An elastica model that predicts radial corrugations in a double- walled carbon nanotube

• We study a variation on the classical problem of a ring subject to a uniform radial load.
• An initially circular elastic ring interacts by a van der Waals forces with second circular, rigid ring.
• This problem is in general motivated by an interest in understanding the mechanics of carbon nanotubes.
• We use this model to study the buckling of the elastic ring as the radius of the rigid ring is varied.
• Our model predicts radial corrugations, which have been studied recently in the physics literature on carbon nanotubes.

In this paper we study a variation on the classical problem of a ring subject to a uniform radial load. An initially circular elastic ring, modeled as an elastica, is concentric with a second circular ring, which is rigid and is either outside or inside the elastic ring. On each point of the elastic ring, the rigid ring exerts a nonuniform radial load that depends on the distance between the point and the rigid ring. The two rings can be viewed as a continuum description of the cross-section of a double-walled carbon nanotube. The force between the elastic ring and the rigid ring is a continuum approximation to the van der Waals interaction between atoms on the two walls of the double-walled tube. We use this model to study the buckling of the elastic ring as the radius of the rigid ring is varied. Our model predicts radial corrugations, a type of deformation studied recently in (Shima and Sato, 2008, 2009; Shima et al., 2010).

The top and bottom middle figures show the initially circular elastic ring with the circular rigid ring either outside or inside. From each of these initial geometries, we can either decrease or increase R.Figure optionsDownload as PowerPoint slide