnarizine), 400 (clofoctol), above 500 (nifedipine), above 1000 (dibucaine) and above 1910 °C/min (acetaminophen), against Rcrit,cool of 5 °C/min or less for all of them baird2013 R9. After quench cooling, bifonazole and celecoxib needed less than 10 °C/min, below the 10 °C/min line that separates classes II and III baird2013 R9, C31. Benzamide and lidocaine crystallized erratically with cooling rate over 5–1004 and 5–839 °C/min as they had over 2–20 °C/min baird2013 R1, R8. Under shear in the rheometer, class I-A melts crystallized at "uniformly higher" temperatures than in DSC baird2012 R5.

Figure

Read down the second column, which is the critical heating rate after 20 °C/min cooling although its printed head says Rcrit,cool: within class II it runs from 12.5 to above 1910 °C/min, while the first column stays at 5 °C/min or below baird2013 R9, X4.

Why

The authors read the spread within class I-B as compounds that "may have" very different temperature dependencies of nucleation and growth baird2013 C15. For class II, which did not crystallize on slow cooling, they consider it "likely" that nucleation and growth do not overlap much in temperature, so that differences in Rcrit,heat "can be inferred" as differences in relative nucleation and growth rates spanning orders of magnitude baird2013 C23. Nucleation and growth rates were not measured as functions of temperature in either paper baird2013 C23; baird2010 C52. They attribute the scatter of crystallization temperatures "most likely" to the stochastic nature of nucleation and to unavoidable heterogeneous nucleation in the DSC pans baird2010 C19; baird2013 C18. The higher crystallization temperatures under shear are put down to heterogeneous nucleation at the upper rheometer plate baird2012 C8. (synthesis: each class boundary is a fixed rate, 20 °C/min on cooling and 10 °C/min on reheating, so any drug whose own critical rate lies near one of these values can move between classes with the protocol; the 2013 critical rates replace the three bins by a continuous measure baird2010 P1; baird2013 R9.)

Conditions and limits

Neat drugs in DSC pans; conventional DSC used 3–5 mg samples in triplicate, the rapid calorimeter 30–50 µg crystals with an unstated number of replicates baird2013 P1, P2, X9. Table 4 of the 2013 paper mixes values from two instruments without stating which gave each, and heating rates of 1900–2000 °C/min lie outside the calibrated range baird2013 X9, X10. The quench rate before reheating is printed for only three compounds baird2013 X5. The 2010 tests used 1 °C/min cooling but no 2 °C/min cooling, so the statement that classes II and III form glasses at 1–2 °C/min holds for class III and 7 of 11 class II molecules only baird2010 X13.

Counterexamples and conflicts

The extreme classes held: no class III molecule crystallized on cooling at 1 °C/min or reheating at 10 °C/min, and all eight class I-A molecules crystallized up to 800–1100 °C/min baird2010 R7, R9; baird2013 R1, R3. Rates above 1000 °C/min were reached for only four of the eight class I-A molecules, so "above 1000 °C/min" is a bound per compound baird2013 X6. The Table 4 value for clofoctol (400 °C/min) conflicts with the text, which names 500 °C/min as the rate that removes the endotherm baird2013 X14.

Transfer check

Test the neat drug at the cooling rate of the intended process (for example the cooling after melt extrusion) and reheat at the rates the product will meet, rather than relying on the 20/10 °C/min class baird2010 X12; trasi2012a C7. Treat a drug that changes behaviour between 1 and 20 °C/min cooling, or between 2 and 20 °C/min reheating, as borderline baird2010 R7, R8, R9. Where a fast-scanning calorimeter is available, measure Rcrit,cool and Rcrit,heat directly, because these spread over orders of magnitude within one class baird2013 C13, C22. Run replicates, since single crystallization temperatures can scatter by tens of degrees baird2010 R12.

History

Baird in 2010 found most assignments robust while recording the deviations baird2010 C13, R7, R8, R9. Trasi in 2012 stated that the class of a compound can be altered by the heating and cooling rates trasi2012a C7. Baird in 2013 measured the spread of critical rates within classes and proposed borderline classes I-B/II and II/III baird2013 C13, C22, C31.

How it was shown

The critical cooling rate Rcrit, the slowest cooling that avoids detectable crystallization, is the usual measure of glass-forming ability baird2010 C50, E2. Inorganic-glass science offers a shortcut: measure the undercooling \Delta T = T_m - T_{cryst,max} at several cooling rates, regress \ln(\text{rate}) on 1/\Delta T^2, and take Rcrit from the intercept A as R_{crit} = \exp(A) (Barandiaran–Colmenero, BC) or, with Cabral's correction, as R_{crit} = \exp\left(A^* - \frac{B^*}{T_m^2}\right) baird2010 E1, E2, E3. These methods had given reasonable values for inorganic glasses but had not been tested on organic molecules baird2010 C22, R31. Baird and co-workers (2010) applied both to the 23 class I molecules of their DSC screen, using undercooling at 5, 10, 15 and 20 °C/min; the four molecules that crystallized only partly on cooling were left out, leaving 19 fits baird2010 P2, P9, R13. Where crystallization was so fast that it heated the thermocouple, the peak temperature was estimated from the time to maximum heat flow baird2010 P2. The estimates were checked against the outcome of quenching 1–2 mg melts in liquid N2 baird2010 P6, R3. In 2013 the same group refitted eight class I-A molecules and indoprofen with undercooling measured from 5 °C/min (conventional DSC) to the maximum rate of a rapid heat/cool calorimeter, 800–1100 °C/min baird2013 P3, R1.

What the data show

Of the 19 fits in 2010, seven had r² 0.74–0.99 and twelve had r^2 < 0.55, because undercooling often did not rise steadily with cooling rate and crystallization temperatures scattered between runs baird2010 R13, C18. Where the fits worked, Rcrit ran from 20 K/min (haloperidol) to 3.28 × 10⁴ K/min by BC and 3.26 × 10⁴ K/min by Cabral (4-biphenylmethanol) baird2010 R13. The estimates contradicted the quench test: haloperidol (20 K/min) and phenacetin (64 K/min) still crystallized in liquid N2, whereas carbamazepine (118 K/min by BC, 117 by Cabral) and griseofulvin (588 and 579 K/min) were quenched amorphous, the reverse of the order the estimates predict baird2010 R13, R3, C21. The authors conclude that the approach "may be of limited utility" for organic molecules and that rates spanning several orders of magnitude "may be needed", noting that for inorganic glasses accurate predictions need cooling rates at least two orders of magnitude below Rcrit baird2010 C20, C22, R31. Over the wider 2013 range, the fits gave r² 0.89–0.99 for six compounds, with printed BC estimates of 8.1 × 10³ (4-biphenylmethanol), 3.2 × 10³ (atenolol), 6.2 × 10³ (benzocaine), 3.0 × 10³ (felbinac), 6.6 × 10³ (haloperidol) and 2.7 × 10³ K/min (phenacetin) baird2013 R7. Atenolol, benzocaine and felbinac, which had given r^2 < 0.55 over 2–20 °C/min, now gave r^2 \geq 0.93, so a wider range "seems to improve" the fits baird2013 R8, C20. Benzamide, lidocaine and indoprofen still failed (r^2 < 0.55), because their undercooling rose and fell with rate baird2013 R7, C16. Three printed values do not follow from their own inputs: haloperidol's intercept 6.5 gives \exp(6.5) \approx 6.6 \times 10^2 K/min, not 6.6 × 10³; the 4-biphenylmethanol intercept lacks a digit; and the felbinac fit cannot be reproduced baird2013 X2, X3, X13.

