Electrical Properties of Carbon Black Polymer Composites: Filler Particle Rearrangement
The practical application of semi-conducting carbon black polymer composites often involves temperature variations resulting in changes in their electrical properties. Study of cross-linked ethylene butylacrylate copolymer (EBA) filled with acetylene black has shown that these changes are due to carbon black network re-arrangement.
The dependence of a composite's dc conductivity on filler concentration is determined by the network formed by the filler particles. The network has an effective volume fraction greater than the volume fraction of the solid carbon black forming it. Their ratio is given by an empirical factor f. During isothermal annealing at 90°C f grows uniformly with time for all investigated filler concentrations indicating that the re-arrangement is independent on the filler concentration although the change in conductivity varies greatly for different concentrations.
The carbon black network has been characterised using the diffusion limited cluster aggregation model (DLCA) and the reaction limited cluster aggregation model (RLCA). The correlation length and the mass fractal dimension of carbon black agglomerates have been determined from image analysis of SEM micrographs. An increase in the filler concentration is accompanied by a decrease of the correlation length. At the same time the fractal dimension changes from 1.8 to 2.1, which has been interpreted as a transition from DLCA to RLCA
However, the carbon black network cannot alone explain the electrical properties of the composite. Therefore, the critical frequency .omega.c denoting the crossover from the dc plateau of the conductivity to its frequency dependent behaviour has been analysed. This analysis is based on the scaling of .omega.c with the dc conductivity .sigma.dc according to .omega.c is proposional to.sigma.dcz. Results indicate that the conducting network consists not only of links between touching particles, but also of gaps between them. During thermal cycling and annealing these gaps open and close (z > 1) when the carbon black network re-arranges above the melting range of EBA. However, re-arrangement below the melting range is due to variations in the gap width distribution without gap opening or closing (z » 1). This switch is discussed in terms of polymer relaxation in the vicinity of the filler surface.