Crystal nucleation along an entropic pathway: Teaching liquids how to transition

Abstract

We combine machine learning (ML) with Monte Carlo (MC) simulations to study the crystal nucleation process. Specifically, we use ML to infer the canonical partition function of the system over the range of densities and temperatures spanned during crystallization. We achieve this on the example of the Lennard-Jones system by training an artificial neural network using, as a reference dataset, equations of state for the Helmholtz free energy for the liquid and solid phases. The accuracy of the ML predictions is tested over a wide range of thermodynamic conditions, and results are shown to provide an accurate estimate for the canonical partition function, when compared to the results from flat-histogram simulations. Then, the ML predictions are used to calculate the entropy of the system during MC simulations in the isothermal-isobaric ensemble. This approach is shown to yield results in very good agreement with the experimental data for both the liquid and solid phases of argon. Finally, taking entropy as a reaction coordinate and using the umbrella sampling technique, we are able to determine the Gibbs free energy profile for the crystal nucleation process. In particular, we obtain a free energy barrier in very good agreement with the results from previous simulation studies. The approach developed here can be readily extended to molecular systems and complex fluids, and is especially promising for the study of entropy-driven processes.