Figure

Each row gives the intercept, slope, r² and the two Rcrit estimates; three compounds fail with r^2 < 0.55, and the haloperidol value should be read as about 6.6 × 10² rather than 6.6 × 10³ K/min baird2013 R7, X2.

Why

Both methods assume that a higher cooling rate always lowers the crystallization temperature, so that undercooling grows in a regular way toward a limit as the rate approaches Rcrit baird2013 C17; baird2010 R31. The authors attribute the failures to undercooling that did not rise consistently with rate and to scattered crystallization temperatures, which they put down "most likely" to the stochastic nature of nucleation and to heterogeneous nucleation in DSC pans baird2010 C18, C19; baird2013 C18. A rate window of 5–20 °C/min lies far below the Rcrit of class I molecules, which crystallize even when quenched in liquid N2, so the extrapolation is long baird2010 C22, R3. The 2013 estimates, except haloperidol's, are much larger than the maximum rates reached and so "may be reasonable estimates" baird2013 C19. (synthesis: with the corrected haloperidol value of about 6.6 × 10² K/min, the extrapolated Rcrit lies below the 913 °C/min at which haloperidol still crystallized, so even the wide-range fit underestimates for this compound; this repeats in milder form the 2010 contradiction with the quench test baird2013 X2, R1.) The formulas are on the Barandiaran-Colmenero critical cooling rate and Cabral critical cooling rate pages.

Conditions and limits

Neat class I molecules only; class II and III molecules do not crystallize on cooling at these rates and cannot be fitted this way baird2010 P9. The liquid-N2 cooling rate used as the check was not measured baird2010 C21. In 2013 the points used per fit and the definition of Tcryst are not fully stated, and the indoprofen undercooling row duplicates phenacetin's, so indoprofen's own data are missing baird2013 X16, X1. Replicate numbers of the fast runs are not stated baird2013 X9.

Counterexamples and conflicts

None found in the library supporting the narrow-range method for organic molecules. Within the 2010 data some fits were good (carbamazepine r² 0.99), so a good fit did not guarantee a correct ranking against the quench test baird2010 R13, C21. The 2013 paper partly revises the 2010 verdict: the method works for some compounds when the rate range is wide baird2013 C20.

Transfer check

For a new drug, answer the practical question directly with a quench test or a fast-scanning DSC run rather than extrapolating from a conventional DSC baird2013 C21; baird2010 C20. If an extrapolation is attempted, use cooling rates spanning several orders of magnitude, check that undercooling rises steadily with rate across replicates, and compare the estimate with the outcome at the fastest rate available baird2010 C22; baird2013 C17, C20. A drug that crystallizes at 500 °C/min or faster falls inside the "difficult to make and keep amorphous" group regardless of the exact estimate baird2013 C21.

History

The BC (1981) and Cabral (2003) methods came from inorganic glass science and are cited baird2010 E1, E3. Baird in 2010 found them of "limited utility" for organic molecules over 5–20 °C/min baird2010 C20. Baird in 2013 found that a much wider rate range improves the fits but still fails for compounds with erratic crystallization baird2013 C20, C16.

How it was shown

Inorganic-glass science offers simple predictors of glass-forming ability: the reduced glass transition temperature T_{rg} = \frac{T_g}{T_m} (in kelvin), for which a higher value is taken to mean a more viscous liquid between Tg and Tm and so more resistance to crystallization, with a typical value of 0.66 proposed baird2010 E4, C1, R29. Glass-stability parameters (KLL, KH, KW, KSP, K1, K2 and the reduced temperature Tred) combine Tg, the crystallization temperatures on reheating and Tm, and had risen as the measured Rcrit fell in inorganic glasses baird2010 E5, E11, C2, R28. Good glass formers were also expected to be "strong" liquids, whose mobility changes little near Tg baird2010 C3. Baird and co-workers (2010) calculated Trg for all 51 molecules of their DSC screen, using measured or literature Tg and, for 16 class I molecules that crystallized too fast to show a Tg, a value estimated from a regression of Trg on molecular weight baird2010 E4, E27, P8. Glass-stability parameters were calculated for the 11 class II molecules and three class I-B molecules baird2010 P11. Fragility m, strength D and the Kauzmann temperature came from the shift of Tg with heating and cooling rate (5–20 °C/min) and from the heat-capacity step, for classes II and III baird2010 P3, P10. Baird and co-workers (2012) measured the steady-shear viscosity of 34 of the same molecules from Tm downward at 30 s⁻¹, fitted the VTF equation \eta = \eta_0 \exp\left(\frac{D\,T_0}{T - T_0}\right) to 28 curves of classes I-B, II and III, and plotted all data on a Tg-scaled (Angell) plot baird2012 P1, P5, P6, E4.

What the data show

Mean Trg was 0.69 (±0.01) for class I-A and 0.7 (±0.03) for class I-B, not different, so Trg did not predict which class I molecules could be quenched to a glass baird2010 R14, C23. Class I as a whole averaged 0.69 ± 0.02 against 0.73 ± 0.04 for class III, the expected order but not a significant difference, so Trg is "clearly not an infallible predictor" baird2010 R14, C37. Trg spanned 0.65–0.76 in class II and 0.65–0.81 in class III, and the two class III molecules that crystallized on slow reheating did not have lower values (nilutamide 0.72, nimesulide 0.70) baird2010 R18, C36. Within class II, Tred and the glass-stability parameters pointed to bifonazole, celecoxib, cinnarizine and droperidol as the best glass formers, yet celecoxib, dibucaine, flurbiprofen and nifedipine were the ones that crystallized on cooling at 1 °C/min baird2010 C27, R7, C28. Tred after 20 °C/min cooling ran from 0.33 (acetaminophen) to 0.72 (celecoxib), but celecoxib also had the lowest KSP (1.464) and K2 (1.118), so the ranking depended on the parameter chosen baird2010 R16, R17, X15. The fragility index m ran from 18 (tolazamide) to 731 (itraconazole) across classes II and III, and neither fragility nor strength correlated with the glass-stability parameters baird2010 R18, C31. From viscosity, all 28 fitted compounds had D between 4.3 and 8.7, below the fragile limit of 10, with class III (4.3–6.3) no less fragile than class I-B (4.5–7.3) or class II (4.4–8.7) baird2012 R12, C39. On the Angell plot the data of all four classes lie in one band near the D = 5 curve, far from the strong D = 100 line baird2012 R13, C42. Chlorpropamide (class I-B), celecoxib (class II) and ketoconazole (class III) have Tm − Tg of 108, 105 and 105 °C, yet their viscosity rose about 10-, 20- and 36-fold over 40 °C of undercooling baird2012 M9, M14, M26, R3. Class means of Tm − Tg (123, 119, 126 and 108 °C for classes I-A to III) did not differ significantly baird2012 R10. Later, pretomanid and delamanid were placed in class I with reduced Tg 0.67 and 0.64 nguyen2023a C59.

