Defect patterns of two-dimensional nematic liquid crystals in confinement

TL;DR

This paper develops a geometric theory to relate defect patterns and winding numbers in two-dimensional nematic liquid crystals confined by boundaries, validated by experimental and theoretical comparisons.

Contribution

It introduces a general geometric framework linking boundary confinement geometry to defect configurations in 2D nematic liquid crystals.

Findings

The total winding number depends on confinement angles and curvature.

The theory matches observed defect patterns in experiments.

Provides a predictive rule for defect arrangements based on boundary shape.

Abstract

A two-dimensional or quasi-two-dimensional nematic liquid crystal refers to a surface confined system. When such a system is further confined by external line boundaries or excluded from internal line boundaries, the nematic directors form a deformed texture that may display defect points or defect lines, for which winding numbers can be clearly defined. Here, a particular attention is paid to the case when the liquid crystal molecules prefer to form a boundary nematic texture in parallel to the wall surface (i.e., following the homogeneous boundary condition). A general theory, based on geometric argument, is presented for the relationship between the sum of all winding numbers in the system (the total winding number) and the type of confinement angles and curved segments. The conclusion is validated by comparing the theoretical defect rule with existing nematic textures observed experimentally and theoretically in recent years.