Crystal Growth Kinetics via Isothermal Seeded Batch Crystallization

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Ind. Eng. Chem. Res. 2005, 44, 1012-1020

Crystal Growth Kinetics via Isothermal Seeded Batch Crystallization: Evaluation of Measurement Techniques and Application to Mandelic Acid in Water Anett Perlberg,* Heike Lorenz, and Andreas Seidel-Morgenstern Max-Planck-Institut fu¨ r Dynamik komplexer technischer Systeme, Sandtorstrasse 1, 39106 Magdeburg, Germany

Measurements of crystal growth kinetics are often performed by isothermal seeded batch experiments. On the basis of measurements for the chiral system mandelic acid/water, this work deals with (a) the experimental evaluation of different analytical techniques to determine simultaneously the solute concentration in the liquid phase and crystal-size-related data and (b) their application to isothermal seeded batch experiments. Calibrations of the applied measurement techniques and the accuracy obtainable are depicted. Metastable zone width measurements are presented, establishing a basis for growth kinetics investigations via isothermal seeded batch experiments. The applicability of the analytical techniques for monitoring isothermal seeded batch experiments is assessed by evaluating measurement results obtained under various experimental conditions. General tendencies with regards to the crystal growth of mandelic acid in water are discussed. 1. Introduction Crystallization is one of the most important separation and purification processes for the pharmaceutical and chemical industry. Besides the knowledge of the underlying thermodynamic equilibria, a quantitative understanding of crystallization kinetics (nucleation and growth) is important for the design and optimization of crystallizers.1-5 In this context, the isothermal seeded batch technique (later called the isothermal growth technique or experiment) is an approved laboratory-scale method for the determination of crystal growth rates.4 The measured data deliver a relationship between the crystal growth rate and supersaturation averaged with regard to a larger crystal population. The resulting kinetic parameters obtained under conditions similar to those of industrial situations provide useful information for crystallizer design and enable the determination of the overall mass-transfer rates in a controlled environment.1 Unfortunately, the successful design and performance of such isothermal growth experiments is difficult because of (a) a lack of information on the properties of the crystallizing system (solubility and metastable zone width data particularly for specialty chemicals and pharmaceuticals) and/or (b) the limited availability and/ or accuracy of measurement techniques. Concerning point (a), some assumptions have to be made, e.g., with regard to the exemption of nucleation and the negligence of attrition or breakage, which could overlay and influence the growth process. Recent publications6,7 suggest a theoretical prediction of metastable zone widths based on kinetic parameters (orders of nucleation, growth rate constants, and diffusion coefficients) and the size of detectable nuclei. However, the available models currently do not take into account * To whom correspondence should be addressed. Tel.: (0049) 391 6110 281. Fax: (0049) 391 6110 546. E-mail: perlberg@ mpi-magdeburg.mpg.de.

temperature-dependent changes of the solution density and/or solute and solvent activity coefficients. On the other hand, the parameters necessary for calculation are also not always available or the object of the experiment itself and must be determined carefully. A comparison between the experimental and calculated data shows that only an estimation of the order of magnitude with regard to the width of the metastable region is achievable up to now.7,8 Attrition and breakage are influenced by the hydrodynamic conditions in the reactor and the physical properties of the crystals (hardness, solid density, etc.). By measurement of only solution-related changes or the changing crystal mass, these processes are not detectable. Only the determination of the changing crystal size distribution or at least of a median crystal size will indicate the occurrence of attrition fragments or broken crystals. Growth rate dispersion9,10 and size-dependent growth11,12 are other complex issues affecting the results. Concerning point (b), a literature review reveals several experimental techniques for monitoring the crystal growth process by directly measuring the solidphase properties (e.g., crystal size and/or mass) or indirectly measuring the concentration changes in the solution, thermal responses, or transients of other system properties under different hydrodynamic conditions. An applicability study and a comparison of different inline particle size measurement techniques for monitoring crystallization were performed, e.g., by Abbas et al.18 The solute concentration was determined by online densitometry,4 inline refractometry,13 or inline ultrasonic sensors.15 Mohan et al.14 determined growth kinetics by measuring the crystallization heat with differential scanning calorimetry. Besides, combinations of different methods for simultaneous measurements of both solid- and solutionspecific data have also already been applied. Monnier et al.16 combined calorimetric heat effect measurements with an inline crystal size distribution determination.

