Article pubs.acs.org/IECR
Evidence of Hydrogen-Bond Formation during Crystallization of Cefodizime Sodium from Induction-Time Measurements and In Situ Raman Spectroscopy Penglei Cui,† Xinwei Zhang,† Qiuxiang Yin,*,†,‡ and Junbo Gong†,‡ †
School of Chemical Engineering and Technology, State Key Laboratory of Chemical Engineering, and ‡Tianjin Key Laboratory of Modern Drug Delivery and High-Efficiency, Tianjin University, Tianjin 300072, People’s Republic of China ABSTRACT: In this article, the nucleation process of cefodizime sodium was analyzed from two perspectives: induction time and hydrogen-bond formation. According to classical nucleation theory, the correlation of the induction time indicated that heterogeneous nucleation dominates the nucleation process at lower supersaturation whereas homogeneous nucleation is the main mechanism at higher supersaturation. Then, in situ Raman spectroscopy was used to investigate the probability of hydrogen-bond formation in the supersaturated solution and the nucleation process of cefodizime sodium. A central feature of the hydrogen bonding is that the probability reaches a maximum value at the nucleation point, which can be used to relate the probability of hydrogen-bond formation to the induction time. Furthermore, SEM imaging affords fundamental information to illustrate the effect of supersaturation on the morphology of cefodizime sodium crystals: agglomerated small needlelike particles preferentially formed at a high supersaturation, whereas large needlelike particles formed at low supersaturation.
1. INTRODUCTION Nucleation has a significant impact on the size distribution, polymorph selection, and shape of growing crystals.1−4 The nucleation process, a phase transformation from solution to solid, is highly sensitive to the supersaturation, which is the principal driving force for solution crystallization processes.5 When the nucleation rate is lower than the crystal growth rate, the supersaturation in the solution drops slowly, resulting in a larger crystal size distribution and a perfect crystal morphology. In contrast, when the nucleation rate is higher than the crystal growth rate, the supersaturation decreases sharply, ultimately resulting in the simultaneous appearance of many fine crystals. Therefore, the relation between supersaturation and nucleation has great importance on the control of the solution crystallization process. At the molecular level, nucleation is the process whereby solute molecules dispersed in a solvent assemble together through intermolecular interactions, such as hydrogen and π−π bonding.6−8 For some substances, hydrogen bonding plays a critical role in nucleation,9,10 from governing the macromolecular arrangement of the supersaturated solution to driving molecular self-assembly into crystals. Although nucleation has been intensively studied, there are still uncertainties concerning hydrogen bonding and macromolecular arrangement in supersaturated solutions.11 According to classical nucleation theory, the induction time, defined as the period between the creation of supersaturation and the formation of a new phase, is employed as the basic parameter to determine the nucleation mechanism.12,13 At the same time, the analysis of induction time is very helpful in determining the crystal−solution interfacial tension and further understanding the effects of supersaturation and temperature on the nucleation process. On the other hand, the further study of the macromolecular arrangement of supersaturated solutions provides a preliminary understanding of nucleation at the molecular level, that the driving force for nucleation is © 2012 American Chemical Society
supersaturation in the solution. Raman spectroscopy is a wellknown powerful tool for studying hydrogen bonding because Raman spectra can sensitively provide direct information on inter- and intramolecular vibrations and can also effectively contribute to an understanding of hydrogen bonding.14,15 Hence, in situ Raman spectroscopy is a suitable method for monitoring the characteristic peak intensity of the hydrogenbond framework, whose strength could correspond to the stability of supersaturated solutions during the nucleation process. Cefodizime sodium (Figure 1) is a third-generation cephalosporin with a high antibacterial activity in the treatment
Figure 1. Chemical structure of cefodizime sodium.
