1102.2066 (Xiaohua Zhou)

A one-dimensional continuous model for carbon nanotubes    [PDF]

Xiaohua Zhou

The continuous two-dimensional (2D) elastic model for single-walled carbon
nanotubes (SWNTs) provided by Tu and Ou-Yang in [Phys. Rev. B \textbf{65},
235411 (2003)] is reduced to a one-dimensional (1D) curvature elastic model
strictly. This model is in accordance with the isotropic 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 reduce to the string model in [Phys. Rev. Lett.
\textbf{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 $\pi/6$, 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.

View original: http://arxiv.org/abs/1102.2066