Why two look-alike glasses crystallize at different rates: amorphous nifedipine and felodipine, alone and in PVP

Background and motivation

An amorphous drug dissolves faster and reaches a higher apparent solubility than its crystal, which "may lead" to higher bioavailability, but it pays for this with lower physical and chemical stability (Chiou and Riegelman 1971; Serajuddin 1999) C1. The usual remedy is to mix the drug at the molecular level with a polymer, making an amorphous solid dispersion. How such a polymer slows crystallization is normally explained by properties of the glass: a higher glass transition temperature (Tg), lower molecular mobility, and specific drug–polymer interactions such as hydrogen bonds (Miyazaki et al. 2004; Khougaz and Clas 2000; Taylor and Zografi 1997) C2.

The introduction points out that this picture does not always hold. Crowley and Zografi (2003) saw better stability at low PVP levels with no rise in Tg, and others argued that a drug that is stable on its own stays stable with a polymer whether or not specific interactions exist (Weuts et al. 2004; Van den Mooter et al. 2001; Law et al. 2001) C3. The authors take a step back: it is "clear" to them that physical stability must depend on two things at once, the free energy of the glass relative to the crystal (the thermodynamic driving force) and the kinetics of crystallization. Since crystallization starts with nucleation, a study of stability should ask how the polymer changes the thermodynamics and kinetics of nucleation, not only how it changes the glass C4·C5.

Two dihydropyridine calcium channel blockers make a sharp test of this idea. Nifedipine and felodipine share a 1,4-dihydropyridine ring with one NH donor and two ester groups; nifedipine carries a 2-nitrophenyl ring and two methyl esters, felodipine a 2,3-dichlorophenyl ring with a methyl and an ethyl ester (Figure 1) M1·M2. Their glasses have nearly the same Tg R4.c–e. Earlier spectroscopy by the same group (Tang, Pikal and Taylor 2002) had shown that in this family the hydrogen-bond strength varies among the crystals but is uniform among the glasses, and that nifedipine bonds more strongly in its crystal while felodipine bonds more strongly in its glass R20. Zhou et al. (2002) had found, for a set of glasses heated through Tg, that the larger the entropy of crystallization, the less readily the glass crystallized, with no correlation to the enthalpy or the total driving force R21.

The objective, in the authors' words, was to examine the thermodynamic, kinetic and structural factors behind the different isothermal nucleation rates of nifedipine and felodipine, alone and with PVP A1·A2. Without PVP, the thermodynamic difference between glass and crystal can be measured directly by calorimetry; with PVP it cannot, so the authors use Flory–Huggins theory to estimate how mixing lowers the drug's activity C6. Kinetics enter through the activation energy of nucleation from Arrhenius plots, and through the two "metrics" commonly used for dispersions, molecular mobility and Tg; structure enters through infrared spectra of the NH group A1.

Background concepts

Nucleation rate and its activation energy. The paper counts crystal nuclei that appear in thin amorphous films stored at constant temperature and humidity. The number of nucleation sites per unit volume rises linearly with time once nucleation is steady, and the slope is the steady-state nucleation rate $I$ P4·C7. Its temperature dependence is described by an Arrhenius relation (Eq. 2):

In plain terms: the rate falls exponentially as temperature falls, and the activation energy $\Delta E$ sets how steeply; $A$ is a pre-exponential factor, $R$ the gas constant and $T$ the absolute temperature E2. A plot of $\ln I$ against $1/T$ is a straight line of slope $-\Delta E/R$. The authors fit it separately above and below Tg, because the plot bends at Tg R2·R3.

Classical nucleation theory. The discussion uses the classical expression for the rate of homogeneous nucleation (Eq. 9; Turnbull and Fisher 1949):

In plain terms: two barriers slow nucleation. $\Delta G^{*}$ is the free energy needed to build a nucleus of critical size, a balance between the cost of creating a new crystal surface ($\Delta G_s$) and the free energy gained by forming crystal ($\Delta G_v$); $\Delta G_a$ is the activation energy for moving a molecule from the amorphous phase onto the nucleus; $k$ is the Boltzmann constant E9·C31. As temperature falls, the driving force grows and $\Delta G^{*}$ shrinks, but molecular motion slows and $\Delta G_a$ matters more. The authors note that the equation does not describe their glasses completely: it ignores stresses that build up in a solid when a nucleus forms with a volume change, and it ignores the lower barrier of heterogeneous nucleation. They still use it as a framework for the balance between driving force and kinetics C32.

