# Structural characterization of carbon nanotubes via the vibrational density of states

## TL;DR

This paper demonstrates that the vibrational density of states (VDOS) can be used to determine the structural properties of carbon nanotubes, including diameter, chirality, and defects, through characteristic vibrational modes.

## Contribution

The study introduces a method to extract detailed structural information of carbon nanotubes from VDOS measurements, highlighting the significance of low-frequency vibrational modes.

## Key findings

- VDOS contains identifiable features related to nanotube diameter and chirality.
- Characteristic low-frequency peaks can distinguish different nanotube structures.
- Defects produce distinct signatures in the VDOS, especially in low-frequency modes.

## Abstract

The electrical and chemical properties of carbon nanotubes vary significantly with different chirality and diameter, making the experimental determination of these structural properties important. Here, we show that the vibrational density of states (VDOS) contains information on the structure of carbon nanotubes, particularly at low frequencies. We show that the diameter and chirality of the nanotubes can be determined from the characteristic low frequency $L$ and $L'$ modes in the VDOS. For zigzag nanotubes, the $L$ peak splits into two peaks giving rise to another low energy $L"$ peak. The significant changes in the frequencies and relative intensities of these peaks open up a route to distinguish among structurally different nanotubes. A close study of different orientations of Stone-Wales defects with varying defect density reveals that different structural defects also leave distinct fingerprints in the VDOS, particularly in the $L$ and $L'$ modes. With our results, more structural information can be obtained from experiments which can directly measure the VDOS, such as inelastic electron and inelastic neutron spectroscopy.