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In Situ Measurement of Particle Size during the Crystallization of L-Glutamic Acid under Two Polymorphic Forms: Influence of Crystal Habit on Ultrasonic Attenuation Measurements

CRYSTAL GROWTH & DESIGN 2002 VOL. 2, NO. 3 227-234

Patricia Mougin* and Derek Wilkinson Centre for Molecular and Interface Engineering, Department of Mechanical and Chemical Engineering, Heriot-Watt University, Riccarton, Edinburgh EH14 4AS, United Kingdom

Kevin J. Roberts Institute for Particle Science and Engineering, Department of Chemical Engineering, University of Leeds, Leeds LS2 9JT, United Kingdom Received December 20, 2001;

Revised Manuscript Received February 26, 2002

ABSTRACT: Ultrasonic attenuation spectroscopy was successfully applied for in-situ determination of particle size during the crystallization of a molecular crystal in two different polymorphic forms. The crystallization of L-glutamic acid was carried out under different cooling conditions by which the R- or β-polymorphic form of L-glutamic was obtained preferentially. It is shown that each polymorph yields a characteristic acoustic attenuation due to the different habits of the two polymorphs. While it was found that ultrasonic attenuation measurements were less sensitive than turbidometric measurements for the determination of the onset of crystallization, ultrasonic attenuation measurements proved to be well behaved and provided particle sizing data for the prismatic crystals of the R-form of L-glutamic acid and an estimation of the primary dimensions of the β-form needles. Growth rate and supersaturation data were derived from particle size and solid concentration results and correlated. Introduction Batch crystallization from solution is routinely used in the fine chemicals industry for purification and separation in the production of pharmaceuticals, agrochemicals, and other speciality chemicals. The quality and reproducibility of the end-product depend on control of the different parameters that govern the process such as supersaturation, crystallinity, and crystal size distribution (CSD). The CSD in particular is important as it dictates the behavior of the product in downstream operations such as filtration, drying, transport, and storage, and it also is likely to be defined by customer specifications. Yet, on-line control of the CSD is difficult as most conventional measurement techniques cannot operate at high concentration of solid product and thus require a difficult and time-consuming dilution step that can itself lead to modification of the CSD. For this reason, a new technique that does not require the transmission of light was used in this study of batch crystallization processes. This technique is based on the measurement of attenuation of ultrasonic waves as a function of frequency (in the range 1 to 150 MHz) and can examine optically opaque or concentrated systems without the need for analyte dilution,1 giving rise to numerous applications.2,3 The extended size range (0.02-1000 µm) is also a major advantage over techniques such as laser diffraction in which a wide size range can only be achieved using several lenses and beam expanders. The CSD is derived by data inversion using the mathematical model of Epstein and Carhart,4 * Corresponding author current address: SSCI, Inc., 3065 Kent Avenue, West Lafayette, IN 47906; phone 765-463-0112; e-mail: [email protected].

Allegra and Hawley5 (ECAH theory) relating attenuation of sound through a suspension to the particle size distribution of the suspension. Following previous experiments reported on the crystallization of the model compound urea,6 this work focuses on in-situ monitoring of the crystallization of L-glutamic acid, which, depending on the conditions of crystallization, may be crystallized under two different polymorphic forms, polymorphs R and β. Crystallization of L-Glutamic Acid The polymorphs R and β of L-glutamic acid crystallize from aqueous solutions under two characteristic crystal habits, polymorph R being prismatic and polymorph β being needle-shaped. While the R-form is generally preferred for industrial purposes, it is under the β-form that L-glutamic acid is the more commonly found and purchased as this form is less soluble than the R-form in aqueous solution (Figure 1) and therefore is the stable form obtained from these solutions. However, due to differences in the growth kinetics of the two forms, the crystallization of the R-form of L-glutamic acid may be achieved by rapid cooling of aqueous solutions of L-glutamic acid.7 The product in the R-form remained for a long period of time if kept at low temperature. Transition between R- and β-polymorph in aqueous solution is possible, as a suspension of R-polymorph heated to an intermediate temperature (typically ∼40 °C for a solution saturated at 70 °C) below the saturation temperature has been shown to result in the slow dissolution of the R-polymorph and subsequent crystallization of the thermodynamically favored β-polymorph.7

10.1021/cg0155752 CCC: $22.00 © 2002 American Chemical Society Published on Web 04/04/2002

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Mougin et al. Table 1. Physical Properties of L-Glutamic Acid and a Saturated Aqueous Solution of L-Glutamic Acid at 25 °Ca property density sound speed thermal expansion thermal conductivity heat capacity viscosity shear rigidity attenuation

Figure 1. Solubility curves of R- and β-forms of L-glutamic acid.7

Figure 2. Acoustic spectroscopy - key analysis steps.

