Overpotential dependence

The physical mechanism described allows one to answer two basic questions (1) Why does the electrochemical process usually require activation and (2) Why is there no inverted region in the current-overpotential dependence ... 

These aquo redox couples, therefore, exhibit a markedly different overpotential dependence of the anodic and cathodic rate constants this contrasts with the symmetrical dependence predicted by eq 16. An example of this behavior is shown in... 

The quadratic rate equation [Eq. (1)] of the continuum theory arises because it implicitly assumed the parabolic dependence of the free energy profile on the solvent coordinate q. One of the consequences of this quadratic equation is the generation of a maximum in the dependence of the rate of reaction on the free energy of reaction and also in current density-overpotential dependence. 

It is important to note that as early as 1931, the density of electronic states in metals, the distribution of electronic states of ions in solution, and the effect of adsorption of species on metal electrode surfaces on activation barriers were adequately taken into account in the seminal Gurney-Butler nonquadratic quantum mechanical treatments, which provide excellent agreement with the observed current-overpotential dependence. 

The experimental data for the rate of stationary two-dimensional nucleation in electrocrystallization of cadmium on the surface of the Cd(OOOl) crystal face in 2.5 M CdS04 aqueous solution at 45 °C were presented [234]. The overpotential dependence of the nucleus size was determined. 

When the overpotential goes into the exponential i vs. T) region, the surface coverage may change from 0C to 0 where 0 is the (overpotential-dependent) coverage at rj. So one has to write... 

Since both OCV and activation overpotential depend on some gas species concentration, and since in a PEN lumped structure the mass transport cannot be directly modeled within the domain thickness, the so-called concentration losses are introduced. They represent the voltage reduction due to the fact that the gas species concentration reacting in the reaction zone is different from that used in the calculation (i.e. the concentration relative to the gas channel, also referred to as the bulk ). 

The sensitivity of the heterogeneous electron transfer rate constant to the overpotential depends on the extent of electronic coupling between the reactant and the electrode [19]. For strongly coupled reactants, electron transfer occurs predominantly through states near the Fermi level of the electrode and the adiabatic potential-dependent rate constant is given by the product of the frequency factor, vn, and the density of acceptor states in the molecule, Dox, according to the following ... 

The manner in which the overpotential depends on the intensity of the current passing has been studied by numerous investigators. The only point on which there seems to be universal agreement is that an equation,... 

The electrochemical evolution of hydrogen has long been one of the most studied electrochemical processes. The mechanism of this process and the - overpotential depend on the electrode material. The - Tafel equation was formulated by Tafel as an empirical relationship for the evolution of hydrogen. The electrocat-alytic character of her follows from the marked dependence of the constants of the Tafel equation. According to the mechanistic interpretations the her consists of two steps, in the first of which adsorbed hydrogen is formed from the reactants (H30+ or H20) ... 

The interpretation of the nucleation rate equation in terms of its overpotential dependence is rather difficult to perceive as represented in the form of eq. (4.42). It has been shown already that the products in the denominator of this equation contain the formation energy AG(iV) of clusters of class N (cf. eq. (4.47)), and that, at a given overpotential, AG has a maximum determining the critically sized cluster, N=Ncnt-The n terms in the sum of the denominator of eq. (4.42) show a maximum for the critically sized cluster. All terms other than that for this cluster can be neglected including the unity in the denominator [4.13, 4.14). Note that/is always much smaller than the impingement rate ti att.o times the adsorption sites Z<, and hence the denominator is much larger than unity. Then ... 

Chapter 5). The measured overpotential dependence of the steady state current density of the transients (c.f. Fig. 6.15) indicates a multilayer growth mode generated by screw dislocations [4.62, 4.63, 4.68, 4,69]. It can be assumed that the screw dislocations of a real Au.Qikl) substrate are inherited by the growing ultra-thin Ag film, determining the growth mechanism under these experimental conditions. 

Overpotential depends on the structure of a solution near an electrode, which differs from that in the bulk solution. Near an electrode, electrons are transferred across an electrode-solution interface that depends on the solution and the condition of the electrode. 

The high overpotential needs to be reduced in order to improve the low energy utilization efficiency. The formation of anion radical CO2 " is presumed to be responsible for the high overpotential. The overpotential depends on electrode... 

The calculated value E° = +1.23 V for the O2, 4H /2H20 electrode implies that electrolysis of water using this applied potential difference at pH 0 should be possible. Even with a platinum electrode, however, no O2 is produced. The minimum potential for O2 evolution to occur is about 1.8V. The excess potential required ( 0.6V) is the overpotential of O2 on platinum. For electrolytic production of H2 at a Pt electrode, there is no overpotential. For other metals as electrodes, overpotentials are observed, e.g. 0.8 V for Hg. In general, the overpotential depends on the gas evolved, the electrode material and the current density. It may be thought of as the activation energy for conversion of the species discharged at the electrode into that liberated from the electrolytic cell, and an example is given in worked example 16.3. Some metals do not liberate H2 from water or acids because of the overpotential of H2 on them. 

The spontaneous process is actually the reverse reaction (i.e. formation of H2O from H2 and O2) and for this at pH 7, iiceU = 1-23V (see the self-study exercises below). In order to drive the electrolysis of H2O, the electrical power source must be able to supply a minimum of 1.23 V. In practice, however, this potential is insufficient to cause the electrolysis of H2O and an additional potential (the overpotential) is needed. The size of the overpotential depends on several factors, one being the nature of the electrode surface. For Pt electrodes, the overpotential for the electrolysis of H2O is 0.60V. Thus, in practice, CI2 (or a mixture of CI2 and... 

These parameters arise from the boundary conditions on Laplace s equation when finite kinetic rates are included. The first is a ratio between the exchange current density and ohmic parameters such as length and conductivity. The second parameter is a dimensionless current level. Values of either or both parameters much greater than unity indicate that ohmic effects dominate and the current distribution resembles the primary case. Low values of both parameters indicate that kinetics limit the process and the current distribution is uniform. Even though a low value of J indicates substantial kinetic effects, the current distribution resembles the primary case at high values of 6 because the linear ohmic dependence on current density dominates the logarithmic overpotential dependence. These... 

Solution pH significantly affects the magnitudes of both the polarographi-cally measured diffusion coefficient and the overpotential for cytochrome c reduction. The overpotential dependence on pH was first described by Griggio and Pinamonti and later by others. The former authors found that... 

Figure 3.3 shows the oxygen overpotential dependence on pH. Assuming that the applied potential of platinum remains at 0.515 V vs. SCE, the oxygen reduction reaction occurs only when the pH is less than or equal to 8. 

Fig. 8.7 Hydrogen permeation current-overpotential dependence obtained on an AiSi 4340 steel membrane in an electrolyte containing 0.5 iVI HCi04 and 0.25 M NaCi04 (pH 0.3) and the membrane thickness=0.3 mm [3]. Reproduced by the permission of The Electrochemical...

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