Boojums in Liquid Crystals Around a Colloid

TL;DR

This paper analyzes the structure of boojum disclinations in liquid crystals around a spherical colloid using the Landau-de Gennes theory, revealing the local structure and conditions for their formation.

Contribution

It provides a detailed mathematical characterization of boojum disclinations in liquid crystals near colloids under specific boundary conditions.

Findings

Energy minimizers exhibit boojum disclinations at poles

Local structure of boojum disclinations characterized

Axially symmetric solutions analyzed

Abstract

We study the Landau-de Gennes theory in the one constant limit. The bulk domain is the exterior of a spherical colloid. A Rapini-Papoular surface potential is imposed on the colloid surface, supplemented by a homogeneous far-field condition at spatial infinity. Under the axially symmetric ansatz and the Lyuksyutov constraint, we show that energy minimizers exhibit boojum disclinations at the two poles of the colloid. The local structure of these boojum disclinations is also characterized.