Examination of the Semi-Batch Crystallization of Benzophenone

CRYSTAL GROWTH & DESIGN

Examination of the Semi-Batch Crystallization of Benzophenone from Saturated Methanol Solution via Aqueous Antisolvent Drowning-Out as Monitored In-Process Using ATR FTIR Spectroscopy

2004 VOL. 4, NO. 5 1053-1060

A. Borissova,* Z. Dashova,† X. Lai, and K. J. Roberts Institute of Particle Science and Engineering, Department of Chemical Engineering, University of Leeds, Leeds, LS2 9JT, UK Received February 2, 2004

ABSTRACT: In-process ATR FTIR spectroscopy is used to measure concentration and supersaturation in drowningout of benzophenone from methanol/water solution and to study the effect of the rate of the aqueous antisolvent addition. A selected peak ratio in terms of IR transmittance or absorbance is monitored on-line and used to develop calibration equations for the concentration of the solute in the mixed solvent as a function of the ratio and the quantity of the antisolvent added. The benzophenone solubility in the mixed methanol/water solvent is found to be a nonlinear function of the respective solubilities of the solvents accounting not only for the dilution effect, but also for the binding of solvent molecules by the antisolvent molecules. 1. Introduction Drowning-out is routinely used as an alternative to cooling and evaporative crystallization processes for the isolation and separation of organic fine chemical processes such as pharmaceuticals due to its cost, energy efficiency, and sensitivity to operational conditions, such as antisolvent addition rate, stirring rate, ionic strength, etc. It is considered as one of the most important separation techniques, especially when separation of solutes from multicomponent solutions is required.1 Drowning-out is a reactive crystallization technique based upon the addition of specific substances (drowning-out antisolvents/salting-out agents/precipitants) to the initial solution, with the aim to reduce the solubility of the solute and hence create supersaturation. It can be characterized as a physical reaction as opposed to precipitation, which is usually based on a chemical reaction between two phases. The drowning-out agents can be solids, liquids (antisolvents), or gases. They must be soluble in the original solvent (gas or solid drowningout agents) or miscible with it (liquid drowning-out agents) and should not react with the solute to be precipitated. The drowning-out precipitation of highly water-soluble ionic solids, for example, is normally induced by adding organic antisolvents miscible in water, such as monovalent alcohols (methanol, ethanol), acetone, and some hydrocarbons.2-4 From all of these, methanol is the most commonly used antisolvent. The addition of salting-out agents has been found to be of great importance for the nucleation kinetics, the size, the distribution, and the morphology of the crystals.5-8 The correct choice of the drowning-out agent is essential. The precipitation by drowning-out is very sensitive to operational conditions, such as the rate of addition and the nature of the drowning-out agent, stirring rate, the geometry of the experimental setup, etc.2 * Communicating author: e-mail [email protected]. † Visiting student from the University of Chemical Technology and Metallurgy, Sofia, Bulgaria, funded under the European Union ERASMUS Programme.

This paper presents the results of a study in which the thermodynamics and the kinetics of the drowningout crystallization of benzophenone-methanol with water are investigated. An automated batch reactor system, equipped with a number of sensors (FTIR spectroscopy, turbidity, and temperature) was used to carry out in-process measurements of the supersaturation, solubility, and concentration of benzophenone in water/methanol solution. 2. Solubility in Mixed Solvent System for Drowning-Out Crystallization Process The supersaturation, as a driving force of the process of crystal formation, is a result of complex physicochemical interactions between solute, solvent, and antisolvent. It is usually expressed as a difference or a ratio between the concentration of the solution c and the solubility c*. Theoretically, crystallization should occur / , where when c gc*, i.e., in drowning-out cSAS g cSAS / cSAS and cSAS are the concentration and the solubility of the solute in the solvent/antisolvent (SAS) mixture. The on-set of the process varies, however, within a range, specific for the process conditions as represented by the metastable zone width (MSZW). The concentration (cSAS) of the solute in the mixed (solvent/antisolvent) solvent system can be represented by the following ratio:

cSAS )

c0S 1+R

(1)

where c0S is the initial concentration of the solute in the solvent, R is the ratio of the mass of the antisolvent MAS to the mass of the solvent MS, R ) MAS/MS. Assuming a linear dependence of the solubility in the / mixed solvent cSAS , on the solubilities in the solvent c/S and the antisolvent c/AS, such that

c/SAS) βc/AS + (1 - β)c/S

10.1021/cg049947t CCC: $27.50 © 2004 American Chemical Society Published on Web 09/01/2004

(2)

1054 Crystal Growth & Design, Vol. 4, No. 5, 2004

Borissova et al.

