Quaternions and hybrid nematic disclinations

TL;DR

This paper introduces a quaternion-based geometric framework to classify and analyze the complex director profiles of disclination lines in nematic liquid crystals, linking topological theory with observable features.

Contribution

It develops a robust quaternion decomposition method for disclination loops, bridging abstract topological classification with local geometric features.

Findings

Quaternion description effectively classifies disclination profiles.

Topological classification aligns with observable disclination features.

Framework applies to linked loops with varying director profiles.

Abstract

Disclination lines in nematic liquid crystals can exist in different geometric conformations, characterised by their director profile. In certain confined, colloidal and even more prominently in chiral nematics, the director profile may vary along the disclination line. We construct a robust geometric decomposition of director profile variations in closed disclination loops based on a quaternion description and use it to apply topological classification to linked loops with arbitrary variation of the profile. The description bridges the gap between the known abstract classification scheme derived from homotopy theory and the observable local features of disclinations. We compare the resulting decomposition of disclination loop features to a similar decomposition of nematic textures on closed surfaces.