To the core of autocatalysis in cyclohexane autoxidation

Despite their industrial importance, the detailed reaction mechanism of autoxidation reactions is still insufficiently known. In this work, complementary experimental and theoretical techniques are employed to address the radical-chain initiation in the autoxidation of cyclohexane with a particular focus on the "lighting-off" of the oxidation by (added) cyclohexanone. We used a newly developed method to quantify the intrinsic rate of chain initiation as well as the rate enhancement by cyclohexanone and several other (oxygenated) molecules. On the basis of first principles, the hitherto assumed perhemiketale mechanism was found to be many orders of magnitude too slow to account for the observed initiation enhancement by the ketone. Instead, it is shown that the pronounced chain-initiation enhancement by the ketone is attributable to a newly proposed concerted reaction between cyclohexyl hydroperoxide and cyclohexanone, in which the (.)OH radical breaking away from the hydroperoxide abstracts an alphaH atom from the ketone, thereby energetically assisting in the cleavage of the RO--OH bond. This reaction is highly efficient in generating radicals as it quasi-excludes geminate in-cage recombination. As a result, the ketone oxidation product at a level of 1 mol % increases the initiation rate by one order of magnitude, and so acts as a highly efficient "autocatalyst" in autoxidation reactions. An analogous reaction with cyclohexanol, although estimated to be even faster, has only a marginal effect on the overall kinetics, owing to the fast subsequent formation of HO(2) (.) radicals that very rapidly terminate with other ROO(.) radicals. Finally, solid evidence is presented that, also in absence of oxygenates, ROOH initiation is actually a bimolecular reaction, involving concerted H abstraction from the alkane substrate by the nascent (.)OH.     

Origin of byproducts during the catalytic autoxidation of cyclohexane

The formation of byproducts during the Co(acac)2 and Cr(acac)3-catalyzed cyclohexane autoxidation is compared with the noncatalyzed thermal process. CoII ions seem to cause only a moderate perturbation of the reaction mechanism, causing a fast conversion of the cyclohexyl hydroperoxide via a redox cycle, rather than via abstraction of the alphaH-atom by chain carrying peroxyl radicals. Nevertheless, both the radical propagation and the CoII-induced decomposition of the hydroperoxide cause the formation of cyclohexoxy radicals that are partially transformed to 6-hydroxyhexanoic acid, the major primary byproduct for these systems. However, during the CoII-catalyzed reaction, the concentration of cyclohexanone increases much faster than that of the hydroperoxide, causing the ketone to take over the role of dominant byproduct source. A mechanism for the conversion of cyclohexanone to ring-opened byproducts is put forward. Cr(acac)3 seems to catalyze additional reactions, some of them probably leading directly to byproducts. Indeed, the evolution of (by)products is significantly different from the CoII-catalyzed and the thermal systems, in the sense that they all seem to be primary in origin.     

Radical autoxidation and autogenous O2 evolution in manganese-porphyrin catalyzed alkane oxidations with chlorite

A manganese porphyrin catalyst employing chlorite (ClO(2)(-)) as a "shunt" oxidant displays remarkable activity in alkane oxidation, oxidizing cyclohexane to cyclohexanol and cyclohexanone with >800 turnover numbers. The ketone is apparently formed without the intermediacy of alcohol and accounts for an unusually large fraction of the product ( approximately 40%). Radical scavenging experiments indicate that the alkane oxidation mechanism involves both carbon-centered and oxygen-centered radicals. The carbon-radical trap CBrCl(3) completely suppresses cyclohexanone formation and reduces cyclohexanol turnovers, while the oxygen-radical trap Ph(2)NH inhibits all oxidation until it is consumed. These observations are indicative of an autoxidation mechanism, a scenario further supported by TEMPO inhibition and (18)O(2) incorporation into products. However, similar cyclohexane oxidation activity occurs when air is excluded. This is explained by mass spectrometric and volumetric measurements showing catalyst-dependent O(2) evolution from the reaction mixture. The catalytic disproportionation of ClO(2)(-) into Cl(-) and O(2) provides sufficient O(2) to support an autoxidation mechanism. A two-path oxidation scheme is proposed to explain all of the experimental observations. The first pathway involves manganese-porphyrin catalyzed decomposition of ClO(2)(-) into both O(2) and an unidentified radical initiator, leading to classical autoxidation chemistry providing equal amounts of cyclohexanol and cyclohexanone. The second pathway is a "rebound" oxygenation involving a high-valent manganese-oxo intermediate, accounting for the excess of alcohol over ketone. This system highlights the importance of mechanistic studies in catalytic oxidations with highly reactive oxidants, and it is unusual in its ability to sustain autoxidation even under apparent exclusion of O(2).     

