Radicals bimolecular reaction

All known free radical bimolecular reactions can be divided into the following five types ... 

The second-order rate law for bimolecular reactions is empirically well confinned. Figure A3.4.3 shows the example of methyl radical recombination (equation (A3.4.36)) in a graphical representation following equation (A3.4.38) [22, 23 and 24]. For this example the bimolecular rate constant is... 

A kinetic analysis of the two modes of termination is quite straightforward, since each mode of termination involves a bimolecular reaction between two radicals. Accordingly, we write the following ... 

Bimolecular reactions of peroxy radicals are not restricted to identical radicals. When both peroxy radicals are tertiary, reaction 15 is not possible. When an a-hydrogen is present, reaction 15 is generally the more effective competitor and predominates. 

The thermal decompositions described above are unimolecular reactions that should exhibit first-order kinetics. Under many conditions, peroxides decompose at rates faster than expected for unimolecular thermal decomposition and with more complicated kinetics. This behavior is known as induced decomposition and occurs when part of the peroxide decomposition is the result of bimolecular reactions with radicals present in solution, as illustrated below specifically for diethyl peroxide. 

Since it is well known that chloroalkenes are often much less stable than the corresponding alkanes, olefinic unsaturation may be an important source of thermal instability in PVC. Chain-end unsaturation could arise by disproportionation during bimolecular reaction of polymer radicals Eq. (2). 

Atom or radical transfer reactions generally proceed by a SH2 mechanism (substitution, homolytie, bimolecular) that can be depicted as shown in Figure 1.6. This area has been the subject of a number of reviews.1 3 27 97 99 The present discussion is limited, in the main, to hydrogen atom abstraction from aliphatic substrates and the factors which influence rate and specificity of this reaction. 

The radicals formed by imimolecular rearrangement or fragmentation of the primary radicals arc often termed secondary radicals. Often the absolute rate constants for secondary radical formation are known or can be accurately determined. These reactions may then be used as radical clocks",R2° lo calibrate the absolute rate constants for the bimolecular reactions of the primary radicals (e.g. addition to monomers - see 3.4). However, care must be taken since the rate constants of some clock reactions (e.g. f-butoxy [3-scission21) are medium dependent (see 3.4.2.1.1). 

The most important mechanism for the decay of propagating species in radical polymerization is radical-radical reaction by combination or disproportionation as shown in Scheme 5.1. This process is sometimes simply referred to as bimolecular termination. However, this term is misleading since most chain termination processes are bimolecular reactions. 

The polymerizations (a) and (b) owe their success to what has become known as the persistent radical effect."1 Simply stated when a transient radical and a persistent radical are simultaneously generated, the cross reaction between the transient and persistent radicals will be favored over self-reaction of the transient radical. Self-reaction of the transient radicals leads to a build up in the concentration of the persistent species w hich favors cross termination with the persistent radical over homotermination. The hoinolermination reaction is thus self-suppressing. The effect can be generalized to a persistent species effect to embrace ATRP and other mechanisms mentioned in Sections 9.3 and 9.4. Many aspects of the kinetics of the processes discussed under (a) and (b) are similar,21 the difference being that (b) involves a bimolecular activation process. 

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. 

Correlated or geminate radical pairs are produced in unimolecular decomposition processes (e.g. peroxide decomposition) or bimolecular reactions of reactive precursors (e.g., carbene abstraction reactions). Radical pairs formed by the random encounter of freely diffusing radicals are referred to as uncorrelated or encounter (P) pairs. Once formed, the radical pairs can either collapse, to give combination or disproportionation products, or diffuse apart into free radicals (doublet states). The free radicals escaping may then either form new radical pairs with other radicals or react with some diamagnetic scavenger... 

Bimolecular reaction between a pair of chain radicals accounts for annihilation of active centers. Two obvious processes by which this may occur are chain coupling (or combination)... 

On the other hand, oxidation of a DNA base by a triplet state of the an-thraquinone (AQ5"3) generates a contact ion pair in an overall triplet state, and back electron transfer from this species to form ground states is prohibited by spin conservation rules. Consequently, the lifetime of the triplet radical ion pair is long enough to permit the bimolecular reaction of AQ- with 02 to form superoxide (02 ) and regenerate the anthraquinone. 

