Lateral and normal forces between patterned substrates induced by nematic fluctuations

TL;DR

This paper investigates how thermal fluctuations in a nematic liquid crystal confined between patterned substrates induce lateral and normal forces, which depend on the substrate patterning and can be comparable to van der Waals forces.

Contribution

It introduces a Gaussian approximation model to analyze fluctuation-induced forces between patterned substrates in nematic liquid crystals, highlighting the oscillatory nature of lateral forces and the conditions for attractive or repulsive normal forces.

Findings

Lateral force oscillates with lateral shift between substrates.

Fluctuation-induced normal force can be attractive or repulsive.

Lateral fluctuation force can be comparable to van der Waals force.

Abstract

We consider a nematic liquid crystal confined by two parallel flat substrates whose anchoring conditions vary periodically in one lateral direction. Within the Gaussian approximation, we study the effective forces between the patterned substrates induced by the thermal fluctuations of the nematic director. The shear force oscillates as function of the lateral shift between the patterns on the lower and the upper substrates. We compare the strength of this fluctuation-induced lateral force with the lateral van der Waals force arising from chemically structured adsorbed monolayers. The fluctuation-induced force in normal direction is either repulsive or attractive, depending on the model parameters.