Geminate escape probability

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. 

The latter quantity is called the escape probability, and describes the probability that the two oppositely charged particles of the geminate pair will never recombine with each other and become free ions. 

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. 

Calculation of the electric field dependence of the escape probability for boundary conditions other than Eq. (11b) with 7 = 0 poses a serious theoretical problem. For the partially reflecting boundary condition imposed at a nonzero R, some analytical treatments were presented by Hong and Noolandi [11]. However, their theory was not developed to the level, where concrete results of (p(ro,F) for the partially diffusion-controlled geminate recombination could be obtained. Also, in the most general case, where the reaction is represented by a sink term, the analytical treatment is very complicated, and the only practical way to calculate the field dependence of the escape probability is to use numerical methods. 

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. 

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

According to Fig. 3, the Onsager result [Eq. (15)], which shows the escape probability in the diffusion-controlled geminate recombination, gives the lower bound for the simulation results. The simulation results obtained for the lowest value of x (x = 0.05) are... 

Computer simulation has also been used to calculate the external electric field effect on the geminate recombination in high-mobility systems [22]. For the mean free time x exceeding -0.05, the field dependence of the escape probability was found to significantly deviate from that obtained from the diffusion theory. Furthermore, the slope-to-intercept ratio of the field dependence of the escape probability was found to decrease with increasing x. Unlike in the diffusion-controlled geminate recombination, this ratio is no longer independent of the initial electron-ion separation [cf. Eq. (24)]. 

The number of free ions (i.e. those which have escaped geminate recombination) formed per 100 eV of radiation absorbed by the liquid is termed Gfi (see the end of Sect. 2.4). It is directly proportional to the escape probability, P(E), of the ion-pair in an applied electric field, E. 

Another effect of crystal anisotropy is that the diffusion coefficient D turns out to become the diffusion tensor D [73-75]. It results in the asymmetric escape probabilities of geminate pairs in different directions. 

There is no general consensus on why the difference in the quantum yield of photosubstitutions is so large for 02-adducts (4> 10 3) and CO-adducts and on which excited states are responsible for this difference. An explanation based on a different efficiency of the recoordination of released 02 or CO molecules (geminate recombination) can be ruled out, as in the systems with the same biocomplex (e.g. Hb02 and HbCO) both molecules (02 and CO) have nearly identical escaping probability from the protein cage due to their similar size, mass and polarity. The reason could, therefore, lie in the different photoreactive excited states involved. 

The conformational orientation between the excited CNA and CHD should be restricted very much to produce a photocycloadduct in the collision complex indicated in the scheme 1. In the fluid solvents like hexane, the rotational relaxation times of the solute molecules are rather fast compared to the reaction rate, which increases the escape probability of the reactants from the solvent cavity due to the large value of ko. On the other hand, the transit time in the reactive conformation, probably symmetrical face to face, may be longer in the liquid paraffin. This means that the observed kR may be expressed as a function of the mutual rotational relaxation time of reactants and the real reaction rate in the face-to-face conformation. In this sense, it is very important to make precise time-dependent measurements in the course of geminate recombination reaction indicated in Scheme 2, because the initial conformation after photodecomposition of cycloadduct is considered to be close to the face-to-face conformation. The studies on the geminate processes of the system in solution by the time resolved spectroscopy are now progress in our laboratory. 

When Mg reacts with RX by pathway R, the result is a reactive geminate pair XMg R-[. This pair may suffer geminate reaction (probability in or escape (1 - [Pg.232]

Tachiya, M. and Schmidt, W. E, Escape probability of geminate electron-ion recombination in the limit of large electron mean free path, /. Chem. Phys., 90, 2471,1989. 

Cage escape yield (< >cage) to the yield of separated electron-transfer products (corrected for fraction of excited states unquenched) that can be intercepted and/or utilized in other secondary reactions. It is a measure of the escape probability from the geminate pair and is given by ... 

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