Figure 1. Experimental setup: (a) FTIR spectrometer mounted on an in-house made stand to enable exact insertion of the ATR immersion probe into the crystallizer; (b) 500-mL jacketed batch crystallizer housing an on-line ATR FTIR immersion probe, a turbidity probe, and a temperature probe.

where β is the mass fraction of the antisolvent in the solution, given by

β)

MAS R ) MS + MAS 1 + R

(3)

the following expression for the solubility in the antisolvent can be obtained:

c/AS e

c0S - c/S R

(4)

According to eq 4, the solubility in the antisolvent would have to be less than zero. The experience shows,2,8 however, that precipitation as a result of drowning-out occurs when saturated solutions are mixed with an antisolvent with low, but not zero, solubility of the solute. A linear relationship between these solubilities, represented by eq 2, reflects only the dilution effect of adding antisolvent to the solution, but not the effect of binding solvent molecules by the antisolvent molecules that leads to a decrease of the solubility of the solute in the mixed solvent and hence to a solid-phase separation. Thus, the linear relationship in eq 2 is clearly insufficient to explain the phenomenon, and it should be replaced by a nonlinear relationship to take account for the nonideal behavior. The use of liquid-liquid interaction parameters as developed for vapor-liquid equilibria is a possible approach. 3. Materials and Methods 3.1 Materials. The system chosen for these studies comprised of three compounds: benzophenone, methanol, and water (as a precipitating agent). Benzophenone (diphenyl ketone, C6H5COC6H5, minimum purity 99%) was obtained from Sigma-Aldrich, and methanol (methyl alcohol, minimum purity 99%, acidity < 0.004%) from P&R Laboratory Suppliers Ltd. 3.2 Solubility Studies. Physicochemical studies were carried out to determine the solubility of benzophenone in the

mixed solvent and the MSZW during cooling crystallization of benzophenone from methanol solution. Solubility studies of benzophenone in pure (methanol) and mixed (methanol/water) solvents were carried out in the temperature range 20-40 °C at 5 °C intervals. The solvent was placed in a water bath to provide temperature uniformity and was added in small quantities to the compound, usually 0.5 g or less. Homogeneity of the solution during the experiments was maintained by continuous stirring. The Van’t Hoff equation1,9-12,15 was used to determine the enthalpy and entropy of dissolution based on experimental data for the solubility of benzophenone:

ln x ) -

∆Hd ∆Sd + RT R

(5)

where x is the mole fraction of the solute in the solvent, T is the solution temperature (K), and ∆Hd and ∆Sd are the enthalpy and the entropy of dissolution. ∆Hd and ∆Sd can be found from the slope and intercept of the straight line plotting ln x versus T-1. 3.3 Batch Crystallization Experiments. 3.3.1 Experimental Setup. The crystallization experiments were carried out using a HEL Autolab reactor system (Figure 1) comprising a 500-mL jacketed glass reactor, a Julabo FP50-HD thermostated bath, a data interface board (A/D), and a PC running WinNT with WinISO process control software. Reactor stirring was provided using a pitched blade stainless steel stirrer rotating at a constant speed of 330 rpm. Temperature and turbidity of the solution and recrystallized slurry were measured using a platinum resistance thermometer (PT100) and an in-house built turbidometric fiber optic probe. The reduction in the light transmittance upon the presence of nuclei in the saturated solution was observed on an in-house built colorimeter. The antisolvent (water) was added using a feed dosing pump. The WinISO software included control and monitoring of process parameters, such as time, temperature, stirrer speed, feed rate, and the total amount of the antisolvent added. All control parameters can be modified during operation. In-process measurements of concentration were performed using a Dipper-210 ATR FTIR immersion probe equipped with a ZnSe conical internal reflection element manufactured by Axiom Analytical Incorporated, together with a Bomen WorkIR FTIR spectrometer connected to a PC equipped with Grams software (Galactic Industries Corporation). The IR light

