The course of an encounter

The encounter pair and the surrounding solvent cage constitute a many-body problem of great complexity, and theoretical treatments necessarily have recourse to correspondingly complex mathematics. Rigorous treatments have been developed [22], but the results are not easy to apply to experimental data. We can, however, gain some insight by the application of simple collision and random-walk theories to a hard-sphere model [23]. 

We make the supposition that the total collision rate between A and B solute molecules in a solution (including the solvent-cage region) is the same as in the gas phase. The 

The equality of the collision number in solution to that in the gas phase cannot be derived from simple kinetic theory. It does, however, lead to reasonable conclusions (see below). Equality within an order of magnirnde for hard-sphere non-interacting equal-sized molecules is indicated by the following argument based on consideration of free volumes [18,a]. The collision number Z in an assembly of such molecules depends on (a) their translational energies (b) their diameters and (c) the space in which they are free to move. Both (a) and (b) are the same in 

For hard-sphere molecules with radius in the range 2-5 A (which includes many ordinary organic reactants), in solvents such as water or cyclohexane with viscosity about 1 cp, this expression gives the average number of recollisions per encounter as 25 to 150, increasing approximately with r g [23,c]. 

Extending the argument, it is possible, without a specific model of the encounter cage, to deduce the average frequency of recollisions in an encounter [23,a] and hence its reciprocal, which is the average time between such recollisions (fiecoii). This comes out to be  

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