Figure

Points of every class sit in one band around the fragile D = 5 curve; the class colours do not separate, so fragility on this scale carries no class information baird2012 R13, C42.

Trg rises only weakly with molecular weight (R² 0.44), and the 16 estimated class I values lie on this line, so their Trg is a function of molecular weight alone baird2010 R19, X17.

Why

The reduced Tg rests on the assumption that all liquids have the same viscosity at Tg, so that a higher Tg/Tm means a more viscous liquid over the undercooled range baird2010 C1. The 2012 data contradict that premise: compounds with similar viscosity at Tm and similar Tm − Tg can differ in how fast viscosity rises on cooling, as chlorpropamide and ketoconazole do, so Tg/Tm "should not be considered a reliable predictor" baird2012 C36. The glass-stability parameters measure crystallization of the reheated liquid above Tg, where nucleation and growth are much faster than in the glass, and their inverse relation to Rcrit was assumed from inorganic glasses rather than shown for organic molecules baird2010 C43, C26. Celecoxib's inconsistent parameters are "believed to be" due to its high Tg and crystallization temperature relative to Tm baird2010 C29. For fragility the authors note that organic liquids are held together by non-covalent forces much weaker than covalent networks, so non-Arrhenius (fragile) behaviour is general among them, and on a log scale the large absolute viscosity differences between compounds shrink baird2012 C40, C42. Hence Angell plots "give minimal information" on crystallization tendency, and kinetic fragility "may not accurately assess" glass-forming ability; crystallization also depends on thermodynamic factors baird2012 C43, C44. The authors summarize that none of the inorganic-glass parameters correlated strongly with crystallization behaviour, "suggesting these parameters may not be ideal" for organic molecules baird2010 C38. A 2010 library paper on felodipine–PVP dispersions notes from the literature that crystallization tendency cannot be predicted from relaxation times and Tg alone marsac2010 C29. The formulas are on the reduced glass transition temperature and Vogel-Tammann-Fulcher equation pages.

Conditions and limits

No statistical test is named for the Trg comparisons, and 16 class I Tg values are estimates from molecular weight baird2010 R14, X17. Tred and the glass-stability parameters cannot be reproduced from the printed temperatures, and chlorpropamide's KSP and K2 are printed identical baird2010 X8, X1. The fragility category depends on whether m or D is used: aceclofenac, tolazamide and nifedipine are strong by m and D^a but fragile by D^b baird2010 X14. Class I-A was not fitted with VTF, and the fitted T0 values do not satisfy the paper's own relation between T0, D and Tg baird2012 X7, X5. All data are for neat melts, without polymer baird2010 A1; baird2012 A1.

Counterexamples and conflicts

The class means of Tg/Tm do follow the expected order, class I lowest and class III highest baird2010 C37. For crystal growth rates, slow growers had a small Tm − Tg trasi2014a R8 (synthesis: a small Tm − Tg means a high Tg/Tm, so the reduced-Tg idea keeps some value as a class-level trend for growth while failing to rank molecules by DSC class; see F5).

Transfer check

Do not screen candidates by Tg/Tm, glass-stability parameters or fragility alone baird2010 C38; baird2012 C36, C43. For a new drug, the heat–cool–heat test, a seeded growth rate and the melt viscosity at Tm with its rise over the first 40 °C of undercooling carried more information in these data sets baird2012 C45; baird2010 C64. If Tg/Tm is reported, measure Tg rather than estimating it from molecular weight baird2010 X17.

History

Trg goes back to Kauzmann and Turnbull, with a typical value of 0.66 proposed baird2010 R29, C1. Baird in 2010 tested Trg, the glass-stability parameters and calorimetric fragility on 51 molecules and found none of them reliable baird2010 C38. Baird in 2012 confirmed the fragility result with viscosity-based fits and showed that Tg/Tm misses differences in the rise of viscosity baird2012 C43, C36. Nguyen in 2023 still reported Tg/Tm alongside the class for two antitubercular drugs nguyen2023a C59.

How it was shown

Baird and co-workers (2010) ran a PCA (SIMCA-P+) on all 51 molecules of their DSC screen with seven descriptors: melting onset, Tg midpoint, ΔHfus, ΔSfus and ΔGv (Hoffman at 293.15 K), the last three per unit volume via the crystal density, molecular weight and number of rotatable bonds baird2010 P8. Data were centred and scaled, components were chosen by cross-validation, and no class information was given to the model baird2010 P8. For 16 class I molecules that crystallized too fast to show a Tg, Tg was estimated from a regression of Tg/Tm on molecular weight baird2010 P8, E27, X17. Van Eerdenbrugh and co-workers (2010) repeated the analysis for the 40 drugs of their spin-coating screen with the same descriptors, then built one PCA model per class and projected three compounds not used in the models (PABA, piroxicam, clarithromycin) onto them in a Coomans' plot vaneerdenbrugh2010a P11, P12. Class membership was compared with the descriptors as each class's mean deviation from the overall mean in standard deviations baird2010 R22; vaneerdenbrugh2010a R20. Trasi and co-workers (2014) did the same for three groups of drugs sorted by crystal growth rate, over 11 properties trasi2014a P6, E5, R8.

What the data show

The 2010 melt model explained 97.8% of the descriptor variance with three components (56.3, 30.4 and 11.0%) and predicted 91.1% in cross-validation baird2010 R20, C66. On the first two components, class means lay at about (−1.1, −0.3) for class I, (0.0, 0.0) for class II and (1.4, 0.4) for class III, with outliers in every class (most notably lidocaine and tolbutamide in class I) baird2010 R21, C39. Class I had lower molecular weight (about −0.63 SD) and fewer rotatable bonds (−0.54), higher ΔHfus (+0.45), ΔSfus (+0.41) and melting onset (+0.25), and a more negative ΔGv (−0.40); class III showed the opposite signs (MW +0.79, rotatable bonds +0.66, ΔHfus −0.63, ΔSfus −0.59, melting onset −0.29, ΔGv +0.57) baird2010 R22. Tg barely differed between classes (all within ±0.08 SD) baird2010 R22.e, C41. The solvent model explained 97.6% (89.8% cross-validated), with class means at about (−0.9, −0.6), (0.4, −0.2) and (0.7, 0.7) vaneerdenbrugh2010a R18, R19. Its class contributions ran MW −0.68 / +0.70, rotatable bonds −0.42 / +0.57, ΔHfus +0.41 / −0.26 and ΔSfus +0.46 / −0.33 for class I / III, and here Tg did separate the classes (−0.34 / +0.46) vaneerdenbrugh2010a R20, C40. The per-class models explained 97.9, 99.1 and 96.1% for classes I, II and III; the class III model could not discriminate and was not used vaneerdenbrugh2010a R21, C42. PABA (class I) and clarithromycin (class III) were "well predicted", while piroxicam (class II) fitted both models vaneerdenbrugh2010a R22, C44. Among growth groups, fast growers had lower molecular weight (about −0.28 SD), fewer rotatable bonds (−0.35) and higher Tm (+0.55) trasi2014a R8, C25. Close relatives split: benzocaine and lidocaine were class I but procaine class III, haloperidol class I but droperidol class II baird2010 R10, C14. Haloperidol (375.9 g/mol) is class I-A and acetaminophen (151.2 g/mol) class II, against class means of 217 g/mol for I-A and 324 g/mol for II in the 2013 set baird2013 X11. Nilutamide, small with one rotatable bond, "would be expected" to crystallize readily but is a slowly crystallizing good glass former trasi2014b M1, C36, C5.

