Effect of curvature on structures and vibrations of zigzag carbon nanotubes: A first-principles study

First-principles pseudopotential-based density functional theory calculations of atomic and electronic structures, full phonon dispersions and thermal properties of zigzag single wall carbon nanotubes (SWCNTs) are presented. By determining the correlation between vibrational modes of a graphene sheet and of the nanotube, we understand how rolling of the sheet results in mixing between modes and changes in vibrational spectrum of graphene. We find that the radial breathing mode softens with 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.