Induced polarization response of porous media with metallic particles - Part 1: A theory for disseminated semiconductors

A model is proposed regarding the polarization of dispersed metallic conductors (e.g., pyrite and magnetite) in porous media free of redox-active ionic species in the pore water. We studied two cases corresponding to having a background material with or without chargeability. The model was based on the polarization mechanism of a single particle using well-established bounds for the reflection coefficient entering the definition of the dipole moment of the metallic grains. We used the Maxwell-Clausius-Mossotti mixing equation to obtain the complex conductivity of the mixture of dispersed metallic particles in the background porous material composed of the pore water and the insulating grains coated by an electric double-layer. This equation can be generalized to a mixture of various types of metallic particles (with their own properties) dispersed in the background porous material. Our model led to a very simple linear relationship between the chargeability and the volume content of metallic particles in the material. In addition, the chargeability depended weakly only on the shape of the spheroidal metallic particles as long as their orientation was random. The relaxation time defined from the phase peak frequency related to the diffusion coefficient of the n-and p-charge carriers in the metallic particles. This diffusion coefficient was consistent with the mobility of the charge carriers derived from theoretical considerations or electric conductivity measurements. In the presence of a polarizable background (e.g., a clayey matrix), we found that the total chargeability of the material can be determined from the chargeability of the metallic particles and the chargeability of the background material.