Kinetics radical copolymerization

It was recently found that j3-PCPY can also be used as a radical initiator to obtain an alternate copolymer of MMA with styrene [35], which was only possible in the presence of Lewis acids [36,37] in the past. The kinetics of the system has been formulated as Rp a[/3-PCPY] a[MMA] (l/a[Styrene] The values of kp /k, and AE were evaluated as 1.43 x 10 L mol -s and 87 kJ/ mol, respectively, for the system. NMR spectroscopy was used to determine the structure composition and stereochemistry of copolymers. Radical copolymerization of AN with styrene [38] by using /3-PCPY as the initiator at 55-65°C also resulted in an alternate copolymer. Rp is a direct function of /3-PCPY and AN, and is inversely related to styrene. 

Any understanding of the kinetics of copolymerization and the structure of copolymers requires a knowledge of the dependence of the initiation, propagation and termination reactions on the chain composition, the nature of the monomers and radicals, and the polymerization medium. This section is principally concerned with propagation and the effects of monomer reactivity on composition and monomer sequence distribution. The influence of solvent and complcxing agents on copolymerization is dealt with in more detail in Section 8.3.1. 

The ends of polymer chains are often not representative of the overall chain composition. This arises because the initiator and transfer agent-derived radicals can show a high degree of selectivity for reaction with a particular monomer type (Section 3.4). Similarly, there is specificity in chain tennination. Transfer agents show a marked preference for particular propagating species (Section 6.2.2 and 6.2.3). The kinetics of copolymerization are such that the probability for termination of a given chain by radical-radical reaction also has a marked dependence on the nature of the last added units (Section 7.4.3). 

Monomer concentrations Ma a=, ...,m) in a reaction system have no time to alter during the period of formation of every macromolecule so that the propagation of any copolymer chain occurs under fixed external conditions. This permits one to calculate the statistical characteristics of the products of copolymerization under specified values Ma and then to average all these instantaneous characteristics with allowance for the drift of monomer concentrations during the synthesis. Such a two-stage procedure of calculation, where first statistical problems are solved before dealing with dynamic ones, is exclusively predetermined by the very specificity of free-radical copolymerization and does not depend on the kinetic model chosen. The latter gives the explicit dependencies of the instantaneous statistical characteristics on monomers concentrations and the rate constants of the elementary reactions. 

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... 

To elucidate the reaction mechanism, the kinetics of free-radical copolymerization of the monomers concerned was investigated. 

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]. 

Thus, the problem on the growth of a block copolymer chain in the course of the interphase radical copolymerization may be formulated in terms of a stochastic process with two regular states corresponding to two types of terminal units (i.e. active centers) of a macroradical. The fact of independent formation of its blocks means in terms of a stochastic process the independence of times ta of the uninterrupted residence in every a-th stay of any realization of this process. Stochastic processes possessing such a property have been scrutinized in the Renewal Theory [75]. On the basis of the main ideas of this theory, the set of kinetic equations describing the interphase copolymerization have been derived [74],... 

Substituting expressions (Eq. 78) for and w2(q) into relationships Eqs. 73 and 74 we get a closed set of kinetic equations describing radical copolymerization in the framework of the simplest model in hand. The values of the rates of initiation in phases 1 and 2 entering in Eq. 74 are determined as follows... 

PolylStyrene co-n-Butyl Methacrylate) Fractionation. OC was developed with the particular idea of elucidating the kinetics of the free radical copolymerization of styrene n-butyl methacrylate. Thus, this polymer provided the main focus of the work. 

An alternative rationale for the unusual RLi (hydrocarbon) copolymerization of butadiene and styrene has been presented by O Driscoll and Kuntz (71). Rather than invoking selective solvation, these workers stated that classical copolymerization kinetics is sufficient to explain this copolymerization. They adapted the copolymer-composition equation, originally derived from steady-state assumptions for free-radical copolymerizations, to the anionic copolymerization of butadiene and styrene. Equation (20) describes the relationship between the instantaneous copolymer composition c/[M,]/rf[M2] with the concentrations of the two monomers in the feed, M, and M2, and the reactivity ratios, rt, r2, of the monomers. The rx and r2 values are measures of the preference of the growing chain ends for like or unlike monomers. 