Figure

Class I (red) lies mostly left and low, class III (green) up and right and class II (blue) between; triangles are class means, and outliers of every class sit inside the other clusters baird2010 R21.

Black (class I) bars point down for molecular weight, rotatable bonds and Tg and up for ΔHfus and ΔSfus; white (class III) bars point the other way vaneerdenbrugh2010a R20.

Why

The authors' explanation for size and flexibility is conformational: flexible molecules exist in the melt as energetically similar conformers, and more rotatable bonds lower the chance that a molecule is in the orientation needed to join a nucleus or crystal baird2010 C59. Van Eerdenbrugh and co-workers call this "intuitive" vaneerdenbrugh2010a C37. The thermal descriptors are read through the driving force: higher ΔHfus and ΔSfus give a more negative ΔGv and so, by classical nucleation theory, a lower barrier (see F6) baird2010 C60, C61; vaneerdenbrugh2010a C38, C39. A higher melting point means more energy to disrupt the lattice baird2010 C62. Conformer populations, interfacial energies and nucleation rates were not measured baird2010 C59, C61. Tg separated the solvent classes but not the melt classes because a week of storage at room temperature favours compounds whose Tg is above the storage temperature, whereas the melt test takes every sample above Tg ("can be readily understood") vaneerdenbrugh2010a C41; baird2010 C41. Because several descriptors were needed, the authors conclude that multiple properties "appear to play a role" and that no single descriptor can predict crystallization baird2010 C42, C63; vaneerdenbrugh2010a C45. Other library papers use the same reasoning for single drugs: pretomanid's high tendency is "attributed" to its low Tg, low molecular weight and linear structure, and ritonavir's slow solution nucleation "most likely" to its size and flexibility nguyen2023a C61; ilevbare2013c C25. For nilutamide the authors propose that the issue is which conformer the crystal needs, not the number of rotatable bonds (see F7) trasi2014b C51. (synthesis: the descriptor trends describe the average of a class, and both PCAs share estimated Tg values for the fastest crystallizers, so the trends are a prior for a new drug rather than a model of it baird2010 X17; vaneerdenbrugh2010a X9.)

Conditions and limits

Class-average trends with wide spread baird2010 R21; vaneerdenbrugh2010a R19. Tg was estimated for 16 molecules in both PCAs baird2010 X17; vaneerdenbrugh2010a X9. Per-compound descriptor values are not printed in the solvent study, and its class bars are plot readings vaneerdenbrugh2010a R20. The prediction was tested on three compounds only vaneerdenbrugh2010a X8. The descriptor set holds no measure of hydrogen bonding or crystal packing beyond ΔHfus and Tm baird2010 P8.

Counterexamples and conflicts

Nilutamide trasi2014b C36; haloperidol and acetaminophen baird2013 X11; structural relatives in different classes baird2010 R10. For four weak bases a reduced-conformational-freedom argument did not follow the printed rotatable-bond counts hsieh2014 X12. Polyphenols with many hydroxyl groups (naringenin, quercetin) crystallized readily, which the authors attribute to an extensive hydrogen-bonded network rather than to size wegiel2013a C26.

Transfer check

Use molecular size, flexibility and ΔHfus only as a prior for a new drug: a small, rigid molecule with a high heat of fusion starts with a higher risk, a large flexible one with a lower one baird2010 C40; vaneerdenbrugh2010a C36. The class itself has to be measured, by the DSC cycle or the spin-coat test (see F9, F14) baird2010 C64; vaneerdenbrugh2010a C47. If a PCA model is used, include the drug's measured Tg and check that the drug falls within the descriptor range of the 51 molecules vaneerdenbrugh2010a C46.

History

Both PCAs date from 2010 baird2010 C40; vaneerdenbrugh2010a C36. Baird in 2013 restated the low-MW tendency baird2013 C39. Trasi in 2014 found similar descriptors for fast growth and a small, rigid exception in nilutamide trasi2014a C25; trasi2014b C36. Later papers used size and flexibility to explain slow solution nucleation of ritonavir (2013) and fast crystallization of pretomanid (2023) ilevbare2013c C25; nguyen2023a C61.

How it was shown

Van Eerdenbrugh, Baird and Taylor (2010) asked how readily drugs crystallize after rapid solvent evaporation, whether the solvent or the route to the amorphous state changes that, and which compound properties go with it vaneerdenbrugh2010a A1, A2, A4. They took the 51 compounds of the melt screen, measured their solubility in dichloromethane (DCM), ethanol (EtOH) and a 1:1 (w/w) mixture (MIX), and removed combinations that degraded in solution (griseofulvin, nifedipine, procaine, tolfenamic acid) or sublimed under vacuum (antipyrin, ibuprofen), keeping 93 of 153 combinations of 40 drugs vaneerdenbrugh2010a P5, P6, R5, R6, R7. A standard concentration of 0.26 M was chosen with felodipine, because below it the films crystallized only in patches at 94% RH; six combinations were run at 0.20 M vaneerdenbrugh2010a P3, P4, R3, P1. 200 µL of solution was spun for 20 s at 8000 rpm on an 18 × 18 mm cover slip, in triplicate, giving films about 1 µm thick, which the authors liken to spray drying ("some similarity") vaneerdenbrugh2010a P2, C12. Films were scored by polarized light within 30 min (day 0), after a night under vacuum (day 1) and after 2, 4 and 6 more days over P2O5 at room temperature (days 3, 5, 7), on a five-step scale from AAAA (no birefringence) to CCCC (fully crystalline) vaneerdenbrugh2010a P8. Class I meant at least AACC at day 0, class II at least AACC by day 7, class III AAAA or AAAC at day 7 vaneerdenbrugh2010a P9. For every class III combination, 400 µL of the same solution was also left to evaporate at ambient conditions in a glass vessel 12 mm wide and 6 mm high, in triplicate vaneerdenbrugh2010a P7. The spin-coating classes were compared with the melt classes of the 2010 DSC screen, which used cooling at 20 °C/min and reheating at 10 °C/min vaneerdenbrugh2010a P10; baird2010 P1.