of lower-respiratory-tract infections. This drug is an antimicrobial agent that was developed by Hoechst AG and Roussel Uclaf.16,17 Considering its broad spectrum of activity against gram-positive and gram-negative organisms, cefodizime sodium is widely used in clinical treatments. As a heat-sensitive pharmaceutical that is soluble in water but sparingly soluble in Received: Revised: Accepted: Published: 13663
June 13, 2012 September 18, 2012 September 23, 2012 September 24, 2012 dx.doi.org/10.1021/ie301557b | Ind. Eng. Chem. Res. 2012, 51, 13663−13669
Industrial & Engineering Chemistry Research
Article
directly observe the critical nuclei as they formed in solution, and the critical nuclei were observed after they had grown to a critical size. Usually, the induction time refers to the time that elapsed after the creation of supersaturation in solution until the appearance of a certain detectable size of particles. Induction-time measurements were carried out in the range of temperature from 278.15 to 293.15 K. Three reproducible experiments were carried out at each temperature, and the average value for the induction time, which had a reproducibility of 5%, was used in the analysis of the final results. 2.3. Construction of the Calibration Curve. The calibration curve was constructed according to the following procedure: First, standard solutions of cefodizime sodium ranging in concentration from 0 to 0.18 mol/L were prepared by dissolving certain amounts of cefodizime sodium in 100 mL of the binary solvent (ethanol/water = 4/1, v/v) at 298.15 K. Second, the Raman spectra of 10 standard solutions were acquired at a laser wavelength of 785 nm with a resolution of 8 cm−1 and were averaged over two consecutive scans using an exposure time of 5 s. In addition, the background of pure binary solvent was also collected and removed from the Raman spectra of the standard solutions. Finally, the characteristic peak area was obtained by a multipeak Lorentzian fitting to interpret the Raman spectra.20 Therefore, the calibration curve was constructed by correlating the area of the characteristic peaks to the concentration of the solution, as shown in Figure 3.
ethanol, cefodizime sodium is generally isolated by antisolvent crystallization from its aqueous solution upon addition of ethanol.18 However, the antisolvent crystallization of cefodizime sodium, especially the nucleation mechanism, has been scarcely studied. In this article, we selected cefodizime sodium as the model substance and combined induction time measurements with in situ Raman spectroscopy to investigate the nucleation mechanism and the probability of hydrogen-bond formation in the process, as a means of gaining initial insight into the extent and nature of the intermolecular association during the nucleation process.
2. EXPERIMENTAL SECTION 2.1. Materials and Instrumentation. Cefodizime sodium was provided by Shandong Lukang Pharmaceutical Group Co., Ltd., with a purity of 99% in mass fraction. The ethanol used was analytical reagent grade. Distilled deionized water of highperformance liquid chromatography grade was used. Raman spectra were collected using a RamanRXN2 spectrometer (Kaiser Optical Systems, Inc.). 2.2. Induction-Time Measurements. Induction times were measured by a laser monitoring technique.19 The experimental apparatus consisted of four parts: reagent feeding system, crystallizer with temperature control, mixing system, and laser monitoring observation system (Figure 2). The laser
Figure 2. Experimental setup for induction-time measurements. Figure 3. Calibration curves between the concentration of cefodizime sodium and the peak areas at 1372 and 1397 cm−1.
