Effective free energy method for nematic liquid crystals in contact with structured substrates

TL;DR

This paper introduces an effective free energy method to analyze the phase behavior of nematic liquid crystals confined between structured substrates, enabling accurate phase diagram predictions and energy barrier calculations.

Contribution

The study develops a novel effective free energy approach that simplifies the analysis of nematic liquid crystals on patterned substrates, matching direct minimization results.

Findings

Good agreement between effective energy and direct minimization phase boundaries

Method enables calculation of energy barriers in bistable nematic devices

Effective free energy simplifies complex phase behavior analysis

Abstract

We study the phase behavior of a nematic liquid crystal confined between a flat substrate with strong anchoring and a patterned substrate whose structure and local anchoring strength we vary. By first evaluating an effective surface free energy function characterizing the patterned substrate we derive an expression for the effective free energy of the confined nematic liquid crystal. Then we determine phase diagrams involving a homogeneous state in which the nematic director is almost uniform and a hybrid aligned nematic state in which the orientation of the director varies through the cell. Direct minimization of the free energy functional were performed in order to test the predictions of the effective free energy method. We find remarkably good agreement between the phase boundaries calculated from the two approaches. In addition the effective energy method allows one to determine the energy barriers between two states in a bistable nematic device.