Concomitant Crystallization of Glycine on ... - ACS Publications

Jan 2, 2008 - In Sung Lee, Ki Tae Kim, Alfred Y. Lee,† and Allan S. Myerson*. Department of Chemical and Biological Engineering, Illinois Institute ...
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Part of the Special Issue: Facets of Polymorphism in Crystals

Concomitant Crystallization of Glycine on Patterned Substrates: The Effect of pH on the Polymorphic Outcome

CRYSTAL GROWTH & DESIGN 2008 VOL. 8, NO. 1 108–113

In Sung Lee, Ki Tae Kim, Alfred Y. Lee,† and Allan S. Myerson* Department of Chemical and Biological Engineering, Illinois Institute of Technology, Chicago, Illinois 60616 ReceiVed September 15, 2007; ReVised Manuscript ReceiVed December 2, 2007

ABSTRACT: This study demonstrates the effect of the solution pH on the polymorphic outcome of glycine by evaporation-driven crystallization from aqueous solution. More than 2000 solution droplets under identical conditions were generated using a patterned self-assembled monolayers (SAMs) substrate. Each droplet on the substrate serves as an independent crystallization trial. Glycine nucleated inside the droplets through solvent evaporation, and their polymorphic forms were identified via Raman microscopy. Three different polymorphic forms of glycine (R-, β-, and γ-forms) simultaneously crystallized at all conditions employed. The probability of producing the thermodynamically stable γ-glycine from acidic (pH 3.40) or basic solution (pH 10.10) droplets significantly increased when compared with neutral aqueous solution (pH ∼ 6.00) droplets. Introduction The phenomenon of a chemical species having more than one possible crystal form is known as polymorphism.1 The ability of a molecule to exist in more than one solid-state structure is a result of differences in the molecular packing arrangement and/or molecular conformation.2,3 Polymorphism is one of the important challenges in pharmaceutical engineering because different solid forms lead to different physical properties such as solubility, dissolution rate, density, heat capacity, melting point, thermal conductivity, optical activity, and particle morphology, which can affect the process acceptability and bioavailability of drug substances.4 Consequently, the control of polymorphism is indispensable for producing high-quality pharmaceutical products.5 One such molecule that exhibits multiple crystal forms is glycine, the simplest amino acid. This pharmaceutical excipient has been studied extensively in many aspects of crystallization including nucleation mechanism6–10 and polymorphic behavior.11–19 Six distinct polymorphic forms of glycine are known in the literature: R,-20 β-,21 and γ-forms22 at ambient environment, and δ-, ε-,23 and β′-forms,24 under high pressure. The R-form is built from centrosymmetric zwitterionic dimers,20 while the β- and γ-forms in non-centrosymmetric structure.11 At room temperature, γ-glycine is the thermodynamically most stable form.25 However, in neutral aqueous solution of pH ca. 6.20, the kinetic R-form is normally obtained.20 Typically, the γ-form is produced from acidic and basic solutions.22,25 β-Glycine is the least stable form compared to R- and γ-forms. It can be obtained from an ethanol–water mixture and readily converts to the R-modification in the presence of water or upon heating.11 It has been a conundrum that the metastable R-form of glycine is usually produced from aqueous solution in the pH range between 3.8 and 8.9, and the thermodynamically most stable γ-form is generated from acidic and basic solutions.12 Towler * To whom correspondence should be addressed. E-mail: [email protected]. † Present address: Strategic Technologies, Chemical Development, GlaxoSmithKline PLC, P.O. Box 1539, King of Prussia, PA 19406, USA.

