Why nifedipine crystallizes faster than felodipine from wet PVP dispersions: mobility versus supersaturation

Background and motivation

Amorphous drugs are more soluble than their crystals, but they are also less stable: given time and molecular mobility, they crystallize. A common way to slow this down is to dissolve the drug at the molecular level in a polymer with a high glass transition temperature ($T_g$), such as poly(vinylpyrrolidone) (PVP), to make an amorphous solid dispersion (ASD; the paper calls these "amorphous molecular level solid dispersions"). The introduction builds the problem from two well-established facts. First, amorphous solids take up water into their bulk, not only onto their surface, so they are more hygroscopic than their crystals; the absorbed water lowers $T_g$ (it acts as a plasticizer) and so raises molecular mobility at room temperature, which can speed crystallization, as reported for indomethacin (Andronis and colleagues, 1997) and lamotrigine mesylate (Schmitt and colleagues, 1996) C1·C2. Second, the polymers added to raise $T_g$ are usually more hygroscopic than the drug, so adding them also brings in more water: a kinetic tug-of-war between the polymer's higher $T_g$ and the lower $T_g$ caused by the water it attracts C3.

The authors add a thermodynamic layer to this picture. The driving force for crystallization is the degree of supersaturation, the difference between the chemical potential of the drug in the amorphous mixture and its chemical potential at the solubility limit (Equation 1) C4·E1. A miscible polymer lowers the drug's chemical potential and so this driving force (Marsac and colleagues, 2006) C4·C25. But if the polymer raises the water content of the dispersion, the water could raise the chemical potential of a hydrophobic drug again, increasing supersaturation: a second competition between polymer and moisture, this time thermodynamic C5. Since no amorphous product can be made completely dry, the authors argue that the influence of small amounts of water needs to be understood C5.

The two drugs were chosen with care. Nifedipine and felodipine are structural analogues from the dihydropyridine class with similar $T_g$, and earlier work by the same group had compared them dry. That work found that a small amount of PVP sharply reduces their nucleation at 0% relative humidity (RH) (Konno and Taylor, 2006; Marsac and colleagues, 2006), that the polymer raises the activation energy for crystallization and may act as a physical barrier, and that nifedipine has the larger thermodynamic driving force for crystallization, attributed to its larger enthalpic driving force, with a lower estimated solubility in PVP C8·C29·C31·C32. What was missing was the behaviour with water present: little work had weighed the stabilizing effect of more polymer against the water uptake that comes with it C24.

The paper therefore measures how the nucleation rate of nifedipine and felodipine dispersions with PVP changes with storage RH, and asks whether the relative stability of the two drugs is explained by kinetic factors ($T_g$ and mobility) or by thermodynamic ones (supersaturation in the presence of water) A1·A3·C5.

Background concepts

Nucleation rate in a thin film. Crystallization from a glass starts with nucleation, the appearance of new crystal sites, followed by growth. The paper measures only nucleation. Crystal sites are counted under a polarized light microscope, where crystals appear bright against the dark amorphous film, and the count per unit area is turned into a count per unit volume by dividing by the depth of field of the objective lens P3·E4. The depth of field is calculated from optics (Equation 2):

In plain terms: the thickness of film that is in focus, $D_{\mathrm{t}\mathrm{o}\mathrm{t}}$, grows with the wavelength of the light $\lambda$ (550 nm) and the refractive index of the medium $n$ (1.000 for air), and shrinks with the numerical aperture NA and the lateral magnification $M$ of the lens; $e$ is the smallest distance the detector can resolve (14 µm) E2·P3. For the 10× objective this gives 0.0144 mm P3. The paper does not print the numerical apertures; an aperture of 0.25 would give exactly the stated 0.0144 mm (a check by the AI writer, card row E2) E2. The nucleation rate is then the slope of the volumetric site density against time, in number per cubic metre per second (#/m³/s) E4.