monitoring system consisted of a laser generator, a photoelectric transformer, and a digital display of the receptor. The temperature of the crystallizer was maintained by circulating water through the outer jacket from a thermostat. The experimental procedure is described briefly below. Prior to use, all solutions were filtered through 0.45-μm membrane filters. A desired quantity (0.16 mol/L) of a solution of cefodizime sodium in ethanol + water was poured into the crystallizer and mixed with a stirrer (500 rpm). After the solution temperature became steady at a fixed value, a certain amount of ethanol was added as quickly as possible to the crystallizer with a pipet, and the timer was switched on at the same time. When the solution was clear and transparent, the laser light intensity reached its maximum, which was seen in the receptor of the laser monitoring system. A decrease of the light intensity detected by the receptor indicated the formation of solid particles. Therefore, the time elapsed between the addition of ethanol and the decay of the light intensity was defined as the induction time. However, it was not possible to
2.4. In Situ Raman Spectroscopy Experiments. The experimental procedure was similar to the induction-time measurements, including two parts: dissolution and nucleation. The experimental setup is shown in Figure 4. In the dissolution part, 100 mL of the binary solution (ethanol/water = 4/1) was poured into the crystallizer (250 mL) and mixed with a stirrer (500 rpm) at constant temperature 298.15 K. The probe of Raman was immersed in the binary solution to collect the background spectra. When the intensity reached stable state, the cefodizime sodium was slowly added into the solution as step addition of 0.5 or 1 g until the concentration reached 0.16 mol/L. At every step of the cefodizime sodium addition, the Raman spectra were collected after waiting for enough time to attain the equilibrium in the system. In nucleation part, a certain amount of ethanol was added into the crystallizer by a pipet as quickly as possible, and the solution was monitored by Raman at intervals of 5 s until some small solid particles can be 13664
dx.doi.org/10.1021/ie301557b | Ind. Eng. Chem. Res. 2012, 51, 13663−13669
Industrial & Engineering Chemistry Research
Article
Figure 4. Experimental setup for in situ Raman spectroscopy experiments.
observed visually. All the Raman spectra were interpreted by the multipeaks Lorentzian fitting,20 and the peak area can be used to calculate the probability of hydrogen-bond formation.
Figure 6. Induction time versus supersaturation at different temperatures.
3. RESULTS AND DISCUSSION 3.1. Study of the Nucleation Mechanism by Induction Time Measurements. The classical nucleation theory was applied to study the relationship between nucleation and induction time in crystallization, assuming that spherical nuclei were formed. However, in many cases, this assumption was not valid for the needlelike crystals of cefodizime sodium formed (see Figure 5). Therefore, classical nucleation theory should be
solution. As expected, the induction time of cefodizime sodium became independent of the supersaturation. As shown in Figure 6, the induction time continuously decreased with increasing supersaturation, and this decrease was particularly strong at high temperature. This behavior can also be explained from the point of view of hydrogen bonding; that is, the increase of supersaturation could induce a higher diffusivity and a higher collision frequency of clusters, thereby enhancing the probability of forming a hydrogen-bond framework between cefodizime sodium and ethanol. In accordance with classical nucleation theory and and observations reported in the literature, we also found that, over a range of supersaturation and temperature values, the value of ln tind was proportional to 1/(ln S)2, as follows21 ln t ind = K +
4fs 3 γ 3v 2 27fv 2 k3T 3(ln S)2
(2)
where K is a dimensionless empirical constant. According to classical nucleation theory (eq 2), the experimental data on induction time were plotted in the form of ln tind verus 1/(ln S)2 (see Figure 7), revealing two straight lines with different slopes. The straight line at high supersaturation represents that homogeneous nucleation is the most important mechanism under these conditions, and the other at low supersaturation indicates that heterogeneous nucleation dominates the nucleation process.21,24,25
Figure 5. Microscope images of cefodizime sodium particles in the nucleation step of antisolvent crystallization (×1000).
