A tube model for predicting the stress and dielectric relaxations of polydisperse linear polymers

We present an algorithm to predict the linear relaxation spectra for linear polymers of fully general and arbitrary polydispersity. As is 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. We 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 propose a novel but minimal description involving five embedded tubes. Building on prior work for binary blends, we derive the scaling level descriptions of the relaxation pathways. We use a large number of existing experimental results on the stress and dielectric relaxations to validate our model, ensuring we explore a very broad range of parameter space.