(337cg) Crystal Growth Modeling and Morphology Predictions of Organic Molecular AB Crystals

Mechanistic crystal growth models provide a rapid in-silico pathway to morphology predictions. In contrast to the empirical growth models, mechanistic models provide flexibility by accounting for the growth environment such as supersaturation, temperature, solvent effects along with crystalline solid-state interactions.¹ The mechanistic models geared towards asymmetric organic molecules are based on equilibrium assumptions in kink density calculation, a fundamental parameter in growth models.^2,3 This restricts the model application to small organic molecules and low driving forces.

In this work, nonequilibrium kink density and step velocity models, which are fundamental growth parameters, are derived based on a simplified steady-state framework (SSSF). The framework draws upon Frank-Voronkov^4,5’s steady-state principle, Cuppen et al.⁶’s nonequilibrium framework for Kossel crystals and extends Padwal and Doherty⁷’s SSSF to Organic molecular crystals with growth units in the unit cell. In the framework, steady-state analysis is conducted accounting for the rates at which kink are formed, destroyed for single and double height kinks since they constitute majority of kinks along the step. The steady-state equations or master equations are then solved simultaneously, numerically to yield nonequilibrium kink densities. The step velocity is then estimated as a function of kink densities by summation of rates of all the surface events. The resulting growth model is validated against kMC simulations from literature⁸ and experimental shape observations.

The step velocity models are then applied for morphology predictions by estimation of relative growth rates of the slow-growing faces.⁹ The model has been successful in providing crystal shapes for pharmaceutical APIs such as doravirine precursor, celecoxib, ritonavir I, among others. Such a multiscale modeling approach can aid optimization of process parameters for engineering crystals with desired properties.

References:

1. Li, J., Tilbury, C.J., Kim, S.H. and Doherty, M.F., 2016. A design aid for crystal growth engineering. Progress in Materials Science, 82, pp.1-38.
2. Kuvadia, Z.B. and Doherty, M.F., 2011. Spiral growth model for faceted crystals of non-centrosymmetric organic molecules grown from solution. Crystal growth & design, 11(7), pp.2780-2802.
3. Tilbury, C.J., Joswiak, M.N., Peters, B. and Doherty, M.F., 2017. Modeling step velocities and edge surface structures during growth of non-centrosymmetric crystals. Crystal Growth & Design, 17(4), pp.2066-2080.
4. Voronkov, V. V. Movement of an elementary step by means of formation of one-
   dimensional nuclei. Soviet Physics Crystallography 1970, 15, 8.
5. Frank, F. C. Nucleation-controlled growth on a one-dimensional growth of finite length. Journal of Crystal Growth 1974, 22, 233–236.
6. Cuppen, H. M.; Meekes, H.; van Veenendaal, E.; van Enckevort, W. J. P.; Bennema, P.; Reedijk, M. F.; Arsic, J.; Vlieg, E. Kink density and propagation velocity of the [010] step on the Kossel (100) surface. Surface Science 2002, 506, 183–195.
7. 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.
8. Joswiak, M. N.; Peters, B.; Doherty, M. F. Nonequilibrium Kink Density from One-Dimensional Nucleation for Step Velocity Predictions. Crystal Growth & Design 2018, 18, 723–727.
9. Lovette, M. A.; Doherty, M. F. Predictive modeling of supersaturation-dependent crystal shapes. Crystal growth & design 2012, 12, 656–669.

Research Interests: Crystal growth modeling, kMC simulations, and morphology predictions