Breathinglike phonon modes of multiwalled carbon nanotubes

The breathinglike phonon modes of multiwalled carbon nanotubes are studied within a valence force field model for nanotubes with two and three layers of armchair type and within a continuum model for nanotubes with a large number of layers. A bond-polarizability model is used to calculate the nonresonant Raman intensity of the breathinglike modes. It is obtained that among all breathinglike modes of a given multiwalled tube, the in-phase one has a maximal intensity. The predicted intensity of the breathinglike modes is compared to available low-frequency experimental Raman data. Special attention is given to the comparison with Raman data on double-walled carbon nanotubes.