Rheology and Microscopic Topology of Entangled Polymeric Liquids

Abstract

The viscoelastic properties of high molecular weight polymeric liquids are dominated by topological constraints on a molecular scale. In a manner similar to that of entangled ropes, polymer chains can slide past but not through each other. Tube models of polymer dynamics and rheology are based on the idea that entanglements confine a chain to small fluctuations around a primitive path that follows the coarse-grained chain contour. Here we provide a microscopic foundation for these highly successful phenomenological models. We analyze the topological state of polymeric liquids in terms of primitive paths and obtain parameter-free, quantitative predictions for the plateau modulus, which agree with experiment for all major classes of synthetic polymers.

Polymer dynamics: long time simulations and topological constraints

“…The d T values can be obtained from the contour length of the primitive path, L pp (which is the sum of the lengths of all the back bone bonds of a chain averaged over all the chains in the melt) using d T = R 2 /L pp . For details refer [24,25]. Fig.…”

“…[17,24] ( ) and a semi-atomistic polycarbonate melt [16] (♦) under an elongational strain, and (iii) predictions of the tube model Eq. 6 based on the results of our PPA for bead-spring melts ( ), and the semiatomistic polycarbonate melt ( ).…”

“…Similar to the tube, the primitive path is usually discussed without specifying the relation between the obstacles and the melt structure. However the obstacles themselves are chains, which has to be taken into account, when constructing the primitive path [24][25][26]. In Ref.…”

“…In Ref. [24] we introduced a primitive path analysis (PPA) where all polymers in the system are contracted simultaneously in a way, that a linear stress strain relationship is kept. This allows us to establish the microscopic foundations of the tube model and to endow a highly successful phenomenological model with predictive power for structure-property relations.…”

Polymer Dynamics: Long Time Simulations and Topological Constraints

“…[17,24] ( ) and a semi-atomistic polycarbonate melt [16] (♦) under an elongational strain, and (iii) predictions of the tube model Eq. 6 based on the results of our PPA for bead-spring melts ( ), and the semiatomistic polycarbonate melt ( ).…”