Heterogeneous electron transfer steps

The preceding approach applies to all linear systems that is, those involving mechanisms in which only first-order or pseudo-first-order homogeneous reactions are coupled with the heterogeneous electron transfer steps. As seen, for example, in Section 2.2.5, it also applies to higher-order systems, involving second-order reactions, when they obey pure kinetic conditions (i.e., when the kinetic dimensionless parameters are large). If this is not the case, nonlinear partial derivative equations of the type... 

Finally, self-assembled monolayers (SAMs) on gold electrodes constitute electrochemical interfaces of supramolecular structures that efficiently connect catalytic reactions, substrate and product diffusion and heterogeneous electron transfer step when enzymes are immobilised on them. Resulting enzyme-SAM electrodes have demonstrated to exhibit good performance and long-term enzyme stability. 

If the RDS is a heterogeneous electron-transfer step, then the current-potential characteristic has the form of (3.5.11). For most mechanisms, this equation is of limited direct utility, because O and R are intermediates, whose concentration cannot be controlled directly. Still, (3.5.11) can serve as the basis for a more practical current-potential relationship, because one can use the presumed mechanism to reexpress Cq (0, t) and Cr (0, t) in terms of the concentrations of more controllable species, such as O and R (36). 

The electrochemical reduction of triorganosulfonium salts (21) to a diorganosul-fane and a hydrocarbon proceeds via an ECE mechanism [27] wherein two heterogeneous electron transfer steps are associated with the veiy fast (chemical) decomposition of the transient sulfuranyl radical (22) to the sulfane and an alkyl (or aryl) radical (Scheme 9). Nevertheless, from irreversible one-electron reduction peaks observed in cyclic voltammograms of phenyldialkylsulfonium salts... 

In the catalytic EC process, the product of an initial heterogeneous electron transfer step, for example, B in Equation 7.36, reacts with a species Y, presents in the solution, to regenerate A, the starting material (Equation 7.37), while Y is converted to products. It is usually assumed that Y is electroin-active at the electrode over the same potential range ... 

FIG. 11 General mechanism for the heterogeneous photoreduction of a species Q located in the organic phase by the water-soluble sensitizer S. The electron-transfer step is in competition with the decay of the excited state, while a second competition involved the separation of the geminate ion-pair and back electron transfer. The latter process can be further affected by the presence of a redox couple able to regenerate the initial ground of the dye. This process is commonly referred to as supersensitization. (Reprinted with permission from Ref. 166. Copyright 1999 American Chemical Society.)... 

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. 

Clearly, the overall rate of the reduction process will be conditioned by the slowest elementary step, which can be associated either with the mass transport (from the bulk of the solution to the electrode surface, and vice versa) or with the heterogeneous electron transfer (from the electrode to the electroactive species, or vice versa). 

This current-potential relationship, also known as the Butler-Volmer equation, governs all the (fast and single step) heterogeneous electron transfers. 

Of hundreds of theoretically possible pathways, the list can be trimmed to four using linear sweep voltammetry (LSV) and chemical arguments [22]. The LSV method is an exceptionally powerful one for analyzing electrochemical processes [24-27]. From LSV studies, it was concluded that a single heterogeneous electron transfer precedes the rate-determining step, cyclization is first order in substrate, and that proton transfer occurs before or in the rate-determining step. The candidates include (a) e-c-P-d-p (radical anion closure). 

If the first e step, i.e., heterogeneous electron transfer, is slow (non-Nernstian) or if the cyclization reaction is faster than the electron transfer itself, the electron transfer becomes rate-determining and nothing can be done about the mechanism of cyclization. 

The discrimination between e-c-P-e (Scheme 3.) and e-c-P-d mechanisms requires the answer to the question of whether the second electron is transferred through heterogeneous electron transfer (e-step) or through solution electron transfer (d-step). The following solution electron transfers (Eqs. 1-3) could be considered ... 

Fig. 2. Heterogenous (anodic) and homo neous (Med ) electron transfer steps in a mediated oxidation...

As shown by the cyclic voltammetric response in Fig. 10, the peak potential separation of the initial Mn(II,II) — Mn(II,III) electrode reaction is much larger than that of the other steps. This suggests significant inner-shell reorganization and a small rate of heterogenous electron transfer for oxidation of the fully reduced Mn(II,II) state. Similar kinetic sluggishness is observed for Mn(III)/Mn(II) electron-transfer reactions of some mononuclear complexes (see Sects 16.1.2 and 16.1.3). 

The net result of a photochemical redox reaction often gives very little information on the quantum yield of the primary electron transfer reaction since this is in many cases compensated by reverse electron transfer between the primary reaction products. This is equally so in homogeneous as well as in heterogeneous reactions. While the reverse process in homogeneous reactions can only by suppressed by consecutive irreversible chemical steps, one has a chance of preventing the reverse reaction in heterogeneous electron transfer processes by applying suitable electric fields. We shall see that this can best be done with semiconductor or insulator electrodes and that there it is possible to study photochemical primary processes with the help of such electrochemical techniques 5-G>7>. 

Fig. 4. Schematic representation of the effect of a change in electrode potential, E, on the free energy—reaction coordinate curves for a heterogeneous single electron transfer step (O + n e - R) at two different electrode potentials (1) E = Ee (solid line) and (2) E

If M is unstable then ipb/fpf will be less than unity. Its magnitude will depend upon the scan rate, the value of the first-order constant k, and the conditions of the experiment. At fast scan rates the ratio ipb/ ip, may approach one if the time gate for the decomposition of M is small compared with the half-life of M-, (In 2jk). As the temperature is lowered, the magnitude of k may be sufficiently decreased for full reversible behaviour to be observed. The decomposition of M- could involve the attack of a solution species upon it, e.g. an electrophile. In such cases, ipb/ipf, will of course be dependent upon the concentration of the particular substrate (under pseudo-first-order conditions, k is kapparent). Quantitative cyclic voltammetric and related techniques allow the evaluation of the rate constants for such electrochemical—chemical, EC, processes. At the limit, the electron-transfer process is completely irreversible if k is sufficiently large with respect to the rate of heterogeneous electron transfer the electrochemical and chemical steps are concerted on the time-scale of the cyclic voltammetric experiment.1-3... 

If the heterogeneous electron transfer of the redox species with the electrode itself is slow, the current after the potential step is necessarily less than in a system in which the electron transfer is rapid. This aspect of chronoamperometry has been used for the measurement of heterogeneous rate constants... 

---