(189a) Critical Supersaturation in Solution Crystallization as a Function of Equilibrium Cluster Size Distribution

Crystallization of pharmaceutical compounds from solution is usually limited by an inadequate understanding of crystal nucleation and growth processes. Significant interest exists in industry and academia towards innovative methods and techniques that facilitate rapid determination of useful kinetic data. Towards that end, we developed an evaporation-based crystallization platform. Solution droplets at various initial conditions are introduced into a micro-device, in which crystallization is driven by different rates of evaporation of the solvent. The droplets are observed periodically using an optical microscope and the nucleation time for any crystals formed is recorded.

Our earlier studies using this platform revealed the existence of a ?critical supersaturation' in the crystallization of a wide range of model compounds [1]. We observed that this critical supersaturation is strongly correlated to the solubility of the compound. In this work, we present an analysis of this observation using the classical nucleation theory. Since the rate of evaporation of solvent (and thus the rate of generation of supersaturation) is very slow, we consider the droplet to be in a stationary nucleation regime at all points of time and examine the evolution of the ?quasi-equilibrium cluster size distribution' in the droplet [2]. The critical supersaturation can then be explained as the minimum driving force required for the formation of ?critical nuclei' in a given volume of solution. Preliminary analysis suggests that the classical nucleation theory qualitatively explains the experimental data and the critical supersaturation predicted is insensitive to the cluster-monomer attachment / detachment frequencies. The meaning of this ?critical supersaturation' in light of present analysis is explored and the implications toward solution crystallization are discussed.

References:

[1] Guangwen He, Venkateswarlu Bhamidi, Reginald B. H. Tan, Paul J. A. Kenis and Charles F. Zukoski, ?Determination of Critical Supersaturation from Microdroplet Evaporation Experiments?, Cryst. Growth & Design, 2006, 6, 1175-1180

[2] Kashchiev, D., ?Nucleation: Basic Theory with Applications?, 2000, Butterworth-Heinemann, Oxford.