How fast must a drug melt be cooled, or its glass reheated, to escape crystallization? Fast-scanning calorimetry on 25 compounds

Background and motivation

Many new drug candidates dissolve poorly in water, and making them amorphous is one way to raise their dissolution rate and apparent solubility. Amorphous drugs are usually mixed with a polymer to form an amorphous solid dispersion that resists crystallization, but keeping the drug amorphous over the shelf life of a product remains, in the authors' words, an "enduring problem" (refs 3–7). C6 When the amorphous product is made by cooling a melt, as in melt extrusion, the inherent tendency of the drug to crystallize from its undercooled melt is an important criterion for whether the drug suits an amorphous formulation at all. C1

The starting point is the authors' own earlier study (Baird, van Eerdenbrugh and Taylor, J. Pharm. Sci. 99, ref 8). There, drug-like molecules were cooled from the melt and reheated in a conventional differential scanning calorimeter (DSC) and sorted into three classes: class (I) crystallized on cooling, class (II) formed a glass on cooling but crystallized on reheating, and class (III) did neither. Class (I) was split further by quenching the melt in liquid nitrogen: class (I–A) compounds crystallized even then, class (I–B) compounds could be trapped as a glass. The labels used in this paper are very high (I–A), high (I–B), moderate (II) and low (III) crystallization tendency, and classes (II) and (III) were separated by whether crystallization occurred on reheating at 10 °C/min. P5

That scheme had a resolution problem. Crystallization during cooling or reheating is "extremely time dependent" and might be suppressed simply by scanning fast enough, but a conventional DSC cannot cool or heat at controlled fast rates; its controlled cooling stopped at 20 °C/min, and quenching in liquid nitrogen is fast but uncontrolled. C7·R6 The critical cooling rate, the slowest cooling that avoids crystallization, could therefore not be measured for most compounds, and compounds within one class could not be told apart. C7

Fast calorimeters had become available. High performance DSC reaches controlled rates of hundreds of degrees per minute with sub-milligram samples and had been used mainly to detect small amorphous contents (refs 9–12). Chip calorimetry, with a thin film spin-coated on a sensor chip, reaches up to 10⁷ °C/s and had been used mainly for fast-crystallizing polymers (refs 13–16). The prototype rapid heat/cool (RHC) DSC from TA Instruments reaches about 2000 °C/min, and preliminary studies on organic compounds suggested it "could be an ideal technique" for their crystallization kinetics (refs 13, 17). C8

A second motivation came from glass science. It had been suggested that cooling faster than the critical rate for crystallization, but slower than the critical rate for nucleation, gives a glass that contains quenched-in nuclei (Angell, ref 21), and the earlier study had proposed that class (II) compounds crystallize on reheating partly for this reason (ref 8). C27

The paper therefore sets out to determine or estimate the critical cooling rate (R_crit,cool) and the critical heating rate (R_crit,heat, the slowest reheating of the glass that avoids crystallization) for class (I–A), (I–B) and (II) compounds, using both the conventional and the RHC DSC, and to test for quenched-in nuclei in compounds that form glasses easily but crystallize on reheating. The test set has eight class (I–A), seven class (I–B) and ten class (II) compounds. A1·P2·P4

Background concepts

The undercooled melt and the glass. When a crystalline compound is melted and cooled, the liquid may stay liquid below its melting temperature $T_m$; it is then an undercooled (supercooled) melt. On further cooling its viscosity rises steeply, and at the glass transition temperature $T_g$ it becomes a glass. Crystallization can happen anywhere between $T_m$ and $T_g$: on the way down (crystallization on cooling) or, if the glass forms, on the way back up when the glass is reheated (devitrification). Table 1 of the paper gives $T_m$ and $T_g$ for all 25 compounds; the $T_g$ values come from ref 8 and are marked as estimates for all class (I–A) compounds and for 4-biphenylcarboxaldehyde; the paper does not say how they were estimated. M1–M25

Degree of undercooling. How far below its melting point a melt gets before it crystallizes is the degree of undercooling (Table 2, footnote a):

