Monte Carlo simulations of effective electrical conductivity of graphene/poly(methyl methacrylate) nanocomposite: Landauer-Buttiker approach

• Electrical conductivities of graphene/PMMA nanocomposite were studied using Landauer-Buttiker formula and three-dimensional Monte Carlo simulation.
• The simulation results showed that the tunneling resistance of a graphene-polymer-graphene junction could be several orders larger in magnitude than the intrinsic resistance of graphene sheets.
• It is worth mentioning that the effect of image potential, contributes to increasing the conductivity while decreasing the percolation threshold.

Three-dimensional Monte Carlo simulation was used to investigate the percolation phenomenon and electrical conductivity of graphene/poly(methyl methacrylate) (PMMA) nanocomposite. The electrical conductivity of this nanocomposite was investigated based on three-dimensional resistor network. By employing Landauer-Buttiker (L-B) formula for calculating tunneling resistance of a graphene-polymer-graphene junction and the intrinsic resistance of graphene sheets, transmission probabilities were estimated by scattering theory and Wentzel-Kramers-Brillouin approximation. Effects of cubic representative volume element size, tunneling distance, graphene diameter, orientation of graphene, and image potential on conductivities of graphene/PMMA nanocomposite were studied using this model. The simulation results showed that, as tunneling distance increased, volume fraction of graphenes required for creating an electrically conductive model was decreased. Also, the nanocomposite with a larger diameter of graphene had lower percolation threshold and lower conductivity. Graphene disperse in polymer with normal vector parallel to the electric field had minimum conductivity and maximum percolation threshold. Taking into account the effect of image potential increased the conductivity of graphene/PMMA and decreased percolation threshold.