Free radical polymerization chain termination

For anionic polymerizations in protic media, you get the same expressions as those obtained for free radical polymerization with termination by disproportionation (p is still the probability of chain growth, but now 1 -p is the probability of chain transfer). Again, the averages and distributions you can obtain are only valid for low degrees of conversion. For cationic polymerization, there are several types of transfer and termination reactions that occur m most reactions, so you... 

The number-average degree of polymerization can be obtained from the rates of propagation (eqn 10.65) and chain breaking (sum of eqns 10.66 and 10.67) as in free-radical polymerization with termination by chain transfer to a transfer agent (see eqn 10.42) ... 

The distribution is as in free-radical polymerization with termination by disproportionation or terminating chain transfer (eqn 10.45 in Section 10.3.4) and, with increase of the progression factor as conversion increases, in step-growth polymerization of bifimctional monomers (eqn 10.19 in Section 10.2.3). According to eqn 10.81, the progression factor is... 

There is an important difference between the distributions calculated for equilibrium, bifunctional step-growth polymerization in Chapter 5 and for the free-radical polymerizations with termination by disproportionation or chain transfer that are being considered here. The distribution functions in the step-growth case apply to the whole reaction mixture in the free-radical polymerization this distribution describes only the polymer which has been formed. There is obviously a strong parallel between the probability S of this section and the extent of reaction p used in the step-growth calculations in Chapter 5. Many authors use the same symbol for both parameters. Different notations are used here, however, for clarity. 

Problem 6.44 Consider a case of free-radical polymerization where termination involves both disproportionation and coupling of chain radicals but chain transfer reactions can be neglected. Derive an expression for the distribution function for the degree of polymerization of polymer in terms of the kinetic chain length and the ratio of termination by disproportionation to that by coupling [65]. Simplify the expression for two limiting cases where (a) termination is solely by coupling and (b) termination is solely by disproportionation. 

The chain lengthening of the polymeric radical is the propagation step. The polymer can be formed as any combination of 1,2-, 1,4-cis or 1,4-trans additions the polymer can be a result of one or all of the three addition processes. The termination step of a polymerization reaction puts a stop to the growing polymer. In free radical polymerization, the termination step rids the growing polymer of its free electron. This generally proceeds by any one of three different methods dimerization, disproportionation and abstraction. Dimerization involves the joining of two growing polymer radicals. It can be shown as ... 

Chain polymerizations which do not terminate by bimolecular chain coupling generally result in polymers with the most probable molecular weight distribution of 2.0 free radical polymerizations which terminate by bimolecular chain coupling result in pdi = 1.5. However, chain transfer to polymer, autoacceleration, slow initiation, and slow exchange between active species of different reactivities result in much higher polydispersities. 

In the older literature one can encounter quite a number of papers suggesting that bimolecular termination is not chain-length dependent e.g. 36, 66, 68, 139-143] Experimental evidence, however, has disproved these suggestions and numerous papers have proven termination to be chain-length dependent. The evidence takes several forms and has been obtained employing different experimental approaches, which can roughly be divided in three classes (i) termination studies of free-radical polymerizations, (ii) termination studies of non-propagating species and (iii) diffusion-controlled mimic reactions. 

If ideal free-radical polymerization chains are formed very quickly with respect to the total time of monomer conversion, then any given propagating chain sees an environment (concentration of radicals, monomers, solvent, etc.) that changes httle during its formation. It is of interest to know after N free-radical events, what the probability is that there were N-l consecutive events (j=N - 1) that chained monomers to the free radical, and a final chain killing event that terminated the chain by a radical-radical encounter. Although there are A/ /[(A/-l) l ]=A different sequences of events that give N-1 monomers and one terminated radical in a chain, the only physically possible sequence is when the terminated radical is at the end of the chain. 

Scheme 1 The underlying initiation, propagation, activation/deactivation, and termination reactions for living and free-radical polymerization (chain transfer is not...

The molecular weight distribution for a polymer like that described above is remarkably narrow compared to free-radical polymerization or even to ionic polymerization in which transfer or termination occurs. The sharpness arises from the nearly simultaneous initiation of all chains and the fact that all active centers grow as long as monomer is present. The following steps outline a quantitative treatment of this effect ... 

The free-radical polymerization of methacrylic monomers follows a classical chain mechanism in which the chain-propagation step entails the head-to-taH growth of the polymeric free radical by attack on the double bond of the monomer. Chain termination can occur by either combination or disproportionation, depending on the conditions of the process (36). 

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). 

The block copolymer produced by Bamford s metal carbonyl/halide-terminated polymers photoinitiating systems are, therefore, more versatile than those based on anionic polymerization, since a wide range of monomers may be incorporated into the block. Although the mean block length is controllable through the parameters that normally determine the mean kinetic chain length in a free radical polymerization, the molecular weight distributions are, of course, much broader than with ionic polymerization and the polymers are, therefore, less well defined,... 

In the period 1910-1950 many contributed to the development of free-radical polymerization.1 The basic mechanism as we know it today (Scheme 1.1), was laid out in the 1940s and 50s.7 9 The essential features of this mechanism are initiation and propagation steps, which involve radicals adding to the less substituted end of the double bond ("tail addition"), and a termination step, which involves disproportionation or combination between two growing chains. 

The polymerization rate equations are based on a classical free radical polymerization mechanism (i.e., initiation, propagation, and termination of the polymer chains). 

Free radical polymerization does not go on indefinitely, because sometimes two free radicals collide and react. This destroys two free radicais and terminates the chain. For example, another initiator fragment can react with the... 

Such a mechanism is open to serious objections both on theoretical and experimental grounds. Cationic polymerizations usually are conducted in media of low dielectric constant in which the indicated separation of charge, and its subsequent increase as monomer adds to the chain, would require a considerable energy. Moreover, termination of chains growing in this manner would be a second-order process involving two independent centers such as occurs in free radical polymerizations. Experimental evidence indicates a termination process of lower order (see below). Finally, it appears doubtful that a halide catalyst is effective without a co-catalyst such as water, alcohol, or acetic acid. This is quite definitely true for isobutylene, and it may hold also for other monomers as well. 

Free radical polymerization Relatively insensitive to trace impurities Reactions can occur in aqueous media Can use chain transfer to solvent to modify polymerization process Structural irregularities are introduced during initiation and termination steps Chain transfer reactions lead to reduced molecular weight and branching Limited control of tacticity High pressures often required... 

Figure 2,3 Chain growth polymerization exemplified by free radical polymerization of polyethylene a) initiation, b) propagation, c) chain transfer, and d) termination...

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