Ultrasonic Spectroscopy for Particle Size Determination Ultrasonic attenuation spectroscopy for the determination of particle size in suspensions and emulsions consists of measuring the acoustic attenuation of ultrasound waves passing through a sample volume at various frequencies, resulting in the measurement of an attenuation spectrum characteristic of the solid concentration and size of particles in suspension. To derive the particle size distribution and particle concentration from spectral data measurements, the spectra associated with all conceivable particle size distributions and particle concentrations are first predicted for the particle/liquid system using the Epstein and Carhart, Allegra and Hawley (ECAH) model.4,5 Although theoretically limited to dilute systems, as it does not take into account particle-particle interactions, this model has been shown to give good results even in concentrated systems,2,5,8,9 in particular when the density contrast between particle and liquid medium is low. In the case studied here, the solid content at the end of the crystallization did not exceed 2v%, below the limit at which multiple scattering occurs for particles of L-glutamic acid crystals dispersed in water. A mathematical inversion procedure is then used for the deconvolution of the measured attenuation spectrum (see Figure 2 for a schematic of the procedure). Monomodal or bimodal log-normal distributions are assumed, allowing description of symmetric and skewed distributions, fully described in terms of geometric mean and geometric deviation of first and second mode. The ECAH model describes the physical phenomena associated with the propagation of an acoustic wave inside a suspension through fundamental equations based on the laws of conservation of mass, energy, and momentum, thermodynamic equations of state, and stress-strain relations

units

glutamic acid

saturated solution

kg m-3 m s-1

1.54 × 103 4.07 × 103

1.00 × 103 1.48 × 103

K-1

2.0 × 10-5

2.6 × 10-4

J m-1 s-1 K-1 4.22 × 10-1 5.9 × 10-1 J kg-1 K-1

1.24 × 103

N s m-2 N m-2 dB m-1

8 × 109 4 × 10-4

4.2 × 103 1.0 × 10-3 (3.2 × 10-1 2.2 × 10-5 × T) × f (1.99-2.9 × 10-3 × T)b

a And at T in °C for the acoustic attenuation of the mother liquor. b f in MHz.

for isotropic elastic solids or viscous fluids, i.e., by formulating the wave equations that describe the interaction between sound and particulates. A set of physical properties describing both liquid and particulate solid properties of the system is therefore required to retrieve CSD information from attenuation. The physical properties of L-glutamic acid and the mother liquor required for the CSD analysis using ECAH model are presented in Table 1. The same properties were used to characterize the R- and β-polymorphs, and implicitly a random set of particle orientations was assumed within the reaction vessel. The temperature dependence of the physical properties of L-glutamic acid crystals was assumed to be negligible. The physical properties characterizing the liquid medium were taken equal to those of water, based on the low working solute concentration (2w%). The temperature dependence of the acoustic attenuation of the mother liquor was assessed in the temperature range 35-50 °C and was extrapolated to 15 °C. Experimental Methods Experimental Setup. In this study, ultrasonic attenuation measurements were carried out using an Ultrasizer (Malvern Instruments Ltd.) working in the frequency range 1-150 MHz and size range 0.02-1000 µm. Crystallization of L-glutamic acid was carried out within the 3-L sample chamber of the ultrasonic spectrometer (see Figure 3). Measurement of ultrasonic attenuation was performed using two pairs of dynamic transducers (emitter and receiver, low and high-frequency ranges) allowing measurement at variable spacings, between 0.08 and 10 cm, depending on the frequency of the ultrasonic wave and the evolution of the crystallizing system. The onset of crystallization was ascertained from simultaneous turbidimetric measurements and compared with attenuation measurements. Temperature control was ensured by cooling coils within the chamber connected to a thermostated bath. A computer interface was used to control the temperature in the crystallization vessel and also to log the data measured by the turbidimetric probe. The chamber was equipped with a marine turbine running at 300 rpm for effective stirring. Materials and Methods. L-Glutamic acid was purchased from Aldrich. Solutions at 2w% (20 g of glutamic acid/1000 g of water) were prepared from freshly distilled water and poured into the chamber of the ultrasonic spectrometer. The solution was stirred at 200 rpm throughout the crystallization process using a marine-type turbine. Measurements of the ultrasonic attenuation of the solution were carried out prior

