# Bistable curvature potential at hyperbolic points of nematic shells

## TL;DR

This paper investigates the curvature-induced effects on nematic liquid crystal shells, revealing that at hyperbolic points, the curvature potential becomes bistable, influencing molecular alignment.

## Contribution

It introduces a systematic method to extract a curvature potential from the elastic energy of nematic shells, highlighting bistability at hyperbolic points.

## Key findings

- Curvature potential influences molecular alignment on nematic shells.
- Bistability occurs specifically at hyperbolic points on the surface.
- The fossil energy component relates to surface curvature and affects director configurations.

## Abstract

Nematic shells are colloidal particles coated with nematic liquid crystal molecules which may freely glide and rotate on the colloid's surface while keeping their long axis on the local tangent plane. We describe the nematic order on a shell by a unit director field on an orientable surface. Equilibrium fields can then be found by minimising the elastic energy, which in general is a function of the surface gradient of the director field. We learn how to extract systematically out of this energy a fossil component, related only to the surface and its curvatures, which expresses a curvature potential for the molecular torque. At hyperbolic points on the colloid's surface, and only there, the alignment preferred by the curvature potential may fail to be a direction of principal curvature. There the fossil energy becomes bistable.