Why small amorphous particles crystallize first: surface growth, particle size and a polymer inhibitor in felodipine powders

Background and motivation

A poorly soluble drug dissolves faster and to a higher concentration from its amorphous form than from its crystals, which is why amorphous formulations, usually amorphous solid dispersions with a polymer, are used to raise oral absorption. The price is physical instability: an amorphous solid can revert to the more stable crystal, and once it does, its solubility advantage is gone. Polymers that inhibit crystallization are a well recognized way to slow this reversion (Simonelli 1969; Ford 1986; Yoshioka 1995; Serajuddin 1999; refs 1–4 of the paper).

The introduction (Section 1) adds a manufacturing angle. Different ways of making a material amorphous give products of different physical stability, and an amorphous formulation then passes through unit operations such as milling and compression that change its particle size and surface area. The authors argue that these changes can "potentially" alter crystallization rates and cause batch-to-batch variation, so a robust amorphous product needs control of particle size and surface area and an understanding of how they act on crystallization.

The physical reason why surface area might matter comes from the work of Yu and co-workers. For indomethacin (Wu and Yu 2006), nifedipine (Zhu et al. 2008) and griseofulvin (Zhu et al. 2010), crystals were found to grow much faster along a free surface than inside the bulk of the same glass, especially below the glass transition temperature. A thin polymer or gold coating that buries the surface suppresses this surface-enhanced growth (Wu et al. 2007), which makes coating a possible stabilization strategy. Real formulations, however, are powders with free surface everywhere, and the amount of that surface depends on particle size. The authors note that the size dependence of crystallization was not well understood and that crystallization is usually treated as a bulk process.

Two earlier particle studies frame the questions. For indomethacin, the smallest sieve fraction crystallized fastest (Wu and Yu 2006; Crowley and Zografi 2003). In the study of Yu and co-workers, amorphous indomethacin particles also crystallized in two stages, a fast initial stage followed by a much slower one that left crystallization incomplete; the same biphasic pattern was seen for griseofulvin and for indomethacin dispersed with low levels of PVP. In those studies the fast stage was ascribed to surface crystallization and the slow stage to bulk crystallization.

The paper therefore sets out to measure how particle size affects the crystallization of an amorphous drug below its glass transition temperature, without and with a polymeric crystallization inhibitor, and to test whether separately measured surface and bulk growth rates can explain the powder kinetics. A third strand, the dissolution of fresh and partly crystallized powders, connects stability to performance. The model drug is felodipine, an antihypertensive dihydropyridine, and the inhibitor is poly(vinylpyrrolidone) (PVP, grade K-29/32) at 3 wt%. Earlier studies from the same group supply important background on this system: 3% PVP lowers the nucleation rate of amorphous felodipine about 150-fold at 30 °C (Konno and Taylor 2006), nucleation in 3% PVP–felodipine rises about 7-fold from 30 to 50 °C (Marsac et al. 2006), felodipine crystals grow around PVP without piling it up at the growth front (Kestur et al. 2010), and PVP is a poor inhibitor of felodipine crystallization from solution (Konno et al. 2008).

Background concepts

Surface-enhanced crystal growth

A glass below its glass transition temperature ($T_g$) is a solid in which molecules move very slowly, so crystals that form in it grow slowly. Molecules at a free surface, with neighbours on one side only, are more mobile than those inside; the authors cite work that attributes faster surface growth to this enhanced mobility. The result is that a crystal touching the free surface can spread along it far faster than a crystal grows into the interior. The ratio of surface to bulk growth rate is the key number: about 100 for indomethacin at 40 °C, according to the earlier work the authors cite, and, as this paper measures, about 6 for felodipine at 30 °C. The difference between surface and bulk growth is reported to be much larger below $T_g$ than above it (nifedipine, Zhu et al. 2008), a point the authors use when they discuss storage at 50 °C.

