Second-Order Impedance Spectroscopy of an Electroreduction Reaction with Allowance for the Frumkin Correction

A theory of second-order impedance spectroscopy is developed. The theory is good for analyzing an electroreduction reaction in surface-inactive supporting electrolytes with allowance made for the structure of the electrical double layer (the Frumkin correction). According to the theory, a measured second-order impedance contains, as a factor, an effective charge transfer coefficient. The latter's dependence on potential has a minimum connected with the diffuseness of the electrical double layer. The theoretical notions are experimentally confirmed on the basis of a real system.     

On the asymmetry of thermodynamic fluctuations of the electrode potential

The asymmetry of thermodynamic fluctuations of the equilibrium electrode potential and the asymmetry of thermodynamic fluctuations of the electrical double layer charge is characterized quantitatively on the basis of third-order noise spectra.Translated from Elektrokhimiya, Vol. 41, No. 2, 2005, pp. 131–136.Original Russian Text Copyright © 2005 by Grafov.This revised version was published online in April 2005 with corrections to the article note and article title and cover date.     

Simulation of the electrical double layer of a macroion with different counterion charges

An electrical double layer of a spherical macroion with single-, double-, and triple-charged counterions in aqueous solution of 1: 1 background electrolyte at different concentrations are studied by the molecular dynamics method for models with discrete and continuous surface charge distribution. Radial profiles of ion partial densities and the electric potential distribution in the double layer are calculated. The degree of counterion binding with a macroion is determined. The effect of water permittivity on the structure of electrical double layer is studied.     

Parameters of electrical double layer on the boundary copper electrode/water-organic solution of copper sulfate

By the method of impedance spectroscopy the properties of the phase boundary of Cu|H₂O + i-C₃H₇OH + CuSO₄ system were investigated. The impedance hodographs were obtained, in the form of circles with displaced centers. The capacity values of electrical double layer, exchange currents, and resistance of the electrolyte solution depending on the mole fraction of 2-propanol were determined. The role of organic component in the formation of the electrical double layer in the studied system is elucidated.     

Double-layer phenomena in electrochemistry: controversial views on some fundamental notions related to electrified interfaces

The problem of the distinction between the so-called free charge and the thermodynamic (total) charge of electrodes was discussed in the light of the relevant IUPAC definitions calling attention to the strict relationships existing between charge and mass balances during the formation of a double layer at electrodes or/and particles. It is demonstrated that the origins of controversial views concerning partial charge transfer and electrosorption valency, notions widely used nowadays in the electrochemical literature, could be ascribed to confusion of the free and thermodynamic charges. Although there are, even if sporadic, evidences and theoretical considerations in the literature proving that electrosorption valency as usually defined is an extrathermodynamic and self-contradictory concept, it is widely used by many authors for the interpretation of electrosorption phenomena. One of the most important aims of the present work was to demonstrate that independent of the thermodynamic considerations, the concept of electrosorption valency cannot be reconciled with elementary laws of electrochemistry. On the basis of analysis of real processes occurring in the interfacial layer of electrodes it was urged to avoid the treatment of some double-layer phenomena in terms of electrosorption valency in order to eliminate far-reaching misinterpretations leading to serious contradictions.     

Efficiently accounting for ion correlations in electrokinetic nanofluidic devices using density functional theory

The electrokinetic behavior of nanofluidic devices is dominated by the electrical double layers at the device walls. Therefore, accurate, predictive models of double layers are essential for device design and optimization. In this paper, we demonstrate that density functional theory (DFT) of electrolytes is an accurate and computationally efficient method for computing finite ion size effects and the resulting ion-ion correlations that are neglected in classical double layer theories such as Poisson-Boltzmann. Because DFT is derived from liquid-theory thermodynamic principles, it is ideal for nanofluidic systems with small spatial dimensions, high surface charge densities, high ion concentrations, and/or large ions. Ion-ion correlations are expected to be important in these regimes, leading to nonlinear phenomena such as charge inversion, wherein more counterions adsorb at the wall than is necessary to neutralize its surface charge, leading to a second layer of co-ions. We show that DFT, unlike other theories that do not include ion-ion correlations, can predict charge inversion and other nonlinear phenomena that lead to qualitatively different current densities and ion velocities for both pressure-driven and electro-osmotic flows. We therefore propose that DFT can be a valuable modeling and design tool for nanofluidic devices as they become smaller and more highly charged.     

Kinetics of an Elementary Charge Transfer Act Involving Polyatomic Dipole Polarizable Species: A Spectroscopic Study

The possibilities of optical and radiowave spectral methods in investigating the kinetics of elementary acts of charge transfer and phototransfer in irregular condensed systems are studied. It is proposed to study the effect of the electrical double layer on the adsorption of dipole polarizable polyatomic species using the IR spectra of adsorbed species and theoretical quantum-mechanical calculations. An analytical equation is obtained for the extinction coefficient of outer-sphere electron phototransfer between species, which accounts for the interaction of intramolecular vibrations of reacting species with fluctuations of the environment polarization. A method based on the recording of nonlinear electromagnetic radiation and microcurrents of the electrochemical system is theoretically substantiated.     

