Hydrodynamic Modeling of Odd Nematic Elasticity in Liquid Crystals

TL;DR

This paper introduces the concept of odd nematic elasticity in liquid crystals, revealing how non-reciprocal interactions influence defect dynamics and domain wall behavior, with potential applications in manipulating topological defects.

Contribution

It generalizes odd elasticity to nematic liquid crystals using a complex Ginzburg--Landau framework, revealing novel defect behaviors and proposing a new approach to control topological defects.

Findings

Domain walls become self-propelled with bidirectional flow

Point defects can self-spin and form spiral patterns

Defect interactions exhibit unique dynamics different from active nematics

Abstract

There is a recent interest in studying odd elasticity in soft solids. Current focus has been on simple solids. However, many soft solids are structured and can exhibit nematic elasticity or viscoelasticity. Here we generalize the concept of odd elasticity to nematic elasticity. By rewriting the governing equation for two-dimensional nematic liquid crystals (LCs) in terms of complex Ginzburg--Landau equation, we propose an odd nematic elastic term and its stress term in the hydrodynamic model of nematic LCs. The odd nematic elasticity can be physically interpreted as non-reciprocal interactions between neighboring directors. In odd nematics we find that domain walls become self-propelled and are accompanied by a bidirectional flow, and point defects can self-spin, develop a spiral pattern, and induce a vortical flow. Interactions of a pair of defects show rich dynamics that are distinct from those in active nematics. As such, we have developed an odd general elasticity, which can be further generalized to other viscoelastic materials, and proposed a novel way to manipulate topological defects in nematic LCs.