Electrochemical case

In the electrochemical case, the predicted and experimental values of the intrinsic barrier for the reduction of butyl and benzyl halides on a glassy carbon electrode were found to agree satisfactorily.22,31... 

In the electrochemical case, starting with a molecule R—X, the dissociative... 

V -dimethylformamide (DMF) and for the reaction of the same compound with anthracene anion radical in the same solvent.12 The results are shown in Figure 3.3. In the electrochemical case, the values predicted for the cyclic voltammetric peak potential (at 0.2 V/s) and the entropy of activation are plotted as functions of the ratio C/AS. Validation of the theory derives from the observation that the agreement between theoretical and experimental values is reached for the same value of AS C/AS for the peak potential and the entropy of activation. The same is true for the homogeneous reactions. That this common value of AS°F c/ASi]h- is smaller in the latter case than in the former falls in line with the fact that the presence of anthracene renders more difficult the mutual displacement of the R and X moieties within the solvent cage. 

In the electrochemical case, using, for example, cyclic voltammetry, one way of driving the potential toward more negative values is to increase the scan rate. This is true whether the linearization procedure or the convolution approach is followed. In the first case, equation (3.4) shows that the activation free energy at the peak, AG, is a decreasing function of the scan rate as a result of the kinetic competition between electron transfer and diffusion. The larger the scan rate, the faster the diffusion and thus the faster the electron transfer has to be in order to compete. This implies a smaller value AG, which is achieved by a shift of the peak potential toward more negative values. 

Generally speaking, detection of a mechanism change is more difficult in the homogeneous case than in the electrochemical case. Figure 3.16 summarizes a case where passage from a stepwise to a concerted mechanism... 

Similar derivations apply for the electrochemical case when taking the image force effect into account. More precisely, in the expression of the potential at the surface of the A sphere, the contribution of the electrical image of A (which bears an opposite charge and which center is located at a distance d, from the center of A) has to be taken into account. 

In the electrochemical case, this ought to be reflected both in slow exhange kinetics and also in a value of the transfer coefficient significantly different from one-half. Dr. Vlcek originally attributed the observed slow electrochemical rate to transfer via excited electronic states. I do not think that is correct. I believe that slow kinetics of ligand exchange in the first solvation shells are generally responsible... 

In the homogeneous case, Aq is given by (7), where is the electron charge, Dop and Dg the optical and static dielectric constants of the solvent respectively, and a I and 2 e equivalent hard sphere radii of the two reactants (and products). For the electrochemical case, there are two versions for the expression of A., . In Marcus s treatment (Marcus, 1965) the reaction site is assumed to be located at a distance from the electrode equal to its radius, a, and the effect of image forces in the electrode is taken into account (8). In Hush s treatment (Hush, 1961) the reaction site is assumed to be located farther from the electrode surface and the effect of image forces is neglected (9). 

The rate constants, k+ and k of the forward and backward reactions are finally derived from (12) and (13) according to the transition-state theory, i.e. assuming that the transition and the initial states, on the one hand, and the transition and final states, on the other, are in equilibrium (Glasstone et al., 1941). Thus, estimating the partition function of these three states in the classical way gives (18) and (19), where p is the reduced mass of the two reactants in the homogeneous case and m the mass of the reactant in the electrochemical case. 

The experimental construction of the activation-driving force relationship is particularly simple in the electrochemical case since an easy and accurate way of making the driving force vary is to change the electrode potential. The theory predicts that the activation-driving force relationships should be... 

In electrochemical kinetics, there is a need to determine a similar quantity. However, there are eomplexities in the electrochemical case, because the reversible potential of the electrode reaction under examination varies with temperature.46 Thus, for a simple one-step electrode reaction, and substituting in the equation of the absolute reaction rate theory for the rate constant, k (cf. Eq. 4.112) ... 

The resolution obtained with the laser spot technique is far exceeded by scanning tunneling microscopy where, in some cases, atomic resolution in electrochemical cases has been reached (Szklarczyk and Velev, 1989). The first successful studies of semiconductors in air (Fig. 10.31) and in an electrochemical situation (Fig. 10.32) were made onp-Si 111 (Gonzalez-Martin, 1990). It was found that the electrochemical formation of SiOx and SiOH induces surface states at 0.25 V above the valence band at the surface (Fig. 10.33). 

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