Influence of adsorption phenomenon on the impedance spectroscopy of a cell of liquid

Ions, adsorption and electric response of a ferrofluid cell

We show that the electric response of a cell in the shape of a slab containing a ferrofluids (magnetic particles in kerosene) can be interpreted by means of a model...

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.

Reanalysis of the electrode polarization in electrolytic cells limited by blocking electrodes

We evaluate the effect of ions on the electric response of an insulting liquid by means of the total electric polarization induced in a cell by an external field. The limiting surfaces are assumed blocking and identical and the ions pointike nonpolarizable charged particles. The analysis is limited to the case where the selective ionic adsorption is absent, in such a manner that in the absence of external electric field the sample is locally and globally neutral. We obtain formulas for the effective dielectric constant renormalized by the presence of the ions in the absence and presence of adsorption from the surfaces. Our results coincide with those obtained by means of the electric impedance of the cell. From the coincidence of the results relevant to the effective dielectric constant we infer that the ions in an insulating liquid do not have a conductive or dielectric nature. They are just electric charges dissolved in an insulating liquid.

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.

Investigation of various types of inverse micelles in nonpolar liquids using transient current measurements

Transient current measurements are used to characterize a wide variety of charge carriers in nonpolar liquids. The transient current method allows us to obtain both the concentration and mobility of charge carriers and therefore also the hydrodynamic radius using Stokes' law. In this article, five different surfactants in dodecane are investigated: OLOA11K, Solsperse13940, Span80, Span85, and AOT. We show that different types of currents are observed depending on the size of the inverse micelles. For large inverse micelles such as for OLOA11K, Solsperse13940, and Span80, the measurement of the transient current is straightforward because of the low steady-state current level. However, for small inverse micelles such as AOT and Span85, the current from the generation of charges is much larger such that high voltages, a small distance between the electrodes, and dielectric coatings on the electrodes are required to measure the signal related to the initially present charged inverse micelles. The estimated hydrodynamic radii of AOT and Span85, the two smallest inverse micelles, are in good agreement with the values reported in the literature. The comparison of the transient currents with simulations indicates that the dynamics of the charge transport are well-understood.

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.

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

Dilute electrolytic cells filled with chlorobenzene containing small amounts of tetrabutylammonium tetraphenylborate show anomalous dielectric dispersions in low-frequency regions. We propose a new model for electrode polarization in order to analyze the dielectric behavior of the dilute electrolytic cells. The model comprises two capacitive components: One is the space-charge polarization accompanied with a specific ionic adsorption on electrodes, and the other is the electrode capacitance which is brought about by an electronic spillover from the electrode surface. This model can primarily explain the anomalous frequency-dependent dielectric behavior of the electrolytic cells not only with low electrolyte concentrations, but also with high concentrations and can correctly describe the characteristics of the electrode polarization reflected in the dielectric spectra.

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.

One sign ion mobile approximation

The electrical response of an electrolytic cell to an external excitation is discussed in the simple case where only one group of positive and negative ions is present. The particular case where the diffusion coefficients of the negative ions, D(m), is very small with respect to that of the positive ions, D(p), is considered. In this framework, it is discussed under what conditions the one mobile approximation, in which the negative ions are assumed fixed, works well. The analysis is performed by assuming that the external excitation is sinusoidal with circular frequency ω, as that used in the impedance spectroscopy technique. In this framework, we show that there exists a circular frequency, ω*, such that for ω > ω*, the one mobile ion approximation works well. We also show that for D(m) ≪ D(p), ω* is independent of D(m).

The influence of adsorption phenomena on the impedance spectroscopy of an electrolytic cell

In this work we investigate the influence of the adsorption of ions on the impedance spectroscopy of an electrolytic cell. We consider that the positive and negative ions present in a dielectric liquid are adsorbed in the electrode surfaces with different adsorption energies. This difference in adsorption energies causes an additional plateaux in the limit of the low-frequency range of the real part of the impedance Z. In the same frequency range, a second minimum in the imaginary part of Z is predicted. The theory is illustrated with measurements of the impedance of an electrolytic solution in the frequency range from 10(-2) Hz to 1 KHz. A comparison between the present model and others from the literature to describe the experimental results is also made.

Complex dielectric constant of a nematic liquid crystal containing two types of ions: limit of validity of the superposition principle

We investigate the influence of two groups of ions on the complex dielectric constant of a nematic liquid crystal limited by perfectly blocking electrodes. The analysis is performed by solving the equations of continuity for the two groups of cations and anions, and the equation of Poisson relating the actual electric field to the net density of charge. We consider a typical experiment of impedance spectroscopy, and evaluate the equivalent resistance and reactance of the cell, in the series representation, versus the frequency of the applied voltage to the cell. We show that the presence of two groups of ions gives rise to two plateaux in the spectrum of the resistance, similar to those related to the ambipolar and free diffusion in the case where there is only one type of ions, but for which the cations and anions have different diffusion coefficients. The correspondence between the usual ambipolar and free diffusion coefficients and those related to the presence of two groups of ions is discussed. The spectra of the real and imaginary parts of the complex dielectric constant are obtained, and their dependence on the bulk densities of the two types of ions is investigated. The nonvalidity of the superposition principle is discussed.

