Kinetics copolymerization reactions

The kinetic order of the copolymerization reaction with respect to the initiator is equal to 0,5, and the total activation energy amounts to 14,4 kcal/mol (60,3 kJ/mol). 

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. 

Now let us make a short survey of quite different approaches to the problem of identifying the kinetic copolymerization models based on the investigations of the model reactions between the low-molecular compounds only. In this very promising direction it is hard to overestimate the paramount contribution made by Bevington, Tirrell et al. [286-295], whose publications could be divided into two groups. 

Lastly, let us point out that in 1953 the photochemical oxidations of mixtures of benzaldehyde and of n-decanal were studied by Ingles and Melville. The kinetic characteristics of the reactions indicate that in mixtures these aldehydes do not undergo oxidation independently of one another the two molecules are involved in a single kinetic chain, exactly as in a copolymerization reaction. 

The composition of copolymers obtained in a free radical polymerization can be predicted based on several kinetic parameters of copolymerization reaction. For a copolymer starting with two species of monomer P and P , it can be assumed that the rate of addition of the monomer to a growing free radical depends only on the nature of the end group. If the chain is indicated by X, this is equivalent with the assumption that the radical Ri will act equivalently with X-R, and the radical R will act equivalently with X-Ri . The following reactions will take place in the system ... 

Copolymers and copolymerization reactions have been extensively studied for the last 50 years. However, the complexity of the kinetics and the difficulties encountered in the characterization of the reaction products have long obscured details of the reaction kinetics as well as characteristics of the resulting products. 

Comprehensive Models. This class of detailed deterministic models for copolymerization are able to describe the MWD and the CCD as functions of the polymerization rate and the relative rate of addition of the monomers to the propagating chain. Simha and Branson (3) published a very extensive and rather complete treatment of the copolymerization reactions under the usual assumptions of free radical polymerization kinetics, namely, ultimate effects SSH, LCA and the absence of gel effect. They did consider, however, the possible variation of the rate constants with respect to composition. Unfortunately, some of their results are stated in such complex formulations that they are difficult to apply directly (10). Stockmeyer (24) simplified the model proposed by Simha and analyzed some limiting cases. More recently, Ray et al (10) completed the work of Simha and Branson by including chain transfer reactions, a correction factor for the gel effect and proposing an algorithm for the numerical calculation of the equations. Such comprehensive models have not been experimentally verified. 

The kinetics of copolymerization provides a partial explanation for the copolymerization behavior of styrenes with dienes. One useful aspect of living anionic copolymerizations is that stable carbanionic chain ends can be generated and the rates of their crossover reactions with other monomers measured independently of the copolymerization reaction. Two of the four rate constants involved in copolymerization correspond at least superficially to the two homopolymerization reactions of butadiene and styrene, for example, and k, respectively. The other... 

It was found that racemic binaphthalenes could take part in the reactions and kinetic resolution was realized with a modest s factor in the presence of the Cu"-(-)-sparteine complex. " Asymmetric oxidative cross-coupling copolymerization reactions were also reported. A Lewis acid such as Yb(OTf)3 was found to be an effective co-catalyst for these reactions. ... 

The kinetic propagation reaction equations for radical copolymerization of two monomers, Mj and M2, are written in Fig. 3.45. The complications due to additional, different monomers, as well as transfer, reverse, and termination reactions increase the numbers of equations and rate constants, so that the resulting reaction equations are unhandy, and it needs much experimental work to establish the rate constants. Also, the computational effort to solve the many equations becomes excessive. 

O DriscoU [407] developed the kinetics of ionic copolymerization of dissimilar monomers. It is based on the assumption, that the ratio of monomers in the copolymer d[Afi]/d[M2] is directly proportional to the square of the initial monomer rate in the copolymerization reaction. 

The quantities k , k,p, kpp, and kp, are the rate constants of the four basic propagation reactions of copolymerization. The Stockmayer distribution function takes into account only a chemical polydispersity resulting fi om the statistical nature of copolymerization reactions. This means that all units of all chains are formed under identical conditions. If a monomer is removed from the reacting mixture at a rate which changes the monomer concentration ratio, the monomer concentration will drift, forming a copolymer which varies in the average composition and is broader in the chemical distribution. No such chemical polydispersity can be described by the Stockmayer distribution. Therefore, Eq. (84) has to be restricted in its application to random copolymers synthesized at very low conversions or under azeotropic conditions. For azeotropic copolymers, the feed monomer concentrations [a ] and are chosen in such a way that the second factor on the right-hand side of the basic relation of copolymerization kinetics... 

The standard kinetic scheme for ethylene/a-olefin copolymerization reactions usually includes several chain initiation reactions, chain propagation reactions, and chain termination reactions as shown below. In this scheme, C represents an active center and m is the number of ethylene and/or comonomer units in a polymer chain. 

Figure 2.19 Kinetics of ethylene/1-hexene copolymerization reaction at 85oC in absence of hydrogen. The points are experimental data and the lines are calculated rates for each of the five active centers [66].

The reactivity of various cycloolefins in copolymerization reactions with ethylene and 2-butene has been examined using V(acac)3/Et2AlCl and VCl4/Hex3Al as the catalysts [21]. It was observed that, while the catalyst system has little effect on the relative reactivity of the cycloolefin, the nature of the cyclic and acychc monomer proved to be quite determinant for reaction kinetics and stereospecificity. In this respect, cyclopentene and cycloheptene displayed high reactivity compared to cyclohexene and cyclooctene, while cis-2-butene was more reactive than tra 5-2-butene. These observations were rationalized by considering steric factors induced by monomers rather than catalyst activity and specificity. 

It is possible to construct a kinetic scheme for a general addition copolymerization reaction between two types of monomer, A and B and this can go some way towards explaining the effect outlined above. As chain growth takes place there are in general two types of monomer unit at the active centre ... 

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