10.1021/ie040127n CCC: $30.25 © 2005 American Chemical Society Published on Web 01/19/2005

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Sessiecq et al.17 simultaneously applied inline turbidimetry and inline electrical conductometry. Granberg et al.19 monitored crystallization offline by a gravimetric analysis of the solution concentration and electrosensing zone measurements of the crystal size distribution. In using offline methods, usually a fast solid-liquid separation is crucial to “freeze” the present state of the liquid and solid phases. Once the two phases are properly separated, one of the many classical analytical methods can be applied (e.g., laser diffraction, microscopy, chromatography, etc.). As this short and incomplete survey reveals, various very different measurement techniques were applied either as single methods or in combination. A general observation is that frequently the fulfillment of the overall mass balance could not be or was not checked thoroughly by considering results obtained simultaneously for the liquid and solid phases. This study is concerned with the experimental application and assessment of different in-, on-, and offline measurement techniques to determine kinetic data considering mandelic acid in water as a compound-forming chiral model system. First, the applied measurement techniques and their calibration are presented. Then, the results of the metastable zone width measurements are shown. The applicability of the presented analytical techniques for monitoring isothermal growth experiments is evaluated based on seven selected experiments. Finally, general requirements for a successful application of the isothermal growth technique are discussed, and first results with regard to the specific growth behavior of mandelic acid crystals in water are given. 2. Experimental Section 2.1. Chemical System. Experiments were performed to study crystal growth on the example of mandelic acid (purity > 99%; Merck KGaA, Darmstadt, Germany) in deionized water. Mandelic acid represents an organic chiral substance from the fine chemical and pharmaceutical background and belongs to the large group of chiral systems forming a racemic compound in the solid state. Detailed solubility data in water were previously published by Lorenz et al.20 In the experimental part, the pure (S)-enantiomer, the racemic mixture, and nonracemic mixtures of both enantiomers in water were used. 2.2. Analytical Techniques. Concentration. The total solute concentration of mandelic acid was determined by an ultrasonic probe (LiquiSonic probe; SensoTech GmbH, Magdeburg-Barleben, Germany). It measures the ultrasound velocity and the temperature of the solution in the reactor and has a working frequence of 1.5 MHz. Because of the resulting low power input, cavitation effects in the solution can be neglected. The probe has to be calibrated regarding the solute concentration. For this reason, the ultrasound velocity in the system mandelic acid/water was determined in a temperature range between 15 and 45 °C. Concentration ranges from 0 to 51.33 wt % for the racemate and from 0 to 22.56 wt % for the pure (S)-enantiomer were covered. All calibration data were measured in a crystalfree solution. To keep solid material from entering the measurement zone, the probe was jacketed by a polypropylene screen cloth of 200-µm mesh size. The mesh size of this screen cloth has to be taken into account when choosing the seed crystal size fraction for the isothermal growth experiments.

Figure 1. Experimental setup with the ultrasonic probe and online polarimeter.

The optical rotation of the solution was measured using an online polarimeter (Polarmonitor; IBZ Messtechnik, Hannover, Germany). A crystal-free solution was taken continuously, heated to 40 °C during the transport to the polarimeter, and placed in the measurement cell (optical path length, 6 mm; measurement temperature, 40 °C). After measurement, the solution was pumped back into the reactor (volumetric flow rate, 5.9 mL/min; total time between filter frit and re-entrance into the reactor, 2 min). A scheme of the experimental setup including the ultrasonic probe and the online polarimeter is given in Figure 1. The determination of the total solute concentration by measuring the optical rotation can only be done in solutions of a single enantiomer. If both enantiomers are present, the optical rotation provides the difference of the weight fractions of the enantiomers in the solution. By application of a further measurement technique for the determination of the total solute concentration (e.g., the ultrasonic probe, density or refractive index measurements), the enantiomeric excess (ee) can be calculated from both signals.21 Furthermore, offline concentration determination was performed by sampling using a sampling tube filled with glass wool and subsequent density measurements (Density Meter DE40; Mettler-Toledo, Giessen, Germany) or measurements of the refractive index (Refractometer RE40; Mettler-Toledo, Giessen, Germany) of the crystalfree solution. Particle Size. The monitoring of particle size and particle number changes was performed using a FBRM probe (D600L; Lasentec, Redmond, WA). The measurement principle of focused beam reflectance gives primarily a specific chord-length distribution as a function of the particle size, shape, refractive indices, and other operating conditions. These complex relationships are not completely understood up to now; therefore, the results cannot always be transferred accurately into a particle size distribution. A detailed elaboration of these aspects can be found, e.g., in work by Ruf et al.22 and Mahoney et al.23 A measurement range of 1-1000 µm divided into 100 size classes and a measurement duration of 5 s were chosen in the measurement settings for the FBRM probe. In a first rough approach, only the cube-weighted median of the chord-length distribution [later called the FBRM median (µm)] and the overall number of counted chord lengths per second [later called the FBRM count number (no./s)] were used for measurement and evaluation.

