Does Crystal Density Control Fast Surface Crystal Growth in Glasses

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Does Crystal Density Control Fast Surface Crystal Growth in Glasses? A Study with Polymorphs Published as part of a virtual special issue of selected papers presented at the 2010 Annual Conference of the British Association for Crystal Growth (BACG), Manchester, UK, September 5 7, 2010 Erica M. Gunn, Ilia A. Guzei, and Lian Yu* School of Pharmacy and Department of Chemistry, University of Wisconsin - Madison, Madison, Wisconsin 53705, United States ABSTRACT: As organic liquids are cooled to become glasses, crystal growth at the free surface can be substantially faster than in the interior, a phenomenon uncommon for other materials and for which different explanations exist. We have measured the surface and bulk growth rates of three polymorphs in carbamazepine glasses. Crystal density has no controlling effect on the extent to which surface crystal growth is enhanced over bulk crystal growth, in contradiction to models that relate fast surface crystal growth to the release of crystallization-induced tension.

’ INTRODUCTION Glasses are amorphous solids formed by cooling liquids, evaporating solutions, or condensing vapors without crystallization. Amorphous materials are useful for many applications,1 including the delivery of poorly soluble drugs.2 In their applications, glasses are often required to resist crystallization, and while their existence is due to avoidance of crystallization, glasses can crystallize (devitrify), sometimes surprisingly fast. In studies of glass crystallization, it is of interest to learn whether the free surface crystallizes faster than the interior. This question has been answered in the affirmative for many systems, including selenium,3 silicon,4,5 metals,6 silicates,7 12 small-molecule organics,13 15 and polymers.16 18 Because crystallization consists of nucleation and growth, a further question is whether faster crystallization at surfaces results from faster nucleation, faster growth, or both. Not all prior studies answered this question; some did not distinguish the two steps of crystallization. Those that answered the question have reached different conclusions. Koster writes, “Whereas in many metallic glasses nucleation has been observed to be enhanced at the surface, growth rates are usually quite comparable with those in the bulk.” For μ-cordierite6 and anorthite,9 surface and bulk crystal growth rates were found equal, though the crystallization temperatures of these studies are slightly higher than the glass transition temperature Tg. In contrast to these observations, recent studies of organic glasses have found that crystal growth at the free surface can be orders of magnitude faster than in the bulk.11 13 This surfaceenhanced crystal growth can be suppressed with a coating only a few nanometers thick.19 Fast surface crystal growth has also been r 2011 American Chemical Society

reported for amorphous selenium3 and amorphous silicon.4,5 A related but different phenomenon exists for liquid n-alkanes, which show “surface freezing” above the bulk freezing point.20 Current views differ on how crystal growth rate should change on going from the bulk to the surface of a glass. Schmelzer and coworkers argue that the growth of higher-density crystals in lowerdensity glasses creates an elastic strain and lowers the thermodynamic driving force and the rate of crystallization, and that the effect should diminish on going from the bulk to the surface, resulting in faster crystallization at the surface.7 In contrast, Konishi and Tanaka argue that the tension around a crystal growing inside a glass should increase molecular mobility and accelerate crystal growth.21 According to this model, crystal growth should be slower at the surface, where tension should be more efficiently relieved. Another view of surface crystallization13 15 focuses on surface molecular mobility, reasoning that, if crystal growth rate is limited by molecular mobility, the enhanced mobility at surfaces can accelerate crystal growth. Given the attention to the role of volume contraction during glass crystallization, we studied the growth of polymorphs in a glass. Polymorphs have different structures and densities but share the same liquid or glass. The different growth rates of polymorphs can reveal how crystal growth depends on the structure being developed.22,23 In the context of this study, the model of Schmelzer and co-workers7 would predict that the ratio of surface and bulk crystal growth rates, us/ub, should increase on Received: April 30, 2011 Revised: June 28, 2011 Published: July 13, 2011 3979

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Crystal Growth & Design going from a less dense polymorph to a denser one, whereas the opposite would be predicted by the model of Konishi and Tanaka.21 We used carbamazepine (CBZ), an anticonvulsant drug, as a model system. CBZ has four known polymorphs whose densities differ by several percent.24 26 Its relatively high Tg (319 K) makes it convenient to study CBZ glasses under ambient conditions. We report here that three polymorphs can grow at the surface and in the bulk of CBZ glasses. We find no consistent increase or decrease of us/ub with crystal density. Our finding indicates that crystal density has no controlling effect on the difference between surface and bulk crystal growth rates. We discuss the significance of our results for understanding crystal growth in glasses.

