Toroidal Crystals

TL;DR

This paper analyzes the structural properties of toroidal crystals, providing a unified elastic theory description and revealing defect arrangements influenced by the torus aspect ratio, with implications for designing functionalized templates.

Contribution

It offers a unified elastic theory framework for toroidal crystals and links defect arrangements to the aspect ratio, enabling controlled template design.

Findings

Ground states have 5-fold disclinations on the exterior and 7-fold inside.

Number of disclinations depends mainly on the torus aspect ratio.

Potential for creating functionalized toroidal templates with controlled defect sites.

Abstract

Crystalline assemblages of identical sub-units packed together and elastically bent in the form of a torus have been found in the past ten years in a variety of systems of surprisingly different nature, such as viral capsids, self-assembled monolayers and carbon nanomaterials. In this Letter we analyze the structural properties of toroidal crystals and we provide a unified description based on the elastic theory of defects in curved geometries. We find ground states characterized by the presence of 5-fold disclinations on the exterior of the torus and 7-fold disclinations in the interior. The number of excess disclinations is controlled primarily by the aspect ratio of the torus, suggesting a novel mechanism for creating toroidal templates with precisely controlled valency via functionalization of the defect sites.