Autoxidation of cyclohexane: conventional views challenged by theory and experiment.

In spite of its industrial importance, the detailed reaction mechanism of cyclohexane autoxidation by O2 is still insufficiently known. Based on quantum chemical potential energy surfaces, rate coefficients of the primary and secondary chain propagation steps involving the cyclohexylperoxyl (CyOO) radical were evaluated using multiconformer transition-state theory. Including tunneling and hindered-internal-rotation effects, the rate coefficient for hydrogen-atom abstraction from cyclohexane (CyH) by CyOO was calculated to be k(T)= 1.46 x 10(-11) x exp(-17.8 kcal mol(-1)/ RT) cm3s(-1) (300-600K), close to the experimental data. A "Franck-Rabinowitch cage" reaction between the nascent cyclohexylhydroperoxide (CyOOH) and cyclohexyl radical, products from CyOO + CyH, is put forward as an initially important cyclohexanol (CyOH) formation channel. alphaH abstraction by CyOO. from cyclohexanone was calculated to be only about five times faster than that from CyH, too slow to explain all the observed side products. The a-hydrogen (alphaH) abstractions from CyOH and CyOOH by CyOO. are predicted to be about 10 and 40 times faster, respectively, than the CyOO. +CyH reaction. The very fast CyOO.+CyOOH reaction proceeds through the unstable Cy-alphaH .OOH radical that decomposes spontaneously into the ketone (Q=O) plus the OH radical; the "hot" .OH is found to produce the bulk of the alcohol via a second, "activated cage" reaction analogous to that above. It is thus shown how the very reactive CyOOH intermediate is the predominant source of ketone and alcohol, while it also leads to some side products. The alpha-hydroxycyclohexylperoxyl radical formed during the moderately fast oxidation of CyOH is shown to decompose fast into HO2 + cyclohexanone in a rapidly equilibrated reaction, which constitutes a smaller, second ketone source. These two fast cyclohexanone forming routes avoid the need for unfavorable molecular routes hitherto invoked as ketone sources. The theoretical predictions are supported and complemented by experimental findings. The newly proposed scheme is also largely applicable to the oxidation of other hydrocarbons, such as toluene, xylene, and ethylbenzene.     

Liquid-phase oxidation of cyclohexane. Elementary steps in the developed process,reactivity, catalysis,and problems of conversion and selectivity

The literature data concerning features of the kinetics and mechanisms of elementary steps of liquid-phase oxidation of cyclohexane and its oxygen derivatives are considered and analyzed. A comparison of rates of intermolecular and intramolecular reactions of cyclohexylperoxyl radicals under the industrial conditions indicated a necessity to take into account intramolecular interactions. The occurrence of cross recombination of hydroperoxyl and α-hydroxyperoxyl radicals without chain termination in the course of cyclohexanol and 2-hydroxycyclohexanol oxidation was proved. A significance of degenerate branching reactions involving cyclohexyl hydroperoxide in the industrial process of cyclohexane oxidation at 423 K was evaluated. The influence of the electron-withdrawing functional groups on the reactivity of carbon–hydrogen bonds of organic compounds in the reactions with electrophilic peroxyl radicals was studied. The low conversion of a substrate in the industrial process are mainly caused by the radicalchain oxidation of cyclohexanone leading only to by-products. The catalysts of cyclohexane oxidation, viz., compounds of variable valence metals, affect the reaction rate and ratio of the yields of the target products (cyclohexyl hydroperoxide, cyclohexanol, and cyclohexanone) but exert no effect on their relative reactivity. The use of the catalytic additives increasing the yield of cyclohexanone in the step of cyclohexane oxidation in the production of caprolactam is revealed to be inexpedient.     

