Free energy simulations along entropic pathways: From crystal nucleation to capillary phase transitions

We carry out free energy simulations to unravel nucleation processes, in the bulk and in nanoconfined systems, using entropy as a reaction coordinate. We first 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 determine the Gibbs free energy profile for the crystal nucleation process and obtain a free energy barrier in very good agreement with the results from previous simulation studies. We then analyze the capillary condensation and evaporation processes in fluids confined in a cylindrical nanopore. For this purpose, we define the entropy of the adsorbed fluid as a reaction coordinate and determine the free energy associated with both processes along entropic pathways. For capillary condensation, we identify a complex free energy profile resulting from the multi-stage nature of this phenomenon. We find capillary condensation to proceed through the nucleation of a liquid bridge across the nanopore, followed by its expansion throughout the pore to give rise to the stable phase of high density. In the case of capillary evaporation, the free energy profile along the entropy pathway also exhibits different regimes, corresponding to the initial destabilization of the layered structure of the fluid followed by the formation, and subsequent expansion, of a bubble across the nanopore.