Concomitant Crystallization of Cefuroxime Acid ... - ACS Publications

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Concomitant Crystallization of Cefuroxime Acid and Its Acetonitrile Solvate in Acetonitrile and Water Solution Guan Wang,† Yongli Wang,†,‡ Youguang Ma,† Hongxun Hao,*,†,‡ Huihui Wang,† and Jie Zhang† †

School of Chemical Engineering and Technology, Tianjin University, Tianjin 300072, China The Co-Innovation Center of Chemistry and Chemical Engineering of Tianjin, Tianjin 300072, China

‡

ABSTRACT: The appearance of concomitant crystals will affect the quality of the crystalline pharmaceutical products. Although many researchers have investigated the concomitant polymorphs, rather little attention has been paid to the solvate systems, which is also a very important solid formation in the pharmaceutical industry. In this study, the concomitant crystallization of pure cefuroxime acid and its acetonitrile solvate was found in the binary mixture of acetonitrile and water. The concomitant crystals were confirmed and verified by a series of off-line and online techniques, including optical microscopy, powder X-ray diffraction, DSC, and Raman spectra. Furthermore, this concomitant crystallization phenomenon was explained with the discontinuity point in the solubility curve of pure cefuroxime acid. Finally, the nucleation and growth mechanisms of the concomitant crystals were identified by fitting the induction period data.

1. INTRODUCTION Concomitant formation of crystals is a very common phenomenon in the process of crystallization.1−4 After Wöhler and Liebig first discovered the concomitant polymorphs in 1832,5 it attracted lots of researchers’ attention not only because the appearance of concomitant crystals would affect the quality of the crystalline product, but also the understanding of the concomitant crystallization could provide necessary information, such as nucleation and growth conditions, for designing and controlling the crystallization process more robustly and explicitly.6−10 When a compound (C) is crystallized out from a solvent (S), depending on the interactions between C and S, there are generally two possibilities for C: either crystallized with S,11−13 or crystallized without S (Figure 1).14−16 As referred to by Sato

(ii) the overlap in the domain of its solvate; and (iii) the overlap in the domain of its solvate and nonsolvate polymorph (Figure 1). So far, there are many reports about phenomena and mechanisms of type (i) concomitant crystals.18−22 Ter et al. even built a new approach to predict the nucleation rates of concomitant polymorphs.23 Possibility (ii) has also been found in the crystallization of hexakis (4-cyanophenyloxy) benzene in a mixture of methanol and acetonitrile by Das et al.24 Yet to the best of our knowledge, no report about the concomitant crystallization of possibility (iii) has ever been published, although it is theoretically possible. In this Article, a case of possibilities (iii) was found and reported for the first time when preparing cefuroxime acid (Figure 2), an active pharmaceutical

Figure 2. Structure of cefuroxime acid.

ingredient (API), which is a common antibiotic drug used for the treatment of bacterial infections.25 As the concomitant crystallization of cefuroxime acid and its acetonitrile solvate (ACN solvate) may cause a series of product quality problems, it is necessary to characterize this phenomenon and to research its mechanism, which would be useful to control the occurrence of concomitant crystallization in the pharmaceutical industry.

Figure 1. Different possibilities of crystal formation.

et al.,17 either possibility could be defined by the occurrence domain, which contained the solvent, temperature, and other operating conditions of crystallization. If there is an overlap among these domains, two or more substances could crystallize out simultaneously under the same conditions. In other words, the concomitant formations of crystals would happen. In principle, there are three possible types of overlap in these domains: (i) the overlap in the domain of its polymorphism; © 2014 American Chemical Society

Received: Revised: Accepted: Published: 14028

February 28, 2014 August 18, 2014 August 21, 2014 August 21, 2014 dx.doi.org/10.1021/ie5021602 | Ind. Eng. Chem. Res. 2014, 53, 14028−14035