In plain terms: $T_{\mathrm{c}\mathrm{r}\mathrm{y}\mathrm{s}\mathrm{t}}$ is the temperature of the crystallization exotherm seen in the cooling thermogram, and $\Delta T$ is how many degrees below $T_m$ that happened. The larger $\Delta T$ at a given cooling rate, the more sluggish the crystallization. The paper does not say which point of the exotherm defines $T_{\mathrm{c}\mathrm{r}\mathrm{y}\mathrm{s}\mathrm{t}}$; its remark that the exotherm peaks could not be located for partly crystallizing samples implies the peak. E4·X16

Critical cooling and heating rates. If a melt is cooled faster, it spends less time at temperatures where crystals can form and grow, so above some cooling rate crystallization is avoided; that rate is R_crit,cool. In the same way, a glass reheated fast enough passes through the undercooled range before crystals can form and grow; that rate is R_crit,heat. The paper reports both in °C/min. P2·P4

Nucleation and growth, and their temperature windows. Crystallization needs two steps: nuclei must form, and then grow. Each step has its own rate and its own temperature dependence below $T_m$. C32 In the authors' picture, growth is fastest at small undercooling and nucleation at larger undercooling, closer to $T_g$, where the melt is viscous and growth is slow. C36 Figure 5 of the paper draws these as two bell-shaped curves (red for nucleation, blue for growth) against the degree of undercooling, from $T_m$ to $T_g$. In panel (a) the curves overlap strongly; in panel (b) the nucleation maximum lies near $T_g$, far from the growth maximum. The figure is a schematic: no nucleation or growth rate was measured in this paper. C33·C35·C36

Quenched-in nuclei. If nucleation is fastest at temperatures where growth is already slow, a melt cooled at a moderate rate can form many nuclei near $T_g$ that never grow during cooling. They stay in the glass. On reheating, the glass passes back through the temperature range where growth is fast, and these nuclei can grow into crystals even when the heating is fast. Such nuclei are called quenched-in nuclei. C27·C36

Estimating a critical cooling rate that cannot be reached. For compounds that crystallize at every rate a calorimeter can achieve, R_crit,cool can only be extrapolated. The paper uses two methods from inorganic glass science, those of Barandiarán and Colmenero (BC, ref 18) and of Cabral (ref 19). Both start from the crystallization temperatures measured at several cooling rates: the natural logarithm of the cooling rate is plotted against $1/(\Delta T{)}^2$ and fitted with a straight line, whose y-intercept is called $A$ (or $A^{*}$) and whose slope is called $B^{*}$ (the paper states this regression in words). E3 The BC estimate is (eq 1):

In plain terms: the intercept is the value of ln(cooling rate) where $1/(\Delta T{)}^2$ falls to zero, that is, where the extrapolated undercooling becomes infinitely large, and its exponential is taken as the critical cooling rate. E1 The Cabral estimate is (eq 2):

In plain terms: the same straight line is read at an undercooling equal to $T_m$ itself, with $T_m$ in kelvin. Because $B^{*}/T_m^2$ is small for these compounds, the two estimates are almost the same in Table 3. For the method to work at all, a faster cooling rate must give a lower crystallization temperature; the authors call this condition obvious. E2·C17·R7

Methods in detail

The work has three parts: cooling series that locate or bound the critical cooling rate, an extrapolation of that rate where it could not be reached, and reheating series that measure the critical heating rate after slow and after fast cooling. The flow below shows how they fit together.

The two instruments

Conventional DSC. The conventional data come from the earlier study (ref 8): a TA Q2000 DSC with a refrigerated cooling accessory and nitrogen purge (50 ml/min), calibrated for temperature with benzophenone, indium and tin and for enthalpy with indium, runs in triplicate. For class (II) compounds, about 3–5 mg in hermetically sealed pans were heated at 10 °C/min to about 10 °C above $T_m$, held for 3 min, cooled at 20 °C/min to −75 °C and reheated at rates from 10 to 200 °C/min; the heating rate that prevented recrystallization was recorded as R_crit,heat. The 5 °C/min cooling data in Table 2 also come from this instrument. P1

