Controlling Factors and Mechanism of Polymorphic ... - ACS Publications

Controlling Factors and Mechanism of Polymorphic Crystallization Mitsutaka Kitamura* Department of Chemical Engineering, Hiroshima University, 1-4-1, Kagamiyama, Higashi-Hiroshima City, 739-8527, Japan

CRYSTAL GROWTH & DESIGN 2004 VOL. 4, NO. 6 1153-1159

Received July 7, 2004

ABSTRACT: The mechanism and controlling factors of polymorphic crystallization were investigated using amino acids and a thiazole derivative (BPT) (pharmaceutical). The controlling factors depend on the system and crystallization method. In the cooling crystallization of amino acids, supersaturation hardly influenced the crystallization behavior of either L-glutamic acid or L-histidine polymorphs. On the other hand, the effects of temperature and polymorphous seeds were remarkable in the polymorphic crystallization of L-glutamic acid, whereas no effect appeared in the crystallization of L-histidine polymorphs. Such a difference between the amino acids may be due to the conformational difference and/or the exchange rate between the conformers (or embryos) corresponding to each polymorph. The controlling factor in antisolvent crystallization of 2-(3-cyano-4-isobutyloxyphenyl)-4-methyl5- thiazolecarboxylic acid (BPT) was also examined in water-methanol mixture solvents. The thermodynamic stability of each polymorph and the transformation behavior between the polymorphs appeared to be affected by the methanol composition. The transformation behavior, comprised of two steps, was explained by the chemical potential difference between the stable and metastable form, and the preferable nucleation and growth of the other metastable forms, due to the specific solute-solvent interaction. In the crystallization of BPT by addition of water, it is clear that the initial concentration and the water addition rate are controlling factors, and the crystallization zone of the polymorphs was shown with respect to these factors. It was also found that the transformation occurs after the crystallization and the rate depends on the initial concentration of BPT and the addition rate of the antisolvent. From these results, the controlling factors of polymorphic crystallization were grouped and shown on the scheme. 1. Introduction Polymorphs and solvated crystals, which are pseudopolymorphs, frequently decide the functionality and properties (e.g., bioavailability, morphology and purity) of many kinds of materials.1-3 On account of this, the precise control of the crystallization of these polymorphous crystals, including solvated crystals, is important for obtaining highly functional crystals in industries. It is known that the crystallization of polymorphs is affected by, for example, additives,4,5 solvents,6,7 and interfaces.5,8 However, the mechanism of these effects is not known and the quantitative relationship between the operational factors and the crystallization characteristics of polymorphs is not clearly understood. The crystallization process of polymorphous crystals is composed of competitive nucleation, growth, and the transformation from a metastable to a stable form.3 To selectively crystallize polymorphs, the mechanism of each elementary step in the crystallization process needs to be clear in relation to the operational conditions and the key controlling factors.3 Practically speaking, the nucleation process is the most important for the control of the polymorphous crystallization. Recently, the molecular modeling approach for the prediction of polymorphic nucleation was reported, in which the dependence of interfacial energy on cluster size was calculated.9 On the other hand, the nucleation behavior of polymorphs seems to be related to molecular structure. Amino acids have a common structure including chiral carbon. We investigated the crystallization pro* Tel.: 0824-24-7715. Fax: 0824-24-5494. E-mail: mkitamu@ hiroshima-u.ac.jp.

