(205a) Modeling Impurity-Mediated Crystal Growth

Crystallization is the process by which growth units, such as molecules and ions, organize to form a structured solid state. High purity crystals grow via a layer-by-layer process known as spiral growth, which is fundamental to various applications including the development and manufacture of pharmaceuticals, catalysts, and organic light-emitting diodes (OLEDs). Given the ubiquity of crystal growth in industrial processes, there is substantial demand for predictive and mechanistic modelling of crystallization. Crystallization of organic molecules is well understood for ideal systems--i.e., Kossel crystals with a single centrosymmetric growth unit (simple cubic single molecules with equal surfaces). There is interest in studying crystal systems in which non-idealities are introduced, as these are more representative of realistic conditions. One such non-ideality involves the presence of impurities.

The goal of this work is to investigate the effect of impurities or ‘imposter molecules’ on the crystal growth process and to develop theoretical models for the mechanisms by which impurities influence crystal growth and hence affect crystal morphology and size. Herein, an impurity, or imposter, typically refers to a structurally similar species to, or one which inhibits the growth of, the primary crystallizing species. Structurally similar additives may influence crystallization of active pharmaceutical ingredients, such as paracetamol. While these systems are prevalent in many relevant fields, there is currently no comprehensive model that captures the full effect of impurities on crystal growth processes. A deeper understanding of the underlying growth mechanisms would promote control of crystallization processes via tailor-made additives and enable identification and proper treatment of impurities that alter growth rates. We employ Kinetic Monte Carlo (KMC) to simulate the time evolution of centrosymmetric organic crystal growth and developed model equations to quantify the effect of inhibition on the crystal face for systems populated with impurities.

In order to validate these simulations, we have developed a classification algorithm to distinguish amongst distinct crystal edge sites on the moving step. We have compared the densities of such sites from simulation results to predictions according to kink density expressions such as the Frenkel expression as well as more thorough site probability expressions developed by Lovette and Doherty (Phys. Rev. E 2012, 85, 021604). We observe excellent agreement between the two approaches which we take as validation of both.

The validated KMC simulations were then used to test the classical mechanistic step velocity model which states that step velocity is proportional to the product of kink density and kink rate (net attachment rate of growth units into kink sites). The agreement is demonstrated to be very good over a range of bond energies and supersaturations, thus validating the classical mechanistic approach. Given the agreement over various growth conditions, we then incorporate impurities in the KMC simulation methodology to investigate their effect on crystal growth. For the cases studied, our results generally suggest a decrease of the step velocity with increasing impurity concentration, though the form of this dependence is based on the mobility and distribution of the impurities, as well as the energetic interactions between impurities and the primary crystallizing species. We use these model equations to predict morphology changes for adipic acid grown from aqueous solution. These results are visualized within the framework of ADDICT, a practical engineering tool developed in the Doherty group to compute relative growth rates and visualize morphology of solution-grown faceted crystals on the order of seconds.