Mechanical coupled vibrations in an individual double-walled carbon nanotube

In this paper we calculate the Raman spectra of different double-walled carbon nanotubes (DWCNTs) by using the spectral moments method. Using a convenient Lennard-Jones expression of the van der Waals intermolecular interaction between the inner and outer tubes, the optimized structures of DWCNT are derived. We found that the C-C bond length in DWCNT is depending on the metallic (M) or semiconducting (Sc) character of the inner and outer nanotubes. We show that the radial breathing-like modes (RBLM) of DWCNT are characterized by concerted inner and outer wall motions. Comparison with Raman spectra measurements is given.