SLIP-LINK MODELING OF ENTANGLED POLYMERS: RHEOLOGICAL APPLICATIONS AND EXTRACTING FRICTION FROM ATOMISTIC SIMULATION
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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 the university observed in the shape of the relaxation modulus of linear monodisperse melts. For this type of polymer we present 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. We find consistency in the friction used for both fast and slow modes. Using these analytic expressions, the polymer density, the molecular weight of a Kuhn step, Mk, and the low-frequency cross-over between the storage and loss moduli, G' and G", it is now straightforward to estimate model parameter values and obtain predictions over the experimentally accessible frequency range. Moreover it has previously been shown that the two static parameters can be obtained from primitive path analysis of molecular dynamics simulations. In this work, two ways are shown for obtaining the friction parameter (i) from atomistic simulations of short chains using the free-volume theory, and (ii) from atomistic simulations of entangled chains by scaling the chain center-of-mass mean-square displacement from the slip-link model to that of the atomistic simulation. Futhermore three standing challenges for molecular theories of polymers (i) predictions for uniaxial extension of star-branched polymer melts (ii) predictions for blends of star-branched and linear chains and (iii) predictions for normal stress differences in start-up of shear and followoing cessation are addressed here using the DSM. Additionally the DSM is used to predict the mechanical properties of a cross-linked polydimethylsiloxane (PDMS) network swollen with non-reactive entangled PDMS solvent. These successful predictions strongly suggest that the observed rheological modification in the swollen blend arises from the constraint dynamics between the network chains and the dangling ends.