Glass transition and $T_g-T$. Below $T_g$ a glass is rigid and its molecules move slowly; above it, mobility rises steeply. A common way to compare glasses is the distance between $T_g$ and the storage temperature $T$: the larger $T_g-T$, the less mobile the glass and, if mobility controls crystallization, the slower the nucleation C30. Water lowers $T_g$, so a humid glass sits closer to its $T_g$ C1·C16. If two drugs crystallized at the same rate at the same $T_g-T$, mobility alone would explain their stability; if not, something else is at work C23.

Supersaturation and chemical potential. The thermodynamic driving force for crystallization is written in Equation 1:

In plain terms: the degree of supersaturation $\sigma$ is the chemical potential of the drug in the supersaturated system, ${\mu }^1$, minus its chemical potential in a saturated solution, ${\mu }^0$, divided by the gas constant $R$ times the absolute temperature $T$ E1. A drug dissolved in a polymer far above its solubility in that polymer has a large $\sigma$ and a strong push to crystallize; anything that raises its solubility in the matrix lowers $\sigma$ C4. The paper uses this relation only as a framework: it computes no value of $\sigma$ for any dispersion E1·X4.

Splitting solubility into a lattice term and a mixing term. The solubility of a crystal in a liquid is given by Equation 3:

In plain terms: the mole fraction solubility $x_{\mathrm{a}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{a}\mathrm{l}}$ has two parts E3. The first is the ideal solubility, set only by the crystal: its enthalpy of fusion $\Delta H_{\mathrm{f}\mathrm{u}\mathrm{s}}$ and melting temperature $T_M$; a stronger crystal lattice gives a more negative first term and a lower solubility E3. The second is the activity coefficient $\gamma$, which carries the heat of mixing and any non-ideal entropy of mixing between drug and solvent E3. If the mixing entropy is ideal, $\gamma$ below 1 means exothermic, favourable mixing and solubility above ideal, and $\gamma$ above 1 means endothermic, unfavourable mixing and solubility below ideal C34. The paper does not print $\Delta H_{\mathrm{f}\mathrm{u}\mathrm{s}}$ or $T_M$; it states only that both are higher for nifedipine M1·C35.

Co-solvent and anti-solvent. In solution chemistry, adding a second solvent that lowers a solute's solubility makes it an anti-solvent. Mixtures of a good solvent with water often show solubility falling roughly log-linearly with water content (log-linear cosolvency, after Yalkowsky, 1999) C39. The authors borrow this picture for the dispersion: they treat PVP plus sorbed water as the "co-solvent" in which the drug is dissolved, and water as an anti-solvent that may raise the drug's chemical potential C26·C33. Because the drug's solubility in PVP cannot be measured directly, they use 1-methyl-2-pyrrolidone (NMP), in the paper's words a low molecular weight analog of PVP, and its mixtures with water as stand-ins M7·C33.

Methods in detail

The study has three strands that meet in the discussion: a kinetic data set (nucleation, water sorption, $T_g$), cross-plots that test whether water content or $T_g-T$ explains the nucleation data, and a thermodynamic data set (crystal solubility) that is turned into a supersaturation argument.

Nucleation in films

Nifedipine (from Hawkins, Inc.) or felodipine (a gift from AstraZeneca) and PVP K29/32 (Sigma-Aldrich) were dissolved together in 50:50 wt% dichloromethane/ethanol or in acetone, and a drop was spin-coated onto a glass coverslip with a KW-4A spin-coater inside a glovebox below 10% RH M1·M2·M3·P1. The film was heated to 90 °C for several minutes to remove residual solvent, which left an optically transparent film that went straight into a desiccator P1·R14. Six compositions were made, with 0, 7, 10, 15, 20 and 25 wt% PVP P1·A2. The films were stored over phosphorous pentoxide ("0% RH") or over saturated salt solutions; nucleation was followed at 11% (lithium chloride), 33% (magnesium chloride), 58% (sodium bromide) and 75% RH (sodium chloride) M10·P2. The storage temperature is given as 25 °C in the caption of Figure 1 and as 22 °C in the caption of Figure 7; the methods do not state it P2·X1.

At each time point, 12 sections of each of three replicate films were examined under polarized light at 10×–50× magnification, and the site density per area was converted to a site density per volume with the depth of field of Equation 2 P3·E2. The nucleation rate is the slope of that volumetric density against time E4. Crystals sometimes appeared first at the film edges; those sites were left out R14. The paper does not give the storage durations, the number of time points per slope or the film thickness X10.

