Identifying the Threshold Chain Length for Stress Overshoot in Ring-Linear Polymer Blends under Uniaxial Elongation: The Role of Multiple Threading

Abstract

The rheological behavior of ring-linear polymer blends under uniaxial elongational flow has remained a subject of intense debate, particularly regarding the emergence of stress overshoot. Herein, we employ coarse-grained molecular dynamics simulations to investigate the chain-length dependence of elongational viscosity in 1:1 ring-linear blends of flexible chains with the equal molecular weight. Our results reveal a distinct threshold in the degree of threading, quantified by the number of entanglements Z = N /Ne (where N is the number of beads per chain and Ne is the entanglement chain length), for the appearance of stress overshoot: while blends with shorter chains (Z $\le$ 2) exhibit monotonic stress growth, a clear stress overshoot emerges when the chain length reaches a threshold value (Z $\approx$ 4). Consistent with previous reports, this overshoot originates from a thread-to-unthread transition. At the threshold chain length, multiple linear chains penetrate a single ring, providing sufficient topological constraints to significantly stretch the ring under elongational flow. We predict that this transition can be experimentally validated via 2D small-angle neutron scattering patterns in the plane of the stretching and perpendicular directions, offering a direct structural signature of the ring recoil process for future experimental verification.

45 pages, 11 figures, 2 tables

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