Eur. Phys. J. B (2012) 85: 81
https://doi.org/10.1140/epjb/e2012-21061-0

Regular Article

A one-dimensional continuous model for carbon nanotubes

Department of Mathematics and Physics, Fourth Military Medical University, Xi’an 710032, P.R. China

^a e-mail: xhzhou08@gmail.com

Received: 21 December 2011
Received in final form: 15 January 2012
Published online: 29 February 2012

Abstract

The two-dimensional (2D) continuous elastic energy model for isotropic tubes is reduced to a one-dimensional (1D) curvature elastic energy model strictly. This 1D model is in accordance with the Kirchhoff elastic rod theory. Neglecting the in-plane strain energy in this model, it is suitable to investigate the nature features of carbon nanotubes (CNTs) with large deformations and can also reduce to the string model in [Z.C. Ou-Yang et al., Phys. Rev. Lett. 76, 4055 (1997)] when the deformation is small enough. For straight chiral shapes, this general model indicates that the difference of the chiral angle between two equilibrium states is about π/6, which is consistent with the lattice model. It also reveals that the helical shape has lower energy for per atom than the straight shape has in the same condition. By solving the corresponding equilibrium shape equations, the helical tube solution is in good agreement with the experimental result, and super helical shapes are obtained and we hope they can be found in future experiments.