The formation of byproducts in the autoxidation of cyclohexane

In this work, a complementary experimental and theoretical approach is used to unravel the formation of byproducts in the autoxidation of cyclohexane. The widely accepted vision that cyclohexanone would be the most important precursor of undesired products was found inconsistent with several experimental observations. However, the propagation reaction of cyclohexyl hydroperoxide, which we recently put forward as the missing source of cyclohexanol and cyclohexanone, is now unambiguously identified also as the dominant path leading to byproducts. Indeed, this overlooked reaction produces large amounts of cyclohexoxy radicals, able to ring-open via a beta-C--C cleavage to omega-formyl radicals. The pathway by which these radicals are converted into the observed and quantified byproducts is derived in this work. In this liquid-phase reaction, solvent cages were found very important, steering the fate of nascent species.     

Kinetics and mechanism of cyclohexane oxidation with molecular oxygen in the presence of propionic aldehyde

The kinetics and mechanism of the liquid-phase oxidation of cyclohexane with molecular oxygen in the presence of the additives of propionic aldehyde are studied at 303.0, 322.5, and 341.5 K by measuring the rates of oxygen and propionic aldehyde consumption and the yields of the main reaction products (cyclohexanol (COL), cyclohexanone (CON), cyclohexyl hydroperoxide, and propionic acid and peracid). A kinetic scheme is proposed and rate constants of elementary reactions are estimated based on the analysis of their rates and the yields of the main cyclohexane products. The key reactions of the main steps (including chain initiation, propagation, and termination) are determined. An increase in the rate of cyclohexane oxidation and the yield of the target products (cyclohexanol, cyclohexanone, and cyclohexyl hydroperoxide) in the presence of propionic aldehyde suggests that highly active acylperoxy radicals participate in chain propagation. The [CON]/[COL] ratio indicates that these products are mainly formed in chain propagation. The strong effect of the Baeyer-Villiger rearrangement on both the rate of oxygen consumption and the yield of the target products at the initial stages of the process and at high propionic aldehyde concentrations is explained.     

Increasing the ketone selectivity of the cobalt-catalyzed radical chain oxidation of cyclohexane

A variety of heterogeneous catalysts for the radical chain oxidation of cyclohexane has been prepared by immobilization of the well-defined cobalt acetate oligomers [py(3)Co(3)(mu(3)-O)(OH)(O(2)CCH(3))(5)](PF(6)) (1) and [py(4)Co(2)(OH)(2)(O(2)CCH(3))(3)](PF(6)) (2) on carboxy-modified mesoporous silica supports A-D by carboxylate exchange. The catalytic oxidation of cyclohexane with tert-butyl hydroperoxide (TBHP) in the presence of these homogeneous and immobilized cobalt acetate complexes afforded the corresponding alcohol and ketone in high yield. The immobilization of 1 and 2 results in a significant increase of catalytic activity. TBHP acts as a radical initiator and as source of molecular oxygen, which is also involved in the overall oxidation process. The rate of cyclohexane conversion is limited by the diffusion of molecular oxygen, and steady-state concentrations of cyclohexanone (K, ketone) and cyclohexanol (A, alcohol) are established; these determine the maximum K:A ratio.     

Mechanism of Thermal Toluene Autoxidation

Aerobic oxidation of toluene (PhCH₃) is investigated by complementary experimental and theoretical methodologies. Whereas the reaction of the chain‐carrying benzylperoxyl radicals with the substrate produces predominantly benzyl hydroperoxide, benzyl alcohol and benzaldehyde originate mainly from subsequent propagation of the hydroperoxide product. Nevertheless, a significant fraction of benzaldehyde is also produced in primary PhCH₃ propagation, presumably via proton rather than hydrogen transfer. An equimolar amount of benzyl alcohol, together with benzoic acid, is additionally produced in the tertiary propagation of PhCHO with benzylperoxyl radicals. The “hot” oxy radicals generated in this step can also abstract aromatic hydrogen atoms from PhCH₃, and this results in production of cresols, known inhibitors of radical‐chain reactions. The very fast benzyl peroxyl‐initiated co‐oxidation of benzyl alcohol generates HO₂^. radicals, along with benzaldehyde. This reaction also causes a decrease in the overall oxidation rate, due to the fast chain‐terminating reaction of HO₂^. with the benzylperoxyl radicals, which causes a loss of chain carriers. Moreover, due to the fast equilibrium PhCH₂OOH+HO₂^.?PhCH₂OO^.+H₂O₂, and the much lower reactivity of H₂O₂ compared to PhCH₂OOH, the fast co‐oxidation of the alcohol means that HO₂^. gradually takes over the role of benzylperoxyl as principal chain carrier. This drastically changes the autoxidation mechanism and, among other things, causes a sharp decrease in the hydroperoxide yield.     

