Shaping thin nematic films with competing boundary conditions

TL;DR

This paper investigates how nematic liquid crystal films with opposing boundary conditions deform and become unstable, revealing thresholds and bifurcations influenced by elastic anisotropy and capillarity.

Contribution

It introduces an analytical framework for understanding shape instabilities and director configurations in nematic films with competing boundary conditions.

Findings

Identified threshold thickness for flat film instability.

Analyzed bifurcation from circular to m-fold symmetric structures.

Provided insights into elastic-capillary interactions in liquid crystalline films.

Abstract

Free interfaces of liquid crystals tend to minimise both capillarity and anchoring forces. Here we study nematic films in planar and radial geometries with antagonistic anchoring boundary conditions and one deformable interface. Assuming a perturbation ansatz we study possible couplings of the director configuration with the shape of free interfaces. In the long-wavelength limit independent of the surface tension, we find analytically threshold thickness when flat film becomes unstable. Next we quantify the bifurcation of a circular ring towards structures with $m$-fold rotational symmetry, induced by elastic anisotropy of nematic director in the bulk. We believe that our simplified approach can give additional insight into elastic and capillary phenomena of materials with inherent liquid crystalline order and free interfaces.