modified by surface and volume shape factors ( fs, f v) to accommodate needlelike crystals.21,22 The modified equation is given by ⎛ −4f 3 γ 3v 2 ⎞ s ⎟ J = A exp⎜⎜ 3 3 3 2⎟ ⎝ 27fv k T (ln S) ⎠
(1)
where J is the nucleation rate; A is the pre-exponential factor; k is the Boltzmann constant; T is the absolute temperature; γ is the interfacial tension of the solid in the solution; v is the molecular volume; and S is the supersaturation, which can be calculated from the concentration of solution and solubility of cefodizime sodium.23 The dependence of the induction time on the supersaturation at 278.15, 283.15, 288.15, and 293.15 K is shown in Figure 6. Plotting induction time versus supersaturation is useful for showing the metastability of the supersaturated
Figure 7. Plots of ln tind versus (ln S)−2 at different temperatures. 13665
dx.doi.org/10.1021/ie301557b | Ind. Eng. Chem. Res. 2012, 51, 13663−13669
Industrial & Engineering Chemistry Research
Article
compared with those of other compounds, such as dexamethasone sodium phosphate19 (3−7 mJ/m2), tolazamide21 (1.94− 2.80 mJ/m2), and asparagine26 (4.4 mJ/m2). The interfacial tension parameters of cefodizime sodium were smaller than those of other systems, indicating that the nucleation can be carried out very easily. The variation of temperature not only changed the fluid dynamics of the solution but also influenced the solubility of cefodizime sodium, which directly related to the supersaturation. Determining the morphology of cefodizime sodium by scanning electron microscopy (SEM) is a direct method for investigating the effect of supersaturation on crystal shape. From Figure 8, it can be seen that agglomerated small needlelike particles preferentially formed at high supersaturation, whereas large needlelike particles formed at low supersaturation. The aspect ratios were 13.3 (S = 4.43), 10.5 (S = 2.57), 6.9 (S = 1.83), and 3.1 (S = 1.37). This variable tendency of the aspect ratio can be explained by twodimensional kinetics according to which the crystal growth rate related to the supersauration is different. 3.2. In Situ Investigation of the Probability of Hydrogen-Bond Formation in the Nucleation Process. On comparing the Raman spectra of a solution of cefodizime sodium in ethanol + water with solid-state cefodizime sodium, differences in the characteristic peaks were observed. As can be seen in Figure 9, a red shift of −NH2 (from 1588 to 1580 cm−1) was found in the spectrum of cefodizime sodium solution, resulting from the formation of hydrogen bonds. The Raman spectrum of solid-state cefodizime sodium contained three C−O stretching bonds at 1658, 1555, and 1315 cm−1. However, the corresponding bands at 1658 and 1555 cm−1 were missing in the spectrum of cefodizime sodium solution, and the 1315 cm−1 band was replaced by a peak at 1304 cm−1 that was assigned to O−H of ethanol. This hint indicates that the C−O might form hydrogen bonds with the solvent. It should be pointed out that the carboxyl group signal (1397
Induction-time measurements are useful for determining the crystal−solution interfacial tension. Interfacial tension is an important characteristic parameter of homogeneous nucleation that is strongly dependent on the macromolecular arrangement of the supersaturated solution. The interfacial tensions at different solvent compositions and temperatures can be estimated from the slope of the straight-line plots of homogeneous nucleation according to the equation19 ⎛ 27αf 2 k3T 3 ⎞1/3 v ⎟⎟ γ = ⎜⎜ 3 2 4 f v ⎝ ⎠ s
(3)
where α = 4fs3γ3v2/(27f v2k3T3) is the slope of the straight lines of homogeneous nucleation. fs, f v, and v can be calculated from the information on cefodizime sodium in Table 1. Table 1. Basic Crystal Information on Cefodizime Sodium parameter molecular formula molar mass density crystal sizea characteristic dimension surface shape factor volume shape factor a
value C20H18N6Na2O7S4 M = 628.64 kg/mol ρs = 1.2830 × 103 kg/m3 length = 17.8 μm, width = 1.7 μm, thickness = 0.5 μm D = 1.7 μm fs = Sarea/d2 = 27.69 f v = V/d3 = 3.08
Estimated from scanning electron microscopy (SEM) images.