et al.12 suggested that charged glycine species, protonated (+H3NCH2CO2H) at low pH (less than 3.8) and deprotonated (H2NCH2CO2-) at high pH (greater than 8.9), inhibit the growth of R-glycine, enabling the crystallization of the γ-form. Consequently, controlling the precise pH domain (less than 3.8 and greater than 8.9) favored the formation of γ-glycine. However, it was demonstrated that γ-glycine can be crystallized in neutral aqueous solutions with additives13,14 or by irradiation of intense polarized laser light,6–7 DC electric field,9 slow evaporation of solvent using an evaporation-based crystallization platform,17 in a microporous membrane,18 and by thin film evaporation of solution on the walls of a glass container.19 Recently, our group has engineered patterned substrates of self-assembled monolayers (SAMs) which consist of hydrophilic gold islands surrounded by a hydrophobic domain.15,16,26 Arrays of small solution droplets on the nano- and picoliter scale are generated using patterned substrates of SAMs. Crystals are formed within each droplet through solvent evaporation. With this approach, we have demonstrated the concomitant nucleation of multiple polymorphic forms under the same conditions with glycine,15,16 mefenamic acid,26 and sulfathiazole.26 Furthermore, it was observed that the polymorph distribution of crystals produced on the gold islands was strongly dependent on the feature size of the islands and the solution concentration.15 This fact indicates that several polymorphic forms competitively nucleate, and the likelihood of their appearance is strongly affected by the rate of solvent evaporation.15,16,26 In this paper, crystallization experiments were conducted using patterned substrates of SAMs with aqueous glycine solutions at three different pHs and concentrations. Solution droplets were created on the patterned surface, and each droplet served as an independent crystallization trial. More than 2000 islands per substrate were analyzed to achieve the statistical accuracy of the polymorph distribution of crystals formed on the substrate due to the stochastic nature of polymorphism from solution crystallization. The aim of this work is to investigate

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Concomitant Glycine Crystallization

Crystal Growth & Design, Vol. 8, No. 1, 2008 109

Figure 1. (a) A patterned substrate having more than 2000 square gold islands with a dimension of 500 µm and (b) crystals of glycine produced on 500 µm islands.

the concomitant crystallization of glycine and the role of pH on the probability for forming each polymorphic modification. Experimental Methods Gold Islands and Self-Assembled Monolayers (SAMs) Preparation. The patterned substrates were prepared in the same way as described previously.15,16,26 Metallic gold islands were formed by allowing titanium to evaporate through a brass mesh onto a glass substrate by using an electron beam evaporator. Gold was deposited on top of the titanium using the same evaporation method. The dimensions and pattern of the islands are dependent upon the size and shape of the holes on the mesh. Typically, square-shaped islands in a variety of sizes have been prepared. 4-Mercaptobenzoic acid (4-MBA) was used as the thiol monolayer and was self-assembled onto the gold surface while octadecyltrichlorosilane (OTS) was applied to the exposed glass surface. The metallic gold island substrates were immersed in a 4-MBA solution (10 mM) in ethanol overnight, which was followed by immersing them in a toluene solution containing OTS (2 mM) for 1 h. Through the above processes, patterned substrates having a bifunctional surface were generated. Solution Preparation, Crystallization and Characterization. Glycine from Fisher Scientific was used without further purification. Hydrochloric acid (6 N), HCl, and sodium hydroxide, NaOH, pellets were purchased from LabChem Inc. and Sigma-Aldrich, respectively. Neutral aqueous glycine solutions (pH ∼ 6.0) of three different concentrations were prepared by dissolving a fixed amount of glycine in deionized (DI) water. The pH of the solution was measured using an Accumet AP63 portable ISE/pH/mV meter from Fisher Scientific equipped with an Accumet glass calomel pH electrode. The measured pH values of the solutions were in the range of 5.90–6.20, close to the isoelectric point of glycine of 5.97.11 Acidic and basic glycine solutions of three different concentrations were prepared by dissolving fixed amount of glycine in DI water, followed by adjusting the pH of solutions to 3.40 and 10.10 by adding appropriate amounts of hydrochloric acid and sodium hydroxide, respectively. Arrays of small solution droplets were created using patterned SAMs by immersing and withdrawing the substrates from the solution. Each substrate had at least 2000 gold islands on the surface. The evaporation of solvent from droplets was conducted under ambient conditions (∼23 °C and 35% RH). Glycine crystallized and was attached to the gold islands (Figure 1). Raman spectra of glycine on the gold islands were obtained using a Raman Microprobe from Kaiser Optical System, Inc., equipped with a 450 mW external cavity stabilized diode laser as the excitation source, operating at 785 nm. The Raman spectra of glycine were different for

