We use molecular dynamics (MD) simulations to explore the lattice thermal transport in freestanding and supported single-wall carbon-nanotube (SWCNT) in comparison to that in graphene nanoribbon (GNR) and graphene sheet. We find the lattice thermal conductivity of freestanding SWCNT and GNR increases with diameter/width and approaches that of graphene. This is partly attributed to the curvature that shortens phonon lifetime in SWCNT. In contrast to GNR, there is only weak chirality dependence in the thermal conductivity of freestanding SWCNT. When SWCNT is put on substrate, an effective boundary along the SWCNT axial direction at the SWCNT-substrate interface is created, rendering resemblance between the phonon transport in supported SWCNT and that in freestanding GNR. As a result, the thermal conductivity of supported SWCNTs differ by around 10%, depending on chirality. The thermal conductivity of SWCNT decreases by about 34–41% when supported, which is less than that of the reduction seen in supported graphene.

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