A kinetic study of the reactions of 2-propyl radicals in the liquid phase in the presence and absence of oxygen

2-Propyl radicals have been generated from the photolysis of solutions of 2,2-azopropane and 2,4-dimethyl-3-pentanone in decane in a glass and a metal cell. The time course of their reactions in the presence and absence of oxygen has been monitored between 323 and 373 K. The primary process involves the formation of solvent-caged radical pairs, two 2-propyl radicals and a 2-propyl and a 2-methylpropanoyl radical from the azo and ketone precursors, respectively. Subsequently these radicals are partitioned between cage escape and dimerization and disproportionation within the cage. In oxygenated solution the free 2-propyl radicals are effectively trapped as 2-propylperoxyl radicals. However, oxygen does not react with the solvent-caged radicals. This leads to a major difference in the hydrocarbon products from the two precursors. 2,2′-Azopropane gives propane, propene, and 2,3-dimethylbutane from the start of the reaction whereas the ketone only gives propene. Following the depletion of oxygen or in the absence of oxygen, both precursors behave analogously and give all three hydrocarbons. The 2-propylperoxyl radicals undergo self-reaction and hydrogen abstraction from the solvent to give 2-propanol, propanone, and 2-propyl hydroperoxide and, under conditions of low oxygen concentration, by reaction with 2-propyl radicals they give 2,2′-dipropylperoxide. Although the two cells lead to different overall rates of reaction, the relative rates and product distributions are unaffected by the cell design. A unified mechanism is described and the known and best estimates of rate constants for the individual steps are used to simulate the time dependence of the product yields from the photolysis of both precursors. © 1996 John Wiley & Sons, Inc.     

Oxidation of Cycloalkanes by Hydrogen Peroxide in a Biomimetic Iron Porphyrin System

The kinetics of cyclohexane and cyclopentane oxidation by hydrogen peroxide catalyzed by iron porphyrins (FeTPP and FeTDCPP) in acetonitrile solutions is studied at room temperature by analyzing product accumulation with the GLC method. The effects of various additives (acetic acid, imidazole, and hydroquinone) on the substrate selectivity of the competitive oxidation of C₆H₁₂ and C₅H₁₀ are studied. In the FeTDCPP/H₂O₂/O₂/AcOH/CH₃CN system, cyclohexane is oxidized to the corresponding alcohol, ketone, and hydroperoxide. The fraction of the product (hydroperoxide) formed by the radical mechanism is 20–30%. The alcohol and ketone are formed by the molecular pathway in a ratio of (6–7) : 1. Kinetic parameters of cycloalkane oxidation are compared in a biomimetic system with hydrogen peroxide (the shunt system) and the system based on dioxygen with electron and proton donors. The latter system modeled cytochrome P-450. It is shown that active species are the same in both systems. The kinetic scheme of the alkane oxidation process is proposed for the shunt system.     

附加试剂及反应介质对TPPFeCl催化环己烷仿生氧化反应性能的影响

研究了某些附加试剂及反应介质对四苯基卟吩合铁(Ⅲ)[TPPFeCl或(TPPFe)₂O]模拟细胞色素P-450催化PhIO羟化环己烷反应的影响。发现适量的异丙醇、吡啶及NaOH能促进反应,加入盐酸及增大介质的极性对反应不利。证明了副产物环己酮主要是由PhIO直接氧化主产物环己醇生成的,TPPFeCl的存在不利于酮的生成,醇的存在能延长催化剂的寿命。     

金属卟啉催化环己烷羟基化反应中环己酮的形成机理研究

单金属卟啉和双金属卟啉催化下PhIO常温氧化环己烷的羟基化反应中金属卟啉结构和反应溶剂、反应温度、反应时间等环境因素对产物酮含量及酮形成反应动力学的影响进行了系统研究, 并与金属卟啉催化下PhIO氧化环己醇的反应进行了对比, 提出了金属卟啉催化下环己烷羟基化反应中产物酮的形成机理。     

