Model Development and Parameter Estimation for Styrene Polymerization

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Woloszyn, John
mathematical modeling , polystyrene
A model is developed to describe the bulk thermally-initiated free-radical polymerization of styrene between 100 °C and 170 °C. This model incorporates a comprehensive thermal initiation mechanism including generation and consumption of a Diels-Alder adduct intermediate species. A semi-empirical break-point treatment of diffusion control on reaction kinetics is used to account for autoacceleration behaviour. Using recently-developed statistical techniques, parameters are ranked based on their influence on model predictions, uncertainty in their initial values and correlation between their effects. The four top-ranked parameters (of the 40 total model parameters) are chosen for estimation to improve the fit between model predictions and literature data. After estimation of these four parameters, and hand-tuning of two additional autoacceleration parameters, the model predicts conversion data with a standard error of 5 %. The model also provides an excellent fit to a single MWD curve obtained from a literature experiment performed at 100 °C. Simulations are used to show that chain-end degradation reactions are not important in the temperature range of interest. The model is then extended to include industrially-relevant dicumyl peroxide and biphenyl peroxide chemical initiation. Additional peroxide-induced mid-chain scission reactions are considered as they may have an important influence on the molecular weight of polystyrene. To improve trends in predictions of Mn and Mw, the stationary-state hypothesis is applied to the initial adduct concentration. Parameters are then ranked, and selected for estimation using recently-developed statistical techniques. While significant improvements in predictions of conversion data are obtained, it is necessary to manually tune several parameters and scrutinize the reaction scheme in detail. To improve trends in predictions of Mn and Mw, mid-chain scission reactions are turned off and chain-transfer to monomer is implemented. Nine of the 48 total parameters are selected for estimation, resulting in a 73 % decrease in the objective function value compared with predictions using literature values. The final step of this work will be to estimate parameters using a large, proprietary industrial data set. Using this data set, it may be possible to estimate additional parameters which may lead to improved model predictions.
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