Compact layer at the interface

We consider dehydration-adsorption of hydrated protons (cathodic proton transfer) and desorption-hydration of adsorbed protons (anodic proton transfer) on the interface of semiconductor electrodes. Since these adsorption and desorption of protons are ion transfer processes across the compact layer at the interface of semiconductor electrodes, the adsorption-desorption equilibrium is expressed as a function of the potential of the compact layer in the same way as Eqns. 9-60 and 9-61. In contrast to metal electrodes where changes with the electrode potential, semiconductor electrodes in the state of band edge level pinning maintain the potential d(hi of the compact layer constant and independent of the electrode potential. The concentration of adsorbed protons, Ch , is then determined not by the electrode potential but by the concentration of h3 ated protons in aqueous solutions. 

The subsequent three chapters are devoted to the electric double-layer structure at the interface between immiscible electrolytes examined by the electrocapillary curves method (Prof. Senda and coauthors) and by measurement of the electric double-layer capacity (Dr. Samec and Dr. Mare ek) as well as to the investigation of the Galvani and Volta potentials in the above-mentioned systems (Prof. Koczorowski). These chapters will be of interest to many electrochemists since the results obtained here are comparable with the thoroughly studied metal/electrolyte solution interface. An insignificant potential shift in the compact layer at the interface between immiscible electrolytes in the absence of specific ion adsorption - this is the main conclusion arrived at by the authors of Chaps. 4 and 5. Chapter 6 deals with the scale of potentials in a system of immiscible electrolytes and the thermodynamic relation between the distribution coefficients and the Volta potentials. 

The electrode potential at which the electron energy band is flat in semiconductor electrodes is caUed the flat band potential, . The flat band potential is used as a characteristic potential of individual semiconductor electrodes in the same way as the potential of zero charge is used for metal electrodes. At the flat band potential the space charge, Ogc, is zero but the interfacial charge, + oh + o, is not zero. The electrode interface is composed of only the compact layer at the flat band potential if no diffuse layer exists on the solution side. 

In the active state, the dissolution of metals proceeds through the anodic transfer of metal ions across the compact electric double layer at the interface between the bare metal and the aqueous solution. In the passive state, the formation of a thin passive oxide film causes the interfadal structure to change from a simple metal/solution interface to a three-phase structure composed of the metal/fUm interface, a thin film layer, and the film/solution interface [Sato, 1976, 1990]. The rate of metal dissolution in the passive state, then, is controlled by the transfer rate of metal ions across the film/solution interface (the dissolution rate of a passive semiconductor oxide film) this rate is a function of the potential across the film/solution interface. Since the potential across the film/solution interface is constant in the stationary state of the passive oxide film (in the state of band edge level pinning), the rate of the film dissolution is independent of the electrode potential in the range of potential of the passive state. In the transpassive state, however, the potential across the film/solution interface becomes dependent on the electrode potential (in the state of Fermi level pinning), and the dissolution of the thin transpassive film depends on the electrode potential as described in Sec. 11.4.2. 

An oxide surface in water is covered with a layer of highly structured, chemisorbed water molecules (34, 35). When exposed to an electric field caused by charging of the surface, these water molecules approach dielectric saturation. As a consequence, the dielectric strength (e) of the solvent within the compact layer of the interface is lowered. The dependency of log K (stability constant) at constant temperature varies linearly with the reciprocal of the dielectric constant (e) of the media (36, 37), resulting in a displacement of the equilibrium towards the adduct in association reactions (32). As e decreases, the stability of complexes... 

These deviations were first explained by the presence of a compact, ion-free layer at the interface this is known as the modified Verwey-Niessen model. Obviously, the presence of an ion-free layer can only reduce the capacity, so the theory had to be modified further. For a few systems a consistent interpretation of the experimental capacity was achieved [78-80] by combining this model with the soolled modified Poisson-Boltzmann (MPB) theory [81], which attempts to correct the GC theory by accounting for the finite size of the ions and for image effects, while the solvent is still treated as a dielectric continuum. The combined model has an adjustable parameter, so it is difficult to judge whether the agreement with experimental data is significant. The existence... 

Fanelli N, Zalis S, Pospisil C (1989) The growth of compact layers at the electrode interface. Part III. Monte Carlo simulations of the formation of fractal stmctuies by diflusion-fimited aggregation. J Electroanal Chem 262 35 4... 

