Utility of continuum diffusion models for analyzing mobile-ion immittance data: electrode polarization, bulk, and generation-recombination effects

Consequences of the well-known Poisson-Nernst-Planck (PNP) continuum equations of charge motion in liquids or solids for ordinary or anomalous diffusion are investigated for an electrochemical cell with completely blocking electrodes. Previous work is summarized and much of it is shown to be independent of earlier published results and incomplete, with little comparison made between ordinary and anomalous diffusion. Such comparison is provided here and also includes variation of the mobility ratio of the mobilities of positive and negative charges from equality to charge of only one sign mobile. New generation-recombination effects are demonstrated for a range of mobility ratios, with particular attention given to those present for the case of charge of only one sign mobile. No previous analyses of experimental data with PNP models using complex-least-squares fitting have been published. Here such a model is found to fit frequency response data well for a hydrogel and to lead to estimates of physically meaningful parameters such as the diffusion constant and ionic concentration. PNP analysis of a synthetic data set derived from experimental results for liquid electrolytes refutes claims made in the original publication dealing with it, but verifies and extends an interesting analysis equation proposed there. PNP fitting of data for solids, including ones showing colossal low-frequency-limiting dielectric constants, suggests that they may often be well described as arising from simple diffuse-charge double-layer effects, and that continuum microscopic models such as the PNP, in series with a conducting Debye response model, may be sufficient for fitting well an appreciable amount of data involving ion hopping and trapping behavior.