Semi-Batch Crystallization of Benzophenone

Crystal Growth & Design, Vol. 4, No. 5, 2004 1055

penetrates only a fraction of the wavelength into the solution and thus is affected by the continuous phase only. Figure 1 shows the stand20 that was designed to house the FTIR spectrometer and allows easy insertion into the batch crystallizer. It can be vertically adjusted by a traverse mechanism and horizontally manoeuvred via wheels, which enables the ATR immersion probe to be inserted easily into one of the ports on the jacketed lid of the crystallizer. 3.3.2 Crystallization Process Protocol. To determine the basic nucleation parameters in the mixed solvent system, experiments to determine the MSZW during cooling crystallization of benzophenone from methanol and mixed (methanol/ water) solvents were also conducted. Each run consisted of five stages: (1) dissolution of benzophenone crystals in the solvent through increasing the reactor temperature to 30 °C; (2) maintaining constant temperature of 30 °C to achieve complete dissolution; (3) cooling using rates of 0.1, 0.25, 0.5, and 0.75 °C/min; (4) heating to 30 °C; (5) maintaining constant temperature at 30 °C. The nucleation kinetics were determined using the Nyvlt method:13,14

log b ) (m - 1) log

dc* + log kn + m log ∆tmax dt

(6)

where kn and n are kinetic constants of nucleation. The nucleation rate is calculated according to the equation J ) m kn ∆cm max, where ∆cmax is the maximum possible supersaturation. Plotting log b against log ∆tmax results in a straight line with slope equal to the order of nucleation, m. The nucleation constant kn can be evaluated from the intercept. Optical microscopy was employed to study the shape and size of the crystals produced. The analysis was carried out using an Olympus microscope linked to a JVC 3-CCD Color Video camera. The samples were examined under transmitted light at various magnifications. It was important to analyze the samples immediately after the completion of the experiment, as it proved difficult to observe single crystals after a certain period of time because of aggregation processes. 3.3.3 ATR FTIR Calibration and Supersaturation Determination. Concentration, solubility, and supersaturation in the system studied were determined using the methodology based on the application of ATR FTIR spectroscopy for in-process monitoring of concentration and supersaturation in crystallizing systems.16-20 The change in intensity (absorbance or transmittance) of the IR spectral peaks specific for the solute, solvent and antisolvent is proportional to their concentration in the solution (Lambert-Beer law). The calibration curves for concentration were developed using specific absorbance ratios linked with the characteristic peaks of the substance and solvent (solvents). The methodology was initially developed for monitoring cooling crystallization, and thus the calibration models were derived considering temperature as a controlling parameter of crystallization. In this work, the amount of antisolvent was the parameter used to control the process, and thus it was included in the calibration model instead of temperature. An appropriate equation for calculation of concentration c on the basis of the amount of the antisolvent (water) added W and the absorbance peak ratio R, was selected from exponential, linear, and power types: (i) exponential calibration model (absorbance obeying the Lambert-Beer Law in transmittance mode)

R ) (wW + x) exp{(yW + z)c}

(7)

(ii) linear calibration model (absorbance obeying the Lambert-Beer Law in absorption mode)

R ) (wW + x)c + (yW + z)

(8)

(iii) calibration power model (the Lambert-Beer Law is not applicable)

R ) (wW + x)c(yW + z)

(9)

The parameters of the above equations, w, x, y, z, were determined using experimental spectroscopic data of the ratio R, concentration c, and the amount of antisolvent (water) W. Two types of experiments were conducted to determine the constants of the calibration model: at a constant amount of water added and at a constant concentration of benzophenone. The data obtained, keeping the amount of water added constant, were used to determine the values of the overall constants: (wW + x) and (yW + z), i.e., each of the three models were determined in a simplified form: exponential R ) a1 exp{b1c}; linear R ) a2c + b2; power R ) a3cb3; a1, a2, and a3 are linked to (wW + x), and b1, b2, and b3 are linked to (yW + z), correspondingly. The values of w, x, y, and z were subsequently determined using the experimental values of the amount of water added and the calculated values of a constants for w and x, and the values of b constants for y and z. The calibration model was selected on the basis of the best prediction of the experimental data. In the setup, used in this study, up to eight wavenumbers (cm-1) within the spectral range of 4000-650 cm-1 can be chosen and the intensity of corresponding ATR FTIR peaks read into the reactor control software for utilization of quantitative analysis of the concentration of the solute. The ratio R, used in the methodology described above, was calculated on the basis of two peak heights (absorbances). Such a general presentation of ATR FTIR calibration relationships with respect to concentration and the possibility to select different types and parameters included in the calibration model, makes the system developed versatile and applicable to modeling concentration in different solute-solvent systems.

