Modelling of the Polymorph Nucleation based on Classical Nucleation Theory

Abstract

To elucidate the relative nucleation rates of different polymorphs, a competitive kinetic model is developed based on classical nucleation theory to describe the time evolution of two different polymorphic cluster size distributions controlled by the association and dissociation of the solute molecules during polymorph nucleation. Although there is only one type of the solute molecules, the agglomerated solute clusters are divided into two types–A form and B form, which resemble the structures and morphologies of the different mature polymorphs and eventually lead to the formation of two polymorphic crystals. A dissociation kernel is incorporated into the proposed model to account for gradual dissolution of the solute clusters smaller than a critical nucleus size due to the thermodynamic instability. By fitting the experimental induction period data and the final measured weight fractions of eflucimibe polymorphs with the proposed model, the association and dissociation rate constants for two polymorphs are determined. The developed model is satisfactory to explain the competitive mechanism of polymorph nucleation for eflucimibe that B form dominates at higher supersaturation while A form dominates at lower supersaturation. The results also indicate that A form is more stable than B form with a transition energy of 3.1kJ/mole at 35°C.