Rate constants in free radical

Table II - Rate constants in free radical polymerizations at 30°C.

Where kp is the rate constant, R, is the rate of initiation, and kt is the termination rate constant. In free radical polymerization initiated by thermal decomposition of... 

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],... 

Ketones play an important role in the decomposition of peroxides to form radicals in alcohols undergoing oxidation. The formed hydroxyhydroperoxide decomposes to form radicals more rapidly than hydrogen peroxide. With an increase in the ketone concentration, there is an increase in the proportion of peroxide in the form of hydroxyhydroperoxide, with the corresponding increase in the rate of formation of radicals. This was proved by the acceptor radical method in the cyclohexanol-cyclohexanone-hydrogen peroxide system [59], The equilibrium constant was found to be K — 0.10 L mol 1 (373 K), 0.11 L mol 1 (383 K), and 0.12 L mol 1 (393 K). The rate constant of free radical generation results in the formation of cyclohexylhydroxy hydroperoxide decomposition and was found to be ki = 2.2 x 104 exp(—67.8/7 7) s 1 [59]. 

Rate Constants of Free Radical Generation by Hydroperoxides in Amides... 

Huyser, E. S., Free Radical Chain Reactions, Chap. 10 and pp. 314—330, Wiley, New York, 1970. Ingold, K. U., Rate Constants for Free Radical Reactions in Solution, Chap. 2 in Free Radicals, Vol. I, J. K. Kochi, ed., Wiley, New York, 1973. 

II/IV Rate constants for free radical reactions in solutions, including IVIRa (M = Si, Ge, or Sn) 107... 

Reactivity-selectivity relationships play an important part in free radical chemistry for the same reasons as in carbene chemistry and electrophilic substitution. Absolute rate constants for free radical reactions are not generally available (and when they are known they are often associated with large systematic errors), and the use of relative rate studies is an important technique in the study of free radical reactions. A comprehensive monograph dealing with various... 

The antioxidant efficiency of phenolic acids, as determined by the accelerated autooxidation of methyl linoleate and scavenging of the free radical 2,2-diphenyl-1-picrylhydrazyl (141) ° methods, was found to be inversely proportional to the maximal detector response potential in the voltammetric determination of these compounds. No similar correlation was found for the flavonoids . A good correlation was found between the O—H bond dissociation energy of a phenolic compound and its effectiveness as antioxidant, expressed as the rate constant of free radical scavenging . The bond dissociation energy of the phenol O—H bond was estimated by a three-dimensional quantitative structme-activity relationship method incorporating electron densities computed using the Austin Method 1 (AMI) followed by correlation of the... 

Figure 14.21. Rate constant of free radical decay at 40"C vs. content of silica in PE. [Adapted, by permission, from Szocs F, Klimova M, Chodak I, Chorvath 1, Eur. Polym. J., 32, No.3, 1996, 401-2.]...

By referring to Figures 2.15(b) and 2.17, it is possible to rationalize the clock data of Newcomb in a simple manner. The apparent lifetimes are determined from the rate constant of free radical rearrangement and the ratio R/U of rearranged to unrearranged alcohol product, assuming a... 

Figure 1 is quite simple but, to our knowledge, no determination of the individual values of the activation parameters for the k(, and kd processes have previously been available. One of the primary purposes of the present work is to discuss an analysis that yields such values. These activation parameters, in turn, are used to illustrate the curvatures that exist in Eyring or Arrhenius treatments of the temperature dependences of the observed rate constants for free radical recombination, trapping and formation by thermolysis of a covalent precursor in solution. 

There is a considerable potential for the determination of rate constants for free radical reactions in discharge-flow systems. Such measurements have so far been carried out in any detail only for the OH, CIO, BrO, NFj and, to a more limited extent, the CN radial. However, these few studies have made a significant contribution to the theory of reactivity of these radicals. 

The use of organometallic compounds as chain-transfer catalysts in free-radical polymerization has been widely studied. One objective is the production of polymers with terminal vinyl groups and lower molecular weight components compared with polymerization in the absence of chain-transfer catalysts. Gomplexes of cobalt(ii) have been used as effective catalysts, but the instability of the intermediate cobalt hydride does not permit firm establishment of the reaction mechanism. To address this issue, several chromium compounds have been applied as catalysts for the polymerization of methylmethacrylate (MMA) and styrene. The temperature dependence of the rate constant for free-radical polymerization of MMA for catalyzed chain transfer by (GsPh5)Gr(GO)3 has been determined using the Mayo equation. ... 

Considerable advances have been made in the direct measurement of rate constants for free-radical systems. - References given earlier for -O- atom and OH- radical reactions cover the wealth of new direct techniques. Recent developments in pulse and modulation techniques, shock-tube design, and the use of e.s.r. 

Rate constants for free radical propagation increase with decreasing polymer free radical resonance stabilization (Table 20-2). The activation energies, however, are more or less independent of the constitution. Consequently the rate constants are predominantly determined by the preexponential factors of the Arrhenius equation. In addition, they also depend on the viscosity of the reaction medium to a slight extent. 

If all these conditions are fulfilled, samples exhibiting both controlled molar mass and narrow molar mass distribution (Dm 1) can be obtained. However, taking into consideration the respective rate constant of free radical capture and that of irreversible termination, one can wonder how the condition of a rate of reversible termination notably higher than that of their irreversible deactivation could be reasonably satisfied. The only way to favor the former reaction against termination is to increase the nitroxide concentration in the reaction medium to a level higher... 

Note that this inquiry into copolymer propagation rates also increases our understanding of the differences in free-radical homopolymerization rates. It will be recalled that in Sec. 6.1 a discussion of this aspect of homopolymerization was deferred until copolymerization was introduced. The trends under consideration enable us to make some sense out of the rate constants for propagation in free-radical homopolymerization as well. For example, in Table 6.4 we see that kp values at 60°C for vinyl acetate and styrene are 2300 and 165 liter mol sec respectively. The relative magnitude of these constants can be understod in terms of the sequence above. 

As the polymerization reaction proceeds, scosity of the system increases, retarding the translational and/ or segmental diffusion of propagating polymer radicals. Bimolecular termination reactions subsequently become diffusion controlled. A reduction in termination results in an increase in free radical population, thus providing more sites for monomer incorporation. The gel effect is assumed not to affect the propagation rate constant since a macroradical can continue to react with the smaller, more mobile monomer molecule. Thus, an increase in the overall rate of polymerization and average degree of polymerization results. 

The value of initiator association and the rate constant may be evaluated. Viscosity is not expected to have a significant cage effect as in free radical systems, but the extent of association may be dependent on viscosity, or other properties of the fluid media. 

The theory of radiation-induced grafting has received extensive treatment [21,131,132]. The typical steps involved in free-radical polymerization are also applicable to graft polymerization including initiation, propagation, and chain transfer [133]. However, the complicating role of diffusion prevents any simple correlation of individual rate constants to the overall reaction rates. Changes in temperamre, for example, increase the rate of monomer diffusion and monomer... 

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