Single-Electron Charge Transfer Reactions

The rectification ratio is obtained by multiplying JFR by the reaction resistance Rr  

Substituting ac + aa = 1, for single-electron charge transfer reactions, the above expression reduces to that of Delahay et al.n 

By assuming D0 = DR (as a first approximation for the sake of simplicity), the equation can be written as 

In any fast multielectron transfer reaction all the electrons cannot be transferred in one step but only by a succession of single-electron transfer steps, whereas Eq. (6) was arrived at by Devanathan31 for the simple case in which it is assumed that the same step is rate determining in both directions, irrespective of the number of electrons involved in the reaction. 

If a two-electron charge transfer reaction takes place in two separate steps, each being accompanied by transfer of a single electron, the mathematical expression for the determination of kinetic parameters becomes more involved and complicated. 

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The present chapter will cover detailed studies of kinetic parameters of several reversible, quasi-reversible, and irreversible reactions accompanied by either single-electron charge transfer or multiple-electrons charge transfer. To evaluate the kinetic parameters for each step of electron charge transfer in any multistep reaction, the suitably developed and modified theory of faradaic rectification will be discussed. The results reported relate to the reactions at redox couple/metal, metal ion/metal, and metal ion/mercury interfaces in the audio and higher frequency ranges. The zero-point method has also been applied to some multiple-electron charge transfer reactions and, wheresoever possible, these results have been incorporated. Other related methods and applications will also be treated. 

Earlier studies generally involved the evaluation of kinetic parameters of reactions which are accompanied by single-electron charge transfer.116 Some reactions involving two-electron charge transfer were also studied, assuming either that both electrons are transferred in a single step or that the slower step in the two-step reaction is in overall control of the rate process. As described in this chapter for the first time, the faradaic rectification theory for... 

By using Delahay s equation, assuming that both electron charge transfers occur in a single step. In this case, the rate constant obtained for the slowest reaction is of the order of 10-5 cm/s (Table 2). 

This chapter offers a study of the application of the multipulse and sweep techniques Cyclic Staircase Voltammetry (CSCV) and Cyclic Voltammetry (CV) to the study of more complex electrode processes than single charge transfer reactions (electronic or ionic), which were addressed in Chap. 5. 

So far, we have considered the dynamics of chemical reactions within the adiabatic approximation. The motion of the atomic nuclei is, however, not always confined to a single electronic state as assumed in Eq. (1.5). This situation can, e.g., occur when two potential energy surfaces come close together for some nuclear geometry. The dynamics of such processes are referred to as non-adiabatic. This is a purely non-classical phenomenon [15]. Examples of reactions that involve non-adiabatic transitions are charge-transfer reactions, i.e., reactions in which charge is transferred between reactants. 

The discussions in sections 3.2.1 and 3.2.2 and the form of Butler-Volmer equation presented above are based on the assumption of single step electron transfer reaction as the rate limiting process. However, in SOFC modeling literature it is quite common to consider the charge transfer reactions in a global picture. Generally the Butler-Volmer equation is written as... 

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