A three-dimensional Monte Carlo model for electrically conductive polymer matrix composites filled with curved fibers

Abstract

A three-dimensional (3-D) Monte Carlo model is developed for predicting electrical conductivity of polymer matrix composites filled with conductive curved fibers. The conductive fillers are modeled as a 3-D network of finite sites that are randomly positioned. The percolation behavior of the network is studied using the Monte Carlo method, which leads to the determination of the critical fiber volume fraction (or the percolation threshold). The effect of fiber curliness on the percolation behavior is incorporated in the current model by using 3-D arm-shaped fibers, each of which needs five independent geometrical parameters (i.e., three coordinates for its vertex and two orientation angles) for its identification. There are three controlling parameters for such fibers, namely the fiber arm length, the fiber aspect ratio, and the fiber arm angle. The new model also considers the sample size and scaling effects. The simulation results reveal an exponential relationship between the fiber aspect ratio and the percolation threshold: the higher the aspect ratio, the lower the threshold. It is also found that the curliness largely influences the percolation threshold: the more curved the fiber, the higher the threshold. However, the effect of curliness diminishes with the increase of the fiber aspect ratio. With the percolation threshold obtained from the Monte Carlo model, the effective electrical conductivity of the composite is then determined by applying the theory of percolation. The numerical results indicate that the composite conductivity decreases as the fibers become more curved and as the fiber aspect ratio decreases. These predicted trends of the percolation threshold and composite conductivity are in good agreement with existing experimental and simulation results.