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Under isothermal conditions, phase transitions occur through a nucleation event when conditions are sufficiently close to coexistence. The formation of a nucleus of the new phase requires the system to overcome a free energy barrier of formation, whose height rapidly rises as supersaturation decreases. This phenomenon occurs both in the bulk and under confinement and leads to a very slow kinetics for the transition, ultimately resulting in hysteresis, where the system can remain in a metastable state for a long time. This has broad implications, for instance, when using simulations to predict phase diagrams or screen porous materials for gas storage applications. Here, we leverage simulations in an adiabatic statistical ensemble, known as adiabatic grand-isochoric ensemble (μ, V, L) ensemble, to reach equilibrium states with a greater efficiency than its isothermal counterpart, i.e., simulations in the grand-canonical ensemble. For the bulk, we show that at low supersaturation, isothermal simulations converge slowly, while adiabatic simulations exhibit a fast convergence over a wide range of supersaturation. We then focus on adsorption and desorption processes in nanoporous materials, assess the reliability of (μ, V, L) simulations on the adsorption of argon in IRMOF-1, and demonstrate the efficiency of adiabatic simulations to predict efficiently the equilibrium loading during the adsorption and desorption of argon in MCM-41, a system that exhibits significant hysteresis. We provide quantitative measures of the increased rate of convergence when using adiabatic simulations. Adiabatic simulations explore a wide temperature range, leading to a more efficient exploration of the configuration space. 

Using molecular simulations, we study the processes of capillary condensation and capillary evaporation in model mesopores. To determine the phase transition pathway, as well as the corresponding free energy profile, we carry out enhanced sampling molecular simulations using entropy as a reaction coordinate to map the onset of order during the condensation process and of disorder during the evaporation process. The structural analysis shows the role played by intermediate states, characterized by the onset of capillary liquid bridges and bubbles. We also analyze the dependence of the free energy barrier on the pore width. Furthermore, we propose a method to build a machine learning model for the prediction of the free energy surfaces underlying capillary phase transition processes in mesopores. 

In this review, we examine how machine learning (ML) can build on molecular simulation (MS) algorithms to advance tremendously our ability to predict the thermodynamic properties of a wide range of systems. The key thermodynamic properties that govern the evolution of a system and the outcome of a process include the entropy, the Helmholtz and the Gibbs free energy. However, their determination through advanced molecular simulation algorithms has remained challenging, since such methods are extremely computationally intensive. Combining MS with ML provides a solution that overcomes such challenges and, in turn, accelerates discovery through the rapid prediction of free energies. After presenting a brief overview of combined MS–ML protocols, we review how these approaches allow for the accurate prediction of these thermodynamic functions and, more broadly, of free energy landscapes for molecular and biological systems. We then discuss extensions of this approach to systems relevant to energy and environmental applications, i.e. gas storage and separation in nanoporous materials, such as metal–organic frameworks and covalent organic frameworks. We finally show in the last part of the review how ML models can suggest new ways to explore free energy landscapes, identify novel pathways and provide new insight into assembly processes.