Prediction of Bivariate Molecular Property Distributions in Free-Radical Polymerization Systems Using Monte Carlo and Sectional Grid Methods (original) (raw)
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Chemical Engineering Science, 2008
In the present study, a two-dimensional fixed pivot technique (2-D FPT) and an efficient Monte Carlo (MC) algorithm are described for the calculation of the bivariate molecular weight-copolymer composition (MW-CC) distribution in batch free-radical copolymerization reactors. A comprehensive free-volume model is employed to describe the variation of termination and propagation rate constants as well as the variation of the initiator efficiency with respect to the monomer conversion. Simulations are carried out, under different reactor conditions, to calculate the individual monomer conversions, the leading moments of the`live' and`dead' polymer chain length distributions as well as the dynamic evolution of the distributed molecular properties (i.e., molecular weight distribution (MWD), copolymer composition distribution (CCD) and joint MW-CC distribution). The validity of the numerical calculations is examined via a direct comparison of the simulation results, obtained by the two numerical methods, with experimental data on the styrene-methyl methacrylate batch free-radical copolymerization. Additional comparisons between the 2-D FPT and the MC methods are carried out for different polymerization conditions. It is clearly shown that both numerical methods are capable of predicting the distributed molecular and copolymer properties, with high accuracy, up to very high monomer conversions. It is also shown that the proposed dynamic MC algorithm is less computationally demanding than the 2-D FPT.
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.
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.
2001
A kinetic gelation model that incorporates the kinetics of free radical homopolymerization is implemented to determine the effects of kinetics on polymerization statistics and microstructures. The simulation is performed on a simple cubic lattice that has 100 sites in each direction. A new algorithm for random selecting of the next step in a self-avoiding random walk and very efficient mechanisms of mobility of components are introduced to improve the generality of the predictions by removing commonly occurring deficiencies due to early trapping of radicals. A first order kinetics is considered for decomposition of initiator that enables us to consider the effect of temperature on polymerization reaction. Better understanding of microstructural evolution during polymerization and providing a framework to produce a realistic system of highly packed random chains within polymer network are among the benefits of model.
Polymer, 2005
In the present work, two different approaches to model diffusion controlled free radical polymerization, namely the free volume model and the entanglement theory are compared. These approaches are applied to methyl methacrylate bulk polymerization in a batch reactor to calculate the conversion, total radical concentration, the number and weight average molecular weights as well as the entire molecular weight distribution as a function of the polymerization time and the process conditions. All the diffusion-controlled phenomena were taken into account, including gel, glass and cage effects as well as residual termination. The molecular weight distribution is calculated by direct numerical integration of a large system of non-linear ordinary differential equations describing the conservation of the mass of macromolecular species in the batch reactor. Model predictions are in good agreement with available experimental data for conversion, number and weight average molecular weights as well as the entire molecular weight distribution, thus justifying the ability of these models to describe the main issues of the diffusion-controlled free radical polymerization.
Initiator Feeding Policies in Semi-Batch Free Radical Polymerization: A Monte Carlo Study
Processes, 2020
A Monte Carlo simulation algorithm is developed to visualize the impact of various initiator feeding policies on the kinetics of free radical polymerization. Three cases are studied: (1) general free radical polymerization using typical rate constants; (2) diffusion-controlled styrene free radical polymerization in a relatively small amount of solvent; and (3) methyl methacrylate free radical polymerization in solution. The number- and weight-average chain lengths, molecular weight distribution (MWD), and polymerization time were computed for each initiator feeding policy. The results show that a higher number of initiator shots throughout polymerization at a fixed amount of initiator significantly increases average molecular weight and broadens MWD. Similar results are also observed when most of the initiator is added at higher conversions. It is demonstrated that one can double the molecular weight of polystyrene and increase its dispersity by 50% through a four-shot instead of a ...