each solid-state form.16 In particular, the wavenumbers of several Raman peaks of glycine in the range of 1320-1460 cm-1 and 2950-3010 cm-1 were selected to differentiate each polymorphic form of glycine on the patterned substrate (Figure 2).16

Results and Discussion Table 1 summarizes the polymorph distribution of glycine crystals formed on the patterned substrate with respect to the solution concentration and pH. A minimum of 2000 islands were examined for each condition. For neutral aqueous glycine solution in the pH range of 5.90–6.20, glycine nucleated on several islands instantaneously, and crystals were observed on all the islands after 5-10 min. The kinetic form, R-glycine, was the predominantly observed form at all concentrations as expected with some appearance of the unstable β-form. The frequency of β-glycine crystals increased with diminishing concentration, consistent with previous results with smaller sampling size.15,16 A small percentage of the thermodynamically stable form, γ-glycine, was also observed at all concentrations indicating that the γ-form also nucleates but at a rate considerably less than that of the R-form. During crystallization of glycine from an acidic solution with pH of 3.40, the time for crystallization increased compared with the neutral solution. It took roughly 8-25 min for crystals to be observed on the entire substrate (Figure 3). The R-form of glycine was preferentially produced at the higher concentration of 3.20 M, but the percentage of the γ-form significantly increased to 26.2% from 4.9%, when compared to identical conditions in neutral solutions. As the concentration of the glycine solution decreased from 3.20 to 1.60 M, the percentage of the γ-form increased from 26.2% to 63.3%.The percentages of the β-form produced with acidic solutions were generally similar to those obtained with neutral solutions. With basic solutions (pH 10.10), solution droplets resided for a longer time on the gold islands. Crystals started to appear in the droplets on the gold islands after 30 min (Figure 3). With increasing concentration of 1.60, 2.40, and 3.20 M, the times it took for particles to appear on the entire patterned substrate were 100, 220, and 480 min, respectively. In each concentration level, R-glycine was the main solid-state form produced on the

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Figure 2. Raman spectra of the three different polymorphic forms of glycine. Table 1. Polymorph Distribution of Glycine for Different pHs and Solution Concentrations pH 3.40 5.90–6.20 10.10

a

concentration (M)

size of island (µm)

total samples

crystallization time (min)a

R-form (%)

β-form (%)

γ-form (%)

1.60 2.40 3.20 1.60 2.40 3.20 1.60 2.40 3.20

500 500 500 500 500 500 500 500 500

2000 2000 2000 2000 2000 3000 2000 2000 2000

8 not measured 25 5 5 10 100 220 450

36.3 54.1 66.0 90.3 88.3 92.2 58.2 68.2 83.8

0.4 10.4 7.8 7.3 5.8 2.9 6.4 10.3 4.9

63.3 35.5 26.2 2.4 5.9 4.9 35.4 21.5 11.3

The crystallization time corresponds to the time when crystals are observed on 99% islands of the patterned substrate.

islands, but the percentage of the γ-form significantly increased compared with the results produced with the neutral aqueous solution of glycine. Similar to the acidic conditions, as the concentration of glycine in solution decreased, γ-form crystals were observed more frequently on the patterned gold islands. In this work, we denote Pi as the probability of yielding an i form crystal on the surface of a gold island. With the assumption that each island is an independent trial of crystallization and that Pi is constant for a given set of conditions, Pi can be expected to be estimated from the experimental data acquired using a large number of samples generated from the patterned SAMs, through the formula for the binomial probability given as27 P (T, Si, k) )

T! (k)Si(1 - k)T-Si (T - Si) ! · (Si)!

