Thermal conductivity of carbon nanotubes using nonequilibrium molecular dynamics combined with a machine learning potential

Large-scale and long-time-span nonequilibrium molecular dynamics simulations have been performed to determine the thermal conductivity of single-walled and double-walled carbon nanotubes (CNTs) using a machine learning potential trained on atomic energies and forces from density functional theory calculations for sp²-hybridized carbon. The size dependence of graphene and CNTs up to 1 μm has been studied with 200000 atoms and simulation times up to 5 ns. The simulations reveal that thermal transport, whether ballistic, quasi-ballistic, or diffusive, is determined by the relationship between the sample length and the effective mean-free path (MFP). The system size has less effect on thermal conductivity when the sample length significantly exceeds the MFP. Radial tensile strain in CNTs causes the C–C bond length to increase in smaller-diameter CNTs, resulting in a phonon softening effect that subsequently reduces thermal conductivity. An analytical function is proposed to describe the relationship between phonon relaxation time and nanotube diameter. The thermal conductivity of the double-walled CNT is lower than that of an equivalent-size single-walled CNT. Phonon–phonon scattering, interlayer van der Waals interactions, and degenerate coupling of transverse acoustic modes are considered to contribute to the reduction in thermal transport.