Rate constants for electron transfer

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]. 

Bimolecular Rate constants for Electron Transfer between Carotenoid Pairs in Argon Saturated Hexane (CAR/- + CAR2 CAR, + CAR/-)... 

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. 

Bimolecular Rate Constants for Electron Transfer between Carotenoid Pairs in Argon Saturated Benzene... 

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 one series of experiments the cytochrome c oxidase mutations replaced acidic residues by neutral ones, and some of them were thus expected to alter the nature of binding of the protein to cytochrome c. From the pattern of dependence of the heme c to Cua electron-transfer rate constant on these mutations it was deduced that the binding of cytochrome c to cytochrome c oxidase is mediated by electrostatic interactions between four specific acidic residues on cytochrome c oxidase and lysines on cytochrome c. In another series of experiments, tryptophan 143 of cytochrome c oxidase was mutated to Phe or Ala. These mutations had an insignificant effect on the binding of the two proteins, but they dramatically reduced the rate constant for electron transfer from heme c to Cua- It was concluded that electron transfer from... 

Fig. 4.5. Variations of the rate constant for electron transfer versus AC0 according to the Marcus theory.

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 biological systems the movement of an electron from a donor to an acceptor site is a quite common and apparently simple event. In reality, however, electron transfers over distances greater than 10 A are frequently necessary, which means that the electron transfer can be a slow process. In fact, according to the Marcus theory, the rate constant for electron transfer between two redox sites, ket (s-1), is given by 5... 

Fe(CN)g] , Fig. 16. However, experiments with the two Ru-modified derivatives clearly indicate that rate constants for electron transfer from His59 are small. Residues 42-45 are more distant from the Cu and are considered less likely lead-in groups. Moreover, attachment of cytochrome c(II) at 42-45 by the car-bodiimide method does not lead to a productive electron transfer (see below) [138]. Therefore Tyr83 (Fig. 17) becomes a prime focus as a lead-in group for electron transfer. 

The rate constants for electron transfer achieved by plugging the nanotubes into the proteins as described above are an order of magnitude or more greater than those reported by Guiseppi-Elie et al. [92] and Zhao ef al. [95] when interfacing wild-type... 

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... 

In the ensuing discussion, the following symbols will be used kt, = bimolecular rate constant for electron transfer between a radical-anion and the substrate ... 

For this simple case, Marcus theory predicts the rate constant for electron transfer to be... 

Equation (25) gives the rate constant for electron transfer between a pair of reactants for which the levels of the various normal modes occupied are specified by X,R = XviXt. .. to give products having the distribution X p = vx specifies the quantum level occupied in normal mode... 

The expression in equation (25) gives the rate constant for electron transfer from a particular vibrational distribution of the reactants to a particular distribution of the products. In order to calculate the total electron transfer rate constant it is necessary to include two additional features. One is all possible transitions from a particular vibrational distribution of the reactants to all of the possible vibrational distributions of the products. In addition, it is necessary to recognize that a statistical distribution exists in solution amongst the various vibrational distributions of the reactants. The total transition rate will include contributions from each distribution of the reactants to all distributions of the products. 

Equation (36), which attempts to include both t and re, has been proposed as a more general expression for et.48 Note that in the limit, when Te -4 t , the expression for the electron transfer rate constant (equation 37) no longer depends on the extent of electronic coupling since vel > vn. In this limit the rate constant for electron transfer for a vibrational distribution near the intersection region is dictated by rates of repopulation of those intramolecular and/or solvent modes which cause the trapping of the exchanging electron. 

From the expression for ket in equation (55), assuming the appropriateness of the dielectric continuum approximation so the AE can be replaced by AGet0, the rate constant for electron transfer in the classical limit is given by equation (59). 

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 ... 

The qualitative operation of Marcus theory can be illustrated most easily by considering how it might estimate the rate constant for electron transfer between two metal complexes M and N. If we assume M and N to be structureless spheres, the first step leading to electron exchange involves diffusion of the two reagents toward each other, either aided or impeded by electro-... 

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