P (T, Si, Pi ) k) shows the probability of obtaining the experimental polymorph outcome with the assumption that the unknown parameter, Pi, is equal to k. T is the total number of the islands used for the experiment, and Si is the number of islands among the total samples that produce the i form. For instance, we obtained the R-form on 2766 islands out of 3000 at the concentration of 3.20 M and pH of ∼6.00 (Table 1). With the hypothesis that the probability of producing an R-form

crystal on a island (PR) is 92%, the probability of obtaining this is 2.7%; P (T ) 3000, SR ) 2766, PR ) 92%) ) 2.7%. Furthermore, the PR is estimated to exist in the range between 90.9% and 93.5% with a 99% confidence level.27 Hence, it is a rare event that PR exists in the range of less than 90.9% or greater than 93.5%. As the sample size increases, the confidence interval for PR decreases. Therefore, large sample sizes allow a more precise estimate of the unknown parameter Pi (i ) R, β, or γ) and a higher probability for detection of a polymorphic form having small Pi. Figure 4 presents the probability {P (T, Si, Pi ) k)} of i ) R, β, and γ-glycine in terms of different pH values of solution with the hypothesis that the unknown parameter, Pi, is equal to k. As illustrated in Figure 4a, at the solution concentration of 3.20 M, PR for the low and high pH is less relative to PR in the neutral solution. Conversely, Pγ is less in the neutral glycine solution but higher under the acidic and basic conditions. Figure 4b shows that Pγ in acidic and basic solutions increases with diminishing concentrations, suggesting that the nucleation of the γ-form depends on the solution concentrations at these conditions. Large-sample hypothesis tests for the null hypothesis H0: Pi (acidic or basic solution) ) Pi (neutral solution), i ) R, β, or γ-glycine, were also conducted to determine if there is a

Concomitant Glycine Crystallization

Crystal Growth & Design, Vol. 8, No. 1, 2008 111

Figure 3. Crystallization in the solution droplets generated on the islands at a concentration of 3.20 M for solutions of three different pH values. (The dimension of each square island is 500 µm.)

Figure 4. (a) Probability of PR, Pγ, and Pβ for different pHs at a concentration of 3.20 M. (b) Probability of Pγ for different concentrations at pH 3.40 and 10.10.

statistically significant difference in the proportion of polymorphic forms produced on the islands under acidic or basic conditions relative to neutral pHs. On the basis of the normal distribution approximation to binominal distribution, the statistics are obtained by the following27 Z)

Pˆ1 )

Pˆ1 - Pˆ2



^

^

(

p(1 - p)

1 1 + T1 T2

)

S1 S2 S1 + S2 ^ , Pˆ2 ) , and p ) T1 T2 T1 + T2

where S1 and S2, and T1 and T2 are the number of islands that produced R-, β-, or γ-glycine, and total islands investigated in experiments 1 (acidic or basic solution) and 2 (neutral solution), respectively. With Z calculated and Φ(|Z|) obtained from ref 27, the P value can be acquired by using: P value ) 2[1 - Φ(|Z|)] The results of the hypothesis tests are summarized in Table 2. For all polymorphic forms and concentrations other than Pβ at the concentration of 1.60 M, the null hypotheses; H0: Pi (acidic or basic solution) ) Pi (neutral solution), i ) R, β, or γ, are rejected with P values of 0.000. These test results indicate that the relative possibility of forming polymorphic forms of glycine,

