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.     

Bimolecular self-reactions of ketyl radicals of acetophenone and diphenylaminyl radicals

The rate constants of self-reactions of ketyl radicals of acetophenone in n-heptane [2k = (3.2 ± 0.5) × 10⁹ M^?1 s^?1] and diphenylaminyl radicals in toluene [2k = (3.3 ± 0.5) × 10⁷ M^?1 s^?1] have been determined at 298 K using the flash photolysis technique. The rate constant of ketyl radicals is equal to the calculated diffusion constant and, therefore, this reaction is diffusion-controlled. The aminyl radical recombination rate is independent of the viscosity of the toluene/vaseline oil binary mixture (0.55 ? η ? 12 cP) and this reaction is activation-controlled. Reactivity anisotropy averaging due to the cage effect has been considered for ketyl and some other radicals. On the basis of the analysis it has been proposed that ketyl recombination involves formation of not only pinacol, but also iso-pinacols.     

Rate constants for radical recombination. III. The trifluoromethyl radical

Products of the radical reactions arising from t-Bu₂O₂, CF₃I, and CH₃I at 146°C in the vapor phase have been measured over a 33-fold range of CH₃I/CH₃I ratios and shown to be governed by the rapidly established equilibrium Together with K estimated by thermochemical methods, the results yield, for the rate of recombination for CF₃· radicals, k_r = 10^{9.7 ± 0.5} M^?1 sec^?1.     

An absolute measurement of the rate constant for t-butyl radical combination

The rate constant for tert-butyl radical recombination has been measured near 700°K by the very-low-pressure pyrolysis (VLPP) technique and was found to be 10^8.8±0.3 M^?1·sec^?1 with neglibible temperature dependence. The thermochemical parameters for tert? butyl radicals were varied within reasonable limits to bring into agreement the data for the decomposition of 2,2,3,3-tetramethyl butane and the recombination of tert-butyl radicals. The revised thermochemistry also makes the gas-phase results and liquid-phase results compatible.     

Radical ion and triplet formation in electron transfer fluorescence quenching studied by nanosecond laser spectroscopy

Application of nanosecond laser flash photolysis led to the detection of delayed triplet production (from initially produced radical ions) in electron transfer fluorescence quenching. From both, the second order radical ion decay and the triplet growing-in, a diffusion-controlled recombination rate constant in acetonitrile of (4.3 ± 0.3) × 10¹⁰ M^?1 sec^?1 (ca. 1.2 × 10¹⁰ M^?1 in n-propanol) is obtained.     

Kinetics and rate constants for the reaction of tri-n-butylgermanium hydride with methyl iodide and carbon tetrachloride. The combination of methyl and trichloromethyl radicals in solution.

The kinetics of the photoinitiated reductions of methyl iodide and carbon tetrachloride by tri-n-butylgermanium hydride in cyclohexane at 25°C have been studied and absolute rate constants have been measured. Rate constants for the combination of CH₃? and CCl₃? radicals are equal within experimental error and are also equal to the values found for the self-reactions of most non-polymeric radicals in low viscosity solvents, i.e. ～1–3 × 10⁹ M^?1 sec^?1. Rate constants for hydrogen atom abstraction by CH₃? and CCl₃? radicals are both ～1?2 × 10⁵ M^?1 sec^?1. Tri-n-butyltin hydride is about 10–20 times as good a hydrogen donor to alkyl radicals as is tri-n-butylgermanium hydride. The strength of the germanium–hydrogen bond, D(n-Bu₃Ge–H) is estimated to be approximately 84 kcal/mole.     

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.     