Rapid heat/cool DSC. The prototype RHC DSC was calibrated for temperature and enthalpy with indium at heating rates from 10 to 1700 °C/min, with helium purge at 10 ml/min. Single crystalline particles of about 30–50 µg were placed in specially designed Tzero pans under a stereomicroscope, crimped, heated at 10 °C/min to about 10 °C above $T_m$ and held for 3 min. The samples are thus about a hundred times smaller than in the conventional DSC. P2·P1 The number of RHC runs per condition is not stated, and Table 2 gives standard deviations only "if available". X9

Part 1: cooling series

Class (I–A) and (I–B) compounds were cooled from the melt at 100 and 500 °C/min and at the fastest rate the RHC could reach for each sample, which ranged from 687 °C/min (4-biphenylcarboxaldehyde) to 1220 °C/min (carbamazepine). The crystallization temperature, and from it the degree of undercooling, was read from each cooling trace. Together with the 5 °C/min data from ref 8, this gives four cooling rates per compound spanning more than two orders of magnitude (Table 2). P2·R1 Class (I–B) compounds that did not crystallize even at the fastest rate were then cooled at progressively slower rates, to find the slowest that still gave a glass. P2·R5

Part 2: extrapolating the critical cooling rate

Where crystallization could not be avoided, the BC and Cabral methods (eqs 1 and 2) were applied to the crystallization temperatures of Table 2. They were applied to the eight class (I–A) compounds and to indoprofen; 4-biphenylcarboxaldehyde and carbamazepine were left out because, with partial crystallization, the exotherm peaks could not be located accurately. P3 The earlier study had applied the same methods to cooling rates of only 2–20 °C/min. R8 The text gives the range used here as "5 °C to over 500 °C min⁻¹" in one place and "5–800 °C min⁻¹" in another, while the fastest rates in Table 2 reach 1100 °C/min; the points entering each fit are not listed. X16

Part 3: reheating series after slow and after fast cooling

Class (I–B) compounds that formed a glass, and the class (II) compounds, were reheated at various rates after cooling at 20 °C/min, in the conventional DSC (up to 200 °C/min) and in the RHC (up to about 2000 °C/min), to find R_crit,heat. They were then reheated after cooling at the maximum rate the RHC could reach. P4·R9 The text gives this quench rate as ">500 °C min⁻¹ in all cases"; figure captions print it for three compounds: flufenamic acid 1025, dibucaine 800 and clofoctol 860 °C/min. P4·X5 Crystallization on reheating shows up either as a crystallization exotherm or as a melting endotherm at $T_m$, the crystals formed on reheating melting again. P4

One control addresses where the crystals form. If clofoctol crystallized partly during cooling, a faster reheating rate would not remove the melting endotherm. The authors therefore cooled clofoctol at a constant 20 °C/min and reheated it at 200, 300, 400 and 500 °C/min (Figure 4b). P4·R12

Experimental analysis

Class (I–A): no rate the instrument reached could stop crystallization

All eight class (I–A) compounds crystallized at the fastest cooling rate the RHC reached for them, between 800 and 1100 °C/min (Table A). R1·R3 Figure 1 shows two of them. For phenacetin the crystallization exotherm peak moved from about 113 °C at 100 °C/min to about 109.5 °C at 500 °C/min and about 107 °C at 1026 °C/min; for benzamide from about 97.5 to about 90.5 and about 85.5 °C at 100, 500 and 1004 °C/min (read from Figure 1, approximate). Faster cooling pushed the exotherm to lower temperature but never removed it. R2·C9

Table A. Degree of undercooling ΔT = T_m − T_cryst (°C) before crystallization on cooling, with standard deviations in parentheses where the paper gives them (Table 2). The 5 °C/min column comes from the conventional DSC of ref 8; * partial crystallization during cooling. The indoprofen row is printed with exactly the values of the phenacetin row. R1·X1

Two things stand out in Table A, and the authors point to both. First, compounds differ widely in how far they can be undercooled: at 500 °C/min 4-biphenylmethanol crystallized only 15.1 °C below its melting point and haloperidol 90.8 °C below. R1·C10 Second, the sensitivity to cooling rate differs: going from 5 to 500 °C/min lowered the crystallization temperature by about 6 °C for 4-biphenylmethanol but about 23 °C for benzocaine. R4·C11 The authors note that this sensitivity "seemed to correlate" with the absolute undercooling for most compounds, with "some exceptions": compounds that crystallize close to $T_m$ "tended to" change least. C11 The exceptions are visible in the table: benzamide (32.3, 28.5, 36.5, 42.9 °C) and lidocaine (43.3, 39.4, 45.1, 45.5 °C) did not undercool steadily more as cooling became faster. R1.c·R1.g

