Phonon modes in single-wall nanotubes with a small diameter

Abstract Phonon modes in single-walled nanotubes (SWNTs) of carbon are reexamined within the framework of a force constant model. In order to explore the effect of curvature of tubules with a small diameter, the dynamical matrices are formulated in terms of cylindrical coordinates. The curvature effect of tubules is discussed by comparing with the results obtained by the zone folding model. The diameter dependent properties of phonon modes are shown to be useful for analyzing the size distribution of SWNT in the synthesized samples.