Geminate radical recombination. Theory

Before defining a few quantities of interest in the theory of radical recombination, it is worthwhile to mention briefly a few of the systems which have been studied experimentally and the type of information 

The rate of reaction of methyl radicals is in excellent agreement with the predictions of the Smoluchowski theory (see Chap. 2, Sect. 2.6). Consequently, it appears that geminate radicals move towards and away from each other at a diffusion-limited rate. Once an encounter pair is formed, reaction is very rapid (primary recombination). Furthermore, the encounter pair is held together for a considerable time ( 0.1ns in mobile solvents) because the surrounding solvent molecules hinder their separation (solvent caging). There is much evidence which lends some support for this view the most important influences on the recombination probability are listed below. 

With so many uncertainties, it is hardly surprising that the difficulties inherent in a successful application of the diffusion equation (or molecular pair analysis) to recombination probability experiments are very considerable. Chemically induced dynamic polarisation (Sect. 4) is a fairly new technique which may assist in the study of recombination of radicals following their diffusive separation from the solvent cage. 

Recently, experiments have been reported where the time dependence of the radical survival probability has been measured. Not only is the (long time) escape or recombination probability measured, but also the time scale over which the initial concentration of radicals decays to the final radical concentration has been noted [266—68]. Such studies provide extremely valuable additional information, because the time scale for reaction is the time scale it takes for the radicals to diffuse together again and hence these experiments give some insight into the distribution of initial separation distances. For instance, radicals separated by r0 1 nm take rl/6D 0.16 ns to diffuse together in a solvent of diffusion coefficient 10 9 m2 s-1. Once the theory of radical recombination has been discussed in the remainder of this section, these time-dependent studies will be reconsidered in Sect. 3. 

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There have been many other theoretical analyses of geminate radical recombination probabilities, some of which are considered further below. They can be divided into three types (a) diffusion equation treatments, (b) first passage time methods, and (c) kinetic theory applications. 

Geminate recombinations and spur reactions have been widely studied in water, both experimentally and theoretically [13-16], and also in a few alcohols [17,18]. Typically, recombinations occur on a timescale of tens to hundreds of picoseconds. In general, the primary cation undergoes a fast proton transfer reaction with a solvent molecule to produce the stable solvated proton and the free radical. Consequently, the recombination processes are complex and depend on the solvent. The central problem in the theory of geminate ion recombination is to describe the relative motion and reaction between the two particles with opposite charges initially separated by a distance rg. In water, the primary products of solvent radiolysis are the hydrated electron e ", the hydroxyl radical OH and the hydronium cation H3O+ ... 

The spinless variant of the present theory was already discussed in Section V.D and its interrelationship with IET and a number of other theories of exciplexes or stable complexes was disclosed. In the next Section XI.D we also consider not an excited-state but a ground-state particle. It is subjected to thermal dissociation to radicals followed by their geminate and subsequent bimolecular recombination into the fluorescent product. 

The reaction in the bulk can be really neglected if the free radicals are unstable as a result of fast decomposition, discharging, or other reasons. But even in this case neither of the abovementioned models is an appropriate tool for the explanation of the phenomenon. The contact diffusional theory provides the alternative interpretation of the effect originating from either geminate recombination alone or together with the reaction in the bulk. 

The mechanism can be best understood within the framework of the conventional theory of radical chain kinetics, provided that certain of the usual simplifying assumptions are omitted. A solution is given to the problem of steady-state polymerization rate as a function of monomer and initiator concentration, taking into account termination reactions of primary radicals and recombination of geminate chains arising from the same initiation event. This model is shown to account for the kinetic data reported herein. With appropriate rate constants it should be generally applicable to radical polymerizations. 

Diffusion models of geminate pair combination connect the time-dependent pair survival probability, P t), with the macroscopic properties of the host solvent. Radicals are treated as spherical particles immersed in a uniformly viscous medium. The pair is assumed to undergo random Brownian movements that ultimately lead to either recombination or escape. The expression of P i) depends on the degree of sophistication of the theory chosen for analyzing the process. In the simplest theory,... 

The theory underlying this effect depends critically on two selection principles the nuclear spin-dependence of intersystem crossing in a radical pair, and the electron spin-dependence of the rates of radical pair reactions. The combination of these selection principles causes a sorting of nuclear spin states into different products, formed by geminate recombination (allowed for singlet pairs but spin-forbidden for triplet pairs) or by free-radical ( escape ) products (whose formation is electron spin-independent). As a result, geminate reaction products are formed with characteristic non-equilibrium populations of nuclear spin levels, whereas escape products show complementary non-equilibrium spin level populations. 

With the intensive development of ultrafast spectroscopic methods, reaction dynamics can be investigated at the subpicosecond time scale. Femtosecond spectroscopy of liquids and solutions allows the study of sol-vent-cage effects on elementary charge-transfer processes. Recent work on ultrafast electron-transfer channels in aqueous ionic solutions is presented (electron-atom or electron-ion radical pairs, early geminate recombination, and concerted electron-proton transfer) and discussed in the framework of quantum theories on nonequilibrium electronic states. These advances permit us to understand how the statistical density fluctuations of a molecular solvent can assist or impede elementary electron-transfer processes in liquids and solutions. 

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