Evaluation of models combining rheological data with the molecular weight distribution

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Abstract
The aim of this article is to test and to improve existing models combining rheological data with the molecular weight distribution (MWD). This process of testing and improving was separated into two distinct steps: First, the mixing behavior of the relaxation modulus obtained from a polymer blend was investigated and compared with the proposed mixing behavior derived from the linear and the quadratic mixing rules with a mixing parameter β equal to 1 and 2. Second, for the first time, kernel functions weighted with the MWD are estimated directly from experimental data and compared to the weighted kernel functions published in the literature. This procedure was performed with polystyrene blends composed of two monodisperse polymers with narrow MWD determined using size exclusion chromotography. It was shown that the existing mixing rules are not able to adequately describe the mixing behavior of the polystyrene blends. An improved mixing rule was derived with β of 3.84. Furthermore, a kernel function exists only for the improved model, which is able to describe the experimental data over a wide molecular range. It is shown how improved estimates of the MWD of a polymer can be determined using the new model.