Kinetics of electron transfer reactions

Electron transfer can generally be described as an exchange of electrons between occupied and vacant energy levels. Since electron transfer is a very fast process, fast compared to the relaxation times of most other energy modes, the Franck-Condon principle has to be applied on a description of this process with respect to the structural conditions and, besides this, the energy has to be conserved. This leads to a description of the rate of electron transfer as shown in the following equations  

At interfaces, the electron transfer occurs between occupied and vacant states at both sides of the interface. The distribution of electronic states in metals as well as in semiconductors is given by their band structure. If we know the position of the band edges relative to the electrolyte, we know in principle the average state density and energy distribution. 

The energy positions of the maxima of these distribution functions are related to the standard redox potential identical with the standard Fermi level of the redox system, following 

The energy level of the standard redox potential can be reached with equal probability by a thermal fluctuation of the occupied or the vacant redox species as equ, (11) and (12) indicate. 

Applying the general formula for the electron transfer reactions one can describe the electron transfer at a metal electrode as shown in Fig. 11,8 and II.9, At equilibrium, the Fermi levels in the redox electrolyte and in the metal coincide and, as one sees, electron transfer occurs at energy levels in the close neighborhood of the Fermi level. If one applies a voltage, the Fermi level in the electrode is shifted upwards (cathodic) or downwards (anodic) relative 

General Kinetic Considerations For an electron transfer reaction of the type represented by Eq. (2), 

The three basic steps in this mechanism are (1) reactant association, (2) electron transfer, and (3) product dissociation. Equilibrium constants associated with these three steps may be defined K] - k lk., Ki = k lk-i, and Ki, = ky/k.T,. 

The general kinetic expression for this reaction mechanism is quite involved, but, clearly, the overall velocity will depend on the detailed kinetics of all three steps. If the back electron transfer rate is neglected (i.e., k 3[Ar][Bo] = 0), and the steady-state approximation is applied to the two central complexes, then the reaction velocity, v, may be derived  

Various limiting forms for v may apply under special conditions. If the electron transfer steps are rate limiting ( 2 and. 2 small), then 

V = / 2 fi Ao] Br) (electron transfer step rate limiting) (22) If the substrate association step is rate limiting, then 

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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. 

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. 

Both the thermodynamics and kinetics of electron transfer reactions (redox potentials and electron transfer rates) have steric contributions, and molecular mechanics calculations have been used to identity them. A large amount of data have been assembled on Co3+/Co2+ couples, and the majority of the molecular mechanics calculations reported so far have dealt with hexaaminecobalt (III/II) complexes. 

Armstrong D, Sun Q, Schuler RH (1996) Reduction potentials and kinetics of electron transfer reactions of phenylthiyl radicals comparisons with phenoxyl radicals. J Phys Chem 100 9892-9899 Asmus K-D (1979) Stabilization of oxidized sulfur centers in organic sulfides. Radical cations and odd-electron sulfur-sulfur bonds. Acc Chem Res 12 436-442 Asmus K-D (1990a) Sulfur-centered free radicals. Methods Enzymol 186 168-180 Asmus K-D (1990b) Sulfur-centered three-electron bonded radical species. In Chatgilialoglu C, Asmus K-D (eds) Sulfur-centered reactive intermediates in chemistry and biology. Plenum, New York, pp 155-172... 

Tubbesing, K., Meissner, D., Memming, R., Kastening, B. 1986. On the kinetics of electron transfer reactions at illuminated InP electrodes. J. Electroanal. Chem. 214. 685-698. 

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... 

Franzen, S., Lao, K. Q., and Boxer, S. G., 1992, Electric-Field Effects On Kinetics Of Electron-Transfer Reactions Connection Between Experiment and Theory Chem. Phys. Lett. 197 380n388. 

The mentioned effect seems to be of general importance for the detailed interpretation of the kinetics of electron transfer reactions. In the present case we have two reaction lines ... 

