Analytic slip-link expressions for universal dynamic modulus predictions of linear monodisperse polymer melts

The discrete slip-link model (DSM) is a robust mesoscopic theory that has great success predicting the rheology of flexible entangled polymer liquids and gels. In the most coarse-grained version of the DSM, we exploit heavily the universality observed in the shape of the relaxation modulus of linear monodisperse melts. For this type of polymer, we present here analytic expressions for the relaxation modulus. The high-frequency dynamics which are typically coarse-grained out from the DSM are added back into these expressions by using a Rouse chain with fixed ends to represent the fast motion of Kuhn steps between entanglements. We find consistency in the friction used for both fast and slow modes. We test these expressions against experimental data for three chemistries and molecular weights with good agreement. Using these analytic expressions, the polymer density, the molecular weight of a Kuhn step, M K, and the low-frequency cross-over between the storage and loss moduli, \(G^{\prime }\) and \(G^{\prime \prime }\), it is now straightforward to estimate model parameter values and obtain predictions over the experimentally accessible frequency range without performing expensive numerical calculations.