Water sorption and $T_g$

For thermal analysis, the pure amorphous drugs were made by melting and cooling the crystals inside the DSC, and the dispersions by co-dissolving dried PVP and drug in ethanol and removing the solvent on a rotary evaporator, followed by at least 12 h under vacuum P4·P5. Before sorption or DSC, the bulk samples were heated just above the melting point of the drug to remove any crystals and ground gently in a dry glovebox P6·P7. Water uptake was measured at 25 °C in a gravimetric analyzer: 10–15 mg of sample was dried for 3 h under nitrogen and then held at one RH (5, 15, 25, 35, 45, 55, 65 or 75%) until its weight stopped changing; the plateau value was recorded P6. The plateau took about 600 min for the pure drugs and about 1,000 min for the dispersions R3.

For $T_g$, 4–6 mg samples in open pans were stored over salts at 0, 11, 22, 33, 43, 53, 64 and 75% RH until sorption equilibrium, sealed, cooled to −20 °C and heated at 10 °C/min in a TA 2920 DSC; three samples were measured per condition P7. No ice melting was seen, which the authors take as "indicating" that the water stayed intimately mixed with the solid R9·C6.

Cross-plots

Two derived plots carry the kinetic argument. In Figure 4, nucleation rates are re-plotted against the water content taken from the sorption data R5·P9. In Figure 7 they are re-plotted against $T_g-T$, using the $T_g$ values of Figure 5 R8·P9. Two details matter for a careful reader. The sorption isotherms were measured only for 0, 10 and 25% PVP and at RH values in steps of 10%, yet Figure 4 also shows 7% and 15% PVP and the nucleation RH values of 11, 33 and 58%; the paper does not say how these water contents were obtained X5. And the $T_g-T$ values plotted in Figure 7 match the $T_g$ of Figure 5 minus 25 °C, not minus the 22 °C named in the caption (a check by the AI writer) X1.

Crystal solubility

Crystal solubility in NMP was measured at 25 °C: excess crystals were stirred in a jacketed vessel for at least 24 h in the dark, the liquid was centrifuged, filtered through a 0.2 µm filter, diluted with ethanol and analysed by UV against a standard curve P8. Solubilities in water and in NMP–water mixtures (about 24 and 39 wt% water) are reported without a separate method description, with three replicates P8·R12. Activity coefficients were obtained through Equation 3, and Figure 8 shows the two terms of Equation 3 for each drug in NMP and in water R10·R11·E3.

The co-solvent composition

Finally, the authors compute, for each dispersion and RH, the water fraction of the "co-solvent" made of polymer plus water, leaving the drug out. The relation is given in words with a worked example: for nifedipine with 10% PVP at 75% RH, 3 wt% water divided by 3 wt% water plus 10 wt% PVP gives 23 wt% water E6·R13. Written as an equation:

In plain terms: $w_{\mathrm{c}\mathrm{o}}$ is how much of the drug's surrounding "solvent" is water, where $w_{\mathrm{w}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{r}}$ is the sorbed water and $w_{\mathrm{P}\mathrm{V}\mathrm{P}}$ the polymer, both per 100 g of dry dispersion E6. A dispersion with more PVP can sorb more water in total and still have a drier co-solvent C45.

Experimental analysis

Result 1: nifedipine nucleates faster, everywhere

Figure 1 is the central data set: nucleation rate against PVP content at five humidities, for nifedipine (a) and felodipine (b) R1. In all 30 combinations of PVP content and RH, nifedipine nucleated faster than felodipine R1·C7. The pure amorphous drugs differed least: about 4.7×10⁵ against 1.4×10⁵ #/m³/s dry, and about 6.8×10⁶ against 3.0×10⁶ #/m³/s at 75% RH (read from Figures 1 and 2) R1.a·R1.g. The gap grew with polymer content: with 25% PVP the text gives about 2,000 against roughly 300 #/m³/s dry and about 400,000 against roughly 2,000 #/m³/s at 75% RH R1·R1.f·R1.l.

