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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Simulation results of the primitive chain network (PCN) model for entangled polymers are compared here to existing data of diffusion coefficient, linear and nonlinear shear and elongational rheology of monodisperse polystyrene melts. Since the plateau modulus of polystyrene is well known from the literature, the quantitative comparison between the whole set of data and simulations only requires a single adjustable parameter, namely, a basic time. The latter, however, must be consistent with the known rheology of unentangled polystyrene melts, i.e., with Rouse behavior, and is therefore not really an adjustable parameter. The PCN model adopted here is a refined version of the original model, incorporating among other things a more accurate description of chain end dynamics as well as finite extensibility effects. In the new version, we find good agreement with linear rheology, virtually without adjustable parameters. It is also shown that, at equilibrium, Gaussian statistics are well obeyed in the simulated network. In the nonlinear range, excellent agreement with data is found in shear, whereas discrepancies and possible inadequacies of the model emerge in fast uniaxial elongational flows, even when accounting for finite extensibility of the network strands.

For branched polymers, the curvilinear motion of the branch point along the backbone is a significant relaxation source but details of this motion have not been well understood. This study conducts multi-chain sliplink simulations to examine effects of the spatial fluctuation and curvilinear hopping of the branch point on the viscoelastic relaxation. The simulation is based on the primitive chain network model that allows the spatial fluctuations of sliplink and branch point and the chain sliding along the backbone according to the subchain tension, chemical potential gradients, drag force against medium, and random force. The sliplinks are created and∕or disrupted through the motion of chain ends. The curvilinear hopping of the branch point along the backbone is allowed to occur when all sliplinks on a branched arm are lost. The simulations considering the fluctuation and the hopping of the branch point described well the viscoelastic data for symmetric and asymmetric star polymers with a parameter set common to the linear polymer. On the other hand, the simulations without the branch point motion predicted unreasonably slow relaxation for asymmetric star polymers. For asymmetric star polymers, further tests with and without the branch point hopping revealed that the hopping is much less important compared to the branch point fluctuation when the lengths of the short and long backbone arms are not very different and the waiting time for the branch point hopping (time for removal of all sliplinks on the short arm) is larger than the backbone relaxation time. Although this waiting time changes with the hopping condition, the above results suggest a significance of the branch point fluctuation in the actual relaxation of branch polymers.

The polymer dynamics under fast flow has not been fully elucidated yet. In addition to the relaxation mechanisms under equilibrium 1) , further relaxation mechanisms (such as convective constraint release 2) ) that work only under fast flows were proposed. However, experiments suggest that there still exist missing mechanisms. For example, the established relaxation mechanisms cannot explain the different elongational behavior of polystyrene (PS) melts and solutions. 3-5)As an additional relaxation mechanism under fast flows, we have recently suggested the reduction of local friction.We examined literature data 6) for stress relaxation of PS melts after cessation of transient uniaxial flow, and found that the relaxation is accelerated depending on the strain rate before the cessation 7). This acceleration seems not to be explained by the conventional relaxation mechanisms and we suggested that it is due to change of the local friction coefficient induced by stretch and orientation. We obtained the relaxation acceleration factor, and we converted the stress at the flow cessation into a stretch/orientation factor F so to obtain an empirical relationship between the local friction coefficient and F so . In our hypothesis, the friction ζ is a function of F so ,-where the stretch l is the ratio of the subchain current length to its maximum possible value, and S -is the mean orientation of all components in the system (polymer. This z(F so ) (determined from the experiment) stays at its equilibrium value when F so is smaller than a certain critical value ( = 0.15), and then steeply decreases with increasing F so . We utilized this z (F so ) in the sliplink simulations to show that the reduction of friction can explain the elongational thinning of melts. 7)Although stress relaxation after uniaxial stretch strongly supports the idea of a change of friction, experimental data are understandably rare due to experimental difficulties. Indeed, melt data are available only for one specific PS sample 6) .There is also a couple of datasets for PS solutions where the acceleration is not observed 8) . In our interpretation, this is because the solvent (essentially isotropic) effectively reduces the mean orientation S -. Experiments in shear can be more easily realized, but the acceleration has not been observed because in shear the stretch ratio l never becomes sufficiently large. 7) On the other hand, further investigation is certainly required to clarify the origin of the acceleration of stress relaxation.In this study, we performed molecular dynamics simulations of the stress relaxation after uniaxial elongations. We used the standard Kremer-Grest bead spring simulation

