A simple model for the semicontinuous heterophase polymerization: Ethyl methacrylate as a case example (original) (raw)
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Journal of Applied Polymer Science, 1997
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.
2020
A mathematical model to describe the emulsion polymerization kinetics of co- and ter-polymerizations is developed. The model is based on the classical Smith-Ewart (SE) equations, within the pseudo-homopolymerization approach, with state-of-the-art models for radical entry and desorption. For co- and ter-polymerizations there are unknown parameters in the model which are related to monomer-specific gel-effect coefficients, that are needed to compute the bimolecular termination reaction rates. The unknown parameters are determined through extensive calibration of the model on literature data for homo- and co-polymerizations of n-butyl acrylate (n-BA) and methyl methacrylate (MMA). The so-obtained predictive model is then applied to the modelling of the ter-polymerization of n-BA and MMA with 2-hydroxyethyl methacrylate (2-HEMA) with sodium persulphate (SPR) as initiator: predictions for the time-evolution of particle size and conversion are in excellent agreement with experimental mea...
Polymer-Plastics Technology and Engineering, 2005
An alternative approach to model emulsion polymerization is presented that is capable of rigorously solving both particle and radical kinetics for emulsion polymerization: the explicit radical-particle size distribution approach. The method is based on a direct solution of all population balances and fully covers the strong influence of compartmentalization on rates of reactions between macroradicals and, consequently, on chain length averages. An essential and new feature is the compartmentalization factor (D f), which accounts for compartmentalization in a transparent manner. The generic approach allows for studying the complete emulsion polymerization conversion range, including gel-effect, and the effect of various parameters on both chain length and particle size distribution. Well-known kinetic regimes for emulsion polymerization naturally arise as limiting cases from our model. The dynamic behavior of the model was studied by simulating several realistic seeded emulsion polymerization reactions for styrene. The model dealt with compartmentalization accurately and was able to correctly reproduce the dynamic behavior known to be typical for emulsion polymerization.
Journal of Macromolecular Science, Part A, 2015
In Part 2 of this series of two extensive overviews of multi-component polymerization case studies, we again present mathematical modeling results with experimental confirmations. Part 2 represents a refinement and expansion of the detailed and extensive 2 mathematical model presented in Part 1 for free-radical, bulk and/or solution multicomponent polymerizations. The expansion is mainly with respect to depropagation, thus making the model more fluent at elevated polymerization temperatures and, in parallel, with additional features as backbiting (with systems involving butyl acrylaye). The model considers up to six monomers (unique in the literature), for either batch or semi-batch reactor modes. As the simulator database contains several monomers, initiators, solvents, chain transfer agents and inhibitors, all tested over a wide range of polymerization conditions, from data in both academic and industrial laboratories, several hundred combinations of ingredients can be modeled. The many outputs generated by the model include conversion, molecular weight, polymer composition, branching indicators, sequence length, as well as many other polymerization characteristics related to both production rate and polymer quality. Although the only literature data found to date contain a maximum of four monomers, model predictions for homo-, co-, ter-and tetrapolymerizations show reasonable agreement against the data at both regular and elevated temperatures. With these expansions, this model is directed towards becoming a complete free-radical polymerization tool for training and educational uses both in industry and academia.
Kinetic modeling of bulk free-radical polymerization of methyl methacrylate
Polymer Journal (2013) 45, 631–636, 2013
The free-radical bulk polymerization of many monomers is characterized by a sudden rise in the rate of polymerization, a phenomenon called autoacceleration. Many mathematical models have been developed to describe this phenomenon. In this paper, the development of a new kinetic model is described. The model very successfully describes experimental data obtained by differential scanning calorimetry of the bulk free-radical polymerization of methyl methacrylate. The proposed model is composed of two contributions to the conversion of the monomer, one originating from polymerization according to the classical theory of radical polymerization and the other originating from polymerization during the autoacceleration. The rate constant of the autoacceleration (second contribution) is about eightfold higher than the rate constant of the first-order reaction (first contribution).
Iranian Polymer Journal, 1998
The batch bulk isothermal polymerization of methyl methacrylate (MMA), in which the initiation is achieved by the decay of an initiator and termination by disproportionation is considered for modeling . According to the kinetic diagram one can make a deduction of the mathematical model in terms of the moment generating function and in terms of moments which give the distribution of the molecular weights . In order to quantify the gel and glass effects, the relations proposed by Chiu et al . are used [1] . The results given by the two solving techniques, generating function and moments, are compared and discussed . The comparison of the simulation and the experimental data represents the model validation and thus a guarantee for its use in various studies of polymer engineering.
1997
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A Novel Method to Model Emulsion Polymerization Kinetics
2005
An alternative approach to model emulsion polymerization is presented that is capable of rigorously solving both particle and radical kinetics for emulsion polymerization: the explicit radical-particle size distribution approach. The method is based on a direct solution of all population balances and fully covers the strong influence of compartmentalization on rates of reactions between macroradicals and, consequently, on chain length averages. An essential and new feature is the compartmentalization factor (D f), which accounts for compartmentalization in a transparent manner. The generic approach allows for studying the complete emulsion polymerization conversion range, including gel-effect, and the effect of various parameters on both chain length and particle size distribution. Well-known kinetic regimes for emulsion polymerization naturally arise as limiting cases from our model. The dynamic behavior of the model was studied by simulating several realistic seeded emulsion polymerization reactions for styrene. The model dealt with compartmentalization accurately and was able to correctly reproduce the dynamic behavior known to be typical for emulsion polymerization.