Potential density

The potential dependence of the velocity of an electrochemical phase boundary reaction is represented by a current-potential curve I(U). It is convenient to relate such curves to the geometric electrode surface area S, i.e., to present them as current-density-potential curves J(U). The determination of such curves is represented schematically in Fig. 2-3. A current is conducted to the counterelectrode Ej in the electrolyte by means of an external circuit (voltage source Uq, ammeter, resistances R and R") and via the electrode E, to be measured, back to the external circuit. In the diagram, the current indicated (0) is positive. The potential of E, is measured with a high-resistance voltmeter as the voltage difference of electrodes El and E2. To accomplish this, the reference electrode, E2, must be equipped with a Haber-Luggin capillary whose probe end must be brought as close as possible to... 

Fig. 2-4 Current-density-potential curves for an electrochemical partial reaction as in Eq. (2-35).

There are no eurrent-density-potential eurves for mixed eleetrodes, only eur-rent-density-potential bands whieh ean be represented in a three-dimensional J-U-x... 

In this type of corrosion, metal ions arising as a result of the process in Eq. (2-21) migrate into the medium. Solid corrosion products formed in subsequent reactions have little effect on the corrosion rate. The anodic partial current-density-potential curve is a constant straight line (see Fig. 2.4). 

Because of possible errors in determining pitting potentials from I(t/) curves, it is safest to take them from pit density-potential diagrams which can be determined by chronopotentiostatic experiments. Figure 2-16 shows the results of experiments on 1.4031 CrNi stainless steel (AISI304) in neutral waters [52]. 

The current-density-potential graph for a working galvanic anode is given by Eq. (6-8) in which the polarization resistance /j, is dependent on loading ... 

According to the current density-potential curves in Figs. 2-18 and 21-11, carbon steels can be passivated in caustic soda [27-32]. In the active range of the... 

Fig. 21-11 Current density-potential curves for plain carbon steel in hot caustic soda from Refs. 28-31.

The generally applicable relations for a two-conductor model are derived in the following section. For simplicity, local potential uniformity is assumed for one of the two conductor phases. Relationships for the potential and current distributions, depending on assumed current density-potential functions, are derived for various applications. 

A ground with locally constant values of S and I in full space is regarded as conductor phase II. Therefore d0 = dU. A linear current density-potential function is assumed for the current transfer ... 

Fig. 5.61 Current density-potential characteristics of n-semiconductor electrode in the dark and upon illumination...

On the basis of obtained data of cyclic voltammograms for 3d metals oxides electrodeposition the optimal conditions (current density, potential, process time, electrolyte composition, temperature) for dense oxide films (Ni, Cr and Co) deposition on steel foil have been elaborated. Data relating to several best films are summarized in Table 1. 

The practical problems associated with the evaluation of exchange integrals led Slater (1974) many years ago to introduce a localized approximation to the exchange. This has been widely utilized and more recently has been modified to include additional correlation effects. Potentials so obtained are called local-density potentials. ... 

Local-density potentials greatly simplify the computational problems associated with defect calculations. In practice, however, such calculations still are very computer-intensive, especially when repeated cycles for different atomic positions are treated. In most cases the cores are eliminated from the calculation by the use of pseudopotentials, and considerable effort has gone into the development of suitable pseudopotentials for atoms of interest (see Hamann et al., 1979). 

As illustrated in Figure 26, which is a varied presentation for a single pore from the scheme shown in Figure 19, there are five possible phases in the current path in which significant potential drops may occur. The distribution of the applied potential in the different phases of the current path depends on doping type and concentration, HF concentration, current density, potential, illumination intensity and direction. The phases in the current path... 

Figure 1 shows typical current density-potential curves of an electroorganic reaction. In this example, the thin line represents the anodic oxidation of the electrolyte without reactants at a higher potential, here at more than 0.8 V versus NHE. If the reactant 1 is present, it can be converted according to the thick compact lines at lower potentials above 0.2 V versus NHE, and this selectively can occur up to 0.5 V versus NHE. Over 0.5 V versus NHE also, an additional reactant... 

Flg.1 Current density-potential curves for the anodic oxidation of two various reactants and finally of the solvent. The electrode potential is measured against a reference electrode (RE), here for example, the normal hydrogen electrode (NHE). 