The authors conclude that cooling at more than 1000 °C/min was insufficient to suppress crystallization of class (I–A) compounds, "confirming" the very high crystallization tendencies seen earlier, and the abstract places their R_crit,cool "above 1000" °C/min. C2 Strictly, Table A shows crystallization above 1000 °C/min for four of the eight compounds (atenolol, benzamide, felbinac, phenacetin); the other four were cooled at most at 800–913 °C/min, so for them the data show R_crit,cool above that rate. X6 The authors also argue that, although these compounds were already known to crystallize during liquid nitrogen quenching, the controlled rates give "a tangible estimate" of their relative crystallization rates. C12

Class (I–B): one class, two very different behaviours

The seven class (I–B) compounds did not behave as one group. Antipyrin, chlorpropamide, flufenamic acid and tolbutamide did not crystallize at the fastest RHC cooling, and further runs at progressively slower rates showed that cooling at only 25 °C/min already gave a glass. R5·R9.a–d In contrast, 4-biphenylcarboxaldehyde and carbamazepine still crystallized partly at the fastest rates reached (687 and 1220 °C/min), and indoprofen crystallized completely. R5·R1.i–j So within one class R_crit,cool differs by orders of magnitude, a difference the earlier study could not detect because its controlled cooling stopped at 20 °C/min. The authors write that the four glass formers "may be more appropriately classified" as borderline class (I–B)/(II). C13

For the partly crystallizing pair, the authors argue by analogy. In ref 8, chlorpropamide, flufenamic acid and tolbutamide also crystallized partly when cooled at 20 °C/min, just below their R_crit,cool of about 25 °C/min; partial crystallization therefore seems to mark a rate close to the critical one. They "conjecture" that the R_crit,cool of 4-biphenylcarboxaldehyde and carbamazepine is "probably only slightly faster" than the maximum rates reached, which fits the earlier finding that both formed a glass when quenched in liquid nitrogen. R6·C14 Their reading of the class as a whole is that class (I–B) compounds "may have very different temperature dependencies of nucleation and/or growth rates". C15

Note by the AI writer (not discussed in the paper): the indoprofen row of Table 2 repeats the phenacetin row in all five columns. Those values rise steadily with cooling rate and would fit the extrapolation well, yet Table 3 and the text place indoprofen among the compounds whose undercooling was erratic. The printed row is therefore most likely a duplicate, and indoprofen's own cooling data are not available from the paper. X1

Extrapolated critical cooling rates

Table B lists the extrapolations. Where the crystallization temperature fell steadily with cooling rate, the fits were good (r² 0.89–0.99) and gave R_crit,cool estimates of a few thousand K/min. For benzamide, lidocaine and indoprofen the undercooling both rose and fell with cooling rate, r² was below 0.55, and the authors call the methods "clearly inappropriate" for them. R7·C16 They attribute the erratic behaviour of benzamide and lidocaine, already seen over 2–20 °C/min in ref 8, "most likely" to the stochastic nature of nucleation and to the difficulty of avoiding heterogeneous nucleation in DSC pans. R8·C18

Table B. Regression intercept A, slope B, r² and the critical cooling rates by eq 1 (BC) and eq 2 (Cabral), as printed in Table 3. The last column is the AI writer's recalculation of eq 1 from the printed intercept, which is rounded to one decimal; the printed column heading of A is "K min⁻¹". R7·E1·X2·X3

Three printed entries do not follow from their own inputs, and the reader should know this before using the numbers. First, haloperidol's intercept of 6.5 gives exp(6.5) ≈ 6.65 × 10² K/min, not the printed 6.6 × 10³; a regression of its four Table 2 points reproduces the printed intercept, slope and r², and the authors' own remark that the estimates are much larger than the fastest RHC rates "with the exception of haloperidol" only makes sense for the smaller value, which lies below the 913 °C/min at which haloperidol still crystallized. The printed exponent is most likely a misprint. X2·C19 Second, 4-biphenylmethanol's intercept is printed as "8.", but its R_crit,BC of 8.1 × 10³ requires an intercept of about 9.0. X3 Third, the felbinac fit cannot be reproduced from the four Table 2 points (recalculated slope about 617 and r² about 0.989 against the printed 768 and 0.93), whereas the other fitted compounds reproduce within rounding. X13·E3