The polymerization described so far is homo-polymerization based on single monomers. Some polymers used in pharmaceutical applications are copolymers. They have properties that each homo-polymer does not exhibit. For example, the copolymer of hydroxyethyl methacrylate and methyl methacrylate is synthesized in order to obtain a polymer exhibiting a hydrophilic/hydrophobic balance. A variety of copolymers (alternating, block, random) can be formed from two different monomers. Special processes produce alternating and block copolymers, while random copolymers are produced by free-radical copolymerization of two monomers. The polymerization steps, such as initiation, propagation, and termination, are the same as in free-radical homo-polymerization. Copolymerization kinetics are depicted as follows ... 

Iwatsuki and Yamashita (46, 48, 50, 52) have provided evidence for the participation of a charge transfer complex in the formation of alternating copolymers from the free radical copolymerization of p-dioxene or vinyl ethers with maleic anhydride. Terpolymerization of the monomer pairs which form alternating copolymers with a third monomer which had little interaction with either monomer of the pair, indicated that the polymerization was actually a copolymerization of the third monomer with the complex (45, 47, 51, 52). Similarly, copolymerization kinetics have been found to be applicable to the free radical polymerization of ternary mixtures of sulfur dioxide, an electron donor monomer, and an electron acceptor monomer (25, 44, 61, 88), as well as sulfur dioxide and two electron donor monomers (42, 80). 

Usually or most widely applied, polymer latexes are made by emulsion polymerization [ 1 ]. Without any doubt, emulsion polymerization has created a wide field of applications, but in the present context one has to be aware that an inconceivable restricted set of polymer reactions can be performed in this way. Emulsion polymerization is good for the radical homopolymerization of a set of barely water-soluble monomers. Already heavily restricted in radical copolymerization, other polymer reactions cannot be performed. The reason for this is the polymerization mechanism where the polymer particles are the product of kinetically controlled growth and are built from the center to the surface, where all the monomer has to be transported by diffusion through the water phase. Because of the dictates of kinetics, even for radical copolymerization, serious disadvantages such as lack of homogeneity and restrictions in the accessible composition range have to be accepted. 

The practical value of the quantitative theory of radical copolymerization depends to a great extent on the adequacy of the applied kinetic model to the real systems. Hence, in Sect. 6 we shall discuss the issues of model discrimination and also the problems of reliability and validity of the calculations of the model parameters with an account of the potentialities of the modern experimental techniques. 

A quite different explanation of the deviations from traditional behavior of radical copolymerization has been suggested by Tudos [44], who has advanced a hot-radical theory. In the kinetic scheme corresponding to this theory one should account for the reactions of the monomers with the intermediate ( hot ) radicals which have not yet lost the reaction heat stored in the course of the previous reaction step. 

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]. 

In our laboratory, much attention has been devoted to the investigation of in situ sequential polyurethane/poly(methyl methacrylate) interpenetrating polymer networks (SEQ PUR/PAc IPNs) (2- ) in which the elastomeric polyurethane network is completely formed in the presence of the methacrylic monomers before the onset of the radical copolymerization which leads to the second network. To each polymerization process corresponds a typical kinetics, which however is not completely independent from each other ( -8). The results obtained with such SEQ IPNs show that the properties do in... 

Fig. 9 Kinetic plots of the radical copolymerization of a 1 1 molar mixture of CD-complexed styrene (filled triangles) and diethyl fumarate (filled squares) in water at room temperature (using 2.5 mol% redox initiator KjSjOg/NajSjOs)...

This paper, which is divided into three sections, critically reviews the state-of-the-art of free-radical copolymerization kinetics, characterization, reactor design, operation and control from the view point of their possible implementation to industrial processes. 

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