What the data show

The 93 combinations split into 39 class I, 23 class II and 31 class III; by compound, 14 were class I, 9 class II and 13 class III in every solvent tested, and clofoctol, flurbiprofen (I or II), cinnarizine and loratadine (II or III) changed class with the solvent vaneerdenbrugh2010a R8, R9. Of the 33 drugs tested in more than one solvent, 10 differed in category at one or more time points, but only those 4 changed class vaneerdenbrugh2010a R11. About half of the class II drugs showed a little crystallinity right after spin coating, and no class III drug did vaneerdenbrugh2010a R10. Against the melt classes, 35% of the 93 combinations were class I by both routes, 8% class II by both and 25% class III by both, 68% in all; 30% were one class apart and 2% opposite, the 2% being atenolol in MIX and EtOH (spin-coat class III, melt class I) vaneerdenbrugh2010a R16, R17. No combination was class I by evaporation and class III from the melt vaneerdenbrugh2010a R16. Counted per drug, 13 of 14 spin-coat class I drugs were also melt class I and 10 of 13 spin-coat class III drugs melt class III, but only 2 of 9 spin-coat class II drugs were melt class II; 25 of 40 drugs agree in every solvent vaneerdenbrugh2010a R14, X6. Slow evaporation reversed the picture for slow crystallizers: 22 of the 31 class III combinations were CCCC at the first look, including celecoxib, felodipine and indomethacin in every solvent tested vaneerdenbrugh2010a R12, R13. Only clotrimazole, ketoprofen, miconazole and ritonavir were not fully crystalline at once, and their outcome then depended on the solvent: miconazole was CCCC from DCM but AAAA for 7 days from MIX, and ritonavir CCCC from DCM but AAAA to AACC from MIX vaneerdenbrugh2010a R12, R13. Later work met the same drying-rate limit: rotary evaporation gave no amorphous naringenin or quercetin, while spin coating gave amorphous naringenin; curcumin could be made amorphous by spin coating but not in larger amounts by rotary evaporation wegiel2013a R7; wegiel2014 C9. For delamanid, a class I drug, rotary-evaporated dispersions above about 10% drug loading held crystals, which the authors put down to an evaporation rate "not fast enough" duong2022a C44, C45.

Figure

Most rows read CCCC from day 0 onward, although every one of these combinations stayed mostly amorphous for a week after spin coating; the four exceptions vary with the solvent vaneerdenbrugh2010a R12, R13.

The diagonal (35, 8 and 25%) is the 68% agreement; the class I evaporation, class III melt cell is empty and the opposite cell holds only atenolol vaneerdenbrugh2010a R16, R17.

Why

The authors explain the small solvent effect by the very short drying time of spin coating, which would suppress any solvent-specific effect on nucleation or growth ("can be explained") vaneerdenbrugh2010a C25. The thin film and the fast process "should minimize" nucleation and growth in the supersaturated solution vaneerdenbrugh2010a C11. Slow evaporation keeps the solution supersaturated longer before its viscosity rises, so crystallization becomes "an obvious result", and the solvent then matters more ("implies") vaneerdenbrugh2010a C27, C28. They read the classes kinetically: class I crystallized at once, "suggesting" extremely fast nucleation and growth; class II crystals come from nuclei formed during spin coating, from nucleation in the film, or both ("may be due", "probably important"); class III "implying" slow nucleation and/or growth vaneerdenbrugh2010a C18, C20, C22. None of these rates was measured, and the duration of supersaturation was not measured either vaneerdenbrugh2010a C18, C22, C25. From the agreement with the melt classes they conclude ("suggests") that under rapid solidification crystallization tendency is dominated by the physicochemical properties of the drug vaneerdenbrugh2010a C33. Part of the difference between the routes is built into the definitions: the melt test is a short temperature excursion above Tg, while the solvent test is a week of storage, which favours drugs whose Tg lies above room temperature ("can be readily understood") vaneerdenbrugh2010a C30, C41. Duong and co-workers later state the same principle for dispersions: the evaporation rate decides whether a drug is trapped before nucleation and growth ("Clearly") duong2022a C45. (synthesis: both 2010 routes are fast, so their agreement shows that the drug ranks alike under fast solidification, not that the process is irrelevant; the slow-evaporation result shows that the drying rate can override the class vaneerdenbrugh2010a X7, R13.)

Conditions and limits

Neat drugs, three solvents of different polarity, mostly 0.26 M, films about 1 µm thick, room temperature and dry storage for 7 days vaneerdenbrugh2010a P1, P2, P8. Crystallinity was scored by eye in five steps, and the per-sample data are in a supporting information file that was not available vaneerdenbrugh2010a P8, R10. The melt classes are cited from the 2010 DSC study and defined by different criteria and time scales vaneerdenbrugh2010a P10, C30. Slow evaporation was run on the class III combinations only vaneerdenbrugh2010a P7. Polymers, humidity, higher temperatures and storage beyond 7 days were not part of the study vaneerdenbrugh2010a A1, A5, P8. Eleven of the 51 compounds were dropped, five of them without a stated reason vaneerdenbrugh2010a X3.

Counterexamples and conflicts

Atenolol is spin-coat class III but melt class I vaneerdenbrugh2010a R17. The intermediate class agrees poorly between routes: of 9 spin-coat class II drugs, 3 were melt class I and 4 melt class III vaneerdenbrugh2010a R14. Per drug the agreement is 25 of 40, lower than the 68% per combination vaneerdenbrugh2010a X6. The statement that the compound rather than the processing decides holds only across the two rapid routes, not across drying rates vaneerdenbrugh2010a X7.

Transfer check

A spin-coat screen of the neat drug ranks it for fast-drying processes such as spray drying; the authors expect a drug that crystallizes readily during solvent evaporation also to crystallize easily from a melt vaneerdenbrugh2010a C12, C32. For slow solvent removal (rotary evaporation, film casting, slow tray drying), test the drug at the process drying rate, because 22 of 31 slow crystallizers became fully crystalline when dried slowly vaneerdenbrugh2010a R13. A drug in the intermediate class, or one whose class changes with solvent, should be tested in the actual process solvent vaneerdenbrugh2010a R11, R14. Check Tg against the storage temperature, since a Tg above it went with the slow class after evaporation vaneerdenbrugh2010a R20, C41.

History

Baird and co-workers in 2010 classified the 51 compounds from the melt baird2010 R1. Van Eerdenbrugh and co-workers in the same year established the solvent classes, their agreement with the melt classes and the drying-rate limit vaneerdenbrugh2010a C31, C26, and used the classes that year to choose drugs for a polymer screen vaneerdenbrugh2010b R11. Polyphenol studies in 2013 and 2014 met the drying-rate limit with rotary evaporation wegiel2013a R7; wegiel2014 C9. Duong in 2022 made the evaporation rate the explanation for residual crystallinity in delamanid dispersions duong2022a C45.

How it was shown

Baird and co-workers (2010) defined glass-forming ability as the ease of vitrifying on cooling and glass stability as resistance to crystallization of the glass, noting that "glass stability" as usually measured on reheating is "somewhat of a misnomer", since it measures the reheated undercooled liquid baird2010 C4. In their screen, class II glasses were reheated at 10 and 20 °C/min, and class I-B glasses made by liquid-N2 quenching were reheated in the Raman experiments baird2010 P4, R8, R15. In 2013 the same group measured, in a rapid heat/cool calorimeter, both the slowest cooling that avoids crystallization (Rcrit,cool) and the slowest reheating that avoids it (Rcrit,heat), for 4 class I-B and 10 class II compounds baird2013 P2, P4, R9. Trasi and co-workers (2014) measured seeded growth rates of 31 drugs from the undercooled melt and coloured each by its glass-forming class from the 2010 test, red for classes I and II and blue for class III trasi2014a P1, R1. Trasi and Taylor (2014) compared nilutamide's glass formation on cooling with the growth rate of its seeded crystals trasi2014b R2, R8.

