Prediction of the Bivariate Molecular Weight - Long Chain Branching Distribution in Highly Branched Polymerization Systems Using Monte Carlo and Sectional Grid Methods

In the present work, an efficient Monte Carlo (MC) algorithm and a two-dimensional fixed pivot technique (FPT) are described for the calculation of the molecular weight distribution (MWD) for linear polymers (e.g., poly(methyl methacrylate), PMMA) and the bivariate molecular weight−long chain branching distribution (MW−LCBD) for highly branched polymers (e.g., poly(vinyl acetate), PVAc), produced in chemically initiated free-radical batch polymerization systems. The validity of the numerical calculations is first examined via a direct comparison of simulation results obtained by both methods with experimental data on monomer conversion and MWD for the free-radical MMA polymerization. Subsequently, the developed FPT and MC numerical algorithms are applied to a highly branched polymerization system (i.e., VAc). Simulation results are directly compared with available experimental measurements on M n, M w and B n . Additional comparisons between the MC and the FP numerical methods are carried out under different polymerization conditions. In general, the 2-D FPT can provide very accurate predictions of the molecular weight averages and MWD for both linear and highly branched polymers in relatively short times but its numerical complexity requires special computational skills. On the other hand, the stochastic MC algorithm described in the present study is quite easy to implement but often requires large computational times, especially for highly branched polymers at high monomer conversions. It is important to point out that, to our knowledge, this is the first time that the joint (MW−LCB) distribution for branched polymers is calculated by two independent numerical methods via the direct solution of the governing population balance equations for both “live” and “dead” polymer chains.