Nucleation versus growth

Crystallization of a glass has two steps: new crystal nuclei must form (nucleation), and existing crystals must grow. A polymer can slow either. The overall rate seen in a powder, for example as % crystallinity per day, mixes both, while a linear growth rate measured on a single crystal (in m s⁻¹) isolates growth. Much of the paper's argument rests on comparing these two kinds of rate: if the overall rate falls far more than the growth rate when PVP is added, the difference must lie in nucleation.

Felodipine's two polymorphs

Felodipine has at least two crystal forms. Form I is the stable form supplied by AstraZeneca and the reference crystal throughout the paper. When a felodipine glass is sandwiched between two cover glasses and left unseeded, form II nucleates and grows inside it; to measure the bulk growth of form I, the authors therefore had to seed the film with form I crystals. At a free surface, form I always appeared. This polymorph behaviour matters because the powders crystallized only to form I, which the authors use as a clue to where crystals start in a powder.

Measuring % crystallinity in a powder

Raman spectroscopy and powder X-ray diffraction (PXRD) both distinguish crystal from glass, but neither gives % crystallinity directly. The authors built multivariate calibration models from physical mixtures of crystalline and amorphous felodipine spanning 0–100% crystallinity: a partial least squares (PLS) model for Raman, an orthogonal PLS (OPLS) model for PXRD of the pure drug, and a full-pattern fit (a least-squares combination of the starting amorphous pattern and the crystalline pattern) for PXRD of the dispersions. Calibration errors (root mean square error of estimation, RMSEE) were 6.9% and 4.5% for Raman and 4.7% and 3.9% for PXRD of the small and large fractions, so differences of a few percentage points between techniques are within error. The authors suggest that Raman is the more surface-sensitive of the two, which matters when crystals start at particle surfaces.

Supersaturation from an amorphous solid

When an amorphous powder dissolves, the solution concentration can rise above the crystalline solubility, a state called supersaturation. It lasts only while the solid dissolves faster than drug is lost to crystallization, either of the dissolving solid or from the supersaturated solution (Alonzo et al. 2010). The concentration–time profile therefore shows a peak followed by a fall, called desupersaturation. The height of the peak depends on how fast the powder dissolves relative to how fast crystals form, which is where particle size enters. The "amorphous advantage" in the paper's words is the extra concentration reached over the crystal.

Methods in detail

The design is compact: one drug, two compositions (pure amorphous felodipine and a 3 wt% PVP dispersion), two sieve fractions, and dry storage at 30 °C, with one extra storage condition at 50 °C. Four strands of work are combined.

Contribution 1: crystallization kinetics of two sieve fractions

The problem. To see a size effect, the powders must differ only in particle size: same composition, same thermal history, same storage. The dispersion must also be homogeneous at a polymer level as low as 3 wt%.

What they did. Amorphous felodipine was made by melting form I on an aluminum pan, holding it for 5 min just above the melting temperature and quenching it on a cold surface. The dispersion was made in two steps, because rotary evaporation of mixtures with less than 5 wt% polymer would, in the authors' account, partly crystallize the drug and give non-homogeneous material: first a 10 wt% PVP dispersion was made by rotary evaporation from a 1:1 (by weight) ethanol–dichloromethane solution and dried for 48 h under vacuum; it was then diluted with crystalline felodipine in a cryogenic mill to 3 wt% PVP and melt quenched (Section 2.1). Both glasses were ground lightly with pestle and mortar in a glove box under dry nitrogen (RH below 10%) and sieved into two fractions: size 1, 150–250 µm, which the paper calls "200 µm", and size 2, 500–710 µm, called "605 µm". The powders were packed into aluminum X-ray holders and stored at 30 °C over phosphorus pentoxide. The size-1 dispersion was also stored at 50 °C for one month.

