Some alternate models for nearly constant loss in conductive systems

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The qualitative serial-response approach recently suggested by Le\'on, Rivera, and co-authors for describing nearly constant loss (NCL) in conductive systems proposes that NCL arises entirely from vibrating ions confined in cages by potential barriers. Their identification of the cage potential-well activation energy as that of single ions and also as that of the thermally activated crossover between hopping and NCL behavior is inconsistent with prior identification of the single-ion energy in the Ngai coupling model, casting doubt on the physical basis of the serial approach. Its authors suggested that their experimental data, showing hopping and NCL behavior, could not be described by means of a parallel (sum) combination of expressions describing these two processes. Here, using essentially exact synthetic data of the same character as the experimental frequency-response data of these authors, it is demonstrated that either a parallel or a series complex constant-phase response element (CPE) can lead to NCL results similar to theirs with a crossover between hopping and NCL response not of exact Arrhenius form. A plausible alternate to the serial NCL model is discussed. It involves a quantitative parallel CPE model that identifies NCL frequency response as being primarily a bulk-dielectric phenomenon arising from interactions between oscillating mobile charge carriers and the dipoles of the bulk material.