ARTICLE pubs.acs.org/crystal
Evaluation of Growth Kinetics of Antisolvent Crystallization of Paracetamol in an Oscillatory Baffled Crystallizer Utilizing Video Imaging Cameron J. Brown and Xiong-Wei Ni* School of Engineering and Physical Science, Heriot-Watt University, Edinburgh, Scotland ABSTRACT: This work aims to show the potential of applying video imaging techniques to antisolvent crystallization of paracetamol in an oscillatory baffled crystallizer for the determination of crystal size distribution and mean crystal size with a high level of accuracy in comparison with the values measured with a Mastersizer. From these data, the effects of supersaturation, addition rate, and mixing on growth rate are examined and crystal growth kinetics extracted for various operational parameters. The kinetic data so generated are in good agreement with these from previous studies in stirred tank systems. It was found that the degree of supersaturation has the most significant effect on the overall growth rates, followed closely by the degree of mixing and then the rate of antisolvent addition. Both the kinetics and process data could be used as the tool for the design and operation of antisolvent crystallization.
1. INTRODUCTION Crystallization is a purification and separation process closely linked with particle technology, and it encompasses aspects of phase equilibrium, thermodynamics, and solid state chemistry. It is estimated that more than 90% of all active pharmaceutical compounds involve a crystallization step in their production.1 When considering the rate at which crystallization takes place, we realize the kinetics of both nucleation (rate at which new crystals form) and growth (rate at which present crystals grow) are of paramount importance. At a process level, the control of crystal size and size distribution is vital to meeting stringent pharmaceutical standards; both rely significantly on growth kinetics. For mass transfer-controlled crystallization processes, crystal growth can generally be considered in three steps:2 (1) movement of the solute from the bulk to the crystal surface, (2) movement from the solution to the solid state, and (3) dissipation of the heat of crystallization. Steps 1 and 2 are dependent on the mass transfer of the solute, while step 3 is heat transfer-dependent. Therefore, mass transfer is critically important in this type of crystallization process. The need for better mass transfer is greater in antisolvent crystallization where a second liquid (the antisolvent) is added to the solvent/solute mixture to decrease the solubility of the solute. Here the antisolvent must quickly be dispersed within the crystallizer to ensure a uniform supersaturation throughout. Many different experimental techniques have been employed to facilitate crystal growth rate measurements.3 The single-crystal growth techniques, which focus on individual face growth rates, are predominately used for fundamental studies relating to growth mechanisms.47 Measurements taken on the population balance of crystals are useful for determining overall mass transfer rates under controlled conditions and for observing size-dependent r 2011 American Chemical Society
growth or growth rate dispersion.811 Although there is no simple or generally accepted method of expressing the rate of growth of a crystal, because it has a complex dependence on temperature, supersaturation, size, habit, fluid dynamics, etc., for crystallizer design purposes, crystal growth rates in terms of mass produced per unit time per unit area of crystal surface are often utilized rather than the individual face growth rates. This was expressed as6 G¼
β KG Δcg 3RFc
ð1Þ
where G is the overall linear growth rate (meters per second), KG is the overall crystal growth coefficient (kilograms per square meter per second), Δc is the degree of supersaturation (Δc = c c*, kilograms per kilogram), Fc is the crystal density (kilograms per cubic meter), and R and β are the volume and surface shape factors, respectively. Therefore, plotting G versus Δc and fitting a power law relationship (G = AΔcg) would allow us to extract growth kinetics for various values of Δc. The determination of the overall linear growth rates requires the data of crystal size distribution and crystal mean sizes that are collected in this work online using a video imaging technique developed in-house. The motivation for this work stemmed from the need at a process control level to be able to actively monitor the crystal sizes and size distribution. Attempts to determine size distribution have been made previously. Caillet et al.12 used a CCD camera to record images during crystallization and determine a size distribution offline. Eggers et al.13 evaluated the size distribution on Received: May 3, 2011 Revised: June 20, 2011 Published: July 11, 2011 3994
dx.doi.org/10.1021/cg200560b | Cryst. Growth Des. 2011, 11, 3994–4000
Crystal Growth & Design the basis of the axial length of preformed carbon fibers with better correlation. Both works, however, focused only on a small section of sample. Although bulk imaging has been used to detect the point of nucleation14 and the mass growth rate,15 detailed kinetic information has yet to be recorded. In our imaging method, we cover a much larger sample area of 1408 mm2, compared to 201 mm2 12 and 10 mm2,13 allowing a more representative bulk sample of the crystallizer. With the laser providing focused illumination, we are able to detect smaller crystals than would be possible under normal conditions. Following our previous study of online evaluation of mass growth rates in paracetamol antisolvent crystallization using a video imaging technique,15 we now present our extended methodology for extracting growth kinetics and establishing a general correlation of crystal growth with a number of process parameters.
