Unraveling Dynamics of Entangled Polymers in StrongExtensional Flows

The traditional Doi–Edwards tube model, applied to extensional flows at strain rates above the inverse Rouse time, predicts that the tube deforms affinely, which implies that the extensional stress reaches its plateau as soon as the chain has become locally fully stretched, even if the chain is still folded, and far from being completely unraveled. By starting from a state in which the chain is in a locally fully stretched, but folded, state, we develop an “entangled kink dynamics algorithm” that predicts the final unraveling of an ensemble of mutually entangled, folded chains, driven by a combination of drag forces and chain tension, with negligible Brownian motion. Equations for motions of both entangled folds and unentangled folds in which two chains hook together at a single fold point are derived and solved, including the effects of constraint release that occurs when the end of one chain passes through the fold at which that chain is entangled. This model predicts that the stress approaches its fina...