Driving force for crystallization. The driving force is the free-energy difference between the amorphous form and the crystal at the same temperature; it is zero at the melting point and grows on cooling. A quick estimate needs only the heat of fusion $\Delta H_f$ and the melting temperature $T_M$, the Hoffman equation (Eq. 3; Hoffman 1958):

In plain terms: the driving force rises roughly in proportion to the undercooling $T_M-T$, scaled by the heat of fusion; the equation assumes that the enthalpies of liquid and crystal both change linearly with temperature and was derived for temperatures above Tg E3. A more exact value comes from the configurational heat capacity $C_p^{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{f}\mathrm{i}\mathrm{g}}$, the heat capacity of the supercooled liquid or glass minus that of the crystal, integrated down from the melting point (Eqs. 4–6):

In plain terms: at the melting point the enthalpy and entropy differences between amorphous form and crystal are the heat and entropy of fusion, with $\Delta S_f=\Delta H_f/T_M$; on cooling, both shrink by the integrals of the excess heat capacity, and their combination gives the free-energy difference at any temperature E4·E5·E6·E11. The enthalpy term favours crystallization, the entropy term ($T\Delta S$, the loss of configurational freedom) opposes it.

Molecular mobility from enthalpy recovery. A glass held below Tg slowly relaxes toward the supercooled liquid and loses enthalpy; on reheating, the lost enthalpy is recovered as an endotherm. The enthalpy recovered after aging time $t$, $\Delta H_{t,T}$, is fitted with the Kohlrausch–Williams–Watts (KWW) equation, printed as Eq. 7, with the maximum recovery given by Eq. 8:

In plain terms: the fraction of the possible enthalpy that has been recovered grows with aging time along a stretched exponential; $\tau$ is a mean relaxation time (longer means less mobile) and $\beta$ (between 0 and 1) measures how broad the distribution of relaxation times is. The maximum that could be recovered is the heat-capacity step at Tg, $\Delta C_P^{T_g}$, times the distance of the aging temperature below Tg E7·E8. The exponent $\beta$ is printed outside the parenthesis in Eq. 7, which would make it a mere rescaling of $\tau$; the standard KWW form is $\exp [-(t/\tau {)}^{\beta }]$, and that form reproduces the paper's nifedipine curve (Note by the AI writer, from the card's extractor note) X4.

Drug activity in a polymer. In a miscible dispersion the drug is diluted by the polymer, so its chemical potential, and with it the driving force for crystallization, must be lower than in the pure glass C45. The authors estimate the drug activity with Flory–Huggins lattice theory, treating the amorphous drug as the solvent (Eq. 10):

In plain terms: the activity $a_{\mathrm{d}\mathrm{r}\mathrm{u}\mathrm{g}}$ falls as the drug volume fraction ${\Phi }_{\mathrm{d}\mathrm{r}\mathrm{u}\mathrm{g}}$ falls, partly offset by the size difference between drug and polymer (the term in $m$, the ratio of the molecular volume of PVP to that of the drug) and lowered further when the interaction parameter $\chi$ is negative (favourable mixing) E10. The authors acknowledge that the theory has known limitations and that these glasses are not at equilibrium, and use it only to compare the two drugs C46.

Infrared NH stretch. Each drug has one NH donor. When the NH group forms a stronger hydrogen bond, its stretching band moves to lower wavenumber. In felodipine films the authors assign a shoulder at 3,420 cm⁻¹ to free NH, a band at 3,345 cm⁻¹ to drug–drug hydrogen bonds, and a band at 3,288 cm⁻¹ that grows with PVP to NH bonded to the PVP carbonyl R13·C27.

Methods in detail

The study measures one outcome, the nucleation rate, and sets beside it every property that might explain it, for both drugs and for their PVP dispersions. All work was done dry: films were stored at 0% relative humidity (RH) over phosphorous pentoxide, and spectra and calorimetry were run under dry gas, so that water does not enter the comparison P1·P4·P6·P7. The workflow is shown below.

