Universality and speedup in equilibrium and nonlinear rheology predictions of the fixed slip-link model

Abstract

The discrete slip-link model (DSM) was developed to describe the dynamics of flexible entangled polymer melts. With just three molecular-weight- and chain-architecture-independent parameters—the molecular weight of a Kuhn step MK; entanglement activity β; and Kuhn step shuffling characteristic time τK—DSM is able to predict simultaneously the linear viscoelasticity of monodisperse linear, polydisperse linear, and branched systems. Without any adjustment, DSM shows excellent agreement with shear flow experiments and elongational flows with stretch up to ∼10–20. Universality observed between entangled melts with the notable exception of high-strain elongations suggests that the average number of entanglements per chain is the primary characteristic of the system. Therefore, theoretical predictions for systems with differing numbers of Kuhn steps per chain but roughly the same number of entanglements should be equivalent when rescaled. In this work, we present a scaling of the DSM parameters, which has no significant effect on model predictions yet reduces greatly computational cost. The idea behind the scaling is clustering several Kuhn steps together. Thus, we call this implementation of the DSM the clustered fixed slip-link model (CFSM). The model is limited to at least one cluster between entanglements. The CFSM assumes two clusters between entanglements on average, which appears to be a reasonable minimum. We find that clustering results in a loss of some of the high frequency modes in G* predictions, sometimes called “longitudinal modes” in tube models. Matching the low-frequency rubbery plateau height allows us to derive Mc—the molecular weight of a cluster, as a function of the DSM parameters β, MK. We also find an empirical relationship between timescale parameters τK and τc, the characteristic time for shuffling a cluster through the entanglement. We compare G* predictions of the CFSM with predictions of the DSM for monodisperse linear, polydisperse linear, and branched systems, and observe no difference. Comparison with shear flow predictions shows that only rates with a Weissenberg number based on the strand relaxation time τe of 1 and higher are affected. For elongational flow at high strains and high rates, significant difference can occur, which is perhaps not surprising given the observation above. For the systems shown in this work, we report CFSM computational savings of several hundred times. We then apply CFSM to the shear flow of a star-branched polymer melt with molecular weight not accessible to DSM without rescaling. Excellent agreement with experimental data is observed. Additionally, we report first normal stress theoretical predictions for this system.