Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions

TL;DR

This paper reviews Monte Carlo simulation methods for estimating interfacial free energies and line tensions in condensed matter systems, focusing on thermodynamic integration and order parameter sampling techniques applied to simple models.

Contribution

It introduces and compares two Monte Carlo methods for calculating interfacial properties, including extensions to off-lattice systems and complex geometries.

Findings

Thermodynamic integration effectively estimates line tensions at three-phase contact lines.

Order parameter sampling provides interfacial free energies for various geometries.

Curvature effects on interfacial free energy are analyzed and compared.

Abstract

Excess contributions to the free energy due to interfaces occur for many problems encountered in the statistical physics of condensed matter when coexistence between different phases is possible (e.g. wetting phenomena, nucleation, crystal growth, etc.). This article reviews two methods to estimate both interfacial free energies and line tensions by Monte Carlo simulations of simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is based on thermodynamic integration. This method is useful to study flat and inclined interfaces for Ising lattices, allowing also the estimation of line tensions of three-phase contact lines, when the interfaces meet walls (where "surface fields" may act). A generalization to off-lattice systems is described as well. The second method is based on the sampling of the order parameter distribution of the system throughout the two-phase coexistence region of the model. Both the interface free energies of flat interfaces and of (spherical or cylindrical) droplets (or bubbles) can be estimated, including also systems with walls, where sphere-cap shaped wall-attached droplets occur. The curvature-dependence of the interfacial free energy is discussed, and estimates for the line tensions are compared to results from the thermodynamic integration method. Basic limitations of all these methods are critically discussed, and an outlook on other approaches is given.