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Table 1. Experimental Parameters of the Isothermal Growth Experiments* experiment no. initial total solute concentration (wt %) total solute concentration in equilibrium (wt %) ee0 ee of seed crystals size of seed crystals (µm) portion of seeds in the final solid phase (wt %) ϑgrowth (°C) ∆T0 (K) ∆Tmax (K)f

1a-c

2a-c

3a,c-e

4c-e

5a,c-e

6a,c,e

7a-c,e

8.96 8.31 1.00 1.00 300-355 ≈4 20 1 4.8g

9.34 8.33 1.00 1.00 300-355 ≈5 20 2 4.8g

20.78 17.15 0.00 0.00 300-355 ≈6 25 2 2.9h

42.73 36.71 0.00 0.00 250-355 ≈58 35 2 2.9h

18.04 16.07 0.60 1.00 300-355 ≈4 25 2 4.0g/5.0i

17.38 15.72 1.00 1.00 300-355 ≈7 35 1 2.1g/4.3i

15.15 14.43 0.49 1.00 300-355 ≈7 20 1 4.8g/5.2i

*Measurement techniques and data used: (a) ultrasonic probe; (b) online polarimeter; (c) microscopy; (d) FBRM probe; (e) offline density and/or refractometry; (f) see Figure 6 (partially interpolated); (g) pure enantiomer solution ee0 ) 1.00; (h) racemic solution ee0 ) 0.00; (i) solution of eutectic mixture ee0 ) 0.38.

Figure 2. Microscopic images and mass density distribution q3,log of seed crystal fractions of size 300-355 µm: (A) (S)-mandelic acid; (B) racemic mandelic acid.

Offline particle size characterization was done additionally by microscopy and laser diffraction (Granulometer 1180 LD; Cilas, Orleans, France). The crystalcontaining samples were filtered, and the crystals were washed with ice water and dried. Dry crystalline samples were dispersed in a saturated solution of mandelic acid in water at a constant temperature and measured by laser diffraction in wet dispersion mode. 2.3. Metastable Zone Width. The metastable zone width with regard to secondary nucleation was measured at different temperatures and ee’s of mandelic acid in an aqueous solution in a 0.5-L reactor according to the polythermal method proposed, e.g., by Nyvlt et al.1 The maximum achievable subcooling ∆T was measured at different cooling rates and extrapolated linearly to cooling rate “zero” to obtain ∆Tmax. For solutions of pure (S)-mandelic acid (ee ) 1.00) and the eutectic mixture [ee ) 0.38, excess of (S)-mandelic acid],20 in water pure (S)-mandelic acid crystals of >1 mm were used as the seed material. Racemic mandelic acid crystals of >1 mm were used in the case of a racemic solution (ee ) 0.00). Nucleation points were detected simultaneously in the same reactor (a) acoustically by the ultrasonic probe and (b) optically by a turbidity probe as the reference (QRSystem; BASF AG, Ludwigshafen, Germany). 2.4. Characterization of Seed Crystals. Seed crystals of mandelic acid for the isothermal growth experiments were produced by sieving (mesh sizes of 250, 300, and 355 µm). The crystal fractions obtained were studied by laser diffraction and microscopy. Seed characteristics are shown in Figure 2 for the 300-355µm sieve fraction of racemic and enantiomerically pure mandelic acid. The nonuniform rounded crystal shape is evident. It is caused essentially by irregular abrasion during the sieving process.

2.5. Isothermal Growth Experiments. Isothermal growth experiments with mandelic acid were carried out in two different double-walled thermostated glass reactors of 0.5- and 2-L volume. The temperature of the crystallizing system was measured in the reactor using a Pt-100. Agitation was performed with a magnetic stirrer in the small reactor and a three-bladed marine propeller in the 2-L vessel. Solutions were prepared directly in the reactor at a temperature of 5 K above the current saturation temperature ϑsat (°C). After complete dissolution, they were rapidly cooled (technically limited cooling rate, 30 K/h) to the desired growth temperature ϑgrowth (°C), and crystals of defined mass and size were added. Experiments were conducted with mandelic acid at three growth temperatures with varying ee with regard to (S)-mandelic acid in the initial solution ee0, seed characteristics (ee, size, and mass), and initial subcooling ∆T0 (K) according to eq 1.

