Liquid-crystalline Casimir effect in the presence of a patterned substrate

TL;DR

This paper studies how a patterned substrate influences the Casimir force in a nematic liquid crystal cell, revealing that at large distances the effect can be approximated by an effective anchoring energy, with new numerical insights at smaller separations.

Contribution

It introduces a continuum theory analysis of the liquid-crystalline Casimir effect with patterned substrates, providing new numerical results for small separations.

Findings

At large distances, patterned substrate effects are captured by an effective anchoring energy.

Numerical results are presented for the Casimir force at smaller separations.

The patterned substrate modifies the Casimir force depending on the separation distance.

Abstract

We consider a nematic liquid crystal confined by two parallel planar interfaces, one being laterally homogeneous and the other provided by a substrate endowed with a periodic chemical stripe pattern. Based on continuum theory we analyze the influence of the lateral pattern on the liquid-crystalline Casimir force acting on the interfaces of the nematic cell at distance d due to the thermal fluctuations of the nematic director. For d much larger than the pattern periodicity, the influence of the patterned substrate can be described by a homogeneous, effective anchoring energy. By tuning this parameter we recover previous results for the liquid-crystalline Casimir force. For the general case, i.e., smaller separations, we present new numerical results.