Leaving these aside, the authors judge that the estimates "may be reasonable" values of the true R_crit,cool, and that a wide range of cooling rates "seems to improve" the fits: atenolol, benzocaine and felbinac gave r² below 0.55 over 2–20 °C/min in ref 8, but 0.99, 0.99 and 0.93 here. C19·C20·R8 They then add a practical shortcut: for pharmaceutical systems it is "probably sufficient to know" that a compound with R_crit,cool above 500 °C/min will be difficult to render and keep amorphous, so its exact critical rate need not be estimated. C21

Reheating: the asymmetry between cooling and heating

Table C collects the critical rates for the four borderline class (I–B) compounds and the ten class (II) compounds. In the printed Table 4 all three rate columns are headed "R_crit,cool", but footnotes a and b and the text define the second and third columns as critical heating rates; Table C uses the corrected headings. R9·X4

Table C. Critical cooling rate and critical heating rates (°C/min) from Table 4, with the column headings corrected as the footnotes define them. Which instrument and which study produced each value is not stated per entry. R9·X4·X9

Three results come out of Table C. The first is the spread within class (II): after cooling at 20 °C/min, R_crit,heat runs from 12.5 °C/min for bifonazole and 15 °C/min for celecoxib to above 1910 °C/min for acetaminophen, a "huge variation" over about four orders of magnitude. R9.e–n·C22 Since these compounds did not crystallize on slow cooling, the authors consider it "likely" that nucleation and growth do not overlap much in temperature for them and "surmise" that growth happened only on reheating; differences in R_crit,heat "can be inferred" as differences in relative nucleation and/or growth rates. C23

The second result is the asymmetry between cooling and heating. Every compound in Table C needs a much faster reheating rate than cooling rate. Acetaminophen forms a glass at cooling rates below 1 °C/min yet still crystallizes on reheating at 1910 °C/min, a difference of over three orders of magnitude; the four borderline class (I–B) compounds need only 25 °C/min on cooling but more than 1500–2000 °C/min on reheating. R9·C24 Figure 2 shows it for flufenamic acid. Cooled at 25 °C/min, it gives no exotherm, and on reheating a glass transition appears (the instrument labels the step 19.45 °C, 0.4787 J/(g·°C)), "indicating" that a glass formed. Cooled at 1025 °C/min and reheated at 1900 °C/min, it still shows a crystallization exotherm (labelled onset 84.20 °C, peak about 108 °C) followed by melting near 131 °C (read from Figure 2, approximate). R10·C25 Similar asymmetries had been reported for inorganic bulk metallic glasses (Schroers et al., ref 20); "to the best of the authors' knowledge" this is the first report for organic systems. R13·C26

The third result is the effect of the cooling history. Glasses made at the maximum cooling rate needed a lower R_crit,heat than glasses made at 20 °C/min in all ten cases where the table allows a comparison: slightly for antipyrin (>2000 → 2000 °C/min), tolazamide (35 → 30) and droperidol (175 → 125), somewhat for bifonazole (12.5 → <10) and celecoxib (15 → <10), about two-fold for cinnarizine (300 → 135) and clofoctol (400 → 200), at least two-fold for nifedipine (>500 → 250) and chlorpropamide (>2000 → 1000), and more than three-fold for dibucaine (>1000 → 300). For acetaminophen, flufenamic acid and tolbutamide the limit of the instrument was reached both times, and D(−) salicin has no value after quench cooling. R9·X8 The authors' reading is that R_crit,heat "was reduced, suggesting a reduction in the number of nuclei formed". C28

