Electron transfer electrochemical

In Chapter 16 we have focused on electron transfer processes of the following characteristics (1) Two electronic states, one associated with the donor species. 

While the process (17.1) involves two electronic states, one on each reactant, a macroscopic metal electrode is characterized by a continuum of electronic states with average occupation given by the Fermi function in terms of the 

In a typical electrochemical setup the potential difference between the interiors of the metal and the solution is controlled, so that the direction and rate of electron transfer can be monitored as functions of this voltage. 

It gives 1 and dir/Lz in the limit of large and small values of the Landau-Zener parameter, respectively. 

The expression for the transition probability per unit time W taking into account the process of activation has the form 

The change in the inner-sphere structure of the reacting partners usually leads to a decrease in the transition probability. If the intramolecular degrees of freedom behave classically, their reorganization results in an increase in the activation barrier. In the simplest case where the intramolecular vibrations are described as harmonic oscillators with unchanged frequencies, this leads to an increase in the reorganization energy  

In the case where they represent quantum vibrational modes, this leads to the appearance of a small tunnel factor in the transmission coefficient k.  

Let us consider a cathode electron transfer process at metal electrode. The role of the electron donor is played here by the metal electrode. The specific feature of this donor consists of the fact that its electron energy spectrum is practically continuous 

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The smallness of the electron transmission coefficient for the transition from individual energy levels does not mean that aU electrochemical electron transfer reactions should be nonadiabatic. If the inequality opposite to Eq. (34.33) is fulfilled. 

Electrochemical Electron Transfer From Marcus Theory to Electrocatalysis... 

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. 

Figure 2.1 Classification of electrochemical electron transfer reaction on metal electrodes. (See color insert.)...

Schmickler W. 1996. Interfacial Electrochemistry. New York Oxford University Press. Schmickler W, Koper MTM. 1999. Adiabahc electrochemical electron-transfer reactions involving frequency changes of iimer-sphete modes. Electrochem Comm 1 402-405. Schmickler W, Mohr J. 2002. The rate of electrochemical electron-transfer reachons. J Chem Phys 117 2867-2872. 

Marcus, R. A., Chemical and electrochemical electron-transfer theory, Ann. Rev. Phys. Chem., 15, 155 (1964). 

Both the initial- and the final-state wavefunctions are stationary solutions of their respective Hamiltonians. A transition between these states must be effected by a perturbation, an interaction that is not accounted for in these Hamiltonians. In our case this is the electronic interaction between the reactant and the electrode. We assume that this interaction is so small that the transition probability can be calculated from first-order perturbation theory. This limits our treatment to nonadiabatic reactions, which is a severe restriction. At present there is no satisfactory, fully quantum-mechanical theory for adiabatic electrochemical electron-transfer reactions. 

A. Insights into the Mechanism of the Tl3+/ Tl+ Self-Exchange Reaction VII. Electrochemical Electron-Transfer Reactions... 

Here kf and kb are the adsorption and desorption constants when 9 —> 0. The derivation of the equation above is similar to establishment of the Butler-Volmer kinetic law for electrochemical electron transfer reactions, where the symmetry factor, a, is regarded as independent from the electrode potential. Similarly, in the present case, the symmetry factor, a, is assumed to be independent of the coverage, 9. 

However, for electrochemical electron transfer reactions at a metal electrode, one gets ... 

The best way to search for the existence of an inverted region (if any) would be to use a single electrochemical electron transfer reaction in one solvent medium at a particular electrode and determine the effect of high overpotential on the reaction rate or the current density. Many experiments were carried out at organic spacer-covered ( 2.0 nm thick) electrodes to search for the inverted region for the outer-sphere ET reactions however, no inverted region was observed." ... 

In general, the experimental resnlts presented emphasize some distinction between chemical and electrochemical electron-transfer reactions. At the same time, both kinds of reactions share a fair number of features. A greater combination of these two methods in the organic chemistry of ion-radicals would seem to be fruitful. 

Electrochemical electron-transfer rate constants have been measured less frequently... 

From a description of the geometric structure of electrified interfaces we moved to a description of models for electrochemical electron transfer across an electrode interface. The science of atomic scale electrochemistry was presented with an emphasis on the bonding of water molecules and anions on electrode surfaces. Subsequently, we presented an in-depth description of the role of surface bonding in a number of important electrocatalytic processes for energy conversion. We have attempted to illustrate how closely surface bonding and catalytic activity are related. 

The value for X2 is the same as that for this same reactant in an ordinary homogeneous or electrochemical electron transfer occurring at the same R and can be estimated from them, as described later (6). AF0/int is known for many reactions of the solvated electron, and w can be estimated approximately. Accordingly, a theoretical value of AF can be calculated from Equation 7 once X/ is known. Either X/ can be calculated from other sources (it depends on the model of the solvated electron) or a value can be used which best fits data on k t for several reactions, or both. In making such calculations it should be noted that AF is not highly accurately given by Equation 7, because of the various... 

In electrochemical electron transfer reactions, the value of the rate constant kei at zero activation overpotential yields a value of AF ei. The latter equals — RT n(kei/ 0A cm. sec. 1)> and the theoretical expression for AF ei is (5)... 

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