Molecular Imaging. Markus Rudin

assumption made in the derivation of Eq. (3.4) for ΔF^*. However, it is possible that the dielectric saturation by the anion is relatively small. For example, studies [78, 79] of the dielectric constant of aqueous salt solutions indicate less dielectric saturation in the vicinity of anions, as compared with cations. It is of interest, too, though not necessarily significant, that the ‘experimental’ free energy of solvation of anions agree reasonably well [80, 81] with those calculated from the Born formula [82]. The Born formula assumes that the dielectric is unsaturated.

      In the interest of simplicity, we shall assume that as a first approximation there is little dielectric saturation in the vicinity of the QH⁻ ion. Accordingly it follows that a will be the crystallographic radius of the oxygen group, which is about 1.4Å.”

      M. will later remove the assumption of absence of dielectric saturation.

“The may be regarded as an ellipsoid of revolution whose [83] semimajor axis was found crystallographically to be 2.02 and whose semiminor axis is 1.51Å. As a first approximation, this molecule will be treated as a sphere of radius 1.7Å which has the same volume as the ellipsoid. This ‘crystallographic’ radius will be taken as the value of a for for the same reason given previously for the choice of the crystallographic radius as the a value of the oxygen atom in the hydroquinone ion” [2, p. 877].

       NOTES

      1.M: “κ is the probability of electron tunneling from one electronic configuration to the other, the rate constant is then proportional to κ. If one wants to phrase that in terms of the Eyring theory, since κ is not an energy dependent factor, that would contribute to the energy independent part of the free energy of activation. The energy independent part is the entropy of activation.”

      2.M: “For a typical bimolecular frequency, where we don’t have to worry about charges, the number would be of the order of 10¹⁴, so this is higher than that by a factor of 500, it is a strange because the charges would orient more, would reduce below the entropy, making the number below 10¹⁴. Now, of course, you have all sorts of ion pairing effects. . .”

       References

1.R. A. Marcus, J. Chem. Phys. 26, 867, (1957).

2.R. A. Marcus, J. Chem. Phys. 26, 872, (1957).

3.R. A. Marcus, Trans. N.Y. Acad. Sci. 19, 423, (1957).

4.R. A. Marcus, Can. J. Chem. 37, 155, (1959).

5.R. A. Marcus, “A Theory of Electron Transfer Processes at Electrodes,” in Transactions of the Symposium on Electrode Processes, p. 239, E. Yeager, Editor, Wiley, New York (1961).

6.R. A. Marcus, J. Phys. Chem. 67, 853, 2889, (1963).

7.R. A. Marcus, “Electron Transfer at Electrodes,” in Encyclopaedia of Electrochemistry, p. 529, C. A. Hampel, Editor, Reinhold, New York (1964).

8.R. A. Marcus, P. Siddarth, in Photoprocesses in Transition Metal Complexes, Biosystems and Other Molecules: Experiment and Theory, Vol. 376, pp. 49–88, Kluwer Academic Publishers (1992).

      9.R. A. Marcus, Angew. Chem. Int. Ed. Engl 32, 1111–1121, (1993).

10.R. A. Marcus, in Lecture Notes, International Summer School on the Quantum Mechanical Aspects of Electrochemistry, pp. 1–75, P. Kirkov, Editor, Ohrid, Yugoslavia (1971).

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      12.R. A. Marcus, Phys. Chem. Sci. Res. Rep. 1, 477, (1975).

13.R. A. Marcus, “Theory and Applications of Electron Transfers at Electrodes and in Solution,” in Special Topics in Electrochemistry, p. 161, P. A. Rock, Editor, Elsevier Scientific Publishing Company, Amsterdam, Oxford, New York (1977).

14.M. Maimonides, The Guide of the Perplexed, Translated and with an Introduction and Notes by Shlomo Pines, Introductory Essay by Leo Strauss, 2 volumes, The University of Chicago Press, Chicago and London (1963).

15.S. Glasstone, K. J. Laidler, H. Eyring, The Theory of Rate Processes, McGraw-Hill, New York and London (1941).

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17.A. J. Bard, L. R. Faulkner, Electrochemical Methods, Fundamentals and Applications, John Wiley and Sons, Inc., New York, Chichester, Brisbane (1980).

18.R. A. Marcus, J. Chem. Phys. 43, 679–701, (1965).

19.R. A. Marcus, “Electrostatic Free Energy and Other Properties of States Having Non-Equilibrium Polarization. II. Electrode Systems”, Office of Naval Research, Technical Report No. 11 Contract Nonr 839(09), Task No. 051-339, in Special Topics In Electrochemistry, p. 210, P. A. Rock, Editor, Elsevier Scientific Publishing, Amsterdam, Oxford, New York (1977).

20.R. A. Marcus, “On the Theory of Overvoltage for Electrode Processes Possessing Electron Transfer Mechanisms. I”, Office of Naval Research, Technical Report No. 12 Contract Nonr 839, Task No. 051-339, inSpecial Topics in Electrochemistry, p. 180, P. A. Rock, Editor, Elsevier Scientific Publishing Company, Amsterdam, Oxford, New York (1977).

21.J. O’M. Bockris, A. K. N. Reddy, A. M. Gamboa-Aldeco, Modern Electrochemistry 2A, Fundamentals of Electrodics, 2nd Edition, Kluwer Academic/ Plenum Publishers, New York, Boston, Dordrecht (2000).

22.K.