Multicentered chain reactions

This chapter provides a formal kinetic description of multicenter chain reactions, where in the rate-limiting steps several carrier chains participate simultaneously. Internal system relations in a multicenter chain reaction are discriminated by the chain length, components These quantities are considered as a response of the rate of formation of some reaction product, due to a small change in the rate of origination of certain chain carrier. The issues of organic coimection of value quantities with characteristic quantities of multicenter chain reactions ate discnssed. 

This Chapter is plaimed in the following logical sequence. In the begirming, a formal-kinetic description of multicentered chain reactions [9] is presented. Then, arguments are listed relative to what additional information may be retrieved by applying the value approach, as already stated in the preceding Chapters. Finally, in summary the value approach... 

Let us pass to a brief description of the formal kinetics of multicentered chain reactions. A multicentered non-branching chain reaction with linear steps of transformation of the active reactive centers (chain carriers) may be represented in the form of a formal scheme [9], as some kind of a flow graph for the dynamic process (see Section 4.5). 

Selective initiation and selective inhibition of multicentered chain reaction as a whole are identical in nature. Expressions (5.11) and (5.12) may be also considered with certain reservations as conditions for the selective inhibition. More detailed formal-kinetic analysis of the possibility to realize selective inhibition in the framework of multicentered consideration of chain conversion may be found in [9]. 

From a methodical viewpoint it seems practical to address first the possibilities of the selective inhibition of the undesirable direction of the reaction for liquid-phase oxidation of a-methylaerolein, by using the formal kinetic tool for the multicentered chain reactions presented in the Section 5.1. Now, by analogy with the scheme (5.1), we present the above-listed set of steps (1-18) as the flow graph (Figmc 6.3) for the multicentered chain process [10]. 

Diverio D, Rossi V, Awisati G, De Santis S, PistiUi A, Pane F, et al. Early detection of relapse by prospective reverse transcriptase-polymerase chain reaction analysis of the PML/RARalpha fusion gene in patients with acute promyelocytic leukemia enrolled in the GIMEMA-AIEOP multicenter AIDA trial. GIMEMA-AIEOP Multicenter AIDA Trial. Blood 1998 92 784-9. 

Tetrafunctional monomers or polymers with vinyl side chains offer the unique possibility of quantum amplification by spatial polymerization. This reaction is also shown in Figure 6. Multicentered polymerization by chain reaction provides high speed and the mechanical-physical strength of a crosslinked polymer. However, because of the rapid increase in viscosity, the amplification may not be as large as expected ... 

Kinetics of Multicentered Chain Chemical Reactions. Approach... 

Formal Kinetics of Multicentered Non-Branching Chain Reactions... 

Multicentered consideration of a chain reaction, unlike the one-centered one, takes into account from the outset the possibility of the decisive role of a great number of individual steps involving the different active reaction centers. Moreover, very often such important reaction features as the reactivity of initial reagents, the yield of target products, etc. are determined by the intensity of the chain reaction occurring by means of different paths . It is easy to conceive that the one-centered approach is not appropriate when studying such problems. 

Figure 5. 1. Schematic illustration of a multicentered non-branching chain reaction. R, is an active reaction center (atom, free radical, excited particle, etc.). Arrows between active reaction centers, chain carriers, R, and R , denote the reactions resulting in mutual transformations ky is the effective rate constant for the formation of the R reaction center with participation of the R reaction center A, is the...

The concept on multicentered reaction system of chain conversion [9] (Section 5.1) enables to consider the conditions of both the selective inhibition and selective initiation of chain reactions from the more general viewpoint. 

Detailed review of studies on the auto- and catalytic-oxidation of unsaturated aldehydes in the liquid phase may be found in [2,9], Here we just note the main specific feature of the unsaturated aldehydes oxidation, briefly cited in Section 5.2. It implies that the free-radical chain process of the aldehyde group oxidation stimulates undesirable reactions, including the copolymerization of aldehyde with oxygen through the aldehyde s double bond, and in some cases also the copolymerization of the reaction products, the unsaturated acids and peroxyacids with oxygen. The oxidation reactions of unsaturated aldehydes are defined as the multicentered chain processes with two types of reaction centers acyl monomeric and polyperoxide free radicals. 

The solvent used for most of polymerizations is THF or dioxane. However, it is also possible to use toluene, benzene, or hexane with an addition of polar substances (ether, amines). In those cases, it is necessary to use mild conditions and gentle catalysts because if the dissociation of the amides of phosphides is weakened, multicenter processes, for example, have an effect. These are favored by the free electron pair on the nitrogen or phosphorus, and they lead to chain-terminating reactions. 

Several reaction mechanisms were also proposed to explain stereospecific placement with insoluble catalysts. Furukawa [46] suggested that here the mechanism for cationic polymerization of vinyl ethers depends upon multicentered coordinations. He felt that coordinations of the polymeric chains and monomers with the catalysts are possible if the complexed counteranions have electrically positive centers. This can take place in the case of aluminum alkyl and boron fluoride ... 

It might be interesting to note that the proponents of the carbene mechanism (mentioned earlier), point out that this is also consistent with their mechanism [254, 255], The reaction can consist of (a) an insertion of a metal into an a-CH bond of a metal alkyl to form a metal-carbene hydride complex. This is followed by (b) reaction of the metal-carbene unit with an alkene to form a metal-cyclobutane-hydride intermediate. The final step (c), is a reductive elimination of hydride and alkyl groups to produce a chain-lengthened metal alkyls. This assures that a chiral metal environment is maintained [254]. It is generally believed [258], however, that stereospecific propagation comes from concerted, multicentered reactions, as was shown in the Cossee-Arlman mechanism. The initiator is coordinated... 

Now let us derive the analytie dependence for the rate of the P product formation and the chain length component vj, on the quantitative characteristics of individual steps (r°, ku, ki), for the multicentered non-branching chain process [9]. In accordance with the reaction scheme illustrated in Figure 5.1 the rates of the chain carrier formation are ... 

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