Rates of Electron Transfer Reactions

In the same way that we considered two limiting extremes for ligand substitution reactions, so may we distinguish two types of reaction pathway for electron transfer (or redox) reactions, as first put forth by Taube. For redox reactions, the distinction between the two mechanisms is more clearly defined, there being no continuum of reactions which follow pathways intermediate between the extremes. In one pathway, there is no covalently linked intermediate and the electron just hops from one center to the next. This is described as the outer-sphere mechanism (Fig. 9-4). 

The second mechanism involves the formation of a covalent bridge through which the electron is passed in the electron transfer process. This is known as the inner-sphere mechanism (Fig. 9-5). 

The inner-sphere mechanism is restricted to those complexes containing at least one ligand which can bridge between two metal centers. The commonest examples of such ligands are the halides, hydroxy or oxo groups, amido groups, thiocyanate 

The scheme in Fig. 9-5 above illustrates the case in which the bridging ligand, X, is transferred from metal center Mi to M2 in the course of the reaction. Although this is not a necessary consequence of an inner-sphere pathway, it is often observed, and provides one method for establishing the mechanism. 

In the case of other systems in which one or both of the reactants is labile, no such generalization can be made. The rates of these reactions are uninformative, and rate constants for outer-sphere reactions range from 10 to 10 sec b No information about mechanism is directly obtained from the rate constant or the rate equation. If the reaction involves two inert centers, and there is no evidence for the transfer of ligands in the redox reaction, it is probably an outer-sphere process. 

---

The field of modified electrodes spans a wide area of novel and promising research. The work dted in this article covers fundamental experimental aspects of electrochemistry such as the rate of electron transfer reactions and charge propagation within threedimensional arrays of redox centers and the distances over which electrons can be transferred in outer sphere redox reactions. Questions of polymer chemistry such as the study of permeability of membranes and the diffusion of ions and neutrals in solvent swollen polymers are accessible by new experimental techniques. There is hope of new solutions of macroscopic as well as microscopic electrochemical phenomena the selective and kinetically facile production of substances at square meters of modified electrodes and the detection of trace levels of substances in wastes or in biological material. Technical applications of electronic devices based on molecular chemistry, even those that mimic biological systems of impulse transmission appear feasible and the construction of organic polymer batteries and color displays is close to industrial use. 

An interesting approach to measuring rates of electron transfer reactions at electrodes is through the study of surface bound molecules (43-451. Molecules can be attached to electrode surfaces by irreversible adsorption or the formation of chemical bonds (461. Electron transfer kinetics to and from surface bound species is simplified because there is no mass transport and because the electron transfer distance is controlled to some degree. 

The rates of electron-transfer reactions can be well predicted provided that the electron transfer is a type of adiabatic outer-sphere reaction and the free-energy change of electron transfer and the reorganization energy (X) associated with the electron transfer are known [1-7]. This means that electron-transfer reactions can be designed quantitatively based on the redox potentials and the reorganization energies of molecules involved in the electron-transfer reactions. 

In a paper, Jortner stated that information about solvation dynamics can be obtained from (1) solvation of the electron, (2) solvation of a dipole, and (3) extracting information from the rates of electron transfer reaction [3,4]. We have added to these... 

When the above factors are put under control, the possibility of changing the ligand L in the pentacyano(L)ferrate complexes adds a further dimension for studying systematic reactivity changes, brought out by the controlled modification of the redox potentials of the Fe(II)-Fe(III) redox couples. In this way, the rates of electron transfer reactions between a series of [Fen(CN)5L]re complexes toward a common oxidant like [Coin(NH3)5(dmso)]3+ showed a variation in agreement with Marcus predictions for outer-sphere electron transfer processes, as demonstrated by linear plots of the rate constants versus the redox potentials (123). 

Charged interphases may also be exploited to create high local concentrations of electron acceptors which affect the rate of electron transfer reactions confined within these restricted reaction volumes and diminish considerably the efficiency of the corresponding back-transfer [24], These results have been primarily applied in photochemical conversion projects [22,25], but technically more interesting applications may be found in their use for the development of new specific analytical procedures (e.g., optical or photoelectrochemical probes). High local concentrations are also of considerable interest in the optimization of photochemical dimerization reactions [22], as the rate of bimolecular reactions between excited and ground state molecules confined in an extremely restricted reaction volume (microreactor) will be considerably enhanced. In addition, spatial gradients of polarity may lead to preferential structures of the solvated substrate and, hence, to the synthesis of specific isomers [24, 22, 26], Similar selectivities have been found when monomolecular photochemical or photoinduced reactions [2,3] are made via inclusion complexes [27,28]. 

