Termination by disproportionation

The results of the kt determination, including the various ratios of termination by disproportionation over combination are shown in figure 3.23. It is gratifying, though at the same time surprising, to see that the MWD procedure is rather insensitive towards the presence of disproportionation. Even in the case when termination is exclusively by disproportionation, the obtained kt curve is still a fair representation for the exact input values of the simulation. For small amounts of disproportionation this can be easily understood. Chains of a specific chain length formed by disproportionation were formed at a much later time than chains of the exact same chain length formed by combination. As a consequence 

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Termination by disproportionation comes about when an atom, usually hydrogen, is transferred from one polymer radical to another ... 

The degree of polymerization in Eq. (6.41) can be replaced with the kinetic chain length, and the resulting expression simplified. To proceed, however, we must choose between the possibilities described by Eqs. (6.34) and (6.35). Assuming termination by disproportionation, we replace n, by v, using Eq. (6.37) ... 

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. 

These various expressions differ from their analogs in the case of termination by disproportionation by the appearance of occasional 2 s. These terms arise... 

This contrasts with a limiting ratio of 2 for the case of termination by disproportionation. Since and can be measured, this difference is potentially a method for determining the mode of termination in a polymer system. In most instances, however, termination occurs by some proportion of both modes. Although general expressions exist for the various averages and their ratio when both modes of termination are operative, molecular weight data are generally not sufficiently precise to allow the proportions of termination modes to be determined in this way. 

In these equations I is the initiator and I- is the radical intermediate, M is a vinyl monomer, I—M- is an initial monomer radical, I—M M- is a propagating polymer radical, and and are polymer end groups that result from termination by disproportionation. Common vinyl monomers that can be homo-or copolymeri2ed by radical initiation include ethylene, butadiene, styrene, vinyl chloride, vinyl acetate, acrylic and methacrylic acid esters, acrylonitrile, A/-vinylirnida2ole, A/-vinyl-2-pyrrohdinone, and others (2). 

Although primary and secondary alkyl hydroperoxides are attacked by free radicals, as in equations 8 and 9, such reactions are not chain scission reactions since the alkylperoxy radicals terminate by disproportionation without forming the new radicals needed to continue the chain (53). Overall decomposition rates are faster than the tme first-order rates if radical-induced decompositions are not suppressed. 

The minimum polydispersity index from a free-radical polymerization is 1.5 if termination is by combination, or 2.0 if chains ate terminated by disproportionation and/or transfer. Changes in concentrations and temperature during the reaction can lead to much greater polydispersities, however. These concepts of polymerization reaction engineering have been introduced in more detail elsewhere (6). 

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. 

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. 

Note, however, that chain ends 4 and 5 may give different chemistry to those formed in termination by disproportionation (2, see Scheme 8.5) or the processes under (a) above. Chain scission (3 to the double bond will not lead to a MMA propagating species. It is not established whether the presence of these ends will give impaired thermal stability. 

Figure 9.2 Calculated (a) number and (b) GPC distributions for three polymers each with =100. The number distributions of chains formed by conventional radical polymerization with termination by disproportionation or chain transfer...

A further problem with these iniferters is loss of living ends through primary radical termination by disproportionation. The ratio of reported for the cross... 

The free radicals combine to form a carbon-to-carbon bond and give a saturated polymer molecule with initiator fragments on both ends. Termination by disproportionation produces two polymer molecules, one of which will contain a double bond ... 

Based on the literature data available for styrene polymerized with benzoyl peroxide, (10,12,14) transfer to monomer and termination by disproportionation will be neglected. For the Initiation step, only primary and Induced decomposition reactions will be considered. 

In the absence of any transfer, only the type of termination reaction has to be taken into account to obtain the number average degree of polymerisation (or chain length) Xn. Indeed, if the reaction terminates by addition, two radicals give one chain, while if the reaction terminates by disproportionation, one radical generates one chain. Using 0.5 < x < 1, one obtains... 

The mechanisms of chain termination by disproportionation of secondary and tertiary peroxyl radicals are sufficiently different (see Chapter 2). Secondary R02 disproportionate by reaction [4-6]... 

The rate constants of chain termination by disproportionation of two acylperoxyl radicals are collected in Table 8.4. 

When the termination involves only combination, the polymerization gives a polymer with two initiator fragments at its chain ends. Because termination in the bulk polymerization of St with AIBN at a moderate temperature occurs by combination, the polymer obtained has two initiator fragments at both chain ends. In the radical polymerization of most monomers, however, termination by disproportionation and chain transfer reactions occur it is therefore impossible to control these termination reactions, i.e., the chain-end structure. Therefore, the number of initiator fragments per one molecule is always less than two. 

The kinetic chain length for termination by disproportionation is DP = v (compared with the relationship for coupling of DP = 2v. The extent of the two types of termination is experimentally found by determining the number of head-to-head sites [coupling] and unsaturated end groups [disproportionation]). 

For termination by disproportionation (Eq. 3-16b) the kinetic chain length is synonymous with the number-average degree of polymerization... 

Consider the situation where one polymer molecule is produced from each kinetic chain. This is the case for termination by disproportionation or chain transfer or a combination of the two, but without combination. The molecular weight distributions are derived in this case in exactly the same manner as for linear step polymerization (Sec. 2-7). Equations 2-86, 2-88, 2-89, 2-27, 2-96, and 2-97 describe the number-fraction, number, and weight-fraction... 

For a radical polymerization with bimolecular termination, the polymer produced contains 1.30 initiator fragments per polymer molecule. Calculate the relative extents of termination by disproportionation and coupling, assuming that no chain-transfer reactions occur. 

The kinetic chain length is given by the number of monomer molecules consumed per initiation step. Since the efficiency of most initiators is not known quantitatively it is necessary to compare the rate of the propagation reaction with either the rate of initiation or the rate of termination. If there is no chain transfer, the kinetic chain length v for termination by disproportionation is equal to the number-average degree of polymerization ... 

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