Primitive chain network simulations for asymmetric star polymers.
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.
Simulating the flow of entangled polymers.
To optimize automation for polymer processing, attempts have been made to simulate the flow of entangled polymers. In industry, fluid dynamics simulations with phenomenological constitutive equations have been practically established. However, to account for molecular characteristics, a method to obtain the constitutive relationship from the molecular structure is required. Molecular dynamics simulations with atomic description are not practical for this purpose; accordingly, coarse-grained models with reduced degrees of freedom have been developed. Although the modeling of entanglement is still a challenge, mesoscopic models with a priori settings to reproduce entangled polymer dynamics, such as tube models, have achieved remarkable success. To use the mesoscopic models as staging posts between atomistic and fluid dynamics simulations, studies have been undertaken to establish links from the coarse-grained model to the atomistic and macroscopic simulations. Consequently, integrated simulations from materials chemistry to predict the macroscopic flow in polymer processing are forthcoming.
Tube dilation and reptation in binary blends of monodisperse linear polymers
We extend the Milner−McLeish theory for monodisperse linear polymers to binary blends, where the reptation time of the long chain is set to either the reptation time in the undilated tube or the reptation time in the dilated tube depending on the value of the “Graessley parameter” Gr ≡ M2Me2/M13, where M1 is the short chain molecular weight, M2 is the long chain molecular weight, and Me is the entanglement molecular weight. We find experimentally that, in blends in which Gr is much smaller than the critical value Grc ≈ 0.064 established by an observed crossover in diffusivity measurements [Green et al. Phys. Rev. Lett. 1984, 26, 2145], the long-chain motion in the binary blend is well predicted by the Milner−McLeish model using reptation in the undilated tube. However, for Gr larger than Grc, reptation must to be assumed to occur in a dilated tube to obtain agreement with the experimental data. These results confirm that the crossover behavior observed in diffusivity also occurs in rheology and show that ...