On the equivalence between specific adsorption and kinetic equation descriptions of the admittance response in electrolytic cells

Introduction of effective dielectric constant to the Poisson-Nernst-Planck model

The Poisson-Nernst-Planck (PNP) model has been widely used for analyzing impedance or dielectric spectra observed for dilute electrolytic cells. In the analysis, the behavior of mobile ions in the cell under an external electric field has been explained by a conductive nature regardless of ionic concentrations. However, if the cell has parallel-plate blocking electrodes, the mobile ions may also play a role as a dielectric medium in the cell by the effect of space-charge polarization when the ionic concentration is sufficiently low. Thus the mobile ions confined between the blocking electrodes can have conductive and dielectric natures simultaneously, and their intensities are affected by the ionic concentration and the adsorption of solvent molecules on the electrodes. The balance of the conductive and dielectric natures is quantitatively determined by introducing an effective dielectric constant to the PNP model in the data analysis. The generalized PNP model with the effective dielectric constant successfully explains the anomalous frequency-dependent dielectric behaviors brought about by the mobile ions in dilute electrolytic cells, for which the conventional PNP model fails in interpretation.

Use of electrochemical impedance spectroscopy to determine double-layer capacitance in doped nonpolar liquids

Electrochemical impedance spectroscopy in a thin cell (10 μm) was used to infer conductivity, permittivity and the differential double-layer capacitance of solutions of dodecane doped with OLOA 11000 [poly(isobutylene) succinimide] for concentrations of dopant between 0.1% and 10% by weight. All spectra (frequencies between 1 Hz and 100 kHz) were well fit by an equivalent circuit having four elements including a constant-phase element representing the double-layer capacitance. Using Gouy-Chapman theory for small zeta potentials and assuming univalent charge carriers, the double-layer capacitances were converted into charge carrier concentration which was found to be directly proportional to the weight percent of dopant with a 1 wt% solution having 87 carriers/μm(3) (the concentration of either positive or negative charges). This is only 17 ppm of the total monomer concentration calculated from the average molecule weight of the dopant. Dividing the measured conductivities by the charge carrier concentration, we inferred the mobility and hydrodynamic diameters for the charged micelles. The hydrodynamic diameters of carriers were significantly larger than the average diameter of all micelles measured independently by dynamic light scattering. This suggests that only large micelles become charged.

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.