Defects in nematic membranes can buckle into pseudospheres

TL;DR

This paper investigates how topological defects in nematic membranes induce buckling into pseudospherical shapes, revealing the influence of elastic and bending energies on membrane morphology.

Contribution

It formulates the free energy of nematic membranes using differential geometry, highlighting defect-induced buckling and shape variations due to elastic anisotropies.

Findings

Defects cause membranes to buckle into pseudospherical shapes.

Bending rigidity modifies the defect-induced shapes.

Different defect types lead to distinct membrane morphologies.

Abstract

A nematic membrane is a sheet with embedded orientational order, which can occur in biological cells, liquid crystal films, manufactured materials, and other soft matter systems. By formulating the free energy of nematic films using tensor contractions from differential geometry, we elucidate the elastic terms allowed by symmetry, and indicate differences from hexatic membranes. We find that topological defects in the orientation field can cause the membrane to buckle over a size set by the competition between surface tension and in-plane elasticity. In the absence of bending rigidity the resulting shape is universal, known as a parabolic pseudosphere or a revolved tractrix. Bending costs oppose such buckling and modify the shape in a predictable manner. In particular, the anisotropic rigidities of nematic membranes lead to different shapes for aster and vortex defects, in principle enabling measurement of couplings specific to nematic membranes.