Heat transport in carbon nanotubes: Length dependence of phononic conductivity from the Boltzmann transport equation and molecular dynamics

TL;DR

This study compares quantum mechanical Boltzmann transport equation calculations and molecular dynamics simulations to understand how the length of carbon nanotubes affects their phononic thermal conductivity, revealing ballistic and diffusive regimes.

Contribution

It provides a comparative analysis of BTE and MD methods for heat transport in CNTs, highlighting the length-dependent transition from ballistic to potentially diffusive regimes.

Findings

Ballistic heat transport dominates for tubes shorter than 1 μm.

BTE predicts saturation of thermal conductivity at long lengths.

MD simulations up to 10 μm are inconclusive on diffusive regime existence.

Abstract

In this article, we address lattice heat transport in single-walled carbon nanotubes (CNTs) by a quantum mechanical calculation of three-phonon scattering rates in the framework of the Boltzmann transport equation (BTE) and classical molecular dynamics (MD) simulation. Under a consistent choice of an empirical, realistic atomic interaction potential, we compare the tube length dependence of the lattice thermal conductivity (TC) at room temperature determined from an iterative solution of the BTE and from a nonequilibrium MD (NEMD) approach. Qualitatively similar trends are found in the limit of short tubes, where an extensive regime of ballistic heat transport prevailing in CNTs of lengths $L\lesssim 1\,\rm{\mu m}$ is independently confirmed. In the limit of long tubes, the BTE approach suggests a saturation of TC with tube length, whereas direct NEMD simulations of tubes extending up to $L=10\,\rm{\mu m}$ are demonstrated to be insufficient to settle the question of whether a fully diffusive heat transport regime and an intrinsic value of TC exist for CNTs. Noting that acoustic phonon lifetimes lie at the heart of a saturation of TC with tube length as per the BTE framework, we complement the quantum mechanical prediction of acoustic phonon lifetimes with an analysis of phonon modes in the framework of equilibrium MD (EMD). A normal mode analysis (NMA) with an emphasis on long wavelength acoustic modes corroborates the BTE prediction that heat transport in CNTs in the long tube limit is governed by the low attenuation rates of longitudinal and twisting phonons.