Bruggeman exponent

Patel et al. showed that a Bruggeman exponent of 1.5 is often not valid for real separator materials, which do not have uniform spherical shape.Porous networks based on other morphologies such as oblate (disk-type) ellipsoids or lameller increase the tortuous path for ionic conductivity and result either in a significant increase of the exponent a, or in a complete deviation from the power law. They showed that spherical or slightly prolate ellipsoidal pores should be preferred for separators, as they lead to higher ionic conductivity separators. 

Equation (2b) is a scaling law depicting the conductive behavior in the vicinity of the percolation threshold, the value of the critical exponent y being 1.6 to within 0.2. Equation (2c) expresses the composite conductivity dependence upon conductor concentration beyond the percolation threshold. Equation (2c) is a simplified form, valid in the case of conductor-insulator mixtures, of a more general equation derived in different ways by Bruggeman (70), Bottcher (71) and Landauer (72) and known as the Effective Medium Theory, (E.M.T.), formula ... 

Bruggeman equation for different exponents L. The curve for Z,=0.33 is the same as for the CRIM equation (see Section 8.7.4.3). (Turves are compared with experimental data for water-saturated sandstone. Pooley et al. (1978). 

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