Similarities and differences among the models proposed for real electrodes in the Poisson-Nernst-Planck theory

The ionic distribution induced by an external field is investigated by means of the Poisson-Nernst-Planck model, by taking into account the non-blocking properties of the limiting electrodes. Three types of models proposed for the description of real electrodes are considered. The first two assume an ionic current on the electrodes proportional to the variation of the bulk density of ions and to the surface electric field, respectively. The third model assumes that the sample is limited by perfectly blocking electrodes with a true resistance in parallel to the cell. Here we show that the first two models are equivalent, in the sense that it is possible to find a phenomenological parameter by means of which the predictions of the two models, for what concerns the spectra of the real and imaginary parts of the impedance of the cell, are the same. On the contrary, the third model is equivalent to the others only if the conduction current across the electrodes is small with respect to the displacement current.