The interfacial tensions calculated by eq 3 were 0.597 mJ/m2 at 293.15 K, 0.628 mJ/m2 at 288.15 K, 0.739 mJ/m2 at 283.15 K, and 0.993 mJ/m2 at 278.15 K. Accordingly, the smaller the interfacial tension, the easier the homogeneous nucleation at a higher rate. The results for the interfacial tension parameter (0.597−0.993 mJ/m2) estimated using induction time were
Figure 8. Morphologies of cefodizime sodium at different supersaturations (T = 293.15 K). The aspect ratio is defined as the ratio of length to width. 13666
dx.doi.org/10.1021/ie301557b | Ind. Eng. Chem. Res. 2012, 51, 13663−13669
Industrial & Engineering Chemistry Research
Article
Figure 9. Comparison of Raman spectra between a solution of cefodizime sodium in ethanol + water and the solid state of cefodizime sodium.
cm−1) exhibited a significant difference. The intensity of the 1397 cm−1 band in solution was higher than that in the solid state. Aside from that at 1397 cm−1, the Raman shift at 1372 cm−1 increased obviously with a slight red shift. It seems reasonable to assume that the hydrogen bonding between cefodizime sodium and solvent has great complexity. On the basis of this evidence, we inferred that hydrogen bonds might exist in six-membered form, namely, the carboxylic group (−COO) of one cefodizime sodium molecule and the amino group (−NH2) of another cefodizime sodium molecule, combined simultaneously with the hydroxyl group (−OH) of ethanol to yield a six-membered hydrogen-bond framework (see Figure 10), corresponding to the peaks of the Raman spectra between 1340−1430 cm−1. These overlapping peaks appeared as an M shape (see Figure 11), and multipeak Lorentzian fitting was used to interpret the Raman spectra. In this case, the Raman shift at 1372 cm−1 was assigned to the characteristic peak of the six-membered hydrogen-bond framework, whereas that at 1397 cm−1 was assigned to the
Figure 11. Raman spectra of solutions with different concentrations and curve fitting using the Lorentzian model.
characteristic peak of the carboxylic group (−COO), which does not form a hydrogen-bond framework with ethanol. Based on this analysis, the percentage characteristic peak area was proposed to represent the probability of hydrogen-bond formation. Thus, the probability could be calculated quantitatively as probability =
S1 S1 + S2
(4) −1
where S1 is the area of the peak at 1372 cm and S2 is the area of the peak at 1397 cm−1. Given the probabilities of hydrogen-bond formation calculated from the Raman spectra (Figure 12), three regions were chosen for study, namely, regions I, II, and III, corresponding to dissolution, induction time, and crystal growth, respectively. In the dissolution region (region I), it is apparent that the probability profile of hydrogen bonding increased gradually in accordance with the concentration of cefodizime sodium solution and then reached a plateau corresponding to the saturated solution. This is an indication that the formation of hydrogen-bond frameworks would be enhanced at higher concentration. It should be mentioned that, during the period from saturation of the solution to supersaturation of the solution, the probability of hydrogen-bond formation changed slightly. Generally, the internal structures of the saturated and supersaturated solutions were different. However, supersaturation could provide an impetus to make the molecules form liquid aggregates. We considered that the process is the re-
Figure 10. Hydrogen-bond frameworks between cefodizime sodium and ethanol. 13667
dx.doi.org/10.1021/ie301557b | Ind. Eng. Chem. Res. 2012, 51, 13663−13669
Industrial & Engineering Chemistry Research
Article
preferentially formed at high supersaturation at a higher nucleation rate whereas large needlelike products formed at low supersaturation at a lower nucleation rate.
■
AUTHOR INFORMATION
Corresponding Author
*Tel.: 86-22-27405754. Fax: 86-22-27314971. E-mail: qxyin@ tju.edu.cn. Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (Nos. 20836005 and 21176173) and the Tianjin Municipal Natural Science Foundation (Nos. 10JCYBJC14200 and 11JCZDJC20700). The analysis tools used in this study were supported by the State Key Laboratory of Chemical Engineering (No. SKL-ChE-11B02).
