Consecutive charge-transfer reactions

The simplest type of complex electrochemical reactions consists of two steps, at least one of which must be a charge-transfer reaction. We now consider two consecutive electron-transfer reactions of the type  

For simplicity we assume that the intermediate stays at the electrode surface, and does not diffuse to the bulk of the solution. Let (j l0 and 0oo denote the standard equilibrium potentials of the two individual steps, and cred, Cint, cox the surface concentrations of the three species involved. If the two steps obey the Butler-Volmer equation the current densities j and j2 associated with the two steps are  

On application of an overpotential rj we have under stationary conditions  

For high anodic or cathodic overpotentials one of the partial current densities can be neglected  

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Some experimental methods to compensate or to minimize the influence of the capacitive current have been reviewed by MacDonald [22]. The reader is directed to the same reference for the theoretical treatments of more complex systems involving parallel and consecutive charge transfer reactions, coupled chemical reactions, as well as of more sophisticated performances of large amplitude galvanostatic techniques, e.g. current reversal and cyclic methods. 

Using the Berzins and Delahay equation for the case in which a single substance undergoes two consecutive charge transfer reactions (diffusion-controlled electrode processes) at sufficiently different potentials [19] ... 

There is another way of looking at these situations where the lack of a sufficient supply of the needs of the interface compels one to look at the transport processes in solution. The broader view demands that one see the charge-transfer reaction as preceded by adrift of the reaction participants to the interface. In fact, one must think of transport in solution and charge transfer as consecutive steps of an overall reaction. 

If these conditions are not satisfied, some process will be involved to prevent accumulation of the intermediates at the interface. Two possibilities are at hand, viz. transport by diffusion into the solution or adsorption at the electrode surface. In the literature, one can find general theories for such mechanisms and theories focussed to a specific electrode reaction, e.g. the hydrogen evolution reaction [125], the reduction of oxygen [126] and the anodic dissolution of metals like iron and nickel [94]. In this work, we will confine ourselves to outline the principles of the subject, treating only the example of two consecutive charge transfer processes O + n e = Z and Z 4- n2e — R. 

When a sequence of p consecutive potential pulses of the same length t is applied, the analytical expression of the surface excess of species O is, in line with the above discussion, identical to that given for a simple charge transfer reaction in Eq. (6.127) by changing k p for k p with ... 

More properly, the above remark refers to the initial step of this reaction. Studies performed using platinum and Sn02 electrodes indicate that the quinone/hydroquinone redox reaction involves two distinct, consecutive charge transfer steps. Also the hydroquinone oxidation at the Ti02 photoanode follows presumably a two-step mechanism. 

The electrolytic reduction of CO2 in neutral aqueous solution at a mercury pool cathode has been studied to establish the reaction mechanism and to obtain kinetic parameters by a steady-state galvanostatic method. The most plausible reaction is thought to involve the consecutive charge-transfer steps ... 

The overvoltage depends on the current density. When there is no net current flow, the overvoltage is equal to zero. Electrochemical processes are heterogeneous reactions consisting of consecutive steps. The overvoltage controls the kinetics of the charge-transfer reaction at the interface and is associated with the slowest step, abbreviated as the rate determining step. 

Two water molecules are oxidized by four consecutive charge-separation reactions through photosystem II to form a molecule of diatomic oxygen and four hydrogen ions. The outcoming electron in each step is transferred to a redox-active tyrosine residue followed by the reduction of a photoxidized... 

The consecutive reaction which preserves some of the light energy on an intermediate energy level can consist in a change of the chemical structure of the material. It is very often an ionization step or a charge transfer reaction. The reasons that the two latter... 

If in boundary metal solution, a consecutive charge transfer takes place in several steps, there is probability that complexes formed of partly reduced metal ions will accumulate in the solution till a certain equiUbrium concentration is reached. Then, the above-specified two groups of reactions become related, and the process of the equilibration acquires pecuUarities. Some of them were established in studying the system Cu Cu +, Cu+ [5] however, as far as we know, analogous complex systems have not been investigated thus far. In this relation, the analysis of the systems formed of metal ions of different oxidation number becomes important. 

There are also some questionable explanations for the inconsistency between a low Tafel slope and the inductive behavior that characterizes the consecutive charge transfer. One of them is to accept that the symmetry factor has a totally asymmetric value, such as the limiting values 0 or 1, and that it is strongly potential dependent the other is to deny the mechanistic significance of steady-state characteristics, that is, of the Tafel slope and reaction orders, because they are influenced by the sweep rate and waiting time arbitrarily chosen by the experimentalists. ... 

Most of the studies of ions formed by charge transfer have been concentrated on the unimolecular reactions of M+ ions formed in well-defined internal-energy states (e.g., fragmentation patterns6) and more recently have been concerned with rate-coefficient measurements.118 Some work has also been reported on consecutive ion-molecule reactions of M+ ions produced in well-defined internal states (mostly... 

Electrode reaction — The electrode reaction is an interfacial reaction (see -> interface) that necessarily involves a -> charge transfer step. The electrode (or interfacial) reaction involves all the processes (chemical reaction, structural reorganization, -> adsorption) accompanying the charge transfer step. The rate of this type of reaction is determined by one of the consecutive steps (i.e., by the most hindered or slowest one) and the overall rate is related to the unit area of the interface [i-v]. 

With or without additives in the electrolyte, the charge-transfer Cu/Cu2+ occurs in two consecutive one-electron steps, with Cu+ being formed as an intermediate (Eq. (20)). The reduction of cupric ion is a slow reaction, whereas the reduction of cuprous ion to metallic copper is a fast one. This means that without additives the formation of Cu(I) ions is the rate-determining step. 

Proton-coupled electron transfer (pcet) is an important mechanism for charge transfer in biology. In a pcet reaction, the electron and proton may transfer consecutively (et/pt or pt/et) or conceitedly (etpt). These mechanisms are analyzed and expressions for their rates presented. Features that lead to dominance of one mechanism over another are outlined. Dissociative etpt is also discussed, as well as a new mechanism for highly exergonic proton transfer. 

Figure 10. Coupled consecutive proton transfer pathway across the membrane. The actual number of binding sites is not known. For simplicity, only five binding sites (A1 througji As) are shown. Site A3 designates the Schiff base proton binding site. It is understood that the Schiff base is neutral when deprotonated and carries a positive charge when protonated. The reverse reactions are not shown but are important for the discussion. (Reproduced with permission from reference 82. Copyright 1990.)...

The dependence of the reaction rate on the film thickness suggests that the reaction takes place within the polymer layer, however, the depth of penetration into the layer depends on several parameters, including (among others) the time-scale of the experiment, the charge state, the morphology and the relative rate of consecutive transport and charge transfer steps. It is important to account for the fact that thick films are usually less dense than thin ones [363-370] (see also Chaps. 4-6). 

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