4. Results and Discussion 4.1 Solubility Studies for the Mixed Solvent System. The solubility of benzophenone in pure methanol at low temperatures is low (Figure 2, 0%H2O), but increases rapidly around 35 °C. The solubility curve was approximated with a polynomial curve, from which the equation for the solubility S (g of benzophenone in 1 g of pure methanol) can be determined:

S ) 0.0078T2 - 0.3179T + 3.5237

(10)

where T is the temperature (°C). The solubility of benzophenone in mixed solvent (methanol/water) as a function of temperature at different weight percent water (10, 20, and 30%) is given in Figure 2. The solubility decreases with increasing the amount of water due to the low solubility of benzophenone in water. The solubility curves of benzophenone in the mixed solvent exhibit a nonlinear character and can be approximated with power or polynomial curves. For 20 wt % H2O, the temperature dependence of the solubility in the mixed solvent can be represented as:

S ) 0.0005T2 - 0.017T + 0.217

(11)

where T is the temperature (°C). The experimentally obtained values were plotted in the form of the natural logarithm of the mole fraction as a function of the inverse of the temperature (Figure 2b). Hence, applying Van’t Hoff’s equation, the enthalpy and entropy of dissolution were determined (Table 1). The values for the enthalpies and entropies calculated applying Van’t Hoff’s equation do not show any consistent change with changing the composition of the mixed solvent (Table 1). The same is demonstrated by the different slopes of the solubility diagrams of the mixed solvents presented in logarithmic scale (Figure 2b). A likely explanation of this might be found in the deviation


Borissova et al.

Figure 2. Solubility of benzophenone in mixed solvent: (a) temperature dependence, (b) Van’t Hoff plot. The solubility of benzophenone is plotted as the natural logarithm of the mole fraction vs the inverse temperature. The linear nature of this plot allows the calculation of the entropy and enthalpy of dissolution (Table 1). Table 1. Data for the Enthalpies and Entropies of Dissolution in the Case of Pure Methanol and in the Case of Mixed Solvent water, wt %

∆Hd, kJ/mol × 10-3

∆Sd, J/mol × 10-3

0 10 20 30

-95.6 -111.6 -59.3 -85.7

-299 -348 -164 -243

of solutions in a mixed solvent from that expected for an ideal solution, in which case the Van’t Hoff equation would be not applicable.1 An equation for the solubility of benzophenone in the mixed solvent (water/methanol) as function of the water added was derived in the form:

S ) (0.066T - 0.98)e(-0.0017T-0.052)W

(12)

W is the amount of water added (in wt %). The exponential form of the solubility function showed the best fit to the experimental data. 4.2 Determination of Metastable Zone Width and Nucleation Kinetics. Temperature and turbidity profiles of cooling crystallization runs in the cases of pure methanol (Figure 3a, concentration 33 wt % benzophenone) and mixed solvent (Figure 3b, concentration 6.376 wt % benzophenone in mixed solvent (20 wt % water) were obtained. After 160 min from the start of the experiment (Figure 3a) nucleation took place and the turbidity decreased as a result of crystal formation. Another effect observed during the cooling was the slight temperature increase, represented by the small peak, seen in the plot around 160 min for crystallization from pure methanol (Figure 3a) and 620 min for crystallization from mixed solvent-20% water, (Figure 3b). It was due to the release of the heat of crystallization. The intensity of the thermal peak, the heat release,

Figure 3. Change of temperature and turbidity during temperature-induced crystallization as a function of time: (a) concentration 33 wt % benzophenone in pure methanol; cooling/heating rate 0.25 °C/min; (b) concentration 6.4 wt % benzophenone in mixed solvent (20 wt % water); cooling/ heating rate 0.25 °C/min. Note the larger enthalpy of crystallization (A) for the pure solvent system.