Figure 12. Probability of hydrogen-bond formation during the crystallization of cefodizime sodium.
formation and reassignment of internal hydrogen bonds, so that the general energy changed only slightly. Region II covered range from the generation of supersaturation to the nucleation point, during which the probability of hydrogen-bond formation was observed to reach the highest point and small crystal particles appeared. Based on the above analysis, the cefodizime sodium and ethanol molecules can be induced to form macromolecular structures through hydrogen bonding. In other words, the probability of hydrogen-bond formation can reflect the change in the macromolecular structure of supersaturation. It can be inferred that, when the supersaturation is high, the probability of hydrogen-bond formation is large enough to overcome the resistance of phase transition and convert the liquid aggregate into crystal nuclei. From the microscopic standpoint, hydrogen bonds have a significant improving effect on homogeneous nucleation. This also indicates that the probability of hydrogen-bond formation is closely related to the induction time. Therefore, this region (region II) can be considered equivalent to the induction time. According to the principle of energy minimization, once the crystal nuclei are formed, the overall energy is lowered. The crystal nuclei have higher stability than liquid aggregates in solution, so that the probability of hydrogen-bond formation decreased gradually after the point of nucleation, which can be clearly observed from region III.
■
REFERENCES
(1) Peter, G. V. Nucleation. Cryst. Growth Des. 2010, 10, 5007−5019. (2) Browning, A. R.; Doherty, M. F.; Fredrickson, G. H. Nucleation and polymorph selection in a model colloidal fluid. Phys. Rev. E 2008, 77, 041604. (3) Abu Bakar, M. R.; Nagy, Z. K.; Saleemi, A. N.; Rielly, C. D. The impact of direct nucleation control on crystal size distribution in pharmaceutical crystallization processes. Cryst. Growth Des. 2009, 9, 1378−1384. (4) Mizev, A. I.; Schwabe, D. Flow suspended solution growthA new method. J. Cryst. Growth 2009, 311, 2443−2453. (5) Garside, J., Davey, R. J., Jones, A. G., Eds. Advances in Industrial Crystallization; Butterworth-Heinemann: Oxford, U.K., 1991. (6) Terech, P.; Furman, I.; Weiss, R. G. Structures of organogels based upon cholesteryl 4-(2-anthryloxy) butanoate, a highly efficient luminescing gelator: Neutron and X-ray small-angle scattering investigations. J. Phys. Chem. 1995, 99, 9558−9566. (7) Suzuki, M.; Nakajima, Y.; Yumoto, M.; Kimura, M.; Shirai, H.; Hanabusa, K. Effects of hydrogen bonding and van der Waals interactions on organogelation using designed low-molecular-weight gelators and gel formation at room temperature. Langmuir 2003, 19, 8622−8624. (8) Michael, A. R.; Alejandro, G. M. Solvent-modulated nucleation and crystallization kinetics of 12-hydroxystearic acid: A nonisothermal approach. Langmuir 2009, 25, 8556−8566. (9) Sanz, M. J.; Nogales, A.; Martiny, M. D.; Ezquerra, T. A. Hydrogen-Bond Network Breakage as a First Step to Isopropanol Crystallization. Phys. Rev. Lett. 2004, 93, 015503. (10) Djikaev, Y. S.; Ruckenstein, E. Effect of hydrogen bond networks on the nucleation mechanism of protein folding. Phys. Rev. E 2009, 80, 061918. (11) Erdemir, D.; Lee, A. Y.; Myerson, A. S. Nucleation of crystals from solution: Classical and two-step models. Acc. Chem. Res. 2009, 42, 621−629. (12) Amedeo, L.; Dino, M.; Marina, P. Measuring induction period for calcium sulfate dihydrate precipitation. AIChE J. 1999, 45, 390− 397. (13) Izmailov, A. F.; Myerson, A. S.; Arnold, S. A statistical understanding of nucleation. J. Cryst. Growth 1999, 196, 234−242. (14) Naoki, T.; Hiromi, K.; Norio, I. Raman spectroscopic study of hydrogen bonding in aqueous carboxylic acid solutions. J. Phys. Chem. 1990, 94, 6290−6292. (15) Beaudoin, J. L.; Eloundou, J. P. Raman spectroscopy of the hydrogen bond in crystallized normal and deuterated glycerol: Influence of the anharmonic multiphonon interactions on νOH, νOD, and γOH vibrations. J. Chem. Phys. 1979, 71, 47−53.
