Density-potential curve

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).

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). 

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.

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]. 

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. 

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...

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.)...

Fig. 11. Current density-potential curve at (111) n-GaP in aqueous 10 mol 1 K3Fe(CN)6 +...

In order to determine the kinetic parameters of the reaction corrected from diffusion phenomenon, a voltammetric investigation was pursued with a rotating platinum ring disk electrode. Figure 21.10 represents current density-potential curves obtained for different rotation speeds and for the positive variations of potential. It appears that the current density of the rotating disk increases with the rotation rate. 

Fig. 15. Potentiodynamic current density/potential curve of a 3-methylthiophene polymer film on a germanium crystal with an evaporated gold layer. Electrolyte solution as in Fig. 13, sweep range 0.1-1.0V, sweep rate 0.002 V s-1. The numbered vertical bars indicate the potentials at which ATR-FTIR spectra (each spectrum originating from 20 interferograms) were recorded.

In this case, values of the rates of individual steps may be obtained from measurements of current density potential curves. In addition, measurements of steady-state potentials provide pertinent information. Methods for the determination of the predominating mechanism of the two alternative mechanisms have recently been outlined by Wagner 124) and applied to the hydrogenation of quinone, allyl alcohol, and vinyl acetate by Takehara (125). 

Figure 11.57. Corrosion current density-potential curves of various metals, both original and passivated [106],... 

Figure 17. Effect of time on the current density-potential curves by potentio-static measurements (calculated for K + B —10 sec Hm...

Figure 18. Current density-potential curves calculated for t = showing dependence on the sum of the constants K and B f IS)...

Fig. 1 Schematic current density potential curve of metals with active, passive, and transpassive potential range and the critical potentials Ep and E restricting the pitting range. Valve metals with insulating passive layers showing neither transpassive metal dissolution nor oxygen evolution.

Fig. 14 Measurement of the current density-potential curves for the interfacial reaction Ag Ag+ (in Ag2S) + e at the phase boundary Ag/Ag2S. (a) Experimental setup and (b) curves measured at 300 and 220°C [15].

The results of such measurements are known as current density-potential curves. They represent cumulative curves given by the superimposition of the current density-potential curves of the individual reactions. For simple electrodes with defined electrode processes, these are the overpotential curves. For metals exposed to electrolytic attack, superimposition of several overpotential curves gives the actual current density-potential curves that are of significance in corrosion testing and research. Figure 20.9 shows the superimposition of the overpotential curves of a hydrogen electrode... 

FIGURE 20.9 Superimposition of the overpotential curves to form a current density-potential curve. 

Even though normal corrosion without external current is only shown by the point of intersection of the cumulative current density-potential curve and the abscissa the anode and cathode branches (i.e., the full course of the curve measurable with external current supply) are still of interest since they reflect aU the peculiarities of the polarization curves involved. 

The procedure for determining a current density-potential curve is to immerse the metal electrode in the corrosive medium. After an incubation period, the mixed potential corresponding to the outwardly currentless state becomes established on the metal. If a circuit is now placed on the electrode and external current is applied, the result is a shift in potential polarization. Current density-potential curves are therefore also known as polarization curves. Depending on the direction of the external current imposed, this is termed anodic or cathodic polarization, and anodic potential becomes positive while cathodic potential becomes negative. 

Simple, purely transfer-related electrode reactions give cumulative current density-potential curves of the type shown by the unbroken Une in Figure 20.11. At the points pi and pj, it swings into the overpotential curves of the respective part reactions because beyond these points, only the anodic or cathodic reaction exists. At these points, the equilibrium potentials of the reverse reaction exceeded and superimposition no longer occurs. These pure overpotential curves thus form linear Tafel lines, which, after reflection of the cathode curve in the x-axis, can be made to intersect by extrapolation in the direction of the abscissa. The ordinate section at the point of intersection is then log that is, the log of the corrosion current density, rest potential, from which the corrosion rate can be calculated by Faraday s law. 

The correlation between polarization resistance and corrosion rate at the free corrosion potential was developed and applied in practice. By this method, the corrosion rate is estimated from the gradient of the current density-potential curve, polarization resistance ... 

FIGURE 20.20 Current density-potential curve of passiviable alloy, with and without pitting corrosion. 

Current density-potential curves for stressed and unstressed tensile test specimens in crack inducing media show that the unstressed specimen exhibits no rise in current until approximately... 

In the description given outlining electrochemical systems in which a current flows, key parameters include the variations of the anodic and cathodic polarisations (or overpotentials if applicable) as a function of current and time. These relationships are generally represented in the form of current-potential curves of an electrode, /= f(E), where E is the voltage between the electrode in question and a reference electrode . The experimental results can also be presented in the form of current density-potential curves. However, when the study concerns the whole electrochemical system and is not just focused on the working electrode, it is best to keep the current-potential representation I... 

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