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.

In the present study, two numerical methods, namely the orthogonal collocation on finite elements and the fixed pivot technique, are employed to calculate the MWD in an MMA free‐radical batch suspension polymerization reactor operating up to very high conversions (e.g., ≥95%). The theoretical MWD predictions are directly compared with experimentally measured MWDs, obtained from a pilot‐scale batch MMA suspension polymerization reactor. It is shown that there is a very good agreement between model predictions and experimental measurements on both monomer conversion and MWD. Subsequently, two different time‐optimal temperature trajectories are calculated to obtain a polymer having either a narrow or a bimodal MWD in minimum batch time. The calculated time optimal trajectories are then applied, as set point temperature changes, to a pilot plant batch polymerization reactor. It is shown that the measured MWDs are in very good agreement with the off‐line calculated optimal MWDs.

In the present study, an efficient Monte Carlo (MC) algorithm and a fixed pivot technique (FPT) are described for the prediction of the dynamic evolution of the droplet/particle size distribution (DSD/PSD) in both non-reactive liquid-liquid dispersions and reactive liquid(solid)-liquid suspension polymerization systems. Semi-empirical and phenomenological expressions are employed to describe the breakage and coalescence rates of dispersed monomer droplets/particles, in terms of the type and concentration of suspending agent, quality of agitation, and evolution of the physical, thermodynamic and transport properties of the polymerization system. Moreover, the validity of the numerical calculations is first examined via a direct comparison of simulation results obtained by both numerical methods with experimental data on average particle diameter and droplet/particle size distributions for both non-reactive liquid-liquid dispersions and the free-radical suspension polymerization of methyl methacrylate (MMA). Additional comparisons between the MC and the FP numerical methods are carried out under different polymerization conditions. The simulation results reveal that both numerical methods are capable of predicting the mean and the distributed particulate properties of both non-reactive and reactive suspension processes.On décrit dans cet article un algorithme de Monte Carlo (MC) efficace et une technique de pivot fixe (FPT) pour prédire l'évolution dynamique de la distribution de taille de gouttelettes/particules (DSP/PSD)à la fois dans des dispersions liquide-liquide non réactives et des systèmes de polymérisation par suspensions liquide (solide)-liquide réactifs. On emploie des expressions semi empiriques et phénoménologiques pour décrire les taux de rupture et de coalescence de gouttelettes/particules de monomères dispersés, en fonction du type et de la concentration d'agent de suspension, de la qualité de l'agitation et de l'évolution des propriétés physiques, thermodynamiques et de transport du système de polymérisation. En outre, la validité des calculs numériques est d'abord examinée par une comparaison directe des résultats de simulation obtenus par les deux méthodes numériques avec les données expérimentales du diamètre de particule et de la distribution de taille de gouttelettes/particules moyensà la fois pour les dispersions liquide-liquide non réactives et la polymérisation par suspensions de radicaux libres du méthacrylate de méthyle (MMA). D'autres comparaisons entre les méthodes numériques MC et FP sont effectuées pour des différentes conditions de polymérisation. Les résultats de simulation révèlent que les deux méthodes numériques sont capables de prédire les propriétés particulaires moyennes et distribuées des deux procédés par suspension non réactif et réactif.

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