Radical combination reactions rate constants

Equation (l) shows the rate of polymerization is controlled by the radical concentration and as described by Equation (2) the rate of generation of free radicals is controlled by the initiation rate. In addition. Equation (3) shows this rate of generation is controlled by the initiator and initiator concentration. Further, the rate of initiation controls the rate of propagation which controls the rate of generation of heat. This combined with the heat transfer controls the reaction temperature and the value of the various reaction rate constants of the kinetic mechanism. Through these events it becomes obvious that the initiator is a prime control variable in the tubular polymerization reaction system. 

The inhibition method has found wide usage as a means for determining the rate at which chain radicals are introduced into the system either by an initiator or by illumination. It is, however, open to criticism on the ground that some of the inhibitor may be consumed by primary radicals and, hence, that actual chain radicals will not be differentiated from primary radicals some of which would not initiate chains in the absence of the inhibitor. This possibility is rendered unlikely by the very low concentration of inhibitor (10 to 10 molar). The concentration of monomer is at least 10 times that of the inhibitor, yet the reaction rate constant for addition of the primary radical to monomer may be less than that for combination with inhibitor by only a factor of 10 to 10 Hence most of the primary radicals may be expected to react with monomer even in the presence of inhibitor, the action of the latter being confined principally to the termination of chain radicals of very short length. ... 

Two steady state conditions apply one to the total radical concentration and the other to the concentrations of the separate radicals Ml- and M2-. The latter has already appeared in Eq. (2), which states that the rates of the two interconversion processes must be equal (very nearly). It follows from Eq. (2) that the ratio of the radical population, Mi - ]/ [Mpropagation reaction rate constants. The steady-state condition as applied to the total radical concentration requires that the combined rate of termination shall be equal to the combined rate of initiation, i.e., that... 

The extension of equilibrium measurements to normally reactive carbocations in solution followed two experimental developments. One was the stoichiometric generation of cations by flash photolysis or radiolysis under conditions that their subsequent reactions could be monitored by rapid recording spectroscopic techniques.3,4,18 20 The second was the identification of nucleophiles reacting with carbocations under diffusion control, which could be used as clocks for competing reactions in analogy with similar measurements of the lifetimes of radicals.21,22 The combination of rate constants for reactions of carbocations determined by these methods with rate constants for their formation in the reverse solvolytic (or other) reactions furnished the desired equilibrium constants. 

The rate of combination of the 02 and G(-H) radicals positioned in single- and double-stranded oligonucleotides can be determined from the decay kinetics of the characteristic narrow absorption band of G(-H) radicals at 315 nm [29]. The rate constant of this bimolecular combination reaction was found to be around 4.7 x 108M 1s 1. The Cu,Zn-SOD reacts with 02 radicals with nearly diffusion-controlled rates [74, 75] and thus dramatically enhances the lifetimes of the DNA-bound G(-H) radicals from 4— 7ms to 0.2-0.6 s in the presence of micromolar concentrations of Cu,Zn-SOD (around 5gM) [29]. Thus, radical-radical combination reactions can play important roles in shortening the lifetimes of guanine radicals in DNA, as mentioned earlier. 

Rate constants for alkoxy radical isomerizations can be combined with rate constants for alkoxy radical decomposition and reaction with O2 to predict the relative importance of the three pathways (Atkinson 1994). Alkoxy radicals can also react with NO and N02, but under ambient tropospheric conditions these reactions are generally of negligible importance. 

TABLE I. Rate Constants for Metal-Alkyl Radical and Metal-Metal Radical Combination Reactions... 

What is the explanation Stable molecules hardly react, only when they form free radicals, carbenes or complex intermediates, ions, or valences. These very reactive species combine easily with molecules or other intermediate species, reacting in successive or parallel steps. These intermediate mechanisms should be known to determine the reaction kinetics. This proves that the overall reaction rate constant is not always true but includes several other constants relative to different intermediate steps of the mechanism. 

Rate constants for the reactions of OH radicals with n-nitroalkanes, n-alkyl nitrates and n-alkyl nitrites have been determined at 298 K and 1 atmosphere total pressure using both pulse radiolysis combined with kinetic spectroscopy and a conventional relative rate method. In order to provide more mechanistic information for these reactions, rate constants for the reaction of Cl atoms with these compounds were determined using the relative rate method. The data indicate that the reaction of OH radicals with these nitrogen-containing compounds involves both an abstraction and an addition channel. These results are discussed in terms of reactivity trends and compared with the data from the literature. 

The polymer-nitroxyl adduct P-X reversibly dissociates thermally, in process 1 into the polymer radical P and the nitroxyl radical X. The rate constants of dissociation and combination are and kc, respectively. The, so-called, degenerative transfer takes place in process 11. The second-order rate constant for active species in either direction is k y. Here all the rate constants are assumed to be independent of chain length. Since the frequency of cleavage of the P-X bond is proportional to [P-X] in process 1 and to [P l [P -X]] in process 11, the overall frequency,/ per unit time and per unit volume, of the bond-cleaving or activation reactions, may be expressed by [277] ... 

The collision rate constants, and k, are given by Langevin theory [2, 3] nicely. It is detailed later in this section. It has already been pointed out (see Sect. 1.1) that this type of reaction is totally analogous to neutral radical combination reactions. 

The rate constants of radical combination reactions, which form the basis from which absolute rates of addition reactions are determined, have been the subject of a vigorous controversy in recent years. That of methyl radicals is well established at 2 X 10 1. mol s", but for other alkyl radicals evidence has been presented for both "low" values and "high" values, and the final outcome remains in doubt (22). 

This situation is expected to apply to radical termination, especially by combination, because of the high reactivity of the trapped radicals. Only one constant appears which depends on the diffusion of the polymer radicals, so it cannot cancel out and may be the source of a dependence of the rate constant on the extent of reaction or degree of polymerization. 

In practice it is found that the concentration of radicals rapidly reaches a constant value and the reaction takes place in the steady state. Thus the rate of radical formation Ej becomes equal to the rate of radical disappearance V. It is thus possible to combine equations (2.1) and (2.3) to obtain an expression for [M—] in terms of the rate constants... 

Chains with uttdesired functionality from termination by combination or disproportionation cannot be totally avoided. Tn attempts to prepare a monofunctional polymer, any termination by combination will give rise to a difunctional impurity. Similarly, when a difunctional polymer is required, termination by disproportionation will yield a monofunctional impurity. The amount of termination by radical-radical reactions can be minimized by using the lowest practical rate of initiation (and of polymerization). Computer modeling has been used as a means of predicting the sources of chain ends during polymerization and examining their dependence on reaction conditions (Section 7.5.612 0 J The main limitations on accuracy are the precision of rate constants which characterize the polymerization. 

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