Theory of depletion induced phase transition from chiral smectic A twisted ribbons to semi-infinite flat membranes

TL;DR

This paper presents a theoretical model explaining a first-order phase transition from twisted ribbons to flat membranes in chiral smectic A liquid crystal assemblies, aligning well with experimental data.

Contribution

It introduces a mean field model incorporating Helfrich and de Gennes energies to describe the phase transition in chiral smectic A systems with depletion forces.

Findings

Identifies a first-order phase transition controlled by edge energy.

Shows the transition line and tilt profile are similar across models.

Predicts the ribbon pitch varies with model parameters.

Abstract

We consider a theoretical model for the chiral smectic A twisted ribbons observed in assemblies of fd viruses condensed by depletion forces. The depletion interaction is modeled by an edge energy assumed to be proportional to the depletant polymer in solution. Our model is based on the Helfrich energy for surface bending and the de Gennes model of chiral smectic A liquid crystals with twist penetration at the edge. We consider two variants of this model, one with the conventional Helfrich Gaussian curvature term, and a second with saddle-splay energy. A mean field analysis of both models yields a first-order phase transition between ribbons and semi-infinite flat membranes as the edge energy is varied. The phase transition line and tilt angle profile are found to be nearly identical for the two models; the pitch of the ribbon, however, does show some differences. Our model yields good qualitative agreement with experimental observations if the sign of the Gaussian curvature or saddle-splay modulus is chosen to favor negative Gaussian curvature.