Particle Size during Crystallization of L-Glutamic Acid

Figure 3. Schematic of the experimental setup capable of recording ultrasonic, turbidimetric, and temperature data during temperature-programmed cycles.

Crystal Growth & Design, Vol. 2, No. 3, 2002 229

Figure 6. Evolution of the acoustic attenuation spectra recorded during the crystallization of L-glutamic acid from a 2w% aqueous solution, by linear cooling at 0.75 °C/min from 50 °C down to 15 °C. The legend indicates the temperature expressed in °C. Table 2. Onset of Crystallization (Crystallization Temperature Tcrys) Derived from Acoustic Attenuation Measurements at 10 MHz and Turbidity Measurements, for Three Cooling Crystallizations

Figure 4. Turbidity data recorded during the crystallization of L-glutamic acid from an aqueous solution at 2w% at three cooling rates.

cooling rate (°C/min)

Tcrys, ultrasonic method (°C)

Tcrys, optical method (°C)

0.1 0.4 0.75

30.6 22.5 20

38.0 27.8 22.1

transmittance and attenuation at 10 MHz vs temperature, respectively, for the three cooling rates studied. Under fast cooling rates (0.75 and 0.4 °C/min) and cooling to 15 °C, the R-form was found to be predominant, although a detectable fraction of β-form was apparent from microscope images in the case of the 0.4 °C/min cooling rate. At a cooling rate of 0.1 °C/min, the β-form was found to be predominant. The onsets of crystallization were determined from the attenuation and turbidity measurements, a summary of which is presented in Table 2. It can be seen that the onset of crystallization is detected earlier by turbidometric measurements than by ultrasonic measurements, showing that the ultrasonic measurements are less sensitive to the presence of crystals at low solid concentration, as expected from this method adapted for suspensions of solid concentration higher than 0.1v%. It is interesting to note however that the ultrasonic method is useful for the determination of the onset of crystallization in the case of colored systems, the study of which can prove difficult using standard optical methods.

Crystallization of L-Glutamic Acid r-Form

Figure 5. Attenuation at 10 MHz recorded during the crystallization of L-glutamic acid from an aqueous solution at 2w% at three cooling rates. to the crystallization, and bubbles removed from the walls of the chamber and faces of transducers when detected. Although the solutions were not deaerated, no problems related to air bubbles dispersed in solution were encountered. The crystallization experiments were carried out by linear cooling of the solution at 0.75, 0.4, and 0.1 °C/min from 50 to 15 °C. The polymorphic form of L-glutamic acid was verified off-line by XRD using an X-ray diffractometer Siemens D5000 (Cu KR radiation). Influence of Cooling Rate on the Onset of Crystallization: Comparative Study of Turbidometric and Acoustic Attenuation Methods. Figures 4 and 5 compare the plots of

Experimental Results. Very good quality ultrasonic data could be obtained during the whole crystallization of L-glutamic acid R-form by fast cooling, an example of which is presented in Figure 6 for a cooling rate of 0.75 °C/min. Figure 7 shows the evolution of the CSD for the 0.75 °C/min cooling rate. It can be seen that following the first monomodal CSD at 25.4 °C giving a mean size of 2.6 µm, a bimodal distribution is seen at 21.1 °C, possibly due to growth rate dispersion or simultaneous secondary nucleation. As the particles grow, the second mode of the distribution (bigger sizes) becomes predominant, growing to a mean size of ∼180 µm, whereas a tail of finer particles can still be seen in the final distribution. Figure 8 shows the evolution of solid concentration during the crystallization of L-glutamic acid at 0.75 and 0.4 °C/min.

