Analytical Functions for the dc and ac Conductivity of Conductor-Insulator Composites

The Maxwell-Wagner and the Bruggeman Symmetric and Asymmetric Media equations are introduced and the well defined microstructures for which these effective media equations apply are emphasized. The microstructures characterising percolation systems and the resultant critical volume fractions are then discussed. After this the concept of scaling, the percolation expressions and a new two exponent analytical phenomenological equation are introduced and their interrelationship is examined. The information obtainable from dc measurements is investigated and then simulations of impedance and modular spectra obtained from the effective media equations are given and the implications of these results discussed. Followed this, results for the complex ac conductivity of a nearly ideal continuum systems are given and it is shown that the conductivity above and the dielectric term below the critical volume fraction can be scaled onto analytical curves, using parameters obtained from dc conductivity measurements. Lastly simulations of the type of impedance spectra and dispersion relations that might be observed for systems with a percolation microstructure but non ideal insulating and conducting components are given and discussed.