Kinetics and mechanisms of substitution reactions with sulfur-containing nucleophiles in aqueous acid solutions. I—rates of reactions of some tetrahalopalladate (II) anions with thiourea and selenourea

The activation energy parameters for the reaction of PdX (X=Cl^?, Br^?) in aqueous halide acid solution with thiourea (tu) and selenourea (seu) have been determined. High rates of reaction parallel low enthalpies and appreciable negative entropy of activation. The rate law in each case simplifies to k_obs=k[L] where L=tu or seu, and only ligand-dependent rate constants are observed at 25°C. The ligand-dependent rate constants for the first identifiable step in the PdCl + X system is (9.1±0.1) × 10³ M^?1 sec^?1 and (4.5±0.1) × 10⁴ M^?1 sec^?1 for X=tu and seu, respectively, while for the PdBr + X system it is (2.0±0.1) × 10⁴ M^?1 sec^?1 and (9.0±0.1) × 10⁴ M^?1 sec^?1 for X=tu and seu, respectively.     

Rate constants for the termination of benzyl radicals in solution

The rate constant for the bimolecular combination of benzyl radicals in cyclohexane and toluene is determined as a function of temperature. Further, it is studied in cyclohexane–toluene mixtures of different compositions. In the entire range covered, 9.8 × 10⁸ ? 2k_t ? 9.0 × 10⁹M^?1·sec^?1, the data are very well described by the Smoluchowski equation for a diffusion-controlled reaction to ground-state products using a spin statistical factor of 1/4, a temperature- and solvent-independent reaction distance, and the known diffusion coefficient of toluene.     

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.     

The decomposition of chemically activated n–butane,isopentane, neohexane,and n–pentane and the correlation of their decomposition rates with radical recombination rates.

The total decomposition rates of the chemically activated alkanes n-butane, n-pentane, isopentane, and neohexane were measured using an internal comparison technique. Chemical activation was by the C? H insertion reaction of excited singlet-state methylene radicals. A total of ten rate constants ranging from 4.6 × 10⁵ to 2.3 × 10⁷ sec^?1 were measured for these alkanes at different excitation energies. These rates correlate via RRKM theory calculations with thermal A-factors in the range of 10^16.1 to 10^17.1 sec^?1 for free rotoractivated complex models and in the range of 10^16.4 to 10^17.8 sec^?1 for vibrator-activated complex models. It was found that high critical energies for decomposition, “tight” radical models, and activated complex models with free internal rotations were required to correlate the decomposition rates of these alkanes with estimated alkyl radical recombination rates. The correlation is just barely possible even for these favorable extremes, indicating that there may be a basic discrepancy between the recombination rate and decomposition rate data for alkanes.     

Reaction of methoxy radicals with oxygen. I. Using dimethyl peroxide as a thermal source of methoxy radicals

Using dimethyl peroxide as a thermal source of methoxy radicals overthe temperature range of 110–160°C, and the combination of methoxy radicals and nitrogen dioxide as a reference reaction: a value was determined of the rate constant for the reaction of methoxy radicals with oxygen: is independent of nitrogen dioxide or oxygen concentration and added inert gas (carbon tetrafluoride). No heterogeneous effects were detected. The value of k₄ is given by the expression In terms of atmospheric chemistry, this corresponds to a value of 10^5.6 M^?1·sec^?1 at 298 K. Extrapolation to temperatures where the combustion of organic compounds has been studied (813 K) produces a value of 10^7.7 M^?1·sec^?1 for k₄. Under these conditions, reaction (4) competes with hydrogen abstraction or disproportionation reactions of the methoxy radical and its decomposition (3): In particular k₃ is in the falloff region under these conditions. It is concluded that reaction (4) takes place as the result of a bimolecular collision process rather than via the formation of a cyclic complex.     

