A new model for Brownian dynamics simulations of entangled polymeric liquids is proposed here. Chains are coarse grained at the level of segments between consecutive entanglements; hence, the system is in fact a network of primitive chains. The model incorporates not only the “individual” mechanisms of reptation and tube length fluctuation, but also collective contributions arising from the 3D network structure of the entangled system, such as constraint release. Chain coupling is achieved by fulfilling force balance on the entanglement nodes. The Langevin equation for the nodes contains both the tension in the chain segments emanating from the node and an osmotic force arising from density fluctuations. Entanglements are modeled as slip links, each connecting two chain strands. The motion of monomers through slip links, which ultimately generates reptation as well as tube length fluctuations, is also described by a suitable Langevin equation. Creation and release of entanglements is controlled by the number of monomers at the chain ends. In a creation event, the partner chain segment is chosen randomly among those spatially close to the advancing chain end. To validate the model, equilibrium dynamics simulations were run for monodisperse linear chains containing up to Z=40 entanglements. The results show, in agreement with experiments, (i) a Z3.5±0.1 dependence of the longest relaxation time, (ii) a Z−2.4±0.2 dependence of the self-diffusion coefficient, and (iii) a relaxation modulus proportional to the square of the end-to-end vector correlation function, consistently with the dynamic tube dilation concept.

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Starting from the united atom model, we construct a coarse-grained model for a flexible polymer chain, in which some successive CH 2 atoms are combined into an effective segment. To connect the coarse-grained model with the atomistic model, we propose a scheme to obtain the effective potentials acting between bonded and nonbonded segments from atomistic molecular dynamics simulation for a single isolated chain. We assume that the total effective potential is a sum of potential components for independent coarse-grained variables. The effective bond potentials are determined by simply taking the logarithm of the corresponding distribution functions calculated from the atomistic simulations. On the other hand, to consider the characteristic entropy effects of the polymer chain system, the effective nonbonded potentials are evaluated using the canonical ensemble average for fixed distance between the segments. We confirmed that the coarse-grained model using these effective potentials can reproduce the radii of gyration and various distribution functions of the coarse-grained variables over a wide temperature range. We also confirmed that the effective potentials obtained for the isolated chain system are applicable to the melt system. A detailed analysis of the distribution functions showed that the effective bond length and the effective torsion angle correlate strongly with the effective bond angle. In order to improve the quality of our coarse-grained potentials, these correlations should be taken into account.

The modelling of molecular entanglement in polymeric materials is an old problem, and has evolved gradually over the last 60 years, with two key approaches: the network model of Green & Tobolsky, and the tube model of Edwards and de Gennes. We will show that these models can be merged together in a straightforward manner. The resulting model, called the dual slip-link model, can be handled by computer simulation, and it can predict the linear and nonlinear rheological behaviours of linear and star polymers with arbitrary molecular weight distribution.

Coarse-grained molecular dynamics simulation of a bead–spring polymer model has been conducted for polymer melt confined between two solid walls. The wall effect was studied by changing the distance between the walls and the wall–polymer interaction. It was observed that the polymers near the walls are compressed towards the walls: the component of the radius of gyration tensor perpendicular to the wall surfaces decreases in a layer near the walls. The thickness of this surface layer, estimated from the analysis of the static polymer structure, is about 1.0–1.5 times the radius of gyration Rg in the bulk, and is independent of the distance between the walls and the wall–polymer interaction. The relaxation time of the polymers, obtained from the autocorrelation of normal modes, increases with increasing the strength of the wall–polymer interaction and with decreasing the distance between the walls. These wall effects are observed at a distance much larger than Rg. This result is in agreement with the recent dielectric measurements of cis-polyisoprene confined between mica surfaces reported by Cho, Watanabe, and Granick [J. Chem. Phys. 110, 9688 (1999)]. The thickness of the surface layer was also estimated by the position dependence of the static and dynamic properties, and was found to agree with that estimated by the viscoelastic measurements.

We have developed a single-chain theory that describes dynamics of associating polymer chains carrying multiple associative groups (or stickers) in the transient network formed by themselves and studied linear viscoelastic properties of this network. It is shown that if the average number N of stickers associated with the network junction per chain is large, the terminal relaxation time τ(A) that is proportional to τ(X)N(2) appears. The time τ(X) is the interval during which an associated sticker goes back to its equilibrium position by one or more dissociation steps. In this lower frequency regime ω<1/τ(X), the moduli are well described in terms of the Rouse model with the longest relaxation time τ(A). The large value of N is realized for chains carrying many stickers whose rate of association with the network junction is much larger than the dissociation rate. This associative Rouse behavior stems from the association/dissociation processes of stickers and is different from the ordinary Rouse behavior in the higher frequency regime, which is originated from the thermal segmental motion between stickers. If N is not large, the dynamic shear moduli are well described in terms of the Maxwell model characterized by a single relaxation time τ(X) in the moderate and lower frequency regimes. Thus, the transition occurs in the viscoelastic relaxation behavior from the Maxwell-type to the Rouse-type in ω<1/τ(X) as N increases. All these results are obtained under the affine deformation assumption for junction points. We also studied the effect of the junction fluctuations from the affine motion on the plateau modulus by introducing the virtual spring for bound stickers. It is shown that the plateau modulus is not affected by the junction fluctuations.

We present a "slip-link" model for relaxation of entangled star polymers that accounts for chain-end fluctuations and constraint release and that explains deviations from the "dynamic dilution" equation observed in recent dielectric and stress relaxation data. In the terminal regime where tube expansion fails to keep up with chain relaxation, relaxation is controlled by rare events in which newly created entanglements near the branch point draw the chain end towards the last remaining old entanglement, where a shallow fluctuation releases it.

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