Combined Application of in Situ FBRM, ATR-FTIR, and Raman on

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Combined Application of in Situ FBRM, ATR-FTIR, and Raman on Polymorphism Transformation Monitoring During the Cooling Crystallization Yingying Zhao,†,‡,§ Junsheng Yuan,† Zhiyong Ji,† Jingkang Wang,‡ and Sohrab Rohani*,§ †

Engineering Research Center of Seawater Utilization Technology of Ministry of Education, Hebei University of Technology, Tianjin 300130, People’s Republic of China ‡ School of Chemical Engineering and Technology, State Research Center of Industrialization for Crystallization Technology, Tianjin University, Tianjin 300072, People’s Republic of China § Department of Chemical and Biochemical Engineering, The University of Western Ontario, London, Ontario N6A 5B9, Canada ABSTRACT: This study evaluates the potential use of the FBRM, ATR-FTIR, and Raman for on line detection of polymorphic transformation of carbamazepine (CBZ) during the cooling crystallization. Changes in solution concentration as a function of time were quantified from the ATR-FTIR data. A new quantitative method of polymorphs ratio was developed using Raman spectroscopy for in situ monitoring during a solution-mediated transformation of carbamazepine from form II to form III in 1propanol. The polymorphic forms initially crystallized from solution, in the absence of seeds, could be clearly identified by FBRM and showed good agreement with results of microscopic images. Furthermore, the kinetics of the conversion of carbamazepine from metastable form to the stable form at different cooling rates could be readily followed. the problems with fluorescence for some compounds and the relatively low sensitivity. To our best knowledge, in-line monitoring of crystallization with Raman spectroscopy is still in a relatively early stage, and most of the polymorphic transformation characterizations have been conducted in aqueous solutions. Fourier transform infrared (FT-IR) and FBRM are important complementary tools for online solution concentration measurement and chord length distribution measurement of a solid phase, which allows for the determination of the desupersaturation curve and calculation of the mass of solid produced at any point in the process. On some occasions, the FBRM has been reported to monitor the identification of morphology change during polymorphic transformation.6,11 The studies of the polymorphic transformation by combining the in situ technologies have been the focus of many investigations over the past few years. O’Sullivan et al. used in situ FBRM, PVM, and ATR-FTIR to monitor the polymorphic transformation of D-mannitol,5,6 and the effect of particle dimension on Raman spectra was investigated offline.5 In situ Raman spectroscopy was also used to determine the rate of polymorph turnover for MK-A, a multipolymorphic compound, at Merck Research Laboratories.12 Ono et al. carried out the batch transformation experiments of L-glutamic acid at several temperatures with quantification of polymorphic fraction by Raman; however, the quantification was done by taking samples and drying in the experimental process.7 The conversion kinetics of carbamazepine polymorphs to the

1. INTRODUCTION Batch crystallization is mostly involved in the pharmaceutical manufacturing processes from solution as a process of purification, final crystal form selection, and/or particle size control.1 Crystallization is an extremely complex process, particularly when multiple crystal forms (polymorphs) can be produced, which is common with many pharmaceutical materials. Polymorphs have different physical and chemical properties, such as lattice energy, melting point, heat of fusion, solubility, dissolution rate, density, and processability. Such differences may affect stability, formulation, potency, bioavailability, and storage of pharmaceuticals and their performance,2 and ultimately have a profound effect on the therapeutic efficacy. Therefore, solid composition is crucial in understanding polymorphism, which is of key importance in the pharmaceuticals.3,4 With the aim of improving the understanding of pharmaceutical manufacturing processes and better controlling product quality, the control and consistency of solid phase properties through crystallization has been the focus of considerable industrial and academic researches. The studies of the polymorphic transformation by in situ technologies, such as FBRM, PVM, Raman, and ATR-FTIR, have been the focus of many investigations over the past few years.5−7 There are many advantages of Raman spectroscopy,3,8 including the following: (i) no special sample preparation is required, (ii) the technique is noninvasive, and (iii) it is relatively insensitive to aqueous media. Especially, Raman spectroscopy can be used for remote detection through fiberoptic coupling of sampling probes, and facilitate the in-line monitoring of polymorphic transformation whereby data are generated in real time by direct analysis of the process.3,7−10 However, Raman spectroscopy has some disadvantages, such as © 2012 American Chemical Society

