Wetting and drying transitions in mean-field theory: Describing the surface parameters for the theory of Nakanishi and Fisher in terms of a microscopic model

The theory of Nakanishi and Fisher [Phys. Rev. Lett. 49, 1565 (1982)] describes the wetting behavior of a liquid and vapor phase in contact with a substrate in terms of the surface chemical potential h(1) and the surface enhancement parameter g. Using density functional theory, we derive molecular expressions for h(1) and g and compare with earlier expressions derived from Landau lattice mean-field theory. The molecular expressions are applied to compare with results from density functional theory for a square-gradient fluid in a square-well fluid-substrate potential and with molecular dynamics simulations.