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Prediction of Bivariate Molecular Property Distributions in Free-Radical Polymerization Systems Using Monte Carlo and Sectional Grid Methods

An efficient Monte Carlo (MC) algorithm and a two-dimensional fixed pivot technique (2-D FPT) are described for the calculation of the average and distributed molecular properties of polymers in batch free-radical polymerization and copolymerization reactors. 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), long chain branching distribution (LCBD), copolymer composition distribution (CCD), joint LCB-MW and CC-MW distributions, etc.). 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 and vinyl acetate batch free-radical polymerization systems. Additional comparisons between the MC and the 2-D FPT methods are carried out for both polymerization systems, under different polymerization conditions. It is clearly shown that both numerical methods are capable of predicting the distributed molecular, branching and copolymer properties, with high accuracy, up to very high monomer conversions.