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.

A comprehensive kinetic model is developed for the suspension free-radical polymerization of vinyl chloride (VC) initiated by a mixture of monofunctional and bifunctional initiators. The model predicts the monomer concentrations in the gas, aqueous, and polymer phases; the overall monomer conversion; the polymerization rate; the polymer chain structural characteristics (e.g., number-and weight-average molecular weights, short chain branching, and number of terminal double bonds); the reactor temperature and pressure; and the coolant flow rate and temperature in the reactor's jacket over the whole batch polymerization cycle. The capabilities of the model are demonstrated by a direct comparison of model predictions with experimental data on monomer conversion, number-and weight-average molecular weights, and reactor pressure. It is shown that high molecular weights and high polymerization rates can be obtained in the presence of a mixture of monofunctional and bifunctional initiators. Moreover, the use of bifunctional initiators results in a significant reduction of the polymerization time without impairing the final molecular weight properties of the polymer. To our knowledge, this is the first comprehensive kinetic modeling study on the combined use of monofunctional and bifunctional initiators on the free-radical suspension polymerization of VC. Taking into consideration the excellent agreement of the model predictions with the experimental measurements, the proposed model should find wide application in the design, optimization, and control of industrial poly(vinyl chloride) batch reactors.

In the present study, a comprehensive mathematical model is developed for the free‐radical polymerization of styrene to predict the polymerization rate and the molecular‐weight distribution of the polymer. The kinetic model accounts for both chemical and thermal radical generation and, thus, can be employed over an extended range of polymerization temperatures (e.g., 60–200 °C). The thermal initiation mechanism includes the reversible Diels‐Alder dimerization of styrene, radical formation via the reaction of the Diels‐Alder adduct with monomer, the formation of dead trimers, and the initiation of new polymer chains. Moreover, a comprehensive free‐volume model is employed to describe the variation of termination and propagation rate constants as well as of the initiator efficiency with respect to the monomer conversion. The cumulative molecular‐weight distribution of the polystyrene is calculated by the weighted sum of all the ‘instantaneous’ weight chain‐length distributions formed during the batch run. The capabilities of the present model are demonstrated by a direct comparison of model predictions with experimental data on monomer conversion, number‐ and weight‐average molecular weights, and molecular‐weight distribution. It should be noted that previously published kinetic models cannot describe the combined thermal and chemical free‐radical polymerization of styrene in terms of a unified, fundamental, kinetic model, which further underlines the significance of this study.Predicted and experimental weight‐average molecular weights with respect to monomer conversion (experimental conditions same as in Figure 1).magnified imagePredicted and experimental weight‐average molecular weights with respect to monomer conversion (experimental conditions same as in Figure 1).

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