Example of a radical chain reaction

If B and E are unstable short-lived intermediates and the Bodenstein hypothesis can be applied, the following relationships are obtained, since b = Q  

Using the second Bodenstein assumption b = e = 0), the changes in the degree of advancement amount to 

Introducing the common degree of advancement j = jtj = jc, for the overall reaction, then 

In Fig. 2.13 the relationship between a and r is graphed, taking u as the parameter. It turns out that the time dependence of cr for m 1 can be repre- 

---

This type of reaction is important industrially since it is one of the few that allows compounds containing functional groups to be made from alkanes. As you might guess, since it needs light for initiation, the process is another example of a radical chain reaction. As with the radical addition of HBr to alkenes, we can identify initiation, propagation, and termination steps in the mechanism. 

Raising the temperature of a radical chain reaction causes an increase in the overall rate of polymerization since the main effect is an increase in the rate of decomposition of the initiator and hence the number of primary radicals generated per unit time. At the same time the degree of polymerization falls since, according to Eq. 3.3, the rate of the termination reaction depends on the concentration of radicals (see Example 3-2). Higher temperatures also favor side reactions such as chain transfer and branching, and in the polymerization of dienes the reaction temperature can affect the relative proportions of the different types of CRUs in the chains. 

Termination— radical recombinations destroy chain-carrying species and end the chain reaction. The success of a chain reaction depends on the relative success of the chain-carrying and termination steps. Figure 11.26 gives an example of a typical chain reaction. 

A typical example of a nonpolymeric chain-propagating radical reaction is the anti-Markovnikov addition of hydrogen sulfide to a terminal olefin. The mechanism involves alternating abstraction and addition reactions in the propagating steps ... 

Initiator (Section 5.3) A substance with an easily broken bond that is used to initiate a radical chain reaction. For example, radical chlorination of alkanes is initiated when light energy breaks the weak Cl-Cl bond to form Cl-radicals. 

Anything that breaks the chain by converting the active chain-carrying species into an ordinary uncreactive molecule inhibits the reaction, and since the chains are often long an inhibitor may be effective in very small traces. The chain-starting catalysts may also be effective in very small amounts provided that no inhibitor is also present. The fact that a reaction is a chain reaction sensitive to small amounts of catalysts and inhibitors does not necesssarily mean that it is a radical chain, but the nature of the substances effective as catalysts or inhibitors will usually differentiate a radical chain from an ionic one. An example of an ionic chain reaction is the polymerization of an olefin-Lewis acid system when water is added as a co-catalyst. Water is so very effective that it is suspected that the polymerization observed in some cases with the driest obtainable reaction mixtures is due to the presence of minute and unavoidable amounts of water. 

For stannanes, there exists one example of a rearrangement (133 —> 134) which at first sight resembles a prototropic rearrangement, but is in fact a radical chain reaction [341] (Scheme 1.59). 

The oxidative addition of alkyl halides can proceed in different ways, although the result is usually atrans addition independent of the mechanism. In certain cases the reaction proceeds as an SN2 reaction as in organic chemistry. That is to say that the electron-rich metal nucleophile attacks the carbon atom of the alkyl halide, the halide being the leaving group. This process leads to inversion of the stereochemistry of the carbon atom (only when the carbon atom is asymmetric can this be observed). There are also examples in which racemisation occurs. This has been explained on the basis of a radical chain... 

In the early days of alkene chemistry, some researchers found that the hydrohalogenation of alkenes followed Markovnikov s rule, while others found that the same reaction did not. For example, when freshly distilled but-l-ene was exposed to hydrogen bromide, the major product was 2-bromopropane, as expected by Markovnikov s rule. However, when the same reaction was carried out with a sample of but-l-ene that had been exposed to air, the major product was 1-bromopropane formed by antl-Markovnikov addition. This caused considerable confusion, but the mystery was solved by the American chemist, Morris Kharasch, in the 1930s. He realised that the samples of alkenes that had been stored in the presence of air had formed peroxide radicals. The hydrohalogenation thus proceeded by a radical chain reaction mechanism and not via the mechanism involving carbocation intermediates as when pure alkenes were used. 

Halogenation reactions of alkanes provide good examples of radical processes, and may also be used to illustrate the steps constituting a radical chain reaction. Alkanes react with chlorine in the presence of light to give alkyl chlorides, e.g. for cyclohexane the product is cyclohexyl chloride. 

A number of other substances, for example CC14, CCl3Br, and several other alkyl poly halides, aldehydes, and thiols, add successfully to olefins.150 Addition of Cl2, frequently looked upon as ionic, often occurs as a radical chain reaction, particularly in nonpolar solvents and in the presence of light or peroxides.151... 

As mentioned above, catalytic oxidation of olefins via coordination catalysis with an intermediate such as LnM (olefin) 02 seemed an attractive possibility, and Collman s group (45) tentatively invoked such catalysis in the 02-oxidation of cyclohexene to mainly 2-cyclo-hexene-1-one promoted by IrI(CO)(PPh3)2, a complex known to form a dioxygen adduct. Soon afterwards (4, 46, 47) such oxidations involving d8 systems generally were shown to exhibit the characteristics of a radical chain process, initiated by decomposition of hydroperoxides via a Haber-Weiss mechanism, for example Reactions 10 and 11. Such oxidations catalyzed by transition-metal salts such as... 

The 1,5-biradicaI BRi formed during the Patemo—Biichi reaction of excited benzo-quinone B with quadricyclane Q (for the formulas, see Chart 9.4) provides one of the extremely rare examples of a short-chain biradical that produces CIDNP of the radical pair type. Extracts of the CIDNP spectra are displayed in Fig. 9.7. The occurrence of both absorption and emission in the same product is clear evidence for this mechanism of polarization generation. 

Coupling of ketones with electron-deficient alkenes via a methylene group (cf. 11, 315-316). This modified Giese reaction involves cyclopropanation of the silyl enol ether of a ketone, mercuration, and finally demercuration and coupling with an alkene via a radical chain reaction.7 Example ... 

The bimolecular termination reaction in free-radical polymerization is a typical example of a diffusion controlled reaction, and is chain-length-depen-dent [282-288]. When pseudobulk kinetics appUes, the MWD formed can be approximated by that resulting from bulk polymerization, and it can be solved numerically [289-291]. As in the other extreme case where no polymer particle contains more than one radical, the so-caUed zero-one system, the bimolecular termination reactions occur immediately after the entrance of second radical, so unique features of chain-length-dependence cannot be found. Assuming that the average time interval between radical entries is the same for all particles and that the weight contribution from ohgomeric chains formed... 

Xanthate 446 undergoes cyclization in the presence of camphorsulfonic acid via a radical chain reaction initiated by a small amount of lauroyl peroxide to give pyrroloimidazoles 449 in 56% yield. The use of an acid and anhydrous medium inhibits nucleophilic attack of the basic heterocycles at the xanthate moiety and allows radical reactions to occur. Fused heteroaromatic compounds can also be prepared directly from benzimidazole carrying an N-alkenyl substituent and xanthates by a tandem radical addition/cyclization to provide, for example, pyrrolobenzimidazole 453 in 57% yield (Scheme 106) <2002OL4345>. 

---