Kinetics of Chain-Growth Copolymerization

Kinetic aspects of step-growth copolymerization have been examined in Section 10.2.2. The principal features of chain-growth copolymerization are very different, but are alike for all types of chain growth, that is, for free-radical, anionic, cationic, and coordination polymerization. 

Many chain-growth copolymerizations include dienes such as divinyl benzene or divinyl adipate that act as crosslinking agents and lead to gel formation. Polymerization kinetics in such cases are complex and are beyond the scope of a book on homogeneous reactions. Here, only binary copolymerization of monofunctional monomers will be examined. For an excellent and extensive treatment that includes copolymerization of more than two monomers as well as crosslinking by bifunctional monomers, the reader is refer to Odian s book [123]. 

Moreover, in chain-growth copolymerizations, which involve the polymerization of two or more comonomers, different comonomer sequences have to be tracked by chain length, as illustrated in Fig. 10.2, for simplicity considering only well-defined monomer sequences (Matyaszewski et al., 2012). This clearly complicates the mathematical description of the polymerization kinetics. In addition, if different CLDs can be obtained by type of active center leading to an observed CLD that is a superposition of individual CLDs, the computational cost increases further (Soares and Hamielec, 1995). 

In copolymerization, the presence of more than one type of monomer adds an extra degree of complexity to the kinetics. The different monomers form different radical structures, and the relative rates of chain growth depend on the structure of both monomer and radical. It is these propagation mechanisms that control polymer composition (the relative amounts of each monomer unit incorporated into the copolymer) and sequence distribution (the way in which these monomer units are arranged within the chain). Developing a set of mechanisms to describe how radical structure affects termination and transfer rates is required to represent copolymer chain length and molecular weight distributions. 

Qince the discovery (6) of supported chromium oxide catalysts for polymerization and copolymerization of olefins, many fundamental studies of these systems have been reported. Early studies by Topchiev et al. (18) deal with the effects of catalyst and reaction variables on the over-all kinetics. More recent studies stress the nature of the catalytically active species (1, 2, 9,13, 14,16, 19). Using ESR techniques, evidence is developed which indicates that the active species are Cr ions in tetrahedral environment. Other recent work presents a more detailed look at the reaction kinetics. For example, Yermakov and co-workers (12) provide evidence which suggests that chain termination in the polymerization of ethylene on the catalyst surface takes place predominantly by transfer with monomer, and Clark and Bailey (3, 4) give evidence that chain growth occurs through a Langmuir-Hinshelwood mechanism. 

Wallace and Morrow used halogenated alcohols, such as 2,2,2-trichloroethyl, to activate the acyl donor and thereby improve the polymerization kinetics [53, 56], They also removed by-products periodically during reactions to further shift the equilibrium toward chain growth instead of chain degradation. They copolymerized bis(2,2,2-trichloroethyl) tmns-3,4-epoxyadipate and 1,4-butanediol using porcine pancreatic lipase as the catalyst. After 5 days, an enantioenriched polyester with Mw = 7900 g mol-1 and an optical purity in excess of 95% was formed (Scheme 4.6). 

The process of synthesizing high-molecular-weight copolymers by the polymerization of mixed cyclics is well established and widely used in the silicone industry. However, the microstructure which depends on several reaction parameters is not easily predictable. The way in which the sequences of the siloxane units are built up is directed by the relative reactivities of the monomers and the active chain-ends. In this process the different cyclics are mixed together and copolymerized. The reaction is initiated by basic or acidic catalysts and a stepwise addition polymerization kinetic scheme is followed. Cyclotrisiloxanes are most frequently used in these copolymerizations since the chain growth mechanism dominates the kinetics and redistribution reactions involving the polymer chain are of negligible importance. Several different copolymers may be obtained by this process. They will be monodisperse and free from cyclics and their microstructure can be varied from pure block to pure random copolymers. 

To address polymer network formation from nonlinear chain-growth polymerization (or copolymerization), kinetic methods are more appropriate [23, 75-83], Some of the most successful kinetic models to address this type of system are based on the method of moments [23, 75-77, 79, 80, 82, 84], Some divergence problems at the vicinity of the gelation point are common with the method of moments, although there are practical ways to avoid this situation [80], A more refined kinetic method to address the issue of modeling the dynamics of gelation in... 

Compared to the CO insertion, fewer reports have appeared on the olefin insertion into an acyl palladium. Direct observation of this process has been reported very recently by Rix and Brookhart [89-92] using cationic l,10-phenanthroline-Pd(II) complexes. They have investigated the microscopic steps responsible for the alternating copolymerization of ethene with CO using the same 1,10-phenanthroline system. On the basis of the kinetic and thermodynamic data, they proposed an accurate model for the polymer chain growth. In support stepwise isolation of the intermediates have been accomplished by norbornene as a substrate where symmetrical bidentate nitrogen ligands were used [93-95]. 

The first example of a copolymerization of polar monomers in LCCP was described in our group, copolymerizing the styrene monomer (13) with isobutylene in amounts of 1-5 mol% of comonomer (Figure 3.7) (Hackethal etal, 2010). Incorporation of the polar monomer (13) can be achieved in amounts up to 2.5 mol%, as proven by NMR spectroscopy and MALDI methods. As followed by in-situ kinetic analysis, the polymerization follows a linear chain growth, together with a linear consumption of monomer when plotted as ln[Mo]/[Mt] vs. time t). 

In addition, kinetic models allow to change the ratio between the rate constant of polymer chain growth and decay both at homopolymerization and copolymerization and to observe the effect of this ratio on general kinetics of the process what is impossible during the experiment. All that allows anticipating and managing the process of copolymerization. 

It is possible to construct a kinetic scheme for a general addition copolymerization reaction between two types of monomer, A and B and this can go some way towards explaining the effect outlined above. As chain growth takes place there are in general two types of monomer unit at the active centre ... 

Thus, the problem on the growth of a block copolymer chain in the course of the interphase radical copolymerization may be formulated in terms of a stochastic process with two regular states corresponding to two types of terminal units (i.e. active centers) of a macroradical. The fact of independent formation of its blocks means in terms of a stochastic process the independence of times ta of the uninterrupted residence in every a-th stay of any realization of this process. Stochastic processes possessing such a property have been scrutinized in the Renewal Theory [75]. On the basis of the main ideas of this theory, the set of kinetic equations describing the interphase copolymerization have been derived [74],... 

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