Copolymerization monomer complex models

Mechanisms for copolymerization involving complexes between the monomers were first proposed to explain the high degree of alternation observed in some copolymerizations. They have also been put forward, usually as alternatives to the penultimate model, to explain anomalous (not consistent with the terminal model) composition data in certain copolymerizations.65"74... 

As mentioned above, hw-maleimides are often copolymerized with vinyl monomers to improve processability and impact resistance. Winter and van der Velden [24] reported a study of the mechanism of reaction of a complex BMI mixture with styrene monomer. The copolymerization of the model system, A-methyl maleimide with styrene, was found to result in polymers having approximately equimolar styrene-maleimide compositions across- the whole range of monomer feed ratios, with alternation of the two monomers. The solid-state C CPMAS spectra of the cured resins were less informative. However, the absence of peaks at 147 ppm due to styrene-rich triads strongly suggest that the copolymerization with styrene results in an alternating copolymer. 

While there is clear evidence for complex formation between certain electron donor and electron acceptor monomers, the evidence for participation of such complexes in copolymerization is oflen less compelling. One of the most studied systems is S-MAH copolymerization." However, the models have been applied to many copolymerizations of donor-acceptor pairs. Acceptor monomers have substituents such as carboxy, anhydride, ester, amide, imide or nitrile on the double bond. Donor monomers have substituents such as alkyl, vinyl, aryl, ether, sulfide and silane. A partial list of donor and acceptor monomers is provided in Table 7.6. ... 

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. 

It was reported by Barb in 1953 that solvents can affect the rates of copolymerization and the composition of the copolymer in copolymerizations of styrene with maleic anhydride [145]. Later, Klumperman also observed similar solvent effects [145]. This was reviewed by Coote and coworkers [145]. A number of complexation models were proposed to describe copolymerizations of styrene and maleic anhydride and styrene with acrylonitrile. There were explanations offered for deviation from the terminal model that assumes that radical reactivity only depends on the terminal unit of the growing chain. Thus, Harwood proposed the bootstrap model based upon the study of styrene copolymerized with MAA, acrylic acid, and acrylamide [146]. It was hypothesized that solvent does not modify the inherent reactivity of the growing radical, but affects the monomer partitioning such that the concentrations of the two monomers at the reactive site (and thus their ratio) differ from that in bulk. 

The f22 values are in general lower than those obtained for propene or other a-olefms, in agreement with the low homopolymerization activity of norbomene. The f22 value for catalyst 1-5 is much greater than ri2 this shows the tendency of this catalyst to insert a third norbomene after the second one. It was clear that the next-to-last E or norbomene monomer unit exerts an influence on the reactivity of the propagating Mt-E or Mt-N species, which depends upon the catalyst stmc-ture. The second-order Markov model must be used to describe E-N copolymerizations promoted by metallocenes I-l, 1-2, and IV-1. A third-order or a more complex model may be required to fit the experimental data obtained with catalyst 1-6, where more sterically hindered indene substitutions are dominant. At higher norbomene concentrations, copolymers with all catalysts may need more complex models. These results allowed the conclusion that E-N copolymerization is dominated by the bulkiness of the norbomene monomer and of the copolymer chain. 

Versions of the Bootstrap model have also been fitted to systems in which monomer-monomer complexes are known to be present, demonstrating that the Bootstrap model may provide an alternative to the MCP and MCD models in these systems. For instance, Klumperman and co-woikers have snccessfiilly fitted versions of the penultimate Bootstrap model to the systems styiene with maleic anhydride in butanone and toluene, " and styrene with acrylonitrile in varions solvents. This latter woik confirmed the earUer observations of Hill et alP for the behavior of styrene with aciylonitiile in bulk, acetonitrile and toluene. They had concluded that, based on sequence distribution data, penultimate unit effects were operating but, in addition, a Bootstrap effect was evident in the coexistent curves obtained when triad distribution was plotted against copolymer composition for each system. In the copolymerization of styrene with aciylonitiile Klumperman et alP a variable Bootstrap effect was required to model the data. Given the strong polarity effects expected in this system (see Section 12.2.2), part of this variation may in fact be caused by the variation of the solvent polarity and its affect on the reactivity ratios. In aity case, as this work indicates, it may be necessary to simultaneously consider a number of different influences (such as, for instance, penultimate unit effects. Bootstrap effects, and polarity effects) in order to model some copolymerization systems. 

