Scaling of the elastic contribution to the surface free energy of a nematic on a sawtoothed substrate

TL;DR

This paper investigates how the elastic energy contribution to the surface free energy of a nematic liquid crystal scales with substrate periodicity, using numerical and analytical methods to account for defect nucleation effects.

Contribution

It provides a combined numerical and analytical analysis of the elastic surface free energy scaling in nematics on sawtooth substrates, highlighting defect-induced contributions.

Findings

Elastic contribution scales as qlnq with substrate periodicity.

Disclination lines nucleate at wedge and apex regions.

Analytical and numerical methods agree on scaling behavior.

Abstract

We characterize the elastic contribution to the surface free energy of a nematic in presence of a sawtooth substrate. Our findings are based on numerical minimization of the Landau-de Gennes model and analytical calculations on the Frank-Oseen theory. The nucleation of disclination lines (characterized by non-half-integer winding numbers) in the wedges and apexes of the substrate induces a leading order proportional to qlnq to the elastic contribution to the surface free energy density, q being the wavenumber associated with the substrate periodicity.