Design of Optimal Experiments for Terpolymerization Reactivity Ratio Estimation

Abstract

A model-based design of experiments is implemented for the problem of reactivity ratio estimation in terpolymerizations for the first time in the literature. Optimal terpolymerization feed compositions are calculated using a design criterion, based on the Error-in-Variables-Model (EVM) approach. The results show that there are three optimal feed compositions with their locations naturally dependent on the values of the reactivity ratios. However, the interesting observation is that in almost all cases the optimal feed compositions are located close to the corners of the terpolymerization composition triangular plot. In addition, the impact of the reactivity ratio values on the location of the optimal feed compositions is explored and "practical heuristics" are presented. This paper demonstrates that by implementing appropriate design of experiments and parameter estimation techniques, reliable reactivity ratios for terpolymerizations can be estimated from only three optimal feed compositions. The first ever model-based design of experiments criterion for terpolymerization reactivity ratio estimation is presented in this paper, which is as significant as the Tidwell-Mortimer criterion in copolymerization studies.