Modeling Of Free Radical Polymerization Research Articles

Modeling of free-radical polymerization with crosslinking: monoradical assumption and stationary-state hypothesis

The validity of the monoradical assumption and the stationary-state hypothesis in modeling of free-radical polymerization with branching and/or cross-linking was evaluated using the method of moments. The polymerization system involved the reactions of chain transfer to polymer and radical recombination. Therefore, the system was capable of gelation. The gelation behavior was controlled by the three groups of parameters: K fp M 0 /K t R, K tc /K t , and K p /K r . It can be shown that polyradical chains accumulate only in the vicinity of the gel point and beyond. The presence of polyradical chains gives higher chain growth rates and thus promotes gelation

Non-steady state model for free radical polymerization

The non-steady state theory for the kinetics of free radical polymerization taking no account of gel-effect is reviewed. Considering the facts that the monomer consumption in chain propagation is much higher than that in chain initiation and the rate constant of chain termination is much larger than that of chain propagation or transfer, a few very close approximations are introduced to solve the set of kinetical differential equations of free radical polymerization. The expressions for various molecular parameters, such as the molecular size function, the number- and weight-average degrees of polymerization and the dispersity, are derived. In accord with the non-steady state theory, the curves of free radical decay with reaction time or monomer conversion and the molecular parameters mentioned can be predicted from the reaction conditions. Several numerical examples are given.

Computation of molecular weight distributions for free radical polymerization systems

Modeling of free radical polymerization leads to very large and usually stiff systems of ordinary differential equations which cannot be solved directly in an efficient way. This paper presents the application of a new approach called the discrete Galerkin method to a realistic example—the polymerization of methyl methacrylate (MMA). The method is characterized by a Galerkin approximation on the basis of orthogonal polynomials of a discrete variable which represents the polymer degree. It allows the efficient computation of solutions of complete kinetic schemes with time- or moment-dependent reaction coefficients by reducing the complexity to a few differential equations. The approximation error can be controlled by an error estimation. In the case of MMA polymerization a reduction of computational effort by a factor of about 25 compared to a standard method can be obtained for the quasi-steady-state approximation of the model. In addition solutions of the un-stationary kinetic scheme can be easily computed.

Modeling of free radical polymerization of styrene catalyzed by unsymmetrical bifunctional initiators

A detailed kinetic model for the bulk polymerization of styrene initiated by unsysmmetrical bifunctional initiators is presented. When chain termination occurs via combination termination mechanism, 10 distinct polymeric species are identified for this initiator system according to the nature of polymer end units. It is shown that the unequal thermal decomposition characteristics of the labile groups in the bifunctional initiator system lead to the formation of polymers having considerbly higher molecular weight than those obtained by conventional monofunctional initiators or mixed initiator systems of those monofunctional initiators. It has also been found that high monomer conversion and high molecular weight can be obtained simultaneously within a short reaction time period by using the bifunctional initiators at high reaction temperature. This is due to the sequential decomposition of peroxides of different thermal stabilities distributed in various types of polymeric species.

Free radical polymerization engineering—II: Modeling of homogeneous polymerization of styrene in a batch reactor, influence of initiator

A “tendency” model of free radical polymerization is used to re-investigate batch polymerization of styrene in solution in cyclohexane with slow and fast decomposing initiators. It is impossible to account for experimental data when a conventional mechanism involving only transfer to the monomer is assumed. In order to sucessfully represent mononer consumption and average molecular weights by number and by weight as a function of time for both initiators, two additional processes are required, i.e. transfer to and induced decomposition of the initiator (if transfer sites are available). The coresponding set of rate constants was determined. When a fast initiator is used, this polymerization is sensitive to mixing effects and could be utilized as a test reaction in polymer reactors. The elucidation of the role of the initiator is a good example of the usefulness of the “tendency” model for studying complex polymerization mechanisms.