Cross-propagation

Table 7.2 lists a few cross-propagation constants calculated by Eq. (7.20). Far more extensive tabulations than this have been prepared by correlating copolymerization and homopolymerization data for additional systems. Examination of Table 7.2 shows that the general order of increasing radical activity is... 

Table 7.2 Values of the Cross-Propagation Constants k 12 for Four Monomer-Radical Combinations...

For the reaction of radical i with monomer j, Price and Alfrey assume that the cross-propagation rate constant can be written as... 

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. 

Certain monomers may act as inhibitors in some circumstances. Reactivity ratios for VAc-S copolymerization (r< 0.02, rVu -2.3) and rates of cross propagation are such that small amounts of S are an effective inhibitor of VAc polymerization. The propagating chain with a terminal VAc is very active towards S and adds even when S is present in small amounts. The propagating radical with S adds to VAc only slowly. Other vinyl aromatics also inhibit VAc polymerization.174... 

In traditional treatments of copolymerizaiion kinetics, the values of the ratios sA and % are implicitly set equal to unity (Section 7.3.1.2.2). Since they contain no terms from cross propagation, these parameters have no direct influence on either the overall copolymer composition or the monomer sequence distribution they only influence the rate of polymerization. 

Monomers not amenable to direct homopolymerization using a particular reagent can sometimes be copolymcrizcd. For example, NMP often fails with methacrylates (e.g. MMA, BMA), yet copolymerizalions of these monomers with S are possible even when the monomer mix is predominantly composed of the methacrylate monomer,15j This is attributed to the facility of cross propagation and the relatively low steady state concentration of propagating radicals with a terminal MMA (Section 7.4.3.1). MMA can also be copolymerized with S or acrylates at low temperature (60 C).111 Under these conditions, only deactivation of propagating radicals with a terminal MMA unit is reversible, deactivation of chains with a terminal S or acrylate unit is irreversible. Molecular weights should then be controlled by the reactivity ratios and the comonomer concentration rather than by the nitroxide/alkoxyamine concentration. 

However, ionic copolymerizations are much more selective than radical copolymerizations and the number of copolymer pairs which undergo ionic copolymerization is relatively limited. Cross-propagation rarely occurs between monomer pairs... 

A cross sequence such as illustrated here may be associated with the following cross propagation steps,... 

Only a few quantitative data are available on copolymerization of methacrylates. Direct determination of the cross-propagation constants is readily achieved in living polymer systems whenever the absorption spectra of the two propagating species are different. Unfortunately, this is not the case in the methacrylate series. A new approach to this problem was developed by Muller 43). A mixture of two monomers is copolymerized, the reaction is interrupted at various times, and the concentrations of the residual monomers are determined as functions of time. The pertinent differential equations include 4 constants ku, k12, k21, and k22. Since kn and k22 were independently determined, the remaining cross-propagation constants are obtained by computer fitting the experimental conversion curves to the calculated ones. 

The correct explanation of the peculiar behaviour of the butadiene-styrene system was provided by O Driscoll and Kuntz 144). As stated previously, under conditions of these experiments butadiene is indeed more reactive than styrene, whether towards lithium polystyrene or polybutadiene, contrary to a naive expectation. This was verified by Ells and Morton 1451 and by Worsfold 146,147) who determined the respective cross-propagation rate constants. It is germane to stress here that the coordination of the monomers with Li4, assumed to be the cause for this gradation of reactivities, takes place in the transition state of the addition and should be distinguished from the formation of an intermediate complex. The formation of a complex ... 

It was possible to formulate a rule describing how the copolymerization parameters depend on the polarity of the solvent used. This rule is a result of contemplation about the connection between the copolymerization parameters and propagation rate constants during the cationic polymerization as well as about the changes of solvation of educts and activated complexes of the crossed propagation steps in solvents with varied polarity 14 U7). The rule is as follows ... 

Aqueous Phase Hass Balances. The usual material balances for the active species in the aqueous solution are considered. With respect to the case of homopolymerization (4) the conplexity of the resulting equations is increased because of the cross propagation and termination terms. For the batch reactor considered in this wortt, the following equations arise ... 

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... 

By studying mixtures of L- and D-LA of varying composition, Spassky et al. have demonstrated that (256) yields PLA containing long isotactic sequences, with a ratio of homo cross propagation of 2.8.796 Hence, an 80/20 L D mixture when polymerized to 70% conversion displayed an optical purity of 87%. Even at the relatively low optical purity of 65/35 L D, isotactic block lengths of >12 repeat units were reported. Achiral (259) converts rac-LA into highly isotactic PLA a Tm of 192 °C indicates that the chains of P(L-LA) and P(D-LA) form a stereocomplex.792 797-799... 

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

Rate Constants of the Cross-Propagation in Co-Oxidation of Hydrocarbons... 

During polymerization, a polymeric radical with a perfluoro(alkyl vinyl ether)-derived active center can have one of two fates it can cross-propagate to tetrafluoroethylene or it can undergo P-scission to yield an acid-fluoride-terminated polymer chain and generate a peduoroalkyl radical capable of initiating further polymerization (ie., chain transfer to monomer). These scenarios are illustrated in Scheme 3. 

When rx =, kx2 = kn, i.e. rate constant for self-propagation and cross propagation are same, the radical M can add to M, or M2 with equal probability. 

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. 

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