Crystallinity was followed by two techniques (Sections 2.2–2.3). Raman spectra (785 nm excitation, non-contact fiber-optic probe) were collected at 6–10 spots of each powder bed and averaged, in triplicate experiments, and converted to % crystallinity with a PLS model built for each particle size over 1800–1400 cm⁻¹ (Figure 1 shows the spectra and the region used). PXRD of pure felodipine (Shimadzu XRD-6000, 5–35° 2θ) used an OPLS model built for each size after normalizing each pattern to a silicon standard and then to unit area (Figure 2 shows the patterns). PXRD of the dispersions was measured in transmission on a PANalytical X'Pert Pro and analysed with PatternMatch, which fits each pattern as a linear combination of the starting amorphous pattern and the 100% crystalline pattern. The peak marked with an asterisk in Figures 1 and 2 was used to identify the polymorph.

How it differs from earlier work. The indomethacin studies looked at pure drug; here the same size comparison is run on a dispersion with a crystallization inhibitor, which turns out to change not only the rate but the extent of crystallization.

Contribution 2: separate growth rates at the free surface and in the bulk

The problem. A powder crystallizes from both its surfaces and its interior, and the powder kinetics cannot tell the two apart. The authors therefore measured each growth mode on its own.

What they did. Crystalline felodipine was melted between an 18 × 18 mm cover glass and an 18 mm round cover glass and cooled rapidly (Section 2.4). For free-surface growth, the top cover glass was removed and crystals that nucleated at the exposed surface were followed. For bulk growth, the top glass was left in place and form I seeds were placed in contact with the film edge, or, for the pure drug, crystals were only partly melted so that the remnants seeded growth; seeding was needed because unseeded sandwiched films grow form II. The same procedures were used for the 3% PVP dispersion. Films were stored at 0% RH and 30 °C and removed at intervals; the growth of edge-seeded crystals into the film, or the size of spherulites, was measured under polarized light. Crystal size rose linearly with time, the slope was taken as the growth rate, and the rates did not depend on the seeding method. The crystal forms were identified by Raman spectroscopy and melting point.

Why it works. Removing or keeping the cover glass switches the free surface on or off for the same material at the same temperature, so the ratio of the two rates measures the surface effect directly. Its limit is that the films are not powders: the rates are measured on thin films between cover glasses, not on particles of 150–710 µm.

Contribution 3: linking film growth to powder kinetics

Two analyses connect the growth rates to the powders (Section 4).

Two-stage slopes. The PXRD kinetics of the dispersions (Figure 12, the data of Figure 6 replotted) have a steep early part and a shallow late part. The authors fitted a straight line to each and took the slope as a crystallization rate (Table 2). The ratio of early to late slope was then set against the ratio of surface to bulk growth rate from Table 1. In a second comparison (Table 3), the early slopes of the pure drug and the dispersion were set side by side, and their ratio compared with the factors by which PVP slows surface and bulk growth. The fitted time ranges are not printed; the PVP-felodipine values in Table 3 are the Table 2 PXRD slopes divided by 24 (0.905/24 ≈ 0.037 h⁻¹), while the source and range of the pure-felodipine slopes are not stated.

A crystallized shell of constant depth. To explain why the dispersion plateaus at different crystallinities for the two sizes, the authors treat each particle as a sphere whose radius is half the midpoint of its sieve cut (100 µm for 150–250 µm, 302.5 µm for 500–710 µm) and assume that crystallization starts at the surface and moves inward. The relation is stated in words in the paper; in symbols it reads

In plain terms: the crystallinity $X$ of a particle is the volume of a crystallized surface layer of depth $d$ divided by the volume of the whole particle of radius $r$. With the Raman crystallinity of the small particles after 56 days, 43.5%, the authors obtain a depth of about 17.3 µm. Assuming the same depth for the large particles gives a predicted crystallinity of 16.2%, against 16.5% measured. The arithmetic checks: a shell 17.3 µm deep occupies one minus the cube of 82.7/100, that is 43.5%, of a 100 µm sphere, and one minus the cube of 285.2/302.5, that is 16.2%, of a 302.5 µm sphere.

