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Extensive molecular simulations are applied to characterize the equilibriumdynamics, entanglement topology, and nonlinear extensional rheology ofsymmetric ring-linear polymer blends with systematically varied ring fraction$\phi_R$. Chains with degree of entanglement $Z\approx14$ mixed to produce 10well-entangled systems with $\phi_R$ varying from neat linear to neat ringmelts. Primitive path analysis are used to visualize and quantify the structureof the composite ring-linear entanglement network. We directly measure thequantity of ring-linear threading and linear-linear entanglement as a functionof $\phi_R$, and identify with simple arguments a ring fraction$\phi_R\approx0.4$ where the topological constraints of the entanglementnetwork are maximized. These topological analyses are used to rationalize the$\phi_R$-dependence of ring and linear chain dynamics, conformations, and blendviscosity. Complimentary simulations of startup uniaxial elongation flowsdemonstrate the extensional stress overshoot observed in recent filamentstretching experiments, and characterize how it depends on the blendcomposition and entanglement topology. The overshoot is driven by anoverstretching and recoil of ring polymer conformations that is caused by theconvective unthreading of rings from linear chains. This produces significantchanges in the entanglement structure of blends that we directly visualize andquantify with primitive path analyses during flow.

Composite Entanglement Topology and Extensional Rheology of Symmetric Ring-Linear Polymer Blends