Saddle-splay elasticity and field induced soliton in nematics

TL;DR

This paper investigates how saddle-splay elasticity influences the non-linear ground state of nematic liquid crystals under magnetic fields, identifying conditions for soliton instability related to elastic constants.

Contribution

It introduces a detailed analysis of saddle-splay effects on nematic solitons and determines the critical elastic constant ratio for instability bifurcation.

Findings

Instability occurs when |K_{24}/K| > 0.707.

Saddle-splay elasticity significantly affects the stability of nematic solitons.

The bifurcation point is identified for the kink-soliton under magnetic fields.

Abstract

The symmetry breaking Freedericksz transitions, when a uniformly aligned nematic state is replaced by a homogeneously or periodically distorted state, have been extensively studied before. Here we analyse the influence of the saddle-splay elasticity on the non-linear ground state of nematic liquid crystal in presence of magnetic field above the Freedericksz threshold. We identify the bifurcation point when the kink-soliton is linearly unstable with respect to the perturbations of the wave vector in the direction perpendicular to the initial plane of soliton. This instability occurs only if the ratio of saddle-splay elastic constant to elastic modulus of nematics in one-constant approximation is above the critical value |K_{24}/K|>0.707.