Contribution 4: dissolution of fresh and stored powders

What they did. About 5 mg of drug, as amorphous felodipine or as the 3% PVP dispersion, was added to 18 mL of 50 mM pH 6.8 phosphate buffer at 30 °C, stirred at 300 rpm (Section 2.5). Concentration was followed in situ with a six-channel UV fiber-optic system, one spectrum every 30 s for 2 h, using second-derivative spectra (270–450 nm) to suppress particle scattering; calibration solutions were made in methanol because water cannot hold the supersaturated concentrations. For the pure amorphous drug, PVP was pre-dissolved in the medium at 250 µg/mL to prevent immediate crystallization of the solid (Alonzo et al. 2010); for the dispersions the medium also started at 250 µg/mL PVP and could rise to 259 µg/mL as the particles dissolved. Crystalline felodipine of both sizes served as reference, and dispersions stored for 24 weeks were tested the same way. Experiments were run in triplicate.

Why the PVP in the medium matters. Since the solution contains almost the same PVP in both tests, the comparison of pure amorphous felodipine with the dispersion isolates the effect of the 3 wt% PVP inside the solid.

Experimental analysis

Pure amorphous felodipine: size sets the rate, not the end point

At 30 °C the pure glass started to crystallize within 3–6 h and was fully crystalline within 72–120 h, depending on particle size: about 3 days for the 150–250 µm fraction and 5 days for the 500–710 µm fraction (Section 3.1). The abstract summarizes this as crystallization "within 7 days". Raman and PXRD showed the growth of form I peaks from 24 h onward (Figures 1 and 2), and only form I appeared. Table A gives the time course read from Figures 3 and 4.

Table A. % crystallinity of pure amorphous felodipine at 30 °C, read from Figures 3 (Raman) and 4 (PXRD), approximate; means of triplicates (card R3, R4).

Both techniques put the small fraction ahead, and both end near 95–96% for the two sizes. The gap is larger by Raman: at 24 h it is about 46 against 12% by Raman but about 31 against 19% by PXRD, and up to 12 h the PXRD values of the two sizes overlap. The authors call the Raman difference significant and say the PXRD difference "may be smaller", adding that this "may be due to the more surface sensitive nature of Raman spectroscopy". No statistical test is reported.

With 3% PVP: slower, and stopped at a plateau that depends on size

Adding just 3 wt% PVP changed the timescale from hours to weeks and, more strikingly, the end point. Neither fraction was fully crystalline at the end of the study (24 weeks in the text, 6 months in the abstract; the last stability point in the figures is at about 161 days). Crystallization was rapid during the first 8 weeks and then slow or negligible. Table B gives the readings.

Table B. % crystallinity of the 3% PVP dispersions at 30 °C, read from Figures 5 (Raman) and 6 (PXRD), approximate (card R6, R7). Error bars are wide, for example about 40–55% for the PXRD value of the small fraction at 161 days.

The authors summarize the plateaus as 45–50% for the small fraction and 15–20% for the large one, or about 45% and 17%, reached after 50–60 days by both. The rate and the extent both fall with increasing particle size "as a general trend". This is the observation that the constant-depth estimate was built to explain.

The early crystallization slope shows how strongly PVP slows the process (Table 3): 2.21 against 0.037 h⁻¹ for the small fraction (ratio 60) and 1.41 against 0.018 h⁻¹ for the large one (ratio 77).

Growth rates: the surface is faster, and PVP mainly slows the bulk

Table C. Linear growth rates of form I at 30 °C and 0% RH (from Table 1 of the paper; the last row is the authors' text). No uncertainty or number of crystals is printed (card R12).