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34.2 °C.9 It is important to clearly understand the polymorph transformation from form II to form III in solvents, for form II has been observed in the preparation process of form III in the cooling crystallization and was responsible for the decreased purity of CBZ form III. Therefore, on the basis of the previous research,9 a further study of the polymorph transformation from form II to form III in the unseeded cooling crystallization was done.

dihydrate in aqueous suspension were studied by Tian et al.13using Raman spectroscopy in the isothermal crystallization process. An advanced calibration strategy for in situ quantitative monitoring of phase transition processes in suspensions using FT-Raman spectroscopy was proposed by Chen et al., but the temperature effects on Raman intensities were not successfully avoided.14 ATR-FTIR and FBRM were applied in the crystallization of the metastable α-form of L-glutamic acid, and pure metastable form with uniform size was successfully obtained using concentration feedback control by Kee et al.15,16 Then, the authors also did semiautomated identification of the phase diagram for enantiotropic crystallizations using ATR-FTIR spectroscopy and laser backscattering.17 ATR-FTIR spectroscopy in combination with optical turbidometric measurements provided direct experimental evidence for a crystallization mechanism, dissolution, and associated pseudopolymorphic behavior of citric acid crystals from aqueous solution by Roberts et al.,18 revealing new physical insights into molecular scale processes prior to and during nucleation and crystal growth. However, to the best of our knowledge, there have been no reports describing the simultaneous monitoring of solution concentration and polymorphic ratio using Raman spectroscopy in conjunction with ATR-FTIR and FBRM during cooling crystallization using organic solvent. Most of the polymorphs are obtained by cooling crystallization in organic solvents. Therefore, the aim of this study is to investigate the utility of these three combined techniques for in-line monitoring of polymorphism transformation as a function of time and temperature during cooling crystallization in organic solutions. It is crucial to monitor the concentration, crystal form present, and its transformation during crystallization in understanding and controlling polymorphism during the crystallization process. So in this paper, ATR-FTIR was used to monitor the solution concentrations as a function of time; FBRM was successfully applied to trace the nucleation, growth, and polymorph transformation; and a new in situ quantitative method was developed to measure the fraction of form II by Raman spectroscopy. This study illustrates the ability of combination of in situ FBRM, ATR-FTIR, and Raman spectroscopy to monitor the complex process during polymorphism transformation, and the potential application of these techniques in the industrial online optimization and control. In this study, carbamazepine (CBZ), a drug used in epilepsy and trigeminal neuralgia treatment, was used as the model compound (Figure 1) considering its simple structure,

2. EXPERIMENTAL SECTION 2.1. Materials. The solvent 1-propanol was 99+% reagent grade, supplied by Alfa Aesar Johnson Matthey Company (Lancs, U.K.). Carbamazepine in form III was recrystallized by cooling crystallization to prepare the form II as described in previous reference.9 The quality of the carbamazepine polymorphs was analyzed by X-ray powder diffraction (XRPD) spectra on a Rigaku-Miniflex powder diffractometer (Carlsbad, CA) using monochromatic radiation (30 kV and 15 mA) in the 2θ range from 5.0° to 40.0°, at a step size of 0.05° with a counting time of 5 s for each step. 2.2. Apparatus and Procedure. The experimental apparatus is shown in Figure 2. All crystallization experiments were performed in a 250 mL jacketed glass vessel. A Neslab RTE digital plus 740 bath circulator (Portmouth, NH) was used for temperature control. A Teflon-coated thermocouple was used for reading the temperature in the flask. For mixing, a top-mounted, two-bladed, flat electromagnetically driven stirrer was employed. An ATR-FTIR (Hamilton Sundstrand, Pomona, CA) was used for concentration measurements. A FBRM (Lasentec, Redmond, WA) was used with a measurement scan rate of 10 s to detect the onset of crystallization and polymorphic transformation based on the number of the particles. The fraction of each form suspended in solution, during the cooling process at a linear cooling rate from 75 to 15 °C, was determined by a Raman spectrometer (Kaiser Optical Systems, Inc. RXN1-785). A mixture of 12.01 g of CAZ and 150 mL of 1-propanol was added to a 250-mL crystallizer. The solution was initially saturated with respect to form II at 64 °C. Before adding any solute, the reference background of the solvent was obtained by FTIR and Raman. Subsequently, the mixture was heated to 75 °C in 30 min, and then clear solution was kept at 75 °C for 20 min. The FBRM readings ensured all the crystals were dissolved and nucleation did not occur during these two steps. The cooling profiles as well as online monitoring by FBRM, FTIR, and Raman were initiated and ran until the end of the process. In the process, a small drop was taken off from solution each 30 min and covered by coverslip which was just taken out of 1-propanol at experimental temperature, and then the picture of the sample was taken quickly by an Axioskop 40 microscope with polarizer (Carl Zeiss, Oberkochen, Germany) and an attached CCD video camera (Qimaging, Surrey, BC) to avoid new nucleation. 3. QUANTITATIVE METHOD 3.1. FTIR Quantitative Method. ATR-FTIR was used for the dissolved CBZ concentration measurement. The spectrum of 1-propanol at room temperature was used as the background for each sample. Mao et al.20 have demonstrated that the relative height of chosen characteristic peaks increased proportionally with the solute concentration and was almost insensitive to temperature. With a comparison of all the peaks,

