Spatial distribution of the reagents

Due to the extremely low translational mobility of the molecules in vitreous matrices, the kinetics of the chemical reactions in these matrices depends substantially on the form of the initial spatial distribution of the reagents. The study of the kinetics of electron tunneling reactions in vitreous matrices is often conducted in such a manner that one of the reagents is generated after vitrification of the solution by means of y- or / -radiolysis or photolysis, and the other is either generated in the similar manner or is introduced into the solution prior to freezing. In this connection, let us dwell upon the spatial distribution of both these types of reagent in vitreous matrices. 

In ref. 5, a method has been suggested of controlling the character of the spatial distribution of the additive in solid matrices, which is based on analyzing the EPR spectra of spin-labelled molecules introduced into the system under study. Due to the magnetic dipole dipole interactions of the paramagnetic spin-labelled molecules, the width of their EPR lines in the diluted (concentration N 1 M) vitrified solutions changes in proportion to their concentration 

In eqn. (2), AH°m is the EPR line width in the limit of such dilution that one can neglect the dipole-dipole interaction and A is a coefficient depending on the EPR line shape and on the character of the spatial distribution of the spin-labelled molecules. In the case of random spatial distribution according to theoretical calculations A = 35 GM 1 for the Gaussian EPR line shape and A = 56GM-1 for the Lorentzian EPR line shape. 

As a characteristic example, in Fig. 3 EPR spectra of the paramagnetic complex of copper (II) with ethylenediamine, Cu(en)2+, in a vitreous solution of 10M NaOH in H20 at 77K are presented. In Fig. 4, the concentration 

The above data show that the spin labelling technique indeed allows one to control the random character and the uniformity of the spatial distribution of the additives in vitreous matrices. The criterion of random character and uniformity of distribution is the linear dependence of the EPR line width on the concentration of paramagnetic additives and the coincidence of the experimentally measured coefficients A in eqn. (2) with the theoretical value of A for such distribution. 

---

To summarise, the form of kinetic equations for electron tunneling reactions must strongly depend on two factors the type of dependence of the tunneling probability on the distance between the reagents and the form of the spatial distribution of the reagents. 

The form of the initial spatial distribution of the reagents is determined by the structure and the phase state (solid or liquid) of the solution in which the reaction takes place, the method of generating the reagents (electron donors and acceptors), and also by the spatial distribution of the particles which are the precursors of the donors and acceptors. Two radically different forms of spatial distribution of donors and acceptors are possible the pairwise distribution, i.e. the distribution in isolated pairs, and the nonpair distribution. The difference between them is that, in the case of the pairwise distribution, the reaction occurs only in the isolated pairs of the reagents, i.e. the reaction between the donor and the acceptor from two different pairs is impossible. 

In the present chapter, (1) the macroscopic kinetics of the electron tunneling reaction is considered for various types of spatial distribution of the reagents and for situations when the reagents can be both immobile and mobile (2) the applicability of various kinetic models is analyzed under typical conditions of experimental studies on electron tunneling reactions and (3) methods are described of the determination, from the kinetic data, of various parameters which characterize the rates and distances of electron tunneling. 

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

Kinetic equations for the recombination luminescence intensity in the presence of a permanent electric field for the arbitrary non-pair initial spatial distribution of the reagents in the case when the concentration of one of them considerably exceeds that of the other, have been obtained in ref. 21. These equations have the form... 

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... 

The parameters ve and ae can be found from the experimental data on the kinetics of electron tunneling reactions only in the case when the form of the spatial distribution of the reagents as well as their initial concentrations (0) and N(Q) are known. Let us consider methods of determining the parameters ve and ac from kinetic data for various practically important forms of the spatial distribution of the reagents. 

As noted above, the calculation of the parameters ve and ac, the main kinetic characteristics of electron tunneling reactions, from kinetic data is possible only if the spatial distribution of the reagents is known. For this reason experiments on the quantitative investigation of electron tunneling... 