Form I grew about 6 times faster at the free surface than in the bulk without polymer and about 23 times faster with PVP (Section 3.2; Figure 8 shows a spherulite grown at the surface and one grown in the bulk, at different magnifications). The authors point out that the larger ratio with PVP comes "mainly" from the slower bulk growth: PVP cuts bulk growth about 7-fold but surface growth only about 2-fold. For a sense of scale (a conversion by the AI writer, not in the paper): 2.7 × 10⁻⁹ m s⁻¹ is about 230 µm per day, and 6.37 × 10⁻¹¹ m s⁻¹ is about 5.5 µm per day.

Biphasic kinetics and the constant-depth estimate

Table D. Slopes from Tables 2 and 3 of the paper and the constant-depth estimate from Section 4. Slopes are in % crystallinity per unit time, printed as day⁻¹ or h⁻¹ (card R14, R15, R16).

The average ratio of early to late slope, 14, is "reasonably similar" to the surface-to-bulk growth ratio with PVP, about 23, which the authors take as "suggesting that the rapid initial crystallization is probably due to the much faster surface growth rate"; the abstract and conclusions state the same attribution without the hedge. The constant-depth estimate reproduces the large particles' crystallinity within 0.3 percentage points, and the authors introduce it with "It can be speculated".

Two details matter when reading these numbers. First, the 43.5% used for the depth matches the 30 °C series of Figure 7 (about 43.5% at 56 days) rather than Figure 5 (about 42% at 56 days), although both series show the same sample by Raman. Second, Figure 12 is presented as the data of Figure 6 with fitted lines, and so it is for the small fraction, but from day 56 on its large-fraction points lie about 2 percentage points above those of Figure 6 (about 15.0, 17.0, 17.9 and 18.9% against about 12.9, 15.2, 15.5 and 16.5%). The late slope is about 0.03 per day either way.

Why PVP works, by elimination

Table D's last comparison drives the authors' main mechanistic conclusion. Pure felodipine crystallizes 60–77 times faster in the early stage than the dispersion, yet PVP slows growth only 2-fold (surface) and 7-fold (bulk). "This analysis suggests that the inhibitory effect of PVP on the growth rate of felodipine (either surface or bulk) cannot alone explain the slower overall crystallization". Since overall crystallization is nucleation followed by growth, the authors conclude that "it appears that PVP must also have a substantial inhibitory effect on the nucleation rate", consistent with the 150-fold reduction measured earlier, and that the improved stability "can be attributed to a large degree" to nucleation, with a more minor contribution from slower growth ("The data thus suggest"). Nucleation itself was not measured in this paper.

Storage at 50 °C

The small-fraction dispersion stored at 50 °C crystallized very slowly for about 5 days, then rapidly to about 70% by 2 weeks, and plateaued around 85% over the next 2 weeks (Figure 7). Based on the initial slopes, crystallization was about 8 times faster than at 30 °C, where the plateau is about 45%; the slope values are not printed. The authors explain the difference with two cited facts: surface-enhanced growth matters less above $T_g$, which they take the 50 °C sample to be (nifedipine: the surface-to-bulk difference is much larger below $T_g$), and the nucleation rate of 3% PVP–felodipine rises about 7-fold from 30 to 50 °C. No $T_g$ value is printed in the paper.

Dissolution: a size advantage that storage reverses

Table E. Solution concentrations of felodipine (µg/mL) at 30 °C in pH 6.8 buffer with 250 µg/mL PVP in the medium. Peaks from the text; values "about" read from Figures 9–11, approximate (card R18–R21).

Crystalline felodipine reached about 1.3 µg/mL within 5 min; the text reports no difference between sizes, although Figure 9 shows plateaus of about 1.0–1.2 for the small and 1.3–1.4 µg/mL for the large crystals. Amorphous felodipine dissolved fastest from the small fraction, peaked within 30–35 min at about 7.0 and 5.4 µg/mL, and then lost its supersaturation quickly, though it was still above the crystalline level at 2 h. The authors attribute this incomplete fall to the "constantly decreasing supersaturation", which slows crystal growth from solution.