Industrial & Engineering Chemistry Research

Article

then was kept still for 2 h to allow the particles to settle. After that, the upper clear solution was first filtered through 0.45 μm membrane filters, and the concentration of the filtrate was determined by HPLC analysis. The undissolved crystals suspended in the solution were filtered, dried, and then characterized. The uncertainty of the HPLC analysis was estimated to be 2%. The concentration of cefuroxime acid was determined on an Agilent 1200 with the Agilent C18 (250 mm × 4.6 mm, 5 μm). The mobile phase was a buffer solution of sodium acetate and acetonitrile (10:1, v/v). The pH value of the sodium acetate solution was adjusted by acetic acid to 4.3 ± 0.1. The velocity of the mobile phase was 1.0 mL/min, and the analysis was conducted at 298.15 K and under 254 nm UV light. To ensure the accuracy of the solubility data, each point of cefuroxime acid solubility was repeated at least three times, and the average value was used to calculate the solubility. The uncertainty of the solubility experiments was estimated to be 5%. The mole fraction solubility of the solute (x) in solution was calculated as follows:

Besides, it would be helpful to better understand the mechanism of concomitant crystallization. In the present work, the concomitant crystallization of cefuroxime acid and its acetonitrile solvate (ACN solvate) was experimentally investigated and verified by both off-line and in situ techniques, including optical microscopy, powder X-ray diffraction (PXRD), DSC, and Raman spectroscopy. The thermodynamic data, specifically the solubility of cefuroxime acid in the binary mixture of water and acetonitrile, were determined using the gravimetric method to explain this concomitant crystallization phenomenon. Moreover, the induction period was also determined by using a laser monitoring system. The nucleation and growth mechanisms of the concomitant crystallization were then discussed by using the induction period data.

2. EXPERIMENTAL SECTION 2.1. Materials. Cefuroxime acid (mass purity ≥99%) was supplied by NCPC Hebei Huamin Pharmaceutical Co., Ltd. Acetonitrile (analytical grade) used in the experiments was purchased from Tianjin Kewei Chemical Co., Ltd. and was used without further purification. Deionized water was used throughout. 2.2. Preparation and Characterization of Concomitant Crystals. Two grams of cefuroxime acid was first dissolved into 68 g of a mixture of acetonitrile and water (4:1, w/w) at 298.15 K. To obtain the concomitant crystals, 163.2−217.6 g of water was then added into the solution. After being stirred for about 1 h at 298.15 K, crystals with two different morphologies were obtained. The obtained samples were characterized by optical microscopy, PXRD, and DSC. The crystal habits were observed using an optical microscope of Nikon Eclipse E200 with a magnification of 100×. PXRD investigations were carried out at 298.15 K on a Rigaku D/max2500 diffractometer at 40 kV and 100 mA with Cu Kα (λ = 1.5418 Å) radiation. The PXRD patterns were recorded between 2° and 40°. The melting property was determined by DSC 1/500 (Mettler Toledo, Switzerland) with a heating rate of 10 K/min under the protection of nitrogen. The relative standard uncertainty of the measurements was estimated to be 3%. Raman spectra were collected with a Kaiser RamanRXN2 Hybrid system from Kaiser Optical Systems, Inc. The analyzer was equipped with an MR probe and a PhAT probe for noncontact or contact sampling, respectively. The PhAT probe was used to ex situ collect the Raman spectra of the solid-state cefuroxime acid and its ACN solvate. The MR probe was used to in situ measure the Raman spectra of the liquid-state sample in the process of crystallization. All data of Raman spectra were recorded by iC Raman software. 2.3. Solubility Determination. The isothermal method similar to the method of the literature26 was applied to determine the solubility of cefuroxime acid in a mixture of acetonitrile and water at 298.15 K. An excess amount of cefuroxime acid was added into the mixture of acetonitrile and water in a jacketed glass vessel. The temperature of solution was controlled by a thermostat (type 501A, Shanghai Laboratory Instrument Works Co., Ltd., China) with an accuracy of ±0.05 K. The solution was kept under agitation for 5 h. It had been confirmed by taking samples at different time that the concentration of the solution reached a maximum after 5 h, which indicated that 5 h was long enough to reach equilibrium for the cefuroxime acid solutions. The solution

x=

m/M m /M + mA /MA + mW /MW

(1)

where m, mA, and mW are the masses of cefuroxime acid, acetonitrile, and water, and M, MA, and MW are the molecule masses of cefuroxime acid, acetonitrile, and water, respectively. The initial mole fraction of water in the solution xW was calculated as follows: xW =

mW /MW mA /MA + mW /MW

(2)

