Spin-Controlled Reactions

The fundamental processes involved in the physical formation of a radiation track and in its subsequent evolution by diffusion and reaction are stochastic in nature. Every track is unique and even identical tracks may evolve differently. Thus most recent simulation methods [5-8] are stochastic in these senses (i.e. for the underlying track and for the diffusion and reaction of the reactive particles that can take place). Unfortunately, these methods ignore the spin-dynamics because of the complexity it introduces. As most radicals in radiation chemistry are paramagnetic species, there is a possibility of spin-controlled reactions and other spin effects such as quantum beats [9], chemically induced dynamic nuclear polarisation (CIDNP) [10-13] and chemically induced dynamic electron polarisation (CIDEP) [11, 12], which would... 

Sect. 2.3.4) currently the only solvable realistic model is the diffusion equation. From the viewpoint of spin dynamics, this theory is considered incomplete, since for a spin-controlled reaction the species are required to be in the correct spin state for reaction to occur. An alternative treatment for spin controlled reactions is presented later in this Sect. 2.7.1), which analytically treats re-encounters differently to first encounter and still retains the diffusion equation. 

Sometimes for a spin controlled reaction, the probability of reaction of first encounter has a physical origin, and if this first encounter is unreactive then the spin state is also unreactive, and therefore all subsequent rapid re-encounters will not react either [due to condition (3)]. The radiation boundary condition is clearly not appropriate to use for such reactions, where an appropriate model for spin dynamics is not incorporated. 

Matheson and Rabani (1965) measured the rate of the reaction eh + eh— H2 + 20H at pH 13 under 100 atmospheres H2 pressure, where all radicals are converted to eh. From a pure second-order decay, the rate constant was determined as 6 x 109 M 1s 1. There are contradictory views on this reaction. According to some, this rate is too low for a diffusion-controlled reaction between like charges, by a factor of -4 (see Farhataziz, 1976). This factor of 4 can be accounted for by spin considerations, since each electron is a doublet but the end product H2is a singlet. To be consistent, then, one has to consider the rate of reaction eh + O—-O2- as normal for diffusion control. 

J. Saltiel and B. W. Atwater, Spin-statistical factors in diffusion-controlled reactions, Adv. Photochem. 14, 1-90 (1988). 

Diffusion-Controlled Reactions, Spin-Satistical Factors in (Saltiel and Atwater). 

While many of the important reactions in radiation and photochemistry are fast, not all are diffusion-limited. The random flight simulation methodology has been extended to include systems where reaction is only partially diffusion-controlled or is spin-controlled [54,55]. The technique for calculating the positions of the particles following a reflecting encounter has been described in detail, but (thus far) this improvement has not been incorporated in realistic diffusion kinetic simulations. Random flight techniques have been successfully used to model the radiation chemistry of aqueous solutions [50] and to investigate ion kinetics in hydrocarbons [48,50,56-58]. 

Similar considerations apply to the role of spin equilibria in electron transfer reactions. For many years spin state restrictions were invoked to account for the slow electron exchange between diamagnetic, low-spin cobalt(III) and paramagnetic, high-spin cobalt(II) complexes. This explanation is now clearly incorrect. The rates of spin state interconversions are too rapid to be competitive with bimolecular encounters, except at the limit of diffusion-controlled reactions with molar concentrations of reagents. In other words, a spin equilibrium with a... 

E. B. Krissinel and N. V. Shokhirev, Differential approximation of spin-controlled and anisotropic diffusional kinetics (Russian), in Siberian Academy Mathematical Methods in Chemistry, Preprint 30 (1989) Diffusion-controlled reactions 22, in DCR User s Manual 11-20-1990. 

This is obviously incorrect as, on chemical grounds, the o-Ps and p-Ps reaction rate constants cannot be different the statistical spin substate factor should not appear in the rate at which the reaction occurs but rather, as in reaction XI, in the yield of the products of the reaction. Formally, reaction schemes XI and XII lead to exactly the same type of kinetic equations to describe the PALS parameters, particularly, A,3. However, if one wishes to compare the experimentally determined k with some theoretical expression such as the diffusion-controlled reaction rate constant, reaction XII will lead to a value of k which is 4 times lower than that yielded by reaction XI if o-... 

Table 4.4 Comparison between experimental Ps reaction rate constants (k ) and diffusion-controlled reaction rate constants calculated from eq. (18) by using either the bubble (kDd, Rb) or the free Ps (kD, RPs = 0.053 nm) radius, (a), unpublished results (b), [82] (c) [61] (d), [84], ox = oxidation sp = spin conversion bs = bound-state formation. The rate constants are in M W. NDMA N-dimethylacetamide 0-NO2 ...

The hypothesis that the HO2 formed in reaction (iv) is rapidly removed (thus preventing its re-dissociation) has recently been examined for flame systems by Dixon-Lewis et al. [182]. On the assumption of equilibration of the fast, bimolecular, electron spin conserving reactions (i), (ii) and (iii), it is possible to compute concentration profiles for all the chemical species in the recombination region of a wide variety of flame systems. The calculation requires knowledge of the rate coefficients 4, Sa and ki 7— 225 which control the rate of electron spin removal (recombination). The rate of recombination via HO2 is calculated as the difference... 

To obtain numbers corresponding to 100% displacement, the substrate in control reactions is heated at 95°C for 30 min in helicase assay reaction mix in a siliconized 1.5-mL microfuge tube. After a brief spin in the microfuge, the substrate is hybridized to capture oligo bound to 96-well plates and processed in the same manner as the enzyme reactions. The data (cpm) from the heated substrate control reactions correspond to 100% displacement of the substrate. 

Diffusion-Controlled Reactions in Solution, Spin Statistics... 

Saltiel, J., Atwater, B. W., Spin statistical Factors in Diffusion controlled Reactions, Advances in Photochemistry, Vol. 14, John Wiley Sons, Inc., New York, 1988, pp. 1 90. 

SPIN-STATISTICAL FACTORS IN DIFFUSION-CONTROLLED REACTIONS... 

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