Star Polymers and the Failure of Time-Temperature Superposition

We model the arm of a star polymer as an anchored random walk in an array of fixed obstacles with the added assumption of an energetic cost associated with the walk retracing its previous step. By including this energetic penalty for such “hairpin” turns on the chain, we are able to account for the thermorheological complexity of long-branched hydrogenated polybutadiene yet not introduce deviations from time-temperature superposition in a melt of the linear chains. We also show that the same assumption leads to a prediction for the thermal expansion coefficient of the linear chains that is in reasonable agreement with the latest data.