Counting nuclei in thin films

Problem. Nucleation is the first step of crystallization, and it is slow and rare in a glass, so it has to be followed as the accumulation of new crystals over days in a sample whose volume is known. What they did. Drug, or drug with PVP K29/32, was dissolved in 50:50 wt% dichloromethane:ethanol or in acetone and spin coated in a glovebox below 10% RH onto glass slides; the films were heated to 90 °C for several minutes to drive off solvent and placed at once in a desiccator at 0% RH. They were optically transparent P1. Films stored over phosphorous pentoxide at 22 °C were taken out at each time point and examined with a polarized light microscope at 10×–50×; crystals show up as bright spots. Twelve sections of each film and three films per time point were counted P4. Sites at the film edge, where nucleation and growth were sometimes faster, were excluded P4.

The number of sites per unit area was turned into a number per unit volume by dividing by the depth of field of the objective, $D_{\mathrm{t}\mathrm{o}\mathrm{t}}$ (Eq. 1):

In plain terms: the depth over which the microscope sees crystals in focus depends on the wavelength $\lambda$ (550 nm), the refractive index $n$ of the medium (1.000 for air), the numerical aperture $NA$, the lateral magnification $M$ and the smallest distance $e$ resolved by the detector (14 µm); for the 10× objective it is 0.0144 mm E1·P4. The paper does not print the NA values or the film thickness; with an NA of 0.25, a typical value for a 10× objective, the equation gives 14.4 µm (calculation by the AI writer) E1·X10. Because the volume is set by the optics rather than by the film thickness, the per-volume rates are comparable within the paper but not easily with other studies X10.

Activation energy from Arrhenius plots

Nucleation rates were measured at several temperatures for the pure drugs and for dispersions with 3 wt% PVP, and $\Delta E$ was taken from the slope of $\ln K$ against $1/T$ (Eq. 2), fitted separately above and below Tg, with three replicates (Figure 3, Table I) P5·R2·R3. The temperatures are not listed in the text; from the $1/T$ axis they run from about 25 to about 75 °C, and the y-axis carries no unit X2. As a check, the AI writer read the pure nifedipine points at about 45 °C and about 25 °C (ln K about 17.5 and 14.5) and obtained a slope of about 14,700 K, that is about 122 kJ/mol, the value in Table I E2·R2.g·R2.k.

Thermodynamics from heat capacity

Pure glasses for calorimetry were made by melting the crystal in the DSC pan and cooling it P2. A TA 2920 modulated DSC, calibrated with benzophenone, indium and a sapphire standard (2 K/min underlying rate, ±0.5 K amplitude, 1 min period, the same pan for standard and sample), gave the heat capacity of the glass, the supercooled liquid and the crystal (Figure 5 shows felodipine) P7·R9. Their difference, $C_p^{\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{f}\mathrm{i}\mathrm{g}}$, is plotted in Figure 6: about 0.05–0.07 mJ/mg/°C in the glass and about 0.41–0.44 mJ/mg/°C just above Tg R10. Amorphous nifedipine crystallizes when heated to 87 (±1) °C, so its liquid heat capacity could not be measured above that point and was extrapolated linearly up to the melting point, 172.1 °C P8·R5. Integrating from the melting point with Eqs. 4–6 gave the free-energy curves of Figure 7 and the 25 °C values of Table II, which were compared with the Hoffman estimate P8·R4.i–l·R11.

Glass transition and mobility

Tg (onset, midpoint and offset, n = 3) and the heat-capacity step at Tg were measured for the pure glasses; for dispersions, drug and PVP were dissolved in ethanol, the solvent removed in a rotary evaporator and the solid dried under vacuum for at least 12 h before DSC P3·P7. The Tg of dispersions from 0 to 100 wt% PVP was compared with the Gordon–Taylor and Couchman–Karasz mixing equations, whose parameters are not printed (Figure 10) R17. Mobility was measured by aging the pure glasses and 10 wt% PVP dispersions at 23.5 °C for up to 16 h and fitting the enthalpy recovered to Eq. 7 (Figure 4) P9·R6.

Hydrogen bonding

Films on ZnS were examined with a Bio-Rad FTS-6000 FT-IR spectrometer (128 scans, 4 cm⁻¹ resolution, purge with dry CO2-free air). Amorphous references were made by spin coating and then melting and cooling, crystalline references by letting a spin-coated film crystallize completely. Dispersions were made at PVP hydrogen-bond acceptor to drug donor ratios of 0, 0.25, 0.5, 1.0, 1.5, 2.0, 2.5, 3.0 and 4.0 (each PVP repeat unit has one carbonyl acceptor, each drug one NH donor), so the comparison is at equal numbers of donors and acceptors rather than at equal weight fractions P6·R14·R15.

