LAUSR

Abstract Due to the extremely thin aspect ratio of graphene fillers, graphene-graphene contact could easily develop and this would introduce a new contact resistance to thermal transport in the graphene-polymer nanocomposites. The effect of this contact resistance has never been considered before. In this paper we present a new theory of thermal conductivity that includes both interfacial Kapitza resistance (filler-matrix type) and the graphene-graphene contact resistance (filler-filler type). To account for the effect of graphene-graphene contact, we treat the development of filler networks as a statistical process that can be described by Cauchy's cumulative probabilistic function. With it, a new effective medium theory with a percolation threshold, Kapitza resistance, and graphene-graphene contact resistance is presented. We highlight this new theory by comparing it to four sets of latest experiments on the conductivity of graphene/epoxy nanocomposites, and demonstrate that both Kapitza resistance and graphene-graphene contact resistance are essential factors, with the latter gaining increasing importance as graphene loading increases. Several other interesting features of the theory, including the issue of percolation phenomenon and the dependence of filler shape, are also addressed.