Geminate recombination exponential model

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],... 

The geminate recombination is actually controlled by diffusion, if the initial separation of ions is so large that their transport from there to the contact takes more time than the reaction itself. The exponential model excludes such a situation from the very beginning, assuming that ions are bom in the same place where they recombine. Thus, EM confines itself to the kinetic limit only and fixes Z = z = const. The kinetic recombination in the contact approximation does not imply that the starts are taken from the very contact. If they are removed a bit and diffusion is fast, the recombination is also controlled by the reaction and its efficiency Z = qz is constant although smaller than in EM. 

Neither the maximum nor the descending branches of the upper curves, representing geminate recombination, are reproduced in the Markovian theory. It predicts the monotonous ion accumulation and still further decrease in the ionization quantum yield /. This is because the Markovian theory does not account for either static or subsequent nonstationary electron transfer. When ionization is under diffusional control, both these are faster than the final (Markovian) transfer. EM is a bit better in this respect. As a non-Markovian theory, it accounts at least for static ionization and qualitatively reproduces the maximum in the charge accumulation kinetics. However, the subsequent geminate recombination develops exponentially in EM because the kinematics of ion separation is oversimplified in this model. It roughly contradicts an actual diffusional separation of ions, characterized by numerous recontacts and the power dependence of long-time separation kinetics studied in a number of works [20,21,187],... 

More rigorous treatments of the geminate combination also take into consideration the probability that the radicals of a pair escape from each other, reencounter in a later event, and finally recombine (Scheme 13.2). This model leads to time-dependent radical pair combination rates and, accordingly, they predict that P t) does not follow a simple exponential decay. For instance, even for the simple case of a contact-start recombination process (ro = o), the survival probabihty is a complex function as shown in Equation 13.2... 

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