Effect of solvent viscosity on the kinetics of reversible dimerization of phenoxy radicals

Flash photolysis technique has been used to obtain the rate and thermodynamic parameters of the reversible dimerization reactions of a range of ten phenoxy radicals (I–X) in a toluene–dibutylphthalate mixture (0.6 cP ≤η≤18.4 cP):\documentclass{article}\pagestyle{empty}\begin{document}$$ {\rm R}^{.} + {\rm R}^{.} {\mathop{{\buildrel{-\!\!\longrightarrow}\over{\longleftarrow}}}\limits_{k_{-1}}^{k_1}}{\rm D} $$\end{document}The main reason for the difference in the k 1 values are the different steric hindrances in radicals. It has been found that the values of k 1 for 2,6‐diphenyl‐4‐methoxy‐ (I), 2‐phenyl‐(III), and 2‐methoxyphenoxy (IV) radicals are 3–5 times smaller than the respective diffusion constants calculated according to the Debye formula with regard to the spin‐statistical factor:\documentclass{article}\pagestyle{empty}\begin{document}$$ k_{diff} = \sigma \frac{{8{\rm RT}}}{{3000{\rm \eta }}} $$\end{document}The resultant Δ H 1 ≠ values for these radicals in toluene and dibutylphthalate are close to the activation energies of the viscous flow of the solvents B . Linear relationships with a slope equal to unity are observed between log k 1 and log( T /η). The recombination of radicals I, III, and IV is limited by translational diffusion. The k 1 values for 2,6‐diphenyl‐ (VII), 2,6‐di‐ tert ‐butyl‐ (IX), and 2,6‐di‐ tert ‐butyl‐4‐methylphenoxy (X) radicals are 10–60 times smaller than k diff and Δ H ≠ B . In the case of radical X in toluene Δ H 1 ≠ 0. The recombination of these three radicals includes an intermediate step of complex formation:\documentclass{article}\pagestyle{empty}\begin{document}$${{\rm R}^\cdot+{\rm R}^\cdot}{\mathop {{\scriptstyle\longleftarrow}^{\hskip-13pt\longrightarrow}}}{\rm R^\cdot}\ldots {\rm R}^\cdot \rightarrow {\rm D}$$ \end{document}For 4‐phenyl‐ (II), 2,6‐ dimethoxy‐ (V), 2,4‐diphenyl‐ (VI), and radicals VII, IX, and X the linear relationships between log k 1 and log ( T /η) have a slope of from 0.5 ± 0.05 to 0.8 ± 0.05. The k 1 ‐1 versus η relationships for these radicals are not straight lines. The recombination of these six radicals is limited by translational and rotational diffusion. With the aid of theoretical models, the k 1 versus η relationships have been used to derive the steric factor f in radical recombination and the angle θ between the axis and the solid angle generatrix. The solid angle defines the reaction spot on the radical‐sphere surface. The recombination of the 2,6‐diphenyl‐4‐diphenylmethylphenoxy radical (VIII) takes place in the region intermediate between the diffusion and the kinetic ones, and the relationship between log k 1 and log ( T /η) for this radical has a plateau portion. The log k ‐1 versus log ( T /η) relationships have precisely the same form as the corresponding k 1 relationships, which is quite in line with the theory of diffusion‐controlled reversible recombination reactions.