Electrochemical Electron-Transfer Reactions

As the field of electrochemical kinetics may be relatively unfamiliar to some readers, it is important to realize that the rate of an electrochemical process is the current. In transient techniques such as cyclic and pulse voltammetry, the current typically consists of a nonfaradaic component derived from capacitive charging of the ionic medium near the electrode and a faradaic component that corresponds to electron transfer between the electrode and the reactant. In a steady-state technique such as rotating-disk voltammetry the current is purely faradaic. The faradaic current is often limited by the rate of diffusion of the reactant to the electrode, but it is also possible that electron transfer between the electrode and the molecules at the surface is the slow step. In this latter case one can define the rate constant as  

i is the faradaic current, n is the number of electrons transferred per molecule, F is the Faraday constant, A is the electrode surface area, k is the rate constant, and Cr is the bulk concentration of the reactant in units of mol cm-3. In general, the rate constant depends on the applied potential, and an important parameter is ke, the standard rate constant (more typically designated as k°), which is the forward rate constant when the applied potential equals the formal potential. Since there is zero driving force at the formal potential, the standard rate constant is analogous to the self-exchange rate constant of a homogeneous electron-transfer reaction. 

Experimental values of AG and the pre-exponential factor were obtained from a plot of In k,. vs 1/T under the assumption that the slope is — AG /R, and the hidden assumption that AG is temperature independent (AS is zero). Comparison between the calculated and observed pre-exponential factor was used to infer significant non-adiabaticity, but one may wonder whether inclusion of a nonzero AS would alter this conclusion. From an alternative perspective, reasonable agreement was noted for the values of ke and the homogeneous self-exchange rate constant after a standard Marcus-type correction was made for the differing reaction types. 

Activation Parameters for Coupled Electron Transfer and Spin Change 

In a new twist on this subject, electrochemical activation parameters have been obtained for two series of redox couples that undergo coupled spin-state change and electron transfer (28). One series is [M(tacn)2]3+/2+ where M = Fe, Co, Ni, and Ru, and tacn = 1,4,7-triazacyclononane. The other is [Fe(pzb)2]+/0, where pzb-= hydrotris(pyrazol-l-yl)borate 

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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. 

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. 

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. 

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)... 

Medvedev, LG. (2006) The effect of the electron-electron interaction on the pre-exponential factor of the rate constant of the adiabatic electrochemical electron transfer reaction. Journal of Eiectroanaiytical Chemistry, 598,1-14. 

Schmickler W. and Mohr J. (2002), The rate of electrochemical electron-transfer reactions , J. Chem. Phys. 117, 2867-2872. 

As a consequence of these difficulties, a number of new methods and techniques have been developed for these purposes.In recent years, electrochemical electron transfer reactions have been shown to be highly efficient and, consequently, they serve as new tools in fluoro-organic synthesis. However, only a limited number of examples of electrosyntheses of fluoro-organic compounds, except for the well-established anodic perfluorination and anodic trifluoromethylation processes, were reported prior to the 1980s. 

This chapter deals with recent advances in the application of electrochemical electron transfer reactions to the synthesis of fluorinated organic substances. The effect of fluorine atoms on the reduction and oxidation potentials of organic compounds is discussed first. Subsequently, recent applications of the electrochemistry to the conversion and functionalization of fluoro-organics (building-block approach) are described. Finally, methods for selective electrochemical fluorination of organic molecules (direct fluorination approach) are briefly considered. 

Hence, we came to some apparently paradoxical situation when the kinetics of IVR in the bulk and electrochemical electron transfer reactions at the interface happen to be inherently entangled. Then, could one disentangle a pure electrochemical step from the impact of chemical electron transfer reaction and study it separately So far, this is the question with no clear answer. 

The title paper was enormously important by itself, but in addition it was the first step (and the cornerstone) in a long series of papers on electron-transfer reactions which were published by Marcus from 1956 to 1965. During those years he extended [3, 4] the theory to include, for instance, intramolecular vibrational effects, numerically calculated rates of self-exchange and cross reactions, electrochemical electron-transfer reactions (i.e. including electrodes), chemiluminescent electron transfers, the relation between nonequilibrium and... 

Quantum Theory of Electrochemical Electron-Transfer Reactions... 

After fifty years of research, the theory of electrochemical electron-transfer reactions is well developed, and has provided us with a basic understanding of the essentials. However, a number of important questions are still open, and remain the subject of ongoing research. We list what we believe to be the most important points ... 

Development of the quantum theory of electrochemical kinetics originates from the work of Gurney (1931), who suggested that an electrochemical electron transfer reaction be considered as a process of electron tunneling from the metal to the ion in the solution. Since that time, the theory has been developed further in the works of many investigators. At present, two main approaches in the theory of the elementary act of the electrochemical process can be distinguished. 

Subsequently, Marcus extended his theory to electrochemical electron transfer reactions/ " However, the role played by the electron energy spectrum in the electrode in these works was not elaborated. All the calculations were performed for a simplified model, where the potential energy surfaces for different electronic states were replaced by two potential energy surfaces (one for the initial state and one for the final state). Further calculations have shown that such considerations do not enable us to explain the fact that the transfer coefficient, a, for electrochemical reactions takes values in the interval from 0 to 1. In particular, it does not enable us to explain the existence of barrierless and activationless process (see Chapter 3 by Krishtalik in this volume). 

The first quantum mechanical calculations for nonadiabatic electrochemical electron transfer reactions at metals and semiconductors were performed by Dogonadze, Chizmadzhev, and Kuznetsov(1962-1964). In Ref. 27 the totally degenerated Fermi gas model was used to describe the state of the electrons in the electrode, and in Ref. 28 an integration over the energy spectrum was performed, taking account of the Fermi distribution of the electrons over a range of energy. Later that theory was extended to other processes at semiconductors and thin semiconductor films. 

Zhang, Y, Zhou, J., Lin, L., and Lin, Z. 2008. Determination of electrochemical electron-transfer reaction standard rate constants at nanoelectrodes Standard rate constants for ferrocenylmethyltrimethylam monium(III)/(II) and hexacyanoferrate(III)/(II). Electroanalysis 20 1490-1494. 

Long-term water-detergent (surfactant) interactions in systems where the water leak into the oil was stopped (or limited water presence occurred due to humidity condensation, which subsides when the oil becomes hot during the equipment exploitation) result in the formation of inverse micelles. It was also shown that the electrochemical electron-transfer reactions (either as direct redox charge transfer or through adsorption-mediated processes) for separated detergent and water are several orders of magnitude faster than the... 

Koper, M.T.M., Mohr, J.H., Schmickler, W. (1997). Quantum effects in adiabatic electrochemical electron-transfer reactions. Chem. Phys. 220 95-114. 

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