2. ANTISOLVENT CRYSTALLIZATION For crystallization processes, an understanding of solubility and metastable zone width (MSZW) greatly aids in the design and control of these processes. In cooling crystallization, solubility is expressed as a profile of solute concentration versus temperature; the MSZW is simply a temperature range having a unit of temperature. The same principle would apply to antisolvent crystallization processes, where the solubility is obtained from a plot of solute concentration versus solvent concentration. Unlike cooling crystallization, there are now three elements in the definition of antisolvent crystallization: solute, solvent, and antisolvent. Because of different expressions of concentrations that were used, the solubility curve takes on different formats; for example, paracetamol solubility for the wateracetone system in the work by Granberg and Rasmuson16 was illustrated in terms of grams of paracetamol per kilogram of total solution versus the mass % of the antisolvent (water). Because there was no antisolvent addition in their work, the mass percentage of antisolvent remained constant and the total solution was the sum of the solvent (acetone) and the initial antisolvent (water) present in the system. O’Grady and co-workers1719 defined the solubility in terms of grams of paracetamol per kilogram of solvent versus kilograms of antisolvent per kilogram of solvent, because the antisolvent was constantly added to the crystallizer. The solubility curve produced in this way is better; the y-axis variable not only is now affected by the mass of solute (paracetamol), instead of the aggregated mass of the solute and the solution, allowing for the study of the effect of the antisolvent on crystal growth, but also provides a clearer way of expressing and determining the equilibrium concentration as well as the degree of supersaturation. We adopted this method in our work, and Figure 1 shows the solubility of the paracetamolactonewater system (solid curve), as well as the typical pathway the concentration of solute in solution takes during an antisolvent crystallization process (dashed curve). It is clear that the concentration initially remains constant with the addition of the antisovlent (the dash curve), then decreases dramatically, indicating that crystallization has occurred, and finally reaches the saturation concentration (c*). The metastable zone is thus defined as the width of concentration expressed in terms of kilograms of water per kilogram of acetone from the start of antisolvent addition to the point when a sudden decrease in solute concentration has occurred, as shown in Figure 1. In addition, this also gives clear definitions of the solution concentration, c,
ARTICLE
Figure 1. Solubility curve (—) and typical concentration pathway (---).
Figure 2. Experimental setup with dual light sheets. The light gray shaded area represents one baffled cell and the image capture area.15
as the starting initial paracetamol concentration and the equilibrium concentration, c*, as the final paraceamol concentration, also shown in Figure 1, from which the mean degree of supersaturation, Δc (c c*), and the supersaturation ratio, S (c/c*), can be determined.
3. EXPERIMENTAL SETUP, OPERATION, AND ANALYSIS PROCEDURES Experimental Setup. A 630 mL oscillatory baffled crystallizer (OBC) (internal diameter of 32 mm) was utilized in this investigation, further description of which can found elsewhere.15,20 As in the previous work,15 fluid oscillation was applied via a diaphragm driven by an electric motor. Illumination for the camera was provided by a continuous 4 W argon ion laser (Spectra Physics), the beam of which was split to produce two light sheets, 1 mm thick by 60 mm. The OBC consisted of a square jacketed column with five equally spaced stationary baffles (the provision of the square jacket is to minimize the curvature effect of the crystallizer when using optical equipment). To provide the most uniform illumination across the images, both sides of the crystallizer were illuminated simultaneously through the center of the OBC (see Figure 2). Images were then recorded directly to a personal computer drive with a gray CCD camera (SensiCam). Experimental Procedure. Paracetamol (PA) (Sigma-Aldrich, USP specification, 98.0101.0%), acetone (Sigma-Aldrich, g99.5%), and distilled filtered water were prepared at their compositions detailed in Table 1 in a volume of 230 mL. To ensure a complete dissolution of the paracetamol crystals before crystallization, each sample was heated to 28 °C and mixed well before being added to the OBC and cooled to the operating temperature of 23 °C. Before imaging, the camera was positioned perpendicular to the crystallizer and light sheets and adjusted to ensure that the focused area was on one baffled cell (space between a pair of baffles). The OBC was then oscillated at the required frequency (Table 1) with a constant amplitude of 15 mm. Simultaneously, images 3995
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Crystal Growth & Design
ARTICLE