The fresh dispersions reached the same peaks as the amorphous drug (6.97 and 5.28 µg/mL) but lost supersaturation more slowly, ending near 3.5–3.75 µg/mL at 116 min in Figure 10, which the text rounds to 4 µg/mL, against about 2.5 µg/mL for the pure amorphous drug. Since the solution PVP was nearly the same, the slower decline belongs to the PVP inside the solid. The authors describe the size effect as significant during the first 40 min, after which the sizes reach similar concentrations; this holds for the dispersions, which converge from about 48 min, but the two amorphous drug curves are still apart at 64 min (about 4.5 against 3.7 µg/mL).

After 24 weeks of storage the picture flips. Both stored dispersions fell far short of the fresh peaks, and the small fraction, now about 45% crystalline, peaked lowest at 2.5 µg/mL near 18 min, while the large fraction, about 17% crystalline, rose more slowly to 3.4 µg/mL near 48 min (Figure 11). The authors say this "could be attributed to higher crystallinity of the starting material" and that the supersaturation reached "appears to be correlated" with the extent of crystallization.

Discussion

The authors' picture, step by step

Put together, the paper argues as follows. Crystals in a powder start at particle surfaces and grow inward: only form I, the form that grows from free surfaces, appeared in the powders, which the authors read as "suggesting perhaps that this polymorph readily crystallizes at the surface and grows inwards". What happens next depends on the contrast between surface and bulk growth, and on whether PVP is present.

For pure felodipine the authors find it "reasonable" that the size dependence "can be attributed in large part" to the different surface-area-to-volume ratios combined with the somewhat faster surface growth. They explain why felodipine, unlike indomethacin, shows a weak size dependence and no biphasic kinetics: the surface-to-bulk contrast of form I (about 6) is much smaller than that of indomethacin (about 100 at 40 °C), a link they present with "may be due to". For the dispersion, the biphasic kinetics and the size-dependent plateaus are read as surface crystallization that proceeds fast at first and then reaches a limit in depth. They considered and set aside the explanation proposed for PVP–indomethacin, namely that PVP accumulates at the growth front and slows it, because their earlier work on PVP–felodipine indicates that felodipine crystals grow around PVP without such accumulation.

What the dissolution data add

The dissolution strand turns a stability study into a formulation trade-off. When the powder is fresh, smaller particles dissolve faster and win the race against crystallization from solution, so they reach a higher peak; the authors write that a smaller particle size "may be advantageous in terms of dissolution behavior when precipitation from solution is very rapid, as for felodipine and PVP dispersions, where PVP is a poor inhibitor of solution crystallization". But smaller particles also crystallize faster on storage, and "the presence of crystallinity in the sample dramatically decreases the supersaturation levels achieved and hence the 'amorphous advantage'". The results, in their words, "highlight the need to preserve the physical stability of the amorphous systems during the manufacturing and storage phase".

Accelerated storage

At 50 °C the dispersion crystallized faster and much further than at 30 °C. The authors take this as a warning: the change in both rate and extent "highlights the difficulty of using accelerated storage conditions to try and predict crystallization at lower temperatures". Their explanation, that surface crystallization matters less above $T_g$ and nucleation is faster at 50 °C, rests on cited work, and the $T_g$ of the dispersion is not given.

What remains open

Three questions are left without a direct test. Nucleation in the powders, which the authors identify as PVP's main target, was not measured. The crystallized layer was never imaged or sectioned, so the constant depth is an inference from two crystallinity values. And the paper does not ask why the surface layer stops growing inward. Note by the AI writer (not discussed in the paper): the bulk growth rate of form I measured with PVP, 6.37 × 10⁻¹¹ m s⁻¹, corresponds to about 5.5 µm per day. A front moving inward at that rate would advance roughly 300 µm in the 56 days used for the estimate, yet the inferred depth is 17.3 µm and the small-fraction crystallinity barely changes from about day 56 to day 161. The plateau therefore cannot be explained by the film growth rates alone; something else, perhaps the absence of new nuclei inside the particles or a difference between film and powder, must stop it, and the paper does not test which.

