Theory and simulation of the confined Lebwohl-Lasher model

TL;DR

This paper investigates the phase behavior of the Lebwohl-Lasher model for nematic liquid crystals confined between parallel plates, revealing a single isotropic-nematic transition influenced by surface interactions through simulation and mean-field theory.

Contribution

It demonstrates the existence of a single phase transition in confined Lebwohl-Lasher models with different surface anchoring, extending understanding beyond narrow cell regimes.

Findings

Single phase transition observed in symmetric and asymmetric cells.

Transition corresponds to the isotropic-nematic (capillary) transition.

Wider cells exhibit the same transition, influenced by surface anchoring.

Abstract

We discuss the Lebwohl-Lasher model of nematic liquid crystals in a confined geometry, using Monte Carlo simulation and mean-field theory. A film of material is sandwiched between two planar, parallel plates that couple to the adjacent spins via a surface strength $\epsilon_s$. We consider the cases where the favoured alignments at the two walls are the same (symmetric cell) or different (asymmetric or hybrid cell). In the latter case, we demonstrate the existence of a {\it single} phase transition in the slab for all values of the cell thickness. This transition has been observed before in the regime of narrow cells, where the two structures involved correspond to different arrangements of the nematic director. By studying wider cells, we show that the transition is in fact the usual isotropic-to-nematic (capillary) transition under confinement in the case of antagonistic surface forces. We show results for a wide range of values of film thickness, and discuss the phenomenology using a mean-field model.