Generalized Collins-Kimball model

Figure 3.8. (a) The linear viscosity dependence of the inverse ionization rate in the reaction studied in Ref. 98. Bullets—experimental points solid line—fit performed with the generalized Collins—Kimball model, (b) The effective quenching radius for the same reaction in the larger range of the viscosity variation. Bullets—experimental points solid fine—fit performed with the encounter theory for the exponential transfer rate. The diffusion coefficient D given in A2/ns was calculated from the Stokes—Einstein relationship corrected by Spemol and Wirtz [100]. 

The more general result extended to the kinetic limit is given by the Collins-Kimball model. The integral over t from the rate constant, Eq. (3.21), is well... 

The simplest theory of diffusion-assisted ET assumes that the reaction occurs only when donor and acceptor make contact (Collins-Kimball or the gray sphere model) [334-336]. Some experiments were analyzed on the basis of such theory [16, 337]. However, according to the Marcus expression, the ET rate can exhibit a peculiar dependence on the interparticle distance [17, 329, 338] as a result of the interplay between different dependencies of V, E, and AG, as shown in Figure 9.31. While in the normal region conventional exchange-type exponential dependence is at least qualitatively valid, kjyj(r) is generally nonmonotonic and acquires a bell-shaped form with increasing exothermicity. 

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