Modeling of free radical polymerization up to high conversion. II. Development of a mathematical model

Abstract

ABSTRACT:In free radical polymerization diffusion-controlled processes take place simultaneously to the normal chemical reactions. Despite extensive efforts to model such processes a consistent model for the design of a polymerization reactor has not yet been established. In this article a semiempirical model describing the conversion, polymerization degree, and molecular weight distribution ( MWD ) for the free radical polymerization is developed for the entire course of the reaction. The model includes the change of termination, propagation, transfer, and initiation rate. By simultaneous parameter estimation from the conversion and degrees of polymerization data the model parameters have been determined for isothermal polymerizations of methyl methacrylate ( MMA ) and styrene ( ST ) . The simulation results for the conversion, degrees of polymerization, and MWD are in good accordance with experimental data for suspension and bulk polymerization of MMA and ST up to very high conversions. The influence of diffusion on the propagation rate in case of polymerization of MMA is negligible compared to the influence of the cage effect on the radical efficiency; in case of ST polymerization both effects must be included in the kinetic model. The model presented is also tested for polymerizations conducted in the presence of solvent and / or chain transfer agents.

Comparison of two algorithms for calculation of the apparent rate constant in the kinetic modelling of diallyl terephthalate bulk polymerization

“…It enables the calculation of the dependence of diffusion coefficient on conversion from the physical properties of pure DAT monomer and polymer. Due to its simplicity, free-volume theory is widely used in the kinetic modelling of various radical polymerizations [7][8][9][10][11][12][13], although other theories may be used, too [7]. All necessary parameters used in free-volume theory were calculated as it was proposed by Zielinski and Duda [18].…”

“…Kinetic modelling of free-radical polymerization is well understood and various algorithms for apparent rate constant calculation were developed in the past [2,[7][8][9][10]. Some of them are semi-empirical [1,8], others are based on parameters with clear physico-chemical meanings [2,7].…”

“…Nevertheless, comparison of two most widely used algorithms such as CCS [1] and S [2] cannot be found in the available literature. In addition, due to a lack of physicochemical parameters used for kinetic modelling of multifunctional monomers authors usually compare different algorithms for apparent rate constant calculation in the kinetic modelling of monomers such as MMA, styrene and others [7][8][9][10]. Only few studies were done so far on the kinetic modelling of more complicated multifunctional monomers [3][4][5][6][11][12][13].…”

Concerning Chain Growth Specific Reaction Rate as a Part of the Process of Methyl Methacrylate Mass Radical Polymerization

“…Having approximated the average values of chain growth reaction rates ( The chain growth reaction rates determined using the SIP method [10][11] were found on the initial polymerization section that proves the correct nature of the chain growth reaction rate value in qua sisteady approximation. mma polymerization simulation using the mC method algorithm description The MC method is thought to be an efficient for solving complex systems of equations.…”

“…The SIP method is similar to the 'rotating sector' method as the monomer and initiator solution flows through an unlit tubular reactor past regularly placed splits that permit light through. The chain growth reaction rate determined using the SIP method can be found in [10][11] (Table 1). The value obtained was applied in [15][16] to describe mass radical polymerization of methyl methacrylate (MMA) in theory.…”