Radical pair escape probability

DY-x e dissociation energy of Y X bond probability of formed free radical pair to escape the cage of solvent or polymer kJ moU1... 

The chain termination is a result of tertiary alkylperoxyl radical recombination in the solvent cage. The values of the rate constants for chain termination through the disproportionation of tertiary peroxyl radicals are collected in Table 2.15. They vary in the range 103 to 105 L mol 1 s 1 at room temperature. The probability of a pair of alkoxyl radicals to escape cage recombination is sufficiently higher than that of cage recombination. The values of rate constants of the reaction 2 R02 > 2 RO + 02 measured by the EPR technique are presented in Table 2.16. 

The introduction of a free radical acceptor (scavenger) helps to measure the probability (e) of radical pairs to escape from geminate combination and diffuse out of the cage. The value of e for the fixed initiator or photoinitiator depends on the viscosity 17 of the solvent. The following empirical dependence for the photodecomposition of initiators was found... 

The probability of the radical pair to escape from geminate recombination (e) depends on the rate constants according to the following equation ... 

Chain Lenth v, Probability of Radical Pair to Escape the Cage e and Rate... 

The decay of ester hydroperoxides was found to occur more rapidly than free radical generation. The probability e for the radical pair formed from hydroperoxide to escape from... 

Escape Probability of an Isolated, Intimate Radical Pair in Liquids and Bulk Polymers... 

Diffusion models of geminate pair combination connect the time-dependent pair survival probability, P t), with the macroscopic properties of the host solvent. Radicals are treated as spherical particles immersed in a uniformly viscous medium. The pair is assumed to undergo random Brownian movements that ultimately lead to either recombination or escape. The expression of P i) depends on the degree of sophistication of the theory chosen for analyzing the process. In the simplest theory,... 

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... 

Estimates of the probability of escape of radical pairs in conventional solvents have been made by product analysis of the decomposition of diacyl peroxides. For example, Braun et al. [22] estimated that 60 to 80% of the methyl radicals produced in the thermolysis of acetyl peroxide escape geminate cage recombination. However, Guillet and Gilmer [25] showed that for longer chain and Cjj radicals the probability was much lower, ranging from 5% at 760C to 16% at 262<>C (Table VI). 

Northrup and Hynes [103] have remarked that the effects of the potential of mean force as well as hydrodynamic repulsion are very much more apparent in their effect on the survival (and escape) probability of a reactant pair of radicals than their effect on the rate coefficient. For instance, considering the escape probability of Fig. 20, suppose that an escape probability of 0.75 had been determined experimentally. Initial distances of separation Tq = 4i or 312 would have been deduced from the diffusion equation analysis alone or from the diffusion equation with the potential of mean force and hydrodynamic repulsion included. Again, the effect of a moderately slow rate of reaction of encounter pairs further reduces the recombination probability. Consequently, as the inherent uncertainty in the magnitudes of U r), D(r) and feact may be as much as a factor of 2, the estimation of an initial separation distance, Tq, of a radical pair from experimental measurements of escape probabilities may be in doubt by a factor of 30% or more. Careful and detailed analysis of the recombination of radical pairs has been made by Northrup and Hynes... 

Cr[1 - q] An A radical, having escaped from its geminate pair, may encounter several different B radicals and thus form several F-pairs before finally reacting. We have therefore to sum the F-polarization over all these pairs to find the total contribution from the F-pair process. The polarization in A arising from the (n l)the F-palr formed by an A radical is simply Up multiplied by the probability that A has survived the previous n pairs, i.e. [1 - 4 p]. The total polarization per mole of A is therefore given by the summation ... 

Secondary cage recombination of peroxy radicals [698]. In a solid polymer, a pair of polymer peroxy radicals (POO 2) is trapped in the polymer matrix. When a radical pair, produced by photoinitiation, escapes the initial cage, the probability of its recombination remains high even after several propagation steps. This phenomenon, known as secondary cage recombination, has a pronounced effect on the kinetics of oxidation and on the distribution of kinetic chain lengths in the oxidation process. 

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