Rate constants, free radical reactions

Which is better for isothermal chemical reactions, pressure driven flow or drag flow between flat plates Assume laminar flow with first-order chemical reaction and compare systems with the same values for the slit width (2Y=H), length, mean velocity, and reaction rate constant. Free-radical polymerizations tend to be highly exothermic. The following data are representative of the thermal (i.e., spontaneous) polymerization of styrene ... 

Buxton G.V., Measurements of Rate Constants for Radical Reactions in the Liquid Phase in "General Aspects ofthe Chemistry of Free Radicals" Z.B. Alfassi (ed), Wiley, Chichester, 1999,51-78. 

EPR spectroscopy can only be applied to systems in which the balance between radical decay and radical formation keeps the free-radicals concentration above the detection limit of the spectrometer used. This can be a particularly severe problem in studying reactions in liquids. An alternative approach is to slow down reactions by studying samples held at cryogenic temperatures, such as 77 K (liquid nitrogen) or 4.2 K (liquid helium). An example of this work is the study of radical reactions in single crystals of amino acids exposed to x-rays, work that sometimes leads to activation energies and rate constants for radical reactions. 

The absolute rate constants for the reaction of a variety of electrophilic free radicals with 4-(dimethylamino)-l,5-dimethyl-2-phenyl-l,2-dihydro-3//-pyrazol-3-one (aminopyrine) and l,5-dimefliyl-2-phenyl-l,2-dihydro-3//-pyrazol-3-one... 

Radiolytic ethylene destruction occurs with a yield of ca. 20 molecules consumed/100 e.v. (36, 48). Products containing up to six carbons account for ca. 60% of that amount, and can be ascribed to free radical reactions, molecular detachments, and low order ion-molecule reactions (32). This leaves only eight molecules/100 e.v. which may have formed ethylene polymer, corresponding to a chain length of only 2.1 molecules/ ion. Even if we assumed that ethylene destruction were entirely the result of ionic polymerization, only about five ethylene molecules would be involved per ion pair. The absence of ionic polymerization can also be demonstrated by the results of the gamma ray initiated polymerization of ethylene, whose kinetics can be completely explained on the basis of conventional free radical reactions and known rate constants for these processes (32). An increase above the expected rates occurs only at pressures in excess of ca. 20 atmospheres (10). The virtual absence of ionic polymerization can be regarded as one of the most surprising aspects of the radiation chemistry of ethylene. 

Initiation occurs as a molecule of intiator decomposes to free radicals (Reaction 2.9), where is the rate constant for the reaction. These newly generated free radicals can then interact with monomer molecules preserving the free radical centre (Reaction 2.10). These two processes may be considered to form part of the initiation stage, the first of them being rate determining. 

Our treatment of chain reactions has been confined to relatively simple situations where the number of participating species and their possible reactions have been sharply bounded. Most free-radical reactions of industrial importance involve many more species. The set of possible reactions is unbounded in polymerizations, and it is perhaps bounded but very large in processes such as naptha cracking and combustion. Perhaps the elementary reactions can be postulated, but the rate constants are generally unknown. The quasi-steady hypothesis provides a functional form for the rate equations that can be used to fit experimental data. 

The accepted kinetic scheme for free radical polymerization reactions (equations 1-M1) has been used as basis for the development of the mathematical equations for the estimation of both, the efficiencies and the rate constants. Induced decomposition reactions (equations 3 and 10) have been Included to generalize the model for initiators such as Benzoyl Peroxide for... 

For the values of rate constants of the free radical reactions in the gas and the liquid phases, see Table 3.9. 

Rate Constants of Free Radical Reactions with Ozone (Experimental Data)... 

Due to these reactions, hydrogen peroxide is an intermediate product of radiolysis of aerated water. Rate constants of free radical reactions with dioxygen and hydrogen peroxide are collected in Table 3.19. For the characteristics of solvated electron and information about its reactions, see monographs [219-223],... 

This reaction was proposed by Farmer [44]. Miller and Mayo observed this reaction experimentally in oxidized styrene [45]. The rate constant of this reaction was measured by the free radical acceptor method by Denisova and Denisov [46]. This reaction is endothermic. The activation energies of these reactions are sufficiently higher than their enthalpy values. 