三氯化钌催化下环己烷和环己醇在离子液体中的氧化反应研究

在三氯化钌催化下,使用叔丁基过氧化氢在离子液体中可将环己烷和环己醇氧化为环己酮,结果表明环己醇的氧化具有较高的转化率和选择性．离子液体(bmim)^ PF6^-和催化剂三氯化钌均有一定的重复使用性．     

Aging and degradation of polyolefins. I. Peroxide-initiated oxidations of atactic polypropylene

Efficiencies of polymer radical production by thermal decomposition of di-tert-butylperoxy oxalate (DBPO) have been measured in bulk atactic polypropylene (PP) at 25–55°C; they range from 1 to 26%, depending on [DBPO], temperature, and presence of oxygen. Most of the polymer radicals thus produced disproportionate in the absence of oxygen but form peroxy radicals in its presence. Most of the pairs of peroxy radicals interact by a first-order reaction in the polymer cage. The fraction that escapes gives hydroperoxide in a reaction that is half order in rate of initiation. In interactions of polymer peroxy radicals, in or out of the cage, about one-third give dialkyl peroxides and immediate chain termination, two-thirds give alkoxy radicals. About one-third of the later cleave at 45°C; the rest abstract hydrogen to give hydroxy groups and new polymer and polymer peroxy radicals. The primary peroxy radicals from cleavage account for the rest of the chain termination. Cleavage of alkoxy radicals and crosslinking of PP through dialkyl peroxides nearly compensate. Up to 70% of the oxygen absorbed has been found in hydroperoxides. The formation of these can be completely inhibited, but cage reactions are unaffected by inhibitors. Concentrations of free polymer peroxy radicals have been measured by electron spin resonance and found to be very high, about 10^?3M at 58–63°C. Comparison with results on 2,4-dimethylpentane indicate that rate constants for both chain propagation and termination in the polymer are much smaller than those for the model hydrocarbon but that the ratio, k_p/(2k_t)^½, is about the same.     

Kinetics and products from reaction of Cl radicals with dioctyl sebacate (DOS) particles in O(2): a model for radical-initiated oxidation of organic aerosols

The reaction of Cl radicals with bis (2-ethylhexyl) sebacate (also known as dioctyl sebacate, DOS) particles in the presence of O(2) is studied as a model of radical-initiated oxidation of organic aerosols. The uptake coefficient as measured from the rate of loss of DOS is gamma(DOS) = 1.7 (+/-0.3) indicating that a radical chain is operative. It is observed that nearly all of the detected products, accounting for 86% (+/-12%) of the reacted DOS, remain in the particles indicating that they are not efficiently volatilized. Correspondingly, the particles do not decrease in volume even after 60% of the DOS has reacted; upon further reaction the volume does decrease by up to 20%. Additionally, the mass of a DOS film increases with reaction indicating that the density increases. The two primary products identified are the ketone (38 +/- 10% yield) and alcohol (14 +/- 4% yield) resulting from reactions of alkylperoxy radicals originating from DOS oxidation. The fact that the ketone/alcohol ratio is >1 implies that the Russell mechanism, the typical fate of alkylperoxy radicals in liquids whereby both a ketone and an alcohol are generated, is not the only source of ketones. In fact, the ketone yield demonstrates a Langmuir-Hinshelwood type dependence on the O(2) concentration indicating that 44% (+/-8%) of the ketone is created from the reaction of alkoxy radicals with O(2) at the surface of the particles (at 20% O(2)). While this is a common reaction in the gas phase, it is generally not considered to occur in organic solvents. Furthermore, the appearance of gas-phase H(2)O(2) suggests that peroxy radicals react to form two ketones and H(2)O(2)via the Bennett and Summers mechanism. The absence of aldehyde products, both in the gas phase and in the particles, indicates that beta-scission of the alkoxy radicals is not significant. The results of this study suggest that organic aerosols in the troposphere are efficiently oxidized by gas-phase radicals but that their chemical transformation does not lead to their removal through volatilization.     

