Electron transfer reactions, rate constants for

Among the dynamical properties the ones most frequently studied are the lateral diffusion coefficient for water motion parallel to the interface, re-orientational motion near the interface, and the residence time of water molecules near the interface. Occasionally the single particle dynamics is further analyzed on the basis of the spectral densities of motion. Benjamin studied the dynamics of ion transfer across liquid/liquid interfaces and calculated the parameters of a kinetic model for these processes [10]. Reaction rate constants for electron transfer reactions were also derived for electron transfer reactions [11-19]. More recently, systematic studies were performed concerning water and ion transport through cylindrical pores [20-24] and water mobility in disordered polymers [25,26]. 

With Eq. 4.6 we can formulate the free-activation-energy dependence of the rate constant for electron-transfer reactions... 

Next we turn to the interpretation of the rate constants for electron-transfer reactions of cytochrome c that are accompanied by a net chemical change (Tables III and IV). The rate constants for the reaction of cytochrome c with both negatively charged (Fe(CN)5L3" and Ru[-(OSO30)2phen]34 ) and positively charged (Fe(bipy)2(CN)2+ and Ru(bipy)32+) complexes can be very great. 

Table V. Observed and Calculated Rate Constants for Electron Transfer Reactions betwen Two Metalloproteins0...

Miscellaneous Physical Chemistry. A kinetic study has been made of the electrochemical reduction of /8-carotene. The photoelectron quantum yield spectrum and photoelectron microscopy of /3-carotene have been described. Second-order rate constants for electron-transfer reactions of radical cations and anions of six carotenoids have been determined. Electronic energy transfer from O2 to carotenoids, e.g. canthaxanthin [/8,/3-carotene-4,4 -dione (192)], has been demonstrated. Several aspects of the physical chemistry of retinal and related compounds have been reported, including studies of electrochemical reduction, the properties of symmetric and asymmetric retinal bilayers, retinal as a source of 02, and the fluorescence lifetimes of retinal. Calculations have been made of photoisomerization quantum yields for 11-cis-retinal and analogues and of the conversion of even-7r-orbital into odd-TT-orbital systems related to retinylidene Schiff bases. ... 

The forty-year-old Marcus cross-rate theory for calculating the rate constant for electron-transfer reactions between different species ky of Eq. 1) was derived classically and ignores separation of Ay and As, tunneling, and variations in both the preexponential factor and Ke [21]. 

Absolute rate constants for electron transfer reactions of aromatic molecules in solution have been determined by the pulse radiolysis method for three additional pairs of aromatic compounds. In two of these cases in which an electron transfer equilibrium is established, the rate constant for the back reaction has also been determined. The equilibrium constant has been estimated from the kinetic data. A correlation of the experimental rate constants with the theory for homogeneous electron transfer rates is considered. 

A bsolute rate constants for electron transfer reactions of some aromatic molecules in solution have been reported in our earlier work (2) using the pulse radiolysis method. The transfer of an electron from various radical anions to a second aromatic compound in solution was observed directly. Of the rate constants for nine donor-acceptor pairs investigated, two were found to be lower than the diffusion controlled values, and a correlation with such parameters as the reduction potential difference of the pair was considered. These measurements have been extended to additional transfer pairs for which the reduction potential difference is small. The objective of this work, in addition to furnishing new data for electron transfer rates, is to provide an adequate test of theories of the rate of homogeneous electron transfer in polar liquids (10, 11,12,13, 14, 15,16,17). 

Pulse radiolysis has been used to study elementary reactions of importance in photosynthesis. Early experiments provided rate constants for electron transfer reactions of carotenoid radical cations and radical anions with chlorophyll pigments.More recent experiments dealt with intramolecular electron transfer in covalently bound carotenoid-porphyrin and carotenoid-porphyrin-quinone compounds. Intramolecular electron transfer reactions within metalloproteins have been studied by various authors much of that work has been reviewed by Buxton, and more recent work has been published. Pulse radiolysis was also used to study charge migration in stacked porphyrins and phthalocyanines. Most of these studies were carried out by pulse radiolysis because this techruque allowed proper initiation of the desired processes and pemtitted determination of very high reaction rate constants. The distinct character of radiolysis to initiate reactions with the medium, in contrast with the case of photolysis, and the recent developments in pulse radiolysis techniques promise continued application of this technique for the study of porphyrins and of more complex chemical systems. 

The Marcus analysis of the rate constants for electron transfer reactions of the [Ni((-)-(R)-Me[9]aneN3)2] couple with nickel and cobalt complexes yields a self-exchange rate constant of 1.2 x 10" The oxidations of... 

Several studies have been carried out on the electron exchange and transfer reactions of Pseudomonas aeruginosa azurin. The AzCu(I)/(II) exchange rate constant has been measured at 4 °C by fast-flow/rapid-freeze EPR methods and at 25 °C using H NMR relaxation techniques/ and shows only a small dependence on pH (4.5-9.0). The rate constants for electron transfer reactions between... 

Table 9.2 Test of the Marcus cross-relation Comparison of observed rate constants for electron-transfer reactions between metal complex ions with values calculated from rate constants observed for the related electron-exchange reactions (Equation (9.41)). Data from R.A. Marcus and N. Sutin, Ref. [13]...