Polymerization of methyl acrylate with triphenylbismuthonium 1,2,3,4‐tetraphenylcyclopentadienylide as a new radical initiator

Triphenylbismuthonium 1,2,3,4‐tetraphenylcyclopentadienylide in 1,4‐dioxan initiated radical polymerization of methyl acrylate to ～30% conversion without gelation because of autoacceleration. The polymer had a viscosity‐average molecular weight of 200,000. The kinetic expression was R_pα[I]^0.3[M]^1.16, that is, the system followed nonideal kinetics because of primary radical termination and degradative chain‐transfer reactions. The values of kk_t and the energy of activation were computed as 3.12 × 10^?5 Lmol^?1s^?1 and 28 kJ/mol, respectively. The ylide dissociated to form a phenyl radical, which brought about polymerization of methyl acrylate. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2060–2065, 2004     

A quantitative study of alkyl radical reactions by kinetic spectroscopy. IV. The flash photolysis of azopropanes

The flash photolysis of azo?n?propane and of azoisopropane has been studied by kinetic spectroscopy. Transient absorption spectra in theregion of 220–260 nm have been assigned to the n-propyl and isopropyl radicals. For the n-propyl radical, ?_max = 744 ± 39 l/mol cm at 245 nm and the rate constants for the mutual reactions were measured to be k_c = (1.0 ± 0.1) × 10¹⁰ l/mol sec (combination) and k_d = (1.9 ± 0.2) × 10⁹ l/mol sec (disproportionation). For the isopropyl radical, ?_max = 1280 ± 110 l/mol cm at 238 nm, with k_c = (7.7 ± 1.6) × 10⁹ l/mol sec and k_d = (5.0 ± 1.2) × 10⁹ l/mol sec The rate constant for the dissociation of the vibrationally excited triplet state of the azopropanes into radicals was measured from the variation in the quantum yield of radicals with pressure. For azo-n-propane k = (6.6 ± 1.3) × 10⁷ sec^?1, and for azoisopropane k = (1.6 ± 0.4) × 10⁸ sec^?1. Collisional deactivation of the vibrationally excited singlet and triplet states was found to occur on every collision for n-pentane; but nitrogen and argon were inefficient with a rate constant of 1.1 × 10¹⁰ l/mol sec. Spectra observed in the region of 220–260 and 370–400 nm areattributed to the cis isomers of the parent trans-azopropanes. These are formed, as permanent products, in increasing amounts as the pressure is increased.     

Rotating sector study of the gas phase photolysis of the carbon tetrachloride–cyclohexane system

The rate constant for the combination of trichloromethyl radicals in the gas phase has been measured by applying the rotating sector technique to the gas phase carbon tetrachloride–cyclohexane photochemical system. A temperature-independent rate constant, k₅, of 3.9 ± 1.0 × 10¹² cc mole^?1 sec^?1 was found. Arrhenius parameters for the reaction were found to be given by the expression log k₄ = 11.79 – (10,700/2.3 RT).     

The decomposition of dimethyl peroxide and the rate constant for CH3O + O2 → CH2O + HO2

The decomposition of dimethyl peroxide (DMP) was studied in the presence and absence of added NO₂ to determine rate constants k₁ and k₂ in the temperature range of 391–432°K: The results reconcile the studies by Takezaki and Takeuchi, Hanst and Calvert, and Batt and McCulloch, giving log k₁(sec^?1) = (15.7 ± 0.5) - (37.1 ± 0.9)/2.3 RT and k₂ ≈ 5 × 10⁴M^?1· sec^?1. The disproportionation/recombination ratio k_7b/k_7a = 0.30 ± 0.05 was also determined: When O₂ was added to DMP mixtures containing NO₂, relative rate constants k₁₂/k_7a were obtained over the temperature range of 396–442°K: A review of literature data produced k_7a = 10^9.8±0.5M^?1·sec^?1, giving log k₁₂(M^?1·sec^?1) = (8.5 ± 1.5) - (4.0 ± 2.8)/2.3 RT, where most of the uncertainty is due to the limited temperature range of the experiments.     