Oxidation of Cyclohexane by Molecular Oxygen Photoassisted by meso-Tetraarylporphyrin Iron(III)-Hydroxo Complexes

The photochemical and photocatalytic properties of iron meso-tetraarylporphyrins bearing an OH(-) axial ligand and different substituents in the beta-positions of the porphyrin ring are reported. Irradiation (lambda = 365 nm) in the absence of dioxygen leads to the reduction of Fe(III) to Fe(II) with the formation of OH(*) radicals. Substituents at the pyrrole beta-positions are found to markedly affect the photoreduction quantum yields. Under aerobic conditions, this photoreaction can induce the subsequent oxidation of cyclohexane to cyclohexanone and cyclohexanol by O(2) itself. The process occurs under mild conditions (22 degrees C; 760 Torr of O(2)) and without the consumption of a reducing agent. The polarity of the solvent and the nature of the porphyrin ring have a remarkable effect on the selectivity of the photooxidation process, likely controlling the cleavage of O-O bonds of possible iron peroxoalkyl intermediates. In particular, in pure cyclohexane, oxidation occurs with the selective formation of cyclohexanone; in contrast, in dichloromethane/cyclohexane mixed solvent, the main oxidation product is cyclohexanol. Phenyl-tert-butylnitrone (pbn) has been found to quench the radical chain autooxidation of the substrate thus increasing the yield of cyclohexanol. This becomes the only oxidation product when iron 5,10,15,20-tetrakis(2,6-dichlorophenyl)porphyrin hydroxide (Fe(III)(TDCPP)(OH)) is used as photocatalyst.     

Hybrid Silsesquioxane/Benzoate Cu7-Complexes: Synthesis,Unique Cage Structure,and Catalytic Activity

A series of phenylsilsesquioxane-benzoate heptacopper complexes 1–3 were synthesized and characterized by X-ray crystallography. Two parallel routes of toluene spontaneous oxidation (into benzyl alcohol and benzoate) assisted the formation of the cagelike structure 1. A unique multi-ligation of copper ions (from (i) silsesquioxane, (ii) benzoate, (iii) benzyl alcohol, (iv) pyridine, (v) dimethyl-formamide and (vi) water ligands) was found in 1. Directed self-assembly using benzoic acid as a reactant afforded complexes 2–3 with the same main structural features as for 1, namely heptanuclear core coordinated by (i) two distorted pentameric cyclic silsesquioxane and (ii) four benzoate ligands, but featuring other solvate surroundings. Complex 3 was evaluated as a catalyst for the oxidation of alkanes to alkyl hydroperoxides and alcohols to ketones with hydrogen peroxide and tert-butyl hydroperoxide, respectively, at 50 °C in acetonitrile. The maximum yield of cyclohexane oxidation products as high as 32% was attained. The oxidation reaction results in a mixture of cyclohexyl hydroperoxide, cyclohexanol, and cyclohexanone. Upon the addition of triphenylphosphine, the cyclohexyl hydroperoxide is completely converted to cyclohexanol. The specific regio- and chemoselectivity in the oxidation of n-heptane and methylcyclohexane, respectively, indicate the involvement of of hydroxyl radicals. Complex 3 exhibits a high activity in the oxidation of alcohols.     

N-Hydroxyphthalimide in combination with Cu(II), Co(II) or Mn(II) salts as catalytic systems for the oxidation of isopropyl-aromatic hydrocarbons with oxygen

Catalytic systems consisting of N-hydroxyphthalimide in combination with copper(II), cobalt(II) and manganese(II) acetylacetonate, acetate or chloride were applied to the oxidation of cumene with oxygen. The use of these catalytic systems decreases cumyl hydroperoxide selectivity as a result of the decomposition reaction of hydroperoxide to 2-phenyl-2-propanol and acetophenone. It has been demonstrated that the use of N-hydroxyphthalimide in combination with copper salts at 60 °C results in high alcohol content whereas ketone is the major product at 90 °C. The results can be used to develop a method for alcohol or ketone synthesis from other isopropyl-aromatic hydrocarbons.     

Magnetic Field Effects on the Dynamics of Radical Pairs in Micelles: A New Approach to Understanding the "Cage Effect"

The effect of temperature on the photolysis of dibenzyl ketone and 4-methyldibenzyl ketone in sodium dodecyl sulfate micelles was studied by laser flash photolysis and product distributions derived from steady-state photolysis. At high temperatures, the product distribution and radical decay kinetics are primarily due to random encounters of radicals, and the "cage effect" cannot be rationalized by geminate recombination reactions that occur before the radicals escape from the micelles. A mechanism is proposed in which the enhancement of the crosstermination product derived from random encounters is due to the different partitioning of each radical species between the micelles and the aqueous phase, thereby leading to different rates for the self-termination reactions.