Generalized Berreman's model of the elastic surface free energy of a nematic liquid crystal on a sawtoothed substrate

TL;DR

This paper generalizes Berreman's model to describe the elastic surface free energy of nematic liquid crystals on sawtooth substrates, accounting for surface structure effects and comparing with Landau-de Gennes results.

Contribution

It extends Berreman's model to include additional contributions and validates it against Landau-de Gennes simulations for strong anchoring conditions.

Findings

Non-analytic $q\ln q$ contribution due to disclination lines

Next-to-leading $q$ contribution consistent with predictions

Model accuracy confirmed for $wL>1$ with strong anchoring

Abstract

In this paper we present a generalization of Berreman's model for the elastic contribution to the surface free-energy density of a nematic liquid crystal in presence of a sawtooth substrate which favours homeotropic anchoring, as a function of the wavenumber of the surface structure $q$, the tilt angle $\alpha$ and the surface anchoring strength $w$. In addition to the previously reported non-analytic contribution proportional to $q\ln q$, due to the nucleation of disclination lines at the wedge bottoms and apexes of the substrate, the next-to-leading contribution is proportional to $q$ for a given substrate roughness, in agreement with Berreman's predictions. We characterise this term, finding that it has two contributions: the deviations of the nematic director field with respect to the corresponding to the isolated disclination lines, and their associated core free energies. Comparison with the results obtained from the Landau-de Gennes model shows that our model is quite accurate in the limit $wL>1$, when strong anchoring conditions are effectively achieved.