Thermal conductivity of single-walled carbon nanotubes

We study numerically the thermal conductivity of single-walled carbon nanotubes for the cases of an isolated nanotube and a nanotube interacting with a substrate. We employ two different numerical methods: (i) direct modeling of the heat transfer by molecular-dynamics simulations and (ii) analysis of the equilibrium dynamics by means of the Green-Kubo formalism. For the numerical modeling of the effective interatomic interactions, we employ both the Brenner potentials and the intermolecular potentials used in the study of the dynamics of large macromolecules. We demonstrate that, quite independently of the methods employed and the potentials used, the character of the thermal conductivity depends crucially on the interaction between a nanotube and a substrate. While an isolated nanotube demonstrates anomalous thermal conductivity due to ballistic transport of long-wave acoustic phonons, the nanotube interacting with a flat substrate displays normal thermal conductivity due to both the appearance of a gap in the frequency spectrum of acoustic phonons and the absorption of long-wave acoustic phonons by the substrate. We study the dependence of the thermal conductivity on chirality, radius, and temperature of the single-walled carbon nanotubes in both the regimes and compare our findings with experimental data and earlier theoretical results for the thermal conductivity.