’ EXPERIMENTAL SECTION Carbamazepine was obtained from Aldrich and from Fluka as a mixture of Forms I and III according to X-ray diffraction. The Aldrich material also contained small amounts of Form IV. Samples of pure polymorphs were prepared to serve as seeds. Forms II and III were crystallized from 1.5 g/10 mL methanolic solutions following a reported procedure.23 Solutions were left to evaporate at room temperature in a glass vial covered with a Kimwipe or perforated parafilm. Fine, opaque needles of Form II grew on the sides of the vial at the liquid contact line. Large, transparent blocks of Form III crystals deposited more slowly at the bottom of the vial. Once a pure sample of Form III crystals had been obtained, it was possible to crystallize larger quantities by seeding. Form I was obtained by heating the commercial powder from Fluka for 3 h at 423 K. Form IV was obtained by seeding a melt with the Aldrich powder containing small amounts of Form IV and allowing crystals to grow at 313 K. Once a sample had been grown by this method, it was used as seeds to crystallize additional Form IV. A carbamazepine glass for crystal growth studies was prepared by melting 2 3 mg of a commercial powder on a glass coverslip. A second coverslip was added over the liquid immediately upon melting to reduce air exposure and avoid decomposition. This “sandwiched” sample was held at 483 K for 2 min and quenched to room temperature to form a glass film approximately 15 μm thick. The sandwiched sample was used for measuring crystal growth in the bulk of a CBZ glass. To measure crystal growth at a free surface, the top coverslip was removed to yield “an open-faced sandwich.” This procedure occasionally produced cracks in the film. In such cases, the sample was annealed at 343 K for a few seconds to heal the cracks. To observe the growth of Forms III and IV in the bulk of CBZ glasses, the edge of a sandwiched glass film was seeded with a commercial powder or scratched with a tungsten needle. Mechanical disturbance alone often nucleated a mixture of Forms III and IV, with Form III typically being the dominant polymorph due to its faster growth and shorter induction period. Bulk growth of Form III could also be initiated with solution-grown crystals as seeds. Once more crystals were grown, they could serve as seeds for future experiments. This was important for Form IV, as we were unable to obtain seeds by solution crystallization. Form I was difficult to observe in the bulk glass because of its slow growth rate. Form I could nucleate around air bubbles in a glass and be initiated at the edge of a glass film by contact with seeds collected from surface-crystallized samples. Seeding to initiate the growth of Form I proved difficult because the process often caused enough mechanical disturbance to nucleate the faster-growing III and IV. Gently blowing seeds onto the edges of the sample with a stream of dry nitrogen proved the most effective method of seeding only Form I. Amorphous samples stored for several months at 323 K showed dense spontaneous nucleation of Form I in the bulk glass.

