Self-exchange electron-transfer reaction rates

The relationship between the rate constants kei for an electrode reaction and fee for the corresponding self-exchange electron transfer reaction is not obvious because kgi can be strongly influenced by the nature and history of the electrode surface and by solvent dynamic effects if present. Electrode properties, however, are not expected to be sensitive to pressures in the 0-200 MPa range. Moreover, the signature of solvent dynamical effects is a dependence of reaction rate on solvent viscosity, but the viscosity of water is effectively independent of such pressures at near-ambient temperatures. Consequently, for typical aqueous electrode reactions, Ai/, = O.SAV, regardless of any involvement of solvent dynamics, and so AVg can be predicted from transition state theory (TST) according to Eqs (5.5)-... 

The rate constants from electron transfer reactions in which reactant and products are chemically indistinguishable, self-exchange electron transfer reactions. 

At the microscopic level, polaron hopping can be viewed as a self-exchange electron-transfer reaction where a charge hops from an ionized oligomer or chain segment to an adjacent neutral unit. In the framework of semiclassical Marcus theory, the electron-transfer rate is written as... 

Electron transfers are perhaps the simplest of all chemical reactions, at least when no chemical bonds are broken or formed. The availability of many radioactive isotopes due to nuclear developments in World War II made possible the early experiments in the electron-transfer field. Artificial radioactivity made it possible to measure the rates of a large number of isotopic-exchange (self-exchange) electron-transfer reactions in aqueous solution. Prior to about 1950, it was commonly believed that a self-exchange reaction such as [where the asterisk marks a radioactive isotope]... 

Although the solvent-reorganisation expression (9.10) has been derived purely from electrostatic theory, there is some direct experimental support for the implied dependence of AG j. on the dielectric and optical properties of the solvent. This comes from rate measurements (by nmr line-broadening) on some self-exchange electron-transfer reactions where one of the reactants is neutral, such as the ruthenium-complex system (L = hexaflu-oroacetylacetonate) [6,a] ... 

Figure 9.6 Pressure-effect on rates of some self-exchange electron-transfer reactions between metal ions comparison of observed volumes of activation with values calculated from classical Marcus theory for adiabatic reactions. The plot shows calculated and observed AP values (cm mol ) at mid-range of pressure (100 MPa, except 70 MPa for Fe(H20)g ) for adiabatic (filled symbols) and nonadiabatic (open circles) self-exchange in couples with rigid ligands. Solvents (o, ) water ( ) CD3CN (A) (CD3)2CO (V) CD3OD. Key (A,B) (C,D) Cu(dmp)2 (E-G) Ru(hfac)j (H) Fe(C5H5)2 (I-K) Mn(CN-t-Bu)g ...

Outer-sphere electron transfer reactions involving the [Co(NH3)6]3+/2+ couple have been thoroughly studied. A corrected [Co(NH3)6]3+/2+ self-exchange electron transfer rate (8 x 10-6M-1s-1 for the triflate salt) has also been reported,588 which is considerably faster than an earlier report. A variety of [Co(NH3)g]3+/2+ electron transfer cross reactions with simple coordination compounds,589 organic radicals,590,591 metalloproteins,592 and positronium particles (electron/ positron pairs)593 as redox partners have been reported. 

The self-exchange electron-transfer (SEET) process, in which a radical is trapped by the parent molecule, has been studied using the intersecting-state model (ISM).91 Absolute rate constants of SEET for a number organic molecules from ISM show a significant improvement over classical Marcus theory92-94 in the ability to predict experimental SEET values. A combination of Marcus theory and the Rips and Jortner approach was applied to the estimation of the amount of charge transferred in the intramolecular ET reactions of isodisubstituted aromatic compounds.95... 

The rate constants (kex) of the electron exchange reactions between ZnTPP+ and ZnTPP [Eq. (1)] were determined using Eq. (2), where AHms( and AH°msi are the maximum slope linewidths of the ESR spectra in the presence and absence of ZnTPP+, respectively, and P, is a statistical factor [14]. From the linear plots of (AHmsi - Afi°msl) and [ZnTPP] at various temperatures are obtained the self-exchange electron-transfer rate constant (k ). The Arrhenius plots are shown in Fig. 13.3 together with the observed activation enthalpies (AHols ), where the effect of diffusion (kdiff) is taken into account. The AHol/ values are all positive and decrease in order toluene > MeCN > CH2C12 [16],... 

A powerful application of outer-sphere electron transfer theory relates the ET rate between D and A to the rates of self exchange for the individual species. Self-exchange rates correspond to electron transfer in D/D (/cjj) and A/A (/c22)- These rates are related through the cross-relation to the D/A electron transfer reaction by the expression... 

The NO/NO+ and NO/NO- self-exchange rates are quite slow (42). Therefore, the kinetics of nitric oxide electron transfer reactions are strongly affected by transition metal complexes, particularly by those that are labile and redox active which can serve to promote these reactions. Although iron is the most important metal target for nitric oxide in mammalian biology, other metal centers might also react with NO. For example, both cobalt (in the form of cobalamin) (43,44) and copper (in the form of different types of copper proteins) (45) have been identified as potential NO targets. In addition, a substantial fraction of the bacterial nitrite reductases (which catalyze reduction of NO2 to NO) are copper enzymes (46). The interactions of NO with such metal centers continue to be rich for further exploration. 

Here, i is the faradaic current, n is the number of electrons transferred per molecule, F is the Faraday constant, A is the electrode surface area, k is the rate constant, and Cr is the bulk concentration of the reactant in units of mol cm-3. In general, the rate constant depends on the applied potential, and an important parameter is ke, the standard rate constant (more typically designated as k°), which is the forward rate constant when the applied potential equals the formal potential. Since there is zero driving force at the formal potential, the standard rate constant is analogous to the self-exchange rate constant of a homogeneous electron-transfer reaction. 

A values have been obtained for oxidation of benzenediols by [Fe(bipy)(CN)4], including the effect of pH, i.e., of protonation of the iron(III) complex, and the kinetics of [Fe(phen)(CN)4] oxidation of catechol and of 4-butylcatechol reported. Redox potentials of [Fe(bipy)2(CFQ7] and of [Fe(bipy)(CN)4] are available. The self-exchange rate constant for [Fe(phen)2(CN)2] has been estimated from kinetic data for electron transfer reactions involving, inter alios, catechol and hydroquinone as 2.8 2.5 x 10 dm moF s (in dimethyl sulfoxide). 

The simplest electron transfer reaction that cytochrome c can undergo, at least in principle, is the self-exchange reaction. The rate of this... 

The efficiency of electron-transfer reduction of Cgo can be expressed by the selfexchange rates between Coo and the radical anion (Ceo ), which is the most fundamental property of electron-transfer reactions in solution. In fact, an electrochemical study on Ceo has indicated that the electron transfer of Ceo is fast, as one would expect for a large spherical reactant. This conclusion is based on the electroreduction kinetics of Ceo in a benzonitrile solution of tetrabutylammonium perchlorate at ultramicroelectrodes by applying the ac admittance technique [29]. The reported standard rate constant for the electroreduction of Ceo (0.3 cm s ) is comparable with that known for the ferricenium ion (0.2 cm s l) [22], whereas the self-exchange rate constant of ferrocene in acetonitrile is reported as 5.3 x 10 s , far smaller than the diffusion limit [30, 31]. 

Given the importance and great variety of electron-transfer reactions of polypyridine complexes, systematic kinetic studies are surprisingly scarce and only few kinetic data are available. Some representative rate constant values for homogeneous self-exchange redox reactions were reported ... 

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