2.4. Induction Period Measurements. The induction period of cefuroxime acid in the binary mixture of water and acetonitrile was determined by a laser monitoring system similar to that described by Hao et al.27 The laser monitoring system consisted of a He−Ne laser generator (type GY-22, Tianjin TUOPU instruments Co., Ltd., China) and a lightintensity display (type WGN-1, Tianjin TUOPU instruments Co., Ltd., China) with an accuracy of ±3%. All experiments were carried out in a jacketed glass vessel maintained at 298.15 K by a thermostat. The initial solution was prepared by adding 0.5−0.6 g of cefuroxime acid into 17 g of solvent mixture of acetonitrile and water (4:1, w/w). A certain mass of water (40.8−54.4 g) with the same temperature then was added quickly into the solution. The solution was mixed by a magnetic stirrer. The time that elapsed between the addition of water and the appearance of the first crystals determined by the laser scattering method was defined as the induction period. The same experiments for each supersaturation level were repeated three times, and the average data were used to calculate the induction period. The maximum relative deviation is 5%.

3. THEORY BASIS As referred to in the literature,27−30 the primary nucleation rate (J) could be expressed as follows: ⎛ −16πγ 3υ2 ⎞ J = A exp⎜ 3 3 ⎟ ⎝ 3k T (ln S)2 ⎠

(3)

where A is the pre-exponential factor, γ is the interfacial free energy between crystal and solution, υ is the molecular volume 14029

dx.doi.org/10.1021/ie5021602 | Ind. Eng. Chem. Res. 2014, 53, 14028−14035


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Table 1. Expressions of f(S) for Different Growth Mechanisms

a

growth mechanisms

normal growth

spiral growth

volume diffusion-controlled growth

2D nucleation-mediated growth

f(S)

S−1

(S − 1) ln S

S−1

(S − 1)2/3S1/3 exp[−B2D/(3 ln S)]a

The constant B2D = β2Dκ2α/(kT)2, β2D is a numerical 2D shape factor, κ is the specific edge free energy of the nucleus, and α is the molecular area.

Figure 3. Habits of (a) the obtained crystals, (b) cefuroxime acid crystals, and (c) cefuroxime acid ACN solvate crystals.

As the value of the first part is much lower than that of the second one,31,34 eq 7 usually could be given as follows:

of the crystal, k is the Boltzmann constant, T is the absolute temperature, and S is the supersaturation, which is calculated as c/s with c being the concentration of solute and s being the solubility of solute. In the above equation, the spherical particles are assumed to be formed. Because many crystals are actually not spherical, eq 3 needs to be modified to fit different situations. As reported by Kuldipkumar et al.,31 eq 3 could be rewritten to accommodate other shapes as follows: ⎛ −4f 3 γ 3υ2 ⎞ S ⎟ J = A exp⎜⎜ 2 3 3 2⎟ ⎝ 27f V k T (ln S) ⎠

⎛ α ⎞1/ n t ind = ⎜ ⎟ ⎝ anJGn − 1 ⎠

The relationship between G and S is usually expressed by the following equation: G = K Gf (S)

(4)

⎛ −B ⎞ J = KJS exp⎜ 2 ⎟ ⎝ ln S ⎠

⎛ B ⎞ ⎟ t ind = A p[f (S)]−(n − 1)/ n S −1/ n exp⎜ ⎝ n ln 2 S ⎠

4fS3 γ 3υ2 27f V2 k3T 3

(6)

By fitting the ln tind and ln S, the straight lines with different slopes suggest that the homogeneous and heterogeneous nucleation mechanisms may exist.29 The behavior of the lower slope zone is more consistent with a heterogeneous nucleation mechanism in contrast to the higher slope zone where homogeneous nucleation is more likely. Furthermore, the growth mechanism could also be deduced from the induction period. A general expression of the induction period in unseeded crystallization was proposed by Kashchiev et al.,32 and the expression was written as follows:33 t ind

(11)

with

−2

⎛ α ⎞1/ n 1 ⎟ = +⎜ n−1 JV ⎝ anJG ⎠

(10)

where KJ is the nucleation rate constant. Combining eqs 8, 9, and 10, the following expression could be deduced as

(5)

with B=

(9)

where KG is the growth rate constant and f(S) is the function of supersaturation related to the growth mechanism. As reported by Teychene and Biscans,35 the expressions of f(S) are listed in Table 1. For the steady-state nucleation rate, J is given as follows:

where f S is the surface shape factor, and f V is the volume shape factor. As suggested by Mullin,29 the induction period tind is inversely proportional to the nucleation rate J, and then eq 4 can be rewritten as ln t ind = K + B ln−2 S