Drug activity in the dispersions

Eq. 10 was evaluated with interaction parameters of −3.8 for nifedipine–PVP and −4.2 for felodipine–PVP, taken from the group's companion work, where they were estimated by melting point depression (Marsac, Shamblin and Taylor 2006) P11·R18. The molecular-volume ratio $m$ is not printed. For a polymer $1/m$ is small; setting it to zero, the AI writer reproduces the curve of Figure 13: at a PVP volume fraction of 0.2, $\exp (\ln 0.8+0.2-3.8\times 0.04)=0.839$ for nifedipine against about 0.84 read from the figure E10·R19.b.

Experimental analysis

The ranking: nifedipine nucleates faster

In the pure glasses at 22 °C and 0% RH, nucleation sites accumulated linearly over 5 days, reaching about 8.0 ×10^10 m⁻³ for nifedipine and about 3.5 ×10^10 m⁻³ for felodipine (Figure 2, read from the plot) R1·C7. Table II gives the steady rates as 0.39 (0.09) ×10^10 and 0.17 (0.07) ×10^10 m⁻³ day⁻¹, a ratio of about 2.3 R4.a. The Arrhenius plots (Figure 3) put nifedipine above felodipine at every temperature from about 25 to about 75 °C, above and below Tg R2·C8. A non-isothermal test pointed the same way: a melt-quenched nifedipine glass heated through Tg at 2 °C/min crystallized to its metastable polymorph at 87 (±1) °C, while felodipine showed no exotherm and no melting endotherm (data not shown) R5·C11.

The absolute size of the rate is less settled than the ranking. The table and two figures give different values for the same pure glasses X1:

Table A. Three statements of the pure-glass nucleation rate R4.a·R1·R16.a·X1.

Converted to a common unit by the AI writer (86,400 s per day), the Figure 9 values are about 1.0 and 0.28 ×10^10 m⁻³ day⁻¹, so the three sources span a factor of about 4 for each drug X1. Every source ranks nifedipine first; the absolute rates should be treated as uncertain.

Tg and mobility do not separate the glasses

Table B. Properties of the two drugs, mean (SD), n = 3, from Table II R4. Unit corrections follow the card's extractor note X3.

Tg onset differs by 0.8 °C, β by 0.01, and τ by 2.1 h in the direction opposite to the nucleation ranking: the faster-nucleating nifedipine relaxes slightly more slowly R4.c·R4.m–n. The enthalpy-recovery curves of the two glasses overlap (Figure 4: about 5.0 and 5.3 mJ/mg after 16 h) R6.a–b. For the authors it is "immediately obvious" that the difference in crystallization cannot be explained by mobility measured this way, and they offer two readings: either other factors dictate nucleation, or this measure of mobility does not describe the motion involved in nucleation ("suggests either") C13·C37. The ΔCp row is printed in J/mol/°C, but 0.32 and 0.35 match the heat-capacity step of Figures 5 and 6 in mJ/mg/°C, and with felodipine's onset Tg they reproduce the stated maximum recovery: $0.32\times (43.1-23.5)=6.27$ mJ/mg against 6.3 (±0.3) in the text E8·R8·X3·X12.

The driving force: larger for nifedipine, and enthalpic

At 25 °C the free energy of crystallization is 9.6 kJ/mol for nifedipine and 6.2 kJ/mol for felodipine (Table B) R4.k. The split into enthalpy and entropy explains why: nifedipine gains more enthalpy on crystallizing (22.1 against 16.1 kJ/mol) and also loses more entropy ($T\Delta S$ 12.5 against 10.0 kJ/mol), but the enthalpy difference is larger, so the net driving force is larger R4.i–j·C15. The MDSC values "agree well" with the Hoffman estimate (8.8 and 6.2 kJ/mol), and in Figure 7 the measured points sit close to the Hoffman lines over the whole range, nifedipine about −30 and felodipine about −18 J/g at 0 °C, both reaching zero at their melting points R4.l·R11·C14. Table II is internally consistent: Hoffman's equation with Table II's $\Delta H_f$ and $T_M$ gives 6.22 and 8.83 kJ/mol, $\Delta H-T\Delta S$ gives 6.1 and 9.6 kJ/mol, and $\Delta H_f/T_M$ gives 74.3 and 89.6 J/mol/K (recalculations in the card) E3·E6·E11.

