Reactivity Ratio Estimation from Cumulative Copolymer Composition Data

Abstract

The goal is to present an alternative technique for reactivity ratio estimation in copolymerization. Typically, reactivity ratios are estimated using the instantaneous copolymer composition equation, based on low conversion copolymer composition data. However, using experimental data from the full copolymerization trajectory would, in principle, be more advantageous, and shy away from commonly used restrictive assumptions. Estimation using cumulative copolymerization data and models eliminates the difficulties associated with stopping reactions at low conversion, while one gains to study the full polymerization trajectory. The error‐in‐variables‐model (EVM) method is used for parameter estimation. Two cumulative model forms, the analytical integration of the differential composition equation and the one resulting from the direct numerical integration of this equation, are employed. Using these two types of models improves the reactivity ratio estimation and, in particular, the latter model form is a more reliable and direct method of estimating reactivity ratios.

Computational Package for Copolymerization Reactivity Ratio Estimation: Improved Access to the Error-in-Variables-Model

“…DNI is a direct numerical approach and does not rely on model transformations or other potentially restrictive assumptions. This is a significant advantage over other estimation approaches with copolymerization models [3,6].…”

Optimal Design for Reactivity Ratio Estimation: A Comparison of Techniques for AMPS/Acrylamide and AMPS/Acrylic Acid Copolymerizations

“…However, linearizing the kinetic models (which are inherently non-linear in the parameters) requires making imprecise, subjective and invalid assumptions. An additional consideration is the use of the instantaneous copolymerization model in these linear techniques; the reaction must be kept at low conversion so that the assumption of "constant composition" in the feed is somewhat valid [8]. However, polymerizations at low conversions are extremely error-prone, and it is impossible to guarantee that the feed composition will remain constant (especially when dealing with an unstudied system).…”

“…The experimental data are presented in Appendix A (Tables A1 and A2), and details regarding the implementation of this technique have been presented previously by Kazemi et al [8].…”

“…The cumulative composition model was applied to the data (using direct numerical integration as described in Kazemi et al [8]) through EVM. Point estimates from the literature [28], the preliminary experiments and the optimally designed experiments are presented in Figure 5, along with their corresponding JCRs.…”

“…Through EVM and direct numerical model integration, we are also able to estimate reactivity ratios using cumulative composition data (as opposed to standard analysis of low-conversion data). This provides additional advantages, including eliminating unnecessary assumptions and avoiding the experimental challenges associated with collecting low-conversion data [8]. Copolymerizations of both AMPS/AAm and AMPS/AAc are designed using Tidwell-Mortimer (T-M) and error-in-variables-model (EVM) techniques.…”