Shear Banding in Entangled Polymers: Stress Plateau, Banding Location, and Lever Rule

Abstract

Using molecular dynamics simulation, we study shear banding of entangled polymer melts under a steady shear. The steady shear stress vs shear rate curve exhibits a plateau spanning nearly two decades of shear rates in which shear banding is observed, and the steady shear stress remains unchanged after switching the shear rates halfway in the range of shear rates within the plateau region. In addition, we find strong correlation in the location of the shear bands between different shear rates starting from the same microstate configurations at equilibrium, which suggests the importance of the inherent structural heterogeneity in the entangled polymer network for shear banding. Furthermore, for the steady shear bands persisting to the longest simulated time of 9.0τ d0 (disengagement time), the shear rate in the slow band and the relative proportion of the bands do not change very much with the increase of imposed shear rate, but the shear rate in the fast band increases approximately in proportion to the imposed shear rates, in contradiction to the lever rule.

Multiple Entanglements between Two Chains in Polymer Melts: An Analysis of Primitive Paths Based on Frenet Trihedron

“…From this set of rules, we have determined the entanglement number per chain ( Z F ) to be 20 for chain length N = 300 at equilibrium. We note that this number is larger than the entanglement number Z = 14 given in previous literature ,, but still less than Z k as determined by the Z1+ code . Hsu and Kremer , have recently developed an improved method that also resulted in a larger Z k than Z . , The discrepancy between Z obtained from other methods and Z F can be attributed to differences in the definition of entanglement and variation in the calculation method.…”

“…Furthermore, Kröger and co-workers − and Tzoumanekas and Theodorou , proposed two different geometry minimization algorithms in the spirit of a constrained steepest descent method, which are named Z1/Z1+ code − and CReTA , algorithms, respectively. These methods have enabled systematic investigation into the relationship between the spatial distribution of kinks and various physical quantities, such as the flow field distribution and crystalline orientation distribution in entangled polymer systems. An alternative approach to obtaining the PP is the mean path method. , In this mean-field method, the average is taken over all possible fluctuation patterns of a tagged chain.…”

“…As commented on by these authors and shown in our work here, for longer chains with free ends, these multiple entanglements can become more important. These types of entanglements, and any intervening entanglements formed by other chains, are expected to have strong spatial and topological correlations that should eventually influence the dynamic and rheological properties of entangled polymer melts, particularly concerning localized strain phenomena such as melt fracture − and shear banding. − …”

Non-Rouse behavior of short ring polymers in melts by molecular dynamics simulations

“…sub-diffusion or the same mechanism with the linear polymer melts holds here is an important issue that needs to be addressed. Fortunately, molecular simulations, particularly coarse-grained molecular dynamics (CGMD) simulations that are widely used to investigate the dynamics and structures of polymers, [43][44][45] provide powerful tools for directly probing the sub-diffusion behavior at the molecular level in situ and a relevant systematic study is instructive for a better understanding of the non-Rouse dynamics in short flexible rings.…”

Nature of Steady-State Fast Flow in Entangled Polymer Melts: Chain Stretching, Shear Thinning, and Viscosity Scaling

“…More confusion arises in steady-state shear at Wi R > 1 where experiments based on cone and partitioned plate (CPP) and cone-plate rheometers have found a wide range of scaling exponents of the steady-state shear stress, σ ∼ Wi R 0.08–0.25 for melts ,,, and σ ∼ Wi R 0.08–0.43 for solutions, ,− depending on polymer chemistry, degree of entanglement, and the range of dimensionless shear rates probed. Computer simulations of coarse-grained and atomistic lightly entangled models also find very different steady-state scaling laws in polymer melts at Wi R > 1, σ ∼ Wi R 0–0.38 . ,,− The lack of consensus within (and between) the experimental and simulation studies in the presence of strong chain stretching frustrates the pursuit of a fundamental theoretical understanding.…”