Population balance modeling of the solution mediated transformation of polymorphs: Limitations and future trends

Abstract

Many of the chemical species prepared or purified using crystallization from solution exist in a number of polymorphic forms, and this can create challenges in the design and operation of industrial crystallizers, particularly where a polymorphically pure product is required. Where two or more polymorphs may crystallize from a solution simultaneously, the metastable polymorph may nucleate first, and will undergo a transformation to the stable polymorph over time. In a solution-based crystallizer the transformation between the metastable polymorph and the stable polymorph will usually occur via a solution mediated transformation (SMT) rather than a solid state transformation. Solution mediated transformation occurs via dissolution of the metastable polymorph crystals simultaneously with the nucleation and growth of the crystals of the stable polymorph. Theoretical models for these mechanisms (dissolution, nucleation, and growth) are all well known, and it is simple to measure the kinetic rates for fitting the models. An essentially exact model for the SMT can thus be created using a population balance model for each of the crystalline phases in the system, and this model can be parameterized based on models fitted using experimental data for the basic mechanisms. However to have a fully a priori model of the SMT is rarely attempted, and when it is it tends to be unsuccessful. More common is to use the nucleation or growth kinetics as fitted parameters in a model fitting the SMT data. This tends to fit the experimental data successfully but there is no guarantee that the model is fundamentally correct rather than simply a good fit to a set of data. Better a priori population balance models of the SMT should be achievable, however mechanisms which need to be better treated in the simulations include the induction time, crystal growth rate and dissolution rate dispersion, null supersaturation for crystal growth and null undersaturation for dissolution, the effect of crystal size and perfection on dissolution kinetics, and variations in crystal shape factors during the growth which may modify the mass balance terms in the model.