Theoretical Study of van der Waals Dispersion Pressures Considering One-Dimensional Material Distributions in In-Plane Direction

The van der Waals (vdW) dispersion pressures between a half-space consisting of a uniform material and a half-space with one-dimensional material distribution in the in-plane direction have been theoretically derived. Two patterns of material distribution were considered here, i.e., a periodic distribution of materials (Pattern 1) and a distribution of two materials with single interface (Pattern 2). The vdW pressure for Pattern 1 was derived based on a Fourier series, while the vdW pressure for Pattern 2 was derived as elementary functions. The basic characteristics of these vdW pressures were clarified.