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Figure 7. Evolution of the CSD during the crystallization of L-glutamic acid R-form from an aqueous solution at 2w% cooled from 50 °C down to 15 °C at 0.75 °C/min. The legend indicates the temperature as the cooling experiments takes place.

Mougin et al.

Figure 9. Size evolution during the crystallization of Lglutamic acid R-form as crystallized under two different cooling rates. Polynomial fitting of degree 4 (R-squared value > 0.98). Table 4. Evolution of the CSD during the Crystallization of L-Glutamic Acid r-Polymorph from a 2w% Aqueous Solution, by Linear Cooling at 0.4 °C/min from 50 °C down to 15 °C 0.4 °C/min

Figure 8. Evolution of the solid concentration during the crystallization of L-glutamic acid R-form from an aqueous solution at 2w% cooled from 50 °C down to 15 °C at two different cooling rates. Table 3. Comparison of Size Distributions at the End of the Crystallization of L-Glutamic Acid r-Form as Crystallized under Various Conditions percentiles (µm)

0.75 °C/min cooling rate

0.4 °C/min cooling rate

D16 D50 D84 D99

77 154 248 442

75 130 191 305

Both set of data gave a final solid concentration of 0.80v%, as expected from solubility data, proving the accuracy of the technique for estimation of solid content. Furthermore, the combined use of solubility data at the recorded temperature with solid concentration data enable the determination of the supersaturation during crystallization, providing a useful tool for process design purposes. Effect of Cooling Rate on the Crystallization of L-Glutamic Acid. Comparing results obtained at 0.75 and 0.4 °C/min (Table 3) shows that the higher cooling rate gave slightly bigger particles at the end of the crystallization. This difference cannot be explained by the difference in crystallization temperature Tcrys and thereby supersaturation level at the beginning of the crystallization, normally conducive to the production of smaller particles at higher cooling rate. However, due to the coexistence of the two polymorphic forms, com-

0.75 °C/min

T (°C)

time (min)

C (v%)

(dL h )/(dt) (m/s)

T (°C)

time (min)

C (v%)

(dL h )/(dt) (m/s)

25.1 24.1 21.8 20.8 19.8 16.3 15

0 2 7 10 12 18 36

0.17 0.16 0.25 0.45 0.38 0.56 0.79

1.5 × 10-7 1.3 × 10-7 9.5 × 10-8 7.8 × 10-8 6.8 × 10-8 4.3 × 10-8 3.7 × 10-9

25.4 21.1 18.1 15.6 15.0 15.0 15.0

0 6 12 17 29 39 58

0.1 0.14 0.23 0.46 0.69 0.72 0.81

1.5 × 10-7 1.4 × 10-7 1.2 × 10-7 1.0 × 10-7 4.5 × 10-8 1.1 × 10-8

petitive nucleation of each form may be expected. This is influenced by the cooling rate, as at very slow cooling rate (0.1 °C/min) only the β-form is produced. It can therefore be expected that the fastest cooling rate leads to lower nucleation of β, leading in turn to slightly bigger R-crystals. At 0.4 °C/min, slightly smaller crystals should be seen as the result of higher nucleation of the β-form, leading to a higher proportion of β-crystals (although the R-form is still predominant) and smaller R-crystals. Growth Rate vs Supersaturation. The overall linear growth rate was estimated by polynomial fitting of the size data, based on the evolution of the geometric mean of the larger mode describing the distribution (GM2) (Figure 9). A summary of the results obtained for both cooling rates is presented in Table 4. Solid concentration data may easily be converted to a measure of the solute concentration at any time t and thence to relative supersaturation σ:

c(t) ) co - FsCs(t)

(1)

c(t) - c*(t) c*(t)

(2)

σ(t) )

where c(t) and c*(t) are the solute concentration and solubility expressed in units of mass per unit volume of solution at the time t, Fs is the density of the solid phase, and Cs is the solid volume fraction. Using supersaturation data calculated from solid concentration measurements throughout the crystallization at both cooling rates, the evolution of the growth rate was plotted versus supersaturation (Figure 10).

