Shear banding in simulated telechelic polymers

The response of simulated telechelic polymers to shear is investigated. End groups of short polymeric chains form temporary junctions that are continuously broken and formed over time. As in experiments, two shear bands coexist for some shear rates. This allows us to study the microscopic differences between these shear bands. We find that the lifetime of a junction is lower in the high shear rate band. In addition, the average aggregate size is lower in this band since more dangling chains exist. Microstructural differences between the sheared and unsheared system are reported as well. Some of the chains, that bridge between two aggregates before shear is applied, form loops that connect with both ends to the same aggregate instead. In addition and more importantly, an increase of chains connecting the same two aggregates is observed. Such restructuring lowers the network connectivity and hence the stress needed to shear the system. Shear banding is a common phenomenon in many complex systems. When these systems are sheared at a rate that is higher than the inverse relaxation time, homogeneous flow becomes unstable. As a consequence two bands with different shear rates form. Although this effect has been observed in a wide variety of systems, such as emulsions, dispersions, granular materials, and foams, it has been most extensively studied experimentally in wormlike micelles [1–9]. A theoretical explanation for shear banding lies in the behavior of the underlying constitutive curve, relating shear stress r to the shear rate _ c [4,8,10]. In homogeneous flow, there is a range of shear rates for which the curve decreases, indicating a mechanical instability. Hence, it is predicted that the flow splits in two bands and the stress plateaus. This theory also predicts the width of the bands; the so-called lever rule states that the location of the interface between both bands changes gradually with the applied shear rate, while the local shear rates in both bands are constant. The interface is located such that _ c ¼ a 1 _ c 1 þ a 2 _ c 2 ð1Þ where a 1 and a 2 are the relative widths of the shear bands. Although some experiments confirm the lever rule [3,6], others indicate that the picture of two smooth bands separated by a stable interface is insufficient to explain the complex behavior at the interface [1,7,9,11]. The position of the interface seems to fluctuate and drift, long …