Simulation of Carbon Black Network in Filled Rubber

Carbon black (CB) is one of the most important fillers for rubber and plastics materials. How to describe the CB network is a fundamental problem for establishing relationships between the CB network and the mechanical properties of filled rubber. In view of the electrical conductivity of CB, an infinite circuit consisting of numerous contact resistors, interconnected with each other, is proposed to simulate the CB network in filled rubber; the resistances were determined by considering the tunneling conduction mechanism and a Gaussian distribution for the CB aggregate junction width. As an example, the electrical resistivity of CB (N330) filled natural rubber during uniaxial deformation was studied. It was found that the logarithm of resistivity was an approximately linear function of the extension ratio, and the resistivity increased with the increase of average number of primary particles per aggregates. Additionally, some published experimental points lie between the curves calculated for five primary particles and for seven primary particles per aggregate at extension ratios below 1.2. The calculations suggested that the average number of primary particles per aggregate for CB type N330 might be between five and seven.