Competing Alignments of Nematic Liquid Crystals on Square Patterned Substrates

TL;DR

This paper investigates how nematic liquid crystals align on square-patterned substrates using simulations and continuum theory, revealing bistable alignments and potential anchoring transitions influenced by pattern strength.

Contribution

It combines Monte Carlo simulations and continuum theory to analyze nematic alignment on square patterns, highlighting new bistability and anchoring transition phenomena.

Findings

Bistable degenerate azimuthal alignment along square edges

Potential anchoring transition to diagonal alignment with weak polar anchoring

No bridging transition observed in thin cells

Abstract

A theoretical analysis is presented of a nematic liquid crystal confined between substrates pat- terned with squares that promote vertical and planar alignment. Two approaches are used to eluci- date the behavior across a wide range of length scales: Monte Carlo simulation of hard particles and Frank-Oseen continuum theory. Both approaches predict bistable degenerate azimuthal alignment in the bulk along the edges of the squares; the continuum calculation additionally reveals the possi- bility of an anchoring transition to diagonal alignment if the polar anchoring energy associated with the pattern is sufficiently weak. Unlike the striped systems previously analyzed, the Monte Carlo simulations suggest that there is no "bridging" transition for sufficiently thin cells. The extent to which these geometrically patterned systems resemble topographically patterned substrates, such as square wells, is also discussed.