Figure 1. Structure of carbamazepine.

polymorph diversity, and great industrial demands.19 Four polymorphs and a hydrate as well as other solvates of CBZ have been reported in the literature.13 Form II is the most commonly encountered form during the production of form III. Form III is the stable form at room temperature, and forms III and II are enantiotropic, with a transition temperature of 12531

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Figure 2. Schematic diagram of the experimental apparatus: (1) Raman probe; (2) ATR-FTIR probe; (3) FBRM; (4) thermometer; (5) crystallizer; (6) impeller; (7) magnetic stirrer; (8) bath circulator.

it was found that the intensity peak heights at 1251 cm−1 changed very little at each run no matter what temperature, polymorphs ratio, or experimental environment variations. Therefore, in order to reduce the effect of noise, the absorbance intensity at 1251 cm−1 was subtracted from absorbance intensity peak heights at 1400 and 1677 cm−1. The quantitative model is

form III. To achieve this objective, a linear cooling strategy was adopted in runs 1−3, and online FBRM, FTIR, and Raman were applied to monitor the evolution of the process. Optical microscopy was also used for the off-line observation. 4.1. FBRM and Microscope Results. For a cooling profile from 75 to 15 °C at a rate of 10 °C/h, Figure 3 shows the

Ccal = 2.831 × (P1400 − P1251) − 0.8896 × (P1677 − P1251) + 0.0039

(1)

where Ccal is the CBZ concentration calculated from the ATRFTIR measurements. The veracity of this model has been verified in a previous reference.9 3.2. Raman Quantitative Method. Distinctive peaks of the Raman trace at 857 and 1450 cm−1 for form III and form II, respectively, are chosen as the characteristic peaks. The intensity at 1271 cm−1 was found to be suitable for background to reduce the effects such as temperature, concentration, and so on. To reduce the effect of the overall solids concentration and solution content, the results were divided by the calculated value of pure form II in each run. The following equation was used to quantify the polymorphs ratio during the polymorphic transformation process. In eq 2, H represents the height of chosen Raman characteristic peaks, and Y represents the mass fraction of solid form II in suspension.

Figure 3. FBRM trends of carbamazepine in the cooling process from 75 to 15 °C at the cooling rate of 10 °C/h.

Y= 9.71 × 10−6 × (H857 − H1271)sol + 7.51 × 10−4 × (H1271 − H1450)sol

FBRM trend for the transformation process. Microscope images of the samples taken from the crystallizer at an interval of 30 min were also obtained to facilitate the interpretation of the FBRM data. As shown in Figure 3, during the first stage 1 (75 to 61.2 °C), there were no changes in the FBRM fine particle population statistic (#/s, 0−20 μm) or coarse population statistics (#/s, 20−50 μm and #/s, 50−200 μm). After 61.2 °C (stage 2), the fine population (#/s, 0−20 μm) began to increase sharply, and later, the population in the ranges 20−50 μm and 50−100 μm

9.71 × 10−6 × (H857 − H1271)ll + 7.51 × 10−4 × (H1271 − H1450)ll

(2)

4. RESULTS AND DISCUSSION The objective of these batch cooling crystallizations was to study the effects of cooling rate on the nucleation of the metastable form, the appearance of the stable form, and the duration of transformation from metastable form II to stable 12532

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Figure 4. Microscopic images of carbamazepine taken during run 2 at different temperatures (×50): (a) 60 °C, (b) 55 °C, (c) 49 °C, (d) 35 °C.