This result runs against the entropy argument of Zhou et al.: if a larger entropy of crystallization made a glass more resistant, felodipine, with the smaller entropy loss, should crystallize more easily. It does not, and for this pair the authors read the data as pointing to the enthalpy of crystallization, which "makes the dominating contribution" to the free energy C35·R21. They also consider the interfacial term. Turnbull found for metals that the crystal–melt interfacial energy scales with the heat of fusion; if that held here, nifedipine, with the higher heat of fusion (39.9 against 30.8 kJ/mol), would face the larger surface penalty, the opposite of what its faster nucleation needs C36·R22·R4.g.

The nucleation barrier below Tg

Table C. Activation energy for nucleation, mean (SD), n = 3, from Table I R3.

Both pure glasses show a break in the Arrhenius plot at Tg: below Tg the rate falls much more steeply with temperature, giving a higher ΔE, "presumably" because mobility drops below Tg R2·C10. Above Tg the two drugs do not differ significantly (78 and 95 kJ/mol); below Tg felodipine's barrier is significantly higher (145 against 122 kJ/mol) R3.a–b·C9. The authors take this as "evidence that kinetic factors are also important" C38. With 3 wt% PVP all four average values rise, though the rise is significant only for felodipine below Tg and nifedipine above Tg, and below Tg the gap widens to 201 against 127 kJ/mol: "it appears" that the barrier is higher for felodipine with and without polymer R3.c–d·C20·C48. The statistical test is not named R3. The abstract states nifedipine's lower activation energy without the below-Tg restriction X6.

Hydrogen bonds in the glass and in the crystal

In the pure glasses the NH band sits at about 3345 cm⁻¹ for both drugs, so the average hydrogen-bond strength is similar; the amorphous nifedipine band is broader, so "there appears to be" a broader spread of bond strengths (Figure 8) R12·C16. The crystals differ in opposite directions. Crystalline nifedipine absorbs at about 3318 cm⁻¹, lower than its glass, so its hydrogen bonds are stronger in the crystal; crystalline felodipine absorbs at about 3363 cm⁻¹, higher than its glass, so its bonds are weaker in the crystal. This matches the earlier study by Tang et al. R12·R20·C17.

PVP dispersions: same drop, same ranking

Table D. Nucleation rate (read from the log axis of Figure 9) and Tg (read from Figure 10) of the dispersions, approximate R16·R17.

PVP cut the nucleation rate of both drugs by about two orders of magnitude at 7 wt%, with a smaller decline from 7 to 25 wt% (Table D); in the authors' words PVP "dramatically" reduced nucleation, and its stabilizing ability was similar for the two drugs R16·C18·C19. Every nifedipine dispersion stayed above its felodipine counterpart, by a factor of about 3.5 to 6 R16·C19. The lower felodipine error bars at 10 and 20 wt% reach down by one to two orders of magnitude on the log axis (to about 2 and about 7 m⁻³ s⁻¹), so individual points are uncertain R16.c·R16.e. Moisture was excluded "as far as possible" P4.

The glass properties of the dispersions stay alike. Each composition showed a single Tg, which the authors take as miscibility over the whole range, and Tg rose from about 43 °C to 168 °C for PVP in a way the authors call "relatively ideal" against the Gordon–Taylor and Couchman–Karasz curves R17·C21·C23. Felodipine with 10 wt% PVP was the exception: its Tg, 40.5 °C, fell below that of the pure drug, a lack of antiplasticization at low polymer content seen before R8·C22. The authors call the Tgs of the two systems "virtually identical" C24; read from Figure 10, nifedipine dispersions are about 6–15 °C higher at 20–40 wt% PVP, and its points lie above both fitted curves from 20 to 90 wt% X5.

Enthalpy recovery fell for both drugs with 10 wt% PVP, to about 3.55 and 3.4 mJ/mg after 16 h, and the fitted relaxation times rose to 42.1 h (nifedipine, β 0.57) and 16.7 h (felodipine, β 0.45) R6.c–d·R7. For felodipine, 3.4 (±0.1) of an expected 5.3 (±0.3) mJ/mg (65%) was recovered with PVP against 5.4 (±0.3) of 6.3 (±0.3) mJ/mg (84%) without, although its Tg fell, "highlighting the fact that Tg alone does not completely describe the reduction in molecular mobility" R8·C26. Note by the AI writer (not discussed in the paper): the nifedipine dispersion, which nucleates faster, has the longer relaxation time, so in the dispersions too the mobility measure runs opposite to the nucleation ranking R7·R16.

