The kinetics of electron tunneling reactions for immobile reagents

The kinetics of electron tunneling reactions for immobile reagents 

It is expedient to begin the analysis of the kinetics of electron tunneling reactions for immobile reagents with the simplest case, i.e. when the probability of tunneling depends only upon the distance between the reagents and this dependence is purely exponential 

It will be shown further that the employment of this simple formula allows a good enough description to be given of the kinetics observed for the majority of electron tunneling reactions which have been experimentally studied so far. 

Let us consider the kinetic equations for various types of spatial distribution of the reagents provided that lT(i ) is described by eqn. (2). 

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Here, D is the diffusion coefficient of the reacting particles and n(t) and N(t) are the current concentrations of the two reagents. The solution of the system of equations (46) is written in the form of a complex series (see, for example, ref. 27). However, it is substantially simplified in two practically important limits t td and t > td, where td = a2/D is the time of diffusion travel of the reagents at a distance of the order of a. For the sake of simplicity we shall consider only the case of random spatial distribution of the reagents and assume that n(0) N. If t tu, then the solution of eqns. (46) is given by expression (35), i.e. it coincides with the equation for the kinetics of electron tunneling reactions for immobile reagents. At t > tu, from eqn. (46) it is possible to obtain... 

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