increased. Therefore, stage 2 was identified as the nucleation and growth step of CBZ metastable form II. This is further confirmed by the pictures taken at 60 °C, shown in Figure 4a. Subsequently, the fine particle counts plateaued (stage 3), which suggests the growth of the metastable form particles. Since the metastable form is needlelike, the growth in the length may not be detected by FBRM. However, this process can be verified by comparing the micropicture taken at 55 °C (Figure 4b) with Figure 4a. After a certain period, the FBRM statistics showed a sudden increase at 49.2 °C in the channels from 20−50 μm to 50−200 μm and finally to 0−20 μm (stage 4). This is attributed to the appearance of the stable form III. Form III crystals are platelike; therefore, after they nucleated, not only the fine population but also coarse population statistics would increase rapidly. As described in other literature,21 solution-mediated transformation involves simultaneous crystal growth of the stable nuclei and the continuous dissolution of the metastable crystals. The pictures taken at 49 °C (Figure 4c) confirmed the appearance of block-like form III crystals. Hence, stage 4 was characterized by the nucleation of the stable form III followed by the growth of the new stable form III nuclei as a result of the continuous dissolution of the metastable form II crystals. Over time, the fine and coarse counts showed a sudden decrease in stage 5, indicating an increase in the dissolution of the metastable form II followed by the agglomeration of the stable form III crystals. This was confirmed by the micropicture taken at 35 °C (Figure 4d). The plateau in the FBRM statistics (stage 6) showed the end point of the whole process, indicating that there was no further big change in the size, number, or morphology of the crystals. 4.2. FTIR Results. The solution concentrations measured by FTIR with the solubility and metastable limits9 of the two forms of carbamazepine during run 2 are shown in Figure 5. The initial concentration was equal to the solubility of form II at about 64 °C. From 75 to 61 °C, the concentration stayed

Figure 5. Comparison between the solution concentration and the solubility and metastable limits of carbamazepine polymorphs.

around the initial value, which confirmed the reliability of the calibration equation to calculate the solution concentration by FTIR. In addition, it showed that no nuclei were formed in the solution. The solution concentration began to decrease from about 61 °C, indicating the consumption of solution concentration by appearance of the metastable form, which was in agreement with the FBRM results. The solution concentration was higher than the metastable limits of both of the two forms above 36 °C, which can drive the nucleation and growth of both forms. The crystallization driving force, relative supersaturation σ, can be defined by the following equation. The relative supersaturation changes of both forms in run 2 are shown in Figure 6. 12533

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* CCal − CCal * CCal

Figure 7. Combination of the FBRM, FTIR, and Raman results with time in run 2.

Raman spectrum showed the pure form II’s spectrum. The calculated weight ratio of form II by Raman quantification measurement was around “1” from 61.2 to 49.2 °C, demonstrating that only metastable form II was present in the solution in zone 1. As discussed on the FBRM counts before, this zone was also inferred to as the nucleation and growth zone of the metastable form II. Suddenly the weight fraction of form II calculated by Raman spectrum decreased sharply at the beginning of zone 2, which means that stable form III nucleated at 49.2 °C. The sudden increase of the FBRM counts was also an indication of the nucleation of form III at 49.2 °C. The fraction of form II continued to decrease until 0 at the end of zone 2, which was at 31.8 °C. At this point, all of the metastable form crystals had transformed to the stable form, which was also confirmed by the XRPD. Then, the fraction of form II continued to stay around “0” until the end of the experiment. From Figure 7, we can conclude that the results analyzed from the FBRM, FTIR, and Raman agreed with each other, and the results verified the efficacy and reliability of the proposed online quantification method of polymorphs ratio by Raman which can be applied not only in the isothermal but also in the cooling crystallization. 4.4. Effect of Cooling Rate on Polymorphic Transformation. To study the effect of cooling rate on the polymorphic transition process, the combination of FBRM, FTIR, and Raman was also used during runs 1 and 3. The trends of FBRM and FTIR, as well as Raman, were similar to those of run 2. The difference lies in the temperature when the nucleation of the metastable form occurred (the starting point of zone 1), the temperature at which the metastable form began to convert to the stable form (the starting point of zone 2), and the duration of transformation from metastable form to stable form (the end point of zone 2), as shown in Table 1. Table 1 shows that the nucleation temperature of the metastable form II is lower at a higher cooling rate, which means that the metastable form nucleates at higher relative supersaturation when increasing cooling rates. Meanwhile, the stable form appeared at lower temperatures (transition temperature), and the duration of transformation from metastable form II to stable form III is longer at increased cooling rates, implying that it was more difficult for metastable form to transform to stable form at higher cooling rates. For example, the transformation continued down to a temperature

Figure 6. Comparison between the relative supersaturation of form II and form III of carbamazepine.