Table A. Nucleation rate (#/m³/s) of films with 0–25% PVP, dry and at 75% RH, read from Figures 1 and 2 (approximate; n = 3) R1.

Result 2: PVP protects, but humidity erodes the protection, more for nifedipine

Dry, only 7% PVP lowered the nucleation rate of both drugs by about two orders of magnitude, and more PVP lowered it further but more gently, as the group had reported before R1·C8. As RH rose, this first drop became smaller; at 75% RH the rate fell log-linearly over the whole PVP range C9. Humidity affected nifedipine more: with 7% PVP its nucleation rate rose by a factor of about 400 from dry to 75% RH, felodipine's by about 100 R1·C10. With 25% PVP the contrast is stronger: the nifedipine rate rose about 250-fold and the felodipine rate only about eightfold (ratios of Figure 1 readings) R1.f·R1.l. In the authors' words, the difference between felodipine at 75% and 0% RH is greater at low than at high polymer content, whereas for nifedipine it depends less on polymer content C10. The pure drugs, by contrast, responded to RH to a similar extent (about 14-fold and 21-fold, read from Figure 2) R1.a·R1.g·C11.

Result 3: nifedipine systems take up more water

Water uptake rose with RH, and at every RH the nifedipine systems held more water than the felodipine systems with the same PVP content (Figure 3) R2·C12. At 75% RH the pure drugs took up about 1.8 (nifedipine) and 1.1 g water per 100 g (felodipine), the 10% PVP dispersions about 3.0 and 1.9, and the 25% PVP dispersions about 5.5 and 4.6 g/100 g R2.a–f. PVP itself is very hygroscopic (data not shown) R4·C13. The abstract calls the nifedipine systems "significantly more hygroscopic"; the isotherms carry no error bars and no statistical test is described C12·X9. Water content stays below about 6% for all systems in the isotherms, which the authors call "a small amount of water" R2·C27.

Result 4: with more PVP, nucleation is less sensitive to water

Figure 4 replots nucleation rate against sorbed water. The authors call it "the most dramatic conclusion" that the nucleation rate is less sensitive to water content at higher polymer content: larger increases in water are needed to raise the rate C15. Pure felodipine rose from about 1.4×10⁵ to about 2.9×10⁶ #/m³/s as its water content went from 0 to about 1.1 g/100 g; felodipine with 25% PVP rose only from about 3.1×10² to about 2.4×10³ #/m³/s while its water content went from 0 to about 4.6 g/100 g R5.b·R5.h. For nifedipine, the pure drug rose from about 4.9×10⁵ to about 6.4×10⁶ #/m³/s with about 1.8 g/100 g water, and the 25% PVP dispersion from about 1.9×10³ to about 4.4×10⁵ #/m³/s with about 5.5 g/100 g R5.a·R5.g. At a given water content "most" nifedipine systems crystallized more easily than the felodipine systems, and the difference grew with polymer content C15. The authors draw from Figures 1, 2 and 4 that, for these systems, "the benefits of the polymer outweigh the drawbacks of increased water content" C27.

Result 5: $T_g$ is the same for both drugs at the same water content

$T_g$ fell with RH for every system (Figure 5) R6·C17. Pure nifedipine went from about 43 °C dry to about 26 °C at 75% RH, and with 25% PVP from about 54 °C to about 29 °C; pure felodipine went from about 46 °C to about 33 °C, and with 25% PVP from about 48 °C to about 28 °C R6.a·R6.c·R6.d·R6.f. At high RH, $T_g$ was similar in all systems, so the polymer's dry $T_g$ gain disappeared as it took up water C17. The authors report the $T_g$ of corresponding nifedipine and felodipine systems as "statistically equivalent" against RH, except for the pure drugs above 54% RH, where nifedipine had the lower $T_g$ C18.

