Utility and Importance of Poisson–Nernst–Planck Immittance-Spectroscopy Fitting Models

Abstract

This feature article highlights work done by the author and others since 1953 on the Poisson–Nernst–Planck (PNP) continuum model for analyzing and fitting wide-range immittance-spectroscopy (IS) frequency-response data for unsupported materials with diffusing mobile charge species present. The small-signal PNP approach, one relevant for analyzing data involving ordinary or anomalous diffusion, is particularly important because it leads to estimates of the values of far more physically significant parameters than do other available IS fitting models. Unfortunately, its virtues were not well appreciated until recently, and it has thus not been used as widely as it should be. The present work aims at remedying this lack by providing a thorough description of the strengths and weaknesses of the model, its response possibilities, and its broad applicability. It deals with a neutral species that can fully or partially dissociate into positive and negative charged species of equal concentrations but arbitrary mo...