Electron transfer, kinetics

Continuing the study of simple outer-sphere electron transfer reactions, 

The first formulation is more directly suited to the case of reactants in solution and the second to attached reactants. In the first case, the rate constants have the dimensions length time typically cm s, whereas in the second case, they have the dimensions of time-1, typically s When these rate constants are very large, equilibrium is achieved, corresponding to Nernst s law  

The standard free energy of the reaction, AG° = E — °, is fixed for each reactant couple as soon as the electrode potential is fixed. For simplicity we have written above that AG° is equal to E — E° rather than the usual relationship AG° = F(E — E°). This convention, which is used throughout the book, implies that when potentials are expressed in volts, energies are expressed in electron volts. The term driving force will be used frequently to designate —AG°, in line with the expectation that an increase in the driving force usually speeds up the reaction. 

The forward and backward rate constants are related to the corresponding activation free energies, AG and AGf, by equation (1.25) below, introducing koo (and kf ) as the maximal rate constants, reached when A Gf or A Gf vanish. The main laws and models describing the way in which the forward and backward rate constants, or the corresponding free energies of activation, vary with the driving force are discussed in Section 1.4.2. 

The next section is devoted to the influence of the electron transfer kinetics on the electrochemical responses for both attached and free-moving 

The addition of MMOH does not affect the rates of electron transfer between NADH and oxidized FAD. However, in the MMO Bath system, the presenee of MMOH results in less semiquinone formation, and the reduction of the [Fe2S2] cluster is delayed. This suggests that when the iron-sulfur cluster of MMOR is reduced, intermolecular electron transfer to the diiron center of MMOH is very fast. Subsequently, the second electron is 

FIGURE 7. Electron transfer pathway and rates from NADH through MMOR to MMOH isolated from M. capsidatus Bath. (From Gassner et al., 1999). 

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Influence of the Kinetics of Electron Transfer on the Faradaic Current The rate of mass transport is one factor influencing the current in a voltammetric experiment. The ease with which electrons are transferred between the electrode and the reactants and products in solution also affects the current. When electron transfer kinetics are fast, the redox reaction is at equilibrium, and the concentrations of reactants and products at the electrode are those specified by the Nernst equation. Such systems are considered electrochemically reversible. In other systems, when electron transfer kinetics are sufficiently slow, the concentration of reactants and products at the electrode surface, and thus the current, differ from that predicted by the Nernst equation. In this case the system is electrochemically irreversible. 

This chapter attempts to give an overview of electrode processes, together with discussion of electron transfer kinetics, mass transport, and the electrode-solution interface. 

For reversible systems (with fast electron-transfer kinetics), the shape of the polarographic wave can be described by the Heyrovsky—Ilkovic equation ... 

Substantial loss in sensitivity is expected for analytes with slow electron-transfer kinetics. This may be advantageous for measurements of species with fast electron-transfer kinetics in the presence of a species (e.g., dissolved oxygen) that is irreversible. (For the same reason, the technique is very useful for the study of electron processes.) Theoretical discussions on AC voltammetry are available in the literature (16-18). 

S.3.3 Electrocatalytic Modified Electrodes Often the desired redox reaction at the bare electrode involves slow electron-transfer kinetics and therefore occurs at an appreciable rate only at potentials substantially higher than its thermodynamic redox potential. Such reactions can be catalyzed by attaching to the surface a suitable electron transfer mediator (45,46). Knowledge of homogeneous solution kinetics is often used to select the surface-bound catalyst. The function of the mediator is to facilitate the charge transfer between the analyte and the electrode. In most cases the mediated reaction sequence (e.g., for a reduction process) can be described by... 

R.L. McCreery, Carbon Electrodes Structural Effects on Electron Transfer Kinetics, in A.J. Bard, Ed., Electroanalytical Chemistry, Vol 18, Marcel Dekker, New York, 1991. 

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... 

EPR studies on electron transfer systems where neighboring centers are coupled by spin-spin interactions can yield useful data for analyzing the electron transfer kinetics. In the framework of the Condon approximation, the electron transfer rate constant predicted by electron transfer theories can be expressed as the product of an electronic factor Tab by a nuclear factor that depends explicitly on temperature (258). On the one hand, since iron-sulfur clusters are spatially extended redox centers, the electronic factor strongly depends on how the various sites of the cluster are affected by the variation in the electronic structure between the oxidized and reduced forms. Theoret-... 

The interpretation of phenomenological electron-transfer kinetics in terms of fundamental models based on transition state theory [1,3-6,10] has been hindered by our primitive understanding of the interfacial structure and potential distribution across ITIES. The structure of ITIES was initially studied by electrochemical and thermodynamic analyses, and more recently by computer simulations and interfacial spectroscopy. Classical electrochemical analysis based on differential capacitance and surface tension measurements has been extensively discussed in the literature [11-18]. The picture that emerged from... 

To gain insight into electron-transfer kinetics of copper(II/I) complexes of macrocyclic thioethers,446,447 Rorabacher and co-workers reported448,4 7 structures of five complexes (complexes (548)-(552)). 

As the immunocomplex structure is generally electroinactive, its coverage on the electrode surface will decrease the double layer capacitance and retard the interfacial electron transfer kinetics of a redox probe present in the electrolyte solution. In this case, Ra can be expressed as the sum of the electron transfer resistance of the bare electrode CRbare) and that of the electrode immobilized with an immunocomplex (R immun) ... 

The quantitative effects of steric encumbrance on the electron-transfer kinetics reinforce the notion that the inner-sphere character of the contact ion pair D+, A- is critical to the electron-transfer paradigm in Scheme 1. Charge-transfer bonding as established in the encounter complex (see above) is doubtless an important consideration in the quantitative treatment of the energetics. None the less, the successful application of the electron-transfer paradigm to the... 

In essence, these empirical findings allow control of the rate of electron-transfer processes by creating the appropriate structural conditions. It is, of course, straightforward to extend such a correlation of structure and electron-transfer kinetics to higher homologues. 

Brederode ME, Jones MR, Van Grondelle R (1997) Primary electron transfer kinetics in membrane-bound Rhodobacter sphaeroides reaction centers a global and target analysis. 

Newton MD (1991) Quantum chemical probes of electron-transfer kinetics the nature of donor-acceptor interactions. Chem Rev 91 767-792... 

C. Electron-Transfer Kinetics of Blue Copper Proteins... 

Ion pairing in aqueous solution often plays a minor role in electron-transfer kinetics, but in low-dielectric solvents such as dichloromethane the effects can be much stronger. Wherland s group has recently uncovered a fascinating case where ion pairing drastically inhibits the rates of outer-sphere electron transfer, even though one of the reactants is uncharged (5). 

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