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): The main reason for the difference in the k₁ values are the different steric hindrances in radicals. It has been found that the values of k₁ 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: The resultant ΔH₁^≠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 k₁ and log(T/η). The recombination of radicals I, III, and IV is limited by translational diffusion. The k₁ 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 ΔH₁^≠ 0. The recombination of these three radicals includes an intermediate step of complex formation: For 4-phenyl- (II), 2,6- dimethoxy- (V), 2,4-diphenyl- (VI), and radicals VII, IX, and X the linear relationships between log k₁ and log (T/η) have a slope of from 0.5 ± 0.05 to 0.8 ± 0.05. The k₁^-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 k₁ 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 k₁ 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 k₁ relationships, which is quite in line with the theory of diffusion-controlled reversible recombination reactions.     

Solvent effect on reversible self-termination reactions of aromatic free radicals

Rates and thermodynamic data have been obtained for the reversible self-termination reaction: Involving aromatic 2-(4′dimethylaminophenyl)indandione-1,3-yl (I), 2-(4′diphenylaminophenyl)indandione-1,3-yl (II), and 2,6 di-tert-butyl-4-(β-phthalylvinyl)-phenoxyl (III) radicals in different solvents. The type of solvent does not tangibly affect the 2k₁ of Radical(I), obviously due to a compensation effect. The log(2k₁) versus solvent parameter E_T(30) curves for the recombination of radicals (II) and (III) have been found to be V shaped, the minimum corresponding to chloroform. The intensive solvation of Radical (II) by chloroform converts the initially diffusion-controlled recombination of the radical into an activated reaction. The log (2k_?1) of the dimer of Radical (I) has been found to be a linear function of the Kirkwood parameter (ε - 1)/(2ε + 1), the dissociation rate increasing with the dielectic constant of the solvent. The investigation revealed an isokinetic relationship for the decay of the dimer of Radical (I), an isokinetic temperature β = 408 K and isoequilibrium relationship for the reversible recombination of Radical (I) with β° = 651 K. For Radical (I) dimer decay In(2k_?1) = const + 0.8 In K, where K is the equilibrium constant of this reversible reaction. The transition state of Radical (I) dimer dissociation reaction looks more like a pair of radicals than the initial dimer. The role of specific solvation in radical self-termination reactions is discussed.     

Kinetics of reversible recombination of aromatic C-centered radicals

The kinetics of the reversible recombination of the 2-phenyl- (I), 2-p-methoxyphenyl-(II), and 2-p-nitrophenyl-3-oxo-2,3-dihydrobenzothiophene-2-yl (III) radicals have been investigated. Recombination rate constants of R(I–III) have been determined in different solvents (2k₁ ～ 10⁹ M^?1 s^?1). The rate of reaction (I) with R(I–III) decreases with increasing solvent viscosity η. In the toluene-vaseline oil mixture (2 ? η ? 120 cP) the recombination of R(I–III) is molecular mobility limited. The thermodynamic parameters of reaction (I) have been determined: ΔH⁰ = 20–30 kcal/mol. Activation volumes ΔV for recombination of R(II) have been measured. In n-propanol ΔV is equal to the viscous flow activation volume of the solvent ΔV. In toluene and chloroform ΔV < ΔV. For the last two solvents the activation volumes of the cage reaction have been estimated ΔV = ?(2–3) cm³/mol. Visible-range absorption spectra and ESR spectra have been recorded for R(I–III). The role of cage effect in the reactivity anisotropy averaging of R(I–III) is discussed. The potential of the high-pressure tests for deriving information about the elementary act of a fast bimolecular reaction is considered.     

Decay kinetics of aryloxy and semiquinone radicals in the presence of copper ions

The decay kinetics of aryloxy and semiquinone radicals in the presence of copper ions in aqueous solutions has been studied by means of the flash photolysis technique. The radicals are involved in electron transfer reactions and those leading to the formation of intermediate complexes with copper ions. The complexes of p-benzosemiquinone anion radicals and 2-hydroxyphenoxy radicals with cupric ions decay in bimolecular self-reactions at a much slower rate than the original radicals. The increased stability of the complexes compared with the initial radicals is attributed to partial delocalization of the unpaired electron over the electron shell of copper and to steric hindrances in the self-reactions of complexes.     

Bimolecular self-reactions of 2-arylindandione- 1,3-yl radicals studied by flash photolysis

Kinetic and thermodynamic data for reaction (1) of certain C-centered aromatic radicals (referred to in this paper by the numbers I to X) in chlorobenzene: have been obtained. The k₁ values of radicals varied between (1.1 ± 0.2) × 10⁶M^?1·sec^?1 (radical VIII) and (3.6 ± 0.7) × 10⁹M^?1 sec^?1 (radical VI) at 20°C. An investigation of the relationship between the recombination rates of radicals I–VIII and X and the solvent viscosity (mixture of toluene and dibutylphthalate, 0.6 < η < 18.4 cP) has shown that the recombination reactions involving radicals I–IV are limited by diffusion in solvents having a viscosity η> 10 cP and are activation reactions in solvents having a viscosity η < 10 cP. The recombination of radicals VIII and IX is an activation reaction, while that of radicals V–VII is diffusion-controlled in the entire viscosity range. The recombination of radical X is limited, in the viscosity range of 18.4 to 2 cP, by intrusion into the first coordination sphere of the partner, the effect of viscosity on the radical X recombination rate in the specified range being the same as its effect on diffusion-controlled reactions. The possible reasons of the discrepancies between the experimental fast recombination rate constants and the theoretical values calculated by the Debye–Smoluchowski theory are discussed. The equilibrium constant depends strongly on the nature of the substituent in the phenyl fragment: the substituents which increase unpaired electron delocalization in the radical intensify the dissociation of the respective dimer. Long-wave absorption bands have been recorded for radicals I–X and their extinction coefficients obtained. Dimers I–V are thermo- and photochromic compounds.     

Kinetics of recombination,dismutation, and disproportionation reactions involving neutral ketyl radicals and radical anions

The kinetics of fast elementary recombination of neutral ketyl radicals of benzophenone and its four derivatives (BPH?), the dismutation of benzophenone radical anions, the disproportionation between BPH? and stable nitroxyl radicals, ( ), and the electron transfer have been investigated in both individual solvents and binary mixtures of different viscosities. Reaction (1) for unsubstituted BPH in water, water glycerol, and n-hexane is controlled by diffusion with 2k₁ ? k_diff. In aliphatic alcohols and toluene, which form solvation complexes with BPH?, reaction (1) is diffusion-enhanced and activation-controlled, respectively, with 2k₁ < k_diff. In a viscous solvent such as 1-propanol–glycerol mixture (100 ? η ? 450 cP) reaction (1) is diffusion-controlled. Reaction (2) in alkaline 1-propanol and alkaline 1-propanol–glycerol mixture is activation controlled. The rates of reactions (3) and (4) for benzophenone radicals and nitroxyl radicals of the imidazoline series decrease as the viscosity of the water–glycerol and 1-propanol–glycerol mixtures is increased. The reactions are molecular mobility limited; nevertheless, the numerical values of k₃ (k₄) are 2–6 times as small as the corresponding k_diff values due to the low steric factor of the reactions (therefore called pseudodiffusion-controlled reactions). The theoretical estimates of k₃ (k₄) are in good agreement with the experimental results. The elimination of spin forbiddance in the process of radical recombination in viscous solvents is discussed.