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, ${\alpha }_R$ . 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.

Electrical conductivity is one of several outstanding features of graphene–polymer nanocomposites, but calculations of this property require the intricate features of the underlying conduction processes to be accounted for. To this end, a novel Monte Carlo method was developed. We first established a randomly distributed graphene nanoplatelet (GNP) network. Then, based on the tunneling effect, the contact conductance between the GNPs was calculated. Coated surfaces (CSs) were next set up to calculate the current flow from the GNPs to the polymer. Using the equipotential approximation, the potentials of the GNPs and CSs met Kirchhoff’s current law, and, based on Laplace equation, the potential of the CSs was obtained from the potential of the GNP by the walk-on-spheres (WoS) method. As such, the potentials of all GNPs were obtained, and the electrical conductivity of the GNP polymer composites was calculated. The barrier heights, polymer conductivity, diameter and thickness of the GNP determining the electrical conductivity of composites were studied in this model. The calculated conductivity and percolation threshold were shown to agree with experimental data.

This work was driven by the need to understand the electromagnetic interference (EMI) shielding effectiveness (SE) of light weight, flexible, and high performance graphene composite foams, but as EMI SE of a material depends on its electrical conductivity, dielectric permittivity, and magnetic permeability, the investigation of these three properties also became a priority. In this paper, we first present a continuum theory to determine these three electromagnetic properties, and then use the obtained properties to evaluate the EMI SE of the foam. A two-scale composite model is conceived to evaluate these three properties, with the large one being the skeleton-void composite and the small one being the graphene-polymer composite that serves as the skeleton of the foam. To evaluate the properties of the skeleton, the effective-medium approach is taken as the starting point. Subsequently, the effect of an imperfect interface and the contributions of electron tunneling to the interfacial conductivity and Maxwell-Wagner-Sillars polarization mechanism to the dielectric constant are also implemented. The derived skeleton properties are then utilized on the large scale to determine the three properties of the composite foam at a given porosity. Then a uniform plane electromagnetic wave is considered to evaluate the EMI SE of the foam. It is demonstrated that the electrical conductivity, dielectric constant, and EMI SE of the foam calculated from the developed theory are in general agreement with the reported experimental data of graphene/PDMS composite foams. The theory is further proven to be valid for the EMI SE of solid graphene/epoxy and solid carbon nanotube/epoxy nanocomposites. It is also shown that, among the three electromagnetic properties, electrical conductivity has the strongest influence on the EMI shielding effectiveness.