Well-Behaved Chain Reactions

When the initiation and termination reactions are the reverse of one another, the kinetic form is usually simpler than when the two are independent. Also, the transition-state composition follows directly from the rate law, which is why the term well-behaved is applied. Imagine, for example, that the termination step in the system most recently presented was the recombination of two sulfate radical ions rather than Eq. (8-38)  

To explore this premise further, imagine that the second initiation step could be neglected. That is, [H2POj ] would be chosen such that k fc2[H2P03 ]. We then have a scheme consisting of Eqs. (8-33), (8-35)—(8-37), and (8-47). With the usual approximations, the rate law is 

Does the transition state composition for the RCS, [S04 H20], really follow from Eq. (8-48) Indeed, from Eq. (8-35), that is exactly the case. There is no indication in this circumstance that a chain mechanism operates. [Keep in mind, however, that this example is fictional, in that Eq. (8-47) is not important compared with Eq. (8-38).] Fractional-order dependences are not necessarily indicative of chains when the reagent is symmetric, like S20 , although the particular examples presented do happen to feature chain mechanisms. 

---

Chain reactions, 181 branching, 189 initiation step, 182 propagation steps, 182 rate laws for, 188 termination step, 182 well-behaved, 187 Chemical mechanism, 9 Chemical relaxation, 255-260 Coalescence temperature, 262 Col, 170... 

Indeed, the formation of esters of the type RO—(COCE CE ),—H was observed when the solvent for the copolymerization reaction was ROH (R=CH3, C2H5). The polyketoesters corresponding to n = 1-5 could be seperated and quantified, and gave well-behaved Schulz-Flory plots indicating the validity of the mechanism involving a single mode of stepwise chain growth as shown in Scheme 1. 

Products are olefins and the corresponding acids. These reactions are among the most widely studied and best understood of all gas phase unimolecular reactions. With few exceptions they are experimentally and kinetically well behaved cleanly first-order, no surface sensitivity, and no free radical chain complications. Reactions involve 1,5-hydrogen transfer from the f -carbon to the carbonyl oxygen, migration of the carbonyl Jt-bond, rupture of the ester (C-O) bond, and formation of a (Cg-Cf) 7t-bond. All present evidence favors a mechanism in which the above occur in a concerted manner. However, a two-step consecutive mechanism (see later) cannot be entirely ruled out at this time. 

A new decarboxylative route to free radicals, which has proved particularly successful in preparative work, embodies the thermal (or photochemical) decomposition reaction of 1-hy-droxypyridine-2(l/f)-thione esters 23 with tributyltin hydride, /er/-butanethiol, or a similar hydrogen donor.These esters can be easily prepared from acyl halides and the sodium salt of l-hydroxypyridine-2(l//)-thione, or from the carboxylic acid, dicyclohexylcarbodiimide and l-hydroxypyridine-2(l/f)-thione. The intermediate radicals were readily reduced to the corresponding hydrocarbons 24 in efficient chain reactions with organotin hydrides or thiols as reaction partners, and the proportion of rearranged to unrearranged products could be controlled by the choice of hydrogen donor, its concentration and the temperature. This system was sufficiently quantitative and well behaved for use in kinetic studies, and the rate constants of the (S-scission reactions of the listed cyclopropylmethyl species were determined. 

The thiophene ring can also be opened up, but in a very different way. Reductive removal of the sulfur atom with Raney nickel reduces not only the C—S bonds but also the double bonds in the ring and the four carbons in the ring form a saturated alkyl chain. If the reduction follows two Friedel—Crafts reactions on thiophene the product is a 1,6-diketone instead of the 1,4-diketones from furan. Thiophene is well behaved in Friedel—Crafts acylations, and reaction occurs at the 2- and 5-positions unless these are blocked. 

Equation 1 has certain desirable features. Apart from fitting the present data, it behaves well mathematically at X = 1 and thus is valuable for extrapolation to low and even zero conversions. Further, the value of Fact obtained is satisfyingly high (78 kcal/mol). The generally accepted, free radical mechanism requires a value of Eact equal to the C-C bond energy in propane (85 kcal), less a number related to one or more of the chain-carrying reactions (5-10 kcal), hence in the range of 75-80 kcal. 

In light of the known dimension dependence of the percolation model, the conclusion drawn above will be a quite unexpected one,but the physicochemical reason is very clear without an ambiguity As the dimensionality increases, the space-freedom should expand, so the probability of one end on a chain encountering the other end must decrease, while just by the same reason, the probability of two functional units on different molecules encountering must decrease as well. As a result of this competition, the minimum of (p- should occur, beyond which cyclization becomes dominant over intermolecular reaction. At sufficiently high dimensions, cyclization finally overwhelms the intermolecular reaction, and the system behaves as if at a dilution limit. 

The last column of table 3 shows the values of k as calculated by the above expression from the values of Vmt C and t given in the same table. It is very probable, therefore, that k expresses the specific inhibitory power of anthraquinone in the reactions studied. Furthermore, anthraquinone seems to behave as a true negative catalyst. Since anthraquinone is not destroyed during the oxidation of anethol, how can its effect be explained in the light of the recently proposed chain mechanism of negative catalysis It is well known that quinones are highly reactive substances and are found to combine with several other organic substances to form imstable and frequently stable complexes. In other words,... 

The copolymerization theory presented here assumes that the reactivity of a growing chain depends on the last mer added to the chain. Chemical theorists point out that there can be penultimate ejfects where reactivity depends on the next to the last (penultimate) mer as well as the last (ultimate) mer. Thus -XX would behave differently than -YX. This is undoubtedly tme, but the extra complexity seldom seems unjustified from a reaction engineering viewpoint. 

---