Stationary electrode potentials

It is possible to attain the theoretical potentials of the reaction (1) only at the special conditions of the electrodes, and provided the deep purification of electrolytes. Stationary electrode potentials are usually lower than the theoretical potentials by 100-500 mV. The reason for that effect is occurance of parallel and side reactions in the cell. 

The spatial variation of the stationary electrode potential, r](x), is small, as long asLp > 2Z. Therefore, the validity criterion of Eq. (103) is... 

If the redox state of the fuel salt is characterized by an uranium ratio [U(IV)]/[U(III)] < 1, the alloy specimens get a more negative stationary electrode potential than equilibrium electrode potentials of some uranium intermetaUic compounds and alloys with nickel and molybdenum. This leads to a spontaneous behavior of alloy formation processes on the specimen siur-face and further diffusion of uranium deep into the metaUic phase. As a consequence, films of intermetaUic compounds and alloys of nickel, molybdenum, and tungsten with uranium are formed on the aUoy specimen surfaces, and IGC does not take place. 

Sereen-plate. separators. These include a metal slide at ground potential that is extended with a conducting screen of suitable screenopening size to allow easy passage of the largest grains being treated, A stationary electrode is placed above the slide and screen sections as... 

It is interesting to note that independent, direct calculations of the PMC transients by Ramakrishna and Rangarajan (the time-dependent generation term considered in the transport equation and solved by Laplace transformation) have yielded an analogous inverse root dependence of the PMC transient lifetime on the electrode potential.37 This shows that our simple derivation from stationary equations is sufficiently reliable. It is interesting that these authors do not discuss a lifetime maximum for their formula, such as that observed near the onset of photocurrents (Fig. 22). Their complicated formula may still contain this information for certain parameter constellations, but it is applicable only for moderate flash intensities. 

This relation shows that the lifetime of PMC transients indeed follows the potential dependence of the stationary PMC signal as found in the experiment shown in Fig. 22. However, the lifetime decreases with increasingly positive electrode potential. This decrease with increasing positive potentials may be understood intuitively the higher the minority carrier extraction (via the photocurrent), the shorter the effective lifetime... 

Equation (40) relates the lifetime of potential-dependent PMC transients to stationary PMC signals and thus interfacial rate constants [compare (18)]. In order to verify such a correlation and see whether the interfacial recombination rates can be controlled in the accumulation region via the applied electrode potentials, experiments with silicon/polymer junctions were performed.38 The selected polymer, poly(epichlorhydrine-co-ethylenoxide-co-allyl-glycylether, or technically (Hydrine-T), to which lithium perchlorate or potassium iodide were added as salt, should not chemically interact with silicon, but can provide a solid electrolyte contact able to polarize the silicon/electrode interface. 

Heterogeneous chemical reactions in which adsorbed species participate are not pure chemical reactions, as the surface concentrations of these substances depend on the electrode potential (see Section 4.3.3), and thus the reaction rates are also functions of the potential. Formulation of the relationship between the current density in the stationary state and the concentrations of the adsorbing species in solution is very simple for a linear adsorption isotherm. Assume that the adsorbed substance B undergoes an... 

Most results of in situ IR studies on Pt in acidic methanol solutions so far have been obtained using a relatively fast (8.5-13.6) Hz) modulation of electrode potential. As already pointed out by Bockris [27], collection of spectral data alternatively at two potentials is not appropriate for processes which are not reversible to follow the change of potential. In this study the SPAIRS version of SNIFTIRS was performed by stepping the potential from a reference potential in the anodic direction, allowing sufficient time at each potential to reach stationary conditions. 

If a stationary electrode is used, such as platinum, gold, or glassy carbon, the technique is called voltammetry. One useful voltammetric technique is called stripping voltammetry, in which the product of a reduction is deposited on the surface on purpose and then stripped off by an oxidizing potential— a potential at which the oxidation of the previously deposited material occurs. This technique can also use a mercury electrode, but one that is held stationary. 

