Nudged elastic band calculation of the binding potential for liquids at interfaces

The wetting behavior of a liquid on solid substrates is governed by the nature of the effective interaction between the liquid-gas and the solid-liquid interfaces, which is described by the binding or wetting potential $g(h)$ which is an excess free energy per unit area that depends on the liquid film height $h$. Given a microscopic theory for the liquid, to determine $g(h)$ one must calculate the free energy for liquid films of any given value of $h$; i.e. one needs to create and analyze out-of-equilibrium states, since at equilibrium there is a unique value of $h$, specified by the temperature and chemical potential of the surrounding gas. Here we introduce a Nudged Elastic Band (NEB) approach to calculate $g(h)$ and illustrate the method by applying it in conjunction with a microscopic lattice density functional theory for the liquid. We show too that the NEB results are identical to those obtained with an established method based on using a fictitious additional potential to stabilize the non-equilibrium states. The advantages of the NEB approach are discussed.