  Extensive molecular simulations are applied to characterize the equilibrium
dynamics, entanglement topology, and nonlinear extensional rheology of
symmetric ring-linear polymer blends with systematically varied ring fraction
$\phi_R$. Chains with degree of entanglement $Z\approx14$ mixed to produce 10
well-entangled systems with $\phi_R$ varying from neat linear to neat ring
melts. Primitive path analysis are used to visualize and quantify the structure
of the composite ring-linear entanglement network. We directly measure the
quantity of ring-linear threading and linear-linear entanglement as a function
of $\phi_R$, and identify with simple arguments a ring fraction
$\phi_R\approx0.4$ where the topological constraints of the entanglement
network are maximized. These topological analyses are used to rationalize the
$\phi_R$-dependence of ring and linear chain dynamics, conformations, and blend
viscosity. Complimentary simulations of startup uniaxial elongation flows
demonstrate the extensional stress overshoot observed in recent filament
stretching experiments, and characterize how it depends on the blend
composition and entanglement topology. The overshoot is driven by an
overstretching and recoil of ring polymer conformations that is caused by the
convective unthreading of rings from linear chains. This produces significant
changes in the entanglement structure of blends that we directly visualize and
quantify with primitive path analyses during flow.
