(27a) Characterization of Crystal Size and Shape

Crystal shape is a ubiquitous property, affecting not only many downstream processing steps in industrial crystallization such as filtration and drying, but also the bioavailability of pharmaceuticals. It is however also an elusive property: unlike the characterization of particle populations with constant shape, which can be described with a single characteristic size L, few techniques have been developed for the characterization of particle populations with non-constant shape.

The characterization of a population of particles with different shapes requires the measurement of a multi-dimensional particle size distribution (PSD). In the simplest approach, particles are described by two independent sizes L1 and L2. Such a bidimensional particle model allows for the description of a wide variety of particles, ranging from parallelepipeds to e.g. cylindrical particles or more complex geometries where the other dimensions are related to L1 and L2. When considering a population of these particles, it needs to be characterized using a two dimensional PSD n(L1, L2). For certain particle geometries it is possible to directly measure L1 and L2 using for example optical microscopy. In the works of Puel et al. [1, 2], bidimensional PSDs were successfully measured in this way. Such an approach is however requires extensive sample preparation to ensure a proper distribution of the particles on the microscope stage and is rather time consuming, leading to the measurement of a very limited number of particles.

In this work, we use a specially constructed view cell through which we pump a suspension of crystals. The view cell is positioned between a bright xenon flash lamp and an optical system with a digital camera. This setup enables us to acquire high quality images of the randomly oriented crystals in suspension at a rate of 10 images per second. These images are then analyzed by a fully automated image analysis routine that identifies the particles in the suspension and measures, amongst other properties, the major and minor axis length of an ellipse with an equal area moment of inertia. This yields a 2D measurement called Axis Length Distribution (ALD). Clearly, the ALD is related to the 2D PSD, but this relation is not straightforward. A measurement model has been developed [3], allowing for the calculation of an ALD for a given 2D PSD. The inverse operation, i.e. the restoration of a 2D PSD from a measured ALD, is obviously of great interest, but is highly ill-posed. To solve this problem, a genetic algorithm was developed [4] that enables us to find the discretized 2D PSD from a measured ALD.

We applied this procedure in real crystallization processes to monitor the bidimensional PSD. In these processes, samples were drawn during the crystallization, which were immediately quenched with a large volume of saturated solution and were analyzed using the view cell to obtain the ALD, with a Coulter counter to obtain the particle volume distribution and by SEM to study particle geometry. From the bidimensional PSDs restored from the measured ALDs, particle volume distributions were calculated. These were found to agree very well with the Coulter counter measurements.

The restored 2D PSDs revealed a great deal of information on interesting aspects of crystallization such as fines generation, bidimensional particle growth and the effects of operating conditions such as supersaturation and stirring rate on particle size and shape. Currently, our research efforts are aimed at the study of agglomeration and breakage using image analysis.

References

1. Puel F., Févotte G., Klein J. P., ?Simulation and analysis of industrial crystallization processes through multidimensional population balance equations. Part 2: a study of semi-batch crystallization?, Chem. Eng. Sci. 58 (2003) 3729-3740.

2. Oullion M., Puel F., Févotte G., Righini S., Carvin P., ?Industrial batch crystallization of a plate-like organic product. In situ monitoring and 2D-CSD modelling: Part 1: Experimental study?, Chem. Eng. Sci. 62 (2007) 820-832.

3. Kempkes M., Eggers J., Mazzotti M., ?Measurement of particle size and shape by FBRM and in-situ microscopy?, (2007), Chem. Eng. Sci. doi: 10.1016/j.ces.2007.10.030

4. Eggers J., Kempkes M., Mazzotti M., ?Measurement of size and shape distributions through image analysis?, (2008) submitted to Chem. Eng. Sci..

* Author to whom correspondence should be addressed.

Phone: +41-44-632 24 56. Fax: +41-44-632 11 41. Email: marco.mazzotti@ipe.mavt.ethz.ch