(8)

⎛ ⎞1/ n α ⎟ A p = ⎜⎜ n−1 ⎟ ⎝ anKJK G ⎠

(12)

By fitting the induction period with eq 11, the growth mechanism of crystals can be determined. To simplify the fitting processes, eq 11 can be rearranged for normal, spiral, and volume diffusion-controlled growth as follows:31 F(S) = ln A p +

B n ln 2 S

(13)

with F(S) = ln{S1/ n[f (S)](n − 1)/ n t ind}

(7)

where V is the volume of the system, α is the volume fraction of the detected new phase, G is the growth rate of nucleus, an is the shape factor, whose value can be obtained from the literature,33 and n = mb + 1, where m refers to the dimensionality of growth and 0.5 < b < 1.

(14)

For 2D nucleation-mediated growth, eq 11 can be rewritten as follows: F(S) = ln A p + (n − 1) 14030

B2D B + 3n ln S n ln 2 S

(15)



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with F(S) = ln[(S − 1)2(n − 1)/3n S(n + 2)/3nt ind] −2

(16) −1

Hence, the plot of F(S) versus ln S or ln S can be built and used to determine the growth mechanism of crystals.

4. RESULTS AND DISCUSSION 4.1. Concomitant Crystallization and Its Characterization. As shown in Figure 3, during the crystallization process of cefuroxime acid from a mixture of water and acetonitrile, two different crystal habits (Figure 3a) were observed at the same time, which are the same as the habits of pure cefuroxime acid (Figure 3b) and its ACN solvate (Figure 3c). The obtained crystals were filtered and characterized by PXRD. For comparison, the same analyses were also applied to pure cefuroxime acid and its ACN solvate, respectively. The PXRD pattern of the obtained crystals, together with the PXRD patterns of pure cefuroxime acid and its ACN solvate, is shown in Figure 4. It can be seen that the characteristic peaks of

Figure 5. DSC curves of cefuroxime acid (blue), concomitant crystals (black), and cefuroxime acid ACN solvate (red).

molecules in the crystal lattice. For the concomitant crystals, the endothermic peak at 394 K and the exothermic peak at 452 K well agreed with those of pure cefuroxime acid and pure ACN solvate, respectively. This also means that the concomitant formation of cefuroxime acid and its ACN solvate did happen in the experiments. To prove that the appearance of two forms of cefuroxime acid is due to the concomitant nucleation of two forms rather than the transformation of different forms, the nucleation experiments of cefuroxime acid in a mixture of ACN and water were in situ monitored by online camera and Raman spectroscopy, respectively. With the help of online cameras, the process of nucleation for concomitant crystals could be easily recorded. This method was previously used to investigate the nucleation mechanism by Kadam et al.36 As shown in Figure 6, the solution was clear Figure 4. PXRD patterns of cefuroxime acid (blue), concomitant crystals (black), cefuroxime acid ACN solvate (red), and concomitant crystals after desolvation (green).

cefuroxime acid at 3.36°, 10.92°, and 14.44° and the characteristic peaks of ACN solvate at 7.54°, 9.36°, and 13.72° could be clearly seen in the PXRD pattern of the obtained crystals from crystallization. This means that both pure cefuroxime acid and its ACN solvate were included in the obtained crystals. It could be preliminarily concluded that the concomitant formation of cefuroxime acid and its ACN solvate did happen under the tested crystallization conditions. To further verify this phenomenon of concomitant crystallization, the experiment of desolvation for the concomitant crystals was carried out by heating the sample at 350 K. As shown in Figure 4, the PXRD pattern of the filtered crystals after desolvation was nearly the same as that of pure cefuroxime acid; this confirmed again that ACN solvates were contained in the mixture of obtained crystals. The DSC results of the concomitant crystals and the two pure crystal formations were plotted in Figure 5. On the basis of the DSC curves, an exothermic peak existed at 455 K for pure cefuroxime acid, which corresponded to its decomposition. Also, an endothermic peak appeared at 393 K for pure ACN solvate, which is caused by the desolvation of the solvent

Figure 6. Photos of real time nucleation: (a) 0 min, (b) 2.5 min, (c) 10 min, (d) 30 min. 14031



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Figure 7. Raman spectra of cefuroxime acid (blue) and its ACN solvate (red).

