Empty smectics of hard nanorings: insights from a second-virial theory

TL;DR

This paper presents a theoretical model explaining why ring-shaped nanostructures tend to form empty smectic liquid crystal phases with antinematic order, contrasting with disk-shaped particles that form nematic phases.

Contribution

It introduces a second-virial theory calculating excluded volume for non-convex nanorings, revealing their tendency to form empty smectic phases with antinematic order.

Findings

Nanorings favor smectic over nematic ordering.

Smectic structures are essentially empty and porous.

Antinematic intralamellar order stabilizes these smectic phases.

Abstract

Inspired by recent simulations on highly open liquid crystalline structures formed by rigid planar nanorings we present a simple theoretical framework explaining the prevalence of smectic over nematic ordering in systems of ring-shaped objects. The key part of our study is a calculation of the excluded volume of such non-convex particles in the limit of vanishing thickness to diameter ratio. Using a simple stability analysis we then show that dilute systems of ring-shaped particles have a strong propensity to order into smectic structures with an unusual antinematic order while solid disks of the same dimensions exhibit nematic order. Since our model rings have zero internal volume these smectic structures are essential empty, resembling the strongly porous structures found in simulation. We argue that the antinematic intralamellar order of the rings plays an essential role in stabilizing these novel smectic structures.