Particle Size during Crystallization of L-Glutamic Acid

Figure 10. Evolution of the overall linear growth rate with relative supersaturation σ during the crystallization of Lglutamic acid R-form as crystallized under two different cooling rates.

Crystal Growth & Design, Vol. 2, No. 3, 2002 231

Figure 12. Evolution of the acoustic attenuation spectra recorded during the crystallization of L-glutamic acid from a 2w% aqueous solution, by linear cooling at 0.1 °C/min from 50 °C down to 15 °C.

Figure 11. Morphology of L-glutamic acid R-polymorph. Three growth directions are highlighted for comparison of overall growth rates with growth rate data from single-crystal studies.10

In this profile, the increase of supersaturation up to 0.8 (relative supersaturation) corresponds to the fast cooling period. As the bottom temperature of 15 °C is reached, the supersaturation progressively decreases. In the cooling phase of the crystallization process, variations of growth rate versus supersaturation are the result of the combined influence of temperature and supersaturation, during which the growth rate was found to decrease slightly at both cooling rates. As soon as the bottom temperature is reached and the supersaturation decreases, the influence of supersaturation on the growth rate translates into a further decrease of the growth rate. Although growth rates data found in the literature could not be found for the same growth conditions, our results may be compared with experimental data in similar conditions. In a recent study of the growth kinetics of L-glutamic acid R- and β-polymorphs, the growth rates of R-L-glutamic acid in three directions were determined10 (Figure 11), using the single-crystal method during isothermal crystallization at 298 K. Results at a relative supersaturation σ ∼ 0.5 yielded the growth rates G(A) ) 7 × 10-8 m/s, G(B) ) 7.5 × 10-8 m/s, and G(C) ) 3.3 × 10-8 m/s in the three directions A, B, and C as seen in Figure 11, while at σ ∼ 0.25 the growth rates G(A) ) 3.2 × 10-8 m/s, G(B) ) 1.2 × 10-8 m/s, and G(C) ) 1.6 × 10-8 m/s could be estimated. These rates may be compared with this study in the isothermal part of the crystallization following fast cooling at 0.75 °C, carried out at 288 K. At σ ∼ 0.5, our measurements yielded an overall growth rate of ∼5 × 10-8 m/s, while at σ ∼ 0.25 the overall growth rate

Figure 13. Evolution of the CSD during the crystallization of L-glutamic acid β-form from an aqueous solution at 2w% cooled from 50 °C down to 15 °C at 0.1 °C/min. The legend indicates the temperature as the cooling experiments takes place.

was estimated at 3 × 10-8 m/s, comparing well with the single-crystal estimations. Crystallization of L-Glutamic Acid β-Form Experimental Results. Good quality ultrasonic data could be obtained during the crystallization of L-glutamic acid β-form by slow cooling at 0.1 °C/min. Figures 12 and 13 show the evolution of the attenuation spectra and the CSD, respectively, throughout the crystallization process. The distribution was found to be bimodal throughout the crystallization. The proportions of the two modes evolved progressively, the proportion of the larger mode increasing compared to that of the smaller mode. The mean of the smaller mode increased from ∼1 µm up to ∼30-35 µm and remained constant thereafter. The mean of the larger mode increased toward the end of the crystallization from ∼80 up to ∼175 µm. Unlike the distribution of R-crystals whose “bimodal” distribution reflects a tail of finer particles commonly found at the end of a crystallization process, the modes of the distribution of β-crystals do not evolve independently of each other. This can be seen by considering the ratio of larger to smaller geometric mean GM2/GM1 (Figure 14) throughout the crystallization. Except at the beginning of the crystallization where this ratio is higher, GM2/GM1 remained approximately constant

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Figure 14. Evolution of the equivalent diameter and geometric means of the first and second mode of the size distribution and their ratio during the crystallization of L-glutamic acid β-form from an aqueous solution at 2w% cooled from 50 °C down to 15 °C at 0.1 °C/min.

