Vibrational Frequencies and Raman Radial Breathing Modes of Multi-Walled Carbon Nanotubes Based on Continuum Mechanics

Abstract

Carbon nanotube structures correspond to the vibrational frequencies and modes of CNTs. In this study, the vibrational frequencies and the Raman RBM (radial breathing mode) of multi-walled carbon nanotubes (MWCNTs), and carbon nanotubes (CNTs) embedded in elastic medium are simulated based on a continuum mechanics. According to this the theoretical analysis, we can understand how the vibrational modes of CNTs effect the RBM frequency shift. It is found that the vibrational frequency of RBM is complicated due to the van der Waals (vdW) interaction between layers of MWCNTs. The highest RBM frequency of MWCNTs depends mostly on the diameter of the innermost layer, being insensitive to the layer numbers. The analytical approximation offers a useful method for determining precisely the diameter of the MWCNTs.