We have used molecular dynamics to calculate the thermal conductivity ofsymmetric and asymmetric graphene nanoribbons (GNRs) of several nanometers insize (up to ~4 nm wide and ~10 nm long). For symmetric nanoribbons, thecalculated thermal conductivity (e.g. ~2000 W/m-K @400K for a 1.5 nm {\times}5.7 nm zigzag GNR) is on the similar order of magnitude of the experimentallymeasured value for graphene. We have investigated the effects of edge chiralityand found that nanoribbons with zigzag edges have appreciably larger thermalconductivity than nanoribbons with armchair edges. For asymmetric nanoribbons,we have found significant thermal rectification. Among varioustriangularly-shaped GNRs we investigated, the GNR with armchair bottom edge anda vertex angle of 30{\deg} gives the maximal thermal rectification. We alsostudied the effect of defects and found that vacancies and edge roughness inthe nanoribbons can significantly decrease the thermal conductivity. However,substantial thermal rectification is observed even in the presence of edgeroughness.
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