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arXiv · 0801.3484

Toroidal Crystals

Luca Giomi·Mark J. Bowick
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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.

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Luca Giomi, Mark J. Bowick. 2008-01-23. Toroidal Crystals. https://doi.org/10.1103/physreve.78.010601

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