correspondingly, is much higher in the case of crystallization from pure methanol compared to the intensity of the peak when crystallization occurs from mixed solvent. It was found that the MSZW for pure methanol solutions was 3.6 °C (Figure 4a) while for mixed


Figure 4. Crystallization and dissolution temperatures for different cooling rates: (a) concentration 33 wt % benzophenone in pure methanol; (b) concentration 6.4 wt % benzophenone in mixed solvent (20 wt % water: 80 wt % methanol).

methanol/water solutions was 6.1 °C (Figure 4b). This increase in MSZW implies a bigger nucleation barrier to growth that perhaps reflects the impact water/ methanol interactions in the mixed solvent has on the hydrophobic solvation of benzophenone by methanol. According to the Nyvlt method,9-14 plotting log of cooling rates against log of the maximum possible supercooling should result in a straight line with a slope equal to the order of nucleation (Figure 5a,b). The crystallization experiments of 33 wt % benzophenone in methanol solution and of 6.4 wt % benzophenone in methanol/water solution were carried out using four different cooling rates (0.1, 0.25, 0.5, 0.75 °C/min) and recording the respective crystallization temperature, Tcryst. The following values for the order of nucleation n were obtained: crystallization from pure methanol, n ) 2.41, mixed solvent n ) 3.27. Given the errors involved, significant analysis of this variation should not be made.


4.3 ATR FTIR Calibration for Mixed Solvent System. The calibration procedure described above was applied for in-process monitoring of the concentration of benzophenone in the mixed solvent (methanol/water). ATR FTIR spectra of benzophenone in methanol/ water solution were taken at a constant temperature of 20 °C and different amount of the antisolvent (water) added (0-40 mass %) (Figure 6). Pachler et al.21 lists eight specific peaks: for methanol: peaks at 2942 and 2832 cm-1, for benzophenone at 1281, 1323, 1594, 1653 cm-1, and for water at 1630 and 3300 cm-1. Some of the benzophenone peaks (e.g., at 1653 cm-1) overlapped with other peaks (methanol, water, or impurities in the solution). Thus, the peaks with the strongest intensities for methanol and benzophenone were selected for the current studies (methanol at 2942 cm-1 and benzophenone at 1281 cm-1). The peak ratio R used in the calibration model was calculated on the basis of these two peak intensities. A selected peak ratio in terms of absorbance (RA) was monitored on-line and used to develop calibration equations for the concentration c of the solute in the mixed solvent as a function of the ratio and the quantity of the antisolvent (water) added W. The calibration results are shown in Figure 7 and Table 2. The best prediction was obtained with the exponential type of the calibration model. The model developed, including the absorbance peak ratio RA, the concentration of benzophenone c, and the amount of water added W, was represented as

RA ) (-0.0204W + 4.3981)c(0.0008W - 0.3356) (13) The model was applied for ATR FTIR on-line determinations of supersaturation, solubility, and concentration during drowning-out crystallization. 4.4 Drowning-Out Crystallization Experiments. Drowning-out experiments were conducted using different rates of addition of the antisolvent (water): 0.1, 0.2, 0.3, 0.4, and 1 g/min. The rate of addition was found to have a strong influence on the nucleation kinetics and changes in the CSD and morphologies of crystals. The concentration of benzophenone in the mixed solvent (water/methanol) during the drowning-out was calculated using the eq 13. Figure 8 showed the results with

Figure 5. The cooling rates plotted as a function of the maximum possible supercooling of the system in the cases of pure methanol and mixed solvent (20 wt % water, 80 wt % methanol). The linear nature of this plot allows the calculation of the order of nucleation. The error bars shown correspond to a deviation of (0.1 °C/min.


Borissova et al.

Figure 6. Spectral data for benzophenone solutions in mixed solvent (20 wt % water, 80 wt % methanol): (a) ATR FTIR spectra of benzophenone in methanol/water solution at 20 °C; (b) enlargement of the spectral part in the range 1260-1300 cm-1. The arrow indicates the change in peak intensity with increasing the amount of the water in the solution. Table 2. ATR FTIR Calibration (Absorbance) Data for Benzophenone in Mixed Solvent: Water-Methanol at Five Different Weight Percent Water and Constant Temperature (20 °C) weight percent water, wt % 0

10

Figure 7. RA calibration curves for benzophenone as a function of concentration of benzophenone in water-methanol solution at constant temperature (20 °C).

