Redox outer-sphere electrode reaction

It is important to notice that the rate of a given outer sphere electrode redox reaction should be independent of the nature of the metal electrode if allowance is made for electrostatic work terms or double layer effects which will, of course, be dependent on the nature of the electrode material. Inner sphere reactions, on the other hand, are expected to be catalytic with kinetics strongly dependent on the electrode surface due to specific adsorption interactions. 

The field of modified electrodes spans a wide area of novel and promising research. The work dted in this article covers fundamental experimental aspects of electrochemistry such as the rate of electron transfer reactions and charge propagation within threedimensional arrays of redox centers and the distances over which electrons can be transferred in outer sphere redox reactions. Questions of polymer chemistry such as the study of permeability of membranes and the diffusion of ions and neutrals in solvent swollen polymers are accessible by new experimental techniques. There is hope of new solutions of macroscopic as well as microscopic electrochemical phenomena the selective and kinetically facile production of substances at square meters of modified electrodes and the detection of trace levels of substances in wastes or in biological material. Technical applications of electronic devices based on molecular chemistry, even those that mimic biological systems of impulse transmission appear feasible and the construction of organic polymer batteries and color displays is close to industrial use. 

In this picture, the electron transfer processes mediated by metallic electrodes (redox reactions in a heterogeneous phase) can also be classified to proceed according to outer-sphere or inner-sphere mechanisms (obviously, considering the electrode surface as a reagent). 

For the electron transfer of hydrated redox particles (the outer-sphere electron transfer), the electrode acts merely as a source or sink of electrons transferring across the compact double layer so that the nature of the electrode hardly affects the reaction kinetics this lack of influence by the electrode has been observed for the ferric-ferrous redox reaction. On the other hand, the electron transfer of adsorbed redox particles (the inner-sphere electron transfer) is affected by the state of adsorption so that the nature of the electrode exerts a definite influence on the reaction kinetics, as has been observed with the hydrogen electrode reaction where the reaction rate depends on the property of electrode. 

We consider a simple electron transfer reaction (an outer-sphere electron transfer) between h3 rated redox particles OX /RED and a metal electrode M as shown in Eqn. 8-1 ... 

We consider a simple redox electron transfer of hydrated redox particles (an outer-sphere electron transfer) of Eqn. -1 at semiconductor electrodes. The kinetics of electron transfer reactions is the same in principal at both metal and semiconductor electrodes but the rate of electron transfer at semiconductor electrodes differs considerably from that at metal electrodes because the electron occupation in the electron energy bands differs distinctly with metals and semiconductors. 

TABLE 8-1. Preference for the conduction band mechanism (CB) and the valence band mechanism (VB) in outer sphere electron transfer reactions of hydrated redox particles at semiconductor electrodes (SC) Eo = standard redox potential referred to NHE c, = band gap of semiconductors. [From Memming, 1983.]... 

In addition to simple reactions of electron transfer (outer-sphere electron transfer) between an electrode and hydrated redox particles, there are more complicated reactions of electron transfer in which complexation or adsorption of redox particles is involved. In such transfer reactions of redox electrons, the redox particles are coordinated with ligands in aqueous solution or contact-adsorbed on the electrode interface before the transfer of their redox electrons occurs after the transfer of electrons, the particles are de-coordinated from ligands or desorbed from the electrode interface. 

Figure 8-40 shows the electron transfer current of two redox reactions (outer-sphere electron transfer) observed at constant potential for platinum electrodes covered with a thin oxide film in acidic solutions as a function of the film thickness. As e3q>ected fium Eqns. 8-84 and 8-85, a linear relationship is observed between the logarithm of the reaction ciirrents and the thicknesses of the film. 

