Electron-transfer reactions electrode kinetics

It should be noticed that, unlike consecutive electron transfer reactions whose kinetics are determined by the slowest process, mixed potentials are determined by the fastest of several possible occurring electrode reactions. 

The rate of an electrochemical process can be limited by kinetics and mass transfer. Before considering electrode kinetics, however, an examination of the nature of the iaterface between the electrode and the electrolyte, where electron-transfer reactions occur, is ia order. 

The oxidation or reduction of a substrate suffering from sluggish electron transfer kinetics at the electrode surface is mediated by a redox system that can exchange electrons rapidly with the electrode and the substrate. The situation is clear when the half-wave potential of the mediator is equal to or more positive than that of the substrate (for oxidations, and vice versa for reductions). The mediated reaction path is favored over direct electrochemistry of the substrate at the electrode because, by the diffusion/reaction layer of the redox mediator, the electron transfer step takes place in a three-dimensional reaction zone rather than at the surface Mediation can also occur when the half-wave potential of the mediator is on the thermodynamically less favorable side, in cases where the redox equilibrium between mediator and substrate is disturbed by an irreversible follow-up reaction of the latter. The requirement of sufficiently fast electron transfer reactions of the mediator is usually fulfilled by such revemible redox couples PjQ in which bond and solvate... 

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. 

An interesting approach to measuring rates of electron transfer reactions at electrodes is through the study of surface bound molecules (43-451. Molecules can be attached to electrode surfaces by irreversible adsorption or the formation of chemical bonds (461. Electron transfer kinetics to and from surface bound species is simplified because there is no mass transport and because the electron transfer distance is controlled to some degree. 

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. 

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 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. 

In Chapter 7 general kinetics of electrode reactions is presented with kinetic parameters such as stoichiometric number, reaction order, and activation energy. In most cases the affinity of reactions is distributed in multiple steps rather than in a single particular rate step. Chapter 8 discusses the kinetics of electron transfer reactions across the electrode interfaces. Electron transfer proceeds through a quantum mechanical tunneling from an occupied electron level to a vacant electron level. Complexation and adsorption of redox particles influence the rate of electron transfer by shifting the electron level of redox particles. Chapter 9 discusses the kinetics of ion transfer reactions which are based upon activation processes of Boltzmann particles. 

M p = (z - l)F(pJRT. E is the electrode potential, is the standard potential, or more exactly the formal potential when activity effects cannot be neglected, and z is the charge number of the reactant. Thus, the current-electrode potential relationship characterizing the kinetics of an outer sphere electron-transfer reaction is given by (22) (/ is the current flowing through... 

Several important energy-related applications, including hydrogen production, fuel cells, and CO2 reduction, have thrust electrocatalysis into the forefront of catalysis research recently. Electrocatalysis involves several physiochemical environmental dfects, which poses substantial challenges for the theoreticians. First, there is the electric potential which can aifect the thermodynamics of the system and the kinetics of the electron transfer reactions. The electrolyte, which is usually aqueous, contains water and ions that can interact directly with a surface and charged/polar adsorbates, and indirectly with the charge in the electrode to form the electrochemical double layer, which sets up an electric field at the interface that further affects interfacial reactivity. 

As shown by the cyclic voltammetric response in Fig. 10, the peak potential separation of the initial Mn(II,II) — Mn(II,III) electrode reaction is much larger than that of the other steps. This suggests significant inner-shell reorganization and a small rate of heterogenous electron transfer for oxidation of the fully reduced Mn(II,II) state. Similar kinetic sluggishness is observed for Mn(III)/Mn(II) electron-transfer reactions of some mononuclear complexes (see Sects 16.1.2 and 16.1.3). 

Fig. 8. Standard free energy diagram for a two-step electron transfer reaction at an electrode with variation of the transition state with potential, (a) At Ej, the rds corresponds to transition state 1. (c) At E2, the transition state controlling the kinetics is 2. (b) corresponds to E. ...

The kinetics of electron transfer reactions at electrodes can be explained either by surmounting an activation barrier due to the chemical reorganization of the reactants or by tunnelling through the potential barrier across the electrode—solution interface. 

At the equilibrium potential, both anodic and cathodic processes of a single electron transfer reaction take place at the same exchange rate (exchange current density) and no net current is observed through the external circuit. The exchange rate reflects the kinetics of the overall reaction and, in many cases, the electrocatalytic properties of the electrode surface. The open circuit potential, in this case, is the equilibrium potential and is therefore a thermodynamic quantity independent of kinetic factors and is related to the activities in solution through the Nemst law. 

The investigation of electrode kinetics has one paramount advantage over other kinetic studies the rate of the electron transfer reaction... 

Quantitative studies using LSV and CV can be carried out for both heterogeneous charge transfer kinetics and the kinetics of homogeneous chemical reactions coupled to charge transfer at electrodes. These methods should continue to play a major role in the study of electron transfer reactions. 

Chlorobenzonitrile and adrenaline, our second example, both give electrode products that are unstable with respect to subsequent chemical reaction. Because the products of these homogeneous chemical reactions are also electroactive in the potential range of interest, the overall electrode reaction is referred to as an ECE process that is, a chemical reaction is interposed between electron transfer reactions. Adrenaline differs from/ -chlorobenzonitrile in that (1) the product of the chemical reactions, leucoadrenochrome, is more readily oxidized than the parent species, and (2) the overall rate of the chemical reactions is sufficiently slow so as to permit kinetic studies by electrochemical methods. As a final note before the experimental results are presented, the enzymic oxidation of adrenaline was known to give adrenochrome. Accordingly, the emphasis in the work described by Adams and co-workers [2] was on the preparation and study of the intermediates. 

In the first region, the current is completely independent of rotation rate of the electrode and increases exponentially, which means that in this region the current (or reaction rate) is mainly controlled by electron transfer and not by transport phenomena. This allows a study of the kinetics and the mechanism of the electron-transfer reaction of the oxidation of dithionite. The third region shows a well-defined limiting-current plateau. This indicates that in this region, electron transfer is so fast that the overall reaction rate is controlled by transport only. This is confirmed by a linear relationship between limiting-current and square root of the rotation rate of the electrode. In this region, it is not possible to study the kinetics and the mechanism, but such conditions are suitable for electroanalytical purposes and sensor development (see sections 6.5 and 6.7). 

The kinetics of an electron transfer reaction are described by the heterogeneous electron transfer rate constants, kj ed and k°x, where the subscript s indicates that the process takes place at an electrode surface. The values of Zcsred and kfx depend exponentially on E as seen in Equations 6.10 and 6.11 ... 

When a constant potential, E, is applied to the electrode immersed in the solution containing species A and L such that the electron transfer reactions take place, the mass transport supposed by pure diffusion to and from the electrode surface, in the presence of an excess of supporting electrolyte, is described by the following differential diffusive-kinetic equations system ... 

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