One sign ion mobile approximation

Free ions in kerosene-based ferrofluid detected by impedance spectroscopy

The influence of the free ions on the electric response of cells filled with kerosene-based ferrofluids in the low-frequency region is explored. The experimental investigations have been performed on cells limited by different types of electrodes, with the same kind of ferrofluid, by means of the impedance spectroscopy technique. The electrodes considered in our study are made of titanium, platinum, gold, brass and surgical steel. The analysis of the spectra of the real and imaginary parts of the electric impedance of the cell data has been done by means of a simplified version of the Poisson-Nernst-Planck model, in which only the carriers of a given sign are mobile. The agreement between the theoretical predictions and the experimental data is rather good on the whole frequency range. From the analysis of the data in the low-frequency range, dominated by the properties of the electrodes, we discovered that only gold electrodes behave in a manner different from the other electrodes. From the best fit of the experimental data the free-ions density is determined as well as their diffusion coefficient in kerosene. The estimated dielectric constant of the kerosene is in good agreement with the values reported in the literature. In the framework of our model, the surface conductivity of the electrodes has been also determined.

Role of the displacement current on Warburg-type behavior

We investigate the role of the displacement current in the analysis of the electric response of an electrolytic cell to an external stimulus. We show that several models proposed to interpret the spectra deduced by means of the impedance spectroscopy technique are questionable. In particular, we demonstrate that even in the frequency range below the Debye frequency the role of the displacement current is fundamental, and its omission leads to incorrect results for the impedance of the cell. In our analysis, the boundary conditions on the bulk current density are of Nernstian and of Ohmic type. The analysis is limited to a fully dissociated electrolyte, and for only one type of mobile ions, as discussed in several papers devoted to the subject. Particular attention is given to the spatial dependence of the current density. We show that Warburg-like behavior is never predicted in the framework of the Poisson-Nernst-Planck model, if the electric impedance of the cell is correctly evaluated. From this conclusion, valid for media with only one type of mobile ions, it follows that if Warburg-like behavior is experimentally observed the theoretical interpretation is still an open problem, and its origin is probably related to the boundary conditions.

Three to six ambiguities in immittance spectroscopy data fitting

Several important ambiguities in immittance spectroscopy (IS) model data-fitting results are identified and illustrated by means of complex-nonlinear-least-squares (CNLS) fits of experimental and synthetic frequency response data. A well-known intrinsic ambiguity, following from Maxwell's electromagnetic equations, arises from the indistinguishability in external measurements of conduction and displacement currents. Usual fit models for either dielectric or conductive-system situations, such as the Davidson-Cole one, only involve a strength parameter, a dielectric constant, a characteristic relaxation time, and a fractional exponent and lead to no additional ambiguities. But the situation is different for more powerful and useful general models, such as ordinary or anomalous diffusion Poisson-Nernst-Planck ones: PNP and PNPA, used here, whose historical background, current status, and applicability are described and discussed herein. They apply to two different kinds of experimental IS situations and involve several additional, potentially free fit parameters, such as the mobilities of positive and negative charge carriers, and generation-recombination parameters that determine the partial or complete dissociation of a neutral entity of concentration N(0) into positive and negative charge carriers of equal concentration, c(0). Then, several additional ambiguities appear that may require information about the material system involved for their adequate resolution.