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To observe the growth of Form I at a free surface, CBZ glasses with exposed surfaces were allowed to crystallize spontaneously. Form I was the only polymorph observed to grow on free surfaces that were not perturbed during sample preparation. Surface growth of Forms III and IV could be initiated by gently touching the glass surface with tweezers or seed crystals. Form II was never observed to grow at the surface or in the bulk glass, spontaneously or by seeding. Polymorphs were identified by X-ray diffraction (Bruker D8 Advance powder diffractometer). Samples were measured in the Bragg Brentano geometry from 2 to 40° (2θ) at 0.02°/step. The integration time was 3 5 s for bulk-crystallized samples and 15 s for thinner, surfacecrystallized crystals. Surface-crystallized samples were analyzed as grown. Surface crystals could be detected by X-ray diffraction (XRD) after 24 48 h of growth at 313 K. For a bulk-crystallized sample, the top coverslip was removed before analysis, and the region of interest was isolated by scraping off the rest with a razor blade. Bulk samples of Forms III and IV of sufficient size for X-ray analysis were grown in 1 2 months at 313 K. Form I grew more slowly in the bulk. At 323 K, Form I crystallized over 5 months in two morphologies, and both were confirmed to be Form I by X-ray diffraction. Only one morphology was observed at the lower temperatures used (313 and 303 K). Because CBZ can decompose after prolonged heating at high temperatures, the purity of glasses prepared for crystallization studies was checked using NMR (Varian Unity-Inova 400 MHz NMR spectrometer). Samples of CBZ glasses prepared between coverslips were scraped off and dissolved in CDCl3. This analysis found that the degradation product iminostilbene was less than 1%. A TA Instruments Q2000 differential scanning calorimeter was used to measure Tg. Ten milligrams of commercial powder was heated in a sealed DSC pan to 483 K for 2 min to ensure complete melting, quenched to room temperature on an aluminum block to form a glass, and heated again at 10 K/min. A glass transition was observed at 319 K (onset), followed by crystallization and then melting at 466 K. The density of Form III was obtained between 100 and 300 K from the diffraction of a single crystal (Bruker AXS APEX II diffractometer equipped with a sealed tube Cu KR radiation source and an Oxford Cryostream 700 cooling device). The diffraction peaks were indexed at each temperature, yielding the corresponding unit-cell volume and crystal density. The density of the CBZ glass was measured at 295 K by volume displacement. One gram of the glass, prepared to be free of air bubbles, was placed in a 10 mL volumetric flask. The volume of the glass was calculated from the volume of water required to fill the flask to mark. The CBZ glass density measured was 1.14 ( 0.02 g/cm3 (n = 3).

’ RESULTS We could observe the growth of three polymorphs on the surface and in the bulk of CBZ glasses. Figure 1 shows the unit cells of these polymorphs:24 28 Form I (P1, a = 5.17 Å, b = 20.57 Å, c = 22.25 Å, R = 84.12°, β = 88.01°, γ = 85.19°, Z = 8); Form III (P21/n, a = 7.54 Å, b = 11.16 Å, c = 13.91 Å, β = 92.86°, Z = 4); Form IV (C2/c, a = 26.61 Å, b = 6.93 Å, c = 13.96 Å, β = 109.70°, Z = 8). Figure 1d shows the radial distribution function (RDF) of molecular centers of mass in each polymorph. This function is a measure of the anisotropy of local molecular packing. By this measure, the packing in Form III is the most isotropic, with each molecule having 13 neighbors 6 9 Å away. Forms III and IV each have one symmetry-independent molecule, whereas Form I has four, for which the RDF shown is the average of the RDFs for the four independent molecules and describes the average local environment. 3980

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Crystal Growth & Design

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Figure 1. Unit cells of (a) Form I, (b) Form III, and (c) Form IV of CBZ. Forms I and IV were solved at 158 K and Form III was solved at room temperature. (d) Radial distribution functions of molecular centers of mass for the three polymorphs (averaged for the four independent molecules in Form I).

Figure 2. Densities of CBZ polymorphs and glass. Solid triangles (Form III) and solid circle (glass) are data from this study. Other symbols are literature values (refs 24 28). For the glass/liquid portion, the lines indicate expected temperature dependences.

Figure 2 shows the densities of CBZ polymorphs and glass. Black triangles are Form III densities from this work; the other symbols indicate the literature data.24 28 Our data agree well with the literature values. The densities of the polymorphs have similar temperature dependences, indicating that their ratios are approximately independent of temperature. The glass density was measured at 295 K. We assume that the CBZ glass has comparable thermal expansion coefficient as the CBZ crystals, as is the case of other organic glasses.29 All three polymorphs are denser than the glass, by factors that are approximately constant at the temperatures of our crystallization experiments (303 and 313 K). Figures 3 5 show results for the growth of three polymorphs at the surface and in the bulk of CBZ glasses. All grew as finegrained polycrystalline domains. Crystals of different polymorphs were distinguishable by their textures, transparency, and degrees of birefringence. X-ray diffraction patterns were used to make definitive assignments of polymorphs, as illustrated in Figures 3 5. The linear velocity of crystal growth u was measured by following the advance of a crystal growth front over time, also illustrated in each figure. Crystal growth rates were constant over the time of observation. Table 1 shows the growth rates for the three polymorphs at the surface and in the bulk of CBZ glasses. The temperatures of measurement were 303 and 313 K, both below Tg. 3981