solvate was due to the concomitant nucleation of these two forms. 4.2. Solubility Data and Concomitant Crystallization Zone. The formation of concomitant crystals is the result of the competition between kinetic and thermodynamic factors. To better understand this phenomenon, it would be helpful to determine the solubility of cefuroxime acid in this system. As shown in Figure 9, the solubility of cefuroxime acid first

before the occurrence of nucleation, while the concomitant crystals of cefuroxime acid and its ACN solvate were actually formed through antisolvent crystallization. The appearances of cefuroxime acid and its ACN solvate crystals were recorded at the same time, which indicated the happening of concomitant nucleation of two different forms. Furthermore, the in situ Raman technology was also used to monitor the process of crystallization of cefuroxime acid in acetonitrile and water solution. The characteristic peaks for solid-state cefuroxime acid and its ACN solvate were determined by the Raman analyzer, and the results are shown in Figure 7. As shown in Figure 7, there are some distinct differences between the cefuroxime acid Raman spectra and its acetonitrile solvate Raman spectra. These differences can be used to distinguish them easily. The peak at 572 cm−1 can be assigned as the characteristic peak of cefuroxime acid, while the peak at 1639 cm−1 can be assigned as the characteristic peak of its ACN solvate. The real time results of Raman spectra were plotted in Figure 8. From Figure 8, it can be found that the

Figure 9. Solubility diagram for cefuroxime acid in the binary mixture of acetonitrile and water (W) at 298.15 K.

increased to its maximum value with the increasing of water fraction until water fraction xC = 0.36, and then started to decrease with the increasing of water fraction. However, the solubility did not decrease smoothly at the point xC = 0.87, which was an apparent discontinuity point. As referred to by Stieger et al.,37 the discontinuity in the solubility curve means that two different crystal forms were probably formed in this range. Similar crystallization experiments then were carried out as described in section 2.2, except for the amount of water added. The crystals obtained from solutions with water fractions xC of 0.84, 0.87, 0.90, and 0.95 were then filtered and characterized by PXRD. The results showed that only the samples obtained from solution with water fractions of 0.87 and 0.90 were a crystal mixture of cefuroxime acid and its ACN solvate, while the sample obtained from solution with water fraction of 0.84 was pure ACN solvate and the sample obtained from solution

Figure 8. Real time change of the characteristic Raman spectra peaks: cefuroxime acid (572 cm−1, blue) and its ACN solvate (1639 cm−1, red).

characteristic Raman peak of cefuroxime acid and its ACN solvate did not change in region I, while both of them started to increase simultaneously after water was added into the solution in region II. This indicated the concomitant nucleation of both cefuroxime acid and its ACN solvate. This confirmed again that the simultaneous appearance of cefuroxime acid and its ACN 14032



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be seen that the value of induction period followed the linear relationship given by eq 5, which means that the nucleation of concomitant crystals could be explained by the classical nucleation theory. However, there are two different straight lines with different slopes in Figure 10. Similar results were also found by Zhi and Liu et al.34,38 The slope change in this case was considered to be caused by the change in the nucleation mechanism from homogeneous nucleation at high supersaturation to heterogeneous nucleation at low supersaturation. The transition from homogeneous to heterogeneous nucleation was also reflected by the intersection point in Figure 10. As described above, the growth mechanism of concomitant crystals could be identified by fitting the F(S) data over a range of supersaturation with eq 13 or eq 15, where the value of F(S) could be obtained with eq 14 or eq 16. For concomitant crystallization, both pure cefuroxime acid and its ACN solvate would grow at the same condition. As referred to by Verdoes et al.,33 the value of m for the crystal of pure cefuroxime acid was 3, while the value of m for needlelike ACN solvate crystal was 1. The values of F(S) for both forms could be obtained, and the growth mechanism could be identified by the fitness of F(S) versus ln−1 S or ln−2 S. As shown in Figures 11 and 12 for cefuroxime acid and its ACN solvate, respectively, for both cases, the 2D nucleation-mediated growth mechanism model could give satisfactory fitting results, while the other growth mechanism models, including the normal growth model, the spiral growth model, and the volume diffusion-controlled growth model, could not give satisfactory fitting results. This means that both the growth of pure cefuroxime acid and its ACN solvate could be represented by the 2D nucleationmediated growth mechanism. This result is reasonable when considering the growth mechanisms of concomitant crystals should be the same. This conclusion is also further confirmed

