Distribution Kinetic Approach for Separation of Polymorphs

Separation of crystals of different polymorphic forms poses a great challenge in the pharmaceutical industry. Understanding the time evolution of polymorph crystal size distributions during crystallization or recrystallization is thus important fundamentally and practically. In this work, a distribution kinetics model for the polymorph crystallization processes is proposed. The model includes the rates of transformation of one polymorph to the other polymorph, coalescence of the polymorphs, Gibbs–Thomson effects of crystal curvature on equilibrium solubility, interfacial and phase-transition energies, critical nucleus sizes for denucleation during ripening by recrystallization, and coarsening of the size distribution by coalescence of the polymorphs. The numerical solutions of the governing population dynamics equations show that interfacial and transition energies, but not activation energies, are significant in causing the less stable dimorph to vanish. Possible ways to control polymorph separation are also discussed.