Double-layer structure, theories

In the region of a very good correspondence has been found between experimental and calculated C,E curves and this has been taken to indicate that the electrical double-layer structure conforms to the GCSG theory. Comparison of the ChE curves for Hg/TMU and Fe/TMU shows that the dependence of Cf on E is less pronounced for an Fe electrode than for Hg/TMU, and the values of Cf for Fe are remarkably lower than for Hg. The same is the case for Fe/DMF, DMAA, MPF, and HMPA interfaces.732-736... 

Double layer emersion continues to allow new ways of studying the electrochemical interphase. In some cases at least, the outer potential of the emersed electrode is nearly equal to the inner potential of the electrolyte. There is an intimate relation between the work function of emersed electrodes and absolute half-cell potentials. Emersion into UHV offers special insight into the emersion process and into double layer structure, partly because absolute work functions can be determined and are found to track the emersion potential with at most a constant shift. The data clearly call for answers to questions involving the most basic aspects of double layer theory, such as the role water plays in the structure and the change in of the electrode surface as the electrode goes frcm vacuum or air to solution. 

The presence of the diffuse layer determines the shape of the capacitance-potential curves. For a majority of systems, models describing the double-layer structure are oversimplified because of taking into account only the charge of ions and neglecting their specific nature. Recently, these problems have been analyzed using new theories such as the modified Poisson-Boltzmann equation, later developed by Lamper-ski. The double-layer capacitanties calculated from these equations are... 

Studies in nonaqueous dipolar aprotic solvents allowed the elucidation of the complicated role of the solvent nature in determining the - double layer structure and kinetics of electrochemical reactions. Special attention was paid to the phenomenon of ion - solvation and its effect on -> standard electrode potentials. Experimental studies of the various electrochemical systems in nonaqueous media greatly contributed to the advancement of the theory of elemental electron-transfer reactions across charged interfaces via the so-called energy of solvent reorganization. 

At the interface between O and W, the presence of the electrical double layers on both sides of the interface also causes the variation of y with Aq<. In the absence of the specific adsorption of ions at the interface, the Gouy-Chapman theory satisfactorily describes the double-layer structure at the interface between two immiscible electrolyte soultions [20,21]. For the diffuse part of the double layer for a z z electrolyte of concentration c in the phase W whose permittivity is e, the Gouy-Chapman theory [22,23] gives an expression... 

Various theories have been proposed to describe and interpret the adsorption of metal ions at hydrous oxide interfaces (10). Most models have stressed either the double layer structure and ion-solvent interactions (11, 12, 13) or surface coordination reactions with amphoteric functional groups (14, 15, 16). Recently Davis (17) and Davis and Leckie (18, 19)... 

Fig. 3. Schematic representation of the double layer structure at the nitrobenzene-water interface at 25 C. The full curve illustrates the potential distribution at Aq 0 = 0.2 V for the interface between a 0.1 M solution of Pn4NPh4B in nitrobenzene and a 0.05 M aqueous solution of LiCl at 25 °C. The thickness of the inner layer is assumed to be 1 nm and the potential distribution is calculated using the Gouy-Chapman theory. (Reprinted from [61]. Copyright Elsevier Seience Publishers, Amsterdam).

A commonly used model for describing counterion distribution at a charged surface is based on the Gouy-Chapman diffuse double-layer (DDL) theory. This model assumes that the surface can be visualized as a structurally featureless plane with evenly distributed charge, while the counterions are considered point charges in a uniform liquid continuum. In this simplified picture, the equilibrium distribution of counterions is described by the Boltzmann equation ... 

This operation determines the values of R and C that, in series, behave as the cell does at the measurement frequency. The impedance is measured as a function of the frequency of the ac source. The technique where the cell or electrode impedance is plotted V5. frequency is called electrochemical impedance spectroscopy (EIS). In modem practice, the impedance is usually measured with lock-in amplifiers or frequency-response analyzers, which are faster and more convenient than impedance bridges. Such approaches are introduced in Section 10.8. The job of theory is to interpret the equivalent resistance and capacitance values in terms of interfacial phenomena. The mean potential of the working electrode (the dc potential ) is simply the equilibrium potential determined by the ratio of oxidized and reduced forms of the couple. Measurements can be made at other potentials by preparing additional solutions with different concentration ratios. The faradaic impedance method, including EIS, is capable of high precision and is frequently used for the evaluation of heterogeneous charge-transfer parameters and for studies of double-layer structure. 

