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.

Small-angle neutron and X-ray scattering data have been obtained for micelles of d-polystyrene−polyisoprene (d-PS−PI) of relatively high molecular weight in n-decane. Contrast variation was performed using mixtures of hydrogenated and deuterated decane. Three samples were investigated with d-polystyrene and polyisoprene molar masses of, respectively, 12 000 and 48 000, 40 000 and 40 000, and 40 000 and 80 000. For the two latter samples, the concentration of the polymer was also varied. The data obtained at relatively high resolution were analyzed together with small-angle X-ray scattering data using scattering functions recently derived from Monte Carlo simulations for a model with a spherical core and a corona of semiflexible chains interacting with a hard-core potential. The scattering from the model can be generated by assuming an analytical form of the radial distribution of the corona and an effective single chain form factor of the random-phase approximation type. In the analysis of the experimental scattering data intermicellar interactions were modeled by an effective hard-sphere model. The analysis of the experimental data provides information on shape, aggregation number, polydispersity, core size, core solvation, corona shape/size, and the interactions between the chains in the corona, which are significant for these micelles. The shape of the corona profile depends on the surface coverage of the micelles as well as the curvature of the core−corona interface. For high curvatures the profile is in agreement with a power-law behavior as predicted by scaling theory. For low curvatures the profile is more compact. The profiles and scattering curves are very well reproduced by Monte Carlo simulations based on the parameters for the structures determined in the analysis of the experimental scattering data. The study shows that two parameters are decisive for the profile shape and internal correlations, namely the reduced surface coverage and the curvature.

The Kremer–Grest (KG) polymer model is a standard model for studying generic polymer properties in molecular dynamics simulations. It owes its popularity to its simplicity and computational efficiency, rather than its ability to represent specific polymers species and conditions. Here we show that by tuning the chain stiffness it is possible to adapt the KG model to model melts of real polymers. In particular, we provide mapping relations from KG to SI units for a wide range of commodity polymers. The connection between the experimental and the KG melts is made at the Kuhn scale, i.e., at the crossover from the chemistry-specific small scale to the universal large scale behavior. We expect Kuhn scale-mapped KG models to faithfully represent universal properties dominated by the large scale conformational statistics and dynamics of flexible polymers. In particular, we observe very good agreement between entanglement moduli of our KG models and the experimental moduli of the target polymers.