Three to six ambiguities in immittance spectroscopy data fitting

Several important ambiguities in immittance spectroscopy (IS) model data-fitting results are identified and illustrated by means of complex-nonlinear-least-squares (CNLS) fits of experimental and synthetic frequency response data. A well-known intrinsic ambiguity, following from Maxwell's electromagnetic equations, arises from the indistinguishability in external measurements of conduction and displacement currents. Usual fit models for either dielectric or conductive-system situations, such as the Davidson-Cole one, only involve a strength parameter, a dielectric constant, a characteristic relaxation time, and a fractional exponent and lead to no additional ambiguities. But the situation is different for more powerful and useful general models, such as ordinary or anomalous diffusion Poisson-Nernst-Planck ones: PNP and PNPA, used here, whose historical background, current status, and applicability are described and discussed herein. They apply to two different kinds of experimental IS situations and involve several additional, potentially free fit parameters, such as the mobilities of positive and negative charge carriers, and generation-recombination parameters that determine the partial or complete dissociation of a neutral entity of concentration N(0) into positive and negative charge carriers of equal concentration, c(0). Then, several additional ambiguities appear that may require information about the material system involved for their adequate resolution.