cess of the polymorphs for L-glutamic acid (R and β; both are orthorhombic with a space group of P212121)10 and L-histidine (A; orthorhombic (P212121) and B; monoclinic (P21)),11 individually. In this paper, we have also examined the relationship between molecular structure and the effect of polymorphous seeds on the crystallization behavior of these polymorphs. In the pharmaceutical industry, antisolvents are often used in the crystallization process. When the antisolvent is continuously added to solutions, the solvent composition changes with time. Several other operational factors also influence the polymorphic crystallization behavior, and the interaction between these influences may be extremely complicated. In this paper, the dependence of the thermodynamic stability and transformation behavior of the thiazole-derivative polymorphs, 2-(3cyano-4-isobutyloxyphenyl)-4-methyl-5- thiazolecarboxylic acid (BPT)12 (an enzyme inhibitor) on the solvent composition, and the controlling factors in antisolvent crystallization were investigated. Finally, the controlling factors for polymorphic crystallization were grouped and discussed. 2. Experimental Procedures 2.1. Crystallization of Amino Acid Polymorphs. The heated solutions of L-glutamic acid and L-histidine at various concentrations (supersaturation) were rapidly cooled to a set temperature (the differential crystallization method).10,11 The effects of polymorphous seed crystals were examined in L-Glu and L-His systems by adding seed crystals of each polymorph (1-20 mg) to 50 mL of the solution just after the solution reached the set temperature. The crystals were sampled and the polymorphous composition was analyzed by X-ray diffraction measurement (Rigaku Corporation RINT 2200).

10.1021/cg0497795 CCC: $27.50 © 2004 American Chemical Society Published on Web 10/19/2004

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2.2. Thermal Analysis, Solubility Measurement, and Crystallization of BPT Polymorphs. BPT has three polymorphs (A, B, and C) and two solvated crystals (a hydrated crystal, BH and a methanolated crystal, D).12 The hydrated crystal BH loses water molecules in an atmosphere and transforms to the B form. TGA and DSC measurements (Seiko Instruments TG/DTA 220; DSC 220c) were carried out for the A, BH, C, and D forms at the increasing temperature rate of 5 K/min (temperature range between 303 and 573 K). The transformation process in solid state due to heat was examined. The solubility of the polymorphous BPT crystals was measured at 323 K by adding excess amounts of each polymorph to the water-methanol mixture solvents while stirring with a magnetic bar and the concentration change was measured by the UV spectroscopic method.12 The transformation behavior of the polymorphs was examined by analyzing the polymorphous composition of crystals by X-ray diffraction measurement (Rigaku Corporation RINT 2200) with elapsed time. In the X-ray diffraction measurement, the range of 2θ is between 5° and 35° and the step size is 1°/min. The methanol volume fraction VMeOH in the solution was changed from 0.5 to 0.9. The BPT (0.5-1 g) was dissolved at the crystallization temperature (323 K) in 40 mL of a methanol and water mixture with a methanol volume fraction of (VMeOH) of 0.95. The initial concentrations (C0) of BPT was 0.04-0.08 mol/L. Crystallization was carried out by adding water, which is an antisolvent, by a pump in the methanol solution at the crystallization temperature. In total, 14 mL of water was added to make the final methanol composition of the solution VMeOH 0.7. The addition rate of water (W) was changed from 0.2 to 2.0 mL/min. After all the water was added, the slurry was filtrated and the composition of the polymorphs was analyzed by XRD analysis.

Kitamura

Figure 1. Effects of the addition of polymorphous L-His seed crystals on polymorphic crystallization behavior.

3. Results and Discussion 3.1. Dependence of Molecular Structure on Nucleation of Amino Acid Polymorphs. From the solubility measurement (293-330 K), it appears that the stable phase is A for L-His and β for L-Glu.10,11 With differential crystallization, the influence of the supersaturation ratio on the polymorphous composition could not be observed at any temperature. Without stirring, the β forms tended to crystallize. This may due to the preferential two-dimensional nucleation of β on the airsolution interface and on the crystallizer wall. Crystallized R transforms to β with a solution-mediated mechanism. Concerning transformation process in stagnant solutions, the epitaxial growth of β on the surface of R crystals has been recently reported.14 In the case of L-His, the polymorphs crystallized with almost the same portion (fraction of A, XA ) 0.4-0.6) at each temperature, regardless of the supersaturation ratio (range for A from 1.34 to 1.90). These results mean that the “Ostwald’s step rule”13 is hardly observed in either the L-Glu and L-His systems under the usual crystallization conditions (at relatively high supersaturation). On the other hand, the temperature effects were different between the systems. In the case of L-Glu at lower temperatures (e.g., 293 K), only the R form crystallized, and as the temperature increased the portion of β in the crystals increased. However, almost no effect was observed in the L-His system. This difference may be attributed to the difference of the molecular structure of each amino acid and the difference of the crystal structure between the polymorphs for each amino acid. We presume that the temperature-dependent crystallization behavior of L-Glu polymorphs may be influenced by the change of relative concentration of

