Copolymerization kinetic considerations

Another unsolved fundamental problem of this theory concerns the correct description of copolymerization kinetics which obviously requires a well-grounded expression, from the physicochemical viewpoint, for the rate constant of the bimolecular chain termination reaction. This elementary reaction of interaction of two macroradicals proves to be diffusion-controlled beginning from the very initial conversions, and therefore, its rate in the course of the entire process is controlled by physical, rather than chemical factors. Naturally, the consideration of the kinetics of bulk copolymerization requires different approaches ... 

Calculations of copolymer composition are based on kinetic considerations and procedures. In spite of this, less attention has been paid to the copropagation rate than to other copolymerization problems. Today a single concise theory is available, solving the rate of the simplest radical binary copolymerization. Other cases described have not been generalized so far they treat the kinetic behaviour of specific monomer pairs or triplets in specific polymerization circumstances. 

Some observations are relevant to the consideration of copolymerization kinetics are... 

Copolymerization involves the simultaneous chain polymerization of a mixture of two or more monomers (Hillmyer, 2012 Ham and Alfrey, 1964 Odian, 2004a Tirrell, 1986). Aside from the general kinetic considerations which govern these chain reactions, as described earlier, there is imposed an additional... 

Copolymerization involves the simultaneous chain polymerization of a mixture of two or more monomers [89-92], Aside from the general kinetic considerations which govern these chain reactions, as described earlier, there is imposed an additional feature, i.e., the relative participation of the different monomers during the growth of the chain. This new parameter is most important, since it controls the composition of the copolymer. Systems involving more than two monomers are difficult to resolve in this respect, but it has been found possible to treat the case of a pair of monomers with relative ease [91,93-95]. 

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]. 

For chainwise polymerizations, the analysis of model systems implies consideration of the homopolymerization or copolymerization of bifunctional monomers. Kinetic results cannot be directly extrapolated to the case of networks, because very important features such as intramolecular cycliza-tion reactions are not present in the case of linear polymers. However, the nature of initiation and termination reactions may be assessed. For example, using electron spin resonance (ESR), Brown and Sandreczki (1990) identified different types of radicals produced during the homopolymerization of a monomaleimide (a model compound of bismaleimides). 

On the other hand copolymer with a trioxane unit at the cationic chain end (Pi+) may be converted intp P2+ by cleavage of several formaldehyde units. These side reactions change the nature of the active chain ends without participation of the actual monomers trioxane and dioxo-lane. Such reactions are not provided for in the kinetic scheme of Mayo and Lewis. In their conventional scheme, conversion of Pi+ to P2+ is assumed to take place exclusively by addition of monomer M2. Polymerization of trioxane with dioxolane actually is a ternary copolymerization after the induction period one of the three monomers—formaldehyde— is present in its equilibrium concentration. Being the most reactive monomer it still exerts a strong influence on the course of copolymerization (9). This makes it impossible to apply the conventional copolymerization equation and complicates the process considerably. 

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]. 

When the copolymerization is carried out under real conditions, each researcher is to answer a question which kinetic model is preferable for the proper description of the experimental data. One should also know the validity of the model under consideration, the numerical values of its parameters, and the expected accuracy of the calculated copolymer characteristics predicted within the framework of this model. Modern experimental methods for analyzing the copolymer composition... 

The Q and e scheme has been the subject of considerable attention. It promised new possibilities of monomer classification, calculation of copolymerization parameters from known values of Q and and predictions about the behaviour of copolymerizing systems. However, to such ends the Q and e values should be known, and they are not directly measurable. In order to calculate them from copolymerization parameters, the easily copolymerized styrene has been selected as the reference monomer, with the assigned values Q = 1 and e = -0.8. Data on the Q and e factors of practically all copolymerizing monomers are now available (see Tables 3 and 3A) some kinetic significance is ascribed to monomer position in the Q — e plane (see Fig. 21). Monomers with a high Q value are expected to form poorly reactive radicals with a low tendency to add further monomer units monomers with widely differing e values usually copolymerize easily, etc. 

Both physical and technological properties of copolymers are influenced by the sequence distribution in the macromolecular chains. The mathematical relationships governing the distribution, first developed by Alfrey and Goldfinger (7), are based upon kinetic and statistical considerations implying three fundamental assumptions a) steady state copolymerization, b) terminal effect only (i.e. influence of the last, but not of the penultimate unit of a growing chain on the addition of the next monomeric unit), and c) constant monomer feed. Under these assumptions, which may be defined as a first order approximation, the copolymers are described by two quantities, the ratio / of the molar fractions of the two monomers and the product of reactivity ratios... 

Three factors are important in the development and implementation of successful control strategies for copolymerization reactors the availability of kinetic models which adequately describe the rate of polymerization and the properties of the resulting polymer as functions of the process variables, the availability of on-line instrumentation which enables rapid characterization of the copolymer throughout the reaction, and the availability of process data which allow for the constraints of the process to be built into the control strategy. This paper discusses the limitations of reported control strategies for copolymerization reactors from the viewpoint of the state-of-the-art of kinetic modeling and copolymer characterization. The critical stages in this process where considerable research effort is required are emphasized. 

A considerable amount of work has been published during the past 20 years on a wide variety of emulsion polymerization and latex problems. A list of 11, mostly recent, general reference books is included at the end of this chapter. Areas in which significant advances have been reported include reaction mechanisms and kinetics, latex characterization and analysis, copolymerization and particle morphology control, reactor mathematical modeling, control of adsorbed and bound surface groups, particle size control reactor parameters. Readers who are interested in a more in-depth study of emulsion polymerization will find extensive literature sources. 

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