Propagation in copolymerization

Propagation in copolymerization could, in principle, be discussed under the same headings as used for the discussion of propagation in Chapter 4. However, remarkably little information is currently available on the tacticity, extents of head vs tail addition, and propensity for rearrangement in copolymerization. 

Studies on radical copolymerization and related model systems have demonstrated that many factors can influence the rate and course of propagation in copolymerization. These include ... 

Scheme 2 Equilibria of propagations in copolymerization hold for any chain length and copolymer sequences (/, y=0,1, 2,a, p,/, and 6 indicate symbolically all possible copolymer unit sequences).

Note that this inquiry into copolymer propagation rates also increases our understanding of the differences in free-radical homopolymerization rates. It will be recalled that in Sec. 6.1 a discussion of this aspect of homopolymerization was deferred until copolymerization was introduced. The trends under consideration enable us to make some sense out of the rate constants for propagation in free-radical homopolymerization as well. For example, in Table 6.4 we see that kp values at 60°C for vinyl acetate and styrene are 2300 and 165 liter mol sec respectively. The relative magnitude of these constants can be understod in terms of the sequence above. 

The and e values of the aHyl group in DAP have been estimated as 0.029 and 0.04, respectively, suggesting that DAP acts as a fairly typical unconjugated, bifunctional monomer (42). Cyclization affects copolymerization, since cyclized radicals are less reactive in chain propagation. Thus DAP is less reactive in copolymerization than DAIP or DATP where cyclization is stericaHy hindered. Particular comonomers affect cyclization, chain transfer, and residual unsaturation in the copolymer products. DiaHyl tetrachloro- and tetrabromophthalates are low in reactivity. 

The incidence of the various structures depends strongly on the comonomer. In copolymerization with acrylates structures 62 and 63 dominate. In copolymerization with VAc structure 61 dominates and 62 and 63 arc not observed. Structure 60 may be present in VAc copolymers to a very small extent but is not observed in acrylate copolymerizations. Structures 62 and 63 arc not observed and cannot be formed in methacrylate copolymerizations.290 The results were interpreted"90 in terms of the PVAc propagating radical having a lesser... 

Frequency factors for addition of small radicals to monomers are higher by more than an order of magnitude than those for propagation (Table 4.12). Activation energies are typically lower. However, trends in the data are very similar suggesting that the same factors are important in determining the relative reactivities for both small radicals and propagating species. The same appears to be true with respect to reactivities in copolymerization (Section 73.1.2)/88... 

Rased on the above data, it would seem unusual if reactivity of the propagating species in copolymerization were insensitive to the nature of the last added monomer units. However, while there are ample experimental data to suggest that copolymerizations should be subject to penultimate unit effects that affect the rate and/or copolymer composition, the origin and magnitude of the effect is not always easily predictable. 

The rate of copolymerization often shows a strong dependence on the monomer feed composition. Many theories have been developed to predict the rate of copolymerization based on the terminal model for chain propagation (Section 7.3.1.1), This usually requires an overall rate constant for termination in copolymerization that is substantially different from that observed in homopolymerization of any of the component monomers. 

More complex models for diffusion-controlled termination in copolymerization have appeared.1 tM7j Russo and Munari171 still assumed a terminal model for propagation but introduced a penultimate model to describe termination. There are ten termination reactions to consider (Scheme 7.1 1). The model was based on the hypothesis that the type of penultimate unit defined the segmental motion of the chain ends and their rate of diffusion. 

Polymerization equilibria frequently observed in the polymerization of cyclic monomers may become important in copolymerization systems. The four propagation reactions assumed to be irreversible in the derivation of the Mayo-Lewis equation must be modified to include reversible processes. Lowry114,11S first derived a copolymer composition equation for the case in which some of the propagation reactions are reversible and it was applied to ring-opening copalymerization systems1 16, m. In the case of equilibrium copolymerization with complete reversibility, the following reactions must be considered. 

Although the basic mechanisms are generally agreed on, the difficult part of the model development is to provide the model with the rate constants, physical properties and other model parameters needed for computation. For copolymerizations, there is only meager data available, particularly for cross-termination rate constants and Trommsdorff effects. In the development of our computer model, the considerable data available on relative homopolymerization rates of various monomers, relative propagation rates in copolymerization, and decomposition rates of many initiators were used. They were combined with various assumptions regarding Trommsdorff effects, cross termination constants and initiator efficiencies, to come up with a computer model flexible enough to treat quantitatively the polymerization processes of interest to us. 

Steric effects similar to those in radical copolymerization are also operative in cationic copolymerizations. Table 6-9 shows the effect of methyl substituents in the a- and 11-positions of styrene. Reactivity is increased by the a-methyl substituent because of its electron-donating power. The decreased reactivity of P-methylstyrene relative to styrene indicates that the steric effect of the P-substituent outweighs its polar effect of increasing the electron density on the double bond. Furthermore, the tranx-fl-methylstyrene appears to be more reactive than the cis isomer, although the difference is much less than in radical copolymerization (Sec. 6-3b-2). It is worth noting that 1,2-disubstituted alkenes have finite r values in cationic copolymerization compared to the values of zero in radical copolymerization (Table 6-2). There is a tendency for 1,2-disubstituted alkenes to self-propagate in cationic copolymerization, although this tendency is low in the radical reaction. 

Some monomers with no tendency toward homopolymerization are found to have some (not high) activity in copolymerization. This behavior is found in cationic copolymerizations of tetrahydropyran, 1,3-dioxane, and 1,4-dioxane with 3,3-bis(chloromethyl)oxetane [Dreyfuss and Dreyfuss, 1969]. These monomers are formally similar in their unusual copolymerization behavior to the radical copolymerization behavior of sterically hindered monomers such as maleic anhydride, stilbene, and diethyl fumarate (Sec. 6-3b-3), but not for the same reason. The copolymerizability of these otherwise unreactive monomers is probably a consequence of the unstable nature of their propagating centers. Consider the copolymerization in which M2 is the cyclic monomer with no tendency to homopolymerize. In homopolymerization, the propagation-depropagation equilibrium for M2 is completely toward... 

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