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

摘要: Percolation phenomena, which include the ac and dc conductivity, dielectric constant, magnetoresistance, are studied in a series of seven cellular composites, consisting small conductor particles embedded on surface larger insulator particles. Carbon black (ground unground), graphite, graphite\char21{}boron-nitride, niobium carbide, nickel, magnetite $({\mathrm{Fe}}_{3}{\mathrm{O}}_{4})$ powders were conducting components with talc-wax powder as common insulating component. The conductivity results fitted to standard percolation equations two-exponent phenomenological equation, yields parameters ${\ensuremath{\sigma}}_{i},$ ${\ensuremath{\sigma}}_{c},$ s, t, ${\ensuremath{\varphi}}_{c}$ ideal limits. Both universal nonuniversal values s t measured systems. Close threshold $({\ensuremath{\varphi}}_{c}),$ $({\ensuremath{\sigma}}_{\mathrm{mr}})$ constant $({\ensuremath{\varepsilon}}_{\mathrm{mr}})$ found scale ${\ensuremath{\sigma}}_{\mathrm{mr}}\ensuremath{\propto}{\ensuremath{\omega}}^{u}$ ${\ensuremath{\varepsilon}}_{\mathrm{mr}}\ensuremath{\propto}{\ensuremath{\omega}}^{\ensuremath{-}v}.$ All these exponents examined using most recent theories compared previous studies. exponent ${(s}^{\ensuremath{'}}),$ from ${\ensuremath{\epsilon}}_{\mathrm{mr}}\ensuremath{\propto}({\ensuremath{\varphi}}_{c}\ensuremath{-}\ensuremath{\varphi}{)}^{\ensuremath{-}{s}^{\ensuremath{'}}},$ is shown be frequency dependent. ${g}_{c}$ (magnetoresistance) ${t}_{m}$ (from magnetoconductivity) composites not yet clearly understood but show that ${t}_{m}gt.$ scaling real composite comprising ${\mathrm{Fe}}_{3}{\mathrm{O}}_{4}$ talc wax.