Electrical conduction mechanism of polymer-carbon black composites below and above the percolation threshold

DC electrical conduction below the percolation p_c is due to a tunneling mechanism between finite clusters because of a non-ohmic behavior of current and the appearance of a current independent of frequency in ac conduction. The temperature dependence of resistivity ρ depending on applied field can be well explained with a tunneling model by incoporating the effect of thermal expansion on a tunneling gap in the model. In the region above p_c, on the other hand, the electrical conduction takes place on conducting pathways between electrodes. The temperature dependence of resistivity ρ above p_c, is discussed with a model where the effects of thermal expansion on the number of conducting pathways and a thermally activated process in electrical conduction are taken into account