Several empirical correlations are known for rate constants and activation energies of bimo-lecular radical reactions [1 4], Evans and Polyany [5] were the first to derive the linear correlation between the activation energy and the enthalpy of reaction of R,X with Na. Later Semenov [1] generalized this empirical equation for different free radical reactions in the following form ... 

Experimental data on the substitution reactions of free radicals with peroxides were analyzed by the IPM method [64]. The calculated parameters are collected in Table 6.27. The activation energies and the rate constants of radical substitution reactions calculated by the IPM method are presented in Table 6.28. 

When a molecule consists of a few similar fragments n, the rate constant of the reactant reaction with this molecule can be expressed as the product of the partial rate constants ky k = nx kj. This was proved many times for free radical reactions for groups of reactants where both reactants or one of them are nonpolar. For example, the rate constants of peroxyl radical reactions with nonbranched aliphatic hydrocarbons Me(CH2) Me can be presented in... 

The intensive mechanistic studies of phenoxyl self-reactions proved a great variety of mechanisms and rate constants of these reactions [2,3,6], The substituents can dramatically influence the mechanism and kinetics of self-reactions. Due to free valence delocalization the phenoxyl radical possesses an excess of the electron density in the ortho- and para-positions. Mono- and disubstituted phenoxyls recombine with the formation of labile dimers that after enolization form bisphenols [3,6],... 

These reactions produce free radicals, as follows from the fact of consumption of free radical acceptor [42]. The oxidation of ethylbenzene in the presence of thiophenol is accompanied by CL induced by peroxyl radicals of ethylbenzene [43]. Dilauryl dithiopropionate induces the pro-oxidative effect in the oxidation of cumene in the presence of cumyl hydroperoxide [44] provided that the latter is added at a sufficiently high proportion ([sulfide]/[ROOH] > 2). By analogy with similar systems, it can be suggested that sulfide should react with ROOH both heterolytically (the major reaction) and homolytically producing free radicals. When dilauryl dithiopropionate reacts with cumyl hydroperoxide in chlorobenzene, the rate constants of these reactions (molecular m and homolytic i) in chlorobenzene are [42]... 

Diffusion of particles in the polymer matrix occurs much more slowly than in liquids. Since the rate constant of a diffusionally controlled bimolecular reaction depends on the viscosity, the rate constants of such reactions depend on the molecular mobility of a polymer matrix (see monographs [1-4]). These rapid reactions occur in the polymer matrix much more slowly than in the liquid. For example, recombination and disproportionation reactions of free radicals occur rapidly, and their rate is limited by the rate of the reactant encounter. The reaction with sufficient activation energy is not limited by diffusion. Hence, one can expect that the rate constant of such a reaction will be the same in the liquid and solid polymer matrix. Indeed, the process of a bimolecular reaction in the liquid or solid phase occurs in accordance with the following general scheme [4,5] ... 

The observed rate constant is kobs = kkn(k + vD)-1. For the fast reactions with k vD the rate constant is kobs = kI). In the case of a slow reaction with k vD the rate constant is k0bs = kx KAb, where KAB = k y vn is the equilibrium constant of formation of cage pairs A and B in the solvent or solid polymer matrix. The equilibrium constant KAB should not depend on the molecular mobility. According to this scheme, the rate constant of a slow bimolecular reaction kobs = kKAB(kobs kD) should be the same in a hydrocarbon solution and the nonpolar polymer matrix. However, it was found experimentally that several slow free radical reactions occur more slowly in the polymer matrix than in the solvent. A few examples are given in Table 19.1. 

FIGURE 19.2 The correlation of rate constants of various free radical reactions with molecular mobility of nitroxyl radical in the polymer matrix of different polymers with addition of plastificator I in IPP, II in preliminary oxidized IPP, III in PE, and IV in PS. Line 1 for the reaction of 2,6-bis(l,l-dimethy-lethyl)phenoxyl radical with hydroperoxide groups at T — 295 K line 2 for the reaction of 2,2,6, 6-tetramethyl-4-bcnzoyloxypiperidinc-/V-oxyl with 1-naphthol at T = 333 K line 3 for the reaction of 2,2,6,6-tetramethyl-4-benzoyloxypiperidine-iV-oxyl with 2,6-bis(l,l-dimethylethyl)phenol at T = 333 K line 4 for the same reaction at 7 — 303 K line 5 for the same reaction at T = 313 K and line 6 for the same reaction at T — 323 K [18]. 

