Electron transfer theory electrodes

In this chapter, we wiU review electrochemical electron transfer theory on metal electrodes, starting from the theories of Marcus [1956] and Hush [1958] and ending with the catalysis of bond-breaking reactions. On this route, we will explore the relation to ion transfer reactions, and also cover the earlier models for noncatalytic bond breaking. Obviously, this will be a tour de force, and many interesting side-issues win be left unexplored. However, we hope that the unifying view that we present, based on a framework of model Hamiltonians, will clarify the various aspects of this most important class of electrochemical reactions. 

The theory of electron transfer to electrodes has been worked out by various... 

The basic division between the roots and the more modern papers is arbitraiy (1931-1964 is about one generation). The basic theory of proton and electron transfer at electrodes was formulated by Gurney in 1931 and by Weiss in 1954. 

However, the mechanisms of conventional redox reactions and electrochemical reactions maybe quite different. Within the formalism of electron transfer theory, the electron transfer reactions at electrodes are usually of the outer-sphere type, whereas those that involve inorganic ions are often of the inner-sphere type [11]. 

Some notions of the mechanism of electron transfer were given in Section 4.2. Any theory must be realistic and take into account the reorientation of the ionic atmosphere in mathematical terms. There have been many contributions in this area, especially by Marcus, Hush, Levich, Dog-nadze, and others5-9. The theories have been of a classical or quantum-mechanical nature, the latter being more difficult to develop but more correct. It is fundamental that the theories permit quantitative comparison between rates of electron transfer in electrodes and in homogeneous solution. 

Refs. [i] Born M (1920) Z Phys 1 45 [ii] Marcus Y (1997) Ion properties. Marcel Dekker, New York [iii] Rashin AA, Honig B (1985) ] Phys Chem 89 5588 [iv] Stilly WC, TempczykA, Hawley RC, Hendrickson TA (1990) ] Am Chem Soc 112 6127 [v] Rashin AA (1990) / Phys Chem 94 1725 [vi] Shoichet BK, Leach AR, Kuntz ID (1999) Proteins 34 4 [vii] Marcus RA (1977) Theory and application of electron transfer at electrodes and in solutions. In Rock PA (ed) Special topics in electrochemistry. Elsevier, Amsterdam, pp 61 [viii] Millery C/ (1995) Heterogeneous electron transfer kinetics at metallic electrodes. In Rubinstein I (ed) Physical electrochemistry. Marcel Dekker, New York, pp 46-47... 

The - Marcus theory [vi-vii] gives a unified treatment of both heterogeneous electron transfer at electrodes and homogeneous electron transfer in solutions. 

The model of Presnov and Trunov [341,345] is based on the transition state theory and modern ideas on electron transfer at electrodes, and allows a quantitative calculation of the rate of oxygen electroreduction based on... 

An important subject in this chapter on Electron transfer at electrodes and interfaces is to draw an analogy between electrochemical and interfacial electron transfer between two solid phases. Any theory dealing with electron transfer has a thermodynamic and a kinetic basis. In Section 4.2, it was shown that electrons flow or tunnel in the direction of decreasing electrochemical potential the gradient of the electrochemical potential is the driving force behind a directed flow of electrons,... 

Mechanism and Theory of Outer Sphere Electron Transfers at Electrodes... 

Hush N. S. (1961), Adiabatic theory of outer sphere electron transfer at electrodes , J. Chem. Soc. Faraday Trans. 57, 557-580. 

Here a value of AG = 0.7 eV is found, which leads to A = 2.8 eV [66]. This rather large value is mainly due to an inner sphere reorganization (see Section 6.1.2). Much smaller values are obtained with pure outer sphere redox systems, for instance metallocenes. In the latter cases AG values in the order of 0.2-0.26 eV have been reported [67], i.e. values which correspond to A = 0.7-1 eV. There are other cases such [Fe(CN)6] where one would also expect an outer sphere reorganization but rather high values have been found (AG = 0.55 eV A = 2.2 eV) [67]. In this context it should also be mentioned that modern theories on electron transfer at electrodes have shown that the A values also depend on the distance of the electron acceptor or donor molecules from the electrode surface [65]. 

In electron-transfer theory, the extent of interaction or electronic coupling between two reactants (or between a reactant and the electrode) is often described in terms of adia-baticity. If the interaction is strong, there is a splitting larger than 4T in the energy curves at the point of intersection (e.g., Figure 3.6.6a). It leads to a lower curve (or surface) pro-... 

One important question in the light of current electron transfer theories [85-87] is that of the transition between stepwise (electron transfer and bond cleavage as separate elementary steps) or concerted (dissociative electron transfer [88]) mechanisms. For the two extremes, one expects largely different activation parameters for the electron transfer at an electrode. In particular, in contrast to the simple Butler-Vohner relationship (Eq. 18) with a constant transfer coefficient, potential dependent a values become evident. The experimentally accessible apparent transfer coefficient... 

During polarization, various electrode processes can occur such as electrochemical dissolution, O2 evolution and oxide formation during anodic polarization, and surface reduction and H2 formation during cathodic polarization. It must be emphasized that the theory derived above is not quantitatively applicable here because, in most processes, a strong interaction between semiconductor and electrolyte is involved, whereas the electron transfer theory is only valid for weak interactions, i.e., it is applicable only for redox processes. The other processes, electrochemical dissolution, etc., will be treated briefly before discussing pure electron transfer reactions (redox processes) because they present the basic behavior of semiconducting electrodes. 

In North America the theory is associated with the name of Marcus and referred to as the Marcus theory. However, Hush in Australia and Levitch and Dogonadze in the U.S.S.R. have made original contributions. Marcus started from the transition-state theory for ionic reactions. Hush from solid-state electron-transfer theory and Levitch from a consideration of reactions at electrodes. All arrived at essentially the same result, although using different terminologies. More recently, Tachiya and co-workers have developed a model based on the electrostatic interaction of the reactants with a polar solvent which also reduces to the same result under certain conditions. The version of the theory developed by Marcus has remained predominant for kinetic studies because it is framed in more familiar terminology and yields relationships that appear simple to test by experiment. 

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