Ac and dc percolative conductivity of magnetite-cellulose acetate composites

Abstract

ac and dc conductivity results for a percolating system, which consists of a conducting powder (magnetite) combined with an ``insulating'' powder (cellulose acetate), are presented. Impedance and modulus spectra are obtained in a percolation system. The temperature dependence of the resistivity of the cellulose acetate is such that at $170\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$, it is essentially a conductor at frequencies below $0.059\ifmmode\pm\else\textpm\fi{}0.002\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$, and a dielectric above. The percolation parameters, from the dc conductivity measured at 25 and $170\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$, are determined and discussed in relation to the ac results. The experimental results scale as a function of composition, temperature, and frequency. An interesting result is the correlation observed between the scaling parameter $({f}_{c\mathrm{e}})$, obtained from a scaling of the ac measurements, and the peak frequency $({f}_{cp})$ of the arcs, obtained from impedance spectra, above the critical volume fraction. Scaling at $170\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$ is not as good as at $25\phantom{\rule{0.2em}{0ex}}\ifmmode^\circ\else\textdegree\fi{}\mathrm{C}$, probably indicating a breakdown in scaling at the higher temperature. The modulus plots show the presence of two materials: a conducting phase dominated by the cellulose acetate and the isolated conducting clusters below the critical volume fraction ${\ensuremath{\phi}}_{c}$, as well as the interconnected conducting clusters above ${\ensuremath{\phi}}_{c}$. These results are confirmed by computer simulations using the two exponent phenomenological percolation equation. These results emphasize the need to analyze ac conductivity results in terms of both impedance and modulus spectra in order to get more insight into the behavior of composite materials.