Calculating the Electrical Conductivity of Graphene Nanoplatelet Polymer Composites by a Monte Carlo Method

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.

Experimental and Numerical Investigation of Flow and Alignment Behavior of Waste Tire-Derived Graphene Nanoplatelets in PA66 Matrix during Melt-Mixing and Injection

“…As Folgar–Tucker model suggests, allocating nonzero value to leads to randomly distributing the particles in the flow domain, causing different orientations along the streamlines [ 47 ]. It is worth mentioning here that since the GNPs are usually treated as 2-dimensional disk shape particles [ 64 ], the amount of in the Equation (6) is equal to −1 and the direction of vector in Equation (4) represents the main axis of the particle which is perpendicular to the surface of the GNPs [ 35 ]. Therefore, the arrow shown in the Figure 11 is the direction of the vector.…”

Computational Study of Graphene–Polypyrrole Composite Electrical Conductivity

“…The graphene is represented by rectangular conducting bars with diameters of and lengths of [21,38]. , , and and , , and , respectively, the cluster representative of the network is [39,40]:…”

“…δ i and θ i are the polar and azimuthal angles, representing the filler orientations. If the start and end points of the cuboid are γ xi , γ yi , and γ zi and γ xj , γ yj , and γ zj , respectively, the cluster representative of the network is [39,40]:…”

“…The filler is periodically arranged in the directions γ x and γ y . Two types of resistance determine the electrical conductivities of nanocomposites [39,40], i.e., the tunneling and intrinsic filler resistances. If the filler is evenly dispersed in the matrix at a low concentration, the transport of electrons in the composite is determined by the tunneling/contact resistance.…”

“… are the polar and azimuthal angles, representing the filler orientations. If the start and end points of the cuboid are and , respectively, the cluster representative of the network is [ 39 , 40 ]: where is a random value (0,1), is the length of the nanorod, and and are the Weibull scaling, shaping, is the probability distribution function, and locator parameters, respectively. The characterizations of the filler length and its diameter were performed using the Weibull distribution (Equation (4)) [ 41 ].…”