Table 1. Variation of Process Parameters initial composition water (kg)
acetone (kg)
PA (g)
c (g/kga)
water added (kg)
c* (g/kga)
Δc (g/kga)
S
Q (mL/min)
Reo
0.058
0.136
81
596
0.210.52
353510
86243
1.171.69
50
1500
2
0.079
0.119
71
595
0.160.43
352509
86243
1.181.69
50
1500
2
0.102
0.101
60
593
0.520.76
350507
86243
1.161.69
50
1500
2
0.125
0.083
45
542
0.080.31
338456
86204
1.191.60
50
1500
2
0.149
0.064
28
438
0.210.40
337352
86101
1.241.30
50
1500
2
0.10
0.10
60
593
0.40
350
243
1.69
133
1500
2
0.10
0.10
60
593
0.40
350
243
1.69
80
1500
2
0.10 0.10
0.10 0.10
60 60
593 593
0.40 0.40
350 350
243 243
1.69 1.69
25 14
1500 1500
2 2
0.10
0.10
60
593
0.40
350
243
1.69
50
770
1
0.10
0.10
60
593
0.40
350
243
1.69
50
2700
3.5
0.10
0.10
60
593
0.40
350
243
1.69
50
3800
5
were captured continuously by the CCD camera at 7.5 frames per second directly to the hard drive. After the sample had been mixed for 5 min and images recording, the addition of the antisolvent (water) began. This was fed into the top of the OBC by a peristaltic pump (Watson Marlow) at the specified rate and for the specific amount (Q and water added, respectively, in Table 1) until the required volume was reached. Once addition of the antisolvent had stopped, the recording continued until the image intensities (mean image value) reached a new steady level, typically 57 min after the addition had been terminated. This period of recording ensured that the images captured covered all stages of crystallization. Once the recording was completed, the OBC was drained and rinsed and the solution filtered to recover the recrystallized paracetamol. The wet sample was then dried until the measured weight remained constant (to two decimal places). Image Analysis. The images were loaded into Matlab as 8 bit gray scale images (pixels can have a value of 0 for black to 255 for white). We stated in our previous work15 that the smallest detectable crystal size was 43 μm (this was the length of 1 pixel based on the camera positioning); therefore, the growth rate kinetics reported in this paper are associated with crystal sizes of g43 μm. With faster shutter speeds, the improved resolution of the camera, and more powerful light sheets, growth kinetics for much smaller crystals can be obtained using the current setup. Once in Matlab an algorithm was developed in house to process the recorded images, the main stages of which are shown in Figure 3. Initially, the majority of the image is black with white pixels representing the position of the baffle support rods; a common baseline image was obtained by averaging images from the first 5 min of recording with no crystals present, as shown in Figure 3A. As crystallization proceeds, more crystals above the minimum size (43 μm) appear as pixels with an increased value ranging from gray to white shown in Figure 3B. By subtracting the baseline image from all further images to remove the background effects, we produce the image in Figure 3C. This is then converted to a binary image (using a threshold value calculated by Otsu’s method21) of black and white (values of 0 and 1, respectively), as shown in Figure 3D, where black represents the solution and the white regions represent potential crystals. Each region of white pixels in the finalized image (Figure 3D) was counted, and the area (px2) and perimeter (px) of the regions were evaluated. From this, the equivalent mean diameter of each region was then determined via deq ¼ 4
area perimeter
ð2Þ
This would result in a diameter in terms of pixels, which is further converted to an equivalent diameter of crystals by multiplying the
frequency (Hz)
Figure 3. Captured images at various stages of processing: (A) baseline image, (B) raw image with crystals present, (C) image with the baseline removed, and (D) conversion to a binary image (Δc = 243 g/kga, Q = 50 mL/min, and Reo = 1500). minimum detectable size of 43 μm: deq ¼ 172
area perimeter
ð3Þ
From this, a histogram of the equivalent mean diameters can be plotted, and in turn the cumulative crystal size distribution along with its mean size. Image Distribution Calibration. To verify our analytical procedure and outcome as well as the robustness of the algorithm, we calibrated our method utilizing three samples of spherical polystyrene/divinylbenzene copolymer particles (Acros Organics, Sigma Aldrich) covering size ranges of 3775, 75152, and 152650 μm. The distribution of each sample was also confirmed using a Malvern Mastersizer. We then added each sample at an identical concentration into the OBC separately and recorded and treated the images as outlined earlier. The aim is to compare the particle size distributions obtained between the Mastersizer and our imaging method. Because the minimum observable size from the current camera setup is 43 μm, counts of particles below this in the Mastersizer were ignored. The initial results are shown in Figure 4. It can clearly be seen in Figure 4 that the image analysis detected a significant quantity of particles in the 477 μm) (Figure 5A) as well as for the smallest particles (
