Liquid Crystals on Deformable Surfaces

TL;DR

This paper develops thermodynamically consistent models for liquid crystals on deformable surfaces, coupling elastic and geometric energies, and explores their complex dynamics and equilibrium shapes through numerical simulations.

Contribution

It introduces new coupled surface liquid crystal models considering surface deformation, unifying elastic and geometric energies in a thermodynamically consistent framework.

Findings

Surface curvature significantly influences liquid crystal configurations.

Coupled models predict asymmetric equilibrium shapes.

Numerical solutions reveal complex dynamics and shape transitions.

Abstract

Liquid crystals with molecules constrained to the tangent bundle of a curved surface show interesting phenomena resulting from the tight coupling of the elastic and bulk free energies of the liquid crystal with geometric properties of the surface. We derive thermodynamically consistent Frank-Oseen-Helfrich and Landau-de Gennes-Helfrich models which consider the simultaneous relaxation of the director/Q-tensor fields and the surface. The resulting systems of vector- or tensor-valued surface partial differential equation and geometric evolution laws are numerically solved to tackle the rich dynamics of these systems and to compute the resulting equilibrium shapes. The results strongly depend on the intrinsic and extrinsic curvature contributions and can lead to unexpected asymmetric shapes.