Geminate ions

Retardation of back ET was also observed with phenanthrene solubilized in the SDS micelle (kb = 6.8 x 107 M-1 s-1) (see Fig. 13) [75]. However, as can be seen from Fig. 13, the transient yield of SPV- for the micellar system is extremely low, presumably because only a small fraction of SPV- can escape from the geminate ion pair. This finding implies that SPV preferably resides inside the micelle and that the electron transfer mainly takes place in the micelle, not across the charged surface. 

Another important factor to determine the charge separation efficiency is the distance between and the mutual orientation of the donor and the acceptor in the geminate ion-pair state. The rate of charge recombination depends on whether... 

In the APh-2-MV2+ system, a tight ion pair can be formed because the motional freedom of the Phen+ residue and a free access of MV + to the Phen + site allow the ion pair to realize an optimal distance and orientation, thus giving rise to a shorter-lived geminate ion pair. This explains why the back ET in the... 

Although the electrostatic potential on the surface of the polyelectrolyte effectively prevents the diffusional back electron transfer, it is unable to retard the very fast charge recombination of a geminate ion pair formed in the primary process within the photochemical cage. Compartmentalization of a photoactive chromophore in the microphase structure of the amphiphilic polyelectrolyte provides a separated donor-acceptor system, in which the charge recombination is effectively suppressed. Thus, with a compartmentalized system, it is possible to achieve efficient charge separation. 

FIG. 11 General mechanism for the heterogeneous photoreduction of a species Q located in the organic phase by the water-soluble sensitizer S. The electron-transfer step is in competition with the decay of the excited state, while a second competition involved the separation of the geminate ion-pair and back electron transfer. The latter process can be further affected by the presence of a redox couple able to regenerate the initial ground of the dye. This process is commonly referred to as supersensitization. (Reprinted with permission from Ref. 166. Copyright 1999 American Chemical Society.)... 

Williams (1964) derived the relation T = kBTrQV3De2, where T is the recombination time for a geminate e-ion pair at an initial separation of rg, is the dielectric constant of the medium, and the other symbols have their usual meanings. This r-cubed rule is based on the use of the Nernst-Einstein relation in a coulom-bic field with the assumption of instantaneous limiting velocity. Mozumder (1968) criticized the rule, as it connects initial distance and recombination time uniquely without allowance for diffusional broadening and without allowing for an escape probability. Nevertheless, the r-cubed rule was used extensively in earlier studies of geminate ion recombination kinetics. 

With the advent of picosecond-pulse radiolysis and laser technologies, it has been possible to study geminate-ion recombination (Jonah et al, 1979 Sauer and Jonah, 1980 Tagawa et al 1982a, b) and subsequently electron-ion recombination (Katsumura et al, 1982 Tagawa et al, 1983 Jonah, 1983) in hydrocarbon liquids. Using cyclohexane solutions of 9,10-diphenylanthracene (DPA) and p-terphenyl (PT), Jonah et al. (1979) observed light emission from the first excited state of the solutes, interpreted in terms of solute cation-anion recombination. In the early work of Sauer and Jonah (1980), the kinetics of solute excited state formation was studied in cyclohexane solutions of DPA and PT, and some inconsistency with respect to the solution of the diffusion equation was noted.1... 

In conclusion we may state that there is evidence for multiple ion-pair recombination in spurs yet a theoretical analysis of free-ion yield and scavenging at low-LET based on the geminate ion-pair picture is meaningful in view of the similarity of the recombination process in the geminate and multiple ion-pair cases. However, if this analogy holds, the geminate ionization yield has to be somewhat less than the true ionization yield. 

Onsager s (1938) formula for the probability of escaping geminate-ion recombination in the presence of an external field E may be written as... 

Fast pulse radiolysis studies have shown that geminate recombination occurs on the picosecond time scale [12,13]. Bartczak and Hummel [14] predicted that for -dodecane, 82% of the geminate ions still remain at 5 psec for 1 MeV irradiation. Future accelerators, with pulses of a few picoseconds length, may soon provide experimental measurements of Gtot directly. 

The central problem in the theory of geminate ion recombination is to describe the relative motion and reaction with each other of two oppositely charged particles initially separated by a distance ro- If we assume that the particles perform an ideal diffusive motion, the time evolution of the probability density, w(r,t), that the two species are separated by r at time t, may be described by the Smoluchowski equation [1,2]... 