As discussed in Sect. 2.3.2.1, electroor-ganic reactions can often be selectively controlled by a constant potential of the working electrode, even at decreasing reactant concentrations (see Fig. 3). A precondition of this operation mode is a suitable potential-measuring equipment in the cell (special practical aspects of potential measurement are discussed in Sect. 2.5.1.6). The optimal potential can be chosen using a current density-potential curve (see Fig. 1), available by cyclovoltammetry with a very low scan rate. 

An exact potential measurement is difficult - particularly in organic electrochemistry - and probably requires very sophisticated techniques to avoid a variety of possible errors (e.g. [75]). Fortunately, for practical applications in electroorganic synthesis, it will usually be sufficient to get reproducible potentials for the current density-potential curves (see Fig. 1) as well as for the synthesis cell. A constant deviation in both measurements may be acceptable, even though the accurate value may be unknown. Some aspects will be discussed here, a more detailed overview is given, for example, in [3a]. 

Intermolecular coupling Many papers on hydrodimerization of aromatic carbonyl compounds have appeared indicating the importance of this reaction. The rac/meso ratio for the pinacolization of acetophenone in aqueous ethanol ranges between 0.9 and 1.4 in acidic medium and between 2.5 and 3.2 in basic medium. The diastereoselectivity is independent of the cathode material mercury, tin, or copper. Electrolysis conditions such as current density, potential, or current-controlled electrolysis also do not influence the diastereoselectivity. The same holds for propiophenone. For benzaldehyde, the rac/meso ratio is 1.1 to 1.2 in acidic as well as in basic media [283]. In the presence... 

The argument can be generalized without restricting it to near the equilibrium. The only difference is that far from equilibrium, exponential current-density-potential relations are operative and the resistances of individual reactions as well as the faradaic... 

Fig. 7.109. Experimental current density-potential relationship for the oxidation of ethylene on platinum and an 80% Pt-20% Ru alloy.

If interface 2 is far from equilibrium, one can use the simple one-term exponential form of the current density-potential law (see Eq. (7.31)]... 

Fig. 13. (a) Schematic representation of the formation of mixed potential, M, at an inert electrode with two simultaneous redox processes (I) and (II) with formal equilibrium potentials E j and E2. Observed current density—potential curve is shown by the broken line, (b) Representation of the formation of corrosion potential, Econ, by simultaneous occurrence of metal dissolution (I), hydrogen evolution, and oxygen reduction. Dissolution of metal M takes place at far too noble potentials and hence does not contribute to EC0Ir and the oxygen evolution reaction. The broken line shows the observed current density—potential curve for the system. 

As regards the double layer charging, the first-order expansion of the charge density—potential relationship is... 

Fig. 3.18 Current density-potential curves for two-electron transfer processes at disc (solid line) and spherical (dashed line) microelectrodes of the same radius. The values of the difference between the formal potentials of the redox centers, AEf (in V), are indicated on the curves. These curves have been calculated with Eq. (3.154) by assuming ra = rd = rs = 5 pm, t = 1 s. D = 10 5 cm2 s-1. T = 298 K...

System 1. Under ideal conditions the adsorption of a surfactant into the EDL proceeds as described in Chap. 3. The border of efficiency of anionic and cationic surfactants is IP or PZC, as follows from the correlation of e.g. adsorption density, potential and notability are dependent on pH [e.g. 44,129,167,174-176]. The course of such an adsorption is shown in Fig. 15. If H+ or OH" react with the surface of one mineral the released ions or their hydrolytic products can adsorb on unequally charged surface of the other mineral and cause an activated adsorption of the surfactant, or they can inhibit the adsorption, as shown on the schemes ... 

Fig. 14.31. Logarithm of the anodic current density-potential curves of the Q/QH2 redox couple on gold electrode covered by (x) three layers of DPPC + gramicidin,(a) five layers of DPPC + gramicidin. (Reprinted from A. Rejou-Michel, M. A. Habib, and J. O M. Bockris, Electron Transfer at Biological Interfaces, in Electrical Double Layers in Biology, M. Blank, ed., Fig. 9, p. 175, Plenum, 1986.)...

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