Dielectric characterization of doped M5

We analyze the dielectric properties of the liquid crystal M5 used to investigate the electrohydrodynamics instability in nematic liquid crystals. We show that the spectra of the electrical impedance of doped samples of M5 with several concentrations of salt and of acid can be interpreted by assuming the doped liquid crystal as a dispersion of ions in a dielectric liquid. The analysis has been performed by considering the electrodes as blocking. From the best fit of the experimental data relevant to the real and imaginary parts of the electrical impedance of the cells, we derive the diffusion coefficients for the positive and negative ions and their bulk density. According to our analysis, in the limit of small concentrations of doping substance, the effective dielectric constant of the resulting liquid is, practically, independent of the doping.

Dielectric process of space-charge polarization for an electrolytic cell with blocking electrodes

The dielectric process of space-charge polarization for an electrolytic cell with blocking electrodes is simulated considering bound charges externally supplied to the electrodes. A numerical calculation is performed to determine the distribution of mobile charges under an ac field satisfying Poisson's equation in which the dielectric constant varies with frequency. An exact frequency-dependent curve of the complex dielectric constant is obtained by including the contribution of bound charges induced by the space-charge polarization itself in Poisson's equation at every frequency. The present model of the space-charge polarization enables one to correctly understand the experimental results on the complex dielectric constant of electrolytic cells in low-frequency regions.

Novel impedance cell for low conductive liquids: determination of bulk and interface contributions

A plane capacitor cell with variable gap has been designed in order to detect the complex permittivity of low conductive liquids (up to 500 microS/cm) and the impedance of the sample-electrode interface. The novelty of the cell consists of the simultaneous presence of the field uniformity ensured by a guard ring, an adjustable gap between 300 microm and 6.75 mm (the electrode axial motion avoiding any rotation), and the immersion of the capacitor in the sample reservoir. The size of the capacitor electrodes and the gap values have been tested via the capacitance detection of the in-air cell at 1 kHz. The sample measurements have been performed by scanning the frequency range between 15 Hz and 2 MHz at four different capacitor gap values. In the paper a method to directly extract the bulk complex permittivity and the interface impedance versus frequency is presented. It is based on the assumption that the interface contribution is independent of the electrode gap, as confirmed (within the measurement accuracy) from measurements on all samples investigated. As samples of interest, we have chosen two certified electrolytic conductivity standards, KCl aqueous solutions having conductivity traceable to SI units; and two polymer latex aqueous dispersions of microspheres. Regarding KCl solutions, the conductivity measurements are compatible with the reference values within the specified uncertainty; the measured permittivities are consistent with the literature. For all samples, we have recovered the expected result that the interface impedance mainly affects the low frequency range (f<10 kHz).

Role of the Adsorption Phenomenon on the Ionic Equilibrium Distribution and on the Transient Effects in Electrolytic Cells

We analyze the influence of the adsorption of ions at the interfaces on the transient phenomena occurring in an electrolytic cell submitted to a steplike external voltage. In the limit of small amplitude of the applied voltage, where the equation of the problem can be linearized, we obtain an analytical solution for the bulk and surface densities of ions and for the electrical potential. We also obtain, in this limit, the relaxation time for the transient phenomena.

Electrical impedance for an electrolytic cell

We analyze in which experimental conditions the concept of electrical impedance is useful for an electrolytic cell. The analysis is performed by solving numerically the differential equations governing the phenomenon of the redistribution of the ions in the presence of an external electric field and comparing the results with the ones obtained by solving the linear approximation of these equations. The control parameter in our study is the amplitude of the applied voltage, assumed a simple harmonic function of the time. We show that the bulk distribution of ions close to the electrodes differs from the one obtained by means of the linear analysis already for small amplitudes of the applied voltage. Nevertheless, the concept of electrical impedance remains valid. For larger amplitudes, the current in the circuit is no longer harmonic at the same frequency of the applied voltage. Therefore the concept of electrical impedance is no longer meaningful.

Excess nonspecific Coulomb ion adsorption at the metal electrode/electrolyte solution interface: role of the surface layer

Excess ion adsorption gamma induced by the polarization image forces in the system of a metal electrode/symmetric electrolyte solution separated by an insulating interlayer has been calculated. The adopted theoretical scheme involves the Coulomb Green's function in a three-layer system with sharp interfaces and specular reflection at them. The influence of the spatial dispersion of the dielectric permittivities epsilon(i)(k) in all the three media on the image force energy W(im) and the adsorption gamma has been analyzed, where k is the wave vector. A comparison with the classical model, where epsilon(i)=const, has been carried out. It has been shown that both the Debye-Hückel ion screening and the spatial dispersion of the solvent contribution epsilon(solv)(k) to the overall dielectric function epsilon(el)(k) of the electrolyte solution lead to the qualitative difference with the results for the classical model. In particular, in a wide range of ion concentrations n0 a thin interlayer L > or = 5-10 angstroms effectively screens out the attractive influence of the metallic electrode, so that the net Coulomb adsorption may become repulsive. The approach and the results obtained qualitatively describe two physically different situations. Specifically, the introduced interlayer corresponds either to the dense near-electrode (inner) electrolyte layer or to the intentionally deposited control coating of arbitrary thickness.