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Table 2. Hypothesis Tests for the Different Solid Forms Nucleated on the Patterned Islands under Acidic or Basic Conditions, Relative to the Neutral Solutions P value concentration (M) 1.60

null hypothesis (H0) Pi Pi Pi Pi Pi Pi

2.40 3.20

(pH (pH (pH (pH (pH (pH

3.40) ) Pi (pH ∼ 6.00) 10.10) ) Pi (pH ∼ 6.00) 3.40) ) Pi (pH ∼ 6.00) 10.10) ) Pi (pH ∼ 6.00) 3.40) ) Pi (pH ∼ 6.00) 10.10) ) Pi (pH ∼ 6.00)

i ) R-form

i ) β-form

i ) γ-form

0.000 0.000 0.000 0.000 0.000 0.000

0.000 0.256 0.000 0.000 0.000 0.000

0.000 0.000 0.000 0.000 0.000 0.000

Table 3. The Polymorph Outcome of Glycine for Different pHs and Island Sizes concentration (M)

size of island (µm)

total samples

crystallization time (min)a

R-form (%)

β-form (%)

γ-form (%)

3.40

3.20

5.90–6.20

3.20

10.10

3.20

250 500 250 500 250 500

3000 2000 3000 3000 2000 2000

10 25 5 10 60 450

11.6 66.0 94.5 92.2 52.4 83.8

14.1 7.8 5.4 2.9 17.1 4.9

73.3 26.2 0.1 4.9 30.5 11.3

pH

a

The crystallization time corresponds to the time when crystals are observed on 99% islands on the substrate.

Pi (i ) R, β, or γ), at the pH of 3.40 and 10.10 is significantly different with respect to Pi (i ) R, β, or γ) for the neutral solutions. Three different polymorphs of glycine: R-, β-, and γ-form were concomitantly produced on the 500 µm islands due to the similarity in the crystal energy of the three forms.16 For neutral solutions, the R-form is preferred at all concentrations investigated, but its frequency significantly decreases at pH values of 3.40 and 10.10. Consequently, the percentage of γ-glycine increases in the acidic and basic solutions without any large difference in the polymorph distribution of the β-form. Towler et al.12 suggested that in glycine solutions of high and low pH values (less than 3.8 or greater than 8.9) charged glycine species may inhibit the growth of R-glycine, thus producing the kinetically less favorable γ-form of glycine of which the growth is not disturbed by charged species. However, using patterned substrates of SAMs, it was observed that R-, β-, and γ-forms of glycine were still concomitantly produced from acidic and basic solutions, although only γ-glycine was consistently obtained in experiments using bulk solution. It is believed that the effect of the charged species reduces the possibility of the formation of R-glycine but does not inhibit it entirely. The probability of γ-glycine formation of ∼5% in a neutral solution may not be enough for γ-glycine to survive against the competitive growth of crystals of other forms in a bulk system, even though γ-glycine is the most stable form. However, the decreased frequency of R-form formation may result in the growth of γ-glycine at the expense of R-glycine in a bulk solution in which the growth of crystals nucleated is influenced by each other. He et al.17 have shown that the γ-form of glycine can be preferably produced even from neutral aqueous glycine solution by slow evaporation-driven crystallization. For acidic and basic solution, the evaporation rate of the solvent from droplets is lower than that for neutral solution of glycine (pH ∼ 6.00) due to the reduction in the vapor pressure of solvent containing HCl and NaOH.28 However, the increased frequency of γ-glycine produced on the patterned SAMs at high and low pH is not likely to be the result of the slow evaporation of solvent because the time of observing crystals in all droplets on a patterned substrate during evaporation decreased with decreasing initial concentration of solution, but the percentage of the γ-form inversely increased. Additionally, the evaporation rate of solvent is higher from the smaller droplets due to the higher vapor

