^{1}

^{1, 2}

^{1, 2}

^{1}

^{2}

A geminate reaction between

More than fifty years ago Monchick [

Under the above conditions, the simplest bulk reaction competing with geminate one is possible on addition of uniformly distributed

In his first work Monchick [

At the same time, only one attempt has been made in the literature to substantiate the phenomenological theory based on relations (

The outline of the paper is as follows: the next section presents conventional theory and superposition approximation. In Section

Commonly,

Conventional theory [

The survival probability of geminate pairs in the absence of competing bulk reaction is defined by the expression:

For dilute solution of reactants the bulk reaction kinetics may be expressed as [

In the absence of initial correlations between reactants the rate constant of the bulk reaction is

Thus in both approximate theories the experimentally measured quantities (

We believe the above independence of bulk and geminate reactions in the “scavenger problem” to be unjustified at least for two physical reasons. First, on intrusion into a geminate pair, an acceptor is to affect essentially the course of geminate reaction, with the most significant changes being determined by the interruption of recontacts between

For further investigation we choose the simplest microscopic model of the reacting system. We shall describe a geminate reaction by the model of isotropic “black” sphere of the radius

Let us take that uncharged

Starting with the initial distance

By analogy with

When calculating the bulk reaction kinetics, in this subsection we shall take that

The model involving jumps of infinite length describes the so-called hopping mechanism of reactions. Physically it is realized when a reactant reaches the reaction zone in one jump. In this case the rate constant is equal to the product of the frequency of jumps and the reaction volume. Being an obvious alternative to diffusion mechanism, the hopping mechanism was first proposed in papers [

The model of the “black” ball of the radius

Kinetics (

The explicit expression for the accumulation kinetics of geminate reaction product in superposition approximation is deduced by substitution of (

Formula (

The more realistic model, we shall take here for the bulk reaction that

The model of a “black” ball of the radius

The first co-factor of (

The kinetics of the bulk reaction

Stationary rate constant (

The expression for the accumulation kinetics of geminate reaction product in the superposition approximation is deduced by substitution of (

The non-Markovian part of the kinetics is defined by the integral

In accordance with (

The choice of the hopping mobility of an excess electron in the above microscopic description of a reacting system makes it possible to use the exactly solvable model of the “scavenger problem” formulated by the authors in [

Assuming the hopping motion of

In this limit of immobile

We begin the examination of time correlation influence with the accumulation kinetics analysis of geminate recombination products. Comparison between (

To analyze errors brought about by superposition approximation at arbitrary mobility of

To find the explicit form of the exact many-particle accumulation kinetics

The behaviour of the accumulation kinetics

Exact accumulation kinetics

Exact product accumulation rate

Before passing to the decay kinetics

To calculate the explicit form of the exact many-particle kinetics of

It is easily seen that the structure of expression (

As one would expect, the influence of correlations disappears under infinite dilution of bulk scavengers: with

Another interpretation of the rate

The behaviour of the kinetics

Exact kinetics

For diffusion motion of scavengers comparison between binary formulae (

To find the accumulation kinetics

The behaviour of the exact accumulation kinetics

Exact accumulation kinetics

The ratio of (

To calculate the decay kinetics

It is interesting to compare

To describe the distinctions between the exact solution and superposition approximation, we introduce relative deviations of the quantities measured:

The behaviour of the relative deviation

Relative deviation

Consider the behaviour of the function

Relative deviation

Using the expansion of the functions

It is easy to see that at the start at the contact (

Thus conditions (

Relative deviation

Now we pass to the analysis of the function

Figure

Relative deviation

In this brief review the “scavenger problem” (

Another consequence of time correlations between bulk and geminate channels of reactions is that the survival probability

Evidently, large distinctions in the theoretical treatment of the measured quantities are to affect experimental data interpretation. In a classical variant [^{2}/s, we get

Another part of experimental works is concerned with the rate constant of the bulk reaction of a geminate partner decay on acceptors. In particular, paper [

In conclusion it should be noted that the exactly solvable model considered above refers to the hopping motion of excess electrons with the mean length of a jump large enough for an electron to leave geminate pair in one jump and change its surroundings in the process of random walks in the bulk in an uncorrelated way. Such a model of excess electron mobility appears to be realizable in such hydrocarbons as isooctane, neopentane, where the mean free path of an excess electron is about 60–200 Å [

Also it should be noted that the exactly solvable model was used to establish the form of kinetic equations [

The authors are grateful to the Russian Foundation of Fundamental Research (projects 05-03-32651, 09-03-00456) and to the Program of Fundamental Research of Chemical Division and Material Science RAS (project 5.1.5) for the support of this work.

^{3+}ion luminescence and an estimation of electron excitation migration along the ions in glass