Figure 2. Scheme of the effects of polymorphous seeds on the crystallization of L-His polymorphs.

the conformers15 with temperature. L-His has a bulky imidazole group, the carbon number is smaller than L-Glu, and the conformational difference between the polymorphs is very small16 in comparison with that of L-Glu polymorphs. Accordingly, the activation energy (∆E) of the L-His conformer exchange may be very small; therefore, the concentration of each conformer corresponding to the A and B forms may be almost the same. This may result in the crystallization of A and B forms with the same probability. Between L-Glu and L-His, a difference in the seed effect was also observed. When the seed crystals of each polymorph were added to the solution, the seed effect appeared in the polymorphic crystallization of L-Glu. In the case of L-His, with the addition of each seed crystal (A or B) the induction time of the nucleation was clearly shortened. However, the polymorphic ratio in the crystallization was not affected at various supersaturations in respect to A crystals (C - C*(A)) (Figure 1). This may indicate that even if the conformer A or embryo A is borne from A seed, fast exchange between the conformers (A and B) or embryos (A and B) may occur, resulting in the nucleation of both A and B polymorphs with the same probability (Figure 2). 3.2. Thermodynamic Stability and Crystallization Behavior of Pharmaceutical Polymorphs (BPT). 3.2.1. Thermal Analysis and the SolidTransformation of BPT Polymorphs. Each polymorphous crystals of BPT can be distinguished by X-ray

Mechanism of Polymorphic Crystallization

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Figure 3. X-ray diffraction patterns of each polymorph of BPT.

Figure 4. (a) TGA curve of each polymorph (temperature increasing rate is 5 K/min). (b) DSC curve of each polymorph (temperature increasing rate is 5 K/min).

diffraction patterns as shown in Figure 3.12 The TGA measurement was performed for each polymorph and the results are shown in Figure 4a. It can be seen that for the A and C forms, almost the same behavior was observed in the weight loss. Around 480 K the weight decreased due to the decomposition of the crystals. In the case of the BH form, the weight decrease began at

about 325 K, and was observed to be 5.3%. This result means that the molar ratio of BPT and water is 1.0. In the previous paper,17 the molar ratio was estimated to be lower because of the rapid escape of water molecules from the crystals. On the other hand, the decrease of the weight began at about 368 K for the D form. This is due to the escape of methanol molecules, and the weight loss (9.2%) supports that the molar ratio of BPT and methanol is 1.0. In Figure 4b, the results of DSC measurement are shown. In the BH and D forms, endothermic peaks at about 328 and 370 K were observed. These peaks correspond to the weight loss in TGA curves, which are due to the escape of water and methanol molecules. The DSC curves are different between the C and A forms, the single endothermic peak of the A form is due to the melting of crystals. According to comparison between the DSC curves of the polymorphs, it is expected that the C form transforms to A form by a melt-mediated mechanism, i.e., the C form melts and the A form crystallizes in the melts. On account of this, the small exothermic peak due to the crystallization of the A form appears just after the endothermic peak due to the melting of the C form in the DSC chart. This means that the A form is the stable form at higher temperatures. It is believed that both the BH and D forms transform to the C form after the discharge of water and methanol molecules, and thereafter the C form transforms to the A form. 3.2.2. The Effects of Solvent Composition on Thermodynamic Stability and the SolutionMediated Transformation of BPT Polymorphs. The solubility of the polymorphous crystals was measured by adding excess amounts of each polymorph to the water-methanol mixture solvents and measuring the concentration at 323 K.12 The transformation behavior of the polymorphs was examined by analyzing the polymorphous composition of the crystals with elapsed time. The dependence of the solubility (C) on the solvent composition (VMeOH) at 323 K is shown in Figure 5. It can be basically seen that the C form is stable and the A form is metastable over the entire methanol composition range. The thermodynamic stability of the BH and D forms is intensively influenced by the solution composition. At high methanol composi-