pressure of a smaller droplet.29 Consequently, as shown in previous reports,15,16,26 metastable forms were consistently more frequently observed with smaller islands. However, using acidic and basic glycine solutions, the frequency of the thermodynamically most stable γ-glycine increases with decreasing island size (Table 3). Therefore, it is apparent that the slow evaporation effect is not the critical factor in the increased percentages of γ-glycine from acidic and basic solutions but rather it is the charged species inhibiting the growth of the R-form. Our investigation using 20 mL glycine solutions shows that the pH of solution decreases for acidic solutions and increases for basic solutions during evaporation of the solvent. This fact is attributed to the increasing concentration of HCl and NaOH, due to the lower vapor pressures of HCl and NaOH compared to that of water. In addition, the pH of solution is further decreased for acidic solutions and increased for basic solutions through crystal growth following nucleation. This is in accordance with the pH shift toward the isoelectric point of glycine of 5.9711 after the dissolution of more glycine in the solution. It is reasonable to assume that the pH change in small acidic or basic solution droplets generated on the patterned substrate of SAMs shows the same trend. Accordingly, the pH at the time of crystallization may be different for different initial concentrations and initial volumes of the solutions. Because of the gradual pH change during the evaporation of solvent from acidic and basic solutions, with low initial concentration of acidic or basic solutions, crystallization occurs at a much lower pH than the initial pH of 3.40 or much higher pH than 10.10, compared with highly concentrated solution. In addition, it was reported by He et al.30 that nucleation occurs at high supersaturation with fast evaporation of solvent. Therefore, the correlation between the pH and the solution concentration through evaporation of solvent indicates that the pH of solution at the time of crystallization may be lower for acidic solutions and higher for basic solutions with fast evaporation of solvent than that with slow evaporation of solvent. The pH change of solution from 3.40 to 3.30 and 3.20 or from 10.10 to 10.20 and 10.30 leads to an increase in the fraction of charged species from 8.7% to 11.0% and 13.8% and from 67.6% to 72.5% and 76.8%, respectively (from pK values of 2.35 for carboxylic acid and 9.78 for amine12). Consequently, it can be suggested that the increased frequency of γ-glycine is due to the increased proportion of charged species at the time of crystallization.

Concomitant Glycine Crystallization

It is worth noting that the 4-MBA assembled on gold islands could be deprotonated on contact with a basic solution due to the carboxyl functional group (-COOH) with a pKa value of 4.79.31 Allen et al.32 had supposed that the clusters of γ-glycine built in the more polarized structure than those of R- and β-glycine can be bound and stabilized for growing to the mature crystal on the charged surface such as an AOT (sodium bis-2ethyl sulfosuccinate) monolayer. Therefore, it cannot be ruled out that the templating effect of the deprotonated 4-MBA monolayer also influences the polymorph outcome of glycine produced on the surface of islands, when basic glycine solution is used. However, the dependence of the polymorph distribution of glycine on the concentration of solution indicates that this templating effect may not be the main cause of increased frequency of obtaining γ-glycine on the islands from a basic solution. Conclusion Three different polymorphic forms of glycine are concomitantly generated on the islands of the patterned SAMs substrate, which indicates that each polymorphic form competitively nucleates in the solution. The probability that each form of glycine can crystallize from the small solution droplet through solution evaporation is significantly dependent on the pH of the solution. At solution pHs less than 3.40 and greater than 10.10, charged glycine species does not appear to entirely inhibit the growth of kinetically favored R-glycine, but reduce the possibility of producing R-form, which increases the chance of forming γ-glycine in the solution. The patterned substrate allows us to conduct a number of crystallization experiments simultaneously, and as a result, it is a useful approach to examine concomitant crystallization and factors that can impact the polymorphic outcome. Acknowledgment. Financial support from the U.S. Army Medical Research and Material Command (W81XWH0410864) is gratefully acknowledged.