∆T0 ) ϑsat - ϑgrowth

(1)

Table 1 summarizes the conditions for the seven experiments discussed below. Additionally, the different analytical techniques applied are indicated. The initial subcooling ∆T0 applied in order to establish an initial supersaturation was chosen with respect to the preliminarily determined metastable zone width data ∆Tmax (see section 3.2). The initial and expected final solute concentrations were calculated based on the known ternary solubility data.20 3. Results and Discussion 3.1. Calibration of Measurement Techniques. Ultrasonic Probe. Figure 3 illustrates the measured relationship between the total solution concentration c, solution temperature ϑ, and ultrasound velocity ν for mandelic acid in water. Generally, the ultrasound velocity increases with concentration in the studied concentration range. However, the influence of temperature on the ultrasound velocity is not trivial in the observed temperature interval. In the lower concentration range up to 30 wt %, the ultrasound velocity increases with increasing temperature. Above this concentration range, the relationship between v and ϑ seems to change into a reverse proportionality. This behavior is typical for water and aqueous solutions. It is attributed to the nonlinear dependence of the solution density F and adiabatic compressibility βad on the temperature in these systems and the relationship of the ultrasound velocity to these two parameters according to eq 2 (Wood equation).24,25 Both the solution


Figure 3. Experimentally determined three-dimensional data field describing the relationship between the solution temperature, total solution concentration, and ultrasound velocity for the system mandelic acid/water (13 341 data points).

Figure 4. Ultrasound velocity vs temperature, a comparison between racemate and enantiomer for two different concentrations.

Figure 5. Functional relationship between the total concentration and optical rotation of the solution for mandelic acid (pure enantiomer) in water at 40 °C (Pearson coefficient of correlation: r ) 0.9996).

density and adiabatic compressibility, furthermore, depend on the solute concentration in an aqueous solution.

v ) 1/xFβad

(2)

Empirical calibration polynomials of higher order were used to fit the gathered data. The calibration polynomials used provided an average accuracy of (0.2 wt % with regard to the calculated concentrations. As Figure 4 illustrates, no difference was found between the enantiomerically pure and racemic solutions. Polarimeter. The obtained calibration data with regard to the relationship between the optical rotation and solution concentration at 40 °C for the pure (S)mandelic acid enantiomer in water are depicted in Figure 5. Obviously, the optical rotation depends lin-

Figure 6. Experimentally determined metastable zone width in the presence of crystals in the system mandelic acid/water depicted as ∆Tmax with regards to the initial solution saturation data (solubility) for varying ee in the solution (lines are just guides to the eyes).

early on the concentration in the analyzed concentration range. For the system studied, an average error of (0.2 wt % was estimated from multiple determinations of samples from the same solution. Density and Refractometry. The calibration of both measurement techniques was performed over a temperature range between 20 and 40 °C and a concentration range between 0 and 30 wt % for racemic mandelic acid in water. A linear dependence was found in the analyzed concentration range for both the density and refractive index. As expected, both parameters increase with decreasing temperature and increasing concentration. The measurement deviation for multiple determinations of samples from the same solution averaged out at a maximum of (0.9% of the expected concentration value. Other Techniques. FBRM, laser diffraction, and microscopy do not require a specific calibration with regards to the chemical system. Therefore, no further description and error estimation are presented here. Concrete results depend strongly on the particle shape, sample treatment, and applied measurement principle. 3.2. Metastable Zone Width. Experimental Results. For isothermal growth experiments, the knowledge of the metastable zone width in the presence of an already crystallized solute material is essential. Figure 6 illustrates the average results with regard to the maximum possible nucleation-free subcooling ∆Tmax at cooling rate “zero” in relation to the initial solution saturation equilibria of the pure mandelic acid enantiomer, the eutectic mixture (ee ) 0.38), and racemic mandelic acid in water. The obtained ∆Tmax data are specific for the experimental setup used and depend, e.g., on the reactor size and geometry, stirrer type, and speed. Solubility data were taken from Lorenz et al.20 An average error of (0.5 K was estimated for the determined ∆Tmax data. The influence of the initial solution saturation temperature and the ee in the solution on ∆Tmax is evident. The metastable zone width increases with decreasing temperature. This could be explained by the decreased mobility and amount (due to reduced solubility) of molecules at lower temperature. Therefore, with decreasing temperature, a stronger subcooling ∆T is necessary to establish a sufficient supersaturation. Furthermore, ∆Tmax varies depending on the ee in the initial solution. One explanation could be given by taking into account that mandelic acid belongs to the compound-forming chiral systems. In the case of an

