The EC Mechanism

We start with the case where the initial electron transfer reaction is fast enough not to interfere kinetically in the electrochemical response.1 Under these conditions, the follow-up reaction is the only possible rate-limiting factor other than diffusion. The electrochemical response is a function of two parameters, the first-order (or pseudo-first-order) equilibrium constant, K, and a dimensionless kinetic parameter, 2, that measures the competition between chemical reaction and diffusion. In cyclic voltammetry, 

FIGURE 2.1. EC reaction scheme in cyclic voltammetry. Kinetic zone diagram showing the competition between diffusion and follow-up reaction as a function of the equilibrium constant, K, and the dimensionless kinetic parameter, X. The boundaries between the zones are based on an uncertainty of 3 mV at 25°C on the peak potential. The dimensionless equations of the cyclic voltammetric responses in each zone are given in Table 6.4. 

COUPLING OF ELECTRODE ELECTRON TRANSFERS WITH CHEMICAL REACTIONS 

The concentration at the electrode surface is much smaller than in the absence of a reaction the more so the faster the reaction. The concentration profile is squeezed within a reaction layer whose thickness, /i, is small compared to the diffusion layer the smaller, the faster the reaction  

We note incidentally that the reaction layer thickness is on the same order as that of the double layer for k+ 1010 s-1 (typical values of the diffusion coefficient are of the order of 10 5 cm2 s 1). It is only for such fast reactions that their kinetics may be perturbed by the strong electric field present in the close vicinity of the electrode.3 

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A special case of the EC mechanism is the catalytic regeneration of O during the chemical step ... 

The natural assumption made by a large number of researchers in the field of electrochemical C02 reduction was that the intermediate was C02, as postulated by Haynes and Sawyer (1967). The observation of oxalate as a major product in addition to, or in competition with, the formation of CO, CO, HCOj and HCOO , increased the attention focused on the reactive intermediate and the mechanisms by which it reacted. However, controversy has arisen over whether the subsequent reaction of the CO 2 was via dimerisation (the EC mechanism) or via attack on another C02 molecule (the ECE mechanism). In addition, the existence of such species as CO 2 (ads) and HCOO (ads) have also been suggested but, as we shall see, these are not now thought to play a major role on simple metals. 

The EC mechanism (Scheme 2.1) associates an electrode electron transfer with a first-order (or pseudo-first-order) follow-up homogeneous reaction. It is one of the simplest reaction schemes where a heterogeneous electron transfer is coupled with a reaction that takes place in the adjacent solution. This is the reason that it is worth discussing in some detail as a prelude to more complicated mechanisms involving more steps and/or reactions with higher reaction orders. As before, the cyclic voltammetric response to this reaction scheme will be taken as an example of the way it can be characterized qualitatively and quantitatively. 

The simplest electrodimerization mechanism occurs when the species formed as the result of a first electron transfer reaction reacts with itself to form a dimer (Scheme 2.7). This mechanism is usually termed radical-radical dimerization (RRD) because the most extensive studies where it occurs have dealt with the dimerization of anion and cation radicals formed upon a first electron transfer step as opposed to the case of radical-substrate dimerizations, which will be discussed subsequently. It is a bimolecular version of the EC mechanism. The bimolecular character of the follow-up reaction leads to nonlinear algebra and thus complicates slightly the analysis and numerical computation of the system. The main features of the cyclic voltammetric responses remain qualitatively similar, however. Unlike the EC case, however, the dimensionless parameter,... 

The peak current is proportional to the substrate concentration and to the square root of the scan rate as for a simple diffusion-controlled wave. The proportionality coefficient is slightly larger, 0.527 instead of 0.446. Correspondingly, the wave is thinner, in the ratio 1.51/1.86. As with the EC mechanism, the peak potential is more sensitive to the follow-up reaction. It varies linearly with the logarithm of the scan rate, of the rate constant of the dimerization reaction, and of the substrate concentration. The rates of these variations are summarized in Table 2.1, where they can be compared to the values characterizing other mechanisms, hence serving as diagnostic... 

As with the other reaction schemes involving the coupling of electron transfer with a follow-up homogeneous reaction, the kinetics of electron transfer may interfere in the rate control of the overall process, similar to what was described earlier for the EC mechanism. Under these conditions a convenient way of obtaining the rate constant for the follow-up reaction with no interference from the electron transfer kinetics is to use double potential chronoamperometry in place of cyclic voltammetry. The variations of normalized anodic-to-cathodic current ratio with the dimensionless rate parameter are summarized in Figure 2.15 for all four electrodimerization mechanisms. 

The transition between the two limiting situations is a function of the parameter (k-e/kc)Cp. The ratio between the catalytic peak current, ip, and the peak current of the reversible wave obtained in the absence of substrate, Pp, is thus a function of one kinetic parameter (e.g., Xe) of the competition parameter, (k e/A c)c and of the excess ratio y = C /Cp, where and Cp are the bulk concentrations of the substrate and catalyst, respectively. In fact, as discussed in Section 2.6, the intermediate C, obtained by an acid-base reaction, is very often easier to reduce than the substrate, thus leading to the redox catalytic ECE mechanism represented by the four reactions in Scheme 2.13. Results pertaining to the EC mechanism can easily be transposed to the ECE mechanism by doubling the value of the excess factor. 

The governing dimensionless partial derivative equations are similar to those derived for cyclic voltammetry in Section 6.2.2 for the various dimerization mechanisms and in Section 6.2.1 for the EC mechanism. They are summarized in Table 6.6. The definition of the dimensionless variables is different, however, the normalizing time now being the time tR at which the potential is reversed. Definitions of the new time and space variables and of the kinetic parameter are thus changed (see Table 6.6). The equation systems are then solved numerically according to a finite difference method after discretization of the time and space variables (see Section 2.2.8). Computation of the... 

