Compact electrical layer

The anodic oxidation of sheet aluminum has been used for a long time to protect aluminum against corrosion by a well-adhering oxide layer. Porous oxide layers are formed if acid electrolytes are used that can redissolve the aluminum oxide (mostly sulfuric or phosphoric acid). A compact oxide layer is formed at the beginning of the electrolysis (Fig. 20.3). Simultaneously, the current decreases, due to the electric resistance of the oxide. Subsequently follows a process in which the oxide is redissolved by the acid, and the current increases until it reaches a steady state. The electrochemical oxidation continues to take place with formation of pores. At the end of a pore, where it has the largest curvature, the electric field has its largest gradient and the process of redisolution is fastest. 

For semiconductor electrodes and also for the interface between two immiscible electrolyte solutions (ITIES), the greatest part of the potential difference between the two phases is represented by the potentials of the diffuse electric layers in the two phases (see Eq. 4.5.18). The rate of the charge transfer across the compact part of the double layer then depends very little on the overall potential difference. The potential dependence of the charge transfer rate is connected with the change in concentration of the transferred species at the boundary resulting from the potentials in the diffuse layers (Eq. 4.3.5), which, of course, depend on the overall potential difference between the two phases. In the case of simple ion transfer across ITIES, the process is very rapid being, in fact, a sort of diffusion accompanied with a resolvation in the recipient phase. 

The central issue which has to be addressed in any comprehensive study of electrode-surface phenomena is the determination of an unambiguous correlation between interfacial composition, interfacial structure, and interfacial reactivity. This principal concern is of course identical to the goal of fundamental studies in heterogeneous catalysis at gas-solid interfaces. However, electrochemical systems are far more complicated since a full treatment of the electrode-solution interface must incorporate not only the compact (inner) layer but also the boundary (outer) layer of the electrical double-layer. The effect of the outer layer on electrode reactions has been neglected in most surface electrochemical studies but in certain situations, such as in conducting polymers and... 

Figure 5-11 shows a simple model of the compact double layer on metal electrodes. The electrode interface adsorbs water molecules to form the first mono-molecular adsorption layer about 0.2 nm thick next, the second adsorption layer is formed consisting of water molecules and hydrated ions these two layers constitute a compact electric double layer about 0.3 to 0.5 nm thick. Since adsorbed water molecules in the compact layer are partially bound with the electrode interface, the permittivity of the compact layer becomes smaller than that of free water molecules in aqueous solution, being in the range from 5 to 6 compared with 80 of bulk water in the relative scale of dielectric constant. In general, water molecules are adsorbed as monomers on the surface of metals on which the affinity for adsorption of water is great (e.g. d-metals) whereas, water molecules are adsorbed as clusters in addition to monomers on the surface of metals on which the affinity for adsorption of water is relatively small (e.g. sp-metals). 

A simple parallel plate condenser model (Fig. 5-12) gives the electric capacity Ch of the compact double layer as shown in Eqn. 5-8 ... 

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. 

Similar types of electric double layer may also be formed at the phase boundary between a solid electrolyte and an aqueous electrolyte solution [7]. They are formed because one electrically-charged component of the solid electrolyte is more readily dissolved, for example the fluoride ion in solid LaFs, leading to excess charge in the solid phase, which, as a result of movement of the holes formed, diffuses into the soUd electrolyte. Another possible way a double layer may be formed is by adsorption of electrically-charged components from solution on the phase boundary, or by reactions of such components with some component of the solid electrolyte. For LaFa this could be the reaction of hydroxyl ions with the trivalent lanthanum ion. Characteristically, for the phase boundary between two immiscible electrolyte solutions, where neither solution contains an amphiphilic ion, the electric double layer consists of two diffuse electric double layers, with no compact double layer at the actual phase boundary, in contrast to the metal electrode/ electrolyte solution boundary [4,8, 35] (see fig. 2.1). Then, for the potential... 

Figure 12. Schematic diagram of the evolution of an anodic Ti02 nanotube array (a) Formation of a compact oxide layer, (b) Formation of pits due to the dissolution and breakdown of the barrier oxide film, (c) The barrier layer at the bottom of the pits is relatively thin and this leads to the enhanced electric field assisted dissolution of Ti02, which results in further pore growth, (d) Voids formed in the inter-pores region, (e) Fully developed nanotube array with a corresponding top view [51].