What the data show

In the rapid calorimeter, four class I-B compounds formed glasses at 25 °C/min but needed above 1500–2000 °C/min on reheating baird2013 R9, C24. Class II compounds had Rcrit,cool of 5 °C/min or less but Rcrit,heat from 12.5 (bifonazole) to above 1910 °C/min (acetaminophen) baird2013 R9, C22. For acetaminophen the gap exceeds three orders of magnitude (below 1 against above 1910 °C/min), which the authors believe is the first report of such an asymmetry for organic systems ("to the best of the authors' knowledge"), similar ones being known in bulk metallic glasses baird2013 R9.e, C24, C26, R13. Flufenamic acid cooled at 25 °C/min gave no exotherm and a glass transition on reheating, yet after cooling at 1025 °C/min it still crystallized on reheating at 1900 °C/min, with an exotherm from a labelled 84.20 °C and melting near 131 °C baird2013 R10, C25. In the 2010 screen, 9 of 11 class II glasses recrystallized on reheating at 20 °C/min, and class I-B glasses crystallized rapidly when reheated above Tg baird2010 R8, R15, C24. Among the 31 drugs, the 19 class III compounds had MCVs from 216 µm/s (nimesulide) to 0.02 µm/s (clotrimazole): 7 were fast growers, 4 intermediate and all 8 slow growers belonged to class III trasi2014a R1, C14. The 12 class I and II compounds had MCVs of 1.8–104 µm/s, none of them slow growers trasi2014a R1, C14. Nilutamide formed a glass on cooling at 15 °C/min that did not crystallize on reheating, although its seeded stable-form crystals grew at about 1.5 µm/s at 70 °C and about 38–40 µm/s at 100 °C trasi2014b R2, R3, R8. Acetaminophen, cited from a 2011 thesis, readily forms a glass even at 1 °C/min cooling yet always recrystallizes on heating trasi2012a R1. Bicalutamide is cited as crystallizing rapidly above Tg despite high glass-forming ability, and celecoxib samples were "quite hard to nucleate" yet easily made amorphous moseson2022b R26; mosqueragiraldo2014 R15.

Figure

Panel (a) has no exotherm on cooling and a glass transition on reheating; panel (b), after cooling at 1025 °C/min, still shows an exotherm and a melting endotherm on reheating at 1900 °C/min baird2013 R10.

Growth runs upward and nucleation to the left; the box for rapid growth with low nucleation (class II, for example nimesulide, nilutamide, celecoxib) holds good glass formers that are at risk once nuclei exist; it is a schematic trasi2014a C17.

Why

In the authors' reading, a melt that forms a glass easily has nucleation and growth windows that overlap little: on cooling, the melt passes the growth maximum while few nuclei exist and forms nuclei only where growth is slow baird2013 C35, C36. On reheating, those nuclei, together with any formed on the way up, are carried into the fast-growth range, where a rate that sufficed on cooling is too slow; "assuming steady-state nucleation" as many nuclei form on reheating as on cooling, and the asymmetry arises because the reheating nuclei meet higher growth rates baird2013 C36. Nuclei formed during cooling are a further contribution (see F16) baird2013 C30, C40. For class III fast growers, Trasi and co-workers argue that ready glass formation can come from low nucleation, low growth, both, or poor overlap, and that the fast-growing class III compounds "clearly" form glasses because they nucleate poorly under the test conditions; nucleation rates were not measured trasi2014a C13, C15. For nilutamide, the authors attribute the glass-forming ability to a low nucleation tendency, since its crystals grow fast ("it appears") trasi2014b C9. Celecoxib's ease of amorphization is likewise attributed "most likely" to a low nucleation rate mosqueragiraldo2014 C7. Trasi and co-workers proposed an extended classification that separates these cases: IA (overlapping fast nucleation and growth, for example carbamazepine), IB (fast nucleation and growth with little overlap, acetaminophen), II (fast growth, low nucleation: nimesulide, nilutamide, celecoxib), III (ready nucleation, slow growth: cinnarizine, droperidol) and IV (slow nucleation and growth: warfarin, miconazole) trasi2014a C17. (synthesis: the 2010 classes rank the cooling step only, so two drugs in the same class III can differ by four orders of magnitude in how fast a nucleus, once formed, will grow; the growth rate is the missing measurement trasi2014a R1, C2.)

Conditions and limits

Neat drugs; DSC scans lasting minutes and growth measured above Tg baird2013 X15; trasi2014a P1. The low nucleation of fast-growing class III drugs is inferred, not measured trasi2014a C15. The 2014 MCVs carry no replicates and several do not match the plotted rates trasi2014a X17, X3. The class labels in the 2014 paper mix two schemes trasi2014a X10. Reheating rates of 1900–2000 °C/min exceed the calibrated range of the rapid calorimeter baird2013 X10.

Counterexamples and conflicts

In a small storage test the class III glasses were the most stable and the class II glasses less so, which fits the reheating results (see F17) baird2010 R24, R25, C47. Under 1–4 h isothermal holds of the undercooled melt, indomethacin (class III) did not nucleate while posaconazole and bicalutamide (also class III) crystallized within 1 h, so class III glasses differ widely in stability above Tg moseson2020 R7, C17, C18.

Transfer check

Always reheat the glass and measure a seeded growth rate; a clean cooling trace is not evidence of stability baird2010 C47; trasi2014a C16. A drug that forms a glass at slow cooling but crystallizes on reheating at 10–20 °C/min (class II), or that grows faster than about 10 µm/s at its maximum, should be treated as at risk once nuclei are present, for example after milling or incomplete melting (synthesis: from the class II and extended class II definitions) baird2010 R1; trasi2014a C16, C17. Where a fast-scanning calorimeter is available, compare Rcrit,cool with Rcrit,heat baird2013 C24.

History

Baird in 2010 separated glass-forming ability from glass stability and found class II much less stable than class III baird2010 C47. Acetaminophen illustrated the point in 2012 trasi2012a R1. Baird in 2013 quantified the cooling–heating asymmetry, reported as a first for organic systems baird2013 C26. Trasi in 2014 showed fast growers among good glass formers, proposed the extended classification, and found nilutamide a nucleation-limited glass former trasi2014a C14, C17; trasi2014b C9. Bicalutamide was cited as a further case in 2022 moseson2022b R26.

