Methods to extract interfacial free energies of flat and curved interfaces from computer simulations

When a computer simulation of a model system that can exist in two phases (e. g., vapor and liquid at the condensation transition, or solid and liquid at the melting transition) is constrained such that the order parameter distinguishing the two phases takes a value in the two-phase coexistence region, the thermodynamic potential of the system contains a contribution due to the interfaces. Studying the chemical potential excess relative to the coexistence curve as a function of the density, for a suitable range of linear dimensions of the simulation box, the interfacial contribution to the thermodynamic potential can be found via thermodynamic integration methods. While for slab-like two-phase configurations this method is well-known (and has been tested for various models by comparison with other methods, such as the analysis of the capillary wave induced broadening of interfacial profiles), for curved interfaces of droplets this technique is new. The question whether it can be used to estimate a Tolman length is considered, and an extension to discuss phase coexistence in systems confined by planar walls is given. Then line-tension corrections need to be considered both for slab-like two-phase geometries and for wall-attached (sphere-cap-shaped) droplets. The methods proposed in this paper yield input for the description of both homogeneous and heterogeneous nucleation and growth.