Here, Ccal is the CBZ concentration calculated by ATR-FTIR quantitative method, and Ccal* is the CBZ solubility calculated by quadratic fitting equation as described in terms of g CBZ/ml 1-propanol: S ll = 0.0469 − 0.0018 × T + 3.127 × 10−5 × T 2

S lll = 0.0299 − 0.0013 × T + 3.250 × 10−5 × T 2

σ is relative supersaturation in solution. It can be seen that for both forms the relative supersaturation is above 0 before 25 °C. According to the “Ostwald’s step rule”, at higher supersaturation difference, the metastable form may tend to precipitate.22 On the other hand, the lower supersaturation difference between polymorphs may preferentially lead to the formation of the stable polymorph. The relative supersaturation difference of the two forms increases and then decreases at about 50 °C. Therefore, above 50 °C, the relative supersaturation difference between form II and form III is relatively high, which favors the nucleation of form II. Then, the relative supersaturation difference decreases, which favors the nucleation of stable form III at 49.2 °C. 4.3. Comparison of FBRM, FTIR, and Raman Results for Detection of Nucleation and Transformation Process. Figure 7 shows the results of particle counts, concentration, and polymorphs ratio trends with time (different temperatures) calculated by FBRM, FTIR, and Raman during run 2. At the beginning, the temperature increased from 25 to 75 °C after adding the solute to the solvent, and the solution concentration measured by FTIR increased while the particle counts in all FBRM channels decreased to near zero, indicating complete dissolution of the crystals until 75 °C. After being stable at 75 °C for 20 min, the cooling profile was initiated. The calibration equation for Raman was obtained by artificially prepared suspending solutions of known polymorph ratios, so it was only valid after there were crystals in the solution, and then the calculation of the polymorphs ratios started after the nucleation commenced. In zone 1, the counts of particles measured by FBRM increased significantly, and the solution concentration decreased sharply below 61.2 °C. Meanwhile, the 12534

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Table 1. Comparison of Polymorph Transition Process in the Cooling Crystallization run number

cooling rate (°C/h)

nucleation temperature of form II (°C)

transition temperature (°C)

concentration at transition temperature (g/ mL solvent)

duration of transformation process (h)

1 2 3

6.7 10.0 13.3

61.9 61.2 54.1

49.6 49.2 48.9

0.0751 0.0720 0.0686

16.08 17.36 >34.57

of 15 °C during run 3. The concentration at which the stable form appeared, measured by FTIR, was lower at increased cooling rates, which indicated that more metastable crystals formed and consumed more supersaturation before transforming to stable crystals. Therefore, metastable form crystals could be obtained by rapid cooling crystallization, and slowing cooling rate is beneficial for the production of stable form.

