Distortional Lifshitz Vectors and Helicity in Nematic Free Energy Density

TL;DR

This paper introduces a compact formulation of nematic liquid crystal free energy density using two distortion vectors and helicity, highlighting their polar and pseudoscalar properties.

Contribution

It presents a novel approach to express nematic free energy density with two vectors and helicity, emphasizing their geometric and physical significance.

Findings

Compact free energy density expression derived

Distortional Lifshitz vectors characterized

Helicity's pseudoscalar nature analyzed

Abstract

Here we discuss the free energy of nematic liquid crystals using two vectors and the helicity, with the aim of having a compact form of its density. The two vectors are due to the splay and bend distortions of the director field. They have a polar nature, whereas the helicity is a pseudoscalar.