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Crystal Growth & Design, Vol. 8, No. 1, 2008 113 (4) Carstensen, J. T. Pharmaceutics of Solids and Solid Dosage Forms; John Wiley & Sons: New York, 1977. (5) Singhal, D.; Curatolo, W. AdV. Drug DeliVery ReV. 2004, 56, 335. (6) Zaccaro, J.; Matic, J.; Myerson, A. S.; Garetz, B. A. Cryst. Growth Des. 2001, 1, 5. (7) Garetz, B. A.; Matic, J.; Myerson, A. S. Phys. ReV. Let. 2002, 89, 175501. (8) Erdemir, D.; Chattopadhyay, S.; Guo, L.; Ilavsky, J.; Amenitsch, H.; Segre, C. U.; Myerson, A. S. Phys. ReV. Lett. 2007, 99, 115702–1. (9) Aber, J. E.; Arnold, S.; Garetz, B. A.; Myerson, A. S. Phys. ReV. Lett. 2005, 94, 145503. (10) Chattopadhyay, S.; Erdemir, D.; Evans, J. M. B.; Ilavsky, J.; Amenitsch, H.; Segre, C. U.; Myerson, A. S. Cryst. Growth Des. 2005, 5, 523. (11) Ferrari, E. S.; Davey, R. J.; Cross, W. I.; Gillon, A. L.; Towler, C. S. Cryst. Growth Des. 2003, 3, 53. (12) Towler, C. S.; Davey, R.; Lancaster, R. W.; Price, C. J. J. Am. Chem. Soc. 2004, 126, 13347. (13) Weissbuch, I.; Zbaida, D.; Addadi, L.; Leiserowitz, L.; Lahav, M. J. Am. Chem. Soc. 1987, 109, 1869. (14) Weissbuch, I.; Torbeev, V. Yu.; Leiserowitz, L.; Lahav, M. Angew. Chem., Int. Ed. 2005, 44, 3226. (15) Lee, A. Y.; Lee, I. S.; Dette, S. S.; Boerner, J.; Myerson, A. S. J. Am. Chem. Soc. 2005, 127, 14982. (16) Lee, A. Y.; Lee, I. S.; Myerson, A. S. Chem. Eng. Technol. 2006, 29, 281. (17) He, G.; Bhamidi, V.; Tan, R. B. H.; Kenis, P. J. A.; Zukoski, C. F. Cryst. Growth Des. 2006, 6, 1746. (18) Profio, G. D.; Tucci, S.; Curcio, E.; Drioli, E. Cryst. Growh Des. 2007, 7, 526. (19) Xu, M.; Harris, K. D. M. J. Phys. Chem. B 2007, 111, 8705. (20) Marsh, R. E. Acta Crystallogr. 1958, 11, 654. (21) Fischer, E. Ber. Dtsch. Chem. Ges. 1905, 38, 2917. (22) Iitaka, Y. Proc. Jpn. Acad. 1954, 30, 109. (23) Dawson, A.; Allan, D. R.; Belmonte, S. A.; Clark, S. J.; David, W. I. F.; McGregor, P. A.; Parsons, S.; Pulham, C. R.; Sawyer, L. Cryst. Growth Des. 2005, 5, 1415. (24) Boldyreva, E. Cryst. Growth Des. 2007, 7, 1662. (25) Iitaka, Y. Acta Crystallogr. 1961, 14, 1. (26) Lee, I. S.; Lee, A. Y.; Myerson, A. S. Pharm. Sci. Res. 2008, accepted for publication, DOI: 10.1007/s11095-007-9424-z. (27) Montogomery D. C.; Runger G. C. Applied Statistics and Probability for Engineers, 3rd ed.; John Wiley & Sons: 2002. (28) Perry, R. H.; Green, D. W. Perry’s Chemical Engineers’ Handbook, 7th ed; McGraw-Hill: London, UK, 1997. (29) Kuz, V. A. Langmuir 1993, 9, 3722. (30) He, G.; Bhamidi, V.; Tan, R. B. H.; Kenis, P. J. A.; Zukoski, C. F. Cryst. Growth Des. 2006, 6, 1175. (31) Hiramatsu, H.; Osterloh, F. E. Langmuir 2003, 19, 7003. (32) Allen, K.; Davey, R. J.; Ferrari, E.; Towler, C.; Tiddy, G. J.; Jones, M. O.; Pritchard, R. G. Cryst. Growth Des. 2002, 2, 523.

CG700890M