The thermograms make the effect concrete. For dibucaine (Figure 3a), reheating at 300 °C/min gave a melting endotherm near 66 °C for the glass made at 20 °C/min but none for the glass made at 800 °C/min; after 20 °C/min cooling the endotherm was still present, though smaller, at 1000 °C/min (Figure 3b; read from the figure, approximate). R11 For clofoctol (Figure 4a), reheating at 200 °C/min gave a small endotherm near 89 °C after 20 °C/min cooling but not after 860 °C/min cooling. R12 In the control of Figure 4b, clofoctol cooled at a constant 20 °C/min showed an endotherm that shrank as the reheating rate rose from 200 to 500 °C/min and was gone at 500 °C/min. "Assuming that the same number of nuclei formed in each sample during constant cooling", the authors take this as confirming that the crystals formed on reheating, "most likely linked" to quenched-in nuclei, and conclude that the smaller asymmetry after quench cooling "strongly suggests" that quenched-in nuclei are generated during the slower cooling. R12·C29·C30 Table 4 lists 400 °C/min as clofoctol's R_crit,heat after slow cooling, while the text names 500 °C/min as the rate that removes the endotherm and Figure 4b at 400 °C/min still shows at most a trace of it; the value is best read as between 300 and 500 °C/min. X14

A side result concerns the class boundaries again. After quench cooling, bifonazole and celecoxib needed less than 10 °C/min on reheating. Since classes (II) and (III) were separated by crystallization at a heating rate of 10 °C/min, the authors call both compounds borderline class (II)/(III), "depending on the cooling rate employed". R9.f–g·C31

Discussion

The authors' explanation: two temperature windows

The discussion turns the rate data into a picture of nucleation and growth (Figure 5). For class (I–A), crystallization at the fastest cooling "indicate[s]" that nucleation and/or growth are very fast and that their temperature windows overlap strongly: as soon as the melt reaches temperatures where nuclei form, growth is fast enough to turn them into crystals. C33 Differences in the undercooling reached before crystallization "suggest" different temperature dependencies; at 5 °C/min 4-biphenylmethanol crystallized at a ΔT of about 9.5 °C and benzocaine at about 31.9 °C, so at about 9.5 °C of undercooling the nucleation and/or growth rates of 4-biphenylmethanol are surmised to be much higher. C34·R1.a·R1.d

For class (I–B) and (II), the authors argue from the asymmetry. If the two windows overlapped as much as in class (I–A), a modest cooling rate could avoid crystallization only if nucleation or growth were slow throughout, and reheating should then need a similar rate; little asymmetry would be expected. Since R_crit,heat is instead far above R_crit,cool, the overlap is taken to be smaller for class (I–B) and minimal for some class (II) compounds (Figure 5b). C35·R9 The chain below follows the authors' scenario for a compound cooled and reheated at the same rate, and how the cooling history changes it.

Two further assumptions carry the argument. "Assuming steady-state nucleation", as many nuclei form on reheating as on cooling; the asymmetry then arises because the nuclei formed on reheating meet higher growth rates as the temperature rises. C36 And although the cooling rate alone can change the properties of a glass and its devitrification below $T_g$ (Yu, ref 22), reheating through $T_g$ "should in principle" erase that thermal history; if no nuclei were trapped during cooling, the cooling rate should then not affect crystallization on reheating, yet it did. C37·R9 On this basis the authors read R_crit,heat after slow and after quench cooling as a pair: after quench cooling, assumed to give a glass free of nuclei, crystallization on reheating needs both nucleation and growth, while after slow cooling it needs only growth. C38

The conclusions put this in firmer and in softer words. Class (I–A) molecules "tend to be" lower molecular weight compounds with simple structures and are therefore poor glass formers. C39 For class (I–B) and (II), "there is evidence" for quenched-in nuclei formed during cooling, which "likely contribute" to their high crystallization tendency on even very rapid reheating, and these compounds "may form glasses that have a high tendency to crystallize during storage". C40·C41

What it means for formulation

The authors draw three practical points. A drug whose R_crit,cool exceeds 500 °C/min will be difficult to render and keep amorphous. C21 In-depth evaluation of a drug's inherent crystallization tendency, for example by thermal analysis, "is critical" to judge whether an amorphous formulation will stay stable over time. C42 And RHC DSC together with conventional DSC "can be valuable tools" for screening new chemical entities early in development. C5