With this source compact electrically-conducting samples can be analyzed directly. They must be flat, and are then taken as the cathode and ablated by cathodic sputtering. The sputtered material is excited in the negative glow of the discharge, which is usually operated at a few mbar of argon. As the sample is ablated layer-by-layer both bulk and in-depth profiling analyses are possible. 

The electric field across electrochemical interfaces is of key importance to understanding electrochemical processes. The barrier heights for the charge transfer processes at such interfaces depend on the field, which in turn depends on the overall electronic properties of the interface. To understand the effect of the field on these barriers requires quantitative insight into the electronic structure of the interface. Theoretical treatments of the physics of electrochemical interfaces are needed. These must handle more effectively such questions as the role of electronic surface states and the interactions of the solvent and ions of the compact double layer with the metal orbitals, as well as the spillover of the conduction band electrons into the interface. The experimental techniques described in the previous section of this chapter will exert a significant influence on the development of such understanding, but this will require the combined efforts of theorists and experimentalists. 

In the case of metallic electrodes, any change in the electrode potential, E, always occurs at the interfacial potential, A4>H> between the metal and the solution. The amount of change in the electrode potential, then, is equal to that in the interfacial potential, which arises across what we call the Helmholtz layer or the electrical compact double layer. This is, however, not the case for nonmetallic solid electrodes such as ionic or covalent semiconductors, at which the interfacial potential usually remains constant irrespective of the electrode potential. 

In semiconductor electrodes, we have a space charge layer in addition to an electrical compact double layer (Helmholz layer) at the electrode interface. The electrode potential, then, is the sum of the space charge potential, Ac[>sc, and the interfacial potential, AH ... 

Transfer of charge carriers from the metal to the electrolyte solution as well as movement of ions in the electrol3de are hampered by the corrosive system. The electrolyte solution induces the formation of a surface layer in the vicinity of the metal electrode surface consisting of spatially separated positive and negative charge carriers, which is called a double electric layer. Spatial separation of charges is always accompanied by a potential difference, therefore the double layer exerts a perceptible influence on the rate of electrode processes. The double layer consists of two parts a compact layer and a diffusive layer (Fig. f.2). 

Clay particles can be thought of as microelectrodes possessing a compact Stern layer and a diffuse layer, which mediates faradic reactions, as depicted in Figure 2.10. As the donated (or accepted) electrons pass across the electrical double layer into and out of the bulk fluid, available species are converted into others via oxidation-reduction reactions (Grahame, 1951,1952). This effect may become significant... 

Atomic Polarization Fields Ionic Fields Electric Dipole Fields The Helmholtz Planes Diffuse Double Layer Compact Double Layer Potential Transients Constant Current Constant Potential Faradaic Processes Non-Faradaic Ideal Polarizable... 

When a metal electrode is placed in an electrolyte solution, an equilibrium difference usually becomes established between the metal and solution. Equilibrium is reached when the electrons left in the metal contribute to the formation of a layer of ions whose charge is equal and opposite to that of the cations in solution at the interface. The positive charges of cations in the solution and the negative charges of electrons in the metal electrode form the electrical double layer [4]. The solution side of the double layer is made up of several layers as shown in Fig. 2.7. The inner layer, which is closest to the electrode, consists of solvent and other ions, which are called specifically adsorbed ions. This inner layer is called the compact Helmholtz layer, and the locus of the electrical centers of this inner layer is called the inner Helmholtz plane, which is at a distance of di from the metal electrode surface. The solvated ion can approach the electrode only to a distance d2. The locus of the centers of the nearest solvated ion is called the outer Helmholtz plane. The interaction of the solvated ion with metal electrode only involves electrostatic force and is independent of the chemical properties of the ions. These ions are called non-specifically adsorbed ions. These ions are distributed in the 3D region called diffusion layer whose thickness depends on the ionic concentration in the electrolyte. The structure of the double layer affects the rate of electrode reactions. 

The film grown on an electrode surface has a duplex structure with a thin, compact first layer that is directly on the electrode surface and a porous second layer contacting the electrolyte. An equivalent circuit can be used to represent the electrical properties of this film. The components of an equivalent circuit can be determined by impedance spectroscopy. Therefore, this method has become one of the key methods for the characterization of conducting polymers. 

