Where a seed crystal comes from decides how well a polymer can stop it growing: felodipine and HPMCAS

Background and motivation

Many poorly water-soluble drugs are formulated as amorphous solids because the amorphous form, with its higher free energy, dissolves faster and can reach concentrations well above the crystalline solubility. Such supersaturated solutions improve membrane transport and absorption, but they are unstable: if the drug crystallizes in the gut, the advantage is lost. Slowing crystal nucleation or growth to prolong supersaturation is therefore a design goal, and polymers are the usual tools (Section 1; refs 1-10). C1

Earlier work had established two ways in which an additive can slow growth: by changing the interfacial energy of the crystal, or by adsorbing on growth steps and pinning them so that the steps advance more slowly. Polymers added to the medium are effective growth inhibitors, and earlier felodipine studies from the same group found that their success depends on adsorbing and covering a large fraction of the crystal surface (Schram et al. 2015, refs 18 and 19). Polymers can also change the macroscopic shape of crystals by blocking particular faces. C2·C3

Most of this knowledge comes from experiments in which pre-made crystals are exposed to a polymer solution. In an amorphous product the situation is different. Seeds can form during manufacture, during storage or while the product dissolves, and they form from the amorphous drug, usually with a polymer close by. The authors point out that little is known about how seeds of different origin affect desupersaturation, and they argue that seeds formed from an amorphous drug are "likely" to differ from solvent-grown crystals, and that a polymer present during their formation "likely" changes them further. C4

The paper therefore set out to study polymer poisoning of felodipine crystal surfaces that had formed under different conditions, and to relate their morphology to their growth rates from supersaturated solution. The authors expected atomic force microscopy (AFM) to reveal differences in both macroscopic morphology and microscopic growth mechanism, and expected these differences to change the growth rates ("It was hypothesized"). The model system is felodipine, a dihydropyridine drug, with hydroxypropylmethyl cellulose acetate succinate (HPMCAS, LF grade) as the polymer. C5·M1·M2

Background concepts

Supersaturation and the growth rate. The driving force for crystal growth is the higher chemical potential of solute in a supersaturated solution. The paper expresses it through the supersaturation ratio (Section 2, eq 1a): C6·E1

In plain terms: S says how many times the bulk concentration C exceeds the equilibrium concentration $C_{eq}$. In the growth experiments C was 2 µg/mL and $C_{eq}$ of felodipine was taken as about 0.5 µg/mL at 25 °C from earlier work, so S = 4 and $\ln S$ = 1.39. P5·M1·R13.e The growth rate is then written as a power law (eq 1b): E2

In plain terms: the mass of solute deposited per unit time, $dm/dt$, grows with the crystal surface area A, with a growth rate coefficient $k_G$, and with supersaturation raised to the overall growth order g. The paper later uses the area term to argue that two seed surfaces with the same area should, other things equal, grow at the same rate. E2·C26

Layer growth and the critical nucleus. In the adsorption layer growth picture that the authors adopt, a new molecular layer starts as a two-dimensional (2D) nucleus on a crystal face. Molecules then join at kink sites on the edge of the layer, so the layer spreads as a step one molecule high. A 2D nucleus can only keep growing once it exceeds a critical radius (eq 2): C6·E3

In plain terms: ${\rho }_c$ is larger when the edge free energy $\gamma$ (the energy cost per unit length of step edge) and the area a occupied by one growth unit are large, and smaller when the temperature T or the supersaturation is high; k is the Boltzmann constant. A smaller ${\rho }_c$ means that new layers start and spread more easily. E3

Step pinning: the Kubota–Mullin model. If impurity molecules, here polymer chains, adsorb along a step edge an average distance l apart, the step is held at those points and bows out between them. The radius of curvature of the bowed segments is $\rho =l/2$, and a curved step advances more slowly than a straight one. Kubota and Mullin expressed the step velocity with impurity, $V_P$, relative to the velocity on a clean surface, $V_0$, as (eq 3): C7·E4·E6