Limitations

Limits the authors state. The authors are careful in several places. They call the PXRD size difference possibly smaller than the Raman one and offer surface sensitivity as a possible reason ("may be due to"). The constant penetration depth is introduced as speculation ("It can be speculated"). The surface origin of the fast stage is "probably" true in the discussion, although the abstract and conclusions state it without hedge. The nucleation role is phrased as what "the data thus suggest". They note that accelerated storage can mislead. They do not discuss limits of sample size or of the two-size design.

The AI writer's own judgement (1): the mechanism is inferred from ratios. The two central mechanistic claims rest on comparing ratios of different quantities. The fast-stage attribution compares the ratio of early to late slopes of powder crystallinity (13–14, in % per day) with the ratio of surface to bulk linear growth rates in films (about 23, in m s⁻¹); agreement within a factor of about 2 is the evidence offered. The nucleation conclusion compares a 60–77-fold drop in the early crystallization slope with 2- and 7-fold drops in growth rate and adds a cited 150-fold nucleation reduction. Both arguments are reasonable, but neither is a measurement of the claimed mechanism. The source and fitted range of the pure-felodipine slopes in Table 3 are not stated, and its caption says "as a function of temperature" although only one temperature is tabulated.

The AI writer's own judgement (2): two sizes and one fit. The constant-depth estimate uses one size to set the depth and the other to test it, which is one prediction. Its agreement (16.2% against 16.5%) is close, but the input crystallinity (43.5%) matches Figure 7 rather than Figure 5, and the Raman and PXRD plateaus of the same powders differ by a few points. With only two sieve fractions, the size dependence cannot distinguish a surface-area scaling from other size effects.

The AI writer's own judgement (3): internal inconsistencies. The figures and text disagree in several small places: Figure 12's late points for the large fraction sit about 2 points above Figure 6; Figures 5 and 7 show slightly different 30 °C series for the same powder; the text gives 4 µg/mL at 2 h for the dispersions where Figure 10 shows about 3.5–3.75; the text reports no size difference for crystalline felodipine where Figure 9 shows a small one; the Raman range is stated as 1800–1400 cm⁻¹ while the box in Figure 1 spans about 1735–1430 cm⁻¹; and the PXRD tube setting is printed as "40 kV and 30 mV". None changes the main conclusions, but plot-derived numbers carry this uncertainty.

The AI writer's own judgement (4): what is not reported. No $T_g$ is printed, although the argument relies on 30 °C lying below and 50 °C above it. Error bars are not defined, growth rates have no uncertainty or number of crystals, the PVP content of the medium for the crystalline reference is not stated, and the crystallinity of the stored powders used for dissolution is taken from the stability study rather than measured on the dissolved portions. Raman and PXRD crystallinities of the same powder differ by up to about 15 points at the same time (for example about 46 against 31% for the small pure fraction at 24 h), so values should be compared within one technique.

Conclusion

For amorphous felodipine stored dry at 30 °C, smaller particles crystallize faster, with and without 3 wt% PVP. Without polymer the size controls only the rate, and the whole powder crystallizes within days; with PVP the size also controls the extent, the small fraction stopping near 45% and the large one near 17% crystallinity. Growth along a free surface is faster than growth into the bulk, about 6 times without and 23 times with PVP, and the authors build their explanation on that contrast: surface-to-volume ratio for the pure drug, a crystallized shell of constant depth for the dispersion, and nucleation inhibition as PVP's main stabilizing action. These links are inferences from rate ratios and two particle sizes, not direct measurements, and the measured bulk growth rate leaves the plateau itself unexplained. The dissolution data make the practical point clearly: fine amorphous particles reach higher supersaturation only while they stay amorphous, and the crystallinity they gain in storage removes much of that gain.