Complex-participation model

Another model used to describe deviations from the terminal model involves the participation of a comonomer complex (Sec. 6-3b-3) [Cais et al., 1979 Coote and Davis, 2002 Coote et al., 1998 Seiner and Litt, 1971]. The comonomer complex competes with each of the individual monomers in propagation. The monomer complex participation model involves eight... 

The complex participation model, like the depropagation model, predicts a variation of the copolymer composition with temperature and monomer concentration. The effect of temperature comes from the change in K, resulting in a decrease in the concentration of the comonomer complex with increasing temperature. Increasing monomer concentration at a constant/i increases the comonomer complex concentration. 

The complex participation model has been tested in the radical copolymerizations of 1,1-diphenylethylene-methyl acrylate, styrene-P-cyanoacrolein, vinyl acetate-hexafluoroace-tone, A-vinylcarbazole diethyl fumarate, A-vinylcarbazole funiaronitrile, maleic anhydride-vinyl acetate, styrene-maleic anhydride [Burke et al., 1994a,b, 1995 Cais et al., 1979 Coote and Davis, 2002 Coote et al., 1998 Dodgson and Ebdon, 1977 Fujimori and Craven, 1986 Georgiev and Zubov, 1978 Litt, 1971 Lift and Seiner, 1971 Yoshimura et al., 1978]. 

A variation of the complex participation model, referred to as the monomer complex dissociation model, involves disruption of the complex during reaction with a propagating chain end [Hill et al., 1983 Karad and Schneider, 1978]. Reaction of the propagating center with... 

The sequence distributions expected for the different models have been described [Hill et al., 1982, 1983 Howell et al., 1970 Tirrell, 1986] (Sec. 6-5a). Sequence distributions obtained by 13C NMR are sometimes more useful than composition data for discriminating between different copolymerization models. For example, while composition data for the radical copolymerization of styrene-acrylonitrile are consistent with either the penultimate or complex participation model, sequence distributions show the penultimate model to give the best fit. 

Copolymer Statistics Within the Framework of the Complex Participation Model... 

Several studies on the reactivities of small radicals with donor-acceptor monomer pairs have been carried out to provide insight into the mechanism of copolymerizations of donor-acceptor pairs. Tirrell and coworkers " reported on the reaction of n-butyl radicals with mixtures of N-phcnylmalcimidc and various donor monomers e.g. S, 2-chloroethyl vinyl ether),. lenkins and coworkers have examined the reaction of t-butoxy radicals with mixtures of AN and VAc. Both groups have examined the S-AN system (see also Section 7.3.1.2). In each of these donor-acceptor systems only simple (one monomer) adducts are observed. Incorporation of monomers as pairs is not an important pathway i.e. the complex participation model is not applicable). Furthermore, the product mixtures can be predicted on the basis of what is observed in single monomer experiments. The reactivity of the individual monomers (towards initiating radicals) is unaffected by the presence of the other monomer i.e. the complex dissociation model is not applicable). Unless propagating species are shown to behave differently, these results suggest that neither the complex participation nor complex dissociation models apply in these systems. 

In these models, the complex formed by the monomer pair competes with the individual monomer molecules for the propagation reaction with the radicals. There are two variations of this approach in the complex participation model, the pair of monomers form a complex and are added to the chain radical [106-109]. On the other hand, in the complex dissociation model, the complex participates in the propagation process, but dissociates upon reaction and only one of the monomers is added to the chain [101, 103]. Although there is ample experimental evidence for the existence of such complexes in these copolymerizations (such as the bright colors associated with them) [76], it is questionable whether the complexes actually participate in the propagation step [76]. Additionally, for several years, Hall and Padias have accumulated experimental and theoretical evidence that refutes the validity of the models based on complex participation [76, 77]. Both the complex participation and the penultimate models were combined in the so-called comppen model [110]. 

Other models sometimes invoked include two-component models based on combinations of the models discussed above [5] and the complex participation model [6]. Examples of the use of these are given in section 2.3. The complex participation model is a modification of the first-order Markov model to take account of the formation of A-B comonomer complexes which compete with monomer during polymerisation. Thus, four propagation steps in addition to those shown for the first-order Markov model are required to describe addition of A-B and B-A complexes (i.e. it can add either way round) to the two types of growing chain and (either A or B). The monomer and comonomer complex addition probabilities are then related to the equilibrium constant for complex formation. As might be expected, this model has been applied particularly to systems that show a marked tendency towards alternation of their comonomers [7]. A probabilistic description of the complex participation model has been given by Cais et al [6]. 

Relationships between second-order Markov addition probabilities and penultimate model reactivity ratios have also been derived and can be found in [5]. Similarly, for the complex participation model, Cais et al have derived expressions which enable calculation of any given sequence from a knowledge of reactivity ratios and the equilibrium constant for complex formation determined by other methods [6]. 

There are several cases where NMR spectroscopy has been used to investigate copolymers which deviate from the terminal model for copolymerisation (see also chapter 3). For example, Hill and co-workers [23, 24] have examined sequence distributions in a number of low conversion styrene/acrylonitrile (S/A) copolymers using carbon-13 NMR spectroscopy. Previous studies on this copolymer system, based on examination of the variation of copolymer composition with monomer feed ratio, indicated significant deviation from the terminal model. In order to explain this deviation, propagation conforming to the penultimate (second-order Markov) and antepenultimate (third-order Markov) models had been proposed [25-27]. Others had invoked the complex participation model as the cause of deviation [28]. From their own copolymer/comonomer composition data. Hill et al [23] obtained best-fit reactivity ratios for the terminal, penultimate, and the complex participation models using non-linear methods. After application of the statistical F-test, they rejected the terminal model as an inadequate description of the data in comparison to the other two models. However, they were unable to discriminate between the penultimate and complex participation models. Attention was therefore turned to the sequence distribution of the polymer. 

As with all of the models, variations are possible by making a different assumption as to which units can affect radical reactivity. For instance. Brown and Fujimori (19) have derived expressions for composition and sequence distribution for the Comppen model, a complex-participation model that is based on the penultimate... 

Many analytical techniques have been utilized to analyze the SAN microstructure including LALLS [38], CNMR [19,31,39-44], infrared spectroscopy [45-49], ultraviolet spectroscopy [50-52], pyrolysis GC [8,27,53], pyrolysis mass spectroscopy [54,55], fluorescence [20,56], GPC-IR [57,58], and GPC-UV [52]. Since the terminal model allows the calculation of sequence distribution, the calculated and measured sequence distributions can be compared. This comparison generally shows deviation of the measured sequence distribution vs that predicted using the terminal model. Ham [59] was the first to notice the deviation and explained the deviation based upon penultimate effects. Since that time several other researchers have also notic deviation of their data from the terminal model and have applied more elaborate copolymerization models (Scheme 4) to explain the mechanism of SAN copolymerization. The penultimate [60,61] and complex participation models [33,62,63] have both been evaluated and give a better fit to the SAN system than the terminal model. 

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