On the theory of mixed electrochemical fluctuations

Mixed correlators of 2^nd order with respect to fluctuations of the electrode free charge, full charge, and potential are analyzed on the basis of classical theory of noise and fluctuations. It is shown that the mixed correlator of free and full charge fluctuations is determined by the electrochemical cell temperature and the electrical capacitance corresponding to the electrode free charge. At the same time, the mixed correlator of the electrode full charge and potential fluctuations equals the product of the Boltzmann constant and temperature. The former result corresponds to both the Gibbs fluctuation theory and the Einstein-Landau theory of the extensive quantities’ mixed correlators. The latter one corresponds to the Einstein-Landau theory for the paired mixed correlators of conjugated (extensive and intensive) quantities. The results obtained evidence that, unlike the 3rd order correlators, the ergodic hypothesis with respect to the 2^nd order correlators works well even in rather complicated electrochemical systems.     

Adsorption of proteins onto charged surfaces: A Monte Carlo approach with explicit ions

A computer model has been developed to simulate the adsorption of proteins onto charged surfaces displaying an electric double layer. Coadsorption of ions onto the surface is included by means of explicit ions. Only electrostatic interactions are considered. Monte Carlo simulations in the canonical ensemble of the enzyme cutinase and 15 variants (modeled from the X-ray tertiary structure of the wild-type) were performed. Adsorption free energies for all variants were calculated by the thermodynamic integration method. Distributions of the electric moment and the vector pointing toward the protein active site and parallel to its central β-sheet were determined to elucidate the mean orientation of the protein with respect to the surface as a function of its distance from the surface. It was found that the free energy of adsorption varied linearly with the total charge of the protein, while the electric moment (dipole moment) had a second-order but significant effect. Though an increase of the electric moment generally resulted in a slightly increased affinity of the protein for the surface, close to the surface the mean force acting on the protein clearly varied linearly with the strength of the electric moment, such that a clear correlation between the latter and the protein orientation with respect to the surface could be established. Wild-type cutinase displayed the highest affinity for the charged surface amongst all proteins having the same total charge, even though it did not have the largest electric moment. © 1996 by John Wiley & Sons, Inc.     

Calculation of parameters of an electrical double layer at the magnetite/solution interface from potentiometric titration data on magnetite suspension

A three-layer model of an electrical double layer at magnetite/aqueous 0.001–1 mol/L KCl solution interfaces has been considered in a pH range of 3.5–9.5. A procedure has been proposed for determining the constants of equilibrium reactions and the parameters of electrical double layers from the acid–base potentiometric titration data of magnetite suspensions in the solutions taking into account the generation of a surface charge. The determination of these constants and the parameters of the electrical double layer is based on the use of the point of zero charge. Software has been developed and used for calculating the main parameters of the electrical double layer within the framework of the three-layer model and the Graham–Parsons concepts.     

The determination of the free energy of an electrical double layer

A well-known charging process is used to obtain the free energy of an electrical double layer, in which the double layer is built up by a transfer of ions from one phase to another. The present study formulates proofs that this charging process cannot determine the free energy of an electrical double layer.     

Electrochemical processes on the copper electrode in water-ethanol solutions of copper sulfate

The system Cu/H₂O-C₂H₅OH-CuSO₄ was studied in a wide range of organic component concentrations by the impedance spectroscopy method. In the studied range of ethanol concentrations the diffusion of ions to an electrode is the limiting stage of the electrode process. An increase in the ethanol concentration results in a decrease in the double electrical layer capacity, which is caused by a change in the double electrical layer structure at the electrode-solution boundary.     

Effect of skimming layer in an electroosmotically driven viscoelastic fluid flow over charge modulated walls

We report a numerical study on the effect of the skimming layer in an EOF of Oldroyd-B fluid over charge modulated walls. Three types of flow conditions were identified on the basis of the relative thickness of the skimming layer and the electrical double layer. We observe maximum slip velocity magnitude when the skimming layer thickness is very less than the thickness of the electrical double layer. For higher skimming layer thickness compared to the thickness of electrical double layer, slip velocity magnitude attenuates, and the polymeric stress inside the skimming layer becomes zero. Enhanced fluid elasticity generates asymmetric flow structures inside the microchannel, which can also be achieved by imposing an asymmetric surface charge along the channel walls. Our present analysis highlights the complex flow dynamics of the EOF of biofluids/polymeric fluids with a near-wall region depleted of macro-molecules.     