At present it is impossible to formulate an exact theory of the structure of the electrical double layer, even in the simple case where no specific adsorption occurs. This is partly because of the lack of experimental data (e.g. on the permittivity in electric fields of up to 109 V m"1) and partly because even the largest computers are incapable of carrying out such a task. The analysis of a system where an electrically charged metal in which the positions of the ions in the lattice are known (the situation is more complicated with liquid metals) is in contact with an electrolyte solution should include the effect of the electrical field on the permittivity of the solvent, its structure and electrolyte ion concentrations in the vicinity of the interface, and, at the same time, the effect of varying ion concentrations on the structure and the permittivity of the solvent. Because of the unsolved difficulties in the solution of this problem, simplifying models must be employed the electrical double layer is divided into three regions that interact only electrostatically, i.e. the electrode itself, the compact layer and the diffuse layer. 

The picture of the compact double layer is further complicated by the fact that the assumption that the electrons in the metal are present in a constant concentration which discontinuously decreases to zero at the interface in the direction towards the solution is too gross a simplification. Indeed, Kornyshev, Schmickler, and Vorotyntsev have pointed out that it is necessary to assume that the electron distribution in the metal and its surroundings can be represented by what is called a jellium the positive metal ions represent a fixed layer of positive charges, while the electron plasma spills over the interface into the compact layer, giving rise to a surface dipole. This surface dipole, together with the dipoles of the solvent molecules, produces the total capacity value of the compact double layer. 

Specific adsorption occurs, i.e. ions enter the compact layer, in a considerable majority of cases. The most obvious result of specific adsorption is a decrease and shift in the maximum of the electrocapillary curve to negative values because of adsorption of anions (see Fig. 4.2) and to positive values for the adsorption of cations. A layer of ions is formed at the interface only when specific adsorption occurs. 

The formation of a membrane potential is connected with the presence of an electrical double layer at the surface of the membrane. For a thick, compact membrane, an electrical double layer is formed at both interfaces. The electrical double layer at a porous membrane is formed primarily in the membrane pores (see Section 6.2). The electrical double layer at thin membranes is formed on both membrane surfaces. It is formed by fixed ions on the surface of the membrane and the diffuse layer in the electrolyte. 

An adsorbed layer of water molecules at the interface separates hydrated ions from the solid surface. The interfacial electric double layer can be represented by a condenser model comprising three distinct layers a diffuse charge layer in the ionic solution, a compact layer of adsorbed water molecules, and a diffuse charge layer in the solid as shown in Fig. 5-8. The interfacial excess charge on the... 

Usually, there is an electrostatic potential of the order of 1 V across the electric double layer at tbe interface between a metal and an aqueous solution this potential produces an intense electric field of the order of 10 V cm in the compact layer 0.3 to 0.5 mn thick. Such an intense electric field can not be realized in any dielectrics of macroscopic size, because of dieleelectron avalanche, but the intense electric field can be sustained in a layer of several atomic thidmess where no electron avalanche can occur. 

In the state of Fermi level pinning, the Fermi level at the interface is at the surface state level both where the level density is high and where the electron level is in the state of degeneracy similar to an allowed band level for electrons in metals. The Fermi level pinning is thus regarded as quasi-metallization of the interface of semiconductor electrodes, making semiconductor electrodes behave like metal electrodes at which all the change of electrode potential occurs in the compact layer. 

When the total overvoltage ti is distributed not only in the space charge layer t)8c but also in the compact layer tih, the Tafel constants of a and a each becomes greater than zero and the Tafel constants of a and each becomes less than one. In such cases, Kiv) and ip(T ) do not remain constant but increase with increasing overvoltage. Further, if Fermi level pinning is established at the interface of semiconductor electrodes, the Tafel constant becomes dose to 0.5 for... 

As shown in Fig. 9-9, the interfacial double layer of semiconductor electrode consists of a space charge layer with the potential of in the semiconductor and a compact layer with the potential of at the electrode interface. The potential 4+sc across the space charge layer controls the process of ionization of smface atoms (Eqn. 9-24) whereas, the potential across the compact layer controls the process of transfer of surface ions (Eqn. 9-33). The overvoltage iiac across the space charge layer and the overvoltage t b across the compact layer are eiq)ressed, respectively, in Eqn. 9-34 ... 

The process in which a hydrated ion is dehydrated to form an adsorbed ion on an electrode interface, and its reverse process, are ion transfer processes across the compact layer on the electrode interface. As an example, we consider proton adsorption (cathodic proton transfer) and proton desorption (anodic proton transfer) at metallic electrodes represented by Eqn. 9-59 ... 

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