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Figure 5. Dependence of the solubility (C) of the polymorphs on the methanol volume fraction (VMeOH) in water-methanol solvent at 323 K.

tions the hydrated BH crystal is the most unstable, and at low methanol compositions the most stable form is the BH crystal. Inversely, the stability of the D form is increased by increasing the methanol composition. It is believed that these behaviors are due to the dissociation equilibrium in eq 1, i.e., with an increase of the solvent molecules the dissociation of D should be suppressed, and the stability of the solvated crystal is increased (eq 1). Inversely, however, the stability of BH crystals decreases. The dissociation equilibrium of the BH and D forms can be written by eqs 1 and 2.

BPT‚H2O (BH) h BPT + H2O

(1)

BPT‚CH3OH (D) h BPT + CH3OH

(2)

The transformation behavior of each polymorph at 323 K is shown in Figure 6. At the methanol volume fraction (VMeOH) of 0.8, A, BH, and D forms transformed to the stable C form. However, sometimes the transformation to the C form proceeded through the formation of the D form. As the BPT molecule builds the framework of the solvated crystals, it is believed that the chemical potential (i.e., the solubility) of BPT in the solvated crystals indicates the thermodynamic stability of the crystals. The chemical potential of BPT in the hydrate (BH) and methanolate (D) crystals can be correlated with the solubility of the BPT (X) in the same manner with that for nonsolvated crystal, and can be written as eq 3.

µBPT(s) ) µBPT(l) ) µBPT(l)0 + RT ln a

(3)

where s and l indicate solid and liquid state, µ0 is a standard chemical potential in liquid state, and a is activity. Then, the driving force of the transformation from a metastable to the stable form is expressed by the

Figure 6. Transformation behavior at 323 K (ms: metastable form, s: stable form).

difference of the chemical potential, ∆µBPT(s) between each form.

ams ∆µBPT(s) ) RT ln as

(4)

where ams and as are the activity of a metastable and a stable forms (mole fraction), respectively. The activity ratio in eq 4 may be substituted by the solubility (X) ratio because the activity coefficient (γ) (a ) γX) is considered to be almost the same for the polymorphs in the same solutions,

Xms ∆µBPT(s) ) RT ln Xs

(5)

The (∆µBPT(s)) for the transformation from A to C and from D to C was estimated by eq 5 to be 360 and 290 J/mol at 0.8 of VMeOH and 323 K. On the other hand, the ∆µBPT(s) between the BH and C form is as large as 550 J/mol, i.e., the BH form is the most unstable. It is expected that the occurrence of the D form in the transformation form BH to C is due to the relatively large free energy difference. This phenomenon seems to follow the “Ostwald’s step rule”.13 Transformation occurs by the “solution-mediated” mechanism,12 i.e., in the transformation process the metastable form dissolves and the stable form nucleates and grows. Therefore, this result seems to indicate that with relatively large chemical potential differences, nucleation of the metastable form tends to occur. At the methanol fraction of 0.7, the A, BH, and D forms transformed to the stable C form. Only the BH form directly transformed to the C form. From the solubility measurements, it is believed that the D form became the most unstable with the decrease of methanol composition from 0.8 to 0.7 of VMeOH. At the methanol fraction (VMeOH) of 0.5, both A and D transformed to the BH form (Figure 6). It appears that the solubility of C is lower than BH, i.e., the C form is the most stable


Figure 7. Crystallization area of the polymorphs on map regarding the initial concentration (C0) and the addition rate of antisolvent (W).