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Figure 7. Results of experiment 1, seeding at t ) 0 h (pure crystal growth).

Figure 8. Results of experiment 2, seeding at t ) 0 h (experiment with nucleation).

enantiopure solution, nuclei are formed by the pure enantiomer. In the case of the racemic solution, the recombination of heterochiral molecules is necessary in connection with the formation of nuclei, considering that the racemic compound exists exclusively in the solid phase. For the eutectic mixture, a selective nucleation could be assumed, keeping in mind the selective seeding with the pure enantiomer with analogy to the “preferential crystallization” processes.26 The counter enantiomer might have a retarding influence on the nucleation process in this case. The depicted experimental ∆Tmax results define the possible range of initial subcooling ∆T0 for isothermal growth experiments. Reliability. During two of the seven isothermal growth experiments presented below (Table 1), unexpected nucleation was observed despite working inside the metastable zone width. The fact that nucleation occurred is illustrated by the results of experiments 1 and 2 (Figures 7 and 8). The experimental conditions of experiment 1 almost agree with those of experiment 2 except for the initial subcooling ∆T0 (see Table 1). In contrast to experiment 1 (∆T0 ) 1 K), nucleation was detected in experiment 2 (∆T0 ) 2 K) by the ultrasonic probe, although subcooling values below the measured ∆Tmax of 4.8 K were chosen in both experiments. The nuclei formed during experiment 2 (Figure 8) were visible by the naked eye and appeared also inside the screen-cloth-protected measurement zone of the ultrasonic probe. Because of this, an erroneous calculation of the concentration from the measured ultrasound velocity and temperature can be seen in the second part of the experiment. The retarded

deviation from the polarimetric data (after 0.5 h) might be explained by the initial small size of the newly formed nuclei and their growth over time (inside the measurement volume of the ultrasonic probe) considering the dependence of the ultrasound velocity on the particle size and amount in suspensions.27,28 For comparison in experiment 1 (Figure 7), the ultrasonic and polarimetric data agree well because no nucleation occurred. Contrary to expectations resulting from the metastable zone width measurements for the racemic aqueous solution (Figure 6, racemate), spontaneous nucleation was also detected in experiment 3 (Figure 9). The nucleation event can be seen in the FBRM signal, in the heat release at the beginning of the experiment observable in the course of the reactor temperature, in the microscopic images that reveal lots of fines in the product, and in the ultrasonic signal. The nucleation detection by the ultrasonic probe is delayed by 2.5 h for the same reason as that mentioned above concerning experiment 2. A possible explanation for the nucleation could be the close nucleation border (approximately 2.9 K at 25 °C) and again the relative impreciseness of the depicted average data in Figure 6 (average error of ∆Tmax, (0.5 K). 3.3. Applicability of Measurement Techniques. Figures 7-11 report the results of the first five isothermal growth experiments conducted with the system mandelic acid/water (see Table 1). In this section, the applicability of the measurement techniques will be discussed in combination with the calibration curves and the system data solubility and metastable zone width. First, the complementary application of different concentration measurement techniques (ultrasonic probe, online polarimeter, and offline methods) will be evaluated, and specific merits and drawbacks will be explored. Furthermore, the capability of the FBRM probe to follow the growth of the crystals is assessed. Ultrasonic Probe. The results of the inline concentration determination by means of the ultrasonic probe can be seen in Figures 7-9 and 11 (experiments 1-3 and 5). While in experiments 1 and 5 (Figures 7 and 11) a continuous concentration decay is obtained until equilibrium is established, experiments 2 and 3 (Figures 8 and 9) show a final increase of the liquid-phase concentration due to the nucleation phenomena, already discussed above. In the case of pure crystal growth (experiments 1 and 5, Figures 7 and 11), this measurement technique is capable of following accurately the continuous concentration decay. The determined concentration data correspond well with data determined offline. Nevertheless, the applicability of this technique is limited by the accuracy of the calibration polynomial, which directly depends on the amount of experimental data gathered for calibration purposes. Especially for concentration changes over the whole experiment smaller than 1 wt %, the gathered data have to be treated with care, and it should be attempted to create higher concentration differences by changing the experimental conditions. However, in isothermal growth experiments, the maximum concentration difference is limited by the metastable zone width of the system in combination with the specific solubility data. In systems where the solubility changes only slightly with temperature, this technique appears to be of limited value. Polarimeter. Experiments 1 and 2 were monitored in addition by means of polarimetry. The resulting


