Mathematical modeling of polymerization reactors

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Polymers are used in everyday products such as plastic containers and textiles, and also in specialized medical applications. Chemical reactions required to produce polymers are carried out in polymerization reactors. Mathematical equations (a model) can be used to describe how polymerization reactor conditions (temperature, and the concentrations of different chemicals) affect the properties of the polymers that are produced. Most of my research is aimed at mathematical modeling of polymerization reactors. Companies use my models to gain improved understanding of their polymerization processes, to improve product quality, and to increase production rates. In recent years, I have expanded my work to include mathematical modeling of polymer gel dosimeters, which are used to calibrate radiation doses delivered by cancer radiotherapy equipment. These models help medical physicists to understand chemical and physical processes that occur in their dosimeters, and will help them to ensure that the correct radiation doses are being delivered to the correct locations in patients' bodies. I also develop mathematical modeling and statistical techniques that assist other modelers. In this proposal, funds are requested for five research topics. In the first, models will be developed to predict product quality in industrial nylon reactors, using experimental data from our lab. In the second, models will be developed for different types of gel dosimeters, so that benefits and short-comings can be better assessed, and improved dosimeters can be designed. In the third, models will be developed to predict the properties of branched polymers, to assist in the design of new materials for biomedical applications. In the fourth and fifth, statistical tools will be developed to assist modelers in finding appropriate values of parameters, which are required when models are used to make predictions. These statistical tools will result in more effective use of experimental data and more reliable model predictions. Most of the budget requested will be spent on salaries for graduate students, who will receive valuable training in polymerization reaction engineering, mathematical modeling and applied statistics.