Theory of self-assembled smectic-A "crenellated disks"

TL;DR

This paper develops an elastic theory to analyze the stability and structure of crenellated disks in smectic-A monolayers formed by chiral fd viruses, explaining their formation and properties.

Contribution

It introduces a phenomenological elastic model for crenellated disks, revealing their stability conditions and matching experimental features.

Findings

Crenellated disks are stable or metastable in a wide phase space.

The model's predictions align qualitatively with experimental observations.

Large energy barriers separate crenellated disks from flat disks.

Abstract

Smectic-A monolayers self-assembled in aqueous solutions of chiral fd viruses and a polymer depletant have been shown to exhibit a variety of structures including large, flat disks and twisted ribbons. The virus particles twist near the edge of the structure in a direction determined by the chirality of the viruses. When fd viruses and their mutants of opposite chirality are mixed together in nearly equal amounts unusual structures referred to as "crenellated disks" can appear. These disks are achiral overall but the twist at the edge alternates between left- and right-handedness. To minimize the mismatch where the two regions of opposing twist meet, the "crenellated" structure exhibits cusps rising out of the plane of the monolayer. We use a phenomenological elastic theory previously applied to flat disks and twisted ribbons to analyze an analytic model proposed to describe the "crenellated" structure . When compared with flat, circular disks, we find that the model "crenellated disks" are stable or at least metastable in a wide region of the phase diagram spanned by the Gaussian curvature modulus and the edge energy modulus, with a large energy barrier separating the two structures. The director pattern and geometric parameters of the "crenellated disks" are found to be in qualitative agreement with experimental observations.