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The Poisson-Nernst-Planck (PNP) diffusional model for the immittance orimpedance spectroscopy response of an electrolytic cell in a finite-lengthsituation is extended to a general framework. In this new formalism, the bulkbehavior of the mobile charges is governed by a fractional diffusion equationin the presence of a reaction term. The solutions have to satisfy a generalboundary condition embodying, in a single expression, most of the surfaceeffects commonly encountered in experimental situations. Among these effects,we specifically consider the charge transfer process from an electrolytic cellto the external circuit and the adsorption-desorption phenomenon at theinterfaces. The equations are exactly solved in the small AC signalapproximation and are used to obtain an exact expression for the electricalimpedance as a funcion of the frequency. The predictions of the model arecompared to and found to be in good agreement with the experimental dataobtained for an electrolytic solution of CdCl2H20.

A framework to investigate the immittance responses for finite  length-situations: fractional diffusion equation, reaction term, and boundary  conditions