Against water content (Figure 6) the two drugs again overlapped at each PVP level ("statistically equivalent") R7·C20. Water lowered $T_g$ more per gram in the pure drugs: pure nifedipine fell from about 43 to about 31 °C with about 1.15 g water per 100 g, whereas the 25% PVP dispersion needed about 2 g per 100 g to fall from about 54 to about 43 °C R7.a·R7.c. The authors read this as water being "a more effective plasticizer for the drug alone" ("This result suggests") C19. Figure 6 also contains a few points at higher water contents than any in the sorption isotherms, with no stated RH (for example nifedipine with 25% PVP at about 7.1 g/100 g and about 20.6 °C) X6.

Result 6: $T_g-T$ does not collapse the data

Figure 7 is the decisive test of the kinetic explanation. Nucleation fell as $T_g-T$ increased for every system ("As expected"): pure felodipine by about one order of magnitude from a $T_g-T$ of 8 to 21, felodipine with 10% PVP by about two orders from 7 to 23, felodipine with 25% PVP by about one order from 3 to 23, pure nifedipine by one order, and nifedipine with 10% or 25% PVP by two orders R8·C21. But at the same $T_g-T$, the curves did not coincide.

Table B. Nucleation rate (#/m³/s) at the plotted point of each series nearest a $T_g-T$ of 15 °C, read from Figure 7 (approximate); points and ratios chosen and computed by the AI writer R8.a–f.

Two observations follow. At a given $T_g-T$, nifedipine dispersions nucleated faster than felodipine dispersions, so the difference between the drugs is "not explained exclusively" by $T_g-T$; the only exception is the pure drugs, whose rates are similar when $T_g-T$ falls below 15 °C C23. And at a given $T_g-T$, more PVP lowered nucleation sharply: for felodipine at a $T_g-T$ of 15 °C, the text gives one order of magnitude lower with 10% PVP and two orders with 25% PVP C22. The plot readings in Table B give about 1.7 orders for 10% PVP (about 2.6×10⁵ against 5.3×10³) and about 2.2 for 25% PVP X8. The authors conclude that "the glass transition temperature alone does not describe the behavior of these systems" and, in the discussion, that "one must conclude that other factors are dictating" the relative stability of the two drugs C22·C23.

Result 7: nifedipine's crystal is harder to dissolve; water hurts felodipine more

The solubility data are the only numbers printed in the text (Table C) R10. In NMP at 25 °C, nifedipine dissolved to a mole fraction of 0.05 (±0.01) and felodipine to 0.10 (±0.02), with activity coefficients of 0.09 (±0.01) and 0.30 (±0.05) R10.a·R10.b. Both coefficients are below 1, so both drugs mix exothermically with NMP; nifedipine's lower solubility therefore "can be attributed" to its higher enthalpy of fusion and melting temperature, a higher "intrinsic tendency to crystallize" C35. Figure 8a shows this as a larger negative lattice term for nifedipine (about −5.3 against about −3.5 in natural-log units) R11.a·R11.b. The authors conclude that, at any drug loading and without water, nifedipine's supersaturation and driving force for crystallization "should be larger" than felodipine's C36.

Table C. Crystal mole fraction solubility $x$ and activity coefficient $\gamma$ at 25 °C (text, p.653–654) and the lattice term read from Figure 8 (approximate) R10·R11.

In water the order reverses: nifedipine is the more soluble, 2.6×10⁻⁶ against 1.3×10⁻⁷, because its activity coefficient in water, 1.89×10³, is about a hundred times smaller than felodipine's, 2.43×10⁵ R10.c·R10.d·C38. The authors write that these large coefficients "suggest strongly endothermic mixing" and, assuming close to ideal mixing entropy, that both drugs mix exothermically with NMP and endothermically with water C37. The data hang together: the lattice term implied by the NMP data (ln $x$ + ln $\gamma$) predicts water activity coefficients of about 1.73×10³ and 2.31×10⁵, within the stated standard deviations of the printed values (a check by the AI writer) E3.

In NMP–water mixtures the solubility of both drugs fell with water (Figure 9), from 0.05 and 0.10 without water to about 0.015 and 0.017 at about 24 wt% water and about 0.0063 and 0.0026 at about 39 wt% water R12. The authors fit log-linear relations, with $S$ the mole fraction solubility and $w$ the water content of the co-solvent in wt%:

In plain terms: each extra wt% of water lowers the logarithm of the solubility by a fixed amount, more for felodipine than for nifedipine E5. The authors read the steeper slope as water being the stronger anti-solvent for felodipine R12·E5·C39. They estimate that the two drugs become equally soluble at about 25 wt% water, so below that water content nifedipine is the less soluble drug C42·C43.