Note by the AI writer (not discussed in the paper): the most useful lesson for a formulator may be that the cooling test alone misjudges some drugs. Acetaminophen looks like an easy glass former on cooling (below 1 °C/min suffices) but crystallizes on reheating at above 1910 °C/min. R9.e Any process that takes a glass back through its undercooled range, such as reheating during extrusion, milling, or storage near or above $T_g$, could then matter more than how easily the glass formed. The cooling-history result also hints that a faster quench may give a glass that is harder to crystallize later, but this was shown only for neat drugs in 30–50 µg DSC samples, on a time scale of minutes, without polymer. R9·P2·A1

Limitations

Limits the authors state. The authors note that the extrapolation methods require the crystallization temperature to fall steadily with cooling rate and fail for benzamide, lidocaine and indoprofen, "most likely" because nucleation is stochastic and heterogeneous nucleation is hard to avoid in DSC pans. C16·C17·C18 They present the R_crit,cool of the partly crystallizing compounds as a conjecture ("probably only slightly faster"). C14 Their mechanism rests on stated assumptions ("Assuming that the same number of nuclei formed", "Assuming steady-state nucleation", "should in principle"), and the storage consequence is put as "may". C29·C36·C37·C41

The AI writer's own judgement (1): the nuclei are inferred. The central explanation, quenched-in nuclei formed during slower cooling, is never observed. The evidence is the effect of the prior cooling rate on R_crit,heat and on the melting endotherm, and the clofoctol control assumes equal nucleation during constant cooling. A direct test, for example counting crystals by microscopy after holding quenched and slowly cooled glasses in the growth range, was not done. X7 The rates themselves are solid DSC observations; the mechanism is the authors' interpretation, as their hedges ("suggesting", "strongly suggests", "likely contribute") indicate. The abstract's statement that quenching "greatly reduced" the asymmetry of class (II) compounds also fits only some of them: the drop is more than three-fold for dibucaine, about two-fold for several others, small for tolazamide and droperidol, and unreadable for acetaminophen. X8

The AI writer's own judgement (2): the tables need care. Several printed values do not hold up: the indoprofen row of Table 2 duplicates phenacetin's X1; the haloperidol estimate in Table 3 is most likely ten times too high X2; one intercept lacks a digit X3; the felbinac fit cannot be reproduced X13; and the Table 4 column headings are wrong X4. The "above 1000 °C/min" for class (I–A) was reached for only four of the eight compounds X6. Lidocaine and dibucaine are listed with the same melting point (68 °C) and glass transition (−39 °C), which cannot be checked here X12. None of these changes the qualitative picture, but a reader taking numbers from the tables should use the corrected readings.

The AI writer's own judgement (3): conditions. Values from two instruments and two studies are combined without saying which entry comes from where; the conventional data were run in triplicate, while the replicate number of the RHC runs is not stated X9. The RHC was calibrated up to 1700 °C/min, but heating rates of 1900–2000 °C/min were used for several compounds X10. The quench rate before reheating is printed for only three compounds X5. The statement that class (I–A) compounds tend to have lower molecular weight holds on average in Table 1 (mean about 217 g/mol for class (I–A), 245 for (I–B), 324 for (II), the AI writer's calculation) but with clear exceptions such as haloperidol (375.9 g/mol, class I–A) and acetaminophen (151.2 g/mol, class II) X11. Finally, the link to storage stability and to formulations with polymers, which motivates the work, was not tested X15.

Conclusion

Fast-scanning calorimetry separated compounds that a conventional DSC had lumped together. The eight class (I–A) compounds crystallized at every cooling rate reached, up to 800–1100 °C/min; four class (I–B) compounds formed a glass at only 25 °C/min, while two others still crystallized partly at 687–1220 °C/min. R1·R3·R5·R9.a–d Glass-forming compounds needed far faster reheating than cooling to avoid crystallization, by more than three orders of magnitude for acetaminophen, and making the glass by faster cooling lowered the reheating rate needed in every comparable case. R9·C24·C28 The authors explain this by nucleation and growth windows that lie apart in temperature, so that slow cooling leaves nuclei in the glass ("strongly suggests"); the nuclei were inferred, not observed, and the suggested consequence for storage stability remains to be tested. C30·C35·C36·C41·X7·X15