Composite Entanglement Topology and Extensional Deformation In Ring-Linear Polymer Blends*

Large-scale molecular simulations are applied to characterize the entanglement structure, topology, and dynamics of architectural blends of ring and linear polymer chains. The mixture of the two chain shapes produces a composite network formed by a combination of conventional linear-chain entanglements and threading of linear chains through ring polymers. We systematically study these networks for symmetric blends of well entangled polymers with the ring fraction $\phi_R$ varying from 0.05 to 0.95. Primitive path analyses are used to visualize and quantify the network structure and measure the quantity of ring-linear threading and linear-linear entanglement as a function of $\phi_R$. We find that the density of topological constraints of the network has a maximum with respect to $\phi_R$ at  a ring fraction $\phi_R\approx0.4$, which we can rationalize with simple constraint-counting arguments. Complimentary simulations of blend elongation are also reported and demonstrate how the changing entanglement structure of blends with $\phi_R$ gives rise to qualitative changes in macroscopic extensional stresses during deformation.