Anisotropic disclination cores in nematic liquid crystals modelled by a self consistent molecular field theory

TL;DR

This paper develops a self-consistent molecular field theory for nematic liquid crystals that models anisotropic disclination cores, capturing biaxial order and elastic effects, and compares well with experimental data on large defect cores.

Contribution

It introduces a tensor order parameter-based theory that handles anisotropic elastic energies without divergences, extending understanding of disclination structures in nematic liquid crystals.

Findings

Biaxial order appears at intermediate distances from the core.

The theory accurately reproduces $ ext{±}1/2$ disclination configurations.

Elastic anisotropy affects disclination polarization and active stress.

Abstract

Disclination configurations of a nematic liquid crystal are studied within a self-consistent molecular field theory. The theory is based on a tensor order parameter, and can accommodate anisotropic elastic energies without the known divergences in the Landau-de Gennes formulation. Our results agree with the asymptotic results of Dzyaloshinsky for the Frank-Oseen energy and far from the defect core, but reveal biaxial order at intermediate distances from the core, crossing over to uniaxial, but isotropic configurations as the core is approached. The elastic terms considered in our energy allow for separate control of surface tension, anchoring, and elasticity contrast, and are used to analyze recent results for lyotropic chromonic liquid crystals. The latter display unusually large defect cores (on the order of tens of microns) which can be used for a quantitative comparison with the theory. Both $\pm 1/2$ disclination configurations are well reproduced by our calculations. Elastic anisotropy is also shown to lead to qualitative changes in the disclination polarization, a quantity that is proportional to the active stress in models of active matter.