In plain terms: the closer the spacing of the pinning points comes to the critical radius, the slower the step; at $l={\rho }_c$ the step stops. The paper states the stopping condition in two ways, as $\rho \le {\rho }_c$ in Section 2 (which with $\rho =l/2$ means $l\le 2{\rho }_c$) and as $l\le {\rho }_c$ in Section 4.4; eq 3 matches the second. For monolayer step growth the step velocity is proportional to the face growth rate, which the authors assume is proportional to the measured overall growth rate. C7·C8·E7·X1

The effectiveness ratio. The paper reports every growth result as a ratio (eq 4): E5

In plain terms: $R_0$ is the growth rate of the control seeds, made in plain buffer, in a supersaturated solution without polymer; $R_P$ is the growth rate in any other experiment. $E_g$ = 1 means no change, $E_g$ = 5 means growth five times slower, and $E_g$ below 1 means faster growth than the control. The authors call it the polymer effectiveness: the larger $E_g$, the more effectively the surface is poisoned and the slower the desupersaturation. E5·C11

What AFM shows. The surfaces were imaged in liquid in tapping mode. Amplitude images are the raw feedback signal and show edges and steps clearly; height images are calibrated in nanometres and give 3D topography, step heights and, through roughness analysis, the true surface area; phase images respond to differences in material properties, and the authors use them to detect adsorbed polymer. Two terms describe growth patterns seen in the images: steps that run straight across a face (layer-by-layer step growth), and birth and spread, in which new layers start as islands at points and spread outward. P7·C12·C17·C22

Methods in detail

The design varies one thing: where and when HPMCAS meets felodipine before and during growth. The drug, the polymer, the polymer concentration (5 µg/mL in solution) and the supersaturation (initial S = 4) stay the same throughout. A1·A2·P3·P5

Making the seed surfaces

The problem. To compare seeds of different origin, the seeds must sit on a support that can be mounted on a rotating disk and then imaged by AFM without being disturbed. What they did. Crystalline felodipine was melted and poured onto AFM pucks seated in custom-made cylindrical Teflon holders, and the surface was flattened with a glass coverslip before the melt cooled. For the solid dispersion, 10% w/w HPMCAS powder was ground with felodipine crystals in a mortar, melted and poured in the same way. Melt temperature, cooling rate and any check that the films were amorphous are not reported. P1·P2·M8

The amorphous surfaces were then crystallized in stirred 50 mM phosphate buffer by four methods (Table 1, Figure 2): P3

• (i) Control: pH 6.8 buffer for up to 24 h. P3.a
• (ii) Pre-adsorbed: as (i), then 3 h in buffer containing 5 µg/mL HPMCAS, "to allow maximum adsorption" of the polymer before the growth test. P3.b
• (iii) Crystallized in polymer solution: pH 6.8 buffer containing 5 µg/mL HPMCAS for up to 24 h. P3.c
• (iv) Crystallized from the ASD: the 10% HPMCAS dispersion in pH 3 buffer for up to a week. P3.d

XRPD of surfaces from methods (i) and (ii) gave the stable felodipine polymorph (CSD reference code DONTIJ); surfaces from (iii) and (iv) were not examined by XRPD. R1·P4 The authors explain the choice: (i) is the control, (ii) tests pre-poisoning, and (iii) and (iv) test the effect of polymer present when crystallization first occurs; (iv) "represents the most likely scenario for an amorphous formulation", while (i) and (ii) resemble the tests used before. C9

Measuring growth

What they did. A small amount of a 10 mg/mL felodipine stock in methanol was added to pH 6.8 buffer, alone or containing 5 µg/mL HPMCAS, 100 µg/mL sodium dodecyl sulfate (SDS) or both, to give 2 µg/mL felodipine, an initial S of 4. The seed holder was mounted at once on a rotating disk apparatus (Princeton Applied Research Model 616) turning at 3000 rpm, and the felodipine concentration was read by a CCD array UV-vis spectrometer at 238 nm every 10 s for 1 h. The slope of concentration against time was taken as the growth rate; every condition was run in triplicate. Method (ii) seeds also received a second growth run, immediately after the first, in a fresh polymer-free supersaturated solution. P5·P6·M3