form. This result indicates that the metastable A and D forms transform to another metastable form, BH. The chemical potential differences (∆µBPT(s)) between D and BH (530 J/mol), and A and BH (480 J/mol) are relatively large. On the other hand, the chemical potential difference (∆µBPT(s)) between the BH and C forms (34 J/mol) is very small. On account of this, for several weeks the transformation from BH to the most stable form, C, was not observed. These results may also indicate that the nucleation and the growth of the metastable form BH occurs in preference to that of the most stable form, C. It is believed that solute-solvent interaction plays an important role in the cluster formation or the nucleation of each polymorph. At the water-rich content as 0.5VMeOH the nucleation of the hydrated BH crystals may be preferable. When the methanol composition was increased to 0.95 VMeOH, every form of A, BH, and C became very unstable and transformed to the stable form, D very quickly. Consequently, the solubility of A, BH, and C could not be measured. 3.2.3. Crystallization Behavior of BPT Polymorphs at 323 K. Crystallization was carried out by adding water as an antisolvent at 323 K. It appears that the crystallized species of polymorphs are BH and D forms, with a few exceptions (A form). Both BH and D are metastable forms and their stabilities may be very close to each other, as shown in Figure 5. It was found that the crystallization behavior of the polymorphic crystals depended on the initial concentration of the solution (C0) and the water addition rate (W). The crystallization zone of polymorphs in respect to the initial concentration of the solution (C0) and the water addition rate (W) is shown in Figure 7. It appears that at the initial concentration of 0.040 mol/L, only the BH form crystallized, independently of the water addition rate (W ) 0.2-2.0 mL/min). At 0.055 mol/L, the BH form also crystallized with small quantities of the D form. At higher initial concentrations (0.079 mol/L) both the BH and the D forms crystallized. At a lower addition rate, the pure D form crystallized, and at a higher addition rate pure BH formed. The A form was also observed in the crystals, more commonly at lower


Figure 8. SEM photographs of crystals SEM photographs of crystals obtained at 323 K. (a) BH crystals obtained at 0.040 mol/L (W ) 1.4 mL/min). (b) D crystals obtained at 0.079 mol/L (W ) 0.3 mL/min). (c) A crystals obtained by the transformation from BH (C0 ) 0.040 mol/L, W ) 0.28 mL/min). (d) C crystals obtained by the transformation from D crystals (C0 ) 0.079 mol/L, W ) 0.28 mL/min).

addition rates. The crystallization area of pure BH is shown in Figure 7. In the other area, three cases occurred: (1) the pure D form; (2) a mixture of the BH and D forms; (3) a mixture of the D, BH, and A forms. The typical morphology of the polymorphous crystals observed by SEM is shown in Figure 8. The BH crystals obtained in crystallization exhibited a fiber bundle type morphology (Figure 8a). The D form (Figure 8b) exhibited a needlelike morphology and was much larger than the BH crystals. From these results, it appears that the crystallization trend of the D form is opposite that of the BH form, and the crystallization of D is accelerated with increase of the initial concentration (C0) and the decrease of the addition rate (W) in comparison to the BH form. The equilibrium constant, K, for each solvated crystals can be written by eqs 6 and 7.

KBH ) KD )

[BPT]e[H2O]e [BPT‚H2O(BH)]

[BPT]e[CH3OH]e [BPT‚CH3OH(D)]

(6)

(7)

where e indicates the equilibrium state. Therefore, the supersaturation ratio (S) is shown by eqs 8 and 9.

SD )

[BPT][CH3OH] KD[BPT‚CH3OH(D)]

SBH )

[BPT][H2O] KBH[BPT‚H2O(BH)]

(8)

(9)

The decrease of the initial concentration means the decrease of the supersaturation ratio for both crystals of the BH (SBH) and D forms (SD). On the other hand,

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Figure 10. Dependence of transformation behavior from BH to A form on W (C0 ) 0.055 mol/L). Figure 9. Dependence of transformation behavior from BH to A form on W (C0 ) 0.040 mol/L).

