Perfectly polarizable electrodes

Indeed, a small current does flow, though not across the interphase. It is called a charging current, i.e., a current observed because there is an electron flow either out of the electrode or into it. But this latter current does not result in any electrons crossing the interphase it s like charging the plates of a condenser. A perfectly polarizable electrode is the analogue of an absolutely leakproof condenser. 

In the mechanisms to be described in this section, one of the idealizations of electrochemistry is being portrayed. Thus, in perfectly polarizable metal electrodes, it is accepted that no charge passes when the potential is changed. However, in reality, a small current does pass across a perfectly polarizable electrode/solution interphase. In the same way, here the statement free from surface states (which has been assumed in the account given above) means in reality that the concentration of surface states in certain semiconductors is relatively small, say, less than 10 states cm. So when one refers to the low surface state case, as here, one means that the surface of the semiconductor, particularly in respect to sites energetically in the energy gap, is covered with less than the stated number per unit area. A surface absolutely free of electronic states in the surface is an idealization. (If 1012 sounds like a large number, it is in fact only about one surface site in a thousand.) A consequence of this is the location of the potential difference at the interphase of a semiconductor with a solution. As shown in Fig. 10.1(a), the potential difference is inside the semiconductor, and outside in the solution there is almost no potential difference at all. 

Perfectly polarizable electrodes pass a current between the electrode and the electrolytic solution by changing the charge distribution within the solution near the electrode. Thus, no actual current crosses the electrode-electrolyte interface. Nonpolarized electrodes, however, allow the current to pass freely across the electrode-electrolyte interface without changing the charge distribution in the electrolytic solution adjacent to the electrode. Although these types of electrodes can be described theoretically, neither can be realized in practice. It is possible, however, to come up with electrode structures that approximate their characteristics. 

Despite of this charge transfer many of these systems may be treated as ideally polarizable electrodes, if the adsorbed species are not transformed into a different component present inside the bulk phase. The latter condition is violated, for example, in the hydrogen adsorption at metals of the platinum group in which the adsorbed hydrogen atoms can be in equilibrium with protons in solution and hydrogen molecules in gas phase or hydrogen dissolved inside the metal. The latter system corresponds to perfectly polarizable electrodes, see Ref. [13] for further discussion. 

In the text that follows, we start with the adsorption phenomena on ideally polarizable electrodes, and then pass to perfectly polarizable electrodes. 

Consideration of perfectly polarizable electrodes presented in the preceding text is related to equilibrium conditions E = const). When dealing with nonpotentio-static modes (linear, stepwise, sinusoidal, etc.), one always observes not only doublelayer capacity but also pseudocapacity induced by the changes of surface coverage with time in the course of reactions (52, 53). Conway, Gileadi and coworkers intensively studied this problem Refs. [85, 86]. 

Surface thermodynamics of perfectly polarizable electrodes forms a basis for various amphyfunctional approaches being of interest for electrochemistry of oxides " and functionally modified electrodes. " Beyond platinum metals electrochemistry, this approach is also important for gold, silver and copper when OH adsorption with charge transfer takes place at these surfaces. 

The links between our knowledge about ideally and perfectly polarizable electrodes should be thoroughly maintained as water and ions adsorption are common phenomena for these types of systems. For ideally plarizable mercury-like) electrodes, pzc (pzfc) data are available for much higher number of metals, and the roles of electron woik function and water adsorption are more apparenL ... 

In 1965, after Frumkin had been transferred to hospital after a heart attack, he started to think about some unsolved problems posed in his early studies back in the 1930s. As a result, he revisited the thermodynamic theory of the perfectly polarizable electrode, and its experimental checkup then appeared [31, 32]. These studies were carried out by O. A. Petrii and coworkers at the Department of Electrochemistry MSU. This not only resulted in the development of some new experimental techniques (e.g., potentiometric titrations under isoelectric conditions) but also led... 

