We present a generic algorithm to predict the linear relaxation spectra for polydisperse linear polymers based on their molecular weight distribution. The algorithm is based on the commonly used "tube model", which described the molecular motion of the polymers. As common in the tube theory descriptions of linear polymers, we assume that the stress relaxation is affected by both the constraint release and tube escape modes. But unlike most existing descriptions, we consider how these two modes of relaxation affect each other and argue that the proper description for relaxation in an arbitrary blend of linear polymers requires consideration of multiple embedded tubes affecting the different relaxation pathways. We derive the scaling level descriptions of these relaxation pathways and use a large number of existing experimental results on the stress and dielectric relaxations of monodisperse and polydisperse polymers to validate our model. <br/><br/>From the point of view of analysis and characterisation of polymers, the algorithm is most straightforwardly used in a forward, predictive mode: given a molecular weight distribution, it predicts rheology with good accuracy. There is, however, potential for using it as a means for inverse modelling, e.g. to find molecular weight distributions consistent with measured rheology.

Predicting the stress and dielectric relaxations of polydisperse linear polymers

ACS Spring 2022

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