Homogeneous electron transfer process

Similar to homogeneous electron-transfer processes, one can consider the observed electrochemical rate constant, k, , to be related to the electrochemical free energy of reorganization for the elementary electron-transfer step, AG, by... 

The theory of homogeneous electron transfer processes, as well as of the closely-related electron exchanges with metallic electrodes, has been the subject of considerable study. The proposal by Hush and by Marcus that these processes are, for simple systems, either usually electronically adiabatic or... 

The homogeneous electron transfer process can then be represented as follows ... 

The direct process includes the reduction of A to B (i) followed by the irreversible reaction of B to a product C (iv). If now a compound P, a so-called mediator, that is easier to reduce than A is added to the solution, the direct reduction of A is replaced by the reaction sequence (ii)-(iii). During the homogeneous electron transfer process (iii) the oxidized form P of the mediator is regenerated. In other words, the reduction of A to B is catalyzed by the redox couple P/Q. Cyclic voltammograms typical for the catalyzed process are shown in Fig. 18. The effect of increasing values of kiji is shown in Fig. 18(a) and the effect of an increasing concentration ratio C /Cp is shown in Fig. 18(b). 

Most of the early mechanistic investigations of anionic polymerization were concerned with reactions taking place in liquid ammonia. The system liquid ammonia-alkali metals will be dicussed first, followed by a review of heterogeneous reactions taking place on alkali or alkali-earth surfaces. Thereafter homogeneous electron-transfer processes and the addition of negative ions to monomer will be discussed. Finally some esoteric reactions, such as initiation by Lewis bases, charge-transfer complex initiation, etc. will be briefly reviewed. 

The study of homogeneous electron transfer processes in biological systems by means of electrochemical methods is now receiving increasing attention. For a number of small-sized redox proteins (e.g. cytochrome c, ferredoxines and azurine) a direct electron transfer at chemically modified electrodes has been achieved [26, 27]. These systems have been investigated by standard electrochemical techniques such as CV, RDEV, and impedance measurements (see chapter 1 of this volume). Information on direct electron transfer between a redox enzyme and the electrode can be found in papers [28-33]. 

The theory outlined here has also been developed to describe homogeneous electron transfer processes. The simplest outer sphere reactions that can be considered involve different oxidation states of the same molecule, e.g. 

In 2008, Weinstock [52] proposed a modification for the Marcus cross relation, which takes into account the relatively small size of 02 , and provides a correction that could, in principle, be applied to any homogeneous electron transfer process characterized by significant differences in size between the donors and acceptors. For this, a single experimentally accessible term was introduced into the general form of the MCR. This term quantitatively accounts for differences in size between electron donors and acceptors. 

Solution of alkali metals in liquid ammonia, containing the so-called solvating electrons, may be used as an alternative homogeneous system to initiate polymerization by an electron transfer process. This system suffers, however, from complications resulting from proton transfer from ammonia leading to the formation of NH2- ions, which in turn initiate further polymerization.4... 

One also obtains analogous findings with trace-crossing effects for the electropolymerization of thiophene and pyrrole. This cannot be explained by a simple linear reaction sequence, as presented in Scheme I, because it indicates competing homogeneous and heterogeneous electron transfer processes. Measurements carried out in a diluted solution of JV-phenylcarbazole provide a more accurate insight into the reaction mechanism (Fig. 2). 

Electron transfer processes leading to a product adsorbed in the interfacial region o are of practical interest. These processes include the deposition of a metal such as Cu or Pd at ITIES, the preparation of colloidal metal particles with catalytic properties for homogeneous organic reactions, or electropolymerization. 

Free radicals generally undergo one-electron transfer processes in homogeneous solution. Two-electron transfer processes, in which two radicals participate, are often highly exoergic. Typical examples are... 

Two-Electron Catalytic Reactions In a number of circumstances, the intermediate C formed upon transformation of the transient species B is easily reduced (for a reductive process, and vice versa for an oxidative process) by the active form of the mediator, Q. This mechanism is the exact counterpart of the ECE mechanism (Section 2.2.2) changing electron transfers at the electrode into homogeneous electron transfers from Q, as depicted in Scheme 2.9. In most practical circumstances both intermediates B and C obey the steady-state approximation. It follows that the current is equal to what it would be for the corresponding EC mechanism with a... 

A preliminary electrochemical overview of the redox aptitude of a species can easily be obtained by varying with time the potential applied to an electrode immersed in a solution of the species under study and recording the relevant current-potential curves. These curves first reveal the potential at which redox processes occur. In addition, the size of the currents generated by the relative faradaic processes is normally proportional to the concentration of the active species. Finally, the shape of the response as a function of the potential scan rate allows one to determine whether there are chemical complications (adsorption or homogeneous reactions) which accompany the electron transfer processes. 

As mentioned in Chapter 1, Section 2.2, it is quite common that a heterogeneous electron transfer process is complicated by homogeneous chemical reactions that involve the species Ox and/or Red. In this light, the chemical complications are classified as ... 

The disproportionation reaction (Eq. 2) of two tetrazolinyl radicals was studied by Umemoto [18a] and it was concluded that this reaction is a slow process, and therefore this process should also be ruled out as a fast d-step. Importantly, the difference between the redox potentials of cR and R (AEp = 0.25 V) favors the backward reaction. The feasibility of the backward reaction is substantiated by ESR experiments by Maender and Russell [20] who found that the mixture of formazan and tetrazolium salt gave rise to tetrazolinyl radicals. Finally, the solution electron transfer (Eq. 3) is possible as a homogeneous electron transfer (d-step) since it would be reasonable to expect that the redox potentials of the reacting species are very close. However, this reaction would imply dEp/dlogv slope of 19.7 mV (Table 1) which was not observed. Taking all the arguments into account it can be concluded that the mechanism shown in... 

Reaction rates for dissociative electron transfer processes are determined by the method of homogeneous electron transfer. The kinetic sequence is illustrated in Scheme 4.1, Linear sweep voltammetry is used to generate the radical-anion fi-om... 

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>. 

As in the homogeneous case, heterogeneous redox electrode reactions involve the chemical reorganization of the coordination spheres of the participating ions, which determines the kinetics of the overall electron transfer process because the electronic transition is a very fast event. 

One of the most intriguing aspects of electrochemistry involves the homogeneous chemical reactions that often accompany heterogeneous electron-transfer processes occurring at the electrode-solution interface. The addition or removal of an electron from a molecule generates a new redox state, which can be chemically reactive. A variety of mechanisms, some of which involve complicated sequences of electrode and chemical reactions, have been characterized. Several of the more common mechanisms with examples of applicable chemical systems are described next. More examples are given in Chaps. 21 and 23. 

To this point, we have considered only the electron transfer reactions that occur between the electrode and soluble substrates, that is, heterogeneous processes. In most cases, heterogeneous electron transfer reactions are sufficient to account completely for the shapes and diagnostic responses of voltammetric curves. It is well known, however, that in the solution layer adjacent to the electrode, second-order electron transfer reactions occur between electrolysis products and reactants. There is a growing body of information showing that under some circumstances these homogeneous electron transfer reactions present a more facile electron transfer pathway than do the heterogeneous reactions and... 

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