4. CONCLUSIONS The nucleation mechanism was determined from the induction time, indicating that heterogeneous nucleation dominates the nucleation process at lower supersaturation whereas homogeneous nucleation dominates at higher supersaturation. Moreover, the tendency of the crystal−solution interfacial tension demonstrated that the macromolecular arrangement of supersaturated solution can also be influenced by temperature. Furthermore, to describe the macromolecular arrangement of the supersaturated solution and nucleation, the probability of hydrogen-bond formation was proposed to investigate the role of hydrogen bonding in the nucleation process. Essentially, hydrogen bonding is influenced by supersaturation, and the probability of hydrogen-bond formation can be related to the nucleation rate. Therefore, the crystallization conditions (temperature, concentration) can be optimized from the viewpoint of both supersaturation and the probability of hydrogen-bond formation. According to SEM images, the results showed that agglomerated small needlelike products 13668
dx.doi.org/10.1021/ie301557b | Ind. Eng. Chem. Res. 2012, 51, 13663−13669
Industrial & Engineering Chemistry Research
Article
(16) Marunaka, T.; Matsushima, E.; Minami, Y. Acidic degradation of cefodizime (THR-221) and structural elucidation of the products. I. Chem. Pharm. Bull. 1989, 37, 367−372. (17) Bryskiera, T. P.; Labrob, M. T. Cefodizime, a new 2aminothiazolyl cephalosporin: Physicochemical properties, toxicology and structure-activity relationships. J. Antimicrob. Chemother. 1990, 26, 1−8. (18) Martin, W. Process for the preparation of cefodizime sodium. U.S. Patent 5,126,445, 1992. (19) Hao, H. X.; Wang, J. K.; Wang, Y. L. Determination of induction period and crystal growth mechanism of dexamethasone sodium phosphate in methanol−acetone system. J. Cryst. Growth 2005, 274, 545−549. (20) Bouhadda, Y.; Bormann, D.; Sheu, E.; Bendedouch, D.; Krallafa, A.; Daaou, M. Characterization of Algerian Hassi-Messaoud asphaltene structure using Raman spectrometry and X-ray diffraction. Fuel 2007, 86, 1855−1864. (21) Anuj, K.; Glen, S. K.; Zhang, G. G. Z. Determining the growth mechanism of tolazamide by induction time measurement. Cryst. Growth Des. 2007, 7, 234−242. (22) Mullin, J. W. Crystallization, 3rd ed.; Butterworth-Heinemann: Oxford, U.K., 2000. (23) Zhang, X. W.; Yin, Q. X.; Cui, P. L.; Liu, Z. K.; Gong, J. B. Correlation of solubilities of hydrophilic pharmaceuticals versus dielectric constants of binary solvents. Ind. Eng. Chem. Res. 2012, 51, 6933−6938. (24) Roger, A. G.; Christelle, D.; Sandra, G.; Rasmuson, A. C. Primary nucleation of paracetamol in acetone−water mixtures. Chem. Eng. Sci. 2001, 56, 2305−2313. (25) Zhang, Y. F.; Li, Y. H.; Zhang, Y. Supersolubility and induction of aluminosilicate nucleation from clear solution. J. Cryst. Growth 2003, 254, 156−163. (26) Mahajan, A. K.; Kirwan, D. J. Nucleation and growth kinetics of biochemicals measured at high supersaturations. J. Cryst. Growth 1994, 144, 281−290.
13669
dx.doi.org/10.1021/ie301557b | Ind. Eng. Chem. Res. 2012, 51, 13663−13669
