Phonon-phonon scattering rates in single walled carbon nanotubes

A theoretical model for the phonon-phonon scattering rates of carbon nanotubes (CNTs) is developed using the carbon specific Brenner's potential. This model allows for the calculation of mode specific phonon-phonon scattering rates, via direct computation of the three-phonon strength of interaction. This direct calculation provides further accuracy to the previously existing model, which relied on continuum mechanics approximations to the strength of interactions. The contributions of each phonon branch to the total phonon-phonon scattering rates are analyzed. The results for longitudinal optical and longitudinal acoustic phonons of a (10, 10) CNT suggest very different behavior for each vibrational mode. While the results presented are specific to the (10, 10) metallic CNTs, the method is directly applicable to CNTs of other chiralities.