Slip-Link Theory Predicts Entangled, Star-Branched Relaxation Measurably Different from Tube Model Predictions

Entangled, linear polymers exhibit a famous molecular-weight scaling of the longest relaxation time with exponent 3.4. However, star-branched polymers exhibit a much stronger dependence closer to exp(γ Ma/Me), where Ma is the arm molecular weight, and Me is an entanglement molecular weight. Several tube models have been proposed to describe star-branched polymer melts. The initial purpose was to predict γ, and later modifications sought to improve the predictions for the shape of the dynamic modulus and to achieve consistency between the parameter values used for linear and star-branched chains. However, a survey of tube models reveals that the addition of new ad hoc terms leads to overall poor and inconsistent predictions. The alternative entanglement theory, slip-links, is more expensive to calculate than tubes, because of the large ratio of longest to entanglement relaxation times and the inclusion of fluctuations not present in tube models. Here, we introduce a corrected algorithm for star-branched relaxation calculations that is orders of magnitude faster than previous studies, allowing a much more complete study. We examine the relaxation spectrum and zero-shear-rate viscosity of stars with up to 12 entanglements per arm. Comparison with existing zero-shear-rate data for several polymer chemistries shows that the slip-link theory can correctly describe the observed molecular-weight dependence.