How it was shown

The 2010 classification left a puzzle: class II melts form a glass on cooling yet crystallize on reheating, which Baird and co-workers explained by nuclei that form during cooling, cannot grow before the glass forms, and then grow on reheating baird2010 C51, C55. In 2013 the same group tested the idea with a prototype rapid heat/cool calorimeter on 30–50 µg crystals baird2013 P2. Glasses of four class I-B and ten class II molecules were made by cooling the melt either at 20 °C/min or at the maximum obtainable rate, stated as above 500 °C/min in all cases and printed as 1025 (flufenamic acid), 800 (dibucaine) and 860 °C/min (clofoctol) baird2013 P4, X5. Each glass was reheated at a series of rates, and the slowest reheating that avoided crystallization (a crystallization exotherm or a melting endotherm at Tm) was recorded as the critical heating rate Rcrit,heat baird2013 P4. To tell crystallization on reheating from crystallization on cooling, clofoctol was cooled at a constant 20 °C/min and reheated at 200, 300, 400 and 500 °C/min baird2013 P4, R12. Trasi and Taylor (2012) had approached the same question for acetaminophen by cooling melts to successively lower temperatures and reheating them in DSC and on a hot stage trasi2012a P6, P7, C40, X9.

What the data show

Rcrit,heat after 20 °C/min cooling against after maximum cooling was: antipyrin above 2000 against 2000, chlorpropamide above 2000 against 1000, cinnarizine 300 against 135, clofoctol 400 against 200, dibucaine above 1000 against 300, droperidol 175 against 125, nifedipine above 500 against 250, tolazamide 35 against 30, bifonazole 12.5 against below 10 and celecoxib 15 against below 10 °C/min baird2013 R9. No change could be read for flufenamic acid (above 1900 both), tolbutamide (above 1500 both) and acetaminophen (above 1910 both), and none was given for D(−) salicin baird2013 R9. The size of the drop therefore ranges from small (droperidol, tolazamide) to at least 3.3-fold (dibucaine) baird2013 X8. For dibucaine reheated at 300 °C/min, the glass made at 20 °C/min showed a melting endotherm near 66 °C and the glass made at 800 °C/min none; after 20 °C/min cooling the endotherm persisted, though shallower, at 300, 500 and 1000 °C/min (about 6, 3 and 1 W/g deep) baird2013 R11. For clofoctol reheated at 200 °C/min, a small endotherm near 89 °C appeared after 20 °C/min cooling and not after 860 °C/min cooling baird2013 R12. After a constant 20 °C/min cooling, the clofoctol endotherm was clear at 200, small at 300, at most barely visible at 400 and absent at 500 °C/min reheating baird2013 R12. Assuming that the same number of nuclei formed during the identical cooling, the authors take this to "confirm" that crystallization occurred during reheating baird2013 C29.

Figure

In panel (a), at the same 300 °C/min reheating, the melting endotherm near 66 °C appears on the trace of the glass made at 20 °C/min (black) but not on the one made at 800 °C/min (red); panel (b) shows that after slow cooling even 1000 °C/min reheating leaves an endotherm baird2013 R11.

Panel (b) is the key test: the cooling was identical, and only the reheating rate changed, yet the endotherm shrinks from 200 to 500 °C/min baird2013 R12.

Why

The authors' explanation starts from two rate curves with maxima at different temperatures, nucleation near Tg and growth closer to Tm baird2013 C35, C36. On cooling at a moderate rate the melt first crosses the growth maximum while few nuclei exist, then forms nuclei near Tg where growth is slow and viscosity high, so the nuclei stay in the glass baird2013 C36. On reheating these nuclei, plus any formed on reheating, enter the fast-growth range, where a rate that sufficed on cooling is too slow to stop growth ("can account for") baird2013 C36. Reheating through Tg "should in principle" erase the cooling history of the glass itself, so a cooling-rate effect on reheating points to something carried over, which they identify as nuclei baird2013 C37. Rapid cooling shortens the time in the undercooled range and so, "assuming" it gives a nucleus-free glass, crystallization on reheating then needs both nucleation and growth, and Rcrit,heat falls baird2013 C38, C28. From the smaller asymmetry after quenching they conclude that this "strongly suggests" nuclei generated during slower cooling, and in the conclusions "there is evidence" for quenched-in nuclei that "likely contribute" to crystallization on reheating baird2013 C30, C40. The 2010 paper had proposed the same nuclei, adding that below Tg, as the glass relaxes, molecules diffuse to them so that they seed crystal growth over long times ("It is believed") baird2010 C57, C58. A 2012 library paper restated that quenched-in nuclei may lead to observable crystallization over longer times trasi2012a C41. What was not measured: nuclei were not seen or counted, nucleation and growth rates were not measured as functions of temperature, and the clofoctol test rests on the stated assumption of equal nucleation during constant cooling baird2013 X7, C35. (synthesis: the glass made by fast cooling also differs in its structural state, which the authors set aside by assuming that reheating through Tg erases it baird2013 C37; a direct count of nuclei, for example by reheating into the growth range and counting crystals, would test the explanation.) The formula behind the argument is on the critical cooling rate to avoid nucleation page.

Conditions and limits

DSC scans lasting minutes on neat drugs, no polymer, no storage baird2013 A1, X15. The quench rate before reheating is printed for three compounds only baird2013 X5. The highest reheating rates (1900–2000 °C/min) exceed the calibrated range of 10–1700 °C/min, and replicate numbers are not stated baird2013 X10, X9. The clofoctol value in Table 4 (400 °C/min) conflicts with the text and figure, which place the threshold near 500 °C/min baird2013 X14.

Counterexamples and conflicts

No change could be read for flufenamic acid, tolbutamide and acetaminophen, whose reheating rates exceeded the instrument range baird2013 R9. The abstract's "greatly reduced" asymmetry holds for some compounds only; for droperidol and tolazamide the drop is small baird2013 X8, C4. In the acetaminophen protocol of 2012 the nucleation zone is passed both on cooling and on reheating, so nuclei formed on cooling were not separated from those formed on reheating trasi2012a X9.

Transfer check

In melt processes such as melt extrusion or melt quenching, record and control the cooling path, and test reheating and storage of material cooled as in the process, because the cooling rate changed the reheating behaviour of the same compound baird2013 R9, C28. Do not take a clean DSC cooling trace as evidence of a nucleus-free glass baird2010 C54. Storage effects of cooling history were not tested in these papers, so a storage study at the product's temperature is needed before relying on the effect baird2013 X15, C41.

History

Quenched-in nuclei were proposed in 2010 to explain the class II behaviour, with a TTT scheme adapted from Angell baird2010 C51, C58. Trasi and Taylor restated the idea for acetaminophen in 2012 trasi2012a C40. Baird in 2013 supported it indirectly with the cooling-rate effect on reheating and the clofoctol constant-cooling test baird2013 C30, C29.

