Contact angles from Young's equation in molecular dynamics simulations

We propose a method to calculate the equilibrium contact angle of heterogeneous 3-phase solid/fluid/fluid systems using molecular dynamics simulations. The proposed method, which combines the phantom-wall method [F. Leroy and F. Müller-Plathe, J. Chem. Phys. 133, 044110 (2010)] and Bennett's acceptance ratio approach [C. H. Bennett, J. Comput. Phys. 22, 245 (1976)], is able to calculate the solid/fluid surface tension relative to the solid surface energy. The calculated relative surface tensions can then be used in Young's equation to estimate the equilibrium contact angle. A fluid droplet is not needed for the proposed method, in contrast to the situation for direct simulations of contact angles. In addition, while prior free-energy based methods for contact angles mainly focused on the wetting of fluids in coexistence with their vapor on solid surfaces, the proposed approach was designed to study the contact angles of fluid mixtures on solid surfaces above the fluid saturation pressures. Using the proposed approach, the contact angles of binary Lennard-Jones fluid mixtures on a non-polar solid substrate were calculated at various interaction parameters and the contact angle of water in equilibrium with CO₂ on a hydrophilic polar silica surface was obtained. For both non-polar and polar systems, the calculated contact angles from the proposed method were in agreement with those obtained from the geometry of a cylindrical droplet. The computational cost of the proposed method was found to be comparable to that of simulations that use fluid droplets, but the new method provides a way to calculate the contact angle directly from Young's equation without ambiguity.