Therefore, the sequence of reactions illustrated in Fig. 1 catalytically (the anthraquinone is regenerated) injects a radical cation into a DNA oligonucleotide that does not simultaneously contain a radical anion. As a result, the lifetime of this radical cation is determined by its relatively slow bimolecular reaction with H20 (or some other diffusible reagent such as 02- ) and not by a rapid intramolecular charge annihilation reaction. This provides sufficient time for the long distance migration of the radical cation in DNA to occur. 

The anthraquinone group of the UAQ sensitizer is intercalated on the 3 -side of its linkage site [15]. Use of UAQ permits assessment of the directionality of long-range radical cation migration. Both AQ and UAQ enable the selective and efficient introduction of a radical cation in duplex DNA, whose lifetime is controlled by its relatively slow bimolecular reaction primarily with H20. 

Termination results in the removal of the activated species from the reaction. It involves the bimolecular reaction between the MA and a specific reactive species, D. Depending on the type of polymerization reaction, the reactive species may be a radical or an ion acceptor. The reaction, then, can be defined as Eq. 4.12. 

The decompositions of hydroperoxides (reactions 4 and 5) that occur as a uni-or bimolecular process are the most important reactions leading to the oxidative degradation (reactions 4 and 5). The bimolecular reaction (reaction 5) takes place some time after the unimolecular initiation (reaction 4) provided that a sufficiently high concentration of hydroperoxides accumulates. In the case of oxidation in a condensed system of a solid polymer with restricted diffusional mobility of respective segments, where hydroperoxides are spread around the initial initiation site, the predominating mode of initiation of free radical oxidation is bimolecular decomposition of hydroperoxides. 

It has been generally accepted that the thermal decomposition of paraffinic hydrocarbons proceeds via a free radical chain mechanism [2], In order to explain the different product distributions obtained in terms of experimental conditions (temperature, pressure), two mechanisms were proposed. The first one was by Kossiakoff and Rice [3], This R-K model comes from the studies of low molecular weight alkanes at high temperature (> 600 °C) and atmospheric pressure. In these conditions, the unimolecular reactions are favoured. The alkyl radicals undergo successive decomposition by [3-scission, the main primary products are methane, ethane and 1-alkenes [4], The second one was proposed by Fabuss, Smith and Satterfield [5]. It is adapted to low temperature (< 450 °C) but high pressure (> 100 bar). In this case, the bimolecular reactions are favoured (radical addition, hydrogen abstraction). Thus, an equimolar distribution ofn-alkanes and 1-alkenes is obtained. 

Productive bimolecular reactions of the ion radicals in the contact ion pair can effectively compete with the back electron transfer if either the cation radical or the anion radical undergoes a rapid reaction with an additive that is present during electron-transfer activation. For example, the [D, A] complex of an arene donor with nitrosonium cation exists in the equilibrium with a low steady-state concentration of the radical pair, which persists indefinitely. However, the introduction of oxygen rapidly oxidizes even small amounts of nitric oxide to compete with back electron transfer and thus successfully effects aromatic nitration80 (Scheme 16). 

Owing to their cationic and radical character, organic cation radicals also participate in a variety of bimolecular reactions with nucleophiles, bases, radicals, etc., as illustrated by the following examples. 

The attachment of an electron to an organic acceptor generates an umpolung anion radical that undergoes a variety of rapid unimolecular decompositions such as fragmentation, cyclization, rearrangement, etc., as well as bimolecular reactions with acids, electrophiles, electron acceptors, radicals, etc., as demonstrated by the following examples.135"137... 

Bimolecular reaction of hydroperoxide decomposition to free radicals was discovered ROOH + ROOH —> R0 + H20 + R00 L. Bateman, H. Hughes, and A. Moris [67]... 

In addition to the bimolecular reactions of organic compounds with dioxygen, free radicals are generated in an oxidized substrate in the liquid phase by the trimolecular reaction [3,8,9]... 

Rate Constants of the Bimolecular Reaction RCH=CH2 + 02 — Free Radicals (Experimental Data)... 

The bimolecular reaction of hydroperoxide decomposition to free radicals... 

The IPM as a semiempirical model of an elementary bimolecular reaction appeared to be very useful and efficient in the analysis and calculation of the activation energies for a wide variety of radical abstraction and addition reactions [108-113]. As a result, it became possible to classify diverse radical abstraction reactions and to differentiate in each class the groups of isotypical reactions. Later this conception was applied to the calculations of activation energies and rate constants of bimolecular reactions of chain generation [114]. In the IPM, the radical abstraction reaction, for example,... 

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