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.

Similar to entangled ropes, polymer chains cannot slide through each other. These topological constraints, the so-called entanglements, dominate the viscoelastic behavior of high-molecular-weight polymeric liquids. Tube models of polymer dynamics and rheology are based on the idea that entanglements confine a chain to small fluctuations around a primitive path which follows the coarse-grained chain contour. To establish the microscopic foundation for these highly successful phenomenological models, we have recently introduced a method for identifying the primitive path mesh that characterizes the microscopic topological state of computer-generated conformations of long-chain polymer melts and solutions. Here we give a more detailed account of the algorithm and discuss several key aspects of the analysis that are pertinent for its successful use in analyzing the topology of the polymer configurations. We also present a slight modification of the algorithm that preserves the previously neglected self-entanglements and allows us to distinguish between local self-knots and entanglements between distant sections of the same chain. Our results indicate that the latter make a negligible contribution to the tube and that the contour length between local self-knots, N lk is significantly larger than the entanglement length N e . c 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: [917][918][919][920][921][922][923][924][925][926][927][928][929][930][931][932][933] 2005

The linear viscoelastic (LVE) spectrum is one of the primary fingerprints of polymer solutions and melts, carrying information about most relaxation processes in the system. Many single chain theories and models start with predicting the LVE spectrum to validate their assumptions. However, until now, no reliable linear stress relaxation data were available from simulations of multichain systems. In this work, we propose a new efficient way to calculate a wide variety of correlation functions and mean-square displacements during simulations without significant additional CPU cost. Using this method, we calculate stress-stress autocorrelation functions for a simple bead-spring model of polymer melt for a wide range of chain lengths, densities, temperatures, and chain stiffnesses. The obtained stress-stress autocorrelation functions were compared with the single chain slip-spring model in order to obtain entanglement related parameters, such as the plateau modulus or the molecular weight between entanglements. Then, the dependence of the plateau modulus on the packing length is discussed. We have also identified three different contributions to the stress relaxation: bond length relaxation, colloidal and polymeric. Their dependence on the density and the temperature is demonstrated for short unentangled systems without inertia.