Geometry and mechanics of disclination lines in 3D nematic liquid crystals

TL;DR

This paper analyzes the geometric and mechanical properties of disclination lines in 3D nematic liquid crystals, introducing new methods to characterize their structure and forces influencing their motion.

Contribution

It develops a comprehensive geometric framework for disclination lines in 3D nematics, including new tensor representations and force analyses, advancing understanding of their behavior.

Findings

Disclination structures vary along their length, including twist and defect-like features.

External stresses and interactions significantly influence disclination dynamics.

The framework applies to both passive and active liquid crystal systems.

Abstract

In 3D nematic liquid crystals, disclination lines have a range of geometric structures. Locally, they may resemble $+1/2$ or $-1/2$ defects in 2D nematic phases, or they may have 3D twist. Here, we analyze the structure in terms of the director deformation modes around the disclination, as well as the nematic order tensor inside the disclination core. Based on this analysis, we construct a vector to represent the orientation of the disclination, as well as tensors to represent higher-order structure. We apply this method to simulations of a 3D disclination arch, and determine how the structure changes along the contour length. We then use this geometric analysis to investigate three types of forces acting on a disclination: Peach-Koehler forces due to external stress, interaction forces between disclination lines, and active forces. These results apply to the motion of disclination lines in both conventional and active liquid crystals.