The applicability of continuum theories, such as the Poisson-Boltzmann model, in nanoscale is the most concerned issue in this field yet. Numerous conflicting results were reported in literature. We have done careful MD simulations of EOF and compared the ion distributions with the PB predictions rigorously to clarify the applicability of the continuum theory. To compare the descriptions from two different scales, above all, the observers have to be stand on the same base to avoid definition gaps. First, when presenting the MD results, the bin size should not be smaller than the solvent molecular diameter in comparison with the continuum theory otherwise, the MD results are not the macroscopic properties at the same level of the continuum. A second gap which departs the MD results from the PB predictions is the effect of the Stem layer. As well known, the PB equation describes only the ion distribution in diffusion (outer) layer of the electric double layer (EDL) [1]. In the continuum theory, the compact (iimer) layer of EDL is too thin (molecular scale) to be considered, and therefore, the PB equation almost governs the ion distribution in the whole domain. However, in nanofluidics the iimer layer which is also termed as Stem layer is comparable to the channel in size. The PB equation is not able to govern the ion behavior in the Stem layer in theory. Therefore, if one compares the MD... 

Another possibility is to develop a direct gas turbine system at high temperature and pressure to increase the efficiency. Since helium has small cross section for neutron capture and is also chemically inactive, no induced radioactivity and no corrosion products can be expected in the coolant. Furthermore, the oxidative microparticle fuel coated with layers such as pyrolytic carbon or silicon carbide is expected to prevent the release of the fission gas into the coolant. Eventually the HTGR is suited to adopt the direct cycle, i.e., the gas turbine cycle, which allows building a more compact electric-power facility than the indirect cycle with a steam turbine system. While the thermal efficiency of electricity generation by steam turbine is about 40%, the gas turbine cycle can increase the efficiency up to ca. 50%. 

When we have a charged surface in the absence of thermal motion, the charge would be neutralized by adsorption of an equal and opposite number of charged ions (counter ions or gegen ions). In fact, thermal motion prevents formation of such a compact double layer and in practice there is a distribution of counter ions (a screening effect) and a distribution of counter ions in the vicinity of the surface, such that the electrical potential gradually falls to zero at... 

If the product layer is nearly free of pores, then the anodic dissolution of metal will practically cease. The metal is then said to be passivated . The thickness of the compact product layer will reach a stationary value. For oxide products which are essentially electronic conductors, this stationary thickness will be determined by the very low ionic conductivity in the oxide on the one hand, and by the rate of dissolution of the oxide in the electrolyte on the other. However, in many cases the oxide layers are porous, so that the electrolyte can continue to attack the metal, independently of the transport of ions and electrons in the oxide. From the above discussion it can be seen that corrosion reactions in aqueous ionic solutions in which a solid product layer is formed on a metal are among the most complicated of all heterogeneous solid state reactions. The reasons for this are the electrochemical nature of these reactions, the great number of possible elementary steps which can occur at the various phase boundaries, and electrical space charge phenomena which occur in the reaction product. 

Figure 4.12 The electrical double layer consists of a compact Stern layer and a more diffuse Gouy-Chapman layer.

In general, the Helmholtz layer can be treated as a linear capacitor. In a theoretical model of the electric double-layer, the compact Helmholtz layer is generally treated as an ideal capacitor with a fixed thickness (d), and its capacitance is considered unchanging with the potential drop across it. Therefore, fhe capacifance of fhe Helmholtz layer can be treated as a constant if fhe femperafure, fhe dielectric constant of the electrolyte solution inside the compact layer, and its thickness are fixed. However, if the specific ion adsorpfion happened on the electrode surface, the dielectric constant of the electrolyte solution inside the compact layer may be affected, leading to non-linear behavior of the Helmholtz layer. This will be discussed more in a later section. 

Extending out into solution from the electrical double layer (or the compact double layer, as it is sometimes known) is a continuous repetition of the layering effect, but with diminishing magnitude. This extension of the compact double layer toward the bulk solution is known as the Gouy-Chapman diffuse double layer. Its effect on electrode kinetics and the concentration of electroactive species at the electrode surface is manifest when supporting electrolyte concentrations are low or zero. 

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