Molecular Insights into the Extensional Flow of Polymers*

Nonlinear extension flows are common in polymer processing but remain a challenging theoretical problem. These flows dramatically stretch chains and deform the entanglement network far from equilibrium. Analytic models make conflicting assumptions about chain dynamics and entanglements in nonlinear flow, and testing these models requires knowledge of molecular conformations that is not available from experiments. Here, we present molecular dynamics simulations of extensional flows in entangled polymer liquids, for Rouse-Weissenberg numbers 0.06 to 52, and Hencky strains up to 12. We measure the transient viscosity, resolving the linear viscoelastic limit and the rate dependence of the nonlinear viscosity. Our generic, bead-spring simulations reproduce experimental trends for polystyrene melts and solutions, implying a universal nonlinear rheology in extension. Characterizing the microscopic structure of flowing liquids reveals a direct connection between stress and chain entropy with a rate-independent entanglement density, and explains the scaling of nonlinear viscosity with chain and entanglement length at different rates. These results answer critical questions about the fundamental nature of entanglement and chain confinement in aligned and deforming polymers.