How it was shown

Baird and co-workers (2010) quenched melts of five molecules in liquid N2 between two cover glasses, which they assumed minimizes surface crystallization, and stored them over P2O5 (0% RH): indoprofen at 30 °C, droperidol and clotrimazole at 15 °C, nifedipine and felodipine at 30 °C, that is 14–20 °C below Tg baird2010 P7, A6, C45. Crystallization was followed by polarized light microscopy at 5 min, 1 day and 3 months, without a crystallinity measurement baird2010 P7, X16. Van Eerdenbrugh and Taylor (2010) spin coated eight drugs of known class with seven polymers at seven drug/polymer ratios from ethanol, scored the films by polarized light at days 0, 1, 3 and 7 of dry storage, and averaged an amorphous index per drug vaneerdenbrugh2010b P1, P2, R2, E4. Marsac and co-workers (2006) had compared nucleation in pure films of nifedipine and felodipine and in their PVP dispersions marsac2006a R1, C52. Zhu and co-workers (2012) measured crystallization of six drugs in 20/80 PEG dispersions against the pure melts at 25 °C, using 50 samples per pure drug for induction-time statistics zhu2012 R1, R2, R3, R23. Later papers used the neat-drug class to choose model drugs or to explain dispersion results for delamanid, pretomanid, lumefantrine, tacrolimus and three melt-extrusion drugs duong2022a C44; nguyen2023a C59; trasi2020 C7; trasi2017 C6; moseson2020 C5.

What the data show

Quenched indoprofen (Tg 50 °C) stored at 30 °C showed one spherulite after 5 min and a fully birefringent field after 1 day baird2010 R23. Droperidol at 15 °C (Tg 29 °C) and nifedipine at 30 °C (Tg 45 °C) crystallized at the edges within 1 day and appeared completely crystalline after 3 months baird2010 R24. Clotrimazole at 15 °C (Tg 30 °C) and felodipine at 30 °C (Tg 45 °C) showed only edge crystallization after 3 months baird2010 R25. The authors conclude "there may be a link" between glass-forming ability and glass stability baird2010 C46, C47. In the polymer screen, average amorphous indices were 47–59% for the five class I drugs, 68% for the class I/II drug and 73–97% for the two class II drugs vaneerdenbrugh2010b R4, C15. The authors conclude that drugs whose pure form crystallizes more readily were harder to stabilize and needed more polymer vaneerdenbrugh2010b C1. Pure nifedipine nucleated faster than felodipine (0.39 against 0.17 × 10¹⁰ m⁻³ day⁻¹ at 22 °C), and the authors suggest that the relative tendency in dispersions "may be dependent" on that of the pure drugs marsac2006a R4.a, C52. In PEG, haloperidol, which crystallizes within seconds as a pure melt, was hardly affected, and benzocaine was slowed by its favourable interaction with PEG zhu2012 R1, C39. Ibuprofen and fenofibrate, which as pure liquids started to crystallize in only 2 and 4 of 50 samples within 1 h, nucleated more readily in the dispersion, with crystals forming at crystalline PEG surfaces zhu2012 R2, R3, C4, C34. The authors state that the link between pure-drug and dispersion crystallization "was found to break down" for these slowly crystallizing drugs zhu2012 C41. Pretomanid (class I) glass crystallized within minutes, yet its HPMCAS dispersions were physically stable under ambient conditions for several months nguyen2023a R4, R27, C62. Delamanid (class I) dispersions made by rotary evaporation held crystals above about 10–15% drug loading duong2022a R8, C44. Pure amorphous tacrolimus did not start to crystallize until after 2 weeks at 40 °C/75% RH, while a commercial formulation crystallized faster than the pure drug, pointing to a formulation or processing factor trasi2017 R16, C28. Under 1–4 h holds of the undercooled melt, posaconazole and bicalutamide (both class III) crystallized within 1 h while indomethacin did not nucleate in 4 h moseson2020 R7, C17, C18.

Figure

Bright areas are crystals and a dark field is glass: indoprofen at 5 min and 1 day (a, b), droperidol and clotrimazole at 15 °C after 3 months (c, d), nifedipine and felodipine at 30 °C after 3 months (e, f); the extractor notes that panels (c) and (d) do not visibly match the text baird2010 R23, R24, R25, X16.

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

Why

Baird and co-workers attribute the faster crystallization of class II and quench-glassy class I glasses below Tg to nuclei formed during cooling, to which molecules diffuse as the glass relaxes ("It is believed"); the nuclei were not detected baird2010 C57, C58. Indoprofen's rapid crystallization below Tg is read as a high inherent tendency from the glass baird2010 C44. For dispersions, the 2010 polymer screen reads the class as how much inhibition a drug needs, and Van Eerdenbrugh and co-workers write that class I drugs "may not be appropriate candidates" for solid dispersions vaneerdenbrugh2010b C1; vaneerdenbrugh2010a C48. Zhu and co-workers explain where the link breaks: both the drug's own tendency and its ability to interact with the carrier matter, and a crystalline carrier can add heterogeneous nucleation zhu2012 C38, C39, C4. Trasi and co-workers grade the risk by the extended classes, class I highest, then class II, class III intermediate and class IV "likely" the most robust, assuming relative growth rates carry over to storage temperatures trasi2014a C18, C16. Tacrolimus authors name inherent crystallization tendency as the most important parameter of physical instability, set by conformational flexibility, configurational entropy, driving force, viscosity and hydrogen bonding, "not fully elucidated" trasi2017 C6. (synthesis: the class is measured on the neat drug at short time scales, whereas stability in a product depends also on the polymer, water, surfaces and process history; the cases above where the class failed involve exactly one of these factors: a nucleating carrier, a strong inhibitor, or a formulation step zhu2012 C41; nguyen2023a C62; trasi2017 C28.)

Conditions and limits

The storage ranking rests on one or two compounds per class, one temperature each, judged by eye, and indoprofen is really class I-B by its quench data baird2010 X16, X3. Only 0% RH and sandwiched samples were used, so humidity and free surfaces were not examined (see F21) baird2010 P7, A6, C45. The polymer screen used spin-coated films over 7 days vaneerdenbrugh2010b P1, P2. The later dispersion results come from single drugs and different preparation routes duong2022a C44; nguyen2023a R27.

Counterexamples and conflicts

PEG dispersions of slowly crystallizing drugs zhu2012 C41. Pretomanid dispersions, class I yet stable for months with HPMCAS nguyen2023a C62. Class III drugs differ widely under isothermal holds of the melt moseson2020 R7. A commercial tacrolimus product crystallized faster than the pure amorphous drug trasi2017 C28.

Transfer check

Treat class I as a warning that strong crystallization inhibition will be needed, and class II as a warning that the glass may carry nuclei vaneerdenbrugh2010a C48; baird2010 C58. Then test the actual dispersion at its drug loading, polymer, humidity, temperature and particle surface, because the class alone did not predict pretomanid, delamanid, PEG or tacrolimus outcomes nguyen2023a C62; duong2022a C44; zhu2012 C41; trasi2017 C28. For a crystalline carrier such as PEG, test whether the carrier nucleates the drug zhu2012 C4.

History

Marsac in 2006 suggested that pure-drug tendency carries into dispersions marsac2006a C52. Baird and Van Eerdenbrugh in 2010 proposed the link from the classes and the polymer screen baird2010 C46; vaneerdenbrugh2010b C1. Zhu in 2012 found where it breaks zhu2012 C41. Trasi in 2014 graded the risk with growth rates trasi2014a C18. Dispersion work from 2017 to 2023 used the class to choose drugs and strategies and found further exceptions trasi2017 C6; moseson2020 C5; duong2022a C44; nguyen2023a C62.