# Theoretical treatment of anharmonicity of vibrational modes of single-walled carbon nanotubes

## TL;DR

This computational study investigates the anharmonic vibrational modes of single-walled carbon nanotubes, revealing mode-dependent anharmonicity levels and the influence of tube diameter, with implications for understanding their thermal and mechanical properties.

## Contribution

The paper introduces a theoretical analysis of vibrational anharmonicity in carbon nanotubes using the moments method, highlighting mode-specific behavior and diameter effects.

## Key findings

- Modes with wall displacements are more anharmonic than radial modes.
- Radial breathing modes are the most anharmonic.
- Larger diameter tubes exhibit increased anharmonicity.

## Abstract

We report a computational study, using the "moments method" [Y. Gao and M. Daw, Modelling Simul. Mater. Sci. Eng. 23 045002 (2015)], of the anharmonicity of the vibrational modes of single-walled carbon nanotubes. We find that modes with displacements largely within the wall are more anharmonic than modes with dominantly radial character, except for a set of modes that are related to the radial breathing mode which are the most anharmonic of all. We also find that periodicity of the calculation along the tube length does not strongly affect the anharmonicity of the modes, but that the tubes with larger diameter show more anharmonicity. Comparison is made with available experiments and other calculations.