Molecular Imaging. Markus Rudin. Читать онлайн. Newlib. NEWLIB.NET

Автор: Markus Rudin
Издательство: Ingram
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Жанр произведения: Медицина
Год издания: 0
isbn: 9781786346865
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57, 62]. The absolute rates of various electrochemical processes [60] are in the general range expected from the values of the chemical rate constants, but further work is desirable, both theoretically on Class II and Class III systems as well as experimentally on salt effects and hydrolysis effects.” [4, p. 159]

      3.21.3.1.Frequency Factor and Activation Energy

      For simple isotopic exchange reactions: “ΔF* equals wr + λ/4. Correspondingly, ΔS* is the sum of two terms. The first, −∂wr/∂T , is the usual entropy change which results when two ions are brought together. The second, −(/dT)/4, is the entropy of formation of the ‘nonequilibrium’ atomic configurations from the equilibrium ones at the same r in order to satisfy the energy restriction. Its value may be computed from Eq. (3.35). It proves to be very small for reactants of Class I.

      Applications of the theoretical equations to Class I reactants by the writer” (M.) “led to good agreement between experimental and calculated frequency factors for the image system and (within a factor of 50) for the image system, the latter system having an extremely small frequency factor.”

      The last frequency factor was measured by A. C. Wahl. “The data were extrapolated to infinite dilution, taking cognizance of the comparative insensitivity of the theoretical activation energy to salt effects.” [4, pp. 159–160]

      Recalling Eq. (3.12) A = A′ exp(−ΔS*/R) = κ Z exp (−ΔS*/R) relating the excess entropy of activation to the frequency factor we see that the smaller the absolute value of ΔS* < 0, the smaller A.

      “These results suggest that the probability of adiabatic reaction may be of the order of unity, at least for these systems. The frequency factors of Class I reactants provide the most direct measure of this probability factor.

      Many of the hydrated metal cations, which are mainly of Class II, tend to hydrolyze and form other complexes easily. In a careful investigation Silverman and Dodson [59] unraveled the rate constant of the Fe+3,+2 system . . .The frequency factor was very small.”

      NOTE that the term −∂wr/∂T of ΔS* in Eq. (3.21) can be influenced by the ionic strength, for instance by the high acidity needed to minimize hydrolysis, because wr is influenced by the ionic strength (see earlier).

      “Baker, Basolo, and Neumann [56] have reported a most interesting result of a very high frequency factor, 5 × 1016 cc mole−1 sec−1 for a Class III system,(2) image

      “The frequency factors of the electrochemical systems. . . Randles and Somerton [61] found them to be typically in the range 3 × 102 to 3 × 104 cm sec−1. The reactants were primarily hydrated metal cations and so were mostly of Class II. In one system, image a rather low frequency factor (10cm sec−1) was found. The electrostatic repulsion between ion and electrode was estimated to be large for this system, and the low A-value was attributed to a small transition probability factor because of the increased R.” [4, p. 160]

      Marcus indicates now two other parameters which are influenced by R:

      “However, we see from Eq. (3.35):

image

      that there is also an image term present. This term would tend to favor small R’s. An alternative explanation for the A-value could be given on the basis of the usual sign of −∂wr/∂T . When two reactants of like sign approach each other, the enhanced electrostatic field polarizes the solvent more strongly and causes a negative ΔS*.”.

      See above.

      “Activation energies for several electrochemical electron transfers have been measured [61]. . .

      The results tentatively indicate the activation energies of the electrode reactions to be more than one-half those of the corresponding exchange processes. Should this result prove to be generally true (at least for Class I and Class II reactants) one possible interpretation would be that the distance between the ion in the activated complex and its electrical image exceeds twice the ionic radius.”

      We have seen that image This is valid in the hypothesis R = 2a. If R > 2a because of the presence of a layer of molecules adjacent to the electrode which the ion cannot penetrate, then λel is greater than for R = 2a and recalling the formula for λel we can explain the earlier experimental result [4, pp. 159–161].

       3.21.4. Salt Effects

      “No detailed study of salt effects for simple electron transfers at electrodes appears to have been reported” until 1958. “Therefore it is not yet possible to adequately test the usual assumption (one not made here) that the work required to transport an ion from the body of the solution to the electrode, wr or wp, equals the ionic charge multiplied by the difference of potential at the initial and final positions of the ion. This assumption is clearly valid when the ionic charge is so small that it does not perturb the configuration of the remaining ions. It is also clearly invalid at the point of zero charge [17, 20]. At this point, the work term estimated on the basis of the above assumption is zero, whereas it actually equals the free energy of interaction of the ion with the image. For infinite dilution, the latter term is −q2/2Ds R, q being the ionic charge, while for dilute salt solutions, an approximate estimate of it is (−q2/2Ds R) exp(−κ R), κ being the usual Debye κ.” [4, p. 161]

      NOTE that the interaction energy is half of what it would be between two real charges [27]. [4, p. 161]

       3.21.5. Solvent Effects

      “Solvent effects for simple electron transfers will occur, according to the theory, whenever there is a change in dielectric constant, refractive index, ionic