Note by the AI writer (not discussed in the paper): the printed fits do not reproduce the points they describe. Their intercepts give solubilities of 0.13 and 0.28 at zero water, against the measured 0.05 and 0.10, and the two printed lines cross at 16.5 wt% water, not 25 wt% E5·X2. A straight line through the three plotted points of each drug gives slopes of about −0.024 and −0.040 per wt% water, crossing near 21 wt% X2. The qualitative reading, a steeper fall for felodipine, holds either way; the water content at which the order of the two solubilities flips is uncertain, between roughly 16 and 25 wt% X2·X3.

Result 8: the co-solvent of nifedipine dispersions is wetter

Figure 10 shows the water fraction of the PVP/water co-solvent at each RH R13. It rises with RH in every dispersion. At 75% RH it is 23 wt% for nifedipine with 10% PVP and 18 wt% with 25% PVP, and about 16 wt% for both felodipine dispersions R13·R13.c·R13.d. So a dispersion with more PVP, although it holds more water in total, has a drier co-solvent: the polymer/water "co-solvent" concentration "may not remain as rich in water" C45. And because nifedipine dispersions sorb more water, their co-solvents are wetter than those of the felodipine dispersions with the same PVP content R13·C48.

Discussion

How the authors connect the results

The discussion weighs two kinds of explanation. On the kinetic side, the authors accept that the polymer raises the activation energy for crystallization and may act as a physical barrier, and add that "Presumably, it will impart a similar effect in the presence of a given amount of water"; mobility may also be reduced by coupling of molecular motions through molecular interactions C29. They grant that the kinetics are "likely to be complex" with both polymer and water present C28. But because the two drugs have the same $T_g$ at the same water content and still nucleate at different rates at the same $T_g-T$, $T_g$ "does not provide a complete description", and the difference between the drugs must have another cause C22·C23.

That cause, they argue, is supersaturation. The chain runs as follows.

Step 4 contains the subtle part of the argument. Water lowers felodipine's solubility more steeply, so for a given amount of water felodipine's driving force rises more; but felodipine, with its much larger activity coefficient in water, takes up less water, which the authors say "can explain—in part" the difference in crystallization tendency C41. Below the water content of about 25 wt% at which the two solubilities are estimated to cross, nifedipine remains the less soluble drug, and since its dispersions also hold more water, "Based on the thermodynamics alone, one would expect nifedipine to crystallize more easily", as observed C42·C43. The same picture offers one reason why nucleation responds less to water at higher PVP content: the 25% PVP dispersion has more polymer to dissolve the drug and a drier co-solvent than the 10% dispersion, so its supersaturation is lower (for nifedipine at 75% RH, 18 against 23 wt% water in the co-solvent) C45·C46. The authors offer a kinetic effect of water as a second, equally possible explanation of that observation C44.

The conclusion is stated with two strengths. The abstract says the relative physical stability "is consistent with differences in the degree of supersaturation", treating polymer and water as a co-solvent; the conclusions section says the difference "was explained by the differences in the degree of supersaturation" C49. In the discussion the key step is introduced as "it is reasoned": all the dispersions are taken to be supersaturated with respect to the estimated solubility in PVP, and water raises supersaturation more for nifedipine because its systems sorb more water C47·C48. The authors also state that water "acts as a strong antisolvent for both nifedipine and felodipine" in the dispersions, and close with a general lesson: "although the properties of the amorphous form are important, they do not completely describe physical stability" C50·C51.

What it suggests for formulation

Stated by the authors: for these drugs, PVP stabilizes more than the water it brings destabilizes, at water contents below about 6% C27; and stability assessments should consider the thermodynamic driving force (supersaturation), not only the properties of the amorphous form such as $T_g$ C51. They propose applying theories of crystallization from solution to amorphous materials, and studying the activation energies of nucleation and the modes of mobility that limit it C52.

