Dynamic prediction of the bivariate molecular weight–copolymer composition distribution using sectional-grid and stochastic numerical methods

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.