the increase of the addition rate may indicate an increase of the local supersaturation around the droplet of water. This fact seems to indicate the contradictory tendency. Such contradiction may indicate that the local solution composition is the influential factor on the nucleation behavior of these polymorphous crystals. When the water droplets fall into the solution, the water molecules diffuse into the bulk solution and BPT and methanol molecules diffuse adversely from the bulk solution. The solubility of BPT is locally decreased (local supersaturation is produced), and the crystals nucleate and grow in the nucleation zone around the water droplet. It is believed that with the increase of the addition rate the water composition in the nucleation zone increases, resulting in the preferential crystallization of the hydrate crystals of BH. On the other hand, with the increase of the initial concentration (C0 ) 0.055 and 0.079 mol/L) the D form tended to crystallize. With an increase of the initial concentration, the water composition in the nucleation zone or the molar ratio of water molecules to BPT decreased. This may also hinder the hydration of BPT, and the crystallization of BH may be decreased, resulting in the crystallization of D. 3.2.4. Transformation Behavior after the Crystallization at 323 K. As shown previously, at the initial concentration of 0.040 mol/L, only the BH form crystallized. It was found that the crystallized BH form transformed to the A form after the end of water addition by a solution-mediated mechanism. On the other hand, it appears that the transformation rate of the BH form changes with the crystallization conditions. In Figure 9, the relationship between the molar fraction of the A form (XA/BH) of crystals in solutions and crystallization time at 0.040 mol/L (Figure 7) is shown. At a high addition rate (1.42 mL/min), no transformation was observed for BH within 300 min. With the decrease of the addition rate, at the ending point of the addition of water, only the BH form existed (XA/BH ) 0), but the fraction of the A form increased with time.

The transformation rate clearly increased with the decrease of the addition rate. We suppose that a very slight amount of the A form is present in BH crystals, even if no peak of the A form is observed in XRD measurement. The amounts of the A form should change with the initial concentrations (C0) and the addition rate (W). The A form included in BH crystals may act as the seed crystals and accelerate the transformation, i.e., the transformation rate decreases with the addition rate. At 0.055 mol/L (C0) the BH and D forms crystallized and both forms transformed to the A form. It appears that the transformation from the BH to the A form increases with the decreasing of the addition rate (Figure 10). Furthermore, the transformation rate of the D form to the A from is faster than that from the BH form to the A form at the same addition rate. This may be mainly due to the difference between driving forces of the transformation, i.e., the solubility difference between the D and the A form is larger than that between the BH and the A form. At 0.079 mol/L the crystallized BH did not transform, but it appears that the crystallized D form transformed to the BH form. This result indicates that the transformation behavior at 0.079 mol/L is different from that at 0.055 mol/L (the D form transformed to the A form). It is believed that with the increase of the initial concentration, the nucleation of A may become more difficult and BH may tend to nucleate. Furthermore, the transformation rate from the D to the BH form decreased with the decrease of the addition rate. At very slow water-addition rates (0.28 mL/min; 0.079 mol/L) the transformation of D to A or C was also sometimes observed. The transformation to A may be related to the crystallization of the mixture of the BH, D, and A forms. Figure 8c depicts the morphology of the A form, which was obtained through the transformation from the BH form at 323 K. The A form possessed a very fine needlelike morphology. The C form (Figure 8d), obtained by transformation from the D form at 323 K, also had a fine needlelike morphology, similar to that of the A form. These results indicate that the transformation


Figure 11. Controlling factors for polymorphic crystallization.

