Van der Waals interactions across stratified media

TL;DR

This paper derives an explicit formula for van der Waals interactions across layered media and compares it with continuum approximations, finding good agreement only for sufficiently thick layers.

Contribution

It provides a complete analytical expression for van der Waals forces in stratified media and assesses the validity of continuum models against discrete-layer calculations.

Findings

Agreement between models improves with layer thickness

Explicit formula for layered van der Waals interactions

Continuum approximation valid for layers of ten or more

Abstract

Working at the Lifshitz level, we investigate the van der Waals interactions across a series of layers with a periodic motif. We derive the complete form of the van der Waals interaction as an explicit function of the number of periodic layers. We then compare our result with an approximation based on an anisotropic-continuum representation of the stratified medium. Satisfactory agreement between discrete-layer and continuum models is reached only for thicknesses of ten or more layers.