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Figure 3. Form III crystals growing (a) at the surface and (b) in the bulk at 313 K. Scale bar = 200 μm. Arrows indicate growth directions. (c) Distance of growth vs time for crystals in (a) and (b). (d) Observed and predicted XRD patterns of Form III crystals.

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Figure 5. Form I crystals growing (a) at the surface and (b) in the bulk at 313 K. The bulk growth began at a bubble. Scale bar = 200 μm. Arrows indicate growth directions. (c) Distance of growth vs time for crystals in (a) and (b). (d) Observed and predicted XRD patterns of Form III crystals.

Table 1. Growth Rates for Three Polymorphs at the Surface and in the Bulk of CBZ Glasses T (K)

polymorph Form I Form III (densest) Form IV (least dense)

Figure 4. Form IV crystals growing (a) at the surface and (b) in the bulk at 313 K. Scale bar = 200 μm. Arrows indicate growth directions. (c) Distance of growth vs time for crystals in (a) and (b). (d) Observed and predicted XRD patterns of Form IV crystals.

Table 1 shows that the CBZ polymorphs have widely different growth rates at the surface and in the bulk. The growth rates

log us (m/s)

log ub (m/s)

303

9.35 (0.11)

11.4 (0.15)

110

313

8.81 (0.16)

10.1 (0.07)

19

303

9.06 (0.06)

9.45 (0.08)

313

8.66 (0.10)

8.90 (0.10)

303

8.62 (0.07)

313

8.21 (0.07)

10.3 (0.17) 9.46 (0.03)

us/ub

2.4 1.8 42 18

follow the order III > IV > I in the bulk and the order IV > III > I at the surface. The ratio of the surface and bulk crystal growth rates, us/ub, spans a large range, 1.8 110. Form III grows at comparable rates at the surface and in the bulk of CBZ glasses, whereas Forms I and IV grow substantially faster at the surface than in the bulk. From 303 to 313 K, the us/ub ratio changes little for Forms III and IV but significantly for Form I. This large change reflects a strong temperature dependence of the Form I bulk growth rate, the cause of which is still unclear. A note is warranted here on any possible difference between the chemical compositions at the surface and in the bulk. Such difference, if present, would affect the interpretation of the us/ub ratio observed. Of the various causes for surface chemical alterations,6 reaction with the atmosphere seems unlikely because CBZ, a pharmaceutical, is chemically stable under ambient conditions. Surface enrichment or depletion of chemical components in the bulk seems irrelevant because CBZ glasses of this study contained a single component. It is conceivable that some level of 3982

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Figure 6. Ratio of surface to bulk crystal growth rate vs crystal density. Data are shown for three CBZ polymorphs at 303 and 313 K (open and closed symbols, respectively). The densest polymorph (III) has the lowest us/ub ratio. The error in scaled density is estimated from independently measured densities of Form III at room temperature (refs 24 28 and this work).

surface contamination could occur during sample preparation and storage; besides storage in desiccators before measurement, our samples were not protected in any special way. We note, however, that the measured surface crystal growth rates were reasonably constant, regardless of storage time, frequency of measurement, and surface seeding, whereas deliberately coating a surface with 10 nm of gold would halt any active surface crystal growth. For a similar organic glass indomethacin,15 comparable surface crystal growth rates were observed in both dry air and vacuum, and with glasses prepared by liquid cooling, spin coating, and vapor deposition. These observations argue that surface contamination (if any) has relatively little effect on the comparison of surface and bulk crystal growth rates. To test whether crystal density has a controlling effect on the surface enhancement of crystal growth, we plot in Figure 6 the us/ub ratio for each polymorph vs its density normalized to the Form III density. Form III (the densest polymorph) has the smallest surface enhancement, while Form IV (the least dense) has an intermediate us/ub ratio.