(4) Doki, N.; Yokota, M.; Kido, K.; Sasaki, S.; Kubota, N. Reliable and selective crystallization of the metastable α-form glycine by seeding. Cryst. Growth Des. 2004, 4, 103−107. (5) O’Sullivan, B.; Barrett, P.; Hsiao, G.; Carr, A.; Glennon, B. In situ monitoring of polymorphic transitions. Org. Process Res. Dev. 2003, 7, 977−982. (6) O’Sullivan, B.; Glennon, B. Application of in situ FBRM and ATR-FTIR to the monitoring of the polymorphic transformation of Dmannitol. Org. Process Res. Dev. 2005, 9, 884−889. (7) Ono, T.; Ter Horst, J.; Jansens, P. Quantitative measurement of the polymorphic transformation of L-glutamic acid using in-situ Raman spectroscopy. Cryst. Growth Des. 2004, 4, 465−469. (8) Wang, F.; Wachter, J. A.; Antosz, F. J.; Berglund, K. A. An investigation of solvent-mediated polymorphic transformation of progesterone using in situ Raman spectroscopy. Org. Process Res. Dev. 2000, 4, 391−395. (9) Zhao, Y.; Bao, Y.; Wang, J.; Rohani, S. In situ focused beam reflectance measurement (FBRM), attenuated total reflectance Fourier transform infrared (ATR-FTIR) and Raman characterization of the polymorphic transformation of carbamazepine. Pharmaceutics 2012, 4, 164−178. (10) Cornel, J.; Lindenberg, C.; Mazzotti, M. Quantitative application of in situ ATR-FTIR and Raman spectroscopy in crystallization processes. Ind. Eng. Chem. Res. 2008, 47, 4870−4882. (11) Liu, W.; Wei, H.; Black, S. An investigation of the transformation of carbamazepine from anhydrate to hydrate using in situ FBRM and PVM. Org. Process Res. Dev. 2009, 13, 494−500. (12) Starbuck, C.; Spartalis, A.; Wai, L.; Wang, J.; Fernandez, P.; Lindemann, C. M.; Zhou, G. X.; Ge, Z. Process optimization of a complex pharmaceutical polymorphic system via in situ Raman spectroscopy. Cryst. Growth Des. 2002, 2, 515−522. (13) Tian, F.; Zeitler, J.; Strachan, C.; Saville, D.; Gordon, K.; Rades, T. Characterizing the conversion kinetics of carbamazepine polymorphs to the dihydrate in aqueous suspension using Raman spectroscopy. J. Pharm. Biomed. Anal. 2006, 40, 271−280. (14) Chen, Z. P.; Fevotte, G.; Caillet, A.; Littlejohn, D.; Morris, J. Advanced calibration strategy for in situ quantitative monitoring of phase transition processes in suspensions using FT-Raman spectroscopy. Anal. Chem. 2008, 80, 6658−6665. (15) Kee, N. C. S.; Tan, R. B. H.; Braatz, R. D. Selective crystallization of the metastable α-form of L-glutamic acid using concentration feedback control. Cryst. Growth Des. 2009, 9, 3044− 3051. (16) Hermanto, M. W.; Kee, N. C.; Tan, R. B. H.; Chiu, M. S.; Braatz, R. D. Robust Bayesian estimation of kinetics for the polymorphic transformation of L-glutamic acid crystals. AIChE J. 2008, 54, 3248−3259. (17) Kee, N. C. S.; Tan, R. B. H.; Braatz, R. D. Semiautomated identification of the phase diagram for enantiotropic crystallizations using ATR-FTIR spectroscopy and laser backscattering. Ind. Eng. Chem. Res. 2011. (18) Groen, H.; Roberts, K. J. Nucleation, growth, and pseudopolymorphic behavior of citric acid as monitored in situ by attenuated total reflection Fourier transform infrared spectroscopy. J. Phys. Chem. B 2001, 105, 10723−10730. (19) Hartley, R.; Aleksandrowicz, J.; Ng, P.; McLain, B.; Bowmer, C.; Forsythe, W. Breakthrough seizures with generic carbamazepine: a consequence of poorer bioavailability? Br. J. Clin. Pract. 1990, 44, 270− 273.

5. CONCLUSIONS Different in situ analytical measurement techniques, ATRFTIR, Raman spectroscopy, and FBRM, were combined to characterize the polymorphic transformation in the cooling crystallization. The counts measured by FBRM were used to detect the nucleation of metastable form and the transformation to stable form, which were in agreement with the offline microscopic images. The solution concentrations were calculated from the FTIR spectrum, and thus, the relative supersaturations were obtained. An online quantitative method for calculating polymorphic forms ratio by Raman spectroscopy was used successfully in cooling crystallization. It has been demonstrated that the quantitative results by FBRM, FTIR, and Raman were consistent with each other. The ability to obtain conversion points, concentrations along with crystal forms ratios, allows for the extraction of data related to the growth rates and conversion rates of polymorphic forms during crystallization operations. The combination of in-line monitoring techniques can provide crucial information in the development and operation of batch crystallization processes for substances with multiple crystal forms.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +519-661-4116. Fax: +519-661-3498. E-mail: srohani@ uwo.ca. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The work was supported by the National Natural Science Foundation of China (NSFC 20836005) and Program for Changjiang Scholars and Innovative Research Team in University (IRT1059), Natural Science Fund of Hebei Province (B2010000042), and Tianjin Natural Science Fund (10JCYBJC04300).

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REFERENCES

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(20) Mao, S.; Zhang, Y.; Rohani, S.; Ray, A. K. Kinetics of (R, S)- and (R)-mandelic acid in an unseeded cooling batch crystallizer. J. Cryst. Growth 2010, 312, 3340−3348. (21) Cardew, P.; Davey, R. The kinetics of solvent-mediated phase transformations. Proc. R. Soc.London 1985, 398, 415−428. (22) Brittain, H. Polymorphism in Pharmaceutical Solids; Marcel Dekker: New York, 1999.

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