Radical polymerization chain transfer reaction

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. 

In a free radical polymerization, chain transfer is an important reaction. Chain transfer to a monomer, solvent, mercaptan, or other growing chain can take place. When a chain transfer reaction to another chain takes place, it creates a radical, which acts as a site for further chain growth and grafting (see Chapter 2 for additional details) ... 

Barriac et aL [110] reported that the number of particles increases with increasing conversion. Thus, the coagulative nucleation seems to be operative. The surface active oligomers formed throughout the polymerization (after the depletion of free emulsifier) should be responsible for this trend, i.e., they take part in stabilization of primary particles. The formation of emulsifier should be responsible for this trend, i.e., they take part in stabilization of primary particles. The formation of emulsifier radicals via chain transfer reactions also increases the stability of new-formed particles. 

The kinetic order of the free-radical polymerization of some vinyl monomers can exceed a 1.5 power dependence on the monomer concentration. Such behavior is observed, for example, in the polymerization of VAc with azo-initiators [46, 58-62], To account for this high reaction order, Ito [58-62] proposed that, under high reaction temperatures and/or low monomer concentrations, the initiator radicals can also be involved in termination reactions with the polymer radicals. The chain initiation and propagation reactions of free and grafted polymer radicals, the chain transfer reactions with monomer and surface, and the termination reactions between polymer radicals remain identical to those given by Eqs (3)-(18). 

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

The three-step mechanism for free-radical polymerization represented by reactions (6.A)-(6.C) does not tell the whole story. Another type of free-radical reaction, called chain transfer, may also occur. This is unfortunate in the sense that it complicates the neat picture presented until now. On the other hand, this additional reaction can be turned into an asset in actual polymer practice. One of the consequences of chain transfer reactions is a lowering of the kinetic chain length and hence the molecular weight of the polymer without necessarily affecting the rate of polymerization. 

Branching occurs especially when free radical initiators are used due to chain transfer reactions (see following section, Free Radical Polymerizations ). For a substituted olefin (such as vinyl chloride), the addition primarily produces the most stable intermediate (I). Intermediate (II) does not form to any appreciable extent ... 

Free radical polymerization of MMA is a well understood process. The kinetic mechanism neglecting the chain transfer reactions is given as follows (Odian (1970), Rudin (1982)). 

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... 

The polymer formation in the radical polymerization of vinyl monomers initiated by a usual initiator R-R is expressed by Eqs. (4) and (5) if termination proceeds via combination and disproportionation and no chain transfer reaction occurs. 

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 molecular weight and chain-end structure of polymers can be modified using the chain transfer reaction [65-68]. When an appropriate chain transfer agent, X-Y, is used in radical polymerization, two types of oligomers or telomers having different end groups, 4 and 5, are formed depending on the value of the chain transfer constant, Ctr> of X-Y used. 

The free radical polymerization of HPMA in the presence of mercaptans involves two different initiation mechanisms (Scheme 2) [26]. One is the initiation by RS radicals from chain transfer agent the other appears to be the direct initiation by the primary isobutyronitrile (IBN) radicals formed by the decomposition of AIBN [27]. The RS are formed by either the free radical transfer reaction of alkyl mercaptans with the IBN radicals or the chain transfer reaction of an active polymer chain with the mercaptans. The initiation by the RS radicals produces the ST polymers with a functional group at one end of the polymer chain. The initiation by IBN radicals leads to nonfunctional polymer chains with an IBN end group. The presence of the polymers with IBN end groups effects the purity and the functionality of ST polymers. As expected, the production of nonfunctionalized polymer chains is affected by reaction conditions. The polymerization is mainly terminated by chain transfer reaction with the mercaptans, but other termination mechanisms, such as disproportionation and recombination, take place depending on the reaction conditions [26]. 

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. 

Let us for the moment disregard chain transfer reactions. Radical polymerization then consists of three component reactions initiation, propagation of the polymer chains, and termination of chain growth. The rate of primary radical formation, v, by decomposition of the initiator I, may be written ... 

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