Recombination probability of radicals

Shin and Kapral have applied the kinetic theory of reactions in solution to the case of two radicals (e.g. iodine atoms) recombining with one another [286]. As it is the behaviour of both radicals which is of interest, Shin and Kapral seek to evaluate the doublet density of A and B, t), rather than the singlet density as used in the case of homogenous reactions of the type [eqn. (306)] where one species is not transformed. The doublet density changes as a result of collision with the solvent and so the triplet density, / BS(123, f), is of concern and the equation for the doublet density is like that of eqn. (295) with a = A, j3 = B and p = S. The triplet density, /f 8, itself depends on a quartet distribution, that of the radical reactants A and B and any two solvent molecules. The second solvent molecule can collide with A, B or the first solvent molecule and thereby change f BS. Following the usual procedure, the triplet density 

Using cluster functions and a super-position approximation which ignores the four-body correlation function x BSS(1234, f it jg possible to write simultaneous equations for the doublet and triplet correlation functions in a manner analogous to the homogeneous reaction case [286]. 

Before discussing the solution of these equations, it is prudent to known where we are aiming to go In Chaps. 6 and 7, the quantities of interest were shown to be the survival and recombination probabilities. From the diffusion equation, the former was found to be the volume integral of the probability density, p(r, and was discussed in Chap, 6, Sect. 2. Recombination probabilities are similarly the time and volume integrals of the rate of reaction of the pair. In a similar manner, the survival probability in Laplace transform space is 

The second term on the right-hand side is the recombination probability, — q(z). Now, X2B a0b is the doublet density f2n and hence the recombination probability is the negative of the integral (or average) over all wave vectors, q, and velocities of A and B (vj and v2) of the reactive collision operator, TAB, and the doublet distribution of A and B, fAB. 

Shin and Kapral found that the equation which the doublet correlation X B satisfies is 

---

Fig. 23. Recombination probability of radical pairs formed in the presence of a radical scavenger (diphenylpicrylhydrazine) plotted against the scavenger concentration and also the most probable distance between scavenger molecules. Radicals are usually termed free when they are essentially uncorrelated with any other radical (i.e. radical—radical distances >100nm). At shorter radical—radical distances, the correlation becomes strong and these are termed secondary pairs or primary pairs if formed as an encounter pair. Taken from Hammond et al. [290] for the recombination of cyanocyclohexyl radicals in chlorobenzene at 80 C.

There have been surprisingly few studies of the time-dependent recombination probability of radicals in solution. The only one, other than those already mentioned or involving magnetic field effects (see Sect. 

For the SiH2 radicals the surface reaction coefficients have been taken as 5 = P = 0.8 [192]. This sticking coefficient is large because there is no barrier for insertion of this species into the a-Si H surface. Kae-Nune et al. [217] specify a surface recombination probability of about 1 for atomic hydrogen on an a-Si H surface during deposition that results mainly in recombination of H with an H-atom bounded to the surface. 

Fig. 21. Inverse recombination probability of f-butyl radicals formed from O, di-f-butyl peroxide (DBP) by photo-dissociation , di-f-butyl hyponitrite (DBH) by thermal dissociation and A, di-f-butyl peroxyoxalate (DBPO) by thermal dissociation plotted against the inverse viscosity of the solvent. The temperature was 45°C. After Kiefer and Traylor [288 ].

Fig. 22. Inverse recombination probability of perfluoromethyl radicals, formed by photo-dissociation of perfluoroazomethane in several solvents at different temperature, plotted against Ti/2 rj 1, where r] is the solvent viscosity in Pa s. After Dobois et al. [289a],...

P ) °n exlernal magnetic field strength Hq. Ps is the recombination probability of the radical pair comprised of GeEt3 and CH2PI1 radicals... 

As shown by calculations, the carbenoid mechanism of dichlorogermylene insertion in ordinary C—Cl bond begins by electrophilic attack of the vacant p-orbital of the Ge atom on the electrons of the bond . The vacant p-orbital does not interact with the unpaired electrons of the chlorine atoms. When the distance between the reactants decreases and becomes close to the value of the C—Cl bond length, inactivated transfer of Cl to the germylene center occurs with formation of a radical pair, followed by its recombination. The closer the components of the radical pair, the smaller the probability of radicals movement away from one another. The theoretical interest concerning the details of the germylene insertion mechanism is continuing. Thus, a quantum-chemical examination of... 

In the encounter RP, the ratio of singlet and triplet spin state populations is 1 3 as shown by reaction (9-12c). The MIE arises almost completely from the T-S conversion of tripler RP. Thus, the recombination probability of peroxy radicals with terminal atoms is higher than that of radicals with terminal 0 or 0 atoms. In the case of polypropylene, the a value of 1.060 0.005 was obtained for O, but 1.015 0.010 for 0. This result certified that (MIE) a(CIE) for reaction (9-12). 

For radiation grafting, the stabilization of radicals in the polymer films is very important. Due to the flexibility of polymer chains, rearrangements and chemical interactions are possible over longer distance, in particular above the glass transition temperature. To lower the probability of radical recombination, exposed polymer substrates can be stored at low temperatures to reduce the chain mobility inside the polymer. Temperatures of -80°C are usually sufficient to stabilize the radicals over weeks to months. 

The main mechanism and proportion of reactive species produced by irradiation depend on the irradiation conditions and the nature of the irradiated material. For example, the probability of radical-radical reactions in the bulk will increase by irradiation at a higher dose rate. On the contrary, recombination reactions in the track will efficiently occur by irradiation at a higher LET value because of the overlap of the spurs along the trace of the ion beam. Therefore, the concentration of reactive species, which will expand into the bulk to react with solutes, will be lower and localized by the irradiation of heavy ion beams rather than gamma ray or high-energy electron beams. 

Localization of Radical Pairs in Micelles. CIDNP can often be enhanced by the use of micelles to enhance the recombination probability of photochemi-cally produced radical pairs. Bagranskaya et al have reviewed this techique. Goez and Heun have used Monte Carlo simulations of diffusional trajectories to calculate reencounter probabilitiies of micellized radical pairs. By varying the initial locations, they found that unless at least one of the radicals starts its diffusional trajectory extremely near the micelle boundary, the reencounter probability is essentially the same as in the case of free diffusion. It was concluded... 

In the previous section, we learned how the recombination probability of a radical pair depended on the coherent mixing of the spin states caused by the S-To mixing. On the other hand, it also depends on the incoherent mixing caused by transversal and longitudinal relaxation. In this section, we will show that one can obtain a qualitative understanding of these effects by considering the spin evolution described by the Bloch equations. From textbooks of Quantum Mechanics, any Hermitian operator F has the following property ... 

An individual radical from the RP may encounter a radical from a different RP to fomi what are known as random RPs or F pairs. F pairs which happen to be in the singlet state have a high probability of recombining, so the remaining F pairs will be in the triplet state. Consequently, the initial condition for F pairs is the triplet state in nearly all cases. 

Recombination reactions between two different macroradicals are readily observable in the condensed state where molecular mobility is restricted and the concentration of radicals is high. Its role in flow-induced degradation is probably negligible at the polymer concentration normally used in these experiments (< 100 ppm), the rate of radical formation is extremely small and the radicals are immediately separated by the velocity gradient at the very moment of their formation. Thus there is no cage effect, which otherwise could enhance the recombination efficiency. 

---