Toroidal Crystals

Physics – Condensed Matter – Soft Condensed Matter

Scientific paper

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4 pages, 4 figures

Scientific paper

10.1103/PhysRevE.78.010601

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.

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