Electrical impedance of an electrolytic cell in the presence of generation and recombination of ions

Abstract

The electrical impedance of an insulating solid containing ions is evaluated in the presence of the generation and recombination of ions. The case of perfectly blocking electrodes is considered. It is shown that in the case where the diffusion coefficients of the positive and negative ions are equal, the expression for the electrical impedance coincides with the one valid in the absence of the generation and recombination of ions, with the bulk density of ions fixed by the chemical reaction describing the generation and recombination of ions. In particular, in the low frequency region, the resistance tends to the value corresponding to the plateau, and the reactance diverges as the inverse of the frequency. The case where the neutral particles, that by decomposition generate the ions, and the positive ions have a vanishing small diffusion coefficient with respect to that of the negative ions is also considered. In this situation, in the series representation, the resistance of the cell presents two plateaus. One in the low frequency region is related to the generation-recombination phenomenon. The other, with a resistance smaller than the previous one, ends at the frequency of Debye. This result is of some importance because it could be the mechanism able to explain the experimental data obtained with hydrogels doped with KCl.

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

“…In addition to the situation treated in Ref. [17], where the sample has the same geometry, we incorporate the adsorptiondesorption process on the surface of the electrode.…”

“…[14,17], we write N n ¼ N n þ n n ; N p ¼ N þ n p , and N m ¼ N þ n m . We assume that the variations in the bulk density of ions due to the action of the external field are very small with respect to the values in thermodynamical equilibrium.…”

“…Thus, to build a more complete model to evaluate the electrical impedance of this system it may also be necessary to take into account the dissociation of neutral particles in ionic products, the recombination of these ions giving rise to neutral particles [3][4][5][6][7][8][9][10][11][12][13], and the adsorption-desorption process occurring at the interfaces [14][15][16]. In a recent paper [17], the importance of the dissociation-association process in the determination of the electrical impedance was analyzed in detail, but without taking into account the adsorption phenomena, in the framework of the Poisson-Nernst-Planck (PNP) model. A conspicuous effect of this dissociation-association process is the appearance of a new plateau in the real part of the electrical impedance of the cell in the dc limit.…”

Warburg's impedance revisited

“…In particular, the parametric plot of the imaginary part versus the real one is a semicircle, whose center is on the real axis, passing for the origin of the cartesian reference frame. Several generalizations of the original model have been proposed to take into account the difference between the ions [1], the electrodes properties [4,5] and the generation/ recombination of ions [6][7][8], fractional diffusion or boundary conditions taking into account memory effects [9][10][11][12][13][14].…”

“…(8) G = q/(εV th ) is an intrinsic length of the problem. The fundamental equations of the problem, (6,7,8), are linear. Consequently if the applied voltage is a simple periodic function of the type ∆V (t) = V 0 exp(iωt), of amplitude V 0 and circular frequency ω, the functions defining the dynamical state, n m (z, t), n f (z, t) and u v (z, t) are of the type…”