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.

The ionic strength (IS) of polyelectrolyte solutions plays an important role in influencing reaction kinetics. The largely unstudied effect of IS on monomer reactivity ratios and copolymerization rates of acrylamide (AAm) and acrylic acid (AAc), in the form of sodium acrylate (NaAc), is investigated. Salt addition affects the nature of overall charges of the polyelectrolyte solution and diminishes the electrostatic repulsions between reacting chains. Therefore, changing the IS of the solution by incorporating salts affect not only the point estimates of the monomer reactivity ratios but also the overall behavior of the copolymerization (with a transition to azeotropic behavior). Experimental results on copolymerization rates confirm the observed trends in reactivity ratio behavior. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2014, 131, 40949.

Reactivity ratios for the important acrylamide (AAm)/acrylic acid (AAc) copolymerization system exhibit considerable scatter in previously published literature, and therefore, there is a need for more definitive values for these reactivity ratios. An appropriate methodology, based on the error‐in‐variables‐model (EVM) framework along with a direct numerical integration procedure, is applied in order to determine reliable reactivity ratios. The reliability of the results is confirmed with extensive and independent replication. Furthermore, via an EVM‐based criterion for the design of experiments using mechanistic models, optimal feed compositions are calculated, and from these optimal reactivity ratios are estimated for the first time (rAAm = 1.33 and rAAc = 0.23) based on information from the full conversion range. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 4819–4827

In typical practice for terpolymerizations so far, binary reactivity ratios have been used directly in the instantaneous Alfrey and Goldfinger (AG) model, effectively ignoring the presence of the third monomer. In addition, the use of the AG model leads to severe estimation problems, if one would like to estimate reactivity ratios from experimental data. Due to the above reasons, the AG model was recast and was subsequently used with terpolymerization data directly to estimate ternary reactivity ratios under the error-in-variables-model framework, based both on instantaneous (low conversion) and cumulative composition data (medium and high conversions). Several examples and counter examples highlight such important issues as the choice of the correct number of responses, accounting for the appropriate error structure, and incorporating the right information content, all with diagnostic checks whose target is the eventual reliability of the reactivity ratio estimates.

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.