Density-functional study of defects in two-dimensional circular nematic nanocavities

TL;DR

This study employs density-functional theory to analyze defect structures in two-dimensional circular nematic nanocavities, revealing differences in defect properties and connecting microscopic details with elastic theory predictions.

Contribution

It provides a detailed, thermodynamically consistent analysis of defect core energies and structures, including elastic constants, in 2D nematic nanocavities, improving upon previous simplified models.

Findings

Radial and tangential defects exhibit significantly different properties.

Elastic constants vary between defect types, contrary to previous models.

Small cavity sizes limit the elastic regime but reveal trend behaviors.

Abstract

We use density--functional theory to study the structure of two-dimensional defects inside a circular nematic nanocavity. The density, nematic order parameter, and director fields, as well as the defect core energy and core radius, are obtained in a thermodynamically consistent way for defects with topological charge $k=+1$ (with radial and tangential symmetries) and $k=+1/2$. An independent calculation of the fluid elastic constants, within the same theory, allows us to connect with the local free--energy density predicted by elastic theory, which in turn provides a criterion to define a defect core boundary and a defect core free energy for the two types of defects. The radial and tangential defects turn out to have very different properties, a feature that a previous Maier--Saupe theory could not account for due to the simplified nature of the interactions --which caused all elastic constants to be equal. In the case with two $k=+1/2$ defects in the cavity, the elastic r\'egime cannot be reached due to the small radii of the cavities considered, but some trends can already be obtained.