Note by the AI writer (not discussed in the paper): three practical points follow from the data, within their limits. First, matching $T_g$ is not enough to predict matching stability between close analogues: at the same $T_g-T$ the nifedipine dispersions nucleated about 3 to 13 times faster (Table B) R8. Second, a cheap solubility screen in a small-molecule analog of the polymer, split into lattice and mixing terms and repeated with added water, pointed the same way as the nucleation data here, because both the lower dry solubility and the larger water uptake favoured crystallization of nifedipine R10·R12·R2. Third, the polymer/water composition around the drug, rather than total water content, is the quantity this framework says to watch: the PVP-rich dispersions held more water yet a drier co-solvent R13.

Limitations

Limitations stated by the authors. The authors acknowledge that the kinetics with polymer and water present are "likely to be complex" and little studied, and that a kinetic effect of water could explain the weaker water sensitivity at high PVP as well as the thermodynamic one C28·C44. The transfer from NMP to PVP is explicitly an assumption: "Assuming that a similar 'solubility' relationship exists in the solid dispersions" C33·C40. Their supersaturation argument "can explain—in part" the observations C41. Sites at the film edges were excluded because of preferential nucleation there R14.

The AI writer's own judgement (1): the explanation is reasoned, not measured. The kinetic observations are direct and consistent: nucleation rates with three replicates, the same ranking in Figures 1, 2, 4 and 7, and $T_g$ and sorption data that agree with each other R1·R5·R7·R8. The thermodynamic explanation is a different kind of evidence. No supersaturation was computed for any dispersion, the solubility of either drug in PVP or in PVP–water was not measured, and the step from NMP–water to PVP–water rests on an assumption X4·C33. The equal-solubility water content, which decides whether nifedipine stays the more supersaturated drug in the wettest dispersions, rests on three water contents, and the printed fits would place it at 16.5 rather than about 25 wt%; nifedipine dispersions at 65–75% RH have co-solvent water fractions of about 0.18–0.23, close to or above that range X2·X3. The conclusion that supersaturation "was explained" is therefore best read as the abstract words it: "consistent with" C49.

The AI writer's own judgement (2): details of the data. The storage temperature is 25 °C in the caption of Figure 1 and 22 °C in that of Figure 7, while the plotted $T_g-T$ values correspond to 25 °C X1. The conclusions say nifedipine "always" crystallized more easily at a given $T_g-T$, but for the pure drugs at a $T_g-T$ of about 8–11 °C felodipine lies at or above the nifedipine curve, as the results section itself notes X7. "Statistically equivalent" and "significantly" are used without a described statistical test X9. Water contents and $T_g$ were measured on bulk powders, not on the films in which nucleation was counted, and the water contents used in Figure 4 for 7% and 15% PVP are of unstated origin X12·X5. Figure 6 contains high-water points with no stated RH X6. The Figure 8 axis is labelled "-ln(solubility contribution)" while the bars carry the two terms of Equation 3 with their own signs X11. Finally, only nucleation was measured, not crystal growth, and only one polymer and two drugs were studied A1·A2.

Conclusion

The paper makes three contributions. First, it measures nucleation rates of nifedipine and felodipine films with 0–25% PVP at 0–75% RH and shows that nifedipine nucleates faster in every case, that PVP's protection weakens with humidity, more so for nifedipine, and that more PVP makes nucleation less sensitive to sorbed water R1·R5·C7·C10·C15. Second, it shows with sorption and DSC data that $T_g$, and the distance between $T_g$ and the storage temperature, cannot explain the difference between the two drugs R6·R7·R8·C23. Third, it proposes a thermodynamic explanation: treating polymer plus water as the drug's solvent, nifedipine is the more supersaturated drug because its crystal is less soluble and its dispersions hold more water, a conclusion the authors present as "consistent with" the stability ranking C48·C49.

For a formulation scientist the main message is a caution about using $T_g$ alone to rank amorphous systems, and a suggestion to look at the solubility of the crystal in the polymer phase, and at how water changes it. The supersaturation picture remains to be tested directly, by measuring drug solubility in the hydrated polymer itself and relating computed supersaturation to the nucleation rates X4.