Group contribution method for rapid estimation of crystal growth rates

Abstract

The morphological evolution of organic crystals during crystallization depends on the face-specific growth rates. Classical growth rate models relate the face-specific growth rates to the crystal lattice, energy of stable facets, growth mechanism, and supersaturation. The complexities of these models have increased over time to account accurately for solution conditions, the structure of growth units, and their attachment rates. Such advanced growth rate models require several layers of computations to obtain attachment energies of facets, nucleation rates, kink density, and attachment rates. Among these, the most intensive and time-consuming computation is for attachment rates, which require molecular dynamic simulations. This substantially increases the overall computation time to predict the absolute growth rate for even one crystallization condition. Since it is nearly impossible to iterate such a growth rate model, optimization schemes cannot be implemented to identify solution conditions that favor specific crystal growth. To reduce the computational time for attachment rate calculations, we implement a group contribution method (GCM) that relates the properties of functional groups in a molecule to their attachment rates to the crystal lattice, thereby rapidly estimating the growth rates of organic crystals. The process of molecular attachment involves partial desolvation of a solvated molecule, referred to as a transition state, followed by total desolvation via spontaneous attachment to a crystal facet. The first step in GCM is to identify the equilibrium states of fully solvated and partially desolvated solute molecules. The degree of supersaturation dictates the extent of this equilibrium and, thereby, the activation barrier for the growth of crystals, according to transition state theory. Identifying this equilibrium phenomenon allows for capturing the functional-group-specific interactions that depend on molecular motion, which could be related to operating conditions such as temperature and pressure. The stochastic optimization technique with Monte-Carlo sampling allows an efficient optimization problem solution to obtain the group interaction parameters. The GCM approach is first validated for the estimation of growth rates of glutamic acid and L-histidine, and then extended to predict growth rates of alanine and glycine rapidly. The optimized parameters and GCM scheme can be used to estimate growth rates in other crystallization systems.