Generalizations of ‘‘universal dielectric response’’ and a general distribution-of-activation-energies model for dielectric and conducting systems

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Abstract
Three empirical equations introduced by Jonscher to represent the imaginary part of the small-signal frequency response of dielectric materials and termed ‘‘universal dielectric response’’ by him are generalized in three ways. The equations may be applied in normalized form at the impedance level as well as at the usual complex dielectric constant level, defining the response of conducting rather than dielectric materials. They are generalized to include real as well as imaginary parts where possible. A unified dielectric or conductive distribution-of-activation-energies (DAE) physical model is proposed whose predictions agree remarkably well with those of all the Jonscher universal dielectric response equations as well as with many other common dielectric response equations. The new model, unlike previous small-signal response models, leads to quantitative predictions for the temperature dependence of the power-law frequency exponent appearing in the ubiquitous constant-phase-response frequency region of the total response.