Polarography is the measurement of the current flowing at a dropping mercury electrode as the potential applied to this electrode is changed. Voltammetry is the measurement of the current flowing at a stationary electrode as the potential applied to this electrode is changed. 

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. 

Thus, in the stationary state, the rate of anodic transfer of metal ions across the metal/film interface equals the rate of anodic transfer of metal ions across the film/solution interface this rate of metal ion transfer represents the dissolution rate of the passive film. The thickness of the passive film at constant potential remains generally constant with time in the stationary state of dissolution, although the thickness of the film depends on the electrode potential and also on the dissolution current of the passive film. 

The rotating disc electrode is constructed from a solid material, usually glassy carbon, platinum or gold. It is rotated at constant speed to maintain the hydrodynamic characteristics of the electrode-solution interface. The counter electrode and reference electrode are both stationary. A slow linear potential sweep is applied and the current response registered. Both oxidation and reduction processes can be examined. The curve of current response versus electrode potential is equivalent to a polarographic wave. The plateau current is proportional to substrate concentration and also depends on the rotation speed, which governs the substrate mass transport coefficient. The current-voltage response for a reversible process follows Equation 1.17. For an irreversible process this follows Equation 1.18 where the mass transfer coefficient is proportional to the square root of the disc rotation speed. 

The technique of cyclic voltammetry is conveniently applied at these stationary electrodes [46], ITie electrode potential is scanned with time between two limits in a triangular fashion depicted in Figure 1.9. The scan rate can be between mV s ... 

Among electrochemical techniques,cyclic voltammetry (CV) utilizes a small stationary electrode, typically platinum, in an unstirred solution. The oxidation products are formed near the anode the bulk of the electrolyte solution remains unchanged. The cyclic voltammogram, showing current as a function of applied potential, differentiates between one- and two-electron redox reactions. For reversible redox reactions, the peak potential reveals the half-wave potential peak potentials of nonreversible redox reactions provide qualitative comparisons. Controlled-potential electrolysis or coulometry can generate radical ions for smdy by optical or ESR spectroscopy. 

In the last section it was shown that instead of representing an electrode potential on a relative scale (arbitrarily setting the standard hydrogen electrode potential equal to zero), it is possible to numerically calculate the actual value of the latter, with a reference state of zero energy for the stationary electron at infinity in a vacuum. 

If the thickness of the diffusion layer (d) is time-independent, a steady limiting current is obtained. However, if the electrode reaction occurs at a stationary electrode that is kept at a constant potential, the thickness of the diffusion layer increases with time by the relation S (7iDt)1/2, where t is the time after the... 

All the electrode kinetic methodology described until now has assumed a steady state (or quasi-steady state in the case of the DME). Many techniques at stationary electrodes involve perturbation of the potential or current in combination with forced convection, this offers new possibilities in the evaluation of a wider range of kinetic parameters. Additionally, we have the possibility of modulating the material flux, the technique of hydrodynamic modulation which has been applied at rotating electrodes. Unfortunately, the mathematical solution of the convective-diffusion equation is considerably more complex and usually has to be performed numerically. 

The potential step provides the theoretical background for any potentiostatic regulation experiment and a basic understanding is necessary for the mathematical solution of any controlled potential, nonsteady-state voltammetric response, such as LSV, pulse or a.c. experiments. At a stationary electrode, the current response to a potential step is described by the Cottrell equation [eqn. (83)] but at hydro-dynamic electrodes, it needs to be modified to take account of forced convection. 

Two voltammetric techniques, stationary-electrode voltammetry (SEV) and cyclic voltammetry (CV), are among the most effective electroanalytical methods available for the mechanistic probing of redox systems. In part, the basis for their effectiveness is the capability for rapidly observing redox behavior over the entire potential range available. Since CV is an extension of SEV, many points pertinent to CV are discussed in the SEV section. 

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