Most recent work is in accord with mechanism (b). In an effort to distinguish these mechanisms studies on model propagating species have been carried out.IS6 liW For S-MMA polymerization initiated by AIBMe- -13C (Scheme 8.13) it has been established by end group analysis that extremely small amounts of ethyl aluminum sesquichloride (<10 3M with 1.75 M monomers) are sufficient to cause a substantial enhancement in specificity for adding S in the initiation step. This result suggests that complexation of the propagating radical may be sufficient to induce alternating copolymerization but does not rule out other hypotheses. 

Cornejo et al. [65] reported the first immobihzation of pyridine-bis(oxa-zoline) chiral hgands and the use of the corresponding solid ruthenium complex in the model cyclopropanation test. They synthesized vinyl-PyBOx, the vinyl functionahty being introduced in the fourth position of the pyridine ring. This monomer was further homo- or copolymerized in the presence of styrene and divinylbenzene. The corresponding ruthenium catalysts proved... 

Currently this model is one of the most commonly used in the theory of free-radical copolymerization. The formation of a donor-acceptor complex Ma... iVlbetween monomers Ma and in some systems is responsible for a number of peculiarities absent in the case of the ideal model. Such peculiarities are due to the fact that besides the single monomer addition to a propagating radical, a possibility also exists of monomer addition in pairs as a complex. Here the role of kinetically independent elements is played by ultimate units Ma of growing chains as well as by free (M ) and complex-bound (M ) monomers, whose constants of the rate of addition to the macroradical with a-th ultimate unit will be... 

This assumption is implicitly present not only in the traditional theory of the free-radical copolymerization [41,43,44], but in its subsequent extensions based on more complicated models than the ideal one. The best known are two types of such models. To the first of them the models belong wherein the reactivity of the active center of a macroradical is controlled not only by the type of its ultimate unit but also by the types of penultimate [45] and even penpenultimate [46] monomeric units. The kinetic models of the second type describe systems in which the formation of complexes occurs between the components of a reaction system that results in the alteration of their reactivity [47-50]. Essentially, all the refinements of the theory of radical copolymerization connected with the models mentioned above are used to reduce exclusively to a more sophisticated account of the kinetics and mechanism of a macroradical propagation, leaving out of consideration accompanying physical factors. The most important among them is the phenomenon of preferential sorption of monomers to the active center of a growing polymer chain. A quantitative theory taking into consideration this physical factor was advanced in paper [51]. 

The ability to determine which copolymerization model best describes the behavior of a particular comonomer pair depends on the quality of the experimental data. There are many reports in the literature where different workers conclude that a different model describes the same comonomer pair. This occurs when the accuracy and precision of the composition data are insufficient to easily discriminate between the different models or composition data are not obtained over a wide range of experimental conditions (feed composition, monomer concentration, temperature). There are comonomer pairs where the behavior is not sufficiently extreme in terms of depropagation or complex participation or penultimate effect such that even with the best composition data it may not be possible to conclude that only one model fits the composition data [Hill et al., 1985 Moad et al., 1989]. 

Two explanations have been advanced for such copolymerization behavior in hydrocarbon solvents. Korotkov (67) suggested that selective complexation or solvation of the lithium chain ends by butadiene causes an increase in the concentration of butadiene about the growing chain ends. In turn, this monomer dominates the early phases of the copolymerization. Consistent with this notion are the high entropies of activation for this copolymerization noted by Morton (68). The work of Oliver and co-workers (64, 65) adds further suggestive support to the concept of preferential solvation. They observed the interaction between the lithium and the double bond of the model compound 3-butenyllithium by 7Li-NMR, UV, and IR spectroscopy. Similar observations were made by Glaze et al. (52) and Halasa el al. (37). 