20

addition rate 0.3 g/min. The water addition started at 65 min, and after 150 min there was only very slight effect on the concentration, i.e., considering water addition rate of 0.3 g/min, 25.5 g of water was added before the drowning-out practically stopped. With increasing the amount of water added, the concentration decreased from 20.65 g/100 g pure methanol (initial concentration of benzophenone in methanol) to 14.02 g/100 g mixed solvent (final concentration of benzophenone in the mixed solvent). The starting quantity of solvent (methanol) was 300 g and the amount of benzophenone was 61.95 g. Then the amount of benzophenone remaining in the solution was 45.63 g and the precipitate was 16.32 g, giving a yield of 26.6%. The addition of extra water beyond this would be counterproductive as it would reduce the yield due to the dilution effect. A slight temperature increase was observed during the drowning-out experiment at 20.3 °C; this was due to the release of the heat of crystallization. It also marked the onset of crystallization of benzophenone at 20.3 °C and when 4.64 g of water had been added.

30

40

RA

conc of benzophenone, g/100 g mixed solvent

4.321 4.233 3.186 1.895 4.139 4.087 3.089 1.866 4.026 3.907 2.992 1.832 3.86 3.776 2.939 1.796 3.672 3.623 2.839 1.747

0.8428 1.264 3.793 9.692 0.8087 1.213 3.639 9.3 0.7773 1.166 3.498 8.939 0.7482 1.122 3.367 8.605 0.7212 1.082 3.246 8.294

approximation with exponential equation RA ) 4.6775e-0.0941c R2 ) 0.9974 RA ) 4.4856e-0.0952c R2 ) 0.9969 RA ) 4.3159e-0.0968c R2 ) 0.9974 RA ) 4.1602.e-0.0982c R2 ) 0.9987 RA ) 3.971e-0.0994c R2 ) 0.9987

The shape and size of the benzophenone crystals, as determined via optical microscopy for samples produced at various antisolvent addition rates is given in Figure 9. The analysis revealed that drowning-out crystallization of benzophenone from methanol solution resulted in the formation of prismatic crystals. This shape is that most commonly observed for benzophenone crystals.22 From the optical micrographs, it was also evident that increasing the rate of addition of water resulted in the formation of smaller crystals. The most probable explanation of this fact was that the addition of increasing amounts of water introduced more potential sites for heterogeneous nucleation, which led to the formation of smaller crystals. However, it should also be noted that crystal size is also dependent on temperature, i.e.,



line determinations of concentration, supersaturation, and solubility of benzophenone in methanol/water solution, using a mathematical model derived from spectral data. No advantage was found in adding more antisolvent after a certain moment during the process as this merely reduces the yield due to the dilution effect. Optical microscopy observations revealed that crystal size decreased when increasing the rate of addition of water.

Figure 8. Concentration, temperature, and total amount of water added during drowning-out experiment at a rate of 0.3 g/min water.

Acknowledgment. We are grateful to the EPSRC through Research Grant GR/N/20300 and associated industrial sponsors for their support of the in-process batch engineering laboratory at Leeds. One of us (A.B.) is grateful to the EPSRC for the financial support, while Z.D. gratefully acknowledges the support of the European Union ERASMUS academic exchange programme. Nomenclature c c* cSAS / cSAS

c0S J

Figure 9. Optical micrographs of prismatic benzophenone crystals produced by drowning-out at a rate of (a) 0.3 g/min water, average crystal size 550 µm; (b) 0.4 g/min water, average crystal size 460 µm; (c) 0.5 g/min water, average crystal size 350 µm; (d) 1 g/min water, average crystal size 250 mm.