Why it works. At 3000 rpm the authors take transport of solute to the crystal surface to have no effect on the rate, citing a companion study then in review (ref 29), so the measured rate reflects only the integration of molecules into the surface, the step that adsorbed polymer interferes with. Expressing every result as $E_g$ against one control removes the need to know the absolute rates, which the paper does not report. C10·E5

Note by the AI writer (not discussed in the paper): two things are held constant only by assumption. S = 4 uses the solubility of felodipine in plain buffer; the solubility in buffer containing HPMCAS or SDS is not reported. And the slope is taken over 1 h while S falls from its initial value, the paper does not say by how much. X9 The rate is also not normalised to the crystal area, although eq 1b contains it, and areas were measured only for seeds (i) and (iii). X12

Imaging the surfaces and calculating the critical radius

AFM. After a growth run the holder was removed and the surface imaged at once in the same liquid, to avoid dissolution, on a Multimode 8 AFM in tapping mode (silicon nitride probes with 0.24 N/m spring constant and 10 or 30 nm tip radius; 512 x 512 pixels; 0.4-0.5 Hz). Scans were 1 x 1 µm for step detail (Figures 5, 9, 12) and 5 x 5 µm for topography (Figure 7). Surface areas came from roughness analysis, step heights h and pinning spacings l from cross-sections. The figure captions give an "incubation time" of about 3 h (Figure 5) or 2-3 h (Figures 7, 9, 12) that is not defined, and only Figure 5 states the growth condition before imaging. P7·P8·X5

The critical radius. Contact angles of water and ethylene glycol (ten drops each) on a felodipine surface crystallized in buffer gave the surface energy by Wu's harmonic mean method, and from it the edge free energy $\gamma$ = 3.9 x 10^-20 J/nm (Table 4). The area of a growth unit, a = 0.584 nm², came from the length and width of one molecule measured in the crystal structure. With k = 1.38 x 10^-23 J/K, T = 298.15 K and $\ln S$ = 1.39, eq 2 gives ${\rho }_c$ = 3.98 nm. P9·P10·R13·R14 Recomputing with these inputs reproduces 3.98 nm. E3 The contact angles, the surface energy and its conversion to an edge energy are not printed, and the uncertainty of $\gamma$ is printed as "± 0.06 J/nm" without its power of ten. X10

Experimental analysis

The overall result: the seed route sets the inhibition

Figure 3 collects all seven combinations of seed route and growth medium. With 5 µg/mL HPMCAS in the growth solution, $E_g$ rose from about 2.7 for control seeds to about 5.5 for pre-adsorbed seeds, about 8.0 for seeds crystallized in HPMCAS solution and 12 for seeds crystallized from the ASD. Without HPMCAS in the growth solution, the same seeds gave about 1.8, 3.0 and 8.4, against 1 for the control by definition. R2 The authors summarise that the preparation method and dissolved HPMCAS both "greatly impacted" the effectiveness, which "ranges from about 2 to 12" ("It is clear"). C13

Table A. Effectiveness ratio by seed route and growth medium; means of three runs with SD, read from Figures 3 and 4 (approximate; the value 12 is given in the text). R2·R3

Two patterns stand out. Every route grew more slowly with HPMCAS in solution than without, which the authors restate in the conclusions as "regardless of the surface preparation method". C16 And the order (i) < (ii) < (iii) < (iv) is the same with and without dissolved HPMCAS. In the authors' words, the ASD seeds were "about three times" (without HPMCAS) and "nearly five times" (with HPMCAS) as effective as the control seeds tested with HPMCAS; from the bars these ratios are about 3.1 and about 4.4. R15·C32

Pre-adsorbed polymer: overgrown when the solution has none

Pre-adsorption was expected to work, since polymers are "generally accepted" to adsorb irreversibly. C15 With HPMCAS also in the growth solution it did help: about 5.5 against about 2.7 for control seeds. The authors had "anticipated" this, because pre-equilibration lets the polymer reach maximum coverage, whereas without it HPMCAS "must compete with felodipine growth units for adsorption to active sites". R2.b·R2.d·C14 Without HPMCAS in the growth solution, however, the pre-adsorbed seeds were only slightly inhibited (about 1.8), and in a second run straight afterwards almost not at all (about 1.1, "close to 1", Figure 4). R2.a·R3

