Abstract
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.
Highlights
Graphene, due to its one-atom-thick 2D structure and excellent performance, has attracted extensive interest in recent years [1,2,3]
By comparing the contact conductance, graphene conductance, and the interlayer conductance, we found that graphene nanoplatelet (GNP) were approximately equipotential if the thickness of the GNP was much smaller than its diameter
When the concentration of the GNP was above the percolation threshold, a conductive network was formed between the two electrodes, and the potential of the GNP, which was close to electrode 1, suddenly increased, resulting in a large tunneling current
Summary
Due to its one-atom-thick 2D structure and excellent performance, has attracted extensive interest in recent years [1,2,3]. Based on the continuum model, Bruggeman’s effective-medium theory [20], as formulated by Maxwell’s far-field matching by setting the property of the reference medium to that of the effective medium (i.e., the composite) in [21], can provide the percolation threshold and an effective conductivity. Based on this approach, Xia et al [22,23] studied the electrical conductivity of graphene composite foams and the influence of the orientation of graphene fillers on the conductivity of highly aligned graphene composites. With the equipotential approximation and the walk-on-spheres (WoS) method, the conductivity of the GNP composite could be obtained near the percolation threshold
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