Besides diffusion, there is another underlying reason for leveling of reactivity of reactants in polymer media. The phenomena of leveling of reactivity of slowly reacting reactants was observed in the study of the reactions of peroxyl radicals with phenols and amines in the solid PS [23]. Later, this peculiarity was detected for different free radical reactions in the polymer matrix. All these reactions occur with rate constants much lower than kV) in polymer and cannot be limited by translational diffusion (see Table 19.6). 

Several compounds can be oxidized by peroxidases by a free radical mechanism. Among various substrates of peroxidases, L-tyrosine attracts a great interest as an important phenolic compound containing at 100 200 pmol 1 1 in plasma and cells, which can be involved in lipid and protein oxidation. In 1980, Ralston and Dunford [187] have shown that HRP Compound II oxidizes L-tyrosine and 3,5-diiodo-L-tyrosine with pH-dependent reaction rates. Ohtaki et al. [188] measured the rate constants for the reactions of hog thyroid peroxidase Compounds I and II with L-tyrosine (Table 22.1) and showed that Compound I was reduced directly to ferric enzyme. Thus, in this case the reaction of Compound I with L-tyrosine proceeds by two-electron mechanism. In subsequent work these authors have shown [189] that at physiological pH TPO catalyzed the two-electron oxidation not only L-tyrosine but also D-tyrosine, A -acetyltyrosinamide, and monoiodotyrosine, whereas diiodotyrosine was oxidized by a one-electron mechanism. 

Various hydroxyl and amino derivatives of aromatic compounds are oxidized by peroxidases in the presence of hydrogen peroxide, yielding neutral or cation free radicals. Thus the phenacetin metabolites p-phenetidine (4-ethoxyaniline) and acetaminophen (TV-acetyl-p-aminophenol) were oxidized by LPO or HRP into the 4-ethoxyaniline cation radical and neutral V-acetyl-4-aminophenoxyl radical, respectively [198,199]. In both cases free radicals were detected by using fast-flow ESR spectroscopy. Catechols, Dopa methyl ester (dihydrox-yphenylalanine methyl ester), and 6-hydroxy-Dopa (trihydroxyphenylalanine) were oxidized by LPO mainly to o-semiquinone free radicals [200]. Another catechol derivative adrenaline (epinephrine) was oxidized into adrenochrome in the reaction catalyzed by HRP [201], This reaction can proceed in the absence of hydrogen peroxide and accompanied by oxygen consumption. It was proposed that the oxidation of adrenaline was mediated by superoxide. HRP and LPO catalyzed the oxidation of Trolox C (an analog of a-tocopherol) into phenoxyl radical [202]. The formation of phenoxyl radicals was monitored by ESR spectroscopy, and the rate constants for the reaction of Compounds II with Trolox C were determined (Table 22.1). 

At the same time the interaction of superoxide with MPO may affect a total superoxide production by phagocytes. Thus, the superoxide adduct of MPO (Compound III) is probably quantitatively formed in PMA-stimulated human neutrophils [223]. Edwards and Swan [224] proposed that superoxide production regulate the respiratory burst of stimulated human neutrophils. It has also been suggested that the interaction of superoxide with HRP, MPO, and LPO resulted in the formation of Compound III by a two-step reaction [225]. Superoxide is able to react relatively rapidly with peroxidases and their catalytic intermediates. For example, the rate constant for reaction of superoxide with Fe(III)MPO is equal to 1.1-2.1 x 1061 mol 1 s 1 [226], and the rate constants for the reactions of Oi and HOO with HRP Compound I are equal to 1.6 x 106 and 2.2 x 1081 mol-1 s-1, respectively [227]. Thus, peroxidases may change their functions, from acting as prooxidant enzymes and the catalysts of free radical processes, and acquire antioxidant catalase properties as shown for HRP [228] and MPO [229]. In this case catalase activity depends on the two-electron oxidation of hydrogen peroxide by Compound I. 

Since glutathione is synthesized in cells in relatively huge amounts, it is seldom applied as pharmacological antioxidant. Furthermore, the mechanism of its antioxidant activity is not so simple as that of vitamins E and C. The major reason is that the GS radical formed during scavenging of free radicals by GSH does not disappear by dimerization but participates in the chain reaction, producing superoxide (Reactions (20)-(23)). Furthermore, it has recently been shown that contrary to previous findings the rate constant for the reaction of GSH with superoxide is relatively small (200-1000 lmol-1 s-1) [211,223],... 

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