Prediction of electrical conductivity of graphene-filled composites considering the tunneling effect

The characteristics of graphene, including good mechanical properties, low density, high thermal conductivity, and high electron mobility, have led to the usage of graphene-filled composites in various fields. So far, the conductive mechanism of graphene-filled composites is controversial. In this paper, a numerical analysis model was developed based on RVE (representative volume element) theory, where the macroscopic model was equivalently replaced by a microscopic model. The graphene filler was modeled as a two-dimensional rectangle that was positioned and angled arbitrarily without intersecting with each other for the sake of numerical calculation. On the finite element model, Ohm's law and the tunneling effect were combined, and a subroutine was constructed for real-time estimation of the distance between graphene fillers in a cell, with Ohm's law being substituted by the tunneling effect for distances less than 3 nm. The electrical conductivity of graphene-filled composites was further numerically analyzed based on the influence of different boundary conditions. The numerical analysis results were in good agreement with the experiments. This work demonstrates that the tunneling effect dominates the conduction mechanism of conductive particle-filled composites at the percolation threshold and above and can be helpful to explain the response mechanism of flexible particle-filled composite sensors.