In the infrared, the 3,288 cm⁻¹ drug–PVP band grows at the expense of the 3,345 cm⁻¹ drug–drug band as PVP is added (Figure 11), and its lower wavenumber "indicates" that the drug–PVP hydrogen bond is stronger than the drug–drug one R14·C28. The height ratio of the two bands falls from about 2.9 to about 0.6 between acceptor:donor ratios of 0 and 4.0 along one curve for both drugs (Figure 12), so for equal numbers of donors and acceptors the interaction is "very similar" R15·C29. Because nifedipine has the lower molecular weight, at equal weight fraction of PVP it "would" form slightly more drug–PVP hydrogen bonds C30. The dispersion spectra also show a second band near 3220 cm⁻¹ that grows with PVP and is not assigned in the text X8.

Finally, Flory–Huggins theory with χ = −3.8 and −4.2 predicts nearly the same drop in drug activity for both drugs: about 0.96, 0.84 and 0.67 at PVP volume fractions of 0.1, 0.2 and 0.3 for nifedipine, a little lower for felodipine (Figure 13) R19·R18. The authors call the reduction small for the PVP range used, so on the driving-force term alone nifedipine "would be expected" to keep nucleating faster at any PVP level C47. Note by the AI writer (not discussed in the paper): the drop in chemical potential that corresponds to an activity of 0.84 at 25 °C is $RT\ln 0.84\approx -0.43$ kJ/mol, small beside the 3.4 kJ/mol gap in driving force between the pure drugs R19.b·R4.k.

Discussion

How the authors put the pieces together. The discussion follows classical nucleation theory. Tg and the average relaxation time are virtually identical, and hydrogen bonding in the two glasses is alike, so the transport barrier as measured by DSC cannot be what separates the rates C13·C37. What does separate the drugs involves the crystal. On the thermodynamic side, nifedipine has the larger driving force C15. On the kinetic side, felodipine has the larger barrier below Tg C38. The authors connect the two through hydrogen bonding, explicitly as a speculation:

The figure above summarizes the argument of the Discussion, page 2313 R12·R4.k·R3.a–b·C39. The authors add that felodipine's lower entropy of crystallization "may also be related" to its hydrogen-bond pattern (Tang et al., ref 44) C40, and they leave open whether the driving force or the barrier dominates: the faster nucleation of nifedipine "may arise" from either or from both, and "further investigations are necessary" C41.

The dispersions. For the PVP systems the authors list the routes by which a polymer is said to stabilize a glass: lower free volume, lower mobility, higher Tg, disrupted drug–drug interactions, new drug–polymer interactions, or simply the pure drug's own tendency to crystallize C42. In their data the first four are either similar for the two drugs or run the wrong way (drug–PVP hydrogen bonding is, if anything, slightly greater for nifedipine at equal weight fraction), so, as for the pure drugs, these common "metrics" do not predict which dispersion crystallizes faster C43. Miscibility does change the drug's environment and could change the driving force, the interfacial term and the barrier C44. The driving force falls by a similar small amount for both drugs, and the barrier stays higher for felodipine below Tg C47·C48. The authors therefore conclude that the relative physical stability "is not explained" by the measured properties of the metastable amorphous form, and correlates instead with nifedipine's larger enthalpic driving force and lower activation energy C49.

What the authors take from it. When judging the physical stability of an amorphous system, "it is important to consider not only the properties of the supercooled liquid/glass but also how these relate to those of the crystalline counterpart", an idea they relate to Turnbull and Cohen's discussion of glass-forming tendency C50. Their results "would also support the conjecture" that within a class of compounds, the more readily the amorphous drug crystallizes, the more polymer it needs for a given stabilization C51. Their closing sentence is that the relative crystallization tendency from dispersions "may be dependent" on that of the pure drugs C52.

