Vibrational properties of single-wall carbon nanotubes: a first-principles study.

We present first-principles pseudopotential-based density functional theory (DFT) calculation of structures, full phonon dispersions and thermal properties of armchair single wall armchair carbon nanotubes (SWCNTs) in the isolated and bundle forms. Comparison between the properties of isolated and bundled nanotubes is used to estimate the intertube interaction. We determine correlation between vibrational modes of a graphene sheet and of the nanotube to understand how rolling of the sheet results in mixing between modes and changes in vibrational spectrum. The radial breathing mode hardens with increasing diameter (or decreasing curvature). We estimate thermal expansion coefficient of nanotubes within a quasiharmonic approximation and identify the modes that dominate thermal expansion of some of these SWCNTs both at low and high temperatures.