The AFM amplitude images after 1 h of growth (Figure 5) show why the authors read this as overgrowth. Control seeds grown without polymer show relatively even, straight steps across the face (Figure 5a), evidence of step growth. Pre-adsorbed seeds grown without polymer look very similar (Figure 5c). R4·R6·C17 The authors conclude that, with no polymer in solution competing for growth sites, felodipine grew around the adsorbed chains ("This suggests") and a pure drug layer covered the poisoned surface, which the second run "confirmed"; they compare this with re-growth on poisoned calcite crystals reported by Gratz and Hillner (ref 22). C19·C20 From this they draw a general point: dissolved polymer must be present during growth for effective inhibition. C21·C33

Note by the AI writer (not discussed in the paper): the burial of the pre-adsorbed polymer is inferred from the second-run ratio and the similar appearance of two amplitude images; no phase image was taken after the first run to show where the polymer went. X7

Dissolved HPMCAS pins the steps

With HPMCAS in the growth solution, the steps on control seeds were no longer even or straight but held back at several points along each step, with curved segments between them (Figure 5b). The authors read this as HPMCAS adsorbed at active sites pinning the steps, slowing them and raising their curvature, which "explains" the slower growth ("The result suggests"). R5·C18 The pinned steps were 0.81 ± 0.2 nm high, about one felodipine molecule, and the pinning points were 68.5 ± 9.4 nm apart (Table 3). R12.b·M1 On pre-adsorbed seeds grown with HPMCAS in solution (Figure 5d), the layers no longer crossed the face; they started at points and spread outward. The authors liken this to the birth and spread mechanism and write that pinning was "so effective" that growth was confined to 2D nuclei between adsorbed polymer ("it appears"), which they call "clear evidence" that surface poisoning can change how crystals evolve. R7·C22

Seeds formed in polymer solution: small crystallites, same area

Seeds crystallized in HPMCAS solution grew about 8.0 times slower than control seeds when HPMCAS was in the growth solution, against about 2.7 for control seeds, and even without polymer in solution they grew about 3.0 times slower (Figure 6). R2.b·R2.c·R2.e·C23 The 5 x 5 µm height maps (Figure 7) show why the authors looked at morphology: control seeds have large, flat features with long straight edges (height scale 0-450 nm), while seeds formed in HPMCAS have much smaller, rough, spike-like crystallites (scale 0-250 nm). R8 The authors conclude that HPMCAS in the crystallization medium "greatly impacts" the size and shape of the seeds and "interfered with the growth mechanism" ("This suggests"). They propose that the morphology "could be" the large-scale result of the point-origin growth of Figure 5d: HPMCAS "may have adsorbed" before crystallization and "likely" forced the crystallites to grow vertically, like islands, rather than as layers. C24·C25

Table B. Morphology and surface area (Table 2, roughness analysis of one image each) against growth ratio (read from Figure 6, approximate). R8·R9·R2.b·R2.e

Because the two areas are almost equal, the authors argue that area cannot explain the difference in rate, as eq 1b might suggest; instead it "must arise" from the availability of active growth sites. Large crystallites carry long steps across large faces, with many high-energy sites; small crystallites cannot have such long, uninterrupted steps, so they offer fewer accessible high-energy sites and grow more slowly. C26 Note by the AI writer (not discussed in the paper): no step or kink density was measured, each area comes from a single image, and the two height maps use different height scales, so the site-availability explanation is an interpretation of the morphology rather than a measured result. X6