behavior strikingly depends on the operational conditions. 3.3. Scheme of Controlling Factors in Polymorphic Crystallization. From the results obtained in our works,10-12,17,18 we grouped the controlling factors for polymorphic crystallization into some groups and a scheme is shown in Figure 11. It should be noticed that the relative importance of each controlling factor depends on systems and crystallization methods. We denoted the basic important factors in the operation of the polymorphic crystallizations as the primary factor group. Supersaturation and temperature are representative in the primary factor (Figure 11). The effects of polymorphous seeds, the stirring rate, the addition rate of antisolvent, and the mixing rate of reactant solutions18 are included in the primary factor group. The factors due to the external substances such as solvents, additives, and interfaces are grouped in the secondary factor group. This factor group includes the interaction with the solute. The host and guest compositions in the case of clathrate compounds are also implied in the secondary factor group. The solubility of each polymorph is not the operational factor, but it is a very important physical property because the relative thermodynamic stability and the direction of the transformation between the polymorphs can be determined by the solubility of polymorphs. Furthermore, the supersaturation of each polymorph is based on the solubility. It should be noted that the primary and secondary factor groups imply both the equilibrium effect and the kinetic effect. For example, temperature may contribute to the equilibrium effect as mentioned above, and the supersaturation may contribute to the kinetic effect. 4. Conclusions 1. The effects of temperature and polymorphous seeds on the crystallization behavior of polymorphs were


observed in the case of L-glutamic acid, whereas no effect appeared in the crystallization of L-histidine polymorphs. The difference may be due to the conformational difference between the polymorphs and/or the exchange rate between the conformers (or embryos) corresponding to each polymorph. 2. The thermodynamic stability of each polymorphs changes with methanol composition, and the transformation behavior is also affected by the methanol composition. The transformation behavior was explained by the chemical potential difference between the stable and metastable form and the preferable nucleation and growth of the stable form due to the specific solute-solvent interaction. 3. The crystallization zone of the polymorphs by the antisolvent method was shown with respect to the controlling factors of the initial concentration and the water addition rate. The mechanism of the increase in the portion of the BH form with an increasing rate of water addition was shown. 4. Transformation behavior after the crystallization was found to depend on the initial concentration of BPT and the addition rate of the antisolvent. 5. The controlling factors of polymorphic crystallization were grouped as primary factor, secondary factor, and solubility. References (1) Rollinger, J. M; Gstrein, E. M.; Burger, A. Eur. J. Pharm. Biopharm. 2002, 53, 75. (2) Murphy, D.; Rodriguez-Cintron, F.; Langevin, B.; Kelly, R. C.; Rodriguz-Hornedo, N. Int. J. Pharm. 2002, 246, 121. (3) Kitamura, M. Crystal Growth Handbook; Japanese Association for Crystal Growth: Kyoritsu-Shuppan, 1995; p 545. (4) Kitamura, M.; Ishizu, T. J. Cryst. Growth 1998, 192, 225. (5) Addadi, L.; Berkovitch-Yellin, Z.; Weissbuch, I.; Mil, J. V.; Shimon, L. J. W.; Lahav, M.; Leiserowitz, L. Angew. Chem. Int. Ed. Engl. 1985, 24, 466. (6) Threlfall, T. Org. Proc. Res. Dev. 2000, 4, 384. (7) Kitamura, M.; Furukawa, H. J. Cryst. Growth 1994, 141, 193-199. (8) Chen, B. D.; et al. J. Am. Chem. Soc. 1998, 120, 1625. (9) Horst, J. H.; Kramer, H. J. M.; Jansens, P. J. Cryst. Growth Des. 2002, 2, 351. (10) Kitamura, M. J. Cryst. Growth 1989, 96, 541. (11) Kitamura, M. J. Chem. Eng. Jpn. 1993, 26, 303. (12) Kitamura, M.; Nakamura, K. J.Cryst. Growth 2002, 236, 676. (13) Ostwald, W. Z. Phys. Chem. 1897, 22, 289. (14) Ferrari E. S.; Davey R. J. Cryst. Growth Des. 2004. (15) Ham, N. S. Molecular and Quantum Pharmacology; Reidel: Dordericht, 1974. (16) Maddin, J. J.; McGandy, E. L.; Seeman, N. C.; Harding, M. M.; Hoy, A. Acta Crystallogr. 1972, B28, 2377. (17) Kitamura, M.; Sugimoto, M. J. Cryst. Growth 2003, 257, 177. (18) Kitamura, M.; Konnno, H.; Yasui A.; Masuoka, H. J. Cryst. Growth 2002, 236, 323.

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