The concept of dynamic tube dilation (DTD) is here used to formulate a new simulation scheme to obtain the linear viscoelastic response of long chains with a large number of entanglements. The new scheme is based on the primitive chain network model previously proposed by some of the authors, and successfully employed to simulate linear and nonlinear behavior of moderately entangled polymers. Scaling laws are generated by the DTD concept, and allow for prediction of the linear response of very long chains on the basis of suitable simulations performed on shorter ones, without introducing adjustable parameters. Tests of the method against existing data for linear monodisperse polyisoprene and polystyrene show good quantitative agreement.

Under elongational flow at strain rates higher than the Rouse relaxation frequency, entangled polymer melts exhibit thinning of their elongational viscosity whereas equally entangled solutions show thickening. Yaoita et al. [Yaoita et al., Macromolecules 2012, 45, 2773 related this difference between the melts and solutions to reduction of segmental friction on enhancement of the stretch/orientation averaged for the components therein (that includes the solvent for the case of solutions). They analyzed the stress relaxation data after cessation of elongational flow to propose an empirical equation describing this friction reduction as a function of the stretch/orientation factor. Multi-chain slip-link (PCN) simulations considering this friction reduction described the thinning of melts and the thickening of solutions consistently and semi-quantitatively. This study further tests the molecular concept of the stretch/orientation-induced friction reduction with the aid of a simple molecular constitutive equation, a toy version of the Mead-Larson-Doi model [Mead et al., Macromolecules 1998, 31, 7895] (MLD toy model) being modified to incorporate this empirical equation of the friction reduction. The modified toy model mimicked the behavior of melts and solutions consistently. This consistency vanished when the friction reduction in the model was artificially switched off, even though the finite extensible nonlinear elasticity was still taken into account. These results lend further support to the molecular concept of the stretch/orientation-induced friction reduction.

Articles you may be interested inNumerical simulation results of the nonlinear coefficient Q from FT-Rheology using a single mode pom-pom model J. Rheol. 57, 1 (2013); 10.1122/1.4754444 Statics, linear, and nonlinear dynamics of entangled polystyrene melts simulated through the primitive chain network model Transient and steady-state solutions of 2D viscoelastic nonisothermal simulation model of film casting process via finite element method Abstract. We here report on some modifications of the Primitive Chain Network (PCN) model, originally proposed in [Y. Masubuchi et al., J. Chem. Phys. 115, 4387 (2001)], which both refine the model and make it suitable for predicting nonlinear rheological response in fast flows. Simulation results are compared with some existing viscoelastic data on monodisperse polystyrene melts [Schweizer et al., J. Rheol. 48, 1345 (2004); Bach et al, Macromolecules 36, 5174], by using as single adjustable parameter (to be assigned once and for all) a basic relaxation time which relates to the coarse graining of the PCN model. Essentially quantitative prediction of linear viscoelasticity is achieved. Without further parameters, the nonlinear behavior of the polystyrene melts in start-up of shear and uniaxial elongational flow is also reproduced by the simulations. Specifically, the viscosity growth fianctions are quantitatively predicted, whereas transient elongational viscosities are reasonably reproduced only up to extensional rates of the order of the reciprocal Rouse time. At higher elongation rates, although the strain hardening effect is correctly captured by the simulations, steady state values are not. Notwithstanding this latter limitation, the simulation model appears adequate to portray the rheological behavior of entangled melts, both in the linear and the nonlinear range.