Seeds formed from the ASD: finer features and closer pinning

Seeds crystallized from the ASD gave the strongest inhibition, 12 with HPMCAS in solution, which the authors describe as "a very significant reduction in growth rate due to highly effective surface poisoning" (Figure 8). R2.g·C27 Their explanation is that "an ASD is an intimate mixture of API and polymer": earlier studies on other systems found that effective ASD stabilisers form strong specific interactions with the drug, and such interactions "can disrupt crystal evolution more effectively" than polymer present only in solution ("likely due to"; refs 33, 34). C28 They predicted that ASD-grown seeds would show even smaller features than seeds formed in polymer solution, and the 1 x 1 µm height images "confirmed" it: terraced crystallites for method (iii) (scale 0-70 nm) against small rounded features over the whole surface for method (iv) (scale 0-20 nm; Figure 9). R10·C29

Cross-sections across steps on the ASD-grown surface (Figure 10) drop by about 0.78 and about 0.81 nm, and the mean step height was 0.77 ± 0.2 nm, the same as the pinned steps of Figure 5b and close to the molecular length of felodipine, about 0.8 nm. The authors therefore "concluded" that the small rounded features are the result of step pinning. R11·R12·M1·C30 The pinning spacing differed strongly between the two surfaces (Table 3):

Table C. Step height and pinning spacing from AFM cross-sections (Table 3; the number of sections is not stated) against the calculated critical radius (eq 2, Table 4). The multiples of ρ_c are the AI writer's arithmetic. R12·R14

The spacing on the ASD-grown surface is "more than four times smaller" (68.5/15.8 = 4.3). Since ${\rho }_c$ is smaller than both spacings, the authors explain why growth was not stopped in either case; and because the ASD value lies "much closer" to ${\rho }_c$, they see "quantitative validation" of why the ASD seeds were about three times (no HPMCAS) and nearly five times (with HPMCAS) as effective as the control seeds with HPMCAS. R15·C31·C32

Note by the AI writer (not discussed in the paper): eq 3 can be evaluated with the printed numbers. It gives $V_P/V_0$ = 1 - 3.98/15.8 = 0.75 for the ASD-grown surface and 1 - 3.98/68.5 = 0.94 for Figure 5b. Under the paper's own assumption that growth rate is proportional to step velocity, this predicts growth ratios of about 1.34 and 1.06, far below the measured about 8.4-12 and about 2.7. The comparison in the paper therefore supports the order of the two surfaces, not their size. The definition of l is also not quite settled: it is defined as the distance between adsorbed polymers, but "determined by measuring the step radii", and Table 5 calls it the "diameter of the pinned steps". X3·X2

SDS: faster growth, although HPMCAS still adsorbs

Surfactants are common in dissolution media, in vivo and in formulations, so the authors also measured growth of control seeds with SDS (Figure 11). HPMCAS alone gave about 2.7; HPMCAS with 100 µg/mL SDS gave about 1.1; SDS alone gave about 0.8, that is, faster growth than with no additive (R₀/R_P < 1). R16·C34 The authors first suspected that adsorbed SDS keeps HPMCAS off the surface by steric hindrance. AFM phase images "provided evidence that this was not the case": a face exposed to HPMCAS and one exposed to HPMCAS with SDS both show dark mottled shading, which the authors take as adsorbed HPMCAS, while the pure face does not (Figure 12). R17·C35 For the acceleration they offer "a possible explanation": the surfactant lowers the interfacial energy $\gamma$ and with it the critical nucleus radius (eq 2), consistent with the report by Chen et al. that some surfactants accelerate crystallization (ref 35). C36 Neither $\gamma$ in SDS solution nor the HPMCAS coverage was measured, and the phase images are single, unquantified pictures. X8·X9

Discussion

The authors connect the results through one idea: HPMCAS slows growth by adsorbing at kink sites on step edges and pinning the steps, and how strongly it does so depends on how and when the polymer met the crystal. C6·C7·C18·C33 The chain below follows their reasoning; the outcomes on the left are good for keeping a solution supersaturated, those on the right bad.

