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

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. In this way, we demonstrate the consequences of the rather different approximations and limitations that are inherent to the two computational approaches. In the limit of long tubes, we show that different conclusions can be drawn with regard to the existence of an intrinsic value of TC. In the BTE framework, a saturation of TC with tube length $L$ is found, whereas NEMD simulations of CNTs with chirality (4,4) in the range up to $L=12.5\,\rm{\mu m}$ suggest a power law divergence of TC. 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 that heat transport in CNTs is governed by the low attenuation rates of longitudinal and twisting phonons.