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.
Highlights
The vibration behavior of carbon nanotubes (CNTs) has been extensively investigated due to their importance in nano-electro-mechanical systems (NEMS) and nanosensor application
We present an analytical solution for Raman radial breathing mode (RBM) frequency of multi-walled carbon nanotubes (MWCNTs) using the circular ring mode
We present an analytical approach for the RBM of MWCNTs considered to be coupled together through the van der Waals (vdW) interaction between tube layers
Summary
The vibration behavior of carbon nanotubes (CNTs) has been extensively investigated due to their importance in nano-electro-mechanical systems (NEMS) and nanosensor application. Based on MD simulation and non-local continuum model, Shi et al showed 2:1 internal resonance between the RBM and the circumferential flexural mode (CFM) in SWCNTs (Shi et al, 2009) They observed that the change of the transformation time from RBM to CFM due to the variation of the perturbation velocity field. Some studies of Raman RBM of double- or multi-walled CNTs have been carried out using continuum mechanics (Wu et al, 2007; Wang & Ru, 2005; Han & Goddard, 2009; Popov & Henrard, 2002) these analytical models were discussed theoretically and there was a lack of experimental investigation. The analytical approximation can offer an estimation for determining the diameter and layer number of the MWCNTs. the elastic medium dependency of embedded matrix on the RBM frequency of double-walled carbon nanotubes (DWCNTs) is simulated and investigated. The calculated results were compared to the experimental observation, showing a good agreement in the frequency shifts
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