Nonequilibrium Crystal Growth Model for Organic Molecules of Real API Complexity

Abstract

Steps play a crucial role in growth of crystal faces. The step velocity is a critical parameter within the growth models and is a function of the density of kinks, which are the most favorable sites of attachment along crystal steps. In this article, we introduce a symbolic-numerical computational tool to generalize the Simplified Steady–State Framework (SSSF), introduced in our earlier articles, to nonequilibrium kink density calculations for crystals with any number of molecules in the unit cell. The tool employs a graph theoretic approach for representation of the crystal surface kinetics, which allows digital implementation of the method for molecules of API complexity. The SSSF is based on identifying a small subset of most-probable surface events which dominate the surface kinetics. Our new model replaces Boltzmann statistics for kink density modeling with a fully nonequilibrium model that captures both the surface correlations between sites (via the use of conditional probabilities) as well as their dependence on supersaturation. The digital tool demonstrates the versatility of the theory for providing key growth parameters within crystal growth models for a wide range of crystals. The tool was successfully used to predict the crystal morphology for three organic compounds with four molecules in the unit cell, one forming platelets and the other two needle-like crystals.