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Geometric and dielectric characterization of porous media

R. Hilfer
Department of Physics, University of Oslo, 0316 Oslo, Norway
Institut für Physik, Universität Mainz, 6500 Mainz, Germany

This paper introduces local porosity distributions and local percolation probabilities as welldefined and experimentally observable geometric characteristics of general porous media. Based on these concepts the dielectric response is analyzed using the effective-medium approximation and percolation scaIing theory. The theoretical origin of static and dynamic scaling laws for the dielectric response incIuding Archie’s law in the low-porosity limit are elucidated. The zero-frequency real dielectric constant is found to diverge as \varepsilon\propto(1-\phi)^{{-m^{\prime}}} in the high-porosity limit, where \phi denotes the porosity and m^{\prime} is analogous to the cementation exponent. ModeI calculations are presented for the interplay between geometric characteristics and the frequency-dependent dieIectric response. Three pureIy geometric mechanisms are identified, each of which can give rise to a large dielectric enhancement.

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PACS: 05.70.Ln,05.30.-d,05.20.-y,03.65.Fd,11.10.Nx,11.10.Jj