Geminate recombination kinetics

In an early attempt, Mozumder (1968) used a prescribed diffusion approach to obtain the e-ion geminate recombination kinetics in the pure solvent. At any time t, the electron distribution function was assumed to be a gaussian corresponding to free diffusion, weighted by another function of t only. The latter function was found by substituting the entire distribution function in the Smoluchowski equation, for which an analytical solution was possible. The result may be expressed by... 

The theory of geminate recombination experienced a similar evolution from primitive exponential model and contact approximation [19,20], to distant recombination carried out by backward electron transfer [21], However, all these theories have an arbitrary parameter initial separation of reactants in a pair, / o. This uncertainty was eliminated by unified theory (UT) proposed in two articles published almost simultaneously [22,23], UT considers jointly the forward bimolecular electron transfer and subsequent geminate recombination of charged products carried out by backward electron or proton transfer. The forward transfer creates the initial condition for the backward one. This is the distribution of initial separations in the geminate ion pair/(ro), closely analyzed theoretically [24,25] and inspected experimentally [26,27], It was used to specify the geminate recombination kinetics accompanied by spin conversion and exciplex formation [28-31], These and other applications of UT have been covered in a review published in 2000 [32],... 

Studies on heterogeneous systems include diffuse reflection laser photolysis of the geminate recombination kinetics of triplet radical pairs generated from 2,4,6-trimethylphenol adsorbed on microcrystallinecellulose, and laser flash photolysis... 

D. F. Kelley and P. M. Rentzepis, Chem. Phys. Lett., 85, 85 (1985). Predissociation and Geminate Recombination Kinetics of I2 in Liquid Xenon and CCI4. 

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. 

In some cases, a long tail can be detected in the decay. It has been assigned to geminate recombination according to the following kinetic scheme ... 

Pathway I was observed for all the 02 complexes studied, strained or unstrained, as well as for the unstrained CO-complexes. This particular pathway is the same one observed in the photodissociation of the natural heme complexes (3,4) (HbCO, MbCO, HbO and MbO ) with the exception that there is no detectable geminate recombination to the limit of our experiment, 50 ps. Pathway II, observed for the strained-CO complexes, reveals the presence of a fifth intermediate X found early in the dissociation that is either absent or undetectable in the natural or synthetic heme complexes following pathway I. The kinetics associated with the evolution of these intermediates will be discussed shortly. First, it is appropriate to examine in some detail the experimental AA difference spectra of two representative complexes, 1 -CO and 1-ET-CO. A discussion of 1-ST-CO and l-ET-O is also included for comparative purposes. ... 

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. 

Further detailed kinetics of the geminate recombination of electrons and positive ions and their application to the advanced technology will be studied by higher time resolution of the femtosecond pulse radiolysis and both by the higher S/N ratio and the wider wavelength monitoring light of the improved subpicosecond pulse radiolysis shown in Fig. 7. 

Due to the existence of two quite different distinctive distances (scale factors) - lo and l - the recombination kinetics also reveals two stages called monomolecular and bimolecular respectively. The defects survived in their geminate pairs go away, separate and start to mix and recombine with dissimilar components from other pairs. It is clear that the problem of kinetics of the monomolecular process is reduced to the time development of the probability w(f) to find any single geminate pair AB as a function of the initial spatial distribution of the pair components f(r), recombination law cr(r) and interaction Uab (r). The smaller the initial concentration of defects, n(0) —> 0, as lo —> oo, the more correct is the separation of the kinetics into two substages, whereas the treatment of the case of semi-mixed geminate pairs is a very difficult problem discussed below. 

Until the geminate pairs start to mix, i.e., at relatively short times r relative diffusion coefficient, the monomolecular kinetics reads n(t) = n(0)u>(t), with n(0) = nA(0) = ne(0) being initial particle concentration. The distinctive feature of this stage is the linearity of the recombination kinetics n(t) with respect to the irradiation dose n(0). 

Strictly speaking, it is correct in the case of complete particle recombination at the black sphere only partial particle reflection is discussed by Doktorov and Kotomin [50]. Incorporation of the back reactions into the kinetics of geminate recombination has been presented quite recently by [74, 75]. The effective radius for an elastic interaction of defects in crystals, (3.1.4), was calculated by Schroder [3], Kotomin and Fabrikant [76],... 

They have calculated the continuous diffusion equation (3.2.30) with U(r) = -a/r3 for several kinds of nn F, H centres in the crystalline lattice. Figure 3.9 demonstrates well that both defect initial separation and an elastic interaction are of primary importance for geminate pair recombination kinetics. The 3nn defects are only expected to have noticeable survival probability. Its magnitude agrees well with equation (3.2.60). 

Recombination of the surface electron Fs+ -centres and of the bulk hole V -centres in y-irradiated highly dispersed oxide CaO has been studied [69]. The recombination kinetics is weakly dependent on temperature in the range 4.2-77 K. The formal activation energy has a value of only 30 cal mol l. At small irradiation doses (less than 2 x 1019eVcm-3) the recombination appears to be of geminate character, i.e. it occurs only in the parent donor-acceptor pairs, the process kinetics being well described by the linear dependence of the concentration of centres on the logarithm of observation... 

Homogeneous kinetics is used instead of diffusion kinetics to express the dependence of intraspur GH, on solute concentration. The rate-determining step for H2 formation is not the combination of reducing species, but first-order disappearance of "excited water." Two physical models of "excited water" are considered. In one model, the HsO + OH radical pair is assumed to undergo geminate recombination in a first-order process with H3O combination to form H2 as a concomitant process. In this model, solute decreases GH, by reaction with HsO. In the other model, "excited water" yields freely diffusing H3O + OH radicals in a first-order process and solute decreases GH, by reaction with "excited water." The dependence of intraspur GH, on solute concentration indicates th,o = 10 9 — 10 10 sec. 

The applicability of homogeneous kinetics is attributed to first-order disappearance of H20, excited water, as the rate-determining step for H2 formation, instead of the combination of reducing species as commonly assumed when using the Samuel-Magee model. Two alternative physical models of H20 are proposed. In one, H20 is the HsO + OH radical pair which is assumed to undergo geminate recombination with... 

---