Model discrimination techniques for the modelling of copolymerization reactions

In recent years, a great deal of work has been done on finding the 'best' model for particular copolymer systems of interest. In examining these efforts, we found that the experiments are often poorly designed for the purpose of discriminating between proposed models. By contrast, statistical model discrimination methods describe how to design and analyze experiments in order to obtain the maximum amount of information with respect to the strengths of competing models.;The objectives of this work were to quantify the benefits of applying model discrimination methods to the problem of copolymerization modelling, to examine the information content of copolymer measurements, and to compare promising statistical model discrimination methods.;The first phase of this work involved extensive computer simulations. Computer simulations were developed to study the application of several model discrimination methods to several copolymer systems. Simulated data were generated for the systems styrene acrylonitrile, styrene methyl methacrylate, and styrene butyl acrylate. Comparisons show that the simulated data are in agreement with existing experimental data. Computer routines were also written to design and analyze experiments using the Buzzi-Ferraris and Forzatti (1983), exact entropy (Reilly, 1970), and Hsiang and Reilly (1971) model discrimination methods. Simulations were then run to study the application of model discrimination methods under different levels of measurement error, different initial values of reactivity ratios (parameters), and with different 'true' models for the systems (terminal or penultimate).;The simulations showed that model discrimination methods should improve the modelling of copolymerization reactions. Based on copolymer composition, the Buzzi-Ferraris and Forzatti method could identify the correct model in 55.6% of the simulations compared to 30.9% of the simulations based on equally spaced experiments. The Buzzi-Ferraris and Forzatti method could identify the correct model in 99% of the simulations based on triad fraction data, and in 96% of the simulations based on the combination of copolymer composition and rate data. The most reliable measurements were triad fraction data and the combination of copolymer composition and rate data.;The simulations showed that the Buzzi-Ferraris and Forzatti method was best able to correctly discriminate between competing nested models. Further studies involving sets of non-nested models showed that the exact entropy and Buzzi-Ferraris and Forzatti methods are very close in terms of reliability, but that the Buzzi-Ferraris and Forzatti method requires more experiments to achieve discrimination. Therefore, it seems the exact entropy method may be best for the more general case of non-nested models.;Experimental work was subsequently done to verify the simulation results. The Buzzi-Ferraris and Forzatti method was applied to the system styrene methyl methacrylate based on triad fraction measurements. The terminal model was picked as the 'best' model for the system after a total of nine experiments. The feed compositions chosen for experiments, the reactivity ratio estimates, and the estimated error level were all what we would have expected based on the preceding simulations involving styrene methylmethacrylate. Therefore, the simulations are valid and we are justified in drawing conclusions from them.