The ensemble switch method and related approaches to obtain interfacial free energies between coexisting phases from simulations: a brief review

Abstract

The accurate estimation of the excess free energy due to an interface between coexisting phases of a model system by computer simulation often is a challenging task. We review here two methods, which rely on constructing paths between a system containing a ‘slab’ of one phase separated by two planar interfaces from the other phase, and a system (with the same total volume) without interfaces. Studying such a system with a slab geometry, it is natural to choose a rectangular geometry (in dimensions), where is the direction perpendicular to the interfaces, and periodic boundary conditions are applied throughout. Since interfaces exhibit large-scale fluctuations, a careful analysis of finite-size effects is mandatory. In the ensemble switch method, an intermediate Hamiltonian is constructed, adding the Hamiltonian of a system with interfaces, multiplied by a fraction , to an equivalent system without interfaces, with fraction . Adding to the state variables of the system, a thermodynamic integration from to yields the desired interfacial free energy. While intermediate states (with ) lack immediate physical meaning, the alternative method discussed here relies on sampling the probability distribution , where is a suitable physical order parameter distinguishing the phases. Advantages and disadvantages of both methods are discussed, using Ising models, Lennard-Jones fluids and the solid-to-liquid transition of the hard sphere model as examples.

Keywords:

• interfacial tension
• ensemble switch method
• Monte Carlo simulations
• solid–liquid interfaces

Acknowledgements

This research was supported by The Deutsche Forschungsgemeinschaft (DFG), grant No VI237/4-3. We are grateful to the Centre for Data Processing (ZDV) of the University of Mainz and the Höchstleistungsrechenzentrum Stuttgart (HLRS) for generous grants on their high performance computers MOGON and HERMIT.

Disclosure statement

No potential conflict of interest was reported by the authors.