Behaviour of molecular pairs in homogeneous reaction

Noyes [5, 265] has developed an analysis of homogeneous chemical reactions in solution by considering all possible combinations of pairs of reactants A and B. If there are initially n and n% reactant molecules in the volume of interest, these can react such that the rate of reaction is kn°An%. As reaction proceeds, the reactants disappear. Ingeniously, Noyes 

At short times (t 0), the rate coefficient has a maximum value of k. This is the rate of reaction between A and B when they are both randomly distributed in space with the equilibrium distribution. Hence, k can be identified as the activation-limited rate coefficient, kact. At later times, the observed time-dependent rate coefficient becomes less than feact because those A and B reactants which were close to each other (within a few times the encounter distance) have reacted. A steady-state is established where reactants A and B diffuse together as fast as they react and the rate coefficient becomes 

The quantity j3 is the probability that a reactant pair of A and B will react at some time after their initial encounter which leads to reaction , i.e. the probability of reaction with each other twice. The steady-state 

The best form of h(f) which can be deduced from the random walk or diffusion equation has been discussed by Berg [278], Pagistas and Kapral [37] and Naqvietal. [38]. They noted that the encounter pair (effectively 

Over long times, this displays the limiting form t 3/2 characteristic of the diffusive recombination of radicals. The various forms of h(t) which have been developed are shown in Fig. 40. There are significant differences between these forms and, in particular, the form of h(t) at short times must be 0(t+ ) where n — 1. The partially reflecting form [eqn. (194)] is satisfactory as its limiting short-time dependence is U1/2, so too is the Noyes random flights form of h(t), though its theoretical justification is limited. The purely diffusive form of h(f), eqn. (193), is an unnecessary contrivance. 

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