Estimation of the characteristic times of solvent diffusion and polymer relaxation in glassy polymer films by a set inversion method

Abstract

This study deals with a multiparameter estimation problem with bounded output errors. It concerns the swelling of polymer films in the glassy state by a solvent. Local thermodynamic equilibrium is no more ensured, and the swelling results of two coupled phenomena, the diffusion of solvent on one hand and the change in solubility due to stress relaxation of the entangled polymer chains on the other. The estimation aims to obtain the parameters that characterize these two phenomena from gravimetric experiments. A set inversion analysis is used to perform the estimation: this global estimation method allows us to determine all the sets of parameters that give a mass uptake consistent with the experimental data and bounded errors. It gives interesting information on the coupling between the parameters and is well appropriate to analyze this ill-conditioned problem. A systematic analysis of the estimation performance as a function of the characteristics of the polymer–solvent system and of the experimental setup have been performed.