The authors' general conclusion is that surface poisoning by polymers "can have a large impact on crystal morphology and consequently, crystal growth rates"; the abstract puts it more cautiously, that polymers present during crystal evolution from an amorphous solid "can impact" crystal size and shape, which "in turn influences" later growth. C38 Their practical message is a recommendation: because seeds prepared in different environments differ in their ability to grow, seed origin "should be considered" when polymers are evaluated as growth inhibitors and when the desupersaturation risk of amorphous formulations with residual crystals is assessed. C39 For surfactants they add that combining a polymer with a surfactant such as SDS "could potentially" weaken stabilisation of the supersaturated solution in vivo and decrease absorption. C37

What it suggests for formulation (note by the AI writer, not discussed in the paper). Seeded-growth tests that use crystals grown in plain buffer, or pre-made crystals soaked in polymer, may describe the wrong seeds for an HPMCAS dispersion: here crystals that grew out of the dispersion were the least able to grow, by a factor of about 4.4 against control seeds tested with the same dissolved polymer. R2.b·R2.g The pre-adsorption result says that a polymer coat on residual crystals does not last on its own; the inhibitor has to remain dissolved while supersaturation lasts, which ties growth inhibition to how the polymer itself dissolves from the product. R2.a·R3 The SDS result is a warning for HPMCAS products that also contain an anionic surfactant, but it comes from one drug, one pair of concentrations and one supersaturation, and its mechanism was not measured. R16·X9

Limitations

Limits the authors state or imply. The authors do not include a limitations paragraph. Their own wording marks several steps as interpretation: the pinning reading of Figure 5b ("suggests"), the island-growth reading of Figure 7b ("could be", "may have", "likely"), the role of intimate mixing in the ASD ("likely due to") and the interfacial-energy explanation for SDS ("a possible explanation"). C18·C25·C28·C36 The SDS consequence for absorption is offered as a possibility ("could potentially"). C37

The AI writer's own judgement (1): what the growth data show and what they do not. The growth ratios are the strongest part of the paper: triplicate means whose SDs are small compared with the differences between routes, and the same bars agree in five figures. R2·R16 The comparison of route (iv) with route (iii) is, however, not a clean test of "polymer mixed into the solid": the ASD was a melt with 10% HPMCAS whose amorphous state and homogeneity were not reported, it crystallized at pH 3 rather than 6.8, and for up to a week rather than a day; the crystal form of the (iii) and (iv) seeds was not checked. X4·X13 The rate is a concentration slope not normalised to area, and areas were measured only for routes (i) and (iii). X12 Supersaturation is nominal: S = 4 uses the buffer solubility in every medium, and S falls during the 1 h run. X9

The AI writer's own judgement (2): how far the mechanism is shown. The AFM evidence consists of single qualitative images per condition, and for Figures 7, 9, 10 and 12 the growth condition before imaging is not stated. X5 The text describes Figure 5a as showing "height features", but the figure is an amplitude image. X11 The Kubota–Mullin comparison is called "quantitative validation", yet eq 3 with the measured spacings predicts much smaller effects than were measured; it supports the order of the two surfaces only. X3 The model's stopping criterion is also stated two ways, differing by a factor of 2 in l. X1 Burial of pre-adsorbed polymer, continued HPMCAS adsorption in the presence of SDS, fewer active sites on small crystallites and drug–polymer interactions in the ASD are all reasonable readings, but none was measured directly. X7·X8·X6·X13 Overall the AI writer rates the paper as moderate: a clear and reproducible effect of seed origin on growth, with a plausible but largely interpretive account of why.

Conclusion

The paper makes three contributions. First, it shows with a simple, controlled design that the same polymer at the same concentration slows felodipine seed growth about 2.7-fold, 5.5-fold, 8-fold or 12-fold depending on how the seeds were made, and that dissolved polymer is needed for the inhibition to last. R2·R3·C16·C21 Second, it pairs every growth result with AFM images of the same surfaces, which show straight steps, pinned steps, point-origin layers, small spiky crystallites and very fine rounded features, and it measures step heights of about one molecule and pinning spacings of 68.5 and 15.8 nm. R4·R5·R7·R8·R10·R12 Third, it places these spacings against a calculated critical nucleus radius of 3.98 nm through the Kubota–Mullin model, which orders the surfaces correctly but does not reproduce the size of the effects. R14·C32·X3 The practical lesson the authors draw is that seed origin has to be part of any judgement of polymer inhibitors and of the desupersaturation risk of amorphous products. C39