The potential dependence of electrochemical rate constants for electron transfer reactions at liquid-liquid interfaces has not yet been studied. Since it has been established that very little of the applied Galvani potential difference occurs across the mixed solvent layer in which the electron transfer reactions are likely to take place, it is not clear if the driving force is affected by the polarization of the interface, and if the apparent electrochemical control of the reaction is not only due to the control of the surface concentrations of the reactants by the applied potential difference. 

These results produce an ordering of the one-electron reduction potentials as shown in Figure 14.9. This order is consistent with results on the reactions of oxygen and porphyrins with carotenoids (McVie at al. 1979, Conn et al. 1992), for example, p-CAR - reacts much more efficiently with oxygen than LYC - and DECA -. Comparative studies have been made in benzene due to the decreased solubility of XANs in hexane and Table 14.8 gives the corresponding bimolecular rate constants for electron transfer. Overall, the one-electron reduction potentials increase in the order ZEA < P-CAR LUT < LYC < APO - CAN < ASTA. 

In the classical limit where the condition << kgT is met for the trapping vibrations, the rate constant for electron transfer is given by eq. 6. In eq. 6, x/4 is the classical vibrational trapping energy which includes contributions from both intramolecular (X ) and solvent (XQ) vibrations (eq. 5). In eq. 6 AE is the internal energy difference in the reaction, vn is the frequen-... 

In this equation g(r) is the equilibrium radial distribution function for a pair of reactants (14), g(r)4irr2dr is the probability that the centers of the pair of reactants are separated by a distance between r and r + dr, and (r) is the (first-order) rate constant for electron transfer at the separation distance r. Intramolecular electron transfer reactions involving "floppy" bridging groups can, of course, also occur over a range of separation distances in this case a different normalizing factor is used. 

In an irreversible reaction, the rate controlling process is usually a single electron transfer step with a rate determined by Equation 1.8. The corresponding po-larographic wave is then described by Equation 1.18 where kconv is the rate constant for electron transfer at the potential of the reference electrode. For an irreversible... 

There has been keen interest in determination of activation parameters for electrode reactions. The enthalpy of activation for a heterogeneous electron transfer reaction, AH X, is the quantity usually sought [3,4]. It is determined by measuring the temperature dependence of the rate constant for electron transfer at the formal potential, that is, the standard heterogeneous electron transfer rate constant, ks. The activation enthalpy is then computed by Equation 16.7 ... 

Theories of Protein-Protein Electron Transfer. The sketch presented here is necessarily brief. Details of the theory can be found in several recent reviews. 3 Like any reaction, the rate constant for electron transfer can be written as the product of a prefactor times an aetivatiog barrier ... 

The rate constants of electron transfer reactions occurring in MLCT excited states can be calculated using expressions similar to those shown in Equations 6.106-6.113 for the electron transfer reactions of LF excited states and the corresponding back electron transfer reactions. 

Kinetics of Energy and Electron Transfer. A semi-quantitative estimate for the rate constants of the various photophysical processes can be obtained from fluorescence quenching. Based on the quenching ratios of the OPV fluorescence and the OPVn singlet excited state lifetimes, the rate constants for energy transfer reactions in toluene solutions were estimated to lie between 1.1 x 1012 and 2.1 x 1012 s-1 for OPV3 Cgo and OPV4 Cgo (Table... 

Fig. 8.13 (a) Potential dependence of the phenomenological rate constant k,r derived for mechanism I. Note that for a two step mechanism, this rate constant contains terms associated with surface recombination, so that it is not the true rate constant for electron transfer. The influence of the modulation of potential due to surface charging is shown, (b) Potential dependence of the phenomenological rate constant k,t for case /. The influence of the dynamic modulation of surface potential by accumulated reaction intermediates is... 

Rate constants for electron transfer may be related to the free energy AG° of the reaction through the classical Marcus equation Eq. (5), where AGq is the intrinsic activation barrier of the reaction process [90, 91]. 

Table 5. Free reaction enthalpies (AGct), rate constants for electron transfer between excited singlet (4k ) and triplet state (3k ) of donor and onium salts, efficiencies of isc-process of the donor in presence of onium salts (ilisc), quantum yields of onium salt decomposition (in) and of polymerization (methyl methacrylate (measured in acetonitrile/water 90 vol%)... 

If it is assumed that this reflects a mechanism in which NH2OH is oxidized, then the rate constant for electron transfer is 7.3 x 103 M 1 sec1. An upper limit of 1 x 1010 M-1 sec-1 for the reverse reaction establishes E° < 1.26 V for the NH2OH+/NH2OH couple. This result should be accepted with some caution because unpublished experiments by the present author indicate that the reaction is catalyzed by adventitious copper (291), as was the case in the oxidation by Fe(CN)63 (58). 

Normal region (for electron transfer) In plots relating rate constants for electron transfer, or quantities related to it, with the standard Gibbs energy for the reaction (AG ), the region for which the rate constants increase with increasing exergoni-... 

As illustrated in the previous section, the kinetics associated with an ET process may be complex when diffusion or relaxation processes create dynamic bottlenecks. In limiting cases, however, a simple model based on transition state theory (TST) suffices. According to TST, the system maintains thermal equilibrium between different positions along the reaction coordinate [87]. We consider the TST rate constant for electron transfer after some preliminary comments about state manifolds and energetics. 

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