Predicting the linear stress and dielectric relaxations of polydisperse linear polymers

We present a generic algorithm to predict the linear relaxation spectrum for polydisperse linear polymers. As common in the tube theory descriptions of linear polymers, we assume that the stress relaxation is affected by both 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 four embedded tubes affecting the different relaxation pathways: the thin tube, the tube for fastest reptation, the constraint release "supertube" and the fully diluted tube. 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 to validate our model. For the particular case of binary blends of long and short polymers, our model is successful at predicting the linear stress and dielectric response for blends throughout the two dimensional space (constraint release rate and degree of entanglement) mapped by the Viovy diagram.