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 $\left({\mathrm{Fe}}_3{\mathrm{O}}_4\right)$ 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 $\left({\phi }_c\right),$ the ac conductivity $\left({\sigma }_{\mathrm{mr}}\right)$ and the dielectric constant $\left({\varepsilon }_{\mathrm{mr}}\right)$ are found to scale as ${\sigma }_{\mathrm{mr}}\propto {\omega }^u$ and ${\varepsilon }_{\mathrm{mr}}\propto {\omega }^{-v}.$ All these exponents are examined using the most recent theories and compared with previous studies. The dielectric constant exponent ${(s}^{\prime }),$ from ${\epsilon }_{\mathrm{mr}}\propto ({\phi }_c-\phi {)}^{-s^{\prime }},$ 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 $t_m>t.\mathrm{}$ dc scaling is shown in a real composite comprising ${\mathrm{Fe}}_3{\mathrm{O}}_4$ and talc wax.

• Received 8 May 2002

DOI:https://doi.org/10.1103/PhysRevB.67.024206