Coil Formation in Multishell Carbon Nanotubes: Competition between Curvature Elasticity and Interlayer Adhesion

TL;DR

This paper models the shape formation of multishell carbon nanotubes, revealing conditions for coiling and identifying an optimal coil ratio that matches experimental observations.

Contribution

It introduces a continuum model with a string equation to describe shape formation in multishell carbon nanotubes, highlighting the role of curvature elasticity and interlayer adhesion.

Findings

Existence of a threshold relation between radii determining bending or twisting.

Regular coiled shapes are solutions of the shape equation.

Optimal pitch-to-radius ratio of 2π matches experimental data.

Abstract

To study the shape formation process of carbon nanotubes, a string equation describing the possible existing shapes of the axis-curve of multishell carbon tubes (MCTs) is obtained in the continuum limit by minimizing the shape energy, that is the difference between the MCT energy and the energy of the carbonaceous mesophase (CM). It is shown that there exists a threshold relation of the outmost and inmost radii, that gives a parameter regime in which a straight MCT will be bent or twisted. Among the deformed shapes, the regular coiled MCTs are shown being one of the solutions of the string equation. In particular,the optimal ratio of pitch $p$ and radius $r_0$ for such a coil is found to be equal to $2\pi $, which is in good agreement with recent observation of coil formation in MCTs by Zhang et al.