Heterogeneous rate constant applied potential

Figure 6. Variation of the heterogeneous rate constant (log kj with the applied potential for some representative organometals.

If the rate of electron transfer is low (or the scan rate is too high), electron transfer will not be able to adjust the surface concentrations of -Fc and -Fc+ to values that are at equilibrium with the applied potential (quasireversible or totally irreversible case, see Chap. 3). In this case, the anodic peak and the cathodic peaks will not be at the same potential that is, AEpk will be greater than zero volts. Kinetic information about the surface-bound redox couple can be obtained from such quasireversible or irreversible voltammograms. For example, methods for obtaining the standard heterogeneous rate constant (see Chap. 2) for the surface-confined redox couple have been developed [41,42]. 

As in BV, the MHC model describes the electrode kinetics as a function of three parameters the formal potential, the standard heterogeneous rate constant, and the reorganization energy. Nevertheless, important differences can be observed between the two kinetic models with respect to the variation of the rate constants with the applied potential. Whereas in BV rate constants vary exponentially and... 

The dependence on time of the current when a constant potential is applied to a plane electrode for different values of the heterogeneous rate constant k° ranging from reversible to totally irreversible processes is shown in Fig. 3.2. 

The potentials Ex and E2 should be chosen in such way that at Ex no electrode process occurs and at E2 the electrode reaction of an electroactive species takes place. If the rate of the electrode process is controlled only by diffusion, the Cottrell equation [Eq. (3.6)] can be applied. Therefore, the observed current should be a linear function of t m with the intercept at the origin (a test for diffusion control). The diffusion coefficient of the electroactive species is directly proportional to the slope of the curve. The heterogeneous rate constant of a kinetically limited electrode reaction (kc or k3) also can be evaluated. 

Using the Marcus theory, the a value (see -> charge-transfer coefficient) can be predicted, and its dependence on the potential applied. For low - over potentials, and when neither Ox nor Red are specifically adsorbed on the electrode surface, a should be approximately equal to 0.5. Further, the theory describes the relation between homogeneous and heterogeneous rate constants characteristic of the same redox system. An interesting prediction from Marcus theory is the existence of a so-called inverted region for the homogeneous electron transfer reactions, of importance to the phenomenon of... 

When the heterogeneous electron-transfer process at the electrode becomes slow and irreversible, the use of the direct OTTLE/Nernst experiment is inconvenient because of the uncertainties associated with a slow equilibration process. A mediated OTTLE/Nernst experiment should rather be considered, where a redox mediator Mox/Mred characterized by a high heterogeneous rate constant is added to the cell (Eq. 111). The concentration ratio of the mediator couple will be adjusted quickly to the applied electrode potential E and, furthermore, it will be in a redox equilibrium (Eq. 112) with the redox pair O/R in the bulk solution, according to Eq. 113. 

This approach was used to study the potential dependence of the rate constant for ET at the ITIES by SECM with no external potential applied (25). The heterogeneous rate constant of ET between ZnPor+ in benzene and aqueous Ru(CN)g were measured with NaCl and NaC104 dissolved in water and tetrahexylammonium perchlorate (THAC104) in benzene. Perchlorate was the only ion common in both phases. The transfer of this ion between the two phases maintained electroneutrality during ET process. 

It is independent of potential and of the applied current density, but inversely proportional to the exchange current density, because the current-potential relationship is linear in this region (cf. Section 5.2.4). In this region the Wagner number is also inversely proportional to the heterogeneous rate constant of the metal deposition reaction. Thus, fast reactions have low value of the Wagner number and tend to lead to primary current distribution. This is a rather unique situation in electrochemistry, where poor catalytic activity (i.e., low specific rate constant) is an advantage. 

Figure 10. Variation in the experimental rate constant (log kj for heterogeneous electron transfer as a function of the applied potential.

In this equation, aua represents the product of the coefficient of electron transfer (a) by the number of electrons (na) involved in the rate-determining step, n the total number of electrons involved in the electrochemical reaction, k the heterogeneous electrochemical rate constant at the zero potential, D the coefficient of diffusion of the electroactive species, and c the concentration of the same in the bulk of the solution. The initial potential is E/ and G represents a numerical constant. This equation predicts a linear variation of the logarithm of the current. In/, on the applied potential, E, which can easily be compared with experimental current-potential curves in linear potential scan and cyclic voltammetries. This type of dependence between current and potential does not apply to electron transfer processes with coupled chemical reactions [186]. In several cases, however, linear In/ vs. E plots can be approached in the rising portion of voltammetric curves for the solid-state electron transfer processes involving species immobilized on the electrode surface [131, 187-191], reductive/oxidative dissolution of metallic deposits [79], and reductive/oxidative dissolution of insulating compounds [147,148]. Thus, linear potential scan voltammograms for surface-confined electroactive species verify [79]... 

The experimentally obtained curves do not always look like the ideal curves this can be caused by several factors. One can be that the rate constant of the heterogeneous electron transfer, which depends on the potential, is not high compared to the time scale of the experiment. This means that it is necessary to apply a more negative potential than in the ideal case to... 

The first exponential term in both equations is independent of the applied potential and is designated as k and A(L for the forward and backward processes, respectively. These represent the rate constants for the reaction at equilibrium, e.g. for a monolayer containing equal concentrations of both oxidized and reduced forms. However, the system is at equilibrium at E0/ and the products of the rate constant and the bulk concentration are equal for the forward and backward reactions, i.e. k must equal Therefore, the standard heterogeneous electron transfer rate constant is designated simply as k°. Substitution into Equations (2.19) and (2.20) then yields the Butler-Volmer equations as follows ... 

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