By solving Eq. (9) subject to boundary conditions (10) and (11b), the escape probability for the totally diffusion-controlled geminate ion recombination is calculated as... 

This expression characterizes the escape probability for the partially diffusion-controlled geminate ion recombination. 

One of the most important experimental methods of studying the electron-ion recombination processes in irradiated systems are measurements of the external electric field effect on the radiation-induced conductivity. The applied electric field is expected to increase the escape probability of geminate ion pairs and, thus, enhance the number of free ions in the system, which will result in an enhanced conductivity. 

In the preceding part of this section, we have concentrated on the electron escape probability, which is an important quantity in the geminate phase of recombination, and can be experimentally observed. However, modern experimental techniques also give us a possibility to observe the time-resolved kinetics of geminate recombination in some systems. Theoretically, the decay of the geminate ion pairs can be described by the pair survival probability, W t), defined by Eq. (4). One method of calculating W t) is to solve the Smoluchowski equation [Eq. (2)] for w r,t) and, then, to integrate the solution over the space variable. Another method [4] is to directly solve Eq. (7) under relevant conditions. 

The analytical solution of the Smoluchowski equation for a Coulomb potential has been found by Hong and Noolandi [13]. Their results of the pair survival probability, obtained for the boundary condition (11a) with R = 0, are presented in Fig. 2. The solid lines show W t) calculated for two different values of Yq. The horizontal axis has a unit of r /D, which characterizes the timescale of the kinetics of geminate recombination in a particular system For example, in nonpolar liquids at room temperature r /Z) 10 sec. Unfortunately, the analytical treatment presented by Hong and Noolandi [13] is rather complicated and inconvenient for practical use. Tabulated values of W t) can be found in Ref. 14. The pair survival probability of geminate ion pairs can also be calculated numerically [15]. In some cases, numerical methods may be a more convenient approach to calculate W f), especially when the reaction cannot be assumed as totally diffusion-controlled. 

Figure 2 Survival probability of geminate ion pairs as a function of time. The two solid lines correspond to two different values of the initial electron-cation distance. The broken lines show the asymptotic kinetics calculated from Eq. (25). The value of the escape probability for Tq = O.Sr is indicated by

When the motion of electrons and positive ions in a particular system may be described as ideal diffusion, the process of bulk recombination of these particles is described by the diffusion equation. The mathematical formalism of the bulk recombination theory is very similar to that used in the theory of geminate electron-ion recombination, which was described in Sec. 10.1.2 ( Diffusion-Controlled Geminate Ion Recombination ). Geminate recombination is described by the Smoluchowski equation for the probability density w(r,i) [cf. Eq. (2)], while the bulk recombination is described by the diffusion equation for the space and time-dependent concentration of electrons around a cation (or vice versa), c(r,i). 

PICOSECOND AND SUBPICOSECOND PULSE-RADIOLYSIS STUDIES OF GEMINATE ION RECOMBINATION IN LIQUID HYDROCARBONS... 

Here the progress in the picosecond and subpicosecond pulse radiolysis is described first and then the experimental studies on the kinetics of the geminate ion recombination is explained in connection with their application to advanced technology such as the next generation nanolithography and nanotechnology. 

With the development of the picosecond pulse radiolysis, the kinetics data of the geminate ion recombination have been directly obtained. The history of picosecond and subpicosecond pulse radiolysis is shown in Fig. 7. Very recently, the first construction of the femtosecond pulse radiolysis and the improvement of the subpicosecond pulse radiolysis started in Osaka University. 

The stroboscopic pulse radiolysis with the single bunch electron pulse instead of pulse trains started in Argonne National Laboratory in 1975 [54]. The research fields have been extended by the stroboscopic pulse radiolysis with the picosecond single electron bunch, although most of researches had been limited to hydrated and solvated electrons in the aqueous and alcoholic solutions. This system was unable to study the kinetics of the geminate ion recombination in liquid hydrocarbons until the modification of the Argonne linac in 1983, which made possible the quality measurements of the weak absorption. 

The combination of the picosecond single electron bunch with streak cameras, independently developed in 1979 at Argonne National Laboratory [55] and at University of Tokyo by us [56], enabled the very high time resolution for emission spectroscopy. The research fields have been extended to organic materials such as liquid scintillators [55-57], polymer systems [58], and pure organic solvents [59]. The kinetics of the geminate ion recombination were studied [55,57,59]. 

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