Surface studies are difficult in the case of many metal electrodes since their regions of ideal or perfect polarizability are very narrow that is, the potentials of anodic dissolution (or oxidation) of the metal and of cathodic hydrogen evolution are close... 

Electrochemical window — In electrochemical experiments the range of potentials that is accessible without appreciable current flow, i.e., the potential range in which the electrode may be considered perfectly polarizable . Electrochemical windows depend on the - electrode material, the - solvent, and the - electrolyte. There is no strict definition for the current density defining the potential limits of the electrochemical window. That depends on the experiment, i.e., the signals to be measured. For highly sensitive measurements of very low current densities, the acceptable current densities at the potential limits are much smaller than in cases where high current density signals are measured. The electrochemical window also depends very much on impurities, e.g., traces of water in nonaqueous solvents, or traces of transition metal ions in aqueous electrolyte solutions. The... 

The interfacial capacitance may also be measured at solid polarizable electrodes in an impedance experiment using phase-sensitive detection. Most experiments are carried out with single crystal electrodes at which the structure of the solid electrode remains constant from experiment to experiment. Nevertheless, capacity experiments with solid electrodes suffer from the problem of frequency dispersion. This means that the experimentally observed interfacial capacity depends to some extent on the frequency used in the a.c. impedance experiment. This observation is attributed to the fact that even a single crystal electrode is not smooth on the atomic scale but has on its surface atomic level steps and other imperfections. Using the theory of fractals, one can rationalize the frequency dependence of the interfacial properties [9]. The capacitance that one would observe at a perfect single crystal without imperfections is that obtained at infinite frequency. Details regarding the analysis of impedance data obtained at solid electrodes are given in [10]. 

The knowledge of the work function of the electrode metal is essential to obtain VNHE(vac. scale) by using Eq. (20). Physical quantities are best known for the perfectly polarizable Hg electrode and it is possible to write for the potential of zero charge of this metal... 

The silver-silver chloride electrode has characteristics similar to a perfectly nonpolarizable electrode and is practical for use in many biomedical applications. The electrode (Figure 4.1a) consists of a silver base structure that is coated with a layer of the ionic compound silver chloride. Some of the silver chloride when exposed to light is reduced to metallic silver hence, a typical silver-silver chloride electrode has finely divided metallic silver within a matrix of silver chloride on its surface. Because silver chloride is relatively insoluble in aqueous solutions, this surface remains stable. Moreover, because there is minimal polarization associated with this electrode, motion artifact is reduced compared to polarizable electrodes such as the platinum electrode. Furthermore, owing to the reduction in polarization, there is also a smaller effect of frequency on electrode impedance, especially at low frequencies. 

As was mentioned in the preceding text, the main difference between perfectly polarizable and ideally polarizable electrodes consists in the fact that the potential of the former is determined by the presence of a certain redox system. 

It is conceivable that direct-current measurement, which is a perfectly valid method for solid electrolytes associated with non-polarizable electrodes, would only allow us to access qualitative information if the electrode is ideally or partially polarizable. 

The simplest interpretation of the compact-layer capacitance is represented by the Helmholtz model of the slab filled with a dielectric continuum and located between a perfect conductor (metal surface) and the outer Helmholtz plane considered as the distance of the closest approach of surface-inactive ions. Experimental determination of its thickness, zh, may be based on Eq. (12). Moreover, its dielectric permittivity, h, is often considered as a constant across the whole compact layer. Then its value can be estimated from the values of the compact-layer capacitance, for example, it gives about 6 or 10 (depending on the choice of zh) for mercury-water interface, that is, a value that is much lower than the one in the bulk water, 80. This diminution was interpreted as a consequence of the dielectric saturation of the solvent in contact with the metal surface, its modified molecular structure or the effects of spatial inhomogeneity. The effective dielectric permittivity of the compact layer shows a complicated dependence on the electrode charge, which cannot be explained by the simple hypothesis of the saturation effects on one hand or by the unperturbed bulk-solvent nonlocal polarizability on the other hand. 

---