’ DISCUSSION We have measured the growth of three polymorphs in CBZ glasses and found that increasing crystal density does not consistently increase or decrease the ratio us/ub (ratio of surface and bulk crystal growth rates). This finding disagrees with the model of Schmelzer and co-workers,7 which predicts that a denser polymorph should have larger us/ub, and the model of Konishi and Tanaka,21 which predicts the opposite. Our finding indicates that for this organic glass, the crystalglass density difference has no controlling effect on the extent to which surface crystal growth is enhanced over bulk crystal growth. This conclusion, reached by observing polymorphs growing in the same glass, is free from complications that could arise in studying crystal growth in glasses of different chemical compositions.

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We consider below a few possible causes for the lack of controlling influence of the crystal density on the extent to which surface crystal growth is enhanced over bulk crystal growth: (1) Tension does not accumulate to levels implied by crystalglass density differences. Tension can be released by flow and cavitation. Neither effect is assumed to occur in glasses during crystallization in the models of Schmelzer and co-workers and of Konishi and Tanaka. If either process occurs, crystallization-induced tension would be lower than that calculated from the crystal-glass density difference. In the case of CBZ, a glass would be stretched by ca. 10% (Figure 2) during crystallization if no cavitation or fracture occurs (assuming no extension of the crystal). Extension of this magnitude in other systems is known to cause mechanical failure. For example, cavitation occurs in the organic liquid o-terphenyl upon stretching by 0.4%, corresponding to a negative pressure of 70 bar.30 (2) A fast growth mode is activated in the bulk and the us/ub ratio is correspondingly smaller. Some organic liquids can develop a fast mode of bulk crystal growth, termed glassto-crystal or GC growth, as they approach Tg.31,32,22,33,34 Upon the activation of GC growth, crystal growth transitions from being limited by bulk diffusion to escaping such control.22 If bulk crystal growth is thus enhanced, us/ub would be correspondingly lower. In the case of CBZ, the model of Konishi and Tanaka would predict that Form III, the densest, grows the fastest in the bulk, followed by Form I and then Form IV. This prediction is in partial agreement with our observations: Form III grows the fastest in the bulk, but the growth rates of the other polymorphs are not ordered by their densities. It is also noteworthy that the fastest growth of Form III in the bulk is consistent with the view22 that GC growth is more likely for more isotropic (liquid-like) crystal structures (Figure 1d). The latter view would give no special importance to crystal density, although for both CBZ and ROY,22 the densest polymorph is also the most isotropically packed by the RDF measure. It is unclear whether the activation of GC growth would reorder us/ub ratios to the ranking observed. (3) Released tension is not the key enabler for fast surface crystal growth. It has been argued that surface molecular mobility is responsible for fast surface crystal growth of glasses.13 This view is consistent with the ability of nanometers-thin coatings to inhibit surface crystal growth19 and observations of surface molecular mobility in glasses.35 38 If this view is valid, the us/ub ratios for different polymorphs need not be ordered by their densities.

’ CONCLUSION Three polymorphs have been observed to grow at the surface and in the bulk of carbamazepine glasses. The polymorphs have widely different ratios of surface to bulk growth rates, us/ub, and these ratios are not ordered according to crystal densities, as predicted by current models of glass crystallization. This finding argues that crystal-glass density difference is not the controlling factor of the degree to which surface crystal growth is enhanced over bulk crystal growth. Better understanding of crystallization in glasses may require considerations of cavitation or fracture during crystallization and the role of surface mobility and attention 3983

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Crystal Growth & Design to molecular-level processes in addition to macroscopic properties such as density changes.

’ AUTHOR INFORMATION Corresponding Author

*Phone: 608-263-2263. E-mail: [email protected].

’ ACKNOWLEDGMENT We thank the NSF (DMR-0804786 and DMR-0907031) for supporting this work. E.G. thanks the PhRMA Foundation for a postdoctoral fellowship.

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