Percolation threshold and electrical conductivity of graphene-based nanocomposites with filler agglomeration and interfacial tunneling

Abstract

The dispersion state or degree of agglomeration of graphene is known to have a significant influence on the percolation threshold and electrical conductivity of graphene-based polymer nanocomposites. In addition, an imperfectly conducting interface and tunneling-assisted interfacial conductivity can also affect the overall conductivity. In this paper, a continuum theory is developed that considers all these factors. We first present a two-scale composite model consisting of graphene-rich regions serving as the agglomerates and a graphene-poor region as the matrix. We then introduce the effective-medium theory to determine the percolation threshold and electrical conductivity of the agglomerate and the composite. To account for the effect of imperfect interfaces, a thin layer of interphase with low conductivity is introduced to build a thinly coated graphene, while to account for the contribution of electron hopping from one graphene to another, Cauchy's statistical function which can reflect the increased tunneling activity near the percolation threshold is introduced. It is shown that the percolation threshold of the nanocomposite is controlled by two dispersion parameters, a and b, and the aspect ratio of agglomerates, αR. It is also shown that the overall conductivity of the nanocomposite mainly depends on the intrinsic conductivity of graphene and polymer matrix, the intrinsic interfacial resistivity, and the tunneling-assisted hopping process. We highlight the conceived theory by demonstrating that a set of recently measured data on the percolation threshold and electrical conductivity of graphene/polystyrene nanocomposites can be well captured by it.