Curvature Energy of Surfactant Interfaces Confined to the Plaquettes of a Cubic Lattice

Abstract

We consider the curvatures of a faceted interface, for which the curvatures are concentrated along the edges and vertices of the underlying lattice. Such a lattice model has been frequently used to generate random monolayer or bilayer surfactant films. We demonstrate that the mean curvature of such an interface is concentrated along the edges, while the Gaussian curvature is confined to the vertices. We analyze in detail all possible interfacial configurations for an interface confined to the plaquettes of a cubic lattice and obtain an exact expression for the curvatures. The contribution of these curvatures to the total free energy of a surfactant solution is calculated, using two different expressions for the bending energy, and the utility of plaquette models is discussed. Show more