Terminal Model for Rate of Radical Copolymerization

The rate of copolymerization, unlike the copolymer composition, depends on the initiation and termination steps as well as on the propagation steps. In the usual case both monomers combine efficiently with the initiator radicals and the initiation rate is independent of the feed composition. Two different models, based on whether termination is diffusion-controlled, have been used to derive expressions for the rate of copolymerization. The chemical-controlled termination model assumed that termination proceeds with chemical control, that is, termination is not diffusion-controlled [Walling, 1949]. But this model is of only historical interest since it is well established that termination in radical polymerization is generally diffusion-controlled [Atherton and North, 1962 Barb, 1953 Braun and Czerwinski, 1987 North, 1963 O Driscoll et al., 1967 Prochazka and Kratochvil, 1983] (Sec. 3-10b). 

The diffusion-controlled termination model considers the termination reaction as the reaction 

Equation 6-71, derived by Fukuda and coworkers [Fukuda et al., 1985 Ma et al., 2001], follows from previous derivations of the rate of copolymerization [Melville et al., 1947 Walling, 1949, 1957], 

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. 

There are also expressions that describe the terminal model in terms of monomer sequence distributions in the copolymer [Burke et al., 1994a,b, 1995 Cheng, 1995, 2000], The Mj centered triad fractions are given by 

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