Wetting transitions and surface critical phenomena at solid-fluid interfaces

Abstract

The van der Waals density functional model of inhomogeneous fluids introduced by Teletzke et al. is applied to construct global phase diagrams that display wetting transition points, thin to thick thin-film transition points, and accompanying surface critical, tricritical, and multicritical points of a solid-fluid interface. The model is based on mean field theory, yields an integral equation for density distributions, can be solved analytically, and predicts both first- and second-order wetting transitions depending on location in field variable space. Here we show that the model, although mathematically simple, predicts thin to thick thin-film transition and surface critical, tricritical, and multicritical phenomena. The various transition and critical points are obtained directly by solution of algebraic equations derived from the model. The global phase diagrams have as coordinates the temperature and chemical potential and an interaction potential parameter W which is the ratio of characteristic energy of two-body solid-fluidinteraction to fluid-fluid interaction. Diagrams are constructed for three values of the three-body interaction potential energy parameter, W 3 = 1 3 , 1, and 3, corresponding to the three phase diagrams of Nakanishi and Fisher who inferred the diagram structure from scaling studies of a magnetic system obeying the Landau-Ginzburg free energy model. Our results agree with their critical exponents Δ and Δ 1 for the ordinary, special, and extraordinary multicritical points. However, we find a quantitative difference between our results and the parameter range over which Nakanishi and Fisher suggested one of the scaling relations holds.