Molecular Imaging. Markus Rudin

can be attributed to the absence of one half of the dielectric medium in the electrode case. (Effectively, the charge is transferred from the ion to its electrostatic image, and the metal surface bisects the line drawn between the two).” [4, p. 158]

       3.21.Interpretation of the Data

      A discussion of data follows on experiments reported in Refs. [4] and [6], from the point of view of the various factors influencing the reaction rate.

       3.21.1. “Standard” Free Energy Change or Activation Overpotentials

      The influence of this only factor alone on the rate constant is more easily investigated for the electrode processes. As a matter of fact, it is obviously much easier to vary the potential of the working electrode at which a substance reacts, than studying the redox reactions of the substance with a variety of reactants.

“When w^p and w^r are sufficiently small, it can be deduced from Eqs. (3.11), (3.33), and (3.34) that the transfer coefficient is 0.5, a value found in a number of simple electron transfer processes [48–50].” “The quantitative effect of ΔF⁰ on the homogeneous bimolecular rate constant has been measured experimentally for some nonspherical reactants [51, 52]. While ion–solvent interactions in these systems (oxidation of hydroquinone-like compounds) were not as simple as assumed in Eq. (3.17) and an atom transfer mechanism could not be ruled out, reasonable agreement with the experimental rate constant was found [2].” [4, p. 158]

      The detailed theoretical description from Ref. [2] is reported in a following section [4, p. 159].

       3.21.2. Ionic Structure and Ligand Field Effects

In order to study the effect of ion size on the rates of homogeneous reaction, it is most convenient to study isotopic exchange reactions because there the reactants merely exchange their charges, ΔF⁰ and w^r − w^p are both zero, and m of Eq. (3.85) is simply Wahl and coworkers have extensively investigated the factor of ion size [53, 54]. The rates of large ions, probably of Class I, were found, as expected, to be much larger than those of the smaller ions, and It is interesting that “the latter two systems had comparable rates in spite of the greater Coulombic repulsion in the second case, perhaps because of larger size of the iron cyanide ion (4.5 vs. 2.9Å). Rather good agreement was obtained between experimental and calculated rate constants using the theoretical equations, taking into consideration the absence of adjustable parameters [55].”

      Marcus theory incorporates the influence of ligand field effects on the rate constants of oxidation–reduction reactions; they influence, in particular, k_i, and ΔF⁰. Accordingly, the discussions of ligand field effects on kinetic problems is then converted into a discussion of the problem of estimating k_i, and ΔF⁰ [6, p. 67].

“The cobalt–nitrogen bonded complexes probably are members of Class III [25, 56] and the rates are therefore extremely slow. The marked increase in rate [56, 57] in the sequence may be partly a reflection of increasing ion size, and partly a reflection of ligand field [58] effects.

The ferrous–ferric system is probably of class II, and its rate [59] is correspondingly much less than that of the or systems. Nevertheless, its rate greatly exceeds that [60] of a probable member of Class III [56]. Reasonable agreement between calculated and experimental between calculated and experimental results for the was found by adapting the theory to Class II reactants [3]. Thus far [1958. . .] there is no experimental evidence which definitely establishes either an electron or an atom transfer mechanism for these homogeneous isotopic exchange reactions of hydrated cations. The general parallelism of various rates in the two processes discussed in the following suggests, however, a common electron transfer mechanism.” [4, p. 159]

       3.21.3. Parallelism between Rates in Solution and at the Electrodes

The theoretical equations suggest a close parallelism between the rates of the two processes, when similar mechanisms are operative, in particular when ΔF⁰ and η_a are zero and the work terms are small, a situation typical of isotopic exchange reactions. “The parallelism becomes very close, therefore, when the rates of isotopic exchange reactions are compared with the corresponding electrochemical exchange currents. The chemical and electrochemical electron transfer rates of the systems and [54, 56, 59, 61] both increase in the order given as do those of the systems and Скачать книгу