Critical Casimir forces between planar and crenellated surfaces

TL;DR

This paper investigates the critical Casimir forces between flat and crenellated surfaces using mean-field theory, revealing significant deviations from the proximity force approximation and proposing a correction based on step contributions.

Contribution

It introduces a first-order correction to the proximity force approximation for critical Casimir forces involving structured surfaces, accounting for edge and sidewall effects.

Findings

Full numerical calculations show deviations from the proximity force approximation.

A step contribution correction improves the approximation accuracy.

Edges and sidewalls significantly influence the Casimir force in structured geometries.

Abstract

We study critical Casimir forces between planar walls and geometrically structured substrates within mean-field theory. As substrate structures, crenellated surfaces consisting of periodic arrays of rectangular crenels and merlons are considered. Within the widely used proximity force approximation, both the top surfaces of the merlons and the bottom surfaces of the crenels contribute to the critical Casimir force. However, for such systems the full, numerically determined critical Casimir forces deviate significantly fromthe pairwise addition formalismunderlying the proximity force approximation. A first-order correction to the proximity force approximation is presented in terms of a step contribution arising from the critical Casimir interaction between a planar substrate and the right-angled steps of the merlons consisting of their upper and lower edges as well as their sidewalls.