Electron Transfer Processes at Electrodes

The basic reaction between two molecules has been given in Eq. (6.1). The corresponding redox reaction at an electrode is given by 

In terms of the Marcus theory the rate constant for the electron transfer is given by 

The reorganization energy can be treated in a similar way. The inner sphere component is only half of that for a self-exchange reaction because only one ion is involved, i.e. 

In the case of the outer sphere component, Aout, it has to be realized that only one molecule needs to be considered, either a donor or an acceptor molecule, i.e. only thel/2rD or the l/ A term has to be considered in Eq. (6.19). It must also be taken into account that the reacting ion forms an image charge in the metal electrode having the same distance from the surface as the ion. For metal electrodes this leads to 

The question arises, however which can be used for reactions at a semiconductor electrode In this context a more general equation is of interest which has recently been derived by Marcus by using a dielectric continuum model [9]. He considered two adjacent dielectrics having charges in both phases, e.g. ions in two immiscible liquids. We omit here the complete derivation because the basic physical picture for the reorganization of the liquid has already been presented above. The final result as derived by Marcus [9] is given by  

The question arises, however which A m can be used for reactions at a semiconductor electrode In this context a more general equation is of interest which has recently been derived by Marcus by using a dielectric continuum model [11,12]. 

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As a result, a stationary voltammogram cannot be expected under these conditions since it shows a behavior similar to that of a macrointerface with respect to the egress of the ion, and features of radial diffusion for the ingress process, reaching a time-independent response [73, 74]. Both are consequences of the markedly different diffusion fields inside and outside the capillaries which give rise to very different concentration profiles (see Fig. 5.21). A similar voltammetric behavior has been reported for electron transfer processes at electrode I solution interfaces where the diffusion fields of the reactant and product species differ greatly. 

Applicability of Time-Dependent Perturbation Theory for Electron Transfer Processes at Electrodes... 

The diagram shown in Fig. 3.10 is now widely used to describe electron transfer processes at electrodes, and it has the merit that it can be extended readily to the discussion of electron transfer at semiconductor and insulator electrodes [16]. The theoretical basis for the diagram is to be found in the fluctuating energy level model of electron transfer which has been discussed by Marcus [12,13], Gerischer [17-19], Levich [20], and Dogonadze [21]. 

An electron-transfer process at electrode/electrolyte interface can often have two types of chemical reactions. One is the electron-transfer reaction coupled with heterogeneous chemical reactions including those surface adsorption processes that... 

C19-0123. A cell is set up using two zinc wires and two solutions, one containing 0.250 M ZnCl2 solution and the other containing 1.25 M Zn (N03)2 solution, (a) What electrochemical reaction occurs at each electrode (b) Draw a molecular picture showing spontaneous electron transfer processes at the two zinc electrodes, (c) Compute the potential of this cell. 

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... 

Lantz, J. M. and Corn, R. M. (1994) Electrostatic field measurements and hand fiattening during electron-transfer processes at single-crystal Ti02 electrodes by electric field-induced optical second harmonic generation. J. Phys. Chem., 98, 4899-4905. 

A solid-liquid interface will have three aspects to its structure the atomic 1.1 structure of the solid electrode, the structure of any adsorbed layer and the Structure structure of the liquid layer above the electrode. All three of these are of fundamental importance in the understanding of the electron transfer processes at the core of electrochemistry and we must consider all three if we are to arrive at a fundamental understanding of the subject. 

The cyclic voltammograms of thiadiazole fused [2,5-(l,3-dithiol-2-ylidene)-l,3,4,6-tetrathiapentalenes], BDT-TTPs 88, in benzonitrile exhibited four pairs of redox waves corresponding to one-electron transfer processes at 4-0.60, 4-0.81, 4-1.30, and 4-1.47 V (vs. saturated calomel electrode (SCE)). The El values are a little higher than that of 4,5-bis(methylthio)-BDT-TTP (4-0.49 V). The difference is attributed to the electron-withdrawing character of the fused thiadiazole ring on the bicycle <1997SM(86)1821>. 

The Role of Interface States in Electron-Transfer Processes at Photoexcited Semiconductor Electrodes... 

A dendrimer consisting of multiple identical and non-interacting redox units, able to reversibly exchange electrons with another molecular substrate or an electrode, can perform as a molecular battery [64, 65]. The redox-active units should exhibit chemically reversible and fast electron transfer processes at easily accessible potential difference and chemical robustness under the working conditions. 

Ftg. 11 Reaction coordinate diagrams for simple heterogeneous electron transfer processes at an electrode held at a potential of for a range of differing values... 

When the heterogeneous electron-transfer process at the electrode becomes slow and irreversible, the use of the direct OTTLE/Nernst experiment is inconvenient because of the uncertainties associated with a slow equilibration process. A mediated OTTLE/Nernst experiment should rather be considered, where a redox mediator Mox/Mred characterized by a high heterogeneous rate constant is added to the cell (Eq. 111). The concentration ratio of the mediator couple will be adjusted quickly to the applied electrode potential E and, furthermore, it will be in a redox equilibrium (Eq. 112) with the redox pair O/R in the bulk solution, according to Eq. 113. 

It is a point peculiar to electrochemical reaction kinetics (77), however, that the rates of charge-transfer processes at electrodes measured, as they have to be, at some well-defined potential relative to that of a reference electrode, are independent of the work function of the electrocatalyst metal surface. This is due to cancellation of electron-transfer energies, O, at interfaces around the measuring circuit. In electrochemistry, this is a well-understood matter, and its detailed origin and a description of the effect may be found, among other places, in the monograph by Conway (77). 

It is fair to say that the effect of ultrasound upon the fundamental electron transfer processes at an electrode have been less widely studied than the effects upon mass transport phenomena. Electrode kinetics is defined by the Butler—Volmer equation, which by a series of practical assumptions reduces to the Tafel equation [44],... 

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