Carbon Nanotube Thermal Transport: Ballistic to Diffusive

TL;DR

This paper introduces a unified model for thermal transport in carbon nanotubes that captures both ballistic and diffusive regimes, revealing how conductance depends on diameter, interfaces, and length, with results aligning with experiments.

Contribution

It proposes a new formula for energy transmission in CNTs that unifies ballistic and diffusive heat conduction regimes, and applies it to analyze thermal properties.

Findings

Thermal conductance scales with diameter for SWCNTs and with diameter squared for MWCNTs.

Interfaces significantly influence thermal conduction due to vibrational mode symmetry.

Thermal conductivity scales with length as L^α, with α decreasing with temperature.

Abstract

We propose to use l_0/(l_0+L) for the energy transmission covering both ballistic and diffusive regimes, where l_0 is mean free path and L is system length. This formula is applied to heat conduction in carbon nanotubes (CNTs). Calculations of thermal conduction show: (1) Thermal conductance at room temperature is proportional to the diameter of CNTs for single-walled CNTs (SWCNTs) and to the square of diameter for multi-walled CNTs (MWCNTs). (2) Interfaces play an important role in thermal conduction in CNTs due to the symmetry of CNTs vibrational modes. (3) When the phonon mean free path is comparable with the length L of CNTs in ballistic-diffusive regime, thermal conductivity \kappa goes as L^{\alpha} . The effective exponent \alpha is numerically found to decrease with increasing temperature and is insensitive to the diameter of SWCNTs for Umklapp scattering process. For short SWCNTs (<0.1 \mu m) we find \alpha \approx 0.8 at room temperature. These results are consistent with recent experimental findings.