The Continuum Approach

Abstract

Low-frequency phonons in carbon nanotubes are studied using a continuummodel which allows consideration of an arbitrary wall thickness forthe nanotube. Phonon dispersion relations are calculated for twoarchetypal examples of carbon nanotubes, the (5,5) and (10,10) tubes.The dependence of the radial breathing mode frequency at Gamma onthe inverse nanotube diameter is verified within this model; furthermore,we prove it to hold for all pure modes within the thin-shell approximation.The effect of the nanotube wall thickness on the eigenfrequenciesof carbon nanotubes is also analyzed, and a criterion to fix thisparameter within a continuum model is presented. We compare our resultsto other continuum approaches, and show that by choosing the appropriateparameters, excellent agreement with recent first-principles calculationscan be achieved.