Figure 9. Results of experiment 3 (experiment with nucleation) including microscopic pictures of the product crystals (top, grown crystals; bottom, crystals formed by nucleation), seeding at t ) 0 h: (1) reactor temperature (°C); (2) FBRM median (µm); (3) concentration measured by the ultrasonic probe (wt %); (4) concentration offline (wt %).

Figure 10. Results of experiment 4 including a microscopic picture of the product crystals, seeding at t ) 0 h: (1) FBRM median (µm); (2) FBRM count number/15000 (no./s); (3) concentration offline (g/gsolvent); (4) concentration calculated from the FBRM median by eq 1 (g/gsolvent).

Figure 11. Results of experiment 5 including a microscopic picture of the product crystals, seeding at t ) 0 h: (1) FBRM median; (2) concentration calculated from the FBRM median (µm) using eq 1 (wt %); (3) concentration offline (wt %); (4) concentration measured by the ultrasonic probe (wt %).

concentration data are illustrated in Figures 7 and 8. Both experiments show a concentration decay over time, and the measured concentrations correlate mostly well with the ultrasonic data. Because a filtered solution is always analyzed, the nucleation event cannot be detected in experiment 2 (Figure 8). The data obtained just show the concentration decay due to crystallization in general (growth and nucleation). Crystallization monitoring using only one method appears to be incapable of following the process in all details. An additional solid-phase-related observation of the crystallization process is indispensable in quantifying experiments with nucleation. Concerning polarimetry, one has to underline that this method can be applied for direct solute concentration measurements only for chiral solutions containing just one enantiomer. An additional total

solute concentration measurement is required to analyze solutions containing both enantiomers. Offline Techniques. As shown in Figures 9-11, the offline concentration measurements based on the determination of the density or refractive index are in general capable of detecting the concentration decay over the experimental run time. However, the drawback of these techniques is obvious. The number of data points over time is low, and errors can happen during sampling and dilution steps prior to the measurement. This could be optimized by taking more samples in shorter intervals and by increasing the individual sample volume to enable multiple measurements, leading to more accurate values. However, these improvements are limited by the total amount of solution used in the experiment. Furthermore, the required concen-

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tration data are obtained with a significant time delay. A notable third aspect is that offline measurements of the solute concentration alone are not capable of detecting the nucleation process that occurred, e.g., in experiment 3 (Figure 8). Thus, the results could lead to the wrong growth rate parameters. FBRM. Figure 10 shows inline FBRM data from the initial seeding point to equilibrium for experiment 4. The seed and final product crystal sizes were determined additionally by laser diffraction. The mass median was found by the latter method at 260 µm for the seed crystals and at 312 µm for the crystalline product. Both values correspond well with the FBRM median of approximately 268 µm in the beginning and 315 µm at the end of the experiment, although the underlying measurement principles of both methods differ significantly. The slight decrease of the FBRM count number and the steady increase of the FBRM median give reason to rule out the occurrence of spontaneous nucleation. Figure 10 additionally contains the solute concentration over time Yt (g/gsolvent) calculated via a mass balance from the initial FBRM median x0 (x0 ) 268 µm), the FBRM median xt (µm) over time, the initial seed crystal mass m0 (g), the solvent mass msolvent (g), and the initial solute concentration Y0 (g/gsolvent) according to the following equation:29

Yt ) Y 0 -

m0 msolvent

[( ) ] xt x0

3

-1

(3)

