Modern theories of the dynamics of concentrated polymeric liquids have not yet accounted for the effects of polydispersity to a sufficient extent. In order to approach quantitatively the problem of polydispersity, a model is proposed here which is based on the concept that the “tube” of constraints around a chain enlarges as the relaxation proceeds. Predictions of linear viscoelasticity obtained with this model compare favorably with experimental results on homopolymeric blends reported in the literature. However, the theory is limited to the case of very long chains and it embodies an arbitrary, if plausible, closure assumption in the self‐consistency scheme. Thus, quantitative agreement remains incomplete.

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.

Well-entangled monodisperse linear polystyrene melts exhibit monotonic thinning of the steady state elongational viscosity with increasing the strain rate ε̇ even beyond the Rouse relaxation frequency, τR ‑1. This behavior is quite different from the thinning followed by hardening at ε̇ > τR ‑1 observed for entangled semidilute solutions. We attempt to elucidate the molecular origin of this difference by focusing on the concept of stretch/orientation-dependent monomeric friction ζ recently proposed by Ianniruberto and co-workers. Specifically, literature data of the stress relaxation after cessation of transient elongational flow, reported for both PS melts and solutions, are analyzed to evaluate the stretch/orientation-dependent decrease of ζ. In our working hypothesis, ζ is expressed as a function of the factor F so = λ̃2 S̅, where λ̃ is the normalized stretch ratio of entangled subchains defined with respect to the fully stretched state, and S̅ is an average orientational anisotropy of the components (polymer plus solvent if any) in the system. The factor F so was estimated from the stress decay data after flow cessation. The resulting functional form of ζ(F so) was then used in the primitive chain network (PCN) simulation including finite extensible nonlinear elasticity (FENE) to examine the elongational behavior of melts and solutions. For melts the simulation indicates that ζ decreases significantly under fast elongation because the entangled subchains are short and approach the fully stretched (and fully oriented) limit rather easily. Hence, the steady elongational viscosity ηE follows this decrease of ζ to exhibit the monotonic thinning even at ε̇ > τR ‑1. In contrast, for solutions, the simulated ηE exhibits thickening at ε̇ > τR ‑1 because the average anisotropy S̅ is governed by the solvent and remains small, thus overwhelming the increase of the subchain stretch λ̃. The simulated results proved to be in satisfactory agreement with the experiments.

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We investigate the nonlinear shear and uniaxial extensional rheology of entangled polystyrene (PS) melts and solutions having the same number Z of entanglements, hence identical linear viscoelasticity. While experiments in extensional flows confirm that PS melts and solutions with the same Z behave differently, respective transient and steady data in simple shear over the largest possible range of rheometric shear rates (corresponding to Rouse−Weissenberg numbers from 0.01 to 40) demonstrate that melts and solutions exhibit identical behavior. Whereas the differences between melts and solutions in elongational flows are due to alignmentinduced friction reduction (more effective in melts than in solutions), in shear flows they disappear since the rotational component reduces monomeric alignment substantially. Recent molecular dynamics simulations of entangled polymers show that rotation induces molecular tumbling at high shear rates, and here a tube-based model involving tumbling effects is proposed in order to describe the response in shear. The main outcome is that tumbling can explain transient stress undershoot (following the overshoot) at high shear rates. Hence, the combination of tumbling in shear and friction reduction in extension successfully describes the whole range of experimental data and provides the basic ingredient for the development of molecular constitutive equations.