The main difference with the EC mechanism (Section 6.2.1) is that C is reduced as soon as it reaches the electrode hence the replacement of the boundary condition (QCc/Qx)x=0 = 0 by the condition (Cc)x=0 = 0. A second difference is the contribution to the current provided by the reduction of C. Introduction of the same normalized variables and parameters as in Sections 6.1.2 and 6.2.1 leads to... 

Fig(I) possibly participated as an intermediate. As a complementary study, redox behavior of the ligands themselves was investigated in DMSO solutions at Hg electrodes. 2-e oxidation of mercury proceeded according to the EC mechanism i.e. involving electrochemical step followed by chemical process ... 

The EC mechanism is a standard departure for discussing electrochemical mechanisms, it represents a one-electron electrode reaction coupled to a chemical reaction in solution ... 

Fig. 4. The zone diagram for the eC mechanism. Zone designations are explained in the text. Reprinted with permission from ref. 29.

Fig. 12. Cyclic voltammograms showing the effect of increasing rate constant for the eC mechanism. Curves with increasing current on the forward scan correspond to increasing rate constant.

The electrode mechanisms treated, along with the rate laws and the appropriate digital simulation parameters, are shown in Table 16. The symbols for mechanisms 5 and 6, RS-2 and RS-3, indicate that these reactions represent cases of radical (primary intermediate B) reacting with substrate (A). Mechanism 5 foDows second-order kinetics while third-order kinetics characterize mechanism 6. The theoretical data for the mechanisms are summarized in Tables 17—23. The calculations are for EX — f revI equal to 300 mV. Data are also available for EX — Eiev — 100 mV. In the following paragraph, the data are explained with reference to the eC mechanism, i.e. Table 17. 

One of the simplest electrode reactions is the EC mechanism (also called a following chemical reaction) in which the electrogenerated species (R) rearranges or reacts with some other solution component (Z) at a rate characterized by the rate constant k. The EC mechanism is summarized by the following reaction sequence, in which the labels E and C identify the heterogeneous electron-transfer reaction (electrode reaction) and the subsequent homogeneous solution reaction (chemical reaction), respectively ... 

Other examples of the EC mechanism include nucleophilic addition of Z (such as H20 or CN") to electrogenerated organic radical cations, ligand exchange reactions in the case of coordination compounds, and redox reactions between R and Z (or O and Z in the case of a reduction). 

The catalytic regeneration mechanism is a variation of the EC mechanism in which the initial electroactive species is regenerated by the homogeneous chemical reaction, as follows ... 

Chronoabsorptometry is useful for the study of homogeneous chemical reactions that involve an electrogenerated species. For example, consider the situation in which an additional species, Z, is also present in solution and is capable of a rapid homogeneous chemical reaction with R at a rate characterized by the second-order rate constant k to form products P (see Chap. 2 for a discussion of the EC mechanism). 

In the simulation of the EC mechanism, a double potential step may be employed these boundary conditions have been discussed previously. Diffusion would be modeled in the usual way. Following the diffusion step, however, the concentration in each element of the resulting array is adjusted according to Equation 20.52 using the input parameter kjtk ... 

The EC mechanism is that of Equation 23.21, the horizontal line in the scheme, encompassing the oxidation of Cd to Cd2+ (E) followed by complexation of Cd2+ by HY3- (C). The electrochemical reactant, Cd2+, was cleverly furnished by a cadmium amalgam working electrode, which upon oxidation gave Cd2+ at the electrode for reaction with HY3. Ca2+ added to the bulk solution served to compete with Cd2+ for available HY3. ... 

Figure 23.15 shows the CV scans obtained after successive additions of CH3CN to a 0.98 mM solution of CpfFe2(CO)2(p-CO)2 in CH2C12. The one-electron oxidation at approximately +0.4 V is that of the reactant diiron complex. Equations 23.23 (E) and 23.22 (C) constitute the EC mechanism. The reduction wave at -0.85 V is that of the ultimate reaction product, Cp Fe(CO)2(NCCH3) +, and although it is a useful indicator of the reaction product, it is not used in the calculations to obtain k. ... 

A second situation is the EC mechanism or the mechanism where the electron-transfer step is followed by a chemical reaction. In addition, different conditions can be defined, resulting in different shapes of the recorded voltammetric waves ... 

When F° for the initial electron transfer reaction is known, the measurements of p give direct access to the rate constant, k. An example of the relationship between p — E° and k for the eC-mechanism is given by Equation 6.49 [36] ... 

When the kinetics of the chemical reaction in solution is very fast with respect to the diffusion transport, the resolution of the problem can be simplified by noting that the concentrations of species B and C are in equilibrium at any point and time (cb(c, t) = Cg, cc(r, t) = c ) and the reaction layer thickness (<5Plane) tends to zero. Taking into account these considerations, the RPV current for the EC mechanism is given by... 

Note that in this limiting case, the oxidative limiting current of the EC mechanism is the same as for the E mechanism given by Eq. (4.72). 

The influence of K = 1 /Kt L[ on the RPV curves is shown in Fig. 4.28. The incidence of the chemical reaction on the voltammograms is more apparent as the chemical equilibrium shifts toward the electroinactive species C, that is, for small K values. Thus, the oxidative limiting current decreases and the voltammogram shifts toward more positive potentials as K decreases. On the other hand, for high K values the effect of the chemical step vanishes and the response of the EC mechanism tends to that of a simple E process (open circles). 

According to these results, the characterization of the subsequent coupled chemical reaction of the EC mechanism can be achieved with RPV by examining the oxidative limiting current. The half-wave potential is also interesting in order to determine the formal potential of the electrode process [79]. 

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