In eq 3, it is assumed that there is no nucleation, no attrition or breakage, and no agglomeration and that there are a nearly constant total crystal surface and shape factors that are size-independent and constant. The calculated data agree quite well with the offlinemeasured concentration data (Figure 10). This good agreement led to the motivation to test the FBRM as a tool to determine both inline particle size and concentration data in further experiments. However, as the results of experiment 5 (Figure 11) show, this simple method cannot be applied in every case. The calculation of the liquid-phase concentration by FBRM data fails to match in this case the offlinemeasured concentrations over time. The mass median (laser diffraction) was determined at 328 µm for the seed crystals and at 840 µm for the final product. While the initial FBRM median still shows a good agreement, the final chord-length values around 600 µm do not correspond with the offline data. The observed discrepancy between the two experiments 4 and 5 (Figures 10 and 11) can be explained by comparing the experimental conditions listed in Table 1. Both experiments were started with nearly the same size fraction of seeds but differ significantly in the mass fraction of the seed crystals in the final product mass and thus in the particle size increase during the experiment. The smoother signal of the FBRM median in experiment 4 compared to those of experiments 3 and 5 is also a consequence of the higher suspension density. As shown above, the seed crystals have a nonuniform rounded shape (see Figure 2). Because of the more pronounced size increase in experiment 5 (Figure 11), the crystals finally have a more healed-up, platelike shape than those in experiment 4 (Figure 10). This can also be seen in the microscopic images in Figures 10 and 11 and leads to a higher detection chance of smaller chord lengths by the FBRM probe in the second half of

Figure 12. Comparison of experiments 1 and 6 (see also Table 1) illustrating the influence of temperature on the growth kinetics of the pure mandelic acid enantiomer.

experiment 5. The assumption of size-independent shape factors is not fulfilled anymore (the crystal shape obviously changed with size), and therefore the final FBRM median is smaller than the final mass median determined by laser diffraction. Hence, the direct determination of desupersaturation data by using just the FBRM median can be very uncertain because of the crystal-shape-influenced measurement principle. This aspect is of larger importance for strongly nonspherical crystal shapes such as needles and plates. Finally, it should be mentioned that by means of the FBRM probe also nucleation can be detected. In Figure 9, the results of experiment 3 are reported. Depicted are the FBRM median, the reactor temperature, and offline- and inline-measured concentration data. The already discussed nucleation event in this experiment can also be seen by the initial decrease of the FBRM median due to the appearance of new small crystals. There is nearly no visible increase in the particle size after nucleation and consumption of the supersaturation. 3.4. Comparative Results with Regard to the Crystal Growth Behavior. In the following, selected results with respect to the influence of the growth temperature and the presence of the counter enantiomer on the crystal growth of the pure mandelic acid enantiomer will be discussed. The obtained total concentration versus time data were determined by means of either the online polarimeter or the ultrasonic probe and were transferred into a dimensionless overall supersaturation St defined as

St ) Yt/Yf - 1

(4)

with the total solute concentration Yt (g/gsolvent) at time t and the total solute concentration in equilibrium Yf (g/gsolvent). In Figure 12, the decay of supersaturation over time is compared for experiments 1 and 6. Similar results for experiments 1 and 7 are shown in Figure 13 (see Table 1). Temperature Effect. Experiments 1 and 6 were performed at different growth temperatures ϑgrowth. As can be seen in Figure 12, the decrease of the initially built-up supersaturation is much faster at 35 °C than at 20 °C. By evaluation of the half-period of the overall supersaturation decay, an average crystallization rate of 31.4 g/(gseeds h) is calculated for a growth temperature of 35 °C in contrast with an average crystallization rate of 4.7 g/(gseeds h) for a growth temperature of 20 °C. Obviously, the growth temperature has a significant effect on the crystal growth process of mandelic acid in water.


Figure 13. Comparison of experiments 1 and 7 (see also Table 1) illustrating the influence of the counter enantiomer on the growth kinetics of the pure mandelic acid enantiomer (ee0 ) ee in the initial solution).

