Electrostatic work terms

Rate constant for homogeneous self exchange, corrected for electrostatic work terms using Debye-Huckel-Bronsted model. Data taken from sources quoted in ref. 15 unless otherwise stated. 

Esr line broadening. When one of the couples if uncharged, the electrostatic work term is approximately zero. Structural differences between the two species are also likely to be small (X small). The effect of solvent is contained in Using Eqns. (5.23) and (5.25)-(5.27), a plot of log A .xch vs (Dop -ZJ " ) should be linear with negative slope. 

There is a decreased electrostatic work term due to a large distance of closest approach with Ru(en)3. This is small at larger and the important factor is a reduced outer-... 

Here v is the number of ions per unit time and area transferring from the solution layer next to the electrode, to the electrode. It will at once be noticed that as long as the interfacial potential difference d< > is negative, the electrostatic work term Pde0 increases the velocity of the ion transfer reaction in an exponential way (Fig. 7.10). 

Finally, we must consider the contribution of the electrostatic work required to transfer one electron into free space. After overcoming the short range chemical forces, the electron must be moved a certain distance against the electric field in the surface. Under the assumption that the lines of force of the electric field are located between the ion defects in the boundary layer and the surface charges represented by the chemisorbed gas atom, we obtain the expression afi for this electrostatic work term. is the boundary field strength represented in Equation (11), and a is the distance between the surface of the oxide and the centers of charge of the chemisorbed atoms in the a-phase. 

It is important to notice that the rate of a given outer sphere electrode redox reaction should be independent of the nature of the metal electrode if allowance is made for electrostatic work terms or double layer effects which will, of course, be dependent on the nature of the electrode material. Inner sphere reactions, on the other hand, are expected to be catalytic with kinetics strongly dependent on the electrode surface due to specific adsorption interactions. 

The analogy between the two physical problems, though with different symmetries, can be also found in the electrostatic work terms associated both to the kinetics of homogeneous ionic reactions and electrode reactions. (For the former, see Vol. 2, Chap. 4 and for the latter, see Sect. 3.5, below.)... 

Probably the most important outcome of the Marcus theory is the relationship between homogeneous homonuclear (fcs) and heterogeneous electron transfer rate coefficients (feei) after corrections for electrostatic work terms... 

E° also contains the electrostatic work term cf. AG° as defined by (46)... 

Variation in the metal surface composition is, then, generally expected to yield large variations in the observed rate constant for inner-sphere pathways since the reaction energetics will be sensitive to the chemical nature of the metal surface. For outer-sphere reactions, on the other hand, the rate constants are anticipated to be independent of the electrode material after correction for electrostatic work terms provided that adiabatic (or equally non-adiabatic) pathways are followed. Although a number of studies of the dependence of the rate constants for supposed outer-sphere reactions on the nature of the electrode material have been reported, relatively few refer to sufficiently well-defined conditions where double-layer corrections are small or can be applied with confidence [111-115]. Several of these studies indeed... 

Since anions and cations adsorb at oxide electrodes positive and negative to the pzc, respectively, electrostatic work terms (double layer corrections) should contribute to the activation free energy barrier for adsorbed electroactive ions depending on the position of the reaction site. Not much attention has been paid to this phenomenon yet. Trasatti and co-workers... 

Fig. 6. Marcus relation Free energies of activation as a function of the driving force (terms (A) + (B) in text) corrected for electrostatic work terms (cyano complexes reaction with hydrazine ( ) methylhydrazine (O) 1,2-dimethylhydrazine ( ). Adapted with permission from Dennis et al. (52). Copyright 1987, American Chemical Society.

For a supramolecular system, A-L-B, the driving force of an excited-state electron transfer process can be easily calculated (Eq. 3) on the basis of electrochemical and spectroscopic data on the isolated molecular components (with, in case, small corrections for electrostatic work terms) [6], F or the case of oxidative PET (Figure lb Eq. 2), the relevant expression is given in Eq. 3. 

This expression relates the second-order rate constant, k, for an outer-sphere electron transfer reaction to the free energy of reaction, AG°, with one adjustable parameter, X, known as the reorganization energy. Wis the electrostatic work term for the coulombic interaction of the two reactants, which can be calculated from the collision distance, the dielectric constant, and a factor describing the influence of ionic strength. If one of the reactants is uncharged, Wis zero. In exact calculations, AG should be corrected for electrostatic work. The other terms in equation 46 can be treated as constants (Eberson, 1987) the diffusion-limited reaction rate constant, k, can be taken to be 10 M" is the equilibrium constant for precursor complex formation and Z is the universal collision frequency factor (see Eberson, 1987). 

In the general case, the electrostatic work terms w that account for the Coulombic attraction of reactants (D, A) and products (D +, A ) are w D, A) = zDzA< 2/(Ansosgi) and ir(D +, A ) zD + zA e2/(4neoegi), where zD and zA are the charge numbers of donor D and acceptor A prior to electron transfer and zD + and zA are those after electron transfer. For neutral species D and A, zD = zA = 0. Choosing convenient units and collecting the constants we obtain the scaled Equation 5.2. 

Sphere series, rates correlate with the Marcus equation, when allowance is made for electrostatic work terms. In the inner-sphere series, the rates increase as the overall equilibrium constant decreases, but the variation is ascribed to work terms. The estimated intrinsic rate constants kex [c/, equation (5)] are all of similar magnitude, between 10 and 10 s h It is suggested that the rate is controlled by substitution in the [Fe(HaO)e] + ion.i ... 

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