A comprehensive modeling approach for polymorph selection in Lennard-Jones crystallization

Computational predictions of the polymorphic outcomes of a crystallization process, referred to as polymorph selection, can accelerate the process development for manufacturing solid products with targeted properties. Polymorph selection requires understanding the interplay between the thermodynamic and kinetic factors that drive nucleation. Moreover, post-nucleation events, such as crystal growth and polymorphic transformation, can affect the resulting crystal structures. Here, the nucleation kinetics of the Lennard-Jones (LJ) fluid from the melt is investigated with a focus on the competition between FCC and HCP crystal structures. Both molecular dynamics (MD) simulations and 2D free energy calculations reveal that polymorph selection occurs not during nucleation but when the cluster sizes exceed the critical cluster size. This result contrasts with the classical nucleation mechanism, where each polymorph is assumed to nucleate independently as an ideal bulk-like cluster, comprised only of its given structure. Using the 2D free energy surface and the MD simulation-derived diffusion coefficients, a structure-dependent nucleation rate is estimated, which agrees with the rate obtained from brute force MD simulations. Furthermore, a comprehensive population balance modeling (PBM) approach for polymorph selection is proposed. The PBM combines the calculated nucleation rate with post-nucleation kinetics while accounting for the structural changes of the clusters after nucleation. When applied to the LJ system, the PBM predicts with high accuracy the polymorphic distribution found in a population of crystals generated from MD simulations. Due to the non-classical nucleation mechanism of the LJ system, post-nucleation kinetic events are crucial in determining the structures of the grown crystals.