Comparison of two generation-recombination terms in the Poisson-Nernst-Planck model

Warburg's impedance revisited

The derivation of Warburg's impedance presented in several books and scientific papers is reconsidered. In the past it was obtained by assuming that the total electric current across the sample is just due to the diffusion, and that the external potential applied to the electrode is responsible for an increase of the bulk density of charge described by Nernst's model. We show that these assumptions are not correct, and hence the proposed derivations are questionable. When the electrochemical impedance of a cell of an insulating material where external charges are injected of a given sign is correctly determined, in the high frequency region the real and imaginary parts do not follow the trends predicted by Warburg's impedance. The analysis presented in this paper is relevant to a symmetric cell, in the Nernstian approximation. It can be easily generalized to the case of an asymmetric cell, assuming boundary conditions where the conduction current across the electrodes is proportional to the surface electric field.

Comment on "Modeling of electrode polarization for electrolytic cells with a limited ionic adsorption"

Recently, Sawada [Phys. Rev. E 88, 032406 (2013)] proposed a model to take into account the dielectric dispersion of ionic origin in a weak electrolyte cell. We first show that the model is based on questionable assumptions. Next, we point out an error in the author's calculation of the current in the external circuit. Finally, we demonstrate why some criticism on recent papers is irrelevant.

Examination of methods to determine free-ion diffusivity and number density from analysis of electrode polarization

Electrode polarization analysis is frequently used to determine free-ion diffusivity and number density in ionic conductors. In the present study, this approach is critically examined in a wide variety of electrolytes, including aqueous and nonaqueous solutions, polymer electrolytes, and ionic liquids. It is shown that the electrode polarization analysis based on the Macdonald-Trukhan model [J. Chem. Phys. 124, 144903 (2006); J. Non-Cryst. Solids 357, 3064 (2011)] progressively fails to give reasonable values of free-ion diffusivity and number density with increasing salt concentration. This should be expected because the original model of electrode polarization is designed for dilute electrolytes. An empirical correction method which yields ion diffusivities in reasonable agreement with pulsed-field gradient nuclear magnetic resonance measurements is proposed. However, the analysis of free-ion diffusivity and number density from electrode polarization should still be exercised with great caution because there is no solid theoretical justification for the proposed corrections.