Toroidal Crystals

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.

4 pages, 4 figures

References in corpus (5)

• Towards a Tetravalent Chemistry of Colloids
• Interacting Topological Defects on Frozen Topographies
• Crystallography on Curved Surfaces
• Vortices in a Thin Film Superconductor with a Spherical Geometry
• Crystalline Order On Riemannian Manifolds With Variable Gaussian Curvature And Boundary

Cited by in corpus (12)

• Two-Dimensional Matter: Order, Curvature and Defects
• Vortices in Superfluid Films on Curved Surfaces
• Particles on curved surfaces - a dynamic approach by a phase field crystal model
• Kinetic Transition Networks for the Thomson Problem and Smale's 7th Problem
• Kibble-Zurek mechanism in curved elastic surface crystals
• Crystalline Particle Packings on Constant Mean Curvature (Delaunay) Surfaces
• Crystalline Order on Catenoidal Capillary Bridges
• Plastic deformation of tubular crystals by dislocation glide
• Viral nematics in confined geometries
• A simple, general criterion for onset of disclination disorder on curved surfaces
• Transitions between phyllotactic lattice states in curved geometries
• Dynamics of Vortex Clusters on a Torus