The paper presents the results of Molecular Dynamics (MD) studies of the thermal properties of Cu and Ag composites with single- (SLG) and multi-layered (MLG) graphene. We show that the thermal boundary conductance (TBC) of the metal-graphene interface drops significantly for the systems containing more than one layer of graphene. It is also concluded that the TBC for a single graphene layer is significantly higher for silver than for copper. For both systems, however, we found that the interface is a barrier for heat transfer with the thermal conductance being at least two orders of magnitude lower than for metal. Moreover, we found that the TBC decreases with an increase in the number of graphene layers. The interfacial effect becomes negligible for a thickness bigger than two graphene layers. Above this thickness the thermal conductivity of the region of multilayered graphene is not influenced by the interface and becomes similar to that of graphite. The results are compared with available experimental data and discussed in terms of the rules for designing composites of a high thermal conductivity.
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