cooling rate. Hence, if a large gradient between the temperatures of the initial solution and the added water existed, smaller crystals would be expected to form. 5. Conclusions Drowning-out as an alternative to cooling crystallization has been studied on the basis of the drowning-out of benzophenone from methanol/water solution. A mathematical model of the solubility of the solute in the mixed solvent has been developed on the basis of the mass balance of the system solute-solvent-antisolvent. It was shown that the solubility of the substance in the mixed solvent was not a linear function of its solubilities in the solvent and the antisolvent but a more complex nonlinear function accounting not only for the dilution effect but also for the binding of solvent molecules by the antisolvent molecules. A nonlinear solubility of the solute in the mixed solvent is also a necessary condition for drowning-out. The solubility of benzophenone in the methanol/water solution was experimentally determined as a function of the weight percent of water antisolvent. ATR FTIR spectroscopy was applied to on-

kn b MAS MS T x R ∆cmax ∆Hd ∆Sd

concentration of the solution, mass/mole units per unit volume solubility of the solute in the solvent, mass/mole units per unit volume concentration of the solute in the solventantisolvent mixture, mass/mole units per unit volume solubility of the solute in the solvent-antisolvent mixture, mass/mole units per unit volume initial concentration of the solute in the solvent, mass/mole units per unit volume rate of nucleation, number of crystals per unit volume per unit time kinetic constant of nucleation kinetic constant of nucleation mass of antisolvent mass of solvent solution temperature (K) mole fraction of the solute in the solvent mass ratio antisolvent /solvent; maximum possible supersaturation ∆c ) c - c* enthalpy of dissolution entropy of dissolution

References (1) Mullin, J. W. In Crystallisation, 4th ed.; Butterworth Heinemann: Woburn, MA, 2001. (2) Pina, C. M.; Fernandez-Diaz, L.; Prieto, M.; VeintemillasVerdaguer S. J. Cryst. Growth 2001, 222, 317. (3) Alfassi, Z. B.; Mosseri, S. AIChE J. 1984, 30, 874. (4) Jones A. G.; Budz J.; Mullin J. W J. Chem. Eng. Sci. 1987, 42, 619. (5) Horst, J. H.; Geertman, R. M.; Van der Heijden, A. E.; Rosmalen, G. M. J. Cryst. Growth 1999, 198/199, 773. (6) Horst, J. H.; Geertman, R. M.; Rosmalen, G. M. J. Cryst. Growth 2001, 230, 277. (7) Jansens, P. J.; Langen, Y. H. M.; Van der Berg, E. P. G.; Geertman, R. M. J. Cryst. Growth 1995, 155, 126. (8) Holmback, X.; Rasmuson, A. C. J. Cryst. Growth 1999, 198/ 199, 780. (9) Gerson, A. R.; Roberts, K. J.; Sherwood, J. N. Powder Technol. 1991, 65, 243-249. (10) Van Gelder, R. N. M.; Roberts, K. J.; Chambers, J.; Instone, T.; J. Cryst. Growth 1996, 166, 189-194. (11) Taggart, A. M.; Voogt, F.; Clydesdale, G.; Roberts, K. J. Langmuir 1996, 12, 5722-5728. (12) Liang, J.; White, G.; Wilkinson, D.; Roberts, K. J.; Ford, L. F.; Wood, W. M. L. Cryst. Growth Des. 2004,4, 1039. (13) Nyvlt, J. In Industrial Crystallisation from Solutions; Butterworths: London 1971. (14) Nyvlt, J.; Sohnel, O.; Matuchova, M.; Broul, M. In The Kinetics of Industrial Crystallisation; Academia Praha and Elsevier: New York, 1985.

1060 Crystal Growth & Design, Vol. 4, No. 5, 2004 (15) Mac Sweeney, S., Ph.D. Thesis, Heriot-Watt University, Scotland, 1999. (16) Groen, H., Ph.D. Thesis, Heriot-Watt University, Scotland, 2001. (17) Groen, H.; Borissova A.; Roberts K. J. Ind. Eng. Chem. Res. 2003, 42, 198. (18) Groen, H.; Roberts K. J. J Phys. Chem. 2001, 105, 1072310730. (19) Groen, H.; Roberts K. J. Cryst. Growth Des. 2004, 4, 929.

Borissova et al. (20) Groen, H.; Mougin P.; Thomas A.; White G.; Wilkinson D.; Hammond R. B.; Lai X.; Roberts K. J. Ind. Eng. Chem. Res. 2003, 42, 4888-4898. (21) Pachler, Klaus G. R. In Merck FT-IR Atlas; Weinheim; Cambridge: VCH, 1988. (22) Doherty, R., Ph.D. Thesis, Strathclyde University, Scotland, 1989.

CG049947T

Examination of the Semi-Batch Crystallization of Benzophenone

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