Topology of orientational defects in confined smectic liquid crystals

TL;DR

This paper introduces a topological framework for understanding orientational defects in confined smectic liquid crystals, linking defect networks to boundary curvature and confinement geometry through simulations and experiments.

Contribution

It develops a formalism to characterize defect networks with topological charges and demonstrates how boundary shape influences defect configurations in smectic liquid crystals.

Findings

Defect networks can be reconstructed from simple topological building blocks.

Wall curvature influences grain boundary anchoring behavior.

Number and position of defect nodes are tunable by boundary geometry.

Abstract

We propose a general formalism to characterize orientational frustration of smectic liquid crystals in confinement by interpreting the emerging networks of grain boundaries as objects with a topological charge. In a formal idealization, this charge is distributed in point-like units of quarter-integer magnitude, which we identify with tetratic disclinations located at the end points and nodes. This coexisting nematic and tetratic order is analyzed with the help of extensive Monte Carlo simulations for a broad range of two-dimensional confining geometries as well as colloidal experiments, showing how the observed defect networks can be universally reconstructed from simple building blocks. We further find that the curvature of the confining wall determines the anchoring behavior of grain boundaries, such that the number of nodes in the emerging networks and the location of their end points can be tuned by changing the number and smoothness of corners, respectively.