The Use of Gauss-hermite Quadrature in the Determination of the Molecular Weight Distribution of Linear Polymers by Rheometry

The molecular weight distribution (MWD) and its parameters are of the fundamental importance in the characterization of polymers. Therefore, the development of techniques for faster MWD determination is a relevant issue. This paper aims at implementing one of the relaxation models from double reptation theory proposed in the literature and analyzing the numeric strategy for the evaluation of the integrals appearing in the relaxation model. The inverse problem, i.e., the determination of the MWD from rheological data using a specified relaxation model and an imposed distribution function was approximated. Concerning the numerical strategy for the evaluation of the integrals appearing in the relaxation models, the use of Gauss-Hermite quadrature using a new change of variables was proposed. In the test of samples of polyethylene with polydispersities less than 10, the application of this methodology led to MWD curves which provided a good fit of the experimental SEC data.