(219c) Symbolic-Numerical Computational Tool for Mechanistic Crystal Growth Models of Molecular Crystals

Controlling crystal properties is vital for product functionality especially in the materials, electronics, and pharmaceutical fields. Crystal growth models enable prediction of crystal properties such as size distribution, shape, morphology, and polymorph, as a function of their growth conditions. On the atomic scale, crystal grows via incorporation of molecules along steps mainly at special sites of attachment called kinks. This brings about key quantities of kink density and step velocity in growth models. The major limitations in existing kink density and step velocity models are twofold: 1. Kink density is modeled at equilibrium utilizing the Boltzmann distribution, which ignores spatial correlations between surface sites, and the nonequilibrium nature of crystallization, 2) step velocity models neglect nucleation rates. This underscores the necessity for a new theory to address the existing deficiencies.

We have developed the Simplified Steady-State Framework (SSSF), which addresses the above deficiencies in a systematic approach for Kossel crystal and AB crystals with two growth units in the cell (Z=2).^1,2 The framework consists of a steady-state master equation analysis and is based on accounting for only a small fraction of most probable surface events at the most likely surface sites. The model predictions based on the novel framework have been validated against kinetic Monte Carlo simulations as well as experimental morphology observations for various active pharmaceutical ingredients such as doravirine precursor, celecoxib, ritonavir I, among others.

In this work, a computational model development and implementation tool is proposed to extend the framework to crystals with any number of non-centrosymmetric growth units in the unit cell (Z>2). The tool consists of two separate engines: symbolic and numerical engines. The symbolic engine utilizes graph network theory to represent the surface kinetics in the form of a network, where the surface sites and rate events become nodes and edges within a network, respectively. Such a network representation allows development of the steady-state master equation model equations, which are then supplied to the numerical engine. Within the numeric sections, the equations are then solved simultaneously employing nonlinear equation solvers. The solvers are utilized in conjunction with a parametric continuation scheme, which incrementally increases parameters within growth models from a known mathematical solution at the Kossel crystal point to the final crystal conditions. Such a computational tool will enable application of SSSF to generate accurate growth rate predictions for complex organic crystals with any number of growth units in the unit cell. This modeling approach is expected to play a crucial role in guiding the design, control, and optimization of crystallization processes, whilst yielding crystals with precisely tailored properties.

References:

1. Padwal, N.A. and Doherty, M.F., 2022. Simple Accurate Nonequilibrium Step Velocity Model for Crystal Growth of Symmetric Organic Molecules. Crystal Growth & Design, 22(6), pp.3656-3661.
2. Padwal, N.A. and Doherty, M.F., 2024. Step Velocity Models for Crystal Growth of Organic Molecules: Two Molecules in the Unit Cell. Crystal Growth & Design. (Accepted for publication)