Charged inclusion in nematic liquid crystals

TL;DR

This paper develops a Ginzburg-Landau theory to describe how charged particles influence the molecular orientation and defect structures in nematic liquid crystals under inhomogeneous electric fields.

Contribution

It introduces a general theoretical framework for charged inclusions in nematic liquid crystals, predicting defect formations based on dielectric anisotropy and charge-to-radius ratio.

Findings

Defects form around charged particles, with structures depending on dielectric anisotropy.

The deformation strength increases with the charge-to-radius ratio.

Different defect types, such as Saturn rings or point defects, emerge based on dielectric properties.

Abstract

We present a general theory of liquid crystals under inhomogeneous electric field in a Ginzburg-Landau scheme. The molecular orientation can be deformed by electric field when the dielectric tensor is orientation-dependent. We then investigate the influence of a charged particle on the orientation order in a nematic state. The director is aligned either along or perpendicular to the local electric field around the charge, depending on the sign of the dielectric anisotropy. The deformation becomes stronger with increasing the ratio $Ze/R$, where $Ze$ is the charge and $R$ is the radius of the particle. Numerical analysis shows the presence of defects around the particle for large $Ze/R$. They are nanometer-scale defects for microscopic ions. If the dielectric anisotropy is positive, a Saturn ring defect appears. If it is negative, a pair of point defects appear apart from the particle surface, each being connected to the surface by a disclination line segment.