A Numerical Simulation of Thermal and Electrical Properties of Nano-fiber Network Polymer Composites Using Percolation Theory and Monte Carlo Method
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Polymer matrix composites reinforced by metal fibers are observed to present an onset of the insulator-to-conductor transition through previous experimental studies. Analytical studies revealed that the percolation threshold occurs when fiber volume fraction reaches the critical value. The numerical study based on Monte Carlo simulations are performed to investigate such a relation. In this work, the conductive fillers are modeled as a three dimensional (3D) network of identical units randomly distributed in the polymer matrix. For the simplest case, straight fibers are used in the simulation. The effects of the aspect ratio and fiber length on the critical volume fraction are also studied. Linearization is made to the logarithm of simulation results. Next, in order to study the effects of emulsion particles and the emulsion particle sizes on the percolation behavior, cubic particles are aligned in the sample model. The gap width to particle size ratio is fixed at 1/10. The calculated critical volume fraction is used in the power-law function to predict the electrical conductivity of the polymer composites. Due to the insensitivity of the thermal conductivity to the percolation threshold, a combination of two empirical equations is used to predict the range of overall thermal conductivity.