Cross-propagation reaction

Copolymerization of methacrylic acid with butadiene and isoprene was photoinitiated by Mn2(CO)io without any halide catalyst [28,29]. The po]ymerization system is accompanied by a Dieis-Alder additive. Cross propagation reaction was promoted by adding trieth-y]aluminum chioride. 

The rate of copolymerization in a binary system depends not only on the rates of the four propagation steps but also on the rates of initiation and termination reactions. To simplify matters the rate of initiation may be made independent of the monomer composition by choosing an initiator which releases primary radicals that combine efficiently with either monomer. The spontaneous decomposition rate of the initiator should be substantially independent of the reaction medium, as otherwise the rate of initiation may vary with the monomer composition. 2-Azo-bis-isobutyronitrile meets these requirements satisfactorily. The rate Ri of initiation of chain radicals of both types Ml and M2 is then fixed and equal to 2//Cd[7], or twice the rate of decomposition of the initiator I if the efficiency / is equal to unity (see Chap. IV). The relative proportion of the two types of chain radicals created at the initiation step is of no real importance, for they wall be converted one into the other by the two cross-propagation reactions of the set (1). Melville, Noble, and Watson presented the first complete theory of copolymerization suitable for handling the problem of the rate. The theory was reduced to a more concise form by Walling, whose procedure is followed here. 

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... 

In addition to cross-propagation reactions, one cross-termination reaction is introduced in addition to two self-termination reactions, viz,... 

When rx> 1 and r2 < 1, the self-propagation reaction of type 11 and cross propagation reaction of type 21 are more probable. The copolymer formed will be richer in Mx. Similarly if r2 > 1 and r < 1, copolymer will be richer in M2. 

Copolymerizations of nonpolar monomers with polar monomers such as methyl methacrylate and acrylonitrile are especially comphcated. The effects of solvent and counterion may be unimportant compared to the side reactions characteristic of anionic polymerization of polar monomers (Sec. 5-3b-4). In addition, copolymerization is often hindered by the very low tendency of one of the cross-propagation reactions. For example, polystyryl anions easily add methyl methacrylate but there is little tendency for poly(methyl methacrylate) anions to add styrene. Many reports of styrene-methyl methacrylate (and similar comonomer pairs) copolymerizations are not copolymerizations in the sense discussed in this chapter. 

In a living system, if Mi is much more reactive than M2 and polymerization is allowed to proceed to completion, the end-product is a tapered block copolymer, in which only the middle section contains units of both monomers, e.g. with anti-1-methylnorbomene (Mi)/syw-7-methylnorbomene (M2), see Section VIII.C.4 also with norbornene (Mi)/cyclooctatetraene (M2), catalysed by 8W (R = Me)360. In the extreme case the cross-propagation reactions may be so slight that the product is indistinguishable from a perfect block copolymer, e.g. with bicyclo[3.2.0]hept-2-ene (Mi)/norbornene (M2) catalysed by 18109,597, or with awft -7-methylnorbornene (Mi) syn-1 -methylnorbomene (M2), catalysed by 7 (R = Me)128. The successive polymerization of the two monomers can be readily followed by NMR. 

The values of relative reactivity of macromonomers (l/r2) in both solution and emulsion were found to decrease slightly with conversion. The r2 values in solution are lower than those for the copolymerization of low-molecular-weight monomers and macromonomers in emulsion. These results support the previous conclusion [95] about the incompatibility of macromonomer with a polymer trunk (polystyrene radical) which suppresses the mutual cross-propagation reactions of comonomers. 

In the random copolymerization process, both types of active species should be able to participate in the cross-propagation reactions. This imposes certain limitations on the choice of comonomers in the cationic polymerization of heterocyclic monomers. Onium ions, being the active species of these polymerizations, differ considerably in reactivity thus, as already discussed, oxonium ions initiate the polymerization of cyclic amines, whereas ammonium ions do not initiate the polymerization of cyclic ethers and the corresponding cross-propagation reaction would not proceed ... 

In many systems, however, the analysis of the cationic copolymerization of heterocyclic monomers is complicated by two factors (1) at least some of the homo- and cross-propagation reactions may be reversible (2) redistribution of the sequences of comonomers within the chain may occur as a result of chain transfer to polymer. Therefore, the conventional treatment involving four irreversible propagation steps is rarely applicable in cationic ring-opening copolymerization. Instead, the diad model should involve four reversible reactions, i.e., eight rate constants... 

By studying the effect of pressure on copolymerizations it is possible to obtain and activation volume difference for various homo- and cross-propagation reactions. For instance, in two of the propagation reactions occurring in the styrene-acrylonitrile polymerization ... 

The ratio kn/ki2 is found to vary with pressure, and AV h — AV i2 has a value of —9.8 cc. per mole (5). Using the value of AV h given by Norrish, AV i2 Is found to be —3.5 cc. per mole. It would be interesting to compare aV values for other cross-propagation reactions as a possible route to an understanding of the nature of the activated complex. 

Oxidation of a mixture of two hydrocarbons simultaneously introduces cross-propagation reactions, where the peroxy radical from one hydro-... 

An expression for the rate constant of the cross-propagation reaction can then be derived as... 

An expression for the ratio [A ]/[B ] is obtained by considering the creation and loss of active centres of a particular typje. The contributions from initiation and termination reactions are negligible compared to that of the cross-propagation reactions and so... 

If monomer loss to start, termination or transfer reactions is small, then the degrees of polymerization will be large. The monomers will only be consumed in the two homopropagation and two cross-propagation reactions. 

But, because of cross-propagation reactions, the individual active species concentrations can vary with time or conversion, and so the concentration ratio [A/J ]/[A/J] can vary with yield in such copolymerizations. If, however, crosspropagation is absent, that is, v /b = Vg/A == 0, then, the ratio [A/ ]/ [A/g] is constant with time. Thus, the first bracketed expression on the right-hand side of Equation (22-12) is also a constant ... 

Table 22-19. Rate Constants for the Homo- and Cross-Propagation Reactions of Anionic Homo- and Copolymerizations in Tetrahydrofuran at 25 C...

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