A Shell Theory for Chiral Single-Wall Carbon Nanotubes

TL;DR

This paper develops a shell theory model for the mechanical behavior of chiral single-wall carbon nanotubes, generalizing previous models to arbitrary chirality and validating it with experimental data.

Contribution

It provides an explicit method to construct the anisotropic shell response for any nanotube chirality based on zigzag or armchair cases.

Findings

The model captures the anisotropic mechanical response of nanotubes.

Analytical solutions for torsion match experimental observations.

Shell response becomes isotropic in the graphene limit.

Abstract

In this paper, we propose a characterization of the mechanical response of the linearly elastic shell we associate to a single-wall carbon nanotube of arbitrary chirality. In Bajaj et al. 2013, we gave such a characterization in the case of zigzag and armchair nanotubes; in particular, we showed that the orthotropic response we postulated for the associated shells is to become isotropic in the graphene-limit, that is, when the shell radius grows bigger and bigger. Here we give an explicit recipe to construct the generally anisotropic response of the shell associated to a nanotube of any chirality in terms of the response of the shell associated to a related zigzag or armchair nanotube. The expected coupling of mechanical effects that anisotropy entrains is demonstrated in the case of a torsion problem, where the axial extension accompanying twist is determined analytically and found in good agreement with the available experimental data.