Partial current densities potential dependence

Thus, while the relation between the partial current densities and potential is exponential, in the region of low polarization a linear relation is obtained between polarization and the net CD, owing to a superposition of the currents of forward and reverse process. At A = 10 mV, the error introduced by the approximation above will be between 1 and 20%, depending on the relative values of a and p it becomes even smaller with decreasing polarization. Hence we can by convention consider the interval of polarization values between -10 and 10 mV as that of low polarization where the linear relation (6.6) is valid. 

FIGURE 63 Potential dependence of the anodic (i) and cathodic (i) partial current densities as well as of the anodic (i ) and cathodic (i ) net current densities. 

Formation of CO2 anion radical and subsequent reduction to formate were studied by photoemission and polarization measurements with Hg electrodes as well as the capacitance and potential decay measurements at Sn and In electrodes all these measurements agreed that very low fraction of the electrode is covered by the adsorbed species. Schififrin investigated reduction of CO2 anion radical formed in a photoemission measurement with a Hg electrode, and showed that the potential of the reduction does not depend on pH. He thus concluded that H2O is the proton donor in the formate formation from CO2 ", as confirmed later by Hori and Suzuki. They demonstrated that the electrode potential is constant in the pH range 2 to 8 at a constant partial current density of HCOO formation 0.5 mA cm at a Hg electrode. 

The problem, in the view of the present authors, is that the partial current density for deposition of, say, nickel is determined from the total amount of nickel deposited per unit time. However, in a solution containing Ni , Mo04 , NH3 and Cit , there can be as many as nine different species from which nickel could be deposited (six complexes with 1-6 molecules of NH3, two with citrate, and one adsorbed mixed-metal complex). The reversible potential for deposition of nickel is, in principle, different for each complex (depending on the stability constants). Hence, although all these parallel paths occur at the same applied potential, the overpotential is different for each of them. Moreover, there is no basis to assume that the exchange current densities or the Tafel slopes would be the same. If the observed Tafel plot would, nevertheless, be linear over at least two decades of current density, it could be argued that one of these parallel paths for deposition of nickel happens to be predominant. However, in the work quoted here, the apparent linearity of the Tafel plots extends only over a factor of about three in current density, namely over half a decade (cf.. Fig. 4a in Ref. 97). 

For the electrode reaction Eq. (6.1) equations for the partial current densities of oxidation and reduction can be derived by formulating the potential dependence of the rate constants. The now generally accepted formulation goes back to work of Erdey-Gruz and Vohner and Butler. ... 

The constants and are the rate constants in Eqs. (6.2) and (6.3) at the electrode potential E = 0, which is related to the chosen reference electrode. The potential dependence of the partial current densities is described by a splitting of the total potential dependence in an anodic part a E and a cathodic part aji = (1 - )E. The factors and are... 

The potential dependence of the partial current densities and of the total current density is shown in Figure 6.1. 

Figure 6.1 Potential dependence of the partial current densities, Eqs. (6.8) and (6.9), and of the total current density (Eq. (6.11)). The dashed, straight line represents the region of linear relation between current and potential.

Figure 10.9 Potential dependence of the partial current densities of iron (spheres) and chromium (rectangles) dissolution from FeCr alloys in sulfuric acid (a) FeCrg gj, Tafel slope 40 mV and (b) FeCr j, Tafel slope 100 mV. (Reproduced with permission from Ref. [17], 1980, Elsevier.)...

The corrosion current density is equal to the anodic partial current density at the corrosion potential. Its value, and therefore the rate of corrosion, depends on the kinetic parameters of both electrode reactions involved in the corrosion process. 

In the subcritical region, the anodic partial current density varies little with potential. Its value, generally small, depends on the applied potential sweep rate and on the alloy... 

As we have seen in Section 3.2.1, the expression for current density of an electrochemical reaction contains a mass transfer and a kinetic element, as shown in Eq. (3.147). Steady state polarization curves and preparative runs are needed to provide information, respectively, on the dependence of total current densities and of partial current densities on electrode potential... 

Clearly, for anodic dissolution to occur, the potential must be positive with respect to the reversible potential for the Fe /Fe couple and negative with respect to the reversible potential for the hydrogen-evolution reaction (HER). Thus, all we could predict from this thermodynamic argument is that at pH = 0 the corrosion potential must be somewhere between -0.617 V and 0.000 V vs. SHE. The rest depends on kinetics. To proceed we need to know the exchange current densities and the Tafel slopes for the two reactions concerned. The two partial current densities are plotted in Figure 18.1 as a function of potential The potential must settle at the point where the anodic and cathodic currents are equal, which is called the corrosion or mixed potential, jeon-... 

Notice that, because of the strong dependence of the kinetics on electrode potential, the determination of the electrochemical reaction order requires that the partial cathodic or anodic current densities are measured at constant potential in addition to the activities of the other species remaining constant. 

The chemical reaction mechanism of electropolymerization can be described as follows. The first step in course of the oxidative electropolymerization is the formation of cation radicals. The further fate of this highly reactive species depends on the experimental conditions (composition of the solution, temperature, potential or the rate of the potential change, galvanostatic current density, material of the electrode, state of the electrode surface, etc.). In favorable case the next step is a dimerization reaction, and then stepwise chain growth proceeds via association of radical ions (RR-route) or that of cation radical with a neutral monomer (RS-route). There might even be parallel dimerization reactions leading to different products or to the polymer of a disordered structure. The inactive ions present in the solution may play a pivotal role in the stabilization of the radical ions. Potential cycling is usually more efficient than the potentiostatic method, i.e., at least a partial reduction... 

A negative partial pressure effect was observed in the oxidation of all the hydrocarbons. The potential decreases by about 70 mv per decade increase of pressure at constant current density. At constant potential, 8 log i/0 pH = 0.5. The usual Arrhenius temperature dependence was observed with an apparent activation energy of 22 kcal mole at the reversible potential, calculated by extrapolation from the Tafel region. Radiotracer studies showed that adsorption isotherm is Langmuirian, and that high coverages are obtained in the potential and concentration range studied. 

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