Director configuration of planar solitons in nematic liquid crystals

TL;DR

This paper investigates how external magnetic fields influence the director configuration of disclination lines in nematic liquid crystals, revealing the potential for elongated defect cores due to magnetic effects.

Contribution

It introduces a combined analytical and numerical approach to evaluate director configurations under magnetic fields, including the effects of elastic anisotropy.

Findings

Director configuration is continuous except along a line segment influenced by magnetic field.

Elongated defect cores are possible in nematics under magnetic fields.

Analytical approximations agree well with numerical results.

Abstract

The director configuration of disclination lines in nematic liquid crystals in the presence of an external magnetic field is evaluated. Our method is a combination of a polynomial expansion for the director and of further analytical approximations which are tested against a numerical shooting method. The results are particularly simple when the elastic constants are equal, but we discuss the general case of elastic anisotropy. The director field is continuous everywhere apart from a straight line segment whose length depends on the value of the magnetic field. This indicates the possibility of an elongated defect core for disclination lines in nematics due to an external magnetic field.