Influence of the Counter Enantiomer. Experiments 1 and 7 were performed under comparable conditions and differ just significantly in the ee of the initial solution. In both cases, only the pure mandelic acid enantiomer should crystallize on the introduced seed crystals, as can be derived from the ternary solubility data.20 Figure 13 shows that the decrease of the initial overall supersaturation is much slower in the presence of the counter enantiomer (ee0 ) 0.49) than in the presence of the pure mandelic acid enantiomer in water (ee0 ) 1.00). Furthermore, the supersaturation decay in the solution containing both enantiomers of mandelic acid shows obviously a change in the growth process mechanism. In the initial part of the experiment, the degradation of supersaturation seems to be inhibited, followed by a comparatively steep decrease in the further course of the experiment. The interpretation of this result appears to be nontrivial. One explanation could originate from the compound-forming nature of the chiral system mandelic acid in water. Both mandelic acid enantiomers are able to join into a crystal lattice forming the racemic compound in a defined region of the ternary phase diagram. The crystallization process in experiment 7 happens outside this region; nevertheless, both species could compete for sites on the crystal surface and therefore might slow the crystal growth process. Other conceivable reasons are, e.g., adsorption of the counter enantiomer on the crystal surface or a change in the physicochemical solution properties by interactions between both enantiomeric species in the solvent. Further systematic experiments are planned to obtain more insight into this interesting phenomenon, which is of a more general interest. 4. Summary and Conclusions The experiments presented illustrated the applicability and limitations of several methods capable of determining liquid-phase concentration profiles and particle sizes in order to characterize crystal growth in isothermal growth experiments. Several constraints were also found during this work and should be considered in the planning of meaningful experiments. Preliminary measurements of solubilities and metastable zone width data appear to be mandatory. The substance characteristics and the overall concentration change in the experiment are important for deciding which measurement techniques should be used and which accuracy the applied methods should have. This fact is especially important for small initial supersaturations. With regards to the scale of isothermal growth experiments, typically some limitations are given and should be balanced. The amount of substance available

for carrying out experiments (especially, e.g., for certain pharmaceuticals) and the solubility behavior in the temperature range of interest limit the number of experiments that could be performed. A small reactor or solution volume, i.e., a small amount of used substances, is often preferred. On the other hand, when offline or online techniques are favored, there should be enough solution to enable sampling without disturbing the system. Furthermore, the sometimes significant geometrical dimensions of potential inline probes define the minimum reactor dimensions and therefore the minimum amount of solution needed for a single experiment. Finally, obviously, a bigger scale reproduces industrial conditions in a better way. These essential points have to be taken into account when applying the isothermal growth technique. Concerning measurement techniques, it is strongly recommended that liquid-phase studies (i.e., following solute concentration or desupersaturation over time) should always be accompanied by solid-phase investigations. This ensures the fulfillment of the usually applied assumptions with regards to nucleation, agglomeration, and breakage and the completeness of the overall mass balance in the system required to determine kinetic data. In this work, it could be shown that this kind of research benefits from using simultaneously different measurement principles. However, some of the methods applied can be used only for a limited number of chemical systems, depending, e.g., on their acoustical and optical properties, crystal shape, or chirality. An inline determination of process data should always be favored to avoid problems with regards to sampling and to provide a high data density. Nevertheless, the implementation and successful application of such inline techniques is not trivial, and there is no standard measurement method that can be applied in general to study a wide range of crystallizing systems. For the enantiomeric system studied in this work, a combination of the ultrasonic probe, online polarimetry, and the FBRM probe currently seems to be the optimal way to determine growth rate data. Crucial requirements for the quantitative analysis of the obtained data are the knowledge of the solubility and metastable zone width with regard to secondary nucleation. For the system investigated (mandelic acid/ water), specific data concerning the metastable zone width were given. The influence of temperature and the presence of the counter enantiomer on the crystal growth process of the pure mandelic acid enantiomer in water was explored and discussed. Both variables have a significant effect on the crystal growth process. More detailed and quantified results obtained will be presented soon. Literature Cited (1) Nyvlt, J.; So¨hnel, O.; Matuchova, M.; Broul, M. The Kinetics of Industrial Crystallization; Elsevier: Amsterdam, The Netherlands, 1985. (2) Tavare, N. S. Industrial CrystallizationsProcess Simulation, Analysis and Design; Plenum Press: New York, 1995. (3) Mullin, J. W. Crystallization; Butterworth-Heinemann: Oxford, U.K., 2001. (4) Myerson, A. S., Ed. Handbook of Industrial Crystallization, 2nd ed.; Butterworth-Heinemann: Oxford, U.K., 2002. (5) Mersmann, A., Ed. Crystallization Technology Handbook; Marcel Dekker: New York, 1995. (6) Lacmann, R.; Herden, A.; Mayer, C. Kinetics of Nucleation and Crystal Growth. Chem. Eng. Technol. 1999, 22, 279-289.

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Received for review April 19, 2004 Revised manuscript received September 24, 2004 Accepted November 3, 2004 IE040127N

Crystal Growth Kinetics via Isothermal Seeded Batch Crystallization

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