Pattern-induced anchoring transitions in nematic liquid crystals

TL;DR

This paper investigates how patterned substrates influence nematic liquid crystal orientations, revealing anchoring transitions linked to substrate geometry and defects, using a modified Frank-Oseen model.

Contribution

It introduces a detailed analysis of anchoring transitions on patterned substrates with different geometries, highlighting the role of topological defects and substrate parameters.

Findings

Homeotropic to planar transition with increased roughness for sawtooth and sinusoidal substrates.

Homeotropic to oblique transition observed for crenellated substrates.

Complex dependence of anchoring phases on substrate roughness and anchoring strength.

Abstract

In this paper we revisit the problem of a nematic liquid crystal in contact with patterned substrates. The substrate is modelled as a periodic array of parallel infinite grooves of well-defined cross section sculpted on a chemically homogeneous substrate which favors local homeotropic anchoring of the nematic. We consider three cases: a sawtooth, a crenellated and a sinusoidal substrate. We analyse this problem within the modified Frank-Oseen formalism. We argue that, for substrate periodicities much larger than the extrapolation length, the existence of different nematic textures with distinct far-field orientations, as well as the anchoring transitions between them, are associated with the presence of topological defects either on or close to the substrate. For the sawtooth and sinusoidal case, we observe a homeotropic to planar anchoring transition as the substrate roughness is increased. On the other hand, a homeotropic to oblique anchoring transition is observed for crenellated substrates. In this case, the anchoring phase diagram shows a complex dependence on the substrate roughness and substrate anchoring strength.