Topological fine structure of smectic grain boundaries and tetratic disclination lines within three-dimensional smectic liquid crystals

TL;DR

This study uses Monte-Carlo simulations to analyze the complex topological structures of grain boundaries and disclination lines in three-dimensional smectic liquid crystals, revealing their tetratic symmetry and defect configurations.

Contribution

It introduces a three-dimensional tetratic order parameter to interpret smectic grain boundaries as disclination lines, advancing understanding of defect topology in confined smectics.

Findings

Grain boundaries are pairs of tetratic disclination lines.

Disclination lines are located on edges of nematic domain boundaries.

Provides a detailed topological characterization of 3D smectic defects.

Abstract

Observing and characterizing the complex ordering phenomena of liquid crystals subjected to external constraints constitutes an ongoing challenge for chemists and physicists alike. To elucidate the delicate balance appearing when the intrinsic positional order of smectic liquid crystals comes into play, we perform Monte-Carlo simulations of rod-like particles in a range of cavities with a cylindrical symmetry. Based on recent insights into the topology of smectic orientational grain boundaries in two dimensions, we analyze the emerging three-dimensional defect structures from the perspective of tetratic symmetry. Using an appropriate three-dimensional tetratic order parameter constructed from the Steinhardt order parameters, we show that those grain boundaries can be interpreted as a pair of tetratic disclination lines that are located on the edges of the nematic domain boundary. Thereby, we shed light on the fine structure of grain boundaries in three-dimensional confined smectics.