The second type of nonideal models takes into account the possible formation of donor-acceptor complexes between monomers. Essentially, along with individual entry of these latter into a polymer chain, the possibility arises for their addition to this chain as a binary complex. A theoretical analysis of copolymerization in the framework of this model revealed (Korolev and Kuchanov, 1982) that the statistics of the succession of units in macromolecules is not Markovian even at fixed monomer mixture composition in a reactor. Nevertheless, an approach based on the "labeling-erasing" procedure has been developed (Kuchanov et al., 1984), enabling the calculation of any statistical characteristics of such non-Markovian copolymers. 

Moreover, a whole set of monomers with bulky and polar substitutors is known, the copolymerization of which cannot, be described by the classic scheme (2.1). In this case, in order to calculate the copolymer composition, molecular structure and composition distribution, one should use a penultimate model or the model of complex formation. 

The formation of the donor-acceptor complexes Mt. .. M2 between the monomers M, and M2 is regarded as being an additional important factor responsible for the deviations of some certain systems from the classic copolymerization model. Also it should be noted that besides the single monomer entrance into the polymer chain a possibility of the monomer addition in pairs as a complex also exists. The corresponding kinetic scheme of the propagation reaction parallel with reactions (2.1) involves four additional ones [36] ... 

This important peculiarity, which allows one to determine the kinetic parameters of m-component copolymerization on the basis of the analysis of the experimental data obtained under the copolymerization of m(m — l)/2 monomer pairs vanishes if one uses other kinetic models instead of the terminal one. There are a number of models describing multicomponent systems which account for the influence of the penultimate unit [47], the formation of the binary [48] and triple [49] complexes and also for the depolymerization reactions [50], However, up to now, all such models have a limited range of application since the current experimental techniques do not allow one to determine correctly a great number of their kinetic parameters. 

In contrast to the above mentioned models, the similar statistical description of the products of the complex-radical copolymerization occurring through the scheme (2.5) has been carried out quite recently [37, 49, 55-60]. Within the framework of this Seiner-Litt model, both copolymer composition [37,49, 55-58] and fractions of the different triads and blocks of the monomer units in the macromolecules were calculated [57]. The probability approaches which were applied in these works, are regarded as being of limited applicability in contrast to the general statistical method [49, 59, 60], By means of the latter method, the sequence distribution and composition inhomogeneity of the copolymer were completely described [49, 60] and also thorough calculations of its microstructure with the account for the tactidty were carried out [59, 60]. 

The consistent kinetic analysis of the copolymerization with the simultaneous occurrence of the reactions (2.1) and (2.5) leads to the conclusion that the probabilities of the sequences of the monomer units M, and M2 in the macromolecules can not be described by a Markov chain of any finite order. Consequently, in this very case we deal with non-Markovian copolymers, the general theory for which is not yet available [6]. However, a comprehensive statistical description of the products of the complex-radical copolymerization within the framework of the Seiner-Litt model via the consideration of the certain auxiliary Markov chain was carried out [49, 59, 60]. 

The kinetic copolymerization models, which are more complex than the terminal one, involve as a rule no less than four kinetic parameters. So one has no hope to estimate their values reliably enough from a single experimental plot of the copolymer composition vs monomer feed composition. However, when in certain systems some of the elementary propagation reactions are forbidden due to the specificity of the corresponding monomers and radicals, the less number of the kinetic parameters is required. For example, when the copolymerization of two monomers, one of which cannot homopolymerize, is known to follow the penultimate model, the copolymer composition is found to be dependent only on two such parameters. It was proposed [26, 271] to use this feature to estimate the reactivity ratios in analogous systems by means of the procedures similar to ones outlined in this section. 

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