Curvature corrections to the nonlocal interfacial model for short-ranged forces

In this paper we revisit the derivation of a nonlocal interfacial Hamiltonian model for systems with short-ranged intermolecular forces. Starting from a microscopic Landau-Ginzburg-Wilson Hamiltonian with a double-parabola potential, we reformulate the derivation of the interfacial model using a rigorous boundary integral approach. This is done for three scenarios: a single fluid phase in contact with a nonplanar substrate (i.e., wall); a free interface separating coexisting fluid phases (say, liquid and gas); and finally a liquid-gas interface in contact with a nonplanar confining wall, as is applicable to wetting phenomena. For the first two cases our approaches identifies the correct form of the curvature corrections to the free energy and, for the case of a free interface, it allows us to recast these as an interfacial self-interaction as conjectured previously in the literature. When the interface is in contact with a substrate our approach similarly identifies curvature corrections to the nonlocal binding potential, describing the interaction of the interface and wall, for which we propose a generalized and improved diagrammatic formulation.

Figure 1

Schematic illustration of a nonplanar interfacial configuration (blue line) for a constrained wetting film of liquid at a nonplanar wall (black line). Conventions for the surface normals are shown. The inset shows the double-parabola approximation for $\mathrm{\Delta }\varphi \left(m\right)$.

Figure 2

Schematic illustration of the coordinates, vectors, and geometry appearing in the curvature expansion for a constrained interfacial configuration. The symbols are described in the text.