The ability of electron tunneling to provide PET at large and various distances when put together with a rather sharp exponential dependence of the tunneling probability on the distance can result in a rather unusual character of the reaction kinetics. The details of these kinetics depend substantially on the character of the spatial distribution of the reagents as well as on how mobile they are. We shall discuss this problem here only very briefly, just to provide better understanding of the data presented below on electron tunneling in PET. For a more detailed discussion see Chapter 4 of Ref. [31],... 

Consider first the kinetics of electron tunneling between immobile reagents. In this case the character of the spatial distribution of the reagents has the strongest influence on the reaction kinetics. From the practical point of view two types of... 

For other than rectangular types of pairwise spatial distribution of the reagents, the kinetics may deviate somewhat from Eq. (4). Note, however, that in most cases this deviation is not expected to be too large since, due to a very sharp exponential dependence of the tunneling probability on R, the kinetics of electron tunneling is not that sensitive to the exact character of a pair-wise distribution. 

Recently, Lepoint-Mullie et al. used Weissler s reagent and starch to trap iodine (levitation cells at 24 kHz or 43 kHz).164 They observed that single bubbles showed a strong chemical activity under certain dynamic regimes (i.e., not only when they luminesce) and the spatial distribution of the chemical species was strongly anisotropic (Fig. 33). Under the most chemically active conditions (with no SL detected by a photo-multiplier tube with sensitivity 3 x 10"H Im), over 10 chlorine radicals were released at each acoustic cycle. Such an experiment (with chemical species as tracers) also enables a study of the liquid flows around a bubble.165... 

When the concentrations of reagents have comparable values, it is necessary to pay attention to the correlation effect in the decay of different donors, i.e. to consider the fact that the spatial distribution of acceptors near the chosen donor can change as a result of the decay of the acceptors in the reactions with other donors neighbouring the chosen one. The rigorous derivation of kinetic equations with the consideration of such a correlation is, as far as we know, unavailable. The approximate description of the kinetics of a biomolecular electron tunneling reaction at n(t) = N t) can be given in terms of the pair density method with the help of eqn. (19) in which, however, N is not a constant quantity but depends on time in the same way as n(t), i.e. 

We have discussed above the influence of reagent mobility on the kinetics of the electron tunneling reaction in two extreme situations, a < a and A > Rz. In the intermediate case, a a 4, i r(the mixed mechanism of reagent mobility), the equations for the kinetics of electron tunneling reactions also have a sufficiently simple form only in two extreme situations small, t r = Rz/D, and large, t > r, observation times [32], If the initial spatial distribution of reagents is random and n(0) N, the kinetics of electron tunneling reactions is described by eqn. (35) at l z, and by the equation... 

In view of the lack of a clear understanding of the physical picture of the process, the thermal diffusion model has no predictive power. On its basis, for example, the manner in which the kinetic curves for low-temperature electron transfer reactions should change with changing concentration or kind of spatial distribution of reagents cannot be predicted. By contrast, the model of electron tunneling permits such predictions, and these predictions have been shown above (see, for example, Chap. 6, Sect. 3) to agree with the experiments. 

Astemizole [152] examined the spatial distribution of astemizole and its metabolites in rat brain slices with and without perfusion with saline solution. The Sprague-Dawley rats were treated orally with the drug at 100 mg/kg in 0.4 % methylcellu-lose. Matrix solution (DHB, 10 ml) coated by 15-20 coats over the entire surface of tissue sections by a glass reagent sprayer. MALDI-MS/MS images showed the distribution of astemizole and its metabolite (M-14) in rat brain slice. Astemizole appeared to be the major drug-related component in rat brain (Fig. 2). 

This effect suggests an interesting possibility for the utilization of kinetic data of ionic reactions in polyelectrolyte solutions to characterize the distribution of the electrostatic potential in such systems. Consider a system in which the local concentrations of two reagents, Ca and Cb, vary widely as a function of the spatial coordinates. If we assume that in any volume element 3F the process takes place at a rate k CACB V,... 

---