Note by the AI writer (not discussed in the paper): what this suggests for formulation. Two drugs with the same Tg and the same DSC relaxation time differed here by a factor of about 2 to 4 in nucleation rate as pure glasses and about 3.5 to 6 in PVP R4.a·R16. Of the quantities in Table II, the one that ranked them correctly with the least effort is the Hoffman driving force, which needs only the melting point and heat of fusion from one DSC run (8.8 against 6.2 kJ/mol) R4.l. The PVP data also show diminishing returns in this dry system: 7 wt% removes about two orders of magnitude, a further 18 wt% only a factor of about 3 to 4, and the ranking of the pure drugs survives throughout R16. Humidity, which raises mobility and competes for hydrogen bonds, was not part of the study.

Limitations

Limitations stated by the authors. They say that their glasses are "not completely described" by the classical homogeneous nucleation equation, which ignores stresses from the volume change of nucleation and the lower barrier of heterogeneous nucleation C32. The interfacial energy "is difficult to measure experimentally with any degree of certainty", particularly for glasses, so one term of the barrier stays unknown C36. Flory–Huggins theory has known limitations and the glasses are "non-equilibrium glasses", so the activity analysis serves only as "a basis for comparison" C46. Whether kinetics or thermodynamics dominates the difference in the glassy region is left to further work C41. Several stabilization factors are "interrelated", which the authors note limits how cleanly they can be separated C42.

The AI writer's own judgement (1): the numbers behind the ranking. The ranking is robust: it appears in Figure 2, Table II, the Arrhenius plots, the PVP series and the heating test R1·R4.a·R2·R16·R5. The absolute nucleation rates are not: Table II, the Figure 2 slopes and Figure 9 differ by up to about 4-fold (Table A), and Figure 3 has no unit on its y-axis, so its heights cannot be placed on the scale of Figure 9 X1·X2. At about 25 °C the 3% PVP points of Figure 3 lie about 6 ln units below the pure drugs, a reduction of about 400-fold, while Figure 9 shows about 85-fold at 7 wt% PVP; the two figures cannot both be on the same scale X2. Table II misprints the units of ΔCp, τ and the TΔS temperature, and Eq. 7 places the KWW exponent outside the parenthesis; none of these changes a conclusion, but a reader re-using the values needs the corrected units X3·X4. The difference in ΔE is significant only below Tg, while the abstract states it without that restriction X6. The "virtually identical" dispersion Tgs differ by up to about 15 °C at 20–40 wt% PVP X5.

The AI writer's own judgement (2): how far the explanation reaches. The paper establishes a correlation, not a mechanism. Two properties (driving force and below-Tg barrier) line up with one ranking from one pair of drugs and one polymer, so the general statements about classes of compounds and polymer levels rest on a single comparison X7·C51·C52. The hydrogen-bond account of felodipine's higher barrier is offered as speculation and no measurement follows hydrogen bonds during nucleation C39. Nucleation was counted in spin-coated films heated to 90 °C, while Tg, heat capacity and relaxation were measured on melt-quenched glasses or rotary-evaporated dispersions at 23.5–25 °C, so linking them assumes that the glasses are the same in both preparations X11. The per-volume rates rest on the optical depth of field rather than a measured film thickness X10. Within those limits, the main point is well supported: for this pair, Tg and DSC mobility would have ranked the two drugs as equal, and they are not R4.c·R4.m–n·R1.

Conclusion

The paper compares the isothermal nucleation of two related dihydropyridines as pure glasses and in PVP dispersions, and sets beside it the driving force, the activation energy for nucleation, Tg, DSC relaxation, hydrogen bonding and the Flory–Huggins drug activity A1·A2. Nifedipine nucleates faster in every comparison, although Tg (42.3 against 43.1 °C onset), relaxation (τ 6.3 against 4.2 h, β 0.36 against 0.37) and hydrogen bonding to PVP are nearly identical R1·R2·R4·R15·R16. What differs is nifedipine's larger free energy of crystallization at 25 °C (9.6 against 6.2 kJ/mol), which is enthalpic, and its lower activation energy for nucleation below Tg (122 against 145 kJ/mol) R4.k·R3.a–b. PVP at 7 wt% lowers nucleation of both drugs by about two orders of magnitude, but the ranking of the pure drugs remains R16. The authors' conclusion, that the crystallization tendency from dispersions "may be dependent" on that of the pure drug and that the crystal must be considered alongside the glass, is a well-argued hypothesis built on one drug pair, and invites tests on more drugs, polymers and humid conditions C50·C52·X7.