Reactions that occur between components in the bulk solution and vesicle-bound components, i.e., reactions occurring across the membrane interface, can be treated mathematically as if they were bimolecular reactions in homogeneous solution. However, kinetic analyses of reactions on the surface of mesoscopic structures are complicated by the finiteness of the reaction space, which may obviate the use of ordinary equations of chemical kinetics that treat the reaction environment as an infinite surface populated with constant average densities of reactant molecules. As was noted above, the kinetics of electron-transfer reactions on the surface of spherical micelles and vesicles is expressed by a sum of exponentials that can be approximated by a single exponential function only at relatively long times [79a, 81], At short times, the kinetics of the oxidative quenching of excited molecules on these surfaces are approximated by the equation [102]... 

The theoretical description of the kinetics of electron transfer reactions starts fi om the pioneering work of Marcus [1] in his work the convenient expression for the free energy of activation was defined. However, the pre-exponential factor in the expression for the reaction rate constant was left undetermined in the framework of that classical (activate-complex formalism) and macroscopic theory. The more sophisticated, semiclassical or quantum-mechanical, approaches [37-41] avoid this inadequacy. Typically, they are based on the Franck-Condon principle, i.e., assuming the separation of the electronic and nuclear motions. The Franck-Condon principle... 

The oxalate complex K3[ri(C204)3(H20)] was prepared by the addition of excess K2[C204] to a solution of [Ti ((112N)2CO)6]Cl 3. The crystal structure revealed a seven-coordinate pentagonal bipyramidal geometry about the Ti center.989 The kinetics of electron transfer reactions between Ti oxalate complexes with Ru and Co complexes have been studied in detail.969,990,991... 

M. A. Hoddenbagh, D. H. Macartney, Kinetics of electron-transfer reactions involving the... 

Much of our earlier work on pressure effects on the kinetics of electron transfer reactions focused upon the rate constants kex and corresponding volume of activation for self-exchange reactions... 

There are several parallels in the reduction chemistry of nitroarenes and aromatic N-oxides, such as similar kinetics of electron transfer reactions of the radical-anions and the effects of prototropic equilibria on radical lifetimes in aqueous solution [16]. The benzotriazine di-N-oxide, tirapazamine (Figure 1,16) is currently in Phase III clinical trial as a hypoxic cell cytotoxin in conjunction with cisplatin [132]. The mechanism of its action appears to involve the one-electron reduction product [133] cleaving DNA [134], probably also sensitizing the damage by a radical-addition step [135-138]. 

The kinetics of electron transfer reactions between spinach plastocyanin and [Fe(CN)6] ", [Co(phen)3] , and Fe(II) cytochrome c have been studied as a function of ionic strength. Applications of the equations of Van Leeuwen support the proposal of two sites of electron transfer, with [Co(phen)3] binding near residues 42-45 and the interaction of [Fe(CN)6] at a hydrophobic region near the copper ion. Pulse radiolysis has been employed to measure the rates of electron transfer from Ru(II) to Cu(II) in plastocyanins from Anabaena variabilis and Scenedesmus obliquus which have been modified at His-59 by [Ru(NH3)5] . The small intramolecular rates (<0.082 and <0.26 s , respectively) over a donor-acceptor distance of 12 A indicate that electron transfer from the His-59 site to the Cu center is not a preferred pathway. A more favorable route, via the acidic (residues 42-44) patch ( 14 A to Cu), is supported by the rate of >5 x 10 s for the reduction of PCu(II) by unattached [Ru(NH3)5im] . The intramolecular electron transfer from Fe(II) in horse cytochrome c to Cu(II) in French bean plastocyanin ( 12 A from heme edge to Cys-84 S), in a carbodiimide cross-linked covalent complex, proceeds with a rate of 1.05 x 10 s . The presence of the... 

The kinetics of electron transfer reactions involving A] have been recently... 

ELECTRODE KINETICS OF ELECTRON-TRANSFER REACTION AND REACTANT TRANSPORT IN ELECTROLYTE SOLUTION... 

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