Influence of the Extrinsic Curvature on 2D Nematic Films

TL;DR

This paper explores how extrinsic curvature influences the shape and stability of 2D nematic films, revealing two main alignment patterns and the impact of parameters on the interface's Gaussian curvature.

Contribution

It introduces a generalized Plateau problem for axisymmetric nematic interfaces, analyzing equilibrium shapes and stability considering extrinsic curvature effects.

Findings

Two classes of equilibrium alignments: along meridians and parallels.

Gaussian curvature varies with parameters, being negative, zero, or positive.

Stability analysis of the equilibrium configurations.

Abstract

Nematic interfaces are thin fluid films, ideally two-dimensional, endowed with an in-plane degenerate nematic order. In this letter we examine a generalisation of the classical Plateau problem to an axisymmetric nematic interface bounded by two coaxial parallel rings. The equilibrium interface shape results from the competition between surface tension, which favours the minimization of the interface area, and the nematic elasticity which instead promotes the alignment of the molecules along a common direction. We find two classes of equilibrium solutions with intrinsically uniform alignments: one in which the molecules are aligned along the meridians, the other along parallels. Depending on two parameters, one geometric and the other constitutive, the Gaussian curvature of the equilibrium interface may be negative, vanishing or positive. The stability of these equilibrium configurations is investigated.