The calculations of phonon dispersion relations for single-wall carbon armchair and zigzag nanotubes.

A 3D single-wall carbon nanotube can be viewed as a 2D graphite sheet rolled into a 3D cylinder. In the study of dispersion relations of carbon nanotubes, the consistent force parameters for 2D graphite sheets have to be modified to include the curvature effect. The present paper reports a series of calculations of phonon dispersion relations for single-wall carbon armchair, zigzag nanotube in which the curvature effect has been properly treated. The symmetry of crystal vibration mode at the centre of Brillouin zone is analyzed based on our numeric results and the structure symmetry of the nanotubes.