Exact study of lattice dynamics of single-walled carbon nanotubes

Based on the model of lattice dynamics with force-constant matrix, we have calculated phonon spectrum and then specific heats of single-walled carbon nanotubes. The results show that with a more complicated phonon spectrum, a single-walled carbon nanotube has analogous good thermal conductivity to the two-dimensional graphite. However, the ratio of thermal conductivity to phonon relaxation time is inversely proportional to the diameter of either zigzag or armchair carbon nanotubes.