Numerical Modeling of the Electrical Resistivity of Carbon Black Filled Rubber

Carbon black (CB) filled rubber is microscopically heterogeneous although homogeneous on a macroscopic scale. CB particles are generally in the form of aggregates, which form the CB network in the rubber matrix. In this work, the junction width between CB aggregates is modeled as a contact resistor and the tunneling conduction mechanism is taken into account, and then an infinite circuit consisting of numerous contact resistors, interconnected with each other, is proposed to simulate the CB network in filled rubber. Prior to determination of the junction width distribution, CB spheres equivalent to CB aggregates in volume is assumed in a specifically random arrangement. Thus, the effect of CB aggregate distribution on the electrical resistivity is discussed. It is found that, for CB (N330) filled natural rubber with volume fraction of 27.5%, the simulated electrical resistivity at a standard deviation of 0.1 mean junction width is in good agreement with the experimental data available in the literature.