Figure 15. Microscope image of β-L-glutamic acid needlelike crystals obtained by crystallization of L-glutamic acid R-form from an aqueous solution at 2w% cooled from 50 °C down to 15 °C at 0.1 °C/min.

throughout the crystallization, irrespective of the shift of GM1 and GM2 toward bigger sizes as the crystals grow. Figure 15 presents a microscope image of β-crystals at the end of the crystallization. Although it is difficult to obtain an exact size from microscope images, particularly because the crystals are prone to agglomerating, the dispersion could be qualified as roughly monodispersed with a length typically around 200 µm and width in the range 15-40 µm. Assuming a random orientation of the particles, ultrasonic attenuation spectroscopy, like laser diffraction methods, gives an estimation of the volume of the scatterers, and the size distribution is given in terms of the diameter of the sphere having the same volume as the particles. While the influence of crystal shape on ultrasonic attenuation may be understood from a physical point of view as the result of variations in viscoinertial scattering (change in viscous drag for particle shape deviating from the spherical shape) and thermal scattering (change in boundary between particle and liquid medium, the effect of which may also be coupled with the effect of anisotropicity of thermal

Mougin et al.

Figure 16. Evolution of the equivalent diameter and solid concentration during the crystallization of L-glutamic acid β-form from an aqueous solution at 2w% cooled from 50 °C down to 15 °C at 0.1 °C/min.

properties also encountered in crystals), the introduction of a shape factor in the ECAH model is not straightforward. The bimodal description of the distribution may be seen however as a deviation from the model of the equivalent sphere, and the comparison with microscope images (e.g., Figure 15) suggests that the two modes are in fact close to the primary dimensions of the crystals. The further use of the CSD results in the next section to retrieve growth rate data was based on the assumption that the geometric means of the two modes of the distribution gave a good approximation of the width and length of the needles. It is important to note in that respect that all cases of needlelike systems studied by the authors gave similar results, that is that the bimodal description of the distribution gave good approximations of the primary dimensions of the crystals on the base of microscope images. Growth Rate. If needlelike particles of L-glutamic acid β-form are modeled as rectangular parallelepipeds of width a and length b then the diameter of the sphere of equivalent volume can be calculated by: 3

x6rπ

Deq ) a

(3)

where r ) b/a. The evolution of the solid concentration and Deq as calculated from (3) is presented in Figure 16. The crystallization can be split into three phases: (i) solid concentration constant but size increases. In addition, the ratio GM2/GM1 decreases sharply to reach its constant value seen in phases 2 and 3. This corresponds to the beginning of the crystallization where it is possible that the dissolution of small nuclei runs in parallel with the growth of the bigger particles. (ii) solid concentration and size both increase, and the ratio GM2/GM1 is constant. This phase corresponds to a period where growth is preponderant over nucleation and attrition. (iii) solid concentration increases, whereas the size levels out and then decreases slightly. The ratio GM2/ GM1 remains constant. This was interpreted as a phase where growth and attrition coexist, and the attrition rate is of the same order of magnitude as the growth rate. Also, the scatter of the size (Deq) measurement is

Particle Size during Crystallization of L-Glutamic Acid

Crystal Growth & Design, Vol. 2, No. 3, 2002 233

Figure 18. Linear growth rates as a function of the supersaturation during the cooling crystallization of L-glutamic acid β-form at 0.1 °C/min from a 2w% aqueous solution. Figure 17. L-Glutamic acid β-form crystal grown from aqueous solution.11

higher than in the previous phases of the crystallization. This may be attributed to oscillations around an optimum size. Polynomial curves were fitted to ratio r ) b/a and Deq data versus time all yielding coefficient of determination values above 0.95. The growth rate in the primary directions of the crystals (Figure 17) was estimated using: 3

x6rπ ‚ dt

1 da 1 〈v(020),v(010)〉 ) ‚ ) ‚ 2 dt 2

dDeq

-

Deq dr ‚ (4) 3r dt

where 〈v(020),v(010)〉 is the average linear growth rate on the faces (021) and (010). As only one type of face grows in the direction of the length of the needle, namely, (101) faces, the linear growth rate of these faces can be derived from db/dt. Given the angle with respect to the b-axis, the linear velocity in the direction perpendicular to the face can be retrieved from its component in the direction of the length of the needle:

v(101) )

x6rπ ‚(r‚ dt

1 db 1 ‚ ) ‚ 2x2 dt 2x2

3

dDeq

)

dr dt

+ Deq‚

(5)

