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Frequency-dependent phonon mean free path in carbon nanotubes from non-equilibrium molecular dynamics

Owing to their long phonon mean free paths (MFPs) and high thermal conductivity, carbon nanotubes (CNTs) are ideal candidates for, e.g., removing heat from electronic devices. It is unknown, however, how the intrinsic phonon MFPs depend on vibrational frequency in non-equilibrium. We determine the spectrally resolved phonon MFPs in isotopically pure CNTs from the spectral phonon transmission function calculated using non-equilibrium molecular dynamics, fully accounting for the resistive phonon-phonon scattering processes through the anharmonic terms of the interatomic potential energy function. Our results show that the effective room temperature MFPs of low-frequency phonons ($f<0.5$ THz) exceed $10$ $μ$m, while the MFP of high-frequency phonons ($f\gtrsim 20$ THz) is in the range 10--100 nm. Because the determined MFPs directly reflect the resistance to energy flow, they can be used to accurately predict the thermal conductivity for arbitrary tube lengths by calculating a single frequency integral. The presented results and methods are expected to significantly improve the understanding of non-equilibrium thermal transport in low-dimensional nanostructures.