Equilibrium configurations of director in a planar nematic cell with one spatially modulated surface

TL;DR

This paper analyzes equilibrium configurations of nematic liquid crystal directors in a cell with one flat and one sinusoidally modulated surface, deriving analytical expressions and studying disclination line positions.

Contribution

It provides analytical solutions for director distribution in a modulated nematic cell with disclinations, linking surface relief parameters to defect positions.

Findings

Disclination lines align above surface extrema.

Disclination distance decreases with increased relief depth.

Analytical expressions describe director configurations.

Abstract

We study two-dimensional equilibrium configurations of nematic liquid crystal (NLC) director in a cell confined between two parallel surfaces: a planar surface and a spatially modulated one. The relief of the modulated surface is described by a smooth periodic sine-like function. The director easy axis orientation is homeotropic at one of the bounding surfaces and is planar at the other one. Strong NLC anchoring with both surfaces is assumed. We consider the case where disclination lines occur in the bulk of NLC strictly above local extrema of the modulated surface. These disclination lines run along the crests and troughs of the relief waves. In the approximation of planar director deformations we obtain analytical expressions describing a director distribution in the bulk of the cell. Equilibrium distances from disclination lines to the modulated surface are calculated and their dependences on the cell thickness and the period and depth of the surface relief are studied. It is shown that the distances from disclination lines to the modulated surface decrease as the depth of the relief increases.