Terminal model for copolymerization

Thus, the terminal model for copolymerization gives us expressions for copolymer composition (Eqs. 6-12 and 6-15), propagation rate constant (Eq. 6-71), and polymerization rate (Eq. 6-70). The terminal model is tested by noting how well the various equations describe the experimental variation of F, kp, and Rp with comonomer feed composition. 

The terminal model for copolymerization can be naturally extended to multicomponent systems involving three or more monomers. Multicomponent copolymerizations And practical application in many commercial processes that involve three to five monomers to impart different properties to the final polymer (e.g., chemical resistance or a certain degree of crosslinking) [134]. There is a classical mathematical development for the terpolymerization or three-monomer case, the Alfrey-Goldfinger equation (Eq. 6.43)... 

Even though the discussion has been mainly on homopolymerization, the same polymerization mechanism steps are valid for copolymerization with coordination catalysts. In this case, for a given catalyst/cocatalyst system, propagation and transfer rates depend not only on the type of coordinating monomer, but also on the type of the last monomer attached to the living polymer chain. It is easy to understand why the last monomer in the chain will affect the behavior of the incoming monomer as the reacting monomer coordinates with the active site, it has to be inserted into the carbon-metal bond and will interact with the last (and, less likely, next-to-last or penultimate) monomer unit inserted into the chain. This is called the terminal model for copolymerization and is also commonly used to describe free-radical copolymerization. In the next section it will be seen that, with a proper transformation, not only the same mechanism, but also the same polymerization kinetic equations for homopolymerization can be used directly to describe copolymerization. 

Start by extending the homopolymerization model shown in Table 2.4 to the terminal model for copolymerization in Table 2.11. It is best to keep the polymerization mechanism as simple as possible at this stage later it will be seen that it is easy to extend this model to include additional polymerization steps. 

The early kinetic models for copolymerization, Mayo s terminal mechanism (41) and Alfrey s penultimate model (42), did not adequately predict the behavior of SAN systems. Copolymerizations in DMF and toluene indicated that both penultimate and antepenultimate effects had to be considered (43,44). The resulting reactivity model is somewhat compHcated, since there are eight reactivity ratios to consider. 

The first quantitative model, which appeared in 1971, also accounted for possible charge-transfer complex formation (45). Deviation from the terminal model for bulk polymerization was shown to be due to antepenultimate effects (46). Mote recent work with numerical computation and C-nmr spectroscopy data on SAN sequence distributions indicates that the penultimate model is the most appropriate for bulk SAN copolymerization (47,48). A kinetic model for azeotropic SAN copolymerization in toluene has been developed that successfully predicts conversion, rate, and average molecular weight for conversions up to 50% (49). 

The rate of copolymerization often shows a strong dependence on the monomer feed composition. Many theories have been developed to predict the rate of copolymerization based on the terminal model for chain propagation (Section 7.3.1.1), This usually requires an overall rate constant for termination in copolymerization that is substantially different from that observed in homopolymerization of any of the component monomers. 

More complex models for diffusion-controlled termination in copolymerization have appeared.1 tM7j Russo and Munari171 still assumed a terminal model for propagation but introduced a penultimate model to describe termination. There are ten termination reactions to consider (Scheme 7.1 1). The model was based on the hypothesis that the type of penultimate unit defined the segmental motion of the chain ends and their rate of diffusion. 

Using the terminal model of copolymerization, there are four possibilities for propagation [Eq. (22)]. 

Scheme 1. The four propagation reactions based on the terminal model for random copolymerization by the stable free radical polymerization process.

TABLE 5.3 Simplified Terminal Model for Binary Copolymerization of Olefins... 

A terminal radical-complex model for copolymerization was formulated by Kamachi. He proposed that a complex is formed between the propagating radical chain and the solvent (which may be the monomer) and that this complexed radical has a different propagation rate constant to the equivalent uncomplexed radical. Under these conditions there are eight different propagation reactions in a binary copolymerization, assuming that the terminal unit is the only unit of the chain affecting the radical reactivity. These are as follows. 

Table 2.11 Simplified terminal model for binary copolymerization of olefins...

This equation follows from the kinetic analysis of copolymerization by Melville and co-workers (8) and Walling (9), who arrived at an expression for the overall rate of copolymerization assuming a terminal model for both propagation and termination. 

It has been known since 1980 that the terminal model for free-radical copolymerization sometimes fails, due to the penultimate unit effect. Direct detection of the penultimate unit effect by ESR has been unsuccessfully attempted many times. In this section, direct detection of the penultimate unit effect using dimeric model radicals generated from dimeric model radical precursors prepared by ATRA is discussed (Fig. 19). The structures of the dimeric model radicals studied are summarized in Fig. 20. For a detailed discussion of the penultimate unit effect, dimeric, monomeric, and polymeric model radicals were examined. The radicals were generated by three methods homolytic cleavage of carbon-bromine bonds of alkyl bromides with hexabutyldistannane, photodecomposition of an azo-initiator, and radical polymerization performed directly in a sample cell in a cavity. 

The polymerization model most commonly adopted for olefin copolymerization is the terminal model, particularly for studies of polymerization kinetics. In the terminal model, only the last monomer molecule added to the chain end influences polymerization and transfer rates. Besides the fact that it is logically expected, there is also significant experimental evidence supporting the terminal model for olefin polymerization. Since monomer propagation and chain-transfer reactions take place by insertion between the chemical bond formed by the metal in the active site and the polymer chain end, it is certainly reasonable to assume that both the nature of the active site and the type of monomer last added to the chain will affect these reactions. On the other hand, higher-order models such as the penultimate and pen-penultimate models have not found widespread use in coordination polymerization. 

Copolymerization models are similar to homopolymerization models, with the added complexity that more polymerization rate constants are required. An accepted form of the terminal model for the binary copolymerization of olefins is shown in Table 8.1. Notice that, except for the fact that the polymerization rate constants now depend on the monomer and the chain end type, the mechanism is essentially the same as the one described in Section 8.3.2.1 for homopolymerization. 

Polymerization Kinetics and Mechanism with Coordination Catalysts 389 Tab. 8.1. Terminal model for blna copolymerization of olefins.M... 

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