ac and dc conductivity, magnetoresistance, and scaling in cellular percolation systems

Percolation phenomena, which include the ac and dc conductivity, dielectric constant, and magnetoresistance, are studied in a series of seven cellular composites, consisting of small conductor particles embedded on the surface of larger insulator particles. Carbon black (ground and unground), graphite, graphite-boron-nitride, niobium carbide, nickel, and magnetite (Fe3O4) powders were the conducting components with talc-wax powder as the common insulating component. The dc conductivity results were fitted to the standard percolation equations and to a two-exponent phenomenological equation, which yields the percolation parameters sigma(i), sigma(c), s, t, and phi(c) in the ideal limits. Both universal and nonuniversal values of s and t are measured in the systems. Close to the percolation threshold (phi(c)), the ac conductivity (sigma(mr)) and the dielectric constant (epsilon(mr)) are found to scale as sigma(mr)proportional toomega(u) and epsilon(mr)proportional toomega(-v). All these exponents are examined using the most recent theories and compared with previous studies. The dielectric constant exponent (s(')), from epsilon(mr)proportional to(phi(c)-phi)(-s'), is shown to be frequency dependent. The exponents g(c) (magnetoresistance) and t(m) (from magnetoconductivity) in composites are not yet clearly understood but these and previous results show that t(m)>t. dc scaling is shown in a real composite comprising Fe3O4 and talc wax.