Numerical study of the effect of structure and geometry on van der Waals forces

TL;DR

This paper investigates how structure and geometry influence van der Waals forces using multipolar expansions and introduces a numerical method to analyze shape and orientation effects on these forces.

Contribution

It presents a detailed analysis of van der Waals forces for coated spheres and develops a numerical approach for arbitrary shapes and orientations.

Findings

Force varies as d^(-2) for small separations on a gold shell.

Force behaves as d^(-5/2) when coating appears two-dimensional.

New numerical method for arbitrary shape interactions.

Abstract

We use multipolar expansions to find the force on a gold coated sphere above a gold substrate; we study both an empty gold shell and a gold coated polystyrene sphere. We find four characteristic separation ranges. In the first region, which for the empty gold shell occurs for distances, d, smaller than the thickness of the coating, the result agrees with that on a solid gold sphere and varies as d^(-2); for larger separations there is a region where the force behaves as if the coating is strictly two dimensional and varies as d^(-5/2); in the third region the dependence is more unspecific; in the forth region when d is larger than the radius, the force varies as d^(-4). For homogeneous objects of more general shapes we introduce a numerical method based on the solution of an integral equation for the electric field over a system of objects with arbitrary shapes. We study the effect of shape and orientation on the van der Waals interaction between an object and a substrate and between two objects.