Theory and molecular simulation of lattice vibrational heat transport in carbon nanotubes

Heat conduction phenomena of carbon nanotubes (CNTs) have attracted great interest both from the viewpoint of engineering applications and fundamental science, but the thermal conductivity of individual single-walled CNTs remains a rather controversial topic. Starting from an empirical, realistic atomic interaction potential, we study the lattice thermal conductivity (LTC) of single-walled CNTs by employing two approaches: quantum mechanical calculations of three-phonon scattering rates in the framework of the Peierls-Boltzmann transport theory (PBTT) and classical molecular dynamics (MD) simulations. First, we compare the system-size and temperature dependence of the LTC determined from an iterative solution of the linearized phonon transport equation in the framework of the PBTT and from a nonequilibrium MD (NEMD) approach. At room temperature, qualitatively similar trends for the tube-length dependence are found in the limit of short tubes, where an extensive regime of ballistic heat transport prevailing in CNTs of lengths L ≲ 1 µm is independently confirmed. In the limit of long tubes, the PBTT-derived LTC diverges. Using PBTT and equilibrium MD approaches, we perform numerical calculations of acoustic phonon lifetimes to clarify the source of divergence. NEMD-derived temperature dependencies obtained for micrometer-long CNTs and temperatures T ≤ 800 K confirm the 1/T behavior of the LTC at moderately high temperatures. Next, we revisit the tube-length dependence of the LTC by use of the relaxation time approximation in the PBTT. Through a combination of numerics and analytical considerations, we derive exact asymptotic scaling laws of the LTC. In particular, we demonstrate the importance of tensile lattice strain, previously overlooked in the long-standing dispute over tube-length convergence vs divergence of the LTC. Namely, it is proved that, in the long-tube limit, the relaxation time approximation yields a finite value for stress-free but an infinite value of the LTC in any stretched tube configuration. Lastly, we pursue a matrix inversion approach to solve the linearized phonon transport equation in the framework of the PBTT. Here, it is shown that violations of acoustic sum rules cause spurious convergent behaviors of a length-dependent LTC.Science, Faculty ofPhysics and Astronomy, Department ofGraduat