Characteristic frequency of carbon black filled rubber

Due to the high electrical conductivity of carbon black (CB) particles, the presence of CB improves the conductivity of filled rubbers. The impedance spectra of CB filled rubber were simulated using an infinite resistor-capacitor (RC) circuit by considering the tunneling conduction mechanism for the CB contact regions. The calculated results had a similar appearance to the experimental results, i.e., the Cole-Cole plot was a semi-circle and a peak appeared in a plot of the imaginary component of complex impedance with respect to the frequency from which the characteristic frequency was obtained. For a simple RC circuit in parallel connection, the logarithm of the characteristic frequency should be a linear function of the 1/3 power of the average number of primary particles per aggregate. A slight deviation from the line found in the simulations was attributed to the network contribution. Additionally, low CB loading had little effect on the characteristic frequency, in accordance with the experimental data, while high loading had a marked effect. Furthermore, the calculations showed that the characteristic frequency was affected not only by the distribution of individual CB aggregates, but also by the percentage of agglomerates at high CB loading.