Modeling of Transient Concentration for Slow Growing Conformational Polymorphs During Batch Crystallization

A simple model to determine the transient concentration during batch crystallization of multiple conformer molecules is presented. The crystallization is assumed to be governed by an advancing step integration mechanism followed by a diffusion period. During the integration period, the concentration of the conformer that crystallizes in solution is considered as the limiting parameter and the low proportion of the right conformer in solution is assumed to be the cause of the observed low nucleation and crystallization rates. This assumption was consolidated by ab initio conformation energy calculations which showed that the conformer that crystallizes has a high energy conformation and thus should be present in minor amount in solution. The model is based on the screw dislocation and the birth and spread theories and assumes a constant step advance velocity (CSAV). The prediction of the combined CSAV model / diffusion model provides a good prediction of the transient concentration during the anti-solvent crystallization of a developmental drug. Simulations of different anti-solvent addition scenarios predict a nearly constant and low supersaturation for parabolic profiles and maxima in supersaturation for linear addition rates.