Chiral fluid membranes with orientational order and multiple edges

TL;DR

This study uses Monte Carlo simulations to explore how chiral liquid crystalline order influences the shape and director configurations of fluid membranes with edges, revealing shape transitions and complex phases under various conditions.

Contribution

It introduces a simulation framework for chiral liquid crystalline membranes with multiple edges, revealing novel shape transformations and phase behaviors not previously characterized.

Findings

Low chirality leads to disk shapes with smectic-A order.

High chirality induces catenoid-like or trinoid-like shapes with cholesteric order.

External stretching results in diverse liquid crystalline phases depending on tilt coupling and chirality.

Abstract

We carry out Monte Carlo simulations on fluid membranes with orientational order and multiple edges in the presence and absence of external forces. The membrane resists bending and has an edge tension, the orientational order couples with the membrane surface normal through a cost for tilting, and there is a chiral liquid crystalline interaction. In the absence of external forces, a membrane initialized as a vesicle will form a disk at low chirality, with the directors forming a smectic-A phase with alignment perpendicular to the membrane surface except near the edge. At large chirality a catenoid-like shape or a trinoid-like shape is formed, depending on the number of edges in the initial vesicle. This shape change is accompanied by cholesteric ordering of the directors and multiple $\pi$ walls connecting the membrane edges and wrapping around the membrane neck. If the membrane is initialized instead in a cylindrical shape and stretched by an external force, it maintains a nearly cylindrical shape but additional liquid crystalline phases appear. For large tilt coupling and low chirality, a smectic-A phase forms. For lower values of the tilt coupling, a nematic phase appears at zero chirality with the average director oriented perpendicular to the long axis of the membrane, while for nonzero chirality a cholesteric phase appears. The $\pi$ walls are tilt walls at low chirality and transition to twist walls as chirality is increased. We construct a continuum model of the director field to explain this behavior.