Figure 8-42 illustrates the anodic and cathodic polarization curves observed for an outer-sphere electron transfer reaction with a typical thick film on a metallic niobium electrode. The thick film is anodically formed n-type Nb206 with a band gap of 5.3 eV and the redox particles are hydrated ferric/ferrous cyano-complexes. The Tafel constant obtained from the observed polarization curve is a- 0 for the anodic reaction and a" = 1 for the cathodic reaction these values agree with the Tafel constants for redox electron transfers via the conduction band of n-lype semiconductor electrodes already described in Sec. 8.3.2 and shown in Fig. 8-27. 

Fig. 1. Schematic representation of the metal—electrolyte interface and reaction sites for outer-sphere (a, c) and inner-sphere (b) redox reaction paths at electrodes [12].

The mass transport rate coefficient, kd, for a RDE at the maximum practical rotation speed of 10000 per min"1 is approximately 2 x 10-2 cms-1 [28], which sets a limit of about 10 3 cms 1 for the electrode reaction kinetics. For the study of very fast electrode processes, such as some outer sphere redox reactions on noble metal electrodes under stationary conditions, higher mass transport rates in the solution adjacent to the electrode must be employed. 

Redox electrode reactions on metal electrodes constitute the simpler case for a theoretical approach to the problem. In particular, outer sphere redox electrode reactions not involving specific adsorption interactions have been treated successfully in analogy with homogeneous redox reactions in solution [54, 56], Approximate extension of the theoretical approach to the case of inner sphere redox reactions at electrodes has been done [56, 57b]. 

The transmission coefficient k — 1 for weak overlap of electronic states of reactants and products in the transition state. It is strong enough to be adiabatic but yet weak enough for the free energy of activation not to have an appreciable contribution from the resonance energy. This condition is almost fulfilled by outer sphere redox reactions at electrodes. 

Experimental attempts to verify the dependence of the transfer coefficient on the electrode potential have been made with simple outer sphere redox electrode reactions (see refs. 5—19 in ref. 70a). Corrections to experimental values of the apparent transfer coefficient due to double layer effects are performed by the use of eqn. (109), but the value of a calculated from experimental data depends on the assumptions about the location of the centre of charge in the transition state in the Helmholtz layer [70b]. 

The effect of upd on outer sphere redox electrode reaction kinetics has been studied [129], but no clear picture emerges because of mass transport limitations for those very fast kinetics. 

Only if the component processes I and II are independent of the electrode material, i.e. outer sphere redox reactions in the absence of double layer effects, is the mixed potential, EM, independent of the electrode. 

However, the mechanisms of conventional redox reactions and electrochemical reactions maybe quite different. Within the formalism of electron transfer theory, the electron transfer reactions at electrodes are usually of the outer-sphere type, whereas those that involve inorganic ions are often of the inner-sphere type [11]. 

Figure 18 gives typical cyclic voltammograms taken in four redox systems at relatively heavily doped diamond electrodes [92]. Outer-sphere reactions proceed in... 

Electron transfer rate constants of outer sphere redox reactions can be measured relatively easily at n-type semiconductor electrodes. This is because electrons are withdrawn from the surface under depletion conditions, so that their concentration is lower than in the bulk. Under ideal... 

In the second chapter, Appleby presents a detailed discussion and review in modem terms of a central aspect of electrochemistry Electron Transfer Reactions With and Without Ion Transfer. Electron transfer is the most fundamental aspect of most processes at electrode interfaces and is also involved intimately with the homogeneous chemistry of redox reactions in solutions. The subject has experienced controversial discussions of the role of solvational interactions in the processes of electron transfer at electrodes and in solution, especially in relation to the role of Inner-sphere versus Outer-sphere activation effects in the act of electron transfer. The author distils out the essential features of electron transfer processes in a tour de force treatment of all aspects of this important field in terms of models of the solvent (continuum and molecular), and of the activation process in the kinetics of electron transfer reactions, especially with respect to the applicability of the Franck-Condon principle to the time-scales of electron transfer and solvational excitation. Sections specially devoted to hydration of the proton and its heterogeneous transfer, coupled with... 

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