The reason for this state of affairs may be seen in past emphasis on surface phenomenological studies which attempted to model the metal surface as an array of surface atoms with some valences saturated by subsurface metal atoms and other valences saturated by ions or molecules making up the environment. This model led to the description of the interface in terms of the Helmholz and Guy-Chapman double layer theories, and inhibitors were visualized as interfering with the double layer structure through adsorption on the surface atoms of the metal, thereby altering the electrochemical reaction rates which are governed by the energetics of the double layer. While this model has been... 

While the electric double layer on a solid surface is relatively well understood and theories are able to account for colloidal stability and coagulation kinetics quite well, there has been much less success in understanding the double-layer structure at liquid-liquid or liquid-gas interfaces. This is despite the fact that the stability of emulsions or dispersion of particles and... 

To date, many excellent reviews regarding electrode materials have been published [11-37], However, there have been rather limited publications focusing on electrolytes for ESs [9,10,12,38-40], and most of them focused on polymer electrolytes for ESs [9,10,38,39]. In the light of the latest achievements in the field of ES electrolytes, the aim of this book is to provide an insight into the development of electrolytes for ESs. This chapter will discuss the fundamental concepts of ESs, including basic structure of different types of ESs, the development of electrical double-layer (EDL) theory, EDL formation in the geometrically confined pore, and performance metrics of various ESs and their relationship with electrolytes. 

Kjellander R, Mitchell DJ (1997) Dressed ion theory for electric double layer structure and interactions an exact analysis. Mol Phys 91 173-188... 

The use of molecular dynamics to study the electric double-layer structure started a little over a decade ago, with the hope of determining more accurate structures because the classical description of an electric double layer based on the Poisson-Boltzmann equation is accurate only for low surface potential and dilute electrolytes. The Poisson-Boltzmann equation only considers the electrostatic interactions between the charged surface and ions in the solution, but not the ion-ion interactions in the solution and the finite molecule size, which can be taken into account in molecular dynamics simulations. It was shown [6, 7] that the ion distribution in the near-wall region could be significantly different from the prediction of classical theory. Typical molecular dynamics simulation results of counterion and co-ion concentrations in a nanochannel are shown in Fig. 2a. The ion distribution obtained... 

At first, however, it seemed that the slow discharge theory was irreconcilably at variance with experimental data since in solutions of pure acids the hydrogen overpotential was found to be independent of the acid concentration. This inconsistency was solved in Frumkin s classical work in which he took into consideration the effects of the double-layer structure on the discharge rate. The numerous studies by Frumkin and his coworkers, as well as the work of other electrochemists, that followed, have provided experimental proof of the limited rate of electrode reactions involving transfer of a charge across the metal-solution interface. 

In the absence of specifically adsorbable ions, the double-layer structure is adequately described in terms of the Gouy-Chapman-Stern theory. The outer Helmholtz plane potential (distinguished by Grahame) is associated with a surface charge density a through the relation... 

Because of the heterogeneous nature of electrode reactions, the rate of charge transfer across the electrochemical interface depends not only on the potential but also on the double layer structure and the adsorption of reactants, intermediates and products, and other eventual solution phase species. Mass-transport limitations are not considered here. The expression relating current to the electrode potential can be obtained from the absolute rate theory applied to the electrochemical interface. For that electrochemical reaction case, the heights of the free energy barriers are functions of the potentials drop across the interface in accordance with the absolute rate theory. 

Oil/water interfaces are classified into the ideal-polarized interface and the nonpolarized interface. The interface between a nitrobenzene solution of tetrabutylam-monium tetraphenylborate and an aqueous solution of lithium chloride behaves as an ideal-polarized interface in a certain potential range. Electrocapillary curves of the interface were measured. The results are analyzed using the electrocapillary equation of the ideal-polarized interface and the Gouy-Chapman theory of diffuse double layers. The electric double layer structure consisting of the inner layer and the two diffuse double layers on each side of the interface is discussed. Electrocapillary curves of the nonpolarized oil/water interface are discussed for two cases of a nonpolarized nitrobenzene/water interface. 

Islam, M. M. Alam, M. T. Okajima, T. Oshaka, T. (2009). Electrical double layer structure in ionic liquids an understanding of the xmusual capacitance-potential curve at a nonmetallic electrode. /. Phys. Chem. C, Vol. 113,3386-3389 Johnson, M. Nordholm, S. (1981). Generalized van der Waals theory. VI. Application to adsorption. /. Chem. Phys., Vbl. 75,1953-1957... 

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