Carbon nanotube thermal transport: Ballistic to diffusive

Abstract

We propose the expression ℓ0∕(ℓ0+L) for the energy transmission covering both ballistic and diffusive regimes, where ℓ0 is mean free path and L is system length. With this formula, calculations of thermal conduction in carbon nanotubes (CNTs) show: (1) Thermal conductance at room temperature is proportional to the diameter for single-walled CNTs (SWCNTs) and to the square of diameter for multiwalled CNTs. (2) Interfaces play an important role in thermal conduction in CNTs due to their symmetry of vibrational modes. (3) For CNTs in ballistic-diffusive regime, thermal conductivity κ goes as Lα. The exponent α is found to decrease with increasing temperature and is insensitive to the diameter of SWCNTs for the Umklapp process, α≈0.8 for short SWCNTs at room temperature. These results are consistent with recent experimental findings.