Electrical probing of endothelial cell behaviour on a fibronectin/polystyrene/thiol/gold electrode by Faradaic electrochemical impedance spectroscopy (EIS)

The electrochemical impedance spectroscopy (EIS) technique has been shown to be an effective tool for monitoring endothelial cell behaviour on a multilayer functionalised gold electrode. Polystyrene, a reproducible model substrate, is deposited as a thin layer on a thiol functionalised gold electrode. Fibronectin, a protein promoting endothelial cell adhesion, is then adsorbed on the polystyrene surface. The different steps of this multilayer assembly are characterized by Faradaic impedance. The charge transfer resistance and the capacitance for the total layer are modified at each step according to the electrical properties of each layer. This gives the endothelial cells' electrical state in terms of its resistive and capacitive properties. In this study, the endothelial cell layer presents a specific charge transfer resistance equal to 1.55 kOmega cm(2) with no large defects in the cell layer, and a specific capacitance equal to few microF cm(-2) explained by the existence of pseudopods. These electrical properties are correlated to the endothelial cell viability, adhesion and cytoskeleton organization.     

A simple algorithm for calculating electrical double layer interactions in asymmetric electrolytes-Poisson-Boltzmann theory

A simple, general, and numerically robust algorithm is presented for calculating the disjoining pressure and interaction free energy per unit area between two identically charged flat plates due to electrical double layer interactions according to the nonlinear Poisson-Boltzmann theory. The result is applicable to electrolytes with any number of ionic species having any combination of valencies as well as to constant potential, constant charge, or charge regulation boundary conditions on the plates. The algorithm is very simple to implement on commonly available numerical software environments and is therefore particularly suitable for use in data analysis.     

The effect of partial charge transfer on the electrochemical turbulent noise

Theoretical analysis of the effect of electrode potential on the spectral density of random alternating current emerged in electrochemical cell under the action of turbulent pulsations of the electrolyte solution velocity is carried out. An impedance model of metal electrode dissolution reaction, including two adsorption stages, is suggested, with allowance for the oxidized ion diffusion in electrolyte solution. It is known that in terms of the Ershler-Randles model, at low frequencies the experimentally measured slope of bilogarithmic frequency dependence of spectral density equals 3, which is characteristic of the diffusion control; at high frequencies the slope equals 4, which is characteristic of the kinetic control. It is shown that for the model of impedance of the two-stage adsorption oxidation process, in the middle segment of the spectrum the local slope must decrease down to 2, provided the first oxidation stage, which proceeds within the inner electrical double layer, is slow; the local slope must increase up to 6 (or 5, for diffusion control), provided the second oxidation stage (the partially oxidized ion desorption to solution) is slow. The “height” and “width” of the slope local changes appeared explicitly depending on the parameters of the partial charge transfer. This makes the turbulent noise method somewhat superior to the impedance method in the studying of the above-specified reaction type.     

Electrical double layers at the oil/water interface

This review presents the historical development and current status of the theory of the electrical double layer at a liquid/liquid interface. It gives rigorous thermodynamic definitions of all basic concepts related to liquid interfaces and to the electrical double layer. The difference between the surface of a solid electrode and the interface of two immiscible electrolyte solutions (ITIES) is analyzed in connection to their electrical properties. The most important classical relationships for the electrical double layer are presented and critically discussed. The generalized adsorption isotherm is derived. After a short review of the classical Gouy-Chapman and Verwey-Niessen models, more recent developments of the double layer theory are presented. These include effects of variable dielectric permittivity, nonlocal electrostatics, hydration forces, the modified Poisson-Boltzmann equation and the ion-dipole plasma. The relative merits of different theories are estimated by comparing them with computer simulation of the ITIES and electrical double layer. Special attention is given to the structure of ITIES and its variation due to adsorption of ions and amphiphilic molecules.     

Thermodynamic and adsorption behavior of N<Subscript>2</Subscript>O<Subscript>4</Subscript> schiff base as a corrosion inhibitor for API-5L-X65 steel in HCl solution

The inhibition ability of N,N′-bis(2,4-dihydroxyacetophenone)-1,3-propandiimine (DHAPP) as a schiff base against the corrosion of API-5L-X65 in 1 M HCl solution was evaluated by polarization, electrochemical impedance spectroscopy, and scanning electron microscopy. Polarization studies indicated that DHAPP retards both the cathodic and anodic reactions through chemical adsorption and blocking the active corrosion sites. The adsorption of this compound obeyed the Langmuir adsorption isotherm. The inhibition efficiency increased with inhibitor concentration and decreased with increasing temperature. EIS data analysed to equivalent circuit model showed that as the inhibitor concentration increased the charge transfer resistance of steel increased whilst double layer capacitance decreased. Kinetic and thermodynamic parameters such as activation energy, enthalpy, entropy, and Gibbs free energy of activation and adsorption were calculated. Gibbs free energy indicated that adsorption occurred through physical and spontaneous process. Scanning electron microscopy was used to study the steel surface with and without inhibitor.