Homopolymerization reaction kinetic models

Kinetic gelation simulations seek to follow the reaction kinetics of monomers and growing chains in space and time using lattice models [43]. In one example, Bowen and Peppas [155] considered homopolymerization of tetrafunctional monomers, decay of initiator molecules, and motion of monomers in the lattice network. Extensive kinetic simulations such as this can provide information on how the structure of the gel and the conversion of monomer change during the course of gelation. Application of this type of model to polyacrylamide gels and comparison to experimental data has not been reported. 

However, for several epoxy-amine systems, the simple kinetic model expressed by the set of Eqs (5.18) (5.21) does not provide a good fitting with experimental results. Reaction mechanisms, including the formation of different kinds of complexes, have been postulated to improve the kinetic description (Flammersheim, 1998). Also, a more general treatment of the kinetics of epoxy-amine reactions would have to include the possibility of the homopolymerization of epoxy groups in the reaction path. Sets of kinetic equations including this reaction have been reported (Riccardi and Williams, 1986 Chiao, 1990 Cole, 1991). 

The simplest kinetics model for free-radical copolymerization, known as the terminal model, will be analysed here. The principal assumption is that the reactivity of an active centre depends only upon the terminal monomer unit in which it is located, hence the name of the model. As in the analysis of homopolymerization kinetics, it is further assumed that the amount of moncHn consumed in reactions other than propagation is negligible and that copolymer molecules of high molar mass are formed. Thus for free-radical copolymerization of monomer A with moncHno- B, only two types of active centre need be considered ... 

In Refs. [15,16], the kinetic models of radical (co)pol5mierization were obtained after the concept of polymerizing system microheterogeneity that considers the process of homopolymerization of polyfimctional monomers till high conversion in two reaction zones and of monofimctional monomers in three reaction zones. 

Example 7.5 In an effort to graft gelatin with polymethyl methacrylate (PMMA), 2g of potassium persulfate and 20 g of gelatin are dissolved in water. This is added to 40 g of methyl methacrylate (MMA), and the reaction mass is made up to 500 cm. This recipe does not contain any surfactant and the polymerization at 70°C is found to give stable emulsion polymenzation. Experimental analyses of samples show a copious formation of gelatin grafts, which suppress the homopolymerization of MMA [29]. Explain this phenomenon through a kinetic model. 

In evaluating the kinetics of copolymerization according to the chemical control model, it is assumed that the termination rate constants k,AA and A,Br are known from studies on homopolymerization. The only unknown in the above expression is the rate constant for cross termination (AtAB)- The rate constant for this reaction in relation to klAA and kmB is given by the parameter . 

The simplest scenario to simulate is a homopolymerization during which the monomer concentration is held constant. We assume a constant reaction volume in order to simplify the system of equations. Conversion of monomer to polymer, Xp defined as the mass ratio of polymer to free monomer, is used as an independent variable. Use of this variable simplifies the model by combining several variables, such as catalyst load, turnover frequency, and degradation rate, into a single value. Also, by using conversion instead of time as an independent variable, the model only requires three dimensionless kinetics parameters. 

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). 

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. 

The basic reaction scheme for free-radical bulk/solution styrene homopolymerization is described below. A complete description of copolymerization kinetics involving styrene is not given here however, the homopolymerization kinetic scheme can be easily extended to describe copolymerization using the pseudo-kinetic rate constant method [6]. Such practice has been used by many research groups [7-10] and has been used extensively for modelling of copolymerization involving styrene by Gao and Penlidis [11]. In this section, all rate constants are defined as chemically controlled, i.e. they are only a function of temperature. 

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