with water fraction of 0.95 was pure cefuroxime acid. Hence, it can be further concluded that the concomitant crystals would happen when the water fraction is between 0.87−0.90 in acetonitrile and water mixed solvents. 4.3. Crystal Nucleation and Growth Mechanisms. To further understand the nucleation and growth mechanisms of concomitant crystallization of cefuroxime acid and its ACN solvate, the induction period of concomitant crystals was determined with the water fraction varied from 0.87 to 0.90 where the solubilities of cefuroxime acid and its ACN solvate were almost the same as each other. The plot of ln tind versus ln−2 S for concomitant crystals of cefuroxime acid and its ACN solvate at 298.15 K was plotted and shown in Figure 10. It can

Figure 10. Plot of ln tind versus ln−2 S for concomitant crystals.

Figure 11. Plot of F(S) versus ln−2 S or ln−1 S for pure cefuroxime acid (m = 3). Data were fitted using (a) normal growth, (b) spiral growth, (c) 2D nucleation-mediated growth, and (d) volume diffusion-controlled growth. 14033



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Figure 12. Plot of F(S) versus ln−2 S or ln−1 S for cefuroxime acid ACN solvate (m = 1). Data were fitted using (a) normal growth, (b) spiral growth, (c) 2D nucleation-mediated growth, and (d) volume diffusion-controlled growth.

phenomenon was also well explained by fitting the induction period data. The 2D nucleation-mediated growth mechanism was identified for the concomitant crystals. Finally, this type of concomitant crystallization may be the real reason for quality problems for some solvate systems, and this problem could be solved by adjusting the solvent ratio out of the range of the concomitant crystals, which would be easily operated and achieved in industrial production.

by the SEM images shown in Figure 13. It can be seen that there are obviously many layers contained in the crystals of both cefuroxime acid and its ACN solvate, which is caused by the growth of 2D nuclei.

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +86-22-27405754. Fax: +86-22-27374971. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We would like to thank Kaiser Optical Systems, Inc. for supporting the RamanRXN2 Hybrid system. We are thankful to the National Natural Science Foundation of China (no. 21376165) and the National Technology R&D Program from the China Ministry of Science and Technology (no. 2011BAD23B02) for financial support.

Figure 13. SEM images of the concomitant crystals: (a) cefuroxime acid, (b) acetonitrile solvate.

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5. CONCLUSIONS The rare occurrence of the concomitant crystallization of cefuroxime acid and its ACN solvate during the antisolvent crystallization of cefuroxime acid in water and acetonitrile was presented in this Article. The concomitant crystallization zone was further verified to happen when the final water fraction was between 0.87−0.90 in acetonitrile and water mixed solvents. Moreover, the nucleation and growth mechanism of this rare 14034

NOTATIONS x = mole fraction solubility of the solute xW = initial mole fraction of water in the solvents m = mass of the compound (g) M = molecular mass of the compound J = primary nucleation rate A = pre-exponential factor T = absolute temperature (K) S = supersaturation [(g/g)/(g/g)] dx.doi.org/10.1021/ie5021602 | Ind. Eng. Chem. Res. 2014, 53, 14028−14035


