Nematic cells with defect-patterned alignment layers

TL;DR

This study uses Monte Carlo simulations to explore how defect-patterned alignment layers influence nematic order in cells, revealing a critical height-to-spacing ratio that determines ordered versus disordered states and examining optical and electric responses.

Contribution

It introduces a detailed simulation analysis of defect-patterned nematic cells, highlighting the critical role of cell height relative to defect spacing in ordering behavior.

Findings

Ordered nematic state when H/a > 0.9 with defect network formation.

Disordered state when H/a < 0.9 with defect lines threading through the cell.

Simulation of optical textures and electric field switching behavior.

Abstract

Using Monte Carlo simulations of the Lebwohl--Lasher model we study the director ordering in a nematic cell where the top and bottom surfaces are patterned with a lattice of $\pm 1$ point topological defects of lattice spacing $a$. We find that the nematic order depends crucially on the ratio of the height of the cell $H$ to $a$. When $H/a \gtrsim 0.9$ the system is very well--ordered and the frustration induced by the lattice of defects is relieved by a network of half--integer defect lines which emerge from the point defects and hug the top and bottom surfaces of the cell. When $H/a \lesssim 0.9$ the system is disordered and the half--integer defect lines thread through the cell joining point defects on the top and bottom surfaces. We present a simple physical argument in terms of the length of the defect lines to explain these results. To facilitate eventual comparison with experimental systems we also simulate optical textures and study the switching behavior in the presence of an electric field.