Identifiability Analysis and Parameter Estimation of Microgel Synthesis: A Set-Membership Approach

Abstract

Functional microgels with tailored structure and specific properties are required for medical and technical applications, thus motivating model-based optimization of their fabrication processes. An important step in the creation of accurate models is parameter estimation. We present a methodology for a parameter identifiability analysis, which approximates the feasible parameter set as a box by solving a series of constrained dynamic optimization problems. The method is applied to the synthesis of microgels based on two monomers, N-vinylcaprolactam and N-isopropylacrylamide, and the cross-linker N,N-methylenebis(acrylamide). The results show that kinetic parameters corresponding to the reaction of the monomers are identifiable as are a subset of the kinetic parameters involving the cross-linker. The reaction kinetics of the cross-linking are faster in comparison to the main polymerization reaction for N-vinylcaprolactam; this allows for an improved understanding of the occurring reaction phenomena. The reaction kinetics of the cross-linking are not identifiable for N-isopropylacrylamide for the given experimental setup; model-based experimental design for parameter precision might enable their identification. The results also indicate potential for model simplification and allow us to make suggestions toward the enhancement of Raman spectroscopy measurements.