Molecular Imaging. Markus Rudin

of the coordination shell, which may include the solvent, naturally alter a, ΔF⁰, and the ease of intramolecular compression or stretching. In addition there are effects which were not incorporated in the theory, effects such as changes in ion pairing, selective solvation of solvent mixtures, and a change of the mechanism itself.”

“Heavy water has been used as a solvent in several studies [64, 65]. Hudis and Dodson [64] have demonstrated the importance, when hydrolyzed species and other complexes are present, of determining the various equilibrium constants so that meaningful electron transfer rate constants for the different species can be obtained and solvent effects evaluated. The rate constant for Fe^+3,+2 was smaller by a factor of two in D₂O [64], while that of was smaller by a somewhat smaller factor [65]. A qualitative interpretation of solvent effects can be given in terms of atom transfer [64, 65] or electron transfer [1] theories. Thus far, [1958], however, comparative studies in the two solvents do not permit either mechanism to be distinguished from the other. This situation results from the fact that ions have different solvation energies in the two media [66], so that water does not behave as an inert solvent.

The rate of the reaction appears to be faster in liquid ammonia [67] than in water, where it was immeasurably slow [57]. The activation energy was high, being in the range found for two other Class III compounds [56, 63]. Possible explanations for the solvent effect include a change of mechanism, such as a dissociation [67] or possibly a hydrolyzed intermediate, [4, pp. 161–162]

       3.21.6. Effects of Electrode Material

      “A dependence of rate constant on electrode material will occur if there is any change in surface contamination [61] and possible metal–solvent binding, or if electrode charge density at a given η_a changes sufficiently to alter w^r or w^p. The rate constants measured for one system with several solid electrodes underwent no great variation (within a factor of 10) but were much smaller than that found for a mercury electrode [61].” [4, p. 162]

       3.21.7. The Image Force Law and Its Implications

“The role of the electrostatic image has been generally ignored in electrochemical theories. A recent investigation [68] of the quantum limitations of the image force law for a vacuum is reassuring. It has been applied by the writer (M.) to dielectric media and to electrochemical theory.

      The effect of this image is to partially neutralize the field of the ion and to reduce, thereby, the configurational rearrangement free energy needed to satisfy the energy restriction. It is noteworthy that its calculated effect remains, even at salt concentrations sufficiently large as to make w^r and w^p negligible. This is because it is impossible for the ionic atmosphere in the activated complex to neutralize the ion–image interactions of the two different hypothetical charge distributions at the same time. A compromise configuration results. A similar behavior exists in the homogeneous case, where the 1/r term remains even if w^r and w^p are zero.

      At the point of zero electric charge [17, 21], there is a net, shielded Coulombic attraction between the ion and its image, which is quite large for very dilute solutions. According to the theory a positive ΔS^* would result, since the attraction lowers the entropy of solvation.”

      See above for the increase of entropy when two ions of opposite charge approach each other.

      “A measurement of the frequency factor in this region would permit a determination of this ΔS^*”

      “If this prediction is verified for Class I reactants, it will be interesting to compare ΔS^* with the theoretical estimates” [4, p. 162]

       3.22.Comparison of Isotopic Exchange Rate and Corresponding Electrochemical Exchange Current

      “A comparison of and k_el/10⁴ on the basis of the existing experimental data is given in Table I.” of Ref. [6], “All rate constants are pseudo-rate constants, their use being justified under the conditions cited [6]. The qualitative trend in both k_el and k_ex is seen to be the same, and the values. . .are relatively close to each other, considering the fact that approximations in the theory enter exponentially (a fairer comparison would be of and that stationary electrodes (with their absorption problems) were usually necessary, and that the work terms may not have been negligible.” [6, p. 854]

       3.23.Comparison of Chemical and Electrochemical Oxidation–Reduction Rates of a Series of Related Reactants

      “In this comparison we shall consider systems in which a constant reagent is used in the chemical system, and a constant electrode potential in the electrochemical one, to oxidize or reduce a series of related compounds. In a series of a given charge type, the work terms are either exactly or roughly constant in each of these two systems. Furthermore, if the ΔF^*’s are in the region where they would depend linearly on ΔF⁰, then according to Eqs. (3.1, 3.78, 3.83, 3.25), the ratio:

should be the same for each member of the series: in both cases, the terms λ₁, ΔF⁰, and, at a constant E, η(= E − E⁰), will normally vary from member to member. λ₂ refers to the constant reagent. However, since ΔF⁰ = −nF E⁰ + const in the series, one sees from Eqs. (3.78, 3.83, 3.25), that these variations in λ₁, ΔF⁰, and E⁰ cancel when one compares values of that is of k_soln/k_el. Vlcek [ Скачать книгу