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(17) Sato, K.; Boistelle, R. Stability and Occurrence of Polymorphic Modifications of the Stearic Acid in Polar and Nonpolar Solutions. J. Cryst. Growth 1984, 66, 441. (18) Jiang, S.; ter Horst, J. H.; Jansens, P. J. Concomitant Polymorphism of o-Aminobenzoic Acid in Antisolvent Crystallization. Cryst. Growth Des. 2007, 8, 37. (19) Kumar, V. S.; Sheela, K.; Nair, V.; Rath, N. P. Concomitant Polymorphism in a Spirobicyclic Dione. Cryst. Growth Des. 2004, 4, 1245. (20) Chun, J.; Jung, I. G.; Kim, H. J.; Park, M.; Lah, M. S.; Son, S. U. Concomitant Formation of N-Heterocyclic Carbene-Copper Complexes within a Supramolecular Network in the Self-Assembly of Imidazolium Dicarboxylate with Metal Ions. Inorg. Chem. 2009, 48, 6353. (21) Lennartson, A.; Wiklund, T.; Håkansson, M. Concomitant Formation of Chiral and Racemic Crystals of a Diaryl Sulfide. CrystEngComm 2007, 9, 856. (22) Lemmerer, A.; Báthori, N. B.; Esterhuysen, C.; Bourne, S. A.; Caira, M. R. Concomitant Polymorphs of the Antihyperlipoproteinemic Bezafibrate. Cryst. Growth Des. 2009, 9, 2646. (23) Ter Horst, J.; Kramer, H.; Jansens, P. A New Molecular Modeling Approach to Predict Concomitant Nucleation of Polymorphs. Cryst. Growth Des. 2002, 2, 351. (24) Das, D.; Barbour, L. J. Concomitant Formation of Two Different Solvates of a Hexa-Host from a Binary Mixture of Solvents. Chem. Commun. 2008, 5110. (25) O’Callaghan, C. H.; Sykes, R.; Griffiths, A.; Thornton, J. Cefuroxime, a New Cephalosporin Antibiotic: Activity in Vitro. Antimicrob. Agents Chemother. 1976, 9, 511. (26) Jing, D.; Wang, J.; Wang, Y. Solubility of Penicillin Sulfoxide in Different Solvents. J. Chem. Eng. Data 2009, 55, 508. (27) Hao, H.; Wang, J.; Wang, Y. Determination of Induction Period and Crystal Growth Mechanism of Dexamethasone Sodium Phosphate in Methanol−Acetone System. J. Cryst. Growth 2005, 274, 545. (28) Liu, B.-w.; Wang, D.-y.; Huang, X.-r. Study on Primary Nucleation of Benzathini Benzylpenicillinum. Chem. Ind. Eng. 2003, 20, 175. (29) Mullin, J. W.; Mullin, J. Crystallization, 3rd ed.; ButterworthHeinemann: Oxford, 1993. (30) Roelands, C. M.; ter Horst, J. H.; Kramer, H. J.; Jansens, P. J. Analysis of Nucleation Rate Measurements in Precipitation Processes. Cryst. Growth Des. 2006, 6, 1380. (31) Kuldipkumar, A.; Kwon, G. S.; Zhang, G. G. Determining the Growth Mechanism of Tolazamide by Induction Time Measurement. Cryst. Growth Des. 2007, 7, 234. (32) Kashchiev, D.; Verdoes, D.; van Rosmalen, G. M. Induction Time and Metastability Limit in New Phase Formation. J. Cryst. Growth 1991, 110, 373. (33) Verdoes, D.; Kashchiev, D.; Van Rosmalen, G. Determination of Nucleation and Growth Rates from Induction Times in Seeded and Unseeded Precipitation of Calcium Carbonate. J. Cryst. Growth 1992, 118, 401. (34) Liu, X.; Xu, D.; Ren, M.; Zhang, G.; Wei, X.; Wang, J. An Examination of the Growth Kinetics of L-Arginine Trifluoroacetate (LATF) Crystals from Induction Period and Atomic Force Microscopy Investigations. Cryst. Growth Des. 2010, 10, 3442. (35) Teychené, S.; Biscans, B. Nucleation Kinetics of Polymorphs: Induction Period and Interfacial Energy Measurements. Cryst. Growth Des. 2008, 8, 1133. (36) Kadam, S. S.; Kramer, H. J.; ter Horst, J. H. Combination of a Single Primary Nucleation Event and Secondary Nucleation in Crystallization Processes. Cryst. Growth Des. 2011, 11, 1271. (37) Stieger, N.; Caira, M. R.; Liebenberg, W.; Tiedt, L. R.; Wessels, J. C.; De Villiers, M. M. Influence of the Composition of Water/ Ethanol Mixtures on the Solubility and Recrystallization of Nevirapine. Cryst. Growth Des. 2010, 10, 3859. (38) Zhi, M.; Wang, Y.; Wang, J. Determining the Primary Nucleation and Growth Mechanism of Cloxacillin Sodium in Methanol−Butyl Acetate System. J. Cryst. Growth 2011, 314, 213.

c = concentration of the solute (g/g) s = solubility of the solute (g/g) f S = surface shape factor f V = volume shape factor tind = induction priod (s) V = volume of the system G = growth rate of nucleus an = shape factor m = dimensionality of growth KG = growth rate constant KJ = nucleation rate constant Greek Letters

γ = interfacial free energy between crystal and solution ν = molecular volume of the crystal κ = Boltzmann constant α = volume fraction of the detected new phase Subscripts

A = acetonitrile W = water

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REFERENCES

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