The effects of temperature, tube length, defects, and surface functionalization on the thermal conductivity (κ) of single-walled carbon nanotubes (SWCNTs) were well documented in literature. However, diameter dependence of thermal conductivity of SWCNTs received less attentions. So far, diverse trends of the diameter dependence have been discussed by different methods and all the previous results were based on empirical interatomic potentials. In this paper, we emphasize to clarify accurate κ values of SWCNTs with different diameters and in-plane κ of graphene. All the studies were under the framework of anharmonic lattice dynamics and Boltzmann transport equation (BTE) based on first principle calculations. We try to infer the right trend of diameter dependent thermal conductivity of SWCNTs. We infer that graphene is the limitation as SWCNT with an infinite diameter. We analyzed the thermal conductivity contributions from each phonon mode in SWCNTs to explain the trend. Meanwhile, we also identify the extremely low thermal conductivity of ultra-thin SWCNTs.
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