The model of thermal diffusion, however, suffers from the following shortcomings. First, it does not agree with the results of direct measurements of the rate of diffusion-controlled electron transfer reactions near the temperatures of solid matrix devitrification (cf. Chap. 6, Sect. 4). Extrapolation of the values obtained in these experiments to the region of lower temperatures has shown that at these temperatures the rate of diffusion must be many orders of magnitude less than the observed rates of electron transfer reactions. 

A review has examined the use of radical anions in elucidation of the role of electron transfer in nucleophilic reactions through the determination of rates of electron-transfer reactions or obtaining reduction potentials of short-lived radical species.203 The control of conjugation and high-spin formation of radical anions of linear and ladder-type n-... 

Buhks E. BixonM. Jortner J. NavonG. Quantum effects on the rates of electron-transfer reactions. J. Phys. Chem. 1981, 85, 3759-3762. 

Marcus theory (Marcus, 1968, 1969), originally developed to interpret the rates of electron transfer reactions, has been successfully applied to proton transfer reactions as well. The theory relates... 

The above equations predict the absolute rates of electron-transfer reactions, but by far the most popular and useful aspect of the Marcus theory is comparison of rates of different, related reactions. 

One particular example of the use of pulse radiolysis to general chemistry was the work of Miller and co-workers on the rates of electron-transfer reactions. These studies, which were begun using reactants captured in glasses, were able to show the distance dependence of the reaction of the electron with electron acceptors. Further work, where molecular frameworks were able to fix the distance between electron donors and acceptors, showed the dependence of electron-transfer rate on the energetics of the reaction. These studies were the first experimental confirmation of the electron transfer theory of Marcus. 

The influence of surface oxide and of adsorbed substances on the rates of electron transfer reactions is still often obscure, especially where irreversible half-reactions are involved. 

It was shown that the rate of electron-transfer reactions substantially changes via the introduction of an additional electrolyte into solution [363, 367]. The variation of reaction rate constants depends on the type of anion added. Thus, this effect is not caused by ionic strength variations and is related to the formation of the outer-sphere complexes. 

Such behaviour is quite common to the semiconductors and also to the oxide-covered metal (especially valve metal) electrodes . It is not unusual that the rates of electron-transfer reactions on the latter materials are by 10 orders of magnitude smaller than on noble metal electrodes. 

The rate of electron transfer reactions depends on the difference in the redox potentials of educts and products. Since an alkyl radical possesses an unpaired electron in a non-bonding orbital, electron transfer reactions to many metals salts often occur with high rates. The higher are the SOMO energies of the radicals, the faster is the electron transfer. 

As suggested above, by recording an approach curve or voltammogram with the tip close to a substrate, one can study the rates of electron transfer reactions at electrode surfaces (Chapter 6). Because mass transfer rates at the small tip electrodes are high, measurements of fast reactions without interference of mass transfer are possible. As a rule of thumb, one can measure k° values (cm/s) that are of the order of Did, where D is the diffusion coefficient (cm2/s). For example, k° for ferrocene oxidation at a Pt electrode in acetonitrile solution was measured at a 1 /xm radius tip at a d of about 0.1 /xm yielded a value of 3.7 cm/s (24). The use of small tips and small currents decreases any interference from uncompensated resistance effects. 

The rate of electron transfer reactions (ETRs) is strongly influenced by the surface composition of the metal. As most materials are covered by oxides, their electronic properties will determine the rate of ETR. Therefore, metals that are covered by electron conducting or semiconducting oxides such as iron or zinc will show a higher ETR rate at the substrate-polymer interface in comparison to materials that form highly insulating oxides such as aluminum. 

In this section we refer, selectively, to studies of medium effects on the rates of electron transfer reactions, which can be classed as equilibrium effects in the sense that they affect the stability, but not the lifetime of the transition state. The principle of calculating solvent reorganization energies, Aout equation (7), in terms of a dielectric continuum model has been critically examined and placed on a sounder thermodynamic basis than before. The two equations frequently cited are (9a) and (9b), where D, and Dy are the displacement, or induction,... 

---