Wetting transitions in systems with van der Waals forces

Abstract

Wetting and drying phase transitions in the presence of van der Waals forces are studied in the Ising lattice-gas model. With low-temperature series and mean-field analyses as a guide, a Landau theory, valid at temperatures below the bulk critical temperature $T_c$, is constructed. From the Landau theory, phase diagrams—including fourth-order, tricritical, critical, and critical end-point wetting transitions—are found. Fourth-order wetting occurs in the idealized case where substrate-adsorbate and adsorbate-adsorbate interactions differ only by an overall factor measuring relative strength. A scaling analysis is presented, and critical exponents, expected to be exact as hyperscaling predicts upper critical dimensions to be less than 3, are obtained. Detailed results from the full mean-field theory, in agreement with the Landau theory, are given, and in one case a detailed mapping from the mean-field theory to the Landau theory is provided. An exact symmetry between wetting and drying transitions, within mean-field theory, is found. The full mean-field equations, supplemented by a scaling analysis, are used to provide predictions of novel wetting and drying phenomena near $T_c$, as a function of variable adsorbate-adsorbate coupling near the adsorbate-substrate interface. Some of these phenomena bear resemblance to, but are distinct from, the special and extraordinary points which appear in the case of short-ranged forces. The relationship between the order of the transitions and the substrate and adsorbate potential parameters is systematically explored. Tuning of substrate-adsorbate interactions by plating the substrate with a monolayer of a third material is proposed as a means of producing critical wetting below $T_c$ as well as, possibly, critical drying at $T_c$.