Surface free energies for nematic shells

TL;DR

This paper develops a continuum model for nematic shells that derives surface free energies from 3D theories, incorporating geometry coupling and predicting shape-dependent nematic configurations.

Contribution

It introduces a novel derivation of surface free energy for nematic shells from 3D theories, including geometry coupling terms, unlike previous models.

Findings

Surface energies include new geometry-coupling terms.

Shell shape influences equilibrium nematic configurations.

Model unifies director and order-tensor approaches.

Abstract

We propose a continuum model to describe the molecular alignment in thin nematic shells. By contrast with previous accounts, the two-dimensional free energy, aimed at describing the physics of thin films of nematics deposited on curved substrates, is not postulated but it is deduced from the conventional three-dimensional theories of nematic liquid crystals. Both the director and the order-tensor theories are taken into account. The so-obtained surface energies exhibit extra terms compared to earlier models. These terms reflect the coupling of the geometry of the shell with the nematic order parameters. As expected, the shape of the shell plays a key role in the equilibrium configurations of nematics coating it.