Kinetics of chemically activated ethane

Chemically activated ethane, with an excitation energy of 114.9 ± 2 kcal/mole, was formed by reaction with methane of excited singlet methylene radicals produced by the 4358 Å photolysis of diazomethane. A decomposition rate constant of (4.6 ± 1.2) × 10⁹ sec^?1 was measured for the chemically activated ethane. This result agrees, via RRKM theory, with most other chemically activated ethane data, and the result predicts, via RRKM and absolute rate theory for E₀ = 85.8 kcal/mole, E* = 114.9 kcal/mole, and k_E = 4.6 × 101 sec^?1, a thermal A-factor at 600°K of 10^16.6±0.2 sec^?1, in approximate agreement with the more recent experimental values. Combining 2 kcal/mole uncertainties in E₀ and E* with the uncertainty in our rate constant yields an A-factor range of 10^16.6±0.7 sec^?1. It is emphasized that this large uncertainty in the A-factor results from an improbable combination of uncertainty limits for the various parameters. These decomposition results predict, via absolute rate theory (with E₀(recombination) = 0) and statistical thermodynamic equilibrium constants, methyl radical recombination rates at 25°C of between 4.4 × 10⁸ to 3.1 × 10⁹ l.-mole^?1-sec^?1, which are 60 to 8 times lower, respectively, than the apparently quite reliable experimental value. A value of E₀(recombination) greater than zero offers no improvement, and a value less than zero would be quite unusual. Activated complexes consistent with the experimental recombination rate and E₀(recombination) = 0 greatly overestimate the experimental chemical activation and high pressure thermal decomposition rate data. Absolute rate theory as it is applied here in a straightforward way has failed in this case, or a significant amount of internally consistent data are in serious error. Some corrections to our previous calculations for higher alkanes are discussed in Appendix II.     

Reactions of the iso-butyl radical during 1,1′-azoisobutane pyrolysis

Quantitative analysis of the products formed in 1,1′-azoisobutane pyrolyses in the temperature range of 553°–602°K has shown that the major reactions of the iso-butyl radical are Analysis of initial rate data gave log₁₀k₄/(k_c)^1/2(cm^?3/2.mol ^1/2.sec^?1/2) = 7.54±0.44 ? (136.5 + 4.8) kJ/mol/2.303RT, the Arrhenius parameters obtained being in good agreement with thermodynamic data for reaction (4). Measured values of k_a/(k_c)^1/2 where k_a is the rate constant of the reaction iC₄H₉ + AIB → iC₄H₁₀ +. AIB were consistent with published parameters determined by photolysis of 1,1′-azoisobutane. Combination of photolysis and pyrolysis data gave log₁₀ k_a/(k_c)^1/2(cm^3/2.mol^?1/22.sec^?1/2) = 3.68 ± 0.15 ? (27.2 ± 1.2) kJ/mol/2.303RT. The crosscombination ratio for methyl and iso-butyl radicals has been found to be 0.25, indicating that the geometric mean rule does not hold for methyl and iso-butyl radicals.     

Rate constants for reactions of iodine atoms in solution

Laser flash photolysis (at 248 or 308 nm) or aryl iodides in water or water/methanol solutions produces iodine atoms and phenyl radicals. Iodine atoms react rapidly with added I^? to form I₂^? but do not react rapidly with O₂ (k ? 10⁷ L mol^?1 s^?1). Iodine atoms oxidize phenols to phenoxyl radicals, with rate constants that vary from 1.6 × 10⁷ L mol^?1 s^?1 for phenol to about 6 × 10⁹ L mol^?1 s^?1 for 4-methoxyphenol and hydroquinone. Ascorbate and a Vitamin E analogue are also oxidized very rapidly. N-Methylindole is oxidized by I atoms to its radical cation with a diffusion-controlled rate constant, 1.9 × 10¹⁰ L mol^?1 s^?1. Iodine atoms also oxidize sulfite and ferrocyanide ions rapidly but do not add to double bonds. The phenyl radicals, produced along with the I atoms, react with O₂ to give phenylperoxyl radicals, which react with phenols much more slowly than I atoms. © 1995 John Wiley & Sons, Inc.