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

Abstract

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 $({\mathrm{Fe}}_{3}{\mathrm{O}}_{4})$ 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 ${\ensuremath{\sigma}}_{i},$ ${\ensuremath{\sigma}}_{c},$ s, t, and ${\ensuremath{\varphi}}_{c}$ in the ideal limits. Both universal and nonuniversal values of s and t are measured in the systems. Close to the percolation threshold $({\ensuremath{\varphi}}_{c}),$ the ac conductivity $({\ensuremath{\sigma}}_{\mathrm{mr}})$ and the dielectric constant $({\ensuremath{\varepsilon}}_{\mathrm{mr}})$ are found to scale as ${\ensuremath{\sigma}}_{\mathrm{mr}}\ensuremath{\propto}{\ensuremath{\omega}}^{u}$ and ${\ensuremath{\varepsilon}}_{\mathrm{mr}}\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{-}v}.$ All these exponents are examined using the most recent theories and compared with previous studies. The dielectric constant exponent ${(s}^{\ensuremath{'}}),$ from ${\ensuremath{\epsilon}}_{\mathrm{mr}}\ensuremath{\propto}({\ensuremath{\varphi}}_{c}\ensuremath{-}\ensuremath{\varphi}{)}^{\ensuremath{-}{s}^{\ensuremath{'}}},$ 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 ${t}_{m}gt.$ dc scaling is shown in a real composite comprising ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ and talc wax.