Radial-breathing-like phonon modes of double-walled carbon nanotubes

TL;DR

This paper presents an analytical model for studying the radial-breathing-like phonon modes in double-walled carbon nanotubes, enabling precise determination of their radii through phonon frequency analysis.

Contribution

It introduces an analytical approach to calculate interaction force constants and phonon modes, improving the accuracy of radius measurement in multi-walled carbon nanotubes.

Findings

Analytical expressions for RBLM frequencies derived

Relationship between phonon frequencies and tube radii established

Model provides a tool for precise radius determination

Abstract

The radial-breathing-like phonon modes (RBLMs) of the double-walled carbon nanotubes are studied in a simple analytical model, in which the interaction force constants (FCs) can be obtained analytically from the continuous model. The RBLMs frequencies are obtained by solving the dynamical matrix, and their relationship with the tube radii can be obtained analytically, offering a powerful experimental tool for determining precisely the radii of the multi-walled carbon nanotubes.