Boundary-roughness effects in nematic liquid crystals

TL;DR

This paper investigates how surface roughness affects the orientation and structure of nematic liquid crystals, revealing a boundary layer with softened orientation and complex tilt behavior influenced by boundary conditions.

Contribution

It introduces a detailed analysis of boundary roughness effects on nematic liquid crystals, linking microscopic anchoring parameters to effective surface properties and highlighting the impact of boundary conditions.

Findings

Rough surfaces induce a softened boundary layer with decreased orientation.

The boundary layer length scale matches the corrugation wavelength.

Boundary conditions significantly influence the nematic configuration.

Abstract

We study the equilibrium configuration of a nematic liquid crystal bounded by a rough surface. The wrinkling of the surface induces a partial melting in the degree of orientation. This softened region penetrates the bulk up to a length scale which turns out to coincide with the characteristic wave length of the corrugation. Within the boundary layer where the nematic degree of orientation decreases, the tilt angle steepens and gives rise to a nontrivial structure, that may be interpreted in terms of an effective weak anchoring potential. We determine how the effective surface extrapolation length is related to the microscopic anchoring parameters. We also analyze the crucial role played by the boundary conditions assumed on the degree of orientation. Quite different features emerge depending on whether they are Neumann- or Dirichlet-like. These features may be useful to ascertain experimentally how the degree of orientation interacts with an external boundary.