Immittance response of an electrolytic cell in the presence of adsorption, generation, and recombination of ions

Frequency-Dependent Dielectric Permittivity in Poisson-Nernst-Planck Model

The approaches developed for studying the polarization of molecules and the dynamics of ions in dielectric materials are usually considered separately. The two effects are often believed to take place in different frequency ranges. The low frequency response is usually dominated by ionic migration, whereas the high frequency response is played by molecular polarization. The goal here is to clarify the interplay between free and bound charge densities and their influences on permittivity and impedance profiles by proposing a version of the Poisson-Nernst-Planck (PNP) model that allows to include the effect of a frequency-dependent (and thus not instantaneous) polarizability.

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

The dielectric properties of dilute electrolytic solution cells have been measured in a low-frequency region, and the dielectric spectra have been analyzed in terms of space-charge polarization by using the Nernst-Planck (NP) model in the presence of ionic adsorption on electrodes [Phys. Rev. E 88, 032406 (2013)]. In the NP model, the internal electric field of the cell is considered to be approximately equal to the external field. In a Comment by Alexe-Ionescu et al. [Phys. Rev. E 89, 056401 (2014).] on our paper [Phys. Rev. E 88, 032406 (2013)], they claim the invalidity of the NP model and the necessity of the conventional Poisson-Nernst-Planck (PNP) model for the data analysis. Their criticisms are, however, originated from a viewpoint for determining the internal electric field, that is different from our approach. In this Reply, we show the validity of the NP model referring to our previous paper in which the conventional PNP model has been modified so as to correctly describe the actual internal field.

The Kramers-Kronig relations for usual and anomalous Poisson-Nernst-Planck models

The consistency of the frequency response predicted by a class of electrochemical impedance expressions is analytically checked by invoking the Kramers-Kronig (KK) relations. These expressions are obtained in the context of Poisson-Nernst-Planck usual or anomalous diffusional models that satisfy Poisson's equation in a finite length situation. The theoretical results, besides being successful in interpreting experimental data, are also shown to obey the KK relations when these relations are modified accordingly.

Electrodiffusion kinetics of ionic transport in a simple membrane channel

We employ numerical techniques for solving time-dependent full Poisson-Nernst-Planck (PNP) equations in 2D to analyze transient behavior of a simple ion channel subject to a sudden electric potential jump across the membrane (voltage clamp). Calculated spatiotemporal profiles of the ionic concentrations and electric potential show that two principal exponential processes can be distinguished in the electrodiffusion kinetics, in agreement with original Planck's predictions. The initial fast process corresponds to the dielectric relaxation, while the steady state is approached in a second slower exponential process attributed to the nonlinear ionic redistribution. Effects of the model parameters such as the channel length, height of the potential step, boundary concentrations, permittivity of the channel interior, and ionic mobilities on electrodiffusion kinetics are studied. Numerical solutions are used to determine spatiotemporal profiles of the electric field, ionic fluxes, and both the conductive and displacement currents. We demonstrate that the displacement current is a significant transient component of the total electric current through the channel. The presented results provide additional information about the classical voltage-clamp problem and offer further physical insights into the mechanism of electrodiffusion. The used numerical approach can be readily extended to multi-ionic models with a more structured domain geometry in 2D or 3D, and it is directly applicable to other systems, such as synthetic nanopores, nanofluidic channels, and nanopipettes.

Non-Debye relaxation in the dielectric response of nematic liquid crystals: surface and memory effects in the adsorption-desorption process of ionic impurities

We demonstrate theoretically that the presence of ions in insulating materials such as nematic liquid crystals may be responsible for the dielectric spectroscopy behavior observed experimentally. It is shown that, at low frequencies, an essentially non-Debye relaxation process takes place due to surface effects. This is accomplished by investigating the effects of the adsorption-desorption process on the electrical response of an electrolytic cell when the generation and recombination of ions is present. The adsorption-desorption is governed by a non-usual kinetic equation in order to incorporate memory effects related to a non-Debye relaxation and the roughness of the surface. The analysis is carried out by searching for solutions to the drift-diffusion equation that satisfy the Poisson equation relating the effective electric field to the net charge density. We also discuss the effect of the mobility of the ions, i.e., situations with equal and different diffusion coefficients for positive and negative ions, on the impedance and obtain an exact expression for the admittance. The model is compared with experimental results measured for the impedance of a nematic liquid crystal sample and a very good agreement is obtained.