Abstract
Consequences of the well-known Poisson–Nernst–Planck (PNP) continuum equations ofcharge motion in liquids or solids for ordinary or anomalous diffusion are investigated foran electrochemical cell with completely blocking electrodes. Previous work is summarizedand much of it is shown to be independent of earlier published results and incomplete, withlittle comparison made between ordinary and anomalous diffusion. Such comparison isprovided here and also includes variation of the mobility ratio of the mobilities ofpositive and negative charges from equality to charge of only one sign mobile. Newgeneration–recombination effects are demonstrated for a range of mobility ratios,with particular attention given to those present for the case of charge of only onesign mobile. No previous analyses of experimental data with PNP models usingcomplex-least-squares fitting have been published. Here such a model is found to fitfrequency response data well for a hydrogel and to lead to estimates of physicallymeaningful parameters such as the diffusion constant and ionic concentration.PNP analysis of a synthetic data set derived from experimental results for liquidelectrolytes refutes claims made in the original publication dealing with it, butverifies and extends an interesting analysis equation proposed there. PNP fitting ofdata for solids, including ones showing colossal low-frequency-limiting dielectricconstants, suggests that they may often be well described as arising from simplediffuse-charge double-layer effects, and that continuum microscopic models such as thePNP, in series with a conducting Debye response model, may be sufficient forfitting well an appreciable amount of data involving ion hopping and trappingbehavior.
Published Version
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