Values of supersaturation throughout the process were retrieved from solid concentration data. Figure 18 shows the plot of 〈v(020),v(010)〉 and v(101) as a function of the relative supersaturation σ. It can be seen from this graph that the linear velocity of the (101) face is constantly higher than the linear velocity of the side faces, which is expected from the habit of the β-crystals. It is interesting to note that the ratio between the two velocities decreases as the temperature decreases (for one value of supersaturation). This however did not have a detectable effect on the overall habit of the crystals. In a single-crystal study of the growth kinetics of L-glutamic acid β-polymorph10 during isothermal crystallization at 298 K, the growth rate of β-crystals was measured in the [100] direction, while the growth rates along the [001] and [010] directions were reported too low to be detected. For comparison, the growth rate in the [100] direction reported at a relative supersaturation σ ∼ 0.5 was G([100]) ) 1.2 × 10-8 m/s. This may be

compared directly to our estimation of db/dt ) 2x2‚v(101) ) 3.1 × 10-8 m/s. However, this value is not obtained in similar conditions, as this supersaturation is achieved during cooling, before the third phase of the process during which the growth rate data cannot be retrieved directly from size data. It is interesting to note, however, as pointed out by Kitamura et al. in their study,11 that this growth rate value of the fastest growing face is lower than that of any of the faces of the R-crystals, as expected from the crystallization behavior of the two polymorphs. Conclusions This study presented an example of ultrasonic study of the crystallization process of an organic crystal, in the particular case of a material displaying polymorphism. It was shown that ultrasonic attenuation data could be recorded throughout the crystallization of L-glutamic acid R- and β-polymorphs. A clear difference was seen in the results obtained with suspensions of each polymorphic form of L-glutamic acid, distinct both in terms of raw data (ultrasonic attenuation spectra) and CSD derived from them. This difference was attributed to the marked difference in the shape of the crystals, one being prismatic, the other being needlelike. The experimental conditions chosen for this study enabled the study of each polymorphic form grown separately. Overall growth rate data were retrieved associated with the growth of the R-form of L-glutamic acid. The influence of crystal shape on ultrasonic attenuation spectra and CSD results was observed during the crystallization of the needlelike β-polymorph of L-glutamic acid where the size distribution was described as consistently bimodal, the mean sizes of the two modes being close to the width and length of the crystals on the basis of microscope images. An estimation of the linear velocities relative to the lateral faces (average on the (020) and (010) faces) and relative to the (101) faces was proposed on the basis of these results. Acknowledgment. This work has been carried out as part of the Chemicals Behaving Badly initiative, a collaborative project funded by EPSRC grant GR/L/ 68797 together with industrial support from AstraZeneca, BASF, GlaxoSmithKline, ICI, Malvern Instruments Ltd., Pfizer, and Syngenta. We gratefully acknowledge

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all members of this academic/industrial team for their contribution to the overall project. References (1) Alba, F. U.S. Patent 5,121,629, 1992. (2) McClements, D. J. Adv. Colloid Interface Sci. 1991, 37, 3372. (3) Povey, M. J. W. Ultrasonic Techniques for Fluids Characterization; Academic: San Diego, CA, 1997. (4) Epstein, P. S.; Carhart, R. R. J. Acoust. Soc. Am. 1953, 25(3), 553-565.

Mougin et al. (5) Allegra, J. R.; Hawley, S. A. J Acoust. Soc. Am. 1972, 51, 1545-1564. (6) Mougin, P.; Roberts, K. J.; Tweedie, R.; Wilkinson, D. J. Acoust. Soc. Am. 2001, 109(1), 274-282. (7) Kitamura, M. J. Cryst. Growth 1989, 96, 541-546. (8) Holmes, A. K.; Challis, R. E.; Wedlock, D. J. J. Colloid Interface Sci. 1994, 168, 339-348. (9) Dukhin, A. S.; Goetz, P. J. Langmuir 1996, 12, 4998-5003. (10) Kitamura, M.; Ishizu, T. J. Cryst. Growth 2000, 209, 138145. (11) Davey, R. J.; Blagden, N.; Potts G. D.; Docherty, R. J. Am. Chem. Soc. 1997, 119(7), 1767-1772.

CG0155752