Termination by combination

This is the simplest form of chain termination. It involves two growing polymer chains which combine with the mutual extinction of the radicals. 

This type of termination reaction will result in a head to head linkage of the two polymer chains involved. 

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Termination by combination results in the simultaneous destruction of two radicals by direct coupling ... 

Only one additional stipulation needs to be made before adapting the results that follow from Eq. (5.24) to addition polymers. The mode of termination must be specified to occur by disproportionation to use the results of Sec. 5.4 in this chapter, since termination by combination obviously changes the particle size distribution. We shall return to the case of termination by combination presently. 

To deal with the case of termination by combination, it is convenient to write some reactions by which an n-mer might be formed. Table 6.5 lists several specific chemical reactions and the corresponding rate expressions as well as the general form for the combination of an (n - m)-mer and an m-mer. On the assumption that all kj values are the same, we can write the total rate of change of [M -] ... 

This expression is plotted in Fig. 6.7 for several large values of p. Although it shows a number distribution of polymers terminated by combination, the distribution looks quite different from Fig. 5.5, which describes the number distribution for termination by disproportionation. In the latter Nj,/N decreases monotonically with increasing n. With combination, however, the curves go through a maximum which reflects the fact that the combination of two very small or two very large radicals is a less probable event than a more random combination. 

Figure 6.7 Number fraction of n-mers as a function of n for termination by combination. Drawn according to Eq. (6.77) for values of p indicated.

One rather different result that arises from the case of termination by combination is seen by examining the limit of Eq. (6.80) for large values of p ... 

In ionic polymerizations termination by combination does not occur, since all of the polymer ions have the same charge. In addition, there are solvents such as dioxane and tetrahydrofuran in which chain transfer reactions are unimportant for anionic polymers. Therefore it is possible for these reactions to continue without transfer or termination until all monomer has reacted. Evidence for this comes from the fact that the polymerization can be reactivated if a second batch of monomer is added after the initial reaction has gone to completion. In this case the molecular weight of the polymer increases, since no new growth centers are initiated. Because of this absence of termination, such polymers are called living polymers. 

In a simple free-radical-initiated addition polymerisation the principal reactions involved are (assuming termination by combination for simplicity)... 

Head-to-head units formed in a molecule have not only been considered as initiation sites for the dehydrochlorination but also as termination points for the growing polyene sequences [19,66,68]. Head-to-head units can either be formed through termination by combination [Eq. (19)] or by head-to-head addition during propagation [Eq. (20)]. 

Depending on the termination reaction of the vinyl monomer, termination by disproportionation or termination by combination occurs. As a result, AB or ABA block copolymers might be obtained. 

Which mechanism of termination will be preferably applied depends largely on the monomer used. Thus, methyl methacrylate chains terminate to a large extent by disproportionation, whereas styrene chains tend to termination by combination. The ratios of termination rate constants 8 = ktJkic (for disproportionation, td, combination,, c) are 5 == 0 and 5 = 2 for styrene [95] and methyl methacrylate [96], respectively. In the case of styrene, however, the values of 8 reported in the literature are at variance. Berger and Meyerhoff [97] found 8 = 0.2, at 52°C. Therefore, it is possible that a fraction of styrene terminates by disproportionation. 

Primary radical termination is also of demonstrable significance when very high rates of initiation or very low monomer concentrations are employed. It should be noted that these conditions pertain in all polymerizations at high conversion and in starved feed processes. Some syntheses of telechelics are based on this process (Section 7.5.1). Reversible primary radical termination by combination with a persistent radical is the desired pathway in many forms of living radical polymerization (Section 9.3). 

The tendency for radicals to give tail addition means that a head-to-head linkage will, most likely, be followed by a tail-to-tail linkage (Scheme 4.5). Thus, head-to-head linkages formed by an "abnormal" addition reaction are chemically distinct from those formed in termination by combination of propagating radicals (Scheme 4.6). 

Chains with uttdesired functionality from termination by combination or disproportionation cannot be totally avoided. Tn attempts to prepare a monofunctional polymer, any termination by combination will give rise to a difunctional impurity. Similarly, when a difunctional polymer is required, termination by disproportionation will yield a monofunctional impurity. The amount of termination by radical-radical reactions can be minimized by using the lowest practical rate of initiation (and of polymerization). Computer modeling has been used as a means of predicting the sources of chain ends during polymerization and examining their dependence on reaction conditions (Section 7.5.612 0 J The main limitations on accuracy are the precision of rate constants which characterize the polymerization. 

Minor (by amount) functionality is introduced into polymers as a consequence of the initiation, termination and chain transfer processes (Chapters 3, 5 and 6 respectively). These groups may either be at the chain ends (as a result of initiation, disproportionation, or chain transfer,) or they may be part of the backbone (as a consequence of termination by combination or the copolymerization of byproducts or impurities). In Section 8.2 wc consider three polymers (PS, PMMA and PVC) and discuss the types of defect structure that may be present, their origin and influence on polymer properties, and the prospects for controlling these properties through appropriate selection of polymerization conditions. 

TC = termination by combination rate constant T = ratio of the termination rate constant for combination to the rate constant for disproportionation CFM = ratio of the rate constant for monomer transfer to the constant for propagation... 

The most comprehensive simulation of a free radical polymerization process in a CSTR is that of Konopnicki and Kuester (15). For a mechanism which includes transfer to both monomer and solvent as well as termination by combination and disproportionation they examined the influence of non-isothermal operation, viscosity effects as well as induced sinuoidal and square-wave forcing functions on initiator feed and jacket temperature on the MWD of the polymer produced. 

The initiator association number y depends upon temperature, solvent and concentration of the system and is reported to be between two and seven (2) The association of polystyryl anions results in species A. Ak which do not react with styrene monomer. The macromolecular association is analogous to a reversible termination by combination. 

In contrast to chain transfer, termination reactions destroy free radicals. Two mechanisms are considered. Termination by combination produces a single molecule of dead polymer ... 

Example 13.5 Determine the instantaneous distributions of chain lengths by number and weight before and after termination by combination. Apply the quasi-steady and equal reactivity assumptions to a batch polymerization with free-radical kinetics and chemical initiation. 

If reactions other than those considered so far did not take place to an appreciable extent, the average degree of polymerization would be directly related to the kinetic chain length v. Assuming termination by combination of radicals, as is indicated by experiments previously cited, each polymer molecule formed in a monoradical-initiated polymerization would consist of two kinetic chains grown from two other-... 

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