Three Dimensional Monte Carlo Simulation of the Electrical Conductivity of Composites Reinforced by Short Fibers

Three-dimensional (3D) Monte Carlo simulation is an effective approach to determine the percolation threshold and reveal the electrical conductivity of nanocomposites that are composed of conducting fillers and insulating matrix polymer. With random nanofiller distribution, composite can be considered as periodic stacking of a representative volume element (RVE), and the composite electrical resistivity is represented by the resistivity of the RVE with periodic boundary conditions. This paper details the 3D Monte Carlo method used to simulate the resistor network used for electrical conductivity calculation. It is found that short fibers in the composite function as hubs that connect junction resistors between fibers. Generally, the short fiber resistance is much smaller than the junction resistance and can be neglected during network resistance determination. This simplification leads to a dramatic improvement in computation efficiency by reducing more than half of the total resistor in network. Previously reported simulations are mostly limited to low concentration and low aspect ratio fillers, and mostly in two dimensional RVEs due to the limited computation capacity on the number of resistors. The simplification approach reported here enables electrical conductivity simulation for 3D system with high large filler aspect ratio.