Can the failure of tube models in blends of branched polymers be salvaged by slip-link models?*

A recent comparison between experiments and theories for the dynamic modulus of linear/star-branched entangled polymer blends revealed that tube models were unable to describe simultaneously two different sets of data. Both the branch-on-branch (BoB) computer algorithm, and the hierarchical model were used with various sets of parameter values. While one set of values could describe one data set, it failed to describe the other.
On the other hand, the discrete slip-link model was able to describe both sets simultaneously, using parameters determined for monodisperse linear chains only. This observation naturally raises the question in our title. Hence, we attempt further coarse graining of the slip-link model to a level of description more like a tube. We consider the simplest case: the primitive path length of a monodisperse star arm without constraint dynamics. Specification of the coarse-grained level of description requires determination of just two 1D objects: free energy and friction, as functions of primitive path length. Statistical mechanics determines the former, and we devise an efficient and accurate method to determine the latter. We can then compare predictions of the coarse-grained and detailed models.