Stability of Texture and Shape of Circular Domains of Langmuir Monolayers

TL;DR

This paper analyzes the stability and shape transformations of circular domains in Langmuir monolayers, revealing a phase transition between textures and conditions for shape instabilities driven by elastic and line tension effects.

Contribution

It introduces a simplified isotropic elastic model to study texture-induced shape instabilities in Langmuir monolayer domains, identifying key conditions for instability onset.

Findings

First-order phase transition between two textures in circular domains.

Shape instabilities depend on elastic constants and line tensions.

Negative effective line tension can trigger shape changes.

Abstract

Finite domains of a Langmuir monolayer in a phase with tilted molecules can be modeled by a simple elastic free energy of an XY order parameter with isotropic and anisotropic line tension terms. The domains can and often do contain nontrivial textures, which in turn influence the shape of the domains. Herein we investigate the properties of a simplified isotropic model with a single elastic constant. For circular domains a first-order phase transition is found between two distinct textures: an exterior defect (or ``virtual boojum'') texture, and an interior defect texture. Starting with a circular domain and either of these two textures as a ground state, we find shape instabilities develop that depend on the elastic constants and line tensions in the simplified model. In both cases a necessary but not sufficient condition for the onset of shape instabilities is the possibility for a local negative effective line tension to develop from the anisotropic line tension term.